LMFDB - Embedded newform 43.8.g.a.24.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, 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:	$13.4325560958$
Analytic rank:	$0$
Dimension:	$300$
Relative dimension:	$25$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			24.13
Character	$\chi$	$=$	43.24
Dual form			43.8.g.a.9.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913875 + 1.14596i) q^{2} +(31.0397 - 4.67849i) q^{3} +(28.0046 + 122.696i) q^{4} +(-325.645 + 222.021i) q^{5} +(-23.0051 + 39.8460i) q^{6} +(-420.198 - 727.804i) q^{7} +(-335.233 - 161.440i) q^{8} +(-1148.26 + 354.191i) q^{9} +O(q^{10})$	\(q+(-0.913875 + 1.14596i) q^{2} +(31.0397 - 4.67849i) q^{3} +(28.0046 + 122.696i) q^{4} +(-325.645 + 222.021i) q^{5} +(-23.0051 + 39.8460i) q^{6} +(-420.198 - 727.804i) q^{7} +(-335.233 - 161.440i) q^{8} +(-1148.26 + 354.191i) q^{9} +(43.1710 - 576.078i) q^{10} +(1281.40 - 5614.16i) q^{11} +(1443.29 + 3677.44i) q^{12} +(-549.896 - 7337.86i) q^{13} +(1218.04 + 183.591i) q^{14} +(-9069.23 + 8415.01i) q^{15} +(-14022.3 + 6752.81i) q^{16} +(23480.6 + 16008.8i) q^{17} +(643.476 - 1639.55i) q^{18} +(-23492.8 - 7246.57i) q^{19} +(-36360.8 - 33737.9i) q^{20} +(-16447.9 - 20625.0i) q^{21} +(5262.59 + 6599.08i) q^{22} +(-61721.3 - 57269.0i) q^{23} +(-11160.9 - 3442.67i) q^{24} +(28209.2 - 71875.9i) q^{25} +(8911.45 + 6075.73i) q^{26} +(-95836.8 + 46152.6i) q^{27} +(77531.3 - 71938.6i) q^{28} +(-177359. - 26732.6i) q^{29} +(-1355.15 - 18083.3i) q^{30} +(114426. + 291554. i) q^{31} +(15674.1 - 68672.6i) q^{32} +(13508.4 - 180257. i) q^{33} +(-39803.8 + 12277.9i) q^{34} +(298423. + 143713. i) q^{35} +(-75614.5 - 130968. i) q^{36} +(-110162. + 190806. i) q^{37} +(29773.8 - 20299.4i) q^{38} +(-51398.7 - 225193. i) q^{39} +(145010. - 21856.8i) q^{40} +(-497656. + 624041. i) q^{41} +38666.7 q^{42} +(247924. + 458642. i) q^{43} +724721. q^{44} +(295288. - 370279. i) q^{45} +(122034. - 18393.6i) q^{46} +(-60316.5 - 264264. i) q^{47} +(-403657. + 275209. i) q^{48} +(58639.2 - 101566. i) q^{49} +(56587.5 + 98012.4i) q^{50} +(803729. + 387055. i) q^{51} +(884928. - 272964. i) q^{52} +(69422.7 - 926381. i) q^{53} +(34693.7 - 152003. i) q^{54} +(829183. + 2.11272e6i) q^{55} +(23367.7 + 311821. i) q^{56} +(-763113. - 115021. i) q^{57} +(192719. - 178817. i) q^{58} +(-2.25610e6 + 1.08648e6i) q^{59} +(-1.28647e6 - 877101. i) q^{60} +(1.16406e6 - 2.96597e6i) q^{61} +(-438681. - 135315. i) q^{62} +(740278. + 686878. i) q^{63} +(-1.17771e6 - 1.47680e6i) q^{64} +(1.80823e6 + 2.26745e6i) q^{65} +(194223. + 180213. i) q^{66} +(874383. + 269712. i) q^{67} +(-1.30665e6 + 3.32930e6i) q^{68} +(-2.18375e6 - 1.48885e6i) q^{69} +(-437412. + 210646. i) q^{70} +(1.38968e6 - 1.28944e6i) q^{71} +(442116. + 66638.2i) q^{72} +(95720.4 + 1.27730e6i) q^{73} +(-117983. - 300615. i) q^{74} +(539337. - 2.36299e6i) q^{75} +(231220. - 3.08542e6i) q^{76} +(-4.62445e6 + 1.42645e6i) q^{77} +(305034. + 146897. i) q^{78} +(-65408.0 - 113290. i) q^{79} +(3.06705e6 - 5.31228e6i) q^{80} +(-587470. + 400530. i) q^{81} +(-260332. - 1.14059e6i) q^{82} +(-3.39479e6 + 511682. i) q^{83} +(2.06999e6 - 2.59568e6i) q^{84} -1.12006e7 q^{85} +(-752158. - 135030. i) q^{86} -5.63025e6 q^{87} +(-1.33592e6 + 1.67519e6i) q^{88} +(441062. - 66479.4i) q^{89} +(154470. + 676778. i) q^{90} +(-5.10946e6 + 3.48357e6i) q^{91} +(5.29821e6 - 9.17677e6i) q^{92} +(4.91580e6 + 8.51441e6i) q^{93} +(357959. + 172384. i) q^{94} +(9.25922e6 - 2.85609e6i) q^{95} +(165235. - 2.20491e6i) q^{96} +(514761. - 2.25532e6i) q^{97} +(62802.1 + 160017. i) q^{98} +(517112. + 6.90038e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9}+O(q^{10}) $ 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9} - 1681 q^{10} + 4580 q^{11} + 9330 q^{12} - 20444 q^{13} - 45798 q^{14} + 50477 q^{15} - 74504 q^{16} - 25312 q^{17} + 2046 q^{18} + 4046 q^{19} + 140781 q^{20} + 100555 q^{21} + 95810 q^{22} + 1648 q^{23} - 292592 q^{24} + 419068 q^{25} + 393435 q^{26} + 274140 q^{27} + 233644 q^{28} + 605697 q^{29} - 1216016 q^{30} + 358580 q^{31} - 19194 q^{32} + 1280291 q^{33} + 1137255 q^{34} + 652739 q^{35} - 8980975 q^{36} - 2360047 q^{37} - 308490 q^{38} + 536339 q^{39} + 3057993 q^{40} - 1376320 q^{41} + 8417790 q^{42} + 7173000 q^{43} - 3856780 q^{44} + 2761486 q^{45} - 7073993 q^{46} + 1437090 q^{47} - 9543469 q^{48} - 16053170 q^{49} - 3046893 q^{50} + 2972901 q^{51} + 17415142 q^{52} + 3320604 q^{53} + 6000486 q^{54} + 13427750 q^{55} - 5450793 q^{56} + 3333100 q^{57} - 7876190 q^{58} - 7084765 q^{59} + 7356443 q^{60} + 3354606 q^{61} - 719427 q^{62} + 14716815 q^{63} - 16086234 q^{64} - 19914646 q^{65} - 8293345 q^{66} + 13025470 q^{67} - 22191927 q^{68} - 33964295 q^{69} + 8094727 q^{70} + 30843495 q^{71} + 93841607 q^{72} - 3067637 q^{73} + 18179570 q^{74} - 41508571 q^{75} - 19751872 q^{76} - 15169179 q^{77} - 69509396 q^{78} - 12090149 q^{79} - 69662530 q^{80} + 3387954 q^{81} + 39226888 q^{82} + 16408777 q^{83} + 98603231 q^{84} - 13423424 q^{85} + 111906660 q^{86} + 49022010 q^{87} + 76213954 q^{88} - 12540205 q^{89} - 92608607 q^{90} - 59091937 q^{91} - 50489370 q^{92} - 52218334 q^{93} - 3441600 q^{94} - 79947551 q^{95} - 23449784 q^{96} - 116467587 q^{97} + 73909552 q^{98} - 20061115 q^{99}+O(q^{100}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9 - 1681 * q^10 + 4580 * q^11 + 9330 * q^12 - 20444 * q^13 - 45798 * q^14 + 50477 * q^15 - 74504 * q^16 - 25312 * q^17 + 2046 * q^18 + 4046 * q^19 + 140781 * q^20 + 100555 * q^21 + 95810 * q^22 + 1648 * q^23 - 292592 * q^24 + 419068 * q^25 + 393435 * q^26 + 274140 * q^27 + 233644 * q^28 + 605697 * q^29 - 1216016 * q^30 + 358580 * q^31 - 19194 * q^32 + 1280291 * q^33 + 1137255 * q^34 + 652739 * q^35 - 8980975 * q^36 - 2360047 * q^37 - 308490 * q^38 + 536339 * q^39 + 3057993 * q^40 - 1376320 * q^41 + 8417790 * q^42 + 7173000 * q^43 - 3856780 * q^44 + 2761486 * q^45 - 7073993 * q^46 + 1437090 * q^47 - 9543469 * q^48 - 16053170 * q^49 - 3046893 * q^50 + 2972901 * q^51 + 17415142 * q^52 + 3320604 * q^53 + 6000486 * q^54 + 13427750 * q^55 - 5450793 * q^56 + 3333100 * q^57 - 7876190 * q^58 - 7084765 * q^59 + 7356443 * q^60 + 3354606 * q^61 - 719427 * q^62 + 14716815 * q^63 - 16086234 * q^64 - 19914646 * q^65 - 8293345 * q^66 + 13025470 * q^67 - 22191927 * q^68 - 33964295 * q^69 + 8094727 * q^70 + 30843495 * q^71 + 93841607 * q^72 - 3067637 * q^73 + 18179570 * q^74 - 41508571 * q^75 - 19751872 * q^76 - 15169179 * q^77 - 69509396 * q^78 - 12090149 * q^79 - 69662530 * q^80 + 3387954 * q^81 + 39226888 * q^82 + 16408777 * q^83 + 98603231 * q^84 - 13423424 * q^85 + 111906660 * q^86 + 49022010 * q^87 + 76213954 * q^88 - 12540205 * q^89 - 92608607 * q^90 - 59091937 * q^91 - 50489370 * q^92 - 52218334 * q^93 - 3441600 * q^94 - 79947551 * q^95 - 23449784 * q^96 - 116467587 * q^97 + 73909552 * q^98 - 20061115 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{20}{21}\right)$

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 $

$2$	−0.913875	+	1.14596i	−0.0807759	+	0.101290i	−0.820577	−	0.571535i	$-0.806348\pi$
$2$	−0.913875	+	1.14596i	−0.0807759	+	0.101290i	0.739801	+	0.672825i	$0.234919\pi$
$3$	31.0397	−	4.67849i	0.663734	−	0.100042i	0.191469	−	0.981499i	$-0.438675\pi$
$3$	31.0397	−	4.67849i	0.663734	−	0.100042i	0.472264	+	0.881457i	$0.343437\pi$
$4$	28.0046	+	122.696i	0.218786	+	0.958564i
$5$	−325.645	+	222.021i	−1.16506	+	0.794328i	−0.982020	−	0.188777i	$-0.939548\pi$
$5$	−325.645	+	222.021i	−1.16506	+	0.794328i	−0.183045	+	0.983105i	$0.558595\pi$
$6$	−23.0051	+	39.8460i	−0.0434805	+	0.0753104i
$7$	−420.198	−	727.804i	−0.463032	−	0.801994i	0.536079	−	0.844168i	$-0.319905\pi$
$7$	−420.198	−	727.804i	−0.463032	−	0.801994i	−0.999110	+	0.0421738i	$0.986572\pi$
$8$	−335.233	−	161.440i	−0.231490	−	0.111480i
$9$	−1148.26	+	354.191i	−0.525039	+	0.161953i
$10$	43.1710	−	576.078i	0.0136519	−	0.182172i
$11$	1281.40	−	5614.16i	0.290274	−	1.27178i	−0.593870	−	0.804561i	$-0.702401\pi$
$11$	1281.40	−	5614.16i	0.290274	−	1.27178i	0.884144	−	0.467214i	$-0.154742\pi$
$12$	1443.29	+	3677.44i	0.241112	+	0.614344i
$13$	−549.896	−	7337.86i	−0.0694191	−	0.926334i	−0.917824	−	0.396987i	$-0.870056\pi$
$13$	−549.896	−	7337.86i	−0.0694191	−	0.926334i	0.848405	−	0.529347i	$-0.177563\pi$
$14$	1218.04	+	183.591i	0.118636	+	0.0178814i
$15$	−9069.23	+	8415.01i	−0.693827	+	0.643777i
$16$	−14022.3	+	6752.81i	−0.855856	+	0.412159i
$17$	23480.6	+	16008.8i	1.15915	+	0.790292i	0.981056	−	0.193722i	$-0.0620561\pi$
$17$	23480.6	+	16008.8i	1.15915	+	0.790292i	0.178089	+	0.984014i	$0.443008\pi$
$18$	643.476	−	1639.55i	0.0260063	−	0.0662630i
$19$	−23492.8	−	7246.57i	−0.785773	−	0.242379i	−0.124198	−	0.992258i	$-0.539636\pi$
$19$	−23492.8	−	7246.57i	−0.785773	−	0.242379i	−0.661575	+	0.749879i	$0.730112\pi$
$20$	−36360.8	−	33737.9i	−1.01631	−	0.943002i
$21$	−16447.9	−	20625.0i	−0.387562	−	0.485988i
$22$	5262.59	+	6599.08i	0.105371	+	0.132131i
$23$	−61721.3	−	57269.0i	−1.05776	−	0.981459i	−0.0579036	−	0.998322i	$-0.518442\pi$
$23$	−61721.3	−	57269.0i	−1.05776	−	0.981459i	−0.999858	+	0.0168630i	$0.994632\pi$
$24$	−11160.9	−	3442.67i	−0.164800	−	0.0508342i
$25$	28209.2	−	71875.9i	0.361078	−	0.920012i
$26$	8911.45	+	6075.73i	0.0994356	+	0.0677940i
$27$	−95836.8	+	46152.6i	−0.937042	+	0.451256i
$28$	77531.3	−	71938.6i	0.667458	−	0.619311i
$29$	−177359.	−	26732.6i	−1.35039	−	0.203539i	−0.566309	−	0.824193i	$-0.691629\pi$
$29$	−177359.	−	26732.6i	−1.35039	−	0.203539i	−0.784085	+	0.620654i	$0.786867\pi$
$30$	−1355.15	−	18083.3i	−0.00916356	−	0.122279i
$31$	114426.	+	291554.i	0.689859	+	1.75773i	0.651721	+	0.758459i	$0.274047\pi$
$31$	114426.	+	291554.i	0.689859	+	1.75773i	0.0381382	+	0.999272i	$0.487857\pi$
$32$	15674.1	−	68672.6i	0.0845584	−	0.370475i
$33$	13508.4	−	180257.i	0.0654343	−	0.873160i
$34$	−39803.8	+	12277.9i	−0.173680	+	0.0535731i
$35$	298423.	+	143713.i	1.17651	+	0.566576i
$36$	−75614.5	−	130968.i	−0.270114	−	0.467850i
$37$	−110162.	+	190806.i	−0.357541	+	0.619279i	−0.987549	−	0.157309i	$-0.949718\pi$
$37$	−110162.	+	190806.i	−0.357541	+	0.619279i	0.630008	+	0.776588i	$0.283051\pi$
$38$	29773.8	−	20299.4i	0.0880221	−	0.0600124i
$39$	−51398.7	−	225193.i	−0.138748	−	0.607894i
$40$	145010.	−	21856.8i	0.358252	−	0.0539978i
$41$	−497656.	+	624041.i	−1.12768	+	1.41407i	−0.230125	+	0.973161i	$0.573913\pi$
$41$	−497656.	+	624041.i	−1.12768	+	1.41407i	−0.897554	+	0.440904i	$0.854658\pi$
$42$	38666.7			0.0805314
$43$	247924.	+	458642.i	0.475530	+	0.879699i
$43$	247924.	+	458642.i	0.475530	+	0.879699i
$44$	724721.			1.28259
$45$	295288.	−	370279.i	0.483060	−	0.605739i
$46$	122034.	−	18393.6i	0.184853	−	0.0278622i
