LMFDB - Embedded newform 312.4.m.a.181.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.23
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.98174 - 2.01809i) q^{2} -3.00000i q^{3} +(-0.145397 + 7.99868i) q^{4} +19.4332 q^{5} +(-6.05428 + 5.94523i) q^{6} +8.53532i q^{7} +(16.4302 - 15.5579i) q^{8} -9.00000 q^{9} +(-38.5117 - 39.2181i) q^{10} -49.3074 q^{11} +(23.9960 + 0.436190i) q^{12} +(-30.7594 - 35.3675i) q^{13} +(17.2251 - 16.9148i) q^{14} -58.2997i q^{15} +(-63.9577 - 2.32596i) q^{16} +117.742 q^{17} +(17.8357 + 18.1628i) q^{18} +26.5911 q^{19} +(-2.82553 + 155.440i) q^{20} +25.6060 q^{21} +(97.7145 + 99.5069i) q^{22} +117.626 q^{23} +(-46.6737 - 49.2906i) q^{24} +252.651 q^{25} +(-10.4177 + 132.165i) q^{26} +27.0000i q^{27} +(-68.2713 - 1.24101i) q^{28} -222.374i q^{29} +(-117.654 + 115.535i) q^{30} -240.158i q^{31} +(122.054 + 133.682i) q^{32} +147.922i q^{33} +(-233.334 - 237.614i) q^{34} +165.869i q^{35} +(1.30857 - 71.9881i) q^{36} +192.722 q^{37} +(-52.6968 - 53.6634i) q^{38} +(-106.103 + 92.2781i) q^{39} +(319.292 - 302.340i) q^{40} +4.97450i q^{41} +(-50.7444 - 51.6752i) q^{42} -184.130i q^{43} +(7.16913 - 394.394i) q^{44} -174.899 q^{45} +(-233.104 - 237.379i) q^{46} +410.488i q^{47} +(-6.97789 + 191.873i) q^{48} +270.148 q^{49} +(-500.689 - 509.873i) q^{50} -353.226i q^{51} +(287.366 - 240.892i) q^{52} -501.688i q^{53} +(54.4885 - 53.5070i) q^{54} -958.203 q^{55} +(132.792 + 140.237i) q^{56} -79.7734i q^{57} +(-448.771 + 440.688i) q^{58} -353.661 q^{59} +(466.321 + 8.47659i) q^{60} +268.231i q^{61} +(-484.661 + 475.931i) q^{62} -76.8179i q^{63} +(27.9039 - 511.239i) q^{64} +(-597.754 - 687.305i) q^{65} +(298.521 - 293.144i) q^{66} +623.874 q^{67} +(-17.1193 + 941.780i) q^{68} -352.877i q^{69} +(334.739 - 328.709i) q^{70} +313.912i q^{71} +(-147.872 + 140.021i) q^{72} -254.390i q^{73} +(-381.926 - 388.932i) q^{74} -757.953i q^{75} +(-3.86626 + 212.694i) q^{76} -420.854i q^{77} +(396.494 + 31.2532i) q^{78} +866.042 q^{79} +(-1242.91 - 45.2010i) q^{80} +81.0000 q^{81} +(10.0390 - 9.85817i) q^{82} -901.650 q^{83} +(-3.72302 + 204.814i) q^{84} +2288.11 q^{85} +(-371.592 + 364.899i) q^{86} -667.122 q^{87} +(-810.131 + 767.119i) q^{88} -701.679i q^{89} +(346.605 + 352.963i) q^{90} +(301.873 - 262.541i) q^{91} +(-17.1024 + 940.849i) q^{92} -720.473 q^{93} +(828.403 - 813.482i) q^{94} +516.752 q^{95} +(401.046 - 366.161i) q^{96} -531.587i q^{97} +(-535.364 - 545.184i) q^{98} +443.767 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.98174	−	2.01809i	−0.700652	−	0.713504i
$2$	−1.98174	−	2.01809i	−0.700652	−	0.713504i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−0.145397	+	7.99868i	−0.0181746	+	0.999835i
