LMFDB - Embedded newform 29.9.f.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,Mod(2,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	29.f (of order $28$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8139796918$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$19$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			2.10
Character	$\chi$	$=$	29.2
Dual form			29.9.f.a.15.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.38682 - 0.381603i) q^{2} +(91.1302 + 57.2609i) q^{3} +(-238.257 - 54.3805i) q^{4} +(116.314 - 92.7574i) q^{5} +(-286.791 - 228.708i) q^{6} +(-926.307 - 4058.42i) q^{7} +(1609.73 + 563.269i) q^{8} +(2179.19 + 4525.14i) q^{9} +O(q^{10})$	\(q+(-3.38682 - 0.381603i) q^{2} +(91.1302 + 57.2609i) q^{3} +(-238.257 - 54.3805i) q^{4} +(116.314 - 92.7574i) q^{5} +(-286.791 - 228.708i) q^{6} +(-926.307 - 4058.42i) q^{7} +(1609.73 + 563.269i) q^{8} +(2179.19 + 4525.14i) q^{9} +(-429.332 + 269.767i) q^{10} +(16170.0 - 5658.11i) q^{11} +(-18598.5 - 18598.5i) q^{12} +(-7748.40 + 16089.7i) q^{13} +(1588.53 + 14098.6i) q^{14} +(15911.1 - 1792.75i) q^{15} +(51129.7 + 24622.8i) q^{16} +(84171.3 - 84171.3i) q^{17} +(-5653.73 - 16157.4i) q^{18} +(-104146. - 165748. i) q^{19} +(-32756.8 + 15774.8i) q^{20} +(147974. - 422886. i) q^{21} +(-56923.9 + 12992.5i) q^{22} +(264640. - 331848. i) q^{23} +(114442. + 143505. i) q^{24} +(-81997.2 + 359253. i) q^{25} +(32382.3 - 51536.2i) q^{26} +(18539.2 - 164540. i) q^{27} +1.01732e6i q^{28} +(-176923. + 684795. i) q^{29} -54572.2 q^{30} +(-1.15962e6 - 130658. i) q^{31} +(-533443. - 335185. i) q^{32} +(1.79756e6 + 410281. i) q^{33} +(-317193. + 252953. i) q^{34} +(-484191. - 386129. i) q^{35} +(-273128. - 1.19665e6i) q^{36} +(204986. + 71727.9i) q^{37} +(289475. + 601102. i) q^{38} +(-1.62742e6 + 1.02258e6i) q^{39} +(239482. - 83798.3i) q^{40} +(1.66890e6 + 1.66890e6i) q^{41} +(-662536. + 1.37577e6i) q^{42} +(-548264. - 4.86598e6i) q^{43} +(-4.16029e6 + 468752. i) q^{44} +(673211. + 324201. i) q^{45} +(-1.02292e6 + 1.02292e6i) q^{46} +(1.62666e6 + 4.64872e6i) q^{47} +(3.24954e6 + 5.17161e6i) q^{48} +(-1.04188e7 + 5.01743e6i) q^{49} +(414802. - 1.18544e6i) q^{50} +(1.24903e7 - 2.85082e6i) q^{51} +(2.72107e6 - 3.41212e6i) q^{52} +(353674. + 443494. i) q^{53} +(-125578. + 550193. i) q^{54} +(1.35596e6 - 2.15800e6i) q^{55} +(794876. - 7.05472e6i) q^{56} -2.10682e7i q^{57} +(860528. - 2.25176e6i) q^{58} -8.80499e6 q^{59} +(-3.88842e6 - 438119. i) q^{60} +(7.19943e6 + 4.52370e6i) q^{61} +(3.87756e6 + 885028. i) q^{62} +(1.63463e7 - 1.30357e7i) q^{63} +(-9.67962e6 - 7.71924e6i) q^{64} +(591192. + 2.59018e6i) q^{65} +(-5.93145e6 - 2.07550e6i) q^{66} +(3.69729e6 + 7.67750e6i) q^{67} +(-2.46317e7 + 1.54771e7i) q^{68} +(4.31186e7 - 1.50879e7i) q^{69} +(1.49252e6 + 1.49252e6i) q^{70} +(-2.49640e6 + 5.18383e6i) q^{71} +(959041. + 8.51173e6i) q^{72} +(3.80473e6 - 428690. i) q^{73} +(-666881. - 321153. i) q^{74} +(-2.80436e7 + 2.80436e7i) q^{75} +(1.58001e7 + 4.51541e7i) q^{76} +(-3.79413e7 - 6.03833e7i) q^{77} +(5.90202e6 - 2.84226e6i) q^{78} +(-8.61152e6 + 2.46103e7i) q^{79} +(8.23105e6 - 1.87868e6i) q^{80} +(3.16569e7 - 3.96965e7i) q^{81} +(-5.01540e6 - 6.28911e6i) q^{82} +(4.84998e6 - 2.12492e7i) q^{83} +(-5.82525e7 + 9.27084e7i) q^{84} +(1.98280e6 - 1.75978e7i) q^{85} +1.66894e7i q^{86} +(-5.53351e7 + 5.22747e7i) q^{87} +2.92163e7 q^{88} +(5.28693e7 + 5.95694e6i) q^{89} +(-2.15633e6 - 1.35491e6i) q^{90} +(7.24762e7 + 1.65422e7i) q^{91} +(-8.10983e7 + 6.46737e7i) q^{92} +(-9.81947e7 - 7.83076e7i) q^{93} +(-3.73524e6 - 1.63651e7i) q^{94} +(-2.74881e7 - 9.61849e6i) q^{95} +(-2.94198e7 - 6.10909e7i) q^{96} +(4.25081e6 - 2.67096e6i) q^{97} +(3.72013e7 - 1.30173e7i) q^{98} +(6.08412e7 + 6.08412e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9}+O(q^{10}) $ 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} - 15884 q^{10} + 8376 q^{11} - 5036 q^{12} - 14 q^{13} - 12742 q^{14} + 35516 q^{15} + 245898 q^{16} - 76248 q^{17} + 465008 q^{18} + 164474 q^{19} - 907274 q^{20} - 628270 q^{21} + 1214962 q^{22} + 173408 q^{23} + 1858618 q^{24} + 43976 q^{25} - 4604204 q^{26} - 1727586 q^{27} + 1079922 q^{29} + 8909208 q^{30} + 3657848 q^{31} + 1160364 q^{32} - 4279184 q^{33} - 8655374 q^{34} - 8269058 q^{35} - 3366854 q^{36} - 5622890 q^{37} + 15536626 q^{38} + 16110008 q^{39} - 23544696 q^{40} - 9561672 q^{41} - 14 q^{42} + 5181008 q^{43} + 51041750 q^{44} - 35245194 q^{45} - 43159224 q^{46} - 12806808 q^{47} + 83954488 q^{48} + 10429400 q^{49} + 80809398 q^{50} + 18760882 q^{51} - 93050550 q^{52} - 30960322 q^{53} - 106220916 q^{54} - 126174004 q^{55} - 40136268 q^{56} + 159368354 q^{58} + 11188020 q^{59} + 255893612 q^{60} + 139657128 q^{61} + 102501616 q^{62} + 9797746 q^{63} - 135941792 q^{64} - 14207858 q^{65} - 447597656 q^{66} - 148930894 q^{67} - 167094904 q^{68} + 66986722 q^{69} + 586255934 q^{70} - 15272096 q^{71} + 41230600 q^{72} - 219415072 q^{73} - 347464696 q^{74} + 391507416 q^{75} + 271512490 q^{76} + 240416780 q^{77} + 141747906 q^{78} + 112667220 q^{79} - 375642638 q^{80} - 358099268 q^{81} - 262154910 q^{82} - 109463350 q^{83} - 694921012 q^{84} - 356627386 q^{85} + 199703522 q^{87} + 251202768 q^{88} + 839849154 q^{89} + 675826020 q^{90} + 533256766 q^{91} + 742339570 q^{92} + 78998570 q^{93} - 209116610 q^{94} - 633414122 q^{95} - 431412576 q^{96} - 402046736 q^{97} - 2192087384 q^{98} - 1966368188 q^{99}+O(q^{100}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9 - 15884 * q^10 + 8376 * q^11 - 5036 * q^12 - 14 * q^13 - 12742 * q^14 + 35516 * q^15 + 245898 * q^16 - 76248 * q^17 + 465008 * q^18 + 164474 * q^19 - 907274 * q^20 - 628270 * q^21 + 1214962 * q^22 + 173408 * q^23 + 1858618 * q^24 + 43976 * q^25 - 4604204 * q^26 - 1727586 * q^27 + 1079922 * q^29 + 8909208 * q^30 + 3657848 * q^31 + 1160364 * q^32 - 4279184 * q^33 - 8655374 * q^34 - 8269058 * q^35 - 3366854 * q^36 - 5622890 * q^37 + 15536626 * q^38 + 16110008 * q^39 - 23544696 * q^40 - 9561672 * q^41 - 14 * q^42 + 5181008 * q^43 + 51041750 * q^44 - 35245194 * q^45 - 43159224 * q^46 - 12806808 * q^47 + 83954488 * q^48 + 10429400 * q^49 + 80809398 * q^50 + 18760882 * q^51 - 93050550 * q^52 - 30960322 * q^53 - 106220916 * q^54 - 126174004 * q^55 - 40136268 * q^56 + 159368354 * q^58 + 11188020 * q^59 + 255893612 * q^60 + 139657128 * q^61 + 102501616 * q^62 + 9797746 * q^63 - 135941792 * q^64 - 14207858 * q^65 - 447597656 * q^66 - 148930894 * q^67 - 167094904 * q^68 + 66986722 * q^69 + 586255934 * q^70 - 15272096 * q^71 + 41230600 * q^72 - 219415072 * q^73 - 347464696 * q^74 + 391507416 * q^75 + 271512490 * q^76 + 240416780 * q^77 + 141747906 * q^78 + 112667220 * q^79 - 375642638 * q^80 - 358099268 * q^81 - 262154910 * q^82 - 109463350 * q^83 - 694921012 * q^84 - 356627386 * q^85 + 199703522 * q^87 + 251202768 * q^88 + 839849154 * q^89 + 675826020 * q^90 + 533256766 * q^91 + 742339570 * q^92 + 78998570 * q^93 - 209116610 * q^94 - 633414122 * q^95 - 431412576 * q^96 - 402046736 * q^97 - 2192087384 * q^98 - 1966368188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{28}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.38682	−	0.381603i	−0.211676	−	0.0238502i	0.00548943	−	0.999985i	$-0.498253\pi$
$2$	−3.38682	−	0.381603i	−0.211676	−	0.0238502i	−0.217166	+	0.976135i	$0.569681\pi$
$3$	91.1302	+	57.2609i	1.12506	+	0.706925i	0.960178	−	0.279388i	$-0.0901315\pi$
$3$	91.1302	+	57.2609i	1.12506	+	0.706925i	0.164886	+	0.986313i	$0.447274\pi$
$4$	−238.257	−	54.3805i	−0.930690	−	0.212424i
$5$	116.314	−	92.7574i	0.186103	−	0.148412i	−0.526007	−	0.850480i	$-0.676311\pi$
$5$	116.314	−	92.7574i	0.186103	−	0.148412i	0.712109	+	0.702068i	$0.247740\pi$
$6$	−286.791	−	228.708i	−0.221289	−	0.176472i
$7$	−926.307	−	4058.42i	−0.385801	−	1.69030i	−0.678908	−	0.734223i	$-0.737547\pi$
$7$	−926.307	−	4058.42i	−0.385801	−	1.69030i	0.293108	−	0.956079i	$-0.405311\pi$
$8$	1609.73	+	563.269i	0.393001	+	0.137517i
$9$	2179.19	+	4525.14i	0.332143	+	0.689703i
$10$	−429.332	+	269.767i	−0.0429332	+	0.0269767i
$11$	16170.0	−	5658.11i	1.10443	−	0.386457i	0.284358	−	0.958718i	$-0.408219\pi$
$11$	16170.0	−	5658.11i	1.10443	−	0.386457i	0.820071	+	0.572261i	$0.193934\pi$
$12$	−18598.5	−	18598.5i	−0.896918	−	0.896918i
$13$	−7748.40	+	16089.7i	−0.271293	+	0.563346i	−0.991453	−	0.130462i	$-0.958354\pi$
$13$	−7748.40	+	16089.7i	−0.271293	+	0.563346i	0.720160	+	0.693808i	$0.244068\pi$
$14$	1588.53	+	14098.6i	0.0413508	+	0.366999i
$15$	15911.1	−	1792.75i	0.314293	−	0.0354124i
$16$	51129.7	+	24622.8i	0.780178	+	0.375714i
$17$	84171.3	−	84171.3i	1.00779	−	1.00779i	0.00781685	−	0.999969i	$-0.497512\pi$
$17$	84171.3	−	84171.3i	1.00779	−	1.00779i	0.999969	−	0.00781685i	$-0.00248821\pi$
$18$	−5653.73	−	16157.4i	−0.0538573	−	0.153915i
$19$	−104146.	−	165748.i	−0.799153	−	1.27184i	−0.958633	−	0.284644i	$-0.908125\pi$
$19$	−104146.	−	165748.i	−0.799153	−	1.27184i	0.159480	−	0.987201i	$-0.449018\pi$
$20$	−32756.8	+	15774.8i	−0.204730	+	0.0985928i
$21$	147974.	−	422886.i	0.760866	−	2.17443i
$22$	−56923.9	+	12992.5i	−0.242999	+	0.0554629i
$23$	264640.	−	331848.i	0.945680	−	1.18584i	−0.0367713	−	0.999324i	$-0.511707\pi$
$23$	264640.	−	331848.i	0.945680	−	1.18584i	0.982451	−	0.186521i	$-0.0597213\pi$
$24$	114442.	+	143505.i	0.344937	+	0.432537i
$25$	−81997.2	+	359253.i	−0.209913	+	0.919688i
$26$	32382.3	−	51536.2i	0.0708622	−	0.112777i
$27$	18539.2	−	164540.i	0.0348848	−	0.309611i
$28$			1.01732e6i			1.65510i
$29$	−176923.	+	684795.i	−0.250146	+	0.968208i
$29$	−176923.	+	684795.i	−0.250146	+	0.968208i
$30$	−54572.2			−0.0673731
$31$	−1.15962e6	−	130658.i	−1.25565	−	0.141478i	−0.541037	−	0.840999i	$-0.681968\pi$
$31$	−1.15962e6	−	130658.i	−1.25565	−	0.141478i	−0.714612	+	0.699521i	$0.753397\pi$
$32$	−533443.	−	335185.i	−0.508731	−	0.319657i
$33$	1.79756e6	+	410281.i	1.51575	+	0.345960i
$34$	−317193.	+	252953.i	−0.237360	+	0.189289i
$35$	−484191.	−	386129.i	−0.322659	−	0.257312i
$36$	−273128.	−	1.19665e6i	−0.162613	−	0.712455i
$37$	204986.	+	71727.9i	0.109375	+	0.0382720i	0.384412	−	0.923162i	$-0.374404\pi$
$37$	204986.	+	71727.9i	0.109375	+	0.0382720i	−0.275037	+	0.961434i	$0.588690\pi$
$38$	289475.	+	601102.i	0.138828	+	0.288279i
$39$	−1.62742e6	+	1.02258e6i	−0.703465	+	0.442016i
$40$	239482.	−	83798.3i	0.0935476	−	0.0327337i
$41$	1.66890e6	+	1.66890e6i	0.590601	+	0.590601i	0.937794	−	0.347193i	$-0.112865\pi$
$41$	1.66890e6	+	1.66890e6i	0.590601	+	0.590601i	−0.347193	+	0.937794i	$0.612865\pi$
$42$	−662536.	+	1.37577e6i	−0.212918	+	0.442129i
$43$	−548264.	−	4.86598e6i	−0.160367	−	1.42330i	−0.773738	−	0.633505i	$-0.781616\pi$
$43$	−548264.	−	4.86598e6i	−0.160367	−	1.42330i	0.613371	−	0.789795i	$-0.289813\pi$
$44$	−4.16029e6	+	468752.i	−1.10997	+	0.125064i
