LMFDB - Embedded newform 91.8.f.a.22.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(22,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("91.22");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.f (of order $3$, degree $2$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.20
Character	$\chi$	$=$	91.22
Dual form			91.8.f.a.29.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.46862 - 14.6681i) q^{2} +(17.8769 - 30.9637i) q^{3} +(-79.4351 - 137.586i) q^{4} +457.543 q^{5} +(-302.785 - 524.440i) q^{6} +(171.500 + 297.047i) q^{7} -522.854 q^{8} +(454.332 + 786.927i) q^{9} +O(q^{10})$	\(q+(8.46862 - 14.6681i) q^{2} +(17.8769 - 30.9637i) q^{3} +(-79.4351 - 137.586i) q^{4} +457.543 q^{5} +(-302.785 - 524.440i) q^{6} +(171.500 + 297.047i) q^{7} -522.854 q^{8} +(454.332 + 786.927i) q^{9} +(3874.76 - 6711.28i) q^{10} +(559.829 - 969.653i) q^{11} -5680.21 q^{12} +(3328.00 - 7188.39i) q^{13} +5809.47 q^{14} +(8179.46 - 14167.2i) q^{15} +(5739.83 - 9941.68i) q^{16} +(4758.45 + 8241.87i) q^{17} +15390.3 q^{18} +(-8060.84 - 13961.8i) q^{19} +(-36345.0 - 62951.3i) q^{20} +12263.6 q^{21} +(-9481.96 - 16423.2i) q^{22} +(-43884.3 + 76009.8i) q^{23} +(-9347.02 + 16189.5i) q^{24} +131221. q^{25} +(-77256.4 - 109691. i) q^{26} +110682. q^{27} +(27246.2 - 47191.8i) q^{28} +(5583.74 - 9671.32i) q^{29} +(-138537. - 239954. i) q^{30} -291968. q^{31} +(-130680. - 226344. i) q^{32} +(-20016.0 - 34668.8i) q^{33} +161190. q^{34} +(78468.7 + 135912. i) q^{35} +(72179.8 - 125019. i) q^{36} +(91763.5 - 158939. i) q^{37} -273057. q^{38} +(-163085. - 231553. i) q^{39} -239229. q^{40} +(-321656. + 557124. i) q^{41} +(103855. - 179883. i) q^{42} +(272247. + 471545. i) q^{43} -177880. q^{44} +(207877. + 360053. i) q^{45} +(743279. + 1.28740e6i) q^{46} -1.22345e6 q^{47} +(-205221. - 355453. i) q^{48} +(-58824.5 + 101887. i) q^{49} +(1.11126e6 - 1.92476e6i) q^{50} +340265. q^{51} +(-1.25338e6 + 113126. i) q^{52} -849222. q^{53} +(937322. - 1.62349e6i) q^{54} +(256146. - 443658. i) q^{55} +(-89669.5 - 155312. i) q^{56} -576411. q^{57} +(-94573.2 - 163806. i) q^{58} +(1.50411e6 + 2.60519e6i) q^{59} -2.59894e6 q^{60} +(-1.76774e6 - 3.06181e6i) q^{61} +(-2.47257e6 + 4.28262e6i) q^{62} +(-155836. + 269916. i) q^{63} -2.95731e6 q^{64} +(1.52270e6 - 3.28900e6i) q^{65} -678033. q^{66} +(-317645. + 550177. i) q^{67} +(755975. - 1.30939e6i) q^{68} +(1.56903e6 + 2.71764e6i) q^{69} +2.65809e6 q^{70} +(-1.64773e6 - 2.85396e6i) q^{71} +(-237550. - 411448. i) q^{72} +3.29083e6 q^{73} +(-1.55422e6 - 2.69199e6i) q^{74} +(2.34582e6 - 4.06309e6i) q^{75} +(-1.28063e6 + 2.21811e6i) q^{76} +384043. q^{77} +(-4.77755e6 + 431207. i) q^{78} -567595. q^{79} +(2.62622e6 - 4.54875e6i) q^{80} +(985024. - 1.70611e6i) q^{81} +(5.44796e6 + 9.43614e6i) q^{82} +5.08785e6 q^{83} +(-974156. - 1.68729e6i) q^{84} +(2.17720e6 + 3.77101e6i) q^{85} +9.22222e6 q^{86} +(-199640. - 345787. i) q^{87} +(-292709. + 506987. i) q^{88} +(2.71604e6 - 4.70432e6i) q^{89} +7.04171e6 q^{90} +(2.70604e6 - 244239. i) q^{91} +1.39438e7 q^{92} +(-5.21949e6 + 9.04043e6i) q^{93} +(-1.03609e7 + 1.79456e7i) q^{94} +(-3.68818e6 - 6.38812e6i) q^{95} -9.34459e6 q^{96} +(2.60026e6 + 4.50379e6i) q^{97} +(996325. + 1.72568e6i) q^{98} +1.01739e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9} + 17800 q^{10} - 11735 q^{11} + 30484 q^{12} - 5622 q^{13} - 5488 q^{14} + 3465 q^{15} - 110364 q^{16} - 3506 q^{17} - 196096 q^{18} - 25291 q^{19} - 13351 q^{20} + 28126 q^{21} + 91579 q^{22} + 82970 q^{23} - 97143 q^{24} + 1263842 q^{25} - 51951 q^{26} - 1080760 q^{27} + 504896 q^{28} + 209315 q^{29} + 1063844 q^{30} + 948356 q^{31} - 495024 q^{32} - 143209 q^{33} + 436128 q^{34} + 90209 q^{35} - 469485 q^{36} - 377142 q^{37} - 198346 q^{38} + 647900 q^{39} - 4780340 q^{40} - 1895174 q^{41} + 178017 q^{42} - 1366459 q^{43} + 8096352 q^{44} - 2154733 q^{45} + 2854528 q^{46} + 2557720 q^{47} - 4102289 q^{48} - 2823576 q^{49} - 2378593 q^{50} - 4369338 q^{51} + 4270295 q^{52} - 4295420 q^{53} + 1447259 q^{54} - 560241 q^{55} + 81291 q^{56} + 15936670 q^{57} - 384326 q^{58} + 6714194 q^{59} + 5267974 q^{60} - 987536 q^{61} + 8520899 q^{62} + 5291461 q^{63} - 8211866 q^{64} - 11284709 q^{65} - 20326376 q^{66} - 1296682 q^{67} - 8400264 q^{68} - 1147530 q^{69} + 12210800 q^{70} - 7723282 q^{71} + 26270290 q^{72} + 15769600 q^{73} + 58033 q^{74} - 928389 q^{75} - 9095520 q^{76} - 8050210 q^{77} - 30641513 q^{78} - 24665908 q^{79} + 16716608 q^{80} - 5846292 q^{81} - 9977079 q^{82} + 32429868 q^{83} + 5228006 q^{84} + 17821519 q^{85} + 89024148 q^{86} - 16967309 q^{87} + 28910709 q^{88} - 27957029 q^{89} - 155228046 q^{90} - 5184102 q^{91} - 5073264 q^{92} + 11673603 q^{93} - 9670145 q^{94} + 38478411 q^{95} + 111942976 q^{96} - 28714467 q^{97} - 941192 q^{98} + 42173094 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9 + 17800 * q^10 - 11735 * q^11 + 30484 * q^12 - 5622 * q^13 - 5488 * q^14 + 3465 * q^15 - 110364 * q^16 - 3506 * q^17 - 196096 * q^18 - 25291 * q^19 - 13351 * q^20 + 28126 * q^21 + 91579 * q^22 + 82970 * q^23 - 97143 * q^24 + 1263842 * q^25 - 51951 * q^26 - 1080760 * q^27 + 504896 * q^28 + 209315 * q^29 + 1063844 * q^30 + 948356 * q^31 - 495024 * q^32 - 143209 * q^33 + 436128 * q^34 + 90209 * q^35 - 469485 * q^36 - 377142 * q^37 - 198346 * q^38 + 647900 * q^39 - 4780340 * q^40 - 1895174 * q^41 + 178017 * q^42 - 1366459 * q^43 + 8096352 * q^44 - 2154733 * q^45 + 2854528 * q^46 + 2557720 * q^47 - 4102289 * q^48 - 2823576 * q^49 - 2378593 * q^50 - 4369338 * q^51 + 4270295 * q^52 - 4295420 * q^53 + 1447259 * q^54 - 560241 * q^55 + 81291 * q^56 + 15936670 * q^57 - 384326 * q^58 + 6714194 * q^59 + 5267974 * q^60 - 987536 * q^61 + 8520899 * q^62 + 5291461 * q^63 - 8211866 * q^64 - 11284709 * q^65 - 20326376 * q^66 - 1296682 * q^67 - 8400264 * q^68 - 1147530 * q^69 + 12210800 * q^70 - 7723282 * q^71 + 26270290 * q^72 + 15769600 * q^73 + 58033 * q^74 - 928389 * q^75 - 9095520 * q^76 - 8050210 * q^77 - 30641513 * q^78 - 24665908 * q^79 + 16716608 * q^80 - 5846292 * q^81 - 9977079 * q^82 + 32429868 * q^83 + 5228006 * q^84 + 17821519 * q^85 + 89024148 * q^86 - 16967309 * q^87 + 28910709 * q^88 - 27957029 * q^89 - 155228046 * q^90 - 5184102 * q^91 - 5073264 * q^92 + 11673603 * q^93 - 9670145 * q^94 + 38478411 * q^95 + 111942976 * q^96 - 28714467 * q^97 - 941192 * q^98 + 42173094 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	8.46862	−	14.6681i	0.748527	−	1.29649i	−0.200001	−	0.979796i	$-0.564095\pi$
$2$	8.46862	−	14.6681i	0.748527	−	1.29649i	0.948529	−	0.316692i	$-0.102572\pi$
$3$	17.8769	−	30.9637i	0.382268	−	0.662108i	−0.609118	−	0.793080i	$-0.708476\pi$
$3$	17.8769	−	30.9637i	0.382268	−	0.662108i	0.991386	+	0.130972i	$0.0418098\pi$
$4$	−79.4351	−	137.586i	−0.620586	−	1.07489i
$5$	457.543			1.63696			0.818478	−	0.574537i	$-0.194818\pi$
$5$	457.543			1.63696			0.818478	+	0.574537i	$0.194818\pi$
$6$	−302.785	−	524.440i	−0.572276	−	0.991211i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$8$	−522.854			−0.361049
$9$	454.332	+	786.927i	0.207742	+	0.359820i
$10$	3874.76	−	6711.28i	1.22531	−	2.12229i
$11$	559.829	−	969.653i	0.126818	−	0.219655i	−0.795624	−	0.605791i	$-0.792857\pi$
$11$	559.829	−	969.653i	0.126818	−	0.219655i	0.922442	+	0.386135i	$0.126190\pi$
$12$	−5680.21			−0.948921
$13$	3328.00	−	7188.39i	0.420127	−	0.907465i
$13$	3328.00	−	7188.39i	0.420127	−	0.907465i
$14$	5809.47			0.565833
$15$	8179.46	−	14167.2i	0.625756	−	1.08384i
$16$	5739.83	−	9941.68i	0.350332	−	0.606792i
$17$	4758.45	+	8241.87i	0.234906	+	0.406869i	0.959245	−	0.282575i	$-0.0911885\pi$
$17$	4758.45	+	8241.87i	0.234906	+	0.406869i	−0.724339	+	0.689444i	$0.757855\pi$
$18$	15390.3			0.622003
$19$	−8060.84	−	13961.8i	−0.269614	−	0.466985i	0.699148	−	0.714977i	$-0.253563\pi$
$19$	−8060.84	−	13961.8i	−0.269614	−	0.466985i	−0.968762	+	0.247992i	$0.920229\pi$
$20$	−36345.0	−	62951.3i	−1.01587	−	1.75954i
$21$	12263.6			0.288968
$22$	−9481.96	−	16423.2i	−0.189854	−	0.328836i
$23$	−43884.3	+	76009.8i	−0.752076	+	1.30263i	0.194739	+	0.980855i	$0.437614\pi$
$23$	−43884.3	+	76009.8i	−0.752076	+	1.30263i	−0.946815	+	0.321778i	$0.895719\pi$
$24$	−9347.02	+	16189.5i	−0.138017	+	0.239053i
$25$	131221.			1.67963
$26$	−77256.4	−	109691.i	−0.862040	−	1.22395i
$27$	110682.			1.08219
$28$	27246.2	−	47191.8i	0.234560	−	0.406269i
$29$	5583.74	−	9671.32i	0.0425140	−	0.0736365i	−0.843985	−	0.536366i	$-0.819797\pi$
$29$	5583.74	−	9671.32i	0.0425140	−	0.0736365i	0.886499	+	0.462730i	$0.153130\pi$
$30$	−138537.	−	239954.i	−0.936791	−	1.62257i
$31$	−291968.			−1.76023			−0.880116	−	0.474759i	$-0.842535\pi$
$31$	−291968.			−1.76023			−0.880116	+	0.474759i	$0.842535\pi$
$32$	−130680.	−	226344.i	−0.704990	−	1.22108i
$33$	−20016.0	−	34668.8i	−0.0969570	−	0.167934i
$34$	161190.			0.703334
$35$	78468.7	+	135912.i	0.309356	+	0.535820i
$36$	72179.8	−	125019.i	0.257844	−	0.446599i
$37$	91763.5	−	158939.i	0.297827	−	0.515851i	−0.677812	−	0.735236i	$-0.737072\pi$
$37$	91763.5	−	158939.i	0.297827	−	0.515851i	0.975638	+	0.219384i	$0.0704049\pi$
$38$	−273057.			−0.807254
$39$	−163085.	−	231553.i	−0.440238	−	0.625065i
$40$	−239229.			−0.591021
$41$	−321656.	+	557124.i	−0.728866	+	1.26243i	0.228497	+	0.973545i	$0.426619\pi$
$41$	−321656.	+	557124.i	−0.728866	+	1.26243i	−0.957363	+	0.288889i	$0.906714\pi$
$42$	103855.	−	179883.i	0.216300	−	0.374643i
$43$	272247.	+	471545.i	0.522183	+	0.904448i	0.999667	+	0.0258074i	$0.00821568\pi$
$43$	272247.	+	471545.i	0.522183	+	0.904448i	−0.477484	+	0.878641i	$0.658451\pi$
$44$	−177880.			−0.314806
