LMFDB - Embedded newform 25.8.d.a.11.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,8,Mod(6,25)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("25.6"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.80962563710$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	25.11
Dual form			25.8.d.a.16.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-13.0050 + 9.44866i) q^{2} +(-6.54660 + 20.1484i) q^{3} +(40.2978 - 124.024i) q^{4} +(-242.876 + 138.334i) q^{5} +(-105.237 - 323.885i) q^{6} -1230.51 q^{7} +(11.9539 + 36.7902i) q^{8} +(1406.22 + 1021.68i) q^{9} +(1851.52 - 4093.89i) q^{10} +(2542.35 - 1847.12i) q^{11} +(2235.06 + 1623.87i) q^{12} +(5800.16 + 4214.06i) q^{13} +(16002.8 - 11626.7i) q^{14} +(-1197.20 - 5799.16i) q^{15} +(13001.1 + 9445.82i) q^{16} +(-11453.8 - 35251.0i) q^{17} -27941.4 q^{18} +(3902.51 + 12010.7i) q^{19} +(7369.42 + 35697.0i) q^{20} +(8055.68 - 24792.8i) q^{21} +(-15610.3 + 48043.6i) q^{22} +(-33120.1 + 24063.2i) q^{23} -819.520 q^{24} +(39852.2 - 67196.1i) q^{25} -115248. q^{26} +(-67274.6 + 48877.9i) q^{27} +(-49587.0 + 152613. i) q^{28} +(13326.9 - 41016.1i) q^{29} +(70363.9 + 64106.0i) q^{30} +(-79645.5 - 245124. i) q^{31} -263280. q^{32} +(20572.8 + 63316.5i) q^{33} +(482031. + 350216. i) q^{34} +(298862. - 170222. i) q^{35} +(183380. - 133234. i) q^{36} +(209750. + 152392. i) q^{37} +(-164237. - 119325. i) q^{38} +(-122878. + 89275.9i) q^{39} +(-7992.66 - 7281.82i) q^{40} +(-591854. - 430007. i) q^{41} +(129495. + 398545. i) q^{42} -212030. q^{43} +(-126636. - 389747. i) q^{44} +(-482871. - 53612.3i) q^{45} +(203361. - 625882. i) q^{46} +(185930. - 572233. i) q^{47} +(-275430. + 200112. i) q^{48} +690622. q^{49} +(116637. + 1.25043e6i) q^{50} +785233. q^{51} +(756378. - 549541. i) q^{52} +(-48694.8 + 149867. i) q^{53} +(413074. - 1.27131e6i) q^{54} +(-361953. + 800315. i) q^{55} +(-14709.4 - 45270.9i) q^{56} -267544. q^{57} +(214231. + 659335. i) q^{58} +(81162.7 + 58968.1i) q^{59} +(-767479. - 85212.0i) q^{60} +(-1.24866e6 + 907208. i) q^{61} +(3.35188e6 + 2.43528e6i) q^{62} +(-1.73038e6 - 1.25719e6i) q^{63} +(1.75982e6 - 1.27858e6i) q^{64} +(-1.99167e6 - 221131. i) q^{65} +(-865804. - 629044. i) q^{66} +(350151. + 1.07765e6i) q^{67} -4.83353e6 q^{68} +(-268009. - 824848. i) q^{69} +(-2.27832e6 + 5.03758e6i) q^{70} +(-22160.3 + 68202.3i) q^{71} +(-20778.1 + 63948.3i) q^{72} +(3.00881e6 - 2.18603e6i) q^{73} -4.16769e6 q^{74} +(1.09300e6 + 1.24286e6i) q^{75} +1.64688e6 q^{76} +(-3.12839e6 + 2.27291e6i) q^{77} +(754483. - 2.32206e6i) q^{78} +(925115. - 2.84721e6i) q^{79} +(-4.46432e6 - 495666. i) q^{80} +(630313. + 1.93990e6i) q^{81} +1.17600e7 q^{82} +(-2.20623e6 - 6.79009e6i) q^{83} +(-2.75028e6 - 1.99819e6i) q^{84} +(7.65827e6 + 6.97717e6i) q^{85} +(2.75745e6 - 2.00340e6i) q^{86} +(739161. + 537032. i) q^{87} +(98347.0 + 71453.3i) q^{88} +(6.12412e6 - 4.44943e6i) q^{89} +(6.78628e6 - 3.86526e6i) q^{90} +(-7.13718e6 - 5.18546e6i) q^{91} +(1.64974e6 + 5.07738e6i) q^{92} +5.46025e6 q^{93} +(2.98883e6 + 9.19866e6i) q^{94} +(-2.60932e6 - 2.37725e6i) q^{95} +(1.72359e6 - 5.30466e6i) q^{96} +(4.53364e6 - 1.39531e7i) q^{97} +(-8.98152e6 + 6.52546e6i) q^{98} +5.46227e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16}+ \cdots + 71266232 q^{99}+O(q^{100}) $ 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−13.0050	+	9.44866i	−1.14949	+	0.835152i	−0.988413	−	0.151790i	$-0.951496\pi$
$2$	−13.0050	+	9.44866i	−1.14949	+	0.835152i	−0.161075	+	0.986942i	$0.551496\pi$
$3$	−6.54660	+	20.1484i	−0.139988	+	0.430839i	−0.996333	−	0.0855660i	$-0.972730\pi$
$3$	−6.54660	+	20.1484i	−0.139988	+	0.430839i	0.856344	+	0.516405i	$0.172730\pi$
$4$	40.2978	−	124.024i	0.314827	−	0.968937i
$5$	−242.876	+	138.334i	−0.868938	+	0.494920i
$5$	−242.876	+	138.334i	−0.868938	+	0.494920i
$6$	−105.237	−	323.885i	−0.198901	−	0.612156i
$7$	−1230.51			−1.35595			−0.677975	−	0.735085i	$-0.737142\pi$
$7$	−1230.51			−1.35595			−0.677975	+	0.735085i	$0.737142\pi$
$8$	11.9539	+	36.7902i	0.00825456	+	0.0254049i
$9$	1406.22	+	1021.68i	0.642991	+	0.467161i
$10$	1851.52	−	4093.89i	0.585500	−	1.29460i
$11$	2542.35	−	1847.12i	0.575918	−	0.418429i	−0.261332	−	0.965249i	$-0.584162\pi$
$11$	2542.35	−	1847.12i	0.575918	−	0.418429i	0.837250	+	0.546820i	$0.184162\pi$
$12$	2235.06	+	1623.87i	0.373384	+	0.271279i
$13$	5800.16	+	4214.06i	0.732214	+	0.531985i	0.890263	−	0.455446i	$-0.150520\pi$
$13$	5800.16	+	4214.06i	0.732214	+	0.531985i	−0.158049	+	0.987431i	$0.550520\pi$
$14$	16002.8	−	11626.7i	1.55865	−	1.13242i
$15$	−1197.20	−	5799.16i	−0.0915900	−	0.443656i
$16$	13001.1	+	9445.82i	0.793521	+	0.576527i
$17$	−11453.8	−	35251.0i	−0.565427	−	1.74021i	−0.666679	−	0.745345i	$-0.732285\pi$
$17$	−11453.8	−	35251.0i	−0.565427	−	1.74021i	0.101252	−	0.994861i	$-0.467715\pi$
$18$	−27941.4			−1.12926
$19$	3902.51	+	12010.7i	0.130529	+	0.401726i	0.994868	−	0.101183i	$-0.0322628\pi$
$19$	3902.51	+	12010.7i	0.130529	+	0.401726i	−0.864339	+	0.502910i	$0.832263\pi$
$20$	7369.42	+	35697.0i	0.205981	+	0.997760i
$21$	8055.68	−	24792.8i	0.189817	−	0.584196i
$22$	−15610.3	+	48043.6i	−0.312559	+	0.961957i
$23$	−33120.1	+	24063.2i	−0.567603	+	0.412388i	−0.834234	−	0.551411i	$-0.814090\pi$
$23$	−33120.1	+	24063.2i	−0.567603	+	0.412388i	0.266631	+	0.963799i	$0.414090\pi$
$24$	−819.520			−0.0121010
$25$	39852.2	−	67196.1i	0.510108	−	0.860110i
$26$	−115248.			−1.28596
$27$	−67274.6	+	48877.9i	−0.657776	+	0.477902i
$28$	−49587.0	+	152613.i	−0.426889	+	1.31383i
$29$	13326.9	−	41016.1i	0.101470	−	0.312293i	−0.887416	−	0.460970i	$-0.847502\pi$
$29$	13326.9	−	41016.1i	0.101470	−	0.312293i	0.988886	+	0.148677i	$0.0475016\pi$
$30$	70363.9	+	64106.0i	0.475801	+	0.433485i
$31$	−79645.5	−	245124.i	−0.480171	−	1.47781i	−0.838855	−	0.544354i	$-0.816775\pi$
$31$	−79645.5	−	245124.i	−0.480171	−	1.47781i	0.358685	−	0.933459i	$-0.383225\pi$
$32$	−263280.			−1.42034
$33$	20572.8	+	63316.5i	0.0996538	+	0.306703i
$34$	482031.	+	350216.i	2.10329	+	1.52813i
$35$	298862.	−	170222.i	1.17824	−	0.671087i
$36$	183380.	−	133234.i	0.655080	−	0.475943i
$37$	209750.	+	152392.i	0.680763	+	0.494603i	0.873611	−	0.486626i	$-0.161772\pi$
$37$	209750.	+	152392.i	0.680763	+	0.494603i	−0.192848	+	0.981229i	$0.561772\pi$
$38$	−164237.	−	119325.i	−0.485544	−	0.352768i
$39$	−122878.	+	89275.9i	−0.331701	+	0.240995i
$40$	−7992.66	−	7281.82i	−0.0197461	−	0.0179900i
$41$	−591854.	−	430007.i	−1.34113	−	0.974388i	−0.999402	−	0.0345899i	$-0.988987\pi$
$41$	−591854.	−	430007.i	−1.34113	−	0.974388i	−0.341729	−	0.939799i	$-0.611013\pi$
$42$	129495.	+	398545.i	0.269700	+	0.830052i
$43$	−212030.			−0.406685			−0.203343	−	0.979108i	$-0.565181\pi$
$43$	−212030.			−0.406685			−0.203343	+	0.979108i	$0.565181\pi$
$44$	−126636.	−	389747.i	−0.224117	−	0.689760i
$45$	−482871.	−	53612.3i	−0.789927	−	0.0877043i
$46$	203361.	−	625882.i	0.308046	−	0.948069i
$47$	185930.	−	572233.i	0.261220	−	0.803953i	−0.731320	−	0.682034i	$-0.761095\pi$
$47$	185930.	−	572233.i	0.261220	−	0.803953i	0.992540	−	0.121918i	$-0.0389046\pi$
$48$	−275430.	+	200112.i	−0.359474	+	0.261173i
$49$	690622.			0.838599
$50$	116637.	+	1.25043e6i	0.131960	+	1.41470i
$51$	785233.			0.828902
$52$	756378.	−	549541.i	0.745980	−	0.541986i
$53$	−48694.8	+	149867.i	−0.0449280	+	0.138274i	−0.971004	−	0.239062i	$-0.923160\pi$
$53$	−48694.8	+	149867.i	−0.0449280	+	0.138274i	0.926076	+	0.377337i	$0.123160\pi$
$54$	413074.	−	1.27131e6i	0.356984	−	1.09869i
$55$	−361953.	+	800315.i	−0.293348	+	0.648622i
$56$	−14709.4	−	45270.9i	−0.0111928	−	0.0344478i
$57$	−267544.			−0.191352
$58$	214231.	+	659335.i	0.144173	+	0.443719i
$59$	81162.7	+	58968.1i	0.0514487	+	0.0373797i	0.613212	−	0.789918i	$-0.289877\pi$
$59$	81162.7	+	58968.1i	0.0514487	+	0.0373797i	−0.561764	+	0.827298i	$0.689877\pi$
$60$	−767479.	−	85212.0i	−0.458709	−	0.0509297i
$61$	−1.24866e6	+	907208.i	−0.704355	+	0.511744i	−0.881348	−	0.472469i	$-0.843363\pi$
$61$	−1.24866e6	+	907208.i	−0.704355	+	0.511744i	0.176993	+	0.984212i	$0.443363\pi$
$62$	3.35188e6	+	2.43528e6i	1.78615	+	1.29771i
$63$	−1.73038e6	−	1.25719e6i	−0.871864	−	0.633446i
$64$	1.75982e6	−	1.27858e6i	0.839145	−	0.609675i
$65$	−1.99167e6	−	221131.i	−0.899539	−	0.0998743i
$66$	−865804.	−	629044.i	−0.370694	−	0.269325i
$67$	350151.	+	1.07765e6i	0.142231	+	0.437741i	0.996644	−	0.0818520i	$-0.0260835\pi$
$67$	350151.	+	1.07765e6i	0.142231	+	0.437741i	−0.854414	+	0.519593i	$0.826083\pi$
$68$	−4.83353e6			−1.86416
$69$	−268009.	−	824848.i	−0.0982151	−	0.302275i
$70$	−2.27832e6	+	5.03758e6i	−0.793909	+	1.75541i
$71$	−22160.3	+	68202.3i	−0.00734803	+	0.0226149i	−0.954663	−	0.297688i	$-0.903785\pi$
$71$	−22160.3	+	68202.3i	−0.00734803	+	0.0226149i	0.947315	+	0.320303i	$0.103785\pi$
$72$	−20778.1	+	63948.3i	−0.00656056	+	0.0201913i
$73$	3.00881e6	−	2.18603e6i	0.905241	−	0.657696i	−0.0345655	−	0.999402i	$-0.511005\pi$
$73$	3.00881e6	−	2.18603e6i	0.905241	−	0.657696i	0.939807	+	0.341706i	$0.111005\pi$
$74$	−4.16769e6			−1.19560
$75$	1.09300e6	+	1.24286e6i	0.299160	+	0.340180i
$76$	1.64688e6			0.430341
$77$	−3.12839e6	+	2.27291e6i	−0.780915	+	0.567368i
$78$	754483.	−	2.32206e6i	0.180019	−	0.554042i
$79$	925115.	−	2.84721e6i	0.211106	−	0.649718i	−0.788301	−	0.615290i	$-0.789039\pi$
$79$	925115.	−	2.84721e6i	0.211106	−	0.649718i	0.999407	−	0.0344283i	$-0.0109610\pi$
$80$	−4.46432e6	−	495666.i	−0.974856	−	0.108237i