$47$	−60316.5	−	264264.i	−0.0847411	−	0.371275i	0.914720	−	0.404087i	$-0.132411\pi$
$47$	−60316.5	−	264264.i	−0.0847411	−	0.371275i	−0.999462	+	0.0328124i	$0.989554\pi$
$48$	−403657.	+	275209.i	−0.526827	+	0.359185i
$49$	58639.2	−	101566.i	0.0712035	−	0.123328i
$50$	56587.5	+	98012.4i	0.0640214	+	0.110888i
$51$	803729.	+	387055.i	0.848426	+	0.408580i
$52$	884928.	−	272964.i	0.872763	−	0.269212i
$53$	69422.7	−	926381.i	0.0640525	−	0.854721i	−0.868961	−	0.494880i	$-0.835212\pi$
$53$	69422.7	−	926381.i	0.0640525	−	0.854721i	0.933014	−	0.359841i	$-0.117169\pi$
$54$	34693.7	−	152003.i	0.0299828	−	0.131363i
$55$	829183.	+	2.11272e6i	0.672018	+	1.71227i
$56$	23367.7	+	311821.i	0.0177811	+	0.237272i
$57$	−763113.	−	115021.i	−0.545792	−	0.0822649i
$58$	192719.	−	178817.i	0.129696	−	0.120340i
$59$	−2.25610e6	+	1.08648e6i	−1.43014	+	0.688717i	−0.979023	−	0.203750i	$-0.934687\pi$
$59$	−2.25610e6	+	1.08648e6i	−1.43014	+	0.688717i	−0.451112	+	0.892467i	$0.648973\pi$
$60$	−1.28647e6	−	877101.i	−0.768901	−	0.524228i
$61$	1.16406e6	−	2.96597e6i	0.656629	−	1.67306i	−0.0800242	−	0.996793i	$-0.525500\pi$
$61$	1.16406e6	−	2.96597e6i	0.656629	−	1.67306i	0.736653	−	0.676271i	$-0.236405\pi$
$62$	−438681.	−	135315.i	−0.233764	−	0.0721067i
$63$	740278.	+	686878.i	0.372995	+	0.346089i
$64$	−1.17771e6	−	1.47680e6i	−0.561576	−	0.704194i
$65$	1.80823e6	+	2.26745e6i	0.816690	+	1.02410i
$66$	194223.	+	180213.i	0.0831567	+	0.0771581i
$67$	874383.	+	269712.i	0.355173	+	0.109556i	0.467207	−	0.884148i	$-0.345260\pi$
$67$	874383.	+	269712.i	0.355173	+	0.109556i	−0.112034	+	0.993704i	$0.535737\pi$
$68$	−1.30665e6	+	3.32930e6i	−0.503941	+	1.28402i
$69$	−2.18375e6	−	1.48885e6i	−0.800259	−	0.545607i
$70$	−437412.	+	210646.i	−0.152422	+	0.0734025i
$71$	1.38968e6	−	1.28944e6i	0.460798	−	0.427558i	−0.415305	−	0.909682i	$-0.636325\pi$
$71$	1.38968e6	−	1.28944e6i	0.460798	−	0.427558i	0.876103	+	0.482124i	$0.160135\pi$
$72$	442116.	+	66638.2i	0.139596	+	0.0210407i
$73$	95720.4	+	1.27730e6i	0.0287988	+	0.384293i	0.992916	+	0.118817i	$0.0379102\pi$
$73$	95720.4	+	1.27730e6i	0.0287988	+	0.384293i	−0.964117	+	0.265476i	$0.914471\pi$
$74$	−117983.	−	300615.i	−0.0338460	−	0.0862381i
$75$	539337.	−	2.36299e6i	0.147620	−	0.646766i
$76$	231220.	−	3.08542e6i	0.0604196	−	0.806243i
$77$	−4.62445e6	+	1.42645e6i	−1.15436	+	0.356074i
$78$	305034.	+	146897.i	0.0727810	+	0.0350495i
$79$	−65408.0	−	113290.i	−0.0149257	−	0.0258521i	0.858466	−	0.512870i	$-0.171418\pi$
$79$	−65408.0	−	113290.i	−0.0149257	−	0.0258521i	−0.873392	+	0.487018i	$0.838085\pi$
$80$	3.06705e6	−	5.31228e6i	0.669739	−	1.16002i
$81$	−587470.	+	400530.i	−0.122825	+	0.0837409i
$82$	−260332.	−	1.14059e6i	−0.0521410	−	0.228445i
$83$	−3.39479e6	+	511682.i	−0.651687	+	0.0982261i	−0.466562	−	0.884489i	$-0.654507\pi$
$83$	−3.39479e6	+	511682.i	−0.651687	+	0.0982261i	−0.185126	+	0.982715i	$0.559269\pi$
$84$	2.06999e6	−	2.59568e6i	0.381057	−	0.477831i
$85$	−1.12006e7			−1.97823
$86$	−752158.	−	135030.i	−0.127516	−	0.0228922i
$87$	−5.63025e6			−0.916664
$88$	−1.33592e6	+	1.67519e6i	−0.208973	+	0.262044i
$89$	441062.	−	66479.4i	0.0663185	−	0.00999591i	−0.115799	−	0.993273i	$-0.536943\pi$
$89$	441062.	−	66479.4i	0.0663185	−	0.00999591i	0.182118	+	0.983277i	$0.441705\pi$
$90$	154470.	+	676778.i	0.0223355	+	0.0978582i
$91$	−5.10946e6	+	3.48357e6i	−0.710771	+	0.484596i
$92$	5.29821e6	−	9.17677e6i	0.709368	−	1.22866i
$93$	4.91580e6	+	8.51441e6i	0.633729	+	1.09765i
$94$	357959.	+	172384.i	0.0444514	+	0.0214067i
$95$	9.25922e6	−	2.85609e6i	1.10800	−	0.341774i
$96$	165235.	−	2.20491e6i	0.0190613	−	0.254356i
$97$	514761.	−	2.25532e6i	0.0572671	−	0.250903i	−0.938189	−	0.346123i	$-0.887498\pi$
$97$	514761.	−	2.25532e6i	0.0572671	−	0.250903i	0.995456	+	0.0952193i	$0.0303552\pi$
$98$	62802.1	+	160017.i	0.00674035	+	0.0171741i
$99$	517112.	+	6.90038e6i	0.0535625	+	0.714743i
$100$	9.60890e6	+	1.44831e6i	0.960890	+	0.144831i
$101$	−6.87157e6	+	6.37588e6i	−0.663638	+	0.615766i	−0.938320	−	0.345769i	$-0.887618\pi$
$101$	−6.87157e6	+	6.37588e6i	−0.663638	+	0.615766i	0.274682	+	0.961535i	$0.411428\pi$
$102$	−1.17806e6	+	567323.i	−0.109917	+	0.0529334i
$103$	1.33341e7	+	9.09105e6i	1.20236	+	0.819754i	0.987612	−	0.156916i	$-0.0501552\pi$
$103$	1.33341e7	+	9.09105e6i	1.20236	+	0.819754i	0.214746	+	0.976670i	$0.431108\pi$
$104$	−1.00028e6	+	2.54867e6i	−0.0871976	+	0.222176i
$105$	9.93535e6	+	3.06465e6i	0.837569	+	0.258356i
$106$	998155.	+	926153.i	0.0814006	+	0.0755287i
$107$	3.22194e6	+	4.04018e6i	0.254257	+	0.318829i	0.892535	−	0.450977i	$-0.148924\pi$
$107$	3.22194e6	+	4.04018e6i	0.254257	+	0.318829i	−0.638278	+	0.769806i	$0.720353\pi$
$108$	−8.34662e6	−	1.04663e7i	−0.637569	−	0.799486i
$109$	−8.80478e6	−	8.16964e6i	−0.651217	−	0.604241i	0.283783	−	0.958889i	$-0.408410\pi$
$109$	−8.80478e6	−	8.16964e6i	−0.651217	−	0.604241i	−0.935000	+	0.354647i	$0.884601\pi$
$110$	−3.17887e6	−	980553.i	−0.227719	−	0.0702419i
$111$	−2.52672e6	+	6.43797e6i	−0.175358	+	0.446805i
$112$	1.08069e7	+	7.36800e6i	0.726837	+	0.495549i
$113$	117500.	−	56585.2i	0.00766063	−	0.00368916i	−0.430050	−	0.902805i	$-0.641504\pi$
$113$	117500.	−	56585.2i	0.00766063	−	0.00368916i	0.437710	+	0.899116i	$0.355790\pi$
$114$	829200.	−	769385.i	0.0524194	−	0.0486381i
$115$	3.28142e7	+	4.94595e6i	2.01196	+	0.303254i
$116$	−1.68689e6	−	2.25099e7i	−0.100342	−	1.33897i
$117$	3.23043e6	+	8.23100e6i	0.186470	+	0.475119i
$118$	816729.	−	3.57832e6i	0.0457605	−	0.200490i
$119$	1.78477e6	−	2.38161e7i	0.0970887	−	1.29556i
$120$	4.39883e6	−	1.35686e6i	0.232382	−	0.0716804i
$121$	−1.23195e7	−	5.93276e6i	−0.632185	−	0.304444i
$122$	2.33509e6	+	4.04450e6i	0.116424	+	0.201653i
$123$	−1.25275e7	+	2.16983e7i	−0.607013	+	1.05138i
$124$	−3.25681e7	+	2.22045e7i	−1.53397	+	1.04584i
$125$	−79947.2	−	350271.i	−0.00366115	−	0.0160406i
$126$	−1.46366e6	+	220611.i	−0.0651843	+	0.00982495i
$127$	−374535.	+	469652.i	−0.0162248	+	0.0203453i	−0.789878	−	0.613264i	$-0.789856\pi$
$127$	−374535.	+	469652.i	−0.0162248	+	0.0203453i	0.773653	+	0.633610i	$0.218427\pi$
$128$	1.17848e7			0.496692
$129$	9.84123e6	+	1.30762e7i	0.403632	+	0.536313i
$130$	−4.25091e6			−0.169700
$131$	−1.69178e7	+	2.12143e7i	−0.657500	+	0.824479i	−0.993068	−	0.117537i	$-0.962500\pi$
$131$	−1.69178e7	+	2.12143e7i	−0.657500	+	0.824479i	0.335569	+	0.942016i	$0.391072\pi$
$132$	2.24952e7	−	3.39060e6i	0.851296	−	0.128312i
$133$	4.59754e6	+	2.01431e7i	0.169451	+	0.742415i
$134$	−1.10816e6	+	755529.i	−0.0397864	+	0.0271259i
$135$	2.09620e7	−	3.63072e7i	0.733270	−	1.27006i
$136$	−5.28702e6	−	9.15739e6i	−0.180229	−	0.312166i
$137$	−2.37228e7	−	1.14243e7i	−0.788213	−	0.379583i	−0.00393434	−	0.999992i	$-0.501252\pi$
$137$	−2.37228e7	−	1.14243e7i	−0.788213	−	0.379583i	−0.784278	+	0.620409i	$0.786967\pi$
$138$	3.70184e6	−	1.14187e6i	0.119906	−	0.0369861i
$139$	662076.	−	8.83479e6i	0.0209101	−	0.279026i	−0.976941	−	0.213508i	$-0.931511\pi$
$139$	662076.	−	8.83479e6i	0.0209101	−	0.279026i	0.997851	−	0.0655178i	$-0.0208699\pi$
$140$	−9.27583e6	+	4.06401e7i	−0.285696	+	1.25172i
$141$	−3.10857e6	−	7.92050e6i	−0.0933885	−	0.237950i
$142$	207651.	+	2.77091e6i	0.00608589	+	0.0812106i
$143$	−4.19006e7	−	6.31549e6i	−1.19824	−	0.180606i
$144$	1.37095e7	−	1.27206e7i	0.382607	−	0.355008i
$145$	6.36914e7	−	3.06721e7i	1.73497	−	0.835519i
$146$	−1.55122e6	−	1.05760e6i	−0.0412512	−	0.0281246i
$147$	1.34497e6	−	3.42693e6i	0.0349222	−	0.0889804i
$148$	−2.64962e7	−	8.17301e6i	−0.671844	−	0.207236i
$149$	−3.78344e7	−	3.51052e7i	−0.936991	−	0.869401i	0.0546399	−	0.998506i	$-0.482599\pi$
$149$	−3.78344e7	−	3.51052e7i	−0.936991	−	0.869401i	−0.991631	+	0.129106i	$0.958789\pi$
$150$	2.21501e6	+	2.77754e6i	0.0535866	+	0.0671955i
$151$	2.93008e7	+	3.67421e7i	0.692565	+	0.868449i	0.996444	−	0.0842614i	$-0.0268531\pi$
$151$	2.93008e7	+	3.67421e7i	0.692565	+	0.868449i	−0.303878	+	0.952711i	$0.598282\pi$
$152$	6.70569e6	+	6.22197e6i	0.154878	+	0.143706i
$153$	−3.26320e7	−	1.00656e7i	−0.736587	−	0.227207i
$154$	2.59151e6	−	6.60305e6i	0.0571781	−	0.145687i
$155$	−1.01994e8	−	6.95380e7i	−2.19994	−	1.49990i
$156$	2.61909e7	−	1.26129e7i	0.552350	−	0.265998i
$157$	4.21824e7	−	3.91396e7i	0.869927	−	0.807175i	−0.112533	−	0.993648i	$-0.535896\pi$
$157$	4.21824e7	−	3.91396e7i	0.869927	−	0.807175i	0.982460	+	0.186473i	$0.0597058\pi$
$158$	189601.	+	28577.7i	0.00382420	+	0.000576405i
$159$	−2.17920e6	−	2.90794e7i	−0.0429940	−	0.573715i
$160$	1.01426e7	+	2.58429e7i	0.195762	+	0.498794i
$161$	−1.57454e7	+	6.89853e7i	−0.297348	+	1.30277i
$162$	77881.3	−	1.03925e6i	0.00143923	−	0.0192052i
$163$	−4.83249e7	+	1.49063e7i	−0.874006	+	0.269595i	−0.699129	−	0.714995i	$-0.746429\pi$
$163$	−4.83249e7	+	1.49063e7i	−0.874006	+	0.269595i	−0.174877	+	0.984590i	$0.555953\pi$
$164$	−9.05041e7	−	4.35845e7i	−1.60219	−	0.771575i
$165$	3.56220e7	+	6.16991e7i	0.617340	+	1.06926i
$166$	2.51604e6	−	4.35792e6i	0.0426914	−	0.0739436i
$167$	−4.07665e6	+	2.77941e6i	−0.0677322	+	0.0461790i	−0.596713	−	0.802455i	$-0.703527\pi$
$167$	−4.07665e6	+	2.77941e6i	−0.0677322	+	0.0461790i	0.528981	+	0.848634i	$0.322574\pi$
$168$	2.18418e6	+	9.56951e6i	0.0355390	+	0.155707i
$169$	8.50590e6	−	1.28206e6i	0.135555	−	0.0204317i
$170$	1.02360e7	−	1.28355e7i	0.159793	−	0.200375i
$171$	2.95425e7			0.451815
$172$	−4.93307e7	+	4.32634e7i	−0.739209	+	0.648292i
$173$	5.80146e7			0.851874			0.425937	−	0.904753i	$-0.359944\pi$
$173$	5.80146e7			0.851874			0.425937	+	0.904753i	$0.359944\pi$
$174$	5.14534e6	−	6.45206e6i	0.0740444	−	0.0928487i
$175$	−6.41651e7	+	9.67133e6i	−0.905035	+	0.136412i
$176$	1.99432e7	+	8.73767e7i	0.275740	+	1.20810i
$177$	−6.49458e7	+	4.42793e7i	−0.880328	+	0.600198i
$178$	−326893.	+	566195.i	−0.00434446	+	0.00752482i
$179$	−2.44825e7	−	4.24049e7i	−0.319058	−	0.552625i	0.661234	−	0.750180i	$-0.270033\pi$
$179$	−2.44825e7	−	4.24049e7i	−0.319058	−	0.552625i	−0.980292	+	0.197555i	$0.936700\pi$
$180$	5.37013e7	+	2.58612e7i	0.686326	+	0.330517i
$181$	9.62008e7	−	2.96740e7i	1.20588	−	0.371964i	0.374266	−	0.927321i	$-0.377895\pi$
$181$	9.62008e7	−	2.96740e7i	1.20588	−	0.371964i	0.831612	+	0.555357i	$0.187418\pi$
$182$	677364.	−	9.03880e6i	0.00832861	−	0.111138i
$183$	2.22558e7	−	9.75090e7i	0.268451	−	1.17616i
$184$	1.14455e7	+	2.91628e7i	0.135448	+	0.345117i
$185$	−6.48928e6	−	8.65935e7i	−0.0753522	−	1.00550i
$186$	−1.42496e7	−	2.14779e6i	−0.162371	−	0.0244735i
$187$	1.19964e8	−	1.11310e8i	1.34154	−	1.24477i
$188$	3.07351e7	−	1.48012e7i	0.337351	−	0.162460i
$189$	7.38604e7	+	5.03572e7i	0.795784	+	0.542557i
$190$	−5.18879e6	+	1.32208e7i	−0.0548819	+	0.139837i
$191$	4.82297e7	+	1.48769e7i	0.500838	+	0.154488i	0.534873	−	0.844932i	$-0.320359\pi$