$45$	207877.	+	360053.i	0.340065	+	0.589010i
$46$	743279.	+	1.28740e6i	1.12590	+	1.95011i
$47$	−1.22345e6			−1.71887			−0.859433	−	0.511248i	$-0.829183\pi$
$47$	−1.22345e6			−1.71887			−0.859433	+	0.511248i	$0.829183\pi$
$48$	−205221.	−	355453.i	−0.267841	−	0.463914i
$49$	−58824.5	+	101887.i	−0.0714286	+	0.123718i
$50$	1.11126e6	−	1.92476e6i	1.25725	−	2.17762i
$51$	340265.			0.359188
$52$	−1.25338e6	+	113126.i	−1.23615	+	0.111571i
$53$	−849222.			−0.783530			−0.391765	−	0.920065i	$-0.628135\pi$
$53$	−849222.			−0.783530			−0.391765	+	0.920065i	$0.628135\pi$
$54$	937322.	−	1.62349e6i	0.810048	−	1.40304i
$55$	256146.	−	443658.i	0.207596	−	0.359566i
$56$	−89669.5	−	155312.i	−0.0682318	−	0.118181i
$57$	−576411.			−0.412259
$58$	−94573.2	−	163806.i	−0.0636458	−	0.110238i
$59$	1.50411e6	+	2.60519e6i	0.953447	+	1.65142i	0.737883	+	0.674928i	$0.235825\pi$
$59$	1.50411e6	+	2.60519e6i	0.953447	+	1.65142i	0.215563	+	0.976490i	$0.430841\pi$
$60$	−2.59894e6			−1.55334
$61$	−1.76774e6	−	3.06181e6i	−0.997157	−	1.72713i	−0.563833	−	0.825888i	$-0.690674\pi$
$61$	−1.76774e6	−	3.06181e6i	−0.997157	−	1.72713i	−0.433324	−	0.901238i	$-0.642659\pi$
$62$	−2.47257e6	+	4.28262e6i	−1.31758	+	2.28212i
$63$	−155836.	+	269916.i	−0.0785192	+	0.135999i
$64$	−2.95731e6			−1.41015
$65$	1.52270e6	−	3.28900e6i	0.687730	−	1.48548i
$66$	−678033.			−0.290300
$67$	−317645.	+	550177.i	−0.129027	+	0.223481i	−0.923300	−	0.384080i	$-0.874519\pi$
$67$	−317645.	+	550177.i	−0.129027	+	0.223481i	0.794273	+	0.607561i	$0.207852\pi$
$68$	755975.	−	1.30939e6i	0.291559	−	0.504995i
$69$	1.56903e6	+	2.71764e6i	0.574989	+	0.995910i
$70$	2.65809e6			0.926245
$71$	−1.64773e6	−	2.85396e6i	−0.546364	−	0.946331i	−0.998520	−	0.0543918i	$-0.982678\pi$
$71$	−1.64773e6	−	2.85396e6i	−0.546364	−	0.946331i	0.452155	−	0.891939i	$-0.350655\pi$
$72$	−237550.	−	411448.i	−0.0750051	−	0.129913i
$73$	3.29083e6			0.990092			0.495046	−	0.868867i	$-0.335151\pi$
$73$	3.29083e6			0.990092			0.495046	+	0.868867i	$0.335151\pi$
$74$	−1.55422e6	−	2.69199e6i	−0.445863	−	0.772257i
$75$	2.34582e6	−	4.06309e6i	0.642068	−	1.11209i
$76$	−1.28063e6	+	2.21811e6i	−0.334638	+	0.579609i
$77$	384043.			0.0958655
$78$	−4.77755e6	+	431207.i	−1.13992	+	0.102886i
$79$	−567595.			−0.129522			−0.0647610	−	0.997901i	$-0.520629\pi$
$79$	−567595.			−0.129522			−0.0647610	+	0.997901i	$0.520629\pi$
$80$	2.62622e6	−	4.54875e6i	0.573478	−	0.993292i
$81$	985024.	−	1.70611e6i	0.205944	−	0.356706i
$82$	5.44796e6	+	9.43614e6i	1.09115	+	1.88993i
$83$	5.08785e6			0.976700			0.488350	−	0.872648i	$-0.337599\pi$
$83$	5.08785e6			0.976700			0.488350	+	0.872648i	$0.337599\pi$
$84$	−974156.	−	1.68729e6i	−0.179329	−	0.310607i
$85$	2.17720e6	+	3.77101e6i	0.384531	+	0.666027i
$86$	9.22222e6			1.56347
$87$	−199640.	−	345787.i	−0.0325035	−	0.0562977i
$88$	−292709.	+	506987.i	−0.0457875	+	0.0793063i
$89$	2.71604e6	−	4.70432e6i	0.408387	−	0.707347i	−0.586322	−	0.810078i	$-0.699425\pi$
$89$	2.71604e6	−	4.70432e6i	0.408387	−	0.707347i	0.994709	+	0.102731i	$0.0327582\pi$
$90$	7.04171e6			1.01819
$91$	2.70604e6	−	244239.i	0.376434	−	0.0339758i
$92$	1.39438e7			1.86691
$93$	−5.21949e6	+	9.04043e6i	−0.672881	+	1.16546i
$94$	−1.03609e7	+	1.79456e7i	−1.28662	+	2.22849i
$95$	−3.68818e6	−	6.38812e6i	−0.441346	−	0.764435i
$96$	−9.34459e6			−1.07798
$97$	2.60026e6	+	4.50379e6i	0.289279	+	0.501045i	0.973638	−	0.228100i	$-0.0732513\pi$
$97$	2.60026e6	+	4.50379e6i	0.289279	+	0.501045i	−0.684359	+	0.729145i	$0.739918\pi$
$98$	996325.	+	1.72568e6i	0.106932	+	0.185212i
$99$	1.01739e6			0.105382
$100$	−1.04235e7	−	1.80541e7i	−1.04235	−	1.80541i
$101$	4.04118e6	−	6.99954e6i	0.390287	−	0.675997i	−0.602200	−	0.798345i	$-0.705709\pi$
$101$	4.04118e6	−	6.99954e6i	0.390287	−	0.675997i	0.992487	+	0.122348i	$0.0390425\pi$
$102$	2.88158e6	−	4.99104e6i	0.268862	−	0.465683i
$103$	−5.14187e6			−0.463650			−0.231825	−	0.972757i	$-0.574470\pi$
$103$	−5.14187e6			−0.463650			−0.231825	+	0.972757i	$0.574470\pi$
$104$	−1.74006e6	+	3.75848e6i	−0.151686	+	0.327639i
$105$	5.61111e6			0.473027
$106$	−7.19174e6	+	1.24565e7i	−0.586494	+	1.01584i
$107$	−4.54328e6	+	7.86919e6i	−0.358531	+	0.620993i	−0.987716	−	0.156262i	$-0.950055\pi$
$107$	−4.54328e6	+	7.86919e6i	−0.358531	+	0.620993i	0.629185	+	0.777256i	$0.283389\pi$
$108$	−8.79202e6	−	1.52282e7i	−0.671592	−	1.16323i
$109$	6.88272e6			0.509058			0.254529	−	0.967065i	$-0.418080\pi$
$109$	6.88272e6			0.509058			0.254529	+	0.967065i	$0.418080\pi$
$110$	−4.33841e6	−	7.51435e6i	−0.310782	−	0.538291i
$111$	−3.28089e6	−	5.68267e6i	−0.227699	−	0.394387i
$112$	3.93752e6			0.264826
$113$	1.93307e6	+	3.34818e6i	0.126030	+	0.218290i	0.922135	−	0.386868i	$-0.126443\pi$
$113$	1.93307e6	+	3.34818e6i	0.126030	+	0.218290i	−0.796105	+	0.605158i	$0.793110\pi$
$114$	−4.88141e6	+	8.45485e6i	−0.308587	+	0.534489i
$115$	−2.00790e7	+	3.47778e7i	−1.23112	+	2.13235i
$116$	−1.77418e6			−0.105535
$117$	7.16875e6	−	647030.i	0.413802	−	0.0373486i
$118$	5.09508e7			2.85472
$119$	−1.63215e6	+	2.82696e6i	−0.0887861	+	0.153782i
$120$	−4.27667e6	+	7.40740e6i	−0.225929	+	0.391320i
$121$	9.11677e6	+	1.57907e7i	0.467834	+	0.810313i
$122$	−5.98812e7			−2.98560
$123$	1.15004e7	+	1.99193e7i	0.557245	+	0.965176i
$124$	2.31925e7	+	4.01706e7i	1.09238	+	1.89205i
$125$	2.42937e7			1.11252
$126$	2.63943e6	+	4.57163e6i	0.117548	+	0.203598i
$127$	−1.52964e6	+	2.64941e6i	−0.0662636	+	0.114772i	−0.897254	−	0.441515i	$-0.854441\pi$
$127$	−1.52964e6	+	2.64941e6i	−0.0662636	+	0.114772i	0.830990	+	0.556287i	$0.187774\pi$
$128$	−8.31732e6	+	1.44060e7i	−0.350549	+	0.607168i
$129$	1.94677e7			0.798456
$130$	−3.53481e7	−	5.01884e7i	−1.41112	−	2.00356i
$131$	1.45619e7			0.565936			0.282968	−	0.959129i	$-0.408681\pi$
$131$	1.45619e7			0.565936			0.282968	+	0.959129i	$0.408681\pi$
$132$	−3.17995e6	+	5.50783e6i	−0.120340	+	0.208436i
$133$	2.76487e6	−	4.78889e6i	0.101905	−	0.176504i
$134$	5.38003e6	+	9.31848e6i	0.193160	+	0.334563i
$135$	5.06417e7			1.77150
$136$	−2.48797e6	−	4.30930e6i	−0.0848125	−	0.146900i
$137$	1.01608e7	+	1.75990e7i	0.337602	+	0.584744i	0.983981	−	0.178272i	$-0.0570508\pi$
$137$	1.01608e7	+	1.75990e7i	0.337602	+	0.584744i	−0.646379	+	0.763017i	$0.723717\pi$
$138$	5.31501e7			1.72158
$139$	−1.47868e7	−	2.56115e7i	−0.467006	−	0.808879i	0.532283	−	0.846566i	$-0.321334\pi$
$139$	−1.47868e7	−	2.56115e7i	−0.467006	−	0.808879i	−0.999290	+	0.0376877i	$0.988001\pi$
$140$	1.24663e7	−	2.15923e7i	0.383964	−	0.665045i
$141$	−2.18714e7	+	3.78824e7i	−0.657068	+	1.13807i
$142$	−5.58161e7			−1.63588
$143$	−5.10713e6	−	7.25127e6i	−0.146050	−	0.207366i
$144$	1.04312e7			0.291115
$145$	2.55480e6	−	4.42505e6i	0.0695936	−	0.120540i
$146$	2.78688e7	−	4.82702e7i	0.741111	−	1.28364i
$147$	2.10320e6	+	3.64285e6i	0.0546097	+	0.0945868i
$148$	−2.91569e7			−0.739309
$149$	−3.60932e7	−	6.25153e7i	−0.893868	−	1.54823i	−0.835199	−	0.549948i	$-0.814647\pi$
$149$	−3.60932e7	−	6.25153e7i	−0.893868	−	1.54823i	−0.0586697	−	0.998277i	$-0.518686\pi$
$150$	−3.97318e7	−	6.88175e7i	−0.961211	−	1.66487i
$151$	−6.63768e6			−0.156891			−0.0784453	−	0.996918i	$-0.524996\pi$
$151$	−6.63768e6			−0.156891			−0.0784453	+	0.996918i	$0.524996\pi$
$152$	4.21464e6	+	7.29998e6i	0.0973438	+	0.168604i
$153$	−4.32383e6	+	7.48910e6i	−0.0975998	+	0.169048i
$154$	3.25231e6	−	5.63317e6i	0.0717579	−	0.124288i
$155$	−1.33588e8			−2.88142
$156$	−1.89037e7	+	4.08316e7i	−0.398668	+	0.861113i
$157$	−1.73502e7			−0.357813			−0.178906	−	0.983866i	$-0.557256\pi$
$157$	−1.73502e7			−0.357813			−0.178906	+	0.983866i	$0.557256\pi$
$158$	−4.80674e6	+	8.32553e6i	−0.0969508	+	0.167924i
$159$	−1.51815e7	+	2.62951e7i	−0.299519	+	0.518781i
$160$	−5.97916e7	−	1.03562e8i	−1.15404	−	1.99885i
$161$	−3.01046e7			−0.568516
$162$	−1.66836e7	−	2.88968e7i	−0.308310	−	0.534008i
$163$	2.44823e7	+	4.24045e7i	0.442787	+	0.766930i	0.997895	−	0.0648485i	$-0.0206564\pi$
$163$	2.44823e7	+	4.24045e7i	0.442787	+	0.766930i	−0.555108	+	0.831778i	$0.687323\pi$
$164$	1.02203e8			1.80930
$165$	−9.15820e6	−	1.58625e7i	−0.158714	−	0.274902i
$166$	4.30871e7	−	7.46290e7i	0.731086	−	1.26628i
$167$	−5.18627e6	+	8.98289e6i	−0.0861683	+	0.149248i	−0.905888	−	0.423516i	$-0.860796\pi$
$167$	−5.18627e6	+	8.98289e6i	−0.0861683	+	0.149248i	0.819720	+	0.572764i	$0.194129\pi$
$168$	−6.41206e6			−0.104331
$169$	−4.05974e7	−	4.78459e7i	−0.646986	−	0.762502i
$170$	7.37514e7			1.15133
$171$	7.32460e6	−	1.26866e7i	0.112020	−	0.194025i
$172$	4.32519e7	−	7.49144e7i	0.648120	−	1.12258i
$173$	−4.47090e7	−	7.74383e7i	−0.656499	−	1.13709i	−0.981516	−	0.191381i	$-0.938703\pi$
$173$	−4.47090e7	−	7.74383e7i	−0.656499	−	1.13709i	0.325017	−	0.945708i	$-0.394630\pi$
$174$	−6.76270e6			−0.0973191
$175$	2.25044e7	+	3.89787e7i	0.317420	+	0.549787i
$176$	−6.42665e6	−	1.11313e7i	−0.0888568	−	0.153904i
$177$	1.07555e8			1.45789
$178$	−4.60023e7	−	7.96783e7i	−0.611377	−	1.05894i
$179$	−7.72027e6	+	1.33719e7i	−0.100611	+	0.174264i	−0.911937	−	0.410331i	$-0.865413\pi$
$179$	−7.72027e6	+	1.33719e7i	−0.100611	+	0.174264i	0.811325	+	0.584595i	$0.198747\pi$
$180$	3.30254e7	−	5.72017e7i	0.422079	−	0.731063i
$181$	8.73901e7			1.09544			0.547718	−	0.836663i	$-0.315497\pi$
$181$	8.73901e7			1.09544			0.547718	+	0.836663i	$0.315497\pi$
$182$	1.93339e7	−	4.17608e7i	0.237722	−	0.513474i
$183$	−1.26407e8			−1.52473
$184$	2.29451e7	−	3.97421e7i	0.271536	−	0.470314i
$185$	4.19858e7	−	7.27215e7i	0.487530	−	0.844426i
$186$	8.84038e7	+	1.53120e8i	1.00734	+	1.74476i
$187$	1.06557e7			0.119161
$188$	9.71845e7	+	1.68328e8i	1.06671	+	1.84759i
$189$	1.89819e7	+	3.28777e7i	0.204515	+	0.354230i
$190$	−1.24935e8			−1.32144