$81$	630313.	+	1.93990e6i	0.131783	+	0.405585i
$82$	1.17600e7			2.35538
$83$	−2.20623e6	−	6.79009e6i	−0.423524	−	1.30347i	−0.904400	−	0.426685i	$-0.859681\pi$
$83$	−2.20623e6	−	6.79009e6i	−0.423524	−	1.30347i	0.480876	−	0.876789i	$-0.340319\pi$
$84$	−2.75028e6	−	1.99819e6i	−0.506290	−	0.367841i
$85$	7.65827e6	+	6.97717e6i	1.35258	+	1.23229i
$86$	2.75745e6	−	2.00340e6i	0.467480	−	0.339644i
$87$	739161.	+	537032.i	0.120343	+	0.0874345i
$88$	98347.0	+	71453.3i	0.0153841	+	0.0111772i
$89$	6.12412e6	−	4.44943e6i	0.920828	−	0.669021i	−0.0229018	−	0.999738i	$-0.507291\pi$
$89$	6.12412e6	−	4.44943e6i	0.920828	−	0.669021i	0.943730	+	0.330717i	$0.107291\pi$
$90$	6.78628e6	−	3.86526e6i	0.981258	−	0.558894i
$91$	−7.13718e6	−	5.18546e6i	−0.992846	−	0.721345i
$92$	1.64974e6	+	5.07738e6i	0.220881	+	0.679802i
$93$	5.46025e6			0.703918
$94$	2.98883e6	+	9.19866e6i	0.371153	+	1.14229i
$95$	−2.60932e6	−	2.37725e6i	−0.312244	−	0.284474i
$96$	1.72359e6	−	5.30466e6i	0.198831	−	0.611939i
$97$	4.53364e6	−	1.39531e7i	0.504366	−	1.55228i	−0.297469	−	0.954732i	$-0.596142\pi$
$97$	4.53364e6	−	1.39531e7i	0.504366	−	1.55228i	0.801834	−	0.597546i	$-0.203858\pi$
$98$	−8.98152e6	+	6.52546e6i	−0.963959	+	0.700357i
$99$	5.46227e6			0.565783
$100$	−6.72797e6	−	7.65048e6i	−0.672797	−	0.765048i
$101$	−1.04111e6			−0.100547			−0.0502736	−	0.998735i	$-0.516009\pi$
$101$	−1.04111e6			−0.100547			−0.0502736	+	0.998735i	$0.516009\pi$
$102$	−1.02119e7	+	7.41940e6i	−0.952812	+	0.692259i
$103$	−5.56978e6	+	1.71420e7i	−0.502236	+	1.54572i	0.303133	+	0.952948i	$0.401967\pi$
$103$	−5.56978e6	+	1.71420e7i	−0.502236	+	1.54572i	−0.805368	+	0.592775i	$0.798033\pi$
$104$	−85702.0	+	263764.i	−0.00747092	+	0.0229931i
$105$	1.47317e6	+	7.13595e6i	0.124191	+	0.601575i
$106$	−782771.	−	2.40912e6i	−0.0638358	−	0.196466i
$107$	−2.32022e7			−1.83099			−0.915497	−	0.402325i	$-0.868202\pi$
$107$	−2.32022e7			−1.83099			−0.915497	+	0.402325i	$0.868202\pi$
$108$	3.35100e6	+	1.03133e7i	0.255972	+	0.787799i
$109$	−720383.	−	523389.i	−0.0532808	−	0.0387108i	0.560826	−	0.827934i	$-0.310484\pi$
$109$	−720383.	−	523389.i	−0.0532808	−	0.0387108i	−0.614107	+	0.789223i	$0.710484\pi$
$110$	−2.85472e6	−	1.38281e7i	−0.204498	−	0.990573i
$111$	−4.44360e6	+	3.22847e6i	−0.308393	+	0.224061i
$112$	−1.59980e7	−	1.16232e7i	−1.07597	−	0.781741i
$113$	8.87013e6	+	6.44452e6i	0.578303	+	0.420161i	0.838112	−	0.545499i	$-0.183660\pi$
$113$	8.87013e6	+	6.44452e6i	0.578303	+	0.420161i	−0.259809	+	0.965660i	$0.583660\pi$
$114$	3.47940e6	−	2.52793e6i	0.219957	−	0.159808i
$115$	4.71531e6	−	1.04260e7i	0.289113	−	0.639258i
$116$	−4.54993e6	−	3.30572e6i	−0.270646	−	0.196636i
$117$	3.85089e6	+	1.18518e7i	0.222285	+	0.684123i
$118$	−1.61269e6			−0.0903573
$119$	1.40940e7	+	4.33769e7i	0.766691	+	2.35963i
$120$	199041.	−	113368.i	0.0105150	−	0.00598902i
$121$	−2.97020e6	+	9.14135e6i	−0.152418	+	0.469096i
$122$	7.66694e6	−	2.35964e7i	0.382263	−	1.17649i
$123$	1.25386e7	−	9.10980e6i	0.607547	−	0.441409i
$124$	−3.36107e7			−1.58308
$125$	−383585.	+	2.18332e7i	−0.0175662	+	0.999846i
$126$	3.43823e7			1.53122
$127$	−1.26352e7	+	9.18001e6i	−0.547355	+	0.397677i	−0.826809	−	0.562482i	$-0.809846\pi$
$127$	−1.26352e7	+	9.18001e6i	−0.547355	+	0.397677i	0.279454	+	0.960159i	$0.409846\pi$
$128$	−391635.	+	1.20533e6i	−0.0165062	+	0.0508008i
$129$	1.38808e6	−	4.27206e6i	0.0569311	−	0.175216i
$130$	2.79910e7	−	1.59428e7i	1.11742	−	0.636447i
$131$	763220.	+	2.34895e6i	0.0296620	+	0.0912902i	0.964792	−	0.263016i	$-0.0847171\pi$
$131$	763220.	+	2.34895e6i	0.0296620	+	0.0912902i	−0.935130	+	0.354306i	$0.884717\pi$
$132$	8.68179e6			0.328549
$133$	−4.80209e6	−	1.47793e7i	−0.176990	−	0.544721i
$134$	−1.47361e7	−	1.07064e7i	−0.529073	−	0.384394i
$135$	9.57787e6	−	2.11776e7i	0.335043	−	0.740814i
$136$	1.15998e6	−	842773.i	0.0395424	−	0.0287293i
$137$	−2.34741e7	−	1.70549e7i	−0.779951	−	0.566667i	0.125014	−	0.992155i	$-0.460103\pi$
$137$	−2.34741e7	−	1.70549e7i	−0.779951	−	0.566667i	−0.904964	+	0.425488i	$0.860103\pi$
$138$	1.12792e7	+	8.19479e6i	0.365342	+	0.265437i
$139$	1.13060e7	−	8.21432e6i	0.357074	−	0.259430i	−0.394756	−	0.918786i	$-0.629171\pi$
$139$	1.13060e7	−	8.21432e6i	0.357074	−	0.259430i	0.751831	+	0.659356i	$0.229171\pi$
$140$	−9.06817e6	−	4.39256e7i	−0.279300	−	1.35291i
$141$	1.03123e7	+	7.49236e6i	0.309807	+	0.225088i
$142$	−356227.	−	1.09635e6i	−0.0104404	−	0.0321323i
$143$	2.25299e7			0.644293
$144$	8.63176e6	+	2.65658e7i	0.240897	+	0.741404i
$145$	2.43715e6	+	1.18054e7i	0.0663888	+	0.321583i
$146$	−1.84744e7	+	5.68584e7i	−0.491288	+	1.51203i
$147$	−4.52123e6	+	1.39149e7i	−0.117394	+	0.361301i
$148$	2.73527e7	−	1.98729e7i	0.693561	−	0.503902i
$149$	−6.89760e7			−1.70823			−0.854115	−	0.520085i	$-0.825900\pi$
$149$	−6.89760e7			−1.70823			−0.854115	+	0.520085i	$0.825900\pi$
$150$	−2.59577e7	−	5.83603e6i	−0.627983	−	0.141188i
$151$	−7.02491e7			−1.66043			−0.830216	−	0.557441i	$-0.811783\pi$
$151$	−7.02491e7			−1.66043			−0.830216	+	0.557441i	$0.811783\pi$
$152$	−395226.	+	287149.i	−0.00912837	+	0.00663215i
$153$	1.99088e7	−	6.12728e7i	0.449391	−	1.38308i
$154$	1.92087e7	−	5.91183e7i	0.423814	−	1.30437i
$155$	5.32530e7	+	4.85169e7i	1.14864	+	1.04648i
$156$	6.12064e6	+	1.88374e7i	0.129081	+	0.397269i
$157$	5.91649e7			1.22016			0.610078	−	0.792341i	$-0.291138\pi$
$157$	5.91649e7			1.22016			0.610078	+	0.792341i	$0.291138\pi$
$158$	1.48713e7	+	4.57690e7i	0.299949	+	0.923149i
$159$	−2.70079e6	−	1.96224e6i	−0.0532846	−	0.0387135i
$160$	6.39443e7	−	3.64207e7i	1.23419	−	0.702956i
$161$	4.07548e7	−	2.96101e7i	0.769641	−	0.559177i
$162$	−2.65267e7	−	1.92728e7i	−0.490208	−	0.356157i
$163$	−4.25442e7	−	3.09102e7i	−0.769456	−	0.559043i	0.132340	−	0.991204i	$-0.457751\pi$
$163$	−4.25442e7	−	3.09102e7i	−0.769456	−	0.559043i	−0.901796	+	0.432162i	$0.857751\pi$
$164$	−7.71816e7	+	5.60757e7i	−1.36634	+	0.992707i
$165$	−1.37555e7	−	1.25321e7i	−0.238387	−	0.217185i
$166$	9.28493e7	+	6.74589e7i	1.57543	+	1.14462i
$167$	−6.44700e6	−	1.98418e7i	−0.107115	−	0.329666i	0.883106	−	0.469173i	$-0.155448\pi$
$167$	−6.44700e6	−	1.98418e7i	−0.107115	−	0.329666i	−0.990221	+	0.139508i	$0.955448\pi$
$168$	1.00843e6			0.0164083
$169$	−3.50683e6	−	1.07929e7i	−0.0558871	−	0.172003i
$170$	−1.65520e8	−	1.83775e7i	−2.58393	−	0.286889i
$171$	−6.78329e6	+	2.08768e7i	−0.103742	+	0.319284i
$172$	−8.54436e6	+	2.62968e7i	−0.128035	+	0.394052i
$173$	9.41412e7	−	6.83976e7i	1.38235	−	1.00434i	0.385695	−	0.922627i	$-0.373962\pi$
$173$	9.41412e7	−	6.83976e7i	1.38235	−	1.00434i	0.996656	−	0.0817100i	$-0.0260381\pi$
$174$	−1.46870e7			−0.211354
$175$	−4.90387e7	+	8.26858e7i	−0.691680	+	1.16627i
$176$	5.05008e7			0.698238
$177$	−1.71945e6	+	1.24925e6i	−0.0233068	+	0.0169334i
$178$	−3.76028e7	+	1.15729e8i	−0.499747	+	1.53806i
$179$	2.19447e7	−	6.75389e7i	0.285986	−	0.880173i	−0.700116	−	0.714029i	$-0.746868\pi$
$179$	2.19447e7	−	6.75389e7i	0.285986	−	0.880173i	0.986102	−	0.166144i	$-0.0531316\pi$
$180$	−2.61078e7	+	5.77270e7i	−0.333670	+	0.737778i
$181$	2.50017e7	+	7.69473e7i	0.313397	+	0.964536i	0.976409	+	0.215928i	$0.0692776\pi$
$181$	2.50017e7	+	7.69473e7i	0.313397	+	0.964536i	−0.663012	+	0.748608i	$0.730722\pi$
$182$	1.41814e8			1.74370
$183$	−1.01042e7	−	3.10977e7i	−0.121878	−	0.375102i
$184$	−1.28120e6	−	930849.i	−0.0151620	−	0.0110158i
$185$	−7.20243e7	−	7.99673e6i	−0.836330	−	0.0928563i
$186$	−7.10103e7	+	5.15920e7i	−0.809145	+	0.587878i
$187$	−9.42324e7	−	6.84639e7i	−1.05379	−	0.765624i
$188$	−6.34780e7	−	4.61195e7i	−0.696740	−	0.506211i
$189$	8.27823e7	−	6.01449e7i	0.891911	−	0.648011i
$190$	5.63959e7	+	6.26155e6i	0.596500	+	0.0662284i
$191$	−1.00564e8	−	7.30637e7i	−1.04430	−	0.758726i	−0.0731767	−	0.997319i	$-0.523314\pi$
$191$	−1.00564e8	−	7.30637e7i	−1.04430	−	0.758726i	−0.971120	+	0.238593i	$0.923314\pi$
$192$	1.42405e7	+	4.38277e7i	0.145201	+	0.446884i
$193$	−2.67089e7			−0.267427			−0.133714	−	0.991020i	$-0.542690\pi$
$193$	−2.67089e7			−0.267427			−0.133714	+	0.991020i	$0.542690\pi$
$194$	7.28783e7	+	2.24296e8i	0.716625	+	2.20555i
$195$	1.74941e7	−	3.86812e7i	0.168955	−	0.373575i
$196$	2.78306e7	−	8.56537e7i	0.264013	−	0.812549i
$197$	6.93389e6	−	2.13403e7i	0.0646168	−	0.198870i	−0.913536	−	0.406758i	$-0.866659\pi$
$197$	6.93389e6	−	2.13403e7i	0.0646168	−	0.198870i	0.978153	+	0.207888i	$0.0666591\pi$
$198$	−7.10367e7	+	5.16112e7i	−0.650361	+	0.472515i
$199$	−1.80136e8			−1.62037			−0.810185	−	0.586175i	$-0.800633\pi$
$199$	−1.80136e8			−1.62037			−0.810185	+	0.586175i	$0.800633\pi$
$200$	2.94855e6	+	662917.i	0.0260617	+	0.00585941i
$201$	−2.40053e7			−0.208507
$202$	1.35396e7	−	9.83706e6i	0.115578	−	0.0839722i
$203$	−1.63990e7	+	5.04709e7i	−0.137588	+	0.423453i
$204$	3.16432e7	−	9.73877e7i	0.260960	−	0.803153i
$205$	2.03232e8	+	2.25645e7i	1.64760	+	0.182931i
$206$	−8.95343e7	−	2.75558e8i	−0.713599	−	2.19623i
$207$	−7.11591e7			−0.557615
$208$	3.56029e7	+	1.09574e8i	0.274324	+	0.844283i
$209$	3.21068e7	+	2.33269e7i	0.243268	+	0.176744i
$210$	−8.65838e7	−	7.88833e7i	−0.645163	−	0.587784i
$211$	6.24284e7	−	4.53569e7i	0.457502	−	0.332395i	−0.335048	−	0.942201i	$-0.608753\pi$
$211$	6.24284e7	−	4.53569e7i	0.457502	−	0.332395i	0.792551	+	0.609806i	$0.208753\pi$
$212$	1.66248e7	+	1.20786e7i	0.119834	+	0.0870648i
$213$	−1.22909e6	−	892986.i	−0.00871475	−	0.00633164i