$191$	4.82297e7	+	1.48769e7i	0.500838	+	0.154488i	−0.0340346	+	0.999421i	$0.510836\pi$
$192$	−4.34650e7	−	4.03296e7i	−0.443185	−	0.411216i
$193$	3.50669e7	+	4.39725e7i	0.351113	+	0.440281i	0.925755	−	0.378123i	$-0.123430\pi$
$193$	3.50669e7	+	4.39725e7i	0.351113	+	0.440281i	−0.574643	+	0.818404i	$0.694859\pi$
$194$	2.11408e6	+	2.65098e6i	0.0207882	+	0.0260675i
$195$	6.67353e7	+	6.19213e7i	0.644517	+	0.598025i
$196$	1.41039e7	+	4.35049e6i	0.133796	+	0.0412707i
$197$	−6.54418e7	+	1.66743e8i	−0.609851	+	1.55387i	0.207807	+	0.978170i	$0.433367\pi$
$197$	−6.54418e7	+	1.66743e8i	−0.609851	+	1.55387i	−0.817658	+	0.575704i	$0.804728\pi$
$198$	−8.38015e6	−	5.71349e6i	−0.0767227	−	0.0523086i
$199$	−9.17838e7	+	4.42008e7i	−0.825620	+	0.397598i	−0.798471	−	0.602034i	$-0.794357\pi$
$199$	−9.17838e7	+	4.42008e7i	−0.825620	+	0.397598i	−0.0271495	+	0.999631i	$0.508643\pi$
$200$	−2.10603e7	+	1.95411e7i	−0.186149	+	0.172721i
$201$	2.84025e7	+	4.28099e6i	0.246701	+	0.0371841i
$202$	−1.02677e6	−	1.37013e7i	−0.00876485	−	0.116959i
$203$	5.50698e7	+	1.40316e8i	0.462038	+	1.17725i
$204$	−2.49821e7	+	1.09454e8i	−0.206027	+	0.902663i
$205$	2.35090e7	−	3.13706e8i	0.190588	−	2.54322i
$206$	−2.26037e7	+	6.97233e6i	−0.180154	+	0.0555703i
$207$	9.11563e7	+	4.38986e7i	0.714316	+	0.343997i
$208$	5.72620e7	+	9.91806e7i	0.441209	+	0.764197i
$209$	−7.07870e7	+	1.22607e8i	−0.536341	+	0.928971i
$210$	−1.25916e7	+	8.58484e6i	−0.0938242	+	0.0639683i
$211$	2.53267e7	+	1.10963e8i	0.185605	+	0.813188i	0.978898	+	0.204349i	$0.0655076\pi$
$211$	2.53267e7	+	1.10963e8i	0.185605	+	0.813188i	−0.793293	+	0.608840i	$0.791635\pi$
$212$	1.15608e8	−	1.74250e7i	0.833318	−	0.125603i
$213$	3.71027e7	−	4.65254e7i	0.263074	−	0.329884i
$214$	−7.57434e6			−0.0528320
$215$	−1.82563e8	−	9.43104e7i	−1.25279	−	0.647180i
$216$	3.95785e7			0.267222
$217$	1.64112e8	−	2.05790e8i	1.09026	−	1.36715i
$218$	1.74086e7	−	2.62392e6i	0.113806	−	0.0171535i
$219$	8.94697e6	+	3.91992e7i	0.0575601	+	0.252187i
$220$	−2.36002e8	+	1.60904e8i	−1.49430	+	1.01879i
$221$	1.04558e8	−	1.81100e8i	0.651607	−	1.12862i
$222$	−5.06857e6	−	8.77902e6i	−0.0310921	−	0.0538531i
$223$	−1.82805e8	−	8.80344e7i	−1.10388	−	0.531600i	−0.209003	−	0.977915i	$-0.567022\pi$
$223$	−1.82805e8	−	8.80344e7i	−1.10388	−	0.531600i	−0.894876	+	0.446314i	$0.852736\pi$
$224$	−5.65664e7	+	1.74484e7i	−0.336272	+	0.103726i
$225$	−6.93370e6	+	9.25237e7i	−0.0405813	+	0.541520i
$226$	−42536.1	+	186363.i	−0.000245120	+	0.00107394i
$227$	−4.98669e7	−	1.27059e8i	−0.282958	−	0.720965i	−0.999720	−	0.0236474i	$-0.992472\pi$
$227$	−4.98669e7	−	1.27059e8i	−0.282958	−	0.720965i	0.716763	−	0.697317i	$-0.245623\pi$
$228$	−7.25807e6	−	9.68523e7i	−0.0405555	−	0.541175i
$229$	1.25881e8	+	1.89735e7i	0.692683	+	0.104405i	0.485943	−	0.873991i	$-0.338476\pi$
$229$	1.25881e8	+	1.89735e7i	0.692683	+	0.104405i	0.206741	+	0.978396i	$0.433714\pi$
$230$	−3.56560e7	+	3.30839e7i	−0.193235	+	0.179295i
$231$	−1.36868e8	+	6.59122e7i	−0.730567	+	0.351823i
$232$	5.51410e7	+	3.75945e7i	0.289912	+	0.197659i
$233$	1.28285e7	−	3.26865e7i	0.0664401	−	0.169287i	−0.893797	−	0.448471i	$-0.851969\pi$
$233$	1.28285e7	−	3.26865e7i	0.0664401	−	0.169287i	0.960238	+	0.279184i	$0.0900640\pi$
$234$	−1.23846e7	−	3.82015e6i	−0.0631870	−	0.0194906i
$235$	7.83140e7	+	7.26648e7i	0.393643	+	0.365247i
$236$	−1.96489e8	−	2.46389e8i	−0.973073	−	1.22019i
$237$	−2.56027e6	−	3.21048e6i	−0.0124930	−	0.0156657i
$238$	2.56614e7	+	2.38103e7i	0.123384	+	0.114484i
$239$	−2.79877e8	−	8.63306e7i	−1.32609	−	0.409046i	−0.450795	−	0.892627i	$-0.648860\pi$
$239$	−2.79877e8	−	8.63306e7i	−1.32609	−	0.409046i	−0.875299	+	0.483581i	$0.839336\pi$
$240$	7.03469e7	−	1.79241e8i	0.328477	−	0.836947i
$241$	−1.59952e8	−	1.09053e8i	−0.736088	−	0.501856i	0.136302	−	0.990667i	$-0.456478\pi$
$241$	−1.59952e8	−	1.09053e8i	−0.736088	−	0.501856i	−0.872390	+	0.488811i	$0.837431\pi$
$242$	1.80572e7	−	8.69589e6i	0.0819024	−	0.0394421i
$243$	1.54171e8	−	1.43050e8i	0.689256	−	0.639536i
$244$	3.96512e8	+	5.97646e7i	1.74740	+	0.263378i
$245$	3.45424e6	+	4.60937e7i	0.0150062	+	0.200244i
$246$	−1.34169e7	−	3.41857e7i	−0.0574618	−	0.146410i
$247$	−4.02557e7	+	1.76372e8i	−0.169976	+	0.744714i
$248$	8.70885e6	−	1.16212e8i	0.0362560	−	0.483803i
$249$	−1.02979e8	+	3.17650e7i	−0.422720	+	0.130392i
$250$	474460.	+	228488.i	0.00192048	+	0.000924854i
$251$	7.88311e7	+	1.36539e8i	0.314659	+	0.545005i	0.979365	−	0.202100i	$-0.0647766\pi$
$251$	7.88311e7	+	1.36539e8i	0.314659	+	0.545005i	−0.664706	+	0.747105i	$0.731443\pi$
$252$	−6.35461e7	+	1.10065e8i	−0.250142	+	0.433259i
$253$	−4.00607e8	+	2.73129e8i	−1.55524	+	1.06034i
$254$	−195926.	−	858407.i	−0.000750194	−	0.00328682i
$255$	−3.47665e8	+	5.24021e7i	−1.31302	+	0.197906i
$256$	1.39977e8	−	1.75526e8i	0.521455	−	0.653884i
$257$	8.53674e7			0.313708			0.156854	−	0.987622i	$-0.449865\pi$
$257$	8.53674e7			0.313708			0.156854	+	0.987622i	$0.449865\pi$
$258$	−2.39785e7	−	672346.i	−0.0869268	−	0.00243738i
$259$	1.85159e8			0.662211
$260$	−2.27569e8	+	2.85362e8i	−0.802983	+	1.00691i
$261$	2.13123e8	−	3.21231e7i	0.741973	−	0.111834i
$262$	−8.85002e6	−	3.87745e7i	−0.0304011	−	0.133196i
$263$	1.20744e8	−	8.23216e7i	0.409278	−	0.279041i	−0.341130	−	0.940016i	$-0.610809\pi$
$263$	1.20744e8	−	8.23216e7i	0.409278	−	0.279041i	0.750408	+	0.660975i	$0.229857\pi$
$264$	−3.36292e7	+	5.82474e7i	−0.112487	+	0.194833i
$265$	1.83069e8	+	3.17085e8i	0.604303	+	1.04668i
$266$	−2.72849e7	−	1.31397e7i	−0.0888866	−	0.0428055i
$267$	1.33794e7	−	4.12701e6i	0.0430178	−	0.0132692i
$268$	−8.60582e6	+	1.14837e8i	−0.0273099	+	0.364426i
$269$	1.18296e8	−	5.18287e8i	0.370540	−	1.62344i	−0.354723	−	0.934972i	$-0.615425\pi$
$269$	1.18296e8	−	5.18287e8i	0.370540	−	1.62344i	0.725263	−	0.688472i	$-0.241718\pi$
$270$	2.24501e7	+	5.72019e7i	0.0694136	+	0.176863i
$271$	8.65290e6	+	1.15465e8i	0.0264101	+	0.352418i	0.994717	+	0.102655i	$0.0327337\pi$
$271$	8.65290e6	+	1.15465e8i	0.0264101	+	0.352418i	−0.968307	+	0.249763i	$0.919647\pi$
$272$	−4.37357e8	−	6.59210e7i	−1.31779	−	0.198624i
$273$	−1.42298e8	+	1.32034e8i	−0.423283	+	0.392749i
$274$	3.47715e7	−	1.67451e7i	0.102117	−	0.0491767i
$275$	−3.67376e8	−	2.50473e8i	−1.06524	−	0.726266i
$276$	1.21522e8	−	3.09632e8i	0.347914	−	0.886471i
$277$	−8.86803e7	−	2.73543e7i	−0.250696	−	0.0773296i	0.166860	−	0.985981i	$-0.446637\pi$
$277$	−8.86803e7	−	2.73543e7i	−0.250696	−	0.0773296i	−0.417556	+	0.908651i	$0.637113\pi$
$278$	9.51929e6	+	8.83261e6i	0.0265734	+	0.0246565i
$279$	−2.34657e8	−	2.94251e8i	−0.646873	−	0.811153i
$280$	−7.68405e7	−	9.63549e7i	−0.209188	−	0.262314i
$281$	−3.05204e8	−	2.83188e8i	−0.820574	−	0.761381i	0.153370	−	0.988169i	$-0.450987\pi$
$281$	−3.05204e8	−	2.83188e8i	−0.820574	−	0.761381i	−0.973944	+	0.226787i	$0.927178\pi$
$282$	1.19174e7	+	3.67604e6i	0.0316454	+	0.00976133i
$283$	−2.92847e7	+	7.46163e7i	−0.0768049	+	0.195696i	−0.964119	−	0.265469i	$-0.914473\pi$
$283$	−2.92847e7	+	7.46163e7i	−0.0768049	+	0.195696i	0.887314	+	0.461165i	$0.152568\pi$
$284$	1.97126e8	+	1.34398e8i	0.510658	+	0.348161i
$285$	2.74042e8	−	1.31971e8i	0.701228	−	0.337694i
$286$	4.55292e7	−	4.22449e7i	0.115082	−	0.106781i
$287$	6.63293e8	+	9.99753e7i	1.65622	+	0.249635i
$288$	6.32533e6	+	8.44056e7i	0.0156030	+	0.208208i
$289$	1.45143e8	+	3.69819e8i	0.353716	+	0.901253i
$290$	−2.30568e7	+	1.01018e8i	−0.0555145	+	0.243225i
$291$	5.42659e6	−	7.24128e7i	0.0129093	−	0.172262i
$292$	−1.54039e8	+	4.75148e7i	−0.362069	+	0.111684i
$293$	2.95213e8	+	1.42167e8i	0.685643	+	0.330188i	0.744068	−	0.668103i	$-0.232894\pi$
$293$	2.95213e8	+	1.42167e8i	0.685643	+	0.330188i	−0.0584252	+	0.998292i	$0.518608\pi$
$294$	2.69800e6	+	4.67307e6i	0.00619193	+	0.0107247i
$295$	4.93468e8	−	8.54711e8i	1.11913	−	1.93840i
$296$	6.77337e7	−	4.61801e7i	0.151804	−	0.103498i
$297$	1.36303e8	+	5.97183e8i	0.301896	+	1.32269i
$298$	7.48053e7	−	1.12751e7i	0.163748	−	0.0246810i
$299$	−3.86291e8	+	4.84394e8i	−0.835730	+	1.04797i
$300$	3.05034e8			0.652264
$301$	2.29625e8	−	3.73160e8i	0.485328	−	0.788701i
$302$	−6.88824e7			−0.143908
$303$	−1.83462e8	+	2.30054e8i	−0.378876	+	0.475096i
$304$	3.78359e8	−	5.70284e7i	0.772407	−	0.116422i
$305$	2.79439e8	+	1.22430e9i	0.563945	+	2.47081i
$306$	4.13564e7	−	2.81963e7i	0.0825122	−	0.0562559i
$307$	−1.13272e8	+	1.96193e8i	−0.223429	+	0.386990i	−0.955847	−	0.293865i	$-0.905058\pi$
$307$	−1.13272e8	+	1.96193e8i	−0.223429	+	0.386990i	0.732418	+	0.680855i	$0.238392\pi$
$308$	−3.04526e8	−	5.27455e8i	−0.593878	−	1.02863i
$309$	4.56420e8	+	2.19800e8i	0.880055	+	0.423812i
$310$	1.72897e8	−	5.33318e7i	0.329627	−	0.101676i
$311$	5.07945e6	−	6.77806e7i	0.00957537	−	0.127774i	−0.990367	−	0.138464i	$-0.955784\pi$
$311$	5.07945e6	−	6.77806e7i	0.00957537	−	0.127774i	0.999943	+	0.0106893i	$0.00340258\pi$
$312$	−1.91245e7	+	8.37899e7i	−0.0356491	+	0.156189i
$313$	6.77172e7	+	1.72541e8i	0.124823	+	0.318043i	0.979602	−	0.200949i	$-0.0644025\pi$
$313$	6.77172e7	+	1.72541e8i	0.124823	+	0.318043i	−0.854779	+	0.518992i	$0.826307\pi$
$314$	6.30304e6	+	8.41082e7i	0.0114894	+	0.153315i
$315$	−3.93570e8	−	5.93211e7i	−0.709471	−	0.106936i
$316$	1.20685e7	−	1.11980e7i	0.0215154	−	0.0199634i
$317$	1.35419e8	−	6.52145e7i	0.238766	−	0.114984i	−0.310675	−	0.950516i	$-0.600555\pi$
$317$	1.35419e8	−	6.52145e7i	0.238766	−	0.114984i	0.549441	+	0.835533i	$0.314841\pi$
$318$	3.53155e7	+	2.40777e7i	0.0615843	+	0.0419875i
$319$	−3.77348e8	+	9.61467e8i	−0.650841	+	1.65832i
$320$	7.11397e8	+	2.19437e8i	1.21363	+	0.374356i
$321$	1.18910e8	+	1.10332e8i	0.200655	+	0.186181i
$322$	−6.46653e7	−	8.10877e7i	−0.107938	−	0.135350i
$323$	−4.35616e8	−	5.46245e8i	−0.719275	−	0.901943i
$324$	−6.55954e7	−	6.08636e7i	−0.107144	−	0.0994146i
$325$	−5.42928e8	−	1.67471e8i	−0.877304	−	0.270612i
$326$	2.70809e7	−	6.90010e7i	0.0432914	−	0.110305i
$327$	−3.11520e8	−	2.12391e8i	−0.492684	−	0.335906i
$328$	2.67576e8	−	1.28858e8i	0.418686	−	0.201629i
$329$	−1.66987e8	+	1.54942e8i	−0.258522	+	0.239874i
$330$	−1.03259e8	−	1.55638e7i	−0.158172	−	0.0238405i
$331$	3.19714e7	+	4.26629e8i	0.0484579	+	0.646625i	0.967566	+	0.252619i	$0.0812920\pi$
$331$	3.19714e7	+	4.26629e8i	0.0484579	+	0.646625i	−0.919108	+	0.394006i	$0.871089\pi$
$332$	−1.57851e8	−	4.02198e8i	−0.236736	−	0.603194i
$333$	5.89127e7	−	2.58114e8i	0.0874288	−	0.383050i
$334$	540444.	−	7.21172e6i	0.000793666	−	0.0105907i
$335$	−3.44621e8	+	1.06301e8i	−0.500823	+	0.154484i
$336$	3.69914e8	+	1.78141e8i	0.532002	+	0.256199i
$337$	7.26594e6	+	1.25850e7i	0.0103416	+	0.0179122i	0.871150	−	0.491017i	$-0.163375\pi$
$337$	7.26594e6	+	1.25850e7i	0.0103416	+	0.0179122i	−0.860808	+	0.508929i	$0.830041\pi$
