LMFDB - Embedded newform 91.8.h.a.16.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(16,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$63$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.10
Character	$\chi$	$=$	91.16
Dual form			91.8.h.a.74.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.9775 q^{2} +(33.7545 - 58.4645i) q^{3} +195.192 q^{4} +(176.342 - 305.434i) q^{5} +(-606.823 + 1051.05i) q^{6} +(544.696 - 725.844i) q^{7} -1207.95 q^{8} +(-1185.23 - 2052.88i) q^{9} +O(q^{10})$	\(q-17.9775 q^{2} +(33.7545 - 58.4645i) q^{3} +195.192 q^{4} +(176.342 - 305.434i) q^{5} +(-606.823 + 1051.05i) q^{6} +(544.696 - 725.844i) q^{7} -1207.95 q^{8} +(-1185.23 - 2052.88i) q^{9} +(-3170.20 + 5490.95i) q^{10} +(-3437.30 + 5953.58i) q^{11} +(6588.61 - 11411.8i) q^{12} +(-7055.91 - 3600.38i) q^{13} +(-9792.29 + 13048.9i) q^{14} +(-11904.7 - 20619.5i) q^{15} -3268.64 q^{16} -6914.72 q^{17} +(21307.6 + 36905.8i) q^{18} +(5751.15 + 9961.29i) q^{19} +(34420.6 - 59618.3i) q^{20} +(-24050.2 - 56345.9i) q^{21} +(61794.3 - 107031. i) q^{22} -11415.1 q^{23} +(-40773.7 + 70622.1i) q^{24} +(-23130.8 - 40063.7i) q^{25} +(126848. + 64725.9i) q^{26} -12385.5 q^{27} +(106320. - 141679. i) q^{28} +(-31375.3 - 54343.6i) q^{29} +(214017. + 370689. i) q^{30} +(-49670.7 - 86032.2i) q^{31} +213379. q^{32} +(232049. + 401921. i) q^{33} +124310. q^{34} +(-125644. - 294366. i) q^{35} +(-231348. - 400706. i) q^{36} -607028. q^{37} +(-103392. - 179080. i) q^{38} +(-448663. + 290991. i) q^{39} +(-213013. + 368949. i) q^{40} +(-315376. - 546247. i) q^{41} +(432363. + 1.01296e6i) q^{42} +(-346455. + 600078. i) q^{43} +(-670934. + 1.16209e6i) q^{44} -836027. q^{45} +205215. q^{46} +(-71391.4 + 123654. i) q^{47} +(-110331. + 191099. i) q^{48} +(-230156. - 790728. i) q^{49} +(415835. + 720247. i) q^{50} +(-233403. + 404266. i) q^{51} +(-1.37726e6 - 702765. i) q^{52} +(356147. + 616865. i) q^{53} +222661. q^{54} +(1.21228e6 + 2.09974e6i) q^{55} +(-657965. + 876782. i) q^{56} +776509. q^{57} +(564050. + 976964. i) q^{58} +1.38082e6 q^{59} +(-2.32370e6 - 4.02477e6i) q^{60} +(-482586. - 835863. i) q^{61} +(892958. + 1.54665e6i) q^{62} +(-2.13566e6 - 257903. i) q^{63} -3.41765e6 q^{64} +(-2.34393e6 + 1.52021e6i) q^{65} +(-4.17167e6 - 7.22554e6i) q^{66} +(-501474. + 868578. i) q^{67} -1.34970e6 q^{68} +(-385310. + 667377. i) q^{69} +(2.25878e6 + 5.29197e6i) q^{70} +(2.80638e6 - 4.86079e6i) q^{71} +(1.43170e6 + 2.47978e6i) q^{72} +(-969122. - 1.67857e6i) q^{73} +1.09129e7 q^{74} -3.12307e6 q^{75} +(1.12258e6 + 1.94436e6i) q^{76} +(2.44909e6 + 5.73784e6i) q^{77} +(8.06586e6 - 5.23131e6i) q^{78} +(-2.35128e6 + 4.07254e6i) q^{79} +(-576399. + 998352. i) q^{80} +(2.17404e6 - 3.76554e6i) q^{81} +(5.66968e6 + 9.82017e6i) q^{82} +497320. q^{83} +(-4.69440e6 - 1.09983e7i) q^{84} +(-1.21936e6 + 2.11199e6i) q^{85} +(6.22842e6 - 1.07879e7i) q^{86} -4.23623e6 q^{87} +(4.15209e6 - 7.19163e6i) q^{88} +2.51738e6 q^{89} +1.50297e7 q^{90} +(-6.45663e6 + 3.16038e6i) q^{91} -2.22813e6 q^{92} -6.70644e6 q^{93} +(1.28344e6 - 2.22299e6i) q^{94} +4.05669e6 q^{95} +(7.20252e6 - 1.24751e7i) q^{96} +(4.76791e6 - 8.25826e6i) q^{97} +(4.13764e6 + 1.42154e7i) q^{98} +1.62960e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9}+O(q^{10}) $ 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9} - 4255 q^{10} + 7423 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} + 410294 q^{16} + 99274 q^{17} - 21111 q^{18} - 4844 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} + 34130 q^{23} - 130304 q^{24} - 810669 q^{25} + 390708 q^{26} + 416614 q^{27} + 69267 q^{28} + 191096 q^{29} + 70666 q^{30} + 183609 q^{31} + 695346 q^{32} + 178591 q^{33} - 742000 q^{34} + 579437 q^{35} - 1732409 q^{36} - 1362898 q^{37} - 877438 q^{38} + 459227 q^{39} - 1502882 q^{40} + 593701 q^{41} + 1442877 q^{42} - 592188 q^{43} + 1254066 q^{44} + 1954226 q^{45} - 1385452 q^{46} + 98278 q^{47} - 374916 q^{48} - 1497637 q^{49} + 289562 q^{50} - 281250 q^{51} - 8455 q^{52} - 1256681 q^{53} - 293814 q^{54} - 3015554 q^{55} - 1646151 q^{56} + 2743072 q^{57} + 1851469 q^{58} - 2279458 q^{59} + 1031485 q^{60} - 1127636 q^{61} - 7724680 q^{62} + 5142530 q^{63} + 11827496 q^{64} - 2789048 q^{65} + 435059 q^{66} + 4373348 q^{67} + 8737122 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} - 11660951 q^{72} - 5060877 q^{73} + 1184002 q^{74} + 22637254 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} - 123568 q^{80} - 30756895 q^{81} + 8626952 q^{82} - 18679806 q^{83} + 11302461 q^{84} + 5330093 q^{85} - 8512356 q^{86} - 16508762 q^{87} - 6438219 q^{88} - 6176684 q^{89} + 53481084 q^{90} + 29236777 q^{91} + 2460546 q^{92} + 27682404 q^{93} - 17421794 q^{94} + 39553398 q^{95} + 26667066 q^{96} + 7705262 q^{97} + 14093080 q^{98} - 60531432 q^{99}+O(q^{100}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9 - 4255 * q^10 + 7423 * q^11 - 18072 * q^12 - 1824 * q^13 - 15916 * q^14 + 11047 * q^15 + 410294 * q^16 + 99274 * q^17 - 21111 * q^18 - 4844 * q^19 + 36626 * q^20 + 73198 * q^21 - 43360 * q^22 + 34130 * q^23 - 130304 * q^24 - 810669 * q^25 + 390708 * q^26 + 416614 * q^27 + 69267 * q^28 + 191096 * q^29 + 70666 * q^30 + 183609 * q^31 + 695346 * q^32 + 178591 * q^33 - 742000 * q^34 + 579437 * q^35 - 1732409 * q^36 - 1362898 * q^37 - 877438 * q^38 + 459227 * q^39 - 1502882 * q^40 + 593701 * q^41 + 1442877 * q^42 - 592188 * q^43 + 1254066 * q^44 + 1954226 * q^45 - 1385452 * q^46 + 98278 * q^47 - 374916 * q^48 - 1497637 * q^49 + 289562 * q^50 - 281250 * q^51 - 8455 * q^52 - 1256681 * q^53 - 293814 * q^54 - 3015554 * q^55 - 1646151 * q^56 + 2743072 * q^57 + 1851469 * q^58 - 2279458 * q^59 + 1031485 * q^60 - 1127636 * q^61 - 7724680 * q^62 + 5142530 * q^63 + 11827496 * q^64 - 2789048 * q^65 + 435059 * q^66 + 4373348 * q^67 + 8737122 * q^68 - 7610377 * q^69 - 8084578 * q^70 - 60067 * q^71 - 11660951 * q^72 - 5060877 * q^73 + 1184002 * q^74 + 22637254 * q^75 + 637438 * q^76 + 21469082 * q^77 - 7230943 * q^78 - 2446486 * q^79 - 123568 * q^80 - 30756895 * q^81 + 8626952 * q^82 - 18679806 * q^83 + 11302461 * q^84 + 5330093 * q^85 - 8512356 * q^86 - 16508762 * q^87 - 6438219 * q^88 - 6176684 * q^89 + 53481084 * q^90 + 29236777 * q^91 + 2460546 * q^92 + 27682404 * q^93 - 17421794 * q^94 + 39553398 * q^95 + 26667066 * q^96 + 7705262 * q^97 + 14093080 * q^98 - 60531432 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−17.9775			−1.58901			−0.794503	−	0.607261i	$-0.792268\pi$
$2$	−17.9775			−1.58901			−0.794503	+	0.607261i	$0.792268\pi$
$3$	33.7545	−	58.4645i	0.721784	−	1.25017i	−0.238500	−	0.971142i	$-0.576656\pi$
$3$	33.7545	−	58.4645i	0.721784	−	1.25017i	0.960284	−	0.279024i	$-0.0900109\pi$
$4$	195.192			1.52494
$5$	176.342	−	305.434i	0.630902	−	1.09275i	−0.356466	−	0.934308i	$-0.616018\pi$
$5$	176.342	−	305.434i	0.630902	−	1.09275i	0.987368	−	0.158446i	$-0.0506482\pi$
$6$	−606.823	+	1051.05i	−1.14692	+	1.98652i
$7$	544.696	−	725.844i	0.600221	−	0.799835i
$7$	544.696	−	725.844i	0.600221	−	0.799835i
$8$	−1207.95			−0.834130
$9$	−1185.23	−	2052.88i	−0.541944	−	0.938675i
$10$	−3170.20	+	5490.95i	−1.00251	+	1.73639i
$11$	−3437.30	+	5953.58i	−0.778652	+	1.34867i	0.154067	+	0.988060i	$0.450763\pi$
$11$	−3437.30	+	5953.58i	−0.778652	+	1.34867i	−0.932719	+	0.360605i	$0.882570\pi$
$12$	6588.61	−	11411.8i	1.10068	−	1.90643i
$13$	−7055.91	−	3600.38i	−0.890740	−	0.454513i
$13$	−7055.91	−	3600.38i	−0.890740	−	0.454513i
$14$	−9792.29	+	13048.9i	−0.953754	+	1.27094i
$15$	−11904.7	−	20619.5i	−0.910750	−	1.57746i
$16$	−3268.64			−0.199502
$17$	−6914.72			−0.341353			−0.170676	−	0.985327i	$-0.554595\pi$
$17$	−6914.72			−0.341353			−0.170676	+	0.985327i	$0.554595\pi$
$18$	21307.6	+	36905.8i	0.861153	+	1.49156i
$19$	5751.15	+	9961.29i	0.192361	+	0.333179i	0.946032	−	0.324072i	$-0.105052\pi$
$19$	5751.15	+	9961.29i	0.192361	+	0.333179i	−0.753671	+	0.657252i	$0.771719\pi$
$20$	34420.6	−	59618.3i	0.962086	−	1.66638i
$21$	−24050.2	−	56345.9i	−0.566697	−	1.32768i
$22$	61794.3	−	107031.i	1.23728	−	2.14304i
$23$	−11415.1			−0.195628			−0.0978141	−	0.995205i	$-0.531185\pi$
$23$	−11415.1			−0.195628			−0.0978141	+	0.995205i	$0.531185\pi$
$24$	−40773.7	+	70622.1i	−0.602061	+	1.04280i
$25$	−23130.8	−	40063.7i	−0.296074	−	0.512815i
$26$	126848.	+	64725.9i	1.41539	+	0.722224i
$27$	−12385.5			−0.121099
$28$	106320.	−	141679.i	0.915299	−	1.21970i
$29$	−31375.3	−	54343.6i	−0.238888	−	0.413766i	0.721507	−	0.692407i	$-0.243450\pi$
$29$	−31375.3	−	54343.6i	−0.238888	−	0.413766i	−0.960396	+	0.278640i	$0.910116\pi$
$30$	214017.	+	370689.i	1.44719	+	2.50660i
$31$	−49670.7	−	86032.2i	−0.299457	−	0.518675i	0.676555	−	0.736392i	$-0.263472\pi$
$31$	−49670.7	−	86032.2i	−0.299457	−	0.518675i	−0.976012	+	0.217717i	$0.930139\pi$
$32$	213379.			1.15114
$33$	232049.	+	401921.i	1.12404	+	1.94689i
$34$	124310.			0.542412
$35$	−125644.	−	294366.i	−0.495342	−	1.16051i
$36$	−231348.	−	400706.i	−0.826432	−	1.43142i
$37$	−607028.			−1.97017			−0.985083	−	0.172079i	$-0.944952\pi$
$37$	−607028.			−1.97017			−0.985083	+	0.172079i	$0.944952\pi$
$38$	−103392.	−	179080.i	−0.305663	−	0.529424i
$39$	−448663.	+	290991.i	−1.21114	+	0.785513i
$40$	−213013.	+	368949.i	−0.526254	+	0.911498i
$41$	−315376.	−	546247.i	−0.714636	−	1.23779i	−0.963100	−	0.269144i	$-0.913259\pi$
$41$	−315376.	−	546247.i	−0.714636	−	1.23779i	0.248464	−	0.968641i	$-0.420074\pi$
$42$	432363.	+	1.01296e6i	0.900484	+	2.10970i
$43$	−346455.	+	600078.i	−0.664519	+	1.15098i	0.314896	+	0.949126i	$0.398030\pi$
$43$	−346455.	+	600078.i	−0.664519	+	1.15098i	−0.979415	+	0.201855i	$0.935303\pi$
$44$	−670934.	+	1.16209e6i	−1.18740	+	2.05663i
$45$	−836027.			−1.36765
$46$	205215.			0.310854
