LMFDB - Embedded newform 21.8.g.b.5.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [21,8,Mod(5,21)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("21.5"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(21, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.56008553517$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	21.5
Dual form			21.8.g.b.17.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(17.0599 + 9.84952i) q^{2} +(-45.1680 - 12.1182i) q^{3} +(130.026 + 225.212i) q^{4} +(-147.583 + 255.621i) q^{5} +(-651.201 - 651.618i) q^{6} +(-45.1728 + 906.368i) q^{7} +2601.29i q^{8} +(1893.30 + 1094.71i) q^{9} +(-5035.49 + 2907.24i) q^{10} +(2530.38 - 1460.92i) q^{11} +(-3143.85 - 11748.0i) q^{12} -12468.8i q^{13} +(-9697.92 + 15017.6i) q^{14} +(9763.71 - 9757.46i) q^{15} +(-8978.17 + 15550.6i) q^{16} +(13752.6 + 23820.2i) q^{17} +(21517.0 + 37323.7i) q^{18} +(-3840.23 - 2217.16i) q^{19} -76758.5 q^{20} +(13023.9 - 40391.4i) q^{21} +57557.3 q^{22} +(34006.6 + 19633.7i) q^{23} +(31523.1 - 117495. i) q^{24} +(-4499.01 - 7792.52i) q^{25} +(122811. - 212716. i) q^{26} +(-72250.5 - 72389.3i) q^{27} +(-209998. + 107678. i) q^{28} +104442. i q^{29} +(262674. - 70293.2i) q^{30} +(-3499.96 + 2020.70i) q^{31} +(-17975.9 + 10378.4i) q^{32} +(-131996. + 35323.0i) q^{33} +541826. i q^{34} +(-225020. - 145312. i) q^{35} +(-363.886 + 568733. i) q^{36} +(188326. - 326191. i) q^{37} +(-43675.9 - 75648.9i) q^{38} +(-151099. + 563190. i) q^{39} +(-664946. - 383907. i) q^{40} +234072. q^{41} +(620022. - 560792. i) q^{42} -655950. q^{43} +(658031. + 379914. i) q^{44} +(-559250. + 322406. i) q^{45} +(386765. + 669897. i) q^{46} +(45057.1 - 78041.2i) q^{47} +(593972. - 593592. i) q^{48} +(-819462. - 81886.3i) q^{49} -177252. i q^{50} +(-332519. - 1.24257e6i) q^{51} +(2.80811e6 - 1.62126e6i) q^{52} +(-401269. + 231672. i) q^{53} +(-519584. - 1.94658e6i) q^{54} +862426. i q^{55} +(-2.35773e6 - 117508. i) q^{56} +(146588. + 146681. i) q^{57} +(-1.02870e6 + 1.78176e6i) q^{58} +(-112563. - 194965. i) q^{59} +(3.46703e6 + 930176. i) q^{60} +(2.12274e6 + 1.22557e6i) q^{61} -79611.7 q^{62} +(-1.07774e6 + 1.66657e6i) q^{63} +1.88952e6 q^{64} +(3.18729e6 + 1.84018e6i) q^{65} +(-2.59975e6 - 697492. i) q^{66} +(-2.21050e6 - 3.82869e6i) q^{67} +(-3.57639e6 + 6.19449e6i) q^{68} +(-1.29808e6 - 1.29892e6i) q^{69} +(-2.40756e6 - 4.69534e6i) q^{70} -4.85818e6i q^{71} +(-2.84767e6 + 4.92502e6i) q^{72} +(1.42104e6 - 820436. i) q^{73} +(6.42564e6 - 3.70984e6i) q^{74} +(108780. + 406493. i) q^{75} -1.15315e6i q^{76} +(1.20982e6 + 2.35945e6i) q^{77} +(-8.12488e6 + 8.11968e6i) q^{78} +(-586188. + 1.01531e6i) q^{79} +(-2.65005e6 - 4.59002e6i) q^{80} +(2.38618e6 + 4.14523e6i) q^{81} +(3.99324e6 + 2.30550e6i) q^{82} +7.03644e6 q^{83} +(1.07901e7 - 2.31879e6i) q^{84} -8.11861e6 q^{85} +(-1.11904e7 - 6.46079e6i) q^{86} +(1.26565e6 - 4.71742e6i) q^{87} +(3.80027e6 + 6.58227e6i) q^{88} +(211992. - 367182. i) q^{89} +(-1.27163e7 - 8136.11i) q^{90} +(1.13013e7 + 563249. i) q^{91} +1.02116e7i q^{92} +(182573. - 48857.8i) q^{93} +(1.53734e6 - 887582. i) q^{94} +(1.13351e6 - 654430. i) q^{95} +(937705. - 250936. i) q^{96} +4.84780e6i q^{97} +(-1.31734e7 - 9.46827e6i) q^{98} +(6.39005e6 + 4088.47i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 84 q^{3} + 1150 q^{4} + 2464 q^{7} - 3516 q^{9} - 630 q^{10} - 3864 q^{12} + 27576 q^{15} - 19594 q^{16} + 33498 q^{18} - 47880 q^{19} + 151788 q^{21} + 105132 q^{22} - 211554 q^{24} - 331252 q^{25}+ \cdots + 35642232 q^{99}+O(q^{100}) $ 32 * q - 84 * q^3 + 1150 * q^4 + 2464 * q^7 - 3516 * q^9 - 630 * q^10 - 3864 * q^12 + 27576 * q^15 - 19594 * q^16 + 33498 * q^18 - 47880 * q^19 + 151788 * q^21 + 105132 * q^22 - 211554 * q^24 - 331252 * q^25 - 353122 * q^28 - 40662 * q^30 + 628152 * q^31 - 66024 * q^33 - 227244 * q^36 - 618748 * q^37 + 1996104 * q^39 + 1986138 * q^40 + 4274802 * q^42 - 1416064 * q^43 - 4757508 * q^45 - 3492840 * q^46 - 6640312 * q^49 + 677340 * q^51 + 11962272 * q^52 - 6743898 * q^54 - 6279408 * q^57 - 2064342 * q^58 + 7521282 * q^60 + 10948728 * q^61 + 13194636 * q^63 - 589508 * q^64 - 6977250 * q^66 - 1944728 * q^67 - 24852702 * q^70 - 1544472 * q^72 + 13351212 * q^73 - 23106048 * q^75 + 1917432 * q^78 + 7626328 * q^79 + 8703036 * q^81 + 14640192 * q^82 + 15191904 * q^84 + 3418848 * q^85 + 15346296 * q^87 + 12313398 * q^88 + 3988992 * q^91 - 24832104 * q^93 - 51594732 * q^94 - 57374730 * q^96 + 35642232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	17.0599	+	9.84952i	1.50789	+	0.870582i	0.999958	+	0.00918721i	$0.00292442\pi$
$2$	17.0599	+	9.84952i	1.50789	+	0.870582i	0.507935	+	0.861395i	$0.330409\pi$
$3$	−45.1680	−	12.1182i	−0.965843	−	0.259128i
$3$	−45.1680	−	12.1182i	−0.965843	−	0.259128i
$4$	130.026	+	225.212i	1.01583	+	1.75947i
$5$	−147.583	+	255.621i	−0.528009	+	0.914539i	0.471458	+	0.881889i	$0.343728\pi$
$5$	−147.583	+	255.621i	−0.528009	+	0.914539i	−0.999467	+	0.0326500i	$0.989605\pi$
$6$	−651.201	−	651.618i	−1.23080	−	1.23158i
$7$	−45.1728	+	906.368i	−0.0497776	+	0.998760i
$7$	−45.1728	+	906.368i	−0.0497776	+	0.998760i
$8$			2601.29i			1.79628i
$9$	1893.30	+	1094.71i	0.865705	+	0.500554i
$10$	−5035.49	+	2907.24i	−1.59236	+	0.919351i
$11$	2530.38	−	1460.92i	0.573207	−	0.330941i	−0.185222	−	0.982697i	$-0.559300\pi$
$11$	2530.38	−	1460.92i	0.573207	−	0.330941i	0.758429	+	0.651755i	$0.225967\pi$
$12$	−3143.85	−	11748.0i	−0.525203	−	1.96260i
$13$		−	12468.8i		−	1.57406i	−0.616913	−	0.787031i	$-0.711617\pi$
$13$		−	12468.8i		−	1.57406i	0.616913	−	0.787031i	$-0.288383\pi$
$14$	−9697.92	+	15017.6i	−0.944562	+	1.46269i
$15$	9763.71	−	9757.46i	0.746957	−	0.746479i
$16$	−8978.17	+	15550.6i	−0.547984	+	0.949136i
$17$	13752.6	+	23820.2i	0.678913	+	1.17591i	0.975309	+	0.220846i	$0.0708819\pi$
$17$	13752.6	+	23820.2i	0.678913	+	1.17591i	−0.296396	+	0.955065i	$0.595785\pi$
$18$	21517.0	+	37323.7i	0.869618	+	1.50845i
$19$	−3840.23	−	2217.16i	−0.128446	−	0.0741582i	0.434400	−	0.900720i	$-0.356960\pi$
$19$	−3840.23	−	2217.16i	−0.128446	−	0.0741582i	−0.562846	+	0.826562i	$0.690294\pi$
$20$	−76758.5			−2.14547
$21$	13023.9	−	40391.4i	0.306884	−	0.951747i
$22$	57557.3			1.15245
$23$	34006.6	+	19633.7i	0.582795	+	0.336477i	0.762243	−	0.647291i	$-0.224098\pi$
$23$	34006.6	+	19633.7i	0.582795	+	0.336477i	−0.179448	+	0.983767i	$0.557431\pi$
$24$	31523.1	−	117495.i	0.465467	−	1.73493i
$25$	−4499.01	−	7792.52i	−0.0575874	−	0.0997443i
$26$	122811.	−	212716.i	1.37035	−	2.37352i
$27$	−72250.5	−	72389.3i	−0.706428	−	0.707785i
$28$	−209998.	+	107678.i	−1.80785	+	0.926986i
$29$			104442.i			0.795207i	0.917557	+	0.397604i	$0.130158\pi$
$29$			104442.i			0.795207i	−0.917557	+	0.397604i	$0.869842\pi$
$30$	262674.	−	70293.2i	1.77620	−	0.475323i
$31$	−3499.96	+	2020.70i	−0.0211007	+	0.0121825i	−0.510513	−	0.859870i	$-0.670545\pi$
$31$	−3499.96	+	2020.70i	−0.0211007	+	0.0121825i	0.489413	+	0.872052i	$0.337211\pi$
$32$	−17975.9	+	10378.4i	−0.0969766	+	0.0559894i
$33$	−131996.	+	35323.0i	−0.639384	+	0.171103i
$34$			541826.i			2.36420i
$35$	−225020.	−	145312.i	−0.887122	−	0.572878i
$36$	−363.886	+	568733.i	−0.00129989	+	2.03165i
$37$	188326.	−	326191.i	0.611230	−	1.05868i	−0.379803	−	0.925067i	$-0.624008\pi$
$37$	188326.	−	326191.i	0.611230	−	1.05868i	0.991033	−	0.133614i	$-0.0426583\pi$
$38$	−43675.9	−	75648.9i	−0.129122	−	0.223645i
$39$	−151099.	+	563190.i	−0.407884	+	1.52030i
$40$	−664946.	−	383907.i	−1.64277	−	0.948453i
$41$	234072.			0.530404			0.265202	−	0.964193i	$-0.414561\pi$
$41$	234072.			0.530404			0.265202	+	0.964193i	$0.414561\pi$
$42$	620022.	−	560792.i	1.29132	−	1.16796i
$43$	−655950.			−1.25815			−0.629073	−	0.777346i	$-0.716565\pi$
$43$	−655950.			−1.25815			−0.629073	+	0.777346i	$0.716565\pi$
$44$	658031.	+	379914.i	1.16456	+	0.672359i
$45$	−559250.	+	322406.i	−0.914876	+	0.527424i
$46$	386765.	+	669897.i	0.585862	+	1.01474i
$47$	45057.1	−	78041.2i	0.0633025	−	0.109643i	−0.832637	−	0.553819i	$-0.813170\pi$
$47$	45057.1	−	78041.2i	0.0633025	−	0.109643i	0.895940	+	0.444176i	$0.146503\pi$
$48$	593972.	−	593592.i	0.775214	−	0.774718i
$49$	−819462.	−	81886.3i	−0.995044	−	0.0994317i
$50$		−	177252.i		−	0.200538i
$51$	−332519.	−	1.24257e6i	−0.351012	−	1.31167i
$52$	2.80811e6	−	1.62126e6i	2.76951	−	1.59898i
$53$	−401269.	+	231672.i	−0.370228	+	0.213751i	−0.673558	−	0.739134i	$-0.735235\pi$
$53$	−401269.	+	231672.i	−0.370228	+	0.213751i	0.303330	+	0.952886i	$0.401902\pi$
$54$	−519584.	−	1.94658e6i	−0.449032	−	1.68227i
$55$			862426.i			0.698960i
$56$	−2.35773e6	−	117508.i	−1.79406	−	0.0894146i
$57$	146588.	+	146681.i	0.104842	+	0.104909i
$58$	−1.02870e6	+	1.78176e6i	−0.692293	+	1.19909i
$59$	−112563.	−	194965.i	−0.0713532	−	0.123587i	0.828141	−	0.560519i	$-0.189398\pi$
$59$	−112563.	−	194965.i	−0.0713532	−	0.123587i	−0.899495	+	0.436932i	$0.856065\pi$
$60$	3.46703e6	+	930176.i	2.07218	+	0.555950i
$61$	2.12274e6	+	1.22557e6i	1.19741	+	0.691325i	0.959977	−	0.280079i	$-0.0903605\pi$
$61$	2.12274e6	+	1.22557e6i	1.19741	+	0.691325i	0.237433	+	0.971404i	$0.423694\pi$
$62$	−79611.7			−0.0424234
$63$	−1.07774e6	+	1.66657e6i	−0.543026	+	0.839716i
$64$	1.88952e6			0.900994
$65$	3.18729e6	+	1.84018e6i	1.43954	+	0.831120i
$66$	−2.59975e6	−	697492.i	−1.11308	−	0.298631i
$67$	−2.21050e6	−	3.82869e6i	−0.897900	−	1.55521i	−0.830174	−	0.557504i	$-0.811759\pi$
$67$	−2.21050e6	−	3.82869e6i	−0.897900	−	1.55521i	−0.0677259	−	0.997704i	$-0.521574\pi$
$68$	−3.57639e6	+	6.19449e6i	−1.37932	+	2.38905i
$69$	−1.29808e6	−	1.29892e6i	−0.475698	−	0.476002i
