LMFDB - Embedded newform 62.8.d.a.33.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,-80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.10
Character	$\chi$	$=$	62.33
Dual form			62.8.d.a.47.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.47214 - 4.70228i) q^{2} +(66.4310 - 48.2650i) q^{3} +(19.7771 + 60.8676i) q^{4} -95.3661 q^{5} -656.906 q^{6} +(418.464 + 1287.90i) q^{7} +(158.217 - 486.941i) q^{8} +(1407.75 - 4332.62i) q^{9} +(617.222 + 448.438i) q^{10} +(-2562.12 - 7885.39i) q^{11} +(4251.58 + 3088.96i) q^{12} +(5741.99 - 4171.80i) q^{13} +(3347.71 - 10303.2i) q^{14} +(-6335.26 + 4602.84i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(3058.58 - 9413.34i) q^{17} +(-29484.4 + 21421.6i) q^{18} +(11094.5 + 8060.62i) q^{19} +(-1886.06 - 5804.71i) q^{20} +(89959.3 + 65359.3i) q^{21} +(-20497.0 + 63083.1i) q^{22} +(30252.1 - 93106.5i) q^{23} +(-12991.7 - 39984.3i) q^{24} -69030.3 q^{25} -56779.9 q^{26} +(-60101.4 - 184973. i) q^{27} +(-70115.3 + 50941.8i) q^{28} +(36788.8 + 26728.6i) q^{29} +62646.5 q^{30} +(-164092. - 24213.5i) q^{31} +32768.0 q^{32} +(-550792. - 400174. i) q^{33} +(-64059.7 + 46542.1i) q^{34} +(-39907.2 - 122822. i) q^{35} +291557. q^{36} +450080. q^{37} +(-33901.7 - 104339. i) q^{38} +(180094. - 554274. i) q^{39} +(-15088.5 + 46437.6i) q^{40} +(-392760. - 285356. i) q^{41} +(-274891. - 846028. i) q^{42} +(469445. + 341072. i) q^{43} +(429294. - 311900. i) q^{44} +(-134252. + 413185. i) q^{45} +(-633609. + 460344. i) q^{46} +(181364. - 131769. i) q^{47} +(-103933. + 319874. i) q^{48} +(-817312. + 593812. i) q^{49} +(446774. + 324600. i) q^{50} +(-251150. - 772960. i) q^{51} +(367487. + 266995. i) q^{52} +(-253786. + 781072. i) q^{53} +(-480811. + 1.47978e6i) q^{54} +(244339. + 751999. i) q^{55} +693339. q^{56} +1.12606e6 q^{57} +(-112417. - 345983. i) q^{58} +(-1.27920e6 + 929394. i) q^{59} +(-405457. - 294582. i) q^{60} -1.09675e6 q^{61} +(948170. + 928322. i) q^{62} +6.16907e6 q^{63} +(-212079. - 154084. i) q^{64} +(-547591. + 397848. i) q^{65} +(1.68307e6 + 5.17996e6i) q^{66} +2.96560e6 q^{67} +633457. q^{68} +(-2.48410e6 - 7.64528e6i) q^{69} +(-319258. + 982575. i) q^{70} +(-1.02481e6 + 3.15404e6i) q^{71} +(-1.88700e6 - 1.37099e6i) q^{72} +(-625928. - 1.92641e6i) q^{73} +(-2.91298e6 - 2.11640e6i) q^{74} +(-4.58575e6 + 3.33174e6i) q^{75} +(-271214. + 834711. i) q^{76} +(9.08343e6 - 6.59950e6i) q^{77} +(-3.77195e6 + 2.74048e6i) q^{78} +(1.12779e6 - 3.47098e6i) q^{79} +(316018. - 229600. i) q^{80} +(-4.86002e6 - 3.53101e6i) q^{81} +(1.20017e6 + 3.69373e6i) q^{82} +(6.92899e6 + 5.03421e6i) q^{83} +(-2.19913e6 + 6.76823e6i) q^{84} +(-291685. + 897713. i) q^{85} +(-1.43450e6 - 4.41493e6i) q^{86} +3.73398e6 q^{87} -4.24509e6 q^{88} +(-279372. - 859818. i) q^{89} +(2.81181e6 - 2.04290e6i) q^{90} +(7.77567e6 + 5.64935e6i) q^{91} +6.26547e6 q^{92} +(-1.20695e7 + 6.31138e6i) q^{93} -1.79342e6 q^{94} +(-1.05804e6 - 768710. i) q^{95} +(2.17681e6 - 1.58155e6i) q^{96} +(1.27549e6 + 3.92555e6i) q^{97} +8.08202e6 q^{98} -3.77712e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) $ 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$3$	66.4310	−	48.2650i	1.42052	−	1.03207i	0.428831	−	0.903385i	$-0.358926\pi$
$3$	66.4310	−	48.2650i	1.42052	−	1.03207i	0.991686	−	0.128681i	$-0.0410744\pi$
$4$	19.7771	+	60.8676i	0.154508	+	0.475528i
$5$	−95.3661			−0.341192			−0.170596	−	0.985341i	$-0.554569\pi$
$5$	−95.3661			−0.341192			−0.170596	+	0.985341i	$0.554569\pi$
$6$	−656.906			−1.24158
$7$	418.464	+	1287.90i	0.461121	+	1.41918i	0.863796	+	0.503841i	$0.168080\pi$
$7$	418.464	+	1287.90i	0.461121	+	1.41918i	−0.402676	+	0.915343i	$0.631920\pi$
$8$	158.217	−	486.941i	0.109254	−	0.336249i
$9$	1407.75	−	4332.62i	0.643691	−	1.98108i
$10$	617.222	+	448.438i	0.195183	+	0.141809i
$11$	−2562.12	−	7885.39i	−0.580397	−	1.78628i	−0.617019	−	0.786948i	$-0.711660\pi$
$11$	−2562.12	−	7885.39i	−0.580397	−	1.78628i	0.0366222	−	0.999329i	$-0.488340\pi$
$12$	4251.58	+	3088.96i	0.710259	+	0.516033i
$13$	5741.99	−	4171.80i	0.724871	−	0.526649i	−0.163066	−	0.986615i	$-0.552138\pi$
$13$	5741.99	−	4171.80i	0.724871	−	0.526649i	0.887937	+	0.459966i	$0.152138\pi$
$14$	3347.71	−	10303.2i	0.326062	−	1.00351i
$15$	−6335.26	+	4602.84i	−0.484669	+	0.352133i
$16$	−3313.73	+	2407.57i	−0.202254	+	0.146946i
$17$	3058.58	−	9413.34i	0.150990	−	0.464700i	−0.846742	−	0.532003i	$-0.821439\pi$
$17$	3058.58	−	9413.34i	0.150990	−	0.464700i	0.997733	+	0.0673033i	$0.0214395\pi$
$18$	−29484.4	+	21421.6i	−1.19162	+	0.865763i
$19$	11094.5	+	8060.62i	0.371082	+	0.269607i	0.757659	−	0.652650i	$-0.226343\pi$
$19$	11094.5	+	8060.62i	0.371082	+	0.269607i	−0.386578	+	0.922257i	$0.626343\pi$
$20$	−1886.06	−	5804.71i	−0.0527171	−	0.162246i
$21$	89959.3	+	65359.3i	2.11972	+	1.54007i
$22$	−20497.0	+	63083.1i	−0.410402	+	1.26309i
$23$	30252.1	−	93106.5i	0.518452	−	1.59563i	−0.258460	−	0.966022i	$-0.583215\pi$
$23$	30252.1	−	93106.5i	0.518452	−	1.59563i	0.776912	−	0.629609i	$-0.216785\pi$
$24$	−12991.7	−	39984.3i	−0.191834	−	0.590405i
$25$	−69030.3			−0.883588
$26$	−56779.9			−0.633560
$27$	−60101.4	−	184973.i	−0.587640	−	1.80857i
$28$	−70115.3	+	50941.8i	−0.603615	+	0.438552i
$29$	36788.8	+	26728.6i	0.280106	+	0.203509i	0.718964	−	0.695048i	$-0.244617\pi$
$29$	36788.8	+	26728.6i	0.280106	+	0.203509i	−0.438857	+	0.898557i	$0.644617\pi$
$30$	62646.5			0.423616
$31$	−164092.	−	24213.5i	−0.989288	−	0.145980i
$31$	−164092.	−	24213.5i	−0.989288	−	0.145980i
$32$	32768.0			0.176777
$33$	−550792.	−	400174.i	−2.66802	−	1.93843i
$34$	−64059.7	+	46542.1i	−0.279517	+	0.203081i
$35$	−39907.2	−	122822.i	−0.157331	−	0.484214i
$36$	291557.			1.04151
$37$	450080.			1.46078			0.730388	−	0.683033i	$-0.239339\pi$
$37$	450080.			1.46078			0.730388	+	0.683033i	$0.239339\pi$
$38$	−33901.7	−	104339.i	−0.100226	−	0.308463i
$39$	180094.	−	554274.i	0.486154	−	1.49623i
$40$	−15088.5	+	46437.6i	−0.0372766	+	0.114726i
$41$	−392760.	−	285356.i	−0.889986	−	0.646613i	0.0458883	−	0.998947i	$-0.485388\pi$
$41$	−392760.	−	285356.i	−0.889986	−	0.646613i	−0.935874	+	0.352334i	$0.885388\pi$
$42$	−274891.	−	846028.i	−0.572517	−	1.76203i
$43$	469445.	+	341072.i	0.900420	+	0.654193i	0.938574	−	0.345079i	$-0.112148\pi$
$43$	469445.	+	341072.i	0.900420	+	0.654193i	−0.0381539	+	0.999272i	$0.512148\pi$
$44$	429294.	−	311900.i	0.759749	−	0.551990i
$45$	−134252.	+	413185.i	−0.219622	+	0.675928i
$46$	−633609.	+	460344.i	−0.959774	+	0.697316i
$47$	181364.	−	131769.i	0.254805	−	0.185127i	−0.453049	−	0.891486i	$-0.649664\pi$
$47$	181364.	−	131769.i	0.254805	−	0.185127i	0.707854	+	0.706359i	$0.249664\pi$
$48$	−103933.	+	319874.i	−0.135647	+	0.417479i
$49$	−817312.	+	593812.i	−0.992433	+	0.721045i
$50$	446774.	+	324600.i	0.505467	+	0.367243i
$51$	−251150.	−	772960.i	−0.265117	−	0.815946i
$52$	367487.	+	266995.i	0.362435	+	0.263325i
$53$	−253786.	+	781072.i	−0.234154	+	0.720652i	0.763078	+	0.646306i	$0.223687\pi$
$53$	−253786.	+	781072.i	−0.234154	+	0.720652i	−0.997232	+	0.0743462i	$0.976313\pi$
$54$	−480811.	+	1.47978e6i	−0.415524	+	1.27885i
$55$	244339.	+	751999.i	0.198027	+	0.609464i
$56$	693339.			0.527579
$57$	1.12606e6			0.805380
$58$	−112417.	−	345983.i	−0.0756541	−	0.232839i
$59$	−1.27920e6	+	929394.i	−0.810880	+	0.589139i	−0.914086	−	0.405521i	$-0.867090\pi$
$59$	−1.27920e6	+	929394.i	−0.810880	+	0.589139i	0.103206	+	0.994660i	$0.467090\pi$
$60$	−405457.	−	294582.i	−0.242335	−	0.176066i
$61$	−1.09675e6			−0.618662			−0.309331	−	0.950954i	$-0.600105\pi$
$61$	−1.09675e6			−0.618662			−0.309331	+	0.950954i	$0.600105\pi$
$62$	948170.	+	928322.i	0.505260	+	0.494684i
$63$	6.16907e6			3.10833
$64$	−212079.	−	154084.i	−0.101127	−	0.0734732i
$65$	−547591.	+	397848.i	−0.247320	+	0.179689i
$66$	1.68307e6	+	5.17996e6i	0.720607	+	2.21780i
$67$	2.96560e6			1.20462			0.602311	−	0.798261i	$-0.294247\pi$
$67$	2.96560e6			1.20462			0.602311	+	0.798261i	$0.294247\pi$
$68$	633457.			0.244307
$69$	−2.48410e6	−	7.64528e6i	−0.910327	−	2.80170i
$70$	−319258.	+	982575.i	−0.111250	+	0.342391i
$71$	−1.02481e6	+	3.15404e6i	−0.339813	+	1.04584i	0.624490	+	0.781033i	$0.285307\pi$
$71$	−1.02481e6	+	3.15404e6i	−0.339813	+	1.04584i	−0.964302	+	0.264803i	$0.914693\pi$
$72$	−1.88700e6	−	1.37099e6i	−0.595810	−	0.432881i
$73$	−625928.	−	1.92641e6i	−0.188319	−	0.579586i	0.811671	−	0.584115i	$-0.198558\pi$
$73$	−625928.	−	1.92641e6i	−0.188319	−	0.579586i	−0.999990	+	0.00452895i	$0.998558\pi$
$74$	−2.91298e6	−	2.11640e6i	−0.835653	−	0.607138i
$75$	−4.58575e6	+	3.33174e6i	−1.25515	+	0.911921i
$76$	−271214.	+	834711.i	−0.0708703	+	0.218116i
$77$	9.08343e6	−	6.59950e6i	2.26742	−	1.64738i
$78$	−3.77195e6	+	2.74048e6i	−0.899983	+	0.653876i
$79$	1.12779e6	−	3.47098e6i	0.257356	−	0.792059i	−0.736001	−	0.676981i	$-0.763288\pi$
$79$	1.12779e6	−	3.47098e6i	0.257356	−	0.792059i	0.993356	−	0.115079i	$-0.0367120\pi$
$80$	316018.	−	229600.i	0.0690075	−	0.0501369i
$81$	−4.86002e6	−	3.53101e6i	−1.01611	−	0.738247i
$82$	1.20017e6	+	3.69373e6i	0.240377	+	0.739804i
$83$	6.92899e6	+	5.03421e6i	1.33014	+	0.966402i	0.999746	+	0.0225580i	$0.00718103\pi$
$83$	6.92899e6	+	5.03421e6i	1.33014	+	0.966402i	0.330392	+	0.943844i	$0.392819\pi$