$191$	7.54202e7	+	1.30632e8i	0.783197	+	1.35654i	0.930070	+	0.367382i	$0.119746\pi$
$191$	7.54202e7	+	1.30632e8i	0.783197	+	1.35654i	−0.146873	+	0.989155i	$0.546921\pi$
$192$	−5.28675e7	+	9.15692e7i	−0.539057	+	0.933674i
$193$	−2.22789e7	+	3.85882e7i	−0.223071	+	0.386371i	−0.955739	−	0.294216i	$-0.904942\pi$
$193$	−2.22789e7	+	3.85882e7i	−0.223071	+	0.386371i	0.732668	+	0.680587i	$0.238275\pi$
$194$	8.80825e7			0.866131
$195$	−7.46185e7	−	1.05946e8i	−0.720651	−	1.02320i
$196$	1.86909e7			0.177310
$197$	−7.10599e7	+	1.23079e8i	−0.662205	+	1.14697i	0.317830	+	0.948148i	$0.397046\pi$
$197$	−7.10599e7	+	1.23079e8i	−0.662205	+	1.14697i	−0.980035	+	0.198826i	$0.936287\pi$
$198$	8.61592e6	−	1.49232e7i	0.0788812	−	0.136626i
$199$	−2.86248e7	−	4.95796e7i	−0.257488	−	0.445982i	0.708080	−	0.706132i	$-0.249561\pi$
$199$	−2.86248e7	−	4.95796e7i	−0.257488	−	0.445982i	−0.965568	+	0.260150i	$0.916228\pi$
$200$	−6.86094e7			−0.606427
$201$	1.13570e7	+	1.96709e7i	0.0986457	+	0.170859i
$202$	−6.84465e7	−	1.18553e8i	−0.584281	−	1.01200i
$203$	3.83045e6			0.0321376
$204$	−2.70290e7	−	4.68156e7i	−0.222907	−	0.386087i
$205$	−1.47171e8	+	2.54908e8i	−1.19312	+	2.06655i
$206$	−4.35445e7	+	7.54213e7i	−0.347055	+	0.601117i
$207$	−7.97522e7			−0.624952
$208$	−5.23626e7	−	7.43460e7i	−0.403459	−	0.572844i
$209$	−1.80508e7			−0.136768
$210$	4.75184e7	−	8.23042e7i	0.354074	−	0.613274i
$211$	−1.14932e7	+	1.99069e7i	−0.0842276	+	0.145886i	−0.905062	−	0.425280i	$-0.860176\pi$
$211$	−1.14932e7	+	1.99069e7i	−0.0842276	+	0.145886i	0.820834	+	0.571166i	$0.193509\pi$
$212$	6.74580e7	+	1.16841e8i	0.486248	+	0.842206i
$213$	−1.17825e8			−0.835431
$214$	7.69506e7	+	1.33282e8i	0.536740	+	0.929661i
$215$	1.24565e8	+	2.15752e8i	0.854792	+	1.48054i
$216$	−5.78705e7			−0.390723
$217$	−5.00726e7	−	8.67283e7i	−0.332653	−	0.576171i
$218$	5.82872e7	−	1.00956e8i	0.381044	−	0.659988i
$219$	5.88299e7	−	1.01896e8i	0.378481	−	0.655548i
$220$	−8.13879e7			−0.515324
$221$	7.50819e7	−	6.77667e6i	0.467910	−	0.0422321i
$222$	−1.11139e8			−0.681757
$223$	−4.96907e7	+	8.60668e7i	−0.300060	+	0.519719i	−0.976149	−	0.217101i	$-0.930340\pi$
$223$	−4.96907e7	+	8.60668e7i	−0.300060	+	0.519719i	0.676089	+	0.736820i	$0.263673\pi$
$224$	4.48231e7	−	7.76359e7i	0.266461	−	0.461524i
$225$	5.96179e7	+	1.03261e8i	0.348930	+	0.604364i
$226$	6.54817e7			0.377347
$227$	5.16020e7	+	8.93774e7i	0.292804	+	0.507151i	0.974472	−	0.224511i	$-0.0720785\pi$
$227$	5.16020e7	+	8.93774e7i	0.292804	+	0.507151i	−0.681668	+	0.731662i	$0.738745\pi$
$228$	4.57873e7	+	7.93059e7i	0.255842	+	0.443132i
$229$	1.24636e8			0.685835			0.342917	−	0.939366i	$-0.388585\pi$
$229$	1.24636e8			0.685835			0.342917	+	0.939366i	$0.388585\pi$
$230$	3.40082e8	+	5.89040e8i	1.84305	+	3.19225i
$231$	6.86550e6	−	1.18914e7i	0.0366463	−	0.0634733i
$232$	−2.91948e6	+	5.05669e6i	−0.0153496	+	0.0265864i
$233$	−2.25786e8			−1.16937			−0.584685	−	0.811260i	$-0.698782\pi$
$233$	−2.25786e8			−1.16937			−0.584685	+	0.811260i	$0.698782\pi$
$234$	5.12187e7	−	1.10631e8i	0.261320	−	0.564446i
$235$	−5.59779e8			−2.81371
$236$	2.38957e8	−	4.13886e8i	1.18339	−	2.04969i
$237$	−1.01468e7	+	1.75748e7i	−0.0495121	+	0.0857575i
$238$	2.76441e7	+	4.78809e7i	0.132918	+	0.230220i
$239$	−1.03673e7			−0.0491218			−0.0245609	−	0.999698i	$-0.507819\pi$
$239$	−1.03673e7			−0.0491218			−0.0245609	+	0.999698i	$0.507819\pi$
$240$	−9.38974e7	−	1.62635e8i	−0.438444	−	0.759408i
$241$	1.19448e7	+	2.06889e7i	0.0549689	+	0.0952090i	0.892201	−	0.451640i	$-0.149161\pi$
$241$	1.19448e7	+	2.06889e7i	0.0549689	+	0.0952090i	−0.837232	+	0.546849i	$0.815827\pi$
$242$	3.08826e8			1.40075
$243$	8.58122e7	+	1.48631e8i	0.383643	+	0.664489i
$244$	−2.80841e8	+	4.86431e8i	−1.23764	+	2.14366i
$245$	−2.69148e7	+	4.66177e7i	−0.116925	+	0.202521i
$246$	3.89571e8			1.66845
$247$	−1.27189e8	+	1.14797e7i	−0.537045	+	0.0484721i
$248$	1.52657e8			0.635529
$249$	9.09550e7	−	1.57539e8i	0.373361	−	0.646680i
$250$	2.05734e8	−	3.56342e8i	0.832752	−	1.44237i
$251$	1.30835e8	+	2.26613e8i	0.522236	+	0.904540i	0.999665	+	0.0258695i	$0.00823543\pi$
$251$	1.30835e8	+	2.26613e8i	0.522236	+	0.904540i	−0.477429	+	0.878670i	$0.658431\pi$
$252$	4.95154e7			0.194912
$253$	4.91354e7	+	8.51050e7i	0.190754	+	0.330395i
$254$	2.59078e7	+	4.48737e7i	0.0992003	+	0.171820i
$255$	1.55686e8			0.587975
$256$	−4.83952e7	−	8.38230e7i	−0.180286	−	0.312265i
$257$	1.75581e8	−	3.04116e8i	0.645227	−	1.11757i	−0.339022	−	0.940778i	$-0.610096\pi$
$257$	1.75581e8	−	3.04116e8i	0.645227	−	1.11757i	0.984249	−	0.176788i	$-0.0565706\pi$
$258$	1.64865e8	−	2.85554e8i	0.597666	−	1.03519i
$259$	6.29497e7			0.225136
$260$	−5.73475e8	+	5.17601e7i	−2.02352	+	0.182637i
$261$	1.01475e7			0.0353278
$262$	1.23319e8	−	2.13595e8i	0.423619	−	0.733730i
$263$	−5.46167e6	+	9.45988e6i	−0.0185131	+	0.0320657i	−0.875134	−	0.483881i	$-0.839227\pi$
$263$	−5.46167e6	+	9.45988e6i	−0.0185131	+	0.0320657i	0.856620	+	0.515947i	$0.172560\pi$
$264$	1.04655e7	+	1.81267e7i	0.0350062	+	0.0606325i
$265$	−3.88556e8			−1.28260
$266$	−4.68292e7	−	8.11106e7i	−0.152557	−	0.264236i
$267$	−9.71089e7	−	1.68198e8i	−0.312226	−	0.540792i
$268$	1.00929e8			0.320289
$269$	2.48777e8	+	4.30894e8i	0.779251	+	1.34970i	0.932374	+	0.361495i	$0.117733\pi$
$269$	2.48777e8	+	4.30894e8i	0.779251	+	1.34970i	−0.153123	+	0.988207i	$0.548933\pi$
$270$	4.28866e8	−	7.42817e8i	1.32601	−	2.29672i
$271$	−1.39662e8	+	2.41902e8i	−0.426272	+	0.738325i	−0.996538	−	0.0831351i	$-0.973507\pi$
$271$	−1.39662e8	+	2.41902e8i	−0.426272	+	0.738325i	0.570266	+	0.821460i	$0.306840\pi$
$272$	1.09251e8			0.329180
$273$	4.08131e7	−	8.81553e7i	0.121403	−	0.262228i
$274$	3.44191e8			1.01082
$275$	7.34613e7	−	1.27239e8i	0.213007	−	0.368939i
$276$	2.49272e8	−	4.31752e8i	0.713661	−	1.23610i
$277$	−1.11242e8	−	1.92677e8i	−0.314478	−	0.544693i	0.664848	−	0.746979i	$-0.268496\pi$
$277$	−1.11242e8	−	1.92677e8i	−0.314478	−	0.544693i	−0.979326	+	0.202286i	$0.935163\pi$
$278$	−5.00896e8			−1.39827
$279$	−1.32651e8	−	2.29758e8i	−0.365675	−	0.633367i
$280$	−4.10277e7	−	7.10621e7i	−0.111692	−	0.193457i
$281$	−2.99978e8			−0.806524			−0.403262	−	0.915085i	$-0.632124\pi$
$281$	−2.99978e8			−0.806524			−0.403262	+	0.915085i	$0.632124\pi$
$282$	3.70442e8	+	6.41624e8i	0.983667	+	1.70376i
$283$	3.06930e8	−	5.31618e8i	0.804983	−	1.39427i	−0.111320	−	0.993785i	$-0.535508\pi$
$283$	3.06930e8	−	5.31618e8i	0.804983	−	1.39427i	0.916303	−	0.400486i	$-0.131159\pi$
$284$	−2.61775e8	+	4.53408e8i	−0.678133	+	1.17456i
$285$	−2.63733e8			−0.674851
$286$	−1.49613e8	+	1.35036e7i	−0.378170	+	0.0341325i
$287$	−2.20656e8			−0.550971
$288$	1.18744e8	−	2.05670e8i	0.292912	−	0.507339i
$289$	1.59884e8	−	2.76927e8i	0.389638	−	0.674874i
$290$	−4.32713e7	−	7.49481e7i	−0.104185	−	0.180455i
$291$	1.85939e8			0.442328
$292$	−2.61407e8	−	4.52771e8i	−0.614438	−	1.06424i
$293$	−8.08601e6	−	1.40054e7i	−0.0187801	−	0.0325281i	0.856483	−	0.516176i	$-0.172645\pi$
$293$	−8.08601e6	−	1.40054e7i	−0.0187801	−	0.0325281i	−0.875263	+	0.483648i	$0.839312\pi$
$294$	7.12448e7			0.163507
$295$	6.88194e8	+	1.19199e9i	1.56075	+	2.70330i
$296$	−4.79789e7	+	8.31019e7i	−0.107530	+	0.186247i
$297$	6.19629e7	−	1.07323e8i	0.137241	−	0.237709i
$298$	−1.22264e9			−2.67634
$299$	4.00342e8	+	5.68418e8i	0.866127	+	1.22975i
$300$	−7.45363e8			−1.59383
$301$	−9.33806e7	+	1.61740e8i	−0.197367	+	0.341849i
$302$	−5.62120e7	+	9.73620e7i	−0.117437	+	0.203407i
$303$	−1.44488e8	−	2.50260e8i	−0.298388	−	0.516824i
$304$	−1.85071e8			−0.377817
$305$	−8.08817e8	−	1.40091e9i	−1.63230	−	2.82723i
$306$	7.32338e7	+	1.26845e8i	0.146112	+	0.253074i
$307$	7.32635e8			1.44512			0.722559	−	0.691309i	$-0.242966\pi$
$307$	7.32635e8			1.44512			0.722559	+	0.691309i	$0.242966\pi$
$308$	−3.05065e7	−	5.28388e7i	−0.0594928	−	0.103045i
$309$	−9.19207e7	+	1.59211e8i	−0.177239	+	0.306986i
$310$	−1.13131e9	+	1.95948e9i	−2.15682	+	3.73573i
$311$	9.30557e8			1.75421			0.877106	−	0.480298i	$-0.159471\pi$
$311$	9.30557e8			1.75421			0.877106	+	0.480298i	$0.159471\pi$
$312$	8.52697e7	+	1.21069e8i	0.158948	+	0.225679i
$313$	4.16673e8			0.768052			0.384026	−	0.923322i	$-0.374537\pi$
$313$	4.16673e8			0.768052			0.384026	+	0.923322i	$0.374537\pi$
$314$	−1.46932e8	+	2.54494e8i	−0.267832	+	0.463899i
$315$	−7.13017e7	+	1.23498e8i	−0.128533	+	0.222625i
$316$	4.50869e7	+	7.80928e7i	0.0803796	+	0.139222i
$317$	−5.05502e8			−0.891283			−0.445642	−	0.895211i	$-0.647024\pi$
$317$	−5.05502e8			−0.891283			−0.445642	+	0.895211i	$0.647024\pi$
$318$	2.57132e8	+	4.45366e8i	0.448396	+	0.776644i
$319$	−6.25188e6	−	1.08286e7i	−0.0107831	−	0.0186769i
$320$	−1.35310e9			−2.30836
$321$	1.62440e8	+	2.81354e8i	0.274110	+	0.474772i
$322$	−2.54945e8	+	4.41577e8i	−0.425550	+	0.737074i
$323$	7.67141e7	−	1.32873e8i	0.126668	−	0.219395i
$324$	−3.12982e8			−0.511224
$325$	4.36703e8	−	9.43267e8i	0.705657	−	1.52420i
$326$	8.29324e8			1.32575
$327$	1.23042e8	−	2.13115e8i	0.194597	−	0.337051i
$328$	1.68179e8	−	2.91295e8i	0.263156	−	0.455800i
$329$	−2.09821e8	−	3.63421e8i	−0.324835	−	0.562631i
$330$	−3.10229e8			−0.475208
$331$	−7.79591e7	−	1.35029e8i	−0.118160	−	0.204658i	0.800879	−	0.598826i	$-0.204366\pi$
$331$	−7.79591e7	−	1.35029e8i	−0.118160	−	0.204658i	−0.919038	+	0.394168i	$0.871033\pi$
$332$	−4.04154e8	−	7.00015e8i	−0.606126	−	1.04984i
$333$	1.66764e8			0.247485
$334$	8.78411e7	+	1.52145e8i	0.128999	+	0.223432i
$335$	−1.45336e8	+	2.51730e8i	−0.211211	+	0.365829i
$336$	7.03908e7	−	1.21920e8i	0.101234	−	0.175343i
$337$	7.06933e8			1.00618			0.503088	−	0.864235i	$-0.332197\pi$
$337$	7.06933e8			1.00618			0.503088	+	0.864235i	$0.332197\pi$