$70$	−2.40756e6	−	4.69534e6i	−0.838947	−	1.63615i
$71$		−	4.85818e6i		−	1.61090i	−0.592661	−	0.805452i	$-0.701923\pi$
$71$		−	4.85818e6i		−	1.61090i	0.592661	−	0.805452i	$-0.298077\pi$
$72$	−2.84767e6	+	4.92502e6i	−0.899136	+	1.55505i
$73$	1.42104e6	−	820436.i	0.427539	−	0.246840i	−0.270759	−	0.962647i	$-0.587275\pi$
$73$	1.42104e6	−	820436.i	0.427539	−	0.246840i	0.698298	+	0.715808i	$0.253941\pi$
$74$	6.42564e6	−	3.70984e6i	1.84334	−	1.06425i
$75$	108780.	+	406493.i	0.0297738	+	0.111260i
$76$		−	1.15315e6i		−	0.301328i
$77$	1.20982e6	+	2.35945e6i	0.301998	+	0.588970i
$78$	−8.12488e6	+	8.11968e6i	−1.93859	+	1.93735i
$79$	−586188.	+	1.01531e6i	−0.133765	+	0.231688i	−0.925125	−	0.379663i	$-0.876040\pi$
$79$	−586188.	+	1.01531e6i	−0.133765	+	0.231688i	0.791360	+	0.611350i	$0.209373\pi$
$80$	−2.65005e6	−	4.59002e6i	−0.578681	−	1.00231i
$81$	2.38618e6	+	4.14523e6i	0.498891	+	0.866665i
$82$	3.99324e6	+	2.30550e6i	0.799792	+	0.461760i
$83$	7.03644e6			1.35076			0.675382	−	0.737468i	$-0.263979\pi$
$83$	7.03644e6			1.35076			0.675382	+	0.737468i	$0.263979\pi$
$84$	1.07901e7	−	2.31879e6i	1.98631	−	0.426859i
$85$	−8.11861e6			−1.43389
$86$	−1.11904e7	−	6.46079e6i	−1.89715	−	1.09532i
$87$	1.26565e6	−	4.71742e6i	0.206060	−	0.768045i
$88$	3.80027e6	+	6.58227e6i	0.594464	+	1.02964i
$89$	211992.	−	367182.i	0.0318754	−	0.0552098i	−0.849648	−	0.527351i	$-0.823185\pi$
$89$	211992.	−	367182.i	0.0318754	−	0.0552098i	0.881523	+	0.472141i	$0.156519\pi$
$90$	−1.27163e7	−	8136.11i	−1.83870	−	0.00117643i
$91$	1.13013e7	+	563249.i	1.57211	+	0.0783530i
$92$			1.02116e7i			1.36721i
$93$	182573.	−	48857.8i	0.0235368	−	0.00629859i
$94$	1.53734e6	−	887582.i	0.190907	−	0.110220i
$95$	1.13351e6	−	654430.i	0.135641	−	0.0783124i
$96$	937705.	−	250936.i	0.108173	−	0.0289477i
$97$			4.84780e6i			0.539316i	0.962956	+	0.269658i	$0.0869107\pi$
$97$			4.84780e6i			0.539316i	−0.962956	+	0.269658i	$0.913089\pi$
$98$	−1.31734e7	−	9.46827e6i	−1.41386	−	1.01620i
$99$	6.39005e6	+	4088.47i	0.661883	+	0.000423484i
$100$	1.16998e6	−	2.02646e6i	0.116998	−	0.202646i
$101$	−1.16442e6	−	2.01683e6i	−0.112457	−	0.194780i	0.804304	−	0.594219i	$-0.202539\pi$
$101$	−1.16442e6	−	2.01683e6i	−0.112457	−	0.194780i	−0.916760	+	0.399438i	$0.869205\pi$
$102$	6.56597e6	−	2.44732e7i	0.612630	−	2.28344i
$103$	−7.78946e6	−	4.49725e6i	−0.702388	−	0.405524i	0.105848	−	0.994382i	$-0.466244\pi$
$103$	−7.78946e6	−	4.49725e6i	−0.702388	−	0.405524i	−0.808236	+	0.588858i	$0.799578\pi$
$104$	3.24350e7			2.82746
$105$	8.40280e6	+	9.29028e6i	0.708372	+	0.783188i
$106$	−9.12745e6			−0.744353
$107$	2.00921e6	+	1.16002e6i	0.158556	+	0.0915424i	0.577179	−	0.816618i	$-0.304154\pi$
$107$	2.00921e6	+	1.16002e6i	0.158556	+	0.0915424i	−0.418623	+	0.908160i	$0.637487\pi$
$108$	6.90847e6	−	2.56841e7i	0.527714	−	1.96192i
$109$	414768.	+	718399.i	0.0306770	+	0.0531340i	0.880956	−	0.473198i	$-0.156900\pi$
$109$	414768.	+	718399.i	0.0306770	+	0.0531340i	−0.850279	+	0.526332i	$0.823567\pi$
$110$	−8.49448e6	+	1.47129e7i	−0.608503	+	1.05396i
$111$	−1.24592e7	+	1.24512e7i	−0.864686	+	0.864133i
$112$	−1.36890e7	−	8.83999e6i	−0.920682	−	0.594550i
$113$		−	1.00544e7i		−	0.655512i	−0.944762	−	0.327756i	$-0.893708\pi$
$113$		−	1.00544e7i		−	0.655512i	0.944762	−	0.327756i	$-0.106292\pi$
$114$	1.05602e6	+	3.94618e6i	0.0667585	+	0.249465i
$115$	−1.00376e7	+	5.79521e6i	−0.615442	+	0.355326i
$116$	−2.35214e7	+	1.35801e7i	−1.39914	+	0.807793i
$117$	1.36497e7	−	2.36071e7i	0.787904	−	1.36267i
$118$		−	4.43476e6i		−	0.248475i
$119$	−2.22111e7	+	1.13889e7i	−1.20825	+	0.619537i
$120$	2.53820e7	+	2.53983e7i	1.34089	+	1.34174i
$121$	−5.47503e6	+	9.48303e6i	−0.280956	+	0.486629i
$122$	2.41425e7	+	4.18160e7i	1.20371	+	2.08489i
$123$	−1.05726e7	−	2.83654e6i	−0.512287	−	0.137443i
$124$	−910170.	−	525487.i	−0.0428693	−	0.0247506i
$125$	−2.04039e7			−0.934392
$126$	−3.48010e7	+	1.78163e7i	−1.54987	+	0.793452i
$127$	−7.32182e6			−0.317180			−0.158590	−	0.987344i	$-0.550695\pi$
$127$	−7.32182e6			−0.317180			−0.158590	+	0.987344i	$0.550695\pi$
$128$	3.45359e7	+	1.99393e7i	1.45558	+	0.840379i
$129$	2.96279e7	+	7.94894e6i	1.21517	+	0.326021i
$130$	3.62498e7	+	6.27864e7i	1.44712	+	2.50648i
$131$	−2.82384e6	+	4.89103e6i	−0.109746	+	0.190086i	−0.915667	−	0.401937i	$-0.868337\pi$
$131$	−2.82384e6	+	4.89103e6i	−0.109746	+	0.190086i	0.805921	+	0.592023i	$0.201671\pi$
$132$	−2.51180e7	−	2.51341e7i	−0.950555	−	0.951163i
$133$	2.18304e6	−	3.38051e6i	0.0804600	−	0.124595i
$134$		−	8.70893e7i		−	3.12678i
$135$	2.91672e7	−	7.78534e6i	1.02030	−	0.272339i
$136$	−6.19634e7	+	3.57746e7i	−2.11227	+	1.21952i
$137$	−1.01085e7	+	5.83612e6i	−0.335864	+	0.193911i	−0.658441	−	0.752632i	$-0.728784\pi$
$137$	−1.01085e7	+	5.83612e6i	−0.335864	+	0.193911i	0.322578	+	0.946543i	$0.395451\pi$
$138$	−9.35146e6	−	3.49448e7i	−0.302902	−	1.13189i
$139$		−	2.02541e7i		−	0.639679i	−0.947472	−	0.319840i	$-0.896371\pi$
$139$		−	2.02541e7i		−	0.639679i	0.947472	−	0.319840i	$-0.103629\pi$
$140$	3.46739e6	−	6.95714e7i	0.106796	−	2.14281i
$141$	−2.98086e6	+	2.97895e6i	−0.0895519	+	0.0894946i
$142$	4.78507e7	−	8.28799e7i	1.40242	−	2.42907i
$143$	−1.82158e7	−	3.15508e7i	−0.520923	−	0.902264i
$144$	−3.40218e7	+	1.96135e7i	−0.949486	+	0.547377i
$145$	−2.66975e7	−	1.54138e7i	−0.727248	−	0.419877i
$146$	3.23236e7			0.859577
$147$	3.60211e7	+	1.36291e7i	0.935291	+	0.353879i
$148$	9.79492e7			2.48362
$149$	5.15532e7	+	2.97643e7i	1.27674	+	0.737129i	0.976248	−	0.216655i	$-0.0695145\pi$
$149$	5.15532e7	+	2.97643e7i	1.27674	+	0.737129i	0.300496	+	0.953783i	$0.402848\pi$
$150$	−2.14798e6	+	8.00614e6i	−0.0519651	+	0.193688i
$151$	−2.38324e7	−	4.12789e7i	−0.563311	−	0.975683i	−0.997205	−	0.0747191i	$-0.976194\pi$
$151$	−2.38324e7	−	4.12789e7i	−0.563311	−	0.975683i	0.433894	−	0.900964i	$-0.357139\pi$
$152$	5.76748e6	−	9.98957e6i	0.133209	−	0.230725i
$153$	−38487.6	+	6.01539e7i	−0.000868761	+	1.35783i
$154$	−2.60002e6	+	5.21681e7i	−0.0573660	+	1.15102i
$155$		−	1.19288e6i		−	0.0257299i
$156$	−1.46484e8	+	3.92000e7i	−3.08925	+	0.826703i
$157$	3.21382e6	−	1.85550e6i	0.0662786	−	0.0382659i	−0.466495	−	0.884524i	$-0.654483\pi$
$157$	3.21382e6	−	1.85550e6i	0.0662786	−	0.0382659i	0.532773	+	0.846258i	$0.321150\pi$
$158$	−2.00006e7	+	1.15473e7i	−0.403406	+	0.232907i
$159$	2.09320e7	−	5.60152e6i	0.412971	−	0.110514i
$160$		−	6.12671e6i		−	0.118252i
$161$	−1.93315e7	+	2.99356e7i	−0.365070	+	0.565324i
$162$	−120567.	+	9.42198e7i	−0.00222806	+	1.74116i
$163$	3.93745e7	−	6.81986e7i	0.712128	−	1.23344i	−0.251928	−	0.967746i	$-0.581065\pi$
$163$	3.93745e7	−	6.81986e7i	0.712128	−	1.23344i	0.964057	−	0.265696i	$-0.0856019\pi$
$164$	3.04355e7	+	5.27158e7i	0.538799	+	0.933227i
$165$	1.04511e7	−	3.89541e7i	0.181120	−	0.675086i
$166$	1.20041e8	+	6.93055e7i	2.03681	+	1.17595i
$167$	−5.01790e7			−0.833709			−0.416854	−	0.908973i	$-0.636868\pi$
$167$	−5.01790e7			−0.833709			−0.416854	+	0.908973i	$0.636868\pi$
$168$	1.05070e8	+	3.38791e7i	1.70961	+	0.551250i
$169$	−9.27219e7			−1.47767
$170$	−1.38502e8	−	7.99644e7i	−2.16215	−	1.24832i
$171$	−4.84355e6	−	8.40169e6i	−0.0740760	−	0.128493i
$172$	−8.52905e7	−	1.47727e8i	−1.27806	−	2.21366i
$173$	6.84856e6	−	1.18621e7i	0.100563	−	0.174180i	−0.811354	−	0.584555i	$-0.801269\pi$
$173$	6.84856e6	−	1.18621e7i	0.100563	−	0.174180i	0.911917	+	0.410375i	$0.134602\pi$
$174$	6.80560e7	−	6.80125e7i	0.979364	−	0.978737i
$175$	7.26612e6	−	3.72575e6i	0.102487	−	0.0525510i
$176$			5.24654e7i			0.725402i
$177$	2.72162e6	+	1.01702e7i	0.0368910	+	0.137856i
$178$	7.23312e6	−	4.17605e6i	0.0961293	−	0.0555003i
$179$	−2.30041e7	+	1.32814e7i	−0.299792	+	0.173085i	−0.642349	−	0.766412i	$-0.722040\pi$
$179$	−2.30041e7	+	1.32814e7i	−0.299792	+	0.173085i	0.342558	+	0.939497i	$0.388707\pi$
$180$	−1.45327e8	−	8.40284e7i	−1.85734	−	1.07392i
$181$			1.45056e8i			1.81828i	0.416496	+	0.909138i	$0.363258\pi$
$181$			1.45056e8i			1.81828i	−0.416496	+	0.909138i	$0.636742\pi$
$182$	1.87251e8	+	1.20921e8i	2.30236	+	1.48680i
$183$	−8.10284e7	−	8.10803e7i	−0.977369	−	0.977994i
$184$	−5.10731e7	+	8.84612e7i	−0.604407	+	1.04686i
$185$	5.55875e7	+	9.62804e7i	0.645470	+	1.11799i
$186$	3.59590e6	+	964752.i	0.0409744	+	0.0109931i
$187$	6.95987e7	+	4.01828e7i	0.778315	+	0.449361i
$188$	2.34344e7			0.257218
$189$	6.88751e7	−	6.22155e7i	0.742072	−	0.670320i
$190$	2.57833e7			0.272710
$191$	−3.13416e7	−	1.80951e7i	−0.325465	−	0.187907i	0.328361	−	0.944552i	$-0.393504\pi$
$191$	−3.13416e7	−	1.80951e7i	−0.325465	−	0.187907i	−0.653826	+	0.756645i	$0.726837\pi$
$192$	−8.53459e7	−	2.28976e7i	−0.870219	−	0.233473i
$193$	−1.02233e7	−	1.77072e7i	−0.102362	−	0.177296i	0.810295	−	0.586022i	$-0.199307\pi$
$193$	−1.02233e7	−	1.77072e7i	−0.102362	−	0.177296i	−0.912657	+	0.408725i	$0.865973\pi$
$194$	−4.77485e7	+	8.27028e7i	−0.469519	+	0.813231i
$195$	−1.21664e8	−	1.21741e8i	−1.17500	−	1.17576i
$196$	−8.81096e7	−	1.95200e8i	−0.835847	−	1.85175i
$197$		−	6.28086e7i		−	0.585312i	−0.956218	−	0.292656i	$-0.905461\pi$
$197$		−	6.28086e7i		−	0.585312i	0.956218	−	0.292656i	$-0.0945391\pi$
$198$	1.08973e8	+	6.30086e7i	0.997680	+	0.576862i
$199$	−1.34048e7	+	7.73924e6i	−0.120579	+	0.0696166i	−0.559077	−	0.829116i	$-0.688844\pi$
$199$	−1.34048e7	+	7.73924e6i	−0.120579	+	0.0696166i	0.438497	+	0.898733i	$0.355511\pi$
$200$	2.02706e7	−	1.17033e7i	0.179169	−	0.103443i
$201$	5.34468e7	+	1.99722e8i	0.464232	+	1.73476i
$202$		−	4.58759e7i		−	0.391611i
$203$	−9.46624e7	−	4.71791e6i	−0.794221	−	0.0395835i
$204$	2.36605e8	−	2.36453e8i	1.95127	−	1.95002i