$5$	19.4332			1.73816			0.869081	−	0.494670i	$-0.164711\pi$
$5$	19.4332			1.73816			0.869081	+	0.494670i	$0.164711\pi$
$6$	−6.05428	+	5.94523i	−0.411941	+	0.404521i
$7$			8.53532i			0.460864i	0.973088	+	0.230432i	$0.0740139\pi$
$7$			8.53532i			0.460864i	−0.973088	+	0.230432i	$0.925986\pi$
$8$	16.4302	−	15.5579i	0.726120	−	0.687568i
$9$	−9.00000			−0.333333
$10$	−38.5117	−	39.2181i	−1.21785	−	1.24018i
$11$	−49.3074			−1.35152			−0.675761	−	0.737121i	$-0.736185\pi$
$11$	−49.3074			−1.35152			−0.675761	+	0.737121i	$0.736185\pi$
$12$	23.9960	+	0.436190i	0.577255	+	0.0104931i
$13$	−30.7594	−	35.3675i	−0.656240	−	0.754552i
$13$	−30.7594	−	35.3675i	−0.656240	−	0.754552i
$14$	17.2251	−	16.9148i	0.328828	−	0.322905i
$15$		−	58.2997i		−	1.00353i
$16$	−63.9577	−	2.32596i	−0.999339	−	0.0363432i
$17$	117.742			1.67980			0.839901	−	0.542740i	$-0.182613\pi$
$17$	117.742			1.67980			0.839901	+	0.542740i	$0.182613\pi$
$18$	17.8357	+	18.1628i	0.233551	+	0.237835i
$19$	26.5911			0.321075			0.160538	−	0.987030i	$-0.448677\pi$
$19$	26.5911			0.321075			0.160538	+	0.987030i	$0.448677\pi$
$20$	−2.82553	+	155.440i	−0.0315904	+	1.73787i
$21$	25.6060			0.266080
$22$	97.7145	+	99.5069i	0.946946	+	0.964316i
$23$	117.626			1.06638			0.533188	−	0.845997i	$-0.320994\pi$
$23$	117.626			1.06638			0.533188	+	0.845997i	$0.320994\pi$
$24$	−46.6737	−	49.2906i	−0.396968	−	0.419225i
$25$	252.651			2.02121
$26$	−10.4177	+	132.165i	−0.0785803	+	0.996908i
$27$			27.0000i			0.192450i
$28$	−68.2713	−	1.24101i	−0.460788	−	0.00837601i
$29$		−	222.374i		−	1.42392i	−0.702218	−	0.711962i	$-0.747807\pi$
$29$		−	222.374i		−	1.42392i	0.702218	−	0.711962i	$-0.252193\pi$
$30$	−117.654	+	115.535i	−0.716021	+	0.703124i
$31$		−	240.158i		−	1.39141i	−0.718329	−	0.695703i	$-0.755093\pi$
$31$		−	240.158i		−	1.39141i	0.718329	−	0.695703i	$-0.244907\pi$
$32$	122.054	+	133.682i	0.674258	+	0.738496i
$33$			147.922i			0.780301i
$34$	−233.334	−	237.614i	−1.17696	−	1.19854i
$35$			165.869i			0.801056i
$36$	1.30857	−	71.9881i	0.00605820	−	0.333278i
$37$	192.722			0.856307			0.428154	−	0.903706i	$-0.359164\pi$
$37$	192.722			0.856307			0.428154	+	0.903706i	$0.359164\pi$
$38$	−52.6968	−	53.6634i	−0.224962	−	0.229088i
$39$	−106.103	+	92.2781i	−0.435641	+	0.378880i
$40$	319.292	−	302.340i	1.26211	−	1.19510i
$41$			4.97450i			0.0189484i	0.999955	+	0.00947422i	$0.00301578\pi$
$41$			4.97450i			0.0189484i	−0.999955	+	0.00947422i	$0.996984\pi$
$42$	−50.7444	−	51.6752i	−0.186429	−	0.189849i
$43$		−	184.130i		−	0.653014i	−0.945195	−	0.326507i	$-0.894128\pi$
$43$		−	184.130i		−	0.653014i	0.945195	−	0.326507i	$-0.105872\pi$
$44$	7.16913	−	394.394i	0.0245634	−	1.35130i
$45$	−174.899			−0.579387