$47$	−71391.4	+	123654.i	−0.100301	+	0.173726i	−0.911808	−	0.410616i	$-0.865314\pi$
$47$	−71391.4	+	123654.i	−0.100301	+	0.173726i	0.811508	+	0.584341i	$0.198647\pi$
$48$	−110331.	+	191099.i	−0.143997	+	0.249410i
$49$	−230156.	−	790728.i	−0.279471	−	0.960154i
$50$	415835.	+	720247.i	0.470463	+	0.814866i
$51$	−233403.	+	404266.i	−0.246383	+	0.426748i
$52$	−1.37726e6	−	702765.i	−1.35832	−	0.693104i
$53$	356147.	+	616865.i	0.328597	+	0.569147i	0.982234	−	0.187661i	$-0.0600907\pi$
$53$	356147.	+	616865.i	0.328597	+	0.569147i	−0.653636	+	0.756809i	$0.726757\pi$
$54$	222661.			0.192427
$55$	1.21228e6	+	2.09974e6i	0.982506	+	1.70175i
$56$	−657965.	+	876782.i	−0.500662	+	0.667166i
$57$	776509.			0.555373
$58$	564050.	+	976964.i	0.379594	+	0.657477i
$59$	1.38082e6			0.875294			0.437647	−	0.899147i	$-0.355812\pi$
$59$	1.38082e6			0.875294			0.437647	+	0.899147i	$0.355812\pi$
$60$	−2.32370e6	−	4.02477e6i	−1.38884	−	2.40554i
$61$	−482586.	−	835863.i	−0.272220	−	0.471499i	0.697210	−	0.716867i	$-0.254425\pi$
$61$	−482586.	−	835863.i	−0.272220	−	0.471499i	−0.969430	+	0.245368i	$0.921091\pi$
$62$	892958.	+	1.54665e6i	0.475839	+	0.824177i
$63$	−2.13566e6	−	257903.i	−1.07607	−	0.129946i
$64$	−3.41765e6			−1.62966
$65$	−2.34393e6	+	1.52021e6i	−1.05864	+	0.686607i
$66$	−4.17167e6	−	7.22554e6i	−1.78610	−	3.09362i
$67$	−501474.	+	868578.i	−0.203698	+	0.352815i	−0.949717	−	0.313109i	$-0.898629\pi$
$67$	−501474.	+	868578.i	−0.203698	+	0.352815i	0.746019	+	0.665924i	$0.231963\pi$
$68$	−1.34970e6			−0.520542
$69$	−385310.	+	667377.i	−0.141201	+	0.244568i
$70$	2.25878e6	+	5.29197e6i	0.787101	+	1.84406i
$71$	2.80638e6	−	4.86079e6i	0.930555	−	1.61177i	0.148179	−	0.988961i	$-0.452659\pi$
$71$	2.80638e6	−	4.86079e6i	0.930555	−	1.61177i	0.782375	−	0.622807i	$-0.214008\pi$
$72$	1.43170e6	+	2.47978e6i	0.452052	+	0.782977i
$73$	−969122.	−	1.67857e6i	−0.291574	−	0.505020i	0.682608	−	0.730784i	$-0.260846\pi$
$73$	−969122.	−	1.67857e6i	−0.291574	−	0.505020i	−0.974182	+	0.225764i	$0.927512\pi$
$74$	1.09129e7			3.13061
$75$	−3.12307e6			−0.854806
$76$	1.12258e6	+	1.94436e6i	0.293339	+	0.508078i
$77$	2.44909e6	+	5.73784e6i	0.611346	+	1.43229i
$78$	8.06586e6	−	5.23131e6i	1.92451	−	1.24818i
$79$	−2.35128e6	+	4.07254e6i	−0.536550	+	0.929332i	0.462537	+	0.886600i	$0.346939\pi$
$79$	−2.35128e6	+	4.07254e6i	−0.536550	+	0.929332i	−0.999087	+	0.0427317i	$0.986394\pi$
$80$	−576399.	+	998352.i	−0.125866	+	0.218006i
$81$	2.17404e6	−	3.76554e6i	0.454537	−	0.787281i
$82$	5.66968e6	+	9.82017e6i	1.13556	+	1.96685i
$83$	497320.			0.0954691			0.0477346	−	0.998860i	$-0.484800\pi$
$83$	497320.			0.0954691			0.0477346	+	0.998860i	$0.484800\pi$
$84$	−4.69440e6	−	1.09983e7i	−0.864178	−	2.02464i
$85$	−1.21936e6	+	2.11199e6i	−0.215360	+	0.373015i
$86$	6.22842e6	−	1.07879e7i	1.05592	−	1.82892i
$87$	−4.23623e6			−0.689702
$88$	4.15209e6	−	7.19163e6i	0.649497	−	1.12496i
$89$	2.51738e6			0.378516			0.189258	−	0.981927i	$-0.439392\pi$
$89$	2.51738e6			0.378516			0.189258	+	0.981927i	$0.439392\pi$
$90$	1.50297e7			2.17321
$91$	−6.45663e6	+	3.16038e6i	−0.898176	+	0.439637i
$92$	−2.22813e6			−0.298321
$93$	−6.70644e6			−0.864573
$94$	1.28344e6	−	2.22299e6i	0.159378	−	0.276051i
$95$	4.05669e6			0.485444
$96$	7.20252e6	−	1.24751e7i	0.830874	−	1.43912i
$97$	4.76791e6	−	8.25826e6i	0.530428	−	0.918729i	−0.468942	−	0.883229i	$-0.655364\pi$
$97$	4.76791e6	−	8.25826e6i	0.530428	−	0.918729i	0.999370	−	0.0354993i	$-0.0113022\pi$
$98$	4.13764e6	+	1.42154e7i	0.444080	+	1.52569i
$99$	1.62960e7			1.68794
$100$	−4.51495e6	−	7.82012e6i	−0.451495	−	0.782012i
$101$	−9.65327e6	+	1.67200e7i	−0.932287	+	1.61477i	−0.152885	+	0.988244i	$0.548856\pi$
$101$	−9.65327e6	+	1.67200e7i	−0.932287	+	1.61477i	−0.779402	+	0.626524i	$0.784477\pi$
$102$	4.19601e6	−	7.26771e6i	0.391504	−	0.678105i
$103$	143556.	−	248647.i	0.0129447	−	0.0224209i	−0.859480	−	0.511169i	$-0.829213\pi$
$103$	143556.	−	248647.i	0.0129447	−	0.0224209i	0.872425	+	0.488748i	$0.162546\pi$
$104$	8.52317e6	+	4.34907e6i	0.742993	+	0.379123i
$105$	−2.14510e7	−	2.59042e6i	−1.80836	−	0.218378i
$106$	−6.40265e6	−	1.10897e7i	−0.522143	−	0.904378i
$107$	7.76509e6			0.612778			0.306389	−	0.951906i	$-0.400879\pi$
$107$	7.76509e6			0.612778			0.306389	+	0.951906i	$0.400879\pi$
$108$	−2.41756e6			−0.184669
$109$	−1.04073e7	−	1.80260e7i	−0.769743	−	1.33323i	−0.937702	−	0.347439i	$-0.887051\pi$
$109$	−1.04073e7	−	1.80260e7i	−0.769743	−	1.33323i	0.167960	−	0.985794i	$-0.446282\pi$
$110$	−2.17939e7	−	3.77481e7i	−1.56121	−	2.70409i
$111$	−2.04899e7	+	3.54896e7i	−1.42203	+	2.46304i
$112$	−1.78041e6	+	2.37252e6i	−0.119745	+	0.159568i
$113$	7.03383e6	−	1.21829e7i	0.458582	−	0.794288i	−0.540304	−	0.841470i	$-0.681691\pi$
$113$	7.03383e6	−	1.21829e7i	0.458582	−	0.794288i	0.998886	+	0.0471821i	$0.0150241\pi$
$114$	−1.39597e7			−0.882490
$115$	−2.01296e6	+	3.48655e6i	−0.123422	+	0.213774i
$116$	−6.12420e6	−	1.06074e7i	−0.364290	−	0.630968i
$117$	971735.	+	1.87522e7i	0.0560915	+	1.08244i
$118$	−2.48237e7			−1.39085
$119$	−3.76642e6	+	5.01901e6i	−0.204887	+	0.273026i
$120$	1.43803e7	+	2.49074e7i	0.759683	+	1.31581i
$121$	−1.38865e7	−	2.40522e7i	−0.712598	−	1.23426i
$122$	8.67571e6	+	1.50268e7i	0.432559	+	0.749214i
$123$	−4.25814e7			−2.06325
$124$	−9.69533e6	−	1.67928e7i	−0.456654	−	0.790947i
$125$	1.12377e7			0.514629
$126$	3.83940e7	+	4.63646e6i	1.70988	+	0.206485i
$127$	2.09646e7	+	3.63118e7i	0.908185	+	1.57302i	0.816584	+	0.577227i	$0.195865\pi$
$127$	2.09646e7	+	3.63118e7i	0.908185	+	1.57302i	0.0916015	+	0.995796i	$0.470801\pi$
$128$	3.41284e7			1.43841
$129$	2.33888e7	+	4.05107e7i	0.959279	+	1.66152i
$130$	4.21382e7	−	2.73297e7i	1.68219	−	1.09102i
$131$	−5.06561e6	+	8.77389e6i	−0.196871	+	0.340991i	−0.947512	−	0.319719i	$-0.896411\pi$
$131$	−5.06561e6	+	8.77389e6i	−0.196871	+	0.340991i	0.750641	+	0.660710i	$0.229745\pi$
$132$	4.52941e7	+	7.84517e7i	1.71409	+	2.96889i
$133$	1.03630e7	+	1.25143e6i	0.381947	+	0.0461240i
$134$	9.01527e6	−	1.56149e7i	0.323677	−	0.560625i
$135$	−2.18409e6	+	3.78296e6i	−0.0764017	+	0.132332i
$136$	8.35263e6			0.284733
$137$	−2.35672e7			−0.783043			−0.391521	−	0.920169i	$-0.628051\pi$
$137$	−2.35672e7			−0.783043			−0.391521	+	0.920169i	$0.628051\pi$
$138$	6.92693e6	−	1.19978e7i	0.224370	−	0.388620i
$139$	1.31003e7	−	2.26904e7i	0.413742	−	0.716621i	−0.581554	−	0.813508i	$-0.697555\pi$
$139$	1.31003e7	−	2.26904e7i	0.413742	−	0.716621i	0.995295	+	0.0968864i	$0.0308884\pi$
$140$	−2.45248e7	−	5.74579e7i	−0.755366	−	1.76971i
$141$	4.81956e6	+	8.34772e6i	0.144791	+	0.250785i
$142$	−5.04518e7	+	8.73850e7i	−1.47866	+	2.56111i
$143$	4.56884e7	−	2.96323e7i	1.30656	−	0.847403i
$144$	3.87409e6	+	6.71013e6i	0.108119	+	0.187267i
$145$	−2.21312e7			−0.602860
$146$	1.74224e7	+	3.01765e7i	0.463312	+	0.802480i
$147$	−5.39983e7	−	1.32347e7i	−1.40207	−	0.343639i
$148$	−1.18487e8			−3.00438
$149$	686036.	+	1.18825e6i	0.0169901	+	0.0294276i	0.874395	−	0.485214i	$-0.161258\pi$
$149$	686036.	+	1.18825e6i	0.0169901	+	0.0294276i	−0.857405	+	0.514642i	$0.827925\pi$
$150$	5.61452e7			1.35829
$151$	−2.91105e7	−	5.04208e7i	−0.688066	−	1.19177i	−0.972463	−	0.233059i	$-0.925127\pi$
$151$	−2.91105e7	−	5.04208e7i	−0.688066	−	1.19177i	0.284397	−	0.958707i	$-0.408207\pi$
$152$	−6.94710e6	−	1.20327e7i	−0.160454	−	0.277915i
$153$	8.19556e6	+	1.41951e7i	0.184994	+	0.320420i
$154$	−4.40286e7	−	1.03152e8i	−0.971432	−	2.27592i
$155$	−3.50362e7			−0.755712
$156$	−8.75754e7	+	5.67992e7i	−1.84691	+	1.19786i
$157$	2.35104e7	+	4.07211e7i	0.484854	+	0.839791i	0.999849	−	0.0174022i	$-0.00553956\pi$
$157$	2.35104e7	+	4.07211e7i	0.484854	+	0.839791i	−0.514995	+	0.857193i	$0.672206\pi$
$158$	4.22703e7	−	7.32143e7i	0.852581	−	1.47671i
$159$	4.80863e7			0.948706
$160$	3.76279e7	−	6.51733e7i	0.726256	−	1.25791i
$161$	−6.21775e6	+	8.28557e6i	−0.117420	+	0.156470i
$162$	−3.90838e7	+	6.76952e7i	−0.722262	+	1.25099i
$163$	−4.19557e7	−	7.26694e7i	−0.758812	−	1.31430i	−0.943457	−	0.331495i	$-0.892447\pi$
$163$	−4.19557e7	−	7.26694e7i	−0.758812	−	1.31430i	0.184645	−	0.982805i	$-0.440886\pi$
$164$	−6.15588e7	−	1.06623e8i	−1.08978	−	1.88755i
$165$	1.63680e8			2.83663
$166$	−8.94060e6			−0.151701
$167$	3.87036e7	+	6.70366e7i	0.643048	+	1.11379i	0.984749	+	0.173984i	$0.0556640\pi$
$167$	3.87036e7	+	6.70366e7i	0.643048	+	1.11379i	−0.341700	+	0.939809i	$0.611003\pi$
$168$	2.90514e7	+	6.80629e7i	0.472699	+	1.10746i
$169$	3.68231e7	+	5.08078e7i	0.586836	+	0.809706i
$170$	2.19211e7	−	3.79684e7i	0.342208	−	0.592722i
$171$	1.36329e7	−	2.36129e7i	0.208498	−	0.361129i
$172$	−6.76253e7	+	1.17131e8i	−1.01335	+	1.75518i
$173$	4.46001e7	+	7.72496e7i	0.654899	+	1.13432i	0.981919	+	0.189300i	$0.0606220\pi$
$173$	4.46001e7	+	7.72496e7i	0.654899	+	1.13432i	−0.327021	+	0.945017i	$0.606045\pi$
$174$	7.61569e7			1.09594
$175$	−4.16792e7	−	5.03318e6i	−0.587877	−	0.0709920i
$176$	1.12353e7	−	1.94601e7i	0.155342	−	0.269061i
$177$	4.66088e7	−	8.07288e7i	0.631773	−	1.09426i
$178$	−4.52564e7			−0.601464
$179$	6.38858e7	−	1.10654e8i	0.832567	−	1.44205i	−0.0634299	−	0.997986i	$-0.520204\pi$
$179$	6.38858e7	−	1.10654e8i	0.832567	−	1.44205i	0.895996	−	0.444061i	$-0.146463\pi$
$180$	−1.63186e8			−2.08559
$181$	−3.91141e7			−0.490296			−0.245148	−	0.969486i	$-0.578837\pi$
$181$	−3.91141e7			−0.490296			−0.245148	+	0.969486i	$0.578837\pi$
$182$	1.16074e8	−	5.68158e7i	1.42721	−	0.698585i
$183$	−6.51578e7			−0.785936
$184$	1.37888e7			0.163179
$185$	−1.07045e8	+	1.85407e8i	−1.24298	+	2.15291i
$186$	1.20565e8			1.37381
$187$	2.37680e7	−	4.11674e7i	0.265795	−	0.460371i
$188$	−1.39350e7	+	2.41362e7i	−0.152952	+	0.264921i
$189$	−6.74634e6	+	8.98996e6i	−0.0726862	+	0.0968593i
$190$	−7.29293e7			−0.771373
$191$	5.36672e7	+	9.29542e7i	0.557304	+	0.965278i	0.997720	+	0.0674846i	$0.0214974\pi$