$205$	−3.45451e7	+	5.98339e7i	−0.280058	+	0.485075i
$206$	−8.85914e7	−	1.53445e8i	−0.706084	−	1.22297i
$207$	4.28914e7	+	7.43999e7i	0.336104	+	0.583010i
$208$	1.93898e8	+	1.11947e8i	1.49400	+	0.862561i
$209$	−1.29563e7			−0.0981681
$210$	5.18458e7	+	2.41254e8i	0.386319	+	1.79766i
$211$	1.77898e7			0.130371			0.0651857	−	0.997873i	$-0.479236\pi$
$211$	1.77898e7			0.130371			0.0651857	+	0.997873i	$0.479236\pi$
$212$	−1.04351e8	−	6.02469e7i	−0.752176	−	0.434269i
$213$	−5.88725e7	+	2.19434e8i	−0.417430	+	1.55588i
$214$	2.28513e7	+	3.95796e7i	0.159390	+	0.276072i
$215$	9.68070e7	−	1.67675e8i	0.664312	−	1.15062i
$216$	1.88306e8	−	1.87945e8i	1.27138	−	1.26894i
$217$	−1.67339e6	−	3.26353e6i	−0.0111170	−	0.0216809i
$218$			1.63410e7i			0.106827i
$219$	−7.41276e7	+	1.98370e7i	−0.476898	+	0.127621i
$220$	−1.94228e8	+	1.12138e8i	−1.22980	+	0.710023i
$221$	2.97009e8	−	1.71478e8i	1.85096	−	1.06865i
$222$	−3.35190e8	+	8.96989e7i	−2.05615	+	0.550240i
$223$		−	7.50760e7i		−	0.453350i	−0.973970	−	0.226675i	$-0.927214\pi$
$223$		−	7.50760e7i		−	0.453350i	0.973970	−	0.226675i	$-0.0727856\pi$
$224$	−8.59464e6	−	1.67616e7i	−0.0510928	−	0.0996434i
$225$	12590.8	−	1.96787e7i	7.36909e−5	−	0.115175i
$226$	9.90307e7	−	1.71526e8i	0.570677	−	0.988442i
$227$	−5.37720e7	−	9.31358e7i	−0.305116	−	0.528477i	0.672171	−	0.740396i	$-0.265362\pi$
$227$	−5.37720e7	−	9.31358e7i	−0.305116	−	0.528477i	−0.977287	+	0.211919i	$0.932029\pi$
$228$	−1.39742e7	+	5.20856e7i	−0.0780825	+	0.291035i
$229$	5.30599e7	+	3.06341e7i	0.291972	+	0.168570i	0.638831	−	0.769347i	$-0.279418\pi$
$229$	5.30599e7	+	3.06341e7i	0.291972	+	0.168570i	−0.346859	+	0.937917i	$0.612752\pi$
$230$	−2.28320e8			−1.23736
$231$	−2.60530e7	−	1.21233e8i	−0.139064	−	0.647109i
$232$	−2.71683e8			−1.42842
$233$	3.02865e8	+	1.74859e8i	1.56857	+	0.905614i	0.996336	+	0.0855222i	$0.0272558\pi$
$233$	3.02865e8	+	1.74859e8i	1.56857	+	0.905614i	0.572233	+	0.820091i	$0.306077\pi$
$234$	4.65381e8	−	2.68291e8i	2.37439	−	1.36883i
$235$	1.32993e7	+	2.30351e7i	0.0668486	+	0.115785i
$236$	2.92722e7	−	5.07009e7i	0.144965	−	0.251087i
$237$	3.87807e7	−	3.87558e7i	0.189233	−	0.189112i
$238$	−4.91094e8	−	2.44758e7i	−2.36127	−	0.117684i
$239$			2.28019e8i			1.08039i	0.841541	+	0.540193i	$0.181649\pi$
$239$			2.28019e8i			1.08039i	−0.841541	+	0.540193i	$0.818351\pi$
$240$	6.40746e7	+	2.39436e8i	0.299190	+	1.11802i
$241$	2.34710e8	−	1.35510e8i	1.08012	−	0.623609i	0.149193	−	0.988808i	$-0.452333\pi$
$241$	2.34710e8	−	1.35510e8i	1.08012	−	0.623609i	0.930929	+	0.365199i	$0.118999\pi$
$242$	−1.86807e8	+	1.07853e8i	−0.847302	+	0.489190i
$243$	−5.75463e7	−	2.16148e8i	−0.257274	−	0.966339i
$244$			6.37422e8i			2.80907i
$245$	1.41871e8	−	1.97387e8i	0.616327	−	0.857506i
$246$	−1.52428e8	−	1.52526e8i	−0.652819	−	0.653237i
$247$	−2.76453e7	+	4.78830e7i	−0.116730	+	0.202182i
$248$	−5.25644e6	−	9.10441e6i	−0.0218832	−	0.0379028i
$249$	−3.17822e8	−	8.52691e7i	−1.30463	−	0.350021i
$250$	−3.48088e8	−	2.00969e8i	−1.40896	−	0.813465i
$251$	2.47202e8			0.986721			0.493360	−	0.869825i	$-0.335768\pi$
$251$	2.47202e8			0.986721			0.493360	+	0.869825i	$0.335768\pi$
$252$	−5.15465e8	−	2.60211e7i	−2.02907	−	0.102429i
$253$	1.14733e8			0.445417
$254$	−1.24909e8	−	7.21164e7i	−0.478274	−	0.276132i
$255$	3.66701e8	+	9.83831e7i	1.38491	+	0.371561i
$256$	2.71856e8	+	4.70868e8i	1.01274	+	1.75412i
$257$	−2.17582e7	+	3.76864e7i	−0.0799572	+	0.138490i	−0.903231	−	0.429154i	$-0.858812\pi$
$257$	−2.17582e7	+	3.76864e7i	−0.0799572	+	0.138490i	0.823274	+	0.567644i	$0.192145\pi$
$258$	4.27155e8	+	4.27429e8i	1.54852	+	1.54951i
$259$	2.87141e8	+	1.85428e8i	1.02694	+	0.663171i
$260$			9.57085e8i			3.37710i
$261$	−1.14333e8	+	1.97739e8i	−0.398044	+	0.688415i
$262$	−9.63486e7	+	5.56269e7i	−0.330972	+	0.191087i
$263$	−4.46496e8	+	2.57785e8i	−1.51347	+	0.873800i	−0.513590	+	0.858036i	$0.671685\pi$
$263$	−4.46496e8	+	2.57785e8i	−1.51347	+	0.873800i	−0.999876	+	0.0157643i	$0.994982\pi$
$264$	−9.18854e7	−	3.43360e8i	−0.307350	−	1.14851i
$265$		−	1.36764e8i		−	0.451451i
$266$	7.05386e7	−	3.61691e7i	0.229795	−	0.117829i
$267$	−1.40249e7	+	1.40159e7i	−0.0450930	+	0.0450642i
$268$	5.74844e8	−	9.95658e8i	1.82422	−	3.15965i
$269$	−1.81917e8	−	3.15089e8i	−0.569822	−	0.986961i	−0.996583	−	0.0825966i	$-0.973679\pi$
$269$	−1.81917e8	−	3.15089e8i	−0.569822	−	0.986961i	0.426761	−	0.904365i	$-0.359655\pi$
$270$	5.74270e8	+	1.54466e8i	1.77559	+	0.477595i
$271$	−7.55684e7	−	4.36294e7i	−0.230647	−	0.133164i	0.380224	−	0.924895i	$-0.375847\pi$
$271$	−7.55684e7	−	4.36294e7i	−0.230647	−	0.133164i	−0.610870	+	0.791731i	$0.709180\pi$
$272$	−4.93893e8			−1.48813
$273$	−5.03631e8	−	1.62392e8i	−1.49811	−	0.483055i
$274$	−2.29932e8			−0.675262
$275$	−2.27684e7	−	1.31454e7i	−0.0660190	−	0.0381161i
$276$	1.23746e8	−	4.61236e8i	0.354282	−	1.32051i
$277$	−7.32333e7	−	1.26844e8i	−0.207028	−	0.358583i	0.743749	−	0.668459i	$-0.233046\pi$
$277$	−7.32333e7	−	1.26844e8i	−0.207028	−	0.358583i	−0.950777	+	0.309876i	$0.899712\pi$
$278$	1.99494e8	−	3.45533e8i	0.556893	−	0.964568i
$279$	−8.83854e6	−	5655.06i	−0.0243650	−	1.55891e-5i
$280$	3.77998e8	−	5.85344e8i	1.02905	−	1.59352i
$281$			3.60876e8i			0.970254i	0.874444	+	0.485127i	$0.161227\pi$
$281$			3.60876e8i			0.970254i	−0.874444	+	0.485127i	$0.838773\pi$
$282$	−8.01944e7	+	2.14605e7i	−0.212947	+	0.0569860i
$283$	−3.67330e8	+	2.12078e8i	−0.963395	+	0.556216i	−0.897216	−	0.441591i	$-0.854414\pi$
$283$	−3.67330e8	+	2.12078e8i	−0.963395	+	0.556216i	−0.0661788	+	0.997808i	$0.521081\pi$
$284$	1.09412e9	−	6.31690e8i	2.83433	−	1.63640i
$285$	−5.91287e7	+	1.58232e7i	−0.151301	+	0.0404891i
$286$		−	7.17669e8i		−	1.81402i
$287$	−1.05737e7	+	2.12156e8i	−0.0264022	+	0.529746i
$288$	−4.53952e7	−	29044.7i	−0.111979	−	7.16461e-5i
$289$	−1.73099e8	+	2.99817e8i	−0.421845	+	0.730657i
$290$	−3.03637e8	−	5.25915e8i	−0.731074	−	1.26626i
$291$	5.87467e7	−	2.18965e8i	0.139752	−	0.520895i
$292$	3.69543e8	+	2.13356e8i	0.868611	+	0.501493i
$293$	−6.57254e8			−1.52650			−0.763249	−	0.646104i	$-0.776397\pi$
$293$	−6.57254e8			−1.52650			−0.763249	+	0.646104i	$0.776397\pi$
$294$	4.80276e8	+	5.87301e8i	1.10224	+	1.34786i
$295$	6.64495e7			0.150701
$296$	8.48517e8	+	4.89892e8i	1.90169	+	1.09794i
$297$	−2.88576e8	−	7.76207e7i	−0.639165	−	0.171921i
$298$	5.86327e8	+	1.01555e9i	1.28346	+	2.22302i
$299$	2.44809e8	−	4.24021e8i	0.529636	−	0.917356i
$300$	−7.74026e7	+	7.73531e7i	−0.165513	+	0.165407i
$301$	2.96311e7	−	5.94532e8i	0.0626274	−	1.25659i
$302$		−	9.38950e8i		−	1.96163i
$303$	2.81541e7	+	1.05207e8i	0.0581423	+	0.217268i
$304$	6.89565e7	−	3.98121e7i	0.140772	−	0.0812750i
$305$	−6.26562e8	+	3.61746e8i	−1.26449	+	0.730052i
$306$	−5.93144e8	+	1.02584e9i	−1.18341	+	2.04670i
$307$		−	9.72539e7i		−	0.191833i	−0.995389	−	0.0959163i	$-0.969422\pi$
$307$		−	9.72539e7i		−	0.191833i	0.995389	−	0.0959163i	$-0.0305781\pi$
$308$	−3.74067e8	+	5.79256e8i	−0.729494	+	1.12965i
$309$	2.97336e8	+	2.97526e8i	0.573314	+	0.573681i
$310$	1.17493e7	−	2.03504e7i	0.0224000	−	0.0387979i
$311$	1.40783e8	+	2.43844e8i	0.265393	+	0.459674i	0.967667	−	0.252233i	$-0.0811649\pi$
$311$	1.40783e8	+	2.43844e8i	0.265393	+	0.459674i	−0.702273	+	0.711907i	$0.747832\pi$
$312$	−1.46502e9	−	3.93054e8i	−2.73088	−	0.732674i
$313$	6.09980e8	+	3.52172e8i	1.12437	+	0.649157i	0.942514	−	0.334167i	$-0.108455\pi$
$313$	6.09980e8	+	3.52172e8i	1.12437	+	0.649157i	0.181860	+	0.983324i	$0.441788\pi$
$314$	7.31031e7			0.133255
$315$	−2.66956e8	−	5.21450e8i	−0.481230	−	0.939996i
$316$	−3.04879e8			−0.543528
$317$	−4.77350e8	−	2.75598e8i	−0.841646	−	0.485924i	0.0161776	−	0.999869i	$-0.494850\pi$
$317$	−4.77350e8	−	2.75598e8i	−0.841646	−	0.485924i	−0.857823	+	0.513945i	$0.828184\pi$
$318$	4.12269e8	+	1.10608e8i	0.718928	+	0.192883i
$319$	1.52580e8	+	2.64277e8i	0.263167	+	0.455818i
$320$	−2.78861e8	+	4.83002e8i	−0.475733	+	0.823994i
$321$	−7.66948e7	−	7.67439e7i	−0.129419	−	0.129502i
$322$	−6.24645e8	+	3.20291e8i	−1.04265	+	0.534624i
$323$		−	1.21967e8i		−	0.201388i
$324$	−6.23288e8	+	1.07638e9i	−1.01808	+	1.75816i
$325$	−9.71632e7	+	5.60972e7i	−0.157004	+	0.0906461i
$326$	1.34345e9	−	7.75639e8i	2.14763	−	1.23993i
$327$	−1.00285e7	−	3.74749e7i	−0.0158606	−	0.0592684i
$328$			6.08891e8i			0.952755i
$329$	6.86987e7	+	4.43637e7i	0.106356	+	0.0686818i
$330$	5.61973e8	−	5.61613e8i	0.860828	−	0.860277i
$331$	−4.73426e8	+	8.19998e8i	−0.717553	+	1.24284i	0.244413	+	0.969671i	$0.421405\pi$
$331$	−4.73426e8	+	8.19998e8i	−0.717553	+	1.24284i	−0.961967	+	0.273167i	$0.911929\pi$
$332$	9.14919e8	+	1.58469e9i	1.37214	+	2.37662i
$333$	7.13642e8	−	4.11413e8i	1.05907	−	0.610552i
$334$	−8.56047e8	−	4.94239e8i	−1.25714	−	0.725812i
$335$	1.30493e9			1.89640
$336$	5.11181e8	+	5.65171e8i	0.735170	+	0.812817i
$337$	7.33822e7			0.104445			0.0522223	−	0.998635i	$-0.483370\pi$
$337$	7.33822e7			0.104445			0.0522223	+	0.998635i	$0.483370\pi$
$338$	−1.58182e9	−	9.13266e8i	−2.22817	−	1.28644i
$339$	−1.21841e8	+	4.54136e8i	−0.169862	+	0.633122i
$340$	−1.05563e9	−	1.82840e9i	−1.45658	−	2.52288i
$341$	−5.90415e6	+	1.02263e7i	−0.00806338	+	0.0139662i
$342$	122230.	−	1.91038e8i	0.000165229	−	0.258243i
$343$	1.11236e8	−	7.39035e8i	0.148839	−	0.988861i
$344$		−	1.70632e9i		−	2.25998i
$345$	5.23606e8	−	1.40120e8i	0.686495	−	0.183711i
$346$	2.33671e8	−	1.34910e8i	0.303276	−	0.175097i
$347$	−9.40391e8	+	5.42935e8i	−1.20825	+	0.697581i	−0.962376	−	0.271722i	$-0.912407\pi$
$347$	−9.40391e8	+	5.42935e8i	−1.20825	+	0.697581i	−0.245870	+	0.969303i	$0.579073\pi$
$348$	1.22698e9	−	3.28348e8i	1.56067	−	0.417645i