$45$	673211.	+	324201.i	0.164173	+	0.0790615i
$46$	−1.02292e6	+	1.02292e6i	−0.228461	+	0.228461i
$47$	1.62666e6	+	4.64872e6i	0.333353	+	0.952670i	0.981552	+	0.191198i	$0.0612372\pi$
$47$	1.62666e6	+	4.64872e6i	0.333353	+	0.952670i	−0.648198	+	0.761472i	$0.724477\pi$
$48$	3.24954e6	+	5.17161e6i	0.612149	+	0.974229i
$49$	−1.04188e7	+	5.01743e6i	−1.80731	+	0.870356i
$50$	414802.	−	1.18544e6i	0.0663683	−	0.189670i
$51$	1.24903e7	−	2.85082e6i	1.84625	−	0.421395i
$52$	2.72107e6	−	3.41212e6i	0.372158	−	0.466671i
$53$	353674.	+	443494.i	0.0448229	+	0.0562062i	0.803738	−	0.594984i	$-0.202842\pi$
$53$	353674.	+	443494.i	0.0448229	+	0.0562062i	−0.758915	+	0.651190i	$0.774270\pi$
$54$	−125578.	+	550193.i	−0.0147686	+	0.0647053i
$55$	1.35596e6	−	2.15800e6i	0.148182	−	0.235831i
$56$	794876.	−	7.05472e6i	0.0808253	−	0.717344i
$57$		−	2.10682e7i		−	1.99585i
$58$	860528.	−	2.25176e6i	0.0760419	−	0.198981i
$59$	−8.80499e6			−0.726642			−0.363321	−	0.931664i	$-0.618357\pi$
$59$	−8.80499e6			−0.726642			−0.363321	+	0.931664i	$0.618357\pi$
$60$	−3.88842e6	−	438119.i	−0.300032	−	0.0338055i
$61$	7.19943e6	+	4.52370e6i	0.519970	+	0.326719i	0.766317	−	0.642463i	$-0.222087\pi$
$61$	7.19943e6	+	4.52370e6i	0.519970	+	0.326719i	−0.246347	+	0.969182i	$0.579230\pi$
$62$	3.87756e6	+	885028.i	0.262417	+	0.0598949i
$63$	1.63463e7	−	1.30357e7i	1.03767	−	0.827510i
$64$	−9.67962e6	−	7.71924e6i	−0.576950	−	0.460102i
$65$	591192.	+	2.59018e6i	0.0331188	+	0.145103i
$66$	−5.93145e6	−	2.07550e6i	−0.312597	−	0.109383i
$67$	3.69729e6	+	7.67750e6i	0.183478	+	0.380996i	0.972339	−	0.233576i	$-0.0750428\pi$
$67$	3.69729e6	+	7.67750e6i	0.183478	+	0.380996i	−0.788860	+	0.614572i	$0.789329\pi$
$68$	−2.46317e7	+	1.54771e7i	−1.15201	+	0.723859i
$69$	4.31186e7	−	1.50879e7i	1.90225	−	0.665627i
$70$	1.49252e6	+	1.49252e6i	0.0621624	+	0.0621624i
$71$	−2.49640e6	+	5.18383e6i	−0.0982383	+	0.203994i	−0.944296	−	0.329097i	$-0.893256\pi$
$71$	−2.49640e6	+	5.18383e6i	−0.0982383	+	0.203994i	0.846058	+	0.533091i	$0.178970\pi$
$72$	959041.	+	8.51173e6i	0.0356868	+	0.316729i
$73$	3.80473e6	−	428690.i	0.133978	−	0.0150957i	−0.0447209	−	0.999000i	$-0.514240\pi$
$73$	3.80473e6	−	428690.i	0.133978	−	0.0150957i	0.178699	+	0.983904i	$0.442811\pi$
$74$	−666881.	−	321153.i	−0.0222393	−	0.0107099i
$75$	−2.80436e7	+	2.80436e7i	−0.886316	+	0.886316i
$76$	1.58001e7	+	4.51541e7i	0.473593	+	1.35345i
$77$	−3.79413e7	−	6.03833e7i	−1.07932	−	1.71773i
$78$	5.90202e6	−	2.84226e6i	0.159449	−	0.0767866i
$79$	−8.61152e6	+	2.46103e7i	−0.221091	+	0.631843i	0.778898	+	0.627151i	$0.215779\pi$
$79$	−8.61152e6	+	2.46103e7i	−0.221091	+	0.631843i	−0.999989	+	0.00469159i	$0.998507\pi$
$80$	8.23105e6	−	1.87868e6i	0.200953	−	0.0458663i
$81$	3.16569e7	−	3.96965e7i	0.735408	−	0.922173i
$82$	−5.01540e6	−	6.28911e6i	−0.110930	−	0.139102i
$83$	4.84998e6	−	2.12492e7i	0.102195	−	0.447744i	−0.897779	−	0.440447i	$-0.854820\pi$
$83$	4.84998e6	−	2.12492e7i	0.102195	−	0.447744i	0.999973	−	0.00729701i	$-0.00232273\pi$
$84$	−5.82525e7	+	9.27084e7i	−1.17003	+	1.86209i
$85$	1.98280e6	−	1.75978e7i	0.0379842	−	0.337119i
$86$			1.66894e7i			0.305104i
$87$	−5.53351e7	+	5.22747e7i	−0.965880	+	0.912462i
$88$	2.92163e7			0.487186
$89$	5.28693e7	+	5.95694e6i	0.842643	+	0.0949431i	0.522724	−	0.852502i	$-0.324916\pi$
$89$	5.28693e7	+	5.95694e6i	0.842643	+	0.0949431i	0.319919	+	0.947445i	$0.396344\pi$
$90$	−2.15633e6	−	1.35491e6i	−0.0328659	−	0.0206510i
$91$	7.24762e7	+	1.65422e7i	1.05689	+	0.241228i
$92$	−8.10983e7	+	6.46737e7i	−1.13204	+	0.902769i
$93$	−9.81947e7	−	7.83076e7i	−1.31267	−	1.04682i
$94$	−3.73524e6	−	1.63651e7i	−0.0478417	−	0.209608i
$95$	−2.74881e7	−	9.61849e6i	−0.337481	−	0.118090i
$96$	−2.94198e7	−	6.10909e7i	−0.346382	−	0.719269i
$97$	4.25081e6	−	2.67096e6i	0.0480159	−	0.0301704i	−0.507810	−	0.861469i	$-0.669545\pi$
$97$	4.25081e6	−	2.67096e6i	0.0480159	−	0.0301704i	0.555826	+	0.831299i	$0.312402\pi$
$98$	3.72013e7	−	1.30173e7i	0.403323	−	0.141129i
$99$	6.08412e7	+	6.08412e7i	0.633369	+	0.633369i
$100$	3.90728e7	−	8.11354e7i	0.390728	−	0.811354i
$101$	1.57876e7	+	1.40119e8i	0.151716	+	1.34651i	0.806741	+	0.590906i	$0.201229\pi$
$101$	1.57876e7	+	1.40119e8i	0.151716	+	1.34651i	−0.655025	+	0.755607i	$0.727342\pi$
$102$	−4.33902e7	+	4.88890e6i	−0.400859	+	0.0451659i
$103$	9.41089e7	+	4.53205e7i	0.836146	+	0.402667i	0.802416	−	0.596764i	$-0.203547\pi$
$103$	9.41089e7	+	4.53205e7i	0.836146	+	0.402667i	0.0337293	+	0.999431i	$0.489262\pi$
$104$	−2.15357e7	+	2.15357e7i	−0.184088	+	0.184088i
$105$	−2.20143e7	−	6.29133e7i	−0.181112	−	0.517589i
$106$	−1.02859e6	−	1.63700e6i	−0.00814742	−	0.0129666i
$107$	−2.08404e7	+	1.00362e7i	−0.158990	+	0.0765656i	−0.511687	−	0.859172i	$-0.670979\pi$
$107$	−2.08404e7	+	1.00362e7i	−0.158990	+	0.0765656i	0.352696	+	0.935738i	$0.385265\pi$
$108$	−1.33648e7	+	3.81945e7i	−0.0982356	+	0.280741i
$109$	1.33234e8	−	3.04097e7i	0.943861	−	0.215430i	0.277218	−	0.960807i	$-0.410588\pi$
$109$	1.33234e8	−	3.04097e7i	0.943861	−	0.215430i	0.666643	+	0.745377i	$0.267731\pi$
$110$	−5.41590e6	+	6.79133e6i	−0.0369913	+	0.0463857i
$111$	1.45733e7	+	1.82743e7i	0.0959985	+	0.120378i
$112$	5.25677e7	−	2.30314e8i	0.334077	−	1.46369i
$113$	9.58299e7	−	1.52512e8i	0.587742	−	0.935387i	−0.411965	−	0.911200i	$-0.635157\pi$
$113$	9.58299e7	−	1.52512e8i	0.587742	−	0.935387i	0.999707	−	0.0241871i	$-0.00769975\pi$
$114$	−8.03968e6	+	7.13542e7i	−0.0476014	+	0.422474i
$115$		−	6.31459e7i		−	0.361039i
$116$	7.93927e7	−	1.53536e8i	0.438479	−	0.847965i
$117$	−8.96934e7			−0.478649
$118$	2.98209e7	+	3.36001e6i	0.153813	+	0.0173306i
$119$	−4.19571e8	−	2.63634e8i	−2.09227	−	1.31466i
$120$	2.66224e7	+	6.07639e6i	0.128387	+	0.0293036i
$121$	6.18607e7	−	4.93323e7i	0.288585	−	0.230139i
$122$	−2.26569e7	−	1.80683e7i	−0.102273	−	0.0815601i
$123$	5.65244e7	+	2.47649e8i	0.246954	+	1.08197i
$124$	2.69181e8	+	9.41907e7i	1.13857	+	0.398402i
$125$	4.90006e7	+	1.01751e8i	0.200706	+	0.416771i
$126$	−6.03365e7	+	3.79119e7i	−0.239385	+	0.150416i
$127$	−497478.	+	174075.i	−0.00191231	+	0.000669148i	−0.331235	−	0.943548i	$-0.607465\pi$
$127$	−497478.	+	174075.i	−0.00191231	+	0.000669148i	0.329323	+	0.944217i	$0.393180\pi$
$128$	1.43881e8	+	1.43881e8i	0.535999	+	0.535999i
$129$	2.28667e8	−	4.74832e8i	0.825742	−	1.71467i
$130$	−1.01384e6	−	8.99808e6i	−0.00354974	−	0.0315048i
$131$	3.08718e8	−	3.47841e7i	1.04828	−	0.118113i	0.429016	−	0.903297i	$-0.358860\pi$
$131$	3.08718e8	−	3.47841e7i	1.04828	−	0.118113i	0.619262	+	0.785184i	$0.287432\pi$
$132$	−4.05969e8	−	1.95504e8i	−1.33720	−	0.643963i
$133$	−5.76203e8	+	5.76203e8i	−1.84149	+	1.84149i
$134$	−9.59230e6	−	2.74132e7i	−0.0297511	−	0.0850239i
$135$	−1.31059e7	−	2.08580e7i	−0.0394578	−	0.0627967i
$136$	1.82904e8	−	8.80821e7i	0.534648	−	0.257473i
$137$	−4.12178e7	+	1.17794e8i	−0.117005	+	0.334380i	−0.987460	−	0.157867i	$-0.949538\pi$
$137$	−4.12178e7	+	1.17794e8i	−0.117005	+	0.334380i	0.870456	+	0.492246i	$0.163824\pi$
$138$	−1.51793e8	+	3.46457e7i	−0.418537	+	0.0955284i
$139$	8.09970e7	−	1.01567e8i	0.216975	−	0.272078i	−0.661418	−	0.750018i	$-0.730045\pi$
$139$	8.09970e7	−	1.01567e8i	0.216975	−	0.272078i	0.878393	+	0.477940i	$0.158616\pi$
$140$	9.43638e7	+	1.18328e8i	0.245637	+	0.308019i
$141$	−1.17952e8	+	5.16783e8i	−0.298422	+	1.30747i
$142$	1.04330e7	−	1.66041e7i	0.0256600	−	0.0408377i
$143$	−3.42538e7	+	3.04011e8i	−0.0819153	+	0.727019i
$144$			2.85027e8i			0.662881i
$145$	4.29412e7	+	9.60623e7i	0.0971408	+	0.217311i
$146$	−1.30495e7			−0.0287199
$147$	−1.23677e9	−	1.39350e8i	−2.64862	−	0.298428i
$148$	−4.49388e7	−	2.82369e7i	−0.0936644	−	0.0588532i
$149$	9.93718e7	+	2.26810e7i	0.201613	+	0.0460168i	0.322135	−	0.946694i	$-0.395600\pi$
$149$	9.93718e7	+	2.26810e7i	0.201613	+	0.0460168i	−0.120522	+	0.992711i	$0.538457\pi$
$150$	1.05680e8	−	8.42771e7i	0.208751	−	0.166473i
$151$	6.82916e8	+	5.44607e8i	1.31359	+	1.04755i	0.995022	+	0.0996515i	$0.0317728\pi$
$151$	6.82916e8	+	5.44607e8i	1.31359	+	1.04755i	0.318566	+	0.947901i	$0.396799\pi$
$152$	−7.42869e7	−	3.25472e8i	−0.139168	−	0.609733i
$153$	5.64312e8	+	1.97461e8i	1.02980	+	0.360343i
$154$	1.05458e8	+	2.18986e8i	0.187498	+	0.389344i
$155$	−1.46999e8	+	9.23658e7i	−0.254676	+	0.160024i
$156$	4.43353e8	−	1.55136e8i	0.748602	−	0.261947i
$157$	8.35367e7	+	8.35367e7i	0.137492	+	0.137492i	0.772503	−	0.635011i	$-0.219004\pi$
$157$	8.35367e7	+	8.35367e7i	0.137492	+	0.137492i	−0.635011	+	0.772503i	$0.719004\pi$
$158$	3.85571e7	−	8.00646e7i	0.0618694	−	0.128473i
$159$	6.83557e6	+	6.06674e7i	0.0106951	+	0.0949220i
$160$	−9.31379e7	+	1.04941e7i	−0.142117	+	0.0160128i
$161$	−1.59192e9	−	7.66626e8i	−2.36928	−	1.14099i
$162$	−1.22365e8	+	1.22365e8i	−0.177663	+	0.177663i
$163$	−4.03354e8	−	1.15272e9i	−0.571394	−	1.63295i	−0.759283	−	0.650760i	$-0.774450\pi$
$163$	−4.03354e8	−	1.15272e9i	−0.571394	−	1.63295i	0.187889	−	0.982190i	$-0.439835\pi$
$164$	−3.06870e8	−	4.88381e8i	−0.424208	−	0.675124i
$165$	2.47138e8	−	1.19016e8i	0.333430	−	0.160571i
$166$	−2.45348e7	+	7.01163e7i	−0.0323109	+	0.0923394i
$167$	3.44047e8	−	7.85264e7i	0.442335	−	0.100960i	0.00444815	−	0.999990i	$-0.498584\pi$
$167$	3.44047e8	−	7.85264e7i	0.442335	−	0.100960i	0.437887	+	0.899030i	$0.355727\pi$
$168$	4.76397e8	−	5.97383e8i	0.598042	−	0.749921i
$169$	3.09759e8	+	3.88425e8i	0.379731	+	0.476168i
$170$	−1.34308e7	+	5.88441e7i	−0.0160807	+	0.0704542i
$171$	5.23078e8	−	8.32474e8i	0.611762	−	0.973613i
$172$	−1.33987e8	+	1.18917e9i	−0.153091	+	1.35872i
$173$			8.31431e8i			0.928200i	0.885783	+	0.464100i	$0.153622\pi$
$173$			8.31431e8i			0.928200i	−0.885783	+	0.464100i	$0.846378\pi$
$174$	2.07358e8	−	1.55929e8i	0.226216	−	0.170110i
$175$	1.53395e9			1.63554
$176$	9.66084e8	+	1.08851e8i	1.00685	+	0.113445i
$177$	−8.02400e8	−	5.04181e8i	−0.817519	−	0.513681i
$178$	−1.76786e8	−	4.03502e7i	−0.176103	−	0.0401944i
$179$	−1.30473e9	+	1.04048e9i	−1.27089	+	1.01350i	−0.272203	+	0.962240i	$0.587752\pi$
$179$	−1.30473e9	+	1.04048e9i	−1.27089	+	1.01350i	−0.998685	+	0.0512594i	$0.983676\pi$
$180$	−1.42767e8	−	1.13853e8i	−0.135999	−	0.108456i
$181$	2.00834e8	+	8.79910e8i	0.187121	+	0.819830i	0.978125	+	0.208019i	$0.0667016\pi$
$181$	2.00834e8	+	8.79910e8i	0.187121	+	0.819830i	−0.791004	+	0.611811i	$0.790441\pi$
$182$	−2.39151e8	−	8.36826e7i	−0.217965	−	0.0762693i
$183$	3.97054e8	+	8.24491e8i	0.354034	+	0.735160i
$184$	6.12919e8	−	3.85122e8i	0.534726	−	0.335991i
$185$	3.04961e7	−	1.06710e7i	0.0260350	−	0.00911004i
$186$	3.02685e8	+	3.02685e8i	0.252895	+	0.252895i
$187$	8.84796e8	−	1.83730e9i	0.723563	−	1.50249i
$188$	−1.34762e8	−	1.19605e9i	−0.107879	−	0.957452i
$189$	−6.84944e8	+	7.71747e7i	−0.536795	+	0.0604822i
$190$	8.94267e7	+	4.30656e7i	0.0686204	+	0.0330458i
$191$	−1.23847e9	+	1.23847e9i	−0.930576	+	0.930576i	−0.997742	−	0.0671659i	$-0.978604\pi$