$338$	−6.30414e6	+	1.09191e7i	−0.00888009	+	0.0153808i
$339$	3.38245e6	−	2.30611e6i	0.00471555	−	0.00321500i
$340$	−3.13670e8	−	1.37428e9i	−0.432809	−	1.89626i
$341$	1.78345e9	−	2.68813e8i	2.43569	−	0.367121i
$342$	−2.69982e7	+	3.38546e7i	−0.0364958	+	0.0457643i
$343$	−7.90662e8			−1.05794
$344$	−9.06911e6	−	1.93777e8i	−0.0120119	−	0.256654i
$345$	1.04168e9			1.36574
$346$	−5.30181e7	+	6.64826e7i	−0.0688110	+	0.0862862i
$347$	−1.01108e9	+	1.52396e8i	−1.29907	+	0.195804i	−0.761914	−	0.647678i	$-0.775740\pi$
$347$	−1.01108e9	+	1.52396e8i	−1.29907	+	0.195804i	−0.537158	+	0.843482i	$0.680502\pi$
$348$	−1.57673e8	−	6.90810e8i	−0.200553	−	0.878681i
$349$	−4.10009e8	+	2.79539e8i	−0.516303	+	0.352009i	−0.793270	−	0.608870i	$-0.791623\pi$
$349$	−4.10009e8	+	2.79539e8i	−0.516303	+	0.352009i	0.276967	+	0.960879i	$0.410671\pi$
$350$	4.75559e7	−	8.23692e7i	0.0592879	−	0.102690i
$351$	3.91361e8	+	6.77857e8i	0.483062	+	0.836688i
$352$	−3.65454e8	−	1.75994e8i	−0.446616	−	0.215079i
$353$	−9.35956e7	+	2.88704e7i	−0.113252	+	0.0349335i	−0.350863	−	0.936427i	$-0.614112\pi$
$353$	−9.35956e7	+	2.88704e7i	−0.113252	+	0.0349335i	0.237611	+	0.971360i	$0.423636\pi$
$354$	8.60991e6	−	1.14891e8i	0.0103154	−	0.137650i
$355$	−1.66261e8	+	7.28438e8i	−0.197238	+	0.864158i
$356$	2.05086e7	+	5.22550e7i	0.0240913	+	0.0613836i
$357$	−5.60246e7	−	7.47597e8i	−0.0651689	−	0.869618i
$358$	7.09684e7	+	1.06968e7i	0.0817475	+	0.0123215i
$359$	−2.73270e8	+	2.53558e8i	−0.311718	+	0.289232i	−0.820480	−	0.571675i	$-0.806294\pi$
$359$	−2.73270e8	+	2.53558e8i	−0.311718	+	0.289232i	0.508762	+	0.860907i	$0.330103\pi$
$360$	−1.58768e8	+	7.64587e7i	−0.179351	+	0.0863710i
$361$	−2.39153e8	−	1.63052e8i	−0.267547	−	0.182410i
$362$	−5.39102e7	+	1.37361e8i	−0.0597298	+	0.152189i
$363$	−4.10151e8	−	1.26515e8i	−0.450060	−	0.138825i
$364$	−5.70509e8	−	5.29355e8i	−0.620023	−	0.575297i
$365$	−3.14759e8	−	3.94695e8i	−0.338807	−	0.424851i
$366$	9.14027e7	+	1.14615e8i	0.0974486	+	0.122197i
$367$	−1.03208e9	−	9.57631e8i	−1.08989	−	1.01127i	−0.999883	−	0.0153287i	$-0.995121\pi$
$367$	−1.03208e9	−	9.57631e8i	−1.08989	−	1.01127i	−0.0900071	−	0.995941i	$-0.528689\pi$
$368$	1.25220e9	+	3.86254e8i	1.30981	+	0.404022i
$369$	3.50409e8	−	8.92826e8i	0.363063	−	0.925070i
$370$	1.05163e8	+	7.16992e7i	0.107934	+	0.0735882i
$371$	−7.03395e8	+	3.38737e8i	−0.715139	+	0.344393i
$372$	−9.07021e8	+	8.41592e8i	−0.913518	+	0.847621i
$373$	−1.09967e9	−	1.65748e8i	−1.09719	−	0.165374i	−0.424591	−	0.905385i	$-0.639582\pi$
$373$	−1.09967e9	−	1.65748e8i	−1.09719	−	0.165374i	−0.672595	+	0.740011i	$0.734820\pi$
$374$	1.79254e7	+	2.39198e8i	0.0177182	+	0.236432i
$375$	−4.12028e6	−	1.04983e7i	−0.00403476	−	0.0102804i
$376$	−2.24426e7	+	9.83276e7i	−0.0217729	+	0.0953933i
$377$	−9.86307e7	+	1.31614e9i	−0.0948020	+	1.26504i
$378$	−1.25207e8	+	3.86211e7i	−0.119236	+	0.0367793i
$379$	6.95535e8	+	3.34952e8i	0.656269	+	0.316042i	0.732219	−	0.681069i	$-0.238485\pi$
$379$	6.95535e8	+	3.34952e8i	0.656269	+	0.316042i	−0.0759503	+	0.997112i	$0.524199\pi$
$380$	6.09732e8	+	1.05609e9i	0.570028	+	0.987318i
$381$	−9.42821e6	+	1.63301e7i	−0.00873357	+	0.0151270i
$382$	−6.11243e7	+	4.16738e7i	−0.0561038	+	0.0382509i
$383$	−2.30475e8	−	1.00978e9i	−0.209618	−	0.918396i	−0.964822	−	0.262906i	$-0.915319\pi$
$383$	−2.30475e8	−	1.00978e9i	−0.209618	−	0.918396i	0.755204	−	0.655490i	$-0.227538\pi$
$384$	3.65797e8	−	5.51350e7i	0.329671	−	0.0496899i
$385$	1.18923e9	−	1.49124e9i	1.06207	−	1.33179i
$386$	−8.24376e7			−0.0729574
$387$	−4.47128e8	−	4.38828e8i	−0.392142	−	0.384863i
$388$	2.91135e8			0.253036
$389$	6.74936e8	−	8.46342e8i	0.581351	−	0.728992i	−0.400991	−	0.916082i	$-0.631334\pi$
$389$	6.74936e8	−	8.46342e8i	0.581351	−	0.728992i	0.982343	+	0.187090i	$0.0599057\pi$
$390$	−1.31947e8	+	1.98879e7i	−0.112635	+	0.0169770i
$391$	−5.32445e8	−	2.33279e9i	−0.450460	−	1.97359i
$392$	−3.60546e7	+	2.45816e7i	−0.0302315	+	0.0206115i
$393$	−4.25875e8	+	7.37637e8i	−0.353922	+	0.613012i
$394$	−1.31276e8	−	2.27376e8i	−0.108130	−	0.187287i
$395$	4.64526e7	+	2.23704e7i	0.0379245	+	0.0182635i
$396$	−8.32169e8	+	2.56690e8i	−0.673408	+	0.207719i
$397$	−1.08706e8	+	1.45058e9i	−0.0871939	+	1.16352i	0.766323	+	0.642456i	$0.222084\pi$
$397$	−1.08706e8	+	1.45058e9i	−0.0871939	+	1.16352i	−0.853517	+	0.521066i	$0.825535\pi$
$398$	3.32265e7	−	1.45575e8i	0.0264176	−	0.115743i
$399$	2.36946e8	+	6.03728e8i	0.186743	+	0.475813i
$400$	8.98047e7	+	1.19836e9i	0.0701599	+	0.936219i
$401$	−3.18882e8	−	4.80638e7i	−0.246959	−	0.0372231i	0.0243960	−	0.999702i	$-0.492234\pi$
$401$	−3.18882e8	−	4.80638e7i	−0.246959	−	0.0372231i	−0.271355	+	0.962479i	$0.587472\pi$
$402$	−3.08622e7	+	2.86359e7i	−0.0236938	+	0.0219847i
$403$	2.07646e9	−	9.99969e8i	1.58036	−	0.761060i
$404$	−9.74733e8	−	6.64562e8i	−0.735446	−	0.501419i
$405$	1.02381e8	−	2.60862e8i	0.0765817	−	0.195127i
$406$	−2.11123e8	−	6.51230e7i	−0.156565	−	0.0482940i
$407$	9.30056e8	+	8.62965e8i	0.683799	+	0.634473i
$408$	−2.06951e8	−	2.59508e8i	−0.150854	−	0.189165i
$409$	7.58369e8	+	9.50964e8i	0.548086	+	0.687278i	0.976306	−	0.216397i	$-0.0694304\pi$
$409$	7.58369e8	+	9.50964e8i	0.548086	+	0.687278i	−0.428219	+	0.903675i	$0.640859\pi$
$410$	3.38011e8	+	3.13629e8i	0.242208	+	0.224736i
$411$	−7.89797e8	−	2.43620e8i	−0.561137	−	0.173088i
$412$	−7.42020e8	+	1.89064e9i	−0.522728	+	1.33189i
$413$	1.73876e9	+	1.18546e9i	1.21454	+	0.828062i
$414$	−1.33612e8	+	6.43440e7i	−0.0925429	+	0.0445663i
$415$	9.91893e8	−	9.20342e8i	0.681234	−	0.632093i
$416$	−5.12529e8	−	7.72513e7i	−0.349053	−	0.0526113i
$417$	−2.07828e7	−	2.77327e8i	−0.0140355	−	0.187291i
$418$	−7.58122e7	−	1.93166e8i	−0.0507718	−	0.129364i
$419$	−3.81390e7	+	1.67098e8i	−0.0253292	+	0.110974i	−0.986012	−	0.166673i	$-0.946698\pi$
$419$	−3.81390e7	+	1.67098e8i	−0.0253292	+	0.110974i	0.960683	+	0.277647i	$0.0895547\pi$
$420$	−9.77853e7	+	1.30485e9i	−0.0644023	+	0.859388i
$421$	2.01720e9	−	6.22224e8i	1.31753	−	0.406406i	0.445251	−	0.895406i	$-0.353114\pi$
$421$	2.01720e9	−	6.22224e8i	1.31753	−	0.406406i	0.872284	+	0.489000i	$0.162638\pi$
$422$	−1.50305e8	−	7.23833e7i	−0.0973601	−	0.0468862i
$423$	1.62859e8	+	2.82080e8i	0.104621	+	0.181210i
$424$	−1.72828e8	+	2.99346e8i	−0.110112	+	0.190719i
$425$	1.81302e9	−	1.23609e9i	1.14562	−	0.781071i
$426$	1.94091e7	+	8.50368e7i	0.0121639	+	0.0532934i
$427$	−2.64778e9	+	3.99089e8i	−1.64583	+	0.248069i
$428$	−4.05486e8	+	5.08463e8i	−0.249990	+	0.313477i
$429$	−1.33013e9			−0.813380
$430$	2.74917e8	−	1.23023e8i	0.166748	−	0.0746186i
$431$	2.41044e9			1.45019			0.725096	−	0.688648i	$-0.241795\pi$
$431$	2.41044e9			1.45019			0.725096	+	0.688648i	$0.241795\pi$
$432$	1.03220e9	−	1.29433e9i	0.615984	−	0.772420i
$433$	−2.17207e9	+	3.27388e8i	−1.28578	+	0.193800i	−0.756134	−	0.654417i	$-0.772914\pi$
$433$	−2.17207e9	+	3.27388e8i	−1.28578	+	0.193800i	−0.529648	+	0.848218i	$0.677676\pi$
$434$	8.58499e7	+	3.76133e8i	0.0504111	+	0.220865i
$435$	1.83346e9	−	1.25003e9i	1.06797	−	0.728131i
$436$	7.55810e8	−	1.30910e9i	0.436727	−	0.756433i
$437$	1.03500e9	+	1.79268e9i	0.593275	+	1.02758i
$438$	−5.30973e7	−	2.55703e7i	−0.0301935	−	0.0145404i
$439$	−9.02692e8	+	2.78444e8i	−0.509230	+	0.157077i	−0.538714	−	0.842489i	$-0.681090\pi$
$439$	−9.02692e8	+	2.78444e8i	−0.509230	+	0.157077i	0.0294844	+	0.999565i	$0.490613\pi$
$440$	6.31081e7	−	8.42119e8i	0.0353184	−	0.471291i
$441$	−3.13592e7	+	1.37394e8i	−0.0174113	+	0.0762837i
$442$	1.11981e8	+	2.85323e8i	0.0616832	+	0.157166i
$443$	6.14844e6	+	8.20453e7i	0.00336010	+	0.0448374i	0.998632	−	0.0522925i	$-0.0166528\pi$
$443$	6.14844e6	+	8.20453e7i	0.00336010	+	0.0448374i	−0.995272	+	0.0971299i	$0.969034\pi$
$444$	−8.60674e8	−	1.29726e8i	−0.466658	−	0.0703373i
$445$	−1.28870e8	+	1.19574e8i	−0.0693253	+	0.0643245i
$446$	2.67945e8	−	1.29036e8i	0.143013	−	0.0688712i
$447$	−1.33861e9	−	9.12650e8i	−0.708889	−	0.483312i
$448$	−5.79951e8	+	1.47769e9i	−0.304732	+	0.776444i
$449$	1.19474e8	+	3.68530e7i	0.0622892	+	0.0192137i	0.325743	−	0.945458i	$-0.394386\pi$
$449$	1.19474e8	+	3.68530e7i	0.0622892	+	0.0192137i	−0.263454	+	0.964672i	$0.584862\pi$
$450$	−9.96923e7	−	9.25009e7i	−0.0515725	−	0.0478522i
$451$	2.86577e9	+	3.59356e9i	1.47104	+	1.84462i
$452$	1.02333e7	+	1.28322e7i	0.00521234	+	0.00653607i
$453$	1.08139e9	+	1.00338e9i	0.546560	+	0.507134i
$454$	1.91177e8	+	5.89702e7i	0.0958826	+	0.0295759i
$455$	8.90445e8	−	2.26882e9i	0.443167	−	1.12917i
$456$	2.37252e8	+	1.61756e8i	0.117175	+	0.0798882i
$457$	−1.88189e9	+	9.06269e8i	−0.922331	+	0.444171i	−0.833903	−	0.551911i	$-0.813899\pi$
$457$	−1.88189e9	+	9.06269e8i	−0.922331	+	0.444171i	−0.0884281	+	0.996083i	$0.528184\pi$
$458$	−1.36782e8	+	1.26915e8i	−0.0665273	+	0.0617283i
$459$	−2.98915e9	−	4.50542e8i	−1.44279	−	0.217466i
$460$	3.12100e8	+	4.16469e9i	0.149500	+	1.99494i
$461$	−1.12712e9	−	2.87187e9i	−0.535820	−	1.36525i	−0.900801	−	0.434232i	$-0.857020\pi$
$461$	−1.12712e9	−	2.87187e9i	−0.535820	−	1.36525i	0.364981	−	0.931015i	$-0.381075\pi$
$462$	4.95474e7	−	2.17081e8i	0.0233762	−	0.102418i
$463$	3.33474e7	−	4.44990e8i	0.0156145	−	0.208361i	−0.983940	−	0.178502i	$-0.942875\pi$
$463$	3.33474e7	−	4.44990e8i	0.0156145	−	0.208361i	0.999554	−	0.0298595i	$-0.00950599\pi$
$464$	2.66751e9	−	8.22818e8i	1.23963	−	0.382376i
$465$	−3.49119e9	−	1.68127e9i	−1.61023	−	0.775446i
$466$	2.57339e7	+	4.45724e7i	0.0117803	+	0.0204040i
$467$	−3.12958e8	+	5.42059e8i	−0.142193	+	0.246285i	−0.928322	−	0.371777i	$-0.878749\pi$
$467$	−3.12958e8	+	5.42059e8i	−0.142193	+	0.246285i	0.786129	+	0.618062i	$0.212082\pi$
$468$	−9.19446e8	+	6.26868e8i	−0.414635	+	0.282693i
$469$	−1.71117e8	−	7.49712e8i	−0.0765928	−	0.335575i
$470$	−1.54840e8	+	2.33384e7i	−0.0687927	+	0.0103688i
$471$	1.12622e9	−	1.41223e9i	0.496649	−	0.622778i
$472$	9.31723e8			0.407840
$473$	2.89258e9	−	8.04181e8i	1.25681	−	0.349413i
$474$	6.01886e6			0.00259591
$475$	−1.18357e9	+	1.48415e9i	−0.506717	+	0.635403i
$476$	2.97213e9	−	4.47977e8i	1.26312	−	0.190384i
$477$	2.48401e8	+	1.08832e9i	0.104795	+	0.459135i
$478$	3.54704e8	−	2.41833e8i	0.148549	−	0.101279i
$479$	1.96645e8	−	3.40599e8i	0.0817538	−	0.141602i	−0.822250	−	0.569127i	$-0.807281\pi$
$479$	1.96645e8	−	3.40599e8i	0.0817538	−	0.141602i	0.904003	+	0.427525i	$0.140615\pi$
$480$	4.35729e8	+	7.54705e8i	0.179834	+	0.311482i
$481$	1.46069e9	+	7.03429e8i	0.598479	+	0.288212i
$482$	2.71147e8	−	8.36378e7i	0.110291	−	0.0340203i
$483$	−1.65988e8	+	2.21495e9i	−0.0670287	+	0.894436i
$484$	3.82924e8	−	1.67770e9i	0.153516	−	0.672598i
$485$	3.33099e8	+	8.48722e8i	0.132580	+	0.337807i
$486$	2.30367e7	+	3.07404e8i	0.00910320	+	0.121474i
$487$	2.00772e9	+	3.02615e8i	0.787684	+	0.118724i	0.530552	−	0.847652i	$-0.321985\pi$