$349$		−	1.20918e9i		−	1.52265i	−0.648369	−	0.761326i	$-0.724549\pi$
$349$		−	1.20918e9i		−	1.52265i	0.648369	−	0.761326i	$-0.275451\pi$
$350$	1.60656e8	+	8.00699e6i	0.200290	+	0.00998231i
$351$	−9.02606e8	+	9.00876e8i	−1.11410	+	1.11196i
$352$	−3.03240e7	+	5.25227e7i	−0.0370584	+	0.0641871i
$353$	−6.38499e8	−	1.10591e9i	−0.772590	−	1.33817i	−0.936139	−	0.351630i	$-0.885628\pi$
$353$	−6.38499e8	−	1.10591e9i	−0.772590	−	1.33817i	0.163549	−	0.986535i	$-0.447706\pi$
$354$	−5.37414e7	+	2.00309e8i	−0.0643869	+	0.239988i
$355$	1.24186e9	+	7.16985e8i	1.47323	+	0.850572i
$356$	1.10258e8			0.129520
$357$	1.14125e9	−	2.45255e8i	1.32752	−	0.285285i
$358$	−5.23262e8			−0.602739
$359$	4.45772e8	+	2.57367e8i	0.508490	+	0.293577i	0.732213	−	0.681076i	$-0.238488\pi$
$359$	4.45772e8	+	2.57367e8i	0.508490	+	0.293577i	−0.223723	+	0.974653i	$0.571821\pi$
$360$	−8.38674e8	−	1.45477e9i	−0.947402	−	1.64338i
$361$	−4.37104e8	−	7.57087e8i	−0.489001	−	0.846975i
$362$	−1.42873e9	+	2.47463e9i	−1.58296	+	2.74176i
$363$	3.62214e8	−	3.61982e8i	0.397458	−	0.397204i
$364$	1.34261e9	+	2.61842e9i	1.45914	+	2.84567i
$365$			4.84330e8i			0.521334i
$366$	−5.83732e8	−	2.18131e9i	−0.622343	−	2.32559i
$367$	−8.63433e8	+	4.98503e8i	−0.911795	+	0.526425i	−0.881008	−	0.473101i	$-0.843135\pi$
$367$	−8.63433e8	+	4.98503e8i	−0.911795	+	0.526425i	−0.0307869	+	0.999526i	$0.509801\pi$
$368$	−6.10634e8	+	3.52550e8i	−0.638725	+	0.368768i
$369$	4.43169e8	+	2.56242e8i	0.459173	+	0.265496i
$370$			2.19004e9i			2.24774i
$371$	−1.91854e8	−	3.74162e8i	−0.195057	−	0.380409i
$372$	3.47426e7	+	3.47648e7i	0.0349915	+	0.0350138i
$373$	1.39545e8	−	2.41699e8i	0.139230	−	0.241154i	−0.787975	−	0.615707i	$-0.788871\pi$
$373$	1.39545e8	−	2.41699e8i	0.139230	−	0.241154i	0.927205	+	0.374553i	$0.122204\pi$
$374$	7.91563e8	+	1.37103e9i	0.782411	+	1.35518i
$375$	9.21605e8	+	2.47259e8i	0.902476	+	0.242127i
$376$	2.03008e8	+	1.17207e8i	0.196950	+	0.113709i
$377$	1.30226e9			1.25171
$378$	1.78779e9	−	3.83002e8i	1.70253	−	0.364736i
$379$	1.69982e9			1.60386			0.801929	−	0.597419i	$-0.203807\pi$
$379$	1.69982e9			1.60386			0.801929	+	0.597419i	$0.203807\pi$
$380$	2.94770e8	+	1.70186e8i	0.275576	+	0.159104i
$381$	3.30712e8	+	8.87275e7i	0.306346	+	0.0821903i
$382$	−3.56455e8	−	6.17399e8i	−0.327178	−	0.566688i
$383$	4.11657e8	−	7.13012e8i	0.374404	−	0.648486i	−0.615834	−	0.787876i	$-0.711181\pi$
$383$	4.11657e8	−	7.13012e8i	0.374404	−	0.648486i	0.990238	+	0.139390i	$0.0445140\pi$
$384$	−1.31829e9	−	1.31913e9i	−1.18810	−	1.18886i
$385$	−7.81675e8	−	3.89582e7i	−0.698094	−	0.0347925i
$386$		−	4.02777e8i		−	0.356459i
$387$	−1.24191e9	−	7.18076e8i	−1.08918	−	0.629770i
$388$	−1.09178e9	+	6.30339e8i	−0.948908	+	0.547852i
$389$	−1.76293e9	+	1.01783e9i	−1.51849	+	0.876702i	−0.518729	+	0.854939i	$0.673595\pi$
$389$	−1.76293e9	+	1.01783e9i	−1.51849	+	0.876702i	−0.999763	+	0.0217634i	$0.993072\pi$
$390$	−8.76470e8	−	3.27522e9i	−0.748188	−	2.79585i
$391$			1.08006e9i			0.913754i
$392$	2.13010e8	−	2.13166e9i	0.178607	−	1.78738i
$393$	1.86818e8	−	1.86698e8i	0.155254	−	0.155155i
$394$	6.18634e8	−	1.07151e9i	0.509562	−	0.882588i
$395$	−1.73023e8	−	2.99684e8i	−0.141258	−	0.244666i
$396$	8.29951e8	+	1.43964e9i	0.671614	+	1.16499i
$397$	−9.90918e8	−	5.72107e8i	−0.794824	−	0.458892i	0.0468339	−	0.998903i	$-0.485087\pi$
$397$	−9.90918e8	−	5.72107e8i	−0.794824	−	0.458892i	−0.841658	+	0.540011i	$0.818420\pi$
$398$	−3.04911e8			−0.242428
$399$	−1.39569e8	+	1.26236e8i	−0.109998	+	0.0994899i
$400$	1.61572e8			0.126228
$401$	1.28973e9	+	7.44625e8i	0.998834	+	0.576677i	0.907903	−	0.419180i	$-0.137682\pi$
$401$	1.28973e9	+	7.44625e8i	0.998834	+	0.576677i	0.0909307	+	0.995857i	$0.471016\pi$
$402$	−1.05537e9	+	3.93365e9i	−0.810237	+	3.01998i
$403$	2.51957e7	+	4.36402e7i	0.0191760	+	0.0332138i
$404$	3.02810e8	−	5.24481e8i	0.228473	−	0.395727i
$405$	−1.41177e9	−	1.80655e6i	−1.05602	−	0.00135132i
$406$	−1.56846e9	−	1.01287e9i	−1.16314	−	0.751123i
$407$		−	1.10052e9i		−	0.809125i
$408$	3.23229e9	−	8.64981e8i	2.35613	−	0.630516i
$409$	1.46963e9	−	8.48488e8i	1.06212	−	0.613217i	0.136105	−	0.990694i	$-0.456542\pi$
$409$	1.46963e9	−	8.48488e8i	1.06212	−	0.613217i	0.926019	+	0.377477i	$0.123208\pi$
$410$	−1.17867e9	+	6.80505e8i	−0.844595	+	0.487627i
$411$	5.27302e8	−	1.41109e8i	0.374639	−	0.100256i
$412$		−	2.33904e9i		−	1.64777i
$413$	1.81795e8	−	9.32163e7i	0.126986	−	0.0651129i
$414$	−1.08239e6	+	1.69171e9i	−0.000749690	+	1.17172i
$415$	−1.03846e9	+	1.79866e9i	−0.713216	+	1.23533i
$416$	1.29406e8	+	2.24138e8i	0.0881309	+	0.152647i
$417$	−2.45444e8	+	9.14839e8i	−0.165759	+	0.617829i
$418$	−2.21033e8	−	1.27614e8i	−0.148027	−	0.0854634i
$419$	9.33561e8			0.620003			0.310002	−	0.950736i	$-0.399670\pi$
$419$	9.33561e8			0.620003			0.310002	+	0.950736i	$0.399670\pi$
$420$	−9.99697e8	+	3.10038e9i	−0.658409	+	2.04194i
$421$	−1.29620e9			−0.846611			−0.423305	−	0.905987i	$-0.639130\pi$
$421$	−1.29620e9			−0.846611			−0.423305	+	0.905987i	$0.639130\pi$
$422$	3.03491e8	+	1.75221e8i	0.196586	+	0.113499i
$423$	1.70739e8	−	9.84307e7i	0.109684	−	0.0632324i
$424$	−6.02648e8	−	1.04382e9i	−0.383958	−	0.665034i
$425$	1.23746e8	−	2.14335e8i	0.0781936	−	0.135435i
$426$	−3.16568e9	+	3.16366e9i	−1.98396	+	1.98269i
$427$	−1.20670e9	+	1.86862e9i	−0.750072	+	1.16151i
$428$			6.03331e8i			0.371965i
$429$	4.40434e8	+	1.64583e9i	0.269327	+	1.00643i
$430$	3.30303e9	−	1.90701e9i	2.00342	−	1.15668i
$431$	6.40769e8	−	3.69948e8i	0.385506	−	0.222572i	−0.294705	−	0.955588i	$-0.595221\pi$
$431$	6.40769e8	−	3.69948e8i	0.385506	−	0.222572i	0.680211	+	0.733016i	$0.261888\pi$
$432$	1.77438e9	−	4.73618e8i	1.05890	−	0.282641i
$433$			5.32389e8i			0.315153i	0.987507	+	0.157577i	$0.0503681\pi$
$433$			5.32389e8i			0.315153i	−0.987507	+	0.157577i	$0.949632\pi$
$434$	3.59628e6	−	7.21575e7i	0.00211174	−	0.0423708i
$435$	1.01908e9	+	1.01974e9i	0.593605	+	0.593985i
$436$	−1.07861e8	+	1.86821e8i	−0.0623250	+	0.107950i
$437$	−8.70622e7	−	1.50796e8i	−0.0499050	−	0.0864381i
$438$	−1.45999e9	−	3.91704e8i	−0.830216	−	0.222740i
$439$	−4.63808e8	−	2.67780e8i	−0.261645	−	0.151061i	0.363440	−	0.931618i	$-0.381602\pi$
$439$	−4.63808e8	−	2.67780e8i	−0.261645	−	0.151061i	−0.625085	+	0.780557i	$0.714936\pi$
$440$	−2.24342e9			−1.25553
$441$	−1.46184e9	−	1.05211e9i	−0.811644	−	0.584152i
$442$	6.75591e9			3.72140
$443$	4.22562e8	+	2.43966e8i	0.230928	+	0.133327i	0.611000	−	0.791630i	$-0.290767\pi$
$443$	4.22562e8	+	2.43966e8i	0.230928	+	0.133327i	−0.380072	+	0.924957i	$0.624101\pi$
$444$	−4.42417e9	−	1.18697e9i	−2.39878	−	0.643575i
$445$	6.25730e7	+	1.08380e8i	0.0336610	+	0.0583025i
$446$	7.39462e8	−	1.28079e9i	0.394679	−	0.683604i
$447$	−1.96787e9	−	1.96913e9i	−1.04212	−	1.04279i
$448$	−8.53550e7	+	1.71260e9i	−0.0448493	+	0.899877i
$449$		−	2.40148e9i		−	1.25204i	−0.779808	−	0.626018i	$-0.784684\pi$
$449$		−	2.40148e9i		−	1.25204i	0.779808	−	0.626018i	$-0.215316\pi$
$450$	1.94040e8	−	3.35592e8i	0.100380	−	0.173607i
$451$	5.92293e8	−	3.41960e8i	0.304031	−	0.175533i
$452$	2.26436e9	−	1.30733e9i	1.15335	−	0.665887i
$453$	5.76235e8	+	2.15329e9i	0.291243	+	1.08833i
$454$		−	2.11851e9i		−	1.06252i
$455$	−1.81186e9	+	2.80573e9i	−0.901746	+	1.39639i
$456$	−3.81562e8	+	3.81317e8i	−0.188446	+	0.188326i
$457$	1.37202e9	−	2.37641e9i	0.672440	−	1.16470i	−0.304770	−	0.952426i	$-0.598580\pi$
$457$	1.37202e9	−	2.37641e9i	0.672440	−	1.16470i	0.977210	−	0.212274i	$-0.0680871\pi$
$458$	6.03463e8	+	1.04523e9i	0.293509	+	0.508372i
$459$	7.30697e8	−	2.71657e9i	0.352690	−	1.31122i
$460$	−2.61030e9	−	1.50706e9i	−1.25037	−	0.721899i
$461$	9.15712e8			0.435317			0.217658	−	0.976025i	$-0.430158\pi$
$461$	9.15712e8			0.435317			0.217658	+	0.976025i	$0.430158\pi$
$462$	7.49622e8	−	2.32482e9i	0.353668	−	1.09684i
$463$	−3.18880e9			−1.49312			−0.746558	−	0.665321i	$-0.768295\pi$
$463$	−3.18880e9			−1.49312			−0.746558	+	0.665321i	$0.768295\pi$
$464$	−1.62413e9	−	9.37694e8i	−0.754760	−	0.435761i
$465$	−1.44556e7	+	5.38802e7i	−0.00666733	+	0.0248510i
$466$	3.44456e9	+	5.96615e9i	1.57682	+	2.73114i
$467$	1.50827e9	−	2.61240e9i	0.685284	−	1.18695i	−0.288063	−	0.957611i	$-0.593011\pi$
$467$	1.50827e9	−	2.61240e9i	0.685284	−	1.18695i	0.973347	−	0.229335i	$-0.0736553\pi$
$468$	7.09141e9	+	4.53721e6i	3.19795	+	0.00204611i
$469$	3.57006e9	−	1.83057e9i	1.59798	−	0.819372i
$470$			5.23968e8i			0.232789i
$471$	−1.67647e8	+	4.48635e7i	−0.0739305	+	0.0197843i
$472$	5.07161e8	−	2.92809e8i	0.221998	−	0.128170i
$473$	−1.65980e9	+	9.58288e8i	−0.721178	+	0.416372i
$474$	1.04332e9	−	2.79199e8i	0.449980	−	0.120417i
$475$			3.99001e7i			0.0170823i
$476$	−5.45293e9	−	3.52135e9i	−2.31743	−	1.49653i
$477$	−1.01334e9	−	648350.i	−0.427503	−	0.000273524i
$478$	−2.24588e9	+	3.88997e9i	−0.940564	+	1.62911i
$479$	2.19531e9	+	3.80239e9i	0.912687	+	1.58082i	0.810253	+	0.586080i	$0.199330\pi$
$479$	2.19531e9	+	3.80239e9i	0.912687	+	1.58082i	0.102434	+	0.994740i	$0.467337\pi$
$480$	−7.42449e7	+	2.76731e8i	−0.0306423	+	0.114213i
$481$	−4.06720e9	−	2.34820e9i	−1.66643	−	0.962114i
$482$	5.33884e9			2.17161
$483$	1.23593e9	−	1.11787e9i	0.499091	−	0.451414i
$484$	−2.84758e9			−1.14161
$485$	−1.23920e9	−	7.15453e8i	−0.493226	−	0.284764i
$486$	1.14722e9	−	4.25426e9i	0.453336	−	1.68111i
$487$	−6.70342e8	−	1.16107e9i	−0.262994	−	0.455518i	0.704042	−	0.710158i	$-0.251376\pi$
$487$	−6.70342e8	−	1.16107e9i	−0.262994	−	0.455518i	−0.967036	+	0.254640i	$0.918043\pi$
$488$	−3.18806e9	+	5.52188e9i	−1.24182	+	2.15089i
$489$	−2.60491e9	+	2.60325e9i	−1.00742	+	1.00678i
$490$	4.36446e9	−	1.97004e9i	1.67588	−	0.756464i
