LMFDB - Embedded newform 71.8.c.a.5.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,8,Mod(5,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("71.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	71.c (of order $5$, degree $4$, 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:	$22.1793368094$
Analytic rank:	$0$
Dimension:	$164$
Relative dimension:	$41$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	71.5
Dual form			71.8.c.a.57.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27884 - 7.01354i) q^{2} +(-19.8378 - 61.0546i) q^{3} +(59.5576 - 43.2711i) q^{4} +(357.700 + 259.884i) q^{5} +(-383.001 + 278.267i) q^{6} +(-219.765 - 676.366i) q^{7} +(-1202.86 - 873.931i) q^{8} +(-1564.80 + 1136.90i) q^{9} +O(q^{10})$	\(q+(-2.27884 - 7.01354i) q^{2} +(-19.8378 - 61.0546i) q^{3} +(59.5576 - 43.2711i) q^{4} +(357.700 + 259.884i) q^{5} +(-383.001 + 278.267i) q^{6} +(-219.765 - 676.366i) q^{7} +(-1202.86 - 873.931i) q^{8} +(-1564.80 + 1136.90i) q^{9} +(1007.57 - 3100.98i) q^{10} +(613.702 + 1888.78i) q^{11} +(-3823.39 - 2777.86i) q^{12} +(2526.97 - 7777.23i) q^{13} +(-4242.91 + 3082.66i) q^{14} +(8771.14 - 26994.8i) q^{15} +(-476.350 + 1466.06i) q^{16} +(8629.66 - 26559.3i) q^{17} +(11539.6 + 8384.00i) q^{18} +(-1879.43 - 5784.30i) q^{19} +32549.2 q^{20} +(-36935.6 + 26835.3i) q^{21} +(11848.5 - 8608.44i) q^{22} -106926. q^{23} +(-29495.3 + 90777.2i) q^{24} +(36267.6 + 111620. i) q^{25} -60304.4 q^{26} +(-13129.3 - 9539.00i) q^{27} +(-42355.8 - 30773.3i) q^{28} +(-2092.52 - 1520.31i) q^{29} -209317. q^{30} +(57927.3 + 178282. i) q^{31} -178945. q^{32} +(103144. - 74938.6i) q^{33} -205941. q^{34} +(97167.2 - 299050. i) q^{35} +(-44001.1 + 135422. i) q^{36} +314396. q^{37} +(-36285.5 + 26363.0i) q^{38} -524965. q^{39} +(-203143. - 625210. i) q^{40} -453520. q^{41} +(272380. + 197896. i) q^{42} +(571609. + 415298. i) q^{43} +(118280. + 85935.6i) q^{44} -855192. q^{45} +(243668. + 749932. i) q^{46} +(-52738.6 + 162313. i) q^{47} +98959.2 q^{48} +(257086. - 186784. i) q^{49} +(700204. - 508728. i) q^{50} -1.79276e6 q^{51} +(-186029. - 572538. i) q^{52} +(42896.0 + 31165.8i) q^{53} +(-36982.6 + 113821. i) q^{54} +(-271343. + 835109. i) q^{55} +(-326751. + 1.00563e6i) q^{56} +(-315874. + 229496. i) q^{57} +(-5894.22 + 18140.5i) q^{58} +(-685538. - 498072. i) q^{59} +(-645707. - 1.98728e6i) q^{60} +(95029.6 - 292471. i) q^{61} +(1.11838e6 - 812551. i) q^{62} +(1.11285e6 + 808530. i) q^{63} +(468760. + 1.44269e6i) q^{64} +(2.92508e6 - 2.12519e6i) q^{65} +(-760633. - 552633. i) q^{66} +(497815. - 361684. i) q^{67} +(-635291. - 1.95523e6i) q^{68} +(2.12119e6 + 6.52835e6i) q^{69} -2.31882e6 q^{70} +(2.92486e6 + 735073. i) q^{71} +2.87581e6 q^{72} +(-214825. - 661163. i) q^{73} +(-716458. - 2.20503e6i) q^{74} +(6.09545e6 - 4.42860e6i) q^{75} +(-362228. - 263174. i) q^{76} +(1.14264e6 - 830174. i) q^{77} +(1.19631e6 + 3.68186e6i) q^{78} +(-4.86390e6 - 3.53383e6i) q^{79} +(-551396. + 400612. i) q^{80} +(-1.62912e6 + 5.01390e6i) q^{81} +(1.03350e6 + 3.18078e6i) q^{82} +(-7.27394e6 - 5.28483e6i) q^{83} +(-1.03860e6 + 3.19649e6i) q^{84} +(9.98919e6 - 7.25757e6i) q^{85} +(1.61011e6 - 4.95540e6i) q^{86} +(-51310.6 + 157918. i) q^{87} +(912464. - 2.80828e6i) q^{88} +(1.75246e6 + 1.27324e6i) q^{89} +(1.94884e6 + 5.99792e6i) q^{90} -5.81559e6 q^{91} +(-6.36828e6 + 4.62683e6i) q^{92} +(9.73578e6 - 7.07346e6i) q^{93} +1.25857e6 q^{94} +(830976. - 2.55748e6i) q^{95} +(3.54989e6 + 1.09254e7i) q^{96} +1.12292e7 q^{97} +(-1.89587e6 - 1.37743e6i) q^{98} +(-3.10767e6 - 2.25785e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 164 q - 24 q^{2} + 23 q^{3} - 2290 q^{4} - 145 q^{5} + 514 q^{6} - 689 q^{7} + 7007 q^{8} - 28870 q^{9}+O(q^{10}) $ 164 * q - 24 * q^2 + 23 * q^3 - 2290 * q^4 - 145 * q^5 + 514 * q^6 - 689 * q^7 + 7007 * q^8 - 28870 * q^9	\( 164 q - 24 q^{2} + 23 q^{3} - 2290 q^{4} - 145 q^{5} + 514 q^{6} - 689 q^{7} + 7007 q^{8} - 28870 q^{9} + 3135 q^{10} - 12985 q^{11} + 18776 q^{12} - 9385 q^{13} + 32591 q^{14} - 8549 q^{15} - 187398 q^{16} - 13646 q^{17} - 76246 q^{18} + 25499 q^{19} + 353436 q^{20} + 34737 q^{21} - 217194 q^{22} + 169250 q^{23} + 331795 q^{24} - 575758 q^{25} + 910386 q^{26} - 804946 q^{27} - 73744 q^{28} + 267827 q^{29} + 148780 q^{30} - 438094 q^{31} - 1526108 q^{32} - 334678 q^{33} + 693478 q^{34} - 2088525 q^{35} - 2044616 q^{36} + 1246506 q^{37} + 153325 q^{38} + 5662314 q^{39} - 1006765 q^{40} + 2523444 q^{41} - 3243385 q^{42} - 610945 q^{43} + 2555635 q^{44} - 2138948 q^{45} - 3308317 q^{46} - 24619 q^{47} + 3151128 q^{48} - 5099094 q^{49} + 1280130 q^{50} + 5652418 q^{51} - 6865861 q^{52} + 7097402 q^{53} + 3114724 q^{54} - 2901298 q^{55} - 5638895 q^{56} + 4376914 q^{57} + 2039661 q^{58} - 5415353 q^{59} + 4266884 q^{60} - 4862842 q^{61} - 698479 q^{62} - 9326945 q^{63} - 7453239 q^{64} - 563874 q^{65} - 1270308 q^{66} - 12169138 q^{67} - 2438715 q^{68} + 4493215 q^{69} + 24169266 q^{70} + 7425657 q^{71} + 74311670 q^{72} + 5888723 q^{73} - 25053117 q^{74} - 23403819 q^{75} - 23428881 q^{76} + 27730932 q^{77} - 4857586 q^{78} - 14763363 q^{79} - 10893310 q^{80} - 52980383 q^{81} + 11235687 q^{82} + 9180561 q^{83} - 57710877 q^{84} + 49461277 q^{85} + 24603299 q^{86} + 22534593 q^{87} + 47400568 q^{88} + 4614244 q^{89} + 36501636 q^{90} - 44327954 q^{91} - 22315930 q^{92} + 11554572 q^{93} + 39127110 q^{94} + 22575615 q^{95} - 16486827 q^{96} + 27532902 q^{97} + 79875624 q^{98} - 47114358 q^{99}+O(q^{100}) \) 164 * q - 24 * q^2 + 23 * q^3 - 2290 * q^4 - 145 * q^5 + 514 * q^6 - 689 * q^7 + 7007 * q^8 - 28870 * q^9 + 3135 * q^10 - 12985 * q^11 + 18776 * q^12 - 9385 * q^13 + 32591 * q^14 - 8549 * q^15 - 187398 * q^16 - 13646 * q^17 - 76246 * q^18 + 25499 * q^19 + 353436 * q^20 + 34737 * q^21 - 217194 * q^22 + 169250 * q^23 + 331795 * q^24 - 575758 * q^25 + 910386 * q^26 - 804946 * q^27 - 73744 * q^28 + 267827 * q^29 + 148780 * q^30 - 438094 * q^31 - 1526108 * q^32 - 334678 * q^33 + 693478 * q^34 - 2088525 * q^35 - 2044616 * q^36 + 1246506 * q^37 + 153325 * q^38 + 5662314 * q^39 - 1006765 * q^40 + 2523444 * q^41 - 3243385 * q^42 - 610945 * q^43 + 2555635 * q^44 - 2138948 * q^45 - 3308317 * q^46 - 24619 * q^47 + 3151128 * q^48 - 5099094 * q^49 + 1280130 * q^50 + 5652418 * q^51 - 6865861 * q^52 + 7097402 * q^53 + 3114724 * q^54 - 2901298 * q^55 - 5638895 * q^56 + 4376914 * q^57 + 2039661 * q^58 - 5415353 * q^59 + 4266884 * q^60 - 4862842 * q^61 - 698479 * q^62 - 9326945 * q^63 - 7453239 * q^64 - 563874 * q^65 - 1270308 * q^66 - 12169138 * q^67 - 2438715 * q^68 + 4493215 * q^69 + 24169266 * q^70 + 7425657 * q^71 + 74311670 * q^72 + 5888723 * q^73 - 25053117 * q^74 - 23403819 * q^75 - 23428881 * q^76 + 27730932 * q^77 - 4857586 * q^78 - 14763363 * q^79 - 10893310 * q^80 - 52980383 * q^81 + 11235687 * q^82 + 9180561 * q^83 - 57710877 * q^84 + 49461277 * q^85 + 24603299 * q^86 + 22534593 * q^87 + 47400568 * q^88 + 4614244 * q^89 + 36501636 * q^90 - 44327954 * q^91 - 22315930 * q^92 + 11554572 * q^93 + 39127110 * q^94 + 22575615 * q^95 - 16486827 * q^96 + 27532902 * q^97 + 79875624 * q^98 - 47114358 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−2.27884	−	7.01354i	−0.201423	−	0.619915i	−0.999841	−	0.0178124i	$-0.994330\pi$
$2$	−2.27884	−	7.01354i	−0.201423	−	0.619915i	0.798419	−	0.602103i	$-0.205670\pi$
$3$	−19.8378	−	61.0546i	−0.424199	−	1.30555i	−0.903759	−	0.428042i	$-0.859204\pi$
$3$	−19.8378	−	61.0546i	−0.424199	−	1.30555i	0.479560	−	0.877509i	$-0.340796\pi$
$4$	59.5576	−	43.2711i	0.465294	−	0.338056i
$5$	357.700	+	259.884i	1.27975	+	0.929791i	0.999545	−	0.0301503i	$-0.00959860\pi$
$5$	357.700	+	259.884i	1.27975	+	0.929791i	0.280202	+	0.959941i	$0.409599\pi$
$6$	−383.001	+	278.267i	−0.723887	+	0.525935i
$7$	−219.765	−	676.366i	−0.242167	−	0.745313i	−0.996090	−	0.0883499i	$-0.971841\pi$
$7$	−219.765	−	676.366i	−0.242167	−	0.745313i	0.753923	−	0.656963i	$-0.228159\pi$
$8$	−1202.86	−	873.931i	−0.830617	−	0.603479i
$9$	−1564.80	+	1136.90i	−0.715502	+	0.519843i
$10$	1007.57	−	3100.98i	0.318621	−	0.980615i
$11$	613.702	+	1888.78i	0.139022	+	0.427865i	0.996194	−	0.0871649i	$-0.0277807\pi$
$11$	613.702	+	1888.78i	0.139022	+	0.427865i	−0.857172	+	0.515030i	$0.827781\pi$
$12$	−3823.39	−	2777.86i	−0.638726	−	0.464062i
$13$	2526.97	−	7777.23i	0.319006	−	0.981800i	−0.655068	−	0.755570i	$-0.727360\pi$
$13$	2526.97	−	7777.23i	0.319006	−	0.981800i	0.974074	−	0.226230i	$-0.0726400\pi$
$14$	−4242.91	+	3082.66i	−0.413253	+	0.300246i
$15$	8771.14	−	26994.8i	0.671022	−	2.06519i
$16$	−476.350	+	1466.06i	−0.0290741	+	0.0894810i
$17$	8629.66	−	26559.3i	0.426012	−	1.31113i	−0.476009	−	0.879440i	$-0.657917\pi$
$17$	8629.66	−	26559.3i	0.426012	−	1.31113i	0.902022	−	0.431691i	$-0.142083\pi$
$18$	11539.6	+	8384.00i	0.466376	+	0.338842i
$19$	−1879.43	−	5784.30i	−0.0628622	−	0.193470i	0.914693	−	0.404149i	$-0.132432\pi$
$19$	−1879.43	−	5784.30i	−0.0628622	−	0.193470i	−0.977555	+	0.210679i	$0.932432\pi$
$20$	32549.2			0.909779
$21$	−36935.6	+	26835.3i	−0.870317	+	0.632323i
$22$	11848.5	−	8608.44i	0.237238	−	0.172363i
$23$	−106926.			−1.83247			−0.916237	−	0.400638i	$-0.868789\pi$
$23$	−106926.			−1.83247			−0.916237	+	0.400638i	$0.868789\pi$
$24$	−29495.3	+	90777.2i	−0.435525	+	1.34041i
$25$	36267.6	+	111620.i	0.464225	+	1.42874i
$26$	−60304.4			−0.672887
$27$	−13129.3	−	9539.00i	−0.128371	−	0.0932673i
$28$	−42355.8	−	30773.3i	−0.364636	−	0.264924i
$29$	−2092.52	−	1520.31i	−0.0159323	−	0.0115755i	0.579791	−	0.814766i	$-0.303134\pi$
$29$	−2092.52	−	1520.31i	−0.0159323	−	0.0115755i	−0.595723	+	0.803190i	$0.703134\pi$
$30$	−209317.			−1.41540
$31$	57927.3	+	178282.i	0.349235	+	1.07483i	0.959277	+	0.282466i	$0.0911523\pi$
$31$	57927.3	+	178282.i	0.349235	+	1.07483i	−0.610043	+	0.792369i	$0.708848\pi$
$32$	−178945.			−0.965373
$33$	103144.	−	74938.6i	0.499627	−	0.363000i
$34$	−205941.			−0.898598
$35$	97167.2	−	299050.i	0.383073	−	1.17898i
$36$	−44001.1	+	135422.i	−0.157183	+	0.483759i
$37$	314396.			1.02040			0.510201	−	0.860055i	$-0.329571\pi$
$37$	314396.			1.02040			0.510201	+	0.860055i	$0.329571\pi$
$38$	−36285.5	+	26363.0i	−0.107273	+	0.0779384i
$39$	−524965.			−1.41711