$84$	−2.19913e6	+	6.76823e6i	−0.404831	+	1.24594i
$85$	−291685.	+	897713.i	−0.0515166	+	0.158552i
$86$	−1.43450e6	−	4.41493e6i	−0.243195	−	0.748478i
$87$	3.73398e6			0.607931
$88$	−4.24509e6			−0.664045
$89$	−279372.	−	859818.i	−0.0420066	−	0.129283i	0.927854	−	0.372944i	$-0.121652\pi$
$89$	−279372.	−	859818.i	−0.0420066	−	0.129283i	−0.969860	+	0.243661i	$0.921652\pi$
$90$	2.81181e6	−	2.04290e6i	0.406571	−	0.295391i
$91$	7.77567e6	+	5.64935e6i	1.08167	+	0.785876i
$92$	6.26547e6			0.838873
$93$	−1.20695e7	+	6.31138e6i	−1.55596	+	0.813644i
$94$	−1.79342e6			−0.222708
$95$	−1.05804e6	−	768710.i	−0.126610	−	0.0919877i
$96$	2.17681e6	−	1.58155e6i	0.251114	−	0.182445i
$97$	1.27549e6	+	3.92555e6i	0.141898	+	0.436717i	0.996599	−	0.0824036i	$-0.0262597\pi$
$97$	1.27549e6	+	3.92555e6i	0.141898	+	0.436717i	−0.854701	+	0.519120i	$0.826260\pi$
$98$	8.08202e6			0.867419
$99$	−3.77712e7			−3.91235
$100$	−1.36522e6	−	4.20171e6i	−0.136522	−	0.420171i
$101$	−3.23300e6	+	9.95016e6i	−0.312235	+	0.960960i	0.664643	+	0.747161i	$0.268584\pi$
$101$	−3.23300e6	+	9.95016e6i	−0.312235	+	0.960960i	−0.976878	+	0.213799i	$0.931416\pi$
$102$	−2.00920e6	+	6.18368e6i	−0.187466	+	0.576961i
$103$	4.62797e6	+	3.36242e6i	0.417311	+	0.303194i	0.776555	−	0.630049i	$-0.216965\pi$
$103$	4.62797e6	+	3.36242e6i	0.417311	+	0.303194i	−0.359244	+	0.933244i	$0.616965\pi$
$104$	−1.12294e6	−	3.45606e6i	−0.0978904	−	0.301276i
$105$	−8.57907e6	−	6.23306e6i	−0.723232	−	0.525459i
$106$	5.31536e6	−	3.86183e6i	0.433473	−	0.314937i
$107$	5.11826e6	−	1.57524e7i	0.403905	−	1.24309i	−0.517901	−	0.855441i	$-0.673286\pi$
$107$	5.11826e6	−	1.57524e7i	0.403905	−	1.24309i	0.921806	−	0.387652i	$-0.126714\pi$
$108$	1.00702e7	−	7.31645e6i	0.769231	−	0.558879i
$109$	1.53485e7	−	1.11513e7i	1.13520	−	0.824771i	0.148757	−	0.988874i	$-0.452473\pi$
$109$	1.53485e7	−	1.11513e7i	1.13520	−	0.824771i	0.986443	+	0.164103i	$0.0524729\pi$
$110$	1.95471e6	−	6.01599e6i	0.140026	−	0.430956i
$111$	2.98992e7	−	2.17231e7i	2.07506	−	1.50762i
$112$	−4.48738e6	−	3.26027e6i	−0.301807	−	0.219276i
$113$	5.87668e6	+	1.80865e7i	0.383140	+	1.17918i	0.937821	+	0.347120i	$0.112840\pi$
$113$	5.87668e6	+	1.80865e7i	0.383140	+	1.17918i	−0.554681	+	0.832063i	$0.687160\pi$
$114$	−7.28804e6	−	5.29507e6i	−0.460727	−	0.334738i
$115$	−2.88503e6	+	8.87920e6i	−0.176892	+	0.544417i
$116$	−899333.	+	2.76786e6i	−0.0534955	+	0.164642i
$117$	−9.99151e6	−	3.07507e7i	−0.576741	−	1.77503i
$118$	1.26494e7			0.708735
$119$	1.34033e7			0.729119
$120$	1.23897e6	+	3.81315e6i	0.0654523	+	0.201442i
$121$	−3.98495e7	+	2.89524e7i	−2.04491	+	1.48571i
$122$	7.09832e6	+	5.15723e6i	0.353913	+	0.257133i
$123$	−3.98641e7			−1.93159
$124$	−1.77145e6	−	1.04668e7i	−0.0834360	−	0.492989i
$125$	1.40336e7			0.642665
$126$	−3.99270e7	−	2.90087e7i	−1.77816	−	1.29191i
$127$	1.68400e7	−	1.22350e7i	0.729506	−	0.530017i	−0.159901	−	0.987133i	$-0.551118\pi$
$127$	1.68400e7	−	1.22350e7i	0.729506	−	0.530017i	0.889407	+	0.457116i	$0.151118\pi$
$128$	648056.	+	1.99451e6i	0.0273135	+	0.0840623i
$129$	4.76475e7			1.95423
$130$	5.41488e6			0.216166
$131$	−4.57466e6	−	1.40794e7i	−0.177791	−	0.547184i	0.821959	−	0.569547i	$-0.192881\pi$
$131$	−4.57466e6	−	1.40794e7i	−0.177791	−	0.547184i	−0.999750	+	0.0223624i	$0.992881\pi$
$132$	1.34646e7	−	4.14397e7i	0.509546	−	1.56822i
$133$	−5.73862e6	+	1.76617e7i	−0.211508	+	0.650955i
$134$	−1.91938e7	−	1.39451e7i	−0.689118	−	0.500674i
$135$	5.73163e6	+	1.76402e7i	0.200498	+	0.617070i
$136$	−4.09982e6	−	2.97869e6i	−0.139759	−	0.101541i
$137$	−1.95413e7	+	1.41976e7i	−0.649278	+	0.471728i	−0.863025	−	0.505161i	$-0.831433\pi$
$137$	−1.95413e7	+	1.41976e7i	−0.649278	+	0.471728i	0.213747	+	0.976889i	$0.431433\pi$
$138$	−1.98728e7	+	6.11622e7i	−0.643698	+	1.98110i
$139$	−2.03983e7	+	1.48202e7i	−0.644232	+	0.468062i	−0.861302	−	0.508094i	$-0.830350\pi$
$139$	−2.03983e7	+	1.48202e7i	−0.644232	+	0.468062i	0.217069	+	0.976156i	$0.430350\pi$
$140$	6.68663e6	−	4.85812e6i	0.205949	−	0.149630i
$141$	5.68838e6	−	1.75070e7i	0.170892	−	0.525952i
$142$	2.14639e7	−	1.55945e7i	0.629071	−	0.457047i
$143$	−4.76079e7	−	3.45892e7i	−1.36145	−	0.989155i
$144$	5.76616e6	+	1.77464e7i	0.160923	+	0.495270i
$145$	−3.50841e6	−	2.54901e6i	−0.0955700	−	0.0694357i
$146$	−5.00742e6	+	1.54113e7i	−0.133162	+	0.409829i
$147$	−2.56345e7	+	7.88950e7i	−0.665602	+	2.04851i
$148$	8.90127e6	+	2.73953e7i	0.225702	+	0.694640i
$149$	4.44234e7			1.10017			0.550085	−	0.835109i	$-0.314595\pi$
$149$	4.44234e7			1.10017			0.550085	+	0.835109i	$0.314595\pi$
$150$	4.53464e7			1.09704
$151$	2.10269e7	+	6.47141e7i	0.496999	+	1.52961i	0.813817	+	0.581121i	$0.197386\pi$
$151$	2.10269e7	+	6.47141e7i	0.496999	+	1.52961i	−0.316818	+	0.948486i	$0.602614\pi$
$152$	5.68038e6	−	4.12704e6i	0.131197	−	0.0953204i
$153$	−3.64787e7	−	2.65033e7i	−0.823416	−	0.598246i
$154$	−8.98219e7			−1.98180
$155$	1.56489e7	+	2.30915e6i	0.337537	+	0.0498071i
$156$	3.72991e7			0.786614
$157$	−9.30050e6	−	6.75721e6i	−0.191804	−	0.139354i	0.487739	−	0.872990i	$-0.337822\pi$
$157$	−9.30050e6	−	6.75721e6i	−0.191804	−	0.139354i	−0.679543	+	0.733636i	$0.737822\pi$
$158$	−2.36208e7	+	1.71615e7i	−0.476424	+	0.346143i
$159$	2.08392e7	+	6.41364e7i	0.411141	+	1.26536i
$160$	−3.12496e6			−0.0603148
$161$	1.32571e8			2.50356
$162$	1.48509e7	+	4.57064e7i	0.274442	+	0.844645i
$163$	4.05970e6	−	1.24945e7i	0.0734238	−	0.225975i	−0.907609	−	0.419816i	$-0.862095\pi$
$163$	4.05970e6	−	1.24945e7i	0.0734238	−	0.225975i	0.981033	+	0.193841i	$0.0620945\pi$
$164$	9.60133e6	−	2.95499e7i	0.169972	−	0.523121i
$165$	5.25269e7	+	3.81630e7i	0.910307	+	0.661377i
$166$	−2.11731e7	−	6.51641e7i	−0.359258	−	1.10568i
$167$	−2.30710e7	−	1.67621e7i	−0.383318	−	0.278497i	0.379394	−	0.925235i	$-0.376133\pi$
$167$	−2.30710e7	−	1.67621e7i	−0.383318	−	0.278497i	−0.762712	+	0.646738i	$0.776133\pi$
$168$	4.60592e7	−	3.34640e7i	0.749435	−	0.544496i
$169$	−3.82383e6	+	1.17685e7i	−0.0609390	+	0.187551i
$170$	6.10912e6	−	4.43854e6i	0.0953691	−	0.0692897i
$171$	5.05419e7	−	3.67208e7i	0.772974	−	0.561599i
$172$	−1.14760e7	+	3.53194e7i	−0.171965	+	0.529254i
$173$	3.04228e7	−	2.21035e7i	0.446723	−	0.324563i	−0.341578	−	0.939854i	$-0.610961\pi$
$173$	3.04228e7	−	2.21035e7i	0.446723	−	0.324563i	0.788301	+	0.615290i	$0.210961\pi$
$174$	−2.41668e7	−	1.75582e7i	−0.347774	−	0.252672i
$175$	−2.88867e7	−	8.89041e7i	−0.407441	−	1.25397i
$176$	2.74748e7	+	1.99616e7i	0.379875	+	0.275995i
$177$	−4.01214e7	+	1.23481e8i	−0.543839	+	1.67376i
$178$	−2.23497e6	+	6.87854e6i	−0.0297032	+	0.0914169i
$179$	−8.16446e6	−	2.51276e7i	−0.106400	−	0.327466i	0.883656	−	0.468136i	$-0.155074\pi$
$179$	−8.16446e6	−	2.51276e7i	−0.106400	−	0.327466i	−0.990057	+	0.140670i	$0.955074\pi$
$180$	−2.78047e7			−0.355356
$181$	−8.23458e7			−1.03221			−0.516103	−	0.856526i	$-0.672618\pi$
$181$	−8.23458e7			−1.03221			−0.516103	+	0.856526i	$0.672618\pi$
$182$	−2.37603e7	−	7.31268e7i	−0.292148	−	0.899139i
$183$	−7.28583e7	+	5.29346e7i	−0.878820	+	0.638500i
$184$	−4.05510e7	−	2.94620e7i	−0.479887	−	0.348658i
$185$	−4.29223e7			−0.498405
$186$	1.07793e8	+	1.59060e7i	1.22828	+	0.181245i
$187$	−8.20643e7			−0.917717
$188$	1.16073e7	+	8.43319e6i	0.127403	+	0.0925634i
$189$	2.13076e8	−	1.54809e8i	2.29572	−	1.66794i
$190$	3.23308e6	+	9.95039e6i	0.0341962	+	0.105245i
$191$	−4.97951e7			−0.517094			−0.258547	−	0.965999i	$-0.583244\pi$
$191$	−4.97951e7			−0.517094			−0.258547	+	0.965999i	$0.583244\pi$
$192$	−2.15255e7			−0.219482
$193$	3.69184e7	+	1.13623e8i	0.369651	+	1.13767i	0.947017	+	0.321184i	$0.104081\pi$
$193$	3.69184e7	+	1.13623e8i	0.369651	+	1.13767i	−0.577366	+	0.816486i	$0.695919\pi$
$194$	1.02039e7	−	3.14044e7i	0.100337	−	0.308805i
$195$	−1.71749e7	+	5.28589e7i	−0.165872	+	0.510501i
$196$	−5.23079e7	−	3.80039e7i	−0.496217	−	0.360523i
$197$	3.37423e7	+	1.03848e8i	0.314444	+	0.967759i	0.975983	+	0.217848i	$0.0699038\pi$
$197$	3.37423e7	+	1.03848e8i	0.314444	+	0.967759i	−0.661539	+	0.749911i	$0.730096\pi$
$198$	2.44461e8	+	1.77611e8i	2.23811	+	1.62608i
$199$	−7.20090e7	+	5.23176e7i	−0.647741	+	0.470611i	−0.862501	−	0.506056i	$-0.831103\pi$
$199$	−7.20090e7	+	5.23176e7i	−0.647741	+	0.470611i	0.214760	+	0.976667i	$0.431103\pi$
$200$	−1.09217e7	+	3.36137e7i	−0.0965355	+	0.297106i
$201$	1.97008e8	−	1.43135e8i	1.71119	−	1.24325i
$202$	6.77129e7	−	4.91963e7i	0.578019	−	0.419955i
$203$	−1.90290e7	+	5.85653e7i	−0.159654	+	0.491365i
$204$	4.20812e7	−	3.05738e7i	0.347042	−	0.252141i
$205$	3.74559e7	+	2.72133e7i	0.303656	+	0.220619i
$206$	−1.41418e7	−	4.35240e7i	−0.112712	−	0.346892i
$207$	−3.60807e8	−	2.62142e8i	−2.82735	−	2.05419i
$208$	−8.98353e6	+	2.76485e7i	−0.0692190	+	0.213034i
$209$	3.51357e7	−	1.08137e8i	0.266218	−	0.819334i
$210$	2.62153e7	+	8.06824e7i	0.195338	+	0.601189i
$211$	−1.61880e8			−1.18633			−0.593165	−	0.805081i	$-0.702122\pi$
$211$	−1.61880e8			−1.18633			−0.593165	+	0.805081i	$0.702122\pi$
$212$	−5.25612e7			−0.378869
$213$	8.41506e7	+	2.58989e8i	0.596662	+	1.83634i
$214$	−1.07198e8	+	7.78841e7i	−0.747721	+	0.543251i
$215$	−4.47691e7	−	3.25267e7i	−0.307216	−	0.223206i
$216$	−9.95800e7			−0.672332