$491$			1.80589e9i			0.688502i	0.938878	+	0.344251i	$0.111867\pi$
$491$			1.80589e9i			0.688502i	−0.938878	+	0.344251i	$0.888133\pi$
$492$	−7.35888e8	−	2.74989e9i	−0.278570	−	1.04097i
$493$	−2.48782e9	+	1.43634e9i	−0.935093	+	0.539876i
$494$	−9.43249e8	+	5.44585e8i	−0.352032	+	0.203246i
$495$	−9.44108e8	+	1.63283e9i	−0.349867	+	0.605094i
$496$		−	7.25688e7i		−	0.0267032i
$497$	4.40330e9	+	2.19458e8i	1.60891	+	0.0801869i
$498$	−4.58214e9	−	4.58507e9i	−1.66251	−	1.66358i
$499$	1.55679e9	−	2.69644e9i	0.560891	−	0.971492i	−0.436528	−	0.899691i	$-0.643792\pi$
$499$	1.55679e9	−	2.69644e9i	0.560891	−	0.971492i	0.997419	−	0.0718014i	$-0.0228748\pi$
$500$	−2.65304e9	−	4.59520e9i	−0.949181	−	1.64403i
$501$	2.26649e9	+	6.08080e8i	0.805232	+	0.216037i
$502$	4.21724e9	+	2.43482e9i	1.48787	+	0.859022i
$503$	−3.44283e9			−1.20622			−0.603112	−	0.797657i	$-0.706073\pi$
$503$	−3.44283e9			−1.20622			−0.603112	+	0.797657i	$0.706073\pi$
$504$	−4.33525e9	−	2.80351e9i	−1.50837	−	0.975428i
$505$	6.87394e8			0.237512
$506$	1.95733e9	+	1.13006e9i	0.671640	+	0.387772i
$507$	4.18806e9	+	1.12362e9i	1.42720	+	0.382907i
$508$	−9.52027e8	−	1.64896e9i	−0.322201	−	0.558068i
$509$	−2.44076e9	+	4.22752e9i	−0.820375	+	1.42093i	0.0850277	+	0.996379i	$0.472902\pi$
$509$	−2.44076e9	+	4.22752e9i	−0.820375	+	1.42093i	−0.905403	+	0.424553i	$0.860431\pi$
$510$	5.28685e9	+	5.29023e9i	1.76482	+	1.76595i
$511$	6.79425e8	+	1.32504e9i	0.225252	+	0.439296i
$512$			5.60613e9i			1.84594i
$513$	1.16960e8	+	4.38183e8i	0.0382496	+	0.143299i
$514$	−7.42385e8	+	4.28616e8i	−0.241134	+	0.139219i
$515$	2.29919e9	−	1.32744e9i	0.741735	−	0.428241i
$516$	2.06221e9	+	7.70612e9i	0.660782	+	2.46923i
$517$		−	2.63299e8i		−	0.0837977i
$518$	3.07222e9	+	5.99157e9i	0.971176	+	1.89403i
$519$	−4.53083e8	+	4.52793e8i	−0.142263	+	0.142172i
$520$	−4.78685e9	+	8.29107e9i	−1.49293	+	2.58582i
$521$	−2.70708e9	−	4.68880e9i	−0.838627	−	1.45254i	−0.891043	−	0.453919i	$-0.850025\pi$
$521$	−2.70708e9	−	4.68880e9i	−0.838627	−	1.45254i	0.0524158	−	0.998625i	$-0.483308\pi$
$522$	−3.89814e9	+	2.24727e9i	−1.19953	+	0.691526i
$523$	−5.19024e8	−	2.99659e8i	−0.158647	−	0.0915948i	0.418575	−	0.908182i	$-0.362530\pi$
$523$	−5.19024e8	−	2.99659e8i	−0.158647	−	0.0915948i	−0.577222	+	0.816588i	$0.695863\pi$
$524$	−1.46869e9			−0.445934
$525$	−3.73346e8	+	8.02323e7i	−0.112604	+	0.0241987i
$526$	−1.01562e10			−3.04286
$527$	−9.62671e7	−	5.55798e7i	−0.0286510	−	0.0165417i
$528$	6.35788e8	−	2.36976e9i	0.187972	−	0.700625i
$529$	−9.31447e8	−	1.61331e9i	−0.273567	−	0.473831i
$530$	1.34706e9	−	2.33317e9i	0.393025	−	0.680739i
$531$	315015.	−	4.92350e8i	9.13061e−5	−	0.142706i
$532$	1.04518e9	+	5.20911e7i	0.300954	+	0.0149994i
$533$		−	2.91860e9i		−	0.834889i
$534$	−3.77312e8	+	1.00971e8i	−0.107228	+	0.0286948i
$535$	−5.93052e8	+	3.42399e8i	−0.167438	+	0.0966705i
$536$	9.95955e9	−	5.75015e9i	2.79359	−	1.61288i
$537$	1.20000e9	−	3.21127e8i	0.334403	−	0.0894883i
$538$		−	7.16716e9i		−	1.98431i
$539$	−2.19318e9	+	9.89962e8i	−0.603273	+	0.272306i
$540$	5.54584e9	+	5.55650e9i	1.51562	+	1.51853i
$541$	−2.03211e8	+	3.51972e8i	−0.0551769	+	0.0955692i	−0.892295	−	0.451454i	$-0.850906\pi$
$541$	−2.03211e8	+	3.51972e8i	−0.0551769	+	0.0955692i	0.837118	+	0.547023i	$0.184239\pi$
$542$	−8.59457e8	−	1.48862e9i	−0.231860	−	0.401594i
$543$	1.75782e9	−	6.55187e9i	0.471166	−	1.75617i
$544$	−4.94432e8	−	2.85461e8i	−0.131677	−	0.0760239i
$545$	−2.44851e8			−0.0647909
$546$	−6.99240e9	−	7.73092e9i	−1.83845	−	2.03262i
$547$	2.37064e9			0.619312			0.309656	−	0.950849i	$-0.399786\pi$
$547$	2.37064e9			0.619312			0.309656	+	0.950849i	$0.399786\pi$
$548$	−2.62872e9	−	1.51769e9i	−0.682359	−	0.393960i
$549$	2.67734e9	+	4.64415e9i	0.690559	+	1.19785i
$550$	−2.58951e8	−	4.48516e8i	−0.0663664	−	0.114950i
$551$	2.31563e8	−	4.01080e8i	0.0589711	−	0.102141i
$552$	3.37886e9	−	3.37670e9i	0.855035	−	0.854488i
$553$	−8.93762e8	−	5.77166e8i	−0.224742	−	0.145132i
$554$		−	2.88525e9i		−	0.720940i
$555$	−1.34403e9	−	5.02241e9i	−0.333721	−	1.24706i
$556$	4.56147e9	−	2.63356e9i	1.12549	−	0.649804i
$557$	2.58993e9	−	1.49530e9i	0.635030	−	0.366635i	−0.147667	−	0.989037i	$-0.547177\pi$
$557$	2.58993e9	−	1.49530e9i	0.635030	−	0.366635i	0.782698	+	0.622402i	$0.213843\pi$
$558$	−1.50729e8	−	8.71518e7i	−0.0367262	−	0.0212352i
$559$			8.17889e9i			1.98040i
$560$	4.27996e9	−	2.19458e9i	1.02987	−	0.528071i
$561$	−2.65669e9	−	2.65839e9i	−0.635289	−	0.635695i
$562$	−3.55445e9	+	6.15649e9i	−0.844686	+	1.46304i
$563$	−2.83286e9	−	4.90666e9i	−0.669031	−	1.15880i	−0.978175	−	0.207781i	$-0.933376\pi$
$563$	−2.83286e9	−	4.90666e9i	−0.669031	−	1.15880i	0.309144	−	0.951015i	$-0.399957\pi$
$564$	−1.05848e9	−	2.83983e8i	−0.248432	−	0.0666523i
$565$	2.57011e9	+	1.48386e9i	0.599491	+	0.346116i
$566$	−8.35548e9			−1.93693
$567$	−3.86489e9	+	1.97551e9i	−0.890424	+	0.455132i
$568$	1.26376e10			2.89364
$569$	4.15379e9	+	2.39819e9i	0.945262	+	0.545747i	0.891606	−	0.452812i	$-0.149579\pi$
$569$	4.15379e9	+	2.39819e9i	0.945262	+	0.545747i	0.0536558	+	0.998559i	$0.482913\pi$
$570$	−1.16458e9	−	3.12447e8i	−0.263395	−	0.0706667i
$571$	3.49349e9	+	6.05091e9i	0.785296	+	1.36017i	0.928822	+	0.370526i	$0.120823\pi$
$571$	3.49349e9	+	6.05091e9i	0.785296	+	1.36017i	−0.143526	+	0.989647i	$0.545844\pi$
$572$	4.73706e9	−	8.20484e9i	1.05834	−	1.83309i
$573$	1.19636e9	+	1.19712e9i	0.265656	+	0.265826i
$574$	−2.27002e9	+	3.51520e9i	−0.501000	+	0.775815i
$575$		−	3.53330e8i		−	0.0775073i
$576$	3.57743e9	+	2.06848e9i	0.779995	+	0.450996i
$577$	−2.41581e9	+	1.39477e9i	−0.523537	+	0.302264i	−0.738381	−	0.674384i	$-0.764409\pi$
$577$	−2.41581e9	+	1.39477e9i	−0.523537	+	0.302264i	0.214843	+	0.976649i	$0.431076\pi$
$578$	−5.90610e9	+	3.40989e9i	−1.27219	+	0.734502i
$579$	2.47185e8	+	9.23688e8i	0.0529233	+	0.197765i
$580$		−	8.01677e9i		−	1.70609i
$581$	−3.17855e8	+	6.37760e9i	−0.0672377	+	1.34909i
$582$	3.15891e9	−	3.15689e9i	0.664213	−	0.663788i
$583$	−6.76908e8	+	1.17244e9i	−0.141478	+	0.245048i
$584$	2.13420e9	+	3.69654e9i	0.443394	+	0.767980i
$585$	4.02001e9	+	6.97317e9i	0.830198	+	1.44007i
$586$	−1.12127e10	−	6.47363e9i	−2.30180	−	1.32894i
$587$	−7.71103e9			−1.57354			−0.786772	−	0.617244i	$-0.788249\pi$
$587$	−7.71103e9			−1.57354			−0.786772	+	0.617244i	$0.788249\pi$
$588$	1.61426e9	+	9.88451e9i	0.327456	+	2.00509i
$589$	1.79209e7			0.00361373
$590$	1.13362e9	+	6.54496e8i	0.227240	+	0.131197i
$591$	−7.61128e8	+	2.83694e9i	−0.151671	+	0.565319i
$592$	3.38165e9	+	5.85719e9i	0.669888	+	1.16028i
$593$	1.75704e9	−	3.04328e9i	0.346011	−	0.599309i	−0.639526	−	0.768769i	$-0.720869\pi$
$593$	1.75704e9	−	3.04328e9i	0.346011	−	0.599309i	0.985537	+	0.169461i	$0.0542027\pi$
$594$	−4.15854e9	−	4.16653e9i	−0.814121	−	0.815685i
$595$	3.66740e8	−	7.35845e9i	0.0713755	−	1.43211i
$596$			1.54805e10i			2.99518i
$597$	6.99252e8	−	1.87124e8i	0.134500	−	0.0359932i
$598$	8.35280e9	−	4.82249e9i	1.59727	−	0.922183i
$599$	−6.87132e9	+	3.96716e9i	−1.30631	+	0.754198i	−0.981478	−	0.191574i	$-0.938641\pi$
$599$	−6.87132e9	+	3.96716e9i	−1.30631	+	0.754198i	−0.324831	+	0.945772i	$0.605307\pi$
$600$	−1.05741e9	+	2.82969e8i	−0.199854	+	0.0534822i
$601$			3.53551e9i			0.664341i	0.943219	+	0.332171i	$0.107781\pi$
$601$			3.53551e9i			0.664341i	−0.943219	+	0.332171i	$0.892219\pi$
$602$	6.36135e9	−	9.85077e9i	1.18840	−	1.84027i
$603$	6.18621e6	−	9.66871e9i	0.00114898	−	1.79580i
$604$	6.19766e9	−	1.07347e10i	1.14445	−	1.98225i
$605$	−1.61604e9	−	2.79907e9i	−0.296694	−	0.513890i
$606$	−5.55934e8	+	2.07212e9i	−0.101477	+	0.378235i
$607$	−5.06105e8	−	2.92200e8i	−0.0918503	−	0.0530298i	0.453371	−	0.891322i	$-0.350221\pi$
$607$	−5.06105e8	−	2.92200e8i	−0.0918503	−	0.0530298i	−0.545222	+	0.838292i	$0.683554\pi$
$608$	9.20424e7			0.0166083
$609$	4.21854e9	+	1.36024e9i	0.756836	+	0.244036i
$610$	−1.42521e10			−2.54228
$611$	−9.73079e8	−	5.61807e8i	−0.172585	−	0.0996422i
$612$	−1.35524e10	+	7.81290e9i	−2.38993	+	1.37779i
$613$	−2.70889e9	−	4.69194e9i	−0.474985	−	0.822698i	0.524604	−	0.851346i	$-0.324213\pi$
$613$	−2.70889e9	−	4.69194e9i	−0.474985	−	0.822698i	−0.999590	+	0.0286477i	$0.990880\pi$
$614$	9.57903e8	−	1.65914e9i	0.167006	−	0.289263i
$615$	2.28541e9	−	2.28395e9i	0.396189	−	0.395935i
$616$	−6.13762e9	+	3.14711e9i	−1.05796	+	0.542474i
$617$			9.10536e9i			1.56063i	0.625389	+	0.780313i	$0.284940\pi$
$617$			9.10536e9i			1.56063i	−0.625389	+	0.780313i	$0.715060\pi$
$618$	2.14202e9	+	8.00437e9i	0.365060	+	1.36417i
$619$	6.39505e9	−	3.69218e9i	1.08374	−	0.625699i	0.151840	−	0.988405i	$-0.451480\pi$
$619$	6.39505e9	−	3.69218e9i	1.08374	−	0.625699i	0.931904	+	0.362706i	$0.118147\pi$
$620$	2.68651e8	−	1.55106e8i	0.0452708	−	0.0261371i
$621$	−1.03572e9	−	3.88026e9i	−0.173549	−	0.650190i
$622$			5.54659e9i			0.924186i
$623$	3.23225e8	+	2.08730e8i	0.0535547	+	0.0345841i
$624$	−7.40137e9	−	7.40611e9i	−1.21946	−	1.22024i
$625$	3.36276e9	−	5.82447e9i	0.550955	−	0.954282i
$626$	6.93745e9	+	1.20160e10i	1.13029	+	1.95772i
$627$	5.85212e8	+	1.57008e8i	0.0948149	+	0.0254381i
$628$	8.35760e8	+	4.82526e8i	0.134655	+	0.0777432i
$629$	1.03599e10			1.65989
$630$	5.81804e8	−	1.15253e10i	0.0927011	−	1.83636i
$631$	5.98860e9			0.948905			0.474452	−	0.880281i	$-0.342646\pi$
$631$	5.98860e9			0.948905			0.474452	+	0.880281i	$0.342646\pi$
$632$	−2.64111e9	−	1.52485e9i	−0.416176	−	0.240279i
$633$	−8.03529e8	−	2.15581e8i	−0.125918	−	0.0337829i
$634$	−5.42901e9	−	9.40333e9i	−0.846074	−	1.46544i
$635$	1.08058e9	−	1.87161e9i	0.167474	−	0.290074i
$636$	3.98323e9	+	3.98577e9i	0.613953	+	0.614346i