$214$	3.01745e8	−	2.19230e8i	2.10470	−	1.52916i
$215$	5.14970e7	−	2.93311e7i	0.353384	−	0.201277i
$216$	−2.60242e6	−	1.89077e6i	−0.0175707	−	0.0127659i
$217$	9.80050e7	+	3.01628e8i	0.651087	+	2.00384i
$218$	1.43139e7			0.0935750
$219$	2.43474e7	+	7.49335e7i	0.156638	+	0.482083i
$220$	8.46723e7	+	7.71418e7i	0.536120	+	0.488439i
$221$	8.21164e7	−	2.52728e8i	0.511749	−	1.57500i
$222$	2.72842e7	−	8.39722e7i	0.167369	−	0.515110i
$223$	3.37871e7	−	2.45478e7i	0.204025	−	0.148233i	−0.481081	−	0.876676i	$-0.659756\pi$
$223$	3.37871e7	−	2.45478e7i	0.204025	−	0.148233i	0.685106	+	0.728443i	$0.259756\pi$
$224$	3.23970e8			1.92591
$225$	1.24694e8	−	5.37765e7i	0.729805	−	0.314741i
$226$	−1.76248e8			−1.01565
$227$	−9.03578e7	+	6.56488e7i	−0.512714	+	0.372508i	−0.813852	−	0.581072i	$-0.802633\pi$
$227$	−9.03578e7	+	6.56488e7i	−0.512714	+	0.372508i	0.301138	+	0.953580i	$0.402633\pi$
$228$	−1.07814e7	+	3.31818e7i	−0.0602427	+	0.185408i
$229$	−2.88867e7	+	8.89040e7i	−0.158955	+	0.489212i	−0.998540	−	0.0540156i	$-0.982798\pi$
$229$	−2.88867e7	+	8.89040e7i	−0.158955	+	0.489212i	0.839585	+	0.543228i	$0.182798\pi$
$230$	3.71895e7	+	1.80143e8i	0.201545	+	0.976272i
$231$	−2.53151e7	−	7.79118e7i	−0.135126	−	0.415874i
$232$	1.66830e6			0.00877136
$233$	6.20080e7	+	1.90841e8i	0.321146	+	0.988385i	0.973150	+	0.230170i	$0.0739283\pi$
$233$	6.20080e7	+	1.90841e8i	0.321146	+	0.988385i	−0.652005	+	0.758215i	$0.726072\pi$
$234$	−1.62064e8	−	1.17747e8i	−0.826861	−	0.600749i
$235$	3.40017e7	+	1.64702e8i	0.170908	+	0.827869i
$236$	1.05841e7	−	7.68982e6i	0.0524159	−	0.0380824i
$237$	5.13103e7	+	3.72791e7i	0.250372	+	0.181906i
$238$	−5.93146e8	−	4.30946e8i	−2.85195	−	2.07206i
$239$	−2.11871e8	+	1.53933e8i	−1.00387	+	0.729357i	−0.962915	−	0.269804i	$-0.913041\pi$
$239$	−2.11871e8	+	1.53933e8i	−1.00387	+	0.729357i	−0.0409580	+	0.999161i	$0.513041\pi$
$240$	3.92130e7	−	8.67038e7i	0.183101	−	0.404854i
$241$	−1.11051e8	−	8.06835e7i	−0.511050	−	0.371300i	0.302171	−	0.953254i	$-0.402288\pi$
$241$	−1.11051e8	−	8.06835e7i	−0.511050	−	0.371300i	−0.813222	+	0.581954i	$0.802288\pi$
$242$	−4.77461e7	−	1.46947e8i	−0.216563	−	0.666512i
$243$	−2.25074e8			−1.00625
$244$	6.21970e7	+	1.91423e8i	0.274098	+	0.843585i
$245$	−1.67735e8	+	9.55368e7i	−0.728691	+	0.415040i
$246$	−7.69882e7	+	2.36945e8i	−0.329725	+	1.01479i
$247$	−2.79786e7	+	8.61093e7i	−0.118137	+	0.363589i
$248$	8.06609e6	−	5.86036e6i	0.0335801	−	0.0243974i
$249$	1.51252e8			0.620876
$250$	−2.01306e8	−	2.87565e8i	−0.814831	−	1.16398i
$251$	1.19404e8			0.476609			0.238304	−	0.971191i	$-0.423408\pi$
$251$	1.19404e8			0.476609			0.238304	+	0.971191i	$0.423408\pi$
$252$	−2.25652e8	+	1.63946e8i	−0.888255	+	0.645355i
$253$	−3.97552e7	+	1.22354e8i	−0.154338	+	0.475003i
$254$	7.75816e7	−	2.38772e8i	0.297058	−	0.914249i
$255$	−1.90714e8	+	1.08625e8i	−0.720265	+	0.410240i
$256$	7.97447e7	+	2.45429e8i	0.297072	+	0.914294i
$257$	2.49969e8			0.918586			0.459293	−	0.888285i	$-0.348103\pi$
$257$	2.49969e8			0.918586			0.459293	+	0.888285i	$0.348103\pi$
$258$	2.23134e7	+	6.86735e7i	0.0808903	+	0.248955i
$259$	−2.58100e8	−	1.87521e8i	−0.923080	−	0.670657i
$260$	−1.07685e8	+	2.38103e8i	−0.379971	+	0.840153i
$261$	6.06460e7	−	4.40619e7i	0.211135	−	0.153399i
$262$	−3.21201e7	−	2.33366e7i	−0.110337	−	0.0801647i
$263$	3.64149e8	+	2.64569e8i	1.23434	+	0.896798i	0.997208	−	0.0746806i	$-0.0237937\pi$
$263$	3.64149e8	+	2.64569e8i	1.23434	+	0.896798i	0.237129	+	0.971478i	$0.423794\pi$
$264$	−2.08350e6	+	1.51375e6i	−0.00696916	+	0.00506339i
$265$	−8.90501e6	−	4.31353e7i	−0.0293950	−	0.142388i
$266$	2.02096e8	+	1.46831e8i	0.658373	+	0.478336i
$267$	4.95566e7	+	1.52520e8i	0.159335	+	0.490384i
$268$	1.47765e8			0.468922
$269$	−3.31300e7	−	1.01964e8i	−0.103774	−	0.319383i	0.885667	−	0.464321i	$-0.153702\pi$
$269$	−3.31300e7	−	1.01964e8i	−0.103774	−	0.319383i	−0.989441	+	0.144938i	$0.953702\pi$
$270$	7.55404e7	+	3.65913e8i	0.233564	+	1.13137i
$271$	6.45894e7	−	1.98786e8i	0.197137	−	0.606727i	−0.802808	−	0.596238i	$-0.796661\pi$
$271$	6.45894e7	−	1.98786e8i	0.197137	−	0.606727i	0.999945	−	0.0104884i	$-0.00333862\pi$
$272$	1.84064e8	−	5.66491e8i	0.554597	−	1.70687i
$273$	1.51203e8	−	1.09855e8i	0.449770	−	0.326777i
$274$	4.66426e8			1.36980
$275$	−2.28015e7	−	2.44448e8i	−0.0661148	−	0.708797i
$276$	−1.13101e8			−0.323806
$277$	9.27670e6	−	6.73992e6i	0.0262249	−	0.0190535i	−0.574596	−	0.818437i	$-0.694841\pi$
$277$	9.27670e6	−	6.73992e6i	0.0262249	−	0.0190535i	0.600821	+	0.799384i	$0.294841\pi$
$278$	−6.94203e7	+	2.13654e8i	−0.193789	+	0.596422i
$279$	1.38439e8	−	4.26071e8i	0.381630	−	1.17454i
$280$	9.83508e6	+	8.96039e6i	0.0267747	+	0.0243935i
$281$	−4.06831e7	−	1.25210e8i	−0.109381	−	0.336640i	0.881353	−	0.472459i	$-0.156633\pi$
$281$	−4.06831e7	−	1.25210e8i	−0.109381	−	0.336640i	−0.990734	+	0.135819i	$0.956633\pi$
$282$	−2.04905e8			−0.544101
$283$	−1.16323e8	−	3.58004e8i	−0.305079	−	0.938936i	−0.979648	−	0.200724i	$-0.935671\pi$
$283$	−1.16323e8	−	3.58004e8i	−0.305079	−	0.938936i	0.674569	−	0.738212i	$-0.264329\pi$
$284$	7.56571e6	+	5.49681e6i	0.0195991	+	0.0142396i
$285$	6.49799e7	−	3.70105e7i	0.166273	−	0.0947039i
$286$	−2.93001e8	+	2.12878e8i	−0.740607	+	0.538082i
$287$	7.28285e8	+	5.29130e8i	1.81851	+	1.32122i
$288$	−3.70230e8	−	2.68988e8i	−0.913268	−	0.663528i
$289$	−7.79476e8	+	5.66322e8i	−1.89959	+	1.38013i
$290$	−1.43240e8	−	1.30501e8i	−0.344883	−	0.314211i
$291$	2.51452e8	+	1.82691e8i	0.598177	+	0.434601i
$292$	−1.49871e8	−	4.61256e8i	−0.352272	−	1.08418i
$293$	5.29005e8			1.22864			0.614318	−	0.789059i	$-0.289431\pi$
$293$	5.29005e8			1.22864			0.614318	+	0.789059i	$0.289431\pi$
$294$	−7.26788e7	−	2.23682e8i	−0.166799	−	0.513353i
$295$	−2.78698e7	−	3.09433e6i	−0.0632057	−	0.00701762i
$296$	−3.09922e6	+	9.53843e6i	−0.00694595	+	0.0213774i
$297$	−8.07519e7	+	2.48529e8i	−0.178857	+	0.550465i
$298$	8.97031e8	−	6.51731e8i	1.96359	−	1.42663i
$299$	−2.93506e8			−0.634991
$300$	1.98190e8	−	8.54729e7i	0.423796	−	0.182770i
$301$	2.60906e8			0.551445
$302$	9.13587e8	−	6.63760e8i	1.90865	−	1.38671i
$303$	6.81570e6	−	2.09766e7i	0.0140754	−	0.0433197i
$304$	−6.27141e7	+	1.93014e8i	−0.128029	+	0.394032i
$305$	1.77772e8	−	3.93072e8i	0.358768	−	0.793273i
$306$	3.20034e8	+	9.84963e8i	0.638515	+	1.96515i
$307$	−7.08625e8			−1.39776			−0.698879	−	0.715240i	$-0.746318\pi$
$307$	−7.08625e8			−1.39776			−0.698879	+	0.715240i	$0.746318\pi$
$308$	1.55828e8	+	4.79589e8i	0.303891	+	0.935280i
$309$	−3.08920e8	−	2.24444e8i	−0.595651	−	0.432766i
$310$	−1.15097e9	−	1.27791e8i	−2.19432	−	0.243631i
$311$	−4.84515e8	+	3.52021e8i	−0.913369	+	0.663601i	−0.941865	−	0.335993i	$-0.890928\pi$
$311$	−4.84515e8	+	3.52021e8i	−0.913369	+	0.663601i	0.0284959	+	0.999594i	$0.490928\pi$
$312$	−4.75335e6	−	3.45351e6i	−0.00886050	−	0.00643753i
$313$	−5.39355e8	−	3.91864e8i	−0.994190	−	0.722321i	−0.0333555	−	0.999444i	$-0.510619\pi$
$313$	−5.39355e8	−	3.91864e8i	−0.994190	−	0.722321i	−0.960835	+	0.277122i	$0.910619\pi$
$314$	−7.69438e8	+	5.59029e8i	−1.40255	+	1.01902i
$315$	5.94179e8	+	6.59707e7i	1.07110	+	0.118923i
$316$	−3.15842e8	−	2.29473e8i	−0.563074	−	0.409097i
$317$	−1.56628e8	−	4.82051e8i	−0.276160	−	0.849935i	−0.988910	−	0.148516i	$-0.952550\pi$
$317$	−1.56628e8	−	4.82051e8i	−0.276160	−	0.849935i	0.712750	−	0.701419i	$-0.247450\pi$
$318$	5.36643e7			0.0935816
$319$	−4.18801e7	−	1.28894e8i	−0.0722338	−	0.222313i
$320$	−2.50545e8	+	5.53979e8i	−0.427425	+	0.945080i
$321$	1.51896e8	−	4.67487e8i	0.256317	−	0.788864i
$322$	−2.50239e8	+	7.70157e8i	−0.417695	+	1.28553i
$323$	3.78691e8	−	2.75135e8i	0.625282	−	0.454294i
$324$	2.65994e8			0.434475
$325$	5.14318e8	−	2.21809e8i	0.831074	−	0.358416i
$326$	8.45346e8			1.35137
$327$	1.52615e7	−	1.10881e7i	0.0241368	−	0.0175364i
$328$	8.74512e6	−	2.69147e7i	0.0136838	−	0.0421144i
$329$	−2.28789e8	+	7.04141e8i	−0.354201	+	1.09012i
$330$	2.97301e8	+	3.30088e7i	0.455405	+	0.0505629i
$331$	3.67667e7	+	1.13156e8i	0.0557258	+	0.171506i	0.975046	−	0.222005i	$-0.0712602\pi$
$331$	3.67667e7	+	1.13156e8i	0.0557258	+	0.171506i	−0.919320	+	0.393511i	$0.871260\pi$
$332$	−9.31040e8			−1.39632
$333$	1.39259e8	+	4.28595e8i	0.206666	+	0.636051i
$334$	2.71322e8	+	1.97127e8i	0.398448	+	0.289490i
$335$	−2.34120e8	−	2.13298e8i	−0.340237	−	0.309977i
$336$	3.38921e8	−	2.46240e8i	0.487428	−	0.354138i
$337$	9.03146e7	+	6.56174e7i	0.128544	+	0.0933930i	0.650200	−	0.759763i	$-0.274685\pi$
$337$	9.03146e7	+	6.56174e7i	0.128544	+	0.0933930i	−0.521655	+	0.853156i	$0.674685\pi$
$338$	1.47585e8	+	1.07227e8i	0.207890	+	0.151041i
$339$	−1.87916e8	+	1.36529e8i	−0.261978	+	0.190338i
$340$	1.17395e9	−	6.68644e8i	1.61984	−	0.922611i
$341$	−6.55260e8	−	4.76075e8i	−0.894898	−	0.650182i
$342$	−1.09042e8	−	3.35595e8i	−0.147401	−	0.453654i
$343$	1.63561e8			0.218852
$344$	−2.53458e6	−	7.80065e6i	−0.00335701	−	0.0103318i
$345$	1.79198e8	+	1.63261e8i	0.234945	+	0.214050i
$346$	−5.78037e8	+	1.77902e9i	−0.750222	+	2.30895i
$347$	−1.53059e8	+	4.71068e8i	−0.196656	+	0.605244i	0.803298	+	0.595578i	$0.203077\pi$
$347$	−1.53059e8	+	4.71068e8i	−0.196656	+	0.605244i	−0.999953	+	0.00966612i	$0.996923\pi$
$348$	9.63914e7	−	7.00324e7i	0.122606	−	0.0890783i
$349$	1.53780e9			1.93647			0.968233	−	0.250051i	$-0.0804475\pi$
$349$	1.53780e9			1.93647			0.968233	+	0.250051i	$0.0804475\pi$
$350$	−1.43524e8	−	1.53868e9i	−0.178931	−	1.91827i
$351$	−5.96178e8			−0.735870