$217$	−3.74822e7	−	2.21467e8i	−0.249009	−	1.47130i
$218$	−1.51774e8			−0.992201
$219$	−1.34559e8	−	9.77628e7i	−0.865682	−	0.628955i
$220$	−4.09401e7	+	2.97447e7i	−0.259220	+	0.188335i
$221$	−2.17082e7	−	6.68111e7i	−0.135286	−	0.416366i
$222$	−2.95660e8			−1.81367
$223$	1.75707e8			1.06102			0.530509	−	0.847680i	$-0.322001\pi$
$223$	1.75707e8			1.06102			0.530509	+	0.847680i	$0.322001\pi$
$224$	1.37122e7	+	4.22019e7i	0.0815154	+	0.250879i
$225$	−9.71776e7	+	2.99082e8i	−0.568758	+	1.75046i
$226$	4.70134e7	−	1.44692e8i	0.270921	−	0.833808i
$227$	1.38706e8	+	1.00776e8i	0.787053	+	0.571827i	0.907087	−	0.420942i	$-0.138301\pi$
$227$	1.38706e8	+	1.00776e8i	0.787053	+	0.571827i	−0.120035	+	0.992770i	$0.538301\pi$
$228$	2.22703e7	+	6.85408e7i	0.124438	+	0.382981i
$229$	−1.55040e8	−	1.12643e8i	−0.853137	−	0.619841i	0.0728719	−	0.997341i	$-0.476784\pi$
$229$	−1.55040e8	−	1.12643e8i	−0.853137	−	0.619841i	−0.926009	+	0.377501i	$0.876784\pi$
$230$	6.04248e7	−	4.39012e7i	0.327467	−	0.237919i
$231$	2.84897e8	−	8.76823e8i	1.52071	−	4.68026i
$232$	1.88359e7	−	1.36851e7i	0.0990325	−	0.0719513i
$233$	1.55590e8	−	1.13043e8i	0.805818	−	0.585461i	−0.106797	−	0.994281i	$-0.534060\pi$
$233$	1.55590e8	−	1.13043e8i	0.805818	−	0.585461i	0.912615	+	0.408820i	$0.134060\pi$
$234$	−7.99321e7	+	2.46006e8i	−0.407817	+	1.25513i
$235$	−1.72960e7	+	1.25663e7i	−0.0869375	+	0.0631638i
$236$	−8.18688e7	−	5.94812e7i	−0.405440	−	0.294569i
$237$	−9.26065e7	−	2.85014e8i	−0.451879	−	1.39074i
$238$	−8.67482e7	−	6.30263e7i	−0.417101	−	0.303042i
$239$	−1.89257e7	+	5.82474e7i	−0.0896727	+	0.275984i	−0.985829	−	0.167755i	$-0.946348\pi$
$239$	−1.89257e7	+	5.82474e7i	−0.0896727	+	0.275984i	0.896156	+	0.443739i	$0.146348\pi$
$240$	9.91173e6	−	3.05052e7i	0.0462818	−	0.142441i
$241$	−1.90587e7	−	5.86567e7i	−0.0877070	−	0.269934i	0.897578	−	0.440857i	$-0.145325\pi$
$241$	−1.90587e7	−	5.86567e7i	−0.0877070	−	0.269934i	−0.985285	+	0.170922i	$0.945325\pi$
$242$	3.94054e8			1.78732
$243$	−6.79259e7			−0.303678
$244$	−2.16905e7	−	6.67566e7i	−0.0955886	−	0.294191i
$245$	7.79438e7	−	5.66295e7i	0.338610	−	0.246015i
$246$	2.58006e8	+	1.87452e8i	1.10499	+	0.802820i
$247$	9.73317e7			0.410975
$248$	−3.77527e7	+	7.60723e7i	−0.157169	+	0.316698i
$249$	7.03276e8			2.88687
$250$	−9.08275e7	−	6.59901e7i	−0.367644	−	0.267109i
$251$	−1.69593e8	+	1.23217e8i	−0.676941	+	0.491826i	−0.872341	−	0.488897i	$-0.837399\pi$
$251$	−1.69593e8	+	1.23217e8i	−0.676941	+	0.491826i	0.195400	+	0.980724i	$0.437399\pi$
$252$	1.22006e8	+	3.75496e8i	0.480264	+	1.47810i
$253$	−8.11691e8			−3.15115
$254$	−1.66523e8			−0.637612
$255$	2.39512e7	+	7.37141e7i	0.0904558	+	0.278394i
$256$	5.18444e6	−	1.59561e7i	0.0193136	−	0.0594410i
$257$	9.72995e7	−	2.99457e8i	0.357557	−	1.10045i	−0.596956	−	0.802274i	$-0.703623\pi$
$257$	9.72995e7	−	2.99457e8i	0.357557	−	1.10045i	0.954512	−	0.298172i	$-0.0963768\pi$
$258$	−3.08381e8	−	2.24052e8i	−1.11794	−	0.812232i
$259$	1.88342e8	+	5.79657e8i	0.673594	+	2.07311i
$260$	−3.50458e7	−	2.54623e7i	−0.123660	−	0.0898443i
$261$	1.67595e8	−	1.21765e8i	0.583470	−	0.423915i
$262$	−3.65973e7	+	1.12635e8i	−0.125717	+	0.386918i
$263$	−3.03769e8	+	2.20701e8i	−1.02967	+	0.748100i	−0.968243	−	0.250011i	$-0.919566\pi$
$263$	−3.03769e8	+	2.20701e8i	−1.02967	+	0.748100i	−0.0614288	+	0.998111i	$0.519566\pi$
$264$	−2.82006e8	+	2.04889e8i	−0.943287	+	0.685338i
$265$	2.42026e7	−	7.44878e7i	0.0798915	−	0.245881i
$266$	1.20191e8	−	8.73240e7i	0.391550	−	0.284478i
$267$	−6.00580e7	−	4.36347e7i	−0.193100	−	0.140295i
$268$	5.86510e7	+	1.80509e8i	0.186124	+	0.572832i
$269$	4.23559e8	+	3.07733e8i	1.32672	+	0.963921i	0.999822	+	0.0188628i	$0.00600457\pi$
$269$	4.23559e8	+	3.07733e8i	1.32672	+	0.963921i	0.326902	+	0.945058i	$0.393995\pi$
$270$	4.58531e7	−	1.41121e8i	0.141774	−	0.436334i
$271$	−5.34900e7	+	1.64625e8i	−0.163260	+	0.502463i	−0.998904	−	0.0468088i	$-0.985095\pi$
$271$	−5.34900e7	+	1.64625e8i	−0.163260	+	0.502463i	0.835644	+	0.549272i	$0.185095\pi$
$272$	1.25279e7	+	3.85570e7i	0.0377475	+	0.116175i
$273$	7.89211e8			2.34760
$274$	1.93235e8			0.567490
$275$	1.76864e8	+	5.44331e8i	0.512832	+	1.57833i
$276$	4.16221e8	−	3.02403e8i	1.19163	−	0.865772i
$277$	−1.54992e8	−	1.12608e8i	−0.438158	−	0.318341i	0.346744	−	0.937960i	$-0.387287\pi$
$277$	−1.54992e8	−	1.12608e8i	−0.438158	−	0.318341i	−0.784903	+	0.619619i	$0.787287\pi$
$278$	2.01710e8			0.563080
$279$	−3.35909e8	+	6.76863e8i	−0.925993	+	1.86589i
$280$	−6.61210e7			−0.180006
$281$	−4.03477e8	−	2.93143e8i	−1.08479	−	0.788147i	−0.106279	−	0.994336i	$-0.533894\pi$
$281$	−4.03477e8	−	2.93143e8i	−1.08479	−	0.788147i	−0.978512	+	0.206189i	$0.933894\pi$
$282$	−1.19139e8	+	8.65596e7i	−0.316360	+	0.229849i
$283$	5.61323e7	+	1.72758e8i	0.147218	+	0.453090i	0.997290	−	0.0735769i	$-0.0234415\pi$
$283$	5.61323e7	+	1.72758e8i	0.147218	+	0.453090i	−0.850072	+	0.526667i	$0.823441\pi$
$284$	−2.12247e8			−0.549829
$285$	−1.07388e8			−0.274789
$286$	1.45477e8	+	4.47732e8i	0.367716	+	1.13171i
$287$	2.03155e8	−	6.25246e8i	0.507271	−	1.56122i
$288$	4.61292e7	−	1.41971e8i	0.113790	−	0.350208i
$289$	2.52715e8	+	1.83608e8i	0.615869	+	0.447455i
$290$	1.07207e7	+	3.29950e7i	0.0258126	+	0.0794430i
$291$	2.74199e8	+	1.99217e8i	0.652289	+	0.473915i
$292$	1.04877e8	−	7.61974e7i	0.246513	−	0.179102i
$293$	−1.03893e8	+	3.19750e8i	−0.241296	+	0.742633i	0.754928	+	0.655808i	$0.227672\pi$
$293$	−1.03893e8	+	3.19750e8i	−0.241296	+	0.742633i	−0.996224	+	0.0868247i	$0.972328\pi$
$294$	5.36897e8	−	3.90078e8i	1.23218	−	0.895233i
$295$	1.21992e8	−	8.86326e7i	0.276666	−	0.201010i
$296$	7.12101e7	−	2.19162e8i	0.159596	−	0.491185i
$297$	−1.30460e9	+	9.47846e8i	−2.88954	+	2.09938i
$298$	−2.87514e8	−	2.08891e8i	−0.629365	−	0.457260i
$299$	−2.14714e8	−	6.60822e8i	−0.464528	−	1.42967i
$300$	−2.93488e8	−	2.13232e8i	−0.627576	−	0.455961i
$301$	−2.42820e8	+	7.47324e8i	−0.513218	+	1.57952i
$302$	1.68215e8	−	5.17713e8i	0.351432	−	1.08160i
$303$	2.65472e8	+	8.17040e8i	0.548239	+	1.68731i
$304$	−5.61707e7			−0.114671
$305$	1.04593e8			0.211083
$306$	1.11469e8	+	3.43066e8i	0.222397	+	0.684467i
$307$	−4.02976e8	+	2.92780e8i	−0.794869	+	0.577506i	−0.909404	−	0.415913i	$-0.863462\pi$
$307$	−4.02976e8	+	2.92780e8i	−0.794869	+	0.577506i	0.114536	+	0.993419i	$0.463462\pi$
$308$	5.81340e8	+	4.22368e8i	1.13371	+	0.823690i
$309$	4.69728e8			0.905714
$310$	−9.04232e7	−	8.85304e7i	−0.172391	−	0.168782i
$311$	−4.92790e8			−0.928967			−0.464483	−	0.885582i	$-0.653760\pi$
$311$	−4.92790e8			−0.928967			−0.464483	+	0.885582i	$0.653760\pi$
$312$	−2.41405e8	−	1.75391e8i	−0.449992	−	0.326938i
$313$	4.46614e8	−	3.24484e8i	0.823241	−	0.598119i	−0.0943982	−	0.995535i	$-0.530093\pi$
$313$	4.46614e8	−	3.24484e8i	0.823241	−	0.598119i	0.917639	+	0.397415i	$0.130093\pi$
$314$	2.84198e7	+	8.74672e7i	0.0518045	+	0.159438i
$315$	−5.88320e8			−1.06054
$316$	2.33575e8			0.416410
$317$	1.62324e8	+	4.99580e8i	0.286203	+	0.880842i	0.986036	+	0.166535i	$0.0532579\pi$
$317$	1.62324e8	+	4.99580e8i	0.286203	+	0.880842i	−0.699833	+	0.714307i	$0.746742\pi$
$318$	1.66713e8	−	5.13091e8i	0.290720	−	0.894745i
$319$	1.16508e8	−	3.58576e8i	0.200951	−	0.618464i
$320$	2.02251e7	+	1.46944e7i	0.0345038	+	0.0250685i
$321$	−4.20277e8	−	1.29348e9i	−0.709199	−	2.18269i
$322$	−8.58019e8	−	6.23387e8i	−1.43219	−	1.04055i
$323$	1.09811e8	−	7.97821e7i	0.181316	−	0.131734i
$324$	1.18807e8	−	3.65651e8i	0.194060	−	0.597254i
$325$	−3.96371e8	+	2.87981e8i	−0.640487	+	0.465341i
$326$	−8.50274e7	+	6.17760e7i	−0.135924	+	0.0987549i
$327$	4.81397e8	−	1.48159e9i	0.761353	−	2.34320i
$328$	−2.01093e8	+	1.46103e8i	−0.314658	+	0.228612i
$329$	2.45599e8	+	1.78438e8i	0.380225	+	0.276250i
$330$	−1.60508e8	−	4.93993e8i	−0.245866	−	0.756696i
$331$	9.31539e7	+	6.76803e7i	0.141190	+	0.102580i	0.656138	−	0.754641i	$-0.272189\pi$
$331$	9.31539e7	+	6.76803e7i	0.141190	+	0.102580i	−0.514948	+	0.857221i	$0.672189\pi$
$332$	−1.69385e8	+	5.21313e8i	−0.254034	+	0.781835i
$333$	6.33601e8	−	1.95002e9i	0.940288	−	2.89391i
$334$	7.04988e7	+	2.16973e8i	0.103531	+	0.318635i
$335$	−2.82818e8			−0.411008
$336$	−4.55458e8			−0.655030
$337$	−1.04031e8	−	3.20176e8i	−0.148067	−	0.455705i	0.849325	−	0.527870i	$-0.177009\pi$
$337$	−1.04031e8	−	3.20176e8i	−0.148067	−	0.455705i	−0.997393	+	0.0721651i	$0.977009\pi$
$338$	8.00874e7	−	5.81869e7i	0.112812	−	0.0819628i
$339$	1.26334e9	+	9.17870e8i	1.76125	+	1.27962i
$340$	−6.04103e7			−0.0833557
$341$	2.29491e8	+	1.35597e9i	0.313419	+	1.85187i
$342$	−4.99786e8			−0.675604
$343$	−2.04550e8	−	1.48614e8i	−0.273697	−	0.198853i
$344$	2.40356e8	−	1.74629e8i	0.318347	−	0.231292i
$345$	2.36899e8	+	7.29100e8i	0.310596	+	0.955917i
$346$	−3.00837e8			−0.390450
$347$	1.41358e8			0.181622			0.0908109	−	0.995868i	$-0.471054\pi$
$347$	1.41358e8			0.181622			0.0908109	+	0.995868i	$0.471054\pi$
$348$	7.38472e7	+	2.27278e8i	0.0939304	+	0.289088i
$349$	2.57324e8	−	7.91962e8i	0.324034	−	0.997276i	−0.647840	−	0.761776i	$-0.724327\pi$
$349$	2.57324e8	−	7.91962e8i	0.324034	−	0.997276i	0.971875	−	0.235499i	$-0.0756725\pi$
$350$	−2.31093e8	+	7.11233e8i	−0.288104	+	0.886693i
$351$	−1.11677e9	−	8.11382e8i	−1.37845	−	1.00150i