$46$	−233.104	−	237.379i	−0.747157	−	0.760862i
$47$			410.488i			1.27395i	0.770883	+	0.636977i	$0.219815\pi$
$47$			410.488i			1.27395i	−0.770883	+	0.636977i	$0.780185\pi$
$48$	−6.97789	+	191.873i	−0.0209827	+	0.576969i
$49$	270.148			0.787605
$50$	−500.689	−	509.873i	−1.41616	−	1.44214i
$51$		−	353.226i		−	0.969834i
$52$	287.366	−	240.892i	0.766355	−	0.642418i
$53$		−	501.688i		−	1.30023i	−0.759836	−	0.650115i	$-0.774721\pi$
$53$		−	501.688i		−	1.30023i	0.759836	−	0.650115i	$-0.225279\pi$
$54$	54.4885	−	53.5070i	0.137314	−	0.134840i
$55$	−958.203			−2.34916
$56$	132.792	+	140.237i	0.316875	+	0.334642i
$57$		−	79.7734i		−	0.185373i
$58$	−448.771	+	440.688i	−1.01598	+	0.997675i
$59$	−353.661			−0.780386			−0.390193	−	0.920733i	$-0.627592\pi$
$59$	−353.661			−0.780386			−0.390193	+	0.920733i	$0.627592\pi$
$60$	466.321	+	8.47659i	1.00336	+	0.0182387i
$61$			268.231i			0.563008i	0.959560	+	0.281504i	$0.0908332\pi$
$61$			268.231i			0.563008i	−0.959560	+	0.281504i	$0.909167\pi$
$62$	−484.661	+	475.931i	−0.992773	+	0.974891i
$63$		−	76.8179i		−	0.153621i
$64$	27.9039	−	511.239i	0.0544998	−	0.998514i
$65$	−597.754	−	687.305i	−1.14065	−	1.31153i
$66$	298.521	−	293.144i	0.556748	−	0.546720i
$67$	623.874			1.13759			0.568794	−	0.822480i	$-0.307410\pi$
$67$	623.874			1.13759			0.568794	+	0.822480i	$0.307410\pi$
$68$	−17.1193	+	941.780i	−0.0305297	+	1.67952i
$69$		−	352.877i		−	0.615672i
$70$	334.739	−	328.709i	0.571556	−	0.561261i
$71$			313.912i			0.524710i	0.964971	+	0.262355i	$0.0844992\pi$
$71$			313.912i			0.524710i	−0.964971	+	0.262355i	$0.915501\pi$
$72$	−147.872	+	140.021i	−0.242040	+	0.229189i
$73$		−	254.390i		−	0.407865i	−0.978985	−	0.203932i	$-0.934628\pi$
$73$		−	254.390i		−	0.407865i	0.978985	−	0.203932i	$-0.0653722\pi$
$74$	−381.926	−	388.932i	−0.599973	−	0.610978i
$75$		−	757.953i		−	1.16694i
$76$	−3.86626	+	212.694i	−0.00583541	+	0.321022i
$77$		−	420.854i		−	0.622868i
$78$	396.494	+	31.2532i	0.575565	+	0.0453684i
$79$	866.042			1.23338			0.616692	−	0.787205i	$-0.288472\pi$
$79$	866.042			1.23338			0.616692	+	0.787205i	$0.288472\pi$
$80$	−1242.91	−	45.2010i	−1.73701	−	0.0631703i
$81$	81.0000			0.111111
$82$	10.0390	−	9.85817i	0.0135198	−	0.0132763i
$83$	−901.650			−1.19240			−0.596198	−	0.802837i	$-0.703323\pi$
$83$	−901.650			−1.19240			−0.596198	+	0.802837i	$0.703323\pi$
$84$	−3.72302	+	204.814i	−0.00483589	+	0.266036i
$85$	2288.11			2.91977
$86$	−371.592	+	364.899i	−0.465928	+	0.457535i
$87$	−667.122			−0.822103
$88$	−810.131	+	767.119i	−0.981367	+	0.929264i
$89$		−	701.679i		−	0.835705i	−0.908515	−	0.417853i	$-0.862783\pi$
$89$		−	701.679i		−	0.835705i	0.908515	−	0.417853i	$-0.137217\pi$
$90$	346.605	+	352.963i	0.405949	+	0.413395i