$352$	−6.69349e8	+	4.86311e8i	−0.818000	+	0.594312i
$353$	−3.89543e8	+	1.19889e9i	−0.471350	+	1.45067i	0.379467	+	0.925205i	$0.376107\pi$
$353$	−3.89543e8	+	1.19889e9i	−0.471350	+	1.45067i	−0.850818	+	0.525461i	$0.823893\pi$
$354$	1.05576e7	−	3.24930e7i	0.0126489	−	0.0389295i
$355$	−4.05254e6	−	1.96302e7i	−0.00480759	−	0.0232877i
$356$	−3.05047e8	−	9.38839e8i	−0.358338	−	1.10285i
$357$	−9.66241e8			−1.12395
$358$	3.52762e8	+	1.08569e9i	0.406341	+	1.25059i
$359$	6.08370e7	+	4.42006e7i	0.0693964	+	0.0504194i	0.621943	−	0.783063i	$-0.286344\pi$
$359$	6.08370e7	+	4.42006e7i	0.0693964	+	0.0504194i	−0.552546	+	0.833482i	$0.686344\pi$
$360$	−3.79976e6	−	1.84058e7i	−0.00429238	−	0.0207920i
$361$	5.94130e8	−	4.31661e8i	0.664671	−	0.482912i
$362$	−1.05220e9	−	7.64465e8i	−1.16578	−	0.846989i
$363$	−1.64738e8	−	1.19689e8i	−0.180768	−	0.131336i
$364$	−9.30734e8	+	6.76218e8i	−1.01151	+	0.734906i
$365$	−4.28363e8	+	9.47154e8i	−0.461092	+	1.01952i
$366$	4.25237e8	+	3.08952e8i	0.453364	+	0.329388i
$367$	−2.79406e8	−	8.59923e8i	−0.295056	−	0.908089i	−0.983203	−	0.182517i	$-0.941575\pi$
$367$	−2.79406e8	−	8.59923e8i	−0.295056	−	0.908089i	0.688147	−	0.725572i	$-0.258425\pi$
$368$	−6.57893e8			−0.688158
$369$	−3.92948e8	−	1.20937e9i	−0.407140	−	1.25305i
$370$	1.01223e9	−	5.76536e8i	1.03890	−	0.591725i
$371$	5.99197e7	−	1.84414e8i	0.0609201	−	0.187493i
$372$	2.20036e8	−	6.77201e8i	0.221612	−	0.682052i
$373$	6.57647e7	−	4.77808e7i	0.0656163	−	0.0476730i	−0.554494	−	0.832188i	$-0.687088\pi$
$373$	6.57647e7	−	4.77808e7i	0.0656163	−	0.0476730i	0.620110	+	0.784515i	$0.287088\pi$
$374$	1.87238e9			1.85073
$375$	−4.37392e8	−	1.50662e8i	−0.428314	−	0.147535i
$376$	2.32752e7			0.0225806
$377$	2.50143e8	−	1.81740e8i	0.240433	−	0.174685i
$378$	−5.08293e8	+	1.56436e9i	−0.484053	+	1.48976i
$379$	5.07634e7	−	1.56234e8i	0.0478975	−	0.147413i	−0.924247	−	0.381794i	$-0.875306\pi$
$379$	5.07634e7	−	1.56234e8i	0.0478975	−	0.147413i	0.972145	+	0.234381i	$0.0753063\pi$
$380$	−3.99986e8	+	2.27820e8i	−0.373940	+	0.212985i
$381$	−1.02245e8	−	3.14676e8i	−0.0947115	−	0.291492i
$382$	1.99818e9			1.83406
$383$	4.48595e7	+	1.38063e8i	0.0407999	+	0.125569i	0.969382	−	0.245558i	$-0.0789713\pi$
$383$	4.48595e7	+	1.38063e8i	0.0407999	+	0.125569i	−0.928582	+	0.371127i	$0.878971\pi$
$384$	−2.17215e7	−	1.57816e7i	−0.0195763	−	0.0142230i
$385$	4.45389e8	−	9.84799e8i	0.397765	−	0.879499i
$386$	3.47348e8	−	2.52363e8i	0.307404	−	0.223342i
$387$	−2.98162e8	−	2.16627e8i	−0.261495	−	0.189987i
$388$	−1.54782e9	−	1.12456e9i	−1.34527	−	0.977397i
$389$	−3.06462e8	+	2.22658e8i	−0.263969	+	0.191785i	−0.711895	−	0.702286i	$-0.752163\pi$
$389$	−3.06462e8	+	2.22658e8i	−0.263969	+	0.191785i	0.447926	+	0.894071i	$0.352163\pi$
$390$	1.37975e8	+	6.68343e8i	0.117781	+	0.570523i
$391$	1.22760e9	+	8.91905e8i	1.03858	+	0.754571i
$392$	8.25561e6	+	2.54082e7i	0.00692226	+	0.0213045i
$393$	−5.23240e7			−0.0434837
$394$	1.11463e8	+	3.43046e8i	0.0918104	+	0.282563i
$395$	1.69179e8	+	8.19494e8i	0.138120	+	0.669046i
$396$	2.20118e8	−	6.77452e8i	0.178124	−	0.548208i
$397$	−4.49795e8	+	1.38433e9i	−0.360784	+	1.11038i	0.591795	+	0.806088i	$0.298419\pi$
$397$	−4.49795e8	+	1.38433e9i	−0.360784	+	1.11038i	−0.952579	+	0.304291i	$0.901581\pi$
$398$	2.34266e9	−	1.70204e9i	1.86259	−	1.35325i
$399$	3.29216e8			0.259464
$400$	1.15284e9	−	4.97184e8i	0.900658	−	0.388425i
$401$	−1.05777e9			−0.819191			−0.409595	−	0.912267i	$-0.634330\pi$
$401$	−1.05777e9			−0.819191			−0.409595	+	0.912267i	$0.634330\pi$
$402$	3.12188e8	−	2.26818e8i	0.239676	−	0.174135i
$403$	5.71010e8	−	1.75739e9i	0.434586	−	1.33752i
$404$	−4.19543e7	+	1.29122e8i	−0.0316550	+	0.0974239i
$405$	−4.21443e8	−	3.83961e8i	−0.315243	−	0.287207i
$406$	−2.63614e8	−	8.11322e8i	−0.195492	−	0.601661i
$407$	8.14744e8			0.599019
$408$	9.38658e6	+	2.88889e7i	0.00684222	+	0.0210582i
$409$	−6.68592e8	−	4.85760e8i	−0.483203	−	0.351067i	0.319362	−	0.947633i	$-0.396532\pi$
$409$	−6.68592e8	−	4.85760e8i	−0.483203	−	0.351067i	−0.802564	+	0.596566i	$0.796532\pi$
$410$	−2.85623e9	+	1.62682e9i	−2.04668	+	1.16572i
$411$	4.97304e8	−	3.61313e8i	0.353326	−	0.256707i
$412$	1.90157e9	+	1.38157e9i	1.33959	+	0.973269i
$413$	−9.98718e7	−	7.25611e7i	−0.0697618	−	0.0506849i
$414$	9.25422e8	−	6.72359e8i	0.640972	−	0.465693i
$415$	1.47514e9	+	1.34395e9i	1.01313	+	0.923027i
$416$	−1.52707e9	−	1.10948e9i	−1.04000	−	0.755601i
$417$	9.14889e7	+	2.81574e8i	0.0617863	+	0.190159i
$418$	−6.37956e8			−0.427242
$419$	3.96214e8	+	1.21942e9i	0.263136	+	0.809851i	0.992117	+	0.125316i	$0.0399945\pi$
$419$	3.96214e8	+	1.21942e9i	0.263136	+	0.809851i	−0.728980	+	0.684535i	$0.760005\pi$
$420$	9.44394e8	+	1.04855e8i	0.621986	+	0.0690581i
$421$	−4.92841e7	+	1.51681e8i	−0.0321899	+	0.0990702i	−0.965861	−	0.259062i	$-0.916586\pi$
$421$	−4.92841e7	+	1.51681e8i	−0.0321899	+	0.0990702i	0.933671	+	0.358133i	$0.116586\pi$
$422$	−3.83317e8	+	1.17973e9i	−0.248293	+	0.764168i
$423$	8.46098e8	−	6.14726e8i	0.543537	−	0.394903i
$424$	−6.09575e6			−0.00388371
$425$	−2.82519e9	−	6.35182e8i	−1.78520	−	0.401363i
$426$	2.44218e7			0.0153054
$427$	1.53650e9	−	1.11633e9i	0.955069	−	0.693898i
$428$	−9.35000e8	+	2.87763e9i	−0.576446	+	1.77412i
$429$	−1.47494e8	+	4.53941e8i	−0.0901933	+	0.277587i
$430$	−3.92577e8	+	8.68028e8i	−0.238114	+	0.526495i
$431$	−2.34974e7	−	7.23175e7i	−0.0141367	−	0.0435084i	0.943739	−	0.330690i	$-0.107282\pi$
$431$	−2.34974e7	−	7.23175e7i	−0.0141367	−	0.0435084i	−0.957876	+	0.287182i	$0.907282\pi$
$432$	−1.33633e9			−0.797483
$433$	−2.36159e8	−	7.26823e8i	−0.139797	−	0.430250i	0.856508	−	0.516133i	$-0.172629\pi$
$433$	−2.36159e8	−	7.26823e8i	−0.139797	−	0.430250i	−0.996305	+	0.0858827i	$0.972629\pi$
$434$	−4.12454e9	−	2.99665e9i	−2.42193	−	1.75963i
$435$	−2.53814e8	−	2.81806e7i	−0.147844	−	0.0164149i
$436$	−9.39426e7	+	6.82533e7i	−0.0542825	+	0.0394385i
$437$	−4.18267e8	−	3.03889e8i	−0.239756	−	0.174193i
$438$	−1.02466e9	−	7.44458e8i	−0.582666	−	0.423332i
$439$	2.29229e8	−	1.66545e8i	0.129313	−	0.0939517i	−0.521248	−	0.853405i	$-0.674533\pi$
$439$	2.29229e8	−	1.66545e8i	0.129313	−	0.0939517i	0.650562	+	0.759453i	$0.274533\pi$
$440$	−3.37705e7	−	3.74949e6i	−0.0188996	−	0.00209840i
$441$	9.71168e8	+	7.05595e8i	0.539212	+	0.391760i
$442$	1.32002e9	+	4.06262e9i	0.727116	+	2.23783i
$443$	−1.10039e9			−0.601357			−0.300678	−	0.953726i	$-0.597213\pi$
$443$	−1.10039e9			−0.601357			−0.300678	+	0.953726i	$0.597213\pi$
$444$	2.21339e8	+	6.81213e8i	0.120010	+	0.369354i
$445$	−8.71890e8	+	1.92784e9i	−0.469031	+	1.03707i
$446$	−2.07457e8	+	6.38486e8i	−0.110728	+	0.340784i
$447$	4.51558e8	−	1.38975e9i	0.239132	−	0.735972i
$448$	−2.16548e9	+	1.57331e9i	−1.13784	+	0.826688i
$449$	3.00770e8			0.156810			0.0784048	−	0.996922i	$-0.475017\pi$
$449$	3.00770e8			0.156810			0.0784048	+	0.996922i	$0.475017\pi$
$450$	−1.11352e9	+	1.87755e9i	−0.576045	+	0.971289i
$451$	−2.29897e9			−1.18009
$452$	1.15672e9	−	8.40407e8i	0.589175	−	0.428061i
$453$	4.59892e8	−	1.41540e9i	0.232441	−	0.715379i
$454$	5.54807e8	−	1.70752e9i	0.278257	−	0.856388i
$455$	2.45078e9	+	2.72105e8i	1.21973	+	0.135425i
$456$	−3.19818e6	−	9.84300e6i	−0.00157953	−	0.00486128i
$457$	1.68082e9			0.823789			0.411894	−	0.911232i	$-0.364867\pi$
$457$	1.68082e9			0.823789			0.411894	+	0.911232i	$0.364867\pi$
$458$	−4.64354e8	−	1.42913e9i	−0.225850	−	0.695094i
$459$	2.49354e9	+	1.81166e9i	1.20357	+	0.874446i
$460$	−1.10306e9	−	1.00496e9i	−0.528380	−	0.481387i
$461$	−1.50383e9	+	1.09260e9i	−0.714900	+	0.519405i	−0.884751	−	0.466065i	$-0.845671\pi$
$461$	−1.50383e9	+	1.09260e9i	−0.714900	+	0.519405i	0.169851	+	0.985470i	$0.445671\pi$
$462$	1.06538e9	+	7.74047e8i	0.502643	+	0.365191i
$463$	−1.56641e8	−	1.13806e8i	−0.0733453	−	0.0532885i	0.550508	−	0.834830i	$-0.314434\pi$
$463$	−1.56641e8	−	1.13806e8i	−0.0733453	−	0.0532885i	−0.623854	+	0.781541i	$0.714434\pi$
$464$	5.60695e8	−	4.07369e8i	0.260564	−	0.189311i
$465$	−1.32616e9	+	7.55340e8i	−0.611661	+	0.348383i
$466$	−2.60961e9	−	1.89599e9i	−1.19460	−	0.867931i
$467$	−3.10256e8	−	9.54870e8i	−0.140965	−	0.433846i	0.855505	−	0.517794i	$-0.173247\pi$
$467$	−3.10256e8	−	9.54870e8i	−0.140965	−	0.433846i	−0.996470	+	0.0839488i	$0.973247\pi$
$468$	1.62509e9			0.732853
$469$	−4.30866e8	−	1.32607e9i	−0.192858	−	0.593555i
$470$	−1.99841e9	−	1.82067e9i	−0.887853	−	0.808890i
$471$	−3.87329e8	+	1.19208e9i	−0.170807	+	0.525691i
$472$	−1.19924e6	+	3.69089e6i	−0.000524941	+	0.00161560i
$473$	−5.39055e8	+	3.91646e8i	−0.234217	+	0.170169i
$474$	−1.01953e9			−0.439718
$475$	9.62595e8	+	2.16419e8i	0.412113	+	0.0926546i
$476$	5.94773e9			2.52771
$477$	−2.21592e8	+	1.60996e8i	−0.0934846	+	0.0679205i
$478$	1.30091e9	−	4.00380e9i	0.544816	−	1.67677i
$479$	1.27633e9	−	3.92815e9i	0.530628	−	1.63311i	−0.222283	−	0.974982i	$-0.571351\pi$
$479$	1.27633e9	−	3.92815e9i	0.530628	−	1.63311i	0.752911	−	0.658123i	$-0.228649\pi$
$480$	3.15199e8	+	1.52680e9i	0.130089	+	0.630143i
$481$	5.74393e8	+	1.76780e9i	0.235343	+	0.724311i
$482$	2.20657e9			0.897538
$483$	3.29789e8	+	1.01499e9i	0.133175	+	0.409869i
$484$	1.01405e9	+	7.36752e8i	0.406539	+	0.295368i
$485$	8.29084e8	+	4.01602e9i	0.329991	+	1.59845i
$486$	2.92708e9	−	2.12665e9i	1.15667	−	0.840368i
$487$	−6.18315e8	−	4.49232e8i	−0.242582	−	0.176246i	0.459851	−	0.887996i	$-0.347903\pi$
$487$	−6.18315e8	−	4.49232e8i	−0.242582	−	0.176246i	−0.702433	+	0.711750i	$0.747903\pi$