$352$	−8.39555e7	−	2.58389e8i	−0.102601	−	0.315772i
$353$	−1.64780e8	−	1.19720e8i	−0.199385	−	0.144862i	0.483613	−	0.875282i	$-0.339324\pi$
$353$	−1.64780e8	−	1.19720e8i	−0.199385	−	0.144862i	−0.682998	+	0.730420i	$0.739324\pi$
$354$	8.40315e8	−	6.10524e8i	1.00677	−	0.731462i
$355$	9.77322e7	−	3.00789e8i	0.115941	−	0.356831i
$356$	4.68099e7	−	3.40094e7i	0.0549874	−	0.0399507i
$357$	8.90397e8	−	6.46911e8i	1.03573	−	0.752499i
$358$	−6.53157e7	+	2.01021e8i	−0.0752362	+	0.231553i
$359$	−3.64306e8	+	2.64684e8i	−0.415562	+	0.301924i	−0.775850	−	0.630918i	$-0.782679\pi$
$359$	−3.64306e8	+	2.64684e8i	−0.415562	+	0.301924i	0.360288	+	0.932841i	$0.382679\pi$
$360$	1.79956e8	+	1.30745e8i	0.203286	+	0.147696i
$361$	−2.18107e8	−	6.71266e8i	−0.244003	−	0.750964i
$362$	5.32953e8	+	3.87213e8i	0.590485	+	0.429013i
$363$	−1.24986e9	+	3.84667e9i	−1.37147	+	4.22096i
$364$	−1.90083e8	+	5.85014e8i	−0.206580	+	0.635787i
$365$	5.96923e7	+	1.83714e8i	0.0642529	+	0.197750i
$366$	7.20462e8			0.768117
$367$	8.85878e8			0.935498			0.467749	−	0.883861i	$-0.345065\pi$
$367$	8.85878e8			0.935498			0.467749	+	0.883861i	$0.345065\pi$
$368$	1.23913e8	+	3.81364e8i	0.129613	+	0.398908i
$369$	−1.78925e9	+	1.29997e9i	−1.85387	+	1.34691i
$370$	2.77799e8	+	2.01833e8i	0.285118	+	0.207151i
$371$	−1.11214e9			−1.13071
$372$	−6.22858e8	−	6.09820e8i	−0.627320	−	0.614188i
$373$	−6.09403e8			−0.608028			−0.304014	−	0.952668i	$-0.598327\pi$
$373$	−6.09403e8			−0.608028			−0.304014	+	0.952668i	$0.598327\pi$
$374$	5.31131e8	+	3.85890e8i	0.524990	+	0.381428i
$375$	9.32268e8	−	6.77332e8i	0.912917	−	0.663273i
$376$	−3.54687e7	−	1.09161e8i	−0.0344103	−	0.105904i
$377$	3.22748e8			0.310219
$378$	−2.10701e9			−2.00653
$379$	−3.49491e8	−	1.07562e9i	−0.329760	−	1.01490i	−0.969246	−	0.246094i	$-0.920853\pi$
$379$	−3.49491e8	−	1.07562e9i	−0.329760	−	1.01490i	0.639486	−	0.768803i	$-0.279147\pi$
$380$	2.58646e7	−	7.96031e7i	0.0241804	−	0.0744196i
$381$	5.28177e8	−	1.62556e9i	0.489263	−	1.50580i
$382$	3.22281e8	+	2.34151e8i	0.295810	+	0.214918i
$383$	2.60341e8	+	8.01246e8i	0.236781	+	0.728736i	0.996880	+	0.0789294i	$0.0251502\pi$
$383$	2.60341e8	+	8.01246e8i	0.236781	+	0.728736i	−0.760099	+	0.649807i	$0.774850\pi$
$384$	1.39316e8	+	1.01219e8i	0.125557	+	0.0912226i
$385$	−8.66252e8	+	6.29369e8i	−0.773627	+	0.562073i
$386$	2.95347e8	−	9.08985e8i	0.261383	−	0.804454i
$387$	2.13860e9	−	1.55378e9i	1.87560	−	1.36270i
$388$	−2.13714e8	+	1.55272e8i	−0.185747	+	0.134953i
$389$	4.62286e8	−	1.42277e9i	0.398187	−	1.22549i	−0.528264	−	0.849080i	$-0.677157\pi$
$389$	4.62286e8	−	1.42277e9i	0.398187	−	1.22549i	0.926451	−	0.376414i	$-0.122843\pi$
$390$	3.59716e8	−	2.61349e8i	0.307067	−	0.223097i
$391$	−7.83914e8	−	5.69547e8i	−0.663208	−	0.481849i
$392$	1.59839e8	+	4.91933e8i	0.134024	+	0.412482i
$393$	−9.83440e8	−	7.14511e8i	−0.817286	−	0.593793i
$394$	2.69939e8	−	8.30786e8i	0.222346	−	0.684309i
$395$	−1.07553e8	+	3.31014e8i	−0.0878077	+	0.270244i
$396$	−7.47005e8	−	2.29904e9i	−0.604492	−	1.86043i
$397$	2.06980e9			1.66020			0.830101	−	0.557613i	$-0.188283\pi$
$397$	2.06980e9			1.66020			0.830101	+	0.557613i	$0.188283\pi$
$398$	7.12065e8			0.566146
$399$	4.71217e8	+	1.45026e9i	0.371378	+	1.14298i
$400$	2.28748e8	−	1.66195e8i	0.178709	−	0.129840i
$401$	1.94077e9	+	1.41005e9i	1.50304	+	1.09202i	0.969153	+	0.246460i	$0.0792674\pi$
$401$	1.94077e9	+	1.41005e9i	1.50304	+	1.09202i	0.533882	+	0.845559i	$0.320733\pi$
$402$	−1.94812e9			−1.49563
$403$	−1.04323e9	+	5.45527e8i	−0.793986	+	0.415191i
$404$	−6.69582e8			−0.505207
$405$	4.63481e8	+	3.36739e8i	0.346689	+	0.251884i
$406$	3.98549e8	−	2.89563e8i	0.295556	−	0.214734i
$407$	−1.15316e9	−	3.54906e9i	−0.847829	−	2.60935i
$408$	−4.16122e8			−0.303326
$409$	1.95925e9			1.41598			0.707992	−	0.706220i	$-0.249601\pi$
$409$	1.95925e9			1.41598			0.707992	+	0.706220i	$0.249601\pi$
$410$	−1.14455e8	−	3.52257e8i	−0.0820147	−	0.252415i
$411$	−6.12902e8	+	1.88632e9i	−0.435456	+	1.34020i
$412$	−1.13135e8	+	3.48192e8i	−0.0796994	+	0.245289i
$413$	−1.73226e9	−	1.25856e9i	−1.21001	−	0.879124i
$414$	1.10253e9	+	3.39324e9i	0.763640	+	2.35024i
$415$	−6.60791e8	−	4.80093e8i	−0.453832	−	0.329729i
$416$	1.88153e8	−	1.36702e8i	0.128140	−	0.0930993i
$417$	−6.39782e8	+	1.96905e9i	−0.432072	+	1.32978i
$418$	−7.35892e8	+	5.34657e8i	−0.492830	+	0.358062i
$419$	1.15920e9	−	8.42207e8i	0.769855	−	0.559332i	−0.132062	−	0.991241i	$-0.542160\pi$
$419$	1.15920e9	−	8.42207e8i	0.769855	−	0.559332i	0.901917	+	0.431909i	$0.142160\pi$
$420$	2.09722e8	−	6.45459e8i	0.138125	−	0.425105i
$421$	−6.77209e8	+	4.92021e8i	−0.442318	+	0.321363i	−0.786555	−	0.617520i	$-0.788138\pi$
$421$	−6.77209e8	+	4.92021e8i	−0.442318	+	0.321363i	0.344237	+	0.938883i	$0.388138\pi$
$422$	1.04771e9	+	7.61207e8i	0.678653	+	0.493070i
$423$	−3.15587e8	−	9.71278e8i	−0.202735	−	0.623954i
$424$	3.40183e8	+	2.47157e8i	0.216736	+	0.157468i
$425$	−2.11135e8	+	6.49806e8i	−0.133413	+	0.410603i
$426$	6.73205e8	−	2.07191e9i	0.421904	−	1.29849i
$427$	−4.58950e8	−	1.41250e9i	−0.285278	−	0.877995i
$428$	1.06004e9			0.653532
$429$	−4.83209e9			−2.95484
$430$	1.36802e8	+	4.21034e8i	0.0829762	+	0.255375i
$431$	1.16370e9	−	8.45474e8i	0.700114	−	0.508663i	−0.179855	−	0.983693i	$-0.557563\pi$
$431$	1.16370e9	−	8.45474e8i	0.700114	−	0.508663i	0.879969	+	0.475030i	$0.157563\pi$
$432$	6.44495e8	+	4.68253e8i	0.384615	+	0.279439i
$433$	−7.09652e6			−0.00420086			−0.00210043	−	0.999998i	$-0.500669\pi$
$433$	−7.09652e6			−0.00420086			−0.00210043	+	0.999998i	$0.500669\pi$
$434$	−7.98810e8	+	1.60962e9i	−0.469061	+	0.945166i
$435$	−3.56095e8			−0.207421
$436$	9.82302e8	+	7.13684e8i	0.567600	+	0.412385i
$437$	1.08613e9	−	7.89118e8i	0.622581	−	0.452332i
$438$	4.11176e8	+	1.26547e9i	0.233813	+	0.719601i
$439$	−1.94889e8			−0.109941			−0.0549706	−	0.998488i	$-0.517507\pi$
$439$	−1.94889e8			−0.109941			−0.0549706	+	0.998488i	$0.517507\pi$
$440$	4.04838e8			0.226567
$441$	1.42219e9	+	4.37704e9i	0.789626	+	2.43022i
$442$	−1.73666e8	+	5.34488e8i	−0.0956613	+	0.294415i
$443$	−5.73755e8	+	1.76584e9i	−0.313555	+	0.965023i	0.662790	+	0.748805i	$0.269372\pi$
$443$	−5.73755e8	+	1.76584e9i	−0.313555	+	0.965023i	−0.976345	+	0.216218i	$0.930628\pi$
$444$	1.91355e9	+	1.39028e9i	1.03753	+	0.753808i
$445$	2.66426e7	+	8.19975e7i	0.0143323	+	0.0441103i
$446$	−1.13720e9	−	8.26225e8i	−0.606967	−	0.440987i
$447$	2.95109e9	−	2.14409e9i	1.56281	−	1.13545i
$448$	1.09698e8	−	3.37615e8i	0.0576401	−	0.177398i
$449$	1.02731e9	−	7.46382e8i	0.535596	−	0.389134i	−0.286851	−	0.957975i	$-0.592608\pi$
$449$	1.02731e9	−	7.46382e8i	0.535596	−	0.389134i	0.822447	+	0.568842i	$0.192608\pi$
$450$	2.03531e9	−	1.47874e9i	1.05290	−	0.764978i
$451$	−1.24385e9	+	3.82818e9i	−0.638485	+	1.96505i
$452$	−9.84662e8	+	7.15399e8i	−0.501536	+	0.364388i
$453$	4.52026e9	+	3.28416e9i	2.28465	+	1.65990i
$454$	−4.23847e8	−	1.30447e9i	−0.212576	−	0.654241i
$455$	−7.41535e8	−	5.38757e8i	−0.369056	−	0.268135i
$456$	1.78162e8	−	5.48326e8i	0.0879910	−	0.270808i
$457$	−9.64707e8	+	2.96906e9i	−0.472812	+	1.45517i	0.376073	+	0.926590i	$0.377274\pi$
$457$	−9.64707e8	+	2.96906e9i	−0.472812	+	1.45517i	−0.848886	+	0.528576i	$0.822726\pi$
$458$	4.73759e8	+	1.45808e9i	0.230425	+	0.709174i
$459$	−1.92504e9			−0.929170
$460$	−5.97513e8			−0.286217
$461$	−1.07759e9	−	3.31649e9i	−0.512273	−	1.57661i	−0.788190	−	0.615433i	$-0.788981\pi$
$461$	−1.07759e9	−	3.31649e9i	−0.512273	−	1.57661i	0.275917	−	0.961182i	$-0.411019\pi$
$462$	−5.96696e9	+	4.33525e9i	−2.81518	+	2.04535i
$463$	−1.23503e9	−	8.97300e8i	−0.578287	−	0.420150i	0.259819	−	0.965657i	$-0.416337\pi$
$463$	−1.23503e9	−	8.97300e8i	−0.578287	−	0.420150i	−0.838106	+	0.545507i	$0.816337\pi$
$464$	−1.86259e8			−0.0865576
$465$	1.15102e9	−	6.01892e8i	0.530881	−	0.277609i
$466$	−1.53856e9			−0.704310
$467$	−2.29808e9	−	1.66965e9i	−1.04413	−	0.758608i	−0.0730464	−	0.997329i	$-0.523272\pi$
$467$	−2.29808e9	−	1.66965e9i	−1.04413	−	0.758608i	−0.971088	+	0.238720i	$0.923272\pi$
$468$	1.67412e9	−	1.21632e9i	0.754963	−	0.548513i
$469$	1.24100e9	+	3.81940e9i	0.555477	+	1.70958i
$470$	1.71032e8			0.0759862
$471$	−9.43978e8			−0.416283
$472$	2.50169e8	+	7.69941e8i	0.109506	+	0.337024i
$473$	1.48671e9	−	4.57562e9i	0.645970	−	1.98809i
$474$	−7.40852e8	+	2.28011e9i	−0.319527	+	0.983403i
$475$	−7.65856e8	−	5.56427e8i	−0.327883	−	0.238221i
$476$	2.65079e8	+	8.15829e8i	0.112655	+	0.346717i
$477$	3.02682e9	+	2.19911e9i	1.27695	+	0.927755i
$478$	3.96386e8	−	2.87991e8i	0.166005	−	0.120610i
$479$	−1.46304e8	+	4.50277e8i	−0.0608248	+	0.187200i	−0.976852	−	0.213917i	$-0.931378\pi$
$479$	−1.46304e8	+	4.50277e8i	−0.0608248	+	0.187200i	0.916027	+	0.401117i	$0.131378\pi$
$480$	−2.07594e8	+	1.50826e8i	−0.0856782	+	0.0622489i
$481$	2.58435e9	−	1.87764e9i	1.05887	−	0.769316i
$482$	−1.52470e8	+	4.69254e8i	−0.0620182	+	0.190872i
$483$	8.80684e9	−	6.39854e9i	3.55635	−	2.58384i
$484$	−2.55037e9	−	1.85295e9i	−1.02245	−	0.742857i
$485$	−1.21638e8	−	3.74365e8i	−0.0484144	−	0.149004i
$486$	4.39626e8	+	3.19407e8i	0.173723	+	0.126217i
$487$	−1.22713e9	+	3.77673e9i	−0.481439	+	1.48172i	0.355635	+	0.934625i	$0.384265\pi$