$487$	2.00772e9	+	3.02615e8i	0.787684	+	0.118724i	0.257131	+	0.966376i	$0.417223\pi$
$488$	−8.69057e8	+	8.06367e8i	−0.338516	+	0.314097i
$489$	−1.43025e9	+	6.88774e8i	−0.553136	+	0.266376i
$490$	−5.59784e7	−	3.81654e7i	−0.0214948	−	0.0146549i
$491$	3.41604e8	−	8.70394e8i	0.130238	−	0.331841i	−0.850848	−	0.525411i	$-0.823911\pi$
$491$	3.41604e8	−	8.70394e8i	0.130238	−	0.331841i	0.981086	+	0.193570i	$0.0620066\pi$
$492$	−3.01313e9	−	9.29429e8i	−1.14062	−	0.351834i
$493$	−3.73654e9	−	3.46700e9i	−1.40445	−	1.30314i
$494$	−1.65327e8	−	2.07313e8i	−0.0617020	−	0.0773718i
$495$	−1.70043e9	−	2.13227e9i	−0.630144	−	0.790175i
$496$	−3.57333e9	−	3.31557e9i	−1.31488	−	1.22003i
$497$	−1.52240e9	−	4.69597e8i	−0.556263	−	0.171585i
$498$	5.77089e7	−	1.47040e8i	0.0209382	−	0.0533498i
$499$	−1.58113e8	−	1.07800e8i	−0.0569661	−	0.0388389i	0.534502	−	0.845167i	$-0.320499\pi$
$499$	−1.58113e8	−	1.07800e8i	−0.0569661	−	0.0388389i	−0.591468	+	0.806328i	$0.701452\pi$
$500$	4.07381e7	−	1.96184e7i	0.0145749	−	0.00701890i
$501$	−1.13535e8	+	1.05345e8i	−0.0403363	+	0.0374266i
$502$	−2.28511e8	−	3.44425e7i	−0.0806203	−	0.0121515i
$503$	2.70591e8	+	3.61078e9i	0.0948037	+	1.26507i	0.818321	+	0.574761i	$0.194905\pi$
$503$	2.70591e8	+	3.61078e9i	0.0948037	+	1.26507i	−0.723517	+	0.690306i	$0.757476\pi$
$504$	−1.37276e8	−	3.49775e8i	−0.0477627	−	0.121697i
$505$	8.22113e8	−	3.60191e9i	0.284061	−	1.24455i
$506$	5.31087e7	−	7.08687e8i	0.0182238	−	0.243180i
$507$	2.58023e8	−	7.95895e7i	0.0879286	−	0.0271224i
$508$	−6.81133e7	−	3.28016e7i	−0.0230520	−	0.0111013i
$509$	−1.69070e9	−	2.92838e9i	−0.568270	−	0.984272i	−0.996737	−	0.0807151i	$-0.974280\pi$
$509$	−1.69070e9	−	2.92838e9i	−0.568270	−	0.984272i	0.428467	−	0.903557i	$-0.359054\pi$
$510$	2.57672e8	−	4.46301e8i	0.0860144	−	0.148981i
$511$	8.89402e8	−	6.06384e8i	0.294866	−	0.201036i
$512$	4.08887e8	+	1.79145e9i	0.134635	+	0.589875i
$513$	2.58592e9	−	3.89765e8i	0.845677	−	0.127465i
$514$	−7.80151e7	+	9.78279e7i	−0.0253401	+	0.0317755i
$515$	−6.36060e9			−2.05198
$516$	−1.32880e9	+	1.57368e9i	−0.425782	+	0.504245i
$517$	−1.56091e9			−0.496776
$518$	−1.69213e8	+	2.12186e8i	−0.0534907	+	0.0670752i
$519$	1.80076e9	−	2.71420e8i	0.565418	−	0.0852230i
$520$	−2.40123e8	−	1.05205e9i	−0.0748896	−	0.328113i
$521$	1.90297e9	−	1.29742e9i	0.589522	−	0.401930i	−0.231492	−	0.972837i	$-0.574361\pi$
$521$	1.90297e9	−	1.29742e9i	0.589522	−	0.401930i	0.821015	+	0.570907i	$0.193408\pi$
$522$	−1.57956e8	+	2.73587e8i	−0.0486059	+	0.0841878i
$523$	−2.96015e9	−	5.12713e9i	−0.904811	−	1.56718i	−0.821171	−	0.570682i	$-0.806679\pi$
$523$	−2.96015e9	−	5.12713e9i	−0.904811	−	1.56718i	−0.0836394	−	0.996496i	$-0.526654\pi$
$524$	−3.07669e9	−	1.48166e9i	−0.934168	−	0.449871i
$525$	−1.94642e9	+	6.00391e8i	−0.587055	+	0.181083i
$526$	−1.60071e7	+	2.13599e8i	−0.00479580	+	0.0639955i
$527$	−1.98062e9	+	8.67768e9i	−0.589474	+	2.58266i
$528$	1.02782e9	+	2.61885e9i	0.303878	+	0.774268i
$529$	2.75338e8	+	3.67413e9i	0.0808670	+	1.07910i
$530$	−5.30670e8	−	7.99857e7i	−0.154831	−	0.0233371i
$531$	2.20577e9	−	2.04666e9i	0.639337	−	0.593218i
$532$	−2.34274e9	+	1.12820e9i	−0.674579	+	0.324860i
$533$	4.85278e9	+	3.30857e9i	1.38818	+	0.946444i
$534$	−7.49774e6	+	1.91039e7i	−0.00213077	+	0.00542910i
$535$	−1.94621e9	−	6.00328e8i	−0.549481	−	0.169492i
$536$	−2.49580e8	−	2.31577e8i	−0.0700057	−	0.0649558i
$537$	−9.58321e8	−	1.20170e9i	−0.267055	−	0.334877i
$538$	4.85830e8	+	6.09212e8i	0.134508	+	0.168667i
$539$	−4.95068e8	−	4.59356e8i	−0.136177	−	0.126354i
$540$	5.04179e9	+	1.55518e9i	1.37786	+	0.425015i
$541$	−1.39086e8	+	3.54385e8i	−0.0377652	+	0.0962243i	−0.948512	−	0.316741i	$-0.897412\pi$
$541$	−1.39086e8	+	3.54385e8i	−0.0377652	+	0.0962243i	0.910747	+	0.412965i	$0.135507\pi$
$542$	−1.40226e8	−	9.56047e7i	−0.0378296	−	0.0257918i
$543$	2.84722e9	−	1.37115e9i	0.763170	−	0.367523i
$544$	1.46740e9	−	1.36155e9i	0.390799	−	0.362608i
$545$	4.68107e9	+	7.05558e8i	1.23868	+	0.186700i
$546$	−2.12627e7	−	2.83731e8i	−0.00559042	−	0.0745989i
$547$	−2.51789e8	−	6.41547e8i	−0.0657780	−	0.167600i	0.894205	−	0.447657i	$-0.147742\pi$
$547$	−2.51789e8	−	6.41547e8i	−0.0657780	−	0.167600i	−0.959983	+	0.280058i	$0.909646\pi$
$548$	7.37370e8	−	3.23063e9i	0.191405	−	0.838600i
$549$	−2.86120e8	+	3.81800e9i	−0.0737981	+	0.984767i
$550$	6.22768e8	−	1.92099e8i	0.159609	−	0.0492328i
$551$	3.97294e9	+	1.91327e9i	1.01177	+	0.487242i
$552$	4.91704e8	+	8.51657e8i	0.124428	+	0.215515i
$553$	−5.49686e7	+	9.52084e7i	−0.0138222	+	0.0239407i
$554$	1.12390e8	−	7.66260e7i	0.0280829	−	0.0191466i
$555$	−6.06552e8	−	2.65748e9i	−0.150606	−	0.659849i
$556$	1.10254e9	−	1.66181e8i	0.272039	−	0.0410033i
$557$	−1.19507e9	+	1.49857e9i	−0.293022	+	0.367438i	−0.906450	−	0.422313i	$-0.861218\pi$
$557$	−1.19507e9	+	1.49857e9i	−0.293022	+	0.367438i	0.613429	+	0.789750i	$0.289790\pi$
$558$	5.51648e8			0.134413
$559$	3.22912e9	−	2.07143e9i	0.781884	−	0.501568i
$560$	−5.15506e9			−1.24044
$561$	3.20289e9	−	4.01629e9i	0.765899	−	0.960407i
$562$	6.03441e8	−	9.09541e7i	0.143403	−	0.0216145i
$563$	1.15215e9	+	5.04790e9i	0.272101	+	1.19215i	0.907528	+	0.419991i	$0.137967\pi$
$563$	1.15215e9	+	5.04790e9i	0.272101	+	1.19215i	−0.635427	+	0.772161i	$0.719176\pi$
$564$	8.84761e8	−	6.03220e8i	0.207658	−	0.141579i
$565$	−2.57003e7	+	4.45143e7i	−0.00599472	+	0.0103832i
$566$	−5.87449e7	−	1.01749e8i	−0.0136180	−	0.0235870i
$567$	5.38361e8	+	2.59261e8i	0.124032	+	0.0597305i
$568$	−6.74034e8	+	2.07912e8i	−0.154334	+	0.0476058i
$569$	−2.68685e8	+	3.58535e9i	−0.0611436	+	0.815904i	0.879368	+	0.476143i	$0.157965\pi$
$569$	−2.68685e8	+	3.58535e9i	−0.0611436	+	0.815904i	−0.940512	+	0.339762i	$0.889654\pi$
$570$	−9.92053e7	+	4.34647e8i	−0.0224374	+	0.0983048i
$571$	−1.39439e8	−	3.55284e8i	−0.0313442	−	0.0798637i	0.914345	−	0.404937i	$-0.132706\pi$
$571$	−1.39439e8	−	3.55284e8i	−0.0313442	−	0.0798637i	−0.945689	+	0.325073i	$0.894611\pi$
$572$	−3.98522e8	−	5.31790e9i	−0.0890361	−	1.18810i
$573$	1.56664e9	+	2.36133e8i	0.347879	+	0.0524343i
$574$	−7.20735e8	+	6.68745e8i	−0.159068	+	0.147594i
$575$	−5.85737e9	+	2.82076e9i	−1.28489	+	0.618770i
$576$	1.87539e9	+	1.27862e9i	0.408895	+	0.278780i
$577$	2.63121e9	−	6.70422e9i	0.570218	−	1.45289i	−0.296959	−	0.954890i	$-0.595973\pi$
$577$	2.63121e9	−	6.70422e9i	0.570218	−	1.45289i	0.867177	−	0.498000i	$-0.165932\pi$
$578$	−5.56442e8	−	1.71640e8i	−0.119859	−	0.0369717i
$579$	1.29419e9	+	1.20083e9i	0.277092	+	0.257104i
$580$	5.54701e9	+	6.95573e9i	1.18049	+	1.48028i
$581$	1.79889e9	+	2.25573e9i	0.380529	+	0.477168i
$582$	7.80232e7	+	7.23949e7i	0.0164056	+	0.0152222i
$583$	−5.11190e9	−	1.57681e9i	−1.06842	−	0.329564i
$584$	1.74118e8	−	4.43647e8i	0.0361743	−	0.0921706i
$585$	−2.87943e9	−	1.96316e9i	−0.594650	−	0.405425i
$586$	−4.32706e8	+	2.08380e8i	−0.0888282	+	0.0427774i
$587$	3.85178e8	−	3.57393e8i	0.0786010	−	0.0729311i	−0.639894	−	0.768463i	$-0.721022\pi$
$587$	3.85178e8	−	3.57393e8i	0.0786010	−	0.0729311i	0.718495	+	0.695532i	$0.244831\pi$
$588$	4.58136e8	+	6.90530e7i	0.0929339	+	0.0140075i
$589$	−5.75432e8	−	7.67861e9i	−0.116035	−	1.54839i
$590$	5.28500e8	+	1.34660e9i	0.105941	+	0.269932i
$591$	−1.25119e9	+	5.48183e9i	−0.249326	+	1.09237i
$592$	2.56253e8	−	3.41945e9i	0.0507624	−	0.677377i
$593$	−5.26395e9	+	1.62371e9i	−1.03662	+	0.319755i	−0.765939	−	0.642913i	$-0.777725\pi$
$593$	−5.26395e9	+	1.62371e9i	−1.03662	+	0.319755i	−0.270682	+	0.962669i	$0.587249\pi$
$594$	−8.08914e8	−	3.89552e8i	−0.158361	−	0.0762629i
$595$	4.70649e9	+	8.15187e9i	0.915983	+	1.58653i
$596$	3.24774e9	−	5.62525e9i	0.628376	−	1.08838i
$597$	−2.64215e9	+	1.80139e9i	−0.508215	+	0.346495i
$598$	−2.02076e8	−	8.85352e8i	−0.0386420	−	0.169302i
$599$	−2.10880e9	+	3.17850e8i	−0.400905	+	0.0604267i	−0.346400	−	0.938087i	$-0.612596\pi$
$599$	−2.10880e9	+	3.17850e8i	−0.400905	+	0.0604267i	−0.0545046	+	0.998514i	$0.517358\pi$
$600$	−5.62284e8	+	7.05082e8i	−0.106274	+	0.133263i
$601$	4.37582e9			0.822240			0.411120	−	0.911581i	$-0.365138\pi$
$601$	4.37582e9			0.822240			0.411120	+	0.911581i	$0.365138\pi$
$602$	2.17780e8	+	6.04163e8i	0.0406845	+	0.112867i
$603$	−1.09955e9			−0.204223
$604$	−3.68756e9	+	4.62405e9i	−0.680941	+	0.853873i
$605$	5.32899e9	−	8.03216e8i	0.978365	−	0.147465i
$606$	−9.59723e7	−	4.20482e8i	−0.0175183	−	0.0767526i
$607$	2.66752e9	−	1.81869e9i	0.484114	−	0.330064i	−0.296547	−	0.955018i	$-0.595835\pi$
$607$	2.66752e9	−	1.81869e9i	0.484114	−	0.330064i	0.780661	+	0.624955i	$0.214883\pi$
$608$	−8.65868e8	+	1.49973e9i	−0.156239	+	0.270614i
$609$	2.36582e9	+	4.09772e9i	0.424444	+	0.735159i
$610$	−1.65838e9	−	7.98632e8i	−0.295821	−	0.142460i
$611$	−1.90596e9	+	5.87912e8i	−0.338042	+	0.104272i
$612$	3.21170e8	−	4.28571e9i	0.0566375	−	0.755775i
$613$	−2.23452e9	+	9.79006e9i	−0.391807	+	1.71662i	0.266470	+	0.963843i	$0.414143\pi$
$613$	−2.23452e9	+	9.79006e9i	−0.391807	+	1.71662i	−0.658277	+	0.752775i	$0.728715\pi$
$614$	−1.21314e8	−	3.09102e8i	−0.0211505	−	0.0538905i
$615$	−7.37957e8	−	9.84735e9i	−0.127929	−	1.70709i
$616$	1.78056e9	+	2.68376e8i	0.306919	+	0.0462605i
$617$	−2.85892e9	+	2.65269e9i	−0.490009	+	0.454662i	−0.886063	−	0.463565i	$-0.846570\pi$
$617$	−2.85892e9	+	2.65269e9i	−0.490009	+	0.454662i	0.396053	+	0.918227i	$0.370379\pi$
$618$	−6.68994e8	+	3.22170e8i	−0.114015	+	0.0549068i
$619$	−1.70946e9	−	1.16549e9i	−0.289696	−	0.197511i	0.409748	−	0.912199i	$-0.365617\pi$
$619$	−1.70946e9	−	1.16549e9i	−0.289696	−	0.197511i	−0.699444	+	0.714687i	$0.746569\pi$
$620$	5.67576e9	−	1.44616e10i	0.956431	−	2.43695i
$621$	8.55828e9	+	2.63988e9i	1.43406	+	0.442348i
$622$	7.30321e7	+	6.77639e7i	0.0121688	+	0.0112910i
$623$	−2.33717e8	−	2.93072e8i	−0.0387242	−	0.0485587i
$624$	2.24141e9	+	2.81064e9i	0.369297	+	0.463084i
$625$	4.52579e9	+	4.19932e9i	0.741505	+	0.688017i
$626$	−2.59610e8	−	8.00792e7i	−0.0422972	−	0.0130470i
$627$	−1.62360e9	+	4.13686e9i	−0.263052	+	0.670246i
$628$	5.98358e9	+	4.07954e9i	0.964057	+	0.657283i
$629$	−5.64125e9	+	2.71668e9i	−0.903853	+	0.435273i
$630$	4.27653e8	−	3.96804e8i	0.0681397	−	0.0632244i
$631$	−1.11104e10	−	1.67462e9i	−1.76046	−	0.265347i	−0.812324	−	0.583207i	$-0.801798\pi$
$631$	−1.11104e10	−	1.67462e9i	−1.76046	−	0.265347i	−0.948138	+	0.317860i	$0.897036\pi$
$632$	3.63742e6	+	4.85380e7i	0.000573171	+	0.00764843i
$633$	1.30527e9	+	3.32579e9i	0.204545	+	0.521172i
$634$	−4.90229e7	+	2.14783e8i	−0.00763988	+	0.0334725i
$635$	1.76929e7	−	2.36095e8i	0.00274214	−	0.0365914i
$636$	3.50691e9	−	1.08174e9i	0.540536	−	0.166733i
$637$	−7.77523e8	−	3.74435e8i	−0.119186	−	0.0573969i
$638$	−7.56957e8	−	1.31109e9i	−0.115398	−	0.199875i
$639$	−1.13901e9	+	1.97282e9i	−0.172693	+	0.299112i