$191$	5.36672e7	+	9.29542e7i	0.557304	+	0.965278i	−0.440417	+	0.897793i	$0.645169\pi$
$192$	−1.15361e8	+	1.99811e8i	−1.17627	+	2.03735i
$193$	3.68156e7	−	6.37666e7i	0.368622	−	0.638473i	−0.620728	−	0.784026i	$-0.713163\pi$
$193$	3.68156e7	−	6.37666e7i	0.368622	−	0.638473i	0.989350	+	0.145553i	$0.0464962\pi$
$194$	−8.57152e7	+	1.48463e8i	−0.842853	+	1.45986i
$195$	9.76029e6	+	1.88351e8i	0.0942631	+	1.81906i
$196$	−4.49246e7	−	1.54344e8i	−0.426175	−	1.46418i
$197$	−3.16628e7	−	5.48416e7i	−0.295065	−	0.511068i	0.679935	−	0.733273i	$-0.262008\pi$
$197$	−3.16628e7	−	5.48416e7i	−0.295065	−	0.511068i	−0.975000	+	0.222205i	$0.928675\pi$
$198$	−2.92962e8			−2.68215
$199$	−9.60950e7			−0.864401			−0.432200	−	0.901778i	$-0.642263\pi$
$199$	−9.60950e7			−0.864401			−0.432200	+	0.901778i	$0.642263\pi$
$200$	2.79408e7	+	4.83949e7i	0.246964	+	0.427754i
$201$	3.38540e7	+	5.86369e7i	0.294052	+	0.509313i
$202$	1.73542e8	−	3.00584e8i	1.48141	−	2.56588i
$203$	−5.65349e7	−	6.82716e6i	−0.474330	−	0.0572801i
$204$	−4.55584e7	+	7.89095e7i	−0.375719	+	0.650764i
$205$	−2.22456e8			−1.80346
$206$	−2.58079e6	+	4.47006e6i	−0.0205692	+	0.0356269i
$207$	1.35295e7	+	2.34338e7i	0.106020	+	0.183631i
$208$	2.30632e7	+	1.17683e7i	0.177704	+	0.0906761i
$209$	−7.90738e7			−0.599130
$210$	3.85636e8	+	4.65694e7i	2.87350	+	0.347003i
$211$	−1.10204e8	−	1.90879e8i	−0.807624	−	1.39885i	−0.914506	−	0.404573i	$-0.867420\pi$
$211$	−1.10204e8	−	1.90879e8i	−0.807624	−	1.39885i	0.106882	−	0.994272i	$-0.465913\pi$
$212$	6.95171e7	+	1.20407e8i	0.501091	+	0.867915i
$213$	−1.89456e8	−	3.28147e8i	−1.34332	−	2.32670i
$214$	−1.39597e8			−0.973708
$215$	1.22190e8	+	2.11638e8i	0.838493	+	1.45231i
$216$	1.49611e7			0.101012
$217$	−8.95014e7	−	1.08082e7i	−0.594594	−	0.0718032i
$218$	1.87098e8	+	3.24063e8i	1.22313	+	2.11851i
$219$	−1.30849e8			−0.841813
$220$	2.36628e8	+	4.09852e8i	1.49826	+	2.59506i
$221$	4.87896e7	+	2.48956e7i	0.304057	+	0.155149i
$222$	3.68359e8	−	6.38016e8i	2.25962	−	3.91378i
$223$	−9.78661e7	−	1.69509e8i	−0.590970	−	1.02359i	−0.994102	−	0.108448i	$-0.965412\pi$
$223$	−9.78661e7	−	1.69509e8i	−0.590970	−	1.02359i	0.403132	−	0.915142i	$-0.367921\pi$
$224$	1.16227e8	−	1.54880e8i	0.690937	−	0.920721i
$225$	−5.48307e7	+	9.49696e7i	−0.320911	+	0.555835i
$226$	−1.26451e8	+	2.19019e8i	−0.728690	+	1.26213i
$227$	−2.52467e8			−1.43257			−0.716283	−	0.697810i	$-0.754158\pi$
$227$	−2.52467e8			−1.43257			−0.716283	+	0.697810i	$0.754158\pi$
$228$	1.51568e8			0.846909
$229$	3.08747e7	−	5.34766e7i	0.169894	−	0.294266i	−0.768488	−	0.639864i	$-0.778991\pi$
$229$	3.08747e7	−	5.34766e7i	0.169894	−	0.294266i	0.938383	+	0.345598i	$0.112324\pi$
$230$	3.61881e7	−	6.26797e7i	0.196119	−	0.339687i
$231$	4.18128e8	+	5.04931e7i	2.23186	+	0.269519i
$232$	3.78997e7	+	6.56442e7i	0.199264	+	0.345135i
$233$	1.64602e8	−	2.85100e8i	0.852493	−	1.47656i	−0.0264591	−	0.999650i	$-0.508423\pi$
$233$	1.64602e8	−	2.85100e8i	0.852493	−	1.47656i	0.878952	−	0.476911i	$-0.158243\pi$
$234$	−1.74694e7	−	3.37119e8i	−0.0891298	−	1.72000i
$235$	2.51787e7	+	4.36107e7i	0.126560	+	0.219208i
$236$	2.69525e8			1.33477
$237$	1.58733e8	+	2.74933e8i	0.774547	+	1.34155i
$238$	6.77110e7	−	9.02295e7i	0.325567	−	0.433840i
$239$	−2.21408e7			−0.104906			−0.0524530	−	0.998623i	$-0.516704\pi$
$239$	−2.21408e7			−0.104906			−0.0524530	+	0.998623i	$0.516704\pi$
$240$	3.89121e7	+	6.73978e7i	0.181696	+	0.314707i
$241$	1.66597e8			0.766666			0.383333	−	0.923610i	$-0.374776\pi$
$241$	1.66597e8			0.766666			0.383333	+	0.923610i	$0.374776\pi$
$242$	2.49646e8	+	4.32399e8i	1.13232	+	1.96124i
$243$	−1.60311e8	−	2.77666e8i	−0.716705	−	1.24137i
$244$	−9.41969e7	−	1.63154e8i	−0.415119	−	0.719007i
$245$	−2.82102e8	−	6.91414e7i	−1.22553	−	0.300370i
$246$	7.65509e8			3.27852
$247$	−4.71519e6	−	9.09922e7i	−0.0199095	−	0.384207i
$248$	5.99997e7	+	1.03923e8i	0.249786	+	0.432642i
$249$	1.67868e7	−	2.90756e7i	0.0689081	−	0.119352i
$250$	−2.02027e8			−0.817748
$251$	1.36036e8	−	2.35621e8i	0.542994	−	0.940493i	−0.455737	−	0.890115i	$-0.650624\pi$
$251$	1.36036e8	−	2.35621e8i	0.542994	−	0.940493i	0.998730	−	0.0503780i	$-0.0160426\pi$
$252$	−4.16865e8	−	5.03406e7i	−1.64094	−	0.198160i
$253$	3.92371e7	−	6.79607e7i	0.152326	−	0.263837i
$254$	−3.76893e8	−	6.52797e8i	−1.44311	−	2.49954i
$255$	8.23177e7	+	1.42578e8i	0.310887	+	0.538472i
$256$	−1.76086e8			−0.655971
$257$	−2.56759e7			−0.0943539			−0.0471770	−	0.998887i	$-0.515022\pi$
$257$	−2.56759e7			−0.0943539			−0.0471770	+	0.998887i	$0.515022\pi$
$258$	−4.20474e8	−	7.28282e8i	−1.52430	−	2.64016i
$259$	−3.30646e8	+	4.40608e8i	−1.18253	+	1.57581i
$260$	−4.57517e8	+	2.96734e8i	−1.61436	+	1.04703i
$261$	−7.43740e7	+	1.28819e8i	−0.258928	+	0.448477i
$262$	9.10672e7	−	1.57733e8i	0.312829	−	0.541836i
$263$	−7.59536e7	+	1.31555e8i	−0.257456	+	0.445927i	−0.965560	−	0.260182i	$-0.916218\pi$
$263$	−7.59536e7	+	1.31555e8i	−0.257456	+	0.445927i	0.708104	+	0.706108i	$0.249551\pi$
$264$	−2.80303e8	−	4.85499e8i	−0.937593	−	1.62396i
$265$	2.51216e8			0.829251
$266$	−1.86301e8	−	2.24977e7i	−0.606916	−	0.0732912i
$267$	8.49730e7	−	1.47178e8i	0.273207	−	0.473208i
$268$	−9.78838e7	+	1.69540e8i	−0.310627	+	0.538021i
$269$	8.98592e7			0.281468			0.140734	−	0.990047i	$-0.455054\pi$
$269$	8.98592e7			0.281468			0.140734	+	0.990047i	$0.455054\pi$
$270$	3.92646e7	−	6.80083e7i	0.121403	−	0.210276i
$271$	4.82975e8			1.47412			0.737058	−	0.675829i	$-0.236214\pi$
$271$	4.82975e8			1.47412			0.737058	+	0.675829i	$0.236214\pi$
$272$	2.26017e7			0.0681005
$273$	−3.31706e7	+	4.84161e8i	−0.0986697	+	1.44019i
$274$	4.23680e8			1.24426
$275$	3.18030e8			0.922155
$276$	−7.52095e7	+	1.30267e8i	−0.215323	+	0.372951i
$277$	−7.20161e7			−0.203587			−0.101794	−	0.994806i	$-0.532458\pi$
$277$	−7.20161e7			−0.203587			−0.101794	+	0.994806i	$0.532458\pi$
$278$	−2.35511e8	+	4.07917e8i	−0.657438	+	1.13872i
$279$	−1.17743e8	+	2.03936e8i	−0.324578	+	0.562186i
$280$	1.51772e8	+	3.55579e8i	0.413180	+	0.968016i
$281$	5.86269e8			1.57625			0.788124	−	0.615516i	$-0.211052\pi$
$281$	5.86269e8			1.57625			0.788124	+	0.615516i	$0.211052\pi$
$282$	−8.66439e7	−	1.50072e8i	−0.230073	−	0.398498i
$283$	−2.63301e8	+	4.56050e8i	−0.690557	+	1.19608i	0.281099	+	0.959679i	$0.409301\pi$
$283$	−2.63301e8	+	4.56050e8i	−0.690557	+	1.19608i	−0.971656	+	0.236401i	$0.924032\pi$
$284$	5.47783e8	−	9.48787e8i	1.41904	−	2.45785i
$285$	1.36931e8	−	2.37172e8i	0.350386	−	0.606886i
$286$	−8.21366e8	+	5.32717e8i	−2.07613	+	1.34653i
$287$	−5.68274e8	−	6.86247e7i	−1.41896	−	0.171354i
$288$	−2.52904e8	−	4.38043e8i	−0.623853	−	1.08055i
$289$	−3.62525e8			−0.883478
$290$	3.97864e8			0.957947
$291$	−3.21877e8	−	5.57507e8i	−0.765709	−	1.32625i
$292$	−1.89165e8	−	3.27643e8i	−0.444632	−	0.770125i
$293$	1.83599e8	−	3.18002e8i	0.426415	−	0.738573i	−0.570136	−	0.821550i	$-0.693110\pi$
$293$	1.83599e8	−	3.18002e8i	0.426415	−	0.738573i	0.996551	+	0.0829773i	$0.0264429\pi$
$294$	9.70758e8	+	2.37927e8i	2.22790	+	0.546044i
$295$	2.43497e8	−	4.21748e8i	0.552225	−	0.956481i
$296$	7.33259e8			1.64337
$297$	4.25728e7	−	7.37382e7i	0.0942941	−	0.163322i
$298$	−1.23332e7	−	2.13618e7i	−0.0269973	−	0.0467607i
$299$	8.05437e7	+	4.10986e7i	0.174254	+	0.0889156i
$300$	−6.09599e8			−1.30353
$301$	2.46850e8	+	5.78333e8i	0.521736	+	1.22235i
$302$	5.23335e8	+	9.06443e8i	1.09334	+	1.89372i
$303$	6.51682e8	+	1.12875e9i	1.34582	+	2.33103i
$304$	−1.87984e7	−	3.25598e7i	−0.0383764	−	0.0664698i
$305$	−3.40401e8			−0.686976
$306$	−1.47336e8	−	2.55193e8i	−0.293957	−	0.509148i
$307$	−4.61538e8			−0.910381			−0.455191	−	0.890394i	$-0.650429\pi$
$307$	−4.61538e8			−0.910381			−0.455191	+	0.890394i	$0.650429\pi$
$308$	4.78043e8	+	1.11998e9i	0.932265	+	2.18415i
$309$	−9.69134e6	−	1.67859e7i	−0.0186866	−	0.0323661i
$310$	6.29865e8			1.20083
$311$	−4.64757e8	−	8.04982e8i	−0.876122	−	1.51749i	−0.855563	−	0.517698i	$-0.826789\pi$
$311$	−4.64757e8	−	8.04982e8i	−0.876122	−	1.51749i	−0.0205583	−	0.999789i	$-0.506544\pi$
$312$	5.41962e8	−	3.51502e8i	1.01025	−	0.655220i
$313$	−2.46610e8	+	4.27141e8i	−0.454575	+	0.787347i	−0.998664	−	0.0516807i	$-0.983542\pi$
$313$	−2.46610e8	+	4.27141e8i	−0.454575	+	0.787347i	0.544089	+	0.839028i	$0.316876\pi$
$314$	−4.22659e8	−	7.32066e8i	−0.770435	−	1.33443i
$315$	−4.55380e8	+	6.06825e8i	−0.820894	+	1.09390i
$316$	−4.58952e8	+	7.94928e8i	−0.818206	+	1.41717i
$317$	8.48156e7	−	1.46905e8i	0.149544	−	0.259017i	−0.781515	−	0.623886i	$-0.785553\pi$
$317$	8.48156e7	−	1.46905e8i	0.149544	−	0.259017i	0.931059	+	0.364869i	$0.118886\pi$
$318$	−8.64474e8			−1.50750
$319$	4.31385e8			0.744043
$320$	−6.02677e8	+	1.04387e9i	−1.02816	+	1.78082i
$321$	2.62107e8	−	4.53982e8i	0.442294	−	0.766075i
$322$	1.11780e8	−	1.48954e8i	0.186581	−	0.248632i
$323$	−3.97676e7	−	6.88796e7i	−0.0656630	−	0.113732i
$324$	4.24355e8	−	7.35004e8i	0.693141	−	1.20056i
$325$	1.89642e7	+	3.65965e8i	0.0306438	+	0.591355i
$326$	7.54260e8	+	1.30642e9i	1.20576	+	2.08843i
$327$	−1.40517e9			−2.22235
$328$	3.80958e8	+	6.59838e8i	0.596099	+	1.03247i
$329$	5.08666e7	+	1.19173e8i	0.0787493	+	0.184498i
$330$	−2.94257e9			−4.50742
$331$	6.29054e7	+	1.08955e8i	0.0953433	+	0.165139i	0.909752	−	0.415153i	$-0.136272\pi$
$331$	6.29054e7	+	1.08955e8i	0.0953433	+	0.165139i	−0.814409	+	0.580292i	$0.802938\pi$
$332$	9.70730e7			0.145585
$333$	7.19470e8	+	1.24616e9i	1.06772	+	1.84935i
$334$	−6.95796e8	−	1.20515e9i	−1.02181	−	1.76982i
$335$	1.76862e8	+	3.06334e8i	0.257027	+	0.445183i
$336$	7.86113e7	+	1.84174e8i	0.113057	+	0.264875i
$337$	5.66090e8			0.805714			0.402857	−	0.915263i	$-0.368017\pi$
$337$	5.66090e8			0.805714			0.402857	+	0.915263i	$0.368017\pi$
$338$	−6.61989e8	−	9.13400e8i	−0.932485	−	1.28663i