$487$	−1.22713e9	+	3.77673e9i	−0.481439	+	1.48172i	−0.837074	+	0.547090i	$0.815735\pi$
$488$	−1.73524e8	+	5.34053e8i	−0.0675913	+	0.208025i
$489$	−3.33355e8	−	1.02596e9i	−0.128922	−	0.396780i
$490$	−7.70751e8			−0.295956
$491$	−1.24490e9			−0.474622			−0.237311	−	0.971434i	$-0.576266\pi$
$491$	−1.24490e9			−0.474622			−0.237311	+	0.971434i	$0.576266\pi$
$492$	−7.88396e8	−	2.42643e9i	−0.298447	−	0.918524i
$493$	3.64127e8	−	2.64554e8i	0.136864	−	0.0994375i
$494$	−6.29944e8	−	4.57681e8i	−0.235103	−	0.170812i
$495$	3.60209e9			1.33486
$496$	6.02054e8	−	3.14827e8i	0.221539	−	0.115847i
$497$	−4.49094e9			−1.64093
$498$	−4.55169e9	−	3.30700e9i	−1.65147	−	1.19986i
$499$	7.10859e8	−	5.16469e8i	0.256113	−	0.186077i	−0.452319	−	0.891856i	$-0.649403\pi$
$499$	7.10859e8	−	5.16469e8i	0.256113	−	0.186077i	0.708432	+	0.705779i	$0.249403\pi$
$500$	2.77544e8	+	8.54193e8i	0.0992972	+	0.305605i
$501$	−2.34165e9			−0.831937
$502$	1.67703e9			0.591668
$503$	1.14826e8	+	3.53398e8i	0.0402302	+	0.123816i	0.969155	−	0.246454i	$-0.0792653\pi$
$503$	1.14826e8	+	3.53398e8i	0.0402302	+	0.123816i	−0.928924	+	0.370269i	$0.879265\pi$
$504$	9.76050e8	−	3.00397e9i	0.339598	−	1.04517i
$505$	3.08319e8	−	9.48908e8i	0.106532	−	0.327872i
$506$	5.25337e9	+	3.81680e9i	1.80265	+	1.30970i
$507$	3.13987e8	+	9.66353e8i	0.107000	+	0.329312i
$508$	1.07776e9	+	7.83038e8i	0.364753	+	0.265009i
$509$	1.96083e8	−	1.42462e8i	0.0659063	−	0.0478838i	−0.554344	−	0.832287i	$-0.687031\pi$
$509$	1.96083e8	−	1.42462e8i	0.0659063	−	0.0478838i	0.620251	+	0.784404i	$0.287031\pi$
$510$	1.91609e8	−	5.89713e8i	0.0639619	−	0.196854i
$511$	2.21909e9	−	1.61226e9i	0.735702	−	0.534519i
$512$	−1.08584e8	+	7.88912e7i	−0.0357538	+	0.0259767i
$513$	8.24203e8	−	2.53664e9i	0.269540	−	0.829559i
$514$	−2.03787e9	+	1.48060e9i	−0.661919	+	0.480912i
$515$	−4.41351e8	−	3.20660e8i	−0.142383	−	0.103448i
$516$	9.42329e8	+	2.90019e9i	0.301946	+	0.929293i
$517$	−1.50372e9	−	1.09252e9i	−0.478576	−	0.347706i
$518$	1.50674e9	−	4.63726e9i	0.476303	−	1.46591i
$519$	9.54196e8	−	2.93671e9i	0.299607	−	0.922095i
$520$	1.07090e8	+	3.29591e8i	0.0333994	+	0.102793i
$521$	−5.41983e9			−1.67901			−0.839506	−	0.543351i	$-0.817155\pi$
$521$	−5.41983e9			−1.67901			−0.839506	+	0.543351i	$0.817155\pi$
$522$	−1.65727e9			−0.509971
$523$	−1.32288e9	−	4.07140e9i	−0.404356	−	1.24448i	−0.921431	−	0.388541i	$-0.872979\pi$
$523$	−1.32288e9	−	4.07140e9i	−0.404356	−	1.24448i	0.517075	−	0.855940i	$-0.327021\pi$
$524$	7.66504e8	−	5.56898e8i	0.232731	−	0.169089i
$525$	−6.20992e9	−	4.51177e9i	−1.87296	−	1.36079i
$526$	3.00384e9			0.899966
$527$	−7.29820e8	+	1.47060e9i	−0.217209	+	0.437680i
$528$	2.78863e9			0.824463
$529$	−4.99907e9	−	3.63203e9i	−1.46823	−	1.06673i
$530$	−5.06905e8	+	3.68288e8i	−0.147898	+	0.107454i
$531$	2.22591e9	+	6.85065e9i	0.645174	+	1.98564i
$532$	−1.18852e9			−0.342227
$533$	−3.44567e9			−0.985663
$534$	1.83521e8	+	5.64820e8i	0.0521544	+	0.160515i
$535$	−4.88109e8	+	1.50224e9i	−0.137809	+	0.424133i
$536$	4.69208e8	−	1.44407e9i	0.131610	−	0.405054i
$537$	−1.75516e9	−	1.27520e9i	−0.489109	−	0.355359i
$538$	−1.29428e9	−	3.98338e9i	−0.358336	−	1.10284i
$539$	6.77649e9	+	4.92341e9i	1.86399	+	1.35427i
$540$	−9.60359e8	+	6.97742e8i	−0.262455	+	0.190685i
$541$	1.60369e9	−	4.93565e9i	0.435442	−	1.34015i	−0.457192	−	0.889368i	$-0.651145\pi$
$541$	1.60369e9	−	4.93565e9i	0.435442	−	1.34015i	0.892633	−	0.450783i	$-0.148855\pi$
$542$	1.12031e9	−	8.13952e8i	0.302232	−	0.219584i
$543$	−5.47032e9	+	3.97442e9i	−1.46627	+	1.06531i
$544$	1.00224e8	−	3.08456e8i	0.0266915	−	0.0821481i
$545$	−1.46372e9	+	1.06346e9i	−0.387321	+	0.281405i
$546$	−5.10788e9	−	3.71109e9i	−1.34297	−	0.975726i
$547$	8.82583e8	+	2.71631e9i	0.230569	+	0.709617i	0.997678	+	0.0681012i	$0.0216941\pi$
$547$	8.82583e8	+	2.71631e9i	0.230569	+	0.709617i	−0.767110	+	0.641516i	$0.778306\pi$
$548$	−1.25064e9	−	9.08644e8i	−0.324639	−	0.235864i
$549$	−1.54395e9	+	4.75180e9i	−0.398227	+	1.22562i
$550$	1.41491e9	−	4.35465e9i	0.362627	−	1.11605i
$551$	1.92704e8	+	5.93081e8i	0.0490749	+	0.151037i
$552$	−4.11582e9			−1.04153
$553$	4.94221e9			1.24275
$554$	4.73614e8	+	1.45763e9i	0.118342	+	0.364221i
$555$	−2.85137e9	+	2.07164e9i	−0.707993	+	0.514387i
$556$	−1.30549e9	−	9.48495e8i	−0.322116	−	0.234031i
$557$	−1.28231e9			−0.314413			−0.157207	−	0.987566i	$-0.550249\pi$
$557$	−1.28231e9			−0.314413			−0.157207	+	0.987566i	$0.550249\pi$
$558$	5.35685e9	−	2.80121e9i	1.30524	−	0.682536i
$559$	4.11843e9			0.997219
$560$	4.27944e8	+	3.10920e8i	0.102974	+	0.0748152i
$561$	−5.45162e9	+	3.96083e9i	−1.30363	+	0.947144i
$562$	1.23292e9	+	3.79452e9i	0.292992	+	0.901737i
$563$	−1.19770e9			−0.282858			−0.141429	−	0.989948i	$-0.545170\pi$
$563$	−1.19770e9			−0.282858			−0.141429	+	0.989948i	$0.545170\pi$
$564$	1.17811e9			0.276509
$565$	−5.60436e8	−	1.72484e9i	−0.130724	−	0.402328i
$566$	4.49059e8	−	1.38206e9i	0.104099	−	0.320383i
$567$	2.51384e9	−	7.73682e9i	0.579159	−	1.78247i
$568$	1.37369e9	+	9.98045e8i	0.314536	+	0.228524i
$569$	−1.15041e9	−	3.54061e9i	−0.261795	−	0.805722i	−0.992414	−	0.122937i	$-0.960769\pi$
$569$	−1.15041e9	−	3.54061e9i	−0.261795	−	0.805722i	0.730619	−	0.682785i	$-0.239231\pi$
$570$	6.95031e8	+	5.04970e8i	0.157196	+	0.114210i
$571$	−3.46811e9	+	2.51973e9i	−0.779590	+	0.566406i	−0.904856	−	0.425718i	$-0.860022\pi$
$571$	−3.46811e9	+	2.51973e9i	−0.779590	+	0.566406i	0.125266	+	0.992123i	$0.460022\pi$
$572$	1.16382e9	−	3.58185e9i	0.260015	−	0.800243i
$573$	−3.30794e9	+	2.40336e9i	−0.734541	+	0.533676i
$574$	−4.25493e9	+	3.09139e9i	−0.939076	+	0.682278i
$575$	−2.08831e9	+	6.42717e9i	−0.458098	+	1.40988i
$576$	−9.66144e8	+	7.01944e8i	−0.210651	+	0.153047i
$577$	4.80251e9	+	3.48923e9i	1.04077	+	0.756161i	0.970435	−	0.241363i	$-0.0775945\pi$
$577$	4.80251e9	+	3.48923e9i	1.04077	+	0.756161i	0.0703309	+	0.997524i	$0.477594\pi$
$578$	−7.72228e8	−	2.37667e9i	−0.166341	−	0.511944i
$579$	7.93654e9	+	5.76623e9i	1.69925	+	1.23457i
$580$	8.57659e7	−	2.63960e8i	0.0182523	−	0.0561747i
$581$	−3.58402e9	+	1.10305e10i	−0.758147	+	2.33334i
$582$	−8.37876e8	−	2.57872e9i	−0.176177	−	0.542217i
$583$	6.80929e9			1.42319
$584$	−1.03708e9			−0.215460
$585$	9.52851e8	+	2.93257e9i	0.196779	+	0.605625i
$586$	2.17597e9	−	1.58093e9i	0.446694	−	0.324542i
$587$	−7.26142e9	−	5.27573e9i	−1.48180	−	1.07659i	−0.976973	−	0.213364i	$-0.931558\pi$
$587$	−7.26142e9	−	5.27573e9i	−1.48180	−	1.07659i	−0.504823	−	0.863223i	$-0.668442\pi$
$588$	−5.30913e9			−1.07697
$589$	−1.62535e9	−	1.59132e9i	−0.327750	−	0.320889i
$590$	−1.20633e9			−0.241815
$591$	7.25377e9	+	5.27017e9i	1.44546	+	1.05019i
$592$	−1.49144e9	+	1.08360e9i	−0.295448	+	0.214656i
$593$	−2.30678e9	−	7.09954e9i	−0.454271	−	1.39810i	−0.871989	−	0.489525i	$-0.837170\pi$
$593$	−2.30678e9	−	7.09954e9i	−0.454271	−	1.39810i	0.417719	−	0.908576i	$-0.362830\pi$
$594$	1.29006e10			2.52555
$595$	−1.27822e9			−0.248770
$596$	8.78565e8	+	2.70395e9i	0.169986	+	0.523162i
$597$	−2.25853e9	+	6.95103e9i	−0.434425	+	1.33702i
$598$	−1.71771e9	+	5.28658e9i	−0.328471	+	1.01093i
$599$	8.22570e8	+	5.97632e8i	0.156379	+	0.113616i	0.663223	−	0.748422i	$-0.269188\pi$
$599$	8.22570e8	+	5.97632e8i	0.156379	+	0.113616i	−0.506844	+	0.862038i	$0.669188\pi$
$600$	8.96820e8	+	2.76013e9i	0.169502	+	0.521675i
$601$	6.12908e9	+	4.45303e9i	1.15169	+	0.836749i	0.988704	−	0.149880i	$-0.0478887\pi$
$601$	6.12908e9	+	4.45303e9i	1.15169	+	0.836749i	0.162982	+	0.986629i	$0.447889\pi$
$602$	5.08569e9	−	3.69497e9i	0.950085	−	0.690277i
$603$	4.17484e9	−	1.28488e10i	0.775405	−	2.38645i
$604$	−3.52314e9	+	2.55971e9i	−0.650581	+	0.472675i
$605$	3.80029e9	−	2.76107e9i	0.697707	−	0.506914i
$606$	2.12378e9	−	6.53632e9i	0.387664	−	1.19311i
$607$	6.37332e9	−	4.63049e9i	1.15666	−	0.840362i	0.167307	−	0.985905i	$-0.446493\pi$
$607$	6.37332e9	−	4.63049e9i	1.15666	−	0.840362i	0.989352	+	0.145543i	$0.0464930\pi$
$608$	3.63544e8	+	2.64130e8i	0.0655986	+	0.0476602i
$609$	1.56253e9	+	4.80898e9i	0.280329	+	0.862765i
$610$	−6.76939e8	−	4.91825e8i	−0.120752	−	0.0877316i
$611$	4.91677e8	−	1.51323e9i	0.0872039	−	0.268386i
$612$	8.91751e8	−	2.74453e9i	0.157258	−	0.483992i
$613$	−1.19792e9	−	3.68681e9i	−0.210046	−	0.646456i	−0.999468	−	0.0326049i	$-0.989620\pi$
$613$	−1.19792e9	−	3.68681e9i	−0.210046	−	0.646456i	0.789422	−	0.613851i	$-0.210380\pi$
$614$	3.98485e9			0.694741
$615$	3.80169e9			0.659042
$616$	−1.77642e9	−	5.46725e9i	−0.306205	−	0.942402i
$617$	2.32698e9	−	1.69065e9i	0.398836	−	0.289772i	−0.370230	−	0.928940i	$-0.620721\pi$
$617$	2.32698e9	−	1.69065e9i	0.398836	−	0.289772i	0.769067	+	0.639168i	$0.220721\pi$
$618$	−3.04014e9	−	2.20879e9i	−0.518124	−	0.376439i
$619$	8.29052e9			1.40496			0.702481	−	0.711702i	$-0.252076\pi$
$619$	8.29052e9			1.40496			0.702481	+	0.711702i	$0.252076\pi$
$620$	1.68936e8	+	9.98176e8i	0.0284677	+	0.168204i
$621$	−1.90404e10			−3.19047
$622$	3.18940e9	+	2.31724e9i	0.531426	+	0.386104i
$623$	9.90452e8	−	7.19605e8i	0.164106	−	0.119230i
$624$	7.37667e8	+	2.27030e9i	0.121539	+	0.374057i
$625$	4.05466e9			0.664316
$626$	−4.41636e9			−0.719539
$627$	−2.88511e9	−	8.87945e9i	−0.467440	−	1.43863i
$628$	2.27358e8	−	6.99737e8i	0.0366313	−	0.112740i