$40$	−203143.	−	625210.i	−0.501871	−	1.54460i
$41$	−453520.			−1.02767			−0.513834	−	0.857890i	$-0.671775\pi$
$41$	−453520.			−1.02767			−0.513834	+	0.857890i	$0.671775\pi$
$42$	272380.	+	197896.i	0.567288	+	0.412159i
$43$	571609.	+	415298.i	1.09638	+	0.796564i	0.980465	−	0.196695i	$-0.0630210\pi$
$43$	571609.	+	415298.i	1.09638	+	0.796564i	0.115912	+	0.993260i	$0.463021\pi$
$44$	118280.	+	85935.6i	0.209328	+	0.152086i
$45$	−855192.			−1.39901
$46$	243668.	+	749932.i	0.369101	+	1.13598i
$47$	−52738.6	+	162313.i	−0.0740945	+	0.228039i	−0.981244	−	0.192768i	$-0.938253\pi$
$47$	−52738.6	+	162313.i	−0.0740945	+	0.228039i	0.907150	+	0.420808i	$0.138253\pi$
$48$	98959.2			0.129155
$49$	257086.	−	186784.i	0.312170	−	0.226805i
$50$	700204.	−	508728.i	0.792190	−	0.575560i
$51$	−1.79276e6			−1.89246
$52$	−186029.	−	572538.i	−0.183471	−	0.564667i
$53$	42896.0	+	31165.8i	0.0395778	+	0.0287549i	0.607398	−	0.794397i	$-0.292213\pi$
$53$	42896.0	+	31165.8i	0.0395778	+	0.0287549i	−0.567821	+	0.823152i	$0.692213\pi$
$54$	−36982.6	+	113821.i	−0.0319609	+	0.0983655i
$55$	−271343.	+	835109.i	−0.219912	+	0.676821i
$56$	−326751.	+	1.00563e6i	−0.248633	+	0.765213i
$57$	−315874.	+	229496.i	−0.225919	+	0.164140i
$58$	−5894.22	+	18140.5i	−0.00396669	+	0.0122082i
$59$	−685538.	−	498072.i	−0.434560	−	0.315726i	0.348910	−	0.937156i	$-0.386552\pi$
$59$	−685538.	−	498072.i	−0.434560	−	0.315726i	−0.783469	+	0.621430i	$0.786552\pi$
$60$	−645707.	−	1.98728e6i	−0.385928	−	1.18776i
$61$	95029.6	−	292471.i	0.0536049	−	0.164979i	−0.920670	−	0.390342i	$-0.872357\pi$
$61$	95029.6	−	292471.i	0.0536049	−	0.164979i	0.974275	+	0.225363i	$0.0723568\pi$
$62$	1.11838e6	−	812551.i	0.595962	−	0.432992i
$63$	1.11285e6	+	808530.i	0.560717	+	0.407384i
$64$	468760.	+	1.44269e6i	0.223522	+	0.687930i
$65$	2.92508e6	−	2.12519e6i	1.32112	−	0.959847i
$66$	−760633.	−	552633.i	−0.325665	−	0.236610i
$67$	497815.	−	361684.i	0.202212	−	0.146915i	−0.482071	−	0.876132i	$-0.660115\pi$
$67$	497815.	−	361684.i	0.202212	−	0.146915i	0.684283	+	0.729217i	$0.260115\pi$
$68$	−635291.	−	1.95523e6i	−0.245014	−	0.754077i
$69$	2.12119e6	+	6.52835e6i	0.777334	+	2.39239i
$70$	−2.31882e6			−0.808025
$71$	2.92486e6	+	735073.i	0.969841	+	0.243740i
$71$	2.92486e6	+	735073.i	0.969841	+	0.243740i
$72$	2.87581e6			0.908023
$73$	−214825.	−	661163.i	−0.0646331	−	0.198920i	0.913525	−	0.406783i	$-0.133349\pi$
$73$	−214825.	−	661163.i	−0.0646331	−	0.198920i	−0.978158	+	0.207862i	$0.933349\pi$
$74$	−716458.	−	2.20503e6i	−0.205532	−	0.632563i
$75$	6.09545e6	−	4.42860e6i	1.66837	−	1.21214i
$76$	−362228.	−	263174.i	−0.0946529	−	0.0687694i
$77$	1.14264e6	−	830174.i	0.285227	−	0.207230i
$78$	1.19631e6	+	3.68186e6i	0.285438	+	0.878489i
$79$	−4.86390e6	−	3.53383e6i	−1.10992	−	0.806401i	−0.127266	−	0.991869i	$-0.540620\pi$
$79$	−4.86390e6	−	3.53383e6i	−1.10992	−	0.806401i	−0.982650	+	0.185467i	$0.940620\pi$
$80$	−551396.	+	400612.i	−0.120406	+	0.0874801i
$81$	−1.62912e6	+	5.01390e6i	−0.340608	+	1.04828i
$82$	1.03350e6	+	3.18078e6i	0.206996	+	0.637067i
$83$	−7.27394e6	−	5.28483e6i	−1.39636	−	1.01451i	−0.995134	−	0.0985324i	$-0.968585\pi$
$83$	−7.27394e6	−	5.28483e6i	−1.39636	−	1.01451i	−0.401223	−	0.915980i	$-0.631415\pi$
$84$	−1.03860e6	+	3.19649e6i	−0.191193	+	0.588431i
$85$	9.98919e6	−	7.25757e6i	1.76427	−	1.28181i
$86$	1.61011e6	−	4.95540e6i	0.272967	−	0.840106i
$87$	−51310.6	+	157918.i	−0.00835391	+	0.0257107i
$88$	912464.	−	2.80828e6i	0.142734	−	0.439289i
$89$	1.75246e6	+	1.27324e6i	0.263502	+	0.191445i	0.711689	−	0.702494i	$-0.247930\pi$
$89$	1.75246e6	+	1.27324e6i	0.263502	+	0.191445i	−0.448188	+	0.893939i	$0.647930\pi$
$90$	1.94884e6	+	5.99792e6i	0.281792	+	0.867265i
$91$	−5.81559e6			−0.809001
$92$	−6.36828e6	+	4.62683e6i	−0.852638	+	0.619478i
$93$	9.73578e6	−	7.07346e6i	1.25511	−	0.911888i
$94$	1.25857e6			0.156289
$95$	830976.	−	2.55748e6i	0.0994388	−	0.306041i
$96$	3.54989e6	+	1.09254e7i	0.409510	+	1.26034i
$97$	1.12292e7			1.24924			0.624621	−	0.780928i	$-0.285254\pi$
$97$	1.12292e7			1.24924			0.624621	+	0.780928i	$0.285254\pi$
$98$	−1.89587e6	−	1.37743e6i	−0.203478	−	0.147835i
$99$	−3.10767e6	−	2.25785e6i	−0.321893	−	0.233869i
$100$	6.98994e6	+	5.07849e6i	0.698994	+	0.507849i
$101$	−2.25625e6			−0.217903			−0.108951	−	0.994047i	$-0.534749\pi$
$101$	−2.25625e6			−0.217903			−0.108951	+	0.994047i	$0.534749\pi$
$102$	4.08541e6	+	1.25736e7i	0.381185	+	1.17317i
$103$	7.07776e6			0.638213			0.319107	−	0.947719i	$-0.396617\pi$
$103$	7.07776e6			0.638213			0.319107	+	0.947719i	$0.396617\pi$
$104$	−9.83636e6	+	7.14653e6i	−0.857468	+	0.622987i
$105$	−2.01859e7			−1.70171
$106$	120829.	−	371874.i	0.00985375	−	0.0303267i
$107$	4.61716e6	−	1.42102e7i	0.364361	−	1.12139i	−0.586019	−	0.810297i	$-0.699306\pi$
$107$	4.61716e6	−	1.42102e7i	0.364361	−	1.12139i	0.950380	−	0.311091i	$-0.100694\pi$
$108$	−1.19471e6			−0.0912600
$109$	−1.27916e7	+	9.29368e6i	−0.946093	+	0.687377i	−0.949880	−	0.312616i	$-0.898795\pi$
$109$	−1.27916e7	+	9.29368e6i	−0.946093	+	0.687377i	0.00378667	+	0.999993i	$0.498795\pi$
$110$	6.47541e6			0.463866
$111$	−6.23695e6	−	1.91953e7i	−0.432854	−	1.33219i
$112$	1.09628e6			0.0737321
$113$	1.81331e7	+	1.31744e7i	1.18222	+	0.858930i	0.992420	−	0.122894i	$-0.0392175\pi$
$113$	1.81331e7	+	1.31744e7i	1.18222	+	0.858930i	0.189795	+	0.981824i	$0.439218\pi$
$114$	2.32941e6	+	1.69241e6i	0.147258	+	0.106989i
$115$	−3.82476e7	−	2.77885e7i	−2.34510	−	1.70382i
$116$	−190411.			−0.0113263
$117$	4.88768e6	+	1.50427e7i	0.282132	+	0.868313i
$118$	−1.93102e6	+	5.94307e6i	−0.108193	+	0.332984i
$119$	−1.98603e7			−1.08037
$120$	−3.41420e7	+	2.48056e7i	−1.80366	+	1.31044i
$121$	1.25746e7	−	9.13598e6i	0.645275	−	0.468820i
$122$	−2.26781e6			−0.113070
$123$	8.99686e6	+	2.76895e7i	0.435936	+	1.34167i
$124$	1.11645e7	+	8.11146e6i	0.525850	+	0.382053i
$125$	−5.36125e6	+	1.65002e7i	−0.245517	+	0.755622i
$126$	3.13466e6	−	9.64750e6i	0.139603	−	0.429653i
$127$	8.75722e6	−	2.69519e7i	0.379361	−	1.16755i	−0.561127	−	0.827729i	$-0.689632\pi$
$127$	8.75722e6	−	2.69519e7i	0.379361	−	1.16755i	0.940489	−	0.339825i	$-0.110368\pi$
$128$	−9.48036e6	+	6.88789e6i	−0.399567	+	0.290303i
$129$	1.40164e7	−	4.31380e7i	0.574873	−	1.76928i
$130$	−2.15709e7	−	1.56722e7i	−0.861126	−	0.625644i
$131$	7.91793e6	+	2.43689e7i	0.307724	+	0.947078i	0.978647	+	0.205550i	$0.0658985\pi$
$131$	7.91793e6	+	2.43689e7i	0.307724	+	0.947078i	−0.670922	+	0.741528i	$0.734102\pi$
$132$	2.90034e6	−	8.92633e6i	0.109759	−	0.337803i
$133$	−3.49927e6	+	2.54237e6i	−0.128973	+	0.0937040i
$134$	−3.67112e6	−	2.66722e6i	−0.131805	−	0.0957619i
$135$	−2.21732e6	−	6.82420e6i	−0.0775639	−	0.238717i
$136$	−3.35913e7	+	2.44055e7i	−1.14509	+	0.831959i
$137$	−1.13901e7	−	8.27537e6i	−0.378447	−	0.274957i	0.382258	−	0.924056i	$-0.375146\pi$
$137$	−1.13901e7	−	8.27537e6i	−0.378447	−	0.274957i	−0.760705	+	0.649098i	$0.775146\pi$
$138$	4.09530e7	−	2.97541e7i	1.32650	−	0.963762i
$139$	−1.21520e7	−	3.73999e7i	−0.383791	−	1.18119i	−0.937354	−	0.348380i	$-0.886732\pi$
$139$	−1.21520e7	−	3.73999e7i	−0.383791	−	1.18119i	0.553562	−	0.832808i	$-0.313268\pi$
$140$	−7.15318e6	−	2.20152e7i	−0.220318	−	0.678070i
$141$	1.09562e7			0.329148
$142$	−1.50981e6	−	2.21887e7i	−0.0442498	−	0.650313i
$143$	1.62403e7			0.464427
$144$	−921358.	−	2.83565e6i	−0.0257134	−	0.0791378i
$145$	−353392.	−	1.08763e6i	−0.00962651	−	0.0296273i
$146$	−4.14754e6	+	3.01337e6i	−0.110295	+	0.0801340i
$147$	−1.65040e7	−	1.19909e7i	−0.428528	−	0.311344i
$148$	1.87247e7	−	1.36043e7i	0.474787	−	0.344953i
$149$	2.26666e7	+	6.97606e7i	0.561350	+	1.72766i	0.678553	+	0.734551i	$0.262607\pi$
$149$	2.26666e7	+	6.97606e7i	0.561350	+	1.72766i	−0.117203	+	0.993108i	$0.537393\pi$
$150$	−4.49507e7	−	3.26586e7i	−1.08747	−	0.790093i
$151$	5.31994e7	−	3.86516e7i	1.25744	−	0.913584i	0.258811	−	0.965928i	$-0.416669\pi$
$151$	5.31994e7	−	3.86516e7i	1.25744	−	0.913584i	0.998629	+	0.0523441i	$0.0166693\pi$
$152$	−2.79438e6	+	8.60021e6i	−0.0645406	+	0.198635i
$153$	1.66915e7	+	5.13712e7i	0.376769	+	1.15958i
$154$	−8.42634e6	−	6.12210e6i	−0.185916	−	0.135076i
$155$	−2.56121e7	+	7.88259e7i	−0.552439	+	1.70023i
$156$	−3.12656e7	+	2.27158e7i	−0.659373	+	0.479063i
$157$	6.14231e6	−	1.89041e7i	0.126673	−	0.389858i	−0.867529	−	0.497386i	$-0.834293\pi$
$157$	6.14231e6	−	1.89041e7i	0.126673	−	0.389858i	0.994202	+	0.107527i	$0.0342934\pi$
$158$	−1.37006e7	+	4.21662e7i	−0.276338	+	0.850481i
$159$	1.05185e6	−	3.23726e6i	0.0207522	−	0.0638686i
$160$	−6.40087e7	−	4.65051e7i	−1.23543	−	0.897595i
$161$	2.34987e7	+	7.23214e7i	0.443764	+	1.36577i
$162$	3.88777e7			0.718452
$163$	−7.44388e7	+	5.40830e7i	−1.34630	+	0.978147i	−0.347117	+	0.937822i	$0.612839\pi$
$163$	−7.44388e7	+	5.40830e7i	−1.34630	+	0.978147i	−0.999187	+	0.0403245i	$0.987161\pi$
$164$	−2.70106e7	+	1.96243e7i	−0.478167	+	0.347409i
$165$	5.63701e7			0.976911
$166$	−2.04892e7	+	6.30593e7i	−0.347654	+	1.06997i
$167$	−1.74632e7	−	5.37463e7i	−0.290146	−	0.892978i	−0.984809	−	0.173642i	$-0.944446\pi$
$167$	−1.74632e7	−	5.37463e7i	−0.290146	−	0.892978i	0.694663	−	0.719335i	$-0.255554\pi$
$168$	6.78806e7			1.10449
$169$	−3.33503e6	−	2.42304e6i	−0.0531491	−	0.0386151i
$170$	−7.36650e7	−	5.35207e7i	−1.14998	−	0.835508i
$171$	9.51709e6	+	6.91457e6i	0.145552	+	0.105750i
$172$	5.20141e7			0.779420
$173$	−1.77700e6	−	5.46906e6i	−0.0260932	−	0.0803065i	0.937162	−	0.348895i	$-0.113443\pi$
$173$	−1.77700e6	−	5.46906e6i	−0.0260932	−	0.0803065i	−0.963255	+	0.268588i	$0.913443\pi$
$174$	1.22449e6			0.0176211
$175$	6.75258e7	−	4.90603e7i	0.952437	−	0.691986i
$176$	−3.06139e6			−0.0423277
$177$	−1.68100e7	+	5.17359e7i	−0.227857	+	0.701271i
$178$	4.93633e6	−	1.51925e7i	0.0656045	−	0.201910i
$179$	8.02934e7			1.04639			0.523196	−	0.852212i	$-0.324740\pi$
$179$	8.02934e7			1.04639			0.523196	+	0.852212i	$0.324740\pi$
$180$	−5.09332e7	+	3.70051e7i	−0.650949	+	0.472942i
$181$	9.71778e7			1.21813			0.609063	−	0.793122i	$-0.291546\pi$
$181$	9.71778e7			1.21813			0.609063	+	0.793122i	$0.291546\pi$
$182$	1.32528e7	+	4.07879e7i	0.162951	+	0.501512i
$183$	−1.97419e7			−0.238128
$184$	1.28618e8	+	9.34463e7i	1.52208	+	1.10586i
$185$	1.12460e8	+	8.17067e7i	1.30586	+	0.948761i
