LMFDB - Embedded newform 33.8.e.b.25.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [33,8,Mod(4,33)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("33.4"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-6] 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:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	33.25
Dual form			33.8.e.b.4.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(14.6841 - 10.6686i) q^{2} +(8.34346 + 25.6785i) q^{3} +(62.2484 - 191.581i) q^{4} +(425.412 + 309.080i) q^{5} +(396.469 + 288.052i) q^{6} +(-184.854 + 568.921i) q^{7} +(-411.912 - 1267.74i) q^{8} +(-589.773 + 428.495i) q^{9} +9544.22 q^{10} +(-2672.22 - 3513.75i) q^{11} +5438.89 q^{12} +(6648.88 - 4830.70i) q^{13} +(3355.18 + 10326.2i) q^{14} +(-4387.31 + 13502.7i) q^{15} +(1286.49 + 934.689i) q^{16} +(-18538.6 - 13469.1i) q^{17} +(-4088.82 + 12584.1i) q^{18} +(-12012.9 - 36972.0i) q^{19} +(85695.1 - 62261.1i) q^{20} -16151.4 q^{21} +(-76725.7 - 23087.2i) q^{22} -14465.5 q^{23} +(29116.8 - 21154.6i) q^{24} +(61303.0 + 188671. i) q^{25} +(46095.8 - 141868. i) q^{26} +(-15923.9 - 11569.4i) q^{27} +(97487.5 + 70828.8i) q^{28} +(-12657.3 + 38955.2i) q^{29} +(79631.8 + 245081. i) q^{30} +(-100999. + 73380.2i) q^{31} +199484. q^{32} +(67932.3 - 97935.5i) q^{33} -415917. q^{34} +(-254481. + 184891. i) q^{35} +(45379.1 + 139663. i) q^{36} +(133858. - 411974. i) q^{37} +(-570838. - 414738. i) q^{38} +(179520. + 130429. i) q^{39} +(216599. - 666624. i) q^{40} +(23931.9 + 73654.8i) q^{41} +(-237167. + 172312. i) q^{42} -803198. q^{43} +(-839509. + 293221. i) q^{44} -383336. q^{45} +(-212412. + 154326. i) q^{46} +(207771. + 639453. i) q^{47} +(-13267.7 + 40833.7i) q^{48} +(376760. + 273732. i) q^{49} +(2.91303e6 + 2.11644e6i) q^{50} +(191190. - 588422. i) q^{51} +(-511587. - 1.57450e6i) q^{52} +(-89459.0 + 64995.7i) q^{53} -357256. q^{54} +(-50766.4 - 2.32072e6i) q^{55} +797384. q^{56} +(849157. - 616949. i) q^{57} +(229737. + 707056. i) q^{58} +(277659. - 854545. i) q^{59} +(2.31377e6 + 1.68105e6i) q^{60} +(-1.11020e6 - 806606. i) q^{61} +(-700215. + 2.15504e6i) q^{62} +(-134758. - 414743. i) q^{63} +(2.76456e6 - 2.00857e6i) q^{64} +4.32159e6 q^{65} +(-47312.5 - 2.16283e6i) q^{66} +1.15170e6 q^{67} +(-3.73441e6 + 2.71321e6i) q^{68} +(-120692. - 371452. i) q^{69} +(-1.76428e6 + 5.42990e6i) q^{70} +(-2.02121e6 - 1.46849e6i) q^{71} +(786154. + 571174. i) q^{72} +(-527486. + 1.62343e6i) q^{73} +(-2.42960e6 - 7.47753e6i) q^{74} +(-4.33332e6 + 3.14834e6i) q^{75} -7.83092e6 q^{76} +(2.49301e6 - 870753. i) q^{77} +4.02757e6 q^{78} +(3.74584e6 - 2.72151e6i) q^{79} +(258394. + 795256. i) q^{80} +(164224. - 505430. i) q^{81} +(1.13721e6 + 826231. i) q^{82} +(-3.66986e6 - 2.66631e6i) q^{83} +(-1.00540e6 + 3.09429e6i) q^{84} +(-3.72351e6 - 1.14598e7i) q^{85} +(-1.17942e7 + 8.56899e6i) q^{86} -1.10592e6 q^{87} +(-3.35378e6 + 4.83502e6i) q^{88} +9.62485e6 q^{89} +(-5.62893e6 + 4.08965e6i) q^{90} +(1.51921e6 + 4.67566e6i) q^{91} +(-900453. + 2.77131e6i) q^{92} +(-2.72698e6 - 1.98127e6i) q^{93} +(9.87298e6 + 7.17314e6i) q^{94} +(6.31686e6 - 1.94413e7i) q^{95} +(1.66438e6 + 5.12244e6i) q^{96} +(-1.41140e7 + 1.02544e7i) q^{97} +8.45271e6 q^{98} +(3.08163e6 + 927280. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{2} - 189 q^{3} + 160 q^{4} + 773 q^{5} - 162 q^{6} + 1289 q^{7} + 2956 q^{8} - 5103 q^{9} - 10640 q^{10} + 13209 q^{11} + 45630 q^{12} + 13499 q^{13} - 3318 q^{14} - 22734 q^{15} - 113196 q^{16}+ \cdots - 6579954 q^{99}+O(q^{100}) $ 28 * q - 6 * q^2 - 189 * q^3 + 160 * q^4 + 773 * q^5 - 162 * q^6 + 1289 * q^7 + 2956 * q^8 - 5103 * q^9 - 10640 * q^10 + 13209 * q^11 + 45630 * q^12 + 13499 * q^13 - 3318 * q^14 - 22734 * q^15 - 113196 * q^16 + 30296 * q^17 + 21141 * q^18 - 6858 * q^19 + 76725 * q^20 - 177012 * q^21 - 48859 * q^22 - 166984 * q^23 + 44442 * q^24 + 99832 * q^25 + 340424 * q^26 - 137781 * q^27 + 657387 * q^28 + 192014 * q^29 - 184410 * q^30 + 396068 * q^31 - 303498 * q^32 + 168453 * q^33 - 1229124 * q^34 - 725859 * q^35 + 116640 * q^36 + 811053 * q^37 + 1548798 * q^38 + 364473 * q^39 - 1427263 * q^40 + 1041497 * q^41 + 300024 * q^42 - 5265288 * q^43 - 5341085 * q^44 + 100602 * q^45 + 1198651 * q^46 + 1667505 * q^47 + 730593 * q^48 + 2968140 * q^49 + 11247432 * q^50 + 340767 * q^51 + 2325763 * q^52 - 1625736 * q^53 - 905418 * q^54 - 8338690 * q^55 - 18201906 * q^56 + 1546479 * q^57 + 14965553 * q^58 - 2587454 * q^59 + 2071575 * q^60 + 5801619 * q^61 + 15631121 * q^62 + 939681 * q^63 - 3732846 * q^64 - 15368174 * q^65 - 235683 * q^66 - 7141262 * q^67 + 17394545 * q^68 - 5063553 * q^69 - 4329200 * q^70 + 3569199 * q^71 + 1199934 * q^72 + 125008 * q^73 - 13691530 * q^74 - 11794221 * q^75 - 19690428 * q^76 - 6038739 * q^77 + 12684438 * q^78 + 17075485 * q^79 + 26606436 * q^80 - 3720087 * q^81 + 19886007 * q^82 - 4645575 * q^83 + 1074519 * q^84 + 12002715 * q^85 - 12296287 * q^86 - 12259512 * q^87 - 50905990 * q^88 + 9601664 * q^89 + 8857350 * q^90 - 14129477 * q^91 - 90776021 * q^92 + 10693836 * q^93 + 1047679 * q^94 + 58935661 * q^95 + 26156304 * q^96 - 22170261 * q^97 + 140532178 * q^98 - 6579954 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	14.6841	−	10.6686i	1.29790	−	0.942979i	0.297966	−	0.954576i	$-0.403692\pi$
$2$	14.6841	−	10.6686i	1.29790	−	0.942979i	0.999933	+	0.0115974i	$0.00369164\pi$
$3$	8.34346	+	25.6785i	0.178411	+	0.549093i
$3$	8.34346	+	25.6785i	0.178411	+	0.549093i
$4$	62.2484	−	191.581i	0.486316	−	1.49673i
$5$	425.412	+	309.080i	1.52200	+	1.10580i	0.960485	+	0.278332i	$0.0897814\pi$
$5$	425.412	+	309.080i	1.52200	+	1.10580i	0.561515	+	0.827466i	$0.310219\pi$
$6$	396.469	+	288.052i	0.749342	+	0.544429i
$7$	−184.854	+	568.921i	−0.203697	+	0.626915i	0.796067	+	0.605208i	$0.206910\pi$
$7$	−184.854	+	568.921i	−0.203697	+	0.626915i	−0.999764	+	0.0217068i	$0.993090\pi$
$8$	−411.912	−	1267.74i	−0.284439	−	0.875414i
$9$	−589.773	+	428.495i	−0.269672	+	0.195928i
$10$	9544.22			3.01815
$11$	−2672.22	−	3513.75i	−0.605338	−	0.795969i
$11$	−2672.22	−	3513.75i	−0.605338	−	0.795969i
$12$	5438.89			0.908606
$13$	6648.88	−	4830.70i	0.839357	−	0.609829i	−0.0828337	−	0.996563i	$-0.526397\pi$
$13$	6648.88	−	4830.70i	0.839357	−	0.609829i	0.922191	+	0.386735i	$0.126397\pi$
$14$	3355.18	+	10326.2i	0.326789	+	1.00575i
$15$	−4387.31	+	13502.7i	−0.335644	+	1.03301i
$16$	1286.49	+	934.689i	0.0785211	+	0.0570489i
$17$	−18538.6	−	13469.1i	−0.915177	−	0.664915i	0.0271421	−	0.999632i	$-0.491359\pi$
$17$	−18538.6	−	13469.1i	−0.915177	−	0.664915i	−0.942319	+	0.334717i	$0.891359\pi$
$18$	−4088.82	+	12584.1i	−0.165251	+	0.508591i
$19$	−12012.9	−	36972.0i	−0.401801	−	1.23662i	−0.923537	−	0.383510i	$-0.874715\pi$
$19$	−12012.9	−	36972.0i	−0.401801	−	1.23662i	0.521735	−	0.853107i	$-0.325285\pi$
$20$	85695.1	−	62261.1i	2.39525	−	1.74025i
$21$	−16151.4			−0.380576
$22$	−76725.7	−	23087.2i	−1.53625	−	0.462266i
$23$	−14465.5			−0.247905			−0.123952	−	0.992288i	$-0.539557\pi$
$23$	−14465.5			−0.247905			−0.123952	+	0.992288i	$0.539557\pi$
$24$	29116.8	−	21154.6i	0.429936	−	0.312367i
$25$	61303.0	+	188671.i	0.784679	+	2.41499i
$26$	46095.8	−	141868.i	0.514346	−	1.58299i
$27$	−15923.9	−	11569.4i	−0.155695	−	0.113119i
$28$	97487.5	+	70828.8i	0.839259	+	0.609757i
$29$	−12657.3	+	38955.2i	−0.0963715	+	0.296601i	−0.987609	−	0.156936i	$-0.949838\pi$
$29$	−12657.3	+	38955.2i	−0.0963715	+	0.296601i	0.891237	+	0.453538i	$0.149838\pi$
$30$	79631.8	+	245081.i	0.538471	+	1.65724i
$31$	−100999.	+	73380.2i	−0.608909	+	0.442398i	−0.849030	−	0.528345i	$-0.822813\pi$
$31$	−100999.	+	73380.2i	−0.608909	+	0.442398i	0.240121	+	0.970743i	$0.422813\pi$
$32$	199484.			1.07617
$33$	67932.3	−	97935.5i	0.329062	−	0.474396i
$34$	−415917.			−1.81481
$35$	−254481.	+	184891.i	−1.00327	+	0.728917i
$36$	45379.1	+	139663.i	0.162105	+	0.498909i
$37$	133858.	−	411974.i	0.434450	−	1.33710i	−0.459199	−	0.888333i	$-0.651864\pi$
$37$	133858.	−	411974.i	0.434450	−	1.33710i	0.893649	−	0.448766i	$-0.148136\pi$
$38$	−570838.	−	414738.i	−1.68760	−	1.22611i
$39$	179520.	+	130429.i	0.484603	+	0.352085i
$40$	216599.	−	666624.i	0.535115	−	1.64691i
$41$	23931.9	+	73654.8i	0.0542292	+	0.166900i	0.974503	−	0.224375i	$-0.0720340\pi$
$41$	23931.9	+	73654.8i	0.0542292	+	0.166900i	−0.920274	+	0.391275i	$0.872034\pi$
$42$	−237167.	+	172312.i	−0.493949	+	0.358875i
$43$	−803198.			−1.54058			−0.770288	−	0.637696i	$-0.779888\pi$
$43$	−803198.			−1.54058			−0.770288	+	0.637696i	$0.779888\pi$
$44$	−839509.	+	293221.i	−1.48573	+	0.518933i
$45$	−383336.			−0.627099
$46$	−212412.	+	154326.i	−0.321756	+	0.233769i
$47$	207771.	+	639453.i	0.291905	+	0.898392i	0.984243	+	0.176819i	$0.0565807\pi$
$47$	207771.	+	639453.i	0.291905	+	0.898392i	−0.692338	+	0.721573i	$0.743419\pi$
$48$	−13267.7	+	40833.7i	−0.0173161	+	0.0532935i
$49$	376760.	+	273732.i	0.457487	+	0.332384i
$50$	2.91303e6	+	2.11644e6i	3.29572	+	2.39448i
$51$	191190.	−	588422.i	0.201822	−	0.621145i
$52$	−511587.	−	1.57450e6i	−0.504554	−	1.55286i
$53$	−89459.0	+	64995.7i	−0.0825388	+	0.0599680i	−0.628289	−	0.777980i	$-0.716245\pi$
$53$	−89459.0	+	64995.7i	−0.0825388	+	0.0599680i	0.545751	+	0.837948i	$0.316245\pi$
$54$	−357256.			−0.308746
$55$	−50766.4	−	2.32072e6i	−0.0411440	−	1.88085i
$56$	797384.			0.606750
$57$	849157.	−	616949.i	0.607332	−	0.441253i
$58$	229737.	+	707056.i	0.154608	+	0.475835i
$59$	277659.	−	854545.i	0.176007	−	0.541693i	−0.823671	−	0.567067i	$-0.808078\pi$
$59$	277659.	−	854545.i	0.176007	−	0.541693i	0.999678	+	0.0253747i	$0.00807787\pi$
$60$	2.31377e6	+	1.68105e6i	1.38290	+	1.00473i
$61$	−1.11020e6	−	806606.i	−0.626247	−	0.454995i	0.228851	−	0.973462i	$-0.426503\pi$
$61$	−1.11020e6	−	806606.i	−0.626247	−	0.454995i	−0.855098	+	0.518466i	$0.826503\pi$