$629$	1.37660e9	−	4.23675e9i	0.220563	−	0.678822i
$630$	3.80769e9	+	2.76645e9i	0.606693	+	0.440788i
$631$	8.14012e8	+	2.50527e9i	0.128982	+	0.396965i	0.994605	−	0.103730i	$-0.0330779\pi$
$631$	8.14012e8	+	2.50527e9i	0.128982	+	0.396965i	−0.865624	+	0.500695i	$0.833078\pi$
$632$	−1.51173e9	−	1.09833e9i	−0.238212	−	0.173071i
$633$	−1.07539e10	+	7.81314e9i	−1.68520	+	1.22437i
$634$	1.29859e9	−	3.99664e9i	0.202376	−	0.622849i
$635$	−1.60596e9	+	1.16680e9i	−0.248902	+	0.180838i
$636$	−3.49169e9	+	2.53686e9i	−0.538190	+	0.391018i
$637$	−2.21573e9	+	6.81932e9i	−0.339648	+	1.04533i
$638$	−2.44019e9	+	1.77290e9i	−0.372006	+	0.270279i
$639$	1.22226e10	+	8.88023e9i	1.85315	+	1.34639i
$640$	−6.18025e7	−	1.90209e8i	−0.00931915	−	0.0286814i
$641$	2.85262e9	+	2.07255e9i	0.427800	+	0.310815i	0.780769	−	0.624820i	$-0.214828\pi$
$641$	2.85262e9	+	2.07255e9i	0.427800	+	0.310815i	−0.352969	+	0.935635i	$0.614828\pi$
$642$	−3.36222e9	+	1.03478e10i	−0.501480	+	1.54340i
$643$	1.31477e9	−	4.04645e9i	0.195035	−	0.600255i	−0.804941	−	0.593354i	$-0.797803\pi$
$643$	1.31477e9	−	4.04645e9i	0.195035	−	0.600255i	0.999976	−	0.00690111i	$-0.00219671\pi$
$644$	2.62187e9	+	8.06929e9i	0.386822	+	1.19051i
$645$	−4.54396e9			−0.666769
$646$	−1.08587e9			−0.158476
$647$	−3.42745e8	−	1.05486e9i	−0.0497515	−	0.153119i	0.923094	−	0.384574i	$-0.125652\pi$
$647$	−3.42745e8	−	1.05486e9i	−0.0497515	−	0.153119i	−0.972846	+	0.231454i	$0.925652\pi$
$648$	−2.48833e9	+	1.80788e9i	−0.359249	+	0.261010i
$649$	1.06061e10	+	7.70578e9i	1.52300	+	1.10652i
$650$	3.91953e9			0.559806
$651$	−1.31791e10	−	1.29032e10i	−1.87220	−	1.83301i
$652$	8.40797e8			0.118802
$653$	3.31506e9	+	2.40853e9i	0.465903	+	0.338498i	0.795842	−	0.605504i	$-0.207028\pi$
$653$	3.31506e9	+	2.40853e9i	0.465903	+	0.338498i	−0.329940	+	0.944002i	$0.607028\pi$
$654$	−1.00825e10	+	7.32537e9i	−1.40944	+	1.02402i
$655$	4.36268e8	+	1.34269e9i	0.0606609	+	0.186695i
$656$	1.98852e9			0.275021
$657$	−9.22754e9			−1.26943
$658$	−7.50483e8	−	2.30975e9i	−0.102695	−	0.316063i
$659$	−3.28014e9	+	1.00952e10i	−0.446472	+	1.37410i	0.434390	+	0.900725i	$0.356964\pi$
$659$	−3.28014e9	+	1.00952e10i	−0.446472	+	1.37410i	−0.880862	+	0.473374i	$0.843036\pi$
$660$	−1.28406e9	+	3.95194e9i	−0.173853	+	0.535065i
$661$	3.03857e9	+	2.20765e9i	0.409226	+	0.297320i	0.773289	−	0.634054i	$-0.218610\pi$
$661$	3.03857e9	+	2.20765e9i	0.409226	+	0.297320i	−0.364062	+	0.931375i	$0.618610\pi$
$662$	−2.84653e8	−	8.76072e8i	−0.0381340	−	0.117365i
$663$	−4.66673e9	−	3.39058e9i	−0.621893	−	0.451832i
$664$	3.54764e9	−	2.57751e9i	0.470275	−	0.341675i
$665$	5.47270e8	−	1.68432e9i	0.0721649	−	0.222101i
$666$	−1.32703e10	+	9.64145e9i	−1.74069	+	1.26469i
$667$	3.60155e9	−	2.61668e9i	0.469947	−	0.341437i
$668$	5.63991e8	−	1.73578e9i	0.0732073	−	0.225309i
$669$	1.16724e10	−	8.48050e9i	1.50719	−	1.09504i
$670$	1.83044e9	+	1.32989e9i	0.235122	+	0.170826i
$671$	2.81001e9	+	8.64831e9i	0.359070	+	1.10510i
$672$	2.94779e9	+	2.14169e9i	0.374717	+	0.272248i
$673$	2.66538e9	−	8.20320e9i	0.337059	−	1.03736i	−0.628639	−	0.777697i	$-0.716388\pi$
$673$	2.66538e9	−	8.20320e9i	0.337059	−	1.03736i	0.965699	−	0.259665i	$-0.0836122\pi$
$674$	−8.32251e8	+	2.56140e9i	−0.104700	+	0.322232i
$675$	4.14882e9	+	1.27687e10i	0.519231	+	1.59803i
$676$	−7.91947e8			−0.0986014
$677$	4.98884e9			0.617929			0.308965	−	0.951073i	$-0.400017\pi$
$677$	4.98884e9			0.617929			0.308965	+	0.951073i	$0.400017\pi$
$678$	−3.86042e9	−	1.18812e10i	−0.475698	−	1.46405i
$679$	−4.52197e9	+	3.28540e9i	−0.554349	+	0.402758i
$680$	3.90984e8	+	2.84066e8i	0.0476846	+	0.0346449i
$681$	1.40783e10			1.70819
$682$	4.89086e9	−	9.85516e9i	0.590391	−	1.18965i
$683$	2.67598e9			0.321374			0.160687	−	0.987005i	$-0.448629\pi$
$683$	2.67598e9			0.321374			0.160687	+	0.987005i	$0.448629\pi$
$684$	3.23468e9	+	2.35013e9i	0.386487	+	0.280799i
$685$	1.86357e9	−	1.35397e9i	0.221529	−	0.160950i
$686$	6.25050e8	+	1.92370e9i	0.0739231	+	0.227512i
$687$	−1.57362e10			−1.85161
$688$	−2.37677e9			−0.278245
$689$	1.80124e9	+	5.54365e9i	0.209800	+	0.645697i
$690$	1.89519e9	−	5.83280e9i	0.219625	−	0.675935i
$691$	−5.19349e8	+	1.59839e9i	−0.0598806	+	0.184294i	−0.976522	−	0.215416i	$-0.930889\pi$
$691$	−5.19349e8	+	1.59839e9i	−0.0598806	+	0.184294i	0.916642	+	0.399710i	$0.130889\pi$
$692$	1.94706e9	+	1.41462e9i	0.223361	+	0.162282i
$693$	−1.58059e10	−	4.86455e10i	−1.80407	−	5.55235i
$694$	−9.14890e8	−	6.64706e8i	−0.103899	−	0.0754869i
$695$	1.94531e9	−	1.41335e9i	0.219807	−	0.159699i
$696$	5.90777e8	−	1.81823e9i	0.0664189	−	0.204416i
$697$	−3.88744e9	+	2.82439e9i	−0.434860	+	0.315944i
$698$	−5.38946e9	+	3.91567e9i	−0.599862	+	0.435825i
$699$	4.88001e9	−	1.50191e10i	0.540443	−	1.66331i
$700$	4.84008e9	−	3.51653e9i	0.533347	−	0.387499i
$701$	−2.02973e9	−	1.47468e9i	−0.222548	−	0.161691i	0.470925	−	0.882173i	$-0.343920\pi$
$701$	−2.02973e9	−	1.47468e9i	−0.222548	−	0.161691i	−0.693473	+	0.720483i	$0.743920\pi$
$702$	3.41255e9	+	1.05027e10i	0.372305	+	1.14584i
$703$	4.99340e9	+	3.62792e9i	0.542067	+	0.393835i
$704$	−6.71644e8	+	2.06711e9i	−0.0725496	+	0.223285i
$705$	−5.42479e8	+	1.66958e9i	−0.0583070	+	0.179451i
$706$	5.03523e8	+	1.54968e9i	0.0538521	+	0.165740i
$707$	−1.41677e10			−1.50776
$708$	−8.30949e9			−0.879950
$709$	6.12796e8	+	1.88599e9i	0.0645735	+	0.198737i	0.978138	−	0.207957i	$-0.0666815\pi$
$709$	6.12796e8	+	1.88599e9i	0.0645735	+	0.198737i	−0.913564	+	0.406694i	$0.866681\pi$
$710$	−2.04693e9	+	1.48718e9i	−0.214634	+	0.155941i
$711$	−1.34508e10	−	9.77257e9i	−1.40347	−	1.01968i
$712$	−4.62882e8			−0.0480607
$713$	−7.21858e9	+	1.45456e10i	−0.745828	+	1.50285i
$714$	−8.80473e9			−0.905258
$715$	4.54018e9	+	3.29864e9i	0.464518	+	0.337492i
$716$	1.36799e9	−	9.93903e8i	0.139280	−	0.101192i
$717$	1.55405e9	+	4.78289e9i	0.157452	+	0.484588i
$718$	3.60246e9			0.363215
$719$	−1.65431e10			−1.65984			−0.829921	−	0.557882i	$-0.811614\pi$
$719$	−1.65431e10			−1.65984			−0.829921	+	0.557882i	$0.811614\pi$
$720$	−5.49896e8	−	1.69240e9i	−0.0549056	−	0.168982i
$721$	−2.39382e9	+	7.36741e9i	−0.237858	+	0.732051i
$722$	−1.74486e9	+	5.37013e9i	−0.172536	+	0.531012i
$723$	−4.09715e9	−	2.97676e9i	−0.403179	−	0.292927i
$724$	−1.62856e9	−	5.01219e9i	−0.159485	−	0.490843i
$725$	−2.53954e9	−	1.84509e9i	−0.247499	−	0.179818i
$726$	2.61774e10	−	1.90190e10i	2.53891	−	1.84463i
$727$	−5.39117e9	+	1.65923e10i	−0.520371	+	1.60154i	0.252921	+	0.967487i	$0.418609\pi$
$727$	−5.39117e9	+	1.65923e10i	−0.520371	+	1.60154i	−0.773292	+	0.634050i	$0.781391\pi$
$728$	3.98114e9	−	2.89247e9i	0.382426	−	0.277849i
$729$	6.11648e9	−	4.44388e9i	0.584730	−	0.424831i
$730$	4.77538e8	−	1.46971e9i	0.0454337	−	0.139831i
$731$	4.64646e9	−	3.37585e9i	0.439958	−	0.319648i
$732$	−4.66293e9	−	3.38782e9i	−0.439410	−	0.319250i
$733$	−3.30446e9	−	1.01701e10i	−0.309911	−	0.953807i	−0.977799	−	0.209546i	$-0.932802\pi$
$733$	−3.30446e9	−	1.01701e10i	−0.309911	−	0.953807i	0.667888	−	0.744262i	$-0.267198\pi$
$734$	−5.73353e9	−	4.16565e9i	−0.535162	−	0.388818i
$735$	2.44467e9	−	7.52391e9i	0.227098	−	0.698937i
$736$	9.91302e8	−	3.05091e9i	0.0916502	−	0.282070i
$737$	−7.59823e9	−	2.33849e10i	−0.699159	−	2.15179i
$738$	1.76931e10			1.62034
$739$	−2.57170e9			−0.234404			−0.117202	−	0.993108i	$-0.537392\pi$
$739$	−2.57170e9			−0.234404			−0.117202	+	0.993108i	$0.537392\pi$
$740$	−8.48879e8	−	2.61258e9i	−0.0770078	−	0.237006i
$741$	6.46584e9	−	4.69771e9i	0.583797	−	0.424153i
$742$	7.19794e9	+	5.22961e9i	0.646836	+	0.469954i
$743$	8.38895e9			0.750321			0.375160	−	0.926960i	$-0.377588\pi$
$743$	8.38895e9			0.750321			0.375160	+	0.926960i	$0.377588\pi$
$744$	1.16368e9	+	6.87569e9i	0.103592	+	0.612084i
$745$	−4.23648e9			−0.375369
$746$	3.94414e9	+	2.86558e9i	0.347829	+	0.252713i
$747$	3.15656e10	−	2.29338e10i	2.77072	−	2.01304i
$748$	−1.62299e9	−	4.99506e9i	−0.141795	−	0.436400i
$749$	2.24293e10			1.95043
$750$	−9.21877e9			−0.797919
$751$	−6.65234e9	−	2.04738e10i	−0.573106	−	1.76384i	−0.642540	−	0.766252i	$-0.722119\pi$
$751$	−6.65234e9	−	2.04738e10i	−0.573106	−	1.76384i	0.0694341	−	0.997587i	$-0.477881\pi$
$752$	−2.83750e8	+	8.73292e8i	−0.0243317	+	0.0748854i
$753$	−5.31921e9	+	1.63708e10i	−0.454009	+	1.39730i
$754$	−2.08887e9	−	1.51765e9i	−0.177464	−	0.128935i
$755$	−2.00525e9	−	6.17153e9i	−0.169572	−	0.521890i
$756$	1.36369e10	+	9.90778e9i	1.14786	+	0.833969i
$757$	1.65627e10	−	1.20335e10i	1.38770	−	1.00822i	0.391586	−	0.920142i	$-0.371927\pi$
$757$	1.65627e10	−	1.20335e10i	1.38770	−	1.00822i	0.996113	−	0.0880808i	$-0.0280734\pi$
$758$	−2.79592e9	+	8.60497e9i	−0.233176	+	0.717641i
$759$	−5.39214e10	+	3.91762e10i	−4.47626	+	3.25219i
$760$	−5.41715e8	+	3.93579e8i	−0.0447635	+	0.0325226i
$761$	3.42386e9	−	1.05375e10i	0.281624	−	0.866749i	−0.705767	−	0.708444i	$-0.749397\pi$
$761$	3.42386e9	−	1.05375e10i	0.281624	−	0.866749i	0.987390	−	0.158304i	$-0.0506027\pi$
$762$	−1.10623e10	+	8.03723e9i	−0.905738	+	0.658057i
$763$	2.07845e10	+	1.51009e10i	1.69397	+	1.23074i
$764$	−9.84802e8	−	3.03091e9i	−0.0798955	−	0.245893i
$765$	3.47883e9	+	2.52752e9i	0.280943	+	0.204117i
$766$	2.08273e9	−	6.40997e9i	0.167429	−	0.515294i
$767$	−3.46791e9	+	1.06731e10i	−0.277514	+	0.854099i