$488$	−4.83028e7	−	3.50940e7i	−0.0188149	−	0.0136698i
$489$	9.01309e8	−	6.54839e8i	0.348572	−	0.253253i
$490$	1.27870e9	−	2.82733e9i	0.491000	−	1.08565i
$491$	2.64435e9	+	1.92123e9i	1.00817	+	0.732477i	0.963824	−	0.266539i	$-0.0858802\pi$
$491$	2.64435e9	+	1.92123e9i	1.00817	+	0.732477i	0.0443442	+	0.999016i	$0.485880\pi$
$492$	−6.24556e8	−	1.92219e9i	−0.236425	−	0.727642i
$493$	−1.59850e9			−0.600827
$494$	−4.49757e8	−	1.38421e9i	−0.167855	−	0.516604i
$495$	−1.32665e9	+	7.55620e8i	−0.491631	+	0.280018i
$496$	1.27992e9	−	3.93918e9i	0.470973	−	1.44951i
$497$	2.72685e7	−	8.39239e7i	0.00996356	−	0.0306647i
$498$	−1.96703e9	+	1.42913e9i	−0.713689	+	0.518525i
$499$	−3.35816e8			−0.120990			−0.0604950	−	0.998168i	$-0.519268\pi$
$499$	−3.35816e8			−0.120990			−0.0604950	+	0.998168i	$0.519268\pi$
$500$	2.69238e9	+	9.27405e8i	0.963257	+	0.331799i
$501$	4.41986e8			0.157028
$502$	−1.55285e9	+	1.12821e9i	−0.547856	+	0.398040i
$503$	−1.53991e9	+	4.73937e9i	−0.539521	+	1.66048i	0.194151	+	0.980972i	$0.437805\pi$
$503$	−1.53991e9	+	4.73937e9i	−0.539521	+	1.66048i	−0.733672	+	0.679504i	$0.762195\pi$
$504$	2.55677e7	−	7.86893e7i	0.00889579	−	0.0273784i
$505$	2.52859e8	−	1.44021e8i	0.0873694	−	0.0497629i
$506$	−6.39066e8	−	1.96684e9i	−0.219290	−	0.674905i
$507$	2.40417e8			0.0819291
$508$	6.29370e8	+	1.93700e9i	0.213002	+	0.655552i
$509$	4.24016e9	+	3.08066e9i	1.42518	+	1.03545i	0.990889	+	0.134683i	$0.0430016\pi$
$509$	4.24016e9	+	3.08066e9i	1.42518	+	1.03545i	0.434293	+	0.900772i	$0.356998\pi$
$510$	1.45387e9	−	3.21465e9i	0.485322	−	1.07310i
$511$	−3.70238e9	+	2.68994e9i	−1.22746	+	0.891803i
$512$	−3.48729e9	−	2.53367e9i	−1.14827	−	0.834266i
$513$	−8.49596e8	−	6.17268e8i	−0.277845	−	0.201866i
$514$	−3.25084e9	+	2.36187e9i	−1.05590	+	0.767159i
$515$	−1.01857e9	−	4.93387e9i	−0.328598	−	1.59170i
$516$	−4.73901e8	−	3.44309e8i	−0.151850	−	0.110325i
$517$	−5.84287e8	−	1.79825e9i	−0.185956	−	0.572313i
$518$	5.12841e9			1.62117
$519$	7.61794e8	+	2.34456e9i	0.239195	+	0.736166i
$520$	−1.56727e7	−	7.59173e7i	−0.00488800	−	0.0236771i
$521$	4.57671e8	−	1.40857e9i	0.141782	−	0.436360i	−0.854801	−	0.518956i	$-0.826321\pi$
$521$	4.57671e8	−	1.40857e9i	0.141782	−	0.436360i	0.996583	+	0.0825956i	$0.0263210\pi$
$522$	−3.72373e8	+	1.14605e9i	−0.114586	+	0.352660i
$523$	1.92244e9	−	1.39673e9i	0.587619	−	0.426930i	−0.253844	−	0.967245i	$-0.581695\pi$
$523$	1.92244e9	−	1.39673e9i	0.587619	−	0.426930i	0.841463	+	0.540315i	$0.181695\pi$
$524$	3.22082e8			0.0977928
$525$	−1.34495e9	−	1.52936e9i	−0.405646	−	0.461266i
$526$	−7.23557e9			−2.16782
$527$	−7.72862e9	+	5.61517e9i	−2.30020	+	1.67119i
$528$	−3.30608e8	+	1.01751e9i	−0.0977451	+	0.300828i
$529$	−5.34243e8	+	1.64423e9i	−0.156908	+	0.482912i
$530$	5.23380e8	+	4.76833e8i	0.152704	+	0.139123i
$531$	5.38862e7	+	1.65845e8i	0.0156188	+	0.0480696i
$532$	−2.02650e9			−0.583521
$533$	−1.62077e9	−	4.98822e9i	−0.463635	−	1.42692i
$534$	−2.08559e9	−	1.51527e9i	−0.592699	−	0.430621i
$535$	5.63526e9	−	3.20967e9i	1.59102	−	0.906196i
$536$	−3.54615e7	+	2.57643e7i	−0.00994673	+	0.00722672i
$537$	1.21713e9	+	8.84299e8i	0.339178	+	0.246428i
$538$	1.39427e9	+	1.01300e9i	0.386020	+	0.280460i
$539$	1.75580e9	−	1.27566e9i	0.482964	−	0.350894i
$540$	−2.24057e9	−	2.04130e9i	−0.612321	−	0.557864i
$541$	−2.74761e9	−	1.99626e9i	−0.746045	−	0.542033i	0.148554	−	0.988904i	$-0.452538\pi$
$541$	−2.74761e9	−	1.99626e9i	−0.746045	−	0.542033i	−0.894598	+	0.446871i	$0.852538\pi$
$542$	1.03828e9	+	3.19549e9i	0.280102	+	0.862064i
$543$	−1.71404e9			−0.459432
$544$	3.01555e9	+	9.28090e9i	0.803100	+	2.47169i
$545$	2.47366e8	+	2.74647e7i	0.0654565	+	0.00726752i
$546$	−9.28402e8	+	2.85733e9i	−0.244097	+	0.751252i
$547$	1.81582e9	−	5.58853e9i	0.474371	−	1.45996i	−0.372433	−	0.928059i	$-0.621476\pi$
$547$	1.81582e9	−	5.58853e9i	0.474371	−	1.45996i	0.846804	−	0.531905i	$-0.178524\pi$
$548$	−3.06118e9	+	2.22407e9i	−0.794614	+	0.577321i
$549$	−2.68278e9			−0.691960
$550$	2.60624e9	+	2.96359e9i	0.667951	+	0.759537i
$551$	5.44641e8			0.138701
$552$	2.71426e7	−	1.97203e7i	0.00686854	−	0.00499029i
$553$	−1.13837e9	+	3.50354e9i	−0.286249	+	0.880985i
$554$	−5.69600e7	+	1.75305e8i	−0.0142326	+	0.0438036i
$555$	6.32635e8	−	1.39882e9i	0.157082	−	0.347325i
$556$	−5.63163e8	−	1.73324e9i	−0.138954	−	0.427658i
$557$	−3.63362e9			−0.890935			−0.445467	−	0.895298i	$-0.646962\pi$
$557$	−3.63362e9			−0.890935			−0.445467	+	0.895298i	$0.646962\pi$
$558$	2.22541e9	+	6.84910e9i	0.542238	+	1.66884i
$559$	−1.22981e9	−	8.93509e8i	−0.297781	−	0.216350i
$560$	5.49341e9	+	6.09924e8i	1.32186	+	0.146763i
$561$	1.99634e9	−	1.45042e9i	0.477379	−	0.346836i
$562$	1.71215e9	+	1.24395e9i	0.406877	+	0.295614i
$563$	5.88817e9	+	4.27801e9i	1.39060	+	1.01033i	0.995800	+	0.0915592i	$0.0291851\pi$
$563$	5.88817e9	+	4.27801e9i	1.39060	+	1.01033i	0.394797	+	0.918768i	$0.370815\pi$
$564$	1.34480e9	−	9.77052e8i	0.315631	−	0.229319i
$565$	−3.04584e9	−	3.38174e8i	−0.710456	−	0.0788807i
$566$	4.89543e9	+	3.55674e9i	1.13484	+	0.824508i
$567$	−7.75609e8	−	2.38708e9i	−0.178691	−	0.549953i
$568$	−2.77408e6			−0.000635185
$569$	7.81951e8	+	2.40660e9i	0.177945	+	0.547660i	0.999756	−	0.0221015i	$-0.00703570\pi$
$569$	7.81951e8	+	2.40660e9i	0.177945	+	0.547660i	−0.821810	+	0.569761i	$0.807036\pi$
$570$	−4.95361e8	+	1.09529e9i	−0.112037	+	0.247724i
$571$	2.54141e9	−	7.82164e9i	0.571278	−	1.75821i	−0.0772382	−	0.997013i	$-0.524610\pi$
$571$	2.54141e9	−	7.82164e9i	0.571278	−	1.75821i	0.648516	−	0.761201i	$-0.275390\pi$
$572$	9.07906e8	−	2.79425e9i	0.202841	−	0.624279i
$573$	2.13046e9	−	1.54787e9i	0.473078	−	0.343711i
$574$	−1.44709e10			−3.19377
$575$	2.97044e8	+	3.18451e9i	0.0651602	+	0.698563i
$576$	3.78099e9			0.824379
$577$	4.99906e9	−	3.63203e9i	1.08336	−	0.787107i	0.105094	−	0.994462i	$-0.466486\pi$
$577$	4.99906e9	−	3.63203e9i	1.08336	−	0.787107i	0.978266	+	0.207356i	$0.0664857\pi$
$578$	4.78607e9	−	1.47300e10i	1.03094	−	3.17289i
$579$	1.74852e8	−	5.38140e8i	0.0374366	−	0.115218i
$580$	1.56236e9	+	1.73467e8i	0.332494	+	0.0369163i
$581$	2.71480e9	+	8.35530e9i	0.574277	+	1.76744i
$582$	−4.99631e9			−1.05055
$583$	1.53024e8	+	4.70960e8i	0.0319831	+	0.0984338i
$584$	1.16391e8	+	8.45633e7i	0.0241811	+	0.0175686i
$585$	−2.57480e9	−	2.34581e9i	−0.531739	−	0.484448i
$586$	−6.87969e9	+	4.99839e9i	−1.41230	+	1.02610i
$587$	−1.97792e9	−	1.43704e9i	−0.403622	−	0.293248i	0.367393	−	0.930066i	$-0.380250\pi$
$587$	−1.97792e9	−	1.43704e9i	−0.403622	−	0.293248i	−0.771015	+	0.636817i	$0.780250\pi$
$588$	1.54358e9	+	1.12148e9i	0.313119	+	0.227495i
$589$	2.63329e9	−	1.91320e9i	0.531000	−	0.385794i
$590$	3.91683e8	−	2.23090e8i	0.0785149	−	0.0447197i
$591$	3.84579e8	+	2.79413e8i	0.0766354	+	0.0556789i
$592$	1.28750e9	+	3.96252e9i	0.255048	+	0.784956i
$593$	−3.35109e9			−0.659925			−0.329963	−	0.943994i	$-0.607036\pi$
$593$	−3.35109e9			−0.659925			−0.329963	+	0.943994i	$0.607036\pi$
$594$	−1.29809e9	−	3.99511e9i	−0.254128	−	0.782125i
$595$	−9.42361e9	−	8.58551e9i	−1.83404	−	1.67092i
$596$	−2.77958e9	+	8.55467e9i	−0.537796	+	1.65517i
$597$	1.17928e9	−	3.62944e9i	0.226832	−	0.698119i
$598$	3.81703e9	−	2.77324e9i	0.729914	−	0.530314i
$599$	−4.20702e9			−0.799798			−0.399899	−	0.916559i	$-0.630955\pi$
$599$	−4.20702e9			−0.799798			−0.399899	+	0.916559i	$0.630955\pi$
$600$	−3.26597e7	+	5.50686e7i	−0.00617280	+	0.0104082i
$601$	−1.61083e9			−0.302684			−0.151342	−	0.988481i	$-0.548360\pi$
$601$	−1.61083e9			−0.302684			−0.151342	+	0.988481i	$0.548360\pi$
$602$	−3.39308e9	+	2.46522e9i	−0.633879	+	0.460540i
$603$	−6.08628e8	+	1.87316e9i	−0.113042	+	0.347909i
$604$	−2.83088e9	+	8.71256e9i	−0.522748	+	1.60885i
$605$	−5.43173e8	−	2.63109e9i	−0.0997227	−	0.483050i
$606$	1.09563e8	+	3.37199e8i	0.0199990	+	0.0615506i
$607$	7.86878e9			1.42806			0.714030	−	0.700115i	$-0.246868\pi$
$607$	7.86878e9			1.42806			0.714030	+	0.700115i	$0.246868\pi$
$608$	−1.02745e9	−	3.16218e9i	−0.185396	−	0.570589i
$609$	−9.09549e8	−	6.60826e8i	−0.163179	−	0.118557i
$610$	1.40208e9	+	6.79160e9i	0.250103	+	1.21148i
$611$	3.48985e9	−	2.53552e9i	0.618960	−	0.449701i
$612$	−6.79702e9	−	4.93832e9i	−1.19864	−	0.870862i
$613$	−1.14446e9	−	8.31497e8i	−0.200672	−	0.145797i	0.482911	−	0.875669i	$-0.339579\pi$
$613$	−1.14446e9	−	8.31497e8i	−0.200672	−	0.145797i	−0.683583	+	0.729872i	$0.739579\pi$
$614$	9.21565e9	−	6.69556e9i	1.60671	−	1.16734i
$615$	−1.78511e9	+	3.94706e9i	−0.309459	+	0.684244i
$616$	−1.21017e8	−	8.79243e7i	−0.0208600	−	0.0151557i
$617$	1.03856e9	+	3.19635e9i	0.178005	+	0.547842i	0.999758	−	0.0220012i	$-0.00700376\pi$
$617$	1.03856e9	+	3.19635e9i	0.178005	+	0.547842i	−0.821753	+	0.569844i	$0.807004\pi$
$618$	6.13819e9			1.04612
$619$	4.77487e8	+	1.46955e9i	0.0809178	+	0.249039i	0.983329	−	0.181837i	$-0.0582044\pi$
$619$	4.77487e8	+	1.46955e9i	0.0809178	+	0.249039i	−0.902411	+	0.430877i	$0.858204\pi$
$620$	8.16323e9	−	4.64952e9i	1.37560	−	0.783497i
$621$	1.05199e9	−	3.23768e9i	0.176275	−	0.542517i
$622$	2.97498e9	−	9.15604e9i	0.495698	−	1.52560i
$623$	−7.53582e9	+	5.47509e9i	−1.24860	+	0.907158i
$624$	−2.44082e9			−0.402152
$625$	−2.92712e9	−	5.35582e9i	−0.479580	−	0.877498i
$626$	1.07169e10			1.74606
$627$	−6.80189e8	+	4.94186e8i	−0.110203	+	0.0800671i
$628$	2.38422e9	−	7.33786e9i	0.384138	−	1.18225i
$629$	2.96956e9	−	9.13936e9i	0.475789	−	1.46433i