$637$	−1.02102e9	+	1.02177e10i	−0.156512	+	1.56626i
$638$			6.01137e9i			0.916434i
$639$	5.31831e9	−	9.19799e9i	0.806344	−	1.39457i
$640$	−1.01938e10	+	5.88541e9i	−1.53712	+	0.887456i
$641$	4.43378e9	−	2.55984e9i	0.664922	−	0.383893i	−0.129228	−	0.991615i	$-0.541250\pi$
$641$	4.43378e9	−	2.55984e9i	0.664922	−	0.383893i	0.794150	+	0.607722i	$0.207916\pi$
$642$	−5.52513e8	−	2.06465e9i	−0.0824081	−	0.307945i
$643$			2.17156e8i			0.0322131i	0.999870	+	0.0161066i	$0.00512710\pi$
$643$			2.17156e8i			0.0322131i	−0.999870	+	0.0161066i	$0.994873\pi$
$644$	−9.25544e9	−	4.61285e8i	−1.36552	−	0.0680564i
$645$	−6.40450e9	+	6.40040e9i	−0.939780	+	0.939179i
$646$	1.20131e9	−	2.08074e9i	0.175325	−	0.303671i
$647$	9.34445e8	+	1.61851e9i	0.135640	+	0.234936i	0.925842	−	0.377911i	$-0.123358\pi$
$647$	9.34445e8	+	1.61851e9i	0.135640	+	0.234936i	−0.790202	+	0.612847i	$0.790024\pi$
$648$	−1.07830e10	+	6.20716e9i	−1.55677	+	0.896150i
$649$	−5.69655e8	−	3.28890e8i	−0.0818003	−	0.0472274i
$650$	−2.21012e9			−0.315660
$651$	3.60358e7	+	1.67686e8i	0.00511918	+	0.0238211i
$652$	2.04788e10			2.89360
$653$	−6.53806e9	−	3.77475e9i	−0.918867	−	0.530508i	−0.0355937	−	0.999366i	$-0.511332\pi$
$653$	−6.53806e9	−	3.77475e9i	−0.918867	−	0.530508i	−0.883273	+	0.468858i	$0.844666\pi$
$654$	1.98024e8	−	7.38093e8i	0.0276819	−	0.103178i
$655$	−8.33501e8	−	1.44367e9i	−0.115894	−	0.200735i
$656$	−2.10154e9	+	3.63998e9i	−0.290653	+	0.503425i
$657$	3.58859e9	+	2.29604e6i	0.493679	+	0.000315865i
$658$	7.35030e8	+	1.43349e9i	0.100581	+	0.196157i
$659$		−	9.85903e9i		−	1.34195i	−0.741481	−	0.670974i	$-0.765876\pi$
$659$		−	9.85903e9i		−	1.34195i	0.741481	−	0.670974i	$-0.234124\pi$
$660$	1.01318e10	−	2.71134e9i	1.37178	−	0.367096i
$661$	4.99500e9	−	2.88386e9i	0.672714	−	0.388391i	−0.124390	−	0.992233i	$-0.539698\pi$
$661$	4.99500e9	−	2.88386e9i	0.672714	−	0.388391i	0.797104	+	0.603842i	$0.206364\pi$
$662$	−1.61532e10	+	9.32603e9i	−2.16399	+	1.24938i
$663$	−1.54933e10	+	4.14611e9i	−2.06465	+	0.552514i
$664$			1.83038e10i			2.42635i
$665$	5.41951e8	+	1.05694e9i	0.0714635	+	0.139371i
$666$	1.62269e10	+	1.03822e7i	2.12850	+	0.00136186i
$667$	−2.05058e9	+	3.55170e9i	−0.267569	+	0.463443i
$668$	−6.52457e9	−	1.13009e10i	−0.846904	−	1.46688i
$669$	−9.09787e8	+	3.39103e9i	−0.117476	+	0.437865i
$670$	2.22619e10	+	1.28529e10i	2.85956	+	1.65097i
$671$	7.16180e9			0.915153
$672$	1.85081e8	+	8.61241e8i	0.0235272	+	0.109479i
$673$	2.03763e9			0.257675			0.128838	−	0.991666i	$-0.458875\pi$
$673$	2.03763e9			0.257675			0.128838	+	0.991666i	$0.458875\pi$
$674$	1.25189e9	+	7.22779e8i	0.157491	+	0.0909276i
$675$	−2.39039e8	+	8.88694e8i	−0.0299162	+	0.111222i
$676$	−1.20562e10	−	2.08820e10i	−1.50106	−	2.59992i
$677$	−3.52871e9	+	6.11191e9i	−0.437075	+	0.757036i	−0.997462	−	0.0711947i	$-0.977319\pi$
$677$	−3.52871e9	+	6.11191e9i	−0.437075	+	0.757036i	0.560388	+	0.828230i	$0.310652\pi$
$678$	−6.55161e9	+	6.54742e9i	−0.807318	+	0.806801i
$679$	−4.39389e9	−	2.18989e8i	−0.538648	−	0.0268458i
$680$		−	2.11189e10i		−	2.57567i
$681$	1.30013e9	+	4.85838e9i	0.157751	+	0.589490i
$682$	−2.01448e8	+	1.16306e8i	−0.0243174	+	0.0140397i
$683$	1.52980e9	−	8.83232e8i	0.183723	−	0.106072i	−0.405318	−	0.914176i	$-0.632839\pi$
$683$	1.52980e9	−	8.83232e8i	0.183723	−	0.106072i	0.589041	+	0.808103i	$0.299506\pi$
$684$	1.26237e9	−	2.18326e9i	0.150831	−	0.260861i
$685$		−	3.44525e9i		−	0.409547i
$686$	9.17681e9	−	1.15122e10i	1.08532	−	1.36152i
$687$	−2.02538e9	−	2.02667e9i	−0.238318	−	0.238471i
$688$	5.88923e9	−	1.02004e10i	0.689444	−	1.19415i
$689$	2.88867e9	+	5.00333e9i	0.336458	+	0.582763i
$690$	1.03128e10	+	2.76683e9i	1.19510	+	0.320635i
$691$	−1.59696e9	−	9.22005e8i	−0.184128	−	0.106307i	0.405102	−	0.914271i	$-0.367236\pi$
$691$	−1.59696e9	−	9.22005e8i	−0.184128	−	0.106307i	−0.589231	+	0.807965i	$0.700569\pi$
$692$	3.56196e9			0.408619
$693$	−2.92362e8	+	5.79155e9i	−0.0333699	+	0.661041i
$694$	−2.13906e10			−2.42921
$695$	5.17739e9	+	2.98917e9i	0.585011	+	0.337756i
$696$	1.22714e10	+	3.29232e9i	1.37963	+	0.370143i
$697$	3.21911e9	+	5.57566e9i	0.360098	+	0.623708i
$698$	1.19098e10	−	2.06284e10i	1.32559	−	2.29600i
$699$	−1.15608e10	−	1.15682e10i	−1.28032	−	1.28114i
$700$	1.78387e9	+	1.15197e9i	0.196571	+	0.126940i
$701$		−	4.95801e9i		−	0.543619i	−0.962351	−	0.271810i	$-0.912378\pi$
$701$		−	4.95801e9i		−	0.543619i	0.962351	−	0.271810i	$-0.0876221\pi$
$702$	−2.42715e10	+	6.47858e9i	−2.64800	+	0.706805i
$703$	−1.44643e9	+	8.35098e8i	−0.157020	+	0.0906554i
$704$	4.78121e9	−	2.76043e9i	0.516456	−	0.298176i
$705$	−3.21560e8	−	1.20162e9i	−0.0345621	−	0.129153i
$706$		−	2.51556e10i		−	2.69041i
$707$	1.88059e9	−	9.64286e8i	0.200137	−	0.102621i
$708$	−1.93657e9	+	1.93533e9i	−0.205077	+	0.204946i
$709$	−2.46660e9	+	4.27227e9i	−0.259918	+	0.450191i	−0.966220	−	0.257720i	$-0.917029\pi$
$709$	−2.46660e9	+	4.27227e9i	−0.259918	+	0.450191i	0.706302	+	0.707911i	$0.250362\pi$
$710$	1.41239e10	+	2.44633e10i	1.48099	+	2.56514i
$711$	−2.22130e9	+	1.28057e9i	−0.231773	+	0.133617i
$712$	9.55148e8	+	5.51455e8i	0.0991723	+	0.0572572i
$713$	−1.58695e8			−0.0163965
$714$	2.18851e10	+	7.05671e9i	2.25012	+	0.725535i
$715$	1.07534e10			1.10021
$716$	−5.98226e9	−	3.45386e9i	−0.609074	−	0.351649i
$717$	2.76319e9	−	1.02992e10i	0.279958	−	1.04348i
$718$	5.06987e9	+	8.78128e9i	0.511165	+	0.885364i
$719$	−2.32589e9	+	4.02855e9i	−0.233366	+	0.404202i	−0.958797	−	0.284094i	$-0.908307\pi$
$719$	−2.32589e9	+	4.02855e9i	−0.233366	+	0.404202i	0.725431	+	0.688295i	$0.241641\pi$
$720$	7.41634e6	−	1.15913e10i	0.000740501	−	1.15736i
$721$	4.42803e9	−	6.85696e9i	0.439984	−	0.681331i
$722$		−	1.72211e10i		−	1.70286i
$723$	−1.22435e10	+	3.27645e9i	−1.20482	+	0.322418i
$724$	−3.26682e10	+	1.88610e10i	−3.19919	+	1.84705i
$725$	8.13863e8	−	4.69884e8i	0.0793173	−	0.0457939i
$726$	9.74466e9	−	2.60773e9i	0.945124	−	0.252921i
$727$		−	1.34967e10i		−	1.30273i	−0.758763	−	0.651367i	$-0.774196\pi$
$727$		−	1.34967e10i		−	1.30273i	0.758763	−	0.651367i	$-0.225804\pi$
$728$	−1.46518e9	+	2.93980e10i	−0.140744	+	2.82396i
$729$	−2.00782e7	+	1.04603e10i	−0.00191945	+	0.999998i
$730$	−4.77042e9	+	8.26260e9i	−0.453864	+	0.786116i
$731$	−9.02102e9	−	1.56249e10i	−0.854171	−	1.47947i
$732$	7.72442e9	−	2.87911e10i	0.727909	−	2.71312i
$733$	−1.39528e10	−	8.05567e9i	−1.30857	−	0.755505i	−0.326716	−	0.945123i	$-0.605942\pi$
$733$	−1.39528e10	−	8.05567e9i	−1.30857	−	0.755505i	−0.981858	+	0.189617i	$0.939275\pi$
$734$	−1.96401e10			−1.83319
$735$	−8.79999e9	+	7.19635e9i	−0.817479	+	0.668508i
$736$	−8.15068e8			−0.0753566
$737$	−1.11868e10	−	6.45870e9i	−1.02937	−	0.594304i
$738$	5.03654e9	+	8.73645e9i	0.461248	+	0.800088i
$739$	6.62049e9	+	1.14670e10i	0.603441	+	1.04519i	0.992296	+	0.123891i	$0.0395373\pi$
$739$	6.62049e9	+	1.14670e10i	0.603441	+	1.04519i	−0.388855	+	0.921299i	$0.627129\pi$
$740$	−1.44556e10	+	2.50379e10i	−1.31137	+	2.27136i
$741$	1.82894e9	−	1.82777e9i	0.165134	−	0.165028i
$742$	4.12312e8	−	8.27282e9i	0.0370521	−	0.743430i
$743$			9.66203e9i			0.864186i	0.901829	+	0.432093i	$0.142225\pi$
$743$			9.66203e9i			0.864186i	−0.901829	+	0.432093i	$0.857775\pi$
$744$	1.27093e8	+	4.74927e8i	0.0113140	+	0.0422787i
$745$	−1.52168e10	+	8.78540e9i	−1.34827	+	0.778421i
$746$	4.76124e9	−	2.74890e9i	0.419888	−	0.242423i
$747$	1.33221e10	+	7.70287e9i	1.16936	+	0.676130i
$748$			2.08992e10i			1.82589i
$749$	−1.14217e9	+	1.76869e9i	−0.0993215	+	0.153803i
$750$	1.32871e10	+	1.32956e10i	1.15005	+	1.15078i
$751$	−8.02143e9	+	1.38935e10i	−0.691054	+	1.19694i	0.280439	+	0.959872i	$0.409520\pi$
$751$	−8.02143e9	+	1.38935e10i	−0.691054	+	1.19694i	−0.971493	+	0.237069i	$0.923813\pi$
$752$	8.09061e8	+	1.40133e9i	0.0693775	+	0.120165i
$753$	−1.11656e10	−	2.99565e9i	−0.953017	−	0.255687i
$754$	2.22163e10	+	1.28266e10i	1.88744	+	1.08971i
$755$	1.40690e10			1.18973
$756$	2.29672e10	+	7.42184e9i	1.93322	+	0.624720i
$757$	7.48622e9			0.627231			0.313615	−	0.949550i	$-0.398460\pi$
$757$	7.48622e9			0.627231			0.313615	+	0.949550i	$0.398460\pi$
$758$	2.89987e10	+	1.67424e10i	2.41845	+	1.39629i
$759$	−5.18226e9	−	1.39036e9i	−0.430202	−	0.115420i
$760$	1.70237e9	+	2.94858e9i	0.140671	+	0.243650i
$761$	−9.05190e9	+	1.56784e10i	−0.744550	+	1.28960i	0.205855	+	0.978582i	$0.434002\pi$
$761$	−9.05190e9	+	1.56784e10i	−0.744550	+	1.28960i	−0.950405	+	0.311015i	$0.899331\pi$
$762$	4.76798e9	+	4.77103e9i	0.390384	+	0.390634i
$763$	−6.69870e8	+	3.43480e8i	−0.0545952	+	0.0279940i
$764$		−	9.41132e9i		−	0.763526i
$765$	−1.53709e10	−	8.88754e9i	−1.24133	−	0.717739i
$766$	1.40456e10	−	8.10925e9i	1.12912	−	0.651899i
$767$	−2.43097e9	+	1.40352e9i	−0.194534	+	0.112314i
$768$	−6.57310e9	−	2.45626e10i	−0.523608	−	1.95663i
$769$			1.28915e10i			1.02226i	0.859504	+	0.511128i	$0.170772\pi$
$769$			1.28915e10i			1.02226i	−0.859504	+	0.511128i	$0.829228\pi$
$770$	−1.29516e10	−	8.36374e9i	−1.02236	−	0.660212i
$771$	1.43947e9	−	1.43855e9i	0.113113	−	0.113040i
$772$	2.65858e9	−	4.60480e9i	0.207965	−	0.360205i
$773$	−6.10830e8	−	1.05799e9i	−0.0475655	−	0.0823859i	0.841262	−	0.540627i	$-0.181813\pi$
$773$	−6.10830e8	−	1.05799e9i	−0.0475655	−	0.0823859i	−0.888828	+	0.458241i	$0.848480\pi$
$774$	−1.41141e10	−	2.44825e10i	−1.09411	−	1.89785i
$775$	3.14927e7	+	1.81823e7i	0.00243027	+	0.00140311i
$776$	−1.26105e10			−0.968764
$777$	−1.07225e10	−	1.18550e10i	−0.820020	−	0.906629i
$778$	−4.01006e10			−3.05297
$779$	−8.98892e8	−	5.18976e8i	−0.0681281	−	0.0393338i
$780$	1.15982e10	−	4.32296e10i	0.875101	−	3.26175i
$781$	−7.09740e9	−	1.22931e10i	−0.533115	−	0.923382i