$191$	−1.23847e9	+	1.23847e9i	−0.930576	+	0.930576i	0.0671659	+	0.997742i	$0.478604\pi$
$192$	−4.40095e8	−	1.25772e9i	−0.323848	−	0.925505i
$193$	−9.16535e8	−	1.45866e9i	−0.660571	−	1.05129i	−0.994091	−	0.108550i	$-0.965379\pi$
$193$	−9.16535e8	−	1.45866e9i	−0.660571	−	1.05129i	0.333520	−	0.942743i	$-0.391764\pi$
$194$	−1.54160e7	+	7.42395e6i	−0.0108834	+	0.00524117i
$195$	−9.44407e7	+	2.69896e8i	−0.0653162	+	0.186663i
$196$	2.75520e9	−	6.28856e8i	1.86693	−	0.426115i
$197$	−2.19898e8	+	2.75743e8i	−0.146001	+	0.183079i	−0.849455	−	0.527662i	$-0.823069\pi$
$197$	−2.19898e8	+	2.75743e8i	−0.146001	+	0.183079i	0.703454	+	0.710741i	$0.251640\pi$
$198$	−1.82841e8	−	2.29275e8i	−0.118963	−	0.149175i
$199$	3.89783e8	−	1.70775e9i	0.248548	−	1.08896i	−0.684445	−	0.729065i	$-0.739955\pi$
$199$	3.89783e8	−	1.70775e9i	0.248548	−	1.08896i	0.932993	−	0.359895i	$-0.117188\pi$
$200$	−3.34350e8	+	5.32114e8i	−0.208969	+	0.332572i
$201$	−1.02686e8	+	9.11363e8i	−0.0629110	+	0.558351i
$202$		−	4.80582e8i		−	0.288643i
$203$	2.94307e9	+	8.36979e7i	1.73307	+	0.0492868i
$204$	−3.13092e9			−1.80780
$205$	3.48919e8	+	3.93137e7i	0.197564	+	0.0222602i
$206$	−3.01436e8	−	1.89405e8i	−0.167389	−	0.105177i
$207$	2.07836e9	+	4.74372e8i	1.13198	+	0.258367i
$208$	−7.92347e8	+	6.31875e8i	−0.423313	+	0.337581i
$209$	−2.62186e9	−	2.09087e9i	−1.37412	−	1.09583i
$210$	5.05506e7	+	2.21477e8i	0.0259926	+	0.113881i
$211$	1.66350e9	+	5.82083e8i	0.839252	+	0.293667i	0.715471	−	0.698643i	$-0.246212\pi$
$211$	1.66350e9	+	5.82083e8i	0.839252	+	0.293667i	0.123781	+	0.992310i	$0.460498\pi$
$212$	−6.01478e7	−	1.24898e8i	−0.0297767	−	0.0618320i
$213$	−5.24328e8	+	3.29457e8i	−0.254733	+	0.160059i
$214$	7.44125e7	−	2.60380e7i	0.0354806	−	0.0124152i
$215$	−5.15127e8	−	5.15127e8i	−0.241079	−	0.241079i
$216$	1.22523e8	−	2.54422e8i	0.0562864	−	0.116880i
$217$	5.43900e8	+	4.82724e9i	0.245290	+	2.17701i
$218$	−4.62843e8	+	5.21499e7i	−0.204931	+	0.0230902i
$219$	3.71273e8	+	1.78796e8i	0.161405	+	0.0777285i
$220$	−4.40420e8	+	4.40420e8i	−0.188008	+	0.188008i
$221$	7.02099e8	+	2.00649e9i	0.294327	+	0.841137i
$222$	−4.23835e7	−	6.74529e7i	−0.0174496	−	0.0277708i
$223$	−1.28917e9	+	6.20833e8i	−0.521305	+	0.251047i	−0.675982	−	0.736918i	$-0.736280\pi$
$223$	−1.28917e9	+	6.20833e8i	−0.521305	+	0.251047i	0.154678	+	0.987965i	$0.450566\pi$
$224$	−8.66187e8	+	2.47542e9i	−0.344048	+	0.983234i
$225$	−1.80436e9	+	4.11833e8i	−0.704033	+	0.160691i
$226$	−3.82758e8	+	4.79963e8i	−0.146720	+	0.183981i
$227$	−1.38968e9	−	1.74260e9i	−0.523372	−	0.656288i	0.447949	−	0.894059i	$-0.352155\pi$
$227$	−1.38968e9	−	1.74260e9i	−0.523372	−	0.656288i	−0.971321	+	0.237771i	$0.923583\pi$
$228$	−1.14570e9	+	5.01963e9i	−0.423966	+	1.85752i
$229$	−2.36899e9	+	3.77022e9i	−0.861431	+	1.37096i	0.0663349	+	0.997797i	$0.478869\pi$
$229$	−2.36899e9	+	3.77022e9i	−0.861431	+	1.37096i	−0.927766	+	0.373162i	$0.878273\pi$
$230$	−2.40967e7	+	2.13864e8i	−0.00861085	+	0.0764234i
$231$		−	7.67529e9i		−	2.69555i
$232$	−6.70523e8	+	1.00268e9i	−0.231452	+	0.346107i
$233$	4.66651e9			1.58332			0.791659	−	0.610963i	$-0.209218\pi$
$233$	4.66651e9			1.58332			0.791659	+	0.610963i	$0.209218\pi$
$234$	3.03776e8	+	3.42273e7i	0.101319	+	0.0114159i
$235$	6.20407e8	+	3.89827e8i	0.203425	+	0.127821i
$236$	2.09785e9	+	4.78820e8i	0.676279	+	0.154356i
$237$	−2.19398e9	+	1.74964e9i	−0.695407	+	0.554569i
$238$	1.32041e9	+	1.05299e9i	0.411529	+	0.328183i
$239$	−5.26821e8	−	2.30815e9i	−0.161462	−	0.707413i	−0.989233	−	0.146347i	$-0.953248\pi$
$239$	−5.26821e8	−	2.30815e9i	−0.161462	−	0.707413i	0.827771	−	0.561066i	$-0.189609\pi$
$240$	8.57673e8	+	3.00113e8i	0.258510	+	0.0904564i
$241$	−1.79504e9	−	3.72743e9i	−0.532114	−	1.10495i	−0.977758	−	0.209736i	$-0.932740\pi$
$241$	−1.79504e9	−	3.72743e9i	−0.532114	−	1.10495i	0.445644	−	0.895210i	$-0.352975\pi$
$242$	−2.28337e8	+	1.43473e8i	−0.0665754	+	0.0418321i
$243$	4.13255e9	−	1.44604e9i	1.18520	−	0.414720i
$244$	−1.46931e9	−	1.46931e9i	−0.414528	−	0.414528i
$245$	−7.46449e8	+	1.55002e9i	−0.207174	+	0.430202i
$246$	−9.69341e7	−	8.60314e8i	−0.0264689	−	0.234918i
$247$	3.47381e9	−	3.91404e8i	0.933293	−	0.105157i
$248$	−1.79308e9	−	8.63501e8i	−0.474015	−	0.228274i
$249$	1.65873e9	−	1.65873e9i	0.431496	−	0.431496i
$250$	−1.27128e8	−	3.63311e8i	−0.0325447	−	0.0930075i
$251$	−1.53725e9	−	2.44652e9i	−0.387302	−	0.616388i	0.594992	−	0.803731i	$-0.297155\pi$
$251$	−1.53725e9	−	2.44652e9i	−0.387302	−	0.616388i	−0.982294	+	0.187344i	$0.940012\pi$
$252$	−4.60350e9	+	2.21693e9i	−1.14153	+	0.549731i
$253$	2.40158e9	−	6.86333e9i	0.586159	−	1.67515i
$254$	1.75130e6	−	399722.i	0.000420751	−	9.60337e-5i
$255$	1.18836e9	−	1.49016e9i	0.281052	−	0.352429i
$256$	1.54373e9	+	1.93578e9i	0.359428	+	0.450708i
$257$	7.70072e8	−	3.37391e9i	0.176522	−	0.773394i	−0.806697	−	0.590965i	$-0.798747\pi$
$257$	7.70072e8	−	3.37391e9i	0.176522	−	0.773394i	0.983219	−	0.182429i	$-0.0583958\pi$
$258$	−9.55652e8	+	1.52091e9i	−0.215685	+	0.343261i
$259$	1.01221e8	−	8.98363e8i	0.0224943	−	0.199642i
$260$		−	6.49277e8i		−	0.142081i
$261$	−3.48434e9	+	6.91698e8i	−0.750860	+	0.149058i
$262$	−1.05885e9			−0.224713
$263$	−3.01232e7	−	3.39407e6i	−0.00629620	−	0.000709411i	0.108816	−	0.994062i	$-0.465294\pi$
$263$	−3.01232e7	−	3.39407e6i	−0.00629620	−	0.000709411i	−0.115112	+	0.993353i	$0.536723\pi$
$264$	2.66249e9	+	1.67295e9i	0.548116	+	0.344404i
$265$	8.22746e7	+	1.87787e7i	0.0166833	+	0.00380786i
$266$	2.17138e9	−	1.73162e9i	0.433720	−	0.345880i
$267$	4.47689e9	+	3.57020e9i	0.880910	+	0.702503i
$268$	−4.63397e8	−	2.03028e9i	−0.0898285	−	0.393565i
$269$	8.13371e8	+	2.84611e8i	0.155339	+	0.0543554i	0.406828	−	0.913505i	$-0.366635\pi$
$269$	8.13371e8	+	2.84611e8i	0.155339	+	0.0543554i	−0.251490	+	0.967860i	$0.580920\pi$
$270$	3.64280e7	+	7.56434e7i	0.00685456	+	0.0142336i
$271$	−1.35166e9	+	8.49306e8i	−0.250606	+	0.157466i	−0.651477	−	0.758668i	$-0.725850\pi$
$271$	−1.35166e9	+	8.49306e8i	−0.250606	+	0.157466i	0.400871	+	0.916134i	$0.368707\pi$
$272$	6.37619e9	−	2.23112e9i	1.16489	−	0.407613i
$273$	5.65754e9	+	5.65754e9i	1.01854	+	1.01854i
$274$	1.84548e8	−	3.83218e8i	0.0327421	−	0.0679897i
$275$	7.06804e8	+	6.27306e9i	0.123586	+	1.09685i
$276$	−1.10938e10	+	1.24997e9i	−1.91180	+	0.215408i
$277$	6.23510e9	+	3.00266e9i	1.05907	+	0.510020i	0.880568	−	0.473919i	$-0.157161\pi$
$277$	6.23510e9	+	3.00266e9i	1.05907	+	0.510020i	0.178500	+	0.983940i	$0.442875\pi$
$278$	−3.13081e8	+	3.13081e8i	−0.0524176	+	0.0524176i
$279$	−1.93579e9	−	5.53216e9i	−0.319478	−	0.913015i
$280$	−5.61922e8	−	8.94294e8i	−0.0914206	−	0.145495i
$281$	−8.58942e9	+	4.13645e9i	−1.37765	+	0.663441i	−0.968497	−	0.249025i	$-0.919890\pi$
$281$	−8.58942e9	+	4.13645e9i	−1.37765	+	0.663441i	−0.409152	+	0.912466i	$0.634175\pi$
$282$	5.96690e8	−	1.70524e9i	0.0943522	−	0.269643i
$283$	−8.69506e8	+	1.98459e8i	−0.135559	+	0.0309404i	−0.289762	−	0.957099i	$-0.593576\pi$
$283$	−8.69506e8	+	1.98459e8i	−0.135559	+	0.0309404i	0.154203	+	0.988039i	$0.450719\pi$
$284$	8.76683e8	−	1.09933e9i	0.134763	−	0.168987i
$285$	−1.95423e9	−	2.45053e9i	−0.296208	−	0.371433i
$286$	2.32023e8	−	1.01656e9i	0.0346791	−	0.151939i
$287$	5.22717e9	−	8.31899e9i	0.770440	−	1.22615i
$288$	3.54282e8	−	3.14434e9i	0.0514966	−	0.457045i
$289$		−	7.19386e9i		−	1.03127i
$290$	−1.08776e8	−	3.41732e8i	−0.0153795	−	0.0483163i
$291$	5.40319e8			0.0753491
$292$	−9.29814e8	−	1.04765e8i	−0.127898	−	0.0144107i
$293$	4.54326e8	+	2.85472e8i	0.0616449	+	0.0387341i	0.562502	−	0.826796i	$-0.309839\pi$
$293$	4.54326e8	+	2.85472e8i	0.0616449	+	0.0387341i	−0.500857	+	0.865530i	$0.666982\pi$
$294$	4.13554e9	+	9.43910e8i	0.553532	+	0.126340i
$295$	−1.02414e9	+	8.16728e8i	−0.135230	+	0.107842i
$296$	2.89571e8	+	2.30925e8i	0.0377214	+	0.0300818i
$297$	−6.31207e8	−	2.76550e9i	−0.0811234	−	0.355425i
$298$	−3.27899e8	−	1.14737e8i	−0.0415791	−	0.0145492i
$299$	3.28880e9	+	6.82927e9i	0.411484	+	0.854456i
$300$	8.20659e9	−	5.15655e9i	1.01316	−	0.636611i
$301$	−1.92403e10	+	6.73248e9i	−2.34394	+	0.820179i
$302$	−2.10509e9	−	2.10509e9i	−0.253071	−	0.253071i
$303$	−6.58460e9	+	1.36731e10i	−0.781194	+	1.62217i
$304$	−1.24380e9	−	1.10390e10i	−0.145632	−	1.29252i
$305$	1.25700e9	−	1.41630e8i	0.145257	−	0.0163665i
$306$	−1.83587e9	−	8.84110e8i	−0.209391	−	0.100837i
$307$	5.20914e7	−	5.20914e7i	0.00586425	−	0.00586425i	−0.704169	−	0.710033i	$-0.748680\pi$
$307$	5.20914e7	−	5.20914e7i	0.00586425	−	0.00586425i	0.710033	+	0.704169i	$0.248680\pi$
$308$	5.75610e9	+	1.64500e10i	0.639625	+	1.82794i
$309$	5.98108e9	+	9.51883e9i	0.656063	+	1.04412i
$310$	5.33108e8	−	2.56731e8i	0.0577256	−	0.0277992i
$311$	2.04581e9	−	5.84660e9i	0.218688	−	0.624974i	−0.781312	−	0.624141i	$-0.785449\pi$
$311$	2.04581e9	−	5.84660e9i	0.218688	−	0.624974i	1.00000		0.000832860i	$-0.000265108\pi$
$312$	−3.19570e9	+	7.29398e8i	−0.337247	+	0.0769744i
$313$	−9.22166e9	+	1.15636e10i	−0.960797	+	1.20480i	0.0179722	+	0.999838i	$0.494279\pi$
$313$	−9.22166e9	+	1.15636e10i	−0.960797	+	1.20480i	−0.978770	+	0.204963i	$0.934292\pi$
$314$	−2.51046e8	−	3.14802e8i	−0.0258247	−	0.0323831i
$315$	6.92144e8	−	3.03248e9i	0.0702998	−	0.308004i
$316$	3.39007e9	−	5.39527e9i	0.339986	−	0.541084i
$317$	−9.68604e8	+	8.59660e9i	−0.0959200	+	0.851314i	0.849971	+	0.526829i	$0.176619\pi$
$317$	−9.68604e8	+	8.59660e9i	−0.0959200	+	0.851314i	−0.945891	+	0.324484i	$0.894809\pi$
$318$		−	2.08078e8i		−	0.0203478i
$319$	1.01381e9	+	1.20742e10i	0.0979021	+	1.16599i
$320$	−1.84189e9			−0.175657
$321$	−2.47387e9	−	2.78738e8i	−0.233000	−	0.0262528i
$322$	5.09899e9	+	3.20391e9i	0.474308	+	0.298027i
$323$	−2.27174e10	−	5.18509e9i	−2.08712	−	0.476372i
$324$	−9.70119e9	+	7.73644e9i	−0.880329	+	0.702039i
$325$	−5.14493e9	−	4.10295e9i	−0.461154	−	0.367758i
$326$	9.26206e8	+	4.05798e9i	0.0820044	+	0.359285i
$327$	1.38829e10	+	4.85784e9i	1.21420	+	0.424866i
$328$	1.74644e9	+	3.62651e9i	0.150889	+	0.313324i
$329$	1.73597e10	−	1.09078e10i	1.48169	−	0.931009i
$330$	−8.82430e8	+	3.08776e8i	−0.0744088	+	0.0260368i
$331$	−1.14545e10	−	1.14545e10i	−0.954250	−	0.954250i	0.0447480	−	0.998998i	$-0.485752\pi$
$331$	−1.14545e10	−	1.14545e10i	−0.954250	−	0.954250i	−0.998998	+	0.0447480i	$0.985752\pi$
$332$	−2.31108e9	+	4.79901e9i	−0.190223	+	0.395002i
$333$	1.22126e8	+	1.08390e9i	0.00993190	+	0.0881481i
$334$	−1.19519e9	+	1.34666e8i	−0.0960398	+	0.0108211i
$335$	1.14219e9	+	5.50051e8i	0.0906901	+	0.0436741i
$336$	1.79785e10	−	1.79785e10i	1.41057	−	1.41057i
$337$	−1.29833e9	−	3.71042e9i	−0.100662	−	0.287676i	0.882528	−	0.470259i	$-0.155840\pi$
$337$	−1.29833e9	−	3.71042e9i	−0.100662	−	0.287676i	−0.983190	+	0.182584i	$0.941554\pi$
$338$	−9.00873e8	−	1.43373e9i	−0.0690235	−	0.109850i
$339$	1.74660e10	−	8.41118e9i	1.32250	−	0.636881i