$339$	−4.74847e8	−	8.22459e8i	−0.661995	−	1.14661i
$340$	−2.38009e8	+	4.12244e8i	−0.328411	+	0.568824i
$341$	6.82933e8			0.932692
$342$	−2.45086e8	+	4.24502e8i	−0.331305	+	0.573836i
$343$	−6.99310e8	−	2.63649e8i	−0.935709	−	0.352774i
$344$	4.18500e8	−	7.24864e8i	0.554295	−	0.960068i
$345$	1.35893e8	+	2.35374e8i	0.178168	+	0.308597i
$346$	−8.01799e8	−	1.38876e9i	−1.04064	−	1.80244i
$347$	−4.37816e7			−0.0562520			−0.0281260	−	0.999604i	$-0.508954\pi$
$347$	−4.37816e7			−0.0562520			−0.0281260	+	0.999604i	$0.508954\pi$
$348$	−8.26878e8			−1.05175
$349$	3.43632e8	+	5.95188e8i	0.432718	+	0.749489i	0.997106	−	0.0760201i	$-0.0242213\pi$
$349$	3.43632e8	+	5.95188e8i	0.432718	+	0.749489i	−0.564388	+	0.825509i	$0.690888\pi$
$350$	7.49290e8	+	9.04843e7i	0.934140	+	0.112807i
$351$	8.73911e7	+	4.45925e7i	0.107868	+	0.0550411i
$352$	−7.33450e8	+	1.27037e9i	−0.896337	+	1.55250i
$353$	1.20630e8	−	2.08938e8i	0.145964	−	0.252817i	−0.783768	−	0.621053i	$-0.786705\pi$
$353$	1.20630e8	−	2.08938e8i	0.145964	−	0.252817i	0.929732	+	0.368237i	$0.120038\pi$
$354$	−8.37911e8	+	1.45131e9i	−1.00389	+	1.73879i
$355$	−9.89767e8	−	1.71433e9i	−1.17418	−	2.03373i
$356$	4.91373e8			0.577213
$357$	1.66300e8	+	3.89616e8i	0.193444	+	0.453209i
$358$	−1.14851e9	+	1.98928e9i	−1.32295	+	2.29142i
$359$	4.23517e8	−	7.33553e8i	0.483103	−	0.836760i	−0.516708	−	0.856161i	$-0.672843\pi$
$359$	4.23517e8	−	7.33553e8i	0.483103	−	0.836760i	0.999812	+	0.0194019i	$0.00617619\pi$
$360$	1.00988e9			1.14080
$361$	3.80784e8	−	6.59538e8i	0.425994	−	0.737844i
$362$	7.03175e8			0.779083
$363$	−1.87493e9			−2.05737
$364$	−1.26028e9	+	6.16880e8i	−1.36966	+	0.670419i
$365$	−6.83589e8			−0.735817
$366$	1.17138e9			1.24886
$367$	−2.30382e8	+	3.99034e8i	−0.243287	+	0.421385i	−0.961648	−	0.274285i	$-0.911559\pi$
$367$	−2.30382e8	+	3.99034e8i	−0.243287	+	0.421385i	0.718362	+	0.695670i	$0.244892\pi$
$368$	3.73117e7			0.0390282
$369$	−7.47587e8	+	1.29486e9i	−0.774586	+	1.34162i
$370$	1.92440e9	−	3.33316e9i	1.97510	−	3.42098i
$371$	6.41740e8	+	7.74965e7i	0.652455	+	0.0787904i
$372$	−1.30904e9			−1.31842
$373$	−1.59057e8	−	2.75494e8i	−0.158698	−	0.274873i	0.775701	−	0.631100i	$-0.217396\pi$
$373$	−1.59057e8	−	2.75494e8i	−0.158698	−	0.274873i	−0.934399	+	0.356227i	$0.884063\pi$
$374$	−4.27290e8	+	7.40089e8i	−0.422350	+	0.731532i
$375$	3.79325e8	−	6.57009e8i	0.371451	−	0.643372i
$376$	8.62371e7	−	1.49367e8i	0.0836637	−	0.144910i
$377$	2.57236e7	+	4.96406e8i	0.0247251	+	0.477136i
$378$	1.21283e8	−	1.61617e8i	0.115499	−	0.153910i
$379$	3.79397e8	+	6.57134e8i	0.357978	+	0.620036i	0.987623	−	0.156847i	$-0.0501329\pi$
$379$	3.79397e8	+	6.57134e8i	0.357978	+	0.620036i	−0.629645	+	0.776883i	$0.716800\pi$
$380$	7.91834e8			0.740272
$381$	2.83060e9			2.62205
$382$	−9.64804e8	−	1.67109e9i	−0.885558	−	1.53383i
$383$	−6.27004e8	−	1.08600e9i	−0.570262	−	0.987723i	−0.996539	−	0.0831298i	$-0.973508\pi$
$383$	−6.27004e8	−	1.08600e9i	−0.570262	−	0.987723i	0.426277	−	0.904593i	$-0.359825\pi$
$384$	1.15199e9	−	1.99530e9i	1.03822	−	1.79825i
$385$	2.18441e9	+	2.63789e8i	1.95084	+	0.235583i
$386$	−6.61855e8	+	1.14637e9i	−0.585743	+	1.01454i
$387$	1.64252e9			1.44053
$388$	9.30657e8	−	1.61195e9i	0.808870	−	1.40100i
$389$	−1.54647e8	−	2.67856e8i	−0.133204	−	0.230716i	0.791706	−	0.610902i	$-0.209193\pi$
$389$	−1.54647e8	−	2.67856e8i	−0.133204	−	0.230716i	−0.924910	+	0.380186i	$0.875860\pi$
$390$	−1.75466e8	−	3.38609e9i	−0.149785	−	2.89049i
$391$	7.89321e7			0.0667783
$392$	2.78017e8	+	9.55159e8i	0.233115	+	0.800893i
$393$	3.41974e8	+	5.92316e8i	0.284197	+	0.492243i
$394$	5.69220e8	+	9.85918e8i	0.468860	+	0.812090i
$395$	8.29262e8	+	1.43632e9i	0.677021	+	1.17263i
$396$	3.18085e9			2.57401
$397$	−3.60239e8	−	6.23951e8i	−0.288950	−	0.500477i	0.684609	−	0.728910i	$-0.259973\pi$
$397$	−3.60239e8	−	6.23951e8i	−0.288950	−	0.500477i	−0.973559	+	0.228434i	$0.926640\pi$
$398$	1.72755e9			1.37354
$399$	4.22961e8	−	5.63625e8i	0.333346	−	0.444206i
$400$	7.56061e7	+	1.30954e8i	0.0590673	+	0.102308i
$401$	−1.00598e9			−0.779086			−0.389543	−	0.921008i	$-0.627367\pi$
$401$	−1.00598e9			−0.779086			−0.389543	+	0.921008i	$0.627367\pi$
$402$	−6.08612e8	−	1.05415e9i	−0.467250	−	0.809301i
$403$	4.07235e7	+	7.85869e8i	0.0309940	+	0.598112i
$404$	−1.88424e9	+	3.26360e9i	−1.42168	+	2.46242i
$405$	−7.66750e8	−	1.32805e9i	−0.573536	−	0.993394i
$406$	1.01636e9	+	1.22735e8i	0.753713	+	0.0910184i
$407$	2.08654e9	−	3.61399e9i	1.53407	−	2.65709i
$408$	2.81939e8	−	4.88333e8i	0.205515	−	0.355963i
$409$	−1.34589e9			−0.972698			−0.486349	−	0.873765i	$-0.661672\pi$
$409$	−1.34589e9			−0.972698			−0.486349	+	0.873765i	$0.661672\pi$
$410$	3.99922e9			2.86571
$411$	−7.95498e8	+	1.37784e9i	−0.565188	+	0.978934i
$412$	2.80211e7	−	4.85339e7i	0.0197399	−	0.0341905i
$413$	7.52125e8	−	1.00226e9i	0.525370	−	0.700091i
$414$	−2.43228e8	−	4.21283e8i	−0.168466	−	0.291791i
$415$	8.76987e7	−	1.51899e8i	0.0602316	−	0.104324i
$416$	−1.50559e9	−	7.68247e8i	−1.02537	−	0.523208i
$417$	−8.84388e8	−	1.53180e9i	−0.597264	−	1.03449i
$418$	1.42155e9			0.952020
$419$	−8.93113e8	−	1.54692e9i	−0.593140	−	1.02735i	−0.993806	−	0.111125i	$-0.964555\pi$
$419$	−8.93113e8	−	1.54692e9i	−0.593140	−	1.02735i	0.400666	−	0.916224i	$-0.368779\pi$
$420$	−4.18707e9	−	5.05630e8i	−2.75764	−	0.333012i
$421$	−1.16821e9			−0.763014			−0.381507	−	0.924366i	$-0.624595\pi$
$421$	−1.16821e9			−0.763014			−0.381507	+	0.924366i	$0.624595\pi$
$422$	1.98120e9	+	3.43154e9i	1.28332	+	2.22277i
$423$	3.38462e8			0.217429
$424$	−4.30208e8	−	7.45142e8i	−0.274093	−	0.474743i
$425$	1.59943e8	+	2.77029e8i	0.101066	+	0.175051i
$426$	3.40595e9	+	5.89928e9i	2.13454	+	3.69713i
$427$	−8.69569e8	−	1.05009e8i	−0.540513	−	0.0652724i
$428$	1.51568e9			0.934449
$429$	−1.90250e8	−	3.67138e9i	−0.116339	−	2.24506i
$430$	−2.19667e9	−	3.80474e9i	−1.33237	−	2.30773i
$431$	−1.11206e9	+	1.92615e9i	−0.669051	+	1.15883i	0.309119	+	0.951023i	$0.399966\pi$
$431$	−1.11206e9	+	1.92615e9i	−0.669051	+	1.15883i	−0.978170	+	0.207806i	$0.933368\pi$
$432$	4.04838e7			0.0241595
$433$	4.07903e7	−	7.06509e7i	0.0241462	−	0.0418225i	−0.853700	−	0.520765i	$-0.825647\pi$
$433$	4.07903e7	−	7.06509e7i	0.0241462	−	0.0418225i	0.877846	+	0.478943i	$0.158980\pi$
$434$	1.60902e9	+	1.94305e8i	0.944814	+	0.114096i
$435$	−7.47026e8	+	1.29389e9i	−0.435134	+	0.753675i
$436$	−2.03142e9	−	3.51853e9i	−1.17381	−	2.03310i
$437$	−6.56499e7	−	1.13709e8i	−0.0376313	−	0.0651793i
$438$	2.35234e9			1.33765
$439$	1.59870e9			0.901865			0.450933	−	0.892558i	$-0.351092\pi$
$439$	1.59870e9			0.901865			0.450933	+	0.892558i	$0.351092\pi$
$440$	−1.46438e9	−	2.53638e9i	−0.819537	−	1.41948i
$441$	−1.35048e9	+	1.40968e9i	−0.749815	+	0.782682i
$442$	−8.77118e8	−	4.47562e8i	−0.483148	−	0.246533i
$443$	1.08456e8	−	1.87851e8i	0.0592707	−	0.102660i	−0.834868	−	0.550451i	$-0.814456\pi$
$443$	1.08456e8	−	1.87851e8i	0.0592707	−	0.102660i	0.894138	+	0.447791i	$0.147789\pi$
$444$	−3.99947e9	+	6.92729e9i	−2.16851	+	3.75598i
$445$	4.43921e8	−	7.68894e8i	0.238806	−	0.413625i
$446$	1.75939e9	+	3.04736e9i	0.939054	+	1.62649i
$447$	9.26272e7			0.0490526
$448$	−1.86158e9	+	2.48068e9i	−0.978158	+	1.30346i
$449$	−1.12020e9	+	1.94024e9i	−0.584026	+	1.01156i	0.410970	+	0.911649i	$0.365190\pi$
$449$	−1.12020e9	+	1.94024e9i	−0.584026	+	1.01156i	−0.994996	+	0.0999144i	$0.968143\pi$
$450$	9.85722e8	−	1.70732e9i	0.509930	−	0.883224i
$451$	4.33617e9			2.22581
$452$	1.37295e9	−	2.37802e9i	0.699310	−	1.21124i
$453$	−3.93044e9			−1.98654
$454$	4.53874e9			2.27635
$455$	−1.73292e8	+	2.52938e9i	−0.0862459	+	1.25885i
$456$	−9.37983e8			−0.463253
$457$	−3.58798e6			−0.00175850			−0.000879251	−	1.00000i	$-0.500280\pi$
$457$	−3.58798e6			−0.00175850			−0.000879251		1.00000i	$0.500280\pi$
$458$	−5.55052e8	+	9.61379e8i	−0.269963	+	0.467590i
$459$	8.56425e7			0.0413375
$460$	−3.92914e8	+	6.80548e8i	−0.188211	+	0.325991i
$461$	−3.39643e8	+	5.88278e8i	−0.161462	+	0.279660i	−0.935393	−	0.353610i	$-0.884954\pi$
$461$	−3.39643e8	+	5.88278e8i	−0.161462	+	0.279660i	0.773932	+	0.633269i	$0.218287\pi$
$462$	−7.51691e9	−	9.07742e8i	−3.54644	−	0.428268i
$463$	2.21995e9			1.03946			0.519732	−	0.854329i	$-0.326032\pi$
$463$	2.21995e9			1.03946			0.519732	+	0.854329i	$0.326032\pi$
$464$	1.02554e8	+	1.77629e8i	0.0476586	+	0.0825471i
$465$	−1.18263e9	+	2.04838e9i	−0.545461	+	0.944766i
$466$	−2.95915e9	+	5.12540e9i	−1.35462	+	2.34626i
$467$	6.51004e8	−	1.12757e9i	0.295784	−	0.512313i	−0.679383	−	0.733784i	$-0.737753\pi$
$467$	6.51004e8	−	1.12757e9i	0.295784	−	0.512313i	0.975167	+	0.221471i	$0.0710859\pi$
$468$	1.89675e8	+	3.66029e9i	0.0855361	+	1.65065i
$469$	3.57302e8	+	8.37103e8i	0.159930	+	0.374692i
$470$	−4.52650e8	−	7.84014e8i	−0.201104	−	0.348322i
$471$	3.17432e9			1.39984
$472$	−1.66796e9			−0.730109
$473$	−2.38174e9	−	4.12530e9i	−1.03486	−	1.79243i
$474$	−2.85363e9	−	4.94263e9i	−1.23076	−	2.13174i
$475$	2.66057e8	−	4.60825e8i	0.113906	−	0.197291i
$476$	−7.35176e8	+	9.79671e8i	−0.312440	+	0.416348i
$477$	8.44235e8	−	1.46226e9i	0.356163	−	0.616893i
$478$	3.98037e8			0.166696
$479$	1.20070e9	−	2.07968e9i	0.499185	−	0.864615i	−0.500814	−	0.865555i	$-0.666966\pi$
$479$	1.20070e9	−	2.07968e9i	0.499185	−	0.864615i	1.00000		0.000940289i	$0.000299303\pi$
$480$	−2.54022e9	−	4.39979e9i	−1.04840	−	1.81588i
$481$	4.28313e9	+	2.18553e9i	1.75491	+	0.895466i
$482$	−2.99500e9			−1.21824
$483$	2.74535e8	+	6.43193e8i	0.110862	+	0.259732i
$484$	−2.71054e9	−	4.69479e9i	−1.08667	−	1.88217i
$485$	−1.68157e9	−	2.91256e9i	−0.669296	−	1.15925i
$486$	2.88199e9	+	4.99175e9i	1.13885	+	1.97254i
$487$	−2.77035e9			−1.08688			−0.543441	−	0.839447i	$-0.682879\pi$
$487$	−2.77035e9			−1.08688			−0.543441	+	0.839447i	$0.682879\pi$
$488$	5.82939e8	+	1.00968e9i	0.227067	+	0.393291i