$91$	301.873	−	262.541i	0.347746	−	0.302437i
$92$	−17.1024	+	940.849i	−0.0193809	+	1.06620i
$93$	−720.473			−0.803329
$94$	828.403	−	813.482i	0.908971	−	0.892598i
$95$	516.752			0.558080
$96$	401.046	−	366.161i	0.426371	−	0.389283i
$97$		−	531.587i		−	0.556438i	−0.960518	−	0.278219i	$-0.910256\pi$
$97$		−	531.587i		−	0.556438i	0.960518	−	0.278219i	$-0.0897441\pi$
$98$	−535.364	−	545.184i	−0.551836	−	0.561959i
$99$	443.767			0.450507
$100$	−36.7346	+	2020.87i	−0.0367346	+	2.02087i
$101$			1194.23i			1.17654i	0.808665	+	0.588269i	$0.200191\pi$
$101$			1194.23i			1.17654i	−0.808665	+	0.588269i	$0.799809\pi$
$102$	−712.843	+	700.003i	−0.691980	+	0.679516i
$103$	334.800			0.320280			0.160140	−	0.987094i	$-0.448805\pi$
$103$	334.800			0.320280			0.160140	+	0.987094i	$0.448805\pi$
$104$	−1055.63	−	102.545i	−0.995315	−	0.0966857i
$105$	497.607			0.462490
$106$	−1012.45	+	994.216i	−0.927718	+	0.911008i
$107$		−	652.991i		−	0.589973i	−0.955501	−	0.294986i	$-0.904685\pi$
$107$		−	652.991i		−	0.589973i	0.955501	−	0.294986i	$-0.0953151\pi$
$108$	−215.964	−	3.92571i	−0.192418	−	0.00349770i
$109$	−1710.98			−1.50351			−0.751754	−	0.659443i	$-0.770792\pi$
$109$	−1710.98			−1.50351			−0.751754	+	0.659443i	$0.770792\pi$
$110$	1898.91	+	1933.74i	1.64595	+	1.67614i
$111$		−	578.167i		−	0.494389i
$112$	19.8528	−	545.899i	0.0167493	−	0.460559i
$113$	−40.3996			−0.0336325			−0.0168162	−	0.999859i	$-0.505353\pi$
$113$	−40.3996			−0.0336325			−0.0168162	+	0.999859i	$0.505353\pi$
$114$	−160.990	+	158.090i	−0.132264	+	0.129882i
$115$	2285.85			1.85353
$116$	1778.70	+	32.3325i	1.42369	+	0.0258793i
$117$	276.834	+	318.308i	0.218747	+	0.251517i
$118$	700.866	+	713.721i	0.546779	+	0.556808i
$119$			1004.97i			0.774160i
$120$	−907.021	−	957.877i	−0.689994	−	0.728682i
$121$	1100.22			0.826611
$122$	541.315	−	531.565i	0.401708	−	0.394472i
$123$	14.9235			0.0109399
$124$	1920.94	+	34.9181i	1.39118	+	0.0252882i
$125$	2480.67			1.77502
$126$	−155.026	+	152.233i	−0.109609	+	0.107635i
$127$	−2128.45			−1.48716			−0.743579	−	0.668648i	$-0.766873\pi$
$127$	−2128.45			−1.48716			−0.743579	+	0.668648i	$0.766873\pi$
$128$	−1087.03	+	956.831i	−0.750628	+	0.660725i
$129$	−552.391			−0.377018
$130$	−202.451	+	2568.39i	−0.136585	+	1.73279i
$131$		−	94.2390i		−	0.0628527i	−0.999506	−	0.0314263i	$-0.989995\pi$
$131$		−	94.2390i		−	0.0628527i	0.999506	−	0.0314263i	$-0.0100050\pi$
$132$	−1183.18	−	21.5074i	−0.780173	−	0.0141817i
$133$			226.964i			0.147972i
$134$	−1236.36	−	1259.04i	−0.797053	−	0.811673i
$135$			524.698i			0.334509i
$136$	1934.53	−	1831.82i	1.21974	−	1.15498i
$137$			2147.19i			1.33903i	0.742801	+	0.669513i	$0.233497\pi$