$340$	−1.42939e9	+	4.08497e9i	−0.106964	+	0.305685i
$341$	−1.94902e10	+	4.44852e9i	−1.44145	+	0.329002i
$342$	−2.08925e9	+	2.61983e9i	−0.152716	+	0.191500i
$343$	1.50515e10	+	1.88740e10i	1.08744	+	1.36360i
$344$	1.85830e9	−	8.14174e9i	0.132703	−	0.581411i
$345$	3.61579e9	−	5.75450e9i	0.255227	−	0.406192i
$346$	3.17277e8	−	2.81591e9i	0.0221378	−	0.196478i
$347$			1.57531e10i			1.08655i	0.839556	+	0.543273i	$0.182815\pi$
$347$			1.57531e10i			1.08655i	−0.839556	+	0.543273i	$0.817185\pi$
$348$	1.60267e10	−	9.44565e9i	1.09276	−	0.644043i
$349$	−1.22854e10			−0.828109			−0.414055	−	0.910252i	$-0.635888\pi$
$349$	−1.22854e10			−0.828109			−0.414055	+	0.910252i	$0.635888\pi$
$350$	−5.19523e9	−	5.85362e8i	−0.346204	−	0.0390079i
$351$	2.50375e9	+	1.57321e9i	0.164954	+	0.103647i
$352$	−1.05223e10	−	2.40164e9i	−0.685392	−	0.156436i
$353$	1.77453e10	−	1.41514e10i	1.14284	−	0.911381i	0.145876	−	0.989303i	$-0.453400\pi$
$353$	1.77453e10	−	1.41514e10i	1.14284	−	0.911381i	0.996959	+	0.0779221i	$0.0248285\pi$
$354$	2.52519e9	+	2.01377e9i	0.160798	+	0.128232i
$355$	1.90472e8	+	8.34512e8i	0.0119927	+	0.0525435i
$356$	−1.22725e10	−	4.29434e9i	−0.764072	−	0.267360i
$357$	−2.31397e10	−	4.80500e10i	−1.42457	−	2.95815i
$358$	4.81593e9	−	3.02605e9i	0.293189	−	0.184223i
$359$	1.76933e10	−	6.19117e9i	1.06520	−	0.372731i	0.259925	−	0.965629i	$-0.416302\pi$
$359$	1.76933e10	−	6.19117e9i	1.06520	−	0.372731i	0.805277	+	0.592898i	$0.202016\pi$
$360$	9.01076e8	+	9.01076e8i	0.0536477	+	0.0536477i
$361$	−9.25706e9	+	1.92225e10i	−0.545060	+	1.13183i
$362$	−3.44412e8	−	3.05674e9i	−0.0200560	−	0.178002i
$363$	8.46219e9	−	9.53460e8i	0.487367	−	0.0549131i
$364$	−1.63683e10	−	7.88258e9i	−0.932394	−	0.449017i
$365$	4.02780e8	−	4.02780e8i	0.0226932	−	0.0226932i
$366$	−1.03012e9	−	2.94392e9i	−0.0574070	−	0.164060i
$367$	−4.77061e9	−	7.59238e9i	−0.262972	−	0.418517i	0.688973	−	0.724787i	$-0.258062\pi$
$367$	−4.77061e9	−	7.59238e9i	−0.262972	−	0.418517i	−0.951945	+	0.306270i	$0.900919\pi$
$368$	2.17020e10	−	1.04511e10i	1.18334	−	0.569865i
$369$	−3.91514e9	+	1.11888e10i	−0.211175	+	0.603503i
$370$	−1.07357e8	+	2.45035e7i	−0.00572827	+	0.00130744i
$371$	1.47227e9	−	1.84617e9i	0.0777127	−	0.0974487i
$372$	1.91371e10	+	2.39972e10i	0.999320	+	1.25311i
$373$	1.42674e9	−	6.25096e9i	0.0737071	−	0.322932i	−0.924611	−	0.380914i	$-0.875609\pi$
$373$	1.42674e9	−	6.25096e9i	0.0737071	−	0.322932i	0.998318	+	0.0579819i	$0.0184666\pi$
$374$	−3.69776e9	+	5.88496e9i	−0.188996	+	0.300786i
$375$	−1.36091e9	+	1.20784e10i	−0.0688182	+	0.610779i
$376$			8.39944e9i			0.420242i
$377$	−9.64729e9	−	8.15271e9i	−0.477573	−	0.403586i
$378$	2.34923e9			0.115069
$379$	−7.84148e8	−	8.83523e7i	−0.0380050	−	0.00428214i	0.0929415	−	0.995672i	$-0.470373\pi$
$379$	−7.84148e8	−	8.83523e7i	−0.0380050	−	0.00428214i	−0.130947	+	0.991389i	$0.541802\pi$
$380$	6.02615e9	+	3.78648e9i	0.289005	+	0.181594i
$381$	−5.53030e7	−	1.26225e7i	−0.00262451	−	0.000599028i
$382$	4.66708e9	−	3.72187e9i	0.219175	−	0.174786i
$383$	7.71604e9	+	6.15333e9i	0.358591	+	0.285967i	0.786169	−	0.618012i	$-0.212062\pi$
$383$	7.71604e9	+	6.15333e9i	0.358591	+	0.285967i	−0.427578	+	0.903978i	$0.640633\pi$
$384$	4.87315e9	+	2.13507e10i	0.224122	+	0.981945i
$385$	−1.00141e10	−	3.50409e9i	−0.455795	−	0.159489i
$386$	2.54751e9	+	5.28996e9i	0.114754	+	0.238289i
$387$	2.08245e10	−	1.30849e10i	0.928389	−	0.583345i
$388$	−1.15803e9	+	4.05213e8i	−0.0510968	+	0.0178795i
$389$	2.16358e10	+	2.16358e10i	0.944875	+	0.944875i	0.998558	−	0.0536834i	$-0.0170962\pi$
$389$	2.16358e10	+	2.16358e10i	0.944875	+	0.944875i	−0.0536834	+	0.998558i	$0.517096\pi$
$390$	4.22847e8	−	8.78051e8i	0.0182778	−	0.0379543i
$391$	−5.65699e9	−	5.02072e10i	−0.242035	−	2.14812i
$392$	−1.95976e10	+	2.20812e9i	−0.829964	+	0.0935144i
$393$	3.01253e10	+	1.45076e10i	1.26288	+	0.608169i
$394$	8.49978e8	−	8.49978e8i	0.0352714	−	0.0352714i
$395$	1.28115e9	+	3.66131e9i	0.0526273	+	0.150400i
$396$	−1.11872e10	−	1.78044e10i	−0.454928	−	0.724013i
$397$	−2.84332e10	+	1.36927e10i	−1.14463	+	0.551224i	−0.907416	−	0.420234i	$-0.861948\pi$
$397$	−2.84332e10	+	1.36927e10i	−1.14463	+	0.551224i	−0.237212	+	0.971458i	$0.576234\pi$
$398$	−1.97181e9	+	5.63510e9i	−0.0785837	+	0.224579i
$399$	−8.55035e10	+	1.95156e10i	−3.37359	+	0.769999i
$400$	−1.30383e10	+	1.63495e10i	−0.509309	+	0.638653i
$401$	1.24805e10	+	1.56501e10i	0.482675	+	0.605255i	0.962224	−	0.272260i	$-0.0877711\pi$
$401$	1.24805e10	+	1.56501e10i	0.482675	+	0.605255i	−0.479549	+	0.877515i	$0.659200\pi$
$402$	6.95558e8	−	3.04744e9i	0.0266335	−	0.116689i
$403$	1.10874e10	−	1.76455e10i	0.420349	−	0.668982i
$404$	3.85823e9	−	3.42427e10i	0.144831	−	1.28541i
$405$		−	7.55368e9i		−	0.280762i
$406$	−9.93571e9	−	1.40655e9i	−0.365675	−	0.0517669i
$407$	3.72047e9			0.135588
$408$	2.17118e10	+	2.44633e9i	0.783528	+	0.0882824i
$409$	2.62180e10	+	1.64739e10i	0.936930	+	0.588712i	0.911650	−	0.410969i	$-0.134809\pi$
$409$	2.62180e10	+	1.64739e10i	0.936930	+	0.588712i	0.0252800	+	0.999680i	$0.491952\pi$
$410$	−1.16672e9	−	2.66297e8i	−0.0412888	−	0.00942390i
$411$	−1.05012e10	+	8.37440e9i	−0.368019	+	0.293485i
$412$	−1.99575e10	−	1.59156e10i	−0.692656	−	0.552375i
$413$	8.15612e9	+	3.57343e10i	0.280339	+	1.22825i
$414$	−6.85801e9	−	2.39972e9i	−0.233452	−	0.0816882i
$415$	−1.40690e9	−	2.92145e9i	−0.0474318	−	0.0984931i
$416$	9.52636e9	−	5.98581e9i	0.318093	−	0.199871i
$417$	1.31971e10	−	4.61786e9i	0.436449	−	0.152720i
$418$	8.08191e9	+	8.08191e9i	0.264733	+	0.264733i
$419$	−5.41884e9	+	1.12523e10i	−0.175813	+	0.365079i	−0.970190	−	0.242346i	$-0.922083\pi$
$419$	−5.41884e9	+	1.12523e10i	−0.175813	+	0.365079i	0.794377	+	0.607425i	$0.207797\pi$
$420$	1.82380e9	+	1.61866e10i	0.0586110	+	0.520187i
$421$	−2.00268e10	+	2.25648e9i	−0.637504	+	0.0718294i	−0.424800	−	0.905287i	$-0.639656\pi$
$421$	−2.00268e10	+	2.25648e9i	−0.637504	+	0.0718294i	−0.212704	+	0.977117i	$0.568227\pi$
$422$	−5.41184e9	−	2.60621e9i	−0.170646	−	0.0821787i
$423$	−1.74913e10	+	1.74913e10i	−0.546338	+	0.546338i
$424$	3.19514e8	+	9.13119e8i	0.00988614	+	0.0282530i
$425$	2.33370e10	+	3.71406e10i	0.715302	+	1.13840i
$426$	1.90153e9	−	9.15728e8i	0.0577384	−	0.0278053i
$427$	1.16902e10	−	3.34086e10i	0.351649	−	1.00496i
$428$	5.51113e9	−	1.25788e9i	0.164235	−	0.0374856i
$429$	−2.05295e10	+	2.57432e10i	−0.606107	+	0.760035i
$430$	1.54807e9	+	1.94122e9i	0.0452810	+	0.0567806i
$431$	1.42482e10	−	6.24255e10i	0.412906	−	1.80906i	−0.157293	−	0.987552i	$-0.550277\pi$
$431$	1.42482e10	−	6.24255e10i	0.412906	−	1.80906i	0.570199	−	0.821507i	$-0.306866\pi$
$432$	4.99933e9	−	7.95639e9i	0.143541	−	0.228445i
$433$	−4.26063e9	+	3.78141e10i	−0.121206	+	1.07573i	0.774960	+	0.632010i	$0.217770\pi$
$433$	−4.26063e9	+	3.78141e10i	−0.121206	+	1.07573i	−0.896166	+	0.443719i	$0.853659\pi$
$434$		−	1.65566e10i		−	0.466671i
$435$	−1.58738e9	+	1.12130e10i	−0.0443326	+	0.313160i
$436$	−3.33975e10			−0.924204
$437$	−8.25645e10	−	9.30278e9i	−2.26395	−	0.255086i
$438$	−1.18921e9	−	7.47228e8i	−0.0323118	−	0.0203028i
$439$	5.53733e10	+	1.26386e10i	1.49088	+	0.340283i	0.888852	−	0.458194i	$-0.151503\pi$
$439$	5.53733e10	+	1.26386e10i	1.49088	+	0.340283i	0.602026	+	0.798477i	$0.294361\pi$
$440$	3.39827e9	−	2.71003e9i	0.0906666	−	0.0723042i
$441$	−4.54091e10	−	3.62126e10i	−1.20057	−	0.957425i
$442$	−1.61220e9	−	7.06353e9i	−0.0422407	−	0.185069i
$443$	5.29001e10	+	1.85106e10i	1.37354	+	0.480623i	0.913342	−	0.407193i	$-0.133492\pi$
$443$	5.29001e10	+	1.85106e10i	1.37354	+	0.480623i	0.460199	+	0.887816i	$0.347778\pi$
$444$	−2.47841e9	−	5.14647e9i	−0.0637736	−	0.132427i
$445$	6.70200e9	−	4.21115e9i	0.170909	−	0.107389i
$446$	4.60311e9	−	1.61070e9i	0.116335	−	0.0407075i
$447$	7.75704e9	+	7.75704e9i	0.194297	+	0.194297i
$448$	−2.23616e10	+	4.64343e10i	−0.555125	+	1.15273i
$449$	−6.35001e9	−	5.63579e10i	−0.156239	−	1.38666i	−0.789989	−	0.613121i	$-0.789914\pi$
$449$	−6.35001e9	−	5.63579e10i	−0.156239	−	1.38666i	0.633750	−	0.773538i	$-0.281515\pi$
$450$	6.26820e9	−	7.06256e8i	0.152860	−	0.0172231i
$451$	3.64288e10	+	1.75432e10i	0.880519	+	0.424035i
$452$	−3.11258e10	+	3.11258e10i	−0.745704	+	0.745704i
$453$	3.10496e10	+	8.87346e10i	0.737331	+	2.10717i
$454$	4.04161e9	+	6.43219e9i	0.0951330	+	0.151403i
$455$	9.96441e9	−	4.79861e9i	0.232491	−	0.111962i
$456$	1.18671e10	−	3.39141e10i	0.274463	−	0.784370i
$457$	2.99919e10	−	6.84545e9i	0.687605	−	0.156941i	0.135577	−	0.990767i	$-0.456711\pi$
$457$	2.99919e10	−	6.84545e9i	0.687605	−	0.156941i	0.552028	+	0.833826i	$0.313854\pi$
$458$	9.46206e9	−	1.18650e10i	0.215042	−	0.269654i
$459$	−1.22891e10	−	1.54100e10i	−0.276865	−	0.347178i
$460$	−3.43391e9	+	1.50449e10i	−0.0766933	+	0.336015i
$461$	2.28200e10	−	3.63178e10i	0.505256	−	0.804111i	−0.492552	−	0.870283i	$-0.663936\pi$
$461$	2.28200e10	−	3.63178e10i	0.505256	−	0.804111i	0.997808	+	0.0661723i	$0.0210787\pi$
$462$	−2.92892e9	+	2.59949e10i	−0.0642894	+	0.570584i
$463$		−	5.73547e10i		−	1.24809i	−0.781389	−	0.624044i	$-0.785489\pi$
$463$		−	5.73547e10i		−	1.24809i	0.781389	−	0.624044i	$-0.214511\pi$
$464$	−2.59076e10	+	3.06570e10i	−0.558927	+	0.661391i
$465$	−1.86850e10			−0.399652
$466$	−1.58046e10	−	1.78075e9i	−0.335151	−	0.0377624i
$467$	−2.86174e10	−	1.79815e10i	−0.601676	−	0.378058i	0.196481	−	0.980508i	$-0.437049\pi$
$467$	−2.86174e10	−	1.79815e10i	−0.601676	−	0.378058i	−0.798157	+	0.602450i	$0.794191\pi$
$468$	2.13701e10	+	4.87758e9i	0.445474	+	0.101676i
$469$	2.77337e10	−	2.21169e10i	0.573213	−	0.457122i
$470$	−1.95245e9	−	1.55703e9i	−0.0400118	−	0.0319083i
$471$	2.82933e9	+	1.23961e10i	0.0574910	+	0.251885i
$472$	−1.41737e10	−	4.95958e9i	−0.285571	−	0.0999256i
$473$	−3.63977e10	−	7.55805e10i	−0.727158	−	1.50996i
$474$	8.09828e9	−	5.08849e9i	0.160428	−	0.100803i
$475$	6.80853e10	−	2.38241e10i	1.33745	−	0.467995i
$476$	8.56290e10	+	8.56290e10i	1.66799	+	1.66799i
$477$	−1.23615e9	+	2.56688e9i	−0.0238779	+	0.0495830i
$478$	9.03450e8	+	8.01834e9i	0.0173058	+	0.153594i
$479$	3.85638e9	−	4.34509e8i	0.0732550	−	0.00825386i	−0.0752609	−	0.997164i	$-0.523979\pi$
$479$	3.85638e9	−	4.34509e8i	0.0732550	−	0.00825386i	0.148516	+	0.988910i	$0.452550\pi$
$480$	−9.08858e9	−	4.37683e9i	−0.171211	−	0.0824507i
$481$	−2.74240e9	+	2.74240e9i	−0.0512330	+	0.0512330i
$482$	4.65707e9	+	1.33091e10i	0.0862828	+	0.246582i
$483$	−1.01174e11	−	1.61017e11i	−1.85900	−	2.95858i
$484$	−1.74214e10	+	8.38972e9i	−0.317470	+	0.152885i
$485$	2.46678e8	−	7.04965e8i	0.00445824	−	0.0127409i
$486$	−1.45480e10	+	3.32049e9i	−0.260771	+	0.0595192i
$487$	2.55420e10	−	3.20286e10i	0.454086	−	0.569406i	−0.501108	−	0.865385i	$-0.667074\pi$
$487$	2.55420e10	−	3.20286e10i	0.454086	−	0.569406i	0.955195	+	0.295978i	$0.0956456\pi$
$488$	9.04108e9	+	1.13372e10i	0.159419	+	0.199906i
$489$	2.92480e10	−	1.28144e11i	0.511518	−	2.24111i