$186$	−7.17962e7	−	5.21630e7i	−0.818100	−	0.594384i
$187$	5.54608e7			0.620212
$188$	3.88247e6	+	1.19490e7i	0.0426143	+	0.131153i
$189$	−3.56650e6	+	1.09766e7i	−0.0384261	+	0.118263i
$190$	−1.98306e7			−0.209749
$191$	1.46361e8	−	1.06338e8i	1.51988	−	1.10426i	0.558337	−	0.829614i	$-0.311440\pi$
$191$	1.46361e8	−	1.06338e8i	1.51988	−	1.10426i	0.961546	−	0.274645i	$-0.0885603\pi$
$192$	7.87839e7	−	5.72398e7i	0.803310	−	0.583639i
$193$	3.62995e7			0.363454			0.181727	−	0.983349i	$-0.441831\pi$
$193$	3.62995e7			0.363454			0.181727	+	0.983349i	$0.441831\pi$
$194$	−2.55894e7	−	7.87562e7i	−0.251625	−	0.774423i
$195$	−1.87780e8	−	1.36430e8i	−1.81355	−	1.31762i
$196$	7.22906e6	−	2.22488e7i	0.0685781	−	0.211062i
$197$	4.92473e7	−	1.51568e8i	0.458934	−	1.41245i	−0.407519	−	0.913197i	$-0.633606\pi$
$197$	4.92473e7	−	1.51568e8i	0.458934	−	1.41245i	0.866453	−	0.499258i	$-0.166394\pi$
$198$	−8.75367e6	+	2.69410e7i	−0.0801423	+	0.246653i
$199$	−1.49308e7	+	1.08479e7i	−0.134307	+	0.0975795i	−0.652910	−	0.757435i	$-0.726452\pi$
$199$	−1.49308e7	+	1.08479e7i	−0.134307	+	0.0975795i	0.518604	+	0.855015i	$0.326452\pi$
$200$	5.39234e7	−	1.65959e8i	0.476620	−	1.46688i
$201$	−3.19580e7	−	2.32189e7i	−0.277584	−	0.201676i
$202$	5.14163e6	+	1.58243e7i	0.0438905	+	0.135081i
$203$	−568422.	+	1.74942e6i	−0.00476908	+	0.0146777i
$204$	−1.06773e8	+	7.75749e7i	−0.880551	+	0.639758i
$205$	−1.62224e8	−	1.17863e8i	−1.31516	−	0.955516i
$206$	−1.61291e7	−	4.96402e7i	−0.128551	−	0.395638i
$207$	1.67319e8	−	1.21564e8i	1.31114	−	0.952598i
$208$	1.01981e7	+	7.40937e6i	0.0785776	+	0.0570899i
$209$	9.77186e6	−	7.09967e6i	0.0740398	−	0.0537931i
$210$	4.60005e7	+	1.41575e8i	0.342764	+	1.05492i
$211$	−1.94912e7	−	5.99877e7i	−0.142840	−	0.439616i	0.853887	−	0.520459i	$-0.174239\pi$
$211$	−1.94912e7	−	5.99877e7i	−0.142840	−	0.439616i	−0.996727	+	0.0808424i	$0.974239\pi$
$212$	3.90336e6			0.0281360
$213$	−1.31432e7	−	1.93158e8i	−0.0931909	−	1.36957i
$214$	−1.10185e8			−0.768555
$215$	9.65352e7	+	2.97105e8i	0.662447	+	2.03880i
$216$	7.45632e6	+	2.29482e7i	0.0503427	+	0.154939i
$217$	1.07854e8	−	7.83602e7i	0.716515	−	0.520579i
$218$	9.43316e7	+	6.85359e7i	0.616680	+	0.448044i
$219$	−3.61054e7	+	2.62321e7i	−0.232283	+	0.168764i
$220$	1.99755e7	+	6.14784e7i	0.126479	+	0.389263i
$221$	−1.84751e8	−	1.34230e8i	−1.15137	−	0.836518i
$222$	−1.20414e8	+	8.74861e7i	−0.738657	+	0.536665i
$223$	−6.75699e7	+	2.07959e8i	−0.408024	+	1.25577i	0.510319	+	0.859985i	$0.329527\pi$
$223$	−6.75699e7	+	2.07959e8i	−0.408024	+	1.25577i	−0.918343	+	0.395784i	$0.870473\pi$
$224$	3.93258e7	+	1.21032e8i	0.233781	+	0.719505i
$225$	−1.83652e8	−	1.33431e8i	−1.07487	−	0.780941i
$226$	5.10771e7	−	1.57199e8i	0.294338	−	0.905881i
$227$	−1.96038e8	+	1.42430e8i	−1.11237	+	0.808183i	−0.983035	−	0.183418i	$-0.941284\pi$
$227$	−1.96038e8	+	1.42430e8i	−1.11237	+	0.808183i	−0.129333	+	0.991601i	$0.541284\pi$
$228$	−8.88216e6	+	2.73365e7i	−0.0496302	+	0.152746i
$229$	1.90042e7	−	5.84890e7i	0.104575	−	0.321847i	−0.885056	−	0.465485i	$-0.845880\pi$
$229$	1.90042e7	−	5.84890e7i	0.104575	−	0.321847i	0.989630	+	0.143638i	$0.0458800\pi$
$230$	−1.07736e8	+	3.31576e8i	−0.583865	+	1.79695i
$231$	−7.33534e7	−	5.32944e7i	−0.391542	−	0.284472i
$232$	1.18838e6	+	3.65744e6i	0.00624807	+	0.0192296i
$233$	2.77130e8			1.43529			0.717643	−	0.696411i	$-0.245221\pi$
$233$	2.77130e8			1.43529			0.717643	+	0.696411i	$0.245221\pi$
$234$	9.43645e7	−	6.85598e7i	0.481452	−	0.349796i
$235$	−6.10471e7	+	4.43533e7i	−0.306851	+	0.222940i
$236$	−6.23811e7			−0.308931
$237$	−1.19267e8	+	3.67067e8i	−0.581972	+	1.79113i
$238$	4.52585e7	+	1.39291e8i	0.217611	+	0.669737i
$239$	−9.21964e7			−0.436839			−0.218419	−	0.975855i	$-0.570090\pi$
$239$	−9.21964e7			−0.436839			−0.218419	+	0.975855i	$0.570090\pi$
$240$	3.53977e7	+	2.57180e7i	0.165286	+	0.120087i
$241$	1.69174e8	+	1.22912e8i	0.778526	+	0.565632i	0.904536	−	0.426397i	$-0.140217\pi$
$241$	1.69174e8	+	1.22912e8i	0.778526	+	0.565632i	−0.126010	+	0.992029i	$0.540217\pi$
$242$	−9.27309e7	−	6.73730e7i	−0.420602	−	0.305585i
$243$	3.02948e8			1.35440
$244$	−6.99581e6	−	2.15309e7i	−0.0308300	−	0.0948851i
$245$	1.40502e8			0.610380
$246$	1.73699e8	−	1.26200e8i	0.743916	−	0.540487i
$247$	−4.97351e7			−0.210002
$248$	8.61275e7	−	2.65073e8i	0.358559	−	1.10353i
$249$	−1.78364e8	+	5.48947e8i	−0.732165	+	2.25337i
$250$	1.27942e8			0.517874
$251$	−2.87307e8	+	2.08741e8i	−1.14680	+	0.833200i	−0.988052	−	0.154119i	$-0.950746\pi$
$251$	−2.87307e8	+	2.08741e8i	−1.14680	+	0.833200i	−0.158749	+	0.987319i	$0.550746\pi$
$252$	1.01264e8			0.398616
$253$	−6.56209e7	−	2.01960e8i	−0.254754	−	0.784052i
$254$	−2.08985e8			−0.800196
$255$	−6.41272e8	−	4.65911e8i	−2.42187	−	1.75959i
$256$	2.26998e8	+	1.64924e8i	0.845633	+	0.614388i
$257$	−1.81905e8	−	1.32161e8i	−0.668464	−	0.485667i	0.201047	−	0.979582i	$-0.435566\pi$
$257$	−1.81905e8	−	1.32161e8i	−0.668464	−	0.485667i	−0.869511	+	0.493914i	$0.835566\pi$
$258$	−3.34491e8			−1.21259
$259$	−6.90933e7	−	2.12647e8i	−0.247108	−	0.760520i
$260$	8.22511e7	−	2.53143e8i	0.290225	−	0.893221i
$261$	5.00282e6			0.0174170
$262$	1.52868e8	−	1.11065e8i	0.525125	−	0.381526i
$263$	−3.17911e8	+	2.30976e8i	−1.07761	+	0.782927i	−0.977264	−	0.212026i	$-0.931994\pi$
$263$	−3.17911e8	+	2.30976e8i	−1.07761	+	0.782927i	−0.100343	+	0.994953i	$0.531994\pi$
$264$	−1.89559e8			−0.634062
$265$	7.24441e6	+	2.22960e7i	0.0239135	+	0.0735981i
$266$	2.58053e7	+	1.87486e7i	0.0840665	+	0.0610779i
$267$	4.29720e7	−	1.32254e8i	0.138164	−	0.425226i
$268$	1.39982e7	−	4.30820e7i	0.0444222	−	0.136718i
$269$	1.06826e8	−	3.28777e8i	0.334615	−	1.02984i	−0.632297	−	0.774726i	$-0.717888\pi$
$269$	1.06826e8	−	3.28777e8i	0.334615	−	1.02984i	0.966912	−	0.255112i	$-0.0821123\pi$
$270$	−4.28089e7	+	3.11025e7i	−0.132361	+	0.0961661i
$271$	8.68785e7	−	2.67384e8i	0.265167	−	0.816100i	−0.726488	−	0.687179i	$-0.758849\pi$
$271$	8.68785e7	−	2.67384e8i	0.265167	−	0.816100i	0.991655	−	0.128921i	$-0.0411514\pi$
$272$	3.48267e7	+	2.53031e7i	0.104935	+	0.0762400i
$273$	1.15369e8	+	3.55069e8i	0.343178	+	1.05619i
$274$	−3.20835e7	+	9.87429e7i	−0.0942226	+	0.289987i
$275$	−1.88568e8	+	1.37003e8i	−0.546770	+	0.397252i
$276$	4.08822e8	+	2.97026e8i	1.17045	+	0.850381i
$277$	8.76276e7	+	2.69690e8i	0.247720	+	0.762405i	0.995177	+	0.0980945i	$0.0312747\pi$
$277$	8.76276e7	+	2.69690e8i	0.247720	+	0.762405i	−0.747457	+	0.664311i	$0.768725\pi$
$278$	−2.34613e8	+	1.70457e8i	−0.654931	+	0.475836i
$279$	−2.93333e8	−	2.13119e8i	−0.808623	−	0.587499i
$280$	−3.78228e8	+	2.74798e8i	−1.02967	+	0.748102i
$281$	1.50379e8	+	4.62818e8i	0.404310	+	1.24434i	0.921470	+	0.388450i	$0.126989\pi$
$281$	1.50379e8	+	4.62818e8i	0.404310	+	1.24434i	−0.517160	+	0.855889i	$0.673011\pi$
$282$	−2.49673e7	−	7.68414e7i	−0.0662978	−	0.204044i
$283$	4.94189e8			1.29611			0.648053	−	0.761595i	$-0.275583\pi$
$283$	4.94189e8			1.29611			0.648053	+	0.761595i	$0.275583\pi$
$284$	2.06005e8	−	8.27826e7i	0.533658	−	0.214449i
$285$	−1.72631e8			−0.441734
$286$	−3.70089e7	−	1.13902e8i	−0.0935460	−	0.287905i
$287$	9.96677e7	+	3.06746e8i	0.248867	+	0.765935i
$288$	2.80014e8	−	2.03442e8i	0.690726	−	0.501842i
$289$	−2.98957e8	−	2.17205e8i	−0.728562	−	0.529331i
$290$	−6.82280e6	+	4.95706e6i	−0.0164274	+	0.0119352i
$291$	−2.22762e8	−	6.85592e8i	−0.529927	−	1.63095i
$292$	−4.14037e7	−	3.00816e7i	−0.0973194	−	0.0707067i
$293$	4.44759e8	−	3.23137e8i	1.03297	−	0.750498i	0.0640705	−	0.997945i	$-0.479592\pi$
$293$	4.44759e8	−	3.23137e8i	1.03297	−	0.750498i	0.968901	+	0.247447i	$0.0795918\pi$
$294$	−4.64884e7	+	1.43077e8i	−0.106691	+	0.328362i
$295$	−1.15776e8	−	3.56321e8i	−0.262567	−	0.808099i
$296$	−3.78176e8	−	2.74761e8i	−0.847564	−	0.615792i
$297$	9.95959e6	−	3.06525e7i	0.0220594	−	0.0678919i
$298$	4.37615e8	−	3.17946e8i	0.957933	−	0.695979i
$299$	−2.70200e8	+	8.31591e8i	−0.584570	+	1.79912i
$300$	1.71400e8	−	5.27514e8i	0.366510	−	1.12800i
$301$	1.55274e8	−	4.77885e8i	0.328184	−	1.01005i
$302$	−3.92317e8	−	2.85035e8i	−0.819621	−	0.595490i
$303$	4.47591e7	+	1.37754e8i	0.0924342	+	0.284483i
$304$	9.37538e6			0.0191395
$305$	1.10001e8	−	7.99202e7i	0.221997	−	0.161290i
$306$	3.22256e8	−	2.34133e8i	0.642949	−	0.467130i
$307$	4.96312e8			0.978973			0.489486	−	0.872011i	$-0.337184\pi$
$307$	4.96312e8			0.978973			0.489486	+	0.872011i	$0.337184\pi$
$308$	3.21301e7	−	9.88864e7i	0.0626592	−	0.192845i
$309$	−1.40408e8	−	4.32130e8i	−0.270730	−	0.833220i
$310$	6.11214e8			1.16527
$311$	6.02883e8	+	4.38020e8i	1.13651	+	0.825720i	0.986629	−	0.162985i	$-0.0521122\pi$
$311$	6.02883e8	+	4.38020e8i	1.13651	+	0.825720i	0.149877	+	0.988705i	$0.452112\pi$
$312$	6.31461e8	+	4.58783e8i	1.17708	+	0.855197i
$313$	1.07083e8	+	7.78001e7i	0.197385	+	0.143408i	0.682088	−	0.731270i	$-0.261072\pi$
$313$	1.07083e8	+	7.78001e7i	0.197385	+	0.143408i	−0.484703	+	0.874679i	$0.661072\pi$
$314$	−1.46582e8			−0.267194
$315$	1.87941e8	+	5.78423e8i	0.338793	+	1.04270i
$316$	−4.42595e8			−0.789045
$317$	−2.09932e8	+	1.52525e8i	−0.370145	+	0.268926i	−0.757271	−	0.653101i	$-0.773468\pi$
$317$	−2.09932e8	+	1.52525e8i	−0.370145	+	0.268926i	0.387126	+	0.922027i	$0.373468\pi$
$318$	−2.51016e7			−0.0437731
$319$	1.58734e6	−	4.88533e6i	0.00273781	−	0.00842611i
$320$	−2.07258e8	+	6.37875e8i	−0.353579	+	1.08821i
$321$	−9.59190e8			−1.61859
$322$	4.53679e8	−	3.29617e8i	0.757275	−	0.550192i
$323$	−1.69846e8			−0.280444
$324$	1.19931e8	+	3.69110e8i	0.195895	+	0.602903i
$325$	9.59742e8			1.55083
$326$	5.48947e8	+	3.98833e8i	0.877543	+	0.637573i
$327$	8.21180e8	+	5.96622e8i	1.29874	+	0.943588i
$328$	5.45522e8	+	3.96345e8i	0.853599	+	0.620176i
$329$	1.21373e8			0.187904
$330$	−1.28458e8	−	3.95354e8i	−0.196772	−	0.605601i
$331$	2.28938e8	−	7.04597e8i	0.346992	−	1.06793i	−0.613517	−	0.789681i	$-0.710246\pi$
$331$	2.28938e8	−	7.04597e8i	0.346992	−	1.06793i	0.960509	−	0.278249i	$-0.0897542\pi$
$332$	−6.61899e8			−0.992678
$333$	−4.91969e8	+	3.57436e8i	−0.730100	+	0.530449i
$334$	−3.37155e8	+	2.44958e8i	−0.495128	+	0.359732i
$335$	2.72064e8			0.395380
$336$	−2.17477e7	−	6.69327e7i	−0.0312771	−	0.0962611i
$337$	8.09578e7	+	5.88193e7i	0.115227	+	0.0837173i	0.643906	−	0.765104i	$-0.277313\pi$