$630$	−8.35062e9	+	4.75625e9i	−1.33054	+	0.757832i
$631$	3.20093e9	+	9.85144e9i	0.507193	+	1.56098i	0.797053	+	0.603909i	$0.206391\pi$
$631$	3.20093e9	+	9.85144e9i	0.507193	+	1.56098i	−0.289860	+	0.957069i	$0.593609\pi$
$632$	1.15808e8			0.0182486
$633$	5.05173e8	+	1.55476e9i	0.0791638	+	0.243641i
$634$	6.59168e9	+	4.78913e9i	1.02727	+	0.746353i
$635$	1.79887e9	−	3.97749e9i	0.278800	−	0.616454i
$636$	−3.52201e8	+	2.55889e8i	−0.0542863	+	0.0394413i
$637$	4.00572e9	+	2.91033e9i	0.614034	+	0.446122i
$638$	1.76252e9	+	1.28055e9i	0.268697	+	0.195220i
$639$	−1.00843e8	+	7.32669e7i	−0.0152895	+	0.0111085i
$640$	−7.16199e7	−	3.46922e8i	−0.0107995	−	0.0523121i
$641$	4.30739e9	+	3.12950e9i	0.645968	+	0.469323i	0.861895	−	0.507086i	$-0.169277\pi$
$641$	4.30739e9	+	3.12950e9i	0.645968	+	0.469323i	−0.215927	+	0.976409i	$0.569277\pi$
$642$	2.44173e9	+	7.51487e9i	0.364187	+	1.12085i
$643$	1.98261e9			0.294102			0.147051	−	0.989129i	$-0.453022\pi$
$643$	1.98261e9			0.294102			0.147051	+	0.989129i	$0.453022\pi$
$644$	−2.03003e9	−	6.24779e9i	−0.299503	−	0.921777i
$645$	2.53843e8	+	1.22960e9i	0.0372483	+	0.180428i
$646$	−2.32520e9	+	7.15624e9i	−0.339350	+	1.04441i
$647$	5.72327e8	−	1.76144e9i	0.0830766	−	0.255684i	−0.900887	−	0.434054i	$-0.857083\pi$
$647$	5.72327e8	−	1.76144e9i	0.0830766	−	0.255684i	0.983963	+	0.178371i	$0.0570826\pi$
$648$	−6.38348e7	+	4.63787e7i	−0.00921605	+	0.00669586i
$649$	3.15265e8			0.0452709
$650$	−4.59289e9	+	7.74423e9i	−0.655978	+	1.10607i
$651$	−6.71891e9			−0.954477
$652$	−5.54804e9	+	4.03089e9i	−0.783922	+	0.569553i
$653$	−1.25048e9	+	3.84858e9i	−0.175744	+	0.540884i	−0.999667	−	0.0258181i	$-0.991781\pi$
$653$	−1.25048e9	+	3.84858e9i	−0.175744	+	0.540884i	0.823923	+	0.566702i	$0.191781\pi$
$654$	−9.37072e7	+	2.88401e8i	−0.0130994	+	0.0403158i
$655$	−5.10308e8	−	4.64923e8i	−0.0709558	−	0.0646453i
$656$	−3.63296e9	−	1.11811e10i	−0.502455	−	1.54640i
$657$	6.46447e9			0.889312
$658$	−3.67779e9	−	1.13191e10i	−0.503265	−	1.54889i
$659$	−1.11256e10	−	8.08325e9i	−1.51435	−	1.10024i	−0.964202	−	0.265170i	$-0.914572\pi$
$659$	−1.11256e10	−	8.08325e9i	−1.51435	−	1.10024i	−0.550147	−	0.835068i	$-0.685428\pi$
$660$	−2.10860e9	+	1.20099e9i	−0.285489	+	0.162606i
$661$	1.96900e9	−	1.43056e9i	0.265180	−	0.192664i	−0.447248	−	0.894410i	$-0.647596\pi$
$661$	1.96900e9	−	1.43056e9i	0.265180	−	0.192664i	0.712427	+	0.701746i	$0.247596\pi$
$662$	−1.54732e9	−	1.12420e9i	−0.207290	−	0.150605i
$663$	4.55448e9	+	3.30902e9i	0.606934	+	0.440963i
$664$	2.23436e8	−	1.62336e8i	0.0296186	−	0.0215192i
$665$	3.21080e9	+	2.92524e9i	0.423387	+	0.385733i
$666$	−5.86070e9	−	4.25805e9i	−0.768759	−	0.558536i
$667$	5.45588e8	+	1.67915e9i	0.0711909	+	0.219103i
$668$	−2.72066e9			−0.353148
$669$	2.73407e8	+	8.41459e8i	0.0353035	+	0.108653i
$670$	5.06010e9	+	5.61815e8i	0.649976	+	0.0721658i
$671$	−1.49881e9	+	4.61287e9i	−0.191522	+	0.589444i
$672$	−2.12090e9	+	6.52746e9i	−0.269605	+	0.829759i
$673$	−1.01873e9	+	7.40150e8i	−0.128827	+	0.0935982i	−0.650333	−	0.759650i	$-0.725370\pi$
$673$	−1.01873e9	+	7.40150e8i	−0.128827	+	0.0935982i	0.521506	+	0.853248i	$0.325370\pi$
$674$	−1.79454e9			−0.225758
$675$	6.03364e8	+	6.46848e9i	0.0755120	+	0.809541i
$676$	−1.47990e9			−0.184255
$677$	1.29899e9	−	9.43775e8i	0.160897	−	0.116898i	−0.504424	−	0.863456i	$-0.668295\pi$
$677$	1.29899e9	−	9.43775e8i	0.160897	−	0.116898i	0.665320	+	0.746558i	$0.268295\pi$
$678$	1.15382e9	−	3.55110e9i	0.142179	−	0.437582i
$679$	−5.57870e9	+	1.71695e10i	−0.683894	+	2.10481i
$680$	−1.65146e8	+	3.65154e8i	−0.0201412	+	0.0445343i
$681$	−7.31179e8	−	2.25034e9i	−0.0887174	−	0.273044i
$682$	1.30199e10			1.57167
$683$	−2.62374e9	−	8.07503e9i	−0.315100	−	0.969777i	−0.975713	−	0.219051i	$-0.929704\pi$
$683$	−2.62374e9	−	8.07503e9i	−0.315100	−	0.969777i	0.660614	−	0.750726i	$-0.270296\pi$
$684$	2.31587e9	+	1.68258e9i	0.276706	+	0.201038i
$685$	8.06058e9	+	8.94952e8i	0.958184	+	0.106386i
$686$	−2.12710e9	+	1.54543e9i	−0.251567	+	0.182774i
$687$	−1.60216e9	−	1.16404e9i	−0.188520	−	0.136968i
$688$	−2.75662e9	−	2.00280e9i	−0.322713	−	0.234465i
$689$	−9.13988e8	+	6.64051e8i	−0.106457	+	0.0773453i
$690$	−3.87306e9	−	4.30019e8i	−0.448830	−	0.0498329i
$691$	1.91396e9	+	1.39058e9i	0.220679	+	0.160333i	0.692632	−	0.721291i	$-0.256451\pi$
$691$	1.91396e9	+	1.39058e9i	0.220679	+	0.160333i	−0.471953	+	0.881624i	$0.656451\pi$
$692$	−4.68925e9	−	1.44320e10i	−0.537938	−	1.65560i
$693$	−6.72141e9			−0.767174
$694$	−2.46043e9	−	7.57243e9i	−0.279417	−	0.859958i
$695$	−1.60964e9	+	3.55907e9i	−0.181879	+	0.402152i
$696$	−1.09217e7	+	3.36135e7i	−0.00122789	+	0.00377904i
$697$	−8.37924e9	+	2.57887e10i	−0.937325	+	2.88479i
$698$	−1.99990e10	+	1.45301e10i	−2.22594	+	1.61724i
$699$	−4.25108e9			−0.470792
$700$	8.27886e9	+	9.41402e9i	0.912279	+	1.03737i
$701$	−8.79390e9			−0.964203			−0.482101	−	0.876115i	$-0.660126\pi$
$701$	−8.79390e9			−0.964203			−0.482101	+	0.876115i	$0.660126\pi$
$702$	7.75327e9	−	5.63308e9i	0.845873	−	0.614563i
$703$	−1.01178e9	+	3.11395e9i	−0.109836	+	0.338040i
$704$	2.11236e9	−	6.50119e9i	0.228173	−	0.702245i
$705$	−3.54107e9	−	3.93159e8i	−0.380603	−	0.0422577i
$706$	−6.26191e9	−	1.92722e10i	−0.669715	−	2.06117i
$707$	1.28110e9			0.136337
$708$	8.56472e7	+	2.63595e8i	0.00906978	+	0.0279139i
$709$	1.30911e10	+	9.51124e9i	1.37948	+	1.00225i	0.996929	+	0.0783133i	$0.0249534\pi$
$709$	1.30911e10	+	9.51124e9i	1.37948	+	1.00225i	0.382548	+	0.923935i	$0.375047\pi$
$710$	2.38182e8	+	2.16999e8i	0.0249750	+	0.0227538i
$711$	4.20986e9	−	3.05864e9i	0.439262	−	0.319143i
$712$	2.36903e8	+	1.72120e8i	0.0245974	+	0.0178711i
$713$	8.53633e9	+	6.20201e9i	0.881978	+	0.640795i
$714$	1.25659e10	−	9.12968e9i	1.29197	−	0.938668i
$715$	−5.47197e9	+	3.11666e9i	−0.559851	+	0.318874i
$716$	−7.49211e9	−	5.44333e9i	−0.762796	−	0.554204i
$717$	−1.71447e9	−	5.27659e9i	−0.173705	−	0.534609i
$718$	−1.20882e9			−0.121878
$719$	5.13509e8	+	1.58042e9i	0.0515225	+	0.158570i	0.973507	−	0.228656i	$-0.0734332\pi$
$719$	5.13509e8	+	1.58042e9i	0.0515225	+	0.158570i	−0.921985	+	0.387226i	$0.873433\pi$
$720$	−5.77141e9	−	5.25812e9i	−0.576260	−	0.525009i
$721$	6.85369e9	−	2.10935e10i	0.681006	−	2.09592i
$722$	−3.64803e9	+	1.12275e10i	−0.360726	+	1.11020i
$723$	2.35265e9	−	1.70930e9i	0.231512	−	0.168203i
$724$	1.05508e10			1.03324
$725$	−2.22502e9	−	2.53010e9i	−0.216845	−	0.246578i
$726$	3.27332e9			0.317476
$727$	1.52802e9	−	1.11017e9i	0.147489	−	0.107157i	−0.511594	−	0.859227i	$-0.670945\pi$
$727$	1.52802e9	−	1.11017e9i	0.147489	−	0.107157i	0.659083	+	0.752071i	$0.270945\pi$
$728$	1.05458e8	−	3.24565e8i	0.0101302	−	0.0311775i
$729$	9.49774e7	−	2.92310e8i	0.00907975	−	0.0279446i
$730$	−3.37849e9	−	1.63652e10i	−0.321435	−	1.55701i
$731$	2.42854e9	+	7.47429e9i	0.229951	+	0.707716i
$732$	−4.26403e9			−0.401820
$733$	−1.75482e9	−	5.40077e9i	−0.164576	−	0.506514i	0.834428	−	0.551116i	$-0.185798\pi$
$733$	−1.75482e9	−	5.40077e9i	−0.164576	−	0.506514i	−0.999005	+	0.0446022i	$0.985798\pi$
$734$	1.17588e10	+	8.54326e9i	1.09756	+	0.797420i
$735$	−8.26814e8	−	4.00503e9i	−0.0768073	−	0.372049i
$736$	8.71987e9	−	6.33536e9i	0.806191	−	0.585732i
$737$	2.88077e9	+	2.09300e9i	0.265077	+	0.192590i
$738$	1.65372e10	+	1.20150e10i	1.51449	+	1.10034i
$739$	1.47372e9	−	1.07072e9i	0.134326	−	0.0975936i	−0.518593	−	0.855021i	$-0.673544\pi$
$739$	1.47372e9	−	1.07072e9i	0.134326	−	0.0975936i	0.652919	+	0.757427i	$0.273544\pi$
$740$	−3.89421e9	+	8.61048e9i	−0.353271	+	0.781117i
$741$	−1.55180e9	−	1.12745e9i	−0.140111	−	0.101796i
$742$	9.63210e8	+	2.96446e9i	0.0865581	+	0.266398i
$743$	−6.40285e9			−0.572680			−0.286340	−	0.958128i	$-0.592439\pi$
$743$	−6.40285e9			−0.572680			−0.286340	+	0.958128i	$0.592439\pi$
$744$	6.52711e7	+	2.00884e8i	0.00581053	+	0.0178830i
$745$	1.67526e10	−	9.54176e9i	1.48435	−	0.845437i
$746$	−4.03802e8	+	1.24278e9i	−0.0356109	+	0.109599i
$747$	3.83485e9	−	1.18024e10i	0.336609	−	1.03598i
$748$	−1.22885e10	+	8.92813e9i	−1.07360	+	0.780018i
$749$	2.85507e10			2.48273
$750$	7.11183e9	−	2.17342e9i	0.615555	−	0.188117i
$751$	−4.47250e9			−0.385311			−0.192655	−	0.981267i	$-0.561710\pi$
$751$	−4.47250e9			−0.385311			−0.192655	+	0.981267i	$0.561710\pi$
$752$	7.82249e9	−	5.68337e9i	0.670784	−	0.487353i
$753$	−7.81692e8	+	2.40580e9i	−0.0667195	+	0.205342i
$754$	−1.53591e9	+	4.72703e9i	−0.130486	+	0.401596i
$755$	1.70618e10	−	9.71786e9i	1.44281	−	0.821782i
$756$	−4.12346e9	−	1.26907e10i	−0.347084	−	1.06822i
$757$	−1.42585e10			−1.19464			−0.597321	−	0.802003i	$-0.703768\pi$
$757$	−1.42585e10			−1.19464			−0.597321	+	0.802003i	$0.703768\pi$
$758$	8.16022e8	+	2.51146e9i	0.0680550	+	0.209452i
$759$	−2.20497e9	−	1.60200e9i	−0.183044	−	0.132989i
$760$	5.62683e7	−	1.24415e8i	0.00464960	−	0.0102807i
$761$	7.49308e9	−	5.44404e9i	0.616331	−	0.447790i	−0.235307	−	0.971921i	$-0.575610\pi$
$761$	7.49308e9	−	5.44404e9i	0.616331	−	0.447790i	0.851638	+	0.524131i	$0.175610\pi$
$762$	4.30296e9	+	3.12628e9i	0.352310	+	0.255968i
$763$	8.86442e8	+	6.44038e8i	0.0722461	+	0.0524899i
$764$	−1.31141e10	+	9.52797e9i	−1.06393	+	0.772990i
$765$	3.64079e9	+	1.76357e10i	0.294023	+	1.42423i
$766$	−1.88791e9	−	1.37165e9i	−0.151768	−	0.110266i
$767$	2.22261e8	+	6.84049e8i	0.0177860	+	0.0547398i
$768$	−5.46705e9			−0.435500
$769$	−6.05969e9	−	1.86498e10i	−0.480516	−	1.47888i	−0.838371	−	0.545100i	$-0.816492\pi$