$338$	−1.04561e9	+	1.90298e8i	−1.47286	+	0.268056i
$339$	1.38229e8			0.192709
$340$	3.45891e8	−	5.99101e8i	0.477269	−	0.826654i
$341$	−1.63452e8	+	2.83108e8i	−0.223229	+	0.386644i
$342$	−1.24058e8	−	2.14875e8i	−0.167701	−	0.290466i
$343$	−4.03536e7			−0.0539949
$344$	−1.42345e8	−	2.46549e8i	−0.188534	−	0.326550i
$345$	7.17899e8	+	1.24344e9i	0.941232	+	1.63026i
$346$	−1.51450e9			−1.96563
$347$	4.71549e8	+	8.16747e8i	0.605862	+	1.04938i	0.991915	+	0.126907i	$0.0405049\pi$
$347$	4.71549e8	+	8.16747e8i	0.605862	+	1.04938i	−0.386053	+	0.922477i	$0.626162\pi$
$348$	−3.17168e7	+	5.49352e7i	−0.0403425	+	0.0698752i
$349$	−1.17691e8	+	2.03847e8i	−0.148202	+	0.256694i	−0.930563	−	0.366132i	$-0.880682\pi$
$349$	−1.17691e8	+	2.03847e8i	−0.148202	+	0.256694i	0.782361	+	0.622825i	$0.214015\pi$
$350$	7.62324e8			0.950389
$351$	3.68349e8	−	7.95624e8i	0.454657	−	0.982049i
$352$	−2.92633e8			−0.357622
$353$	−5.05711e8	+	8.75917e8i	−0.611915	+	1.05987i	0.379003	+	0.925395i	$0.376267\pi$
$353$	−5.05711e8	+	8.75917e8i	−0.611915	+	1.05987i	−0.990917	+	0.134472i	$0.957066\pi$
$354$	9.10843e8	−	1.57763e9i	1.09127	−	1.89013i
$355$	−7.53909e8	−	1.30581e9i	−0.894375	−	1.54910i
$356$	−8.62996e8			−1.01376
$357$	5.83555e7	+	1.01075e8i	0.0678802	+	0.117572i
$358$	1.30760e8	+	2.26483e8i	0.150621	+	0.260883i
$359$	−3.80122e8			−0.433603			−0.216801	−	0.976216i	$-0.569562\pi$
$359$	−3.80122e8			−0.433603			−0.216801	+	0.976216i	$0.569562\pi$
$360$	−1.08689e8	−	1.88255e8i	−0.122780	−	0.212661i
$361$	3.16982e8	−	5.49028e8i	0.354617	−	0.614214i
$362$	7.40074e8	−	1.28184e9i	0.819964	−	1.42022i
$363$	6.51919e8			0.715353
$364$	−2.48558e8	−	3.52911e8i	−0.270130	−	0.383539i
$365$	1.50570e9			1.62074
$366$	−1.07049e9	+	1.85415e9i	−1.14130	+	1.97679i
$367$	6.32146e8	−	1.09491e9i	0.667554	−	1.15624i	−0.311032	−	0.950399i	$-0.600675\pi$
$367$	6.32146e8	−	1.09491e9i	0.667554	−	1.15624i	0.978586	−	0.205838i	$-0.0659920\pi$
$368$	5.03777e8	+	8.72567e8i	0.526952	+	0.912707i
$369$	−5.84554e8			−0.605665
$370$	−7.11123e8	−	1.23170e9i	−0.729858	−	1.26415i
$371$	−1.45642e8	−	2.52259e8i	−0.148073	−	0.256470i
$372$	1.65844e9			1.67032
$373$	−7.93756e8	−	1.37483e9i	−0.791966	−	1.37172i	−0.924748	−	0.380580i	$-0.875725\pi$
$373$	−7.93756e8	−	1.37483e9i	−0.791966	−	1.37172i	0.132782	−	0.991145i	$-0.457609\pi$
$374$	9.02388e7	−	1.56298e8i	0.0891955	−	0.154491i
$375$	4.34296e8	−	7.52222e8i	0.425281	−	0.736609i
$376$	6.39684e8			0.620595
$377$	−5.09386e7	−	7.23242e7i	−0.0489612	−	0.0695167i
$378$	6.43003e8			0.612339
$379$	4.51653e7	−	7.82287e7i	0.0426155	−	0.0738123i	−0.843931	−	0.536452i	$-0.819764\pi$
$379$	4.51653e7	−	7.82287e7i	0.0426155	−	0.0738123i	0.886546	+	0.462640i	$0.153098\pi$
$380$	−5.85942e8	+	1.01488e9i	−0.547787	+	0.948795i
$381$	5.46903e7	+	9.47264e7i	0.0506609	+	0.0877473i
$382$	2.55482e9			2.34498
$383$	−1.05039e9	−	1.81932e9i	−0.955330	−	1.65468i	−0.733610	−	0.679571i	$-0.762166\pi$
$383$	−1.05039e9	−	1.81932e9i	−0.955330	−	1.65468i	−0.221720	−	0.975110i	$-0.571167\pi$
$384$	2.97376e8	+	5.15070e8i	0.268007	+	0.464202i
$385$	1.75716e8			0.156928
$386$	3.77344e8	+	6.53578e8i	0.333950	+	0.578418i
$387$	−2.47381e8	+	4.28476e8i	−0.216959	+	0.375784i
$388$	4.13104e8	−	7.15517e8i	0.359045	−	0.621883i
$389$	−3.86661e8			−0.333048			−0.166524	−	0.986037i	$-0.553254\pi$
$389$	−3.86661e8			−0.333048			−0.166524	+	0.986037i	$0.553254\pi$
$390$	−2.18593e9	+	1.97296e8i	−1.86600	+	0.168419i
$391$	−8.35284e8			−0.706668
$392$	3.07566e7	−	5.32721e7i	0.0257892	−	0.0446682i
$393$	2.60321e8	−	4.50890e8i	0.216339	−	0.374711i
$394$	1.20356e9	+	2.08462e9i	0.991358	+	1.71708i
$395$	−2.59699e8			−0.212022
$396$	−8.08168e7	−	1.39979e8i	−0.0653986	−	0.113274i
$397$	8.56988e8	+	1.48435e9i	0.687398	+	1.19061i	0.972677	+	0.232163i	$0.0745804\pi$
$397$	8.56988e8	+	1.48435e9i	0.687398	+	1.19061i	−0.285279	+	0.958444i	$0.592086\pi$
$398$	−9.69651e8			−0.770947
$399$	−9.88545e7	−	1.71221e8i	−0.0779097	−	0.134944i
$400$	7.53186e8	−	1.30456e9i	0.588426	−	1.01918i
$401$	−2.46742e7	+	4.27370e7i	−0.0191090	+	0.0330978i	−0.875422	−	0.483360i	$-0.839416\pi$
$401$	−2.46742e7	+	4.27370e7i	−0.0191090	+	0.0330978i	0.856313	+	0.516458i	$0.172750\pi$
$402$	3.84713e8			0.295356
$403$	−9.71669e8	+	2.09878e9i	−0.739522	+	1.59735i
$404$	−1.28405e9			−0.968827
$405$	4.50691e8	−	7.80620e8i	0.337122	−	0.583912i
$406$	3.24386e7	−	5.61853e7i	0.0240559	−	0.0416660i
$407$	−1.02744e8	−	1.77957e8i	−0.0755397	−	0.130839i
$408$	−1.77909e8			−0.129684
$409$	−3.52000e8	−	6.09682e8i	−0.254397	−	0.440628i	0.710335	−	0.703864i	$-0.248544\pi$
$409$	−3.52000e8	−	6.09682e8i	−0.254397	−	0.440628i	−0.964731	+	0.263236i	$0.915210\pi$
$410$	2.49268e9	+	4.31744e9i	1.78617	+	3.09374i
$411$	7.26574e8			0.516218
$412$	4.08444e8	+	7.07446e8i	0.287735	+	0.498372i
$413$	−5.15908e8	+	8.93579e8i	−0.360369	+	0.624177i
$414$	−6.75391e8	+	1.16981e9i	−0.467793	+	0.810242i
$415$	2.32791e9			1.59881
$416$	−2.06195e9	+	1.86105e8i	−1.40427	+	0.126745i
$417$	−1.05737e9			−0.714086
$418$	−1.52865e8	+	2.64770e8i	−0.102374	+	0.177318i
$419$	−1.28399e9	+	2.22394e9i	−0.852732	+	1.47698i	0.0260004	+	0.999662i	$0.491723\pi$
$419$	−1.28399e9	+	2.22394e9i	−0.852732	+	1.47698i	−0.878733	+	0.477314i	$0.841610\pi$
$420$	−4.45719e8	−	7.72008e8i	−0.293554	−	0.508451i
$421$	−2.10059e8			−0.137200			−0.0685999	−	0.997644i	$-0.521853\pi$
$421$	−2.10059e8			−0.137200			−0.0685999	+	0.997644i	$0.521853\pi$
$422$	1.94664e8	+	3.37168e8i	0.126093	+	0.218400i
$423$	−5.55851e8	−	9.62762e8i	−0.357081	−	0.618483i
$424$	4.44019e8			0.282893
$425$	6.24408e8	+	1.08151e9i	0.394554	+	0.683388i
$426$	−9.97819e8	+	1.72827e9i	−0.625343	+	1.08313i
$427$	6.06334e8	−	1.05020e9i	0.376890	−	0.652793i
$428$	1.44358e9			0.889997
$429$	−3.15826e8	+	2.85055e7i	−0.193129	+	0.0174312i
$430$	4.21956e9			2.55934
$431$	3.05632e8	−	5.29369e8i	0.183877	−	0.318485i	−0.759320	−	0.650717i	$-0.774468\pi$
$431$	3.05632e8	−	5.29369e8i	0.183877	−	0.318485i	0.943198	+	0.332232i	$0.107802\pi$
$432$	6.35295e8	−	1.10036e9i	0.379125	−	0.656664i
$433$	2.76508e8	+	4.78925e8i	0.163681	+	0.283505i	0.936186	−	0.351504i	$-0.114330\pi$
$433$	2.76508e8	+	4.78925e8i	0.163681	+	0.283505i	−0.772505	+	0.635009i	$0.780996\pi$
$434$	−1.69618e9			−0.995998
$435$	−9.13440e7	−	1.58212e8i	−0.0532068	−	0.0921570i
$436$	−5.46729e8	−	9.46963e8i	−0.315915	−	0.547180i
$437$	1.41498e9			0.811081
$438$	−9.96416e8	−	1.72584e9i	−0.566606	−	0.981391i
$439$	3.04965e7	−	5.28215e7i	0.0172038	−	0.0297978i	−0.857295	−	0.514825i	$-0.827857\pi$
$439$	3.04965e7	−	5.28215e7i	0.0172038	−	0.0297978i	0.874499	+	0.485027i	$0.161190\pi$
$440$	−1.33927e8	+	2.31969e8i	−0.0749522	+	0.129821i
$441$	−1.06903e8			−0.0593549
$442$	5.36439e8	−	1.15870e9i	0.295490	−	0.638251i
$443$	−2.01087e9			−1.09893			−0.549465	−	0.835517i	$-0.685168\pi$
$443$	−2.01087e9			−1.09893			−0.549465	+	0.835517i	$0.685168\pi$
$444$	−5.21236e8	+	9.02807e8i	−0.282614	+	0.489502i
$445$	1.24271e9	−	2.15243e9i	0.668511	−	1.15790i
$446$	8.41623e8	+	1.45773e9i	0.449206	+	0.778048i
$447$	−2.58094e9			−1.36679
$448$	−5.07178e8	−	8.78458e8i	−0.266494	−	0.461581i
$449$	−9.42178e8	−	1.63190e9i	−0.491214	−	0.850808i	0.508735	−	0.860923i	$-0.330113\pi$
$449$	−9.42178e8	−	1.63190e9i	−0.491214	−	0.850808i	−0.999949	+	0.0101157i	$0.996780\pi$
$450$	2.01952e9			1.04473
$451$	3.60145e8	+	6.23789e8i	0.184867	+	0.320199i
$452$	3.07107e8	−	5.31925e8i	0.156425	−	0.270935i
$453$	−1.18661e8	+	2.05527e8i	−0.0599743	+	0.103878i
$454$	1.74799e9			0.876686
$455$	1.23813e9	−	1.11750e8i	0.616207	−	0.0556170i
$456$	3.01379e8			0.148846
$457$	6.45577e8	−	1.11817e9i	0.316403	−	0.548027i	−0.663331	−	0.748326i	$-0.730858\pi$
$457$	6.45577e8	−	1.11817e9i	0.316403	−	0.548027i	0.979735	+	0.200299i	$0.0641914\pi$
$458$	1.05550e9	−	1.82817e9i	0.513366	−	0.889176i
$459$	5.26674e8	+	9.12225e8i	0.254213	+	0.440309i
$460$	6.37989e9			3.05605
$461$	1.38912e9	+	2.40602e9i	0.660367	+	1.14379i	0.980519	+	0.196424i	$0.0629328\pi$
$461$	1.38912e9	+	2.40602e9i	0.660367	+	1.14379i	−0.320152	+	0.947366i	$0.603734\pi$
$462$	−1.16283e8	−	2.01407e8i	−0.0548615	−	0.0950230i
$463$	9.20647e7			0.0431082			0.0215541	−	0.999768i	$-0.493139\pi$
$463$	9.20647e7			0.0431082			0.0215541	+	0.999768i	$0.493139\pi$
$464$	−6.40995e7	−	1.11024e8i	−0.0297880	−	0.0515943i
$465$	−2.38814e9	+	4.13639e9i	−1.10148	+	1.90781i
$466$	−1.91210e9	+	3.31185e9i	−0.875306	+	1.51607i
$467$	−3.88159e9			−1.76360			−0.881800	−	0.471623i	$-0.843668\pi$
$467$	−3.88159e9			−1.76360			−0.881800	+	0.471623i	$0.843668\pi$
$468$	−6.58472e8	−	9.34920e8i	−0.296946	−	0.421613i
$469$	−2.17904e8			−0.0975352
$470$	−4.74056e9	+	8.21089e9i	−2.10614	+	3.64794i
$471$	−3.10168e8	+	5.37226e8i	−0.136780	+	0.236910i
$472$	−7.86428e8	−	1.36213e9i	−0.344241	−	0.596242i
$473$	6.09647e8			0.264889
$474$	1.71859e8	+	2.97669e8i	0.0741224	+	0.128384i
$475$	−1.05775e9	−	1.83208e9i	−0.452851	−	0.784361i
$476$	5.18599e8			0.220398
$477$	−3.85829e8	−	6.68275e8i	−0.162772	−	0.281930i
$478$	−8.77969e7	+	1.52069e8i	−0.0367690	+	0.0636858i
$479$	4.04335e7	−	7.00329e7i	0.0168100	−	0.0291157i	−0.857498	−	0.514487i	$-0.827982\pi$
$479$	4.04335e7	−	7.00329e7i	0.0168100	−	0.0291157i	0.874308	+	0.485371i	$0.161316\pi$
$480$	−4.27555e9			−1.76461
$481$	−8.37127e8	−	1.18858e9i	−0.342992	−	0.486991i
$482$	4.04622e8			0.164583
$483$	−5.38177e8	+	9.32151e8i	−0.217325	+	0.376419i
$484$	1.44838e9	−	2.50867e9i	0.580663	−	1.00574i
$485$	1.18973e9	+	2.06068e9i	0.473536	+	0.820189i
$486$	2.90684e9			1.14867
$487$	−1.71534e9	−	2.97106e9i	−0.672975	−	1.16563i	−0.977056	−	0.212981i	$-0.931683\pi$