$490$	3.11958e9	−	4.96479e9i	0.0541143	−	0.0861224i
$491$	2.38971e8	−	2.12093e9i	0.00411168	−	0.0364922i	−0.991489	−	0.130192i	$-0.958441\pi$
$491$	2.38971e8	−	2.12093e9i	0.00411168	−	0.0364922i	0.995601	+	0.0936995i	$0.0298693\pi$
$492$		−	6.20779e10i		−	1.05944i
$493$	4.27483e10	+	7.25320e10i	0.723653	+	1.22784i
$494$	−1.19145e10			−0.200064
$495$	1.27202e10	+	1.43322e9i	0.211871	+	0.0238721i
$496$	−5.60738e10	−	3.52335e10i	−0.926474	−	0.582142i
$497$	2.33506e10	+	5.32962e9i	0.382712	+	0.0873515i
$498$	−6.25078e9	+	4.98483e9i	−0.101629	+	0.0810463i
$499$	6.66929e10	+	5.31858e10i	1.07567	+	0.857815i	0.990357	−	0.138540i	$-0.0442409\pi$
$499$	6.66929e10	+	5.31858e10i	1.07567	+	0.857815i	0.0853087	+	0.996355i	$0.472812\pi$
$500$	−6.14146e9	−	2.69075e10i	−0.0982633	−	0.430520i
$501$	3.58495e10	+	1.25443e10i	0.569027	+	0.199111i
$502$	4.27279e9	+	8.87255e9i	0.0672817	+	0.139712i
$503$	−8.33838e10	+	5.23935e10i	−1.30260	+	0.818475i	−0.991272	−	0.131829i	$-0.957915\pi$
$503$	−8.33838e10	+	5.23935e10i	−1.30260	+	0.818475i	−0.311323	+	0.950304i	$0.600772\pi$
$504$	3.36558e10	−	1.17767e10i	0.521600	−	0.182516i
$505$	1.48334e10	+	1.48334e10i	0.228073	+	0.228073i
$506$	−1.07528e10	+	2.23284e10i	−0.164029	+	0.340609i
$507$	5.98680e9	+	5.31343e10i	0.0906072	+	0.804161i
$508$	1.27994e8	−	1.44214e7i	0.00192191	−	0.000216548i
$509$	4.52086e8	+	2.17713e8i	0.00673519	+	0.00324350i	0.437248	−	0.899341i	$-0.355953\pi$
$509$	4.52086e8	+	2.17713e8i	0.00673519	+	0.00324350i	−0.430513	+	0.902584i	$0.641667\pi$
$510$	−4.59341e9	+	4.59341e9i	−0.0678977	+	0.0678977i
$511$	−5.26415e9	−	1.50441e10i	−0.0772049	−	0.220639i
$512$	−3.22035e10	−	5.12516e10i	−0.468622	−	0.745808i
$513$	−2.92030e10	+	1.40634e10i	−0.421655	+	0.203058i
$514$	−3.89559e9	+	1.11330e10i	−0.0558111	+	0.159499i
$515$	1.51500e10	−	3.45789e9i	0.215369	−	0.0491567i
$516$	−8.03030e10	+	1.00697e11i	−1.13275	+	1.42042i
$517$	5.26060e10	+	6.59658e10i	0.736331	+	0.923330i
$518$	−6.85636e8	+	3.00397e9i	−0.00952302	+	0.0417231i
$519$	−4.76085e10	+	7.57685e10i	−0.656168	+	1.04429i
$520$	−5.07309e8	+	4.50250e9i	−0.00693840	+	0.0615800i
$521$		−	2.17155e10i		−	0.294726i	−0.989082	−	0.147363i	$-0.952921\pi$
$521$		−	2.17155e10i		−	0.294726i	0.989082	−	0.147363i	$-0.0470786\pi$
$522$	1.20648e10	−	1.01302e9i	0.162494	−	0.0136438i
$523$	1.55816e10			0.208259			0.104130	−	0.994564i	$-0.466794\pi$
$523$	1.55816e10			0.208259			0.104130	+	0.994564i	$0.466794\pi$
$524$	−7.54456e10	−	8.50068e9i	−1.00071	−	0.112753i
$525$	1.39790e11	+	8.78356e10i	1.84008	+	1.15620i
$526$	1.00727e8	+	2.29902e7i	0.00131584	+	0.000300331i
$527$	−1.08604e11	+	8.66090e10i	−1.40800	+	1.12285i
$528$	8.18065e10	+	6.52385e10i	1.05257	+	0.839399i
$529$	−2.26630e10	−	9.92929e10i	−0.289397	−	1.26793i
$530$	−2.71484e8	−	9.49962e7i	−0.00344065	−	0.00120393i
$531$	−1.91878e10	−	3.98438e10i	−0.241349	−	0.501167i
$532$	1.68618e11	−	1.05950e11i	2.10503	−	1.32268i
$533$	−3.97833e10	+	1.39208e10i	−0.492938	+	0.172487i
$534$	−1.38000e10	−	1.38000e10i	−0.169713	−	0.169713i
$535$	−1.49310e9	+	3.10045e9i	−0.0182252	+	0.0378451i
$536$	1.62714e9	+	1.44413e10i	0.0197136	+	0.174963i
$537$	−1.78479e11	+	2.01098e10i	−2.14630	+	0.241830i
$538$	−2.64613e9	−	1.27431e9i	−0.0315851	−	0.0152106i
$539$	−1.40082e11	+	1.40082e11i	−1.65969	+	1.65969i
$540$	1.98831e9	+	5.68225e9i	0.0233834	+	0.0668260i
$541$	−3.82051e10	−	6.08030e10i	−0.445997	−	0.709800i	0.545759	−	0.837942i	$-0.316241\pi$
$541$	−3.82051e10	−	6.08030e10i	−0.445997	−	0.709800i	−0.991756	+	0.128142i	$0.959099\pi$
$542$	4.90194e9	−	2.36065e9i	0.0568029	−	0.0273548i
$543$	−3.20824e10	+	9.16863e10i	−0.369035	+	1.05464i
$544$	−7.31136e10	+	1.66877e10i	−0.834838	+	0.190546i
$545$	1.26762e10	−	1.58955e10i	0.143683	−	0.180172i
$546$	−1.70022e10	−	2.13200e10i	−0.191308	−	0.239893i
$547$	−1.87317e10	+	8.20688e10i	−0.209232	+	0.916703i	0.755848	+	0.654747i	$0.227225\pi$
$547$	−1.87317e10	+	8.20688e10i	−0.209232	+	0.916703i	−0.965080	+	0.261956i	$0.915632\pi$
$548$	1.62261e10	−	2.58237e10i	0.179925	−	0.286349i
$549$	−4.78144e9	+	4.24364e10i	−0.0526343	+	0.467143i
$550$		−	2.15154e10i		−	0.235125i
$551$	1.31929e11	−	4.19943e10i	1.43132	−	0.455600i
$552$	7.79079e10			0.839122
$553$	1.07856e11	+	1.21524e10i	1.15330	+	0.129946i
$554$	−1.99713e10	−	1.25488e10i	−0.212016	−	0.133218i
$555$	3.39015e9	+	7.73780e8i	0.0357312	+	0.00815540i
$556$	−2.48213e10	+	1.97944e10i	−0.259732	+	0.207130i
$557$	−1.10978e11	−	8.85023e10i	−1.15297	−	0.919462i	−0.155312	−	0.987866i	$-0.549638\pi$
$557$	−1.10978e11	−	8.85023e10i	−1.15297	−	0.919462i	−0.997658	+	0.0684030i	$0.978210\pi$
$558$	4.44507e9	+	1.94751e10i	0.0458503	+	0.200883i
$559$	8.25404e10	+	2.88821e10i	0.845316	+	0.295789i
$560$	−1.52490e10	−	3.16648e10i	−0.155056	−	0.321977i
$561$	1.85837e11	−	1.16769e11i	1.87621	−	1.17890i
$562$	3.06693e10	−	1.07317e10i	0.307439	−	0.107578i
$563$	6.66447e10	+	6.66447e10i	0.663334	+	0.663334i	0.956164	−	0.292830i	$-0.0945972\pi$
$563$	6.66447e10	+	6.66447e10i	0.663334	+	0.663334i	−0.292830	+	0.956164i	$0.594597\pi$
$564$	5.62059e10	−	1.16713e11i	0.555476	−	1.15346i
$565$	−3.00029e9	−	2.66283e10i	−0.0294421	−	0.261306i
$566$	3.02060e9	−	3.40339e8i	0.0294325	−	0.00331624i
$567$	−1.90429e11	−	9.17058e10i	−1.84247	−	0.887288i
$568$	−6.93842e9	+	6.93842e9i	−0.0666603	+	0.0666603i
$569$	−3.79824e10	−	1.08548e11i	−0.362355	−	1.03555i	−0.970370	−	0.241625i	$-0.922320\pi$
$569$	−3.79824e10	−	1.08548e11i	−0.362355	−	1.03555i	0.608015	−	0.793925i	$-0.291966\pi$
$570$	5.68350e9	+	9.04524e9i	0.0538414	+	0.0856881i
$571$	−6.50167e10	+	3.13104e10i	−0.611619	+	0.294540i	−0.713935	−	0.700212i	$-0.753089\pi$
$571$	−6.50167e10	+	3.13104e10i	−0.611619	+	0.294540i	0.102316	+	0.994752i	$0.467375\pi$
$572$	2.46935e10	−	7.05699e10i	0.230674	−	0.659228i
$573$	−1.83778e11	+	4.19461e10i	−1.70480	+	0.389111i
$574$	−2.08780e10	+	2.61802e10i	−0.192328	+	0.241171i
$575$	9.75177e10	+	1.22283e11i	0.892097	+	1.11865i
$576$	1.38369e10	−	6.06233e10i	0.125704	−	0.550744i
$577$	−7.44649e9	+	1.18510e10i	−0.0671813	+	0.106918i	−0.878626	−	0.477511i	$-0.841539\pi$
$577$	−7.44649e9	+	1.18510e10i	−0.0671813	+	0.106918i	0.811444	+	0.584430i	$0.198682\pi$
$578$	−2.74520e9	+	2.43643e10i	−0.0245959	+	0.218295i
$579$		−	1.85409e11i		−	1.64975i
$580$	−5.00710e9	−	2.52226e10i	−0.0442460	−	0.222884i
$581$	−9.07305e10			−0.796249
$582$	−1.82996e9	−	2.06187e8i	−0.0159496	−	0.00179709i
$583$	8.22824e9	+	5.17014e9i	0.0712250	+	0.0447536i
$584$	6.36606e9	+	1.45301e9i	0.0547292	+	0.0124916i
$585$	−1.04326e10	+	8.31973e9i	−0.0890778	+	0.0710372i
$586$	−1.42978e9	−	1.14022e9i	−0.0121250	−	0.00966933i
$587$	4.77577e10	+	2.09240e11i	0.402246	+	1.76235i	0.618270	+	0.785966i	$0.287834\pi$
$587$	4.77577e10	+	2.09240e11i	0.402246	+	1.76235i	−0.216025	+	0.976388i	$0.569309\pi$
$588$	2.87091e11	+	1.00457e11i	2.40165	+	0.840373i
$589$	9.91138e10	+	2.05812e11i	0.823518	+	1.71005i
$590$	3.78026e9	−	2.37529e9i	0.0311971	−	0.0196024i
$591$	−3.58286e10	+	1.25370e10i	−0.293684	+	0.102764i
$592$	8.71476e9	+	8.71476e9i	0.0709527	+	0.0709527i
$593$	6.13828e10	−	1.27463e11i	0.496396	−	1.03078i	−0.490801	−	0.871271i	$-0.663296\pi$
$593$	6.13828e10	−	1.27463e11i	0.496396	−	1.03078i	0.987197	−	0.159505i	$-0.0509898\pi$
$594$	1.08246e9	+	9.60712e9i	0.00869495	+	0.0771698i
$595$	−7.32560e10	+	8.25397e9i	−0.584488	+	0.0658559i
$596$	−2.24426e10	−	1.08078e10i	−0.177864	−	0.0856547i
$597$	1.33308e11	−	1.33308e11i	1.04945	−	1.04945i
$598$	−8.53252e9	−	2.43845e10i	−0.0667225	−	0.190682i
$599$	−1.24730e11	−	1.98506e11i	−0.968863	−	1.54194i	−0.834503	−	0.551004i	$-0.814245\pi$
$599$	−1.24730e11	−	1.98506e11i	−0.968863	−	1.54194i	−0.134360	−	0.990933i	$-0.542898\pi$
$600$	−6.09387e10	+	2.93465e10i	−0.470206	+	0.226439i
$601$	−6.92439e9	+	1.97888e10i	−0.0530743	+	0.151677i	−0.967369	−	0.253372i	$-0.918460\pi$
$601$	−6.92439e9	+	1.97888e10i	−0.0530743	+	0.151677i	0.914295	+	0.405050i	$0.132746\pi$
$602$	6.77326e10	−	1.54595e10i	0.515718	−	0.117709i
$603$	−2.66847e10	+	3.34615e10i	−0.201833	+	0.253091i
$604$	−1.33093e11	−	1.66894e11i	−1.00002	−	1.25398i
$605$	2.61934e9	−	1.14761e10i	0.0195511	−	0.0856588i
$606$	2.75185e10	−	4.37955e10i	0.204049	−	0.324742i
$607$	−2.55360e10	+	2.26638e11i	−0.188104	+	1.66947i	0.445099	+	0.895481i	$0.353169\pi$
$607$	−2.55360e10	+	2.26638e11i	−0.188104	+	1.66947i	−0.633203	+	0.773986i	$0.718260\pi$
$608$			1.23326e11i			0.902482i
$609$	2.63410e11	+	1.76150e11i	1.91497	+	1.28060i
$610$	−4.31129e9			−0.0311378
$611$	−8.74006e10	−	9.84768e9i	−0.627119	−	0.0706593i
$612$	−1.23713e11	−	7.77341e10i	−0.881881	−	0.554123i
$613$	2.18279e11	+	4.98208e10i	1.54586	+	0.352833i	0.908551	−	0.417774i	$-0.137190\pi$
$613$	2.18279e11	+	4.98208e10i	1.54586	+	0.352833i	0.637311	+	0.770607i	$0.280047\pi$
$614$	−1.96302e8	+	1.56546e8i	−0.00138119	+	0.00110146i
$615$	2.95459e10	+	2.35621e10i	0.206536	+	0.164707i
$616$	−2.70633e10	−	1.18572e11i	−0.187957	−	0.823492i
$617$	1.09968e11	+	3.84794e10i	0.758795	+	0.265514i	0.681821	−	0.731519i	$-0.261188\pi$
$617$	1.09968e11	+	3.84794e10i	0.758795	+	0.265514i	0.0769745	+	0.997033i	$0.475474\pi$
$618$	−1.66244e10	−	3.45210e10i	−0.113971	−	0.236662i
$619$	1.04571e11	−	6.57066e10i	0.712279	−	0.447555i	−0.126542	−	0.991961i	$-0.540388\pi$
$619$	1.04571e11	−	6.57066e10i	0.712279	−	0.447555i	0.838822	+	0.544406i	$0.183245\pi$
$620$	4.00465e10	−	1.40129e10i	0.271018	−	0.0948332i
$621$	−4.96960e10	−	4.96960e10i	−0.334161	−	0.334161i
$622$	−9.15988e9	+	1.90207e10i	−0.0611968	+	0.127076i
$623$	−2.47975e10	−	2.20084e11i	−0.164610	−	1.46095i
$624$	−1.08388e11	+	1.22124e10i	−0.714899	+	0.0805498i
$625$	−1.14550e11	−	5.51643e10i	−0.750714	−	0.361525i
$626$	3.56448e10	−	3.56448e10i	0.232113	−	0.232113i
$627$	−1.19206e11	−	3.40672e11i	−0.771309	−	2.20427i
$628$	−1.53604e10	−	2.44459e10i	−0.0987562	−	0.157170i
$629$	2.32914e10	−	1.12166e10i	0.148797	−	0.0716567i
$630$	−3.50137e9	+	1.00063e10i	−0.0222268	+	0.0635204i
$631$	−2.01346e11	+	4.59559e10i	−1.27006	+	0.289884i	−0.803874	−	0.594800i	$-0.797231\pi$
$631$	−2.01346e11	+	4.59559e10i	−1.27006	+	0.289884i	−0.466191	+	0.884684i	$0.654374\pi$
$632$	−2.77245e10	+	3.47654e10i	−0.173778	+	0.217911i
$633$	1.18264e11	+	1.48299e11i	0.736612	+	0.923682i
$634$	6.56098e9	−	2.87455e10i	0.0406080	−	0.177915i
$635$	−4.17170e7	+	6.63922e7i	−0.000256577	+	0.000408340i
$636$	1.67050e9	−	1.48261e10i	0.0102098	−	0.0906148i
$637$		−	2.06512e11i		−	1.25426i
$638$	1.17396e9	−	4.12799e10i	0.00708549	−	0.249147i
$639$	−2.88977e10			−0.173324
$640$	3.00815e10	+	3.38937e9i	0.179299	+	0.0202022i
$641$	−7.74921e10	−	4.86915e10i	−0.459014	−	0.288417i	0.282608	−	0.959235i	$-0.408800\pi$
$641$	−7.74921e10	−	4.86915e10i	−0.459014	−	0.288417i	−0.741622	+	0.670818i	$0.765943\pi$
