LMFDB - Embedded newform 62.8.d.a.35.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			35.7
Character	$\chi$	$=$	62.35
Dual form			62.8.d.a.39.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.47214 + 7.60845i) q^{2} +(9.33796 - 28.7393i) q^{3} +(-51.7771 + 37.6183i) q^{4} -490.921 q^{5} +241.746 q^{6} +(1157.34 - 840.856i) q^{7} +(-414.217 - 300.946i) q^{8} +(1030.57 + 748.754i) q^{9} +(-1213.62 - 3735.15i) q^{10} +(-794.813 + 577.466i) q^{11} +(597.629 + 1839.31i) q^{12} +(-3005.37 + 9249.58i) q^{13} +(9258.71 + 6726.85i) q^{14} +(-4584.20 + 14108.7i) q^{15} +(1265.73 - 3895.53i) q^{16} +(9531.29 + 6924.89i) q^{17} +(-3149.15 + 9692.07i) q^{18} +(12257.1 + 37723.5i) q^{19} +(25418.5 - 18467.6i) q^{20} +(-13358.4 - 41113.0i) q^{21} +(-6358.50 - 4619.72i) q^{22} +(-23092.3 - 16777.5i) q^{23} +(-12516.9 + 9094.07i) q^{24} +162879. q^{25} -77804.7 q^{26} +(84607.9 - 61471.2i) q^{27} +(-28292.1 + 87074.2i) q^{28} +(75954.9 + 233765. i) q^{29} -118678. q^{30} +(-137197. + 93218.1i) q^{31} +32768.0 q^{32} +(9174.01 + 28234.7i) q^{33} +(-29125.0 + 89637.6i) q^{34} +(-568163. + 412794. i) q^{35} -81526.8 q^{36} +411994. q^{37} +(-256716. + 186515. i) q^{38} +(237762. + 172744. i) q^{39} +(203348. + 147741. i) q^{40} +(-135299. - 416407. i) q^{41} +(279782. - 203274. i) q^{42} +(-92375.9 - 284304. i) q^{43} +(19429.9 - 59799.0i) q^{44} +(-505929. - 367579. i) q^{45} +(70563.8 - 217173. i) q^{46} +(-378245. + 1.16412e6i) q^{47} +(-100135. - 72752.6i) q^{48} +(377906. - 1.16308e6i) q^{49} +(402659. + 1.23926e6i) q^{50} +(288019. - 209258. i) q^{51} +(-192344. - 591973. i) q^{52} +(666892. + 484526. i) q^{53} +(676863. + 491770. i) q^{54} +(390191. - 283490. i) q^{55} -732442. q^{56} +1.19860e6 q^{57} +(-1.59082e6 + 1.15580e6i) q^{58} +(10372.0 - 31921.8i) q^{59} +(-293389. - 902959. i) q^{60} +3.19752e6 q^{61} +(-1.04841e6 - 813409. i) q^{62} +1.82231e6 q^{63} +(81007.0 + 249314. i) q^{64} +(1.47540e6 - 4.54082e6i) q^{65} +(-192143. + 139600. i) q^{66} -817257. q^{67} -754004. q^{68} +(-697810. + 506989. i) q^{69} +(-4.54530e6 - 3.30235e6i) q^{70} +(-3.42635e6 - 2.48939e6i) q^{71} +(-201545. - 620293. i) q^{72} +(-1.43294e6 + 1.04109e6i) q^{73} +(1.01851e6 + 3.13464e6i) q^{74} +(1.52096e6 - 4.68102e6i) q^{75} +(-2.05373e6 - 1.49212e6i) q^{76} +(-434303. + 1.33665e6i) q^{77} +(-726537. + 2.23605e6i) q^{78} +(-732144. - 531934. i) q^{79} +(-621376. + 1.91240e6i) q^{80} +(-115677. - 356016. i) q^{81} +(2.83373e6 - 2.05883e6i) q^{82} +(159081. + 489602. i) q^{83} +(2.23826e6 + 1.62619e6i) q^{84} +(-4.67911e6 - 3.39957e6i) q^{85} +(1.93475e6 - 1.40567e6i) q^{86} +7.42751e6 q^{87} +503011. q^{88} +(-6.78547e6 + 4.92993e6i) q^{89} +(1.54598e6 - 4.75805e6i) q^{90} +(4.29933e6 + 1.32320e7i) q^{91} +1.82679e6 q^{92} +(1.39788e6 + 4.81341e6i) q^{93} -9.79222e6 q^{94} +(-6.01728e6 - 1.85193e7i) q^{95} +(305986. - 941729. i) q^{96} +(8.68028e6 - 6.30659e6i) q^{97} +9.78344e6 q^{98} -1.25149e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) $ 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	2.47214	+	7.60845i	0.218508	+	0.672499i
$2$	2.47214	+	7.60845i	0.218508	+	0.672499i
$3$	9.33796	−	28.7393i	0.199677	−	0.614542i	−0.800213	−	0.599716i	$-0.795280\pi$
$3$	9.33796	−	28.7393i	0.199677	−	0.614542i	0.999890	−	0.0148265i	$-0.00471959\pi$
$4$	−51.7771	+	37.6183i	−0.404508	+	0.293893i
$5$	−490.921			−1.75637			−0.878187	−	0.478318i	$-0.841247\pi$
$5$	−490.921			−1.75637			−0.878187	+	0.478318i	$0.841247\pi$
$6$	241.746			0.456910
$7$	1157.34	−	840.856i	1.27532	−	0.926571i	0.275914	−	0.961182i	$-0.411019\pi$
$7$	1157.34	−	840.856i	1.27532	−	0.926571i	0.999401	+	0.0346115i	$0.0110194\pi$
$8$	−414.217	−	300.946i	−0.286031	−	0.207813i
$9$	1030.57	+	748.754i	0.471226	+	0.342366i
$10$	−1213.62	−	3735.15i	−0.383782	−	1.18116i
$11$	−794.813	+	577.466i	−0.180049	+	0.130813i	−0.674159	−	0.738586i	$-0.735494\pi$
$11$	−794.813	+	577.466i	−0.180049	+	0.130813i	0.494110	+	0.869399i	$0.335494\pi$
$12$	597.629	+	1839.31i	0.0998384	+	0.307271i
$13$	−3005.37	+	9249.58i	−0.379399	+	1.16767i	0.561063	+	0.827773i	$0.310392\pi$
$13$	−3005.37	+	9249.58i	−0.379399	+	1.16767i	−0.940463	+	0.339897i	$0.889608\pi$
$14$	9258.71	+	6726.85i	0.901784	+	0.655184i
$15$	−4584.20	+	14108.7i	−0.350707	+	1.07937i
$16$	1265.73	−	3895.53i	0.0772542	−	0.237764i
$17$	9531.29	+	6924.89i	0.470522	+	0.341855i	0.797645	−	0.603127i	$-0.206079\pi$
$17$	9531.29	+	6924.89i	0.470522	+	0.341855i	−0.327122	+	0.944982i	$0.606079\pi$
$18$	−3149.15	+	9692.07i	−0.127274	+	0.391708i
$19$	12257.1	+	37723.5i	0.409969	+	1.26175i	0.916674	+	0.399635i	$0.130863\pi$
$19$	12257.1	+	37723.5i	0.409969	+	1.26175i	−0.506706	+	0.862119i	$0.669137\pi$
$20$	25418.5	−	18467.6i	0.710468	−	0.516185i
$21$	−13358.4	−	41113.0i	−0.314766	−	0.968749i
$22$	−6358.50	−	4619.72i	−0.127314	−	0.0924989i
$23$	−23092.3	−	16777.5i	−0.395749	−	0.287529i	0.372058	−	0.928209i	$-0.378652\pi$
$23$	−23092.3	−	16777.5i	−0.395749	−	0.287529i	−0.767807	+	0.640681i	$0.778652\pi$
$24$	−12516.9	+	9094.07i	−0.184824	+	0.134282i
$25$	162879.			2.08485
$26$	−77804.7			−0.868158
$27$	84607.9	−	61471.2i	0.827252	−	0.601034i
$28$	−28292.1	+	87074.2i	−0.243564	+	0.749611i
$29$	75954.9	+	233765.i	0.578313	+	1.77986i	0.624611	+	0.780936i	$0.285257\pi$
$29$	75954.9	+	233765.i	0.578313	+	1.77986i	−0.0462985	+	0.998928i	$0.514743\pi$
$30$	−118678.			−0.802504
$31$	−137197.	+	93218.1i	−0.827139	+	0.561997i
$31$	−137197.	+	93218.1i	−0.827139	+	0.561997i
$32$	32768.0			0.176777
$33$	9174.01	+	28234.7i	0.0444386	+	0.136768i
$34$	−29125.0	+	89637.6i	−0.127084	+	0.391124i
$35$	−568163.	+	412794.i	−2.23993	+	1.62740i
$36$	−81526.8			−0.291234
$37$	411994.			1.33717			0.668583	−	0.743638i	$-0.266901\pi$
$37$	411994.			1.33717			0.668583	+	0.743638i	$0.266901\pi$
$38$	−256716.	+	186515.i	−0.758946	+	0.551407i
$39$	237762.	+	172744.i	0.641825	+	0.466313i
$40$	203348.	+	147741.i	0.502377	+	0.364998i
$41$	−135299.	−	416407.i	−0.306585	−	0.943570i	−0.979081	−	0.203470i	$-0.934778\pi$
$41$	−135299.	−	416407.i	−0.306585	−	0.943570i	0.672497	−	0.740100i	$-0.265222\pi$
$42$	279782.	−	203274.i	0.582704	−	0.423359i
$43$	−92375.9	−	284304.i	−0.177182	−	0.545309i	0.822545	−	0.568701i	$-0.192554\pi$
$43$	−92375.9	−	284304.i	−0.177182	−	0.545309i	−0.999726	+	0.0233912i	$0.992554\pi$
$44$	19429.9	−	59799.0i	0.0343863	−	0.105830i
$45$	−505929.	−	367579.i	−0.827649	−	0.601322i
$46$	70563.8	−	217173.i	0.106888	−	0.328968i
$47$	−378245.	+	1.16412e6i	−0.531411	+	1.63552i	0.219866	+	0.975530i	$0.429438\pi$
$47$	−378245.	+	1.16412e6i	−0.531411	+	1.63552i	−0.751278	+	0.659986i	$0.770562\pi$
$48$	−100135.	−	72752.6i	−0.130690	−	0.0949520i
$49$	377906.	−	1.16308e6i	0.458879	−	1.41228i
$50$	402659.	+	1.23926e6i	0.455556	+	1.40206i
$51$	288019.	−	209258.i	0.304036	−	0.220895i
$52$	−192344.	−	591973.i	−0.189700	−	0.583835i
$53$	666892.	+	484526.i	0.615305	+	0.447045i	0.851278	−	0.524715i	$-0.175828\pi$
$53$	666892.	+	484526.i	0.615305	+	0.447045i	−0.235974	+	0.971759i	$0.575828\pi$
$54$	676863.	+	491770.i	0.584955	+	0.424995i
$55$	390191.	−	283490.i	0.316233	−	0.229757i
$56$	−732442.			−0.557333
$57$	1.19860e6			0.857262
$58$	−1.59082e6	+	1.15580e6i	−1.07059	+	0.777829i
$59$	10372.0	−	31921.8i	0.00657478	−	0.0202351i	−0.947715	−	0.319117i	$-0.896614\pi$
$59$	10372.0	−	31921.8i	0.00657478	−	0.0202351i	0.954290	+	0.298882i	$0.0966137\pi$
$60$	−293389.	−	902959.i	−0.175354	−	0.539683i
$61$	3.19752e6			1.80368			0.901838	−	0.432074i	$-0.142218\pi$
$61$	3.19752e6			1.80368			0.901838	+	0.432074i	$0.142218\pi$
$62$	−1.04841e6	−	813409.i	−0.558679	−	0.433449i
$63$	1.82231e6			0.918188
$64$	81007.0	+	249314.i	0.0386271	+	0.118882i
$65$	1.47540e6	−	4.54082e6i	0.666367	−	2.05087i
$66$	−192143.	+	139600.i	−0.0822661	+	0.0597698i
$67$	−817257.			−0.331968			−0.165984	−	0.986128i	$-0.553080\pi$
$67$	−817257.			−0.331968			−0.165984	+	0.986128i	$0.553080\pi$
$68$	−754004.			−0.290799
$69$	−697810.	+	506989.i	−0.255720	+	0.185792i
$70$	−4.54530e6	−	3.30235e6i	−1.58387	−	1.15075i
$71$	−3.42635e6	−	2.48939e6i	−1.13613	−	0.825447i	−0.149554	−	0.988753i	$-0.547784\pi$
$71$	−3.42635e6	−	2.48939e6i	−1.13613	−	0.825447i	−0.986575	+	0.163307i	$0.947784\pi$
$72$	−201545.	−	620293.i	−0.0636369	−	0.195854i
$73$	−1.43294e6	+	1.04109e6i	−0.431119	+	0.313226i	−0.782096	−	0.623158i	$-0.785849\pi$
$73$	−1.43294e6	+	1.04109e6i	−0.431119	+	0.313226i	0.350977	+	0.936384i	$0.385849\pi$
$74$	1.01851e6	+	3.13464e6i	0.292181	+	0.899242i
$75$	1.52096e6	−	4.68102e6i	0.416296	−	1.28123i
$76$	−2.05373e6	−	1.49212e6i	−0.536656	−	0.389903i
$77$	−434303.	+	1.33665e6i	−0.108411	+	0.333656i
$78$	−726537.	+	2.23605e6i	−0.173351	+	0.533520i
$79$	−732144.	−	531934.i	−0.167071	−	0.121384i	0.501108	−	0.865385i	$-0.332926\pi$
$79$	−732144.	−	531934.i	−0.167071	−	0.121384i	−0.668179	+	0.744000i	$0.732926\pi$
$80$	−621376.	+	1.91240e6i	−0.135687	+	0.417603i
$81$	−115677.	−	356016.i	−0.0241851	−	0.0744341i
$82$	2.83373e6	−	2.05883e6i	0.567558	−	0.412355i
$83$	159081.	+	489602.i	0.0305384	+	0.0939875i	0.965164	−	0.261646i	$-0.0842652\pi$
$83$	159081.	+	489602.i	0.0305384	+	0.0939875i	−0.934626	+	0.355633i	$0.884265\pi$