$137$			2147.19i			1.33903i	−0.742801	+	0.669513i	$0.766503\pi$
$138$	−712.138	+	699.311i	−0.439284	+	0.431372i
$139$		−	451.555i		−	0.275542i	−0.990464	−	0.137771i	$-0.956006\pi$
$139$		−	451.555i		−	0.275542i	0.990464	−	0.137771i	$-0.0439938\pi$
$140$	−1326.73	−	24.1168i	−0.800924	−	0.0145589i
$141$	1231.46			0.735518
$142$	633.503	−	622.092i	0.374383	−	0.367639i
$143$	1516.67	+	1743.88i	0.886922	+	1.01979i
$144$	575.619	+	20.9337i	0.333113	+	0.0121144i
$145$		−	4321.45i		−	2.47501i
$146$	−513.383	+	504.136i	−0.291013	+	0.285771i
$147$		−	810.445i		−	0.454724i
$148$	−28.0212	+	1541.52i	−0.0155630	+	0.856166i
$149$	626.419			0.344418			0.172209	−	0.985060i	$-0.444910\pi$
$149$	626.419			0.344418			0.172209	+	0.985060i	$0.444910\pi$
$150$	−1529.62	+	1502.07i	−0.832619	+	0.817621i
$151$			199.097i			0.107300i	0.998560	+	0.0536499i	$0.0170855\pi$
$151$			199.097i			0.107300i	−0.998560	+	0.0536499i	$0.982915\pi$
$152$	436.898	−	413.702i	0.233139	−	0.220761i
$153$	−1059.68			−0.559934
$154$	−849.323	+	834.025i	−0.444418	+	0.436413i
$155$		−	4667.04i		−	2.41849i
$156$	−722.676	−	862.097i	−0.370900	−	0.442455i
$157$		−	1381.01i		−	0.702017i	−0.936372	−	0.351008i	$-0.885839\pi$
$157$		−	1381.01i		−	0.702017i	0.936372	−	0.351008i	$-0.114161\pi$
$158$	−1716.27	−	1747.75i	−0.864172	−	0.880024i
$159$	−1505.06			−0.750688
$160$	2371.90	+	2597.88i	1.17197	+	1.28363i
$161$			1003.97i			0.491454i
$162$	−160.521	−	163.466i	−0.0778502	−	0.0792782i
$163$	−1581.77			−0.760082			−0.380041	−	0.924970i	$-0.624090\pi$
$163$	−1581.77			−0.760082			−0.380041	+	0.924970i	$0.624090\pi$
$164$	−39.7894	−	0.723276i	−0.0189453	−	0.000344380i
$165$			2874.61i			1.35629i
$166$	1786.84	+	1819.61i	0.835455	+	0.850779i
$167$			3549.13i			1.64455i	0.569091	+	0.822275i	$0.307295\pi$
$167$			3549.13i			1.64455i	−0.569091	+	0.822275i	$0.692705\pi$
$168$	420.711	−	398.375i	0.193206	−	0.182948i
$169$	−304.721	+	2175.77i	−0.138699	+	0.990335i
$170$	−4534.44	−	4617.61i	−2.04574	−	2.08326i
$171$	−239.320			−0.107025
$172$	1472.80	+	26.7719i	0.652906	+	0.0118683i
$173$			1461.00i			0.642066i	0.947068	+	0.321033i	$0.104030\pi$
$173$			1461.00i			0.642066i	−0.947068	+	0.321033i	$0.895970\pi$
$174$	1322.06	+	1346.31i	0.576008	+	0.586574i
$175$			2156.46i			0.931501i
$176$	3153.59	+	114.687i	1.35063	+	0.0491186i
$177$			1060.98i			0.450556i
$178$	−1416.05	+	1390.55i	−0.596279	+	0.585538i
$179$			4222.63i			1.76321i	0.471988	+	0.881605i	$0.343537\pi$
$179$			4222.63i			1.76321i	−0.471988	+	0.881605i	$0.656463\pi$
$180$	25.4298	−	1398.96i	0.0105301	−	0.579292i
$181$			3351.24i			1.37622i	0.725606	+	0.688110i	$0.241560\pi$
$181$			3351.24i			1.37622i	−0.725606	+	0.688110i	$0.758440\pi$