$489$	−5.66477e9			−2.19079
$490$	5.07149e9	+	1.24299e9i	1.94738	+	0.477290i
$491$	−1.55626e9	−	2.69552e9i	−0.593331	−	1.02768i	−0.993780	−	0.111360i	$-0.964479\pi$
$491$	−1.55626e9	−	2.69552e9i	−0.593331	−	1.02768i	0.400450	−	0.916319i	$-0.368854\pi$
$492$	−8.31155e9			−3.14633
$493$	2.16951e8	+	3.75771e8i	0.0815452	+	0.141240i
$494$	8.47676e7	+	1.63582e9i	0.0316363	+	0.610507i
$495$	2.87368e9	−	4.97736e9i	1.06493	−	1.84451i
$496$	1.62356e8	+	2.81208e8i	0.0597422	+	0.103477i
$497$	−1.99955e9	−	4.68464e9i	−0.730610	−	1.71171i
$498$	−3.01785e8	+	5.22708e8i	−0.109495	+	0.189651i
$499$	1.43249e9	−	2.48114e9i	0.516106	−	0.893921i	−0.483720	−	0.875223i	$-0.660715\pi$
$499$	1.43249e9	−	2.48114e9i	0.516106	−	0.893921i	0.999825	−	0.0186981i	$-0.00595213\pi$
$500$	2.19352e9			0.784777
$501$	5.22568e9			1.85657
$502$	−2.44559e9	+	4.23588e9i	−0.862820	+	1.49445i
$503$	−1.90498e9	+	3.29953e9i	−0.667426	+	1.15602i	0.311195	+	0.950346i	$0.399271\pi$
$503$	−1.90498e9	+	3.29953e9i	−0.667426	+	1.15602i	−0.978621	+	0.205670i	$0.934063\pi$
$504$	2.57977e9	+	3.11533e8i	0.897583	+	0.108392i
$505$	3.40456e9	+	5.89687e9i	1.17636	+	2.03752i
$506$	−7.05387e8	+	1.22177e9i	−0.242047	+	0.419238i
$507$	4.21340e9	−	4.37850e8i	1.43584	−	0.149210i
$508$	4.09213e9	+	7.08778e9i	1.38493	+	2.39876i
$509$	1.50760e9			0.506726			0.253363	−	0.967371i	$-0.418463\pi$
$509$	1.50760e9			0.506726			0.253363	+	0.967371i	$0.418463\pi$
$510$	−1.47987e9	−	2.56321e9i	−0.494001	−	0.855635i
$511$	−1.74626e9	−	2.10878e8i	−0.578941	−	0.0699129i
$512$	−1.20285e9			−0.396064
$513$	−7.12310e7	−	1.23376e8i	−0.0232948	−	0.0403477i
$514$	4.61590e8			0.149929
$515$	−5.06301e7	−	8.76940e7i	−0.0163337	−	0.0282907i
$516$	4.56532e9	+	7.90736e9i	1.46284	+	2.53371i
$517$	−4.90788e8	−	8.50069e8i	−0.156198	−	0.270544i
$518$	5.94420e9	−	7.92105e9i	1.87905	−	2.50397i
$519$	6.02181e9			1.89078
$520$	2.83135e9	−	1.83634e9i	0.883043	−	0.572719i
$521$	8.28662e8	+	1.43528e9i	0.256711	+	0.444637i	0.965359	−	0.260925i	$-0.0840277\pi$
$521$	8.28662e8	+	1.43528e9i	0.256711	+	0.444637i	−0.708647	+	0.705563i	$0.750694\pi$
$522$	1.33706e9	−	2.31586e9i	0.411438	−	0.712632i
$523$	6.34249e9			1.93867			0.969335	−	0.245742i	$-0.0790316\pi$
$523$	6.34249e9			1.93867			0.969335	+	0.245742i	$0.0790316\pi$
$524$	−9.88766e8	+	1.71259e9i	−0.300216	+	0.519990i
$525$	−1.70112e9	+	2.26686e9i	−0.513072	+	0.683703i
$526$	1.36546e9	−	2.36504e9i	0.409099	−	0.708580i
$527$	3.43459e8	+	5.94889e8i	0.102221	+	0.177051i
$528$	−7.58483e8	−	1.31373e9i	−0.224247	−	0.388408i
$529$	−3.27452e9			−0.961730
$530$	−4.51624e9			−1.31768
$531$	−1.63659e9	−	2.83466e9i	−0.474361	−	0.821617i
$532$	2.02277e9	+	2.44270e8i	0.582446	+	0.0703362i
$533$	2.58567e8	+	4.98974e9i	0.0739652	+	1.42736i
$534$	−1.52761e9	+	2.64589e9i	−0.434127	+	0.751930i
$535$	1.36931e9	−	2.37172e9i	0.386603	−	0.669616i
$536$	6.05755e8	−	1.04920e9i	0.169910	−	0.294294i
$537$	−4.31287e9	−	7.47011e9i	−1.20187	−	2.08169i
$538$	−1.61545e9			−0.447255
$539$	5.49878e9	+	1.34772e9i	1.51254	+	0.370714i
$540$	−4.26318e8	+	7.38404e8i	−0.116508	+	0.201797i
$541$	−3.55705e9	+	6.16099e9i	−0.965827	+	1.67286i	−0.258452	+	0.966024i	$0.583212\pi$
$541$	−3.55705e9	+	6.16099e9i	−0.965827	+	1.67286i	−0.707376	+	0.706838i	$0.750121\pi$
$542$	−8.68270e9			−2.34238
$543$	−1.32028e9	+	2.28679e9i	−0.353888	+	0.612952i
$544$	−1.47546e9			−0.392945
$545$	−7.34100e9			−1.94253
$546$	5.96326e8	−	8.70402e9i	0.156787	−	2.28847i
$547$	2.26379e9			0.591398			0.295699	−	0.955281i	$-0.404447\pi$
$547$	2.26379e9			0.591398			0.295699	+	0.955281i	$0.404447\pi$
$548$	−4.60013e9			−1.19409
$549$	−1.14395e9	+	1.98138e9i	−0.295056	+	0.511052i
$550$	−5.71740e9			−1.46531
$551$	3.60888e8	−	6.25076e8i	0.0919056	−	0.159185i
$552$	4.65435e8	−	8.06157e8i	0.117780	−	0.204001i
$553$	1.67530e9	+	3.92496e9i	0.421263	+	0.986955i
$554$	1.29467e9			0.323501
$555$	7.22649e9	+	1.25166e10i	1.79433	+	3.10787i
$556$	2.55707e9	−	4.42898e9i	0.630930	−	1.09280i
$557$	−2.26070e9	+	3.91565e9i	−0.554307	+	0.960088i	0.443650	+	0.896200i	$0.353683\pi$
$557$	−2.26070e9	+	3.91565e9i	−0.554307	+	0.960088i	−0.997957	+	0.0638881i	$0.979650\pi$
$558$	2.11672e9	−	3.66627e9i	0.515756	−	0.893316i
$559$	4.60506e9	−	2.98672e9i	1.11505	−	0.723192i
$560$	4.10686e8	+	9.62174e8i	0.0988216	+	0.231524i
$561$	−1.60455e9	−	2.77917e9i	−0.383693	−	0.664577i
$562$	−1.05397e10			−2.50467
$563$	2.41187e9			0.569606			0.284803	−	0.958586i	$-0.408072\pi$
$563$	2.41187e9			0.569606			0.284803	+	0.958586i	$0.408072\pi$
$564$	9.40740e8	+	1.62941e9i	0.220797	+	0.382431i
$565$	−2.48072e9	−	4.29674e9i	−0.578641	−	1.00224i
$566$	4.73350e9	−	8.19866e9i	1.09730	−	1.90058i
$567$	−1.54901e9	−	3.62909e9i	−0.356872	−	0.836097i
$568$	−3.38996e9	+	5.87158e9i	−0.776203	+	1.34442i
$569$	−8.13103e9			−1.85034			−0.925172	−	0.379549i	$-0.876079\pi$
$569$	−8.13103e9			−1.85034			−0.925172	+	0.379549i	$0.876079\pi$
$570$	−2.46169e9	+	4.26378e9i	−0.556765	+	0.964345i
$571$	−2.59388e9	−	4.49274e9i	−0.583074	−	1.00991i	−0.995113	−	0.0987477i	$-0.968516\pi$
$571$	−2.59388e9	−	4.49274e9i	−0.583074	−	1.00991i	0.412038	−	0.911167i	$-0.364817\pi$
$572$	8.91802e9	−	5.78400e9i	1.99243	−	1.29224i
$573$	7.24603e9			1.60901
$574$	1.02162e10	+	1.23370e9i	2.25474	+	0.272282i
$575$	2.64040e8	+	4.57330e8i	0.0579205	+	0.100321i
$576$	4.05071e9	+	7.01604e9i	0.883187	+	1.52973i
$577$	−2.55106e9	−	4.41856e9i	−0.552847	−	0.957558i	−0.998068	−	0.0621377i	$-0.980208\pi$
$577$	−2.55106e9	−	4.41856e9i	−0.552847	−	0.957558i	0.445221	−	0.895421i	$-0.353125\pi$
$578$	6.51731e9			1.40385
$579$	−2.48539e9	−	4.30482e9i	−0.532132	−	0.921679i
$580$	−4.31983e9			−0.919324
$581$	2.70888e8	−	3.60977e8i	0.0573025	−	0.0763595i
$582$	5.78655e9	+	1.00226e10i	1.21672	+	2.10741i
$583$	−4.89675e9			−1.02345
$584$	1.17065e9	+	2.02762e9i	0.243210	+	0.421253i
$585$	5.89893e9	+	3.01001e9i	1.21822	+	0.621617i
$586$	−3.30065e9	+	5.71690e9i	−0.677576	+	1.17360i
$587$	3.83344e9	+	6.63972e9i	0.782268	+	1.35493i	0.930618	+	0.365993i	$0.119271\pi$
$587$	3.83344e9	+	6.63972e9i	0.782268	+	1.35493i	−0.148350	+	0.988935i	$0.547396\pi$
$588$	−1.05400e10	−	2.58330e9i	−2.13807	−	0.524028i
$589$	5.71328e8	−	9.89569e8i	0.115208	−	0.199546i
$590$	−4.37747e9	+	7.58200e9i	−0.877488	+	1.51985i
$591$	−4.27505e9			−0.851893
$592$	1.98415e9			0.393052
$593$	−1.38185e8	+	2.39343e8i	−0.0272125	+	0.0471335i	−0.879311	−	0.476248i	$-0.841996\pi$
$593$	−1.38185e8	+	2.39343e8i	−0.0272125	+	0.0471335i	0.852098	+	0.523382i	$0.175330\pi$
$594$	−7.65354e8	+	1.32563e9i	−0.149834	+	0.259520i
$595$	8.68797e8	+	2.03546e9i	0.169086	+	0.396144i
$596$	1.33909e8	+	2.31937e8i	0.0259088	+	0.0448753i
$597$	−3.24364e9	+	5.61815e9i	−0.623911	+	1.08064i
$598$	−1.44798e9	−	7.38852e8i	−0.276890	−	0.141287i
$599$	−1.68164e8	−	2.91268e8i	−0.0319697	−	0.0553731i	0.849598	−	0.527431i	$-0.176845\pi$
$599$	−1.68164e8	−	2.91268e8i	−0.0319697	−	0.0553731i	−0.881568	+	0.472058i	$0.843511\pi$
$600$	3.77251e9			0.713019
$601$	−2.06883e9	−	3.58332e9i	−0.388745	−	0.673325i	0.603536	−	0.797335i	$-0.293758\pi$
$601$	−2.06883e9	−	3.58332e9i	−0.388745	−	0.673325i	−0.992281	+	0.124010i	$0.960424\pi$
$602$	−4.43776e9	−	1.03970e10i	−0.829042	−	1.94232i
$603$	2.37745e9			0.441572
$604$	−5.68214e9	−	9.84175e9i	−1.04926	−	1.81737i
$605$	−9.79513e9			−1.79832
$606$	−1.17156e10	−	2.02921e10i	−2.13851	−	3.70402i
$607$	−3.32930e8	−	5.76651e8i	−0.0604216	−	0.104653i	0.834232	−	0.551413i	$-0.185911\pi$
$607$	−3.32930e8	−	5.76651e8i	−0.0604216	−	0.104653i	−0.894654	+	0.446760i	$0.852578\pi$
$608$	1.22718e9	+	2.12553e9i	0.221434	+	0.383536i
$609$	−2.30745e9	+	3.07484e9i	−0.413974	+	0.551648i
$610$	6.11958e9			1.09161
$611$	9.48930e8	−	6.15452e8i	0.168302	−	0.109157i
$612$	1.59971e9	+	2.77077e9i	0.282105	+	0.488620i
$613$	6.77111e8	−	1.17279e9i	0.118727	−	0.205641i	−0.800537	−	0.599284i	$-0.795452\pi$
$613$	6.77111e8	−	1.17279e9i	0.118727	−	0.205641i	0.919263	+	0.393643i	$0.128785\pi$
$614$	8.29732e9			1.44660
$615$	−7.50891e9	+	1.30058e10i	−1.30171	+	2.25463i
$616$	−2.95837e9	−	6.93101e9i	−0.509942	−	1.19472i
$617$	2.15003e9	−	3.72397e9i	0.368508	−	0.638275i	−0.620824	−	0.783950i	$-0.713202\pi$
$617$	2.15003e9	−	3.72397e9i	0.368508	−	0.638275i	0.989333	+	0.145675i	$0.0465354\pi$
$618$	1.74227e8	+	3.01769e8i	0.0296930	+	0.0514299i
$619$	−8.05704e8	−	1.39552e9i	−0.136540	−	0.236493i	0.789645	−	0.613564i	$-0.210265\pi$
$619$	−8.05704e8	−	1.39552e9i	−0.136540	−	0.236493i	−0.926185	+	0.377071i	$0.876931\pi$
$620$	−6.83879e9			−1.15241
$621$	1.41382e8			0.0236904
$622$	8.35518e9	+	1.44716e10i	1.39216	+	2.41130i
$623$	1.37121e9	−	1.82723e9i	0.227193	−	0.302750i
$624$	1.46652e9	−	9.51144e8i	0.241624	−	0.156711i
$625$	3.78878e9	−	6.56237e9i	0.620754	−	1.07518i
$626$	4.43344e9	−	7.67895e9i	0.722322	−	1.25110i
$627$	−2.66910e9	+	4.62301e9i	−0.432442	+	0.749012i
$628$	4.58904e9	+	7.94845e9i	0.739372	+	1.28063i
$629$	4.19743e9			0.672522
$630$	8.18662e9	−	1.09092e10i	1.30441	−	1.73821i
$631$	−1.34647e9	+	2.33215e9i	−0.213350	+	0.369533i	−0.952761	−	0.303721i	$-0.901771\pi$
$631$	−1.34647e9	+	2.33215e9i	−0.213350	+	0.369533i	0.739411	+	0.673255i	$0.235104\pi$
$632$	2.84023e9	−	4.91942e9i	0.447552	−	0.775183i
$633$	−1.48795e10			−2.33172
$634$	−1.52478e9	+	2.64099e9i	−0.237626	+	0.411580i
$635$	1.47878e10			2.29190
$636$	9.38607e9			1.44672
$637$	−1.22296e9	+	6.40795e9i	−0.187467	+	0.982271i
$638$	−7.75525e9			−1.18229
$639$	−1.33048e10			−2.01724
$640$	6.01829e9	−	1.04240e10i	0.907493	−	1.57182i
$641$	−1.24396e9			−0.186554			−0.0932768	−	0.995640i	$-0.529734\pi$
$641$	−1.24396e9			−0.186554			−0.0932768	+	0.995640i	$0.529734\pi$
$642$	−4.71204e9	+	8.16149e9i	−0.702807	+	1.21730i