$337$	8.09578e7	+	5.88193e7i	0.115227	+	0.0837173i	−0.528679	+	0.848822i	$0.677313\pi$
$338$	−9.39409e6	+	2.89120e7i	−0.0132326	+	0.0407259i
$339$	4.44639e8	−	1.36846e9i	0.619882	−	1.90780i
$340$	2.80889e8	−	8.64487e8i	0.387577	−	1.19284i
$341$	−3.01185e8	+	2.18824e8i	−0.411333	+	0.298851i
$342$	2.68077e7	−	8.25057e7i	0.0362383	−	0.111530i
$343$	−6.56659e8	−	4.77091e8i	−0.878639	−	0.638369i
$344$	−3.24625e8	−	9.99094e8i	−0.429960	−	1.32328i
$345$	−9.37866e8	+	2.88646e9i	−1.22963	+	3.78441i
$346$	−3.43079e7	+	2.49262e7i	−0.0445275	+	0.0323511i
$347$	4.69018e7	+	3.40762e7i	0.0602610	+	0.0437822i	0.617508	−	0.786565i	$-0.288142\pi$
$347$	4.69018e7	+	3.40762e7i	0.0602610	+	0.0437822i	−0.557247	+	0.830347i	$0.688142\pi$
$348$	3.77735e6	+	1.16255e7i	0.00480462	+	0.0147871i
$349$	−1.08860e9	+	7.90916e8i	−1.37082	+	0.995959i	−0.373147	+	0.927772i	$0.621721\pi$
$349$	−1.08860e9	+	7.90916e8i	−1.37082	+	0.995959i	−0.997673	+	0.0681868i	$0.978279\pi$
$350$	−4.97967e8	−	3.61794e8i	−0.620815	−	0.451048i
$351$	−1.07364e8	+	7.80048e7i	−0.132521	+	0.0962823i
$352$	−1.09819e8	−	3.37988e8i	−0.134208	−	0.413049i
$353$	−1.29588e8	−	3.98829e8i	−0.156802	−	0.482587i	0.841537	−	0.540200i	$-0.181651\pi$
$353$	−1.29588e8	−	3.98829e8i	−0.156802	−	0.482587i	−0.998339	+	0.0576124i	$0.981651\pi$
$354$	4.01159e8			0.480624
$355$	8.55188e8	+	1.02306e9i	1.01452	+	1.21367i
$356$	1.59467e8			0.187325
$357$	3.93986e8	+	1.21256e9i	0.458292	+	1.41048i
$358$	−1.82976e8	−	5.63141e8i	−0.210767	−	0.648674i
$359$	1.28045e6	−	930302.i	0.00146060	−	0.00106119i	−0.587055	−	0.809547i	$-0.699713\pi$
$359$	1.28045e6	−	930302.i	0.00146060	−	0.00106119i	0.588515	+	0.808486i	$0.299713\pi$
$360$	1.02868e9	+	7.47379e8i	1.16204	+	0.844271i
$361$	6.93232e8	−	5.03662e8i	0.775538	−	0.563461i
$362$	−2.21452e8	−	6.81560e8i	−0.245358	−	0.755134i
$363$	−8.07246e8	−	5.86499e8i	−0.885794	−	0.643567i
$364$	−3.46363e8	+	2.51647e8i	−0.376423	+	0.273487i
$365$	9.49831e7	−	2.92328e8i	0.102240	−	0.314663i
$366$	4.49885e7	+	1.38460e8i	0.0479643	+	0.147619i
$367$	6.87999e8	+	4.99861e8i	0.726535	+	0.527859i	0.888466	−	0.458943i	$-0.151772\pi$
$367$	6.87999e8	+	4.99861e8i	0.726535	+	0.527859i	−0.161930	+	0.986802i	$0.551772\pi$
$368$	5.09344e7	−	1.56760e8i	0.0532776	−	0.163971i
$369$	7.09669e8	−	5.15605e8i	0.735299	−	0.534226i
$370$	3.16776e8	−	9.74936e8i	0.325122	−	1.00062i
$371$	1.16524e7	−	3.58625e7i	0.0118470	−	0.0364613i
$372$	2.73763e8	−	8.42556e8i	0.275724	−	0.848591i
$373$	−1.69328e8	−	1.23024e8i	−0.168946	−	0.122747i	0.500099	−	0.865968i	$-0.333297\pi$
$373$	−1.69328e8	−	1.23024e8i	−0.168946	−	0.122747i	−0.669045	+	0.743221i	$0.733297\pi$
$374$	−1.26386e8	−	3.88976e8i	−0.124925	−	0.384479i
$375$	1.11377e9			1.09065
$376$	2.05287e8	−	1.49150e8i	0.199161	−	0.144699i
$377$	−1.71115e7	+	1.24323e7i	−0.0164473	+	0.0119497i
$378$	8.51119e7			0.0810530
$379$	3.07601e8	−	9.46699e8i	0.290236	−	0.893254i	−0.694545	−	0.719450i	$-0.744394\pi$
$379$	3.07601e8	−	9.46699e8i	0.290236	−	0.893254i	0.984780	−	0.173804i	$-0.0556059\pi$
$380$	−6.11742e7	−	1.88275e8i	−0.0571907	−	0.176015i
$381$	−1.81926e9			−1.68523
$382$	−1.07934e9	−	7.84185e8i	−0.990685	−	0.719775i
$383$	2.92121e8	+	2.12238e8i	0.265685	+	0.193031i	0.712649	−	0.701520i	$-0.247495\pi$
$383$	2.92121e8	+	2.12238e8i	0.265685	+	0.193031i	−0.446965	+	0.894552i	$0.647495\pi$
$384$	6.08607e8	+	4.42179e8i	0.548501	+	0.398509i
$385$	6.24471e8			0.557699
$386$	−8.27206e7	−	2.54588e8i	−0.0732079	−	0.225311i
$387$	−1.36661e9			−1.19855
$388$	6.68782e8	−	4.85898e8i	0.581264	−	0.422313i
$389$	−1.89205e9			−1.62970			−0.814852	−	0.579668i	$-0.803182\pi$
$389$	−1.89205e9			−1.62970			−0.814852	+	0.579668i	$0.803182\pi$
$390$	−5.28938e8	+	1.62790e9i	−0.451522	+	1.38964i
$391$	−9.22738e8	+	2.83990e9i	−0.780656	+	2.40261i
$392$	−4.72474e8			−0.396166
$393$	1.33076e9	−	9.66851e8i	1.10592	−	0.803500i
$394$	−1.17525e9			−0.968042
$395$	−8.21431e8	−	2.52811e9i	−0.670628	−	2.06398i
$396$	−2.82785e8			−0.228835
$397$	9.21846e8	+	6.69760e8i	0.739421	+	0.537221i	0.892530	−	0.450989i	$-0.148929\pi$
$397$	9.21846e8	+	6.69760e8i	0.739421	+	0.537221i	−0.153109	+	0.988209i	$0.548929\pi$
$398$	1.10107e8	+	7.99972e7i	0.0875433	+	0.0636040i
$399$	2.24641e8	+	1.63212e8i	0.177045	+	0.128631i
$400$	−1.80917e8			−0.141342
$401$	3.32387e8	+	1.02298e9i	0.257418	+	0.792251i	0.993344	+	0.115188i	$0.0367472\pi$
$401$	3.32387e8	+	1.02298e9i	0.257418	+	0.792251i	−0.735926	+	0.677062i	$0.763253\pi$
$402$	−9.00192e7	+	2.77051e8i	−0.0691105	+	0.212700i
$403$	1.53292e9			1.16668
$404$	−1.34377e8	+	9.76305e7i	−0.101389	+	0.0736632i
$405$	−1.88577e9	+	1.37009e9i	−1.41058	+	1.02484i
$406$	1.35650e7			0.0100595
$407$	1.92946e8	+	5.93826e8i	0.141858	+	0.436595i
$408$	2.15645e9	+	1.56675e9i	1.57191	+	1.14206i
$409$	1.44565e8	−	4.44926e8i	0.104480	−	0.321556i	−0.885128	−	0.465347i	$-0.845929\pi$
$409$	1.44565e8	−	4.44926e8i	0.104480	−	0.321556i	0.989608	+	0.143791i	$0.0459294\pi$
$410$	−4.56953e8	+	1.40636e9i	−0.327437	+	1.00775i
$411$	−2.79295e8	+	8.59582e8i	−0.198434	+	0.610718i
$412$	4.21534e8	−	3.06263e8i	0.296957	−	0.215752i
$413$	−1.86222e8	+	5.73133e8i	−0.130079	+	0.400341i
$414$	−1.23389e9	−	8.96471e8i	−0.854622	−	0.620919i
$415$	−1.22845e9	−	3.78077e9i	−0.843699	−	2.59664i
$416$	−4.52190e8	+	1.39170e9i	−0.307960	+	0.947803i
$417$	−2.04237e9	+	1.48387e9i	−1.37930	+	1.00212i
$418$	−7.20623e7	−	5.23563e7i	−0.0482604	−	0.0350632i
$419$	−2.05743e8	−	6.33212e8i	−0.136639	−	0.420533i	0.859202	−	0.511636i	$-0.170961\pi$
$419$	−2.05743e8	−	6.33212e8i	−0.136639	−	0.420533i	−0.995841	+	0.0911037i	$0.970961\pi$
$420$	−1.20223e9	+	8.73468e8i	−0.791797	+	0.575274i
$421$	−1.10057e9	−	7.99611e8i	−0.718837	−	0.522265i	0.167176	−	0.985927i	$-0.446535\pi$
$421$	−1.10057e9	−	7.99611e8i	−0.718837	−	0.522265i	−0.886012	+	0.463662i	$0.846535\pi$
$422$	−3.76309e8	+	2.73404e8i	−0.243753	+	0.177097i
$423$	−1.02007e8	−	3.13946e8i	−0.0655299	−	0.201680i
$424$	−2.43613e7	−	7.49763e7i	−0.0155210	−	0.0477687i
$425$	3.27753e9			2.07103
$426$	−1.32477e9	+	5.32356e8i	−0.830247	+	0.333633i
$427$	−2.18702e8			−0.135942
$428$	−3.39903e8	−	1.04611e9i	−0.209557	−	0.644949i
$429$	−3.22172e8	−	9.91543e8i	−0.197010	−	0.606333i
$430$	1.86377e9	−	1.35411e9i	1.13045	−	0.821321i
$431$	−7.74148e7	−	5.62451e7i	−0.0465751	−	0.0338388i	0.564254	−	0.825601i	$-0.309164\pi$
$431$	−7.74148e7	−	5.62451e7i	−0.0465751	−	0.0338388i	−0.610829	+	0.791762i	$0.709164\pi$
$432$	2.02389e7	−	1.47044e7i	0.0120779	−	0.00877514i
$433$	−2.04387e8	−	6.29038e8i	−0.120989	−	0.372365i	0.872160	−	0.489220i	$-0.162719\pi$
$433$	−2.04387e8	−	6.29038e8i	−0.120989	−	0.372365i	−0.993149	+	0.116855i	$0.962719\pi$
$434$	−7.95362e8	−	5.77865e8i	−0.467037	−	0.339322i
$435$	−5.93942e7	+	4.31524e7i	−0.0345965	+	0.0251358i
$436$	−3.59692e8	+	1.10702e9i	−0.207839	+	0.639664i
$437$	2.00961e8	+	6.18495e8i	0.115193	+	0.354528i
$438$	2.66258e8	+	1.93448e8i	0.151406	+	0.110003i
$439$	−6.29548e8	+	1.93755e9i	−0.355143	+	1.09302i	0.600784	+	0.799412i	$0.294855\pi$
$439$	−6.29548e8	+	1.93755e9i	−0.355143	+	1.09302i	−0.955927	+	0.293606i	$0.905145\pi$
$440$	1.05622e9	−	7.67386e8i	0.591110	−	0.429466i
$441$	−1.89935e8	+	5.84559e8i	−0.105456	+	0.324559i
$442$	−5.20406e8	+	1.60165e9i	−0.286658	+	0.882244i
$443$	−1.85682e8	+	5.71470e8i	−0.101474	+	0.312306i	−0.988887	−	0.148670i	$-0.952501\pi$
$443$	−1.85682e8	+	5.71470e8i	−0.101474	+	0.312306i	0.887412	+	0.460976i	$0.152501\pi$
$444$	−1.20206e9	−	8.73349e8i	−0.651758	−	0.473530i
$445$	2.95961e8	+	9.10875e8i	0.159212	+	0.490003i
$446$	1.61251e9			0.860655
$447$	3.80955e9	−	2.76780e9i	2.01742	−	1.46574i
$448$	8.72772e8	−	6.34106e8i	0.458594	−	0.333188i
$449$	−1.99831e9			−1.04184			−0.520919	−	0.853606i	$-0.674411\pi$
$449$	−1.99831e9			−1.04184			−0.520919	+	0.853606i	$0.674411\pi$
$450$	−5.17311e8	+	1.59212e9i	−0.267613	+	0.823629i
$451$	−2.78326e8	−	8.56599e8i	−0.142868	−	0.439703i
$452$	1.65003e9			0.840443
$453$	−3.41522e9	−	2.48130e9i	−1.72614	−	1.25411i
$454$	1.44567e9	+	1.05034e9i	0.725061	+	0.526787i
$455$	−2.08024e9	−	1.51138e9i	−1.03532	−	0.752202i
$456$	5.80517e8			0.286707
$457$	−3.20228e8	−	9.85561e8i	−0.156947	−	0.483033i	0.841406	−	0.540403i	$-0.181728\pi$
$457$	−3.20228e8	−	9.85561e8i	−0.156947	−	0.483033i	−0.998353	+	0.0573704i	$0.981728\pi$
$458$	−4.53522e8			−0.220582
$459$	−3.66651e8	+	2.66388e8i	−0.176974	+	0.128579i
$460$	−3.48037e9			−1.66715
$461$	7.38296e8	−	2.27224e9i	0.350976	−	1.08019i	−0.607330	−	0.794450i	$-0.707759\pi$
$461$	7.38296e8	−	2.27224e9i	0.350976	−	1.08019i	0.958306	−	0.285743i	$-0.0922405\pi$
$462$	−2.06622e8	+	6.35916e8i	−0.0974830	+	0.300022i
$463$	−6.47817e8			−0.303332			−0.151666	−	0.988432i	$-0.548464\pi$
$463$	−6.47817e8			−0.303332			−0.151666	+	0.988432i	$0.548464\pi$
$464$	3.22563e6	−	2.34356e6i	0.00149900	−	0.00108909i
$465$	5.32077e9			2.45408
$466$	−6.31535e8	−	1.94366e9i	−0.289099	−	0.889755i
$467$	3.40938e9			1.54905			0.774527	−	0.632541i	$-0.217988\pi$
$467$	3.40938e9			1.54905			0.774527	+	0.632541i	$0.217988\pi$
$468$	9.42014e8	+	6.84413e8i	0.424812	+	0.308644i
$469$	−3.54033e8	−	2.57220e8i	−0.158467	−	0.115133i
$470$	4.50190e8	+	3.27082e8i	0.200011	+	0.145316i
$471$	−1.27603e9			−0.562715
$472$	3.89327e8	+	1.19822e9i	0.170419	+	0.524495i
$473$	−4.33610e8	+	1.33451e9i	−0.188402	+	0.579841i
$474$	2.84623e9			1.22757
$475$	5.77482e8	−	4.19565e8i	0.247236	−	0.179627i
$476$	−1.18283e9	+	8.59379e8i	−0.502689	+	0.365225i
$477$	−1.02556e8			−0.0432660
$478$	2.10100e8	+	6.46623e8i	0.0879892	+	0.270803i
$479$	−3.83373e9	−	2.78537e9i	−1.59385	−	1.15800i	−0.898169	−	0.439650i	$-0.855103\pi$
$479$	−3.83373e9	−	2.78537e9i	−1.59385	−	1.15800i	−0.695681	−	0.718350i	$-0.744897\pi$
$480$	−1.56955e9	+	4.83059e9i	−0.647786	+	1.99368i
$481$	7.94472e8	−	2.44513e9i	0.325515	−	1.00183i
$482$	4.76528e8	−	1.46660e9i	0.193831	−	0.596551i
$483$	3.94939e9	−	2.86940e9i	1.59483	−	1.15871i
$484$	3.53588e8	−	1.08823e9i	0.141755	−	0.436278i
$485$	4.01667e9	+	2.91829e9i	1.59871	+	1.16153i
$486$	−6.90368e8	−	2.12474e9i	−0.272806	−	0.839610i
$487$	−5.67192e8	+	1.74564e9i	−0.222525	+	0.684861i	0.776009	+	0.630722i	$0.217241\pi$