$62$	−700215.	+	2.15504e6i	−0.373130	+	1.14838i
$63$	−134758.	−	414743.i	−0.0678990	−	0.208972i
$64$	2.76456e6	−	2.00857e6i	1.31824	−	0.957760i
$65$	4.32159e6			1.95185
$66$	−47312.5	−	2.16283e6i	−0.0202569	−	0.926017i
$67$	1.15170e6			0.467817			0.233909	−	0.972259i	$-0.424848\pi$
$67$	1.15170e6			0.467817			0.233909	+	0.972259i	$0.424848\pi$
$68$	−3.73441e6	+	2.71321e6i	−1.44026	+	1.04641i
$69$	−120692.	−	371452.i	−0.0442290	−	0.136123i
$70$	−1.76428e6	+	5.42990e6i	−0.614787	+	1.89212i
$71$	−2.02121e6	−	1.46849e6i	−0.670203	−	0.486931i	0.199890	−	0.979818i	$-0.435941\pi$
$71$	−2.02121e6	−	1.46849e6i	−0.670203	−	0.486931i	−0.870093	+	0.492887i	$0.835941\pi$
$72$	786154.	+	571174.i	0.248224	+	0.180345i
$73$	−527486.	+	1.62343e6i	−0.158701	+	0.488433i	−0.998517	−	0.0544389i	$-0.982663\pi$
$73$	−527486.	+	1.62343e6i	−0.158701	+	0.488433i	0.839816	+	0.542872i	$0.182663\pi$
$74$	−2.42960e6	−	7.47753e6i	−0.696984	−	2.14510i
$75$	−4.33332e6	+	3.14834e6i	−1.18606	+	0.861723i
$76$	−7.83092e6			−2.04628
$77$	2.49301e6	−	870753.i	0.622310	−	0.217359i
$78$	4.02757e6			0.960975
$79$	3.74584e6	−	2.72151e6i	0.854780	−	0.621034i	−0.0716795	−	0.997428i	$-0.522836\pi$
$79$	3.74584e6	−	2.72151e6i	0.854780	−	0.621034i	0.926460	+	0.376393i	$0.122836\pi$
$80$	258394.	+	795256.i	0.0564245	+	0.173657i
$81$	164224.	−	505430.i	0.0343352	−	0.105673i
$82$	1.13721e6	+	826231.i	0.227768	+	0.165483i
$83$	−3.66986e6	−	2.66631e6i	−0.704493	−	0.511844i	0.176899	−	0.984229i	$-0.443393\pi$
$83$	−3.66986e6	−	2.66631e6i	−0.704493	−	0.511844i	−0.881392	+	0.472385i	$0.843393\pi$
$84$	−1.00540e6	+	3.09429e6i	−0.185080	+	0.569619i
$85$	−3.72351e6	−	1.14598e7i	−0.657638	−	2.02400i
$86$	−1.17942e7	+	8.56899e6i	−1.99951	+	1.45273i
$87$	−1.10592e6			−0.180055
$88$	−3.35378e6	+	4.83502e6i	−0.524620	+	0.756326i
$89$	9.62485e6			1.44720			0.723601	−	0.690219i	$-0.242486\pi$
$89$	9.62485e6			1.44720			0.723601	+	0.690219i	$0.242486\pi$
$90$	−5.62893e6	+	4.08965e6i	−0.813911	+	0.591341i
$91$	1.51921e6	+	4.67566e6i	0.211336	+	0.650426i
$92$	−900453.	+	2.77131e6i	−0.120560	+	0.371046i
$93$	−2.72698e6	−	1.98127e6i	−0.351554	−	0.255419i
$94$	9.87298e6	+	7.17314e6i	1.22603	+	0.890762i
$95$	6.31686e6	−	1.94413e7i	0.755907	−	2.32644i
$96$	1.66438e6	+	5.12244e6i	0.192001	+	0.590919i
$97$	−1.41140e7	+	1.02544e7i	−1.57017	+	1.14080i	−0.643186	+	0.765710i	$0.722388\pi$
$97$	−1.41140e7	+	1.02544e7i	−1.57017	+	1.14080i	−0.926989	+	0.375089i	$0.877612\pi$
$98$	8.45271e6			0.907203
$99$	3.08163e6	+	927280.i	0.319196	+	0.0960478i
$100$	3.99619e7			3.99619
$101$	2.50214e6	−	1.81791e6i	0.241650	−	0.175569i	−0.460368	−	0.887728i	$-0.652282\pi$
$101$	2.50214e6	−	1.81791e6i	0.241650	−	0.175569i	0.702018	+	0.712159i	$0.252282\pi$
$102$	−3.47019e6	−	1.06801e7i	−0.323782	−	0.996498i
$103$	−3.24962e6	+	1.00013e7i	−0.293024	+	0.901834i	0.690854	+	0.722994i	$0.257235\pi$
$103$	−3.24962e6	+	1.00013e7i	−0.293024	+	0.901834i	−0.983878	+	0.178840i	$0.942765\pi$
$104$	−8.86280e6	−	6.43920e6i	−0.772599	−	0.561326i
$105$	−6.87098e6	−	4.99206e6i	−0.579237	−	0.420840i
$106$	−620207.	+	1.90880e6i	−0.0505785	+	0.155665i
$107$	5.70712e6	+	1.75647e7i	0.450374	+	1.38611i	0.876481	+	0.481437i	$0.159885\pi$
$107$	5.70712e6	+	1.75647e7i	0.450374	+	1.38611i	−0.426107	+	0.904673i	$0.640115\pi$
$108$	−3.20771e6	+	2.33054e6i	−0.245026	+	0.178022i
$109$	−1.17782e7			−0.871133			−0.435567	−	0.900156i	$-0.643452\pi$
$109$	−1.17782e7			−0.871133			−0.435567	+	0.900156i	$0.643452\pi$
$110$	−2.55043e7	−	3.35360e7i	−1.82700	−	2.40235i
$111$	1.16957e7			0.811702
$112$	−769576.	+	559130.i	−0.0517593	+	0.0376053i
$113$	2.27670e6	+	7.00697e6i	0.148433	+	0.456831i	0.997437	−	0.0715569i	$-0.0227967\pi$
$113$	2.27670e6	+	7.00697e6i	0.148433	+	0.456831i	−0.849003	+	0.528388i	$0.822797\pi$
$114$	5.88710e6	−	1.81186e7i	0.372164	−	1.14540i
$115$	−6.15379e6	−	4.47099e6i	−0.377311	−	0.274133i
$116$	6.67518e6	+	4.84980e6i	0.397064	+	0.288484i
$117$	−1.85140e6	+	5.69803e6i	−0.106869	+	0.328908i
$118$	−5.03964e6	−	1.55104e7i	−0.282366	−	0.869033i
$119$	1.10897e7	−	8.05717e6i	0.603264	−	0.438297i
$120$	1.89251e7			0.999778
$121$	−5.20565e6	+	1.87790e7i	−0.267132	+	0.963660i
$122$	−2.49076e7			−1.24186
$123$	−1.69167e6	+	1.22907e6i	−0.0819687	+	0.0595537i
$124$	7.77122e6	+	2.39173e7i	0.366027	+	1.12652i
$125$	−1.95407e7	+	6.01401e7i	−0.894861	+	2.75410i
$126$	−6.40352e6	−	4.65243e6i	−0.285182	−	0.207197i
$127$	2.43910e6	+	1.77211e6i	0.105661	+	0.0767675i	0.639361	−	0.768906i	$-0.279199\pi$
$127$	2.43910e6	+	1.77211e6i	0.105661	+	0.0767675i	−0.533700	+	0.845674i	$0.679199\pi$
$128$	1.12759e7	−	3.47037e7i	0.475244	−	1.46265i
$129$	−6.70145e6	−	2.06249e7i	−0.274856	−	0.845919i
$130$	6.34584e7	−	4.61052e7i	2.53330	−	1.84055i
$131$	1.72518e7			0.670477			0.335239	−	0.942133i	$-0.391183\pi$
$131$	1.72518e7			0.670477			0.335239	+	0.942133i	$0.391183\pi$
$132$	−1.45339e7	−	1.91109e7i	−0.550014	−	0.723222i
$133$	2.32548e7			0.857100
$134$	1.69116e7	−	1.22870e7i	0.607179	−	0.441142i
$135$	−3.19835e6	−	9.84350e6i	−0.111881	−	0.344335i
$136$	−9.43894e6	+	2.90501e7i	−0.321764	+	0.990287i
$137$	2.67607e7	+	1.94428e7i	0.889149	+	0.646005i	0.935656	−	0.352913i	$-0.114809\pi$
$137$	2.67607e7	+	1.94428e7i	0.889149	+	0.646005i	−0.0465067	+	0.998918i	$0.514809\pi$
$138$	−5.73512e6	−	4.16681e6i	−0.185766	−	0.134967i
$139$	9.71050e6	−	2.98859e7i	0.306683	−	0.943874i	−0.672361	−	0.740224i	$-0.734720\pi$
$139$	9.71050e6	−	2.98859e7i	0.306683	−	0.943874i	0.979044	−	0.203650i	$-0.0652804\pi$
$140$	1.95806e7	+	6.02629e7i	0.603084	+	1.85610i
$141$	−1.46867e7	+	1.06705e7i	−0.441222	+	0.320566i
$142$	−4.53462e7			−1.32902
$143$	−3.47411e7	−	1.04538e7i	−0.993499	−	0.298950i
$144$	−1.15925e6			−0.0323525
$145$	−1.74249e7	+	1.26599e7i	−0.474658	+	0.344859i
$146$	9.57413e6	+	2.94661e7i	0.254603	+	0.783589i
$147$	−3.88556e6	+	1.19585e7i	−0.100889	+	0.310504i
$148$	−7.05939e7	−	5.12895e7i	−1.78999	−	1.30051i
$149$	2.52284e7	+	1.83295e7i	0.624796	+	0.453941i	0.854594	−	0.519297i	$-0.173806\pi$
$149$	2.52284e7	+	1.83295e7i	0.624796	+	0.453941i	−0.229797	+	0.973239i	$0.573806\pi$
$150$	−3.00424e7	+	9.24609e7i	−0.726800	+	2.23686i
$151$	8.45791e6	+	2.60308e7i	0.199914	+	0.615273i	0.999884	+	0.0152326i	$0.00484888\pi$
$151$	8.45791e6	+	2.60308e7i	0.199914	+	0.615273i	−0.799970	+	0.600040i	$0.795151\pi$
$152$	−4.19224e7	+	3.04584e7i	−0.968265	+	0.703485i
$153$	1.67050e7			0.377074
$154$	2.73178e7	−	3.93831e7i	0.602731	−	0.868935i
$155$	−6.56467e7			−1.41596
$156$	3.61625e7	−	2.62736e7i	0.762645	−	0.554094i
$157$	−2.47662e7	−	7.62225e7i	−0.510752	−	1.57193i	−0.790880	−	0.611972i	$-0.790377\pi$
$157$	−2.47662e7	−	7.62225e7i	−0.510752	−	1.57193i	0.280127	−	0.959963i	$-0.409623\pi$
$158$	2.59694e7	−	7.99257e7i	0.523796	−	1.61208i
$159$	−2.41539e6	−	1.75488e6i	−0.0476538	−	0.0346225i
$160$	8.48627e7	+	6.16564e7i	1.63794	+	1.19003i
$161$	2.67399e6	−	8.22970e6i	0.0504975	−	0.155415i
$162$	−2.98075e6	−	9.17381e6i	−0.0550837	−	0.169530i
$163$	−5.14642e7	+	3.73909e7i	−0.930783	+	0.676253i	−0.946184	−	0.323628i	$-0.895097\pi$
$163$	−5.14642e7	+	3.73909e7i	−0.930783	+	0.676253i	0.0154017	+	0.999881i	$0.495097\pi$
$164$	1.56006e7			0.276177
$165$	5.91691e7	−	2.06664e7i	1.02542	−	0.358156i
$166$	−8.23343e7			−1.39702
$167$	1.97162e7	−	1.43246e7i	0.327578	−	0.237999i	−0.411824	−	0.911263i	$-0.635108\pi$
$167$	1.97162e7	−	1.43246e7i	0.327578	−	0.237999i	0.739402	+	0.673264i	$0.235108\pi$
$168$	6.65294e6	+	2.04756e7i	0.108251	+	0.333162i
$169$	1.48166e6	−	4.56007e6i	0.0236126	−	0.0726722i
$170$	−1.76936e8	−	1.28552e8i	−2.76214	−	2.00681i
$171$	2.29272e7	+	1.66576e7i	0.350643	+	0.254757i
$172$	−4.99978e7	+	1.53878e8i	−0.749207	+	2.30582i
$173$	−7.68329e6	−	2.36467e7i	−0.112820	−	0.347224i	0.878666	−	0.477437i	$-0.158434\pi$
$173$	−7.68329e6	−	2.36467e7i	−0.112820	−	0.347224i	−0.991486	+	0.130213i	$0.958434\pi$
$174$	−1.62394e7	+	1.17986e7i	−0.233694	+	0.169788i
$175$	−1.18671e8			−1.67383
$176$	−153523.	−	7.01809e6i	−0.00212265	−	0.0970342i
$177$	2.42601e7			0.328841
$178$	1.41332e8	−	1.02684e8i	1.87832	−	1.36468i
$179$	−6.57117e6	−	2.02240e7i	−0.0856362	−	0.263561i	0.899064	−	0.437817i	$-0.144248\pi$
$179$	−6.57117e6	−	2.02240e7i	−0.0856362	−	0.263561i	−0.984700	+	0.174256i	$0.944248\pi$
$180$	−2.38621e7	+	7.34399e7i	−0.304968	+	0.938595i
$181$	6.73322e7	+	4.89197e7i	0.844010	+	0.613209i	0.923488	−	0.383628i	$-0.125325\pi$
$181$	6.73322e7	+	4.89197e7i	0.844010	+	0.613209i	−0.0794780	+	0.996837i	$0.525325\pi$
$182$	7.21909e7	+	5.24497e7i	0.887631	+	0.644902i
$183$	1.14496e7	−	3.52381e7i	0.138105	−	0.425044i
$184$	5.95850e6	+	1.83384e7i	0.0705139	+	0.217019i
$185$	1.84278e8	−	1.33886e8i	2.13979	−	1.55465i
$186$	−6.11804e7			−0.697136
$187$	2.21229e6	+	1.01132e8i	0.0247398	+	1.13095i
$188$	1.35440e8			1.48661
$189$	9.52564e6	−	6.92078e6i	0.102631	−	0.0745657i
$190$	−1.14654e8	−	3.52869e8i	−1.21270	−	3.73229i
$191$	−3.88560e6	+	1.19586e7i	−0.0403497	+	0.124184i	−0.969202	−	0.246266i	$-0.920796\pi$
$191$	−3.88560e6	+	1.19586e7i	−0.0403497	+	0.124184i	0.928853	+	0.370450i	$0.120796\pi$
$192$	7.46430e7	+	5.42313e7i	0.761088	+	0.552963i
$193$	2.44742e7	+	1.77815e7i	0.245051	+	0.178040i	0.703531	−	0.710665i	$-0.251606\pi$
$193$	2.44742e7	+	1.77815e7i	0.245051	+	0.178040i	−0.458479	+	0.888705i	$0.651606\pi$
$194$	−9.78503e7	+	3.01152e8i	−0.962179	+	2.96128i
$195$	3.60570e7	+	1.10972e8i	0.348232	+	1.07175i
$196$	7.58947e7	−	5.51407e7i	0.719971	−	0.523090i
$197$	1.72519e8			1.60770			0.803849	−	0.594834i	$-0.202782\pi$
$197$	1.72519e8			1.60770			0.803849	+	0.594834i	$0.202782\pi$
$198$	5.51436e7	−	1.92604e7i	0.504855	−	0.176334i
$199$	2.61990e7			0.235667			0.117833	−	0.993033i	$-0.462405\pi$