$640$	−3.83766e9	+	2.61647e9i	−0.578678	+	0.394536i
$641$	−1.49805e9	−	6.56338e9i	−0.224658	−	0.984293i	−0.953921	−	0.300059i	$-0.902994\pi$
$641$	−1.49805e9	−	6.56338e9i	−0.224658	−	0.984293i	0.729262	−	0.684234i	$-0.239863\pi$
$642$	−2.35106e8	+	3.54365e7i	−0.0350664	+	0.00528540i
$643$	3.93105e9	−	4.92938e9i	0.583136	−	0.731229i	−0.399508	−	0.916730i	$-0.630819\pi$
$643$	3.93105e9	−	4.92938e9i	0.583136	−	0.731229i	0.982644	+	0.185500i	$0.0593906\pi$
$644$	−8.90518e9			−1.31384
$645$	−6.10795e9	−	2.07325e9i	−0.896266	−	0.304223i
$646$	1.02408e9			0.149458
$647$	6.40516e8	−	8.03182e8i	0.0929748	−	0.116587i	−0.733168	−	0.680048i	$-0.761959\pi$
$647$	6.40516e8	−	8.03182e8i	0.0929748	−	0.116587i	0.826143	+	0.563461i	$0.190530\pi$
$648$	2.61601e8	−	3.94300e7i	0.0377683	−	0.00569265i
$649$	3.20873e9	+	1.40583e10i	0.460761	+	2.01873i
$650$	6.88084e8	−	4.69128e8i	0.0982753	−	0.0670030i
$651$	4.13121e9	−	7.15547e9i	0.586873	−	1.01649i
$652$	−3.18226e9	−	5.51184e9i	−0.449645	−	0.778807i
$653$	−5.03940e9	−	2.42685e9i	−0.708243	−	0.341072i	0.0448426	−	0.998994i	$-0.485721\pi$
$653$	−5.03940e9	−	2.42685e9i	−0.708243	−	0.341072i	−0.753086	+	0.657922i	$0.771436\pi$
$654$	5.28082e8	−	1.62892e8i	0.0738209	−	0.0227707i
$655$	7.99191e8	−	1.06645e10i	0.111124	−	1.48284i
$656$	2.76428e9	−	1.21111e10i	0.382312	−	1.67502i
$657$	−5.62320e8	−	1.43277e9i	−0.0773580	−	0.197105i
$658$	−2.49518e7	−	3.32959e8i	−0.00341438	−	0.0455617i
$659$	5.85547e9	+	8.82570e8i	0.797008	+	0.120130i	0.534907	−	0.844911i	$-0.320347\pi$
$659$	5.85547e9	+	8.82570e8i	0.797008	+	0.120130i	0.262101	+	0.965040i	$0.415585\pi$
$660$	−6.57266e9	+	6.09854e9i	−0.889893	+	0.825700i
$661$	−1.28230e9	+	6.17523e8i	−0.172697	+	0.0831664i	−0.518235	−	0.855238i	$-0.673411\pi$
$661$	−1.28230e9	+	6.17523e8i	−0.172697	+	0.0831664i	0.345538	+	0.938405i	$0.387696\pi$
$662$	−5.18119e8	−	3.53248e8i	−0.0694108	−	0.0473235i
$663$	2.39819e9	−	6.11049e9i	0.319585	−	0.814289i
$664$	1.22065e9	+	3.76521e8i	0.161809	+	0.0499116i
$665$	−5.96937e9	−	5.53877e9i	−0.787142	−	0.730361i
$666$	2.41950e8	+	3.03395e8i	0.0317370	+	0.0397969i
$667$	9.41588e9	+	1.18071e10i	1.22863	+	1.54065i
$668$	−4.55188e8	−	4.22353e8i	−0.0590844	−	0.0548224i
$669$	−6.08610e9	−	1.87731e9i	−0.785864	−	0.242407i
$670$	1.93123e8	−	4.92069e8i	0.0248069	−	0.0632068i
$671$	−1.51598e10	−	1.03358e10i	−1.93716	−	1.32073i
$672$	−1.67417e9	+	8.06240e8i	−0.212818	+	0.102488i
$673$	−5.13692e9	+	4.76636e9i	−0.649606	+	0.602746i	−0.934565	−	0.355794i	$-0.884211\pi$
$673$	−5.13692e9	+	4.76636e9i	−0.649606	+	0.602746i	0.284959	+	0.958540i	$0.408020\pi$
$674$	−2.10621e7	−	3.17460e6i	−0.00264967	−	0.000399373i
$675$	6.13777e8	+	8.19029e9i	0.0768153	+	1.02503i
$676$	3.95508e8	+	1.00774e9i	0.0492427	+	0.125468i
$677$	−1.01872e9	+	4.46331e9i	−0.126181	+	0.552836i	0.871831	+	0.489808i	$0.162933\pi$
$677$	−1.01872e9	+	4.46331e9i	−0.126181	+	0.552836i	−0.998012	+	0.0630283i	$0.979924\pi$
$678$	−448413.	+	5.98366e6i	−5.52554e−5	+	0.000737332i
$679$	−1.85773e9	+	5.73034e8i	−0.227740	+	0.0702483i
$680$	3.75483e9	+	1.80823e9i	0.457941	+	0.220533i
$681$	−2.14230e9	−	3.71057e9i	−0.259935	−	0.450221i
$682$	−1.32181e9	+	2.28944e9i	−0.159559	+	0.276365i
$683$	−6.55396e9	+	4.46841e9i	−0.787102	+	0.536637i	−0.888864	−	0.458172i	$-0.848505\pi$
$683$	−6.55396e9	+	4.46841e9i	−0.787102	+	0.536637i	0.101761	+	0.994809i	$0.467552\pi$
$684$	8.27327e8	+	3.62476e9i	0.0988509	+	0.433094i
$685$	1.02616e10	−	1.54669e9i	1.21983	−	0.183860i
$686$	7.22567e8	−	9.06070e8i	0.0854562	−	0.107159i
$687$	3.99607e9			0.470202
$688$	−6.57359e9	−	4.75706e9i	−0.769561	−	0.556902i
$689$	−6.83583e9			−0.796203
$690$	−9.51969e8	+	1.19373e9i	−0.110319	+	0.138336i
$691$	1.10854e10	−	1.67085e9i	1.27814	−	0.192648i	0.525335	−	0.850896i	$-0.323940\pi$
$691$	1.10854e10	−	1.67085e9i	1.27814	−	0.192648i	0.752801	+	0.658248i	$0.228702\pi$
$692$	1.62468e9	+	7.11817e9i	0.186378	+	0.816577i
$693$	4.80483e9	−	3.27588e9i	0.548418	−	0.373905i
$694$	7.49363e8	−	1.29793e9i	0.0851008	−	0.147399i
$695$	1.74591e9	+	3.02400e9i	0.197276	+	0.341693i
$696$	1.88745e9	+	9.08947e8i	0.212199	+	0.102189i
$697$	−2.16754e10	+	6.68598e9i	−2.42467	+	0.747911i
$698$	5.43552e7	−	7.25320e8i	0.00604988	−	0.0807301i
$699$	2.45270e8	−	1.07460e9i	0.0271628	−	0.119008i
$700$	−2.98355e9	−	7.60197e9i	−0.328769	−	0.837689i
$701$	5.12398e8	+	6.83748e9i	0.0561816	+	0.749692i	0.952161	+	0.305596i	$0.0988558\pi$
$701$	5.12398e8	+	6.83748e9i	0.0561816	+	0.749692i	−0.895980	+	0.444095i	$0.853525\pi$
$702$	−1.13446e9	−	1.70992e8i	−0.123768	−	0.0186550i
$703$	3.97070e9	−	3.68427e9i	0.431046	−	0.399952i
$704$	−9.80011e9	+	4.71949e9i	−1.05859	+	0.509789i
$705$	2.77081e9	+	1.88911e9i	0.297814	+	0.203046i
$706$	5.24503e7	−	1.33641e8i	0.00560959	−	0.0142930i
$707$	7.52781e9	+	2.32202e9i	0.801126	+	0.247115i
$708$	−7.25169e9	−	6.72858e9i	−0.767932	−	0.712536i
$709$	−5.27800e8	−	6.61840e8i	−0.0556170	−	0.0697415i	0.753245	−	0.657740i	$-0.228487\pi$
$709$	−5.27800e8	−	6.61840e8i	−0.0556170	−	0.0697415i	−0.808862	+	0.587999i	$0.799916\pi$
$710$	−6.82821e8	−	8.56230e8i	−0.0715983	−	0.0897814i
$711$	1.15232e8	+	1.06919e8i	0.0120234	+	0.0111561i
$712$	−1.58591e8	−	4.89189e7i	−0.0164664	−	0.00507922i
$713$	9.63444e9	−	2.45482e10i	0.995436	−	2.53633i
$714$	9.07918e8	+	6.19008e8i	0.0933475	+	0.0636433i
$715$	1.50469e10	−	7.24620e9i	1.53949	−	0.741378i
$716$	4.51730e9	−	4.19144e9i	0.459921	−	0.426745i
$717$	−9.09121e9	−	1.37028e9i	−0.921095	−	0.138833i
$718$	−4.08329e7	−	5.44878e8i	−0.00411694	−	0.0549368i
$719$	8.32137e8	+	2.12025e9i	0.0834918	+	0.212734i	0.966523	−	0.256581i	$-0.0825962\pi$
$719$	8.32137e8	+	2.12025e9i	0.0834918	+	0.212734i	−0.883031	+	0.469315i	$0.844501\pi$
$720$	−1.64020e9	+	7.18620e9i	−0.163770	+	0.717523i
$721$	1.01353e9	−	1.35247e10i	0.100708	−	1.34386i
$722$	4.05407e8	−	1.25051e8i	0.0400877	−	0.0123654i
$723$	−5.47507e9	−	2.63665e9i	−0.538773	−	0.259459i
$724$	6.33495e9	+	1.09725e10i	0.620381	+	1.07453i
$725$	−6.92459e9	+	1.19937e10i	−0.674856	+	1.16888i
$726$	5.19808e8	−	3.54399e8i	0.0504155	−	0.0343727i
$727$	2.78767e9	+	1.22136e10i	0.269073	+	1.17889i	0.911094	+	0.412200i	$0.135239\pi$
$727$	2.78767e9	+	1.22136e10i	0.269073	+	1.17889i	−0.642020	+	0.766688i	$0.721903\pi$
$728$	2.27525e9	−	3.42938e8i	0.218559	−	0.0329425i
$729$	5.08569e9	−	6.37726e9i	0.486188	−	0.609660i
$730$	7.39956e8			0.0704005
$731$	−1.52092e9	+	1.47381e10i	−0.144011	+	1.39551i
$732$	1.25873e10			1.18616
$733$	1.74239e9	−	2.18489e9i	0.163411	−	0.204911i	−0.693384	−	0.720569i	$-0.743881\pi$
$733$	1.74239e9	−	2.18489e9i	0.163411	−	0.204911i	0.856795	+	0.515657i	$0.172452\pi$
$734$	2.04060e9	−	3.07571e8i	0.190468	−	0.0287085i
$735$	3.22868e8	+	1.41458e9i	0.0299929	+	0.131408i
$736$	−4.90024e9	+	3.34092e9i	−0.453048	+	0.308883i
$737$	2.63464e9	−	4.56332e9i	0.242429	−	0.419899i
$738$	7.02917e8	+	1.21749e9i	0.0643734	+	0.111498i
$739$	−4.30813e9	−	2.07469e9i	−0.392675	−	0.189102i	0.227119	−	0.973867i	$-0.427069\pi$
$739$	−4.30813e9	−	2.07469e9i	−0.392675	−	0.189102i	−0.619794	+	0.784765i	$0.712784\pi$
$740$	1.04430e10	−	3.22123e9i	0.947355	−	0.292220i
$741$	−4.24373e8	+	5.66287e9i	−0.0383164	+	0.511296i
$742$	2.54635e8	−	1.11563e9i	0.0228825	−	0.100255i
$743$	−5.75531e9	−	1.46643e10i	−0.514764	−	1.31160i	−0.918029	−	0.396513i	$-0.870220\pi$
$743$	−5.75531e9	−	1.46643e10i	−0.514764	−	1.31160i	0.403266	−	0.915083i	$-0.367875\pi$
$744$	−2.73374e8	−	3.64792e9i	−0.0243361	−	0.324743i
$745$	2.01147e10	+	3.03181e9i	1.78224	+	0.268630i
$746$	1.19490e9	−	1.10871e9i	0.105377	−	0.0977755i
$747$	3.71687e9	−	1.78995e9i	0.326253	−	0.157115i
$748$	1.70169e10	+	1.16019e10i	1.48670	+	1.01362i
$749$	1.58661e9	−	4.04261e9i	0.137970	−	0.351541i
$750$	1.57961e7	+	4.87245e6i	0.00136721	+	0.000421729i
$751$	1.37579e10	+	1.27654e10i	1.18525	+	1.09976i	0.992964	+	0.118418i	$0.0377823\pi$
$751$	1.37579e10	+	1.27654e10i	1.18525	+	1.09976i	0.192291	+	0.981338i	$0.438408\pi$
$752$	2.63030e9	+	3.29830e9i	0.225550	+	0.282831i
$753$	3.08570e9	+	3.86934e9i	0.263373	+	0.330259i
$754$	−1.41811e9	−	1.31581e9i	−0.120478	−	0.111788i
$755$	−1.76992e10	−	5.45948e9i	−1.49672	−	0.461676i
$756$	−4.11020e9	+	1.04726e10i	−0.345969	+	0.881514i
$757$	−1.86045e10	−	1.26843e10i	−1.55877	−	1.06275i	−0.966387	−	0.257092i	$-0.917236\pi$
$757$	−1.86045e10	−	1.26843e10i	−1.55877	−	1.06275i	−0.592381	−	0.805658i	$-0.701812\pi$
$758$	−1.01947e9	+	4.90953e8i	−0.0850226	+	0.0409447i
$759$	−1.11569e10	+	1.03521e10i	−0.926184	+	0.859374i
$760$	−3.56508e9	−	5.37350e8i	−0.294593	−	0.0444027i
$761$	5.59103e8	+	7.46072e9i	0.0459881	+	0.613669i	0.971819	+	0.235730i	$0.0757481\pi$
$761$	5.59103e8	+	7.46072e9i	0.0459881	+	0.613669i	−0.925830	+	0.377939i	$0.876633\pi$
$762$	−1.00975e7	−	2.57281e7i	−0.000826748	−	0.00210652i
$763$	−2.24615e9	+	9.84102e9i	−0.183064	+	0.802055i
$764$	−4.74684e8	+	6.33422e9i	−0.0385104	+	0.513886i
$765$	1.28613e10	−	3.96717e9i	1.03865	−	0.320380i
$766$	1.36779e9	+	6.58695e8i	0.109956	+	0.0529521i
$767$	9.21308e9	+	1.59575e10i	0.737260	+	1.27697i
$768$	3.52366e9	−	6.10315e9i	0.280692	−	0.486172i
$769$	−1.04159e10	+	7.10145e9i	−0.825953	+	0.563125i	−0.900882	−	0.434063i	$-0.857079\pi$
$769$	−1.04159e10	+	7.10145e9i	−0.825953	+	0.563125i	0.0749290	+	0.997189i	$0.476127\pi$
$770$	6.22105e8	+	2.72562e9i	0.0491073	+	0.215153i
$771$	2.64978e9	−	3.99390e8i	0.208219	−	0.0313839i
$772$	−4.41322e9	+	5.53400e9i	−0.345219	+	0.432891i
$773$	−1.86236e10			−1.45023			−0.725113	−	0.688630i	$-0.758212\pi$
$773$	−1.86236e10			−1.45023			−0.725113	+	0.688630i	$0.758212\pi$
$774$	9.11500e8	−	1.11358e8i	0.0706583	−	0.00863232i
$775$	2.41836e10			1.86623
$776$	−5.36663e8	+	6.72955e8i	−0.0412274	+	0.0516975i
$777$	5.74730e9	−	8.66266e8i	0.439532	−	0.0662487i
$778$	3.53070e8	+	1.54690e9i	0.0268802	+	0.117770i
$779$	1.62135e10	−	1.10542e10i	1.22884	−	0.837809i
$780$	−5.72862e9	+	9.92225e9i	−0.432234	+	0.748651i
$781$	−5.45837e9	−	9.45417e9i	−0.410000	−	0.710141i
$782$	3.15989e9	+	1.52172e9i	0.236291	+	0.113792i
$783$	1.82313e10	−	5.62361e9i	1.35722	−	0.418648i
$784$	−1.36403e8	+	1.82017e9i	−0.0101092	+	0.134898i
$785$	−5.04670e9	+	2.21110e10i	−0.372360	+	1.63142i
$786$	−4.56108e8	−	1.16215e9i	−0.0335034	−	0.0853653i
$787$	−9.13374e7	−	1.21881e9i	−0.00667939	−	0.0891303i	0.992868	−	0.119221i	$-0.0380396\pi$
$787$	−9.13374e7	−	1.21881e9i	−0.00667939	−	0.0891303i	−0.999547	+	0.0300903i	$0.990421\pi$
$788$	−2.22914e10	−	3.35989e9i	−1.62292	−	0.244615i
$789$	3.36271e9	−	3.12014e9i	0.243736	−	0.226154i
$790$	−6.80875e7	+	3.27892e7i	−0.00491329	+	0.00236612i
$791$	−9.05563e7	−	6.17402e7i	−0.00650580	−	0.00443558i