$487$	−5.67192e8	+	1.74564e9i	−0.222525	+	0.684861i	−0.998533	+	0.0541386i	$0.982759\pi$
$488$	−3.69907e8	+	2.68753e8i	−0.144086	+	0.104685i
$489$	4.77872e9	+	3.47194e9i	1.84812	+	1.34274i
$490$	−3.20180e8	−	9.85414e8i	−0.122944	−	0.378384i
$491$	1.17826e9	−	8.56053e8i	0.449215	−	0.326374i	−0.340071	−	0.940400i	$-0.610451\pi$
$491$	1.17826e9	−	8.56053e8i	0.449215	−	0.326374i	0.789286	+	0.614026i	$0.210451\pi$
$492$	1.73399e9	+	1.25981e9i	0.656398	+	0.476901i
$493$	−5.84362e7	+	4.24564e7i	−0.0219643	+	0.0159580i
$494$	1.13338e8	+	3.48819e8i	0.0422992	+	0.130183i
$495$	−5.24833e8	−	1.61527e9i	−0.194492	−	0.598586i
$496$	−2.88965e8			−0.106331
$497$	−1.45601e8	−	2.13982e9i	−0.0532008	−	0.781861i
$498$	4.25652e9			1.54437
$499$	1.20095e9	+	3.69613e9i	0.432685	+	1.33167i	0.895440	+	0.445182i	$0.146861\pi$
$499$	1.20095e9	+	3.69613e9i	0.432685	+	1.33167i	−0.462755	+	0.886486i	$0.653139\pi$
$500$	3.94680e8	+	1.21470e9i	0.141205	+	0.434584i
$501$	−2.93502e9	+	2.13242e9i	−1.04275	+	0.757601i
$502$	2.11874e9	+	1.53935e9i	0.747505	+	0.543094i
$503$	−1.49609e9	+	1.08698e9i	−0.524168	+	0.380831i	−0.818172	−	0.574974i	$-0.805012\pi$
$503$	−1.49609e9	+	1.08698e9i	−0.524168	+	0.380831i	0.294004	+	0.955804i	$0.405012\pi$
$504$	−6.32002e8	−	1.94510e9i	−0.219893	−	0.676761i
$505$	−8.07061e8	−	5.86364e8i	−0.278860	−	0.202604i
$506$	−1.26692e9	+	9.20470e8i	−0.434732	+	0.315851i
$507$	−8.17779e7	+	2.51687e8i	−0.0278682	+	0.0857694i
$508$	−6.44682e8	−	1.98413e9i	−0.218184	−	0.671501i
$509$	−3.30475e9	−	2.40104e9i	−1.11077	−	0.807025i	−0.127989	−	0.991776i	$-0.540852\pi$
$509$	−3.30475e9	−	2.40104e9i	−1.11077	−	0.807025i	−0.982785	+	0.184751i	$0.940852\pi$
$510$	−1.80633e9	+	5.55932e9i	−0.602979	+	1.85578i
$511$	−3.99978e8	+	2.90601e8i	−0.132606	+	0.0963438i
$512$	1.75896e8	−	5.41353e8i	0.0579178	−	0.178253i
$513$	−3.05008e7	+	9.38718e7i	−0.00997471	+	0.0306990i
$514$	−5.12388e8	+	1.57697e9i	−0.166429	+	0.512215i
$515$	2.53172e9	+	1.83940e9i	0.816752	+	0.593405i
$516$	−1.03185e9	−	3.17570e9i	−0.330629	−	1.01757i
$517$	−3.38939e8			−0.107871
$518$	−1.33396e9	+	9.69176e8i	−0.421684	+	0.306372i
$519$	−2.98659e8	+	2.16988e8i	−0.0937756	+	0.0681320i
$520$	−5.37574e9			−1.67659
$521$	−6.55833e8	+	2.01845e9i	−0.203171	+	0.625295i	0.796613	+	0.604490i	$0.206623\pi$
$521$	−6.55833e8	+	2.01845e9i	−0.203171	+	0.625295i	−0.999784	+	0.0208053i	$0.993377\pi$
$522$	−1.14006e7	−	3.50875e7i	−0.00350818	−	0.0107971i
$523$	1.10142e9			0.336664			0.168332	−	0.985730i	$-0.446162\pi$
$523$	1.10142e9			0.336664			0.168332	+	0.985730i	$0.446162\pi$
$524$	1.52604e9	+	1.10873e9i	0.463347	+	0.336641i
$525$	−4.33492e9	−	3.14951e9i	−1.30745	−	0.949915i
$526$	2.34442e9	+	1.70332e9i	0.702403	+	0.510325i
$527$	5.23495e9			1.55803
$528$	6.07314e7	+	1.86912e8i	0.0179554	+	0.0552610i
$529$	8.02843e9			2.35796
$530$	1.39865e8	−	1.01618e8i	0.0408078	−	0.0296486i
$531$	1.63899e9			0.475056
$532$	−9.83970e7	+	3.02835e8i	−0.0283329	+	0.0871997i
$533$	−1.14603e9	+	3.52713e9i	−0.327832	+	1.00896i
$534$	−1.02549e9			−0.291433
$535$	5.34456e9	−	3.88305e9i	1.50895	−	1.09631i
$536$	−9.14889e8			−0.256621
$537$	−1.59285e9	−	4.90228e9i	−0.443879	−	1.36612i
$538$	−2.54933e9			−0.705811
$539$	5.10567e8	+	3.70949e8i	0.140440	+	0.102036i
$540$	−4.27349e8	−	3.10487e8i	−0.116790	−	0.0848527i
$541$	4.88463e8	+	3.54889e8i	0.132630	+	0.0963612i	0.652122	−	0.758114i	$-0.273879\pi$
$541$	4.88463e8	+	3.54889e8i	0.132630	+	0.0963612i	−0.519492	+	0.854475i	$0.673879\pi$
$542$	−2.07329e9			−0.559323
$543$	−1.92780e9	−	5.93315e9i	−0.516728	−	1.59033i
$544$	−1.54424e9	+	4.75267e9i	−0.411261	+	1.26573i
$545$	−6.99086e9			−1.84988
$546$	2.22738e9	−	1.61829e9i	0.585626	−	0.425482i
$547$	−1.15889e9	+	8.41982e8i	−0.302752	+	0.219962i	−0.728780	−	0.684748i	$-0.759912\pi$
$547$	−1.15889e9	+	8.41982e8i	−0.302752	+	0.219962i	0.426029	+	0.904710i	$0.359912\pi$
$548$	−1.03645e9			−0.269040
$549$	1.83807e8	+	5.65698e8i	0.0474087	+	0.145909i
$550$	1.39059e9	+	1.01032e9i	0.356394	+	0.258935i
$551$	−4.86116e6	+	1.49611e7i	−0.00123797	+	0.00381007i
$552$	3.15383e9	−	9.70648e9i	0.798088	−	2.45626i
$553$	−1.32125e9	+	4.06639e9i	−0.332236	+	1.02252i
$554$	1.69179e9	−	1.22916e9i	0.422730	−	0.307131i
$555$	2.75761e9	−	8.48707e9i	0.684712	−	2.10733i
$556$	−2.34208e9	−	1.70162e9i	−0.577882	−	0.419856i
$557$	1.66321e9	+	5.11883e9i	0.407806	+	1.25510i	0.918529	+	0.395353i	$0.129378\pi$
$557$	1.66321e9	+	5.11883e9i	0.407806	+	1.25510i	−0.510723	+	0.859745i	$0.670622\pi$
$558$	−8.26259e8	+	2.54296e9i	−0.201324	+	0.619613i
$559$	4.67431e9	−	3.39609e9i	1.13182	−	0.822313i
$560$	3.92138e8	+	2.84905e8i	0.0943585	+	0.0685554i
$561$	−1.10022e9	−	3.38614e9i	−0.263094	−	0.809719i
$562$	2.90330e9	−	2.10937e9i	0.689947	−	0.501276i
$563$	2.02657e9	+	1.47239e9i	0.478611	+	0.347731i	0.800788	−	0.598948i	$-0.204415\pi$
$563$	2.02657e9	+	1.47239e9i	0.478611	+	0.347731i	−0.322177	+	0.946680i	$0.604415\pi$
$564$	6.52522e8	−	4.74085e8i	0.153150	−	0.111270i
$565$	3.06237e9	+	9.42500e9i	0.714312	+	2.19843i
$566$	−1.12618e9	−	3.46601e9i	−0.261065	−	0.803476i
$567$	3.74926e9			0.863783
$568$	−2.87580e9	−	3.44031e9i	−0.658475	−	0.787733i
$569$	8.74301e9			1.98961			0.994805	−	0.101802i	$-0.0324608\pi$
$569$	8.74301e9			1.98961			0.994805	+	0.101802i	$0.0324608\pi$
$570$	3.93397e8	+	1.21075e9i	0.0889753	+	0.273838i
$571$	2.20941e9	+	6.79988e9i	0.496650	+	1.52853i	0.814369	+	0.580347i	$0.197083\pi$
$571$	2.20941e9	+	6.79988e9i	0.496650	+	1.52853i	−0.317719	+	0.948185i	$0.602917\pi$
$572$	9.67232e8	−	7.02735e8i	0.216095	−	0.157002i
$573$	−9.39591e9	−	6.82653e9i	−2.08640	−	1.51586i
$574$	1.92425e9	−	1.39805e9i	0.424687	−	0.308553i
$575$	−3.87796e9	−	1.19351e10i	−0.850680	−	2.61812i
$576$	−2.37371e9	−	1.72460e9i	−0.517546	−	0.376019i
$577$	−6.61540e8	+	4.80637e8i	−0.143364	+	0.104160i	−0.657156	−	0.753755i	$-0.728241\pi$
$577$	−6.61540e8	+	4.80637e8i	−0.143364	+	0.104160i	0.513791	+	0.857915i	$0.328241\pi$
$578$	−8.42101e8	+	2.59172e9i	−0.181391	+	0.558265i
$579$	−7.20104e8	−	2.21625e9i	−0.154177	−	0.474508i
$580$	−6.81101e7	−	4.94849e7i	−0.0144948	−	0.0105311i
$581$	−1.97592e9	+	6.08127e9i	−0.417978	+	1.28640i
$582$	−4.30079e9	+	3.12470e9i	−0.904310	+	0.657020i
$583$	−3.25399e7	+	1.00148e8i	−0.00680106	+	0.0209315i
$584$	−3.19406e8	+	9.83031e8i	−0.0663587	+	0.204231i
$585$	−2.16105e9	+	6.65102e9i	−0.446292	+	1.37354i
$586$	−3.27986e9	−	2.38296e9i	−0.673309	−	0.489187i
$587$	2.99107e9	+	9.20557e9i	0.610370	+	1.87853i	0.454493	+	0.890750i	$0.349820\pi$
$587$	2.99107e9	+	9.20557e9i	0.610370	+	1.87853i	0.155877	+	0.987776i	$0.450180\pi$
$588$	−1.50180e9			−0.304643
$589$	9.22366e8	−	6.70138e8i	0.185994	−	0.135133i
$590$	−2.23524e9	+	1.62399e9i	−0.448066	+	0.325539i
$591$	−1.02309e10			−2.03871
$592$	−1.49763e8	+	4.60923e8i	−0.0296673	+	0.0913066i
$593$	−8.05254e8	−	2.47832e9i	−0.158577	−	0.488051i	0.839928	−	0.542697i	$-0.182597\pi$
$593$	−8.05254e8	−	2.47832e9i	−0.158577	−	0.488051i	−0.998506	+	0.0546462i	$0.982597\pi$
$594$	−2.37678e8			−0.0465305
$595$	−7.10405e9	−	5.16139e9i	−1.38260	−	1.00452i
$596$	4.36858e9	+	3.17396e9i	0.845238	+	0.614101i
$597$	9.58507e8	+	6.96396e8i	0.184368	+	0.133951i
$598$	6.44814e9			1.23305
$599$	1.19076e9	+	3.66478e9i	0.226376	+	0.696714i	0.998149	+	0.0608157i	$0.0193702\pi$
$599$	1.19076e9	+	3.66478e9i	0.226376	+	0.696714i	−0.771773	+	0.635898i	$0.780630\pi$
$600$	−1.12023e10			−2.11727
$601$	−2.41320e9	+	1.75329e9i	−0.453454	+	0.329453i	−0.790958	−	0.611871i	$-0.790417\pi$
$601$	−2.41320e9	+	1.75329e9i	−0.453454	+	0.329453i	0.337504	+	0.941324i	$0.390417\pi$
$602$	−3.70551e9			−0.692246
$603$	−3.67785e8	+	1.13193e9i	−0.0683100	+	0.210236i
$604$	1.49593e9	−	4.60399e9i	0.276237	−	0.850169i
$605$	6.87223e9			1.26169
$606$	8.64147e8	−	6.27840e8i	0.157737	−	0.114603i
$607$	3.96435e9			0.719467			0.359734	−	0.933055i	$-0.382868\pi$
$607$	3.96435e9			0.719467			0.359734	+	0.933055i	$0.382868\pi$
$608$	3.36316e8	+	1.03507e9i	0.0606854	+	0.186771i
$609$	1.18087e8			0.0211856
$610$	−8.11197e8	−	5.89369e8i	−0.144701	−	0.105132i
$611$	1.12907e9	+	8.20320e8i	0.200252	+	0.145492i
$612$	3.21699e9	+	2.33728e9i	0.567310	+	0.412175i
$613$	−6.78984e9			−1.19055			−0.595276	−	0.803522i	$-0.702957\pi$
$613$	−6.78984e9			−1.19055			−0.595276	+	0.803522i	$0.702957\pi$
$614$	−1.13101e9	−	3.48090e9i	−0.197187	−	0.606880i
$615$	−3.97789e9	+	1.22427e10i	−0.689588	+	2.12233i
$616$	−2.09995e9			−0.361973
$617$	−7.60465e9	+	5.52510e9i	−1.30341	+	0.946983i	−0.999983	−	0.00587209i	$-0.998131\pi$
$617$	−7.60465e9	+	5.52510e9i	−1.30341	+	0.946983i	−0.303427	+	0.952855i	$0.598131\pi$
$618$	−2.71079e9	+	1.96951e9i	−0.461994	+	0.335659i
$619$	−1.05887e10			−1.79443			−0.897213	−	0.441598i	$-0.854412\pi$
$619$	−1.05887e10			−1.79443			−0.897213	+	0.441598i	$0.854412\pi$
$620$	1.88549e9	+	5.80294e9i	0.317727	+	0.977862i
$621$	1.40387e9	+	1.01997e9i	0.235237	+	0.170910i
$622$	1.69820e9	−	5.22652e9i	0.282958	−	0.870855i
$623$	4.76046e8	−	1.46512e9i	0.0788752	−	0.242753i
$624$	2.50067e8	−	7.69628e8i	0.0412013	−	0.126805i
$625$	1.21208e9	−	8.80627e8i	0.198587	−	0.144282i
$626$	3.01630e8	−	9.28321e8i	0.0491433	−	0.151247i
$627$	−6.27320e8	−	4.55775e8i	−0.101637	−	0.0738438i
$628$	−4.52180e8	−	1.39167e9i	−0.0728538	−	0.224221i
$629$	2.71313e9	−	8.35017e9i	0.434704	−	1.33788i
$630$	3.62850e9	−	2.63626e9i	0.578143	−	0.420046i
$631$	−5.43426e9	−	3.94822e9i	−0.861069	−	0.625603i	0.0671066	−	0.997746i	$-0.478623\pi$
$631$	−5.43426e9	−	3.94822e9i	−0.861069	−	0.625603i	−0.928176	+	0.372143i	$0.878623\pi$
$632$	2.76228e9	+	8.50143e9i	0.435269	+	1.33962i
$633$	−3.27586e9	+	2.38005e9i	−0.513349	+	0.372970i
$634$	1.54814e9	+	1.12479e9i	0.241267	+	0.175291i
$635$	1.01368e10	−	7.36485e9i	1.57107	−	1.14145i
$636$	−7.74342e7	−	2.38318e8i	−0.0119353	−	0.0367330i
$637$	−8.03010e8	−	2.47141e9i	−0.123093	−	0.378841i
$638$	−3.78808e7			−0.00577492
$639$	−5.41253e9	+	2.17501e9i	−0.820629	+	0.329768i
$640$	−5.18118e9			−0.781266
$641$	3.80447e9	+	1.17089e10i	0.570546	+	1.75596i	0.650868	+	0.759191i	$0.274405\pi$
$641$	3.80447e9	+	1.17089e10i	0.570546	+	1.75596i	−0.0803227	+	0.996769i	$0.525595\pi$
$642$	2.18584e9	+	6.72731e9i	0.326021	+	1.00339i