$199$	2.61990e7			0.235667			0.117833	+	0.993033i	$0.462405\pi$
$200$	2.13934e8	−	1.55432e8i	1.89093	−	1.37384i
$201$	9.60913e6	+	2.95739e7i	0.0834637	+	0.256875i
$202$	1.73470e7	−	5.33887e7i	0.148080	−	0.455742i
$203$	−1.98227e7	−	1.44020e7i	−0.166313	−	0.120833i
$204$	−1.00829e8	−	7.32567e7i	−0.831535	−	0.604146i
$205$	−1.25843e7	+	3.87305e7i	−0.102021	+	0.313989i
$206$	5.89823e7	+	1.81529e8i	0.470096	+	1.44681i
$207$	8.53135e6	−	6.19839e6i	0.0668531	−	0.0485716i
$208$	1.30689e7			0.100697
$209$	−9.78090e7	+	1.41008e8i	−0.741083	+	1.06839i
$210$	−1.54152e8			−1.14863
$211$	−6.94208e6	+	5.04372e6i	−0.0508746	+	0.0369626i	−0.612932	−	0.790136i	$-0.710010\pi$
$211$	−6.94208e6	+	5.04372e6i	−0.0508746	+	0.0369626i	0.562057	+	0.827098i	$0.310010\pi$
$212$	6.88327e6	+	2.11845e7i	0.0496157	+	0.152701i
$213$	2.08449e7	−	6.41539e7i	0.147799	−	0.454878i
$214$	2.71194e8	+	1.97034e8i	1.89161	+	1.37434i
$215$	−3.41690e8	−	2.48252e8i	−2.34476	−	1.70357i
$216$	−8.10767e6	+	2.49528e7i	−0.0547404	+	0.168474i
$217$	−2.30775e7	−	7.10251e7i	−0.153313	−	0.471849i
$218$	−1.72951e8	+	1.25656e8i	−1.13064	+	0.821461i
$219$	−4.60885e7			−0.296509
$220$	−4.47766e8	−	1.34735e8i	−2.83512	−	0.853104i
$221$	−1.88326e8			−1.17364
$222$	1.71741e8	−	1.24777e8i	1.05351	−	0.765418i
$223$	−9.15657e7	−	2.81810e8i	−0.552924	−	1.70173i	−0.701362	−	0.712805i	$-0.747425\pi$
$223$	−9.15657e7	−	2.81810e8i	−0.552924	−	1.70173i	0.148438	−	0.988922i	$-0.452575\pi$
$224$	−3.68752e7	+	1.13490e8i	−0.219213	+	0.674669i
$225$	−1.17000e8	−	8.50053e7i	−0.684772	−	0.497516i
$226$	1.08186e8	+	7.86015e7i	0.623433	+	0.452951i
$227$	−4.45493e7	+	1.37109e8i	−0.252785	+	0.777991i	0.741474	+	0.670982i	$0.234127\pi$
$227$	−4.45493e7	+	1.37109e8i	−0.252785	+	0.777991i	−0.994258	+	0.107009i	$0.965873\pi$
$228$	−6.53370e7	−	2.01087e8i	−0.365079	−	1.12360i
$229$	1.23109e7	−	8.94438e6i	0.0677431	−	0.0492182i	−0.553398	−	0.832917i	$-0.686669\pi$
$229$	1.23109e7	−	8.94438e6i	0.0677431	−	0.0492182i	0.621141	+	0.783698i	$0.286669\pi$
$230$	−1.38062e8			−0.748214
$231$	4.31600e7	+	5.67518e7i	0.230377	+	0.302927i
$232$	5.45986e7			0.287061
$233$	2.60177e8	−	1.89030e8i	1.34748	−	0.979005i	0.348352	−	0.937364i	$-0.386741\pi$
$233$	2.60177e8	−	1.89030e8i	1.34748	−	0.979005i	0.999133	−	0.0416408i	$-0.0132585\pi$
$234$	3.36039e7	+	1.03422e8i	0.171449	+	0.527664i
$235$	−1.09254e8	+	3.36249e8i	−0.549160	+	1.69014i
$236$	−1.46431e8	−	1.06388e8i	−0.725171	−	0.526868i
$237$	1.01138e8	+	7.34809e7i	0.493508	+	0.358554i
$238$	7.68837e7	−	2.36624e8i	0.369671	−	1.13773i
$239$	−6.99533e7	−	2.15294e8i	−0.331448	−	1.02009i	−0.968445	−	0.249226i	$-0.919824\pi$
$239$	−6.99533e7	−	2.15294e8i	−0.331448	−	1.02009i	0.636997	−	0.770866i	$-0.280176\pi$
$240$	−1.82651e7	+	1.32704e7i	−0.0852870	+	0.0619646i
$241$	1.92142e8			0.884225			0.442113	−	0.896960i	$-0.354229\pi$
$241$	1.92142e8			0.884225			0.442113	+	0.896960i	$0.354229\pi$
$242$	1.23905e8	+	3.31289e8i	0.562001	+	1.50263i
$243$	1.43489e7			0.0641500
$244$	−2.23638e8	+	1.62483e8i	−0.985558	+	0.716050i
$245$	7.56732e7	+	2.32898e8i	0.328746	+	1.01178i
$246$	−1.17281e7	+	3.60955e7i	−0.0502292	+	0.154590i
$247$	−2.58473e8	−	1.87792e8i	−1.09138	−	0.792934i
$248$	1.34630e8	+	9.78141e7i	0.560479	+	0.407212i
$249$	3.78476e7	−	1.16483e8i	0.155361	−	0.478151i
$250$	3.54674e8	+	1.09157e9i	1.43562	+	4.41838i
$251$	−2.43897e8	+	1.77202e8i	−0.973530	+	0.707311i	−0.956253	−	0.292540i	$-0.905499\pi$
$251$	−2.43897e8	+	1.77202e8i	−0.973530	+	0.707311i	−0.0172763	+	0.999851i	$0.505499\pi$
$252$	−8.78454e7			−0.345794
$253$	3.86549e7	+	5.08280e7i	0.150066	+	0.197325i
$254$	5.47218e7			0.209528
$255$	2.63204e8	−	1.91229e8i	0.994034	−	0.722208i
$256$	−6.94994e7	−	2.13897e8i	−0.258905	−	0.796829i
$257$	−7.96549e7	+	2.45153e8i	−0.292716	+	0.900887i	0.691263	+	0.722603i	$0.257055\pi$
$257$	−7.96549e7	+	2.45153e8i	−0.292716	+	0.900887i	−0.983979	+	0.178284i	$0.942945\pi$
$258$	−3.18444e8	−	2.31363e8i	−1.15442	−	0.838734i
$259$	2.09636e8	+	1.52310e8i	0.749751	+	0.544726i
$260$	2.69012e8	−	8.27934e8i	0.949216	−	2.92139i
$261$	−9.22719e6	−	2.83984e7i	−0.0321238	−	0.0988670i
$262$	2.53326e8	−	1.84052e8i	0.870212	−	0.632246i
$263$	7.50278e7			0.254318			0.127159	−	0.991882i	$-0.459414\pi$
$263$	7.50278e7			0.254318			0.127159	+	0.991882i	$0.459414\pi$
$264$	−1.52138e8	−	4.57793e7i	−0.508891	−	0.153128i
$265$	−5.81458e7			−0.191937
$266$	3.41474e8	−	2.48096e8i	1.11243	−	0.808227i
$267$	8.03046e7	+	2.47152e8i	0.258197	+	0.794648i
$268$	7.16913e7	−	2.20643e8i	0.227507	−	0.700194i
$269$	−5.92561e7	−	4.30521e7i	−0.185609	−	0.134853i	0.491100	−	0.871103i	$-0.336595\pi$
$269$	−5.92561e7	−	4.30521e7i	−0.185609	−	0.134853i	−0.676710	+	0.736250i	$0.736595\pi$
$270$	−1.51981e8	−	1.10421e8i	−0.469912	−	0.341411i
$271$	−4.41818e7	+	1.35978e8i	−0.134850	+	0.415026i	−0.995567	−	0.0940587i	$-0.970016\pi$
$271$	−4.41818e7	+	1.35978e8i	−0.134850	+	0.415026i	0.860717	+	0.509084i	$0.170016\pi$
$272$	−1.12603e7	−	3.46556e7i	−0.0339280	−	0.104420i
$273$	−1.07388e8	+	7.80223e7i	−0.319439	+	0.232086i
$274$	6.00382e8			1.76320
$275$	4.99128e8	−	7.19575e8i	1.44726	−	2.08647i
$276$	−7.86760e7			−0.225248
$277$	−4.13120e8	+	3.00149e8i	−1.16788	+	0.848511i	−0.990753	−	0.135678i	$-0.956679\pi$
$277$	−4.13120e8	+	3.00149e8i	−1.16788	+	0.848511i	−0.177123	+	0.984189i	$0.556679\pi$
$278$	−1.76250e8	−	5.42443e8i	−0.492009	−	1.51425i
$279$	2.81236e7	−	8.65554e7i	0.0775275	−	0.238605i
$280$	3.39217e8	+	2.46455e8i	0.923473	+	0.670942i
$281$	5.74572e7	+	4.17451e7i	0.154480	+	0.112236i	0.662340	−	0.749203i	$-0.269563\pi$
$281$	5.74572e7	+	4.17451e7i	0.154480	+	0.112236i	−0.507860	+	0.861440i	$0.669563\pi$
$282$	−1.01821e8	+	3.13372e8i	−0.270374	+	0.832125i
$283$	−2.00689e8	−	6.17657e8i	−0.526345	−	1.61992i	−0.761641	−	0.648000i	$-0.775606\pi$
$283$	−2.00689e8	−	6.17657e8i	−0.526345	−	1.61992i	0.235296	−	0.971924i	$-0.424394\pi$
$284$	−4.07152e8	+	2.95813e8i	−1.05473	+	0.766309i
$285$	5.51928e8			1.41230
$286$	−6.21668e8	+	2.17135e8i	−1.57137	+	0.548843i
$287$	−4.63276e7			−0.115679
$288$	−1.17650e8	+	8.54778e7i	−0.290214	+	0.210853i
$289$	3.54614e7	+	1.09139e8i	0.0864197	+	0.265973i
$290$	−1.20804e8	+	3.71797e8i	−0.290863	+	0.895186i
$291$	−3.81077e8	−	2.76869e8i	−0.906541	−	0.658640i
$292$	2.78184e8	+	2.02113e8i	0.653871	+	0.475065i
$293$	−1.16993e8	+	3.60068e8i	−0.271721	+	0.836272i	0.718347	+	0.695685i	$0.244899\pi$
$293$	−1.16993e8	+	3.60068e8i	−0.271721	+	0.836272i	−0.990068	+	0.140587i	$0.955101\pi$
$294$	7.05248e7	+	2.17053e8i	0.161855	+	0.498139i
$295$	3.82242e8	−	2.77715e8i	0.866885	−	0.629829i
$296$	−5.77412e8			−1.29409
$297$	1.90027e6	+	8.68684e7i	0.00420889	+	0.192404i
$298$	5.66006e8			1.23898
$299$	−9.61792e7	+	6.98783e7i	−0.208081	+	0.151180i
$300$	3.33420e8	+	1.02616e9i	0.712964	+	2.19428i
$301$	1.48474e8	−	4.56956e8i	0.313811	−	0.965810i
$302$	4.01908e8	+	2.92003e8i	0.839658	+	0.610047i
$303$	6.75579e7	+	4.90837e7i	0.139517	+	0.101365i
$304$	1.91028e7	−	5.87925e7i	0.0389978	−	0.120023i
$305$	−2.22986e8	−	6.86280e8i	−0.450016	−	1.38501i
$306$	2.45297e8	−	1.78219e8i	0.489403	−	0.355572i
$307$	−4.66718e8			−0.920599			−0.460300	−	0.887764i	$-0.652258\pi$
$307$	−4.66718e8			−0.920599			−0.460300	+	0.887764i	$0.652258\pi$
$308$	−1.16336e7	−	5.31817e8i	−0.0226876	−	1.03713i
$309$	−2.83932e8			−0.547469
$310$	−9.63959e8	+	7.00357e8i	−1.83778	+	1.33522i
$311$	5.51024e7	+	1.69588e8i	0.103874	+	0.319693i	0.989465	−	0.144775i	$-0.0462457\pi$
$311$	5.51024e7	+	1.69588e8i	0.103874	+	0.319693i	−0.885590	+	0.464468i	$0.846246\pi$
$312$	9.14028e7	−	2.81309e8i	0.170380	−	0.524375i
$313$	2.83625e8	+	2.06065e8i	0.522804	+	0.379839i	0.817659	−	0.575703i	$-0.195271\pi$
$313$	2.83625e8	+	2.06065e8i	0.522804	+	0.379839i	−0.294855	+	0.955542i	$0.595271\pi$
$314$	−1.17685e9	−	8.55035e8i	−2.14521	−	1.55858i
$315$	7.08610e7	−	2.18088e8i	0.127738	−	0.393137i
$316$	−2.88217e8	−	8.87042e8i	−0.513825	−	1.58139i
$317$	7.36225e8	−	5.34899e8i	1.29808	−	0.943114i	0.298150	−	0.954519i	$-0.403630\pi$
$317$	7.36225e8	−	5.34899e8i	1.29808	−	0.943114i	0.999935	+	0.0114052i	$0.00363048\pi$
$318$	−5.41899e7			−0.0944982
$319$	1.70702e8	−	5.96223e7i	0.294422	−	0.102835i
$320$	1.79688e9			3.06546
$321$	−4.03419e8	+	2.93101e8i	−0.680751	+	0.494594i
$322$	−4.85343e7	−	1.49373e8i	−0.0810127	−	0.249331i
$323$	−2.75276e8	+	8.47211e8i	−0.454526	+	1.39889i
$324$	−8.66082e7	−	6.29245e7i	−0.141466	−	0.102781i
$325$	1.31901e9	+	9.58317e8i	2.13136	+	1.54852i
$326$	−3.56794e8	+	1.09810e9i	−0.570370	+	1.75542i
$327$	−9.82706e7	−	3.02446e8i	−0.155420	−	0.478333i
$328$	8.35169e7	−	6.06786e7i	0.130682	−	0.0949461i
$329$	−4.02205e8			−0.622676
$330$	6.48360e8	−	9.34718e8i	0.993156	−	1.43180i
$331$	−5.63023e8			−0.853352			−0.426676	−	0.904404i	$-0.640316\pi$
$331$	−5.63023e8			−0.853352			−0.426676	+	0.904404i	$0.640316\pi$
$332$	−7.39258e8	+	5.37103e8i	−1.10870	+	0.805516i
$333$	9.75828e7	+	3.00329e8i	0.144817	+	0.445700i
$334$	1.36690e8	−	4.20687e8i	0.200735	−	0.617798i
$335$	4.89945e8	+	3.55966e8i	0.712018	+	0.517311i
$336$	−2.07786e7	−	1.50965e7i	−0.0298832	−	0.0217114i
$337$	6.40034e7	−	1.96982e8i	0.0910957	−	0.280364i	−0.895121	−	0.445824i	$-0.852911\pi$
$337$	6.40034e7	−	1.96982e8i	0.0910957	−	0.280364i	0.986217	+	0.165460i	$0.0529108\pi$
$338$	−2.68928e7	−	8.27676e7i	−0.0378815	−	0.116587i
$339$	−1.60933e8	+	1.16925e8i	−0.224360	+	0.163007i
$340$	−2.42726e9			−3.34920
$341$	5.27732e8	+	1.58797e8i	0.720731	+	0.216872i
$342$	5.14378e8			0.695330
$343$	−6.23933e8	+	4.53314e8i	−0.834851	+	0.606555i
$344$	3.30847e8	+	1.01824e9i	0.438200	+	1.34864i
$345$	6.34645e7	−	1.95324e8i	0.0832078	−	0.256087i
$346$	−3.65099e8	−	2.65260e8i	−0.473854	−	0.344275i