$84$	2.23826e6	+	1.62619e6i	0.412034	+	0.299360i
$85$	−4.67911e6	−	3.39957e6i	−0.826413	−	0.600424i
$86$	1.93475e6	−	1.40567e6i	0.328004	−	0.238309i
$87$	7.42751e6			1.20928
$88$	503011.			0.0786843
$89$	−6.78547e6	+	4.92993e6i	−1.02027	+	0.741270i	−0.966338	−	0.257275i	$-0.917175\pi$
$89$	−6.78547e6	+	4.92993e6i	−1.02027	+	0.741270i	−0.0539318	+	0.998545i	$0.517175\pi$
$90$	1.54598e6	−	4.75805e6i	0.223540	−	0.687986i
$91$	4.29933e6	+	1.32320e7i	0.598076	+	1.84069i
$92$	1.82679e6			0.244586
$93$	1.39788e6	+	4.81341e6i	0.180211	+	0.620530i
$94$	−9.79222e6			−1.21600
$95$	−6.01728e6	−	1.85193e7i	−0.720058	−	2.21611i
$96$	305986.	−	941729.i	0.0352982	−	0.108637i
$97$	8.68028e6	−	6.30659e6i	0.965678	−	0.701606i	0.0112158	−	0.999937i	$-0.496430\pi$
$97$	8.68028e6	−	6.30659e6i	0.965678	−	0.701606i	0.954463	+	0.298331i	$0.0964298\pi$
$98$	9.78344e6			1.05003
$99$	−1.25149e6			−0.129630
$100$	−8.43339e6	+	6.12722e6i	−0.843339	+	0.612722i
$101$	3.37942e6	+	2.45530e6i	0.326376	+	0.237126i	0.738891	−	0.673825i	$-0.235350\pi$
$101$	3.37942e6	+	2.45530e6i	0.326376	+	0.237126i	−0.412515	+	0.910951i	$0.635350\pi$
$102$	2.30415e6	+	1.67406e6i	0.214986	+	0.156197i
$103$	1.24892e6	+	3.84378e6i	0.112617	+	0.346600i	0.991443	−	0.130544i	$-0.0416722\pi$
$103$	1.24892e6	+	3.84378e6i	0.112617	+	0.346600i	−0.878825	+	0.477143i	$0.841672\pi$
$104$	4.02850e6	−	2.92688e6i	0.351177	−	0.255145i
$105$	6.55793e6	+	2.01832e7i	0.552846	+	1.70149i
$106$	−2.03784e6	+	6.27183e6i	−0.166188	+	0.511474i
$107$	−6.32594e6	−	4.59606e6i	−0.499208	−	0.362696i	0.309506	−	0.950897i	$-0.399836\pi$
$107$	−6.32594e6	−	4.59606e6i	−0.499208	−	0.362696i	−0.808714	+	0.588201i	$0.799836\pi$
$108$	−2.06831e6	+	6.36560e6i	−0.157991	+	0.486246i
$109$	−4.86528e6	+	1.49738e7i	−0.359844	+	1.10749i	0.593302	+	0.804980i	$0.297824\pi$
$109$	−4.86528e6	+	1.49738e7i	−0.359844	+	1.10749i	−0.953147	+	0.302508i	$0.902176\pi$
$110$	3.12153e6	+	2.26792e6i	0.223611	+	0.162463i
$111$	3.84719e6	−	1.18404e7i	0.267001	−	0.821744i
$112$	−1.81070e6	−	5.57275e6i	−0.121782	−	0.374806i
$113$	7.82080e6	−	5.68214e6i	0.509890	−	0.370457i	−0.302892	−	0.953025i	$-0.597952\pi$
$113$	7.82080e6	−	5.68214e6i	0.509890	−	0.370457i	0.812782	+	0.582568i	$0.197952\pi$
$114$	2.96311e6	+	9.11952e6i	0.187319	+	0.576508i
$115$	1.13365e7	+	8.23646e6i	0.695084	+	0.505008i
$116$	−1.27266e7	−	9.24639e6i	−0.757021	−	0.550008i
$117$	−1.00229e7	+	7.28207e6i	−0.578553	+	0.420343i
$118$	268516.			0.0150447
$119$	1.68538e7			0.916817
$120$	6.14482e6	−	4.46447e6i	0.324620	−	0.235850i
$121$	−5.72361e6	+	1.76154e7i	−0.293711	+	0.903951i
$122$	7.90470e6	+	2.43282e7i	0.394118	+	1.21297i
$123$	−1.32306e7			−0.641081
$124$	3.59696e6	−	9.98767e6i	0.169418	−	0.470423i
$125$	−4.16075e7			−1.90540
$126$	4.50501e6	+	1.38650e7i	0.200631	+	0.617480i
$127$	6.56147e6	−	2.01941e7i	0.284242	−	0.874807i	−0.702383	−	0.711799i	$-0.747881\pi$
$127$	6.56147e6	−	2.01941e7i	0.284242	−	0.874807i	0.986625	−	0.163007i	$-0.0521194\pi$
$128$	−1.69663e6	+	1.23268e6i	−0.0715077	+	0.0519534i
$129$	−9.03329e6			−0.370495
$130$	3.81960e7			1.52481
$131$	−2.99229e7	+	2.17402e7i	−1.16293	+	0.844919i	−0.990146	−	0.140041i	$-0.955277\pi$
$131$	−2.99229e7	+	2.17402e7i	−1.16293	+	0.844919i	−0.172785	+	0.984960i	$0.555277\pi$
$132$	−1.53714e6	−	1.11680e6i	−0.0581709	−	0.0422636i
$133$	4.59057e7	+	3.33524e7i	1.69194	+	1.22927i
$134$	−2.02037e6	−	6.21806e6i	−0.0725377	−	0.223248i
$135$	−4.15358e7	+	3.01775e7i	−1.45296	+	1.05564i
$136$	−1.86400e6	−	5.73681e6i	−0.0635419	−	0.195562i
$137$	7.79558e6	−	2.39923e7i	0.259016	−	0.797169i	−0.733996	−	0.679154i	$-0.762347\pi$
$137$	7.79558e6	−	2.39923e7i	0.259016	−	0.797169i	0.993012	−	0.118015i	$-0.0376532\pi$
$138$	−5.58248e6	−	4.05591e6i	−0.180822	−	0.131375i
$139$	−490784.	+	1.51048e6i	−0.0155003	+	0.0477049i	−0.958507	−	0.285067i	$-0.907984\pi$
$139$	−490784.	+	1.51048e6i	−0.0155003	+	0.0477049i	0.943007	+	0.332772i	$0.107984\pi$
$140$	1.38892e7	−	4.27466e7i	0.427789	−	1.31660i
$141$	2.99239e7	+	2.17410e7i	0.898983	+	0.653149i
$142$	1.04700e7	−	3.22234e7i	0.306858	−	0.944412i
$143$	−2.95261e6	−	9.08718e6i	−0.0844363	−	0.259868i
$144$	4.22122e6	−	3.06690e6i	0.117806	−	0.0855914i
$145$	−3.72879e7	−	1.14760e8i	−1.01573	−	3.12611i
$146$	−1.14635e7	−	8.32871e6i	−0.304847	−	0.221484i
$147$	−2.98971e7	−	2.17215e7i	−0.776280	−	0.564000i
$148$	−2.13319e7	+	1.54985e7i	−0.540895	+	0.392983i
$149$	−2.58353e7			−0.639825			−0.319913	−	0.947447i	$-0.603654\pi$
$149$	−2.58353e7			−0.639825			−0.319913	+	0.947447i	$0.603654\pi$
$150$	3.93753e7			0.952588
$151$	−2.80192e7	+	2.03571e7i	−0.662272	+	0.481169i	−0.867429	−	0.497560i	$-0.834229\pi$
$151$	−2.80192e7	+	2.03571e7i	−0.662272	+	0.481169i	0.205157	+	0.978729i	$0.434229\pi$
$152$	6.27564e6	−	1.93144e7i	0.144946	−	0.446097i
$153$	4.63764e6	+	1.42732e7i	0.104683	+	0.322181i
$154$	−1.12435e7			−0.248072
$155$	6.73529e7	−	4.57628e7i	1.45277	−	0.987078i
$156$	−1.88090e7			−0.396670
$157$	1.23091e7	+	3.78836e7i	0.253851	+	0.781272i	0.994054	+	0.108889i	$0.0347293\pi$
$157$	1.23091e7	+	3.78836e7i	0.253851	+	0.781272i	−0.740203	+	0.672383i	$0.765271\pi$
$158$	2.23723e6	−	6.88550e6i	0.0451244	−	0.138879i
$159$	2.01523e7	−	1.46415e7i	0.397590	−	0.288866i
$160$	−1.60865e7			−0.310486
$161$	−4.08331e7			−0.771121
$162$	2.42276e6	−	1.76024e6i	0.0447722	−	0.0325289i
$163$	1.45480e7	+	1.05697e7i	0.263116	+	0.191165i	0.711519	−	0.702666i	$-0.248007\pi$
$163$	1.45480e7	+	1.05697e7i	0.263116	+	0.191165i	−0.448404	+	0.893831i	$0.648007\pi$
$164$	2.26699e7	+	1.64706e7i	0.401324	+	0.291579i
$165$	−4.50372e6	−	1.38610e7i	−0.0780508	−	0.240216i
$166$	−3.33184e6	+	2.42073e6i	−0.0565336	+	0.0410740i
$167$	3.48132e6	+	1.07144e7i	0.0578411	+	0.178017i	0.975803	−	0.218652i	$-0.0701661\pi$
$167$	3.48132e6	+	1.07144e7i	0.0578411	+	0.178017i	−0.917962	+	0.396669i	$0.870166\pi$
$168$	−6.83951e6	+	2.10498e7i	−0.111287	+	0.342505i
$169$	−2.57578e7	−	1.87142e7i	−0.410493	−	0.298241i
$170$	1.42981e7	−	4.40050e7i	0.223207	−	0.686959i
$171$	−1.56138e7	+	4.80543e7i	−0.238793	+	0.734930i
$172$	1.54780e7	+	1.12454e7i	0.231934	+	0.168510i
$173$	−2.83142e7	+	8.71421e7i	−0.415760	+	1.27958i	0.495810	+	0.868431i	$0.334871\pi$
$173$	−2.83142e7	+	8.71421e7i	−0.415760	+	1.27958i	−0.911569	+	0.411146i	$0.865129\pi$
$174$	1.83618e7	+	5.65118e7i	0.264237	+	0.813237i
$175$	1.88506e8	−	1.36958e8i	2.65884	−	1.93176i
$176$	1.24351e6	+	3.82713e6i	0.0171931	+	0.0529151i
$177$	−820556.	−	596169.i	−0.0111225	−	0.00808096i
$178$	−5.42838e7	−	3.94395e7i	−0.721440	−	0.524157i
$179$	−8.18890e7	+	5.94958e7i	−1.06719	+	0.775356i	−0.975404	−	0.220424i	$-0.929256\pi$
$179$	−8.18890e7	+	5.94958e7i	−1.06719	+	0.775356i	−0.0917811	+	0.995779i	$0.529256\pi$
$180$	4.00232e7			0.511515
$181$	3.39796e7			0.425935			0.212967	−	0.977059i	$-0.431687\pi$
$181$	3.39796e7			0.425935			0.212967	+	0.977059i	$0.431687\pi$
$182$	−9.00464e7	+	6.54225e7i	−1.10718	+	0.804410i
$183$	2.98583e7	−	9.18944e7i	0.360152	−	1.10844i
$184$	4.51609e6	+	1.38991e7i	0.0534441	+	0.164484i
$185$	−2.02257e8			−2.34856
$186$	−3.31668e7	+	2.25351e7i	−0.377928	+	0.256782i
$187$	−1.15745e7			−0.129436
$188$	−2.42077e7	−	7.45036e7i	−0.265706	−	0.817758i
$189$	4.62316e7	−	1.42286e8i	0.498107	−	1.53301i
$190$	1.26028e8	−	9.15644e7i	1.33299	−	0.968476i
$191$	8.11557e7			0.842757			0.421378	−	0.906885i	$-0.361546\pi$
$191$	8.11557e7			0.842757			0.421378	+	0.906885i	$0.361546\pi$
$192$	7.92154e6			0.0807710
$193$	6.77801e7	−	4.92451e7i	0.678659	−	0.493075i	−0.194254	−	0.980951i	$-0.562228\pi$
$193$	6.77801e7	−	4.92451e7i	0.678659	−	0.493075i	0.872912	+	0.487877i	$0.162228\pi$
$194$	6.94422e7	+	5.04527e7i	0.682838	+	0.496111i
$195$	−1.16723e8	−	8.48039e7i	−1.12729	−	0.819021i
$196$	2.41860e7	+	7.44369e7i	0.229439	+	0.706142i
$197$	2.52416e7	−	1.83391e7i	0.235226	−	0.170902i	−0.463928	−	0.885873i	$-0.653560\pi$
$197$	2.52416e7	−	1.83391e7i	0.235226	−	0.170902i	0.699154	+	0.714971i	$0.253560\pi$
$198$	−3.09386e6	−	9.52191e6i	−0.0283251	−	0.0871758i
$199$	8.72180e6	−	2.68429e7i	0.0784549	−	0.241459i	−0.904135	−	0.427247i	$-0.859484\pi$
$199$	8.72180e6	−	2.68429e7i	0.0784549	−	0.241459i	0.982590	+	0.185787i	$0.0594836\pi$
$200$	−6.74671e7	−	4.90178e7i	−0.596331	−	0.433260i
$201$	−7.63151e6	+	2.34874e7i	−0.0662864	+	0.204009i
$202$	−1.03266e7	+	3.17820e7i	−0.0881511	+	0.271301i
$203$	2.84468e8	+	2.06678e8i	2.38670	+	1.73404i
$204$	−7.04086e6	+	2.16695e7i	−0.0580658	+	0.178708i
$205$	6.64211e7	+	2.04423e8i	0.538477	+	1.65726i
$206$	−2.61577e7	+	1.90047e7i	−0.208480	+	0.151470i
$207$	−1.12360e7	−	3.45809e7i	−0.0880473	−	0.270982i
$208$	3.22280e7	+	2.34150e7i	0.248320	+	0.180415i
$209$	−3.15262e7	−	2.29051e7i	−0.238869	−	0.173548i
$210$	−1.37351e8	+	9.97915e7i	−1.02345	+	0.743577i
$211$	−3.22028e7			−0.235996			−0.117998	−	0.993014i	$-0.537648\pi$
$211$	−3.22028e7			−0.235996			−0.117998	+	0.993014i	$0.537648\pi$
$212$	−5.27567e7			−0.380279
$213$	−1.03538e8	+	7.52251e7i	−0.734130	+	0.533377i
$214$	1.93303e7	−	5.94927e7i	0.134831	−	0.414969i
$215$	4.53493e7	+	1.39571e8i	0.311197	+	0.957767i
$216$	−5.35455e7			−0.361522