$643$	−1.62847e9	+	1.18315e9i	−0.241569	+	0.175510i	−0.701982	−	0.712195i	$-0.747701\pi$
$643$	−1.62847e9	+	1.18315e9i	−0.241569	+	0.175510i	0.460413	+	0.887705i	$0.347701\pi$
$644$	4.52895e9	+	3.29048e9i	0.668186	+	0.485465i
$645$	1.62246e10	−	1.17878e10i	2.38075	−	1.72972i
$646$	3.87052e8	+	1.19122e9i	0.0564878	+	0.173852i
$647$	−2.59374e9	−	1.88446e9i	−0.376496	−	0.273541i	0.383403	−	0.923581i	$-0.374752\pi$
$647$	−2.59374e9	−	1.88446e9i	−0.376496	−	0.273541i	−0.759900	+	0.650040i	$0.774752\pi$
$648$	6.34141e9	−	4.60730e9i	0.915531	−	0.665172i
$649$	5.20033e8	−	1.60050e9i	0.0746749	−	0.229826i
$650$	−2.18710e9	−	6.73119e9i	−0.312371	−	0.961380i
$651$	−6.92383e9	−	5.03046e9i	−0.983587	−	0.714618i
$652$	−2.09317e9	+	6.44210e9i	−0.295758	+	0.910251i
$653$	5.00667e9	−	3.63756e9i	0.703644	−	0.511227i	−0.177473	−	0.984126i	$-0.556792\pi$
$653$	5.00667e9	−	3.63756e9i	0.703644	−	0.511227i	0.881117	+	0.472899i	$0.156792\pi$
$654$	2.31310e9	−	7.11898e9i	0.323349	−	0.995167i
$655$	−3.50085e9	+	1.07745e10i	−0.486775	+	1.49814i
$656$	2.16034e8	−	6.64886e8i	0.0298786	−	0.0919567i
$657$	1.08783e9	+	7.90357e8i	0.149652	+	0.108729i
$658$	−2.76589e8	−	8.51253e8i	−0.0378481	−	0.116485i
$659$	−2.54641e8			−0.0346601			−0.0173300	−	0.999850i	$-0.505517\pi$
$659$	−2.54641e8			−0.0346601			−0.0173300	+	0.999850i	$0.505517\pi$
$660$	3.35727e9	−	2.43920e9i	0.454550	−	0.330250i
$661$	−7.40766e9	+	5.38198e9i	−0.997644	+	0.724831i	−0.961582	−	0.274519i	$-0.911482\pi$
$661$	−7.40766e9	+	5.38198e9i	−0.997644	+	0.724831i	−0.0360625	+	0.999350i	$0.511482\pi$
$662$	−5.46343e9			−0.731918
$663$	−4.53027e9	+	1.39427e10i	−0.603707	+	1.85802i
$664$	4.13098e9	+	1.27138e10i	0.547601	+	1.68534i
$665$	−1.91241e9			−0.252177
$666$	3.62801e9	+	2.63590e9i	0.475892	+	0.345756i
$667$	2.23746e8	+	1.62561e8i	0.0291955	+	0.0212117i
$668$	−3.36573e9	−	2.44534e9i	−0.436879	−	0.317411i
$669$	1.40373e10			1.81255
$670$	−6.19990e8	−	1.90813e9i	−0.0796385	−	0.245102i
$671$	6.10733e8			0.0780410
$672$	6.60945e9	−	4.80205e9i	0.840181	−	0.610427i
$673$	1.10848e9			0.140176			0.0700881	−	0.997541i	$-0.477672\pi$
$673$	1.10848e9			0.140176			0.0700881	+	0.997541i	$0.477672\pi$
$674$	2.28042e8	−	7.01840e8i	0.0286883	−	0.0882935i
$675$	5.88576e8	−	1.81145e9i	0.0736613	−	0.226706i
$676$	−3.03474e8			−0.0377840
$677$	9.38719e8	−	6.82019e8i	0.116272	−	0.0844766i	−0.528130	−	0.849164i	$-0.677106\pi$
$677$	9.38719e8	−	6.82019e8i	0.116272	−	0.0844766i	0.644402	+	0.764687i	$0.277106\pi$
$678$	−1.06110e10			−1.30753
$679$	−2.46777e9	−	7.59503e9i	−0.302525	−	0.931076i
$680$	−1.83582e10			−2.23898
$681$	1.25849e10	+	9.14349e9i	1.52699	+	1.10942i
$682$	2.22108e9	+	1.61371e9i	0.268114	+	0.194796i
$683$	−2.37289e9	−	1.72401e9i	−0.284974	−	0.207046i	0.436110	−	0.899893i	$-0.356356\pi$
$683$	−2.37289e9	−	1.72401e9i	−0.284974	−	0.207046i	−0.721084	+	0.692848i	$0.756356\pi$
$684$	8.66016e8			0.103474
$685$	−1.92359e9	−	5.92021e9i	−0.228663	−	0.703752i
$686$	−1.84967e9	+	5.69271e9i	−0.218757	+	0.673263i
$687$	−3.94802e9			−0.464549
$688$	−8.81137e8	+	6.40184e8i	−0.103154	+	0.0749454i
$689$	3.50780e8	−	2.54857e8i	0.0408571	−	0.0296844i
$690$	2.23815e10			2.59369
$691$	−3.99951e9	−	1.23092e10i	−0.461141	−	1.41925i	−0.863772	−	0.503883i	$-0.831904\pi$
$691$	−3.99951e9	−	1.23092e10i	−0.461141	−	1.41925i	0.402631	−	0.915362i	$-0.368096\pi$
$692$	−3.42486e8	−	2.48831e8i	−0.0392891	−	0.0285452i
$693$	−8.44180e8	+	2.59812e9i	−0.0963538	+	0.296546i
$694$	1.32113e8	−	4.06602e8i	0.0150033	−	0.0461754i
$695$	5.37289e9	−	1.65361e10i	0.607102	−	1.86847i
$696$	1.99729e8	−	1.45112e8i	0.0224548	−	0.0163143i
$697$	−3.91372e9	+	1.20452e10i	−0.437799	+	1.34741i
$698$	8.02787e9	+	5.83259e9i	0.893524	+	0.649183i
$699$	−5.49767e9	−	1.69201e10i	−0.608847	−	1.87384i
$700$	1.89878e9	−	5.84383e9i	0.209233	−	0.643953i
$701$	1.75379e9	−	1.27420e9i	0.192293	−	0.139709i	−0.487473	−	0.873138i	$-0.662081\pi$
$701$	1.75379e9	−	1.27420e9i	0.192293	−	0.139709i	0.679766	+	0.733429i	$0.262081\pi$
$702$	7.91755e8	+	5.75244e8i	0.0863796	+	0.0627584i
$703$	−5.90887e8	−	1.81856e9i	−0.0641447	−	0.197417i
$704$	−2.43725e9	+	1.77077e9i	−0.263267	+	0.191275i
$705$	3.91902e9	+	2.84733e9i	0.421226	+	0.306039i
$706$	−2.50190e9	+	1.81773e9i	−0.267579	+	0.194408i
$707$	4.95844e8	+	1.52605e9i	0.0527688	+	0.162406i
$708$	1.23751e9	+	3.80865e9i	0.131048	+	0.403325i
$709$	4.41014e9			0.464719			0.232360	−	0.972630i	$-0.425355\pi$
$709$	4.41014e9			0.464719			0.232360	+	0.972630i	$0.425355\pi$
$710$	5.22644e9	−	8.32928e9i	0.548027	−	0.873380i
$711$	1.16287e10			1.21335
$712$	−9.95248e8	−	3.06306e9i	−0.103336	−	0.318035i
$713$	−6.19396e9	−	1.90631e10i	−0.639963	−	1.96960i
$714$	7.60654e9	−	5.52647e9i	0.782066	−	0.568204i
$715$	5.80915e9	+	4.22060e9i	0.594349	+	0.431820i
$716$	4.78208e9	−	3.47439e9i	0.486880	−	0.353739i
$717$	1.82898e9	+	5.62901e9i	0.185307	+	0.570316i
$718$	−9.44264e6	−	6.86048e6i	−0.000952046	−	0.000691702i
$719$	−3.83834e9	+	2.78872e9i	−0.385117	+	0.279804i	−0.763452	−	0.645865i	$-0.776497\pi$
$719$	−3.83834e9	+	2.78872e9i	−0.385117	+	0.279804i	0.378335	+	0.925669i	$0.376497\pi$
$720$	4.07371e8	−	1.25376e9i	0.0406749	−	0.125184i
$721$	−1.55544e9	−	4.78716e9i	−0.154554	−	0.475669i
$722$	−5.11221e9	−	3.71424e9i	−0.505509	−	0.367274i
$723$	4.14829e9	−	1.27671e10i	0.408212	−	1.25635i
$724$	5.78767e9	−	4.20499e9i	0.566786	−	0.411794i
$725$	9.38062e7	−	2.88706e8i	0.00914215	−	0.0281367i
$726$	−2.27385e9	+	6.99818e9i	−0.220538	+	0.678746i
$727$	−1.88450e9	+	5.79990e9i	−0.181897	+	0.559822i	−0.999881	−	0.0154192i	$-0.995092\pi$
$727$	−1.88450e9	+	5.79990e9i	−0.181897	+	0.559822i	0.817984	+	0.575241i	$0.195092\pi$
$728$	6.99536e9	+	5.08243e9i	0.671970	+	0.488215i
$729$	−2.44695e9	−	7.53094e9i	−0.233926	−	0.719951i
$730$	−2.26670e9			−0.215658
$731$	1.59628e10	−	1.15977e10i	1.51147	−	1.09815i
$732$	−1.17578e9	+	8.54253e8i	−0.110799	+	0.0805003i
$733$	−9.21433e9			−0.864172			−0.432086	−	0.901833i	$-0.642222\pi$
$733$	−9.21433e9			−0.864172			−0.432086	+	0.901833i	$0.642222\pi$
$734$	1.93795e9	−	5.96441e9i	0.180887	−	0.556713i
$735$	−2.78725e9	−	8.57827e9i	−0.258923	−	0.796882i
$736$	1.91340e10			1.76902
$737$	9.88651e8	+	7.18297e8i	0.0909718	+	0.0660949i
$738$	−5.23343e9	−	3.80231e9i	−0.479280	−	0.348217i
$739$	−6.11360e9	−	4.44179e9i	−0.557239	−	0.404858i	0.273208	−	0.961955i	$-0.411915\pi$
$739$	−6.11360e9	−	4.44179e9i	−0.557239	−	0.404858i	−0.830447	+	0.557097i	$0.811915\pi$
$740$	1.02334e10			0.928341
$741$	9.86637e8	+	3.03656e9i	0.0890828	+	0.274169i
$742$	−2.78077e8			−0.0249892
$743$	−1.34463e10	+	9.76929e9i	−1.20266	+	0.873780i	−0.994543	−	0.104325i	$-0.966732\pi$
$743$	−1.34463e10	+	9.76929e9i	−1.20266	+	0.873780i	−0.208112	+	0.978105i	$0.566732\pi$
$744$	−1.78925e10			−1.59282
$745$	−1.00218e10	+	3.08441e10i	−0.887975	+	2.73291i
$746$	−4.76963e8	+	1.46794e9i	−0.0420629	+	0.129456i
$747$	1.73906e10			1.52648
$748$	3.30311e9	−	2.39985e9i	0.288581	−	0.209666i
$749$	−1.06260e10			−0.924021
$750$	−2.53810e9	−	7.81147e9i	−0.219682	−	0.676111i
$751$	1.42609e8			0.0122859			0.00614294	−	0.999981i	$-0.498045\pi$
$751$	1.42609e8			0.0122859			0.00614294	+	0.999981i	$0.498045\pi$
$752$	−2.12837e8	−	1.54635e8i	−0.0182510	−	0.0132601i
$753$	1.84441e10	+	1.34004e10i	1.57426	+	1.14377i
$754$	1.26188e8	+	9.16813e7i	0.0107206	+	0.00778899i
$755$	2.90744e10			2.45865
$756$	2.62556e8	+	8.08063e8i	0.0221001	+	0.0680173i
$757$	−6.34977e9	+	1.95426e10i	−0.532013	+	1.63737i	0.218003	+	0.975948i	$0.430046\pi$
$757$	−6.34977e9	+	1.95426e10i	−0.532013	+	1.63737i	−0.750016	+	0.661420i	$0.769954\pi$
$758$	−7.34068e9			−0.612201
$759$	−1.10288e10	+	8.01292e9i	−0.915553	+	0.665188i
$760$	−3.23461e9	+	2.35008e9i	−0.267285	+	0.194194i
$761$	5.17686e8			0.0425814			0.0212907	−	0.999773i	$-0.493222\pi$
$761$	5.17686e8			0.0425814			0.0212907	+	0.999773i	$0.493222\pi$
$762$	4.14580e9	+	1.27595e10i	0.339443	+	1.04470i
$763$	9.09708e9	+	6.60942e9i	0.741423	+	0.538676i
$764$	4.11558e9	−	1.26664e10i	0.333891	−	1.02761i
$765$	−7.38001e9	+	2.27133e10i	−0.595994	+	1.83428i
$766$	8.22845e8	−	2.53246e9i	0.0661481	−	0.203583i
$767$	−5.60596e9	+	4.07297e9i	−0.448607	+	0.325932i
$768$	5.56620e9	−	1.71310e10i	0.443399	−	1.36464i
$769$	−1.09439e10	−	7.95123e9i	−0.867823	−	0.630510i	0.0621792	−	0.998065i	$-0.480195\pi$
$769$	−1.09439e10	−	7.95123e9i	−0.867823	−	0.630510i	−0.930002	+	0.367555i	$0.880195\pi$
$770$	−1.42307e9	−	4.37975e9i	−0.112333	−	0.345726i
$771$	−4.46047e9	+	1.37279e10i	−0.350502	+	1.07873i
$772$	2.16191e9	−	1.57072e9i	0.169113	−	0.122868i
$773$	−1.17608e9	−	8.54471e8i	−0.0915815	−	0.0665379i	0.541052	−	0.840989i	$-0.318026\pi$
$773$	−1.17608e9	−	8.54471e8i	−0.0915815	−	0.0665379i	−0.632634	+	0.774451i	$0.718026\pi$
$774$	3.11427e9	+	9.58475e9i	0.241415	+	0.742998i
$775$	−1.77990e10	+	1.29317e10i	−1.37353	+	0.997930i
$776$	−1.35071e10	−	9.81351e9i	−1.03764	−	0.753891i
$777$	−1.16124e10	+	8.43692e9i	−0.888074	+	0.645224i
$778$	4.31167e9	+	1.32700e10i	0.328259	+	1.01028i
$779$	8.52361e8	+	2.62330e9i	0.0646015	+	0.198823i
$780$	−1.70872e10			−1.28926
$781$	4.06598e8	+	5.97553e9i	0.0305412	+	0.448846i
$782$	2.20205e10			1.64666
$783$	1.29712e7	+	3.99212e7i	0.000965635	+	0.00297192i
$784$	1.51372e8	+	4.65876e8i	0.0112186	+	0.0345274i
$785$	7.10998e9	−	5.16570e9i	0.524596	−	0.381141i
$786$	−9.81362e9	−	7.13002e9i	−0.720859	−	0.523735i
$787$	−4.61983e8	+	3.35650e8i	−0.0337842	+	0.0245457i	−0.604549	−	0.796568i	$-0.706647\pi$
$787$	−4.61983e8	+	3.35650e8i	−0.0337842	+	0.0245457i	0.570765	+	0.821113i	$0.306647\pi$
$788$	−3.62545e9	−	1.11580e10i	−0.263949	−	0.812352i
$789$	2.04088e10	+	1.48279e10i	1.47927	+	1.07475i
$790$	−1.58591e10	+	1.15223e10i	−1.14441	+	0.831464i
$791$	4.92574e9	−	1.51599e10i	0.353878	−	1.08912i
$792$	1.76489e9	+	5.43177e9i	0.126235	+	0.388511i
$793$	−2.03448e9	−	1.47813e9i	−0.144876	−	0.105259i
$794$	2.59665e9	−	7.99167e9i	0.184095	−	0.566586i
$795$	1.21756e9	−	8.84609e8i	0.0859420	−	0.0624405i
$796$	−4.19843e8	+	1.29214e9i	−0.0295047	+	0.0908062i
$797$	3.67600e8	−	1.13136e9i	0.0257200	−	0.0791582i	−0.937373	−	0.348328i	$-0.886749\pi$