$487$	−1.71534e9	−	2.97106e9i	−0.672975	−	1.16563i	0.304081	−	0.952646i	$-0.401651\pi$
$488$	9.24270e8	+	1.60088e9i	0.360022	+	0.623577i
$489$	1.75067e9			0.677054
$490$	4.55862e8	+	7.89576e8i	0.175044	+	0.303185i
$491$	−1.02899e9	+	1.78227e9i	−0.392307	+	0.679496i	−0.992753	−	0.120169i	$-0.961656\pi$
$491$	−1.02899e9	+	1.78227e9i	−0.392307	+	0.679496i	0.600446	+	0.799665i	$0.294990\pi$
$492$	1.82707e9	−	3.16458e9i	0.691637	−	1.19795i
$493$	1.06280e8			0.0399472
$494$	−9.08731e8	+	1.96284e9i	−0.339149	+	0.732555i
$495$	4.65502e8			0.172506
$496$	−1.67585e9	+	2.90266e9i	−0.616665	+	1.06809i
$497$	5.65172e8	−	9.78907e8i	0.206506	−	0.357680i
$498$	−1.54053e9	−	2.66827e9i	−0.558942	−	0.968116i
$499$	−3.87081e9			−1.39460			−0.697301	−	0.716779i	$-0.745616\pi$
$499$	−3.87081e9			−1.39460			−0.697301	+	0.716779i	$0.745616\pi$
$500$	−1.92977e9	−	3.34246e9i	−0.690415	−	1.19583i
$501$	1.85429e8	+	3.21172e8i	0.0658788	+	0.114105i
$502$	4.43198e9			1.56363
$503$	3.56745e8	+	6.17901e8i	0.124989	+	0.216487i	0.921728	−	0.387836i	$-0.126777\pi$
$503$	3.56745e8	+	6.17901e8i	0.124989	+	0.216487i	−0.796740	+	0.604322i	$0.793444\pi$
$504$	8.14795e7	−	1.41127e8i	0.0283493	−	0.0491023i
$505$	1.84902e9	−	3.20259e9i	0.638883	−	1.10658i
$506$	1.66444e9			0.571137
$507$	−2.20724e9	+	4.01711e8i	−0.752180	+	0.136894i
$508$	4.86027e8			0.164489
$509$	2.49325e9	−	4.31843e9i	0.838018	−	1.45149i	−0.0535318	−	0.998566i	$-0.517048\pi$
$509$	2.49325e9	−	4.31843e9i	0.838018	−	1.45149i	0.891550	−	0.452923i	$-0.149619\pi$
$510$	1.31845e9	−	2.28362e9i	0.440116	−	0.762303i
$511$	5.64378e8	+	9.77531e8i	0.187110	+	0.324084i
$512$	−3.76860e9			−1.24089
$513$	−8.92188e8	−	1.54531e9i	−0.291773	−	0.505366i
$514$	−2.97386e9	−	5.15088e9i	−0.965940	−	1.67306i
$515$	−2.35263e9			−0.758975
$516$	−1.54642e9	−	2.67848e9i	−0.495511	−	0.858250i
$517$	−6.84921e8	+	1.18632e9i	−0.217983	+	0.377558i
$518$	5.33097e8	−	9.23352e8i	0.168520	−	0.291886i
$519$	−3.19704e9			−1.00383
$520$	−7.96151e8	+	1.71967e9i	−0.248304	+	0.536331i
$521$	1.54041e9			0.477204			0.238602	−	0.971117i	$-0.423311\pi$
$521$	1.54041e9			0.477204			0.238602	+	0.971117i	$0.423311\pi$
$522$	8.59353e7	−	1.48844e8i	0.0264439	−	0.0458021i
$523$	1.38461e9	−	2.39822e9i	0.423225	−	0.733048i	−0.573027	−	0.819536i	$-0.694231\pi$
$523$	1.38461e9	−	2.39822e9i	0.423225	−	0.733048i	0.996253	+	0.0864882i	$0.0275645\pi$
$524$	−1.15672e9	−	2.00350e9i	−0.351212	−	0.608318i
$525$	1.60924e9			0.485358
$526$	9.25056e7	+	1.60224e8i	0.0277152	+	0.0480041i
$527$	−1.38932e9	−	2.40637e9i	−0.413489	−	0.716184i
$528$	−4.59555e8			−0.135868
$529$	−2.14925e9	−	3.72261e9i	−0.631236	−	1.09333i
$530$	−3.29053e9	+	5.69937e9i	−0.960065	+	1.66288i
$531$	−1.36673e9	+	2.36724e9i	−0.396142	+	0.686139i
$532$	−8.78509e8			−0.252962
$533$	2.93436e9	+	4.16629e9i	0.839398	+	1.19180i
$534$	−3.28951e9			−0.934840
$535$	−2.07875e9	+	3.60049e9i	−0.586899	+	1.01654i
$536$	1.66082e8	−	2.87663e8i	0.0465850	−	0.0806876i
$537$	2.76029e8	+	4.78096e8i	0.0769210	+	0.133231i
$538$	8.42719e9			2.33316
$539$	6.58634e7	+	1.14079e8i	0.0181169	+	0.0313793i
$540$	−4.02273e9	−	6.96757e9i	−1.09937	−	1.90416i
$541$	3.26764e9			0.887245			0.443623	−	0.896214i	$-0.353693\pi$
$541$	3.26764e9			0.887245			0.443623	+	0.896214i	$0.353693\pi$
$542$	2.36549e9	+	4.09716e9i	0.638153	+	1.10531i
$543$	1.56226e9	−	2.70592e9i	0.418750	−	0.725297i
$544$	1.24366e9	−	2.15409e9i	0.331213	−	0.573677i
$545$	3.14914e9			0.833306
$546$	−9.47438e8	−	1.34520e9i	−0.249102	−	0.353682i
$547$	7.46922e9			1.95128			0.975641	−	0.219375i	$-0.0704019\pi$
$547$	7.46922e9			1.95128			0.975641	+	0.219375i	$0.0704019\pi$
$548$	1.61425e9	−	2.79596e9i	0.419023	−	0.725769i
$549$	1.60628e9	−	2.78216e9i	0.414303	−	0.717594i
$550$	−1.24423e9	−	2.15507e9i	−0.318883	−	0.552322i
$551$	−1.80038e8			−0.0458495
$552$	−8.20375e8	−	1.42093e9i	−0.207599	−	0.359572i
$553$	−9.73425e7	−	1.68602e8i	−0.0244774	−	0.0423960i
$554$	−3.76828e9			−0.941583
$555$	−1.50115e9	−	2.60007e9i	−0.372734	−	0.645594i
$556$	−2.34918e9	+	4.06890e9i	−0.579635	+	1.00396i
$557$	1.45058e9	−	2.51248e9i	0.355672	−	0.616041i	−0.631561	−	0.775326i	$-0.717585\pi$
$557$	1.45058e9	−	2.51248e9i	0.355672	−	0.616041i	0.987233	+	0.159285i	$0.0509188\pi$
$558$	−4.49347e9			−1.09487
$559$	4.29569e9	−	3.87716e8i	1.04014	−	0.0938798i
$560$	1.80159e9			0.433508
$561$	1.90490e8	−	3.29939e8i	0.0455516	−	0.0788976i
$562$	−2.54040e9	+	4.40010e9i	−0.603705	+	1.04565i
$563$	−2.62044e9	−	4.53873e9i	−0.618863	−	1.07190i	−0.989694	−	0.143201i	$-0.954260\pi$
$563$	−2.62044e9	−	4.53873e9i	−0.618863	−	1.07190i	0.370831	−	0.928700i	$-0.379073\pi$
$564$	6.94943e9			1.63107
$565$	8.84463e8	+	1.53194e9i	0.206305	+	0.357331i
$566$	−5.19854e9	−	9.00414e9i	−1.20510	−	2.08730i
$567$	6.75727e8			0.155679
$568$	8.61524e8	+	1.49220e9i	0.197264	+	0.341672i
$569$	2.52110e9	−	4.36667e9i	0.573715	−	0.993704i	−0.422465	−	0.906379i	$-0.638835\pi$
$569$	2.52110e9	−	4.36667e9i	0.573715	−	0.993704i	0.996180	−	0.0873246i	$-0.0278317\pi$
$570$	−2.23346e9	+	3.86846e9i	−0.505144	+	0.874935i
$571$	−7.10198e9			−1.59644			−0.798221	−	0.602364i	$-0.794225\pi$
$571$	−7.10198e9			−1.59644			−0.798221	+	0.602364i	$0.794225\pi$
$572$	−5.91985e8	+	1.27867e9i	−0.132259	+	0.285676i
$573$	5.39312e9			1.19757
$574$	−1.86865e9	+	3.23660e9i	−0.412417	+	0.714327i
$575$	−5.75853e9	+	9.97407e9i	−1.26321	+	2.18794i
$576$	−1.34360e9	−	2.32718e9i	−0.292948	−	0.507402i
$577$	−3.37193e9			−0.730740			−0.365370	−	0.930862i	$-0.619058\pi$
$577$	−3.37193e9			−0.730740			−0.365370	+	0.930862i	$0.619058\pi$
$578$	−2.70799e9	−	4.69037e9i	−0.583310	−	1.01032i
$579$	7.96557e8	+	1.37968e9i	0.170546	+	0.295395i
$580$	−8.11764e8			−0.172755
$581$	8.72566e8	+	1.51133e9i	0.184579	+	0.319700i
$582$	1.57464e9	−	2.72736e9i	0.331094	−	0.573472i
$583$	−4.75419e8	+	8.23450e8i	−0.0993658	+	0.172107i
$584$	−1.72063e9			−0.357472
$585$	3.28001e9	−	2.96044e8i	0.677377	−	0.0611380i
$586$	−2.73909e8			−0.0562296
$587$	3.33438e9	−	5.77532e9i	0.680428	−	1.17854i	−0.294423	−	0.955675i	$-0.595127\pi$
$587$	3.33438e9	−	5.77532e9i	0.680428	−	1.17854i	0.974850	−	0.222860i	$-0.0715394\pi$
$588$	3.34136e8	−	5.78740e8i	0.0677801	−	0.117399i
$589$	2.35351e9	+	4.07640e9i	0.474583	+	0.822002i
$590$	2.33122e10			4.67306
$591$	2.54066e9	+	4.40056e9i	0.506280	+	0.876903i
$592$	−1.05341e9	−	1.82457e9i	−0.208676	−	0.361438i
$593$	4.46386e8			0.0879062			0.0439531	−	0.999034i	$-0.486005\pi$
$593$	4.46386e8			0.0879062			0.0439531	+	0.999034i	$0.486005\pi$
$594$	−1.04948e9	−	1.81775e9i	−0.205458	−	0.355863i
$595$	−7.46778e8	+	1.29346e9i	−0.145339	+	0.251735i
$596$	−5.73413e9	+	9.93181e9i	−1.10945	+	1.92162i
$597$	−2.04689e9			−0.393718
$598$	1.17279e10	−	1.05853e9i	2.24268	−	0.202418i
$599$	−7.43034e9			−1.41259			−0.706293	−	0.707919i	$-0.749634\pi$
$599$	−7.43034e9			−1.41259			−0.706293	+	0.707919i	$0.749634\pi$
$600$	−1.22652e9	+	2.12440e9i	−0.231818	+	0.401520i
$601$	−2.14367e9	+	3.71294e9i	−0.402807	+	0.697682i	−0.994063	−	0.108802i	$-0.965299\pi$
$601$	−2.14367e9	+	3.71294e9i	−0.402807	+	0.697682i	0.591257	+	0.806483i	$0.298632\pi$
$602$	1.58161e9	+	2.73943e9i	0.295469	+	0.511767i
$603$	−5.77265e8			−0.107217
$604$	5.27264e8	+	9.13249e8i	0.0973642	+	0.168640i
$605$	4.17132e9	+	7.22493e9i	0.765825	+	1.32645i
$606$	−4.89445e9			−0.893408
$607$	−2.97397e9	−	5.15106e9i	−0.539729	−	0.934838i	−0.998918	−	0.0464995i	$-0.985193\pi$
$607$	−2.97397e9	−	5.15106e9i	−0.539729	−	0.934838i	0.459189	−	0.888338i	$-0.348140\pi$
$608$	−2.10677e9	+	3.64904e9i	−0.380150	+	0.658440i
$609$	6.84765e7	−	1.18605e8i	0.0122852	−	0.0212785i
$610$	−2.73983e10			−4.88729
$611$	−4.07162e9	+	8.79461e9i	−0.722143	+	1.55981i
$612$	1.37386e9			0.242276
$613$	−1.99745e9	+	3.45969e9i	−0.350239	+	0.606632i	−0.986291	−	0.165014i	$-0.947233\pi$
$613$	−1.99745e9	+	3.45969e9i	−0.350239	+	0.606632i	0.636052	+	0.771646i	$0.280566\pi$
$614$	6.20441e9	−	1.07464e10i	1.08171	−	1.87358i
$615$	5.26194e9	+	9.11395e9i	0.912185	+	1.57995i
$616$	−2.00799e8			−0.0346121
$617$	−7.10899e8	−	1.23131e9i	−0.121846	−	0.211043i	0.798650	−	0.601796i	$-0.205548\pi$
$617$	−7.10899e8	−	1.23131e9i	−0.121846	−	0.211043i	−0.920496	+	0.390753i	$0.872215\pi$
$618$	1.55688e9	+	2.69660e9i	0.265336	+	0.459575i
$619$	−3.56623e9			−0.604354			−0.302177	−	0.953252i	$-0.597713\pi$
$619$	−3.56623e9			−0.604354			−0.302177	+	0.953252i	$0.597713\pi$
$620$	1.06116e10	+	1.83798e10i	1.78817	+	3.09721i
$621$	−4.85719e9	+	8.41290e9i	−0.813888	+	1.40970i
$622$	7.88054e9	−	1.36495e10i	1.31307	−	2.27431i
$623$	1.86321e9			0.308711
$624$	−3.23811e9	+	2.92262e8i	−0.533514	+	0.0481533i
$625$	8.63775e8			0.141521
$626$	3.52865e9	−	6.11180e9i	0.574908	−	0.995769i
$627$	−3.22692e8	+	5.58919e8i	−0.0522819	+	0.0905550i
$628$	1.37821e9	+	2.38714e9i	0.222054	+	0.384608i
$629$	1.74661e9			0.279845
$630$	1.20765e9	+	2.09172e9i	0.192420	+	0.333282i
$631$	−4.34408e9	−	7.52417e9i	−0.688328	−	1.19222i	−0.972378	−	0.233410i	$-0.925012\pi$
$631$	−4.34408e9	−	7.52417e9i	−0.688328	−	1.19222i	0.284050	−	0.958809i	$-0.408322\pi$
$632$	2.96769e8			0.0467638
$633$	4.10928e8	+	7.11747e8i	0.0643950	+	0.111535i
$634$	−4.28091e9	+	7.41475e9i	−0.667150	+	1.15554i
$635$	−6.99875e8	+	1.21222e9i	−0.108471	+	0.187877i
$636$	4.82376e9			0.743508
$637$	5.36636e8	+	7.61933e8i	0.0822606	+	0.116796i
$638$	−2.11779e8			−0.0322858
$639$	1.49724e9	−	2.59329e9i	0.227006	−	0.393186i
$640$	−3.80553e9	+	6.59138e9i	−0.573833	+	0.993908i
$641$	−4.58966e9	−	7.94952e9i	−0.688299	−	1.19217i	−0.972388	−	0.233371i	$-0.925024\pi$