$643$	5.12182e9	−	8.87125e9i	0.759776	−	1.31597i	−0.183189	−	0.983078i	$-0.558642\pi$
$643$	5.12182e9	−	8.87125e9i	0.759776	−	1.31597i	0.942965	−	0.332893i	$-0.108025\pi$
$644$	−1.21365e9	+	1.61728e9i	−0.179058	+	0.238607i
$645$	1.64978e10			2.42084
$646$	7.14924e8	+	1.23829e9i	0.104339	+	0.180720i
$647$	−4.69128e8	+	8.12554e8i	−0.0680968	+	0.117947i	−0.898064	−	0.439866i	$-0.855026\pi$
$647$	−4.69128e8	+	8.12554e8i	−0.0680968	+	0.117947i	0.829967	+	0.557813i	$0.188359\pi$
$648$	−2.62612e9	+	4.54858e9i	−0.379143	+	0.656694i
$649$	−4.74629e9	+	8.22081e9i	−0.681550	+	1.18048i
$650$	−3.40930e8	−	6.57916e9i	−0.0486932	−	0.939666i
$651$	−3.65297e9	+	4.86783e9i	−0.518935	+	0.691516i
$652$	−8.18942e9	−	1.41845e10i	−1.15714	−	2.00423i
$653$	4.96745e9			0.698131			0.349066	−	0.937098i	$-0.386499\pi$
$653$	4.96745e9			0.698131			0.349066	+	0.937098i	$0.386499\pi$
$654$	2.52616e10			3.53133
$655$	1.78656e9	+	3.09442e9i	0.248413	+	0.430263i
$656$	1.03085e9	+	1.78548e9i	0.142571	+	0.246940i
$657$	−2.29727e9	+	3.97899e9i	−0.316033	+	0.547386i
$658$	−9.14456e8	−	2.14243e9i	−0.125133	−	0.293168i
$659$	−5.62820e9	+	9.74833e9i	−0.766074	+	1.32688i	0.173603	+	0.984816i	$0.444459\pi$
$659$	−5.62820e9	+	9.74833e9i	−0.766074	+	1.32688i	−0.939677	+	0.342063i	$0.888874\pi$
$660$	3.19491e10			4.32568
$661$	−2.09547e9	+	3.62946e9i	−0.282213	+	0.488807i	−0.971929	−	0.235273i	$-0.924402\pi$
$661$	−2.09547e9	+	3.62946e9i	−0.282213	+	0.488807i	0.689717	+	0.724079i	$0.257735\pi$
$662$	−1.13089e9	−	1.95875e9i	−0.151501	−	0.262407i
$663$	3.10238e9	−	2.01212e9i	0.413426	−	0.268137i
$664$	−6.00737e8			−0.0796336
$665$	2.20966e9	−	2.94452e9i	0.291373	−	0.388275i
$666$	−1.29343e10	−	2.24029e10i	−1.69661	−	2.93862i
$667$	3.58151e8	+	6.20336e8i	0.0467333	+	0.0809444i
$668$	7.55464e9	+	1.30850e10i	0.980609	+	1.69846i
$669$	−1.32137e10			−1.70621
$670$	−3.17955e9	−	5.50714e9i	−0.408417	−	0.707399i
$671$	6.63518e9			0.847859
$672$	−5.13182e9	−	1.20231e10i	−0.652347	−	1.52835i
$673$	−1.72428e9	−	2.98655e9i	−0.218050	−	0.377674i	0.736162	−	0.676806i	$-0.236636\pi$
$673$	−1.72428e9	−	2.98655e9i	−0.218050	−	0.377674i	−0.954212	+	0.299132i	$0.903303\pi$
$674$	−1.01769e10			−1.28028
$675$	2.86487e8	+	4.96210e8i	0.0358543	+	0.0621015i
$676$	7.18757e9	+	9.91729e9i	0.894889	+	1.23475i
$677$	−6.04539e9	+	1.04709e10i	−0.748797	+	1.29696i	0.199602	+	0.979877i	$0.436035\pi$
$677$	−6.04539e9	+	1.04709e10i	−0.748797	+	1.29696i	−0.948399	+	0.317078i	$0.897298\pi$
$678$	8.53658e9	+	1.47858e10i	1.05191	+	1.82197i
$679$	−3.39715e9	−	7.95899e9i	−0.416457	−	0.975695i
$680$	1.47292e9	−	2.55118e9i	0.179638	−	0.311143i
$681$	−8.52190e9	+	1.47604e10i	−1.03400	+	1.79095i
$682$	−1.22775e10			−1.48205
$683$	−1.01134e9			−0.121457			−0.0607287	−	0.998154i	$-0.519342\pi$
$683$	−1.01134e9			−0.121457			−0.0607287	+	0.998154i	$0.519342\pi$
$684$	2.66104e9	−	4.60905e9i	0.317947	−	0.550700i
$685$	−4.15589e9	+	7.19822e9i	−0.494023	+	0.855673i
$686$	1.25719e10	+	4.73976e9i	1.48685	+	0.560560i
$687$	−2.08432e9	−	3.61015e9i	−0.245254	−	0.424793i
$688$	1.13244e9	−	1.96144e9i	0.132573	−	0.229623i
$689$	−2.91994e8	−	5.63481e9i	−0.0340100	−	0.656314i
$690$	−2.44302e9	−	4.23144e9i	−0.283111	−	0.490362i
$691$	−1.19233e10			−1.37474			−0.687372	−	0.726306i	$-0.741236\pi$
$691$	−1.19233e10			−1.37474			−0.687372	+	0.726306i	$0.741236\pi$
$692$	8.70558e9	+	1.50785e10i	0.998680	+	1.72976i
$693$	8.87637e9	−	1.18284e10i	1.01314	−	1.35008i
$694$	7.87085e8			0.0893848
$695$	−4.62027e9	−	8.00255e9i	−0.522061	−	0.904236i
$696$	5.11714e9			0.575301
$697$	2.18074e9	+	3.77715e9i	0.243943	+	0.422522i
$698$	−6.17766e9	−	1.07000e10i	−0.687591	−	1.19094i
$699$	−1.11121e10	−	1.92468e10i	−1.23063	−	2.13152i
$700$	−8.13546e9	−	9.82437e8i	−0.896476	−	0.108258i
$701$	3.60649e9			0.395432			0.197716	−	0.980259i	$-0.436648\pi$
$701$	3.60649e9			0.395432			0.197716	+	0.980259i	$0.436648\pi$
$702$	−1.57108e9	−	8.01664e8i	−0.171403	−	0.0874607i
$703$	−3.49111e9	−	6.04678e9i	−0.378983	−	0.656419i
$704$	1.17475e10	−	2.03473e10i	1.26894	−	2.19787i
$705$	3.39957e9			0.365395
$706$	−2.16864e9	+	3.75619e9i	−0.231937	+	0.401727i
$707$	6.87798e9	+	1.61141e10i	0.731970	+	1.71489i
$708$	9.09767e9	−	1.57576e10i	0.963415	−	1.66868i
$709$	3.87952e9	+	6.71952e9i	0.408805	+	0.708070i	0.994756	−	0.102276i	$-0.0326124\pi$
$709$	3.87952e9	+	6.71952e9i	0.408805	+	0.708070i	−0.585952	+	0.810346i	$0.699279\pi$
$710$	1.77936e10	+	3.08194e10i	1.86577	+	3.23161i
$711$	1.11473e10			1.16312
$712$	−3.04087e9			−0.315731
$713$	5.66995e8	+	9.82065e8i	0.0585823	+	0.101467i
$714$	−2.98967e9	−	7.00434e9i	−0.307383	−	0.720151i
$715$	−9.93915e8	−	1.91802e10i	−0.101690	−	1.96238i
$716$	1.24700e10	−	2.15987e10i	1.26961	−	2.19903i
$717$	−7.47351e8	+	1.29445e9i	−0.0757195	+	0.131150i
$718$	−7.61379e9	+	1.31875e10i	−0.767654	+	1.32962i
$719$	3.48355e9	+	6.03368e9i	0.349519	+	0.605385i	0.986164	−	0.165772i	$-0.0530117\pi$
$719$	3.48355e9	+	6.03368e9i	0.349519	+	0.605385i	−0.636645	+	0.771157i	$0.719678\pi$
$720$	2.73267e9			0.272849
$721$	−1.02284e8	−	2.39636e8i	−0.0101633	−	0.0238111i
$722$	−6.84557e9	+	1.18569e10i	−0.676907	+	1.17244i
$723$	5.62338e9	−	9.73998e9i	0.553367	−	0.958461i
$724$	−7.63476e9			−0.747671
$725$	−1.45147e9	+	2.51402e9i	−0.141457	+	0.245011i
$726$	3.37067e10			3.26917
$727$	−1.65258e8			−0.0159511			−0.00797557	−	0.999968i	$-0.502539\pi$
$727$	−1.65258e8			−0.0159511			−0.00797557	+	0.999968i	$0.502539\pi$
$728$	7.79928e9	−	3.81757e9i	0.749195	−	0.366714i
$729$	−1.21356e10			−1.16015
$730$	1.22893e10			1.16922
$731$	2.39564e9	−	4.14938e9i	0.226836	−	0.392891i
$732$	−1.27183e10			−1.19850
$733$	−2.38561e9	+	4.13199e9i	−0.223736	+	0.387522i	−0.955939	−	0.293564i	$-0.905159\pi$
$733$	−2.38561e9	+	4.13199e9i	−0.223736	+	0.387522i	0.732204	+	0.681086i	$0.238492\pi$
$734$	4.14171e9	−	7.17365e9i	0.386584	−	0.669583i
$735$	−1.35645e10	+	1.41591e10i	−1.26008	+	1.31532i
$736$	−2.43574e9			−0.225195
$737$	−3.44744e9	−	5.97114e9i	−0.317220	−	0.549441i
$738$	1.34398e10	−	2.32784e10i	1.23082	−	2.13184i
$739$	1.08280e9	−	1.87547e9i	0.0986945	−	0.170944i	−0.812450	−	0.583031i	$-0.801867\pi$
$739$	1.08280e9	−	1.87547e9i	0.0986945	−	0.170944i	0.911145	+	0.412087i	$0.135200\pi$
$740$	−2.08943e10	+	3.61900e10i	−1.89547	+	3.28305i
$741$	−5.47898e9	−	2.79573e9i	−0.494693	−	0.252424i
$742$	−1.15369e10	−	1.39320e9i	−1.03675	−	0.125198i
$743$	6.51682e9	+	1.12875e10i	0.582874	+	1.00957i	0.995137	+	0.0985024i	$0.0314052\pi$
$743$	6.51682e9	+	1.12875e10i	0.582874	+	1.00957i	−0.412263	+	0.911065i	$0.635261\pi$
$744$	8.10104e9			0.721166
$745$	4.83909e8			0.0428762
$746$	2.85945e9	+	4.95271e9i	0.252172	+	0.436775i
$747$	−5.89440e8	−	1.02094e9i	−0.0517390	−	0.0896145i
$748$	4.63933e9	−	8.03555e9i	0.405321	−	0.702037i
$749$	4.22961e9	−	5.63625e9i	0.367802	−	0.490121i
$750$	−6.81932e9	+	1.18114e10i	−0.590238	+	1.02232i
$751$	1.27113e10			1.09509			0.547546	−	0.836775i	$-0.315562\pi$
$751$	1.27113e10			1.09509			0.547546	+	0.836775i	$0.315562\pi$
$752$	2.33352e8	−	4.04178e8i	0.0200101	−	0.0346586i
$753$	−9.18363e9	−	1.59065e10i	−0.783848	−	1.35767i
$754$	−4.62447e8	−	8.92416e9i	−0.0392882	−	0.758172i
$755$	−2.05337e10			−1.73641
$756$	−1.31683e9	+	1.75477e9i	−0.110842	+	0.147704i
$757$	−4.99872e9	−	8.65804e9i	−0.418816	−	0.725410i	0.577005	−	0.816741i	$-0.304221\pi$
$757$	−4.99872e9	−	8.65804e9i	−0.418816	−	0.725410i	−0.995821	+	0.0913303i	$0.970888\pi$
$758$	−6.82062e9	−	1.18137e10i	−0.568829	−	0.985241i
$759$	−2.64886e9	−	4.58796e9i	−0.219893	−	0.380867i
$760$	−4.90027e9			−0.404923
$761$	9.71307e8	+	1.68235e9i	0.0798933	+	0.138379i	0.903204	−	0.429212i	$-0.141209\pi$
$761$	9.71307e8	+	1.68235e9i	0.0798933	+	0.138379i	−0.823310	+	0.567591i	$0.807875\pi$
$762$	−5.08873e10			−4.16646
$763$	−1.87529e10	−	2.26460e9i	−1.52838	−	0.184567i
$764$	1.04754e10	+	1.81439e10i	0.849853	+	1.47199i
$765$	5.78090e9			0.466853
$766$	1.12720e10	+	1.95237e10i	0.906149	+	1.56950i
$767$	−9.74291e9	−	4.97146e9i	−0.779660	−	0.397833i
$768$	−5.94369e9	+	1.02948e10i	−0.473470	+	0.820073i
$769$	9.57185e8	+	1.65789e9i	0.0759021	+	0.131466i	0.901478	−	0.432824i	$-0.142483\pi$
$769$	9.57185e8	+	1.65789e9i	0.0759021	+	0.131466i	−0.825576	+	0.564291i	$0.809150\pi$
$770$	−3.92703e10	−	4.74228e9i	−3.09989	−	0.374343i
$771$	−8.66678e8	+	1.50113e9i	−0.0681032	+	0.117958i
$772$	7.18612e9	−	1.24467e10i	0.562126	−	0.973632i
$773$	−2.70483e9			−0.210626			−0.105313	−	0.994439i	$-0.533584\pi$
$773$	−2.70483e9			−0.210626			−0.105313	+	0.994439i	$0.533584\pi$
$774$	−2.95285e10			−2.28901
$775$	−2.29785e9	+	3.97999e9i	−0.177323	+	0.307132i
$776$	−5.75939e9	+	9.97555e9i	−0.442446	+	0.766339i
$777$	1.45991e10	+	3.42035e10i	1.11649	+	2.61576i
$778$	2.78017e9	+	4.81539e9i	0.211662	+	0.366609i
$779$	3.62755e9	−	6.28310e9i	0.274936	−	0.476204i
$780$	1.90513e9	+	3.67646e10i	0.143745	+	2.77395i
$781$	1.92927e10	+	3.34160e10i	1.44916	+	2.51001i
$782$	−1.41901e9			−0.106111
$783$	3.88599e8	+	6.73073e8i	0.0289291	+	0.0501067i
$784$	7.52296e8	+	2.58460e9i	0.0557549	+	0.191552i
$785$	1.65835e10			1.22358
$786$	−6.14785e9	−	1.06484e10i	−0.451590	−	0.782177i
$787$	1.54904e10			1.13279			0.566397	−	0.824133i	$-0.308337\pi$
$787$	1.54904e10			1.13279			0.566397	+	0.824133i	$0.308337\pi$
$788$	−6.18033e9	−	1.07047e10i	−0.449956	−	0.779347i
$789$	5.12755e9	+	8.88117e9i	0.371655	+	0.643726i
$790$	−1.49081e10	−	2.58216e10i	−1.07579	−	1.86332i
$791$	−5.01162e9	−	1.17415e10i	−0.360048	−	0.843538i
$792$	−1.96848e10			−1.40796
$793$	3.95657e8	+	7.63526e9i	0.0281749	+	0.543711i
$794$	6.47620e9	+	1.12171e10i	0.459144	+	0.795260i
$795$	8.47965e9	−	1.46872e10i	0.598540	−	1.03670i
$796$	−1.87570e10			−1.31816
$797$	−1.17436e10	+	2.03406e10i	−0.821672	+	1.42318i	0.0827651	+	0.996569i	$0.473625\pi$