$782$	−1.06381e10	+	1.84257e10i	−0.795498	+	1.37784i
$783$	7.56045e9	−	7.54595e9i	0.562836	−	0.561756i
$784$	8.63065e9	−	1.20080e10i	0.639643	−	0.889946i
$785$			1.09536e9i			0.0808191i
$786$	5.02597e9	−	1.34498e9i	0.369183	−	0.0987956i
$787$	−3.27730e9	+	1.89215e9i	−0.239665	+	0.138371i	−0.615023	−	0.788509i	$-0.710853\pi$
$787$	−3.27730e9	+	1.89215e9i	−0.239665	+	0.138371i	0.375358	+	0.926880i	$0.377520\pi$
$788$	1.41452e10	−	8.16675e9i	1.02984	−	0.594576i
$789$	2.32912e10	−	6.23288e9i	1.68820	−	0.451772i
$790$		−	6.81676e9i		−	0.491907i
$791$	9.11296e9	+	4.54184e8i	0.654699	+	0.0326298i
$792$	−1.06353e7	+	1.66224e10i	−0.000760697	+	1.18893i
$793$	1.52813e10	−	2.64680e10i	1.08819	−	1.88480i
$794$	−1.12700e10	−	1.95201e10i	−0.799007	−	1.38392i
$795$	−1.65733e9	+	6.17734e9i	−0.116984	+	0.436031i
$796$	−3.48593e9	−	2.01261e9i	−0.244976	−	0.141437i
$797$	2.25090e10			1.57489			0.787447	−	0.616382i	$-0.211402\pi$
$797$	2.25090e10			1.57489			0.787447	+	0.616382i	$0.211402\pi$
$798$	−3.62440e9	+	7.78885e8i	−0.252479	+	0.0542580i
$799$	2.47861e9			0.171908
$800$	1.61748e8	+	9.33853e7i	0.0111693	+	0.00644857i
$801$	8.03323e8	−	4.63114e8i	0.0552302	−	0.0318401i
$802$	1.46684e10	+	2.54064e10i	1.00409	+	1.73913i
$803$	2.39718e9	−	4.15203e9i	0.163379	−	0.282981i
$804$	−3.80301e10	+	3.80058e10i	−2.58067	+	2.57902i
$805$	−4.79916e9	−	9.35954e9i	−0.324250	−	0.632367i
$806$			9.92660e8i			0.0667772i
$807$	4.39850e9	+	1.64364e10i	0.294610	+	1.10091i
$808$	5.24638e9	−	3.02900e9i	0.349881	−	0.202004i
$809$	2.74883e9	−	1.58704e9i	0.182527	−	0.105382i	−0.405952	−	0.913894i	$-0.633060\pi$
$809$	2.74883e9	−	1.58704e9i	0.182527	−	0.105382i	0.588480	+	0.808512i	$0.299727\pi$
$810$	−2.40668e10	−	1.39361e10i	−1.59118	−	0.921388i
$811$			8.03296e9i			0.528813i	0.964411	+	0.264407i	$0.0851761\pi$
$811$			8.03296e9i			0.528813i	−0.964411	+	0.264407i	$0.914824\pi$
$812$	−1.12460e10	−	2.19325e10i	−0.737146	−	1.43761i
$813$	2.88456e9	+	2.88641e9i	0.188262	+	0.188383i
$814$	1.08395e10	−	1.87746e10i	0.704410	−	1.22007i
$815$	1.16220e10	+	2.01299e10i	0.752021	+	1.30254i
$816$	2.23082e10	+	5.98510e9i	1.43730	+	0.385617i
$817$	2.51900e9	+	1.45434e9i	0.161603	+	0.0933018i
$818$	3.34288e10			2.13542
$819$	2.07801e10	+	1.34381e10i	1.32177	+	0.854757i
$820$	−1.79670e10			−1.13796
$821$	−1.45251e10	−	8.38604e9i	−0.916045	−	0.528879i	−0.0336737	−	0.999433i	$-0.510721\pi$
$821$	−1.45251e10	−	8.38604e9i	−0.916045	−	0.528879i	−0.882371	+	0.470554i	$0.844054\pi$
$822$	1.03856e10	+	2.78637e9i	0.652197	+	0.174979i
$823$	5.54894e9	+	9.61104e9i	0.346985	+	0.600995i	0.985712	−	0.168438i	$-0.0538722\pi$
$823$	5.54894e9	+	9.61104e9i	0.346985	+	0.600995i	−0.638728	+	0.769433i	$0.720539\pi$
$824$	1.16987e10	−	2.02627e10i	0.728436	−	1.26169i
$825$	8.69107e8	+	8.69663e8i	0.0538870	+	0.0539215i
$826$	4.01953e9	+	2.00331e8i	0.248167	+	0.0123685i
$827$			9.97710e9i			0.613388i	0.951808	+	0.306694i	$0.0992228\pi$
$827$			9.97710e9i			0.613388i	−0.951808	+	0.306694i	$0.900777\pi$
$828$	−1.11787e10	+	1.93335e10i	−0.684362	+	1.18360i
$829$	2.05950e10	−	1.18905e10i	1.25551	−	0.724869i	0.283311	−	0.959028i	$-0.408567\pi$
$829$	2.05950e10	−	1.18905e10i	1.25551	−	0.724869i	0.972198	+	0.234159i	$0.0752337\pi$
$830$	−3.54319e10	+	2.04566e10i	−2.15091	+	1.24183i
$831$	1.77068e9	+	6.61674e9i	0.107038	+	0.399982i
$832$		−	2.35600e10i		−	1.41822i
$833$	−9.31919e9	−	2.06459e10i	−0.558625	−	1.23759i
$834$	−1.31980e10	+	1.31895e10i	−0.787818	+	0.787314i
$835$	7.40557e9	−	1.28268e10i	0.440206	−	0.762459i
$836$	−1.68466e9	−	2.91792e9i	−0.0997218	−	0.172723i
$837$	3.99151e8	+	1.07363e8i	0.0235287	+	0.00632870i
$838$	1.59264e10	+	9.19513e9i	0.934898	+	0.539764i
$839$	−2.02872e10			−1.18592			−0.592960	−	0.805232i	$-0.702041\pi$
$839$	−2.02872e10			−1.18592			−0.592960	+	0.805232i	$0.702041\pi$
$840$	−2.41668e10	+	2.18581e10i	−1.40683	+	1.27244i
$841$	6.34184e9			0.367646
$842$	−2.21129e10	−	1.27669e10i	−1.27660	−	0.737044i
$843$	4.37317e9	−	1.63000e10i	0.251420	−	0.937113i
$844$	2.31313e9	+	4.00646e9i	0.132435	+	0.229384i
$845$	1.36842e10	−	2.37017e10i	0.780226	−	1.35139i
$846$	3.88228e9	+	2.48395e6i	0.220440	+	0.000141042i
$847$	−8.34779e9	−	5.39077e9i	−0.472041	−	0.304831i
$848$		−	8.31998e9i		−	0.468529i
$849$	1.91616e10	−	5.12776e9i	1.07462	−	0.287575i
$850$	4.22219e9	−	2.43768e9i	0.235815	−	0.136148i
$851$	1.28087e10	−	7.39509e9i	0.712444	−	0.411330i
$852$	−5.70741e10	+	1.52734e10i	−3.16155	+	0.846052i
$853$			2.42898e10i			1.33999i	0.742365	+	0.669995i	$0.233704\pi$
$853$			2.42898e10i			1.33999i	−0.742365	+	0.669995i	$0.766296\pi$
$854$	−3.89912e10	+	1.99930e10i	−2.14222	+	1.09844i
$855$	2.86248e9	+	1.83146e6i	0.156625	+	0.000100211i
$856$	−3.01755e9	+	5.22656e9i	−0.164436	+	0.284812i
$857$	5.35587e9	+	9.27664e9i	0.290668	+	0.503451i	0.973968	−	0.226686i	$-0.0727892\pi$
$857$	5.35587e9	+	9.27664e9i	0.290668	+	0.503451i	−0.683300	+	0.730138i	$0.739456\pi$
$858$	−8.69687e9	+	3.24157e10i	−0.470065	+	1.75206i
$859$	−1.79777e10	−	1.03794e10i	−0.967739	−	0.558725i	−0.0691930	−	0.997603i	$-0.522042\pi$
$859$	−1.79777e10	−	1.03794e10i	−0.967739	−	0.558725i	−0.898546	+	0.438879i	$0.855376\pi$
$860$	5.03497e10			2.69931
$861$	3.04854e9	−	9.45451e9i	0.162773	−	0.504810i
$862$	1.45752e10			0.775069
$863$	2.38809e10	+	1.37876e10i	1.26477	+	0.730217i	0.973994	−	0.226573i	$-0.0727521\pi$
$863$	2.38809e10	+	1.37876e10i	1.26477	+	0.730217i	0.290780	+	0.956790i	$0.406085\pi$
$864$	2.05006e9	+	5.51421e8i	0.108135	+	0.0290861i
$865$	2.02146e9	+	3.50128e9i	0.106196	+	0.183937i
$866$	−5.24378e9	+	9.08249e9i	−0.274367	+	0.475217i
$867$	1.14518e10	−	1.14445e10i	0.596770	−	0.596388i
$868$	5.17399e8	−	8.01211e8i	0.0268539	−	0.0415842i
$869$			3.42549e9i			0.177073i
$870$	7.34153e9	+	2.74341e10i	0.377980	+	1.41245i
$871$	−4.77391e10	+	2.75622e10i	−2.44800	+	1.41335i
$872$	−1.86877e9	+	1.07893e9i	−0.0954437	+	0.0551045i
$873$	−5.30694e9	+	9.17832e9i	−0.269957	+	0.466889i
$874$		−	3.43008e9i		−	0.173786i
$875$	9.21703e8	−	1.84935e10i	0.0465118	−	0.933233i
$876$	−1.41060e10	−	1.41151e10i	−0.708991	−	0.709445i
$877$	−1.20555e10	+	2.08808e10i	−0.603515	+	1.04532i	0.388769	+	0.921335i	$0.372900\pi$
$877$	−1.20555e10	+	2.08808e10i	−0.603515	+	1.04532i	−0.992284	+	0.123984i	$0.960433\pi$
$878$	−5.27500e9	−	9.13657e9i	−0.263022	−	0.455567i
$879$	2.96868e10	+	7.96475e9i	1.47436	+	0.395559i
$880$	−1.34113e10	−	7.74301e9i	−0.663408	−	0.383019i
$881$	−2.86524e10			−1.41171			−0.705855	−	0.708356i	$-0.749437\pi$
$881$	−2.86524e10			−1.41171			−0.705855	+	0.708356i	$0.749437\pi$
$882$	−1.45761e10	−	3.23473e10i	−0.715320	−	1.58744i
$883$	1.99580e10			0.975561			0.487781	−	0.872966i	$-0.337807\pi$
$883$	1.99580e10			0.975561			0.487781	+	0.872966i	$0.337807\pi$
$884$	7.72378e10	+	4.45932e10i	3.76051	+	2.17113i
$885$	−3.00139e9	−	8.05250e8i	−0.145553	−	0.0390507i
$886$	4.80590e9	+	8.32406e9i	0.232144	+	0.402084i
$887$	−2.92531e9	+	5.06679e9i	−0.140747	+	0.243781i	−0.927778	−	0.373132i	$-0.878284\pi$
$887$	−2.92531e9	+	5.06679e9i	−0.140747	+	0.243781i	0.787031	+	0.616913i	$0.211617\pi$
$888$	−3.23892e10	−	3.24100e10i	−1.55223	−	1.55322i
$889$	3.30747e8	−	6.63627e9i	0.0157885	−	0.316787i
$890$			2.46525e9i			0.117219i
$891$	1.20938e10	+	7.00300e9i	0.572783	+	0.331675i
$892$	1.69080e10	−	9.76183e9i	0.797654	−	0.460526i
$893$	−3.46060e8	+	1.99798e8i	−0.0162619	+	0.00938880i
$894$	−1.41766e10	−	5.29755e10i	−0.663576	−	2.47967i
$895$		−	7.84045e9i		−	0.365562i
$896$	−1.96324e10	+	3.04015e10i	−0.911793	+	1.41194i
$897$	−1.61959e10	+	1.61855e10i	−0.749258	+	0.748779i
$898$	2.36534e10	−	4.09689e10i	1.09000	−	1.88794i
$899$	−2.11045e8	−	3.65541e8i	−0.00968760	−	0.0167794i
$900$	4.43350e9	−	2.55590e9i	0.202721	−	0.116868i
$901$	−1.10370e10	−	6.37220e9i	−0.502705	−	0.290237i
$902$	1.34726e10			0.611262
$903$	−8.54304e9	+	2.64947e10i	−0.386105	+	1.19744i
$904$	2.61544e10			1.17748
$905$	−3.70793e10	−	2.14078e10i	−1.66288	−	0.960066i
$906$	−1.13784e10	+	4.24105e10i	−0.508314	+	1.89463i
$907$	−6.07975e9	−	1.05304e10i	−0.270558	−	0.468620i	0.698447	−	0.715662i	$-0.253875\pi$
$907$	−6.07975e9	−	1.05304e10i	−0.270558	−	0.468620i	−0.969005	+	0.247042i	$0.920541\pi$
$908$	1.39835e10	−	2.42201e10i	0.619891	−	1.07368i
$909$	3.25870e6	−	5.09317e9i	0.000143903	−	0.224913i
$910$	−5.85451e10	+	3.00194e10i	−2.57541	+	1.32056i
$911$		−	1.95438e10i		−	0.856435i	−0.903676	−	0.428217i	$-0.859142\pi$
$911$		−	1.95438e10i		−	0.856435i	0.903676	−	0.428217i	$-0.140858\pi$
$912$	−3.59708e9	+	9.62601e8i	−0.157025	+	0.0420208i
$913$	1.78049e10	−	1.02796e10i	0.774268	−	0.447024i
$914$	4.68129e10	−	2.70275e10i	2.02794	−	1.17083i
$915$	3.26843e10	−	8.74652e9i	1.41047	−	0.377452i
$916$			1.59329e10i			0.684954i
$917$	−4.30551e9	−	2.78038e9i	−0.184388	−	0.119072i
$918$	3.92224e10	−	3.91472e10i	1.67334	−	1.67014i
$919$	−9.10217e9	+	1.57654e10i	−0.386848	+	0.670041i	−0.992024	−	0.126051i	$-0.959770\pi$
$919$	−9.10217e9	+	1.57654e10i	−0.386848	+	0.670041i	0.605176	+	0.796092i	$0.293103\pi$
$920$	−1.50750e10	−	2.61107e10i	−0.638265	−	1.10551i
$921$	−1.17854e9	+	4.39276e9i	−0.0497092	+	0.185280i
$922$	1.56219e10	+	9.01932e9i	0.656411	+	0.378979i
$923$	−6.05756e10			−2.53566
$924$	2.39154e10	−	2.16308e10i	0.997300	−	0.902030i
$925$	−3.38913e9			−0.140797
$926$	−5.44004e10	−	3.14081e10i	−2.25146	−	1.29988i
$927$	−9.82458e9	−	1.70418e10i	−0.405075	−	0.702648i
$928$	−1.08394e9	−	1.87744e9i	−0.0445232	−	0.0771164i
$929$	−1.91356e10	+	3.31438e10i	−0.783046	+	1.35627i	0.147114	+	0.989120i	$0.453002\pi$