$347$	9.73508e8	+	7.07295e8i	1.25080	+	0.908756i	0.998268	−	0.0588334i	$-0.0187381\pi$
$347$	9.73508e8	+	7.07295e8i	1.25080	+	0.908756i	0.252528	+	0.967590i	$0.418738\pi$
$348$	−6.88417e7	+	2.11873e8i	−0.0875637	+	0.269493i
$349$	6.49665e7	+	1.99946e8i	0.0818089	+	0.251782i	0.983592	−	0.180407i	$-0.0577414\pi$
$349$	6.49665e7	+	1.99946e8i	0.0818089	+	0.251782i	−0.901783	+	0.432189i	$0.857741\pi$
$350$	−1.74257e9	+	1.26605e9i	−2.17246	+	1.57839i
$351$	−1.61764e8			−0.199668
$352$	−5.33064e8	−	7.00935e8i	−0.651448	−	0.856600i
$353$	2.82023e8			0.341251			0.170625	−	0.985336i	$-0.445421\pi$
$353$	2.82023e8			0.341251			0.170625	+	0.985336i	$0.445421\pi$
$354$	3.56237e8	−	2.58821e8i	0.426803	−	0.310090i
$355$	−4.05964e8	−	1.24943e9i	−0.481602	−	1.48222i
$356$	5.99132e8	−	1.84394e9i	0.703797	−	2.16607i
$357$	2.99423e8	+	2.17544e8i	0.348294	+	0.253051i
$358$	−3.12253e8	−	2.26865e8i	−0.359680	−	0.261322i
$359$	−8.13172e7	+	2.50269e8i	−0.0927581	+	0.285480i	−0.986663	−	0.162777i	$-0.947955\pi$
$359$	−8.13172e7	+	2.50269e8i	−0.0927581	+	0.285480i	0.893905	+	0.448257i	$0.147955\pi$
$360$	1.57901e8	+	4.85969e8i	0.178372	+	0.548971i
$361$	−4.99461e8	+	3.62880e8i	−0.558762	+	0.405964i
$362$	1.51061e9			1.67368
$363$	−5.25650e8	+	2.30085e7i	−0.576798	+	0.0252473i
$364$	9.90336e8			1.07629
$365$	−7.26170e8	+	5.27593e8i	−0.781652	+	0.567903i
$366$	−2.07815e8	−	6.39589e8i	−0.221561	−	0.681895i
$367$	−1.81187e8	+	5.57637e8i	−0.191336	+	0.588872i	0.808664	+	0.588271i	$0.200191\pi$
$367$	−1.81187e8	+	5.57637e8i	−0.191336	+	0.588872i	−1.00000		0.000600527i	$0.999809\pi$
$368$	−1.86097e7	−	1.35207e7i	−0.0194658	−	0.0141427i
$369$	−4.56751e7	−	3.31849e7i	−0.0473247	−	0.0343834i
$370$	1.27757e9	−	3.93197e9i	1.31123	−	4.03556i
$371$	−2.04406e7	−	6.29097e7i	−0.0207819	−	0.0639601i
$372$	−5.49323e8	+	3.99107e8i	−0.553258	+	0.401966i
$373$	−9.26124e8			−0.924034			−0.462017	−	0.886871i	$-0.652874\pi$
$373$	−9.26124e8			−0.924034			−0.462017	+	0.886871i	$0.652874\pi$
$374$	1.11142e9	+	1.46143e9i	1.09857	+	1.44453i
$375$	−1.70735e9			−1.67191
$376$	7.25074e8	−	5.26797e8i	0.703436	−	0.511076i
$377$	1.04024e8	+	3.20152e8i	0.0999857	+	0.307724i
$378$	6.60400e7	−	2.03250e8i	0.0628906	−	0.193557i
$379$	−5.64442e8	−	4.10091e8i	−0.532577	−	0.386940i	0.288744	−	0.957406i	$-0.406762\pi$
$379$	−5.64442e8	−	4.10091e8i	−0.532577	−	0.386940i	−0.821321	+	0.570467i	$0.806762\pi$
$380$	−3.33137e9	−	2.42038e9i	−3.11444	−	2.26277i
$381$	−2.51546e7	+	7.74180e7i	−0.0233013	+	0.0717141i
$382$	7.05255e7	+	2.17055e8i	0.0647328	+	0.199227i
$383$	−1.22569e9	+	8.90517e8i	−1.11477	+	0.809928i	−0.983408	−	0.181406i	$-0.941935\pi$
$383$	−1.22569e9	+	8.90517e8i	−1.11477	+	0.809928i	−0.131362	+	0.991334i	$0.541935\pi$
$384$	9.85219e8			0.887919
$385$	1.32969e9	+	4.00111e8i	1.18751	+	0.357329i
$386$	5.49083e8			0.485940
$387$	4.73705e8	−	3.44167e8i	0.415451	−	0.301843i
$388$	1.08598e9	+	3.34229e9i	0.943863	+	2.90491i
$389$	2.86014e8	−	8.80260e8i	0.246356	−	0.758207i	−0.749054	−	0.662509i	$-0.769492\pi$
$389$	2.86014e8	−	8.80260e8i	0.246356	−	0.758207i	0.995410	−	0.0956978i	$-0.0305083\pi$
$390$	1.71338e9	+	1.24484e9i	1.46260	+	1.06264i
$391$	2.68169e8	+	1.94836e8i	0.226877	+	0.164836i
$392$	1.91828e8	−	5.90386e8i	0.160846	−	0.495034i
$393$	1.43939e8	+	4.43000e8i	0.119621	+	0.368154i
$394$	2.53327e9	−	1.84053e9i	2.08663	−	1.51602i
$395$	2.43469e9			1.98771
$396$	3.69476e8	−	5.32660e8i	0.298987	−	0.431039i
$397$	1.19176e9			0.955921			0.477961	−	0.878381i	$-0.341376\pi$
$397$	1.19176e9			0.955921			0.477961	+	0.878381i	$0.341376\pi$
$398$	3.84707e8	−	2.79506e8i	0.305872	−	0.222229i
$399$	1.94025e8	+	5.97148e8i	0.152916	+	0.470627i
$400$	−9.74834e7	+	3.00023e8i	−0.0761589	+	0.234393i
$401$	−1.39315e8	−	1.01218e8i	−0.107893	−	0.0783888i	0.532531	−	0.846411i	$-0.321241\pi$
$401$	−1.39315e8	−	1.01218e8i	−0.107893	−	0.0783888i	−0.640423	+	0.768022i	$0.721241\pi$
$402$	4.56612e8	+	3.31748e8i	0.350555	+	0.254693i
$403$	−3.17054e8	+	9.75793e8i	−0.241305	+	0.742660i
$404$	−1.92523e8	−	5.92526e8i	−0.145261	−	0.447067i
$405$	2.26081e8	−	1.64258e8i	0.169111	−	0.122866i
$406$	−4.44726e8			−0.329801
$407$	−1.80527e9	+	6.30541e8i	−1.32728	+	0.463588i
$408$	−8.24716e8			−0.601165
$409$	−9.39343e8	+	6.82473e8i	−0.678880	+	0.493235i	−0.872986	−	0.487746i	$-0.837819\pi$
$409$	−9.39343e8	+	6.82473e8i	−0.678880	+	0.493235i	0.194106	+	0.980981i	$0.437819\pi$
$410$	2.28411e8	+	7.02977e8i	0.163672	+	0.503730i
$411$	−2.75985e8	+	8.49394e8i	−0.196082	+	0.603480i
$412$	1.71378e9	+	1.24513e9i	1.20730	+	0.877153i
$413$	4.34842e8	+	3.15931e8i	0.303743	+	0.220682i
$414$	5.91467e7	−	1.82035e8i	0.0409666	−	0.126082i
$415$	−7.37101e8	−	2.26856e9i	−0.506242	−	1.55805i
$416$	1.32634e9	−	9.63645e8i	0.903294	−	0.656282i
$417$	8.48444e8			0.572990
$418$	6.81207e7	+	3.11405e9i	0.0456207	+	2.08549i
$419$	−1.19401e9			−0.792973			−0.396486	−	0.918041i	$-0.629771\pi$
$419$	−1.19401e9			−0.792973			−0.396486	+	0.918041i	$0.629771\pi$
$420$	−1.38409e9	+	1.00560e9i	−0.911575	+	0.662298i
$421$	−7.51300e8	−	2.31226e9i	−0.490711	−	1.51025i	−0.823536	−	0.567265i	$-0.808002\pi$
$421$	−7.51300e8	−	2.31226e9i	−0.490711	−	1.51025i	0.332824	−	0.942989i	$-0.391998\pi$
$422$	−4.81285e7	+	1.48124e8i	−0.0311752	+	0.0959473i
$423$	−3.96540e8	−	2.88103e8i	−0.254739	−	0.185079i
$424$	1.19247e8	+	8.66377e7i	0.0759741	+	0.0551984i
$425$	1.40475e9	−	4.32339e9i	0.887645	−	2.73189i
$426$	−3.78345e8	−	1.16442e9i	−0.237112	−	0.729756i
$427$	6.64119e8	−	4.82510e8i	0.412808	−	0.299923i
$428$	3.72032e9			2.29365
$429$	−2.14229e7	−	9.79322e8i	−0.0131002	−	0.598859i
$430$	−7.66590e9			−4.64968
$431$	3.70912e8	−	2.69484e8i	0.223152	−	0.162129i	−0.470592	−	0.882351i	$-0.655960\pi$
$431$	3.70912e8	−	2.69484e8i	0.223152	−	0.162129i	0.693744	+	0.720221i	$0.255960\pi$
$432$	−9.67213e6	−	2.97678e7i	−0.00577204	−	0.0177645i
$433$	−6.54516e8	+	2.01439e9i	−0.387447	+	1.19244i	0.547242	+	0.836974i	$0.315678\pi$
$433$	−6.54516e8	+	2.01439e9i	−0.387447	+	1.19244i	−0.934689	+	0.355466i	$0.884322\pi$
$434$	−1.09661e9	−	7.96733e8i	−0.643929	−	0.467841i
$435$	−4.70471e8	−	3.41817e8i	−0.274044	−	0.199105i
$436$	−7.33172e8	+	2.25647e9i	−0.423646	+	1.30385i
$437$	1.73773e8	+	5.34818e8i	0.0996086	+	0.306564i
$438$	−6.76766e8	+	4.91699e8i	−0.384839	+	0.279602i
$439$	2.12795e9			1.20043			0.600213	−	0.799840i	$-0.295082\pi$
$439$	2.12795e9			1.20043			0.600213	+	0.799840i	$0.295082\pi$
$440$	−2.92115e9	+	1.02029e9i	−1.63482	+	0.571005i
$441$	−3.39496e8			−0.188495
$442$	−2.76538e9	+	2.00917e9i	−1.52327	+	1.10672i
$443$	−7.41466e8	−	2.28200e9i	−0.405208	−	1.24710i	−0.920721	−	0.390220i	$-0.872399\pi$
$443$	−7.41466e8	−	2.28200e9i	−0.405208	−	1.24710i	0.515513	−	0.856881i	$-0.327601\pi$
$444$	7.28041e8	−	2.24068e9i	0.394744	−	1.21490i
$445$	4.09453e9	+	2.97485e9i	2.20264	+	1.60031i
$446$	−4.35107e9	−	3.16124e9i	−2.32233	−	1.68727i
$447$	−2.60183e8	+	8.00761e8i	−0.137785	+	0.424059i
$448$	6.31678e8	+	1.94410e9i	0.331912	+	1.02152i
$449$	−9.21953e8	+	6.69838e8i	−0.480669	+	0.349227i	−0.801585	−	0.597881i	$-0.796009\pi$
$449$	−9.21953e8	+	6.69838e8i	−0.480669	+	0.349227i	0.320915	+	0.947108i	$0.396009\pi$
$450$	−2.62492e9			−1.35791
$451$	1.94853e8	−	2.80912e8i	0.100020	−	0.144196i
$452$	1.48412e9			0.755937
$453$	−5.97864e8	+	4.34374e8i	−0.302175	+	0.219543i
$454$	8.08592e8	+	2.48859e9i	0.405540	+	1.24812i
$455$	−7.98860e8	+	2.45864e9i	−0.397586	+	1.22364i
$456$	−1.13191e9	−	8.22378e8i	−0.559028	−	0.406157i
$457$	−2.78259e9	−	2.02167e9i	−1.36377	−	0.990840i	−0.998195	−	0.0600597i	$-0.980871\pi$
$457$	−2.78259e9	−	2.02167e9i	−1.36377	−	0.990840i	−0.365579	−	0.930780i	$-0.619129\pi$
$458$	8.53498e7	−	2.62680e8i	0.0415120	−	0.127761i
$459$	1.39377e8	+	4.28959e8i	0.0672741	+	0.207048i
$460$	−1.23962e9	+	9.00636e8i	−0.593794	+	0.431417i
$461$	−1.08075e9			−0.513774			−0.256887	−	0.966441i	$-0.582697\pi$
$461$	−1.08075e9			−0.513774			−0.256887	+	0.966441i	$0.582697\pi$
$462$	1.23922e9	+	3.72890e8i	0.584660	+	0.175927i
$463$	2.61984e9			1.22671			0.613354	−	0.789808i	$-0.289820\pi$
$463$	2.61984e9			1.22671			0.613354	+	0.789808i	$0.289820\pi$
$464$	−5.26945e7	+	3.82848e7i	−0.0244880	+	0.0177915i
$465$	−5.47720e8	−	1.68571e9i	−0.252623	−	0.777495i
$466$	1.80378e9	−	5.55145e9i	0.825718	−	2.54130i
$467$	−1.59492e9	−	1.15877e9i	−0.724650	−	0.526489i	0.163216	−	0.986590i	$-0.447813\pi$
$467$	−1.59492e9	−	1.15877e9i	−0.724650	−	0.526489i	−0.887867	+	0.460101i	$0.847813\pi$
$468$	9.76388e8	+	7.09387e8i	0.440313	+	0.319906i
$469$	−2.12895e8	+	6.55224e8i	−0.0952929	+	0.293281i
$470$	1.98301e9	+	6.10308e9i	0.881013	+	2.71148i
$471$	1.75065e9	−	1.27192e9i	0.772014	−	0.560901i
$472$	−1.19771e9			−0.524269
$473$	2.14632e9	+	2.82223e9i	0.932569	+	1.22625i
$474$	2.26905e9			0.978632
$475$	6.23913e9	−	4.53299e9i	2.67114	−	1.94070i
$476$	−8.53282e8	−	2.62613e9i	−0.362634	−	1.11607i
$477$	2.49101e7	−	7.66655e7i	0.0105090	−	0.0323434i
$478$	−3.32408e9	−	2.41509e9i	−1.39211	−	1.01143i
$479$	2.41523e9	+	1.75477e9i	1.00412	+	0.729534i	0.962967	−	0.269619i	$-0.0868978\pi$
$479$	2.41523e9	+	1.75477e9i	1.00412	+	0.729534i	0.0411501	+	0.999153i	$0.486898\pi$
$480$	−8.75196e8	+	2.69358e9i	−0.361211	+	1.11169i
$481$	−1.10011e9	−	3.38580e9i	−0.450743	−	1.38724i
$482$	2.82142e9	−	2.04989e9i	1.14764	−	0.833806i
$483$	2.33637e8			0.0943467
$484$	3.27366e9	+	2.16627e9i	1.31243	+	0.868467i
$485$	−9.17368e9			−3.65130
$486$	2.10700e8	−	1.53083e8i	0.0832603	−	0.0604921i
$487$	7.31978e8	+	2.25280e9i	0.287175	+	0.883834i	0.985738	+	0.168286i	$0.0538231\pi$
$487$	7.31978e8	+	2.25280e9i	0.287175	+	0.883834i	−0.698563	+	0.715548i	$0.746177\pi$
$488$	−5.65259e8	+	1.73969e9i	−0.220180	+	0.677644i
$489$	−1.38953e9	−	1.00955e9i	−0.537388	−	0.390435i