$797$	−1.17436e10	+	2.03406e10i	−0.821672	+	1.42318i	−0.904437	+	0.426608i	$0.859708\pi$
$798$	−7.60380e9	+	1.01326e10i	−0.529689	+	0.705846i
$799$	4.93652e8	−	8.55030e8i	0.0342379	−	0.0593018i
$800$	−4.93564e9	−	8.54877e9i	−0.340822	−	0.590322i
$801$	−2.98368e9	−	5.16789e9i	−0.205135	−	0.355304i
$802$	1.80851e10			1.23797
$803$	1.33247e10			0.908138
$804$	6.60803e9	+	1.14455e10i	0.448411	+	0.776670i
$805$	1.43424e9	+	3.36021e9i	0.0969029	+	0.227029i
$806$	−7.32108e8	−	1.41280e10i	−0.0492496	−	0.950403i
$807$	3.03315e9	−	5.25357e9i	0.203159	−	0.351882i
$808$	1.16607e10	−	2.01968e10i	0.777648	−	1.34693i
$809$	−5.42621e9	+	9.39847e9i	−0.360310	+	0.624076i	−0.988012	−	0.154379i	$-0.950662\pi$
$809$	−5.42621e9	+	9.39847e9i	−0.360310	+	0.624076i	0.627702	+	0.778454i	$0.283996\pi$
$810$	1.37843e10	+	2.38751e10i	0.911352	+	1.57851i
$811$	1.78366e10			1.17420			0.587098	−	0.809516i	$-0.300270\pi$
$811$	1.78366e10			1.17420			0.587098	+	0.809516i	$0.300270\pi$
$812$	−1.10352e10	−	1.33261e9i	−0.723324	−	0.0873486i
$813$	1.63026e10	−	2.82369e10i	1.06399	−	1.84289i
$814$	−3.75109e10	+	6.49707e10i	−2.43765	+	4.22214i
$815$	−2.95943e10			−1.91494
$816$	7.62910e8	−	1.32140e9i	0.0491538	−	0.0851370i
$817$	−7.97007e9			−0.511311
$818$	2.41958e10			1.54562
$819$	1.41405e10	+	9.50893e9i	0.899437	+	0.604837i
$820$	−4.34217e10			−2.75016
$821$	1.38809e10			0.875423			0.437711	−	0.899115i	$-0.355789\pi$
$821$	1.38809e10			0.875423			0.437711	+	0.899115i	$0.355789\pi$
$822$	1.43011e10	−	2.47702e10i	0.898086	−	1.55553i
$823$	−2.42970e10			−1.51934			−0.759668	−	0.650311i	$-0.774639\pi$
$823$	−2.42970e10			−1.51934			−0.759668	+	0.650311i	$0.774639\pi$
$824$	−1.73409e8	+	3.00353e8i	−0.0107976	+	0.0187019i
$825$	1.07349e10	−	1.85935e10i	0.665597	−	1.15285i
$826$	−1.35214e10	+	1.80181e10i	−0.834815	+	1.11245i
$827$	1.01888e10			0.626404			0.313202	−	0.949687i	$-0.398598\pi$
$827$	1.01888e10			0.626404			0.313202	+	0.949687i	$0.398598\pi$
$828$	2.64086e9	+	4.57410e9i	0.161673	+	0.280027i
$829$	−6.48944e9	+	1.12400e10i	−0.395609	+	0.685216i	−0.993179	−	0.116602i	$-0.962800\pi$
$829$	−6.48944e9	+	1.12400e10i	−0.395609	+	0.685216i	0.597569	+	0.801817i	$0.296133\pi$
$830$	−1.57661e9	+	2.73076e9i	−0.0957084	+	0.165772i
$831$	−2.43087e9	+	4.21039e9i	−0.146946	+	0.254518i
$832$	2.41146e10	+	1.23048e10i	1.45161	+	0.740704i
$833$	1.59147e9	+	5.46767e9i	0.0953981	+	0.327751i
$834$	1.58991e10	+	2.75381e10i	0.949056	+	1.64381i
$835$	2.73003e10			1.62280
$836$	−1.54346e10			−0.913636
$837$	6.15198e8	+	1.06555e9i	0.0362640	+	0.0628111i
$838$	1.60560e10	+	2.78098e10i	0.942503	+	1.63246i
$839$	5.81476e9	−	1.00715e10i	0.339911	−	0.588742i	−0.644505	−	0.764600i	$-0.722937\pi$
$839$	5.81476e9	−	1.00715e10i	0.339911	−	0.588742i	0.984416	+	0.175858i	$0.0562699\pi$
$840$	2.59117e10	+	3.12910e9i	1.50841	+	0.182155i
$841$	6.65612e9	−	1.15287e10i	0.385865	−	0.668338i
$842$	2.10015e10			1.21243
$843$	1.97892e10	−	3.42759e10i	1.13771	−	1.97057i
$844$	−2.15110e10	−	3.72581e10i	−1.23158	−	2.13315i
$845$	2.20119e10	−	2.28744e9i	1.25505	−	0.130422i
$846$	−6.08471e9			−0.345496
$847$	−2.50221e10	−	3.02166e9i	−1.41492	−	0.170865i
$848$	−1.16412e9	−	2.01631e9i	−0.0655557	−	0.113546i
$849$	1.77752e10	+	3.07875e10i	0.996866	+	1.72662i
$850$	−2.87538e9	−	4.98031e9i	−0.160594	−	0.278157i
$851$	6.92928e9			0.385420
$852$	−3.69803e10	−	6.40517e10i	−2.04848	−	3.54807i
$853$	3.95671e9			0.218279			0.109140	−	0.994026i	$-0.465190\pi$
$853$	3.95671e9			0.218279			0.109140	+	0.994026i	$0.465190\pi$
$854$	1.56327e10	+	1.88781e9i	0.858878	+	0.103718i
$855$	−4.80812e9	−	8.32791e9i	−0.263084	−	0.455674i
$856$	−9.37983e9			−0.511137
$857$	−1.36784e10	−	2.36917e10i	−0.742341	−	1.28577i	−0.951427	−	0.307875i	$-0.900382\pi$
$857$	−1.36784e10	−	2.36917e10i	−0.742341	−	1.28577i	0.209086	−	0.977897i	$-0.432951\pi$
$858$	3.42022e9	+	6.60023e10i	0.184863	+	3.56742i
$859$	1.48659e10	−	2.57485e10i	0.800229	−	1.38604i	−0.119236	−	0.992866i	$-0.538044\pi$
$859$	1.48659e10	−	2.57485e10i	0.800229	−	1.38604i	0.919465	−	0.393172i	$-0.128622\pi$
$860$	2.38504e10	+	4.13102e10i	1.27865	+	2.21469i
$861$	−2.31939e10	+	3.09074e10i	−1.23841	+	1.65026i
$862$	1.99922e10	−	3.46274e10i	1.06312	−	1.84139i
$863$	1.25106e10	−	2.16691e10i	0.662585	−	1.14763i	−0.317349	−	0.948309i	$-0.602792\pi$
$863$	1.25106e10	−	2.16691e10i	0.662585	−	1.14763i	0.979934	−	0.199323i	$-0.0638742\pi$
$864$	−2.64282e9			−0.139402
$865$	3.14595e10			1.65271
$866$	−7.33310e8	+	1.27013e9i	−0.0383685	+	0.0664562i
$867$	−1.22369e10	+	2.11949e10i	−0.637680	+	1.10449i
$868$	−1.74700e10	−	2.10967e9i	−0.906720	−	0.109495i
$869$	−1.61642e10	−	2.79971e10i	−0.835572	−	1.44725i
$870$	1.34297e10	−	2.32609e10i	0.691431	−	1.19759i
$871$	6.66556e9	−	4.32311e9i	0.341801	−	0.221683i
$872$	1.25715e10	+	2.17745e10i	0.642065	+	1.11209i
$873$	−2.26043e10			−1.14985
$874$	1.18022e9	+	2.04421e9i	0.0597963	+	0.103570i
$875$	6.12115e9	−	8.15685e9i	0.308891	−	0.411618i
$876$	−2.55407e10			−1.28371
$877$	5.66089e9	+	9.80495e9i	0.283391	+	0.490848i	0.972218	−	0.234078i	$-0.0752073\pi$
$877$	5.66089e9	+	9.80495e9i	0.283391	+	0.490848i	−0.688827	+	0.724926i	$0.741874\pi$
$878$	−2.87407e10			−1.43307
$879$	−1.23946e10	−	2.14680e10i	−0.615560	−	1.06618i
$880$	−3.96252e9	−	6.86328e9i	−0.196012	−	0.339502i
$881$	−8.95288e9	−	1.55068e10i	−0.441110	−	0.764025i	0.556662	−	0.830739i	$-0.312082\pi$
$881$	−8.95288e9	−	1.55068e10i	−0.441110	−	0.764025i	−0.997772	+	0.0667137i	$0.978749\pi$
$882$	2.42784e10	−	2.53426e10i	1.19146	−	1.24369i
$883$	−5.62088e9			−0.274753			−0.137376	−	0.990519i	$-0.543867\pi$
$883$	−5.62088e9			−0.274753			−0.137376	+	0.990519i	$0.543867\pi$
$884$	9.52335e9	+	4.85943e9i	0.463668	+	0.236593i
$885$	−1.64382e10	−	2.84718e10i	−0.797174	−	1.38075i
$886$	−1.94977e9	+	3.37710e9i	−0.0941815	+	0.163127i
$887$	−1.38766e8			−0.00667652			−0.00333826	−	0.999994i	$-0.501063\pi$
$887$	−1.38766e8			−0.00667652			−0.00333826	+	0.999994i	$0.501063\pi$
$888$	2.47508e10	−	4.28696e10i	1.18616	−	2.05449i
$889$	3.77761e10	+	4.56184e9i	1.80327	+	0.217763i
$890$	−7.98061e9	+	1.38228e10i	−0.379465	+	0.657252i
$891$	1.49456e10	+	2.58866e10i	0.707852	+	1.22604i
$892$	−1.91027e10	−	3.30868e10i	−0.901192	−	1.56091i
$893$	−1.64233e9			−0.0771757
$894$	−1.66521e9			−0.0779449
$895$	−2.25316e10	−	3.90258e10i	−1.05054	−	1.81958i
$896$	1.85896e10	−	2.47719e10i	0.863361	−	1.15049i
$897$	5.12152e9	−	3.32169e9i	0.236933	−	0.153669i
$898$	2.01384e10	−	3.48807e10i	0.928021	−	1.60738i
$899$	−3.11686e9	+	5.39857e9i	−0.143073	+	0.247810i
$900$	−1.07025e10	+	1.85373e10i	−0.489370	+	0.847614i
$901$	−2.46266e9	−	4.26545e9i	−0.112168	−	0.194280i
$902$	−7.79537e10			−3.53683
$903$	4.21442e10	+	5.08934e9i	1.90472	+	0.230014i
$904$	−8.49650e9	+	1.47164e10i	−0.382517	+	0.662539i
$905$	−6.89747e9	+	1.19468e10i	−0.309329	+	0.535773i
$906$	7.06596e10			3.15662
$907$	2.75590e9	−	4.77336e9i	0.122642	−	0.212422i	−0.798167	−	0.602436i	$-0.794197\pi$
$907$	2.75590e9	−	4.77336e9i	0.122642	−	0.212422i	0.920809	+	0.390015i	$0.127530\pi$
$908$	−4.92796e10			−2.18457
$909$	4.57655e10			2.02099
$910$	3.11536e9	−	4.54721e10i	0.137045	−	2.00032i
$911$	7.22234e9			0.316493			0.158246	−	0.987400i	$-0.449416\pi$
$911$	7.22234e9			0.316493			0.158246	+	0.987400i	$0.449416\pi$
$912$	−2.53813e9			−0.110798
$913$	−1.70944e9	+	2.96084e9i	−0.0743372	+	0.128756i
$914$	6.45030e7			0.00279427
$915$	−1.14901e10	+	1.99014e10i	−0.495849	+	0.858835i
$916$	6.02651e9	−	1.04382e10i	0.259079	−	0.448737i
$917$	3.60926e9	+	8.45594e9i	0.154570	+	0.362134i
$918$	−1.53964e9			−0.0656856
$919$	−4.56250e8	−	7.90248e8i	−0.0193909	−	0.0335861i	0.856167	−	0.516699i	$-0.172839\pi$
$919$	−4.56250e8	−	7.90248e8i	−0.0193909	−	0.0335861i	−0.875558	+	0.483113i	$0.839506\pi$
$920$	2.43156e9	−	4.21158e9i	0.102950	−	0.178315i
$921$	−1.55790e10	+	2.69836e10i	−0.657099	+	1.13813i
$922$	6.10594e9	−	1.05758e10i	0.256563	−	0.444381i
$923$	−3.73022e10	+	2.41932e10i	−1.56145	+	1.01272i
$924$	8.16152e10	+	9.85585e9i	3.40345	+	0.411000i
$925$	1.40410e10	+	2.43198e10i	0.583315	+	1.01033i
$926$	−3.99093e10			−1.65172
$927$	−6.80590e8			−0.0280612
$928$	−6.69484e9	−	1.15958e10i	−0.274993	−	0.476302i
$929$	−2.05236e10	−	3.55480e10i	−0.839845	−	1.45465i	−0.890024	−	0.455914i	$-0.849313\pi$
$929$	−2.05236e10	−	3.55480e10i	−0.839845	−	1.45465i	0.0501793	−	0.998740i	$-0.484021\pi$
$930$	2.12608e10	−	3.68248e10i	0.866740	−	1.50124i
$931$	6.55301e9	−	6.84025e9i	0.266144	−	0.277810i
$932$	3.21291e10	−	5.56492e10i	1.30000	−	2.25166i
$933$	−6.27505e10			−2.52948
$934$	−1.17034e10	+	2.02710e10i	−0.470002	+	0.814067i
$935$	−8.38262e9	−	1.45191e10i	−0.335381	−	0.580898i
$936$	−1.17381e9	−	2.26517e10i	−0.0467876	−	0.902892i
$937$	2.64623e10			1.05084			0.525422	−	0.850842i	$-0.323907\pi$
$937$	2.64623e10			1.05084			0.525422	+	0.850842i	$0.323907\pi$
$938$	−6.42341e9	−	1.50491e10i	−0.254130	−	0.595387i
$939$	1.66484e10	+	2.88359e10i	0.656210	+	1.13659i
$940$	4.91467e9	+	8.51247e9i	0.192996	+	0.334278i
$941$	6.48347e7	+	1.12297e8i	0.00253655	+	0.00439344i	0.867291	−	0.497802i	$-0.165859\pi$
$941$	6.48347e7	+	1.12297e8i	0.00253655	+	0.00439344i	−0.864754	+	0.502195i	$0.832526\pi$
$942$	−5.70665e10			−2.22435
$943$	3.60004e9	+	6.23545e9i	0.139803	+	0.242146i
$944$	−4.51339e9			−0.174623
$945$	1.55617e9	+	3.64587e9i	0.0599855	+	0.140537i
$946$	4.28179e10	+	7.41628e10i	1.64440	+	2.84818i
$947$	2.70605e8			0.0103541			0.00517703	−	0.999987i	$-0.498352\pi$
$947$	2.70605e8			0.0103541			0.00517703	+	0.999987i	$0.498352\pi$
$948$	3.09834e10	+	5.36648e10i	1.18114	+	2.04579i
$949$	7.94553e8	+	1.53330e10i	0.0301780	+	0.582366i