$642$	8.27219e9	+	1.88807e9i	0.0486945	+	0.0111142i
$643$	5.59861e10	−	4.46474e10i	0.327519	−	0.261187i	−0.445900	−	0.895083i	$-0.647116\pi$
$643$	5.59861e10	−	4.46474e10i	0.327519	−	0.261187i	0.773419	+	0.633895i	$0.218545\pi$
$644$	3.37595e11	+	2.69223e11i	1.96269	+	1.56520i
$645$	−1.74470e10	−	7.64402e10i	−0.100805	−	0.441655i
$646$	7.49611e10	+	2.62300e10i	0.430433	+	0.150615i
$647$	−9.89606e10	−	2.05494e11i	−0.564735	−	1.17269i	−0.966434	−	0.256913i	$-0.917294\pi$
$647$	−9.89606e10	−	2.05494e11i	−0.564735	−	1.17269i	0.401699	−	0.915772i	$-0.368420\pi$
$648$	7.33189e10	−	4.60693e10i	0.415830	−	0.261283i
$649$	−1.42376e11	+	4.98196e10i	−0.802525	+	0.280816i
$650$	1.58593e10	+	1.58593e10i	0.0888444	+	0.0888444i
$651$	−2.26847e11	+	4.71052e11i	−1.26301	+	2.62268i
$652$	3.34163e10	+	2.96578e11i	0.184913	+	1.64115i
$653$	2.31810e9	−	2.61188e8i	0.0127491	−	0.00143648i	−0.105588	−	0.994410i	$-0.533672\pi$
$653$	2.31810e9	−	2.61188e8i	0.0127491	−	0.00143648i	0.118337	+	0.992974i	$0.462244\pi$
$654$	−4.51651e10	−	2.17504e10i	−0.246884	−	0.118893i
$655$	3.26817e10	−	3.26817e10i	0.177558	−	0.177558i
$656$	4.42374e10	+	1.26423e11i	0.238877	+	0.682670i
$657$	1.02311e10	+	1.62827e10i	0.0549113	+	0.0873908i
$658$	−6.29566e10	+	3.03183e10i	−0.335844	+	0.161734i
$659$	−7.38901e10	+	2.11166e11i	−0.391782	+	1.11965i	0.564051	+	0.825740i	$0.309242\pi$
$659$	−7.38901e10	+	2.11166e11i	−0.391782	+	1.11965i	−0.955833	+	0.293910i	$0.905044\pi$
$660$	−6.53544e10	+	1.49167e10i	−0.344429	+	0.0786136i
$661$	1.03212e11	−	1.29423e11i	0.540659	−	0.677964i	−0.434193	−	0.900820i	$-0.642966\pi$
$661$	1.03212e11	−	1.29423e11i	0.540659	−	0.677964i	0.974851	+	0.222855i	$0.0715378\pi$
$662$	3.44231e10	+	4.31652e10i	0.179233	+	0.224751i
$663$	−5.09107e10	+	2.23054e11i	−0.263484	+	1.15440i
$664$	1.97762e10	−	3.14736e10i	0.101735	−	0.161910i
$665$	−1.35735e10	+	1.20468e11i	−0.0694071	+	0.616005i
$666$		−	3.71758e9i		−	0.0188957i
$667$	1.80427e11	+	2.39936e11i	0.911587	+	1.21225i
$668$	−8.62417e10			−0.433123
$669$	−1.53032e11	−	1.72426e10i	−0.763973	−	0.0860791i
$670$	−3.65850e9	−	2.29879e9i	−0.0181553	−	0.0114077i
$671$	1.42010e11	+	3.24129e10i	0.700533	+	0.159892i
$672$	−2.20681e11	+	1.75987e11i	−1.08215	+	0.862985i
$673$	1.03258e9	+	8.23458e8i	0.00503344	+	0.00401404i	0.626003	−	0.779820i	$-0.284690\pi$
$673$	1.03258e9	+	8.23458e8i	0.00503344	+	0.00401404i	−0.620970	+	0.783834i	$0.713261\pi$
$674$	2.98131e9	+	1.30620e10i	0.0144467	+	0.0632950i
$675$	5.75913e10	+	2.01521e10i	0.277423	+	0.0970744i
$676$	−5.26793e10	−	1.09390e11i	−0.252263	−	0.523829i
$677$	3.22046e10	−	2.02355e10i	0.153307	−	0.0963295i	−0.453194	−	0.891412i	$-0.649715\pi$
$677$	3.22046e10	−	2.02355e10i	0.153307	−	0.0963295i	0.606501	+	0.795083i	$0.292573\pi$
$678$	−6.23639e10	+	2.18221e10i	−0.295131	+	0.103271i
$679$	−1.47774e10	−	1.47774e10i	−0.0695216	−	0.0695216i
$680$	1.31041e10	−	2.72109e10i	0.0612874	−	0.127265i
$681$	−2.68587e10	−	2.38378e11i	−0.124881	−	1.10835i
$682$	6.77076e10	−	7.62881e9i	0.312968	−	0.0352630i
$683$	−1.48967e10	−	7.17388e9i	−0.0684554	−	0.0329664i	0.399343	−	0.916802i	$-0.369238\pi$
$683$	−1.48967e10	−	7.17388e9i	−0.0684554	−	0.0329664i	−0.467798	+	0.883835i	$0.654953\pi$
$684$	−1.69897e11	+	1.69897e11i	−0.776179	+	0.776179i
$685$	6.13203e9	+	1.75243e10i	0.0278511	+	0.0795938i
$686$	−4.37745e10	−	6.96667e10i	−0.197663	−	0.314578i
$687$	−4.31772e11	+	2.07931e11i	−1.93833	+	0.933451i
$688$	9.17813e10	−	2.62296e11i	0.409638	−	1.17068i
$689$	−9.87609e9	+	2.25415e9i	−0.0438236	+	0.0100025i
$690$	−1.44420e10	+	1.81097e10i	−0.0637133	+	0.0798940i
$691$	−4.53309e10	−	5.68432e10i	−0.198830	−	0.249325i	0.672414	−	0.740176i	$-0.265258\pi$
$691$	−4.53309e10	−	5.68432e10i	−0.198830	−	0.249325i	−0.871244	+	0.490850i	$0.836686\pi$
$692$	4.52136e10	−	1.98094e11i	0.197172	−	0.863867i
$693$	1.90561e11	−	3.03277e11i	0.826231	−	1.31494i
$694$	6.01144e9	−	5.33530e10i	0.0259144	−	0.229996i
$695$		−	1.93267e10i		−	0.0828361i
$696$	−1.18519e11	+	5.29797e10i	−0.505071	+	0.225773i
$697$	2.80946e11			1.19040
$698$	4.16085e10	+	4.68815e9i	0.175291	+	0.0197506i
$699$	4.25260e11	+	2.67208e11i	1.78133	+	1.11929i
$700$	−3.65475e11	−	8.34172e10i	−1.52218	−	0.347427i
$701$	−3.62926e10	+	2.89424e10i	−0.150295	+	0.119857i	−0.695751	−	0.718283i	$-0.744928\pi$
$701$	−3.62926e10	+	2.89424e10i	−0.150295	+	0.119857i	0.545455	+	0.838140i	$0.316357\pi$
$702$	−7.87941e9	−	6.28362e9i	−0.0324448	−	0.0258739i
$703$	−9.45985e9	−	4.14463e10i	−0.0387314	−	0.169693i
$704$	−2.00195e11	−	7.00514e10i	−0.815011	−	0.285185i
$705$	3.42159e10	+	7.10501e10i	0.138507	+	0.287613i
$706$	−6.55003e10	+	4.11565e10i	−0.263648	+	0.165661i
$707$	5.54036e11	−	1.93866e11i	2.21748	−	0.775931i
$708$	1.63760e11	+	1.63760e11i	0.651739	+	0.651739i
$709$	1.07574e10	−	2.23379e10i	0.0425717	−	0.0884011i	−0.878598	−	0.477562i	$-0.841521\pi$
$709$	1.07574e10	−	2.23379e10i	0.0425717	−	0.0884011i	0.921170	+	0.389161i	$0.127235\pi$
$710$	−3.26642e8	−	2.89903e9i	−0.00128540	−	0.0114083i
$711$	−1.30131e11	+	1.46623e10i	−0.509218	+	0.0573750i
$712$	8.17500e10	+	3.93687e10i	0.318103	+	0.153190i
$713$	−3.50240e11	+	3.50240e11i	−1.35521	+	1.35521i
$714$	6.00339e10	+	1.71567e11i	0.230996	+	0.660147i
$715$	2.42151e10	+	3.85381e10i	0.0926535	+	0.147457i
$716$	3.67442e11	−	1.76951e11i	1.39809	−	0.673287i
$717$	8.41577e10	−	2.40509e11i	0.318432	−	0.910027i
$718$	−6.22868e10	+	1.42166e10i	−0.234368	+	0.0534929i
$719$	−5.46804e10	+	6.85671e10i	−0.204605	+	0.256566i	−0.873538	−	0.486756i	$-0.838180\pi$
$719$	−5.46804e10	+	6.85671e10i	−0.204605	+	0.256566i	0.668933	+	0.743323i	$0.266751\pi$
$720$	2.64384e10	+	3.31527e10i	0.0983795	+	0.123364i
$721$	9.67556e10	−	4.23914e11i	0.358043	−	1.56869i
$722$	3.86874e10	−	6.15706e10i	0.142371	−	0.226582i
$723$	4.98540e10	−	4.42467e11i	0.182451	−	1.61930i
$724$		−	2.20566e11i		−	0.802757i
$725$	−2.31508e11	−	1.19712e11i	−0.837941	−	0.433295i
$726$	−2.90238e10			−0.104474
$727$	4.24450e10	+	4.78240e9i	0.151946	+	0.0171202i	0.187610	−	0.982244i	$-0.439926\pi$
$727$	4.24450e10	+	4.78240e9i	0.151946	+	0.0171202i	−0.0356639	+	0.999364i	$0.511355\pi$
$728$	1.07349e11	+	6.74521e10i	0.382185	+	0.240143i
$729$	1.34627e11	+	3.07277e10i	0.476675	+	0.108798i
$730$	−1.51784e9	+	1.21044e9i	−0.00534485	+	0.00426238i
$731$	−4.55724e11	−	3.63428e11i	−1.59600	−	1.27277i
$732$	−4.97645e10	−	2.18033e11i	−0.173331	−	0.759411i
$733$	7.96969e10	+	2.78871e10i	0.276074	+	0.0966025i	0.464765	−	0.885434i	$-0.346139\pi$
$733$	7.96969e10	+	2.78871e10i	0.276074	+	0.0966025i	−0.188691	+	0.982036i	$0.560424\pi$
$734$	1.32599e10	+	2.75345e10i	0.0456832	+	0.0948622i
$735$	−1.56780e11	+	9.85111e10i	−0.537205	+	0.337548i
$736$	−2.52401e11	+	8.83189e10i	−0.860160	+	0.300983i
$737$	1.03225e11	+	1.03225e11i	0.349877	+	0.349877i
$738$	1.75296e10	−	3.64006e10i	0.0590944	−	0.122711i
$739$	1.51914e10	+	1.34827e11i	0.0509355	+	0.452065i	0.993132	+	0.117003i	$0.0373287\pi$
$739$	1.51914e10	+	1.34827e11i	0.0509355	+	0.452065i	−0.942196	+	0.335062i	$0.891243\pi$
$740$	−7.84620e9	+	8.84054e8i	−0.0261657	+	0.00294817i
$741$	3.38981e11	+	1.63245e11i	1.12435	+	0.541460i
$742$	−5.69082e9	+	5.69082e9i	−0.0187741	+	0.0187741i
$743$	1.19332e11	+	3.41031e11i	0.391562	+	1.11902i	0.955955	+	0.293514i	$0.0948249\pi$
$743$	1.19332e11	+	3.41031e11i	0.391562	+	1.11902i	−0.564392	+	0.825507i	$0.690889\pi$
$744$	−1.13959e11	−	1.81364e11i	−0.371925	−	0.591916i
$745$	1.36622e10	−	6.57935e9i	0.0443501	−	0.0213579i
$746$	−7.21750e9	+	2.06264e10i	−0.0233040	+	0.0665991i
$747$	1.06724e11	−	2.43592e10i	0.342753	−	0.0782312i
$748$	−3.10722e11	+	3.89633e11i	−0.992579	+	1.24465i
$749$	6.00356e10	+	7.52823e10i	0.190758	+	0.239203i
$750$	9.21830e9	−	4.03880e10i	0.0291344	−	0.127646i
$751$	−2.81315e11	+	4.47710e11i	−0.884367	+	1.40746i	0.0286717	+	0.999589i	$0.490872\pi$
$751$	−2.81315e11	+	4.47710e11i	−0.884367	+	1.40746i	−0.913039	+	0.407873i	$0.866271\pi$
$752$	−3.12939e10	+	2.77741e11i	−0.0978561	+	0.868497i
$753$		−	3.10976e11i		−	0.967269i
$754$	2.95625e10	+	3.12932e10i	0.0914653	+	0.0968199i
$755$	1.29949e11			0.399931
$756$	1.67389e11	+	1.88602e10i	0.512437	+	0.0577378i
$757$	2.26018e10	+	1.42016e10i	0.0688270	+	0.0432469i	0.566006	−	0.824401i	$-0.308488\pi$
$757$	2.26018e10	+	1.42016e10i	0.0688270	+	0.0432469i	−0.497179	+	0.867648i	$0.665631\pi$
$758$	2.62205e9	+	5.98467e8i	0.00794264	+	0.00181286i
$759$	6.11857e11	−	4.87940e11i	1.84367	−	1.47028i
$760$	−3.88306e10	−	3.09664e10i	−0.116391	−	0.0928188i
$761$	9.40130e10	+	4.11898e11i	0.280317	+	1.22815i	0.897388	+	0.441242i	$0.145462\pi$
$761$	9.40130e10	+	4.11898e11i	0.280317	+	1.22815i	−0.617071	+	0.786907i	$0.711681\pi$
$762$	1.82485e8	+	6.38541e7i	0.000541260	+	0.000189395i
$763$	−2.46831e11	−	5.12549e11i	−0.728284	−	1.51230i
$764$	3.62422e11	−	2.27725e11i	1.06375	−	0.668401i
$765$	8.39535e10	−	2.93766e10i	0.245128	−	0.0857740i
$766$	−2.37847e10	−	2.37847e10i	−0.0690848	−	0.0690848i
$767$	6.82245e10	−	1.41670e11i	0.197133	−	0.409351i
$768$	2.98362e10	+	2.64803e11i	0.0857626	+	0.761164i
$769$	−3.52314e11	+	3.96962e10i	−1.00745	+	0.113513i	−0.600239	−	0.799821i	$-0.704928\pi$
$769$	−3.52314e11	+	3.96962e10i	−1.00745	+	0.113513i	−0.407213	+	0.913333i	$0.633499\pi$
$770$	3.25788e10	+	1.56891e10i	0.0926771	+	0.0446309i
$771$	2.63370e11	−	2.63370e11i	0.745330	−	0.745330i
$772$	1.39048e11	+	3.97376e11i	0.391467	+	1.11875i
$773$	3.45113e10	+	5.49244e10i	0.0966593	+	0.153832i	0.891553	−	0.452916i	$-0.149616\pi$
$773$	3.45113e10	+	5.49244e10i	0.0966593	+	0.153832i	−0.794894	+	0.606749i	$0.792473\pi$
$774$	−7.55220e10	+	3.63695e10i	−0.210431	+	0.101338i
$775$	1.42025e11	−	4.05883e11i	0.393692	−	1.12511i
$776$	8.34713e9	−	1.90518e9i	0.0230192	−	0.00525399i
$777$	6.06654e10	−	7.60719e10i	0.166440	−	0.208709i
$778$	−6.50202e10	−	8.15328e10i	−0.177472	−	0.222543i
$779$	1.02807e11	−	4.50426e11i	0.279172	−	1.22313i
$780$	3.71782e10	−	5.91688e10i	0.100441	−	0.159851i
$781$	−1.10360e10	+	9.79472e10i	−0.0296625	+	0.263262i
$782$			1.72201e11i			0.460479i
$783$	1.09396e11	+	4.18065e10i	0.291041	+	0.111224i
$784$	−6.56253e11			−1.73703
$785$	1.74652e10	+	1.96785e9i	0.0459932	+	0.00518219i
$786$	−9.64928e10	−	6.06305e10i	−0.252816	−	0.158855i
$787$	−4.40794e11	−	1.00608e11i	−1.14904	−	0.262262i	−0.394744	−	0.918791i	$-0.629167\pi$
$787$	−4.40794e11	−	1.00608e11i	−1.14904	−	0.262262i	−0.754301	+	0.656529i	$0.772024\pi$
$788$	6.73871e10	−	5.37394e10i	0.174772	−	0.139376i
$789$	−2.55079e9	−	2.03418e9i	−0.00658213	−	0.00524907i
$790$	−2.94185e9	−	1.28891e10i	−0.00755288	−	0.0330913i
$791$	−7.07727e11	−	2.47644e11i	−1.80784	−	0.632590i
$792$	6.36680e10	+	1.32208e11i	0.161816	+	0.336013i
$793$	−1.28569e11	+	8.07853e10i	−0.325120	+	0.204286i