$641$	−4.58966e9	−	7.94952e9i	−0.688299	−	1.19217i	0.284089	−	0.958798i	$-0.408309\pi$
$642$	5.50256e9			0.820714
$643$	−1.59944e9	−	2.77031e9i	−0.237263	−	0.410952i	0.722665	−	0.691199i	$-0.242917\pi$
$643$	−1.59944e9	−	2.77031e9i	−0.237263	−	0.410952i	−0.959928	+	0.280247i	$0.909584\pi$
$644$	2.39136e9	+	4.14196e9i	0.352813	+	0.611090i
$645$	8.90732e9			1.30704
$646$	−1.29933e9	−	2.25050e9i	−0.189629	−	0.328447i
$647$	−3.55777e9	+	6.16224e9i	−0.516432	+	0.894487i	0.483386	+	0.875407i	$0.339407\pi$
$647$	−3.55777e9	+	6.16224e9i	−0.516432	+	0.894487i	−0.999818	+	0.0190793i	$0.993926\pi$
$648$	−5.15024e8	+	8.92048e8i	−0.0743559	+	0.128788i
$649$	3.36817e9			0.483657
$650$	−1.01376e10	−	1.43938e10i	−1.44791	−	2.05578i
$651$	−3.58057e9			−0.508650
$652$	3.88950e9	−	6.73681e9i	0.549575	−	0.951892i
$653$	2.51790e9	−	4.36112e9i	0.353868	−	0.612918i	−0.633055	−	0.774107i	$-0.718199\pi$
$653$	2.51790e9	−	4.36112e9i	0.353868	−	0.612918i	0.986924	+	0.161189i	$0.0515328\pi$
$654$	−2.08399e9	−	3.60957e9i	−0.291322	−	0.504584i
$655$	6.66269e9			0.926414
$656$	3.69250e9	+	6.39560e9i	0.510690	+	0.884540i
$657$	1.49513e9	+	2.58964e9i	0.205684	+	0.356255i
$658$	−7.10758e9			−0.972592
$659$	4.00538e9	+	6.93752e9i	0.545186	+	0.944290i	0.998595	+	0.0529873i	$0.0168743\pi$
$659$	4.00538e9	+	6.93752e9i	0.545186	+	0.944290i	−0.453409	+	0.891302i	$0.649792\pi$
$660$	−1.45496e9	+	2.52007e9i	−0.196992	+	0.341200i
$661$	−7.77371e8	+	1.34645e9i	−0.104694	+	0.181336i	−0.913613	−	0.406584i	$-0.866720\pi$
$661$	−7.77371e8	+	1.34645e9i	−0.104694	+	0.181336i	0.808919	+	0.587920i	$0.200053\pi$
$662$	−2.64082e9			−0.353782
$663$	1.13240e9	−	2.44596e9i	0.150905	−	0.325951i
$664$	−2.66020e9			−0.352636
$665$	1.26505e9	−	2.19112e9i	0.166813	−	0.288929i
$666$	1.41226e9	−	2.44611e9i	0.185249	−	0.320861i
$667$	4.90077e8	+	8.48838e8i	0.0639475	+	0.110760i
$668$	1.64789e9			0.213900
$669$	1.77663e9	+	3.07722e9i	0.229407	+	0.397344i
$670$	2.46160e9	+	4.26361e9i	0.316195	+	0.547666i
$671$	−3.95853e9			−0.505830
$672$	−1.60260e9	−	2.77578e9i	−0.203719	−	0.352852i
$673$	−4.47922e9	+	7.75823e9i	−0.566434	+	0.981092i	0.430481	+	0.902600i	$0.358344\pi$
$673$	−4.47922e9	+	7.75823e9i	−0.566434	+	0.981092i	−0.996915	+	0.0784925i	$0.974989\pi$
$674$	5.98675e9	−	1.03694e10i	0.753150	−	1.30449i
$675$	1.45238e10			1.81767
$676$	−3.35804e9	+	9.38626e9i	−0.418093	+	1.16864i
$677$	1.95666e9			0.242357			0.121178	−	0.992631i	$-0.461333\pi$
$677$	1.95666e9			0.242357			0.121178	+	0.992631i	$0.461333\pi$
$678$	1.17061e9	−	2.02756e9i	0.144248	−	0.249844i
$679$	−8.91890e8	+	1.54480e9i	−0.109337	+	0.189377i
$680$	−1.13836e9	−	1.97169e9i	−0.138834	−	0.240468i
$681$	3.68994e9			0.447718
$682$	2.76843e9	+	4.79507e9i	0.334186	+	0.578828i
$683$	−5.29191e9	−	9.16586e9i	−0.635536	−	1.10078i	−0.986401	−	0.164354i	$-0.947446\pi$
$683$	−5.29191e9	−	9.16586e9i	−0.635536	−	1.10078i	0.350866	−	0.936426i	$-0.385887\pi$
$684$	−2.32732e9			−0.278073
$685$	4.64900e9	+	8.05231e9i	0.552640	+	0.957201i
$686$	−3.41739e8	+	5.91910e8i	−0.0404167	+	0.0700037i
$687$	2.22811e9	−	3.85920e9i	0.262173	−	0.454097i
$688$	6.25060e9			0.731749
$689$	−2.82621e9	+	6.10454e9i	−0.329182	+	0.711026i
$690$	2.43185e10			2.81815
$691$	−1.02177e9	+	1.76976e9i	−0.117809	+	0.204052i	−0.918899	−	0.394492i	$-0.870920\pi$
$691$	−1.02177e9	+	1.76976e9i	−0.117809	+	0.204052i	0.801090	+	0.598544i	$0.204254\pi$
$692$	−7.10293e9	+	1.23026e10i	−0.814829	+	1.41132i
$693$	1.74483e8	+	3.02214e8i	0.0199153	+	0.0344943i
$694$	1.59735e10			1.81402
$695$	−6.76561e9	−	1.17184e10i	−0.764469	−	1.32410i
$696$	1.04383e8	+	1.80796e8i	0.0117354	+	0.0203262i
$697$	−6.12233e9			−0.684860
$698$	1.99336e9	+	3.45261e9i	0.221867	+	0.384285i
$699$	−4.03636e9	+	6.99119e9i	−0.447013	+	0.774249i
$700$	3.57527e9	−	6.19256e9i	0.393973	−	0.682381i
$701$	1.59422e10			1.74797			0.873987	−	0.485949i	$-0.161526\pi$
$701$	1.59422e10			1.74797			0.873987	+	0.485949i	$0.161526\pi$
$702$	−8.55088e9	−	1.21408e10i	−0.932891	−	1.32455i
$703$	−2.95876e9			−0.321193
$704$	−1.65559e9	+	2.86756e9i	−0.178833	+	0.309748i
$705$	−1.00071e10	+	1.73329e10i	−1.07559	+	1.86298i
$706$	8.56535e9	+	1.48356e10i	0.916070	+	1.58668i
$707$	2.77225e9			0.295029
$708$	−8.54364e9	−	1.47980e10i	−0.904746	−	1.56707i
$709$	−8.10775e9	−	1.40430e10i	−0.854355	−	1.47979i	−0.877242	−	0.480049i	$-0.840619\pi$
$709$	−8.10775e9	−	1.40430e10i	−0.854355	−	1.47979i	0.0228863	−	0.999738i	$-0.492714\pi$
$710$	−2.55383e10			−2.67786
$711$	−2.57877e8	−	4.46655e8i	−0.0269072	−	0.0466046i
$712$	−1.42010e9	+	2.45968e9i	−0.147448	+	0.255387i
$713$	1.28128e10	−	2.21925e10i	1.32383	−	2.29294i
$714$	1.97676e9			0.203241
$715$	−2.33674e9	−	3.31777e9i	−0.239077	−	0.339450i
$716$	2.45304e9			0.249752
$717$	−1.85336e8	+	3.21011e8i	−0.0187777	+	0.0325239i
$718$	−3.21911e9	+	5.57565e9i	−0.324563	+	0.562160i
$719$	−1.35046e9	−	2.33907e9i	−0.135497	−	0.234688i	0.790290	−	0.612733i	$-0.209930\pi$
$719$	−1.35046e9	−	2.33907e9i	−0.135497	−	0.234688i	−0.925787	+	0.378045i	$0.876597\pi$
$720$	4.77271e9			0.476542
$721$	−8.81830e8	−	1.52737e9i	−0.0876217	−	0.151765i
$722$	−5.36880e9	−	9.29903e9i	−0.530880	−	0.919512i
$723$	8.54141e8			0.0840515
$724$	−6.94184e9	−	1.20236e10i	−0.679813	−	1.17747i
$725$	7.32704e8	−	1.26908e9i	0.0714077	−	0.123682i
$726$	5.52085e9	−	9.56239e9i	0.535461	−	0.927446i
$727$	−8.56791e9			−0.826998			−0.413499	−	0.910504i	$-0.635694\pi$
$727$	−8.56791e9			−0.826998			−0.413499	+	0.910504i	$0.635694\pi$
$728$	−1.41486e9	+	1.27701e8i	−0.135911	+	0.0122669i
$729$	1.04447e10			0.998506
$730$	1.27512e10	−	2.20857e10i	1.21317	−	2.10127i
$731$	−2.59094e9	+	4.48764e9i	−0.245328	+	0.424920i
$732$	1.00411e10	+	1.73917e10i	0.946224	+	1.63891i
$733$	1.43750e10			1.34817			0.674084	−	0.738655i	$-0.264539\pi$
$733$	1.43750e10			1.34817			0.674084	+	0.738655i	$0.264539\pi$
$734$	−1.07068e10	−	1.85447e10i	−0.999365	−	1.73095i
$735$	9.62305e8	+	1.66676e9i	0.0893938	+	0.154835i
$736$	2.29391e10			2.12082
$737$	3.55654e8	+	6.16011e8i	0.0327259	+	0.0566829i
$738$	−4.95037e9	+	8.57429e9i	−0.453357	+	0.785237i
$739$	3.54353e9	−	6.13758e9i	0.322984	−	0.559424i	−0.658118	−	0.752914i	$-0.728647\pi$
$739$	3.54353e9	−	6.13758e9i	0.322984	−	0.559424i	0.981102	+	0.193490i	$0.0619807\pi$
$740$	−1.33406e10			−1.21022
$741$	−1.91829e9	+	4.14347e9i	−0.173201	+	0.374111i
$742$	−4.93353e9			−0.443348
$743$	1.58018e9	−	2.73695e9i	0.141334	−	0.244797i	−0.786665	−	0.617380i	$-0.788194\pi$
$743$	1.58018e9	−	2.73695e9i	0.141334	−	0.244797i	0.927999	+	0.372582i	$0.121528\pi$
$744$	2.72903e9	−	4.72683e9i	0.242943	−	0.420789i
$745$	−1.65142e10	−	2.86035e10i	−1.46322	−	2.53438i
$746$	−2.68881e10			−2.37123
$747$	2.31157e9	+	4.00376e9i	0.202902	+	0.351436i
$748$	−8.46434e8	−	1.46607e9i	−0.0739499	−	0.128085i
$749$	−3.11669e9			−0.271024
$750$	−7.35577e9	−	1.27406e10i	−0.636669	−	1.10274i
$751$	−8.85893e9	+	1.53441e10i	−0.763205	+	1.32191i	0.177985	+	0.984033i	$0.443042\pi$
$751$	−8.85893e9	+	1.53441e10i	−0.763205	+	1.32191i	−0.941190	+	0.337877i	$0.890291\pi$
$752$	−7.02237e9	+	1.21631e10i	−0.602173	+	1.04299i
$753$	9.35573e9			0.798537
$754$	−1.49224e9	+	1.34685e8i	−0.126776	+	0.0114425i
$755$	−3.03703e9			−0.256823
$756$	3.01566e9	−	5.22328e9i	0.253838	−	0.439660i
$757$	−1.85539e9	+	3.21363e9i	−0.155453	+	0.269253i	−0.933224	−	0.359295i	$-0.883017\pi$
$757$	−1.85539e9	+	3.21363e9i	−0.155453	+	0.269253i	0.777771	+	0.628548i	$0.216350\pi$
$758$	−7.64976e8	−	1.32498e9i	−0.0637978	−	0.110501i
$759$	3.51356e9			0.291676
$760$	1.92838e9	+	3.34006e9i	0.159348	+	0.275998i
$761$	3.80848e9	+	6.59648e9i	0.313260	+	0.542582i	0.979066	−	0.203543i	$-0.0652455\pi$
$761$	3.80848e9	+	6.59648e9i	0.313260	+	0.542582i	−0.665806	+	0.746125i	$0.731912\pi$
$762$	1.85261e9			0.151684
$763$	1.18039e9	+	2.04449e9i	0.0962030	+	0.166628i
$764$	1.19820e10	−	2.07535e10i	0.972083	−	1.68370i
$765$	−1.97834e9	+	3.42659e9i	−0.159767	+	0.276724i
$766$	−3.55813e10			−2.86036
$767$	2.37328e10	−	2.14205e9i	1.89917	−	0.171414i
$768$	−3.46063e9			−0.275671
$769$	−5.72060e9	+	9.90837e9i	−0.453627	+	0.785706i	−0.998608	−	0.0527428i	$-0.983204\pi$
$769$	−5.72060e9	+	9.90837e9i	−0.453627	+	0.785706i	0.544981	+	0.838449i	$0.316537\pi$
$770$	1.48807e9	−	2.57742e9i	0.117465	−	0.203455i
$771$	−6.27771e9	−	1.08733e10i	−0.493299	−	0.854420i
$772$	7.07891e9			0.553740
$773$	2.91525e9	+	5.04935e9i	0.227011	+	0.393195i	0.956921	−	0.290349i	$-0.0937713\pi$
$773$	2.91525e9	+	5.04935e9i	0.227011	+	0.393195i	−0.729910	+	0.683543i	$0.760438\pi$
$774$	4.18995e9	+	7.25721e9i	0.324800	+	0.562569i
$775$	−3.83124e10			−2.95653
$776$	−1.35956e9	−	2.35482e9i	−0.104444	−	0.180902i
$777$	1.12535e9	−	1.94916e9i	0.0860623	−	0.149064i
$778$	−3.27449e9	+	5.67158e9i	−0.249296	+	0.431793i
$779$	1.03713e10			0.786050
$780$	−8.64927e9	+	1.86822e10i	−0.652602	+	1.40960i
$781$	−3.68980e9			−0.277156
$782$	−7.07370e9	+	1.22520e10i	−0.528960	+	0.916186i
$783$	6.18019e8	−	1.07044e9i	0.0460082	−	0.0796886i
$784$	6.75285e8	+	1.16963e9i	0.0500474	+	0.0866846i
$785$	−7.93847e9			−0.585724
$786$	−4.40912e9	−	7.63683e9i	−0.323872	−	0.560963i
$787$	3.96855e9	+	6.87372e9i	0.290215	+	0.502667i	0.973860	−	0.227147i	$-0.0729398\pi$
$787$	3.96855e9	+	6.87372e9i	0.290215	+	0.502667i	−0.683645	+	0.729814i	$0.739607\pi$
$788$	2.25786e10			1.64382
$789$	1.95275e8	+	3.38227e8i	0.0141540	+	0.0245154i
$790$	−2.19929e9	+	3.80929e9i	−0.158704	+	0.274884i
$791$	−6.63043e8	+	1.14842e9i	−0.0476348	+	0.0825058i
$792$	−5.31949e8			−0.0380480
$793$	−2.78925e10	+	2.51750e9i	−1.98624	+	0.179272i
$794$	2.90300e10			2.05814