$792$	9.40643e8	−	2.39672e9i	0.0672801	−	0.171427i
$793$	−2.24040e10	−	6.91071e9i	−1.59540	−	0.492115i
$794$	−1.56297e9	−	1.45022e9i	−0.110810	−	0.102816i
$795$	7.16590e9	+	8.98576e9i	0.505808	+	0.634263i
$796$	−7.99364e9	−	1.00237e10i	−0.561757	−	0.704421i
$797$	−9.53803e9	−	8.85000e9i	−0.667352	−	0.619212i	0.271947	−	0.962312i	$-0.412332\pi$
$797$	−9.53803e9	−	8.85000e9i	−0.667352	−	0.619212i	−0.939299	+	0.343100i	$0.888523\pi$
$798$	−9.08390e8	−	2.80201e8i	−0.0632794	−	0.0195191i
$799$	2.81428e9	−	7.17067e9i	0.195188	−	0.497332i
$800$	−4.49375e9	−	3.06379e9i	−0.310309	−	0.211565i
$801$	−4.82908e8	+	2.32556e8i	−0.0332009	+	0.0159887i
$802$	3.46498e8	−	3.21503e8i	0.0237187	−	0.0220077i
$803$	7.29362e9	+	1.09934e9i	0.497094	+	0.0749249i
$804$	2.70140e8	+	3.60476e9i	0.0183313	+	0.244614i
$805$	−1.01888e10	−	2.59606e10i	−0.688393	−	1.75400i
$806$	−7.51695e8	+	3.29339e9i	−0.0505672	+	0.221549i
$807$	1.24707e9	−	1.66409e10i	0.0835280	−	1.11460i
$808$	3.33290e9	−	1.02806e9i	0.222271	−	0.0685615i
$809$	1.40161e10	+	6.74981e9i	0.930696	+	0.448200i	0.836878	−	0.547390i	$-0.184378\pi$
$809$	1.40161e10	+	6.74981e9i	0.930696	+	0.448200i	0.0938183	+	0.995589i	$0.470093\pi$
$810$	2.05375e8	+	3.55719e8i	0.0135784	+	0.0235185i
$811$	9.78046e9	−	1.69403e10i	0.643853	−	1.11519i	−0.340713	−	0.940167i	$-0.610668\pi$
$811$	9.78046e9	−	1.69403e10i	0.643853	−	1.11519i	0.984565	−	0.175018i	$-0.0559983\pi$
$812$	−1.56740e10	+	1.06863e10i	−1.02739	+	0.700459i
$813$	8.08785e8	+	3.54352e9i	0.0527857	+	0.231269i
$814$	−1.83888e9	+	2.77167e8i	−0.119500	+	0.0180117i
$815$	1.24273e10	−	1.55833e10i	0.804127	−	1.00834i
$816$	−1.38839e10			−0.894530
$817$	−2.50084e9	−	1.25714e10i	−0.160438	−	0.806503i
$818$	−1.78282e9			−0.113886
$819$	4.63313e9	−	5.80977e9i	0.294701	−	0.369543i
$820$	3.91489e10	−	5.90075e9i	2.47954	−	0.373731i
$821$	2.81040e9	+	1.23132e10i	0.177242	+	0.776549i	0.982896	+	0.184162i	$0.0589572\pi$
$821$	2.81040e9	+	1.23132e10i	0.177242	+	0.776549i	−0.805654	+	0.592387i	$0.798186\pi$
$822$	1.00096e9	−	6.82440e8i	0.0628584	−	0.0428562i
$823$	−1.25903e10	+	2.18070e10i	−0.787293	+	1.36363i	0.140327	+	0.990105i	$0.455185\pi$
$823$	−1.25903e10	+	2.18070e10i	−0.787293	+	1.36363i	−0.927620	+	0.373526i	$0.878149\pi$
$824$	−3.00238e9	−	5.20028e9i	−0.186948	−	0.323803i
$825$	−1.25751e10	−	6.05585e9i	−0.779691	−	0.375479i
$826$	−2.94750e9	+	9.09185e8i	−0.181980	+	0.0561335i
$827$	8.85137e8	−	1.18113e10i	0.0544178	−	0.726156i	−0.901548	−	0.432679i	$-0.857569\pi$
$827$	8.85137e8	−	1.18113e10i	0.0544178	−	0.726156i	0.955966	−	0.293477i	$-0.0948124\pi$
$828$	−2.83339e9	+	1.24139e10i	−0.173460	+	0.759980i
$829$	−8.62213e9	−	2.19688e10i	−0.525622	−	1.33926i	−0.909433	−	0.415851i	$-0.863484\pi$
$829$	−8.62213e9	−	2.19688e10i	−0.525622	−	1.33926i	0.383810	−	0.923412i	$-0.374612\pi$
$830$	1.48212e8	+	1.97775e9i	0.00899725	+	0.120060i
$831$	−2.88059e9	−	4.34179e8i	−0.174132	−	0.0262461i
$832$	−1.01889e10	+	9.45395e9i	−0.613334	+	0.569091i
$833$	3.00283e9	−	1.44609e9i	0.180001	−	0.0866837i
$834$	3.36800e8	+	2.29626e8i	0.0201044	+	0.0137069i
$835$	7.10453e8	−	1.81020e9i	0.0422311	−	0.107603i
$836$	−1.70257e10	−	5.25174e9i	−1.00782	−	0.310872i
$837$	−2.44222e10	−	2.26605e10i	−1.43961	−	1.33577i
$838$	−1.56634e8	−	1.96413e8i	−0.00919458	−	0.0115296i
$839$	1.71930e10	+	2.15594e10i	1.00504	+	1.26029i	0.965318	+	0.261075i	$0.0840771\pi$
$839$	1.71930e10	+	2.15594e10i	1.00504	+	1.26029i	0.0397261	+	0.999211i	$0.487351\pi$
$840$	−2.83590e9	−	2.63133e9i	−0.165087	−	0.153179i
$841$	1.42581e10	+	4.39804e9i	0.826561	+	0.254960i
$842$	−1.13042e9	+	2.88028e9i	−0.0652603	+	0.166281i
$843$	−1.07983e10	−	7.36218e9i	−0.620812	−	0.423263i
$844$	−1.29055e10	+	6.21498e9i	−0.738886	+	0.355829i
$845$	−2.48526e9	+	2.30599e9i	−0.141701	+	0.131480i
$846$	−4.72086e8	−	7.11556e7i	−0.0268056	−	0.00404029i
$847$	8.58742e8	+	1.14591e10i	0.0485591	+	0.647976i
$848$	5.28220e9	+	1.34588e10i	0.297461	+	0.757918i
$849$	−5.59899e8	+	2.45308e9i	−0.0314002	+	0.137573i
$850$	−2.40353e8	+	3.20729e9i	−0.0134240	+	0.179131i
$851$	1.77266e10	−	5.46794e9i	0.985990	−	0.304138i
$852$	6.74753e9	+	3.24944e9i	0.373772	+	0.179999i
$853$	1.29232e10	+	2.23836e10i	0.712932	+	1.23483i	0.963752	+	0.266800i	$0.0859664\pi$
$853$	1.29232e10	+	2.23836e10i	0.712932	+	1.23483i	−0.250820	+	0.968034i	$0.580700\pi$
$854$	1.96240e9	−	3.39898e9i	0.107816	−	0.186743i
$855$	−9.62038e9	+	6.55907e9i	−0.526394	+	0.358889i
$856$	−4.27854e8	−	1.87455e9i	−0.0233151	−	0.102150i
$857$	−1.83291e10	+	2.76266e9i	−0.994734	+	0.149932i	−0.626184	−	0.779676i	$-0.715384\pi$
$857$	−1.83291e10	+	2.76266e9i	−0.994734	+	0.149932i	−0.368551	+	0.929608i	$0.620146\pi$
$858$	1.21557e9	−	1.52428e9i	0.0657015	−	0.0823871i
$859$	−3.22202e10			−1.73441			−0.867204	−	0.497952i	$-0.834085\pi$
$859$	−3.22202e10			−1.73441			−0.867204	+	0.497952i	$0.834085\pi$
$860$	6.45891e9	−	2.50410e10i	0.346270	−	1.34248i
$861$	2.10562e10			1.12426
$862$	−2.20284e9	+	2.76227e9i	−0.117141	+	0.146890i
$863$	−2.06632e10	+	3.11448e9i	−1.09436	+	0.164948i	−0.671323	−	0.741165i	$-0.734274\pi$
$863$	−2.06632e10	+	3.11448e9i	−1.09436	+	0.164948i	−0.423036	+	0.906113i	$0.639036\pi$
$864$	1.66726e9	+	7.30476e9i	0.0879440	+	0.385308i
$865$	−1.88922e10	+	1.28805e10i	−0.992489	+	0.676667i
$866$	1.60983e9	−	2.78831e9i	0.0842302	−	0.145891i
$867$	6.23540e9	+	1.08000e10i	0.324936	+	0.562805i
$868$	2.98456e10	+	1.43729e10i	1.54903	+	0.745975i
$869$	−7.19842e8	+	2.22042e8i	−0.0372107	+	0.0114780i
$870$	−2.43064e8	+	3.24346e9i	−0.0125142	+	0.166990i
$871$	1.49828e9	−	6.56441e9i	0.0768300	−	0.336614i
$872$	1.63275e9	+	4.16018e9i	0.0833896	+	0.212473i
$873$	2.07734e8	+	2.77201e9i	0.0105671	+	0.141009i
$874$	−3.00021e9	−	4.52208e8i	−0.152006	−	0.0229112i
$875$	−2.21335e8	+	2.05369e8i	−0.0111692	+	0.0103635i
$876$	−4.55904e9	+	2.19552e9i	−0.229144	+	0.110350i
$877$	−3.02774e10	−	2.06428e10i	−1.51572	−	1.03340i	−0.982248	−	0.187589i	$-0.939933\pi$
$877$	−3.02774e10	−	2.06428e10i	−1.51572	−	1.03340i	−0.533477	−	0.845814i	$-0.679115\pi$
$878$	5.05862e8	−	1.28891e9i	0.0252232	−	0.0642678i
$879$	9.82845e9	+	3.03168e9i	0.488117	+	0.150564i
$880$	−2.58939e10	−	2.40260e10i	−1.28088	−	1.18848i
$881$	1.36431e8	+	1.71079e8i	0.00672199	+	0.00842911i	0.785181	−	0.619266i	$-0.212570\pi$
$881$	1.36431e8	+	1.71079e8i	0.00672199	+	0.00842911i	−0.778459	+	0.627695i	$0.783998\pi$
$882$	−1.28790e8	−	1.61497e8i	−0.00632035	−	0.00792547i
$883$	−1.68637e9	−	1.56473e9i	−0.0824312	−	0.0764849i	0.637881	−	0.770135i	$-0.279811\pi$
$883$	−1.68637e9	−	1.56473e9i	−0.0824312	−	0.0764849i	−0.720312	+	0.693650i	$0.756002\pi$
$884$	2.51485e10	+	7.75727e9i	1.22441	+	0.377682i
$885$	1.13184e10	−	2.88387e10i	0.548886	−	1.39854i
$886$	−9.96398e7	−	6.79332e7i	−0.00481299	−	0.00328144i
$887$	5.48894e9	−	2.64333e9i	0.264092	−	0.127180i	−0.297152	−	0.954830i	$-0.596037\pi$
$887$	5.48894e9	−	2.64333e9i	0.264092	−	0.127180i	0.561245	+	0.827650i	$0.310323\pi$
$888$	1.88638e9	−	1.75031e9i	0.0904034	−	0.0838821i
$889$	4.99193e8	+	7.52413e7i	0.0238294	+	0.00359170i
$890$	−1.92562e7	−	2.56956e8i	−0.000915599	−	0.0122178i
$891$	1.49586e9	+	3.81139e9i	0.0708466	+	0.180514i
$892$	5.68210e9	−	2.48949e10i	0.268060	−	1.17445i
$893$	−4.98003e8	+	6.64539e9i	−0.0234019	+	0.312277i
$894$	2.26919e9	−	6.99951e8i	0.106216	−	0.0327632i
$895$	1.73874e10	+	8.37333e9i	0.810689	+	0.390407i
$896$	−4.95194e9	−	8.57701e9i	−0.229984	−	0.398344i
$897$	−9.72416e9	+	1.68427e10i	−0.449861	+	0.779182i
$898$	−1.51417e8	+	1.03234e8i	−0.00697761	+	0.00475726i
$899$	−1.25006e10	−	5.47686e10i	−0.573814	−	2.51404i
$900$	−1.15465e10	+	1.74035e9i	−0.527960	+	0.0795772i
$901$	1.64603e10	−	2.06406e10i	0.749725	−	0.940125i
$902$	−6.73705e9			−0.305666
$903$	5.38166e9	−	1.26571e10i	0.243226	−	0.572040i
$904$	−4.85251e7			−0.00218463
$905$	−2.47391e10	+	3.10218e10i	−1.10946	+	1.39122i
$906$	−2.13809e9	+	3.22266e8i	−0.0955164	+	0.0143968i
$907$	3.54954e9	+	1.55515e10i	0.157960	+	0.692066i	0.990432	+	0.138000i	$0.0440674\pi$
$907$	3.54954e9	+	1.55515e10i	0.157960	+	0.692066i	−0.832473	+	0.554066i	$0.813075\pi$
$908$	1.41931e10	−	9.67671e9i	0.629184	−	0.428970i
$909$	5.63207e9	−	9.75502e9i	0.248711	−	0.430779i
$910$	1.78622e9	+	3.09383e9i	0.0785762	+	0.136098i
$911$	−1.56228e10	−	7.52355e9i	−0.684612	−	0.329692i	0.0590427	−	0.998255i	$-0.481195\pi$
$911$	−1.56228e10	−	7.52355e9i	−0.684612	−	0.329692i	−0.743655	+	0.668564i	$0.766909\pi$
$912$	1.14774e10	−	3.54030e9i	0.501026	−	0.154546i
$913$	−1.47740e9	+	1.97146e10i	−0.0642467	+	0.857313i
$914$	6.81259e8	−	2.98479e9i	0.0295121	−	0.129301i
$915$	1.44016e10	+	3.66946e10i	0.621493	+	1.58354i
$916$	1.19727e9	+	1.59764e10i	0.0514703	+	0.686824i
$917$	2.25487e10	+	3.39867e9i	0.965670	+	0.145551i
$918$	3.24802e9	−	3.01372e9i	0.138570	−	0.128574i
$919$	−1.61320e10	+	7.76877e9i	−0.685622	+	0.330178i	−0.744060	−	0.668113i	$-0.767102\pi$
$919$	−1.61320e10	+	7.76877e9i	−0.685622	+	0.330178i	0.0584381	+	0.998291i	$0.481388\pi$
$920$	−1.02019e10	−	6.95557e9i	−0.431942	−	0.294493i
$921$	−2.59805e9	+	6.61973e9i	−0.109582	+	0.279210i
$922$	4.32111e9	+	1.33288e9i	0.181567	+	0.0560060i
$923$	−1.02259e10	−	9.48823e9i	−0.428050	−	0.397172i
$924$	−1.19201e10	−	1.49474e10i	−0.497083	−	0.623322i
$925$	1.06068e10	+	1.33005e10i	0.440644	+	0.552550i
$926$	4.79467e8	+	4.44881e8i	0.0198436	+	0.0184122i
$927$	−1.85310e10	−	5.71606e9i	−0.764047	−	0.235677i
$928$	−4.61573e9	+	1.17607e10i	−0.189593	+	0.483076i
$929$	2.29232e10	+	1.56288e10i	0.938037	+	0.639543i	0.932781	−	0.360443i	$-0.117375\pi$
$929$	2.29232e10	+	1.56288e10i	0.938037	+	0.639543i	0.00525593	+	0.999986i	$0.498327\pi$
$930$	5.11718e9	−	2.46430e9i	0.208613	−	0.100462i
$931$	−2.11360e9	+	1.96114e9i	−0.0858420	+	0.0796497i
$932$	4.36977e9	+	6.58637e8i	0.176808	+	0.0266496i
$933$	−1.59446e8	−	2.12766e9i	−0.00642728	−	0.0857661i
$934$	−3.35175e8	−	8.54012e8i	−0.0134604	−	0.0342965i
$935$	−1.43525e10	+	6.28822e10i	−0.574230	+	2.51586i
$936$	2.45864e8	−	3.28083e9i	0.00980007	−	0.130773i
$937$	4.27500e10	−	1.31866e10i	1.69765	−	0.523655i	0.713447	−	0.700709i	$-0.247133\pi$
$937$	4.27500e10	−	1.31866e10i	1.69765	−	0.523655i	0.984201	+	0.177053i	$0.0566565\pi$
$938$	1.01552e9	+	4.89049e8i	0.0401772	+	0.0193483i
$939$	2.90916e9	+	5.03881e9i	0.114667	+	0.198609i
$940$	−6.72254e9	+	1.16438e10i	−0.263989	+	0.457243i
$941$	2.59436e10	−	1.76881e10i	1.01500	−	0.692016i	0.0629697	−	0.998015i	$-0.479943\pi$
$941$	2.59436e10	−	1.76881e10i	1.01500	−	0.692016i	0.952032	+	0.305999i	$0.0989905\pi$
$942$	5.89144e8	+	2.58121e9i	0.0229638	+	0.100611i
$943$	6.64542e10	−	1.00164e10i	2.58066	−	0.388972i
$944$	2.42991e10	−	3.04701e10i	0.940129	−	1.17888i