$217$	−8.04004e7	+	2.23248e8i	−0.534133	+	1.48313i
$218$	−1.25955e8			−0.823413
$219$	1.65395e7	+	5.09032e7i	0.106406	+	0.327484i
$220$	−9.53854e6	+	2.93566e7i	−0.0603952	+	0.185877i
$221$	−9.26973e7	+	6.73485e7i	−0.577689	+	0.419716i
$222$	9.95980e7			0.610964
$223$	−2.62677e8			−1.58619			−0.793095	−	0.609098i	$-0.791532\pi$
$223$	−2.62677e8			−1.58619			−0.793095	+	0.609098i	$0.791532\pi$
$224$	3.79237e7	−	2.75532e7i	0.225446	−	0.163796i
$225$	1.67858e8	+	1.21956e8i	0.982435	+	0.713781i
$226$	6.25664e7	+	4.54571e7i	0.360547	+	0.261953i
$227$	−2.98725e7	−	9.19381e7i	−0.169504	−	0.521681i	0.829835	−	0.558008i	$-0.188434\pi$
$227$	−2.98725e7	−	9.19381e7i	−0.169504	−	0.521681i	−0.999340	+	0.0363270i	$0.988434\pi$
$228$	−6.20602e7	+	4.50894e7i	−0.346770	+	0.251943i
$229$	3.07631e6	+	9.46791e6i	0.0169280	+	0.0520991i	0.959164	−	0.282852i	$-0.0912804\pi$
$229$	3.07631e6	+	9.46791e6i	0.0169280	+	0.0520991i	−0.942236	+	0.334951i	$0.891280\pi$
$230$	−3.46413e7	+	1.06615e8i	−0.187736	+	0.577791i
$231$	3.43588e7	+	2.49631e7i	0.183399	+	0.133247i
$232$	3.88889e7	−	1.19688e8i	0.204464	−	0.629277i
$233$	1.14378e8	−	3.52018e8i	0.592373	−	1.82314i	0.0249845	−	0.999688i	$-0.492046\pi$
$233$	1.14378e8	−	3.52018e8i	0.592373	−	1.82314i	0.567389	−	0.823450i	$-0.307954\pi$
$234$	−8.01832e7	−	5.82565e7i	−0.409099	−	0.297228i
$235$	1.85689e8	−	5.71491e8i	0.933357	−	2.87258i
$236$	663809.	+	2.04299e6i	0.00328739	+	0.0101175i
$237$	−2.21241e7	+	1.60741e7i	−0.107956	+	0.0784347i
$238$	4.16648e7	+	1.28231e8i	0.200332	+	0.616558i
$239$	1.52803e8	+	1.11018e8i	0.723999	+	0.526016i	0.887659	−	0.460501i	$-0.152330\pi$
$239$	1.52803e8	+	1.11018e8i	0.723999	+	0.526016i	−0.163660	+	0.986517i	$0.552330\pi$
$240$	4.91586e7	+	3.57158e7i	0.229541	+	0.166771i
$241$	1.25924e8	−	9.14893e7i	0.579495	−	0.421027i	−0.259047	−	0.965865i	$-0.583409\pi$
$241$	1.25924e8	−	9.14893e7i	0.579495	−	0.421027i	0.838542	+	0.544837i	$0.183409\pi$
$242$	−1.48176e8			−0.672084
$243$	2.17407e8			0.971967
$244$	−1.65558e8	+	1.20285e8i	−0.729602	+	0.530087i
$245$	−1.85522e8	+	5.70979e8i	−0.805962	+	2.48050i
$246$	−3.27080e7	−	1.00665e8i	−0.140081	−	0.431126i
$247$	−3.85764e8			−1.62885
$248$	8.48829e7	+	2.67639e6i	0.353378	+	0.0111421i
$249$	1.55563e7			0.0638571
$250$	−1.02859e8	−	3.16569e8i	−0.416345	−	1.28138i
$251$	6.09105e7	−	1.87463e8i	0.243127	−	0.748269i	−0.752811	−	0.658236i	$-0.771303\pi$
$251$	6.09105e7	−	1.87463e8i	0.243127	−	0.748269i	0.995939	−	0.0900328i	$-0.0286972\pi$
$252$	−9.43541e7	+	6.85523e7i	−0.371415	+	0.269849i
$253$	2.80425e7			0.108867
$254$	1.69867e8			0.650415
$255$	−1.41395e8	+	1.02729e8i	−0.534002	+	0.387975i
$256$	−1.35731e7	−	9.86140e6i	−0.0505636	−	0.0367366i
$257$	3.12030e8	+	2.26703e8i	1.14665	+	0.833090i	0.988032	−	0.154250i	$-0.0492963\pi$
$257$	3.12030e8	+	2.26703e8i	1.14665	+	0.833090i	0.158618	+	0.987340i	$0.449296\pi$
$258$	−2.23315e7	−	6.87293e7i	−0.0809560	−	0.249157i
$259$	4.76817e8	−	3.46428e8i	1.70531	−	1.23898i
$260$	9.44256e7	+	2.90612e8i	0.333183	+	1.02543i
$261$	−9.67556e7	+	2.97783e8i	−0.336848	+	1.03671i
$262$	−2.39383e8	−	1.73922e8i	−0.822316	−	0.597448i
$263$	1.03819e8	−	3.19523e8i	0.351911	−	1.08307i	−0.605868	−	0.795565i	$-0.707174\pi$
$263$	1.03819e8	−	3.19523e8i	0.351911	−	1.08307i	0.957779	−	0.287505i	$-0.0928258\pi$
$264$	4.69710e6	−	1.44562e7i	0.0157114	−	0.0483548i
$265$	−3.27392e8	−	2.37864e8i	−1.08070	−	0.785178i
$266$	−1.40275e8	+	4.31723e8i	−0.456978	+	1.40643i
$267$	7.83203e7	+	2.41045e8i	0.251817	+	0.775013i
$268$	4.23152e7	−	3.07438e7i	0.134284	−	0.0975631i
$269$	−6.33218e7	−	1.94884e8i	−0.198345	−	0.610442i	−0.999921	−	0.0125498i	$-0.996005\pi$
$269$	−6.33218e7	−	1.94884e8i	−0.198345	−	0.610442i	0.801577	−	0.597892i	$-0.203995\pi$
$270$	−3.32287e8	−	2.41420e8i	−1.02740	−	0.746450i
$271$	1.51225e8	+	1.09871e8i	0.461563	+	0.335345i	0.794144	−	0.607730i	$-0.207920\pi$
$271$	1.51225e8	+	1.09871e8i	0.461563	+	0.335345i	−0.332581	+	0.943075i	$0.607920\pi$
$272$	3.90402e7	−	2.83643e7i	0.117631	−	0.0854636i
$273$	4.20425e8			1.25060
$274$	2.01816e8			0.592692
$275$	−1.29458e8	+	9.40569e7i	−0.375375	+	0.272726i
$276$	1.70585e7	−	5.25008e7i	0.0488382	−	0.150309i
$277$	8.37918e7	+	2.57885e8i	0.236877	+	0.729031i	0.996867	+	0.0790969i	$0.0252037\pi$
$277$	8.37918e7	+	2.57885e8i	0.236877	+	0.729031i	−0.759990	+	0.649934i	$0.774796\pi$
$278$	−1.27057e7			−0.0354684
$279$	−2.11189e8	−	6.65886e6i	−0.582178	−	0.0183563i
$280$	3.59571e8			0.978885
$281$	−1.30743e7	−	4.02385e7i	−0.0351517	−	0.108186i	0.931941	−	0.362610i	$-0.118114\pi$
$281$	−1.30743e7	−	4.02385e7i	−0.0351517	−	0.108186i	−0.967093	+	0.254424i	$0.918114\pi$
$282$	−9.14393e7	+	2.81421e8i	−0.242807	+	0.747283i
$283$	5.82665e8	−	4.23331e8i	1.52815	−	1.11027i	0.570898	−	0.821021i	$-0.306595\pi$
$283$	5.82665e8	−	4.23331e8i	1.52815	−	1.11027i	0.957255	−	0.289247i	$-0.0934048\pi$
$284$	2.71053e8			0.702167
$285$	−5.88420e8			−1.50567
$286$	6.18402e7	−	4.49295e7i	0.156311	−	0.113567i
$287$	−5.06725e8	−	3.68157e8i	−1.26528	−	0.919277i
$288$	3.37698e7	+	2.45352e7i	0.0833018	+	0.0605223i
$289$	−8.39102e7	−	2.58249e8i	−0.204490	−	0.629356i
$290$	7.80968e8	−	5.67406e8i	1.88036	−	1.36616i
$291$	−1.00191e8	−	3.08356e8i	−0.238343	−	0.733544i
$292$	3.50293e7	−	1.07809e8i	0.0823363	−	0.253405i
$293$	7.21971e7	+	5.24543e7i	0.167681	+	0.121827i	0.668461	−	0.743747i	$-0.266953\pi$
$293$	7.21971e7	+	5.24543e7i	0.167681	+	0.121827i	−0.500780	+	0.865575i	$0.666953\pi$
$294$	9.13574e7	−	2.81169e8i	0.209666	−	0.645286i
$295$	−5.09185e6	+	1.56711e7i	−0.0115478	+	0.0355404i
$296$	−1.70655e8	−	1.23988e8i	−0.382470	−	0.277881i
$297$	−3.17499e7	+	9.77163e7i	−0.0703227	+	0.216431i
$298$	−6.38683e7	−	1.96566e8i	−0.139807	−	0.430281i
$299$	2.24586e8	−	1.63171e8i	0.485885	−	0.353016i
$300$	9.73412e7	+	2.99585e8i	0.208148	+	0.640614i
$301$	−3.45969e8	−	2.51361e8i	−0.731230	−	0.531270i
$302$	−2.24154e8	−	1.62857e8i	−0.468297	−	0.340238i
$303$	1.02120e8	−	7.41948e7i	0.210893	−	0.153223i
$304$	1.62467e8			0.331672
$305$	−1.56973e9			−3.16793
$306$	−9.71319e7	+	7.05705e7i	−0.193792	+	0.140798i
$307$	4.03662e6	−	1.24235e7i	0.00796222	−	0.0245052i	−0.946996	−	0.321244i	$-0.895899\pi$
$307$	4.03662e6	−	1.24235e7i	0.00796222	−	0.0245052i	0.954959	+	0.296739i	$0.0958991\pi$
$308$	−2.77954e7	−	8.55454e7i	−0.0542057	−	0.166828i
$309$	1.22130e8			0.235487
$310$	5.14689e8	+	3.99320e8i	0.981249	+	0.761298i
$311$	−1.41234e8			−0.266244			−0.133122	−	0.991100i	$-0.542500\pi$
$311$	−1.41234e8			−0.266244			−0.133122	+	0.991100i	$0.542500\pi$
$312$	−4.64984e7	−	1.43107e8i	−0.0866755	−	0.266760i
$313$	6.26266e7	−	1.92745e8i	0.115439	−	0.355286i	−0.876599	−	0.481221i	$-0.840193\pi$
$313$	6.26266e7	−	1.92745e8i	0.115439	−	0.355286i	0.992038	+	0.125936i	$0.0401933\pi$
$314$	−2.57806e8	+	1.87307e8i	−0.469936	+	0.341428i
$315$	−8.94613e8			−1.61268
$316$	5.79187e7			0.103256
$317$	6.51242e8	−	4.73155e8i	1.14825	−	0.834249i	0.159999	−	0.987117i	$-0.448851\pi$
$317$	6.51242e8	−	4.73155e8i	1.14825	−	0.834249i	0.988247	+	0.152868i	$0.0488510\pi$
$318$	1.61219e8	+	1.17132e8i	0.281139	+	0.204259i
$319$	−1.95361e8	−	1.41938e8i	−0.336954	−	0.244812i
$320$	−3.97680e7	−	1.22393e8i	−0.0678437	−	0.208801i
$321$	−1.91159e8	+	1.38885e8i	−0.322572	+	0.234362i
$322$	−1.00945e8	−	3.10677e8i	−0.168496	−	0.518577i
$323$	−1.44405e8	+	4.44433e8i	−0.238437	+	0.733833i
$324$	1.93821e7	+	1.40819e7i	0.0316587	+	0.0230014i
$325$	−4.89511e8	+	1.50656e9i	−0.790990	+	2.43442i
$326$	−4.44547e7	+	1.36818e8i	−0.0710651	+	0.218716i
$327$	3.84904e8	+	2.79649e8i	0.608745	+	0.442279i
$328$	−6.92730e7	+	2.13200e8i	−0.108394	+	0.333602i
$329$	5.41099e8	+	1.66533e9i	0.837704	+	2.57819i
$330$	9.43271e7	−	6.85327e7i	0.144490	−	0.104978i
$331$	−2.70716e8	−	8.33177e8i	−0.410313	−	1.26281i	−0.916376	−	0.400318i	$-0.868900\pi$
$331$	−2.70716e8	−	8.33177e8i	−0.410313	−	1.26281i	0.506063	−	0.862496i	$-0.331100\pi$
$332$	−2.66548e7	−	1.93658e7i	−0.0399753	−	0.0290437i
$333$	4.24589e8	+	3.08482e8i	0.630107	+	0.457800i
$334$	−7.29138e7	+	5.29750e7i	−0.107077	+	0.0777962i
$335$	4.01209e8			0.583061
$336$	−1.77065e8			−0.254651
$337$	6.65769e8	−	4.83709e8i	0.947586	−	0.688462i	−0.00264858	−	0.999996i	$-0.500843\pi$
$337$	6.65769e8	−	4.83709e8i	0.947586	−	0.688462i	0.950235	+	0.311535i	$0.100843\pi$
$338$	7.87090e7	−	2.42241e8i	0.110870	−	0.341224i
$339$	−9.02704e7	−	2.77824e8i	−0.125848	−	0.387321i
$340$	3.70157e8			0.510752
$341$	5.52157e7	−	1.53317e8i	0.0754088	−	0.209388i
$342$	−4.04219e8			−0.546418
$343$	−1.76555e8	−	5.43380e8i	−0.236238	−	0.727067i
$344$	−4.72964e7	+	1.45563e8i	−0.0626432	+	0.192796i
$345$	3.42570e8	−	2.48892e8i	0.449141	−	0.326320i
$346$	−7.33013e8			−0.951361
$347$	−1.38209e9			−1.77575			−0.887875	−	0.460084i	$-0.847819\pi$
$347$	−1.38209e9			−1.77575			−0.887875	+	0.460084i	$0.847819\pi$
$348$	−3.84575e8	+	2.79410e8i	−0.489163	+	0.355397i
$349$	−2.03481e8	−	1.47838e8i	−0.256233	−	0.186164i	0.452252	−	0.891890i	$-0.350621\pi$
$349$	−2.03481e8	−	1.47838e8i	−0.256233	−	0.186164i	−0.708485	+	0.705726i	$0.750621\pi$
$350$	1.50805e9	+	1.09566e9i	1.88008	+	1.36596i
$351$	3.14305e8	+	9.67331e8i	0.387950	+	1.19399i