$182$	−1128.07	−	88.9188i	−0.459439	−	0.0362148i
$183$	804.693			0.325053
$184$	1932.61	−	1830.01i	0.774316	−	0.733206i
$185$	3745.22			1.48840
$186$	1427.79	+	1453.98i	0.562854	+	0.573178i
$187$	−5805.55			−2.27029
$188$	−3283.36	−	59.6836i	−1.27374	−	0.0231536i
$189$	−230.454			−0.0886933
$190$	−1024.07	−	1042.85i	−0.391020	−	0.398192i
$191$	−2384.90			−0.903482			−0.451741	−	0.892149i	$-0.649197\pi$
$191$	−2384.90			−0.903482			−0.451741	+	0.892149i	$0.649197\pi$
$192$	−1533.72	−	83.7116i	−0.576492	−	0.0314655i
$193$			1797.53i			0.670411i	0.942145	+	0.335205i	$0.108806\pi$
$193$			1797.53i			0.670411i	−0.942145	+	0.335205i	$0.891194\pi$
$194$	−1072.79	+	1053.47i	−0.397021	+	0.389869i
$195$	−2061.92	+	1793.26i	−0.757215	+	0.658555i
$196$	−39.2787	+	2160.83i	−0.0143144	+	0.787474i
$197$	3708.67			1.34128			0.670638	−	0.741785i	$-0.266020\pi$
$197$	3708.67			1.34128			0.670638	+	0.741785i	$0.266020\pi$
$198$	−879.431	−	895.562i	−0.315649	−	0.321439i
$199$	−1420.65			−0.506068			−0.253034	−	0.967457i	$-0.581428\pi$
$199$	−1420.65			−0.506068			−0.253034	+	0.967457i	$0.581428\pi$
$200$	4151.11	−	3930.72i	1.46764	−	1.38972i
$201$		−	1871.62i		−	0.656787i
$202$	2410.07	−	2366.66i	0.839465	−	0.824344i
$203$	1898.03			0.656236
$204$	2825.34	+	51.3579i	0.969674	+	0.0176263i
$205$			96.6706i			0.0329354i
$206$	−663.487	−	675.658i	−0.224405	−	0.228521i
$207$	−1058.63			−0.355458
$208$	1885.04	+	2333.57i	0.628383	+	0.777904i
$209$	−1311.14			−0.433940
$210$	−986.128	−	1004.22i	−0.324044	−	0.329988i
$211$		−	5818.86i		−	1.89852i	−0.314499	−	0.949258i	$-0.601837\pi$
$211$		−	5818.86i		−	1.89852i	0.314499	−	0.949258i	$-0.398163\pi$
$212$	4012.84	+	72.9438i	1.30001	+	0.0236311i
$213$	941.735			0.302942
$214$	−1317.80	+	1294.06i	−0.420948	+	0.413365i
$215$		−	3578.25i		−	1.13504i
$216$	420.063	+	443.616i	0.132323	+	0.139742i
$217$	2049.82			0.641249
$218$	3390.73	+	3452.92i	1.05344	+	1.07276i
$219$	−763.170			−0.235481
$220$	139.320	−	7664.35i	0.0426951	−	2.34878i
$221$	−3621.67	−	4164.24i	−1.10235	−	1.26750i
$222$	−1166.79	+	1145.78i	−0.352748	+	0.346395i
$223$		−	5752.76i		−	1.72751i	−0.503916	−	0.863753i	$-0.668108\pi$
$223$		−	5752.76i		−	1.72751i	0.503916	−	0.863753i	$-0.331892\pi$
$224$	−1141.02	+	1041.77i	−0.340346	+	0.310741i
$225$	−2273.86			−0.673736
$226$	80.0615	+	81.5301i	0.0235647	+	0.0239969i
$227$	−2000.89			−0.585037			−0.292519	−	0.956260i	$-0.594493\pi$
$227$	−2000.89			−0.585037			−0.292519	+	0.956260i	$0.594493\pi$
$228$	638.082	+	11.5988i	0.185342	+	0.00336907i
$229$	4617.48			1.33245			0.666226	−	0.745750i	$-0.267909\pi$
$229$	4617.48			1.33245			0.666226	+	0.745750i	$0.267909\pi$
$230$	−4529.96	−	4613.05i	−1.29868	−	1.32250i