$795$	−6.94618e9	+	1.20311e10i	−0.490299	+	0.849223i
$796$	−4.54763e9	+	7.87672e9i	−0.319587	+	0.553541i
$797$	−2.87131e9	−	4.97325e9i	−0.200898	−	0.347966i	0.747920	−	0.663789i	$-0.231053\pi$
$797$	−2.87131e9	−	4.97325e9i	−0.200898	−	0.347966i	−0.948818	+	0.315823i	$0.897719\pi$
$798$	−3.34865e9			−0.233270
$799$	−5.82170e9	−	1.00835e10i	−0.403772	−	0.699354i
$800$	−1.71479e10	−	2.97010e10i	−1.18412	−	2.05096i
$801$	4.93594e9			0.339357
$802$	4.17913e8	+	7.23847e8i	0.0286072	+	0.0495492i
$803$	1.84230e9	−	3.19096e9i	0.125562	−	0.217479i
$804$	1.80429e9	−	3.12512e9i	0.122436	−	0.212066i
$805$	−1.37742e10			−0.930636
$806$	2.25564e10	+	3.20263e10i	1.51739	+	2.15444i
$807$	1.77895e10			1.19153
$808$	−2.11295e9	+	3.65974e9i	−0.140913	+	0.244068i
$809$	−5.63615e9	+	9.76210e9i	−0.374251	+	0.648222i	−0.990215	−	0.139553i	$-0.955433\pi$
$809$	−5.63615e9	+	9.76210e9i	−0.374251	+	0.648222i	0.615964	+	0.787775i	$0.288767\pi$
$810$	−7.63347e9	−	1.32216e10i	−0.504689	−	0.874148i
$811$	3.05210e9			0.200922			0.100461	−	0.994941i	$-0.467968\pi$
$811$	3.05210e9			0.200922			0.100461	+	0.994941i	$0.467968\pi$
$812$	−3.04272e8	−	5.27014e8i	−0.0199441	−	0.0345443i
$813$	4.99346e9	+	8.64893e9i	0.325900	+	0.564476i
$814$	−3.48039e9			−0.226174
$815$	1.12017e10	+	1.94019e10i	0.724823	+	1.25543i
$816$	1.95307e9	−	3.38281e9i	0.125835	−	0.217952i
$817$	4.38907e9	−	7.60210e9i	0.281576	−	0.487704i
$818$	−1.19238e10			−0.761691
$819$	1.42164e9	+	2.01849e9i	0.0904265	+	0.128390i
$820$	4.67623e10			2.96174
$821$	−1.48407e10	+	2.57049e10i	−0.935954	+	1.62112i	−0.163030	+	0.986621i	$0.552127\pi$
$821$	−1.48407e10	+	2.57049e10i	−0.935954	+	1.62112i	−0.772924	+	0.634499i	$0.781207\pi$
$822$	6.15308e9	−	1.06574e10i	0.386404	−	0.669271i
$823$	−7.07499e9	−	1.22542e10i	−0.442411	−	0.766279i	0.555456	−	0.831546i	$-0.312544\pi$
$823$	−7.07499e9	−	1.22542e10i	−0.442411	−	0.766279i	−0.997868	+	0.0652666i	$0.979210\pi$
$824$	2.68845e9			0.167400
$825$	−2.62652e9	−	4.54927e9i	−0.162852	−	0.282067i
$826$	8.73806e9	+	1.51348e10i	0.539492	+	0.934428i
$827$	1.66864e10			1.02587			0.512937	−	0.858427i	$-0.328558\pi$
$827$	1.66864e10			1.02587			0.512937	+	0.858427i	$0.328558\pi$
$828$	6.33512e9	+	1.09727e10i	0.387836	+	0.671752i
$829$	1.60564e10	−	2.78105e10i	0.978828	−	1.69538i	0.312154	−	0.950032i	$-0.398950\pi$
$829$	1.60564e10	−	2.78105e10i	0.978828	−	1.69538i	0.666675	−	0.745349i	$-0.267717\pi$
$830$	1.97142e10	−	3.41460e10i	1.19676	−	2.07284i
$831$	−7.95468e9			−0.480860
$832$	−9.84190e9	+	2.12583e10i	−0.592444	+	1.27967i
$833$	−1.11965e9			−0.0671160
$834$	−8.95446e9	+	1.55096e10i	−0.534513	+	0.925804i
$835$	−2.37294e9	+	4.11006e9i	−0.141054	+	0.244312i
$836$	1.43386e9	+	2.48352e9i	0.0848762	+	0.147010i
$837$	−3.23156e10			−1.90490
$838$	2.17473e10	+	3.76674e10i	1.27659	+	2.21111i
$839$	5.89448e9	+	1.02095e10i	0.344571	+	0.596815i	0.985276	−	0.170973i	$-0.0546910\pi$
$839$	5.89448e9	+	1.02095e10i	0.344571	+	0.596815i	−0.640705	+	0.767787i	$0.721358\pi$
$840$	−2.93379e9			−0.170786
$841$	8.56258e9	+	1.48308e10i	0.496385	+	0.859764i
$842$	−1.77891e9	+	3.08116e9i	−0.102698	+	0.177878i
$843$	−5.36268e9	+	9.28843e9i	−0.308308	+	0.534005i
$844$	3.65187e9			0.209082
$845$	−1.85751e10	−	2.18916e10i	−1.05909	−	1.24818i
$846$	−1.88292e10			−1.06914
$847$	−3.12705e9	+	5.41621e9i	−0.176825	+	0.306269i
$848$	−4.87439e9	+	8.44269e9i	−0.274495	+	0.475440i
$849$	−1.09739e10	−	1.90074e10i	−0.615438	−	1.06597i
$850$	2.11515e10			1.18134
$851$	8.05395e9	+	1.39498e10i	0.447977	+	0.775918i
$852$	9.35947e9	+	1.62111e10i	0.518457	+	0.897994i
$853$	−2.74723e10			−1.51556			−0.757780	−	0.652510i	$-0.773716\pi$
$853$	−2.74723e10			−1.51556			−0.757780	+	0.652510i	$0.773716\pi$
$854$	−1.02696e10	−	1.77875e10i	−0.564225	−	0.977266i
$855$	3.35132e9	−	5.80466e9i	0.183373	−	0.317611i
$856$	2.37547e9	−	4.11444e9i	0.129447	−	0.224209i
$857$	1.76694e10			0.958932			0.479466	−	0.877560i	$-0.340830\pi$
$857$	1.76694e10			0.958932			0.479466	+	0.877560i	$0.340830\pi$
$858$	−2.25649e9	+	4.87396e9i	−0.121963	+	0.263437i
$859$	−1.07258e10			−0.577369			−0.288684	−	0.957424i	$-0.593218\pi$
$859$	−1.07258e10			−0.577369			−0.288684	+	0.957424i	$0.593218\pi$
$860$	1.97896e10	−	3.42766e10i	1.06094	−	1.83761i
$861$	−3.94464e9	+	6.83232e9i	−0.210619	+	0.364802i
$862$	−5.17655e9	−	8.96606e9i	−0.275274	−	0.476789i
$863$	8.21219e9			0.434932			0.217466	−	0.976068i	$-0.430221\pi$
$863$	8.21219e9			0.434932			0.217466	+	0.976068i	$0.430221\pi$
$864$	−1.44639e10	−	2.50521e10i	−0.762932	−	1.32144i
$865$	−2.04563e10	−	3.54314e10i	−1.07466	−	1.86137i
$866$	9.36655e9			0.490080
$867$	−5.71645e9	−	9.90119e9i	−0.297893	−	0.515965i
$868$	−7.95504e9	+	1.37785e10i	−0.412879	+	0.715128i
$869$	−3.17756e8	+	5.50370e8i	−0.0164257	+	0.0284502i
$870$	−3.09423e9			−0.159307
$871$	2.89777e9	+	4.11434e9i	0.148594	+	0.210978i
$872$	−3.59866e9			−0.183795
$873$	−2.36277e9	+	4.09243e9i	−0.120191	+	0.208176i
$874$	1.19829e10	−	2.07550e10i	0.607116	−	1.05156i
$875$	4.16636e9	+	7.21636e9i	0.210247	+	0.364158i
$876$	−1.86926e10			−0.939520
$877$	1.10250e10	+	1.90959e10i	0.551926	+	0.955963i	0.998136	+	0.0610349i	$0.0194401\pi$
$877$	1.10250e10	+	1.90959e10i	0.551926	+	0.955963i	−0.446210	+	0.894928i	$0.647227\pi$
$878$	−5.16527e8	−	8.94650e8i	−0.0257550	−	0.0446090i
$879$	−5.78211e8			−0.0287161
$880$	−2.94047e9	−	5.09305e9i	−0.145455	−	0.251935i
$881$	1.70991e10	−	2.96165e10i	0.842477	−	1.45921i	−0.0453180	−	0.998973i	$-0.514430\pi$
$881$	1.70991e10	−	2.96165e10i	0.842477	−	1.45921i	0.887795	−	0.460240i	$-0.152237\pi$
$882$	−9.05325e8	+	1.56807e9i	−0.0444288	+	0.0769529i
$883$	−5.27884e9			−0.258033			−0.129017	−	0.991642i	$-0.541182\pi$
$883$	−5.27884e9			−0.258033			−0.129017	+	0.991642i	$0.541182\pi$
$884$	−6.89650e9	−	9.79188e9i	−0.335773	−	0.476742i
$885$	4.92111e10			2.38650
$886$	−1.70293e10	+	2.94955e10i	−0.822579	+	1.42475i
$887$	1.52694e10	−	2.64474e10i	0.734665	−	1.27248i	−0.220205	−	0.975454i	$-0.570673\pi$
$887$	1.52694e10	−	2.64474e10i	0.734665	−	1.27248i	0.954870	−	0.297024i	$-0.0959941\pi$
$888$	1.71543e9	+	2.97121e9i	0.0822106	+	0.142393i
$889$	−1.04933e9			−0.0500906
$890$	−2.10480e10	−	3.64563e10i	−1.00080	−	1.73343i
$891$	−1.10289e9	−	1.91026e9i	−0.0522349	−	0.0904735i
$892$	1.57887e10			0.744853
$893$	9.86199e9	+	1.70815e10i	0.463431	+	0.802685i
$894$	−2.18570e10	+	3.78574e10i	−1.02308	+	1.77203i
$895$	−3.53236e9	+	6.11822e9i	−0.164696	+	0.285262i
$896$	−5.70568e9			−0.264990
$897$	2.47572e10	−	2.23451e9i	1.14532	−	0.103373i
$898$	−3.19158e10			−1.47075
$899$	−1.63028e9	+	2.82372e9i	−0.0748346	+	0.129617i
$900$	9.47150e9	−	1.64051e10i	0.433082	−	0.750120i
$901$	−4.04098e9	−	6.99918e9i	−0.184056	−	0.318794i
$902$	1.21997e10			0.553512
$903$	3.33871e9	+	5.78282e9i	0.150894	+	0.261356i
$904$	−1.01071e9	−	1.75061e9i	−0.0455029	−	0.0788133i
$905$	3.99848e10			1.79318
$906$	2.00979e9	+	3.48106e9i	0.0897848	+	0.155512i
$907$	−9.09202e9	+	1.57478e10i	−0.404608	+	0.700802i	−0.994276	−	0.106844i	$-0.965925\pi$
$907$	−9.09202e9	+	1.57478e10i	−0.404608	+	0.700802i	0.589667	+	0.807646i	$0.299259\pi$
$908$	8.19802e9	−	1.41994e10i	0.363420	−	0.629462i
$909$	7.34416e9			0.324316
$910$	8.84610e9	−	1.91074e10i	0.389141	−	0.840535i
$911$	−1.32098e10			−0.578870			−0.289435	−	0.957198i	$-0.593467\pi$
$911$	−1.32098e10			−0.578870			−0.289435	+	0.957198i	$0.593467\pi$
$912$	−3.30850e9	+	5.73050e9i	−0.144427	+	0.250156i
$913$	2.84833e9	−	4.93345e9i	0.123863	−	0.214537i
$914$	−1.09343e10	−	1.89387e10i	−0.473673	−	0.820426i
$915$	−5.78366e10			−2.49591
$916$	−9.90047e9	−	1.71481e10i	−0.425620	−	0.737195i
$917$	2.49736e9	+	4.32556e9i	0.106952	+	0.185246i
$918$	1.78408e10			0.761140
$919$	7.38262e8	+	1.27871e9i	0.0313766	+	0.0543459i	0.881287	−	0.472581i	$-0.156678\pi$
$919$	7.38262e8	+	1.27871e9i	0.0313766	+	0.0543459i	−0.849911	+	0.526927i	$0.823344\pi$
$920$	1.04984e10	−	1.81837e10i	0.444493	−	0.769884i
$921$	1.30973e10	−	2.26851e10i	0.552423	−	0.956824i
$922$	4.70556e10			1.97721
$923$	−2.59990e10	+	2.34659e9i	−1.08831	+	0.0982272i
$924$	−2.18145e9			−0.0909688
$925$	1.20413e10	−	2.08561e10i	0.500238	−	0.866438i
$926$	7.79661e8	−	1.35041e9i	0.0322676	−	0.0558892i
$927$	−2.33612e9	−	4.04627e9i	−0.0963197	−	0.166831i
$928$	−2.91872e9			−0.119888
$929$	−9.60001e9	−	1.66277e10i	−0.392841	−	0.680421i	0.599982	−	0.800013i	$-0.295174\pi$
$929$	−9.60001e9	−	1.66277e10i	−0.392841	−	0.680421i	−0.992823	+	0.119593i	$0.961841\pi$
$930$	4.04486e10	+	7.00590e10i	1.64897	+	2.85610i
$931$	1.89670e9			0.0770326
$932$	1.79354e10	+	3.10649e10i	0.725695	+	1.25694i
$933$	1.66355e10	−	2.88135e10i	0.670579	−	1.16148i
$934$	−3.28717e10	+	5.69354e10i	−1.32010	+	2.28649i
$935$	4.87543e9			0.195062
$936$	−3.74821e9	+	3.38303e8i	−0.149403	+	0.0134847i
$937$	−9.11275e8			−0.0361877			−0.0180938	−	0.999836i	$-0.505760\pi$
$937$	−9.11275e8			−0.0361877			−0.0180938	+	0.999836i	$0.505760\pi$
$938$	−1.84535e9	+	3.19624e9i	−0.0730077	+	0.126453i
$939$	7.44883e9	−	1.29017e10i	0.293602	−	0.508533i
$940$	4.44661e10	+	7.70176e10i	1.74615	+	3.02442i
$941$	5.00547e10			1.95831			0.979154	−	0.203120i	$-0.0651082\pi$
$941$	5.00547e10			1.95831			0.979154	+	0.203120i	$0.0651082\pi$
$942$	5.25339e9	+	9.09913e9i	0.204768	+	0.354668i
$943$	−2.82313e10	−	4.88980e10i	−1.09633	−	1.89889i
$944$	3.45333e10			1.33609
$945$	8.68506e9	+	1.50430e10i	0.334781	+	0.579858i
$946$	5.16287e9	−	8.94235e9i	0.198277	−	0.343426i
$947$	−5.35205e9	+	9.27002e9i	−0.204783	+	0.354695i	−0.950064	−	0.312056i	$-0.898982\pi$
$947$	−5.35205e9	+	9.27002e9i	−0.204783	+	0.354695i	0.745280	+	0.666751i	$0.232316\pi$