$945$	−3.52327e10			−1.35811
$946$	−1.72189e9	+	4.04971e9i	−0.0661283	+	0.155527i
$947$	3.89806e10			1.49150			0.745751	−	0.666225i	$-0.232091\pi$
$947$	3.89806e10			1.49150			0.745751	+	0.666225i	$0.232091\pi$
$948$	3.22214e8	−	4.04044e8i	0.0122833	−	0.0154028i
$949$	9.32001e9	−	1.40477e9i	0.353985	−	0.0533546i
$950$	−6.19145e8	−	2.71265e9i	−0.0234293	−	0.102651i
$951$	3.89827e9	−	2.65780e9i	0.146974	−	0.100205i
$952$	−4.44319e9	+	7.69583e9i	−0.166904	+	0.289085i
$953$	1.05724e10	+	1.83119e10i	0.395684	+	0.685345i	0.993188	−	0.116521i	$-0.0371742\pi$
$953$	1.05724e10	+	1.83119e10i	0.395684	+	0.685345i	−0.597504	+	0.801866i	$0.703841\pi$
$954$	−1.47418e9	−	7.09926e8i	−0.0549706	−	0.0264724i
$955$	−1.90088e10	+	5.86343e9i	−0.706223	+	0.217841i
$956$	2.75459e9	−	3.67575e10i	0.101966	−	1.36064i
$957$	−7.21458e9	+	3.16091e10i	−0.266084	+	1.16579i
$958$	2.10605e8	+	5.36612e8i	0.00773907	+	0.0197188i
$959$	1.65362e9	+	2.20660e10i	0.0605438	+	0.807901i
$960$	2.31082e10	+	3.48300e9i	0.842980	+	0.127059i
$961$	−5.17420e10	+	4.80095e10i	−1.88066	+	1.74500i
$962$	−2.14099e9	+	1.03105e9i	−0.0775357	+	0.0373392i
$963$	−5.13062e9	−	3.49799e9i	−0.185130	−	0.126220i
$964$	8.90104e9	−	2.26795e10i	0.320016	−	0.815386i
$965$	−2.11822e10	−	6.53384e9i	−0.758796	−	0.234058i
$966$	−2.38656e9	−	2.21441e9i	−0.0851830	−	0.0790382i
$967$	−4.53729e8	−	5.68958e8i	−0.0161363	−	0.0202343i	0.773698	−	0.633555i	$-0.218405\pi$
$967$	−4.53729e8	−	5.68958e8i	−0.0161363	−	0.0202343i	−0.789834	+	0.613320i	$0.789833\pi$
$968$	3.17212e9	+	3.97772e9i	0.112405	+	0.140952i
$969$	−1.60770e10	−	1.49173e10i	−0.567639	−	0.526692i
$970$	−1.27701e9	−	3.93907e8i	−0.0449257	−	0.0138577i
$971$	−9.63090e9	+	2.45391e10i	−0.337598	+	0.860185i	0.656759	+	0.754100i	$0.271927\pi$
$971$	−9.63090e9	+	2.45391e10i	−0.337598	+	0.860185i	−0.994357	+	0.106085i	$0.966168\pi$
$972$	2.18692e10	+	1.49101e10i	0.763836	+	0.520775i
$973$	−6.70820e9	+	3.23050e9i	−0.233459	+	0.112428i
$974$	−2.18159e9	+	2.02422e9i	−0.0756514	+	0.0701943i
$975$	−1.76358e10	−	2.65818e9i	−0.609369	−	0.0918476i
$976$	3.70580e9	+	4.94505e10i	0.127588	+	1.70254i
$977$	1.05094e10	+	2.67775e10i	0.360535	+	0.918628i	0.989932	+	0.141544i	$0.0452068\pi$
$977$	1.05094e10	+	2.67775e10i	0.360535	+	0.918628i	−0.629397	+	0.777084i	$0.716698\pi$
$978$	5.17764e8	−	2.26847e9i	0.0176989	−	0.0775439i
$979$	1.91949e8	−	2.56138e9i	0.00653802	−	0.0872438i
$980$	−5.55878e9	+	1.71466e9i	−0.188664	+	0.0581951i
$981$	1.30038e10	+	6.26230e9i	0.439773	+	0.211784i
$982$	6.85256e8	+	1.18690e9i	0.0230921	+	0.0399966i
$983$	1.49748e10	−	2.59371e10i	0.502832	−	0.870931i	−0.497163	−	0.867657i	$-0.665625\pi$
$983$	1.49748e10	−	2.59371e10i	0.502832	−	0.870931i	0.999995	−	0.00327327i	$-0.00104192\pi$
$984$	7.70263e9	−	5.25156e9i	0.257725	−	0.175714i
$985$	−1.57097e10	−	6.88286e10i	−0.523770	−	2.29478i
$986$	7.38779e9	−	1.11353e9i	0.245440	−	0.0369941i
$987$	−4.45836e9	+	5.59060e9i	−0.147593	+	0.185075i
$988$	−2.27675e10			−0.751045
$989$	1.09638e10	−	4.25063e10i	0.360392	−	1.39723i
$990$	3.99748e9			0.130937
$991$	1.99171e10	−	2.49753e10i	0.650084	−	0.815179i	−0.342140	−	0.939649i	$-0.611152\pi$
$991$	1.99171e10	−	2.49753e10i	0.650084	−	0.815179i	0.992223	+	0.124470i	$0.0397230\pi$
$992$	2.18153e10	−	3.28812e9i	0.709528	−	0.106944i
$993$	2.98837e9	+	1.30929e10i	0.0968526	+	0.424339i
$994$	1.92942e9	−	1.31546e9i	0.0623125	−	0.0424839i
$995$	2.00755e10	−	3.47717e10i	0.646078	−	1.11904i
$996$	−6.78134e9	−	1.17456e10i	−0.217474	−	0.376676i
$997$	7.39689e9	+	3.56215e9i	0.236383	+	0.113836i	0.548326	−	0.836265i	$-0.315265\pi$
$997$	7.39689e9	+	3.56215e9i	0.236383	+	0.113836i	−0.311943	+	0.950101i	$0.600980\pi$
$998$	2.68031e8	−	8.26765e7i	0.00853547	−	0.00263285i
$999$	1.75138e9	−	2.33705e10i	0.0555777	−	0.741633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.g.a.24.13	yes	300
43.9	even	21	inner	43.8.g.a.9.13	✓	300

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.g.a.9.13	✓	300	43.9	even	21	inner
43.8.g.a.24.13	yes	300	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913875 + 1.14596i) q^{2} +(31.0397 - 4.67849i) q^{3} +(28.0046 + 122.696i) q^{4} +(-325.645 + 222.021i) q^{5} +(-23.0051 + 39.8460i) q^{6} +(-420.198 - 727.804i) q^{7} +(-335.233 - 161.440i) q^{8} +(-1148.26 + 354.191i) q^{9} +O(q^{10})\)	\(q+(-0.913875 + 1.14596i) q^{2} +(31.0397 - 4.67849i) q^{3} +(28.0046 + 122.696i) q^{4} +(-325.645 + 222.021i) q^{5} +(-23.0051 + 39.8460i) q^{6} +(-420.198 - 727.804i) q^{7} +(-335.233 - 161.440i) q^{8} +(-1148.26 + 354.191i) q^{9} +(43.1710 - 576.078i) q^{10} +(1281.40 - 5614.16i) q^{11} +(1443.29 + 3677.44i) q^{12} +(-549.896 - 7337.86i) q^{13} +(1218.04 + 183.591i) q^{14} +(-9069.23 + 8415.01i) q^{15} +(-14022.3 + 6752.81i) q^{16} +(23480.6 + 16008.8i) q^{17} +(643.476 - 1639.55i) q^{18} +(-23492.8 - 7246.57i) q^{19} +(-36360.8 - 33737.9i) q^{20} +(-16447.9 - 20625.0i) q^{21} +(5262.59 + 6599.08i) q^{22} +(-61721.3 - 57269.0i) q^{23} +(-11160.9 - 3442.67i) q^{24} +(28209.2 - 71875.9i) q^{25} +(8911.45 + 6075.73i) q^{26} +(-95836.8 + 46152.6i) q^{27} +(77531.3 - 71938.6i) q^{28} +(-177359. - 26732.6i) q^{29} +(-1355.15 - 18083.3i) q^{30} +(114426. + 291554. i) q^{31} +(15674.1 - 68672.6i) q^{32} +(13508.4 - 180257. i) q^{33} +(-39803.8 + 12277.9i) q^{34} +(298423. + 143713. i) q^{35} +(-75614.5 - 130968. i) q^{36} +(-110162. + 190806. i) q^{37} +(29773.8 - 20299.4i) q^{38} +(-51398.7 - 225193. i) q^{39} +(145010. - 21856.8i) q^{40} +(-497656. + 624041. i) q^{41} +38666.7 q^{42} +(247924. + 458642. i) q^{43} +724721. q^{44} +(295288. - 370279. i) q^{45} +(122034. - 18393.6i) q^{46} +(-60316.5 - 264264. i) q^{47} +(-403657. + 275209. i) q^{48} +(58639.2 - 101566. i) q^{49} +(56587.5 + 98012.4i) q^{50} +(803729. + 387055. i) q^{51} +(884928. - 272964. i) q^{52} +(69422.7 - 926381. i) q^{53} +(34693.7 - 152003. i) q^{54} +(829183. + 2.11272e6i) q^{55} +(23367.7 + 311821. i) q^{56} +(-763113. - 115021. i) q^{57} +(192719. - 178817. i) q^{58} +(-2.25610e6 + 1.08648e6i) q^{59} +(-1.28647e6 - 877101. i) q^{60} +(1.16406e6 - 2.96597e6i) q^{61} +(-438681. - 135315. i) q^{62} +(740278. + 686878. i) q^{63} +(-1.17771e6 - 1.47680e6i) q^{64} +(1.80823e6 + 2.26745e6i) q^{65} +(194223. + 180213. i) q^{66} +(874383. + 269712. i) q^{67} +(-1.30665e6 + 3.32930e6i) q^{68} +(-2.18375e6 - 1.48885e6i) q^{69} +(-437412. + 210646. i) q^{70} +(1.38968e6 - 1.28944e6i) q^{71} +(442116. + 66638.2i) q^{72} +(95720.4 + 1.27730e6i) q^{73} +(-117983. - 300615. i) q^{74} +(539337. - 2.36299e6i) q^{75} +(231220. - 3.08542e6i) q^{76} +(-4.62445e6 + 1.42645e6i) q^{77} +(305034. + 146897. i) q^{78} +(-65408.0 - 113290. i) q^{79} +(3.06705e6 - 5.31228e6i) q^{80} +(-587470. + 400530. i) q^{81} +(-260332. - 1.14059e6i) q^{82} +(-3.39479e6 + 511682. i) q^{83} +(2.06999e6 - 2.59568e6i) q^{84} -1.12006e7 q^{85} +(-752158. - 135030. i) q^{86} -5.63025e6 q^{87} +(-1.33592e6 + 1.67519e6i) q^{88} +(441062. - 66479.4i) q^{89} +(154470. + 676778. i) q^{90} +(-5.10946e6 + 3.48357e6i) q^{91} +(5.29821e6 - 9.17677e6i) q^{92} +(4.91580e6 + 8.51441e6i) q^{93} +(357959. + 172384. i) q^{94} +(9.25922e6 - 2.85609e6i) q^{95} +(165235. - 2.20491e6i) q^{96} +(514761. - 2.25532e6i) q^{97} +(62802.1 + 160017. i) q^{98} +(517112. + 6.90038e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9}+O(q^{10}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9} - 1681 q^{10} + 4580 q^{11} + 9330 q^{12} - 20444 q^{13} - 45798 q^{14} + 50477 q^{15} - 74504 q^{16} - 25312 q^{17} + 2046 q^{18} + 4046 q^{19} + 140781 q^{20} + 100555 q^{21} + 95810 q^{22} + 1648 q^{23} - 292592 q^{24} + 419068 q^{25} + 393435 q^{26} + 274140 q^{27} + 233644 q^{28} + 605697 q^{29} - 1216016 q^{30} + 358580 q^{31} - 19194 q^{32} + 1280291 q^{33} + 1137255 q^{34} + 652739 q^{35} - 8980975 q^{36} - 2360047 q^{37} - 308490 q^{38} + 536339 q^{39} + 3057993 q^{40} - 1376320 q^{41} + 8417790 q^{42} + 7173000 q^{43} - 3856780 q^{44} + 2761486 q^{45} - 7073993 q^{46} + 1437090 q^{47} - 9543469 q^{48} - 16053170 q^{49} - 3046893 q^{50} + 2972901 q^{51} + 17415142 q^{52} + 3320604 q^{53} + 6000486 q^{54} + 13427750 q^{55} - 5450793 q^{56} + 3333100 q^{57} - 7876190 q^{58} - 7084765 q^{59} + 7356443 q^{60} + 3354606 q^{61} - 719427 q^{62} + 14716815 q^{63} - 16086234 q^{64} - 19914646 q^{65} - 8293345 q^{66} + 13025470 q^{67} - 22191927 q^{68} - 33964295 q^{69} + 8094727 q^{70} + 30843495 q^{71} + 93841607 q^{72} - 3067637 q^{73} + 18179570 q^{74} - 41508571 q^{75} - 19751872 q^{76} - 15169179 q^{77} - 69509396 q^{78} - 12090149 q^{79} - 69662530 q^{80} + 3387954 q^{81} + 39226888 q^{82} + 16408777 q^{83} + 98603231 q^{84} - 13423424 q^{85} + 111906660 q^{86} + 49022010 q^{87} + 76213954 q^{88} - 12540205 q^{89} - 92608607 q^{90} - 59091937 q^{91} - 50489370 q^{92} - 52218334 q^{93} - 3441600 q^{94} - 79947551 q^{95} - 23449784 q^{96} - 116467587 q^{97} + 73909552 q^{98} - 20061115 q^{99}+O(q^{100}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9 - 1681 * q^10 + 4580 * q^11 + 9330 * q^12 - 20444 * q^13 - 45798 * q^14 + 50477 * q^15 - 74504 * q^16 - 25312 * q^17 + 2046 * q^18 + 4046 * q^19 + 140781 * q^20 + 100555 * q^21 + 95810 * q^22 + 1648 * q^23 - 292592 * q^24 + 419068 * q^25 + 393435 * q^26 + 274140 * q^27 + 233644 * q^28 + 605697 * q^29 - 1216016 * q^30 + 358580 * q^31 - 19194 * q^32 + 1280291 * q^33 + 1137255 * q^34 + 652739 * q^35 - 8980975 * q^36 - 2360047 * q^37 - 308490 * q^38 + 536339 * q^39 + 3057993 * q^40 - 1376320 * q^41 + 8417790 * q^42 + 7173000 * q^43 - 3856780 * q^44 + 2761486 * q^45 - 7073993 * q^46 + 1437090 * q^47 - 9543469 * q^48 - 16053170 * q^49 - 3046893 * q^50 + 2972901 * q^51 + 17415142 * q^52 + 3320604 * q^53 + 6000486 * q^54 + 13427750 * q^55 - 5450793 * q^56 + 3333100 * q^57 - 7876190 * q^58 - 7084765 * q^59 + 7356443 * q^60 + 3354606 * q^61 - 719427 * q^62 + 14716815 * q^63 - 16086234 * q^64 - 19914646 * q^65 - 8293345 * q^66 + 13025470 * q^67 - 22191927 * q^68 - 33964295 * q^69 + 8094727 * q^70 + 30843495 * q^71 + 93841607 * q^72 - 3067637 * q^73 + 18179570 * q^74 - 41508571 * q^75 - 19751872 * q^76 - 15169179 * q^77 - 69509396 * q^78 - 12090149 * q^79 - 69662530 * q^80 + 3387954 * q^81 + 39226888 * q^82 + 16408777 * q^83 + 98603231 * q^84 - 13423424 * q^85 + 111906660 * q^86 + 49022010 * q^87 + 76213954 * q^88 - 12540205 * q^89 - 92608607 * q^90 - 59091937 * q^91 - 50489370 * q^92 - 52218334 * q^93 - 3441600 * q^94 - 79947551 * q^95 - 23449784 * q^96 - 116467587 * q^97 + 73909552 * q^98 - 20061115 * q^99

Introduction

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