$769$	−6.05969e9	−	1.86498e10i	−0.480516	−	1.47888i	0.357855	−	0.933777i	$-0.383508\pi$
$770$	3.51277e9	+	1.70156e10i	0.277289	+	1.34317i
$771$	−1.63645e9	+	5.03646e9i	−0.128591	+	0.395763i
$772$	−1.07631e9	+	3.31254e9i	−0.0841931	+	0.259120i
$773$	−3.09698e9	+	2.25009e9i	−0.241162	+	0.175215i	−0.701801	−	0.712373i	$-0.747620\pi$
$773$	−3.09698e9	+	2.25009e9i	−0.241162	+	0.175215i	0.460639	+	0.887588i	$0.347620\pi$
$774$	5.92442e9			0.459254
$775$	−1.96454e10	−	4.41684e9i	−1.51602	−	0.340844i
$776$	5.67532e8			0.0435988
$777$	5.46791e9	−	3.97267e9i	0.418165	−	0.303815i
$778$	1.88171e9	−	5.79131e9i	0.143260	−	0.440908i
$779$	2.85497e9	−	8.78668e9i	0.216381	−	0.665953i
$780$	−4.09241e9	−	3.72845e9i	−0.308780	−	0.281318i
$781$	6.96390e7	+	2.14327e8i	0.00523087	+	0.0160990i
$782$	−2.43922e10			−1.82401
$783$	1.10822e9	+	3.41074e9i	0.0825008	+	0.253911i
$784$	8.97882e9	+	6.52349e9i	0.665446	+	0.483475i
$785$	−1.43697e10	+	8.18455e9i	−1.06024	+	0.603880i
$786$	6.80472e8	−	4.94392e8i	0.0499840	−	0.0363155i
$787$	2.07518e9	+	1.50770e9i	0.151755	+	0.110257i	0.661072	−	0.750323i	$-0.270102\pi$
$787$	2.07518e9	+	1.50770e9i	0.151755	+	0.110257i	−0.509317	+	0.860579i	$0.670102\pi$
$788$	−2.36729e9	−	1.71994e9i	−0.172349	−	0.125219i
$789$	−7.71457e9	+	5.60496e9i	−0.559168	+	0.406259i
$790$	−9.94330e9	−	9.05897e9i	−0.717523	−	0.653709i
$791$	−1.09148e10	−	7.93008e9i	−0.784149	−	0.569718i
$792$	6.52953e7	+	2.00958e8i	0.00467029	+	0.0143737i
$793$	−1.10655e10			−0.787978
$794$	−7.23046e9	−	2.22531e10i	−0.512618	−	1.57768i
$795$	9.27402e8	+	1.02968e8i	0.0654611	+	0.00726804i
$796$	−7.25907e9	+	2.23411e10i	−0.510135	+	1.57004i
$797$	−4.51260e8	+	1.38884e9i	−0.0315735	+	0.0971732i	−0.965601	−	0.260027i	$-0.916269\pi$
$797$	−4.51260e8	+	1.38884e9i	−0.0315735	+	0.0971732i	0.934028	+	0.357200i	$0.116269\pi$
$798$	−4.28145e9	+	3.11065e9i	−0.298250	+	0.216691i
$799$	−2.23014e10			−1.54674
$800$	−1.04923e10	+	1.76914e10i	−0.724528	+	1.22165i
$801$	1.31578e10			0.904625
$802$	1.37562e10	−	9.99449e9i	0.941650	−	0.684148i
$803$	3.61157e9	−	1.11153e10i	0.246145	−	0.757558i
$804$	−9.67359e8	+	2.97722e9i	−0.0656435	+	0.202030i
$805$	−5.80225e9	+	1.28294e10i	−0.392023	+	0.866801i
$806$	9.17900e9	+	2.82501e10i	0.617480	+	1.90041i
$807$	2.27129e9			0.152130
$808$	−1.24453e7	−	3.83025e7i	−0.000829973	−	0.00255439i
$809$	4.77606e9	+	3.47001e9i	0.317139	+	0.230415i	0.734954	−	0.678117i	$-0.237204\pi$
$809$	4.77606e9	+	3.47001e9i	0.317139	+	0.230415i	−0.417815	+	0.908532i	$0.637204\pi$
$810$	9.10877e9	+	1.01133e9i	0.602230	+	0.0668646i
$811$	−1.97440e10	+	1.43449e10i	−1.29976	+	0.944330i	−0.999953	−	0.00967043i	$-0.996922\pi$
$811$	−1.97440e10	+	1.43449e10i	−1.29976	+	0.944330i	−0.299805	+	0.954000i	$0.596922\pi$
$812$	5.59876e9	+	4.06774e9i	0.366983	+	0.266629i
$813$	3.58237e9	+	2.60274e9i	0.233805	+	0.169869i
$814$	−1.05957e10	+	7.69824e9i	−0.688566	+	0.500272i
$815$	1.46089e10	+	1.62200e9i	0.945292	+	0.104954i
$816$	1.02089e10	+	7.41717e9i	0.657751	+	0.477884i
$817$	−8.27450e8	−	2.54663e9i	−0.0530841	−	0.163376i
$818$	1.32848e10			0.848630
$819$	−4.73857e9	−	1.45838e10i	−0.301407	−	0.927637i
$820$	1.09883e10	−	2.42963e10i	0.695958	−	1.53883i
$821$	5.14892e9	−	1.58467e10i	0.324724	−	0.999399i	−0.646840	−	0.762625i	$-0.723910\pi$
$821$	5.14892e9	−	1.58467e10i	0.324724	−	0.999399i	0.971565	−	0.236774i	$-0.0760900\pi$
$822$	−3.05351e9	+	9.39772e9i	−0.191755	+	0.590162i
$823$	1.38588e10	−	1.00690e10i	0.866613	−	0.629631i	−0.0630627	−	0.998010i	$-0.520087\pi$
$823$	1.38588e10	−	1.00690e10i	0.866613	−	0.629631i	0.929676	+	0.368378i	$0.120087\pi$
$824$	−6.97239e8			−0.0434147
$825$	5.07449e9	+	1.14089e9i	0.314633	+	0.0707383i
$826$	1.98444e9			0.122520
$827$	−7.96681e9	+	5.78823e9i	−0.489796	+	0.355858i	−0.805106	−	0.593131i	$-0.797892\pi$
$827$	−7.96681e9	+	5.78823e9i	−0.489796	+	0.355858i	0.315310	+	0.948989i	$0.397892\pi$
$828$	−2.86756e9	+	8.82543e9i	−0.175552	+	0.540294i
$829$	−5.80285e9	+	1.78593e10i	−0.353753	+	1.08874i	0.602976	+	0.797760i	$0.293982\pi$
$829$	−5.80285e9	+	1.78593e10i	−0.353753	+	1.08874i	−0.956729	+	0.290981i	$0.906018\pi$
$830$	−3.18827e10	−	3.53989e9i	−1.93545	−	0.214890i
$831$	7.50674e7	+	2.31034e8i	0.00453782	+	0.0139660i
$832$	1.55952e10			0.938772
$833$	−7.91022e9	−	2.43451e10i	−0.474167	−	1.45933i
$834$	−3.85031e9	−	2.79741e9i	−0.229834	−	0.166984i
$835$	4.31062e9	+	3.92725e9i	0.256234	+	0.233446i
$836$	4.18693e9	−	3.04198e9i	0.247841	−	0.180067i
$837$	1.73392e10	+	1.25977e10i	1.02209	+	0.742595i
$838$	−1.66747e10	−	1.21148e10i	−0.978820	−	0.711154i
$839$	−1.56497e10	+	1.13702e10i	−0.914829	+	0.664662i	−0.942232	−	0.334962i	$-0.891276\pi$
$839$	−1.56497e10	+	1.13702e10i	−0.914829	+	0.664662i	0.0274025	+	0.999624i	$0.491276\pi$
$840$	−2.44923e8	+	1.39501e8i	−0.0142578	+	0.00812080i
$841$	1.24507e10	+	9.04598e9i	0.721786	+	0.524409i
$842$	−7.92242e8	−	2.43827e9i	−0.0457368	−	0.140763i
$843$	2.78910e9			0.160350
$844$	−3.10961e9	−	9.57039e9i	−0.178036	−	0.547937i
$845$	2.34476e9	+	2.13622e9i	0.133690	+	0.121800i
$846$	−5.19514e9	+	1.59890e10i	−0.294986	+	0.907872i
$847$	3.65488e9	−	1.12486e10i	0.206672	−	0.636070i
$848$	−2.04870e9	+	1.48847e9i	−0.115370	+	0.0838213i
$849$	7.97472e9			0.447238
$850$	4.27431e10	−	1.84337e10i	2.38726	−	1.02955i
$851$	−1.06140e10			−0.590371
$852$	−1.60281e8	+	1.16451e8i	−0.00887859	+	0.00645068i
$853$	1.01702e10	−	3.13006e10i	0.561058	−	1.72676i	−0.118326	−	0.992975i	$-0.537753\pi$
$853$	1.01702e10	−	3.13006e10i	0.561058	−	1.72676i	0.679384	−	0.733783i	$-0.262247\pi$
$854$	−9.43428e9	+	2.90357e10i	−0.518330	+	1.59526i
$855$	−1.24049e9	−	6.00883e9i	−0.0678751	−	0.328782i
$856$	−2.77357e8	−	8.53616e8i	−0.0151140	−	0.0465162i
$857$	−8.56748e9			−0.464965			−0.232483	−	0.972601i	$-0.574685\pi$
$857$	−8.56748e9			−0.464965			−0.232483	+	0.972601i	$0.574685\pi$
$858$	−2.37097e9	−	7.29711e9i	−0.128151	−	0.394407i
$859$	−1.38087e10	−	1.00326e10i	−0.743323	−	0.540056i	0.150427	−	0.988621i	$-0.451935\pi$
$859$	−1.38087e10	−	1.00326e10i	−0.743323	−	0.540056i	−0.893750	+	0.448565i	$0.851935\pi$
$860$	−1.56254e9	−	7.56884e9i	−0.0837696	−	0.405774i
$861$	−1.54289e10	+	1.12097e10i	−0.823803	+	0.598528i
$862$	9.88887e8	+	7.18468e8i	0.0525861	+	0.0382061i
$863$	2.77540e10	+	2.01645e10i	1.46990	+	1.06794i	0.980643	+	0.195805i	$0.0627319\pi$
$863$	2.77540e10	+	2.01645e10i	1.46990	+	1.06794i	0.489257	+	0.872140i	$0.337268\pi$
$864$	1.77121e10	−	1.28686e10i	0.934267	−	0.678785i
$865$	−1.34029e10	+	2.96351e10i	−0.704111	+	1.55686i
$866$	9.93875e9	+	7.22093e9i	0.520019	+	0.377816i
$867$	−6.30755e9	−	1.94126e10i	−0.328695	−	1.01162i
$868$	4.13585e10			2.14657
$869$	−2.90719e9	−	8.94740e9i	−0.150281	−	0.462517i
$870$	3.56712e9	−	2.03172e9i	0.183654	−	0.104603i
$871$	−2.51037e9	+	7.72612e9i	−0.128728	+	0.396185i
$872$	1.06442e7	−	3.27596e7i	0.000543634	−	0.00167313i
$873$	2.06309e10	−	1.49892e10i	1.04947	−	0.762481i
$874$	8.31089e9			0.421073
$875$	4.72007e8	−	2.68661e10i	0.0238188	−	1.35574i
$876$	1.02747e10			0.516422
$877$	−2.17476e10	+	1.58005e10i	−1.08871	+	0.790995i	−0.979181	−	0.202989i	$-0.934934\pi$
$877$	−2.17476e10	+	1.58005e10i	−1.08871	+	0.790995i	−0.109530	+	0.993984i	$0.534934\pi$
$878$	−1.40749e9	+	4.33182e9i	−0.0701803	+	0.215993i
$879$	−3.46318e9	+	1.06586e10i	−0.171994	+	0.529344i
$880$	−1.22654e10	+	6.98600e9i	−0.606726	+	0.345572i
$881$	−3.41135e9	−	1.04991e10i	−0.168078	−	0.517290i	0.831172	−	0.556015i	$-0.187670\pi$
$881$	−3.41135e9	−	1.04991e10i	−0.168078	−	0.517290i	−0.999250	+	0.0387249i	$0.987670\pi$
$882$	−1.92969e10			−0.946997
$883$	6.97702e9	+	2.14731e10i	0.341042	+	1.04962i	0.963669	+	0.267100i	$0.0860653\pi$
$883$	6.97702e9	+	2.14731e10i	0.341042	+	1.04962i	−0.622627	+	0.782518i	$0.713935\pi$
$884$	−2.80353e10	−	2.03688e10i	−1.36496	−	0.991705i
$885$	2.44798e8	−	5.41272e8i	0.0118715	−	0.0262491i
$886$	1.43105e10	−	1.03972e10i	0.691252	−	0.502224i
$887$	−2.45702e9	−	1.78513e9i	−0.118216	−	0.0858891i	0.527106	−	0.849799i	$-0.323277\pi$
$887$	−2.45702e9	−	1.78513e9i	−0.118216	−	0.0858891i	−0.645322	+	0.763910i	$0.723277\pi$
$888$	−1.71894e8	−	1.24888e8i	−0.00823789	−	0.00598518i
$889$	1.55478e10	−	1.12961e10i	0.742186	−	0.539230i
$890$	−6.87657e9	−	3.33096e10i	−0.326969	−	1.58382i
$891$	5.18571e9	+	3.76764e9i	0.245605	+	0.178442i
$892$	−1.68296e9	−	5.17963e9i	−0.0793959	−	0.244355i
$893$	7.59851e9			0.357066
$894$	7.25881e9	+	2.23403e10i	0.339769	+	1.04570i
$895$	4.01311e9	+	1.94393e10i	0.187112	+	0.906356i
$896$	4.81913e8	−	1.48318e9i	0.0223816	−	0.0688834i
$897$	1.92146e9	−	5.91366e9i	0.0888912	−	0.273579i
$898$	−3.91151e9	+	2.84188e9i	−0.180251	+	0.130960i
$899$	−1.11155e10			−0.510233
$900$	−1.64468e9	−	1.76321e10i	−0.0752025	−	0.806223i
$901$	5.84071e9			0.266029
$902$	2.98981e10	−	2.17222e10i	1.35650	−	0.985557i
$903$	−1.70805e9	+	5.25683e9i	−0.0771957	+	0.237584i
$904$	−1.31063e8	+	4.03371e8i	−0.00590053	+	0.0181600i
$905$	−1.67168e10	−	1.52300e10i	−0.749691	−	0.683016i
$906$	7.39278e9	+	2.27526e10i	0.330262	+	1.01644i
$907$	−9.63821e9			−0.428915			−0.214457	−	0.976733i	$-0.568798\pi$
$907$	−9.63821e9			−0.428915			−0.214457	+	0.976733i	$0.568798\pi$
$908$	4.50080e9	+	1.38520e10i	0.199521	+	0.614063i
$909$	−1.46403e9	−	1.06368e9i	−0.0646510	−	0.0469717i
$910$	−3.44433e10	+	1.96178e10i	−1.51516	+	0.862990i