$490$	3.59588e9	+	2.61256e9i	1.38076	+	1.00318i
$491$	1.16151e9	−	3.57475e9i	0.442830	−	1.36289i	−0.442017	−	0.897007i	$-0.645737\pi$
$491$	1.16151e9	−	3.57475e9i	0.442830	−	1.36289i	0.884846	−	0.465883i	$-0.154263\pi$
$492$	1.30163e8	+	4.00600e8i	0.0492730	+	0.151647i
$493$	7.59339e8	−	5.51692e8i	0.285411	−	0.207364i
$494$	−5.79891e9			−2.16422
$495$	1.02436e9	+	1.34695e9i	0.379607	+	0.499151i
$496$	−1.98522e8			−0.0730505
$497$	1.20908e9	−	8.78450e8i	0.441783	−	0.320974i
$498$	−6.86953e8	−	2.11422e9i	−0.249244	−	0.767093i
$499$	1.00111e9	−	3.08110e9i	0.360686	−	1.11008i	−0.591952	−	0.805973i	$-0.701642\pi$
$499$	1.00111e9	−	3.08110e9i	0.360686	−	1.11008i	0.952638	−	0.304106i	$-0.0983575\pi$
$500$	1.03053e10	+	7.48726e9i	3.68695	+	2.67872i
$501$	5.32337e8	+	3.86765e8i	0.189127	+	0.137409i
$502$	−1.69091e9	+	5.20408e9i	−0.596564	+	1.83604i
$503$	−5.39421e7	−	1.66017e8i	−0.0188991	−	0.0581653i	0.941162	−	0.337955i	$-0.109735\pi$
$503$	−5.39421e7	−	1.66017e8i	−0.0188991	−	0.0581653i	−0.960061	+	0.279790i	$0.909735\pi$
$504$	−4.70276e8	+	3.41675e8i	−0.163624	+	0.118879i
$505$	1.62632e9			0.561936
$506$	1.10987e9	+	3.33967e8i	0.380844	+	0.114598i
$507$	1.29458e8			0.0441165
$508$	4.91333e8	−	3.56974e8i	0.166285	−	0.120813i
$509$	2.00755e8	+	6.17861e8i	0.0674768	+	0.207672i	0.979110	−	0.203334i	$-0.0651776\pi$
$509$	2.00755e8	+	6.17861e8i	0.0674768	+	0.207672i	−0.911633	+	0.411006i	$0.865178\pi$
$510$	1.82476e9	−	5.61603e9i	0.609129	−	1.87471i
$511$	−8.26098e8	−	6.00195e8i	−0.273879	−	0.198985i
$512$	4.76135e8	+	3.45933e8i	0.156778	+	0.113906i
$513$	−2.36451e8	+	7.27720e8i	−0.0773267	+	0.237987i
$514$	1.44577e9	+	4.44964e9i	0.469602	+	1.44529i
$515$	−4.47363e9	+	3.25029e9i	−1.44323	+	1.04857i
$516$	−4.36850e9			−1.39978
$517$	1.69167e9	−	2.43881e9i	0.538391	−	0.776178i
$518$	4.70324e9			1.48677
$519$	5.43108e8	−	3.94591e8i	0.170530	−	0.123897i
$520$	−1.78011e9	−	5.47863e9i	−0.555183	−	1.70868i
$521$	6.25468e8	−	1.92499e9i	0.193764	−	0.596345i	−0.806225	−	0.591609i	$-0.798493\pi$
$521$	6.25468e8	−	1.92499e9i	0.193764	−	0.596345i	0.999989	−	0.00473515i	$-0.00150725\pi$
$522$	−4.38463e8	−	3.18562e8i	−0.134923	−	0.0980273i
$523$	−2.34057e9	−	1.70053e9i	−0.715429	−	0.519789i	0.169492	−	0.985532i	$-0.445787\pi$
$523$	−2.34057e9	−	1.70053e9i	−0.715429	−	0.519789i	−0.884920	+	0.465742i	$0.845787\pi$
$524$	1.07390e9	−	3.30511e9i	0.326064	−	1.00352i
$525$	−9.90127e8	−	3.04730e9i	−0.298630	−	0.919089i
$526$	1.10171e9	−	8.00441e8i	0.330079	−	0.239817i
$527$	2.86074e9			0.851416
$528$	1.78933e8	−	6.24974e7i	0.0529021	−	0.0184775i
$529$	−3.19558e9			−0.938543
$530$	−8.53816e8	+	6.20334e8i	−0.249114	+	0.180992i
$531$	2.02413e8	+	6.22964e8i	0.0586689	+	0.180564i
$532$	1.44757e9	−	4.45517e9i	0.416821	−	1.28284i
$533$	5.14924e8	+	3.74114e8i	0.147298	+	0.107019i
$534$	3.81596e9	+	2.77246e9i	1.08445	+	0.787899i
$535$	−3.00102e9	+	9.23619e9i	−0.847287	+	2.60768i
$536$	−4.74398e8	−	1.46005e9i	−0.133066	−	0.409534i
$537$	4.64496e8	−	3.37476e8i	0.129441	−	0.0940444i
$538$	−1.32942e9			−0.368066
$539$	−4.49605e7	−	2.05531e9i	−0.0123672	−	0.565350i
$540$	−2.08492e9			−0.569786
$541$	−3.86851e9	+	2.81063e9i	−1.05040	+	0.763157i	−0.972288	−	0.233788i	$-0.924888\pi$
$541$	−3.86851e9	+	2.81063e9i	−1.05040	+	0.763157i	−0.0781077	+	0.996945i	$0.524888\pi$
$542$	8.01921e8	+	2.46806e9i	0.216339	+	0.665822i
$543$	−6.94402e8	+	2.13715e9i	−0.186128	+	0.572843i
$544$	−3.69814e9	−	2.68686e9i	−0.984889	−	0.715564i
$545$	−5.01057e9	−	3.64039e9i	−1.32587	−	0.963298i
$546$	−7.44510e8	+	2.29137e9i	−0.195748	+	0.602449i
$547$	1.34912e8	+	4.15217e8i	0.0352448	+	0.108472i	0.967131	−	0.254278i	$-0.0818378\pi$
$547$	1.34912e8	+	4.15217e8i	0.0352448	+	0.108472i	−0.931886	+	0.362750i	$0.881838\pi$
$548$	5.39067e9	−	3.91655e9i	1.39930	−	1.01665i
$549$	1.00039e9			0.258028
$550$	−3.47626e8	−	1.58913e10i	−0.0890928	−	4.07276i
$551$	1.59230e9			0.405504
$552$	−4.21188e8	+	3.06011e8i	−0.106583	+	0.0774373i
$553$	8.55893e8	+	2.63417e9i	0.215219	+	0.662377i
$554$	−2.86410e9	+	8.81481e9i	−0.715657	+	2.20256i
$555$	4.97550e9	+	3.61491e9i	1.23541	+	0.897579i
$556$	−5.12110e9	−	3.72070e9i	−1.26358	−	0.918042i
$557$	−1.15209e8	+	3.54577e8i	−0.0282484	+	0.0869397i	−0.964187	−	0.265224i	$-0.914554\pi$
$557$	−1.15209e8	+	3.54577e8i	−0.0282484	+	0.0869397i	0.935938	+	0.352164i	$0.114554\pi$
$558$	−5.10456e8	−	1.57102e9i	−0.124377	−	0.382792i
$559$	−5.34037e9	+	3.88001e9i	−1.29309	+	0.939488i
$560$	−5.00203e8			−0.120362
$561$	−2.57847e9	+	9.00600e8i	−0.616583	+	0.215358i
$562$	1.28907e9			0.306336
$563$	1.84059e9	−	1.33727e9i	0.434688	−	0.315819i	−0.348833	−	0.937185i	$-0.613422\pi$
$563$	1.84059e9	−	1.33727e9i	0.434688	−	0.315819i	0.783521	+	0.621366i	$0.213422\pi$
$564$	1.13004e9	+	3.47791e9i	0.265227	+	0.816285i
$565$	−1.19718e9	+	3.68453e9i	−0.279247	+	0.859434i
$566$	−9.53645e9	−	6.92864e9i	−2.21070	−	1.60617i
$567$	2.57192e8	+	1.86861e8i	0.0592540	+	0.0430505i
$568$	−1.02910e9	+	3.16724e9i	−0.235634	+	0.725208i
$569$	8.68062e8	+	2.67162e9i	0.197541	+	0.607970i	0.999938	+	0.0111779i	$0.00355811\pi$
$569$	8.68062e8	+	2.67162e9i	0.197541	+	0.607970i	−0.802396	+	0.596792i	$0.796442\pi$
$570$	8.10454e9	−	5.88830e9i	1.83302	−	1.33177i
$571$	1.78930e9			0.402214			0.201107	−	0.979569i	$-0.435546\pi$
$571$	1.78930e9			0.402214			0.201107	+	0.979569i	$0.435546\pi$
$572$	−4.16533e9	+	6.00501e9i	−0.930601	+	1.34161i
$573$	−3.39499e8			−0.0753872
$574$	−6.80277e8	+	4.94250e8i	−0.150139	+	0.109083i
$575$	−8.86777e8	−	2.72922e9i	−0.194526	−	0.598689i
$576$	−7.69800e8	+	2.36920e9i	−0.167841	+	0.516563i
$577$	2.77033e9	+	2.01276e9i	0.600366	+	0.436192i	0.846009	−	0.533169i	$-0.178999\pi$
$577$	2.77033e9	+	2.01276e9i	0.600366	+	0.436192i	−0.245643	+	0.969360i	$0.578999\pi$
$578$	1.68507e9	+	1.22428e9i	0.362971	+	0.263714i
$579$	−2.52404e8	+	7.76819e8i	−0.0540407	+	0.166320i
$580$	1.34073e9	+	4.12633e9i	0.285326	+	0.878144i
$581$	2.19531e9	−	1.59498e9i	0.464386	−	0.337396i
$582$	−8.54955e9			−1.79768
$583$	4.67433e8	+	1.40653e8i	0.0976965	+	0.0293974i
$584$	2.27536e9			0.472722
$585$	−2.54876e9	+	1.85178e9i	−0.526360	+	0.382423i
$586$	2.12348e9	+	6.53540e9i	0.435920	+	1.34162i
$587$	−1.07808e9	+	3.31798e9i	−0.219997	+	0.677080i	0.778764	+	0.627316i	$0.215847\pi$
$587$	−1.07808e9	+	3.31798e9i	−0.219997	+	0.677080i	−0.998761	+	0.0497634i	$0.984153\pi$
$588$	2.04916e9	+	1.48880e9i	0.415676	+	0.302006i
$589$	3.92631e9	+	2.85263e9i	0.791738	+	0.575231i
$590$	2.65003e9	−	8.15597e9i	0.531214	−	1.63491i
$591$	1.43940e9	+	4.43003e9i	0.286831	+	0.882775i
$592$	5.57275e8	−	4.04884e8i	0.110394	−	0.0802056i
$593$	6.83154e9			1.34533			0.672663	−	0.739949i	$-0.265150\pi$
$593$	6.83154e9			1.34533			0.672663	+	0.739949i	$0.265150\pi$
$594$	9.54667e8	+	1.25531e9i	0.186896	+	0.245752i
$595$	7.20802e9			1.40284
$596$	5.08202e9	−	3.69231e9i	0.983274	−	0.714391i
$597$	2.18590e8	+	6.72751e8i	0.0420456	+	0.129403i
$598$	−6.66798e8	+	2.05219e9i	−0.127509	+	0.392432i
$599$	−6.35728e9	−	4.61883e9i	−1.20859	−	0.878088i	−0.213484	−	0.976947i	$-0.568481\pi$
$599$	−6.35728e9	−	4.61883e9i	−1.20859	−	0.878088i	−0.995102	+	0.0988582i	$0.968481\pi$
$600$	5.77621e9	+	4.19666e9i	1.09173	+	0.793186i
$601$	1.99901e9	−	6.15233e9i	0.375626	−	1.15606i	−0.567430	−	0.823422i	$-0.692062\pi$
$601$	1.99901e9	−	6.15233e9i	0.375626	−	1.15606i	0.943056	−	0.332635i	$-0.107938\pi$
$602$	−2.69488e9	−	8.29397e9i	−0.503444	−	1.54944i
$603$	−6.79240e8	+	4.93496e8i	−0.126157	+	0.0916587i
$604$	5.51350e9			1.01812
$605$	−8.01876e9	+	6.37985e9i	−1.47219	+	1.17130i
$606$	1.51568e9			0.276664
$607$	2.19908e9	−	1.59773e9i	0.399099	−	0.289963i	−0.370075	−	0.929002i	$-0.620668\pi$
$607$	2.19908e9	−	1.59773e9i	0.399099	−	0.289963i	0.769174	+	0.639039i	$0.220668\pi$
$608$	−2.39638e9	−	7.37531e9i	−0.432408	−	1.33081i
$609$	2.04433e8	−	6.29180e8i	0.0366767	−	0.112879i
$610$	−1.05960e10	−	7.69842e9i	−1.89011	−	1.37324i
$611$	4.47045e9	+	3.24797e9i	0.792878	+	0.576060i
$612$	1.03986e9	−	3.20036e9i	0.183377	−	0.564376i
$613$	−3.37774e9	−	1.03956e10i	−0.592263	−	1.82280i	−0.567904	−	0.823095i	$-0.692245\pi$
$613$	−3.37774e9	−	1.03956e10i	−0.592263	−	1.82280i	−0.0243594	−	0.999703i	$-0.507755\pi$
$614$	−6.85332e9	+	4.97923e9i	−1.19485	+	0.868106i
$615$	−1.09954e9			−0.190611
$616$	−2.13079e9	−	2.80180e9i	−0.367288	−	0.482954i
$617$	9.69186e9			1.66115			0.830576	−	0.556906i	$-0.188012\pi$
$617$	9.69186e9			1.66115			0.830576	+	0.556906i	$0.188012\pi$
$618$	−4.16927e9	+	3.02915e9i	−0.710560	+	0.516252i
$619$	−1.81612e9	−	5.58945e9i	−0.307771	−	0.947222i	−0.978629	−	0.205636i	$-0.934074\pi$
$619$	−1.81612e9	−	5.58945e9i	−0.307771	−	0.947222i	0.670857	−	0.741586i	$-0.265926\pi$
$620$	−4.08640e9	+	1.25767e10i	−0.688605	+	2.11931i
$621$	2.30346e8	+	1.67356e8i	0.0385977	+	0.0280428i
$622$	2.61839e9	+	1.90237e9i	0.436282	+	0.316978i
$623$	−1.77919e9	+	5.47578e9i	−0.294791	+	0.907272i
$624$	1.09040e8	+	3.35590e8i	0.0179655	+	0.0552922i
$625$	−1.43624e10	+	1.04349e10i	−2.35314	+	1.70965i
$626$	6.36319e9			1.03673
$627$	−4.43694e9	−	1.33510e9i	−0.718864	−	0.216310i
$628$	−1.61444e10			−2.60114
$629$	−8.03044e9	+	5.83446e9i	−1.28666	+	0.934810i
$630$	−1.28616e9	−	3.95840e9i	−0.204929	−	0.630707i
$631$	1.29138e9	−	3.97447e9i	0.204622	−	0.629762i	−0.795107	−	0.606470i	$-0.792585\pi$
$631$	1.29138e9	−	3.97447e9i	0.204622	−	0.629762i	0.999729	−	0.0232922i	$-0.00741481\pi$
$632$	−4.99312e9	−	3.62771e9i	−0.786795	−	0.571640i
$633$	−1.87436e8	−	1.36180e8i	−0.0293725	−	0.0213403i
$634$	5.10415e9	−	1.57090e10i	0.795447	−	2.44813i
$635$	4.89899e8	+	1.50775e9i	0.0759274	+	0.233680i
$636$	−4.86557e8	+	3.53504e8i	−0.0749953	+	0.0544872i
$637$	3.82735e9			0.586693
$638$	1.87051e9	−	2.69665e9i	0.285159	−	0.411104i