$352$	−2.60444e7	+	1.89224e7i	−0.0318285	+	0.0231247i
$353$	2.14441e8	+	6.59981e8i	0.259475	+	0.798583i	0.992915	+	0.118828i	$0.0379137\pi$
$353$	2.14441e8	+	6.59981e8i	0.259475	+	0.798583i	−0.733440	+	0.679755i	$0.762086\pi$
$354$	2.50740e6	−	7.71697e6i	0.00300408	−	0.00924561i
$355$	1.68207e9	+	1.22210e9i	1.99547	+	1.44979i
$356$	1.65876e8	−	5.10515e8i	0.194854	−	0.599700i
$357$	1.57380e8	−	4.84365e8i	0.183067	−	0.563422i
$358$	−6.55112e8	−	4.75967e8i	−0.754614	−	0.548259i
$359$	−2.31428e8	+	7.12262e8i	−0.263989	+	0.812473i	0.727936	+	0.685645i	$0.240480\pi$
$359$	−2.31428e8	+	7.12262e8i	−0.263989	+	0.812473i	−0.991925	+	0.126828i	$0.959520\pi$
$360$	9.89429e7	+	3.04515e8i	0.111770	+	0.343993i
$361$	−5.49670e8	+	3.99359e8i	−0.614932	+	0.446774i
$362$	8.40021e7	+	2.58532e8i	0.0930701	+	0.286440i
$363$	4.52809e8	+	3.28985e8i	0.496868	+	0.360996i
$364$	−7.20371e8	−	5.23380e8i	−0.782891	−	0.568804i
$365$	7.03459e8	−	5.11093e8i	0.757205	−	0.550142i
$366$	7.72988e8			0.824117
$367$	7.00663e7			0.0739908			0.0369954	−	0.999315i	$-0.488221\pi$
$367$	7.00663e7			0.0739908			0.0369954	+	0.999315i	$0.488221\pi$
$368$	−9.45861e7	+	6.87208e7i	−0.0989373	+	0.0718822i
$369$	1.72351e8	−	5.30442e8i	0.178575	−	0.549599i
$370$	−5.00006e8	−	1.53886e9i	−0.513180	−	1.57940i
$371$	1.17924e9			1.19893
$372$	−2.53450e8	−	1.96638e8i	−0.255266	−	0.198047i
$373$	1.20856e9			1.20583			0.602917	−	0.797804i	$-0.294005\pi$
$373$	1.20856e9			1.20583			0.602917	+	0.797804i	$0.294005\pi$
$374$	−2.86137e7	−	8.80638e7i	−0.0282828	−	0.0870456i
$375$	−3.88529e8	+	1.19577e9i	−0.380464	+	1.17095i
$376$	5.07012e8	−	3.68366e8i	0.491882	−	0.357373i
$377$	−2.39050e9			−2.29770
$378$	1.19687e9			1.13979
$379$	−1.66852e7	+	1.21225e7i	−0.0157432	+	0.0114381i	−0.595629	−	0.803260i	$-0.703097\pi$
$379$	−1.66852e7	+	1.21225e7i	−0.0157432	+	0.0114381i	0.579886	+	0.814698i	$0.303097\pi$
$380$	1.00822e9	+	7.32515e8i	0.942569	+	0.684816i
$381$	−5.19094e8	−	3.77144e8i	−0.480849	−	0.349357i
$382$	2.00628e8	+	6.17469e8i	0.184149	+	0.566753i
$383$	−1.56493e9	+	1.13699e9i	−1.42331	+	1.03410i	−0.432100	+	0.901826i	$0.642227\pi$
$383$	−1.56493e9	+	1.13699e9i	−1.42331	+	1.03410i	−0.991213	+	0.132272i	$0.957773\pi$
$384$	1.95831e7	+	6.02707e7i	0.0176491	+	0.0543184i
$385$	2.13209e8	−	6.56189e8i	0.190411	−	0.586025i
$386$	5.42241e8	+	3.93961e8i	0.479884	+	0.348656i
$387$	1.17674e8	−	3.62162e8i	0.103203	−	0.317625i
$388$	−2.12197e8	+	6.53074e8i	−0.184428	+	0.567612i
$389$	−9.29185e8	−	6.75092e8i	−0.800348	−	0.581487i	0.110669	−	0.993857i	$-0.464701\pi$
$389$	−9.29185e8	−	6.75092e8i	−0.800348	−	0.581487i	−0.911016	+	0.412371i	$0.864701\pi$
$390$	3.56673e8	−	1.09773e9i	0.304469	−	0.937060i
$391$	−1.03917e8	−	3.19823e8i	−0.0879159	−	0.270577i
$392$	−5.06558e8	+	3.68036e8i	−0.424745	+	0.308595i
$393$	3.45380e8	+	1.06297e9i	0.287028	+	0.883380i
$394$	2.01933e8	+	1.46713e8i	0.166330	+	0.120846i
$395$	3.59425e8	+	2.61138e8i	0.293440	+	0.213196i
$396$	6.47986e7	−	4.70789e7i	0.0524363	−	0.0380972i
$397$	−1.00910e9			−0.809412			−0.404706	−	0.914447i	$-0.632626\pi$
$397$	−1.00910e9			−0.809412			−0.404706	+	0.914447i	$0.632626\pi$
$398$	2.25795e8			0.179524
$399$	1.38719e9	−	1.00785e9i	1.09328	−	0.794314i
$400$	2.06161e8	−	6.34499e8i	0.161063	−	0.495702i
$401$	−9.00956e7	−	2.77286e8i	−0.0697747	−	0.214745i	0.910089	−	0.414414i	$-0.136013\pi$
$401$	−9.00956e7	−	2.77286e8i	−0.0697747	−	0.214745i	−0.979863	+	0.199669i	$0.936013\pi$
$402$	−1.97569e8			−0.151680
$403$	−4.49900e8	−	1.54917e9i	−0.342412	−	1.17905i
$404$	−2.67341e8			−0.201711
$405$	5.67881e7	+	1.74776e8i	0.0424781	+	0.130734i
$406$	−8.69258e8	+	2.67530e9i	−0.644626	+	1.98395i
$407$	−3.27458e8	+	2.37912e8i	−0.240755	+	0.174919i
$408$	−1.82278e8			−0.132869
$409$	2.53519e8			0.183222			0.0916112	−	0.995795i	$-0.470798\pi$
$409$	2.53519e8			0.183222			0.0916112	+	0.995795i	$0.470798\pi$
$410$	−1.39114e9	+	1.01072e9i	−0.996845	+	0.724250i
$411$	−6.16728e8	−	4.48079e8i	−0.438175	−	0.318352i
$412$	−2.09262e8	−	1.52038e8i	−0.147418	−	0.107105i
$413$	−1.48377e7	−	4.56657e7i	−0.0103643	−	0.0318981i
$414$	2.35330e8	−	1.70977e8i	0.162996	−	0.118423i
$415$	−7.80965e7	−	2.40356e8i	−0.0536368	−	0.165077i
$416$	−9.84800e7	+	3.03090e8i	−0.0670689	+	0.206417i
$417$	3.88272e7	+	2.82096e7i	0.0262216	+	0.0190511i
$418$	9.63354e7	−	2.96490e8i	0.0645162	−	0.198560i
$419$	−2.42872e8	+	7.47483e8i	−0.161298	+	0.496423i	−0.998744	−	0.0500958i	$-0.984047\pi$
$419$	−2.42872e8	+	7.47483e8i	−0.161298	+	0.496423i	0.837447	+	0.546519i	$0.184047\pi$
$420$	−1.09881e9	−	7.98332e8i	−0.723685	−	0.525788i
$421$	5.09806e8	−	1.56902e9i	0.332979	−	1.02480i	−0.634730	−	0.772734i	$-0.718889\pi$
$421$	5.09806e8	−	1.56902e9i	0.332979	−	1.02480i	0.967709	−	0.252071i	$-0.0811115\pi$
$422$	−7.96097e7	−	2.45013e8i	−0.0515670	−	0.158707i
$423$	−1.26145e9	+	9.16495e8i	−0.810359	+	0.588761i
$424$	−1.30422e8	−	4.01397e8i	−0.0830940	−	0.255737i
$425$	1.55245e9	+	1.12792e9i	0.980968	+	0.712715i
$426$	−8.28308e8	−	6.01801e8i	−0.519109	−	0.377154i
$427$	3.70061e9	−	2.68865e9i	2.30026	−	1.67123i
$428$	5.00434e8			0.308528
$429$	−2.88730e8			−0.176560
$430$	−9.49808e8	+	6.90076e8i	−0.576098	+	0.418560i
$431$	−1.48337e7	+	4.56534e7i	−0.00892439	+	0.0274665i	−0.955420	−	0.295252i	$-0.904597\pi$
$431$	−1.48337e7	+	4.56534e7i	−0.00892439	+	0.0274665i	0.946495	+	0.322718i	$0.104597\pi$
$432$	−1.32372e8	−	4.07399e8i	−0.0789955	−	0.243123i
$433$	−1.64551e9			−0.974073			−0.487037	−	0.873382i	$-0.661922\pi$
$433$	−1.64551e9			−0.974073			−0.487037	+	0.873382i	$0.661922\pi$
$434$	−1.89733e9	−	5.98236e7i	−1.11411	−	0.0351284i
$435$	−3.64632e9			−2.12394
$436$	−3.11378e8	−	9.58322e8i	−0.179922	−	0.553744i
$437$	3.49863e8	−	1.07677e9i	0.200546	−	0.617216i
$438$	−3.46407e8	+	2.51679e8i	−0.196982	+	0.143116i
$439$	2.00923e9			1.13345			0.566727	−	0.823906i	$-0.308209\pi$
$439$	2.00923e9			1.13345			0.566727	+	0.823906i	$0.308209\pi$
$440$	−2.46939e8			−0.138199
$441$	1.26032e9	−	9.15674e8i	0.699753	−	0.508400i
$442$	−7.41579e8	−	5.38788e8i	−0.408488	−	0.296784i
$443$	8.27621e8	+	6.01302e8i	0.452292	+	0.328609i	0.790500	−	0.612462i	$-0.209821\pi$
$443$	8.27621e8	+	6.01302e8i	0.452292	+	0.328609i	−0.338208	+	0.941071i	$0.609821\pi$
$444$	2.46220e8	+	7.57787e8i	0.133500	+	0.410872i
$445$	3.33113e9	−	2.42021e9i	1.79198	−	1.30195i
$446$	−6.49373e8	−	1.99857e9i	−0.346595	−	1.06671i
$447$	−2.41249e8	+	7.42488e8i	−0.127758	+	0.393199i
$448$	3.03390e8	+	2.20425e8i	0.159414	+	0.115821i
$449$	4.94582e8	−	1.52217e9i	0.257855	−	0.793598i	−0.735398	−	0.677635i	$-0.763005\pi$
$449$	4.94582e8	−	1.52217e9i	0.257855	−	0.793598i	0.993254	−	0.115962i	$-0.0369952\pi$
$450$	−5.12929e8	+	1.57863e9i	−0.265347	+	0.816653i
$451$	3.47998e8	+	2.52835e8i	0.178632	+	0.129784i
$452$	−1.91186e8	+	5.88410e8i	−0.0973804	+	0.299706i
$453$	3.23408e8	+	9.95346e8i	0.163458	+	0.503072i
$454$	6.25658e8	−	4.54567e8i	0.313792	−	0.227983i
$455$	−2.11063e9	−	6.49586e9i	−1.05044	−	3.23294i
$456$	−4.96482e8	−	3.60715e8i	−0.245203	−	0.178151i
$457$	2.02800e9	+	1.47343e9i	0.993941	+	0.722140i	0.960781	−	0.277310i	$-0.0894428\pi$
$457$	2.02800e9	+	1.47343e9i	0.993941	+	0.722140i	0.0331602	+	0.999450i	$0.489443\pi$
$458$	−6.44311e7	+	4.68119e7i	−0.0313376	+	0.0227681i
$459$	1.23210e9			0.594707
$460$	−8.96813e8			−0.429585
$461$	1.77727e8	−	1.29126e8i	0.0844891	−	0.0613849i	−0.544739	−	0.838606i	$-0.683371\pi$
$461$	1.77727e8	−	1.29126e8i	0.0844891	−	0.0613849i	0.629228	+	0.777221i	$0.283371\pi$
$462$	−1.04991e8	+	3.23129e8i	−0.0495342	+	0.152451i
$463$	−6.07755e8	−	1.87048e9i	−0.284574	−	0.875829i	−0.986526	−	0.163605i	$-0.947688\pi$
$463$	−6.07755e8	−	1.87048e9i	−0.284574	−	0.875829i	0.701952	−	0.712224i	$-0.252312\pi$
$464$	1.00678e9			0.467865
$465$	−6.86250e8	−	2.36301e9i	−0.316517	−	1.08988i
$466$	2.96107e9			1.35550
$467$	−6.83228e8	−	2.10276e9i	−0.310425	−	0.955389i	−0.977597	−	0.210486i	$-0.932495\pi$
$467$	−6.83228e8	−	2.10276e9i	−0.310425	−	0.955389i	0.667172	−	0.744904i	$-0.267505\pi$
$468$	2.45018e8	−	7.54088e8i	0.110494	−	0.340065i
$469$	−9.45843e8	+	6.87195e8i	−0.423364	+	0.307592i
$470$	4.80721e9			2.13575
$471$	1.20369e9			0.530813
$472$	−1.39030e7	+	1.01011e7i	−0.00608571	+	0.00442153i
$473$	2.37597e8	+	1.72624e8i	0.103235	+	0.0750047i
$474$	−1.76993e8	−	1.28593e8i	−0.0763365	−	0.0554617i
$475$	1.99643e9	+	6.14437e9i	0.854723	+	2.63057i
$476$	−8.72639e8	+	6.34009e8i	−0.370860	+	0.269446i
$477$	3.24490e8	+	9.98676e8i	0.136895	+	0.421318i
$478$	−4.66923e8	+	1.43704e9i	−0.195545	+	0.601827i
$479$	1.38898e9	+	1.00915e9i	0.577460	+	0.419549i	0.837807	−	0.545966i	$-0.183837\pi$
$479$	1.38898e9	+	1.00915e9i	0.577460	+	0.419549i	−0.260348	+	0.965515i	$0.583837\pi$
$480$	−1.50215e8	+	4.62315e8i	−0.0619969	+	0.190807i
$481$	−1.23820e9	+	3.81077e9i	−0.507319	+	1.56137i
$482$	1.00739e9	+	7.31914e8i	0.409765	+	0.297711i
$483$	−3.81298e8	+	1.17352e9i	−0.153975	+	0.473886i
$484$	−3.66311e8	−	1.12739e9i	−0.146856	−	0.451975i
$485$	−4.26133e9	+	3.09604e9i	−1.69609	+	1.23228i
$486$	5.37460e8	+	1.65413e9i	0.212383	+	0.653647i
$487$	2.12808e8	+	1.54614e8i	0.0834902	+	0.0606592i	0.628747	−	0.777610i	$-0.283568\pi$