$950$	−4.78306e9	+	8.28450e9i	−0.180998	+	0.313497i
$951$	−5.72582e9	−	9.91741e9i	−0.215877	−	0.373909i
$952$	4.54964e9	−	6.06271e9i	0.170902	−	0.227739i
$953$	1.64839e10	−	2.85510e10i	0.616930	−	1.06855i	−0.373113	−	0.927786i	$-0.621709\pi$
$953$	1.64839e10	−	2.85510e10i	0.616930	−	1.06855i	0.990043	−	0.140768i	$-0.0449572\pi$
$954$	−1.51773e10	+	2.62878e10i	−0.565945	+	0.980246i
$955$	3.78552e10			1.40642
$956$	−4.32170e9			−0.159975
$957$	1.45612e10	−	2.52207e10i	0.537038	−	0.930178i
$958$	−2.15857e10	+	3.73876e10i	−0.793208	+	1.37388i
$959$	−1.28369e10	+	1.71061e10i	−0.469998	+	0.626305i
$960$	4.06861e10	+	7.04705e10i	1.48422	+	2.57074i
$961$	8.82195e9	−	1.52801e10i	0.320651	−	0.555384i
$962$	−7.70002e10	−	3.92905e10i	−2.78856	−	1.42290i
$963$	−9.20344e9	−	1.59408e10i	−0.332092	−	0.575200i
$964$	3.25183e10			1.16912
$965$	−1.29843e10	−	2.24895e10i	−0.465129	−	0.805627i
$966$	−4.93546e9	−	1.15630e10i	−0.176160	−	0.412716i
$967$	−1.79819e10			−0.639503			−0.319751	−	0.947501i	$-0.603599\pi$
$967$	−1.79819e10			−0.639503			−0.319751	+	0.947501i	$0.603599\pi$
$968$	1.67742e10	+	2.90538e10i	0.594399	+	1.02953i
$969$	−5.36935e9			−0.189578
$970$	3.02305e10	+	5.23607e10i	1.06352	+	1.84206i
$971$	2.05022e10	+	3.55109e10i	0.718677	+	1.24479i	0.961524	+	0.274721i	$0.0885855\pi$
$971$	2.05022e10	+	3.55109e10i	0.718677	+	1.24479i	−0.242847	+	0.970065i	$0.578081\pi$
$972$	−3.12914e10	−	5.41982e10i	−1.09293	−	1.89301i
$973$	−9.33400e9	−	2.18681e10i	−0.324842	−	0.761056i
$974$	4.98040e10			1.72706
$975$	2.20361e10	+	1.12442e10i	0.761410	+	0.388520i
$976$	1.57740e9	+	2.73213e9i	0.0543084	+	0.0940648i
$977$	1.38390e10	−	2.39699e10i	0.474761	−	0.822310i	−0.524821	−	0.851212i	$-0.675868\pi$
$977$	1.38390e10	−	2.39699e10i	0.474761	−	0.822310i	0.999582	+	0.0289024i	$0.00920119\pi$
$978$	1.01839e11			3.48118
$979$	−8.65301e9	+	1.49875e10i	−0.294732	+	0.510491i
$980$	−5.50640e10	−	1.34959e10i	−1.86886	−	0.458046i
$981$	−2.46701e10	+	4.27300e10i	−0.834315	+	1.44508i
$982$	2.79777e10	+	4.84588e10i	0.942805	+	1.63299i
$983$	−2.26378e10	−	3.92098e10i	−0.760145	−	1.31661i	−0.942775	−	0.333429i	$-0.891794\pi$
$983$	−2.26378e10	−	3.92098e10i	−0.760145	−	1.31661i	0.182630	−	0.983182i	$-0.441539\pi$
$984$	5.14361e10			1.72102
$985$	−2.23340e10			−0.744629
$986$	−3.90025e9	−	6.75544e9i	−0.129576	−	0.224432i
$987$	8.68434e9	+	1.04872e9i	0.287493	+	0.0347176i
$988$	−9.20368e8	−	1.77610e10i	−0.0303607	−	0.585892i
$989$	3.95482e9	−	6.84994e9i	0.129999	−	0.225164i
$990$	−5.16617e10	+	8.94807e10i	−1.69218	+	2.93093i
$991$	−7.15364e9	+	1.23905e10i	−0.233490	+	0.404417i	−0.958833	−	0.283971i	$-0.908348\pi$
$991$	−7.15364e9	+	1.23905e10i	−0.233490	+	0.404417i	0.725342	+	0.688388i	$0.241681\pi$
$992$	−1.05987e10	−	1.83575e10i	−0.344717	−	0.597067i
$993$	8.49336e9			0.275269
$994$	3.59470e10	+	8.42184e10i	1.16094	+	2.71991i
$995$	−1.69456e10	+	2.93507e10i	−0.545352	+	0.944577i
$996$	3.27665e9	−	5.67533e9i	0.105081	−	0.182005i
$997$	3.14106e10			1.00379			0.501895	−	0.864929i	$-0.332636\pi$
$997$	3.14106e10			1.00379			0.501895	+	0.864929i	$0.332636\pi$
$998$	−2.57526e10	+	4.46048e10i	−0.820095	+	1.42045i
$999$	7.51836e9			0.238585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.h.a.16.10	yes	126
7.4	even	3		91.8.g.a.81.54	yes	126
13.9	even	3		91.8.g.a.9.54	✓	126
91.74	even	3	inner	91.8.h.a.74.10	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.g.a.9.54	✓	126	13.9	even	3
91.8.g.a.81.54	yes	126	7.4	even	3
91.8.h.a.16.10	yes	126	1.1	even	1	trivial
91.8.h.a.74.10	yes	126	91.74	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-17.9775 q^{2} +(33.7545 - 58.4645i) q^{3} +195.192 q^{4} +(176.342 - 305.434i) q^{5} +(-606.823 + 1051.05i) q^{6} +(544.696 - 725.844i) q^{7} -1207.95 q^{8} +(-1185.23 - 2052.88i) q^{9} +O(q^{10})\)	\(q-17.9775 q^{2} +(33.7545 - 58.4645i) q^{3} +195.192 q^{4} +(176.342 - 305.434i) q^{5} +(-606.823 + 1051.05i) q^{6} +(544.696 - 725.844i) q^{7} -1207.95 q^{8} +(-1185.23 - 2052.88i) q^{9} +(-3170.20 + 5490.95i) q^{10} +(-3437.30 + 5953.58i) q^{11} +(6588.61 - 11411.8i) q^{12} +(-7055.91 - 3600.38i) q^{13} +(-9792.29 + 13048.9i) q^{14} +(-11904.7 - 20619.5i) q^{15} -3268.64 q^{16} -6914.72 q^{17} +(21307.6 + 36905.8i) q^{18} +(5751.15 + 9961.29i) q^{19} +(34420.6 - 59618.3i) q^{20} +(-24050.2 - 56345.9i) q^{21} +(61794.3 - 107031. i) q^{22} -11415.1 q^{23} +(-40773.7 + 70622.1i) q^{24} +(-23130.8 - 40063.7i) q^{25} +(126848. + 64725.9i) q^{26} -12385.5 q^{27} +(106320. - 141679. i) q^{28} +(-31375.3 - 54343.6i) q^{29} +(214017. + 370689. i) q^{30} +(-49670.7 - 86032.2i) q^{31} +213379. q^{32} +(232049. + 401921. i) q^{33} +124310. q^{34} +(-125644. - 294366. i) q^{35} +(-231348. - 400706. i) q^{36} -607028. q^{37} +(-103392. - 179080. i) q^{38} +(-448663. + 290991. i) q^{39} +(-213013. + 368949. i) q^{40} +(-315376. - 546247. i) q^{41} +(432363. + 1.01296e6i) q^{42} +(-346455. + 600078. i) q^{43} +(-670934. + 1.16209e6i) q^{44} -836027. q^{45} +205215. q^{46} +(-71391.4 + 123654. i) q^{47} +(-110331. + 191099. i) q^{48} +(-230156. - 790728. i) q^{49} +(415835. + 720247. i) q^{50} +(-233403. + 404266. i) q^{51} +(-1.37726e6 - 702765. i) q^{52} +(356147. + 616865. i) q^{53} +222661. q^{54} +(1.21228e6 + 2.09974e6i) q^{55} +(-657965. + 876782. i) q^{56} +776509. q^{57} +(564050. + 976964. i) q^{58} +1.38082e6 q^{59} +(-2.32370e6 - 4.02477e6i) q^{60} +(-482586. - 835863. i) q^{61} +(892958. + 1.54665e6i) q^{62} +(-2.13566e6 - 257903. i) q^{63} -3.41765e6 q^{64} +(-2.34393e6 + 1.52021e6i) q^{65} +(-4.17167e6 - 7.22554e6i) q^{66} +(-501474. + 868578. i) q^{67} -1.34970e6 q^{68} +(-385310. + 667377. i) q^{69} +(2.25878e6 + 5.29197e6i) q^{70} +(2.80638e6 - 4.86079e6i) q^{71} +(1.43170e6 + 2.47978e6i) q^{72} +(-969122. - 1.67857e6i) q^{73} +1.09129e7 q^{74} -3.12307e6 q^{75} +(1.12258e6 + 1.94436e6i) q^{76} +(2.44909e6 + 5.73784e6i) q^{77} +(8.06586e6 - 5.23131e6i) q^{78} +(-2.35128e6 + 4.07254e6i) q^{79} +(-576399. + 998352. i) q^{80} +(2.17404e6 - 3.76554e6i) q^{81} +(5.66968e6 + 9.82017e6i) q^{82} +497320. q^{83} +(-4.69440e6 - 1.09983e7i) q^{84} +(-1.21936e6 + 2.11199e6i) q^{85} +(6.22842e6 - 1.07879e7i) q^{86} -4.23623e6 q^{87} +(4.15209e6 - 7.19163e6i) q^{88} +2.51738e6 q^{89} +1.50297e7 q^{90} +(-6.45663e6 + 3.16038e6i) q^{91} -2.22813e6 q^{92} -6.70644e6 q^{93} +(1.28344e6 - 2.22299e6i) q^{94} +4.05669e6 q^{95} +(7.20252e6 - 1.24751e7i) q^{96} +(4.76791e6 - 8.25826e6i) q^{97} +(4.13764e6 + 1.42154e7i) q^{98} +1.62960e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9}+O(q^{10}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9} - 4255 q^{10} + 7423 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} + 410294 q^{16} + 99274 q^{17} - 21111 q^{18} - 4844 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} + 34130 q^{23} - 130304 q^{24} - 810669 q^{25} + 390708 q^{26} + 416614 q^{27} + 69267 q^{28} + 191096 q^{29} + 70666 q^{30} + 183609 q^{31} + 695346 q^{32} + 178591 q^{33} - 742000 q^{34} + 579437 q^{35} - 1732409 q^{36} - 1362898 q^{37} - 877438 q^{38} + 459227 q^{39} - 1502882 q^{40} + 593701 q^{41} + 1442877 q^{42} - 592188 q^{43} + 1254066 q^{44} + 1954226 q^{45} - 1385452 q^{46} + 98278 q^{47} - 374916 q^{48} - 1497637 q^{49} + 289562 q^{50} - 281250 q^{51} - 8455 q^{52} - 1256681 q^{53} - 293814 q^{54} - 3015554 q^{55} - 1646151 q^{56} + 2743072 q^{57} + 1851469 q^{58} - 2279458 q^{59} + 1031485 q^{60} - 1127636 q^{61} - 7724680 q^{62} + 5142530 q^{63} + 11827496 q^{64} - 2789048 q^{65} + 435059 q^{66} + 4373348 q^{67} + 8737122 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} - 11660951 q^{72} - 5060877 q^{73} + 1184002 q^{74} + 22637254 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} - 123568 q^{80} - 30756895 q^{81} + 8626952 q^{82} - 18679806 q^{83} + 11302461 q^{84} + 5330093 q^{85} - 8512356 q^{86} - 16508762 q^{87} - 6438219 q^{88} - 6176684 q^{89} + 53481084 q^{90} + 29236777 q^{91} + 2460546 q^{92} + 27682404 q^{93} - 17421794 q^{94} + 39553398 q^{95} + 26667066 q^{96} + 7705262 q^{97} + 14093080 q^{98} - 60531432 q^{99}+O(q^{100}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9 - 4255 * q^10 + 7423 * q^11 - 18072 * q^12 - 1824 * q^13 - 15916 * q^14 + 11047 * q^15 + 410294 * q^16 + 99274 * q^17 - 21111 * q^18 - 4844 * q^19 + 36626 * q^20 + 73198 * q^21 - 43360 * q^22 + 34130 * q^23 - 130304 * q^24 - 810669 * q^25 + 390708 * q^26 + 416614 * q^27 + 69267 * q^28 + 191096 * q^29 + 70666 * q^30 + 183609 * q^31 + 695346 * q^32 + 178591 * q^33 - 742000 * q^34 + 579437 * q^35 - 1732409 * q^36 - 1362898 * q^37 - 877438 * q^38 + 459227 * q^39 - 1502882 * q^40 + 593701 * q^41 + 1442877 * q^42 - 592188 * q^43 + 1254066 * q^44 + 1954226 * q^45 - 1385452 * q^46 + 98278 * q^47 - 374916 * q^48 - 1497637 * q^49 + 289562 * q^50 - 281250 * q^51 - 8455 * q^52 - 1256681 * q^53 - 293814 * q^54 - 3015554 * q^55 - 1646151 * q^56 + 2743072 * q^57 + 1851469 * q^58 - 2279458 * q^59 + 1031485 * q^60 - 1127636 * q^61 - 7724680 * q^62 + 5142530 * q^63 + 11827496 * q^64 - 2789048 * q^65 + 435059 * q^66 + 4373348 * q^67 + 8737122 * q^68 - 7610377 * q^69 - 8084578 * q^70 - 60067 * q^71 - 11660951 * q^72 - 5060877 * q^73 + 1184002 * q^74 + 22637254 * q^75 + 637438 * q^76 + 21469082 * q^77 - 7230943 * q^78 - 2446486 * q^79 - 123568 * q^80 - 30756895 * q^81 + 8626952 * q^82 - 18679806 * q^83 + 11302461 * q^84 + 5330093 * q^85 - 8512356 * q^86 - 16508762 * q^87 - 6438219 * q^88 - 6176684 * q^89 + 53481084 * q^90 + 29236777 * q^91 + 2460546 * q^92 + 27682404 * q^93 - 17421794 * q^94 + 39553398 * q^95 + 26667066 * q^96 + 7705262 * q^97 + 14093080 * q^98 - 60531432 * q^99

Introduction

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