$639$	1.82130e9			0.276139
$640$	1.55231e10	−	1.12782e10i	2.34072	−	1.70063i
$641$	1.59033e8	+	4.89454e8i	0.0238498	+	0.0734022i	0.962273	−	0.272086i	$-0.0877134\pi$
$641$	1.59033e8	+	4.89454e8i	0.0238498	+	0.0734022i	−0.938423	+	0.345488i	$0.887713\pi$
$642$	−2.79685e9	+	8.60781e9i	−0.417154	+	1.28387i
$643$	9.34337e8	+	6.78835e8i	0.138601	+	0.100699i	0.654925	−	0.755694i	$-0.272700\pi$
$643$	9.34337e8	+	6.78835e8i	0.138601	+	0.100699i	−0.516325	+	0.856393i	$0.672700\pi$
$644$	−1.41020e9	−	1.02457e9i	−0.208056	−	0.151162i
$645$	3.52388e9	−	1.08454e10i	0.517085	−	1.59142i
$646$	4.99639e9	+	1.53773e10i	0.729192	+	2.24422i
$647$	4.08864e9	−	2.97057e9i	0.593491	−	0.431197i	−0.250071	−	0.968227i	$-0.580454\pi$
$647$	4.08864e9	−	2.97057e9i	0.593491	−	0.431197i	0.843563	+	0.537031i	$0.180454\pi$
$648$	−7.08398e8			−0.102274
$649$	−3.74462e9	+	1.30791e9i	−0.537714	+	0.187811i
$650$	2.95923e10			4.22651
$651$	1.63128e9	−	1.18519e9i	0.231736	−	0.168366i
$652$	3.95982e9	+	1.21871e10i	0.559512	+	1.72200i
$653$	3.16890e9	−	9.75288e9i	0.445362	−	1.37068i	−0.436725	−	0.899595i	$-0.643862\pi$
$653$	3.16890e9	−	9.75288e9i	0.445362	−	1.37068i	0.882087	−	0.471087i	$-0.156138\pi$
$654$	−4.66968e9	−	3.39272e9i	−0.652777	−	0.474270i
$655$	7.33911e9	+	5.33218e9i	1.02047	+	0.741413i
$656$	−3.80562e7	+	1.17125e8i	−0.00526335	+	0.0161989i
$657$	−3.84537e8	−	1.18348e9i	−0.0529005	−	0.162811i
$658$	−5.90600e9	+	4.29096e9i	−0.808170	+	0.587170i
$659$	−4.72645e9			−0.643334			−0.321667	−	0.946853i	$-0.604243\pi$
$659$	−4.72645e9			−0.643334			−0.321667	+	0.946853i	$0.604243\pi$
$660$	−2.76112e8	−	1.26221e10i	−0.0373837	−	1.70895i
$661$	−5.59190e9			−0.753103			−0.376552	−	0.926396i	$-0.622890\pi$
$661$	−5.59190e9			−0.753103			−0.376552	+	0.926396i	$0.622890\pi$
$662$	−8.26746e9	+	6.00666e9i	−1.10757	+	0.804693i
$663$	−1.57129e9	−	4.83593e9i	−0.209391	−	0.644440i
$664$	−1.86852e9	+	5.75070e9i	−0.247690	+	0.762312i
$665$	9.89286e9	+	7.18758e9i	1.30451	+	0.947779i
$666$	4.63700e9	+	3.36898e9i	0.608243	+	0.441914i
$667$	1.83094e8	−	5.63506e8i	0.0238910	−	0.0735289i
$668$	−1.51703e9	−	4.66893e9i	−0.196914	−	0.606038i
$669$	6.47250e9	−	4.70254e9i	0.835758	−	0.607214i
$670$	1.09920e10			1.41194
$671$	1.32485e8	+	6.05638e9i	0.0169293	+	0.773899i
$672$	−3.22193e9			−0.409566
$673$	−1.94595e9	+	1.41382e9i	−0.246082	+	0.178789i	−0.703989	−	0.710211i	$-0.748599\pi$
$673$	−1.94595e9	+	1.41382e9i	−0.246082	+	0.178789i	0.457907	+	0.889000i	$0.348599\pi$
$674$	−1.16169e9	−	3.57532e9i	−0.146144	−	0.449785i
$675$	1.20663e9	−	3.71362e9i	0.151012	−	0.464766i
$676$	−7.81393e8	−	5.67715e8i	−0.0972872	−	0.0706833i
$677$	−4.82827e9	−	3.50794e9i	−0.598041	−	0.434502i	0.247142	−	0.968979i	$-0.420509\pi$
$677$	−4.82827e9	−	3.50794e9i	−0.598041	−	0.434502i	−0.845183	+	0.534477i	$0.820509\pi$
$678$	−1.11573e9	+	3.43386e9i	−0.137485	+	0.423134i
$679$	−3.22492e9	−	9.92529e9i	−0.395344	−	1.21674i
$680$	−1.29942e10	+	9.44086e9i	−1.58478	+	1.15141i
$681$	−3.89244e9			−0.472289
$682$	9.44339e9	−	3.29836e9i	1.13994	−	0.398156i
$683$	1.11218e10			1.33567			0.667837	−	0.744307i	$-0.267220\pi$
$683$	1.11218e10			1.33567			0.667837	+	0.744307i	$0.267220\pi$
$684$	4.61847e9	−	3.35551e9i	0.551825	−	0.400925i
$685$	5.37494e9	+	1.65424e10i	0.638935	+	1.96644i
$686$	−4.32565e9	+	1.33130e10i	−0.511584	+	1.57449i
$687$	3.32394e8	+	2.41498e8i	0.0391115	+	0.0284162i
$688$	−1.03331e9	−	7.50741e8i	−0.120968	−	0.0878882i
$689$	−2.80827e8	+	8.64298e8i	−0.0327094	+	0.100669i
$690$	−1.15191e9	−	3.54522e9i	−0.133490	−	0.410839i
$691$	1.53777e9	−	1.11726e9i	0.177304	−	0.128819i	−0.495593	−	0.868555i	$-0.665049\pi$
$691$	1.53777e9	−	1.11726e9i	0.177304	−	0.128819i	0.672898	+	0.739736i	$0.265049\pi$
$692$	−5.00854e9			−0.574566
$693$	−1.09720e9	+	1.58179e9i	−0.125233	+	0.180544i
$694$	2.18409e10			2.48034
$695$	1.33681e10	−	9.71248e9i	1.51051	−	1.09745i
$696$	4.55541e8	+	1.40201e9i	0.0512148	+	0.157623i
$697$	5.48397e8	−	1.68779e9i	0.0613452	−	0.188801i
$698$	3.08712e9	+	2.24292e9i	0.343605	+	0.249643i
$699$	7.02479e9	+	5.10381e9i	0.777970	+	0.565229i
$700$	−7.38709e9	+	2.27351e10i	−0.814011	+	2.50527i
$701$	−2.94798e9	−	9.07294e9i	−0.323229	−	0.994798i	−0.972233	−	0.234013i	$-0.924814\pi$
$701$	−2.94798e9	−	9.07294e9i	−0.323229	−	0.994798i	0.649004	−	0.760785i	$-0.275186\pi$
$702$	−2.37535e9	+	1.72580e9i	−0.259148	+	0.188282i
$703$	−1.68395e10			−1.82804
$704$	−1.44451e10	−	4.34661e9i	−1.56033	−	0.469512i
$705$	−9.54593e9			−1.02602
$706$	4.14124e9	−	3.00879e9i	0.442909	−	0.321792i
$707$	5.71719e8	+	1.75957e9i	0.0608435	+	0.187257i
$708$	1.51015e9	−	4.64777e9i	0.159921	−	0.492185i
$709$	−4.00739e9	−	2.91154e9i	−0.422279	−	0.306804i	0.356275	−	0.934381i	$-0.384047\pi$
$709$	−4.00739e9	−	2.91154e9i	−0.422279	−	0.306804i	−0.778554	+	0.627577i	$0.784047\pi$
$710$	−1.92908e10	−	1.40156e10i	−2.02277	−	1.46963i
$711$	−1.04304e9	+	3.21015e9i	−0.108832	+	0.334952i
$712$	−3.96459e9	−	1.22018e10i	−0.411641	−	1.26690i
$713$	1.46100e9	−	1.06148e9i	0.150951	−	0.109673i
$714$	6.71763e9			0.690673
$715$	−1.15482e10	−	1.51850e10i	−1.18153	−	1.55361i
$716$	−4.28358e9			−0.436125
$717$	4.94478e9	−	3.59259e9i	0.500991	−	0.363991i
$718$	1.47595e9	+	4.54250e9i	0.148811	+	0.457993i
$719$	−1.64960e9	+	5.07695e9i	−0.165511	+	0.509392i	−0.999074	−	0.0430339i	$-0.986298\pi$
$719$	−1.64960e9	+	5.07695e9i	−0.165511	+	0.509392i	0.833562	+	0.552426i	$0.186298\pi$
$720$	−4.93158e8	−	3.58300e8i	−0.0492405	−	0.0357753i
$721$	−5.08925e9	−	3.69756e9i	−0.505685	−	0.367402i
$722$	−3.46270e9	+	1.06571e10i	−0.342401	+	1.05380i
$723$	1.60313e9	+	4.93393e9i	0.157756	+	0.485522i
$724$	1.35634e10	−	9.85439e9i	1.32826	−	0.965039i
$725$	−8.12567e9			−0.791910
$726$	−7.47321e9	+	5.94581e9i	−0.724818	+	0.576677i
$727$	9.41309e9			0.908577			0.454289	−	0.890855i	$-0.349894\pi$
$727$	9.41309e9			0.908577			0.454289	+	0.890855i	$0.349894\pi$
$728$	5.30171e9	−	3.85192e9i	0.509280	−	0.370013i
$729$	1.19720e8	+	3.68459e8i	0.0114451	+	0.0352243i
$730$	−5.03444e9	+	1.54944e10i	−0.478984	+	1.47416i
$731$	1.48901e10	+	1.08183e10i	1.40990	+	1.02435i
$732$	−6.03824e9	−	4.38704e9i	−0.569012	−	0.413411i
$733$	−7.12748e8	+	2.19361e9i	−0.0668454	+	0.205729i	−0.978900	−	0.204340i	$-0.934495\pi$
$733$	−7.12748e8	+	2.19361e9i	−0.0668454	+	0.205729i	0.912055	+	0.410069i	$0.134495\pi$
$734$	3.28864e9	+	1.01214e10i	0.306959	+	0.944722i
$735$	−5.34911e9	+	3.88635e9i	−0.496907	+	0.361024i
$736$	−2.88562e9			−0.266789
$737$	−3.07759e9	−	4.04677e9i	−0.283187	−	0.372368i
$738$	−1.02473e9			−0.0938454
$739$	2.38681e8	−	1.73412e8i	0.0217551	−	0.0158060i	−0.576855	−	0.816847i	$-0.695720\pi$
$739$	2.38681e8	−	1.73412e8i	0.0217551	−	0.0158060i	0.598610	+	0.801041i	$0.295720\pi$
$740$	−1.41789e10	−	4.36383e10i	−1.28627	−	3.95874i
$741$	2.66565e9	−	8.20404e9i	0.240680	−	0.740737i
$742$	−9.71309e8	−	7.05697e8i	−0.0872858	−	0.0634169i
$743$	1.00157e10	+	7.27680e9i	0.895815	+	0.650848i	0.937388	−	0.348288i	$-0.113237\pi$
$743$	1.00157e10	+	7.27680e9i	0.895815	+	0.650848i	−0.0415726	+	0.999135i	$0.513237\pi$
$744$	−1.38845e9	+	4.27320e9i	−0.123601	+	0.380406i
$745$	5.06719e9	+	1.55952e10i	0.448973	+	1.38180i
$746$	−1.35993e10	+	9.88043e9i	−1.19930	+	0.871345i
$747$	3.30689e9			0.290267
$748$	1.95127e10	+	5.87148e9i	1.70475	+	0.512970i
$749$	−1.10479e10			−0.960712
$750$	−2.50708e10	+	1.82150e10i	−2.16997	+	1.57657i
$751$	7.29352e8	+	2.24471e9i	0.0628343	+	0.193384i	0.977546	−	0.210724i	$-0.0675820\pi$
$751$	7.29352e8	+	2.24471e9i	0.0628343	+	0.193384i	−0.914711	+	0.404108i	$0.867582\pi$
$752$	−3.30395e8	+	1.01685e9i	−0.0283316	+	0.0871956i
$753$	−6.58523e9	−	4.78445e9i	−0.562068	−	0.408366i
$754$	4.94306e9	+	3.59135e9i	0.419949	+	0.305111i
$755$	−4.44749e9	+	1.36880e10i	−0.376098	+	1.15751i
$756$	−7.32934e8	−	2.25574e9i	−0.0616934	−	0.189873i
$757$	−8.54417e8	+	6.20770e8i	−0.0715870	+	0.0520110i	−0.623003	−	0.782219i	$-0.714088\pi$
$757$	−8.54417e8	+	6.20770e8i	−0.0715870	+	0.0520110i	0.551416	+	0.834230i	$0.314088\pi$
$758$	−1.26634e10			−1.05611
$759$	−9.82672e8	+	1.41668e9i	−0.0815760	+	0.117605i
$760$	−2.72484e10			−2.25161
$761$	4.62986e9	−	3.36379e9i	0.380822	−	0.276683i	−0.380862	−	0.924632i	$-0.624373\pi$
$761$	4.62986e9	−	3.36379e9i	0.380822	−	0.276683i	0.761684	+	0.647949i	$0.224373\pi$
$762$	4.56569e8	+	1.40517e9i	0.0373821	+	0.115050i
$763$	2.17723e9	−	6.70084e9i	0.177447	−	0.546126i
$764$	2.04918e9	+	1.48881e9i	0.166246	+	0.120785i
$765$	7.10650e9	+	5.16318e9i	0.573906	+	0.416967i
$766$	−8.49756e9	+	2.61528e10i	−0.683114	+	2.10241i
$767$	−2.28193e9	−	7.02306e9i	−0.182607	−	0.562008i
$768$	4.91270e9	−	3.56928e9i	0.391341	−	0.284326i
$769$	−1.16309e10			−0.922297			−0.461148	−	0.887323i	$-0.652562\pi$
$769$	−1.16309e10			−0.922297			−0.461148	+	0.887323i	$0.652562\pi$
$770$	2.37939e10	−	8.31066e9i	1.87822	−	0.656021i
$771$	−6.95975e9			−0.546894
$772$	4.93008e9	−	3.58191e9i	0.385650	−	0.280191i
$773$	−5.00855e9	−	1.54147e10i	−0.390018	−	1.20035i	−0.932774	−	0.360461i	$-0.882619\pi$
$773$	−5.00855e9	−	1.54147e10i	−0.390018	−	1.20035i	0.542757	−	0.839890i	$-0.317381\pi$
$774$	3.28413e9	−	1.01075e10i	0.254582	−	0.783523i
$775$	−2.00363e10	−	1.45572e10i	−1.54619	−	1.12337i
$776$	1.88136e10	+	1.36689e10i	1.44529	+	1.05007i
$777$	−2.16200e9	+	6.65394e9i	−0.165341	+	0.508868i
$778$	−5.19129e9	−	1.59772e10i	−0.395227	−	1.21638i
$779$	2.43567e9	−	1.76962e9i	0.184603	−	0.134122i
$780$	2.35046e10			1.77346
$781$	2.41200e8	+	1.10261e10i	0.0181175	+	0.828218i
$782$	6.01644e9			0.449900
$783$	6.52241e8	−	4.73881e8i	0.0485559	−	0.0352779i
$784$	2.28843e8	+	7.04308e8i	0.0169603	+	0.0521983i
$785$	1.30230e10	−	4.00807e10i	0.960877	−	2.95727i
$786$	6.83980e9	+	4.96941e9i	0.502417	+	0.365027i