$768$	−4.25712e8	−	1.31021e9i	−0.0339118	−	0.104370i
$769$	−1.34120e10			−1.06353			−0.531765	−	0.846892i	$-0.678471\pi$
$769$	−1.34120e10			−1.06353			−0.531765	+	0.846892i	$0.678471\pi$
$770$	8.56597e9			0.676175
$771$	−7.98958e9	−	2.45894e10i	−0.627818	−	1.93222i
$772$	−6.18583e9	+	4.49427e9i	−0.483880	+	0.351559i
$773$	−1.85097e10	−	1.34481e10i	−1.44135	−	1.04720i	−0.987758	−	0.155995i	$-0.950142\pi$
$773$	−1.85097e10	−	1.34481e10i	−1.44135	−	1.04720i	−0.453594	−	0.891208i	$-0.649858\pi$
$774$	−2.11476e10			−1.63934
$775$	1.13274e10	+	1.67147e9i	0.874123	+	0.128986i
$776$	2.11332e9			0.162349
$777$	4.04889e10	+	2.94169e10i	3.09644	+	2.24969i
$778$	−9.68225e9	+	7.03457e9i	−0.737136	+	0.535561i
$779$	−2.05732e9	−	6.33177e9i	−0.155927	−	0.479893i
$780$	−3.55706e9			−0.268387
$781$	2.74966e10			2.06538
$782$	2.39543e9	+	7.37237e9i	0.179126	+	0.551294i
$783$	2.73302e9	−	8.41137e9i	0.203459	−	0.626182i
$784$	1.27871e9	−	3.93547e9i	0.0947689	−	0.291669i
$785$	8.86952e8	+	6.44409e8i	0.0654420	+	0.0475464i
$786$	3.00512e9	+	9.24882e9i	0.220741	+	0.679372i
$787$	−6.53573e8	−	4.74848e8i	−0.0477950	−	0.0347251i	0.563631	−	0.826027i	$-0.309404\pi$
$787$	−6.53573e8	−	4.74848e8i	−0.0477950	−	0.0347251i	−0.611426	+	0.791301i	$0.709404\pi$
$788$	−5.65367e9	+	4.10763e9i	−0.411613	+	0.299054i
$789$	−9.52756e9	+	2.93228e10i	−0.690577	+	2.12538i
$790$	2.25262e9	−	1.63662e9i	0.162552	−	0.118101i
$791$	−2.08345e10	+	1.51371e10i	−1.49680	+	1.08749i
$792$	−5.97604e9	+	1.83924e10i	−0.427440	+	1.31553i
$793$	−6.29753e9	+	4.57542e9i	−0.448450	+	0.325818i
$794$	−1.33960e10	−	9.73277e9i	−0.949737	−	0.690024i
$795$	−1.98735e9	−	6.11643e9i	−0.140278	−	0.431731i
$796$	−4.60858e9	−	3.34833e9i	−0.323870	−	0.235306i
$797$	1.52758e9	−	4.70142e9i	0.106881	−	0.328946i	−0.883286	−	0.468834i	$-0.844674\pi$
$797$	1.52758e9	−	4.70142e9i	0.106881	−	0.328946i	0.990167	+	0.139888i	$0.0446742\pi$
$798$	3.76973e9	−	1.16020e10i	0.262604	−	0.808211i
$799$	−6.85666e8	−	2.11026e9i	−0.0475553	−	0.146360i
$800$	−2.26199e9			−0.156198
$801$	−4.11855e9			−0.283159
$802$	−5.93047e9	−	1.82521e10i	−0.405956	−	1.24940i
$803$	−1.35868e10	+	9.87137e9i	−0.926002	+	0.672780i
$804$	1.26085e10	+	9.16062e9i	0.855594	+	0.621625i
$805$	−1.26428e10			−0.854196
$806$	9.31715e9	+	1.37484e9i	0.626773	+	0.0924868i
$807$	4.29902e10			2.87946
$808$	4.33363e9	+	3.14856e9i	0.289009	+	0.209978i
$809$	−1.41517e10	+	1.02818e10i	−0.939699	+	0.682731i	−0.948348	−	0.317232i	$-0.897247\pi$
$809$	−1.41517e10	+	1.02818e10i	−0.939699	+	0.682731i	0.00864949	+	0.999963i	$0.497247\pi$
$810$	−1.41627e9	−	4.35884e9i	−0.0936374	−	0.288186i
$811$	−1.21775e10			−0.801650			−0.400825	−	0.916155i	$-0.631276\pi$
$811$	−1.21775e10			−0.801650			−0.400825	+	0.916155i	$0.631276\pi$
$812$	−3.94107e9			−0.258326
$813$	4.39224e9	+	1.35179e10i	0.286661	+	0.882253i
$814$	−9.22526e9	+	2.83924e10i	−0.599506	+	1.84509i
$815$	−3.87158e8	+	1.19155e9i	−0.0250516	+	0.0771010i
$816$	2.69320e9	+	1.95672e9i	0.173521	+	0.126071i
$817$	2.45900e9	+	7.56803e9i	0.157755	+	0.485519i
$818$	−1.26805e10	−	9.21295e9i	−0.810030	−	0.588521i
$819$	3.54227e10	−	2.57361e10i	2.25314	−	1.63700i
$820$	−9.15641e8	+	2.81805e9i	−0.0579932	+	0.178485i
$821$	1.02305e10	−	7.43293e9i	0.645205	−	0.468769i	−0.216429	−	0.976298i	$-0.569441\pi$
$821$	1.02305e10	−	7.43293e9i	0.645205	−	0.468769i	0.861634	+	0.507529i	$0.169441\pi$
$822$	1.28368e10	−	9.32646e9i	0.806129	−	0.585687i
$823$	−1.99224e9	+	6.13148e9i	−0.124578	+	0.383412i	−0.993824	−	0.110968i	$-0.964605\pi$
$823$	−1.99224e9	+	6.13148e9i	−0.124578	+	0.383412i	0.869246	+	0.494380i	$0.164605\pi$
$824$	2.36952e9	−	1.72156e9i	0.147542	−	0.107195i
$825$	3.80214e10	+	2.76241e10i	2.35743	+	1.71277i
$826$	5.29333e9	+	1.62912e10i	0.326813	+	1.00583i
$827$	−3.12185e9	−	2.26816e9i	−0.191930	−	0.139445i	0.487670	−	0.873028i	$-0.337847\pi$
$827$	−3.12185e9	−	2.26816e9i	−0.191930	−	0.139445i	−0.679600	+	0.733583i	$0.737847\pi$
$828$	8.82023e9	−	2.71459e10i	0.539975	−	1.66187i
$829$	4.08108e9	−	1.25603e10i	0.248791	−	0.765700i	−0.746199	−	0.665723i	$-0.768123\pi$
$829$	4.08108e9	−	1.25603e10i	0.248791	−	0.765700i	0.994990	−	0.0999767i	$-0.0318768\pi$
$830$	2.01920e9	+	6.21445e9i	0.122576	+	0.377250i
$831$	−1.57313e10			−0.950960
$832$	−1.86056e9			−0.111999
$833$	3.08994e9	+	9.50985e9i	0.185222	+	0.570054i
$834$	1.33998e10	−	9.73550e9i	0.799864	−	0.581135i
$835$	2.20019e9	+	1.59854e9i	0.130785	+	0.0950210i
$836$	7.27690e9			0.430749
$837$	5.38333e9	+	3.18079e10i	0.317331	+	1.87498i
$838$	−1.14628e10			−0.672878
$839$	1.07181e10	+	7.78714e9i	0.626542	+	0.455209i	0.855200	−	0.518297i	$-0.173434\pi$
$839$	1.07181e10	+	7.78714e9i	0.626542	+	0.455209i	−0.228659	+	0.973507i	$0.573434\pi$
$840$	−4.39248e9	+	3.19133e9i	−0.255701	+	0.185778i
$841$	−4.69151e9	−	1.44390e10i	−0.271973	−	0.837048i
$842$	6.69661e9			0.386601
$843$	−4.09519e10			−2.35438
$844$	−3.20152e9	−	9.85327e9i	−0.183298	−	0.564133i
$845$	3.64664e8	−	1.12232e9i	0.0207919	−	0.0639909i
$846$	−2.52470e9	+	7.77022e9i	−0.143355	+	0.441202i
$847$	−5.39633e10	−	3.92066e10i	−3.05145	−	2.21701i
$848$	−1.03951e9	−	3.19927e9i	−0.0585385	−	0.180163i
$849$	1.20671e10	+	8.76724e9i	0.676745	+	0.491684i
$850$	4.42206e9	−	3.21282e9i	0.246978	−	0.179440i
$851$	1.36159e10	−	4.19053e10i	0.757342	−	2.33086i
$852$	−1.40998e10	+	1.02441e10i	−0.781041	+	0.567459i
$853$	5.19863e9	−	3.77703e9i	0.286792	−	0.208367i	−0.435082	−	0.900391i	$-0.643281\pi$
$853$	5.19863e9	−	3.77703e9i	0.286792	−	0.208367i	0.721875	+	0.692024i	$0.243281\pi$
$854$	−3.67160e9	+	1.13000e10i	−0.201722	+	0.620836i
$855$	−4.81998e9	+	3.50192e9i	−0.263733	+	0.191613i
$856$	−6.86069e9	−	4.98458e9i	−0.373861	−	0.271626i
$857$	4.88746e9	+	1.50421e10i	0.265247	+	0.816346i	0.991636	+	0.129063i	$0.0411968\pi$
$857$	4.88746e9	+	1.50421e10i	0.265247	+	0.816346i	−0.726390	+	0.687283i	$0.758803\pi$
$858$	3.12739e10	+	2.27218e10i	1.69035	+	1.22811i
$859$	−9.66372e9	+	2.97419e10i	−0.520198	+	1.60100i	0.253424	+	0.967355i	$0.418443\pi$
$859$	−9.66372e9	+	2.97419e10i	−0.520198	+	1.60100i	−0.773621	+	0.633648i	$0.781557\pi$
$860$	1.09442e9	−	3.36827e9i	0.0586731	−	0.180577i
$861$	−1.66817e10	−	5.13410e10i	−0.890695	−	2.74128i
$862$	−1.15073e10			−0.611922
$863$	−2.54376e8			−0.0134722			−0.00673610	−	0.999977i	$-0.502144\pi$
$863$	−2.54376e8			−0.0134722			−0.00673610	+	0.999977i	$0.502144\pi$
$864$	−1.96940e9	−	6.06120e9i	−0.103881	−	0.319713i
$865$	−2.90131e9	+	2.10792e9i	−0.152418	+	0.110738i
$866$	4.59296e7	+	3.33698e7i	0.00240315	+	0.00174599i
$867$	2.56499e10			1.33666
$868$	1.27389e10	−	6.66142e9i	0.661168	−	0.345739i
$869$	−3.02596e10			−1.56421
$870$	2.30469e9	+	1.67446e9i	0.118658	+	0.0862098i
$871$	1.70285e10	−	1.23719e10i	0.873196	−	0.634414i
$872$	−3.00165e9	−	9.23812e9i	−0.153303	−	0.471820i
$873$	1.88035e10			0.956508
$874$	−1.07402e10			−0.544156
$875$	5.87256e9	+	1.80739e10i	0.296346	+	0.912060i
$876$	3.28940e9	−	1.01237e10i	0.165330	−	0.508835i
$877$	−2.76926e9	+	8.52290e9i	−0.138632	+	0.426667i	−0.996137	−	0.0878090i	$-0.972013\pi$
$877$	−2.76926e9	+	8.52290e9i	−0.138632	+	0.426667i	0.857505	+	0.514476i	$0.172013\pi$
$878$	1.26135e9	+	9.16421e8i	0.0628931	+	0.0456945i
$879$	8.53100e9	+	2.62557e10i	0.423681	+	1.30396i
$880$	−2.62016e9	−	1.90366e9i	−0.129610	−	0.0941673i
$881$	−7.52192e9	+	5.46499e9i	−0.370606	+	0.269261i	−0.757462	−	0.652879i	$-0.773561\pi$
$881$	−7.52192e9	+	5.46499e9i	−0.370606	+	0.269261i	0.386856	+	0.922140i	$0.373561\pi$
$882$	1.13775e10	−	3.50163e10i	0.558350	−	1.71842i
$883$	−2.11353e10	+	1.53557e10i	−1.03311	+	0.750596i	−0.968928	−	0.247343i	$-0.920443\pi$
$883$	−2.11353e10	+	1.53557e10i	−1.03311	+	0.750596i	−0.0641782	+	0.997938i	$0.520443\pi$
$884$	3.63730e9	−	2.64266e9i	0.177091	−	0.128664i
$885$	3.82623e9	−	1.17759e10i	0.185553	−	0.571075i
$886$	1.20169e10	−	8.73078e9i	0.580462	−	0.421730i
$887$	−1.02289e10	−	7.43171e9i	−0.492147	−	0.357566i	0.313862	−	0.949469i	$-0.398377\pi$
$887$	−1.02289e10	−	7.43171e9i	−0.492147	−	0.357566i	−0.806010	+	0.591903i	$0.798377\pi$
$888$	−5.84729e9	−	1.79961e10i	−0.280227	−	0.862449i
$889$	2.28043e10	+	1.65683e10i	1.08858	+	0.790901i
$890$	2.13141e8	−	6.55980e8i	0.0101345	−	0.0311907i
$891$	−1.53915e10	+	4.73700e10i	−0.728967	+	2.24353i
$892$	3.47498e9	+	1.06949e10i	0.163936	+	0.504544i
$893$	3.07428e9			0.144465
$894$	−2.91820e10			−1.36595
$895$	7.78613e8	+	2.39632e9i	0.0363029	+	0.111729i
$896$	−2.29754e9	+	1.66926e9i	−0.106705	+	0.0775258i
$897$	−4.61582e10	−	3.35359e10i	−2.13538	−	1.55145i
$898$	−1.01586e10			−0.468128
$899$	−5.38957e9	−	5.27675e9i	−0.247398	−	0.242219i
$900$	−2.01263e10			−0.920270
$901$	6.57627e9	+	4.77794e9i	0.299532	+	0.217623i
$902$	2.60516e10	−	1.89276e10i	1.18198	−	0.858760i
$903$	1.99388e10	+	6.13652e10i	0.901137	+	2.77342i
$904$	9.73687e9			0.438359
$905$	7.85300e9			0.352181
$906$	−1.38127e10	−	4.25111e10i	−0.617063	−	1.89913i
$907$	−9.04824e9	+	2.78476e10i	−0.402660	+	1.23926i	0.520173	+	0.854061i	$0.325867\pi$
$907$	−9.04824e9	+	2.78476e10i	−0.402660	+	1.23926i	−0.922833	+	0.385199i	$0.874133\pi$
$908$	−3.39078e9	+	1.04357e10i	−0.150314	+	0.462618i