$794$	1.01524e11	−	3.55246e10i	0.255437	−	0.0893814i
$795$	6.42242e9	+	6.42242e9i	0.0160779	+	0.0160779i
$796$	−1.85737e11	+	3.85686e11i	−0.462642	+	0.960687i
$797$	−5.69811e10	−	5.05721e11i	−0.141220	−	1.25337i	−0.841799	−	0.539791i	$-0.818503\pi$
$797$	−5.69811e10	−	5.05721e11i	−0.141220	−	1.25337i	0.700579	−	0.713575i	$-0.252925\pi$
$798$	2.97032e11	−	3.34675e10i	0.732473	−	0.0825299i
$799$	5.28207e11	+	2.54371e11i	1.29604	+	0.624138i
$800$	1.64157e11	−	1.64157e11i	0.400774	−	0.400774i
$801$	8.82565e10	+	2.52222e11i	0.214396	+	0.612708i
$802$	−3.62971e10	−	5.77666e10i	−0.0877354	−	0.139630i
$803$	5.90967e10	−	2.84595e10i	0.142135	−	0.0684487i
$804$	7.40260e10	−	2.11554e11i	0.177158	−	0.506287i
$805$	−2.56272e11	+	5.84925e10i	−0.610265	+	0.139289i
$806$	−4.42847e10	+	5.55313e10i	−0.104933	+	0.131582i
$807$	5.78256e10	+	7.25110e10i	0.136341	+	0.170966i
$808$	−5.35108e10	+	2.34446e11i	−0.125544	+	0.550044i
$809$	−1.75833e11	+	2.79836e11i	−0.410492	+	0.653295i	−0.986427	−	0.164201i	$-0.947495\pi$
$809$	−1.75833e11	+	2.79836e11i	−0.410492	+	0.653295i	0.575935	+	0.817496i	$0.304638\pi$
$810$	−2.88251e9	+	2.55830e10i	−0.00669623	+	0.0594307i
$811$			5.80572e11i			1.34206i	0.741430	+	0.671031i	$0.234148\pi$
$811$			5.80572e11i			1.34206i	−0.741430	+	0.671031i	$0.765852\pi$
$812$	−6.96654e11	−	1.79987e11i	−1.60248	−	0.414016i
$813$	−1.71809e11			−0.393264
$814$	−1.26006e10	−	1.41974e9i	−0.0287007	−	0.00323379i
$815$	−1.53839e11	−	9.66634e10i	−0.348687	−	0.219095i
$816$	7.08820e11	+	1.61783e11i	1.59873	+	0.364900i
$817$	−7.49427e11	+	5.97648e11i	−1.68206	+	1.34140i
$818$	−8.25093e10	−	6.57990e10i	−0.184285	−	0.146962i
$819$	8.30837e10	+	3.64013e11i	0.184663	+	0.809062i
$820$	−8.09943e10	−	2.83411e10i	−0.179143	−	0.0626847i
$821$	−7.01205e10	−	1.45607e11i	−0.154338	−	0.320486i	0.809435	−	0.587209i	$-0.199773\pi$
$821$	−7.01205e10	−	1.45607e11i	−0.154338	−	0.320486i	−0.963773	+	0.266723i	$0.914059\pi$
$822$	3.87613e10	−	2.43553e10i	0.0849006	−	0.0533466i
$823$	4.79406e11	−	1.67752e11i	1.04497	−	0.365651i	0.247424	−	0.968907i	$-0.420416\pi$
$823$	4.79406e11	−	1.67752e11i	1.04497	−	0.365651i	0.797548	+	0.603256i	$0.206130\pi$
$824$	1.25962e11	+	1.25962e11i	0.273232	+	0.273232i
$825$	−2.94790e11	+	6.12137e11i	−0.636351	+	1.32140i
$826$	−1.39870e10	−	1.24138e11i	−0.0300472	−	0.266677i
$827$	5.99771e11	−	6.75779e10i	1.28222	−	0.144472i	0.555565	−	0.831473i	$-0.312502\pi$
$827$	5.99771e11	−	6.75779e10i	1.28222	−	0.144472i	0.726656	+	0.687001i	$0.241073\pi$
$828$	−4.69386e11	−	2.26045e11i	−0.998640	−	0.480920i
$829$	5.05831e11	−	5.05831e11i	1.07099	−	1.07099i	0.0737152	−	0.997279i	$-0.476514\pi$
$829$	5.05831e11	−	5.05831e11i	1.07099	−	1.07099i	0.997279	−	0.0737152i	$-0.0234856\pi$
$830$	3.65007e9	+	1.04313e10i	0.00769111	+	0.0219799i
$831$	3.96270e11	+	6.30661e11i	0.830974	+	1.32249i
$832$	1.99202e11	−	9.59306e10i	0.415719	−	0.200200i
$833$	−4.54640e11	+	1.29929e12i	−0.944252	+	2.69852i
$834$	−4.64584e10	+	1.06038e10i	−0.0960284	+	0.0219179i
$835$	3.27336e10	−	4.10466e10i	0.0673361	−	0.0844367i
$836$	5.10974e11	+	6.40741e11i	1.04610	+	1.31177i
$837$	−4.29968e10	+	1.88381e11i	−0.0876060	+	0.383827i
$838$	2.26466e10	−	3.60418e10i	0.0459226	−	0.0730853i
$839$	2.02895e10	−	1.80075e11i	0.0409472	−	0.363417i	−0.956484	−	0.291785i	$-0.905751\pi$
$839$	2.02895e10	−	1.80075e11i	0.0409472	−	0.363417i	0.997431	−	0.0716317i	$-0.0228206\pi$
$840$		−	1.13673e11i		−	0.228319i
$841$	−4.37643e11	−	2.42313e11i	−0.874854	−	0.484386i
$842$	6.86882e10			0.136658
$843$	−1.01961e12	−	1.14883e11i	−2.01895	−	0.227481i
$844$	−3.64685e11	−	2.29147e11i	−0.718701	−	0.451590i
$845$	7.20586e10	+	1.64469e10i	0.141338	+	0.0322595i
$846$	6.59147e10	−	5.25652e10i	0.128677	−	0.102616i
$847$	−2.57513e11	−	2.05360e11i	−0.500340	−	0.399008i
$848$	7.16323e9	+	3.13842e10i	0.0138524	+	0.0606914i
$849$	−9.06022e10	−	3.17031e10i	−0.174385	−	0.0610198i
$850$	−6.48653e10	−	1.34694e11i	−0.124262	−	0.258032i
$851$	7.80503e10	−	4.90423e10i	0.148818	−	0.0935088i
$852$	1.42841e11	−	4.99821e10i	0.271078	−	0.0948542i
$853$	−3.91502e11	−	3.91502e11i	−0.739500	−	0.739500i	0.232981	−	0.972481i	$-0.425152\pi$
$853$	−3.91502e11	−	3.91502e11i	−0.739500	−	0.739500i	−0.972481	+	0.232981i	$0.925152\pi$
$854$	−5.23414e10	+	1.08688e11i	−0.0984042	+	0.204338i
$855$	−1.63768e10	−	1.45348e11i	−0.0306453	−	0.271985i
$856$	−3.92005e10	+	4.41683e9i	−0.0730123	+	0.00822651i
$857$	5.75309e11	+	2.77054e11i	1.06654	+	0.513620i	0.882991	−	0.469391i	$-0.155526\pi$
$857$	5.75309e11	+	2.77054e11i	1.06654	+	0.513620i	0.183551	+	0.983010i	$0.441241\pi$
$858$	7.93535e10	−	7.93535e10i	0.146426	−	0.146426i
$859$	−3.77634e10	−	1.07922e11i	−0.0693583	−	0.198215i	0.903987	−	0.427561i	$-0.140627\pi$
$859$	−3.77634e10	−	1.07922e11i	−0.0693583	−	0.198215i	−0.973345	+	0.229346i	$0.926341\pi$
$860$	9.47195e10	+	1.50745e11i	0.173159	+	0.275581i
$861$	9.52706e11	−	4.58799e11i	1.73359	−	0.834852i
$862$	−7.20779e10	+	2.05987e11i	−0.130549	+	0.373087i
$863$	−2.05961e11	+	4.70092e10i	−0.371314	+	0.0847500i	−0.404106	−	0.914712i	$-0.632417\pi$
$863$	−2.05961e11	+	4.70092e10i	−0.371314	+	0.0847500i	0.0327918	+	0.999462i	$0.489560\pi$
$864$	−6.50409e10	+	8.15587e10i	−0.116716	+	0.146358i
$865$	7.71214e10	+	9.67072e10i	0.137756	+	0.172740i
$866$	2.88600e10	−	1.26444e11i	0.0513127	−	0.224816i
$867$	4.11927e11	−	6.55578e11i	0.729028	−	1.16024i
$868$	1.32920e11	−	1.17970e12i	0.234160	−	2.07823i
$869$			4.46673e11i			0.783268i
$870$	9.65509e9	−	3.73708e10i	0.0168531	−	0.0652312i
$871$	−1.52177e11			−0.264409
$872$	2.31599e11	+	2.60950e10i	0.400563	+	0.0451326i
$873$	2.13498e10	+	1.34150e10i	0.0367568	+	0.0230958i
$874$	2.76081e11	+	6.30137e10i	0.473142	+	0.107991i
$875$	3.67558e11	−	2.93117e11i	0.627037	−	0.500045i
$876$	−7.87352e10	−	6.27893e10i	−0.133707	−	0.106627i
$877$	1.09261e11	+	4.78702e11i	0.184699	+	0.809220i	0.979353	+	0.202157i	$0.0647952\pi$
$877$	1.09261e11	+	4.78702e11i	0.184699	+	0.809220i	−0.794654	+	0.607063i	$0.792348\pi$
$878$	−1.82716e11	−	6.39353e10i	−0.307468	−	0.107588i
$879$	2.50564e10	+	5.20302e10i	0.0419724	+	0.0871566i
$880$	1.22466e11	−	7.69505e10i	0.204214	−	0.128316i
$881$	−6.19862e11	+	2.16899e11i	−1.02894	+	0.360043i	−0.791377	−	0.611329i	$-0.790635\pi$
$881$	−6.19862e11	+	2.16899e11i	−1.02894	+	0.360043i	−0.237566	+	0.971371i	$0.576350\pi$
$882$	1.39974e11	+	1.39974e11i	0.231298	+	0.231298i
$883$	3.74174e9	−	7.76980e9i	0.00615504	−	0.0127811i	−0.897869	−	0.440263i	$-0.854885\pi$
$883$	3.74174e9	−	7.76980e9i	0.00615504	−	0.0127811i	0.904024	+	0.427482i	$0.140599\pi$
$884$	−5.81661e10	−	5.16239e11i	−0.0952492	−	0.845360i
$885$	−1.40097e11	+	1.57851e10i	−0.228379	+	0.0257321i
$886$	−1.72100e11	−	8.28788e10i	−0.279283	−	0.134496i
$887$	−6.10751e11	+	6.10751e11i	−0.986665	+	0.986665i	−0.999912	−	0.0132468i	$-0.995783\pi$
$887$	−6.10751e11	+	6.10751e11i	−0.986665	+	0.986665i	0.0132468	+	0.999912i	$0.495783\pi$
$888$	1.31657e10	+	3.76253e10i	0.0211734	+	0.0605102i
$889$	1.16729e9	+	1.85773e9i	0.00186883	+	0.00297423i
$890$	−2.43055e10	+	1.17049e10i	−0.0387386	+	0.0186555i
$891$	2.87284e11	−	8.21009e11i	0.455827	−	1.30268i
$892$	3.40915e11	−	7.78117e10i	0.538501	−	0.122909i
$893$	6.01106e11	−	7.53764e11i	0.945247	−	1.18530i
$894$	−2.33116e10	−	2.92318e10i	−0.0364940	−	0.0457621i
$895$	−5.52454e10	+	2.42046e11i	−0.0861002	+	0.377230i
$896$	4.50652e11	−	7.17208e11i	0.699212	−	1.11279i
$897$	−9.13409e10	+	8.10673e11i	−0.141090	+	1.25221i
$898$			1.93297e11i			0.297249i
$899$	2.94637e11	−	7.70985e11i	0.451075	−	1.18034i
$900$	4.52296e11			0.689371
$901$	6.70987e10	+	7.56021e9i	0.101816	+	0.0114719i
$902$	−1.16683e11	−	7.33170e10i	−0.176272	−	0.110759i
$903$	−2.13888e12	−	4.88186e11i	−3.21689	−	0.734233i
$904$	2.40166e11	−	1.91526e11i	0.359615	−	0.286783i
$905$	1.04978e11	+	8.37171e10i	0.156496	+	0.124802i
$906$	−7.12979e10	−	3.12377e11i	−0.105819	−	0.463624i
$907$	6.65169e11	+	2.32753e11i	0.982885	+	0.343926i	0.773423	−	0.633890i	$-0.218543\pi$
$907$	6.65169e11	+	2.32753e11i	0.982885	+	0.343926i	0.209462	+	0.977817i	$0.432829\pi$
$908$	2.36336e11	+	4.90758e11i	0.347686	+	0.721978i
$909$	−5.99652e11	+	3.76787e11i	−0.878302	+	0.551874i
$910$	−3.55788e10	+	1.24496e10i	−0.0518831	+	0.0181547i
$911$	5.87983e11	+	5.87983e11i	0.853673	+	0.853673i	0.990583	−	0.136910i	$-0.0437172\pi$
$911$	5.87983e11	+	5.87983e11i	0.853673	+	0.853673i	−0.136910	+	0.990583i	$0.543717\pi$
$912$	5.18757e11	−	1.07721e12i	0.749868	−	1.55712i
$913$	−4.18061e10	−	3.71040e11i	−0.0601668	−	0.533995i
$914$	−1.04189e11	+	1.17393e10i	−0.149293	+	0.0168212i
$915$	1.22661e11	+	5.90703e10i	0.174993	+	0.0842723i
$916$	7.69453e11	−	7.69453e11i	1.09295	−	1.09295i
$917$	−4.27136e11	−	1.22068e12i	−0.604072	−	1.72634i
$918$	3.57404e10	+	5.68805e10i	0.0503255	+	0.0800926i
$919$	−3.02678e11	+	1.45762e11i	−0.424345	+	0.204354i	−0.633853	−	0.773453i	$-0.718528\pi$
$919$	−3.02678e11	+	1.45762e11i	−0.424345	+	0.204354i	0.209509	+	0.977807i	$0.432813\pi$
$920$	3.55682e10	−	1.01648e11i	0.0496489	−	0.141889i
$921$	7.72990e9	−	1.76430e9i	0.0107432	−	0.00245207i
$922$	−9.11462e10	+	1.14294e11i	−0.126129	+	0.158161i
$923$	−6.40632e10	−	8.03327e10i	−0.0882677	−	0.110684i
$924$	−4.17386e11	+	1.82869e12i	−0.572599	+	2.50872i
$925$	−4.25768e10	+	6.77606e10i	−0.0581575	+	0.0925572i
$926$	−2.18867e10	+	1.94250e11i	−0.0297671	+	0.264191i
$927$			5.24618e11i			0.710435i
$928$	3.23911e11	−	3.05998e11i	0.436752	−	0.412597i
$929$	−4.16680e11			−0.559423			−0.279711	−	0.960084i	$-0.590239\pi$
$929$	−4.16680e11			−0.559423			−0.279711	+	0.960084i	$0.590239\pi$
$930$	6.32829e10	+	7.13027e9i	0.0845969	+	0.00953178i
$931$	1.91671e12	+	1.20435e12i	2.55128	+	1.60307i
$932$	−1.11183e12	−	2.53767e11i	−1.47358	−	0.336335i
$933$	5.21217e11	−	4.15657e11i	0.687847	−	0.548540i
$934$	9.00602e10	+	7.18206e10i	0.118344	+	0.0943761i
$935$	−6.75087e10	−	2.95775e11i	−0.0883310	−	0.387004i
$936$	−1.44382e11	−	5.05215e10i	−0.188109	−	0.0658223i
$937$	2.03527e11	+	4.22628e11i	0.264036	+	0.548276i	0.990268	−	0.139173i	$-0.0444445\pi$
$937$	2.03527e11	+	4.22628e11i	0.264036	+	0.548276i	−0.726232	+	0.687450i	$0.758730\pi$
$938$	−1.02369e11	+	6.43226e10i	−0.132238	+	0.0830907i
$939$	−1.50251e12	+	5.25752e11i	−1.93266	+	0.676268i
$940$	−1.26617e11	−	1.26617e11i	−0.162174	−	0.162174i
$941$	−1.53409e10	+	3.18558e10i	−0.0195656	+	0.0406284i	−0.910523	−	0.413459i	$-0.864320\pi$
$941$	−1.53409e10	+	3.18558e10i	−0.0195656	+	0.0406284i	0.890957	+	0.454088i	$0.150035\pi$
$942$	−4.85204e9	−	4.30631e10i	−0.00616199	−	0.0546892i
$943$	9.95477e11	−	1.12163e11i	1.25888	−	0.141842i
$944$	−4.50196e11	−	2.16803e11i	−0.566910	−	0.273009i
$945$	−7.25102e10	+	7.25102e10i	−0.0909226	+	0.0909226i
$946$	9.44306e10	+	2.69867e11i	0.117909	+	0.336966i