$797$	3.67600e8	−	1.13136e9i	0.0257200	−	0.0791582i	0.963093	+	0.269170i	$0.0867494\pi$
$798$	6.32769e8	−	1.94746e9i	0.0440794	−	0.135662i
$799$	3.85580e9	+	2.80141e9i	0.267424	+	0.194295i
$800$	−6.48991e9	−	1.99739e10i	−0.448150	−	1.37926i
$801$	−4.18980e9			−0.288057
$802$	6.41726e9	−	4.66242e9i	0.439278	−	0.319154i
$803$	1.11695e9	−	8.11514e8i	0.0761256	−	0.0553085i
$804$	−2.90805e9			−0.197336
$805$	−1.03897e10	+	3.19763e10i	−0.701971	+	2.16044i
$806$	−3.49327e9	−	1.07512e10i	−0.234996	−	0.723242i
$807$	−2.21926e10			−1.48645
$808$	2.71396e9	+	1.97181e9i	0.180994	+	0.131500i
$809$	6.69166e9	+	4.86178e9i	0.444339	+	0.322831i	0.787357	−	0.616498i	$-0.211449\pi$
$809$	6.69166e9	+	4.86178e9i	0.444339	+	0.322831i	−0.343018	+	0.939329i	$0.611449\pi$
$810$	1.39066e10	+	1.01037e10i	0.919437	+	0.668010i
$811$	8.08135e9			0.531999			0.265999	−	0.963973i	$-0.414298\pi$
$811$	8.08135e9			0.531999			0.265999	+	0.963973i	$0.414298\pi$
$812$	4.18456e7	+	1.28788e8i	0.00274286	+	0.00844167i
$813$	−1.80485e10			−1.17794
$814$	3.72513e9	−	2.70646e9i	0.242078	−	0.175880i
$815$	−4.06821e10			−2.63240
$816$	8.53984e8	−	2.62829e9i	0.0550217	−	0.169339i
$817$	1.32791e9	−	4.08689e9i	0.0851906	−	0.262190i
$818$	−3.44995e9			−0.220382
$819$	9.10026e9	−	6.61172e9i	0.578842	−	0.420553i
$820$	−1.47617e10			−0.934951
$821$	−4.49079e9	−	1.38212e10i	−0.283219	−	0.871657i	−0.986927	−	0.161168i	$-0.948474\pi$
$821$	−4.49079e9	−	1.38212e10i	−0.283219	−	0.871657i	0.703708	−	0.710489i	$-0.251526\pi$
$822$	6.66518e9			0.418562
$823$	−2.07920e10	−	1.51063e10i	−1.30016	−	0.944623i	−0.300205	−	0.953875i	$-0.597055\pi$
$823$	−2.07920e10	−	1.51063e10i	−1.30016	−	0.944623i	−0.999957	+	0.00925121i	$0.997055\pi$
$824$	−8.51358e9	−	6.18548e9i	−0.530111	−	0.385148i
$825$	1.21055e10	+	8.79512e9i	0.750572	+	0.545322i
$826$	4.44406e9			0.274378
$827$	8.23387e9	+	2.53412e10i	0.506215	+	1.55797i	0.798719	+	0.601704i	$0.205511\pi$
$827$	8.23387e9	+	2.53412e10i	0.506215	+	1.55797i	−0.292505	+	0.956264i	$0.594489\pi$
$828$	4.70488e9	−	1.44801e10i	0.288033	−	0.886475i
$829$	4.35004e9			0.265187			0.132593	−	0.991171i	$-0.457670\pi$
$829$	4.35004e9			0.265187			0.132593	+	0.991171i	$0.457670\pi$
$830$	−2.37171e10	+	1.72315e10i	−1.43976	+	1.04604i
$831$	1.47275e10	−	1.07001e10i	0.890276	−	0.646823i
$832$	1.24047e10			0.746714
$833$	−2.74229e9	−	8.43990e9i	−0.164383	−	0.505918i
$834$	1.50614e10	+	1.09427e10i	0.899049	+	0.653197i
$835$	7.72122e9	−	2.37635e10i	0.458969	−	1.41256i
$836$	2.74778e8	−	8.45679e8i	0.0162652	−	0.0500591i
$837$	9.40086e8	−	2.89329e9i	0.0554151	−	0.170550i
$838$	−3.97220e9	+	2.88597e9i	−0.233172	+	0.169410i
$839$	1.80997e9	−	5.57053e9i	0.105805	−	0.325634i	−0.884114	−	0.467272i	$-0.845237\pi$
$839$	1.80997e9	−	5.57053e9i	0.105805	−	0.325634i	0.989919	+	0.141638i	$0.0452369\pi$
$840$	2.42809e10	+	1.76411e10i	1.41347	+	1.02695i
$841$	−5.32844e9	−	1.63992e10i	−0.308897	−	0.950688i
$842$	−3.10008e9	+	9.54107e9i	−0.178970	+	0.550814i
$843$	2.52740e10	−	1.83626e10i	1.45304	−	1.05569i
$844$	−3.75658e9	−	2.72932e9i	−0.215077	−	0.156263i
$845$	−5.63230e8	−	1.73344e9i	−0.0321135	−	0.0988351i
$846$	−1.96941e9	+	1.43086e9i	−0.111825	+	0.0812459i
$847$	−8.94272e9	−	6.49726e9i	−0.505682	−	0.367400i
$848$	−6.61243e7	+	4.80421e7i	−0.00372371	+	0.00270543i
$849$	−9.80365e9	−	3.01725e10i	−0.549808	−	1.69213i
$850$	−7.46896e9	−	2.29871e10i	−0.417152	−	1.28386i
$851$	−3.36173e10			−1.86986
$852$	−9.14095e9	−	1.09353e10i	−0.506352	−	0.605749i
$853$	1.48484e10			0.819141			0.409571	−	0.912278i	$-0.365679\pi$
$853$	1.48484e10			0.819141			0.409571	+	0.912278i	$0.365679\pi$
$854$	4.98385e8	+	1.53387e9i	0.0273818	+	0.0842726i
$855$	1.60728e9	+	4.94669e9i	0.0879446	+	0.270666i
$856$	−1.79725e10	+	1.30578e10i	−0.979378	+	0.711560i
$857$	−2.24637e10	−	1.63209e10i	−1.21913	−	0.885748i	−0.223100	−	0.974796i	$-0.571618\pi$
$857$	−2.24637e10	−	1.63209e10i	−1.21913	−	0.885748i	−0.996027	+	0.0890480i	$0.971618\pi$
$858$	−6.22005e9	+	4.51913e9i	−0.336193	+	0.244258i
$859$	−4.83715e9	−	1.48872e10i	−0.260384	−	0.801379i	−0.992721	−	0.120437i	$-0.961571\pi$
$859$	−4.83715e9	−	1.48872e10i	−0.260384	−	0.801379i	0.732337	−	0.680942i	$-0.238429\pi$
$860$	1.86055e10	+	1.35177e10i	0.997460	+	0.724697i
$861$	1.67510e10	−	1.21703e10i	0.894398	−	0.649818i
$862$	−2.18062e8	+	6.71125e8i	−0.0115959	+	0.0356885i
$863$	8.60547e9	+	2.64849e10i	0.455760	+	1.40269i	0.870240	+	0.492628i	$0.163964\pi$
$863$	8.60547e9	+	2.64849e10i	0.455760	+	1.40269i	−0.414480	+	0.910059i	$0.636036\pi$
$864$	2.34943e9	+	1.70696e9i	0.123926	+	0.0900378i
$865$	7.85688e8	−	2.41810e9i	0.0412756	−	0.127033i
$866$	−3.94601e9	+	2.86695e9i	−0.206465	+	0.150005i
$867$	−7.33070e9	+	2.25616e10i	−0.382013	+	1.17572i
$868$	3.03276e9	−	9.33388e9i	0.157405	−	0.484444i
$869$	3.68965e9	−	1.13556e10i	0.190728	−	0.587002i
$870$	4.38001e8	+	3.18226e8i	0.0225506	+	0.0163839i
$871$	−1.55493e9	−	4.78558e9i	−0.0797347	−	0.245398i
$872$	2.35086e10			1.20066
$873$	−1.75714e10	+	1.27664e10i	−0.893835	+	0.649409i
$874$	3.87988e9	−	2.81890e9i	0.196575	−	0.142820i
$875$	1.23384e10			0.622631
$876$	−1.01526e9	+	3.12464e9i	−0.0510284	+	0.157049i
$877$	6.13870e9	+	1.88930e10i	0.307311	+	0.945805i	0.978805	+	0.204795i	$0.0656528\pi$
$877$	6.13870e9	+	1.88930e10i	0.307311	+	0.945805i	−0.671494	+	0.741010i	$0.734347\pi$
$878$	1.50237e10			0.749112
$879$	−2.85520e10	−	2.07443e10i	−1.41800	−	1.03024i
$880$	−1.09506e9	−	7.95609e8i	−0.0541688	−	0.0393559i
$881$	1.54074e9	+	1.11941e9i	0.0759125	+	0.0551536i	0.625094	−	0.780549i	$-0.285061\pi$
$881$	1.54074e9	+	1.11941e9i	0.0759125	+	0.0551536i	−0.549182	+	0.835703i	$0.685061\pi$
$882$	4.53266e9			0.222440
$883$	−5.19104e9	−	1.59764e10i	−0.253742	−	0.780937i	−0.994075	−	0.108697i	$-0.965332\pi$
$883$	−5.19104e9	−	1.59764e10i	−0.253742	−	0.780937i	0.740333	−	0.672240i	$-0.234668\pi$
$884$	−1.68116e10			−0.818514
$885$	−1.94583e10	+	1.41373e10i	−0.943634	+	0.685590i
$886$	4.43117e9			0.214042
$887$	3.36488e9	−	1.03560e10i	0.161896	−	0.498266i	−0.836898	−	0.547359i	$-0.815633\pi$
$887$	3.36488e9	−	1.03560e10i	0.161896	−	0.498266i	0.998794	+	0.0490932i	$0.0156331\pi$
$888$	−9.27322e9	+	2.85400e10i	−0.444411	+	1.36776i
$889$	−2.01539e10			−0.962062
$890$	5.71401e9	−	4.15147e9i	0.271691	−	0.197395i
$891$	−1.04700e10			−0.495876
$892$	4.97430e9	+	1.53093e10i	0.234669	+	0.722236i
$893$	1.03798e9			0.0487765
$894$	−2.80934e10	−	2.04110e10i	−1.31499	−	0.955397i
$895$	2.87210e10	+	2.08670e10i	1.33912	+	0.972926i
$896$	6.74218e9	+	4.89848e9i	0.313128	+	0.227501i
$897$	5.61326e10			2.59682
$898$	4.55382e9	+	1.40152e10i	0.209850	+	0.645851i
$899$	1.49829e8	−	4.61127e8i	0.00687761	−	0.0211671i
$900$	−1.67116e10			−0.764133
$901$	1.19792e9	−	8.70340e8i	0.0545621	−	0.0396417i
$902$	−5.37353e9	+	3.90410e9i	−0.243802	+	0.177132i
$903$	−3.22574e10			−1.45788
$904$	−1.02980e10	−	3.16941e10i	−0.463623	−	1.42688i
$905$	3.47605e10	+	2.52550e10i	1.55889	+	1.13260i
$906$	−9.61998e9	+	2.96073e10i	−0.429759	+	1.32266i
$907$	−3.16295e9	+	9.73455e9i	−0.140756	+	0.433202i	−0.996441	−	0.0842952i	$-0.973136\pi$
$907$	−3.16295e9	+	9.73455e9i	−0.140756	+	0.433202i	0.855685	+	0.517497i	$0.173136\pi$
$908$	−5.51243e9	+	1.69655e10i	−0.244367	+	0.752085i
$909$	3.53059e9	−	2.56512e9i	0.155910	−	0.113275i
$910$	−5.85961e9	+	1.80340e10i	−0.257765	+	0.793319i
$911$	−1.06943e10	−	7.76990e9i	−0.468640	−	0.340487i	0.328271	−	0.944584i	$-0.393534\pi$
$911$	−1.06943e10	−	7.76990e9i	−0.468640	−	0.340487i	−0.796911	+	0.604096i	$0.793534\pi$
$912$	−1.85987e8	−	5.72410e8i	−0.00811898	−	0.0249876i
$913$	5.51785e9	−	1.69822e10i	0.239951	−	0.738492i
$914$	−6.18252e9	+	4.49186e9i	−0.267827	+	0.194588i
$915$	−7.06167e9	−	5.13061e9i	−0.304743	−	0.221409i
$916$	−1.39904e9	−	4.30579e9i	−0.0601444	−	0.185105i
$917$	1.47422e10	−	1.07108e10i	0.631349	−	0.458702i
$918$	2.70386e9	+	1.96447e9i	0.115354	+	0.0838099i
$919$	1.93776e9	−	1.40786e9i	0.0823560	−	0.0598351i	−0.545845	−	0.837886i	$-0.683791\pi$
$919$	1.93776e9	−	1.40786e9i	0.0823560	−	0.0598351i	0.628201	+	0.778051i	$0.283791\pi$
$920$	2.17214e10	+	6.68515e10i	0.919666	+	2.83044i
$921$	−9.84576e9	−	3.03021e10i	−0.415280	−	1.27810i
$922$	−1.76189e10			−0.740322
$923$	1.31079e10	−	2.08898e10i	0.548689	−	0.874435i
$924$	−6.67486e9			−0.278349
$925$	1.14024e10	+	3.50930e10i	0.473697	+	1.45789i
$926$	1.47627e9	+	4.54349e9i	0.0610980	+	0.188040i
$927$	−1.10753e10	+	8.04668e9i	−0.456643	+	0.331770i
$928$	3.74447e8	+	2.72052e8i	0.0153806	+	0.0111746i
$929$	−2.27574e10	+	1.65342e10i	−0.931251	+	0.676593i	−0.946299	−	0.323293i	$-0.895210\pi$
$929$	−2.27574e10	+	1.65342e10i	−0.931251	+	0.676593i	0.0150478	+	0.999887i	$0.495210\pi$
$930$	−1.21252e10	−	3.73174e10i	−0.494308	−	1.52132i
$931$	−1.56359e9	−	1.13601e9i	−0.0635036	−	0.0461381i
$932$	1.65052e10	−	1.19917e10i	0.667829	−	0.485206i
$933$	1.47832e10	−	4.54981e10i	0.595914	−	1.83404i
$934$	−7.76942e9	−	2.39118e10i	−0.312014	−	0.960282i
$935$	1.98383e10	+	1.44134e10i	0.793715	+	0.576668i
$936$	7.26710e9	−	2.23658e10i	0.289665	−	0.891496i
$937$	2.69680e10	−	1.95934e10i	1.07093	−	0.778074i	0.0948481	−	0.995492i	$-0.469763\pi$
$937$	2.69680e10	−	1.95934e10i	1.07093	−	0.778074i	0.976079	+	0.217418i	$0.0697635\pi$
$938$	−9.97238e8	+	3.06918e9i	−0.0394538	+	0.121426i
$939$	2.62576e9	−	8.08127e9i	0.103497	−	0.318530i
$940$	−1.71660e9	+	5.28316e9i	−0.0674096	+	0.207466i
$941$	2.57755e10	+	1.87270e10i	1.00842	+	0.732663i	0.963878	−	0.266344i	$-0.0858157\pi$
$941$	2.57755e10	+	1.87270e10i	1.00842	+	0.732663i	0.0445466	+	0.999007i	$0.485816\pi$
$942$	2.90787e9	+	8.94949e9i	0.113343	+	0.348835i
$943$	4.84933e10			1.88317
$944$	1.05676e9	−	7.67780e8i	0.0408859	−	0.0297053i
$945$	−4.12837e9	+	2.99944e9i	−0.159136	+	0.115619i
$946$	1.03478e10			0.397401
$947$	−4.04993e9	+	1.24644e10i	−0.154961	+	0.476921i	−0.998157	−	0.0606856i	$-0.980671\pi$
$947$	−4.04993e9	+	1.24644e10i	−0.154961	+	0.476921i	0.843196	+	0.537606i	$0.180671\pi$
$948$	8.78013e9	+	2.70225e10i	0.334712	+	1.03014i
$949$	−5.68487e9			−0.215918
$950$	−4.25862e9	−	3.09407e9i	−0.161152	−	0.117084i
$951$	1.34769e10	+	9.79156e9i	0.508112	+	0.369165i
$952$	2.38893e10	+	1.73566e10i	0.897374	+	0.651980i