$487$	2.12808e8	+	1.54614e8i	0.0834902	+	0.0606592i	−0.545257	+	0.838269i	$0.683568\pi$
$488$	−1.32447e9	−	9.62281e8i	−0.515907	−	0.374828i
$489$	4.39615e8	−	3.19399e8i	0.170017	−	0.123524i
$490$	−4.80290e9			−1.84424
$491$	4.30938e9			1.64297			0.821485	−	0.570230i	$-0.193146\pi$
$491$	4.30938e9			1.64297			0.821485	+	0.570230i	$0.193146\pi$
$492$	6.85044e8	−	4.97714e8i	0.259323	−	0.188409i
$493$	−8.94849e8	+	2.75406e9i	−0.336345	+	1.03516i
$494$	−9.53661e8	−	2.93507e9i	−0.355918	−	1.09540i
$495$	6.14384e8			0.227678
$496$	1.89479e8	+	6.52444e8i	0.0697228	+	0.240081i
$497$	−6.05867e9			−2.21376
$498$	3.84573e7	+	1.18359e8i	0.0139533	+	0.0429438i
$499$	−1.12277e8	+	3.45552e8i	−0.0404518	+	0.124498i	−0.969243	−	0.246105i	$-0.920849\pi$
$499$	−1.12277e8	+	3.45552e8i	−0.0404518	+	0.124498i	0.928791	+	0.370603i	$0.120849\pi$
$500$	2.15431e9	−	1.56520e9i	0.770751	−	0.559983i
$501$	3.40433e8			0.120948
$502$	1.57688e9			0.556335
$503$	−4.06941e8	+	2.95660e8i	−0.142575	+	0.103587i	−0.656786	−	0.754077i	$-0.728085\pi$
$503$	−4.06941e8	+	2.95660e8i	−0.142575	+	0.103587i	0.514211	+	0.857663i	$0.328085\pi$
$504$	−7.54833e8	−	5.48418e8i	−0.262630	−	0.190812i
$505$	−1.65903e9	−	1.20536e9i	−0.573238	−	0.416482i
$506$	6.93249e7	+	2.13360e8i	0.0237883	+	0.0732127i
$507$	−7.78357e8	+	5.65510e8i	−0.265247	+	0.192714i
$508$	4.19934e8	+	1.29242e9i	0.142121	+	0.437403i
$509$	8.99756e8	−	2.76916e9i	0.302421	−	0.930757i	−0.678205	−	0.734872i	$-0.737242\pi$
$509$	8.99756e8	−	2.76916e9i	0.302421	−	0.930757i	0.980627	−	0.195885i	$-0.0627580\pi$
$510$	−1.13116e9	−	8.21834e8i	−0.377596	−	0.274340i
$511$	−7.82987e8	+	2.40979e9i	−0.259586	+	0.798924i
$512$	4.14756e7	−	1.27649e8i	0.0136568	−	0.0420312i
$513$	3.35596e9	+	2.43825e9i	1.09750	+	0.797383i
$514$	−9.53479e8	+	2.93451e9i	−0.309699	+	0.953157i
$515$	−6.13122e8	−	1.88699e9i	−0.197798	−	0.608759i
$516$	4.67717e8	−	3.39817e8i	0.149868	−	0.108886i
$517$	−3.71604e8	−	1.14368e9i	−0.118267	−	0.363989i
$518$	3.81454e9	+	2.77142e9i	1.20583	+	0.876090i
$519$	2.24000e9	+	1.62746e9i	0.703336	+	0.511004i
$520$	−1.97768e9	+	1.43687e9i	−0.616799	+	0.448131i
$521$	2.50048e9			0.774626			0.387313	−	0.921948i	$-0.373403\pi$
$521$	2.50048e9			0.774626			0.387313	+	0.921948i	$0.373403\pi$
$522$	−2.50486e9			−0.770791
$523$	−3.93592e9	+	2.85962e9i	−1.20307	+	0.874081i	−0.994583	−	0.103944i	$-0.966854\pi$
$523$	−3.93592e9	+	2.85962e9i	−1.20307	+	0.874081i	−0.208487	+	0.978025i	$0.566854\pi$
$524$	7.31489e8	−	2.25129e9i	0.222100	−	0.683554i
$525$	−2.17580e9	−	6.69644e9i	−0.656239	−	2.01970i
$526$	2.68773e9			0.805258
$527$	−1.95319e9	−	6.15848e7i	−0.581309	−	0.0183289i
$528$	1.21601e8			0.0359516
$529$	−8.00380e8	−	2.46332e9i	−0.235072	−	0.723478i
$530$	1.00042e9	−	3.07898e9i	0.291888	−	0.898340i
$531$	3.45907e7	−	2.51316e7i	0.0100260	−	0.00728432i
$532$	−3.63152e9			−1.04568
$533$	4.25821e9			1.21810
$534$	−1.64036e9	+	1.19179e9i	−0.466171	+	0.338693i
$535$	3.10554e9	+	2.25631e9i	0.876796	+	0.637030i
$536$	3.38521e8	+	2.45950e8i	0.0949531	+	0.0689875i
$537$	9.45192e8	+	2.90900e9i	0.263396	+	0.810651i
$538$	1.32623e9	−	9.63562e8i	0.367181	−	0.266773i
$539$	3.71271e8	+	1.14266e9i	0.102125	+	0.314307i
$540$	1.01538e9	−	3.12501e9i	0.277491	−	0.854030i
$541$	−5.28135e8	−	3.83713e8i	−0.143402	−	0.104188i	0.513771	−	0.857927i	$-0.328248\pi$
$541$	−5.28135e8	−	3.83713e8i	−0.143402	−	0.104188i	−0.657173	+	0.753740i	$0.728248\pi$
$542$	−4.62102e8	+	1.42220e9i	−0.124664	+	0.383676i
$543$	3.17300e8	−	9.76549e8i	0.0850493	−	0.261755i
$544$	3.12321e8	+	2.26915e8i	0.0831774	+	0.0604319i
$545$	2.38847e9	−	7.35095e9i	0.632021	−	1.94516i
$546$	1.03935e9	+	3.19878e9i	0.273267	+	0.841028i
$547$	−5.38153e9	+	3.90991e9i	−1.40589	+	1.02144i	−0.411981	+	0.911193i	$0.635163\pi$
$547$	−5.38153e9	+	3.90991e9i	−1.40589	+	1.02144i	−0.993905	+	0.110243i	$0.964837\pi$
$548$	4.98917e8	+	1.53551e9i	0.129508	+	0.398585i
$549$	3.29527e9	+	2.39415e9i	0.849939	+	0.617517i
$550$	−1.03567e9	−	7.52455e8i	−0.265430	−	0.192846i
$551$	−7.88746e9	+	5.73057e9i	−2.00866	+	1.45938i
$552$	4.41621e8			0.111754
$553$	−1.29462e9			−0.325540
$554$	−1.75496e9	+	1.27505e9i	−0.438513	+	0.318598i
$555$	−1.88867e9	+	5.81272e9i	−0.468953	+	1.44329i
$556$	−3.14102e7	−	9.66706e7i	−0.00775013	−	0.0238524i
$557$	2.46246e9			0.603775			0.301888	−	0.953344i	$-0.402383\pi$
$557$	2.46246e9			0.603775			0.301888	+	0.953344i	$0.402383\pi$
$558$	−4.71423e8	−	1.62328e9i	−0.114866	−	0.395525i
$559$	2.90731e9			0.703964
$560$	8.88909e8	+	2.73578e9i	0.213894	+	0.658299i
$561$	−1.08082e8	+	3.32642e8i	−0.0258454	+	0.0795440i
$562$	2.73832e8	−	1.98950e8i	0.0650738	−	0.0472789i
$563$	−4.43660e9			−1.04778			−0.523891	−	0.851785i	$-0.675520\pi$
$563$	−4.43660e9			−1.04778			−0.523891	+	0.851785i	$0.675520\pi$
$564$	−2.36723e9			−0.555602
$565$	−3.83940e9	+	2.78949e9i	−0.895558	+	0.650661i
$566$	4.66132e9	+	3.38665e9i	1.08057	+	0.785078i
$567$	−4.33235e8	−	3.14764e8i	−0.0998121	−	0.0725177i
$568$	6.70080e8	+	2.06230e9i	0.153429	+	0.472206i
$569$	2.07596e9	−	1.50827e9i	0.472417	−	0.343231i	−0.325966	−	0.945382i	$-0.605689\pi$
$569$	2.07596e9	−	1.50827e9i	0.472417	−	0.343231i	0.798382	+	0.602151i	$0.205689\pi$
$570$	−1.45466e9	−	4.47697e9i	−0.329002	−	1.01256i
$571$	1.10310e9	−	3.39498e9i	0.247963	−	0.763152i	−0.747172	−	0.664631i	$-0.768589\pi$
$571$	1.10310e9	−	3.39498e9i	0.247963	−	0.763152i	0.995135	−	0.0985211i	$-0.0314112\pi$
$572$	4.94721e8	+	3.59436e8i	0.110529	+	0.0803037i
$573$	7.57829e8	−	2.33236e9i	0.168279	−	0.517909i
$574$	1.54841e9	−	4.76552e9i	0.341739	−	1.05177i
$575$	−3.76125e9	−	2.73271e9i	−0.825077	−	0.599454i
$576$	−1.03191e8	+	3.17590e8i	−0.0224990	+	0.0692449i
$577$	1.60495e9	+	4.93954e9i	0.347814	+	1.07046i	0.960060	+	0.279794i	$0.0902662\pi$
$577$	1.60495e9	+	4.93954e9i	0.347814	+	1.07046i	−0.612246	+	0.790667i	$0.709734\pi$
$578$	1.75744e9	−	1.27685e9i	0.378558	−	0.275039i
$579$	−7.82342e8	−	2.40780e9i	−0.167503	−	0.515520i
$580$	6.24774e9	+	4.53925e9i	1.32961	+	0.966020i
$581$	5.95796e8	+	4.32871e8i	0.126032	+	0.0915677i
$582$	2.09842e9	−	1.52459e9i	0.441228	−	0.320571i
$583$	−8.09852e8			−0.169264
$584$	9.06857e8			0.188406
$585$	4.92046e9	−	3.57492e9i	1.01616	−	0.738280i
$586$	−2.20615e8	+	6.78982e8i	−0.0452890	+	0.139385i
$587$	2.37193e9	+	7.30006e9i	0.484027	+	1.48968i	0.833386	+	0.552692i	$0.186399\pi$
$587$	2.37193e9	+	7.30006e9i	0.484027	+	1.48968i	−0.349359	+	0.936989i	$0.613601\pi$
$588$	2.36511e9			0.479767
$589$	−5.19815e9	−	4.03297e9i	−1.04820	−	0.813245i
$590$	−1.31821e8			−0.0264241
$591$	−2.91347e8	−	8.96675e8i	−0.0580571	−	0.178681i
$592$	5.21475e8	−	1.60493e9i	0.103302	−	0.317930i
$593$	3.32666e9	−	2.41696e9i	0.655115	−	0.475969i	−0.209895	−	0.977724i	$-0.567312\pi$
$593$	3.32666e9	−	2.41696e9i	0.655115	−	0.475969i	0.865010	+	0.501755i	$0.167312\pi$
$594$	−8.21960e8			−0.160916
$595$	−8.27387e9			−1.61027
$596$	1.33768e9	−	9.71878e8i	0.258815	−	0.188040i
$597$	−6.90003e8	−	5.01317e8i	−0.132721	−	0.0964277i
$598$	1.79669e9	+	1.30537e9i	0.343573	+	0.249620i
$599$	−2.91538e9	−	8.97260e9i	−0.554244	−	1.70579i	−0.697933	−	0.716163i	$-0.745897\pi$
$599$	−2.91538e9	−	8.97260e9i	−0.554244	−	1.70579i	0.143689	−	0.989623i	$-0.454103\pi$
$600$	−2.03874e9	+	1.48123e9i	−0.385330	+	0.279958i
$601$	8.30563e7	+	2.55621e8i	0.0156067	+	0.0480326i	0.958557	−	0.284902i	$-0.0919611\pi$
$601$	8.30563e7	+	2.55621e8i	0.0156067	+	0.0480326i	−0.942950	+	0.332935i	$0.891961\pi$
$602$	1.05719e9	−	3.25369e9i	0.197499	−	0.607838i
$603$	−8.42241e8	−	6.11924e8i	−0.156432	−	0.113655i
$604$	6.84952e8	−	2.10807e9i	0.126483	−	0.389274i
$605$	2.80984e9	−	8.64780e9i	0.515867	−	1.58768i
$606$	8.16963e8	+	5.93558e8i	0.149124	+	0.108345i
$607$	−3.27639e9	+	1.00837e10i	−0.594614	+	1.83003i	−0.0379771	+	0.999279i	$0.512091\pi$
$607$	−3.27639e9	+	1.00837e10i	−0.594614	+	1.83003i	−0.556637	+	0.830756i	$0.687909\pi$
$608$	4.01641e8	+	1.23612e9i	0.0724729	+	0.223049i
$609$	8.59614e9	−	6.24546e9i	1.54221	−	1.12048i
$610$	−3.88059e9	−	1.19432e10i	−0.692218	−	2.13043i
$611$	−9.63084e9	−	6.99722e9i	−1.70813	−	1.24103i
$612$	−7.77055e8	−	5.64564e8i	−0.137032	−	0.0995595i
$613$	−6.67831e9	+	4.85208e9i	−1.17099	+	0.850778i	−0.991128	−	0.132913i	$-0.957567\pi$
$613$	−6.67831e9	+	4.85208e9i	−1.17099	+	0.850778i	−0.179867	+	0.983691i	$0.557567\pi$
$614$	1.04502e8			0.0182195
$615$	6.49521e9			1.12598
$616$	5.82154e8	−	4.22960e8i	0.100347	−	0.0729066i
$617$	5.69328e8	−	1.75221e9i	0.0975808	−	0.300323i	−0.890337	−	0.455302i	$-0.849531\pi$
$617$	5.69328e8	−	1.75221e9i	0.0975808	−	0.300323i	0.987918	+	0.154980i	$0.0495312\pi$
$618$	3.01922e8	+	9.29219e8i	0.0514558	+	0.158365i
$619$	−3.31221e9			−0.561306			−0.280653	−	0.959809i	$-0.590551\pi$
$619$	−3.31221e9			−0.561306			−0.280653	+	0.959809i	$0.590551\pi$
$620$	−1.76582e9	+	4.90316e9i	−0.297561	+	0.826238i
$621$	−2.98513e9			−0.500198
$622$	−3.49151e8	−	1.07458e9i	−0.0581764	−	0.179049i
$623$	−3.70773e9	+	1.14112e10i	−0.614327	+	1.89070i
$624$	9.73874e8	−	7.07561e8i	0.160456	−	0.116578i
$625$	7.70110e9			1.26175
$626$	1.62131e9			0.264154
$627$	−9.52666e8	+	6.92152e8i	−0.154349	+	0.112141i