$929$	−1.91356e10	+	3.31438e10i	−0.783046	+	1.35627i	−0.930160	+	0.367155i	$0.880332\pi$
$930$	−7.77305e8	+	7.76808e8i	−0.0316885	+	0.0316682i
$931$	2.96537e9	+	2.13134e9i	0.120436	+	0.0865623i
$932$			9.09450e10i			3.67979i
$933$	−3.40395e9	−	1.27200e10i	−0.137214	−	0.512744i
$934$	5.14618e10	−	2.97115e10i	2.06667	−	1.19319i
$935$	−2.05432e10	+	1.18606e10i	−0.821915	+	0.474533i
$936$	6.14090e10	+	3.55069e10i	2.44775	+	1.41530i
$937$		−	1.69165e10i		−	0.671774i	−0.941902	−	0.335887i	$-0.890964\pi$
$937$		−	1.69165e10i		−	0.671774i	0.941902	−	0.335887i	$-0.109036\pi$
$938$	7.89349e10	+	3.93406e9i	3.12291	+	0.155644i
$939$	−2.32839e10	−	2.32988e10i	−0.917753	−	0.918341i
$940$	−3.45852e9	+	5.99033e9i	−0.135813	+	0.235236i
$941$	2.42506e10	+	4.20032e10i	0.948765	+	1.64331i	0.748032	+	0.663663i	$0.230999\pi$
$941$	2.42506e10	+	4.20032e10i	0.948765	+	1.64331i	0.200733	+	0.979646i	$0.435668\pi$
$942$	−3.30192e9	−	8.85880e8i	−0.128703	−	0.0345300i
$943$	7.96001e9	+	4.59571e9i	0.309117	+	0.178469i
$944$	4.04244e9			0.156402
$945$	5.73881e9	+	2.67879e10i	0.221213	+	1.03259i
$946$	−3.77547e10			−1.44995
$947$	3.85475e10	+	2.22554e10i	1.47493	+	0.851550i	0.999601	−	0.0282590i	$-0.00899631\pi$
$947$	3.85475e10	+	2.22554e10i	1.47493	+	0.851550i	0.475327	+	0.879809i	$0.342330\pi$
$948$	1.37708e10	+	3.69458e9i	0.524963	+	0.140843i
$949$	−1.02298e10	−	1.77186e10i	−0.388541	−	0.672973i
$950$	−3.92997e8	+	6.80690e8i	−0.0148716	+	0.0257583i
$951$	1.82212e10	+	1.82328e10i	0.686981	+	0.687421i
$952$	−2.96259e10	−	5.77777e10i	−1.11286	−	2.17035i
$953$		−	1.43257e9i		−	0.0536157i	−0.999641	−	0.0268078i	$-0.991466\pi$
$953$		−	1.43257e9i		−	0.0536157i	0.999641	−	0.0268078i	$-0.00853422\pi$
$954$	−1.72810e10	−	9.99192e9i	−0.644390	−	0.372589i
$955$	9.25098e9	−	5.34105e9i	0.343697	−	0.198434i
$956$	−5.13525e10	+	2.96484e10i	−1.90090	+	1.09748i
$957$	−3.68919e9	−	1.37859e10i	−0.136063	−	0.508443i
$958$			8.64910e10i			3.17828i
$959$	−4.83305e9	−	9.42562e9i	−0.176952	−	0.345100i
$960$	1.84487e10	−	1.84369e10i	0.673004	−	0.672573i
$961$	−1.37481e10	+	2.38125e10i	−0.499703	+	0.865511i
$962$	−4.62572e10	−	8.01198e10i	−1.67520	−	2.90153i
$963$	2.53415e9	+	4.39577e9i	0.0914410	+	0.158615i
$964$	6.10369e10	+	3.52397e10i	2.19444	+	1.26696i
$965$	6.03513e9			0.216193
$966$	3.20953e10	−	6.89730e9i	1.14557	−	0.246184i
$967$	−1.81432e10			−0.645240			−0.322620	−	0.946529i	$-0.604564\pi$
$967$	−1.81432e10			−0.645240			−0.322620	+	0.946529i	$0.604564\pi$
$968$	−2.46682e10	−	1.42422e10i	−0.874124	−	0.504675i
$969$	−1.47802e9	+	5.50900e9i	−0.0521852	+	0.194509i
$970$	−1.40937e10	−	2.44111e10i	−0.495821	−	0.858787i
$971$	−4.09980e9	+	7.10107e9i	−0.143713	+	0.248918i	−0.928892	−	0.370351i	$-0.879238\pi$
$971$	−4.09980e9	+	7.10107e9i	−0.143713	+	0.248918i	0.785179	+	0.619269i	$0.212571\pi$
$972$	4.11965e10	−	4.10649e10i	1.43889	−	1.43430i
$973$	1.83577e10	+	9.14936e8i	0.638886	+	0.0318417i
$974$		−	2.64102e10i		−	0.915831i
$975$	5.06847e9	−	1.35635e9i	0.175130	−	0.0468659i
$976$	−3.81167e10	+	2.20067e10i	−1.31232	+	0.757670i
$977$	1.91749e10	−	1.10706e10i	0.657812	−	0.379788i	−0.133631	−	0.991031i	$-0.542664\pi$
$977$	1.91749e10	−	1.10706e10i	0.657812	−	0.379788i	0.791443	+	0.611243i	$0.209330\pi$
$978$	−7.00802e10	+	1.87539e10i	−2.39557	+	0.641070i
$979$		−	1.23881e9i		−	0.0421955i
$980$	6.29007e10	+	6.28547e9i	2.13483	+	0.213327i
$981$	−1.16075e6	+	1.81419e9i	−3.92553e−5	+	0.0613539i
$982$	−1.77871e10	+	3.08082e10i	−0.599398	+	1.03819i
$983$	1.19773e9	+	2.07453e9i	0.0402181	+	0.0696598i	0.885434	−	0.464766i	$-0.153861\pi$
$983$	1.19773e9	+	2.07453e9i	0.0402181	+	0.0696598i	−0.845216	+	0.534425i	$0.820528\pi$
$984$	7.37868e9	−	2.75024e10i	0.246885	−	0.920212i
$985$	1.60552e10	+	9.26949e9i	0.535290	+	0.309050i
$986$	−5.65892e10			−1.88003
$987$	−2.56537e9	−	2.83632e9i	−0.0849260	−	0.0938957i
$988$	−1.43784e10			−0.474309
$989$	−2.23066e10	−	1.28787e10i	−0.733241	−	0.423337i
$990$	−3.21889e10	+	1.85568e10i	−1.05435	+	0.607828i
$991$	−2.62784e10	−	4.55155e10i	−0.857711	−	1.48560i	−0.874107	−	0.485734i	$-0.838552\pi$
$991$	−2.62784e10	−	4.55155e10i	−0.857711	−	1.48560i	0.0163955	−	0.999866i	$-0.494781\pi$
$992$	4.19433e7	−	7.26480e7i	0.00136418	−	0.00236283i
$993$	3.13206e10	−	3.13006e10i	1.01510	−	1.01445i
$994$	7.29581e10	+	4.71143e10i	2.35625	+	1.52160i
$995$		−	4.56873e9i		−	0.147033i
$996$	−2.21215e10	−	8.26643e10i	−0.709426	−	2.65100i
$997$	6.44667e9	−	3.72199e9i	0.206017	−	0.118944i	−0.393442	−	0.919349i	$-0.628716\pi$
$997$	6.44667e9	−	3.72199e9i	0.206017	−	0.118944i	0.599459	+	0.800406i	$0.295383\pi$
$998$	5.31173e10	−	3.06673e10i	1.69153	−	0.976604i
$999$	−3.72194e10	+	9.93463e9i	−1.18111	+	0.315263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.8.g.b.5.15	yes	32
3.2	odd	2	inner	21.8.g.b.5.2	✓	32
7.2	even	3		147.8.c.b.146.7		32
7.3	odd	6	inner	21.8.g.b.17.2	yes	32
7.5	odd	6		147.8.c.b.146.25		32
21.2	odd	6		147.8.c.b.146.26		32
21.5	even	6		147.8.c.b.146.8		32
21.17	even	6	inner	21.8.g.b.17.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.g.b.5.2	✓	32	3.2	odd	2	inner
21.8.g.b.5.15	yes	32	1.1	even	1	trivial
21.8.g.b.17.2	yes	32	7.3	odd	6	inner
21.8.g.b.17.15	yes	32	21.17	even	6	inner
147.8.c.b.146.7		32	7.2	even	3
147.8.c.b.146.8		32	21.5	even	6
147.8.c.b.146.25		32	7.5	odd	6
147.8.c.b.146.26		32	21.2	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(17.0599 + 9.84952i) q^{2} +(-45.1680 - 12.1182i) q^{3} +(130.026 + 225.212i) q^{4} +(-147.583 + 255.621i) q^{5} +(-651.201 - 651.618i) q^{6} +(-45.1728 + 906.368i) q^{7} +2601.29i q^{8} +(1893.30 + 1094.71i) q^{9} +(-5035.49 + 2907.24i) q^{10} +(2530.38 - 1460.92i) q^{11} +(-3143.85 - 11748.0i) q^{12} -12468.8i q^{13} +(-9697.92 + 15017.6i) q^{14} +(9763.71 - 9757.46i) q^{15} +(-8978.17 + 15550.6i) q^{16} +(13752.6 + 23820.2i) q^{17} +(21517.0 + 37323.7i) q^{18} +(-3840.23 - 2217.16i) q^{19} -76758.5 q^{20} +(13023.9 - 40391.4i) q^{21} +57557.3 q^{22} +(34006.6 + 19633.7i) q^{23} +(31523.1 - 117495. i) q^{24} +(-4499.01 - 7792.52i) q^{25} +(122811. - 212716. i) q^{26} +(-72250.5 - 72389.3i) q^{27} +(-209998. + 107678. i) q^{28} +104442. i q^{29} +(262674. - 70293.2i) q^{30} +(-3499.96 + 2020.70i) q^{31} +(-17975.9 + 10378.4i) q^{32} +(-131996. + 35323.0i) q^{33} +541826. i q^{34} +(-225020. - 145312. i) q^{35} +(-363.886 + 568733. i) q^{36} +(188326. - 326191. i) q^{37} +(-43675.9 - 75648.9i) q^{38} +(-151099. + 563190. i) q^{39} +(-664946. - 383907. i) q^{40} +234072. q^{41} +(620022. - 560792. i) q^{42} -655950. q^{43} +(658031. + 379914. i) q^{44} +(-559250. + 322406. i) q^{45} +(386765. + 669897. i) q^{46} +(45057.1 - 78041.2i) q^{47} +(593972. - 593592. i) q^{48} +(-819462. - 81886.3i) q^{49} -177252. i q^{50} +(-332519. - 1.24257e6i) q^{51} +(2.80811e6 - 1.62126e6i) q^{52} +(-401269. + 231672. i) q^{53} +(-519584. - 1.94658e6i) q^{54} +862426. i q^{55} +(-2.35773e6 - 117508. i) q^{56} +(146588. + 146681. i) q^{57} +(-1.02870e6 + 1.78176e6i) q^{58} +(-112563. - 194965. i) q^{59} +(3.46703e6 + 930176. i) q^{60} +(2.12274e6 + 1.22557e6i) q^{61} -79611.7 q^{62} +(-1.07774e6 + 1.66657e6i) q^{63} +1.88952e6 q^{64} +(3.18729e6 + 1.84018e6i) q^{65} +(-2.59975e6 - 697492. i) q^{66} +(-2.21050e6 - 3.82869e6i) q^{67} +(-3.57639e6 + 6.19449e6i) q^{68} +(-1.29808e6 - 1.29892e6i) q^{69} +(-2.40756e6 - 4.69534e6i) q^{70} -4.85818e6i q^{71} +(-2.84767e6 + 4.92502e6i) q^{72} +(1.42104e6 - 820436. i) q^{73} +(6.42564e6 - 3.70984e6i) q^{74} +(108780. + 406493. i) q^{75} -1.15315e6i q^{76} +(1.20982e6 + 2.35945e6i) q^{77} +(-8.12488e6 + 8.11968e6i) q^{78} +(-586188. + 1.01531e6i) q^{79} +(-2.65005e6 - 4.59002e6i) q^{80} +(2.38618e6 + 4.14523e6i) q^{81} +(3.99324e6 + 2.30550e6i) q^{82} +7.03644e6 q^{83} +(1.07901e7 - 2.31879e6i) q^{84} -8.11861e6 q^{85} +(-1.11904e7 - 6.46079e6i) q^{86} +(1.26565e6 - 4.71742e6i) q^{87} +(3.80027e6 + 6.58227e6i) q^{88} +(211992. - 367182. i) q^{89} +(-1.27163e7 - 8136.11i) q^{90} +(1.13013e7 + 563249. i) q^{91} +1.02116e7i q^{92} +(182573. - 48857.8i) q^{93} +(1.53734e6 - 887582. i) q^{94} +(1.13351e6 - 654430. i) q^{95} +(937705. - 250936. i) q^{96} +4.84780e6i q^{97} +(-1.31734e7 - 9.46827e6i) q^{98} +(6.39005e6 + 4088.47i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 84 q^{3} + 1150 q^{4} + 2464 q^{7} - 3516 q^{9} - 630 q^{10} - 3864 q^{12} + 27576 q^{15} - 19594 q^{16} + 33498 q^{18} - 47880 q^{19} + 151788 q^{21} + 105132 q^{22} - 211554 q^{24} - 331252 q^{25}+ \cdots + 35642232 q^{99}+O(q^{100}) \) 32 * q - 84 * q^3 + 1150 * q^4 + 2464 * q^7 - 3516 * q^9 - 630 * q^10 - 3864 * q^12 + 27576 * q^15 - 19594 * q^16 + 33498 * q^18 - 47880 * q^19 + 151788 * q^21 + 105132 * q^22 - 211554 * q^24 - 331252 * q^25 - 353122 * q^28 - 40662 * q^30 + 628152 * q^31 - 66024 * q^33 - 227244 * q^36 - 618748 * q^37 + 1996104 * q^39 + 1986138 * q^40 + 4274802 * q^42 - 1416064 * q^43 - 4757508 * q^45 - 3492840 * q^46 - 6640312 * q^49 + 677340 * q^51 + 11962272 * q^52 - 6743898 * q^54 - 6279408 * q^57 - 2064342 * q^58 + 7521282 * q^60 + 10948728 * q^61 + 13194636 * q^63 - 589508 * q^64 - 6977250 * q^66 - 1944728 * q^67 - 24852702 * q^70 - 1544472 * q^72 + 13351212 * q^73 - 23106048 * q^75 + 1917432 * q^78 + 7626328 * q^79 + 8703036 * q^81 + 14640192 * q^82 + 15191904 * q^84 + 3418848 * q^85 + 15346296 * q^87 + 12313398 * q^88 + 3988992 * q^91 - 24832104 * q^93 - 51594732 * q^94 - 57374730 * q^96 + 35642232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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