$948$	3.22406e9			0.122906
$949$	1.09519e10	−	2.36558e10i	0.415965	−	0.898474i
$950$	−3.58307e10			−1.35589
$951$	−9.03682e9	+	1.56522e10i	−0.340709	+	0.590126i
$952$	8.53375e8	−	1.47809e9i	0.0320561	−	0.0555228i
$953$	1.94575e10	+	3.37014e10i	0.728218	+	1.26131i	0.957636	+	0.287983i	$0.0929847\pi$
$953$	1.94575e10	+	3.37014e10i	0.728218	+	1.26131i	−0.229417	+	0.973328i	$0.573682\pi$
$954$	−1.30698e10			−0.487358
$955$	3.45080e10	+	5.97697e10i	1.28206	+	2.22059i
$956$	8.23529e8	+	1.42639e9i	0.0304843	+	0.0528004i
$957$	−4.47057e8			−0.0164881
$958$	−6.84832e8	−	1.18616e9i	−0.0251655	−	0.0435879i
$959$	−3.48515e9	+	6.03646e9i	−0.127602	+	0.221013i
$960$	−2.41892e10	+	4.18969e10i	−0.882412	+	1.52838i
$961$	5.77329e10			2.09842
$962$	−2.45235e10	+	2.21342e9i	−0.888116	+	0.0801587i
$963$	−8.25663e9			−0.297928
$964$	1.89766e9	−	3.28685e9i	0.0682260	−	0.118171i
$965$	−1.01936e10	+	1.76558e10i	−0.365158	+	0.632472i
$966$	9.11524e9	+	1.57881e10i	0.325348	+	0.563519i
$967$	1.06662e10			0.379330			0.189665	−	0.981849i	$-0.439260\pi$
$967$	1.06662e10			0.379330			0.189665	+	0.981849i	$0.439260\pi$
$968$	−4.76674e9	−	8.25624e9i	−0.168911	−	0.292562i
$969$	−2.74282e9	−	4.75071e9i	−0.0968422	−	0.167736i
$970$	4.03016e10			1.41782
$971$	−5.96052e9	−	1.03239e10i	−0.208938	−	0.361891i	0.742442	−	0.669910i	$-0.233667\pi$
$971$	−5.96052e9	−	1.03239e10i	−0.208938	−	0.361891i	−0.951380	+	0.308019i	$0.900334\pi$
$972$	1.36330e10	−	2.36130e10i	0.476167	−	0.824745i
$973$	5.07188e9	−	8.78475e9i	0.176512	−	0.305727i
$974$	−5.81063e10			−2.01496
$975$	−2.14002e10	−	3.03846e10i	−0.739437	−	1.04988i
$976$	−4.05861e10			−1.39734
$977$	4.74663e8	−	8.22140e8i	0.0162837	−	0.0282043i	−0.857769	−	0.514036i	$-0.828150\pi$
$977$	4.74663e8	−	8.22140e8i	0.0162837	−	0.0282043i	0.874052	+	0.485832i	$0.161483\pi$
$978$	1.48258e10	−	2.56790e10i	0.506793	−	0.877791i
$979$	−3.04104e9	−	5.26724e9i	−0.103582	−	0.179409i
$980$	8.55190e9			0.290249
$981$	3.12704e9	+	5.41620e9i	0.105753	+	0.183169i
$982$	1.74283e10	+	3.01867e10i	0.587306	+	1.01724i
$983$	−1.56829e10			−0.526610			−0.263305	−	0.964713i	$-0.584813\pi$
$983$	−1.56829e10			−0.526610			−0.263305	+	0.964713i	$0.584813\pi$
$984$	−6.01305e9	−	1.04149e10i	−0.201192	−	0.348476i
$985$	−3.25130e10	+	5.63141e10i	−1.08400	+	1.87755i
$986$	9.00043e8	−	1.55892e9i	0.0299016	−	0.0517910i
$987$	−1.50038e10			−0.496697
$988$	1.16827e10	+	1.65875e10i	0.385385	+	0.547182i
$989$	−4.77894e10			−1.57089
$990$	3.94216e9	−	6.82802e9i	0.129125	−	0.223651i
$991$	1.85384e10	−	3.21095e10i	0.605083	−	1.04804i	−0.386955	−	0.922099i	$-0.626473\pi$
$991$	1.85384e10	−	3.21095e10i	0.605083	−	1.04804i	0.992038	−	0.125936i	$-0.0401935\pi$
$992$	3.81543e10	+	6.60852e10i	1.24095	+	2.14938i
$993$	−5.57467e9			−0.180674
$994$	−9.57246e9	−	1.65800e10i	−0.309151	−	0.535466i
$995$	−1.30971e10	−	2.26848e10i	−0.421497	−	0.730054i
$996$	−2.89001e10			−0.926811
$997$	−1.87400e10	−	3.24586e10i	−0.598876	−	1.03728i	−0.992987	−	0.118221i	$-0.962281\pi$
$997$	−1.87400e10	−	3.24586e10i	−0.598876	−	1.03728i	0.394112	−	0.919063i	$-0.371052\pi$
$998$	−3.27804e10	+	5.67774e10i	−1.04390	+	1.80808i
$999$	1.01565e10	−	1.75917e10i	0.322305	−	0.558248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.f.a.22.20	✓	48
13.3	even	3	inner	91.8.f.a.29.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.f.a.22.20	✓	48	1.1	even	1	trivial
91.8.f.a.29.20	yes	48	13.3	even	3	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.46862 - 14.6681i) q^{2} +(17.8769 - 30.9637i) q^{3} +(-79.4351 - 137.586i) q^{4} +457.543 q^{5} +(-302.785 - 524.440i) q^{6} +(171.500 + 297.047i) q^{7} -522.854 q^{8} +(454.332 + 786.927i) q^{9} +O(q^{10})\)	\(q+(8.46862 - 14.6681i) q^{2} +(17.8769 - 30.9637i) q^{3} +(-79.4351 - 137.586i) q^{4} +457.543 q^{5} +(-302.785 - 524.440i) q^{6} +(171.500 + 297.047i) q^{7} -522.854 q^{8} +(454.332 + 786.927i) q^{9} +(3874.76 - 6711.28i) q^{10} +(559.829 - 969.653i) q^{11} -5680.21 q^{12} +(3328.00 - 7188.39i) q^{13} +5809.47 q^{14} +(8179.46 - 14167.2i) q^{15} +(5739.83 - 9941.68i) q^{16} +(4758.45 + 8241.87i) q^{17} +15390.3 q^{18} +(-8060.84 - 13961.8i) q^{19} +(-36345.0 - 62951.3i) q^{20} +12263.6 q^{21} +(-9481.96 - 16423.2i) q^{22} +(-43884.3 + 76009.8i) q^{23} +(-9347.02 + 16189.5i) q^{24} +131221. q^{25} +(-77256.4 - 109691. i) q^{26} +110682. q^{27} +(27246.2 - 47191.8i) q^{28} +(5583.74 - 9671.32i) q^{29} +(-138537. - 239954. i) q^{30} -291968. q^{31} +(-130680. - 226344. i) q^{32} +(-20016.0 - 34668.8i) q^{33} +161190. q^{34} +(78468.7 + 135912. i) q^{35} +(72179.8 - 125019. i) q^{36} +(91763.5 - 158939. i) q^{37} -273057. q^{38} +(-163085. - 231553. i) q^{39} -239229. q^{40} +(-321656. + 557124. i) q^{41} +(103855. - 179883. i) q^{42} +(272247. + 471545. i) q^{43} -177880. q^{44} +(207877. + 360053. i) q^{45} +(743279. + 1.28740e6i) q^{46} -1.22345e6 q^{47} +(-205221. - 355453. i) q^{48} +(-58824.5 + 101887. i) q^{49} +(1.11126e6 - 1.92476e6i) q^{50} +340265. q^{51} +(-1.25338e6 + 113126. i) q^{52} -849222. q^{53} +(937322. - 1.62349e6i) q^{54} +(256146. - 443658. i) q^{55} +(-89669.5 - 155312. i) q^{56} -576411. q^{57} +(-94573.2 - 163806. i) q^{58} +(1.50411e6 + 2.60519e6i) q^{59} -2.59894e6 q^{60} +(-1.76774e6 - 3.06181e6i) q^{61} +(-2.47257e6 + 4.28262e6i) q^{62} +(-155836. + 269916. i) q^{63} -2.95731e6 q^{64} +(1.52270e6 - 3.28900e6i) q^{65} -678033. q^{66} +(-317645. + 550177. i) q^{67} +(755975. - 1.30939e6i) q^{68} +(1.56903e6 + 2.71764e6i) q^{69} +2.65809e6 q^{70} +(-1.64773e6 - 2.85396e6i) q^{71} +(-237550. - 411448. i) q^{72} +3.29083e6 q^{73} +(-1.55422e6 - 2.69199e6i) q^{74} +(2.34582e6 - 4.06309e6i) q^{75} +(-1.28063e6 + 2.21811e6i) q^{76} +384043. q^{77} +(-4.77755e6 + 431207. i) q^{78} -567595. q^{79} +(2.62622e6 - 4.54875e6i) q^{80} +(985024. - 1.70611e6i) q^{81} +(5.44796e6 + 9.43614e6i) q^{82} +5.08785e6 q^{83} +(-974156. - 1.68729e6i) q^{84} +(2.17720e6 + 3.77101e6i) q^{85} +9.22222e6 q^{86} +(-199640. - 345787. i) q^{87} +(-292709. + 506987. i) q^{88} +(2.71604e6 - 4.70432e6i) q^{89} +7.04171e6 q^{90} +(2.70604e6 - 244239. i) q^{91} +1.39438e7 q^{92} +(-5.21949e6 + 9.04043e6i) q^{93} +(-1.03609e7 + 1.79456e7i) q^{94} +(-3.68818e6 - 6.38812e6i) q^{95} -9.34459e6 q^{96} +(2.60026e6 + 4.50379e6i) q^{97} +(996325. + 1.72568e6i) q^{98} +1.01739e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9} + 17800 q^{10} - 11735 q^{11} + 30484 q^{12} - 5622 q^{13} - 5488 q^{14} + 3465 q^{15} - 110364 q^{16} - 3506 q^{17} - 196096 q^{18} - 25291 q^{19} - 13351 q^{20} + 28126 q^{21} + 91579 q^{22} + 82970 q^{23} - 97143 q^{24} + 1263842 q^{25} - 51951 q^{26} - 1080760 q^{27} + 504896 q^{28} + 209315 q^{29} + 1063844 q^{30} + 948356 q^{31} - 495024 q^{32} - 143209 q^{33} + 436128 q^{34} + 90209 q^{35} - 469485 q^{36} - 377142 q^{37} - 198346 q^{38} + 647900 q^{39} - 4780340 q^{40} - 1895174 q^{41} + 178017 q^{42} - 1366459 q^{43} + 8096352 q^{44} - 2154733 q^{45} + 2854528 q^{46} + 2557720 q^{47} - 4102289 q^{48} - 2823576 q^{49} - 2378593 q^{50} - 4369338 q^{51} + 4270295 q^{52} - 4295420 q^{53} + 1447259 q^{54} - 560241 q^{55} + 81291 q^{56} + 15936670 q^{57} - 384326 q^{58} + 6714194 q^{59} + 5267974 q^{60} - 987536 q^{61} + 8520899 q^{62} + 5291461 q^{63} - 8211866 q^{64} - 11284709 q^{65} - 20326376 q^{66} - 1296682 q^{67} - 8400264 q^{68} - 1147530 q^{69} + 12210800 q^{70} - 7723282 q^{71} + 26270290 q^{72} + 15769600 q^{73} + 58033 q^{74} - 928389 q^{75} - 9095520 q^{76} - 8050210 q^{77} - 30641513 q^{78} - 24665908 q^{79} + 16716608 q^{80} - 5846292 q^{81} - 9977079 q^{82} + 32429868 q^{83} + 5228006 q^{84} + 17821519 q^{85} + 89024148 q^{86} - 16967309 q^{87} + 28910709 q^{88} - 27957029 q^{89} - 155228046 q^{90} - 5184102 q^{91} - 5073264 q^{92} + 11673603 q^{93} - 9670145 q^{94} + 38478411 q^{95} + 111942976 q^{96} - 28714467 q^{97} - 941192 q^{98} + 42173094 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9 + 17800 * q^10 - 11735 * q^11 + 30484 * q^12 - 5622 * q^13 - 5488 * q^14 + 3465 * q^15 - 110364 * q^16 - 3506 * q^17 - 196096 * q^18 - 25291 * q^19 - 13351 * q^20 + 28126 * q^21 + 91579 * q^22 + 82970 * q^23 - 97143 * q^24 + 1263842 * q^25 - 51951 * q^26 - 1080760 * q^27 + 504896 * q^28 + 209315 * q^29 + 1063844 * q^30 + 948356 * q^31 - 495024 * q^32 - 143209 * q^33 + 436128 * q^34 + 90209 * q^35 - 469485 * q^36 - 377142 * q^37 - 198346 * q^38 + 647900 * q^39 - 4780340 * q^40 - 1895174 * q^41 + 178017 * q^42 - 1366459 * q^43 + 8096352 * q^44 - 2154733 * q^45 + 2854528 * q^46 + 2557720 * q^47 - 4102289 * q^48 - 2823576 * q^49 - 2378593 * q^50 - 4369338 * q^51 + 4270295 * q^52 - 4295420 * q^53 + 1447259 * q^54 - 560241 * q^55 + 81291 * q^56 + 15936670 * q^57 - 384326 * q^58 + 6714194 * q^59 + 5267974 * q^60 - 987536 * q^61 + 8520899 * q^62 + 5291461 * q^63 - 8211866 * q^64 - 11284709 * q^65 - 20326376 * q^66 - 1296682 * q^67 - 8400264 * q^68 - 1147530 * q^69 + 12210800 * q^70 - 7723282 * q^71 + 26270290 * q^72 + 15769600 * q^73 + 58033 * q^74 - 928389 * q^75 - 9095520 * q^76 - 8050210 * q^77 - 30641513 * q^78 - 24665908 * q^79 + 16716608 * q^80 - 5846292 * q^81 - 9977079 * q^82 + 32429868 * q^83 + 5228006 * q^84 + 17821519 * q^85 + 89024148 * q^86 - 16967309 * q^87 + 28910709 * q^88 - 27957029 * q^89 - 155228046 * q^90 - 5184102 * q^91 - 5073264 * q^92 + 11673603 * q^93 - 9670145 * q^94 + 38478411 * q^95 + 111942976 * q^96 - 28714467 * q^97 - 941192 * q^98 + 42173094 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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