$909$	3.85590e10	+	2.80147e10i	1.70275	+	1.23712i
$910$	2.26593e9	+	6.97381e9i	0.0996785	+	0.306779i
$911$	2.56556e10	+	1.86399e10i	1.12426	+	0.816824i	0.984850	−	0.173411i	$-0.0554788\pi$
$911$	2.56556e10	+	1.86399e10i	1.12426	+	0.816824i	0.139412	+	0.990235i	$0.455479\pi$
$912$	−3.73147e9	+	2.71107e9i	−0.162892	+	0.118348i
$913$	2.19438e10	−	6.75360e10i	0.954254	−	2.93689i
$914$	2.02051e10	−	1.46799e10i	0.875284	−	0.635931i
$915$	6.94821e9	−	5.04817e9i	0.299846	−	0.217851i
$916$	3.79008e9	−	1.16647e10i	0.162935	−	0.501462i
$917$	1.62185e10	−	1.17834e10i	0.694572	−	0.504636i
$918$	1.24591e10	+	9.05207e9i	0.531542	+	0.386188i
$919$	−9.04672e9	−	2.78429e10i	−0.384491	−	1.18334i	−0.936849	−	0.349735i	$-0.886272\pi$
$919$	−9.04672e9	−	2.78429e10i	−0.384491	−	1.18334i	0.552357	−	0.833608i	$-0.313728\pi$
$920$	3.86719e9	+	2.80968e9i	0.163734	+	0.118959i
$921$	−1.26391e10	+	3.88993e10i	−0.533100	+	1.64071i
$922$	−8.62074e9	+	2.65319e10i	−0.362232	+	1.11483i
$923$	7.27359e9	+	2.23858e10i	0.304469	+	0.937058i
$924$	5.90046e10			2.46056
$925$	−3.10691e10			−1.29072
$926$	3.77391e9	+	1.16149e10i	0.156190	+	0.480703i
$927$	2.10831e10	−	1.53178e10i	0.869272	−	0.631563i
$928$	1.20550e9	+	8.75844e8i	0.0495163	+	0.0359757i
$929$	−1.82647e10			−0.747408			−0.373704	−	0.927548i	$-0.621912\pi$
$929$	−1.82647e10			−0.747408			−0.373704	+	0.927548i	$0.621912\pi$
$930$	−1.02798e10	−	1.51689e9i	−0.419078	−	0.0618393i
$931$	−1.38541e10			−0.562673
$932$	9.95778e9	+	7.23475e9i	0.402909	+	0.292730i
$933$	−3.27365e10	+	2.37845e10i	−1.31961	+	0.958755i
$934$	7.02232e9	+	2.16125e10i	0.282011	+	0.867941i
$935$	7.82615e9			0.313118
$936$	−1.65546e10			−0.659862
$937$	3.25520e9	+	1.00185e10i	0.129267	+	0.397844i	0.994654	−	0.103260i	$-0.0329273\pi$
$937$	3.25520e9	+	1.00185e10i	0.129267	+	0.397844i	−0.865387	+	0.501104i	$0.832927\pi$
$938$	9.92798e9	−	3.05552e10i	0.392781	−	1.20886i
$939$	1.40078e10	−	4.31116e10i	0.552129	−	1.69928i
$940$	−1.10694e9	−	8.04240e8i	−0.0434688	−	0.0315819i
$941$	5.89231e8	+	1.81347e9i	0.0230527	+	0.0709490i	0.961921	−	0.273327i	$-0.0881243\pi$
$941$	5.89231e8	+	1.81347e9i	0.0230527	+	0.0709490i	−0.938868	+	0.344276i	$0.888124\pi$
$942$	6.10955e9	+	4.43885e9i	0.238139	+	0.173018i
$943$	−3.84504e10	+	2.79358e10i	−1.49317	+	1.08485i
$944$	2.00135e9	−	6.15953e9i	0.0774322	−	0.238312i
$945$	−2.03203e10	+	1.47635e10i	−0.783281	+	0.569087i
$946$	−3.11381e10	+	2.26231e10i	−1.19584	+	0.868828i
$947$	2.46790e9	−	7.59542e9i	0.0944284	−	0.290621i	−0.892676	−	0.450699i	$-0.851175\pi$
$947$	2.46790e9	−	7.59542e9i	0.0944284	−	0.290621i	0.987104	+	0.160078i	$0.0511747\pi$
$948$	1.55166e10	−	1.12735e10i	0.591518	−	0.429763i
$949$	−1.16307e10	−	8.45016e9i	−0.441746	−	0.320947i
$950$	2.34025e9	+	7.20254e9i	0.0885583	+	0.272554i
$951$	3.48955e10	+	2.53531e10i	1.31564	+	0.955871i
$952$	2.12063e9	−	6.52663e9i	0.0796592	−	0.245166i
$953$	−3.46145e8	+	1.06532e9i	−0.0129549	+	0.0398710i	−0.957325	−	0.289014i	$-0.906673\pi$
$953$	−3.46145e8	+	1.06532e9i	−0.0129549	+	0.0398710i	0.944370	+	0.328885i	$0.106673\pi$
$954$	−9.24914e9	−	2.84659e10i	−0.344891	−	1.06147i
$955$	4.74876e9			0.176429
$956$	−3.91968e9			−0.145093
$957$	−9.56689e9	−	2.94439e10i	−0.352841	−	1.08593i
$958$	3.06422e9	−	2.22629e9i	0.112601	−	0.0818092i
$959$	−2.64623e10	−	1.92260e10i	−0.968865	−	0.703921i
$960$	2.05280e9			0.0748855
$961$	2.63400e10	+	7.94651e9i	0.957380	+	0.288831i
$962$	−2.55555e10			−0.925489
$963$	−6.10439e10	−	4.43510e10i	−2.20267	−	1.60034i
$964$	3.19337e9	−	2.32012e9i	0.114810	−	0.0834143i
$965$	−3.52076e9	−	1.08358e10i	−0.126122	−	0.388164i
$966$	−8.70868e10			−3.10837
$967$	3.36893e10			1.19812			0.599059	−	0.800705i	$-0.295542\pi$
$967$	3.36893e10			1.19812			0.599059	+	0.800705i	$0.295542\pi$
$968$	7.79323e9	+	2.39851e10i	0.276156	+	0.849920i
$969$	3.44415e9	−	1.06000e10i	0.121604	−	0.374260i
$970$	−9.73107e8	+	2.99492e9i	−0.0342342	+	0.105362i
$971$	−8.66731e8	−	6.29717e8i	−0.0303820	−	0.0220738i	0.572491	−	0.819911i	$-0.305977\pi$
$971$	−8.66731e8	−	6.29717e8i	−0.0303820	−	0.0220738i	−0.602873	+	0.797837i	$0.705977\pi$
$972$	−1.34338e9	−	4.13449e9i	−0.0469209	−	0.144408i
$973$	−2.76229e10	−	2.00692e10i	−0.961335	−	0.698451i
$974$	2.57014e10	−	1.86732e10i	0.891253	−	0.647533i
$975$	−1.24320e10	+	3.82617e10i	−0.429560	+	1.32205i
$976$	3.63434e9	−	2.64050e9i	0.125127	−	0.0909101i
$977$	3.01066e10	−	2.18737e10i	1.03284	−	0.750399i	0.0639609	−	0.997952i	$-0.479627\pi$
$977$	3.01066e10	−	2.18737e10i	1.03284	−	0.750399i	0.968874	+	0.247554i	$0.0796267\pi$
$978$	−2.66684e9	+	8.20769e9i	−0.0911614	+	0.280566i
$979$	−6.06422e9	+	4.40591e9i	−0.206555	+	0.150071i
$980$	4.98840e9	+	3.62429e9i	0.169305	+	0.123007i
$981$	−2.67075e10	−	8.21974e10i	−0.903217	−	2.77982i
$982$	8.05713e9	+	5.85385e9i	0.271513	+	0.197266i
$983$	6.39903e9	−	1.96942e10i	0.214871	−	0.661304i	−0.784292	−	0.620392i	$-0.786974\pi$
$983$	6.39903e9	−	1.96942e10i	0.214871	−	0.661304i	0.999163	−	0.0409119i	$-0.0130263\pi$
$984$	−6.30717e9	+	1.94115e10i	−0.211034	+	0.649495i
$985$	−3.21788e9	−	9.90360e9i	−0.107286	−	0.330192i
$986$	−3.60069e9			−0.119623
$987$	2.49277e10			0.825224
$988$	1.92494e9	+	5.92435e9i	0.0634991	+	0.195430i
$989$	4.59577e10	−	3.33902e10i	1.51068	−	1.09757i
$990$	−2.33132e10	−	1.69381e10i	−0.763624	−	0.554805i
$991$	−3.30229e10			−1.07785			−0.538923	−	0.842355i	$-0.681169\pi$
$991$	−3.30229e10			−1.07785			−0.538923	+	0.842355i	$0.681169\pi$
$992$	−5.37698e9	−	7.93428e8i	−0.174883	−	0.0258058i
$993$	9.45489e9			0.306432
$994$	2.90660e10	+	2.11177e10i	0.938712	+	0.682014i
$995$	6.86722e9	−	4.98933e9i	0.221004	−	0.160569i
$996$	1.39087e10	+	4.28067e10i	0.446047	+	1.37279i
$997$	−3.13894e10			−1.00311			−0.501557	−	0.865124i	$-0.667239\pi$
$997$	−3.13894e10			−1.00311			−0.501557	+	0.865124i	$0.667239\pi$
$998$	−7.02936e9			−0.223851
$999$	−2.70504e10	−	8.32526e10i	−0.858410	−	2.64191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.d.a.33.10	✓	40
31.16	even	5	inner	62.8.d.a.47.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.d.a.33.10	✓	40	1.1	even	1	trivial
62.8.d.a.47.10	yes	40	31.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.47214 - 4.70228i) q^{2} +(66.4310 - 48.2650i) q^{3} +(19.7771 + 60.8676i) q^{4} -95.3661 q^{5} -656.906 q^{6} +(418.464 + 1287.90i) q^{7} +(158.217 - 486.941i) q^{8} +(1407.75 - 4332.62i) q^{9} +(617.222 + 448.438i) q^{10} +(-2562.12 - 7885.39i) q^{11} +(4251.58 + 3088.96i) q^{12} +(5741.99 - 4171.80i) q^{13} +(3347.71 - 10303.2i) q^{14} +(-6335.26 + 4602.84i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(3058.58 - 9413.34i) q^{17} +(-29484.4 + 21421.6i) q^{18} +(11094.5 + 8060.62i) q^{19} +(-1886.06 - 5804.71i) q^{20} +(89959.3 + 65359.3i) q^{21} +(-20497.0 + 63083.1i) q^{22} +(30252.1 - 93106.5i) q^{23} +(-12991.7 - 39984.3i) q^{24} -69030.3 q^{25} -56779.9 q^{26} +(-60101.4 - 184973. i) q^{27} +(-70115.3 + 50941.8i) q^{28} +(36788.8 + 26728.6i) q^{29} +62646.5 q^{30} +(-164092. - 24213.5i) q^{31} +32768.0 q^{32} +(-550792. - 400174. i) q^{33} +(-64059.7 + 46542.1i) q^{34} +(-39907.2 - 122822. i) q^{35} +291557. q^{36} +450080. q^{37} +(-33901.7 - 104339. i) q^{38} +(180094. - 554274. i) q^{39} +(-15088.5 + 46437.6i) q^{40} +(-392760. - 285356. i) q^{41} +(-274891. - 846028. i) q^{42} +(469445. + 341072. i) q^{43} +(429294. - 311900. i) q^{44} +(-134252. + 413185. i) q^{45} +(-633609. + 460344. i) q^{46} +(181364. - 131769. i) q^{47} +(-103933. + 319874. i) q^{48} +(-817312. + 593812. i) q^{49} +(446774. + 324600. i) q^{50} +(-251150. - 772960. i) q^{51} +(367487. + 266995. i) q^{52} +(-253786. + 781072. i) q^{53} +(-480811. + 1.47978e6i) q^{54} +(244339. + 751999. i) q^{55} +693339. q^{56} +1.12606e6 q^{57} +(-112417. - 345983. i) q^{58} +(-1.27920e6 + 929394. i) q^{59} +(-405457. - 294582. i) q^{60} -1.09675e6 q^{61} +(948170. + 928322. i) q^{62} +6.16907e6 q^{63} +(-212079. - 154084. i) q^{64} +(-547591. + 397848. i) q^{65} +(1.68307e6 + 5.17996e6i) q^{66} +2.96560e6 q^{67} +633457. q^{68} +(-2.48410e6 - 7.64528e6i) q^{69} +(-319258. + 982575. i) q^{70} +(-1.02481e6 + 3.15404e6i) q^{71} +(-1.88700e6 - 1.37099e6i) q^{72} +(-625928. - 1.92641e6i) q^{73} +(-2.91298e6 - 2.11640e6i) q^{74} +(-4.58575e6 + 3.33174e6i) q^{75} +(-271214. + 834711. i) q^{76} +(9.08343e6 - 6.59950e6i) q^{77} +(-3.77195e6 + 2.74048e6i) q^{78} +(1.12779e6 - 3.47098e6i) q^{79} +(316018. - 229600. i) q^{80} +(-4.86002e6 - 3.53101e6i) q^{81} +(1.20017e6 + 3.69373e6i) q^{82} +(6.92899e6 + 5.03421e6i) q^{83} +(-2.19913e6 + 6.76823e6i) q^{84} +(-291685. + 897713. i) q^{85} +(-1.43450e6 - 4.41493e6i) q^{86} +3.73398e6 q^{87} -4.24509e6 q^{88} +(-279372. - 859818. i) q^{89} +(2.81181e6 - 2.04290e6i) q^{90} +(7.77567e6 + 5.64935e6i) q^{91} +6.26547e6 q^{92} +(-1.20695e7 + 6.31138e6i) q^{93} -1.79342e6 q^{94} +(-1.05804e6 - 768710. i) q^{95} +(2.17681e6 - 1.58155e6i) q^{96} +(1.27549e6 + 3.92555e6i) q^{97} +8.08202e6 q^{98} -3.77712e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) \) 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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