$911$	−4.85290e9	+	3.52584e9i	−0.212661	+	0.154507i	−0.689017	−	0.724746i	$-0.741957\pi$
$911$	−4.85290e9	+	3.52584e9i	−0.212661	+	0.154507i	0.476356	+	0.879252i	$0.341957\pi$
$912$	−3.47835e9	−	2.52717e9i	−0.151842	−	0.110320i
$913$	−1.81511e10	−	1.31876e10i	−0.789326	−	0.573479i
$914$	−2.18591e10	+	1.58815e10i	−0.946935	+	0.687988i
$915$	6.75595e9	+	6.15510e9i	0.291550	+	0.265620i
$916$	9.86215e9	+	7.16527e9i	0.423972	+	0.308034i
$917$	−9.39153e8	−	2.89042e9i	−0.0402202	−	0.123785i
$918$	−4.95462e10			−2.11379
$919$	2.69922e9	+	8.30734e9i	0.114719	+	0.353067i	0.991888	−	0.127113i	$-0.0405711\pi$
$919$	2.69922e9	+	8.30734e9i	0.114719	+	0.353067i	−0.877170	+	0.480181i	$0.840571\pi$
$920$	4.39942e8	+	4.88460e7i	0.0186268	+	0.00206810i
$921$	4.63908e9	−	1.42776e10i	0.195670	−	0.602209i
$922$	9.23368e9	−	2.84183e10i	0.387986	−	1.19410i
$923$	−4.15942e8	+	3.02200e8i	−0.0174111	+	0.0126499i
$924$	−1.06831e10			−0.445496
$925$	1.85992e10	−	8.02122e9i	0.772676	−	0.333230i
$926$	3.11243e9			0.128813
$927$	−2.53460e10	+	1.84150e10i	−1.04503	+	0.759262i
$928$	−3.50872e9	+	1.07987e10i	−0.144122	+	0.443563i
$929$	−3.14682e9	+	9.68492e9i	−0.128771	+	0.396316i	−0.994569	−	0.104077i	$-0.966811\pi$
$929$	−3.14682e9	+	9.68492e9i	−0.128771	+	0.396316i	0.865798	+	0.500393i	$0.166811\pi$
$930$	1.01097e10	−	2.23536e10i	0.412144	−	0.911292i
$931$	2.69516e9	+	8.29485e9i	0.109461	+	0.336887i
$932$	2.61676e10			1.05879
$933$	−3.92072e9	−	1.20667e10i	−0.158045	−	0.486411i
$934$	1.30571e10	+	9.48655e9i	0.524364	+	0.380973i
$935$	3.23577e10	+	3.59262e9i	1.29460	+	0.143738i
$936$	−3.89998e8	+	2.83350e8i	−0.0155452	+	0.0112943i
$937$	−3.82365e9	−	2.77805e9i	−0.151841	−	0.110319i	0.509271	−	0.860606i	$-0.329915\pi$
$937$	−3.82365e9	−	2.77805e9i	−0.151841	−	0.110319i	−0.661112	+	0.750287i	$0.729915\pi$
$938$	1.81330e10	+	1.31744e10i	0.717396	+	0.521219i
$939$	1.14264e10	−	8.30174e9i	0.450379	−	0.327220i
$940$	2.17972e10	+	2.42010e9i	0.855959	+	0.0950357i
$941$	−3.68087e10	−	2.67431e10i	−1.44008	−	1.04628i	−0.988025	−	0.154292i	$-0.950690\pi$
$941$	−3.68087e10	−	2.67431e10i	−1.44008	−	1.04628i	−0.452057	−	0.891989i	$-0.649310\pi$
$942$	−6.22632e9	−	1.91626e10i	−0.242691	−	0.746926i
$943$	2.99496e10			1.16306
$944$	4.98198e8	+	1.53330e9i	0.0192752	+	0.0593231i
$945$	−1.17857e10	+	2.60594e10i	−0.454302	+	1.00451i
$946$	3.30986e9	−	1.01867e10i	0.127113	−	0.391214i
$947$	2.37193e9	−	7.30005e9i	0.0907564	−	0.279319i	−0.895368	−	0.445327i	$-0.853088\pi$
$947$	2.37193e9	−	7.30005e9i	0.0907564	−	0.279319i	0.986125	+	0.166007i	$0.0530875\pi$
$948$	6.69119e9	−	4.86144e9i	0.255079	−	0.185326i
$949$	2.66636e10			1.01272
$950$	−1.45634e10	+	6.28072e9i	−0.551099	+	0.237671i
$951$	1.07379e10			0.404844
$952$	−1.42737e9	+	1.03704e9i	−0.0536175	+	0.0389554i
$953$	−6.28324e9	+	1.93378e10i	−0.235157	+	0.723740i	0.761943	+	0.647644i	$0.224246\pi$
$953$	−6.28324e9	+	1.93378e10i	−0.235157	+	0.723740i	−0.997100	+	0.0760960i	$0.975754\pi$
$954$	1.36060e9	−	4.18750e9i	0.0507354	−	0.156148i
$955$	3.45317e10	+	3.83399e9i	1.28294	+	0.142442i
$956$	1.05535e10	+	3.24802e10i	0.390654	+	1.20231i
$957$	2.87117e9			0.105893
$958$	2.05171e10	+	6.31452e10i	0.753940	+	2.32039i
$959$	2.88852e10	+	2.09863e10i	1.05757	+	0.768372i
$960$	−9.52155e9	−	8.67474e9i	−0.347343	−	0.316451i
$961$	−3.14841e10	+	2.28745e10i	−1.14435	+	0.831419i
$962$	−2.41733e10	−	1.75629e10i	−0.875433	−	0.636039i
$963$	−3.26275e10	−	2.37053e10i	−1.17731	−	0.855368i
$964$	−1.44818e10	+	1.05216e10i	−0.520658	+	0.378280i
$965$	6.48694e9	−	3.69476e9i	0.232378	−	0.132355i
$966$	−1.38792e10	−	1.00838e10i	−0.495386	−	0.359919i
$967$	−7.24969e8	−	2.23122e9i	−0.0257826	−	0.0793506i	0.937337	−	0.348423i	$-0.113283\pi$
$967$	−7.24969e8	−	2.23122e9i	−0.0257826	−	0.0793506i	−0.963120	+	0.269073i	$0.913283\pi$
$968$	−3.71818e8			−0.0131755
$969$	3.06438e9	+	9.43119e9i	0.108196	+	0.332992i
$970$	−4.87283e10	−	4.43945e10i	−1.71427	−	1.56181i
$971$	1.29675e10	−	3.99099e10i	0.454558	−	1.39899i	−0.417096	−	0.908863i	$-0.636952\pi$
$971$	1.29675e10	−	3.99099e10i	0.454558	−	1.39899i	0.871654	−	0.490123i	$-0.163048\pi$
$972$	−9.07000e9	+	2.79146e10i	−0.316793	+	0.974988i
$973$	−1.39122e10	+	1.01078e10i	−0.484175	+	0.351773i
$974$	1.22858e10			0.426037
$975$	1.10205e9	+	1.18147e10i	0.0380790	+	0.408233i
$976$	−2.48033e10			−0.853954
$977$	−2.70253e10	+	1.96350e10i	−0.927127	+	0.673597i	−0.945288	−	0.326238i	$-0.894219\pi$
$977$	−2.70253e10	+	1.96350e10i	−0.927127	+	0.673597i	0.0181609	+	0.999835i	$0.494219\pi$
$978$	−5.53414e9	+	1.70323e10i	−0.189175	+	0.582221i
$979$	7.35098e9	−	2.26240e10i	0.250384	−	0.770602i
$980$	5.08948e9	+	2.46531e10i	0.172736	+	0.836721i
$981$	−4.78283e8	−	1.47200e9i	−0.0161750	−	0.0497814i
$982$	−5.25427e10			−1.77061
$983$	5.19290e9	+	1.59821e10i	0.174370	+	0.536656i	0.999604	−	0.0281348i	$-0.00895676\pi$
$983$	5.19290e9	+	1.59821e10i	0.174370	+	0.536656i	−0.825234	+	0.564791i	$0.808957\pi$
$984$	4.85036e8	+	3.52399e8i	0.0162290	+	0.0117910i
$985$	1.26803e9	+	6.14224e9i	0.0422768	+	0.204786i
$986$	2.07885e10	−	1.51037e10i	0.690644	−	0.501782i
$987$	−1.26895e10	−	9.21946e9i	−0.420082	−	0.305208i
$988$	9.55214e9	+	6.94003e9i	0.315102	+	0.228935i
$989$	7.02247e9	−	5.10212e9i	0.230836	−	0.167712i
$990$	1.01135e10	−	2.23619e10i	0.331266	−	0.732463i
$991$	1.31279e10	+	9.53799e9i	0.428487	+	0.311314i	0.781044	−	0.624476i	$-0.214688\pi$
$991$	1.31279e10	+	9.53799e9i	0.428487	+	0.311314i	−0.352556	+	0.935791i	$0.614688\pi$
$992$	2.09691e10	+	6.45362e10i	0.682007	+	2.09900i
$993$	−2.52061e9			−0.0816926
$994$	4.38342e8	+	1.34908e9i	0.0141567	+	0.0435698i
$995$	4.37506e10	−	2.49190e10i	1.40800	−	0.801954i
$996$	6.09514e9	−	1.87589e10i	0.195468	−	0.601589i
$997$	−1.01080e10	+	3.11094e10i	−0.323024	+	0.994164i	0.649301	+	0.760531i	$0.275061\pi$
$997$	−1.01080e10	+	3.11094e10i	−0.323024	+	0.994164i	−0.972325	+	0.233633i	$0.924939\pi$
$998$	4.36728e9	−	3.17301e9i	0.139077	−	0.101045i
$999$	−2.15594e10			−0.684161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.d.a.11.4	✓	68
25.4	even	10		625.8.a.c.1.6		34
25.16	even	5	inner	25.8.d.a.16.4	yes	68
25.21	even	5		625.8.a.d.1.29		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.d.a.11.4	✓	68	1.1	even	1	trivial
25.8.d.a.16.4	yes	68	25.16	even	5	inner
625.8.a.c.1.6		34	25.4	even	10
625.8.a.d.1.29		34	25.21	even	5

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.0050 + 9.44866i) q^{2} +(-6.54660 + 20.1484i) q^{3} +(40.2978 - 124.024i) q^{4} +(-242.876 + 138.334i) q^{5} +(-105.237 - 323.885i) q^{6} -1230.51 q^{7} +(11.9539 + 36.7902i) q^{8} +(1406.22 + 1021.68i) q^{9} +(1851.52 - 4093.89i) q^{10} +(2542.35 - 1847.12i) q^{11} +(2235.06 + 1623.87i) q^{12} +(5800.16 + 4214.06i) q^{13} +(16002.8 - 11626.7i) q^{14} +(-1197.20 - 5799.16i) q^{15} +(13001.1 + 9445.82i) q^{16} +(-11453.8 - 35251.0i) q^{17} -27941.4 q^{18} +(3902.51 + 12010.7i) q^{19} +(7369.42 + 35697.0i) q^{20} +(8055.68 - 24792.8i) q^{21} +(-15610.3 + 48043.6i) q^{22} +(-33120.1 + 24063.2i) q^{23} -819.520 q^{24} +(39852.2 - 67196.1i) q^{25} -115248. q^{26} +(-67274.6 + 48877.9i) q^{27} +(-49587.0 + 152613. i) q^{28} +(13326.9 - 41016.1i) q^{29} +(70363.9 + 64106.0i) q^{30} +(-79645.5 - 245124. i) q^{31} -263280. q^{32} +(20572.8 + 63316.5i) q^{33} +(482031. + 350216. i) q^{34} +(298862. - 170222. i) q^{35} +(183380. - 133234. i) q^{36} +(209750. + 152392. i) q^{37} +(-164237. - 119325. i) q^{38} +(-122878. + 89275.9i) q^{39} +(-7992.66 - 7281.82i) q^{40} +(-591854. - 430007. i) q^{41} +(129495. + 398545. i) q^{42} -212030. q^{43} +(-126636. - 389747. i) q^{44} +(-482871. - 53612.3i) q^{45} +(203361. - 625882. i) q^{46} +(185930. - 572233. i) q^{47} +(-275430. + 200112. i) q^{48} +690622. q^{49} +(116637. + 1.25043e6i) q^{50} +785233. q^{51} +(756378. - 549541. i) q^{52} +(-48694.8 + 149867. i) q^{53} +(413074. - 1.27131e6i) q^{54} +(-361953. + 800315. i) q^{55} +(-14709.4 - 45270.9i) q^{56} -267544. q^{57} +(214231. + 659335. i) q^{58} +(81162.7 + 58968.1i) q^{59} +(-767479. - 85212.0i) q^{60} +(-1.24866e6 + 907208. i) q^{61} +(3.35188e6 + 2.43528e6i) q^{62} +(-1.73038e6 - 1.25719e6i) q^{63} +(1.75982e6 - 1.27858e6i) q^{64} +(-1.99167e6 - 221131. i) q^{65} +(-865804. - 629044. i) q^{66} +(350151. + 1.07765e6i) q^{67} -4.83353e6 q^{68} +(-268009. - 824848. i) q^{69} +(-2.27832e6 + 5.03758e6i) q^{70} +(-22160.3 + 68202.3i) q^{71} +(-20778.1 + 63948.3i) q^{72} +(3.00881e6 - 2.18603e6i) q^{73} -4.16769e6 q^{74} +(1.09300e6 + 1.24286e6i) q^{75} +1.64688e6 q^{76} +(-3.12839e6 + 2.27291e6i) q^{77} +(754483. - 2.32206e6i) q^{78} +(925115. - 2.84721e6i) q^{79} +(-4.46432e6 - 495666. i) q^{80} +(630313. + 1.93990e6i) q^{81} +1.17600e7 q^{82} +(-2.20623e6 - 6.79009e6i) q^{83} +(-2.75028e6 - 1.99819e6i) q^{84} +(7.65827e6 + 6.97717e6i) q^{85} +(2.75745e6 - 2.00340e6i) q^{86} +(739161. + 537032. i) q^{87} +(98347.0 + 71453.3i) q^{88} +(6.12412e6 - 4.44943e6i) q^{89} +(6.78628e6 - 3.86526e6i) q^{90} +(-7.13718e6 - 5.18546e6i) q^{91} +(1.64974e6 + 5.07738e6i) q^{92} +5.46025e6 q^{93} +(2.98883e6 + 9.19866e6i) q^{94} +(-2.60932e6 - 2.37725e6i) q^{95} +(1.72359e6 - 5.30466e6i) q^{96} +(4.53364e6 - 1.39531e7i) q^{97} +(-8.98152e6 + 6.52546e6i) q^{98} +5.46227e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16}+ \cdots + 71266232 q^{99}+O(q^{100}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more