$628$	−2.06244e9	−	1.49845e9i	−0.332295	−	0.241426i
$629$	3.92684e9	+	2.85301e9i	0.629166	+	0.457116i
$630$	−2.21161e9	−	6.80662e9i	−0.352384	−	1.08453i
$631$	5.59921e9	−	4.06807e9i	0.887206	−	0.644593i	−0.0479422	−	0.998850i	$-0.515266\pi$
$631$	5.59921e9	−	4.06807e9i	0.887206	−	0.644593i	0.935148	+	0.354257i	$0.115266\pi$
$632$	1.43183e8	+	4.40672e8i	0.0225622	+	0.0694393i
$633$	−3.00708e8	+	9.25485e8i	−0.0471229	+	0.145030i
$634$	5.20993e9	+	3.78524e9i	0.811932	+	0.589903i
$635$	−3.22117e9	+	9.91373e9i	−0.499235	+	1.53649i
$636$	−4.92640e8	+	1.51619e9i	−0.0759329	+	0.233698i
$637$	9.62221e9	+	6.99095e9i	1.47498	+	1.07164i
$638$	5.96971e8	−	1.83729e9i	0.0910082	−	0.280095i
$639$	−1.66716e9	−	5.13099e9i	−0.252769	−	0.777944i
$640$	8.32913e8	−	6.05147e8i	0.125594	−	0.0912495i
$641$	−2.48212e9	−	7.63919e9i	−0.372238	−	1.14563i	−0.945323	−	0.326134i	$-0.894254\pi$
$641$	−2.48212e9	−	7.63919e9i	−0.372238	−	1.14563i	0.573086	−	0.819495i	$-0.305746\pi$
$642$	−1.52927e9	−	1.11108e9i	−0.228093	−	0.165719i
$643$	9.63857e8	+	7.00283e8i	0.142980	+	0.103881i	0.656976	−	0.753912i	$-0.271835\pi$
$643$	9.63857e8	+	7.00283e8i	0.142980	+	0.103881i	−0.513996	+	0.857793i	$0.671835\pi$
$644$	2.11422e9	−	1.53607e9i	0.311925	−	0.226627i
$645$	4.43463e9			0.650727
$646$	−3.73844e9			−0.545602
$647$	−2.07906e9	+	1.51053e9i	−0.301789	+	0.219262i	−0.728365	−	0.685189i	$-0.759719\pi$
$647$	−2.07906e9	+	1.51053e9i	−0.301789	+	0.219262i	0.426577	+	0.904451i	$0.359719\pi$
$648$	−5.92264e7	+	1.82280e8i	−0.00855072	+	0.0263164i
$649$	1.01899e7	+	3.13613e7i	0.00146324	+	0.00450338i
$650$	−1.26727e10			−1.80998
$651$	5.66521e9	+	4.39533e9i	0.804790	+	0.624393i
$652$	−1.15087e9			−0.162614
$653$	7.68314e8	+	2.36463e9i	0.107980	+	0.332328i	0.990418	−	0.138100i	$-0.0440996\pi$
$653$	7.68314e8	+	2.36463e9i	0.107980	+	0.332328i	−0.882438	+	0.470428i	$0.844100\pi$
$654$	−1.17616e9	+	3.61986e9i	−0.164416	+	0.506022i
$655$	1.46898e10	−	1.06728e10i	2.04254	−	1.48399i
$656$	−1.79338e9			−0.248032
$657$	−2.25626e9			−0.310392
$658$	−1.13329e10	+	8.23385e9i	−1.55078	+	1.12671i
$659$	2.85585e9	+	2.07489e9i	0.388719	+	0.282421i	0.764930	−	0.644113i	$-0.222773\pi$
$659$	2.85585e9	+	2.07489e9i	0.388719	+	0.282421i	−0.376211	+	0.926534i	$0.622773\pi$
$660$	7.54617e8	+	5.48261e8i	0.102170	+	0.0742308i
$661$	−1.12216e9	−	3.45365e9i	−0.151129	−	0.465129i	0.846619	−	0.532200i	$-0.178635\pi$
$661$	−1.12216e9	−	3.45365e9i	−0.151129	−	0.465129i	−0.997748	+	0.0670712i	$0.978635\pi$
$662$	5.66994e9	−	4.11945e9i	0.759584	−	0.551870i
$663$	1.06995e9	+	3.29295e9i	0.142582	+	0.438822i
$664$	8.14497e7	−	2.50676e8i	0.0107970	−	0.0332296i
$665$	−2.25361e10	−	1.63734e10i	−2.97169	−	2.15906i
$666$	−1.29743e9	+	3.99308e9i	−0.170186	+	0.523779i
$667$	2.16803e9	−	6.67251e9i	0.282895	−	0.870661i
$668$	−5.83310e8	−	4.23800e8i	−0.0757150	−	0.0550102i
$669$	−2.45287e9	+	7.54915e9i	−0.316725	+	0.974780i
$670$	9.91843e8	+	3.05258e9i	0.127403	+	0.392107i
$671$	−2.54143e9	+	1.84646e9i	−0.324750	+	0.235945i
$672$	−4.37729e8	−	1.34719e9i	−0.0556433	−	0.171252i
$673$	−7.70457e9	−	5.59770e9i	−0.974307	−	0.707876i	−0.0178780	−	0.999840i	$-0.505691\pi$
$673$	−7.70457e9	−	5.59770e9i	−0.974307	−	0.707876i	−0.956429	+	0.291965i	$0.905691\pi$
$674$	5.32615e9	+	3.86967e9i	0.670045	+	0.486816i
$675$	1.37808e10	−	1.00124e10i	1.72470	−	1.25306i
$676$	2.03766e9			0.253699
$677$	1.42479e10			1.76479			0.882393	−	0.470514i	$-0.155931\pi$
$677$	1.42479e10			1.76479			0.882393	+	0.470514i	$0.155931\pi$
$678$	1.89065e9	−	1.37364e9i	0.232974	−	0.169265i
$679$	4.74309e9	−	1.45977e10i	0.581456	−	1.78954i
$680$	9.15078e8	+	2.81632e9i	0.111603	+	0.343480i
$681$	−2.92118e9			−0.354441
$682$	1.30301e9	+	4.10844e7i	0.157290	+	0.00495943i
$683$	3.40390e9			0.408794			0.204397	−	0.978888i	$-0.434477\pi$
$683$	3.40390e9			0.408794			0.204397	+	0.978888i	$0.434477\pi$
$684$	−9.99283e8	−	3.07548e9i	−0.119397	−	0.367465i
$685$	−3.82702e9	+	1.17784e10i	−0.454929	+	1.40013i
$686$	3.69781e9	−	2.68662e9i	0.437331	−	0.317740i
$687$	3.00828e8			0.0353972
$688$	−1.22444e9			−0.143343
$689$	−6.48592e9	+	4.71229e9i	−0.755447	+	0.548864i
$690$	2.74056e9	+	1.99113e9i	0.317590	+	0.230743i
$691$	−1.94117e9	−	1.41034e9i	−0.223816	−	0.162612i	0.470227	−	0.882546i	$-0.344172\pi$
$691$	−1.94117e9	−	1.41034e9i	−0.223816	−	0.162612i	−0.694043	+	0.719934i	$0.744172\pi$
$692$	−1.81211e9	−	5.57709e9i	−0.207880	−	0.639789i
$693$	−1.44840e9	+	1.05232e9i	−0.165319	+	0.120111i
$694$	−3.41670e9	−	1.05155e10i	−0.388016	−	1.19419i
$695$	2.40937e8	−	7.41526e8i	0.0272242	−	0.0837876i
$696$	−3.07660e9	−	2.23528e9i	−0.345890	−	0.251304i
$697$	1.59400e9	−	4.90582e9i	0.178309	−	0.548778i
$698$	6.21783e8	−	1.91365e9i	0.0692061	−	0.212995i
$699$	−9.04870e9	−	6.57427e9i	−1.00211	−	0.728077i
$700$	−4.60819e9	+	1.41825e10i	−0.507793	+	1.56283i
$701$	5.45948e9	+	1.68025e10i	0.598602	+	1.84231i	0.535911	+	0.844274i	$0.319968\pi$
$701$	5.45948e9	+	1.68025e10i	0.598602	+	1.84231i	0.0626909	+	0.998033i	$0.480032\pi$
$702$	−6.58289e9	+	4.78275e9i	−0.718185	+	0.521792i
$703$	5.04986e9	+	1.55419e10i	0.548196	+	1.68717i
$704$	−2.08355e8	−	1.51379e8i	−0.0225061	−	0.0163517i
$705$	−1.46903e10	−	1.06731e10i	−1.57895	−	1.14717i
$706$	−4.49131e9	+	3.26312e9i	−0.480348	+	0.348993i
$707$	5.97569e9			0.635946
$708$	6.49128e7			0.00687407
$709$	−1.02713e10	+	7.46255e9i	−1.08234	+	0.786367i	−0.978090	−	0.208183i	$-0.933245\pi$
$709$	−1.02713e10	+	7.46255e9i	−1.08234	+	0.786367i	−0.104252	+	0.994551i	$0.533245\pi$
$710$	−5.13995e9	+	1.58191e10i	−0.538958	+	1.65874i
$711$	−3.56239e8	−	1.09639e9i	−0.0371705	−	0.114399i
$712$	4.29430e9			0.445874
$713$	4.73217e9	+	1.49207e8i	0.488930	+	0.0154161i
$714$	4.07433e9			0.418902
$715$	1.44950e9	+	4.46109e9i	0.148302	+	0.456426i
$716$	2.00184e9	−	6.16104e9i	0.203814	−	0.627276i
$717$	4.61743e9	−	3.35476e9i	0.467825	−	0.339895i
$718$	−5.99133e9			−0.604071
$719$	−5.92197e9			−0.594176			−0.297088	−	0.954850i	$-0.596015\pi$
$719$	−5.92197e9			−0.594176			−0.297088	+	0.954850i	$0.596015\pi$
$720$	−2.07229e9	+	1.50560e9i	−0.206912	+	0.150331i
$721$	4.67749e9	+	3.39840e9i	0.464771	+	0.337676i
$722$	−4.39736e9	−	3.19487e9i	−0.434823	−	0.315917i
$723$	−1.45346e9	−	4.47329e9i	−0.143027	−	0.440193i
$724$	−1.75936e9	+	1.27825e9i	−0.172294	+	0.125179i
$725$	1.23714e10	+	3.80754e10i	1.20569	+	3.71075i
$726$	−1.38366e9	+	4.25847e9i	−0.134200	+	0.413024i
$727$	−6.90473e9	−	5.01658e9i	−0.666464	−	0.484214i	0.202376	−	0.979308i	$-0.435134\pi$
$727$	−6.90473e9	−	5.01658e9i	−0.666464	−	0.484214i	−0.868840	+	0.495094i	$0.835134\pi$
$728$	2.20126e9	−	6.77478e9i	0.211452	−	0.650781i
$729$	2.28312e9	−	7.02673e9i	0.218264	−	0.671749i
$730$	5.62767e9	+	4.08874e9i	0.535425	+	0.389009i
$731$	1.08831e9	−	3.34947e9i	0.103048	−	0.317151i
$732$	1.91093e9	+	5.88124e9i	0.180076	+	0.554218i
$733$	−8.29274e9	+	6.02503e9i	−0.777740	+	0.565061i	−0.904300	−	0.426898i	$-0.859606\pi$
$733$	−8.29274e9	+	6.02503e9i	−0.777740	+	0.565061i	0.126560	+	0.991959i	$0.459606\pi$
$734$	1.73213e8	+	5.33096e8i	0.0161676	+	0.0497587i
$735$	1.46771e10	+	1.06636e10i	1.36344	+	0.990595i
$736$	−7.56689e8	−	5.49767e8i	−0.0699592	−	0.0508284i
$737$	6.49566e8	−	4.71938e8i	0.0597706	−	0.0434259i
$738$	4.46192e9			0.408625
$739$	−5.83359e8			−0.0531717			−0.0265858	−	0.999647i	$-0.508464\pi$
$739$	−5.83359e8			−0.0531717			−0.0265858	+	0.999647i	$0.508464\pi$
$740$	1.04723e10	−	7.60855e9i	0.950013	−	0.690225i
$741$	−3.60225e9	+	1.10866e10i	−0.325244	+	1.00100i
$742$	2.91523e9	+	8.97217e9i	0.261975	+	0.806276i
$743$	−4.27081e9			−0.381988			−0.190994	−	0.981591i	$-0.561171\pi$
$743$	−4.27081e9			−0.381988			−0.190994	+	0.981591i	$0.561171\pi$
$744$	8.69550e8	−	2.41448e9i	0.0774087	−	0.214941i
$745$	1.26831e10			1.12377
$746$	2.98773e9	+	9.19528e9i	0.263484	+	0.810922i
$747$	−2.02647e8	+	6.23683e8i	−0.0177876	+	0.0547446i
$748$	5.99293e8	−	4.35412e8i	0.0523580	−	0.0380403i
$749$	−1.11859e10			−0.972711
$750$	−1.00585e10			−0.870596
$751$	3.46841e8	−	2.51995e8i	0.0298807	−	0.0217096i	−0.572745	−	0.819734i	$-0.694121\pi$
$751$	3.46841e8	−	2.51995e8i	0.0298807	−	0.0217096i	0.602625	+	0.798024i	$0.294121\pi$
$752$	4.05610e9	+	2.94693e9i	0.347813	+	0.252701i
$753$	−4.81878e9	−	3.50105e9i	−0.411296	−	0.298824i
$754$	−5.90964e9	−	1.81880e10i	−0.502067	−	1.54520i
$755$	1.37552e10	−	9.99376e9i	1.16320	−	0.845112i
$756$	2.95882e9	+	9.10631e9i	0.249053	+	0.766507i
$757$	5.26624e9	−	1.62078e10i	0.441230	−	1.35797i	−0.445336	−	0.895363i	$-0.646916\pi$
$757$	5.26624e9	−	1.62078e10i	0.441230	−	1.35797i	0.886566	−	0.462602i	$-0.153084\pi$
$758$	−1.33481e8	−	9.69800e7i	−0.0111321	−	0.00808798i
$759$	2.61860e8	−	8.05922e8i	0.0217382	−	0.0669032i
$760$	−3.08085e9	+	9.48188e9i	−0.254579	+	0.783514i
$761$	1.05643e10	+	7.67543e9i	0.868951	+	0.631330i	0.930305	−	0.366786i	$-0.119542\pi$
$761$	1.05643e10	+	7.67543e9i	0.868951	+	0.631330i	−0.0613541	+	0.998116i	$0.519542\pi$
$762$	1.58621e9	−	4.88185e9i	0.129873	−	0.399708i
$763$	6.96002e9	+	2.14207e10i	0.567250	+	1.74582i
$764$	−4.20201e9	+	3.05294e9i	−0.340902	+	0.247680i
$765$	−2.27671e9	−	7.00701e9i	−0.183863	−	0.565871i
$766$	−1.25195e10	−	9.09593e9i	−1.00643	−	0.731217i