$787$	1.41053e10	+	1.02481e10i	1.03151	+	0.749433i	0.968610	−	0.248587i	$-0.0799662\pi$
$787$	1.41053e10	+	1.02481e10i	1.03151	+	0.749433i	0.0628966	+	0.998020i	$0.479966\pi$
$788$	1.07390e10	−	3.30513e10i	0.781849	−	2.40628i
$789$	6.25991e8	+	1.92660e9i	0.0453731	+	0.139644i
$790$	3.57511e10	−	2.59747e10i	2.57985	−	1.87437i
$791$	−4.40726e9			−0.316629
$792$	−9.38153e7	−	4.28865e9i	−0.00671020	−	0.306748i
$793$	−1.12780e10			−0.803115
$794$	1.74999e10	−	1.27144e10i	1.24069	−	0.901414i
$795$	−4.85137e8	−	1.49310e9i	−0.0342436	−	0.105391i
$796$	1.63085e9	−	5.01923e9i	0.114609	−	0.352729i
$797$	1.69026e10	+	1.22804e10i	1.18263	+	0.859231i	0.992466	−	0.122521i	$-0.0390980\pi$
$797$	1.69026e10	+	1.22804e10i	1.18263	+	0.859231i	0.190164	+	0.981752i	$0.439098\pi$
$798$	9.21981e9	+	6.69858e9i	0.642261	+	0.466630i
$799$	4.76105e9	−	1.46530e10i	0.330209	−	1.01628i
$800$	1.22289e10	+	3.76368e10i	0.844450	+	2.59895i
$801$	−5.67648e9	+	4.12421e9i	−0.390270	+	0.283548i
$802$	−3.12557e9			−0.213953
$803$	7.11390e9	−	2.48472e9i	0.484845	−	0.169346i
$804$	6.26394e9			0.425061
$805$	3.68119e9	−	2.67454e9i	0.248715	−	0.180702i
$806$	5.75469e9	+	1.77111e10i	0.387123	+	1.19144i
$807$	6.11113e8	−	1.88081e9i	0.0409321	−	0.125976i
$808$	−3.33530e9	−	2.42323e9i	−0.222431	−	0.161605i
$809$	−7.34084e7	−	5.33343e7i	−0.00487445	−	0.00354150i	0.585345	−	0.810784i	$-0.300959\pi$
$809$	−7.34084e7	−	5.33343e7i	−0.00487445	−	0.00354150i	−0.590220	+	0.807243i	$0.700959\pi$
$810$	1.56739e9	−	4.82394e9i	0.103629	−	0.318937i
$811$	−4.42734e8	−	1.36260e9i	−0.0291454	−	0.0897003i	0.935426	−	0.353523i	$-0.115017\pi$
$811$	−4.42734e8	−	1.36260e9i	−0.0291454	−	0.0897003i	−0.964571	+	0.263823i	$0.915017\pi$
$812$	−3.99308e9	+	2.90115e9i	−0.261735	+	0.190162i
$813$	−3.86033e9			−0.251946
$814$	−1.97817e10	+	2.85186e10i	−1.28552	+	1.85329i
$815$	−3.34503e10			−2.16445
$816$	7.95955e8	−	5.78295e8i	0.0512829	−	0.0372592i
$817$	9.64877e9	+	2.96958e10i	0.619006	+	1.90510i
$818$	−6.51234e9	+	2.00429e10i	−0.416007	+	1.28034i
$819$	−2.89949e9	−	2.10660e9i	−0.184428	−	0.133995i
$820$	6.63667e9	+	4.82183e9i	0.420341	+	0.305396i
$821$	−4.87600e9	+	1.50068e10i	−0.307512	+	0.946426i	0.671215	+	0.741262i	$0.265773\pi$
$821$	−4.87600e9	+	1.50068e10i	−0.307512	+	0.946426i	−0.978728	+	0.205163i	$0.934227\pi$
$822$	5.00926e9	+	1.54169e10i	0.314574	+	0.968158i
$823$	−4.66237e9	+	3.38741e9i	−0.291546	+	0.211821i	−0.723938	−	0.689865i	$-0.757670\pi$
$823$	−4.66237e9	+	3.38741e9i	−0.291546	+	0.211821i	0.432392	+	0.901686i	$0.357670\pi$
$824$	1.40176e10			0.872826
$825$	2.26421e10	+	6.81313e9i	1.40387	+	0.422433i
$826$	9.75579e9			0.602327
$827$	5.87663e9	−	4.26962e9i	0.361292	−	0.262494i	−0.392299	−	0.919838i	$-0.628320\pi$
$827$	5.87663e9	−	4.26962e9i	0.361292	−	0.262494i	0.753591	+	0.657344i	$0.228320\pi$
$828$	−6.56430e8	−	2.02028e9i	−0.0401867	−	0.123682i
$829$	1.53707e9	−	4.73061e9i	0.0937028	−	0.288388i	−0.893211	−	0.449638i	$-0.851553\pi$
$829$	1.53707e9	−	4.73061e9i	0.0937028	−	0.288388i	0.986913	+	0.161251i	$0.0515528\pi$
$830$	−3.50260e10	−	2.54479e10i	−2.12626	−	1.54482i
$831$	−1.11542e10	−	8.10402e9i	−0.674273	−	0.489888i
$832$	8.67843e9	−	2.67095e10i	0.522408	−	1.60781i
$833$	−3.29768e9	−	1.01492e10i	−0.197675	−	0.608380i
$834$	1.24586e10	−	9.05170e9i	0.743683	−	0.540317i
$835$	1.28150e10			0.761753
$836$	2.09259e10	+	2.75159e10i	1.23869	+	1.62878i
$837$	2.45726e9			0.144848
$838$	−1.75329e10	+	1.27384e10i	−1.02920	+	0.747757i
$839$	6.57377e9	+	2.02320e10i	0.384280	+	1.18269i	0.937001	+	0.349326i	$0.113590\pi$
$839$	6.57377e9	+	2.02320e10i	0.384280	+	1.18269i	−0.552721	+	0.833366i	$0.686410\pi$
$840$	−3.49837e9	+	1.07669e10i	−0.203652	+	0.626776i
$841$	1.25981e10	+	9.15309e9i	0.730332	+	0.530617i
$842$	−3.57007e10	−	2.59381e10i	−2.06103	−	1.49743i
$843$	−5.92561e8	+	1.82372e9i	−0.0340672	+	0.104848i
$844$	5.34147e8	+	1.64393e9i	0.0305817	+	0.0941208i
$845$	2.03974e9	−	1.48196e9i	0.116299	−	0.0844963i
$846$	−8.89648e9			−0.505152
$847$	−9.72148e9	−	6.43297e9i	−0.549719	−	0.363764i
$848$	−1.75839e8			−0.00990214
$849$	1.41861e10	−	1.03068e10i	0.795582	−	0.578025i
$850$	−2.54970e10	−	7.84716e10i	−1.42404	−	4.38275i
$851$	−1.93633e9	+	5.95940e9i	−0.107702	+	0.331474i
$852$	−1.09931e10	−	7.98696e9i	−0.608951	−	0.442428i
$853$	−8.52495e9	−	6.19374e9i	−0.470295	−	0.341689i	0.327261	−	0.944934i	$-0.393874\pi$
$853$	−8.52495e9	−	6.19374e9i	−0.470295	−	0.341689i	−0.797556	+	0.603245i	$0.793874\pi$
$854$	4.60425e9	−	1.41704e10i	0.252963	−	0.778539i
$855$	4.60499e9	+	1.41727e10i	0.251969	+	0.775481i
$856$	1.99166e10	−	1.44702e10i	1.08532	−	0.788528i
$857$	1.55951e10			0.846362			0.423181	−	0.906045i	$-0.360914\pi$
$857$	1.55951e10			0.846362			0.423181	+	0.906045i	$0.360914\pi$
$858$	−1.07626e10	−	1.41519e10i	−0.581714	−	0.764906i
$859$	−3.07221e10			−1.65377			−0.826884	−	0.562373i	$-0.809889\pi$
$859$	−3.07221e10			−1.65377			−0.826884	+	0.562373i	$0.809889\pi$
$860$	−6.88301e10	+	5.00080e10i	−3.69007	+	2.68099i
$861$	−3.86532e8	−	1.18962e9i	−0.0206383	−	0.0635183i
$862$	2.57149e9	−	7.91422e9i	0.136744	−	0.420855i
$863$	6.68643e9	+	4.85797e9i	0.354125	+	0.257287i	0.750597	−	0.660760i	$-0.229766\pi$
$863$	6.68643e9	+	4.85797e9i	0.354125	+	0.257287i	−0.396473	+	0.918047i	$0.629766\pi$
$864$	−3.17655e9	−	2.30790e9i	−0.167555	−	0.121736i
$865$	4.04017e9	−	1.24344e10i	0.212248	−	0.653231i
$866$	1.18798e10	+	3.65622e10i	0.621578	+	1.91302i
$867$	−2.50665e9	+	1.82119e9i	−0.130625	+	0.0949049i
$868$	−1.50436e10			−0.780788
$869$	−1.95724e10	−	5.88945e9i	−1.01175	−	0.304443i
$870$	−1.05551e10			−0.543433
$871$	7.65749e9	−	5.56349e9i	0.392666	−	0.285288i
$872$	4.85157e9	+	1.49316e10i	0.247785	+	0.762603i
$873$	3.93008e9	−	1.20955e10i	0.199918	−	0.615284i
$874$	8.25744e9	+	5.99938e9i	0.418365	+	0.303960i
$875$	−3.06028e10	−	2.22342e10i	−1.54430	−	1.12200i
$876$	−2.86894e9	+	8.82968e9i	−0.144197	+	0.443793i
$877$	−8.90777e8	−	2.74153e9i	−0.0445934	−	0.137244i	0.926281	−	0.376834i	$-0.122987\pi$
$877$	−8.90777e8	−	2.74153e9i	−0.0445934	−	0.137244i	−0.970874	+	0.239589i	$0.922987\pi$
$878$	3.12469e10	−	2.27022e10i	1.55803	−	1.13198i
$879$	−1.02221e10			−0.507669
$880$	2.10384e9	−	3.03303e9i	0.104070	−	0.150033i
$881$	6.73619e9			0.331893			0.165947	−	0.986135i	$-0.446932\pi$
$881$	6.73619e9			0.331893			0.165947	+	0.986135i	$0.446932\pi$
$882$	−4.98518e9	+	3.62195e9i	−0.244648	+	0.177747i
$883$	−3.27886e9	−	1.00913e10i	−0.160273	−	0.493270i	0.838384	−	0.545080i	$-0.183501\pi$
$883$	−3.27886e9	−	1.00913e10i	−0.160273	−	0.493270i	−0.998657	+	0.0518106i	$0.983501\pi$
$884$	−1.17230e10	+	3.60796e10i	−0.570762	+	1.75663i
$885$	1.03205e10	+	7.49831e9i	0.500496	+	0.363632i
$886$	−3.52334e10	−	2.55986e10i	−1.70191	−	1.23651i
$887$	−3.81907e9	+	1.17539e10i	−0.183749	+	0.565522i	−0.999925	−	0.0122824i	$-0.996090\pi$
$887$	−3.81907e9	+	1.17539e10i	−0.183749	+	0.565522i	0.816175	+	0.577804i	$0.196090\pi$
$888$	−4.81761e9	−	1.48271e10i	−0.230880	−	0.710576i
$889$	−1.45907e9	+	1.06007e9i	−0.0696496	+	0.0506034i
$890$	9.18617e10			4.36787
$891$	−2.21480e9	+	7.73579e8i	−0.104897	+	0.0366381i
$892$	−5.96893e10			−2.81592
$893$	2.11459e10	−	1.53634e10i	0.993680	−	0.721951i
$894$	4.72245e9	+	1.45342e10i	0.221048	+	0.680315i
$895$	3.45537e9	−	1.06345e10i	0.161107	−	0.495836i
$896$	1.76592e10	+	1.28302e10i	0.820151	+	0.595875i
$897$	−2.59684e9	−	1.88671e9i	−0.120136	−	0.0872836i
$898$	−6.39178e9	+	1.96719e10i	−0.294547	+	0.906522i
$899$	−1.58016e9	−	4.86324e9i	−0.0725343	−	0.223238i
$900$	−2.35684e10	+	1.71235e10i	−1.07766	+	0.782967i
$901$	2.53387e9			0.115411
$902$	−1.35708e8	−	6.20374e9i	−0.00615721	−	0.281469i
$903$	1.29727e10			0.586306
$904$	7.94518e9	−	5.77251e9i	0.357696	−	0.259881i
$905$	1.35238e10	+	4.16220e10i	0.606498	+	1.86661i
$906$	−4.14491e9	+	1.27567e10i	−0.185168	+	0.569889i
$907$	2.39482e10	+	1.73994e10i	1.06573	+	0.774299i	0.975140	−	0.221589i	$-0.0711245\pi$
$907$	2.39482e10	+	1.73994e10i	1.06573	+	0.774299i	0.0905907	+	0.995888i	$0.471124\pi$
$908$	2.34943e10	+	1.70696e10i	1.04151	+	0.756699i
$909$	−6.96730e8	+	2.14431e9i	−0.0307674	+	0.0946923i
$910$	1.44997e10	+	4.46255e10i	0.637844	+	1.96308i
$911$	−7.17320e9	+	5.21164e9i	−0.314339	+	0.228381i	−0.733756	−	0.679413i	$-0.762235\pi$
$911$	−7.17320e9	+	5.21164e9i	−0.314339	+	0.228381i	0.419417	+	0.907794i	$0.362235\pi$
$912$	1.66909e9			0.0728613
$913$	4.37942e8	+	2.00199e10i	0.0190445	+	0.870593i
$914$	−6.24281e10			−2.70438
$915$	1.57622e10	−	1.14519e10i	0.680209	−	0.494201i
$916$	−9.47240e8	−	2.91531e9i	−0.0407217	−	0.125329i
$917$	−3.18905e9	+	9.81489e9i	−0.136574	+	0.420332i
$918$	6.62302e9	+	4.81190e9i	0.282557	+	0.205290i
$919$	−1.26532e10	−	9.19311e9i	−0.537771	−	0.390713i	0.285486	−	0.958383i	$-0.407845\pi$
$919$	−1.26532e10	−	9.19311e9i	−0.537771	−	0.390713i	−0.823256	+	0.567670i	$0.807845\pi$
$920$	−3.13321e9	+	9.64302e9i	−0.132658	+	0.408278i
$921$	−3.89405e9	−	1.19846e10i	−0.164245	−	0.505494i
$922$	−1.58698e10	+	1.15301e10i	−0.666827	+	0.484478i
$923$	−2.05326e10			−0.859485
$924$	1.35592e10	−	4.73593e9i	0.565435	−	0.197494i
$925$	8.59336e10			3.56999
$926$	3.84699e10	−	2.79500e10i	1.59214	−	1.15676i
$927$	−2.36898e9	−	7.29096e9i	−0.0976746	−	0.300611i
$928$	−2.52493e9	+	7.77093e9i	−0.103712	+	0.319194i
$929$	−3.23381e10	−	2.34950e10i	−1.32330	−	0.961436i	−0.999885	−	0.0151798i	$-0.995168\pi$
$929$	−3.23381e10	−	2.34950e10i	−1.32330	−	0.961436i	−0.323418	−	0.946256i	$-0.604832\pi$
$930$	−2.60269e10	−	1.89096e10i	−1.06104	−	0.770891i
$931$	5.59444e9	−	1.72179e10i	0.227213	−	0.699289i
$932$	−2.00189e10	−	6.16119e10i	−0.809999	−	2.49292i
$933$	−3.89502e9	+	2.82990e9i	−0.157009	+	0.114073i
$934$	−3.57823e10			−1.43699