$953$	−4.86385e10			−1.82035			−0.910174	−	0.414225i	$-0.864053\pi$
$953$	−4.86385e10			−1.82035			−0.910174	+	0.414225i	$0.864053\pi$
$954$	2.33708e8	+	7.19280e8i	0.00871475	+	0.0268212i
$955$	7.99891e10			2.97180
$956$	−5.49099e9	+	3.98944e9i	−0.203258	+	0.147676i
$957$	−3.29762e8			−0.0121621
$958$	−1.07988e10	+	3.32354e10i	−0.396824	+	1.22130i
$959$	−3.09405e9	+	9.52250e9i	−0.113282	+	0.348647i
$960$	4.30568e10			1.57070
$961$	−6.17071e9	+	4.48328e9i	−0.224287	+	0.162954i
$962$	−1.89595e10			−0.686616
$963$	8.93053e9	+	2.74853e10i	0.322244	+	0.991766i
$964$	1.53941e10			0.553458
$965$	1.29843e10	+	9.43367e9i	0.465130	+	0.337937i
$966$	−2.91247e10	−	2.11603e10i	−1.03954	−	0.755270i
$967$	−5.70197e9	−	4.14272e9i	−0.202783	−	0.147331i	0.481759	−	0.876304i	$-0.339998\pi$
$967$	−5.70197e9	−	4.14272e9i	−0.202783	−	0.147331i	−0.684543	+	0.728973i	$0.739998\pi$
$968$	−2.31097e10			−0.818900
$969$	3.36938e9	+	1.03699e10i	0.118964	+	0.366135i
$970$	1.13142e10	−	3.48214e10i	0.398035	−	1.22503i
$971$	3.50124e10			1.22731			0.613656	−	0.789574i	$-0.289698\pi$
$971$	3.50124e10			1.22731			0.613656	+	0.789574i	$0.289698\pi$
$972$	1.80428e10	−	1.31089e10i	0.630192	−	0.457861i
$973$	−2.26255e10	+	1.64384e10i	−0.787413	+	0.572089i
$974$	1.35356e10			0.469377
$975$	−1.90392e10	−	5.85967e10i	−0.657859	−	2.02468i
$976$	3.83511e8	+	2.78637e8i	0.0132040	+	0.00959323i
$977$	−1.05511e10	+	3.24729e10i	−0.361965	+	1.11401i	0.589895	+	0.807480i	$0.299169\pi$
$977$	−1.05511e10	+	3.24729e10i	−0.361965	+	1.11401i	−0.951860	+	0.306534i	$0.900831\pi$
$978$	1.34607e10	−	4.14277e10i	0.460130	−	1.41614i
$979$	−1.32938e9	+	4.09140e9i	−0.0452803	+	0.139358i
$980$	8.36794e9	−	6.07966e9i	0.284006	−	0.206342i
$981$	9.45047e9	−	2.90855e10i	0.319604	−	0.983639i
$982$	−8.68901e9	−	6.31293e9i	−0.292806	−	0.212736i
$983$	8.52297e9	+	2.62310e10i	0.286189	+	0.880800i	0.986040	+	0.166511i	$0.0532500\pi$
$983$	8.52297e9	+	2.62310e10i	0.286189	+	0.880800i	−0.699850	+	0.714289i	$0.746750\pi$
$984$	1.33767e10	−	4.11693e10i	0.447575	−	1.37750i
$985$	5.70058e10	−	4.14172e10i	1.90061	−	1.38087i
$986$	4.30936e8	+	3.13093e8i	0.0143167	+	0.0104017i
$987$	−2.40778e9	−	7.41037e9i	−0.0797088	−	0.245318i
$988$	−2.96210e9	+	2.15209e9i	−0.0977126	+	0.0709924i
$989$	−6.11201e10	−	4.44064e10i	−2.00908	−	1.45968i
$990$	−1.01327e10	+	7.36187e9i	−0.331897	+	0.241138i
$991$	−2.58479e9	−	7.95517e9i	−0.0843661	−	0.259652i	0.899971	−	0.435950i	$-0.143588\pi$
$991$	−2.58479e9	−	7.95517e9i	−0.0843661	−	0.259652i	−0.984337	+	0.176298i	$0.943588\pi$
$992$	−1.03658e10	−	3.19027e10i	−0.337142	−	1.03762i
$993$	−4.75605e10			−1.54143
$994$	−1.46759e10	+	5.89747e9i	−0.473971	+	0.190464i
$995$	−8.15994e9			−0.262607
$996$	1.31306e10	+	4.04120e10i	0.421093	+	1.29599i
$997$	−1.11703e10	−	3.43785e10i	−0.356969	−	1.09864i	−0.954859	−	0.297059i	$-0.903994\pi$
$997$	−1.11703e10	−	3.43785e10i	−0.356969	−	1.09864i	0.597890	−	0.801578i	$-0.296006\pi$
$998$	2.31862e10	−	1.68458e10i	0.738368	−	0.536456i
$999$	−4.12781e9	−	2.99903e9i	−0.130991	−	0.0951703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.8.c.a.5.15	✓	164
71.57	even	5	inner	71.8.c.a.57.15	yes	164

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.8.c.a.5.15	✓	164	1.1	even	1	trivial
71.8.c.a.57.15	yes	164	71.57	even	5	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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	71.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27884 - 7.01354i) q^{2} +(-19.8378 - 61.0546i) q^{3} +(59.5576 - 43.2711i) q^{4} +(357.700 + 259.884i) q^{5} +(-383.001 + 278.267i) q^{6} +(-219.765 - 676.366i) q^{7} +(-1202.86 - 873.931i) q^{8} +(-1564.80 + 1136.90i) q^{9} +O(q^{10})\)	\(q+(-2.27884 - 7.01354i) q^{2} +(-19.8378 - 61.0546i) q^{3} +(59.5576 - 43.2711i) q^{4} +(357.700 + 259.884i) q^{5} +(-383.001 + 278.267i) q^{6} +(-219.765 - 676.366i) q^{7} +(-1202.86 - 873.931i) q^{8} +(-1564.80 + 1136.90i) q^{9} +(1007.57 - 3100.98i) q^{10} +(613.702 + 1888.78i) q^{11} +(-3823.39 - 2777.86i) q^{12} +(2526.97 - 7777.23i) q^{13} +(-4242.91 + 3082.66i) q^{14} +(8771.14 - 26994.8i) q^{15} +(-476.350 + 1466.06i) q^{16} +(8629.66 - 26559.3i) q^{17} +(11539.6 + 8384.00i) q^{18} +(-1879.43 - 5784.30i) q^{19} +32549.2 q^{20} +(-36935.6 + 26835.3i) q^{21} +(11848.5 - 8608.44i) q^{22} -106926. q^{23} +(-29495.3 + 90777.2i) q^{24} +(36267.6 + 111620. i) q^{25} -60304.4 q^{26} +(-13129.3 - 9539.00i) q^{27} +(-42355.8 - 30773.3i) q^{28} +(-2092.52 - 1520.31i) q^{29} -209317. q^{30} +(57927.3 + 178282. i) q^{31} -178945. q^{32} +(103144. - 74938.6i) q^{33} -205941. q^{34} +(97167.2 - 299050. i) q^{35} +(-44001.1 + 135422. i) q^{36} +314396. q^{37} +(-36285.5 + 26363.0i) q^{38} -524965. q^{39} +(-203143. - 625210. i) q^{40} -453520. q^{41} +(272380. + 197896. i) q^{42} +(571609. + 415298. i) q^{43} +(118280. + 85935.6i) q^{44} -855192. q^{45} +(243668. + 749932. i) q^{46} +(-52738.6 + 162313. i) q^{47} +98959.2 q^{48} +(257086. - 186784. i) q^{49} +(700204. - 508728. i) q^{50} -1.79276e6 q^{51} +(-186029. - 572538. i) q^{52} +(42896.0 + 31165.8i) q^{53} +(-36982.6 + 113821. i) q^{54} +(-271343. + 835109. i) q^{55} +(-326751. + 1.00563e6i) q^{56} +(-315874. + 229496. i) q^{57} +(-5894.22 + 18140.5i) q^{58} +(-685538. - 498072. i) q^{59} +(-645707. - 1.98728e6i) q^{60} +(95029.6 - 292471. i) q^{61} +(1.11838e6 - 812551. i) q^{62} +(1.11285e6 + 808530. i) q^{63} +(468760. + 1.44269e6i) q^{64} +(2.92508e6 - 2.12519e6i) q^{65} +(-760633. - 552633. i) q^{66} +(497815. - 361684. i) q^{67} +(-635291. - 1.95523e6i) q^{68} +(2.12119e6 + 6.52835e6i) q^{69} -2.31882e6 q^{70} +(2.92486e6 + 735073. i) q^{71} +2.87581e6 q^{72} +(-214825. - 661163. i) q^{73} +(-716458. - 2.20503e6i) q^{74} +(6.09545e6 - 4.42860e6i) q^{75} +(-362228. - 263174. i) q^{76} +(1.14264e6 - 830174. i) q^{77} +(1.19631e6 + 3.68186e6i) q^{78} +(-4.86390e6 - 3.53383e6i) q^{79} +(-551396. + 400612. i) q^{80} +(-1.62912e6 + 5.01390e6i) q^{81} +(1.03350e6 + 3.18078e6i) q^{82} +(-7.27394e6 - 5.28483e6i) q^{83} +(-1.03860e6 + 3.19649e6i) q^{84} +(9.98919e6 - 7.25757e6i) q^{85} +(1.61011e6 - 4.95540e6i) q^{86} +(-51310.6 + 157918. i) q^{87} +(912464. - 2.80828e6i) q^{88} +(1.75246e6 + 1.27324e6i) q^{89} +(1.94884e6 + 5.99792e6i) q^{90} -5.81559e6 q^{91} +(-6.36828e6 + 4.62683e6i) q^{92} +(9.73578e6 - 7.07346e6i) q^{93} +1.25857e6 q^{94} +(830976. - 2.55748e6i) q^{95} +(3.54989e6 + 1.09254e7i) q^{96} +1.12292e7 q^{97} +(-1.89587e6 - 1.37743e6i) q^{98} +(-3.10767e6 - 2.25785e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 164 q - 24 q^{2} + 23 q^{3} - 2290 q^{4} - 145 q^{5} + 514 q^{6} - 689 q^{7} + 7007 q^{8} - 28870 q^{9}+O(q^{10}) \) 164 * q - 24 * q^2 + 23 * q^3 - 2290 * q^4 - 145 * q^5 + 514 * q^6 - 689 * q^7 + 7007 * q^8 - 28870 * q^9	\( 164 q - 24 q^{2} + 23 q^{3} - 2290 q^{4} - 145 q^{5} + 514 q^{6} - 689 q^{7} + 7007 q^{8} - 28870 q^{9} + 3135 q^{10} - 12985 q^{11} + 18776 q^{12} - 9385 q^{13} + 32591 q^{14} - 8549 q^{15} - 187398 q^{16} - 13646 q^{17} - 76246 q^{18} + 25499 q^{19} + 353436 q^{20} + 34737 q^{21} - 217194 q^{22} + 169250 q^{23} + 331795 q^{24} - 575758 q^{25} + 910386 q^{26} - 804946 q^{27} - 73744 q^{28} + 267827 q^{29} + 148780 q^{30} - 438094 q^{31} - 1526108 q^{32} - 334678 q^{33} + 693478 q^{34} - 2088525 q^{35} - 2044616 q^{36} + 1246506 q^{37} + 153325 q^{38} + 5662314 q^{39} - 1006765 q^{40} + 2523444 q^{41} - 3243385 q^{42} - 610945 q^{43} + 2555635 q^{44} - 2138948 q^{45} - 3308317 q^{46} - 24619 q^{47} + 3151128 q^{48} - 5099094 q^{49} + 1280130 q^{50} + 5652418 q^{51} - 6865861 q^{52} + 7097402 q^{53} + 3114724 q^{54} - 2901298 q^{55} - 5638895 q^{56} + 4376914 q^{57} + 2039661 q^{58} - 5415353 q^{59} + 4266884 q^{60} - 4862842 q^{61} - 698479 q^{62} - 9326945 q^{63} - 7453239 q^{64} - 563874 q^{65} - 1270308 q^{66} - 12169138 q^{67} - 2438715 q^{68} + 4493215 q^{69} + 24169266 q^{70} + 7425657 q^{71} + 74311670 q^{72} + 5888723 q^{73} - 25053117 q^{74} - 23403819 q^{75} - 23428881 q^{76} + 27730932 q^{77} - 4857586 q^{78} - 14763363 q^{79} - 10893310 q^{80} - 52980383 q^{81} + 11235687 q^{82} + 9180561 q^{83} - 57710877 q^{84} + 49461277 q^{85} + 24603299 q^{86} + 22534593 q^{87} + 47400568 q^{88} + 4614244 q^{89} + 36501636 q^{90} - 44327954 q^{91} - 22315930 q^{92} + 11554572 q^{93} + 39127110 q^{94} + 22575615 q^{95} - 16486827 q^{96} + 27532902 q^{97} + 79875624 q^{98} - 47114358 q^{99}+O(q^{100}) \) 164 * q - 24 * q^2 + 23 * q^3 - 2290 * q^4 - 145 * q^5 + 514 * q^6 - 689 * q^7 + 7007 * q^8 - 28870 * q^9 + 3135 * q^10 - 12985 * q^11 + 18776 * q^12 - 9385 * q^13 + 32591 * q^14 - 8549 * q^15 - 187398 * q^16 - 13646 * q^17 - 76246 * q^18 + 25499 * q^19 + 353436 * q^20 + 34737 * q^21 - 217194 * q^22 + 169250 * q^23 + 331795 * q^24 - 575758 * q^25 + 910386 * q^26 - 804946 * q^27 - 73744 * q^28 + 267827 * q^29 + 148780 * q^30 - 438094 * q^31 - 1526108 * q^32 - 334678 * q^33 + 693478 * q^34 - 2088525 * q^35 - 2044616 * q^36 + 1246506 * q^37 + 153325 * q^38 + 5662314 * q^39 - 1006765 * q^40 + 2523444 * q^41 - 3243385 * q^42 - 610945 * q^43 + 2555635 * q^44 - 2138948 * q^45 - 3308317 * q^46 - 24619 * q^47 + 3151128 * q^48 - 5099094 * q^49 + 1280130 * q^50 + 5652418 * q^51 - 6865861 * q^52 + 7097402 * q^53 + 3114724 * q^54 - 2901298 * q^55 - 5638895 * q^56 + 4376914 * q^57 + 2039661 * q^58 - 5415353 * q^59 + 4266884 * q^60 - 4862842 * q^61 - 698479 * q^62 - 9326945 * q^63 - 7453239 * q^64 - 563874 * q^65 - 1270308 * q^66 - 12169138 * q^67 - 2438715 * q^68 + 4493215 * q^69 + 24169266 * q^70 + 7425657 * q^71 + 74311670 * q^72 + 5888723 * q^73 - 25053117 * q^74 - 23403819 * q^75 - 23428881 * q^76 + 27730932 * q^77 - 4857586 * q^78 - 14763363 * q^79 - 10893310 * q^80 - 52980383 * q^81 + 11235687 * q^82 + 9180561 * q^83 - 57710877 * q^84 + 49461277 * q^85 + 24603299 * q^86 + 22534593 * q^87 + 47400568 * q^88 + 4614244 * q^89 + 36501636 * q^90 - 44327954 * q^91 - 22315930 * q^92 + 11554572 * q^93 + 39127110 * q^94 + 22575615 * q^95 - 16486827 * q^96 + 27532902 * q^97 + 79875624 * q^98 - 47114358 * q^99

Introduction

L-functions

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