$767$	2.64091e8	+	1.91874e8i	0.0211335	+	0.0153544i
$768$	−4.10154e8	+	2.97994e8i	−0.0326725	+	0.0237380i
$769$	6.37779e9			0.505741			0.252871	−	0.967500i	$-0.418625\pi$
$769$	6.37779e9			0.505741			0.252871	+	0.967500i	$0.418625\pi$
$770$	5.51966e9			0.435707
$771$	9.42901e9	−	6.85058e9i	0.740928	−	0.538316i
$772$	−1.65694e9	+	5.09954e9i	−0.129612	+	0.398906i
$773$	−3.97603e9	−	1.22370e10i	−0.309614	−	0.952895i	−0.977915	−	0.209004i	$-0.932978\pi$
$773$	−3.97603e9	−	1.22370e10i	−0.309614	−	0.952895i	0.668301	−	0.743891i	$-0.267022\pi$
$774$	3.04640e9			0.236153
$775$	−2.23465e10	+	1.51833e10i	−1.72446	+	1.17168i
$776$	−5.49346e9			−0.422017
$777$	−5.50359e9	−	1.69383e10i	−0.420894	−	1.29538i
$778$	2.83934e9	−	8.73858e9i	0.216166	−	0.665292i
$779$	1.40500e10	−	1.02079e10i	1.06486	−	0.773669i
$780$	9.23373e9			0.696701
$781$	4.16085e9			0.312538
$782$	2.17646e9	−	1.58129e9i	0.162753	−	0.118247i
$783$	2.07962e10	+	1.51093e10i	1.54817	+	1.12481i
$784$	−4.05247e9	−	2.94429e9i	−0.300340	−	0.218210i
$785$	−6.04281e9	−	1.85979e10i	−0.445857	−	1.37221i
$786$	−7.23374e9	+	5.25562e9i	−0.531354	+	0.386051i
$787$	−7.11369e9	−	2.18937e10i	−0.520216	−	1.60106i	−0.773587	−	0.633690i	$-0.781539\pi$
$787$	−7.11369e9	−	2.18937e10i	−0.520216	−	1.60106i	0.253371	−	0.967369i	$-0.418461\pi$
$788$	−6.17052e8	+	1.89909e9i	−0.0449241	+	0.138262i
$789$	−8.21339e9	−	5.96738e9i	−0.595323	−	0.432528i
$790$	−1.09831e9	+	3.38024e9i	−0.0792554	+	0.243923i
$791$	4.27345e9	−	1.31523e10i	0.307016	−	0.944899i
$792$	5.18388e8	+	3.76631e8i	0.0370781	+	0.0269388i
$793$	−9.60973e9	+	2.95757e10i	−0.684313	+	2.10610i
$794$	−2.49464e9	−	7.67773e9i	−0.176863	−	0.544328i
$795$	−9.89321e9	+	7.18784e9i	−0.698317	+	0.507357i
$796$	5.58195e8	+	1.71795e9i	0.0392275	+	0.120730i
$797$	2.75008e9	+	1.99805e9i	0.192416	+	0.139798i	0.679822	−	0.733377i	$-0.262057\pi$
$797$	2.75008e9	+	1.99805e9i	0.192416	+	0.139798i	−0.487406	+	0.873175i	$0.662057\pi$
$798$	1.10975e10	+	8.06283e9i	0.773065	+	0.561665i
$799$	−1.16666e10	+	8.47625e9i	−0.809150	+	0.587882i
$800$	5.33721e9			0.368553
$801$	−1.06842e10			−0.734563
$802$	1.88699e9	−	1.37098e9i	0.129169	−	0.0938468i
$803$	5.37723e8	−	1.65494e9i	0.0366483	−	0.112792i
$804$	−4.88417e8	−	1.50319e9i	−0.0331432	−	0.102004i
$805$	2.00459e10			1.35438
$806$	1.06746e10	−	7.25280e9i	0.718088	−	0.487903i
$807$	−6.19214e9			−0.414747
$808$	−6.60902e8	−	2.03405e9i	−0.0440755	−	0.135651i
$809$	5.15497e9	−	1.58654e10i	0.342300	−	1.05349i	−0.620714	−	0.784037i	$-0.713157\pi$
$809$	5.15497e9	−	1.58654e10i	0.342300	−	1.05349i	0.963014	−	0.269453i	$-0.0868428\pi$
$810$	−1.18939e9	+	8.64139e8i	−0.0786367	+	0.0571329i
$811$	2.63644e10			1.73558			0.867790	−	0.496931i	$-0.165540\pi$
$811$	2.63644e10			1.73558			0.867790	+	0.496931i	$0.165540\pi$
$812$	−2.25038e10			−1.47506
$813$	4.56975e9	−	3.32012e9i	0.298247	−	0.216689i
$814$	−2.61967e9	−	1.90330e9i	−0.170240	−	0.123686i
$815$	−7.14193e9	−	5.18891e9i	−0.462130	−	0.335757i
$816$	−4.50615e8	−	1.38685e9i	−0.0290329	−	0.0893541i
$817$	9.59268e9	−	6.96949e9i	0.615407	−	0.447120i
$818$	6.26733e8	+	1.92888e9i	0.0400355	+	0.123217i
$819$	−5.47673e9	+	1.68556e10i	−0.348360	+	1.07214i
$820$	−1.11291e10	−	8.08578e9i	−0.704876	−	0.512122i
$821$	−7.36371e9	+	2.26632e10i	−0.464403	+	1.42929i	0.395328	+	0.918540i	$0.370631\pi$
$821$	−7.36371e9	+	2.26632e10i	−0.464403	+	1.42929i	−0.859731	+	0.510747i	$0.829369\pi$
$822$	1.88455e9	−	5.80006e9i	0.118347	−	0.364234i
$823$	−1.72930e10	−	1.25641e10i	−1.08136	−	0.785654i	−0.103440	−	0.994636i	$-0.532985\pi$
$823$	−1.72930e10	−	1.25641e10i	−1.08136	−	0.785654i	−0.977920	+	0.208982i	$0.932985\pi$
$824$	6.39447e8	−	1.96802e9i	0.0398162	−	0.122542i
$825$	1.49425e9	+	4.59884e9i	0.0926478	+	0.285141i
$826$	3.10765e8	−	2.25784e8i	0.0191868	−	0.0139400i
$827$	−3.87506e9	−	1.19262e10i	−0.238237	−	0.733218i	−0.996676	−	0.0814733i	$-0.974037\pi$
$827$	−3.87506e9	−	1.19262e10i	−0.238237	−	0.733218i	0.758439	−	0.651744i	$-0.225963\pi$
$828$	1.88264e9	+	1.36782e9i	0.115255	+	0.0837380i
$829$	−1.75625e10	−	1.27599e10i	−1.07064	−	0.777868i	−0.0946160	−	0.995514i	$-0.530162\pi$
$829$	−1.75625e10	−	1.27599e10i	−1.07064	−	0.777868i	−0.976028	+	0.217646i	$0.930162\pi$
$830$	1.63567e9	−	1.18839e9i	0.0992941	−	0.0721414i
$831$	8.19386e9			0.495319
$832$	−2.54950e9			−0.153470
$833$	1.16561e10	−	8.46865e9i	0.698708	−	0.507641i
$834$	−1.18645e8	+	3.65152e8i	−0.00708221	+	0.0217968i
$835$	−1.70906e9	−	5.25994e9i	−0.101591	−	0.312664i
$836$	2.49398e9			0.147629
$837$	−5.87771e9	+	1.63206e10i	−0.346473	+	0.962052i
$838$	−6.28760e9			−0.369089
$839$	−1.15996e9	−	3.56999e9i	−0.0678072	−	0.208689i	0.911412	−	0.411496i	$-0.134994\pi$
$839$	−1.15996e9	−	3.56999e9i	−0.0678072	−	0.208689i	−0.979219	+	0.202807i	$0.934994\pi$
$840$	3.35766e9	−	1.03338e10i	0.195461	−	0.601566i
$841$	−3.49215e10	+	2.53720e10i	−2.02445	+	1.47085i
$842$	1.31981e10			0.761938
$843$	−1.27851e9			−0.0735037
$844$	1.66737e9	−	1.21141e9i	0.0954624	−	0.0693575i
$845$	1.26451e10	+	9.18718e9i	0.720980	+	0.523822i
$846$	−1.00916e10	−	7.33196e9i	−0.573011	−	0.416317i
$847$	8.18790e9	+	2.51998e10i	0.463000	+	1.42497i
$848$	2.73159e9	−	1.98462e9i	0.153826	−	0.111761i
$849$	−6.72533e9	−	2.06984e10i	−0.377170	−	1.16081i
$850$	−4.74385e9	+	1.46001e10i	−0.264951	+	0.815434i
$851$	−9.51390e9	−	6.91225e9i	−0.529182	−	0.384473i
$852$	2.53108e9	−	7.78987e9i	0.140206	−	0.431511i
$853$	−2.56332e8	+	7.88908e8i	−0.0141410	+	0.0435216i	−0.957878	−	0.287175i	$-0.907284\pi$
$853$	−2.56332e8	+	7.88908e8i	−0.0141410	+	0.0435216i	0.943737	+	0.330697i	$0.107284\pi$
$854$	2.96049e10	+	2.15092e10i	1.62653	+	1.18174i
$855$	7.66515e9	−	2.35909e10i	0.419410	−	1.29081i
$856$	1.23714e9	+	3.80753e9i	0.0674157	+	0.207484i
$857$	1.69824e10	−	1.23384e10i	0.921651	−	0.669619i	−0.0222836	−	0.999752i	$-0.507094\pi$
$857$	1.69824e10	−	1.23384e10i	0.921651	−	0.669619i	0.943934	+	0.330133i	$0.107094\pi$
$858$	−7.13781e8	−	2.19679e9i	−0.0385798	−	0.118736i
$859$	−2.70342e10	−	1.96415e10i	−1.45525	−	1.05730i	−0.984569	−	0.174995i	$-0.944009\pi$
$859$	−2.70342e10	−	1.96415e10i	−1.45525	−	1.05730i	−0.470679	−	0.882304i	$-0.655991\pi$
$860$	−7.59846e9	−	5.52061e9i	−0.407363	−	0.295966i
$861$	−1.53123e10	+	1.11251e10i	−0.817581	+	0.594007i
$862$	−3.84023e8			−0.0204212
$863$	8.17007e9			0.432701			0.216351	−	0.976316i	$-0.430585\pi$
$863$	8.17007e9			0.432701			0.216351	+	0.976316i	$0.430585\pi$
$864$	2.77243e9	−	2.01429e9i	0.146239	−	0.106249i
$865$	1.39000e10	−	4.27799e10i	0.730230	−	2.24742i
$866$	−4.06791e9	−	1.25197e10i	−0.212843	−	0.655063i
$867$	−8.20545e9			−0.427598
$868$	−4.23530e9	−	1.45836e10i	−0.219819	−	0.756915i
$869$	8.89091e8			0.0459597
$870$	−9.01420e9	−	2.77429e10i	−0.464098	−	1.42835i
$871$	2.45616e9	−	7.55928e9i	0.125948	−	0.387630i
$872$	6.52158e9	−	4.73821e9i	0.333077	−	0.241995i
$873$	1.36677e10			0.695259
$874$	9.05745e9			0.458898
$875$	−4.81540e10	+	3.49859e10i	−2.42999	+	1.76549i
$876$	−2.77125e9	−	2.01343e9i	−0.139287	−	0.101198i
$877$	2.06799e10	+	1.50249e10i	1.03526	+	0.752162i	0.969355	−	0.245663i	$-0.0790057\pi$
$877$	2.06799e10	+	1.50249e10i	1.03526	+	0.752162i	0.0659076	+	0.997826i	$0.479006\pi$
$878$	4.96709e9	+	1.52871e10i	0.247669	+	0.762246i
$879$	2.18167e9	−	1.58508e9i	0.108350	−	0.0787208i
$880$	−6.10466e8	−	1.87882e9i	−0.0301976	−	0.0929386i
$881$	−9.73149e9	+	2.99504e10i	−0.479472	+	1.47566i	0.360358	+	0.932814i	$0.382655\pi$
$881$	−9.73149e9	+	2.99504e10i	−0.479472	+	1.47566i	−0.839830	+	0.542850i	$0.817345\pi$
$882$	1.00825e10	+	7.32539e9i	0.494800	+	0.359493i
$883$	−4.05260e9	+	1.24726e10i	−0.198094	+	0.609670i	0.801833	+	0.597549i	$0.203859\pi$
$883$	−4.05260e9	+	1.24726e10i	−0.198094	+	0.609670i	−0.999927	+	0.0121217i	$0.996141\pi$
$884$	2.26606e9	−	6.97422e9i	0.110329	−	0.339557i
$885$	4.02829e8	+	2.92672e8i	0.0195352	+	0.0141932i
$886$	−2.52899e9	+	7.78342e9i	−0.122160	+	0.375969i
$887$	−2.46200e9	−	7.57727e9i	−0.118456	−	0.364569i	0.874196	−	0.485573i	$-0.161389\pi$
$887$	−2.46200e9	−	7.57727e9i	−0.118456	−	0.364569i	−0.992652	+	0.121003i	$0.961389\pi$
$888$	−5.15690e9	+	3.74670e9i	−0.247140	+	0.179558i
$889$	−9.38651e9	−	2.88887e10i	−0.448072	−	1.37902i
$890$	2.66491e10	+	1.93617e10i	1.26712	+	0.920615i
$891$	2.97528e8	+	2.16167e8i	0.0140915	+	0.0102380i
$892$	1.36007e10	−	9.88145e9i	0.641627	−	0.466169i
$893$	−4.85509e10			−2.28148
$894$	−6.24558e9			−0.292342
$895$	4.02011e10	−	2.92078e10i	1.87438	−	1.36181i
$896$	−9.27076e8	+	2.85325e9i	−0.0430564	+	0.132514i
$897$	−2.59225e9	−	7.97814e9i	−0.119923	−	0.369086i
$898$	1.28040e10			0.590037
$899$	−3.22119e10	−	2.49915e10i	−1.47862	−	1.14718i
$900$	−1.32790e10			−0.607178
$901$	3.00106e9	+	9.23630e9i	0.136690	+	0.420689i
$902$	−1.06339e9	+	3.27277e9i	−0.0482468	+	0.148488i
$903$	−1.04546e10	+	7.59570e9i	−0.472497	+	0.343289i
$904$	−4.94952e9			−0.222830
$905$	−1.66813e10			−0.748100
$906$	−6.77354e9	+	4.92126e9i	−0.302598	+	0.219851i
$907$	2.36023e10	+	1.71481e10i	1.05034	+	0.763116i	0.972277	−	0.233832i	$-0.0751266\pi$
$907$	2.36023e10	+	1.71481e10i	1.05034	+	0.763116i	0.0780625	+	0.996948i	$0.475127\pi$