$935$	−3.03168e10	+	4.37066e10i	−1.21295	+	1.74866i
$936$	7.98621e9			0.318328
$937$	−8.43982e9	+	6.13189e9i	−0.335154	+	0.243504i	−0.742614	−	0.669719i	$-0.766414\pi$
$937$	−8.43982e9	+	6.13189e9i	−0.335154	+	0.243504i	0.407460	+	0.913223i	$0.366414\pi$
$938$	3.86415e9	+	1.18926e10i	0.152878	+	0.470509i
$939$	−2.92505e9	+	9.00237e9i	−0.115293	+	0.354836i
$940$	5.76180e10	+	4.18619e10i	2.26261	+	1.64389i
$941$	−1.91443e10	−	1.39092e10i	−0.748991	−	0.544174i	0.146523	−	0.989207i	$-0.453192\pi$
$941$	−1.91443e10	−	1.39092e10i	−0.748991	−	0.544174i	−0.895514	+	0.445034i	$0.853192\pi$
$942$	1.21370e10	−	3.73538e10i	0.473078	−	1.45599i
$943$	−3.46186e8	−	1.06545e9i	−0.0134437	−	0.0413754i
$944$	1.15594e9	−	8.39839e8i	0.0447232	−	0.0324933i
$945$	6.19140e9			0.238659
$946$	6.16260e10	+	1.85436e10i	2.36671	+	0.712156i
$947$	2.77942e10			1.06348			0.531741	−	0.846907i	$-0.321538\pi$
$947$	2.77942e10			1.06348			0.531741	+	0.846907i	$0.321538\pi$
$948$	2.03732e10	−	1.48020e10i	0.776659	−	0.564275i
$949$	4.33513e9	+	1.33422e10i	0.164653	+	0.506750i
$950$	4.32551e10	−	1.33125e11i	1.63683	−	5.03765i
$951$	1.98781e10	+	1.44423e10i	0.749450	+	0.544507i
$952$	−1.47824e10	−	1.07400e10i	−0.555283	−	0.403437i
$953$	4.88787e9	−	1.50433e10i	0.182934	−	0.563013i	−0.816973	−	0.576676i	$-0.804349\pi$
$953$	4.88787e9	−	1.50433e10i	0.182934	−	0.563013i	0.999907	+	0.0136636i	$0.00434941\pi$
$954$	−4.52131e8	−	1.39152e9i	−0.0168595	−	0.0518882i
$955$	−5.34915e9	+	3.88639e9i	−0.198734	+	0.144389i
$956$	−4.56007e10			−1.68799
$957$	2.95526e9	+	3.88592e9i	0.108994	+	0.143318i
$958$	5.41863e10			1.99118
$959$	−1.60082e10	+	1.16306e10i	−0.586107	+	0.425832i
$960$	1.49922e10	+	4.61413e10i	0.546911	+	1.68322i
$961$	−3.68568e9	+	1.13434e10i	−0.133963	+	0.412296i
$962$	−5.22758e10	−	3.79806e10i	−1.89316	−	1.37546i
$963$	−1.08923e10	−	7.91372e9i	−0.393032	−	0.285554i
$964$	1.19605e10	−	3.68108e10i	0.430013	−	1.32344i
$965$	4.91569e9	+	1.51289e10i	0.176092	+	0.541955i
$966$	3.43074e9	−	2.49258e9i	0.122453	−	0.0889670i
$967$	−4.19670e10			−1.49250			−0.746251	−	0.665664i	$-0.768148\pi$
$967$	−4.19670e10			−1.49250			−0.746251	+	0.665664i	$0.768148\pi$
$968$	2.59511e10	−	1.13592e9i	0.919584	−	0.0402516i
$969$	−2.40519e10			−0.849211
$970$	−1.34707e11	+	9.78702e10i	−4.73902	+	3.44310i
$971$	−1.60837e10	−	4.95005e10i	−0.563791	−	1.73517i	−0.671517	−	0.740989i	$-0.734357\pi$
$971$	−1.60837e10	−	4.95005e10i	−0.563791	−	1.73517i	0.107726	−	0.994181i	$-0.465643\pi$
$972$	8.93197e8	−	2.74898e9i	0.0311972	−	0.0960151i
$973$	1.52077e10	+	1.10490e10i	0.529258	+	0.384528i
$974$	3.47826e10	+	2.52710e10i	1.20616	+	0.876328i
$975$	−1.36031e10	+	4.18659e10i	−0.470025	+	1.44659i
$976$	−6.74332e8	−	2.07538e9i	−0.0232166	−	0.0714534i
$977$	−7.17311e9	+	5.21157e9i	−0.246080	+	0.178788i	−0.703988	−	0.710212i	$-0.748599\pi$
$977$	−7.17311e9	+	5.21157e9i	−0.246080	+	0.178788i	0.457908	+	0.889000i	$0.348599\pi$
$978$	−3.11745e10			−1.06565
$979$	−2.57197e10	−	3.38193e10i	−0.876046	−	1.15193i
$980$	4.93294e10			1.67423
$981$	6.94645e9	−	5.04689e9i	0.234921	−	0.170680i
$982$	−2.10819e10	−	6.48835e10i	−0.710428	−	2.18647i
$983$	−6.86190e9	+	2.11188e10i	−0.230413	+	0.709139i	0.767284	+	0.641308i	$0.221608\pi$
$983$	−6.86190e9	+	2.11188e10i	−0.230413	+	0.709139i	−0.997697	+	0.0678309i	$0.978392\pi$
$984$	2.25496e9	+	1.63832e9i	0.0754493	+	0.0548171i
$985$	7.33915e10	+	5.33221e10i	2.44692	+	1.77779i
$986$	5.26440e9	−	1.62021e10i	0.174896	−	0.538274i
$987$	−3.35578e9	−	1.03280e10i	−0.111092	−	0.341907i
$988$	−5.20669e10	+	3.78288e10i	−1.71756	+	1.24788i
$989$	1.16186e10			0.381916
$990$	2.94117e10	+	8.85016e9i	0.963380	+	0.289886i
$991$	2.92118e10			0.953455			0.476727	−	0.879051i	$-0.341823\pi$
$991$	2.92118e10			0.953455			0.476727	+	0.879051i	$0.341823\pi$
$992$	−2.01477e10	+	1.46382e10i	−0.655291	+	0.476097i
$993$	−4.69756e9	−	1.44576e10i	−0.152247	−	0.468570i
$994$	8.38241e9	−	2.57984e10i	0.270718	−	0.833183i
$995$	1.11454e10	+	8.09758e9i	0.358685	+	0.260600i
$996$	−1.99600e10	−	1.45018e10i	−0.640107	−	0.465065i
$997$	1.40212e10	−	4.31528e10i	0.448076	−	1.37904i	−0.430998	−	0.902353i	$-0.641839\pi$
$997$	1.40212e10	−	4.31528e10i	0.448076	−	1.37904i	0.879075	−	0.476684i	$-0.158161\pi$
$998$	−1.81706e10	−	5.59235e10i	−0.578646	−	1.78089i
$999$	−6.89783e9	+	5.01156e9i	−0.218894	+	0.159036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.e.b.25.6	yes	28
3.2	odd	2		99.8.f.b.91.2		28
11.2	odd	10		363.8.a.r.1.12		14
11.4	even	5	inner	33.8.e.b.4.6	✓	28
11.9	even	5		363.8.a.o.1.3		14
33.26	odd	10		99.8.f.b.37.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.e.b.4.6	✓	28	11.4	even	5	inner
33.8.e.b.25.6	yes	28	1.1	even	1	trivial
99.8.f.b.37.2		28	33.26	odd	10
99.8.f.b.91.2		28	3.2	odd	2
363.8.a.o.1.3		14	11.9	even	5
363.8.a.r.1.12		14	11.2	odd	10

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(14.6841 - 10.6686i) q^{2} +(8.34346 + 25.6785i) q^{3} +(62.2484 - 191.581i) q^{4} +(425.412 + 309.080i) q^{5} +(396.469 + 288.052i) q^{6} +(-184.854 + 568.921i) q^{7} +(-411.912 - 1267.74i) q^{8} +(-589.773 + 428.495i) q^{9} +9544.22 q^{10} +(-2672.22 - 3513.75i) q^{11} +5438.89 q^{12} +(6648.88 - 4830.70i) q^{13} +(3355.18 + 10326.2i) q^{14} +(-4387.31 + 13502.7i) q^{15} +(1286.49 + 934.689i) q^{16} +(-18538.6 - 13469.1i) q^{17} +(-4088.82 + 12584.1i) q^{18} +(-12012.9 - 36972.0i) q^{19} +(85695.1 - 62261.1i) q^{20} -16151.4 q^{21} +(-76725.7 - 23087.2i) q^{22} -14465.5 q^{23} +(29116.8 - 21154.6i) q^{24} +(61303.0 + 188671. i) q^{25} +(46095.8 - 141868. i) q^{26} +(-15923.9 - 11569.4i) q^{27} +(97487.5 + 70828.8i) q^{28} +(-12657.3 + 38955.2i) q^{29} +(79631.8 + 245081. i) q^{30} +(-100999. + 73380.2i) q^{31} +199484. q^{32} +(67932.3 - 97935.5i) q^{33} -415917. q^{34} +(-254481. + 184891. i) q^{35} +(45379.1 + 139663. i) q^{36} +(133858. - 411974. i) q^{37} +(-570838. - 414738. i) q^{38} +(179520. + 130429. i) q^{39} +(216599. - 666624. i) q^{40} +(23931.9 + 73654.8i) q^{41} +(-237167. + 172312. i) q^{42} -803198. q^{43} +(-839509. + 293221. i) q^{44} -383336. q^{45} +(-212412. + 154326. i) q^{46} +(207771. + 639453. i) q^{47} +(-13267.7 + 40833.7i) q^{48} +(376760. + 273732. i) q^{49} +(2.91303e6 + 2.11644e6i) q^{50} +(191190. - 588422. i) q^{51} +(-511587. - 1.57450e6i) q^{52} +(-89459.0 + 64995.7i) q^{53} -357256. q^{54} +(-50766.4 - 2.32072e6i) q^{55} +797384. q^{56} +(849157. - 616949. i) q^{57} +(229737. + 707056. i) q^{58} +(277659. - 854545. i) q^{59} +(2.31377e6 + 1.68105e6i) q^{60} +(-1.11020e6 - 806606. i) q^{61} +(-700215. + 2.15504e6i) q^{62} +(-134758. - 414743. i) q^{63} +(2.76456e6 - 2.00857e6i) q^{64} +4.32159e6 q^{65} +(-47312.5 - 2.16283e6i) q^{66} +1.15170e6 q^{67} +(-3.73441e6 + 2.71321e6i) q^{68} +(-120692. - 371452. i) q^{69} +(-1.76428e6 + 5.42990e6i) q^{70} +(-2.02121e6 - 1.46849e6i) q^{71} +(786154. + 571174. i) q^{72} +(-527486. + 1.62343e6i) q^{73} +(-2.42960e6 - 7.47753e6i) q^{74} +(-4.33332e6 + 3.14834e6i) q^{75} -7.83092e6 q^{76} +(2.49301e6 - 870753. i) q^{77} +4.02757e6 q^{78} +(3.74584e6 - 2.72151e6i) q^{79} +(258394. + 795256. i) q^{80} +(164224. - 505430. i) q^{81} +(1.13721e6 + 826231. i) q^{82} +(-3.66986e6 - 2.66631e6i) q^{83} +(-1.00540e6 + 3.09429e6i) q^{84} +(-3.72351e6 - 1.14598e7i) q^{85} +(-1.17942e7 + 8.56899e6i) q^{86} -1.10592e6 q^{87} +(-3.35378e6 + 4.83502e6i) q^{88} +9.62485e6 q^{89} +(-5.62893e6 + 4.08965e6i) q^{90} +(1.51921e6 + 4.67566e6i) q^{91} +(-900453. + 2.77131e6i) q^{92} +(-2.72698e6 - 1.98127e6i) q^{93} +(9.87298e6 + 7.17314e6i) q^{94} +(6.31686e6 - 1.94413e7i) q^{95} +(1.66438e6 + 5.12244e6i) q^{96} +(-1.41140e7 + 1.02544e7i) q^{97} +8.45271e6 q^{98} +(3.08163e6 + 927280. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 189 q^{3} + 160 q^{4} + 773 q^{5} - 162 q^{6} + 1289 q^{7} + 2956 q^{8} - 5103 q^{9} - 10640 q^{10} + 13209 q^{11} + 45630 q^{12} + 13499 q^{13} - 3318 q^{14} - 22734 q^{15} - 113196 q^{16}+ \cdots - 6579954 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 189 * q^3 + 160 * q^4 + 773 * q^5 - 162 * q^6 + 1289 * q^7 + 2956 * q^8 - 5103 * q^9 - 10640 * q^10 + 13209 * q^11 + 45630 * q^12 + 13499 * q^13 - 3318 * q^14 - 22734 * q^15 - 113196 * q^16 + 30296 * q^17 + 21141 * q^18 - 6858 * q^19 + 76725 * q^20 - 177012 * q^21 - 48859 * q^22 - 166984 * q^23 + 44442 * q^24 + 99832 * q^25 + 340424 * q^26 - 137781 * q^27 + 657387 * q^28 + 192014 * q^29 - 184410 * q^30 + 396068 * q^31 - 303498 * q^32 + 168453 * q^33 - 1229124 * q^34 - 725859 * q^35 + 116640 * q^36 + 811053 * q^37 + 1548798 * q^38 + 364473 * q^39 - 1427263 * q^40 + 1041497 * q^41 + 300024 * q^42 - 5265288 * q^43 - 5341085 * q^44 + 100602 * q^45 + 1198651 * q^46 + 1667505 * q^47 + 730593 * q^48 + 2968140 * q^49 + 11247432 * q^50 + 340767 * q^51 + 2325763 * q^52 - 1625736 * q^53 - 905418 * q^54 - 8338690 * q^55 - 18201906 * q^56 + 1546479 * q^57 + 14965553 * q^58 - 2587454 * q^59 + 2071575 * q^60 + 5801619 * q^61 + 15631121 * q^62 + 939681 * q^63 - 3732846 * q^64 - 15368174 * q^65 - 235683 * q^66 - 7141262 * q^67 + 17394545 * q^68 - 5063553 * q^69 - 4329200 * q^70 + 3569199 * q^71 + 1199934 * q^72 + 125008 * q^73 - 13691530 * q^74 - 11794221 * q^75 - 19690428 * q^76 - 6038739 * q^77 + 12684438 * q^78 + 17075485 * q^79 + 26606436 * q^80 - 3720087 * q^81 + 19886007 * q^82 - 4645575 * q^83 + 1074519 * q^84 + 12002715 * q^85 - 12296287 * q^86 - 12259512 * q^87 - 50905990 * q^88 + 9601664 * q^89 + 8857350 * q^90 - 14129477 * q^91 - 90776021 * q^92 + 10693836 * q^93 + 1047679 * q^94 + 58935661 * q^95 + 26156304 * q^96 - 22170261 * q^97 + 140532178 * q^98 - 6579954 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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