$947$	5.03625e11	+	8.01515e11i	0.626192	+	0.996579i	0.997676	+	0.0681393i	$0.0217062\pi$
$947$	5.03625e11	+	8.01515e11i	0.626192	+	0.996579i	−0.371484	+	0.928439i	$0.621151\pi$
$948$	6.17876e11	−	2.97554e11i	0.765012	−	0.368410i
$949$	−2.25831e10	+	6.45387e10i	−0.0278431	+	0.0795711i
$950$	−2.39684e11	+	5.47063e10i	−0.294269	+	0.0671650i
$951$	−5.80518e11	+	7.27947e11i	−0.709731	+	0.889974i
$952$	−5.26899e11	−	6.60711e11i	−0.641475	−	0.804384i
$953$	2.76192e11	−	1.21007e12i	0.334841	−	1.46703i	−0.474792	−	0.880098i	$-0.657477\pi$
$953$	2.76192e11	−	1.21007e12i	0.334841	−	1.46703i	0.809633	−	0.586937i	$-0.199666\pi$
$954$	5.16614e9	−	8.22186e9i	0.00623695	−	0.00992605i
$955$	−2.91743e10	+	2.58929e11i	−0.0350741	+	0.311291i
$956$			5.78582e11i			0.692681i
$957$	−5.98989e11	+	1.15837e12i	−0.714120	+	1.38102i
$958$	−1.32267e10			−0.0157032
$959$	5.16237e11	+	5.81659e10i	0.610344	+	0.0687692i
$960$	−1.67852e11	−	1.05468e11i	−0.197625	−	0.124176i
$961$	4.96135e11	+	1.13240e11i	0.581710	+	0.132771i
$962$	1.03345e10	−	8.24150e9i	0.0120667	−	0.00962290i
$963$	−9.08304e10	−	7.24348e10i	−0.105615	−	0.0842252i
$964$	2.24979e11	+	9.85700e11i	0.260516	+	1.14140i
$965$	−2.41907e11	−	8.46470e10i	−0.278958	−	0.0976118i
$966$	2.81213e11	+	5.83945e11i	0.322944	+	0.670600i
$967$	−8.20707e9	+	5.15685e9i	−0.00938604	+	0.00589764i	−0.536717	−	0.843762i	$-0.680336\pi$
$967$	−8.20707e9	+	5.15685e9i	−0.00938604	+	0.00589764i	0.527331	+	0.849660i	$0.323193\pi$
$968$	1.27366e11	−	4.45674e10i	0.145062	−	0.0507594i
$969$	−1.77334e12	−	1.77334e12i	−2.01139	−	2.01139i
$970$	−1.10447e9	+	2.29346e9i	−0.00124758	+	0.00259062i
$971$	1.09505e11	+	9.71885e11i	0.123185	+	1.09330i	0.891436	+	0.453147i	$0.149699\pi$
$971$	1.09505e11	+	9.71885e11i	0.123185	+	1.09330i	−0.768251	+	0.640149i	$0.778873\pi$
$972$	−1.06324e12	+	1.19799e11i	−1.19115	+	0.134211i
$973$	−4.87229e11	−	2.34637e11i	−0.543603	−	0.261786i
$974$	−9.87283e10	+	9.87283e10i	−0.109700	+	0.109700i
$975$	−2.33920e11	−	6.68506e11i	−0.258851	−	0.739753i
$976$	2.56719e11	+	4.08565e11i	0.282916	+	0.450259i
$977$	−7.79436e11	+	3.75356e11i	−0.855465	+	0.411970i	−0.809603	−	0.586978i	$-0.800318\pi$
$977$	−7.79436e11	+	3.75356e11i	−0.855465	+	0.411970i	−0.0458615	+	0.998948i	$0.514603\pi$
$978$	−1.47958e11	+	4.22840e11i	−0.161727	+	0.462190i
$979$	8.88600e11	−	2.02817e11i	0.967332	−	0.220787i
$980$	2.62137e11	−	3.28710e11i	0.284200	−	0.356376i
$981$	4.27950e11	+	5.36632e11i	0.462080	+	0.579430i
$982$	−1.61870e9	+	7.09201e9i	−0.00174069	+	0.00762646i
$983$	−2.52210e10	+	4.01390e10i	−0.0270115	+	0.0429885i	−0.859957	−	0.510366i	$-0.829510\pi$
$983$	−2.52210e10	+	4.01390e10i	−0.0270115	+	0.0429885i	0.832946	+	0.553355i	$0.186653\pi$
$984$	−4.85043e10	+	4.30487e11i	−0.0517368	+	0.459177i
$985$			5.24699e10i			0.0557398i
$986$	−1.17102e11	−	2.61966e11i	−0.123896	−	0.277164i
$987$	2.20658e12			2.32515
$988$	−8.48942e11	−	9.56528e10i	−0.890944	−	0.100385i
$989$	−1.75986e12	−	1.10579e12i	−1.83947	−	1.15582i
$990$	−4.25340e10	−	9.70811e9i	−0.0442788	−	0.0101063i
$991$	−2.67991e11	+	2.13716e11i	−0.277860	+	0.221586i	−0.752497	−	0.658596i	$-0.771151\pi$
$991$	−2.67991e11	+	2.13716e11i	−0.277860	+	0.221586i	0.474637	+	0.880182i	$0.342579\pi$
$992$	5.74796e11	+	4.58385e11i	0.593563	+	0.473351i
$993$	−3.87954e11	−	1.69974e12i	−0.399010	−	1.74818i
$994$	−7.70504e10	−	2.69611e10i	−0.0789277	−	0.0276180i
$995$	−1.13069e11	−	2.34791e11i	−0.115359	−	0.239546i
$996$	−4.85405e11	+	3.05000e11i	−0.493250	+	0.309929i
$997$	−1.75202e11	+	6.13057e10i	−0.177320	+	0.0620469i	−0.417479	−	0.908687i	$-0.637086\pi$
$997$	−1.75202e11	+	6.13057e10i	−0.177320	+	0.0620469i	0.240159	+	0.970734i	$0.422800\pi$
$998$	−2.05581e11	−	2.05581e11i	−0.207234	−	0.207234i
$999$	1.56024e10	−	3.23987e10i	0.0156649	−	0.0325286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.f.a.2.10	✓	228
29.15	odd	28	inner	29.9.f.a.15.10	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.f.a.2.10	✓	228	1.1	even	1	trivial
29.9.f.a.15.10	yes	228	29.15	odd	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.38682 - 0.381603i) q^{2} +(91.1302 + 57.2609i) q^{3} +(-238.257 - 54.3805i) q^{4} +(116.314 - 92.7574i) q^{5} +(-286.791 - 228.708i) q^{6} +(-926.307 - 4058.42i) q^{7} +(1609.73 + 563.269i) q^{8} +(2179.19 + 4525.14i) q^{9} +O(q^{10})\)	\(q+(-3.38682 - 0.381603i) q^{2} +(91.1302 + 57.2609i) q^{3} +(-238.257 - 54.3805i) q^{4} +(116.314 - 92.7574i) q^{5} +(-286.791 - 228.708i) q^{6} +(-926.307 - 4058.42i) q^{7} +(1609.73 + 563.269i) q^{8} +(2179.19 + 4525.14i) q^{9} +(-429.332 + 269.767i) q^{10} +(16170.0 - 5658.11i) q^{11} +(-18598.5 - 18598.5i) q^{12} +(-7748.40 + 16089.7i) q^{13} +(1588.53 + 14098.6i) q^{14} +(15911.1 - 1792.75i) q^{15} +(51129.7 + 24622.8i) q^{16} +(84171.3 - 84171.3i) q^{17} +(-5653.73 - 16157.4i) q^{18} +(-104146. - 165748. i) q^{19} +(-32756.8 + 15774.8i) q^{20} +(147974. - 422886. i) q^{21} +(-56923.9 + 12992.5i) q^{22} +(264640. - 331848. i) q^{23} +(114442. + 143505. i) q^{24} +(-81997.2 + 359253. i) q^{25} +(32382.3 - 51536.2i) q^{26} +(18539.2 - 164540. i) q^{27} +1.01732e6i q^{28} +(-176923. + 684795. i) q^{29} -54572.2 q^{30} +(-1.15962e6 - 130658. i) q^{31} +(-533443. - 335185. i) q^{32} +(1.79756e6 + 410281. i) q^{33} +(-317193. + 252953. i) q^{34} +(-484191. - 386129. i) q^{35} +(-273128. - 1.19665e6i) q^{36} +(204986. + 71727.9i) q^{37} +(289475. + 601102. i) q^{38} +(-1.62742e6 + 1.02258e6i) q^{39} +(239482. - 83798.3i) q^{40} +(1.66890e6 + 1.66890e6i) q^{41} +(-662536. + 1.37577e6i) q^{42} +(-548264. - 4.86598e6i) q^{43} +(-4.16029e6 + 468752. i) q^{44} +(673211. + 324201. i) q^{45} +(-1.02292e6 + 1.02292e6i) q^{46} +(1.62666e6 + 4.64872e6i) q^{47} +(3.24954e6 + 5.17161e6i) q^{48} +(-1.04188e7 + 5.01743e6i) q^{49} +(414802. - 1.18544e6i) q^{50} +(1.24903e7 - 2.85082e6i) q^{51} +(2.72107e6 - 3.41212e6i) q^{52} +(353674. + 443494. i) q^{53} +(-125578. + 550193. i) q^{54} +(1.35596e6 - 2.15800e6i) q^{55} +(794876. - 7.05472e6i) q^{56} -2.10682e7i q^{57} +(860528. - 2.25176e6i) q^{58} -8.80499e6 q^{59} +(-3.88842e6 - 438119. i) q^{60} +(7.19943e6 + 4.52370e6i) q^{61} +(3.87756e6 + 885028. i) q^{62} +(1.63463e7 - 1.30357e7i) q^{63} +(-9.67962e6 - 7.71924e6i) q^{64} +(591192. + 2.59018e6i) q^{65} +(-5.93145e6 - 2.07550e6i) q^{66} +(3.69729e6 + 7.67750e6i) q^{67} +(-2.46317e7 + 1.54771e7i) q^{68} +(4.31186e7 - 1.50879e7i) q^{69} +(1.49252e6 + 1.49252e6i) q^{70} +(-2.49640e6 + 5.18383e6i) q^{71} +(959041. + 8.51173e6i) q^{72} +(3.80473e6 - 428690. i) q^{73} +(-666881. - 321153. i) q^{74} +(-2.80436e7 + 2.80436e7i) q^{75} +(1.58001e7 + 4.51541e7i) q^{76} +(-3.79413e7 - 6.03833e7i) q^{77} +(5.90202e6 - 2.84226e6i) q^{78} +(-8.61152e6 + 2.46103e7i) q^{79} +(8.23105e6 - 1.87868e6i) q^{80} +(3.16569e7 - 3.96965e7i) q^{81} +(-5.01540e6 - 6.28911e6i) q^{82} +(4.84998e6 - 2.12492e7i) q^{83} +(-5.82525e7 + 9.27084e7i) q^{84} +(1.98280e6 - 1.75978e7i) q^{85} +1.66894e7i q^{86} +(-5.53351e7 + 5.22747e7i) q^{87} +2.92163e7 q^{88} +(5.28693e7 + 5.95694e6i) q^{89} +(-2.15633e6 - 1.35491e6i) q^{90} +(7.24762e7 + 1.65422e7i) q^{91} +(-8.10983e7 + 6.46737e7i) q^{92} +(-9.81947e7 - 7.83076e7i) q^{93} +(-3.73524e6 - 1.63651e7i) q^{94} +(-2.74881e7 - 9.61849e6i) q^{95} +(-2.94198e7 - 6.10909e7i) q^{96} +(4.25081e6 - 2.67096e6i) q^{97} +(3.72013e7 - 1.30173e7i) q^{98} +(6.08412e7 + 6.08412e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9}+O(q^{10}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} - 15884 q^{10} + 8376 q^{11} - 5036 q^{12} - 14 q^{13} - 12742 q^{14} + 35516 q^{15} + 245898 q^{16} - 76248 q^{17} + 465008 q^{18} + 164474 q^{19} - 907274 q^{20} - 628270 q^{21} + 1214962 q^{22} + 173408 q^{23} + 1858618 q^{24} + 43976 q^{25} - 4604204 q^{26} - 1727586 q^{27} + 1079922 q^{29} + 8909208 q^{30} + 3657848 q^{31} + 1160364 q^{32} - 4279184 q^{33} - 8655374 q^{34} - 8269058 q^{35} - 3366854 q^{36} - 5622890 q^{37} + 15536626 q^{38} + 16110008 q^{39} - 23544696 q^{40} - 9561672 q^{41} - 14 q^{42} + 5181008 q^{43} + 51041750 q^{44} - 35245194 q^{45} - 43159224 q^{46} - 12806808 q^{47} + 83954488 q^{48} + 10429400 q^{49} + 80809398 q^{50} + 18760882 q^{51} - 93050550 q^{52} - 30960322 q^{53} - 106220916 q^{54} - 126174004 q^{55} - 40136268 q^{56} + 159368354 q^{58} + 11188020 q^{59} + 255893612 q^{60} + 139657128 q^{61} + 102501616 q^{62} + 9797746 q^{63} - 135941792 q^{64} - 14207858 q^{65} - 447597656 q^{66} - 148930894 q^{67} - 167094904 q^{68} + 66986722 q^{69} + 586255934 q^{70} - 15272096 q^{71} + 41230600 q^{72} - 219415072 q^{73} - 347464696 q^{74} + 391507416 q^{75} + 271512490 q^{76} + 240416780 q^{77} + 141747906 q^{78} + 112667220 q^{79} - 375642638 q^{80} - 358099268 q^{81} - 262154910 q^{82} - 109463350 q^{83} - 694921012 q^{84} - 356627386 q^{85} + 199703522 q^{87} + 251202768 q^{88} + 839849154 q^{89} + 675826020 q^{90} + 533256766 q^{91} + 742339570 q^{92} + 78998570 q^{93} - 209116610 q^{94} - 633414122 q^{95} - 431412576 q^{96} - 402046736 q^{97} - 2192087384 q^{98} - 1966368188 q^{99}+O(q^{100}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9 - 15884 * q^10 + 8376 * q^11 - 5036 * q^12 - 14 * q^13 - 12742 * q^14 + 35516 * q^15 + 245898 * q^16 - 76248 * q^17 + 465008 * q^18 + 164474 * q^19 - 907274 * q^20 - 628270 * q^21 + 1214962 * q^22 + 173408 * q^23 + 1858618 * q^24 + 43976 * q^25 - 4604204 * q^26 - 1727586 * q^27 + 1079922 * q^29 + 8909208 * q^30 + 3657848 * q^31 + 1160364 * q^32 - 4279184 * q^33 - 8655374 * q^34 - 8269058 * q^35 - 3366854 * q^36 - 5622890 * q^37 + 15536626 * q^38 + 16110008 * q^39 - 23544696 * q^40 - 9561672 * q^41 - 14 * q^42 + 5181008 * q^43 + 51041750 * q^44 - 35245194 * q^45 - 43159224 * q^46 - 12806808 * q^47 + 83954488 * q^48 + 10429400 * q^49 + 80809398 * q^50 + 18760882 * q^51 - 93050550 * q^52 - 30960322 * q^53 - 106220916 * q^54 - 126174004 * q^55 - 40136268 * q^56 + 159368354 * q^58 + 11188020 * q^59 + 255893612 * q^60 + 139657128 * q^61 + 102501616 * q^62 + 9797746 * q^63 - 135941792 * q^64 - 14207858 * q^65 - 447597656 * q^66 - 148930894 * q^67 - 167094904 * q^68 + 66986722 * q^69 + 586255934 * q^70 - 15272096 * q^71 + 41230600 * q^72 - 219415072 * q^73 - 347464696 * q^74 + 391507416 * q^75 + 271512490 * q^76 + 240416780 * q^77 + 141747906 * q^78 + 112667220 * q^79 - 375642638 * q^80 - 358099268 * q^81 - 262154910 * q^82 - 109463350 * q^83 - 694921012 * q^84 - 356627386 * q^85 + 199703522 * q^87 + 251202768 * q^88 + 839849154 * q^89 + 675826020 * q^90 + 533256766 * q^91 + 742339570 * q^92 + 78998570 * q^93 - 209116610 * q^94 - 633414122 * q^95 - 431412576 * q^96 - 402046736 * q^97 - 2192087384 * q^98 - 1966368188 * q^99

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