$908$	5.00526e9	+	3.63654e9i	0.221884	+	0.161208i
$909$	1.64433e9	+	5.06071e9i	0.0726130	+	0.223480i
$910$	4.42057e10	−	3.21173e10i	1.94461	−	1.41284i
$911$	−3.95302e9	−	1.21661e10i	−0.173227	−	0.533137i	0.826321	−	0.563199i	$-0.190430\pi$
$911$	−3.95302e9	−	1.21661e10i	−0.173227	−	0.533137i	−0.999548	+	0.0300620i	$0.990430\pi$
$912$	1.51711e9	−	4.66919e9i	0.0662271	−	0.203826i
$913$	−4.09168e8	−	2.97278e8i	−0.0177932	−	0.0129275i
$914$	−6.19701e9	+	1.90724e10i	−0.268454	+	0.826217i
$915$	−1.46581e10	+	4.51129e10i	−0.632562	+	1.94683i
$916$	−5.15449e8	−	3.74495e8i	−0.0221591	−	0.0160995i
$917$	−1.63505e10	+	5.03217e10i	−0.700226	+	2.15508i
$918$	3.04593e9	+	9.37440e9i	0.129948	+	0.399939i
$919$	3.88602e9	−	2.82336e9i	0.165159	−	0.119995i	−0.502136	−	0.864789i	$-0.667452\pi$
$919$	3.88602e9	−	2.82336e9i	0.165159	−	0.119995i	0.667294	+	0.744794i	$0.267452\pi$
$920$	−2.21704e9	−	6.82336e9i	−0.0938678	−	0.288895i
$921$	−3.19347e8	−	2.32019e8i	−0.0134696	−	0.00978623i
$922$	1.42182e9	+	1.03301e9i	0.0597428	+	0.0434057i
$923$	3.33233e10	−	2.42108e10i	1.39490	−	1.01345i
$924$	−2.71807e9			−0.113347
$925$	6.71052e10			2.78779
$926$	1.27290e10	−	9.24816e9i	0.526812	−	0.382751i
$927$	−1.59094e9	+	4.89642e9i	−0.0655958	+	0.201883i
$928$	2.48889e9	+	7.66002e9i	0.102232	+	0.314638i
$929$	2.51115e10			1.02759			0.513793	−	0.857914i	$-0.328240\pi$
$929$	2.51115e10			1.02759			0.513793	+	0.857914i	$0.328240\pi$
$930$	1.62823e10	−	1.10630e10i	0.663782	−	0.451005i
$931$	4.85074e10			1.97008
$932$	7.32017e9	+	2.25292e10i	0.296187	+	0.911569i
$933$	−1.31884e9	+	4.05898e9i	−0.0531627	+	0.163618i
$934$	1.43097e10	−	1.03966e10i	0.574667	−	0.417520i
$935$	5.68216e9			0.227338
$936$	6.34316e9			0.252837
$937$	−9.47103e9	+	6.88111e9i	−0.376105	+	0.273256i	−0.759738	−	0.650230i	$-0.774673\pi$
$937$	−9.47103e9	+	6.88111e9i	−0.376105	+	0.273256i	0.383633	+	0.923486i	$0.374673\pi$
$938$	−7.56675e9	−	5.49756e9i	−0.299364	−	0.217501i
$939$	−4.95455e9	−	3.59969e9i	−0.195287	−	0.141885i
$940$	1.18841e10	+	3.65754e10i	0.466679	+	1.43629i
$941$	−1.11441e10	+	8.09665e9i	−0.435994	+	0.316768i	−0.784041	−	0.620709i	$-0.786845\pi$
$941$	−1.11441e10	+	8.09665e9i	−0.435994	+	0.316768i	0.348047	+	0.937477i	$0.386845\pi$
$942$	2.97568e9	+	9.15821e9i	0.115987	+	0.356971i
$943$	−3.86192e9	+	1.18858e10i	−0.149973	+	0.461569i
$944$	−1.11224e8	−	8.08090e7i	−0.00430325	−	0.00312649i
$945$	−2.26961e10	+	6.98513e10i	−0.874861	+	2.69255i
$946$	−7.26032e8	+	2.23450e9i	−0.0278828	+	0.0858145i
$947$	−1.24094e9	−	9.01593e8i	−0.0474815	−	0.0344973i	0.563791	−	0.825917i	$-0.309342\pi$
$947$	−1.24094e9	−	9.01593e8i	−0.0474815	−	0.0344973i	−0.611273	+	0.791420i	$0.709342\pi$
$948$	5.40843e8	−	1.66454e9i	0.0206178	−	0.0634550i
$949$	−5.32313e9	−	1.63829e10i	−0.202179	−	0.622242i
$950$	−4.18137e10	+	3.03794e10i	−1.58229	+	1.14960i
$951$	−7.51686e9	−	2.31345e10i	−0.283403	−	0.872225i
$952$	−6.98111e9	−	5.07207e9i	−0.262238	−	0.190527i
$953$	2.08785e10	+	1.51691e10i	0.781401	+	0.567721i	0.905399	−	0.424561i	$-0.139572\pi$
$953$	2.08785e10	+	1.51691e10i	0.781401	+	0.567721i	−0.123998	+	0.992282i	$0.539572\pi$
$954$	−6.79620e9	+	4.93773e9i	−0.253423	+	0.184123i
$955$	−3.98411e10			−1.48020
$956$	−1.20880e10			−0.447456
$957$	−5.90348e9	+	4.28913e9i	−0.217729	+	0.158189i
$958$	−4.24434e9	+	1.30627e10i	−0.155966	+	0.480015i
$959$	−1.11520e10	−	3.43222e10i	−0.408307	−	1.25664i
$960$	−3.88885e9			−0.141864
$961$	1.01334e10	−	2.55785e10i	0.368318	−	0.929700i
$962$	−3.20551e10			−1.16087
$963$	−3.07801e9	−	9.47314e9i	−0.111065	−	0.341823i
$964$	−3.07832e9	+	9.47409e9i	−0.110674	+	0.340618i
$965$	−3.32747e10	+	2.41755e10i	−1.19198	+	0.866023i
$966$	−9.87126e9			−0.352332
$967$	1.99279e10			0.708712			0.354356	−	0.935111i	$-0.384700\pi$
$967$	1.99279e10			0.708712			0.354356	+	0.935111i	$0.384700\pi$
$968$	7.67211e9	−	5.57412e9i	0.271864	−	0.197521i
$969$	1.14242e10	+	8.30019e9i	0.403361	+	0.293059i
$970$	−3.40907e10	−	2.47683e10i	−1.19932	−	0.871356i
$971$	−2.22924e9	−	6.86090e9i	−0.0781429	−	0.240499i	0.904352	−	0.426787i	$-0.140354\pi$
$971$	−2.22924e9	−	6.86090e9i	−0.0781429	−	0.240499i	−0.982495	+	0.186287i	$0.940354\pi$
$972$	−1.12567e10	+	8.17847e9i	−0.393169	+	0.285654i
$973$	7.02091e8	+	2.16082e9i	0.0244342	+	0.0752008i
$974$	−6.50282e8	+	2.00136e9i	−0.0225499	+	0.0694016i
$975$	3.87264e10	+	2.81364e10i	1.33811	+	0.972193i
$976$	4.04721e9	−	1.24560e10i	0.139342	−	0.428850i
$977$	9.00956e8	−	2.77286e9i	0.0309081	−	0.0951255i	−0.934412	−	0.356193i	$-0.884075\pi$
$977$	9.00956e8	−	2.77286e9i	0.0309081	−	0.0951255i	0.965321	+	0.261068i	$0.0840745\pi$
$978$	3.51692e9	+	2.55519e9i	0.120220	+	0.0873450i
$979$	2.54632e9	−	7.83675e9i	0.0867307	−	0.266930i
$980$	−1.18734e10	−	3.65426e10i	−0.402981	−	1.24025i
$981$	−1.62257e10	+	1.17887e10i	−0.548734	+	0.398678i
$982$	1.06534e10	+	3.27877e10i	0.359002	+	1.10490i
$983$	3.22079e10	+	2.34004e10i	1.08150	+	0.785754i	0.977943	−	0.208870i	$-0.0669785\pi$
$983$	3.22079e10	+	2.34004e10i	1.08150	+	0.785754i	0.103554	+	0.994624i	$0.466979\pi$
$984$	5.48035e9	+	3.98171e9i	0.183369	+	0.133225i
$985$	−1.23916e10	+	9.00306e9i	−0.413145	+	0.300167i
$986$	−2.31663e10			−0.769641
$987$	5.29132e10			1.75168
$988$	1.99737e10	−	1.45118e10i	0.658886	−	0.478708i
$989$	−2.63675e9	+	8.11507e9i	−0.0866725	+	0.266751i
$990$	1.51884e9	+	4.67451e9i	0.0497495	+	0.153113i
$991$	4.60779e10			1.50395			0.751977	−	0.659189i	$-0.229100\pi$
$991$	4.60779e10			1.50395			0.751977	+	0.659189i	$0.229100\pi$
$992$	−4.49567e9	+	3.05457e9i	−0.146219	+	0.0993480i
$993$	−2.64729e10			−0.857982
$994$	−1.49779e10	−	4.60971e10i	−0.483724	−	1.48875i
$995$	−4.28172e9	+	1.31778e10i	−0.137796	+	0.424093i
$996$	−8.05461e8	+	5.85201e8i	−0.0258307	+	0.0187671i
$997$	−2.54670e10			−0.813852			−0.406926	−	0.913461i	$-0.633399\pi$
$997$	−2.54670e10			−0.813852			−0.406926	+	0.913461i	$0.633399\pi$
$998$	−2.90668e9			−0.0925636
$999$	3.48580e10	−	2.53258e10i	1.10617	−	0.803681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.d.a.35.7	✓	40
31.8	even	5	inner	62.8.d.a.39.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.d.a.35.7	✓	40	1.1	even	1	trivial
62.8.d.a.39.7	yes	40	31.8	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.47214 + 7.60845i) q^{2} +(9.33796 - 28.7393i) q^{3} +(-51.7771 + 37.6183i) q^{4} -490.921 q^{5} +241.746 q^{6} +(1157.34 - 840.856i) q^{7} +(-414.217 - 300.946i) q^{8} +(1030.57 + 748.754i) q^{9} +(-1213.62 - 3735.15i) q^{10} +(-794.813 + 577.466i) q^{11} +(597.629 + 1839.31i) q^{12} +(-3005.37 + 9249.58i) q^{13} +(9258.71 + 6726.85i) q^{14} +(-4584.20 + 14108.7i) q^{15} +(1265.73 - 3895.53i) q^{16} +(9531.29 + 6924.89i) q^{17} +(-3149.15 + 9692.07i) q^{18} +(12257.1 + 37723.5i) q^{19} +(25418.5 - 18467.6i) q^{20} +(-13358.4 - 41113.0i) q^{21} +(-6358.50 - 4619.72i) q^{22} +(-23092.3 - 16777.5i) q^{23} +(-12516.9 + 9094.07i) q^{24} +162879. q^{25} -77804.7 q^{26} +(84607.9 - 61471.2i) q^{27} +(-28292.1 + 87074.2i) q^{28} +(75954.9 + 233765. i) q^{29} -118678. q^{30} +(-137197. + 93218.1i) q^{31} +32768.0 q^{32} +(9174.01 + 28234.7i) q^{33} +(-29125.0 + 89637.6i) q^{34} +(-568163. + 412794. i) q^{35} -81526.8 q^{36} +411994. q^{37} +(-256716. + 186515. i) q^{38} +(237762. + 172744. i) q^{39} +(203348. + 147741. i) q^{40} +(-135299. - 416407. i) q^{41} +(279782. - 203274. i) q^{42} +(-92375.9 - 284304. i) q^{43} +(19429.9 - 59799.0i) q^{44} +(-505929. - 367579. i) q^{45} +(70563.8 - 217173. i) q^{46} +(-378245. + 1.16412e6i) q^{47} +(-100135. - 72752.6i) q^{48} +(377906. - 1.16308e6i) q^{49} +(402659. + 1.23926e6i) q^{50} +(288019. - 209258. i) q^{51} +(-192344. - 591973. i) q^{52} +(666892. + 484526. i) q^{53} +(676863. + 491770. i) q^{54} +(390191. - 283490. i) q^{55} -732442. q^{56} +1.19860e6 q^{57} +(-1.59082e6 + 1.15580e6i) q^{58} +(10372.0 - 31921.8i) q^{59} +(-293389. - 902959. i) q^{60} +3.19752e6 q^{61} +(-1.04841e6 - 813409. i) q^{62} +1.82231e6 q^{63} +(81007.0 + 249314. i) q^{64} +(1.47540e6 - 4.54082e6i) q^{65} +(-192143. + 139600. i) q^{66} -817257. q^{67} -754004. q^{68} +(-697810. + 506989. i) q^{69} +(-4.54530e6 - 3.30235e6i) q^{70} +(-3.42635e6 - 2.48939e6i) q^{71} +(-201545. - 620293. i) q^{72} +(-1.43294e6 + 1.04109e6i) q^{73} +(1.01851e6 + 3.13464e6i) q^{74} +(1.52096e6 - 4.68102e6i) q^{75} +(-2.05373e6 - 1.49212e6i) q^{76} +(-434303. + 1.33665e6i) q^{77} +(-726537. + 2.23605e6i) q^{78} +(-732144. - 531934. i) q^{79} +(-621376. + 1.91240e6i) q^{80} +(-115677. - 356016. i) q^{81} +(2.83373e6 - 2.05883e6i) q^{82} +(159081. + 489602. i) q^{83} +(2.23826e6 + 1.62619e6i) q^{84} +(-4.67911e6 - 3.39957e6i) q^{85} +(1.93475e6 - 1.40567e6i) q^{86} +7.42751e6 q^{87} +503011. q^{88} +(-6.78547e6 + 4.92993e6i) q^{89} +(1.54598e6 - 4.75805e6i) q^{90} +(4.29933e6 + 1.32320e7i) q^{91} +1.82679e6 q^{92} +(1.39788e6 + 4.81341e6i) q^{93} -9.79222e6 q^{94} +(-6.01728e6 - 1.85193e7i) q^{95} +(305986. - 941729. i) q^{96} +(8.68028e6 - 6.30659e6i) q^{97} +9.78344e6 q^{98} -1.25149e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) \) 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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