$231$	−1262.56			−0.359613
$232$	−3459.67	−	3653.65i	−0.979046	−	1.03394i
$233$	1716.45			0.482610			0.241305	−	0.970449i	$-0.422425\pi$
$233$	1716.45			0.482610			0.241305	+	0.970449i	$0.422425\pi$
$234$	93.7597	−	1189.48i	0.0261934	−	0.332303i
$235$			7977.12i			2.21434i
$236$	51.4212	−	2828.82i	0.0141832	−	0.780257i
$237$		−	2598.13i		−	0.712094i
$238$	2028.11	−	1991.58i	0.552366	−	0.542416i
$239$			931.378i			0.252075i	0.992026	+	0.126037i	$0.0402259\pi$
$239$			931.378i			0.252075i	−0.992026	+	0.126037i	$0.959774\pi$
$240$	−135.603	+	3728.72i	−0.0364714	+	1.00287i
$241$		−	4468.94i		−	1.19448i	−0.802062	−	0.597240i	$-0.796264\pi$
$241$		−	4468.94i		−	1.19448i	0.802062	−	0.597240i	$-0.203736\pi$
$242$	−2180.35	−	2220.35i	−0.579167	−	0.589790i
$243$		−	243.000i		−	0.0641500i
$244$	−2145.49	−	38.9999i	−0.562915	−	0.0102324i
$245$	5249.86			1.36898
$246$	−29.5745	−	30.1170i	−0.00766505	−	0.00780565i
$247$	−817.927	−	940.462i	−0.210702	−	0.242268i
$248$	−3736.35	−	3945.84i	−0.956687	−	1.01033i
$249$			2704.95i			0.688431i
$250$	−4916.05	−	5006.22i	−1.24367	−	1.26649i
$251$		−	680.070i		−	0.171018i	−0.996337	−	0.0855092i	$-0.972748\pi$
$251$		−	680.070i		−	0.171018i	0.996337	−	0.0855092i	$-0.0272517\pi$
$252$	614.441	+	11.1691i	0.153596	+	0.00279200i
$253$	−5799.81			−1.44123
$254$	4218.03	+	4295.40i	1.04198	+	1.06109i
$255$		−	6864.32i		−	1.68573i
$256$	4085.18	+	297.527i	0.997358	+	0.0726383i
$257$	7670.60			1.86179			0.930893	−	0.365293i	$-0.119031\pi$
$257$	7670.60			1.86179			0.930893	+	0.365293i	$0.119031\pi$
$258$	1094.70	+	1114.78i	0.264158	+	0.269004i
$259$			1644.95i			0.394641i
$260$	5584.45	−	4681.31i	1.33205	−	1.11663i
$261$			2001.37i			0.474642i
$262$	−190.183	+	186.757i	−0.0448456	+	0.0440378i
$263$	2160.00			0.506431			0.253216	−	0.967410i	$-0.418512\pi$
$263$	2160.00			0.506431			0.253216	+	0.967410i	$0.418512\pi$
$264$	2301.36	+	2430.39i	0.536511	+	0.566592i
$265$		−	9749.42i		−	2.26001i
$266$	458.034	−	449.784i	0.105578	−	0.103677i
$267$	−2105.04			−0.482495
$268$	−90.7093	+	4990.17i	−0.0206752	+	1.13740i
$269$			6377.13i			1.44543i	0.691147	+	0.722714i	$0.257106\pi$
$269$			6377.13i			1.44543i	−0.691147	+	0.722714i	$0.742894\pi$
$270$	1058.89	−	1039.82i	0.238674	−	0.234375i
$271$			4253.92i			0.953532i	0.879030	+	0.476766i	$0.158191\pi$
$271$			4253.92i			0.953532i	−0.879030	+	0.476766i	$0.841809\pi$
$272$	−7530.51	−	273.864i	−1.67869	−	0.0610493i
$273$	−787.623	−	905.619i	−0.174612	−	0.200771i
$274$	4333.22	−	4255.17i	0.955399	−	0.938190i
$275$	−12457.6			−2.73171
$276$	2822.55	+	51.3071i	0.615570	+	0.0111896i
$277$			4986.70i			1.08167i	0.841130	+	0.540833i	$0.181891\pi$
$277$			4986.70i			1.08167i	−0.841130	+	0.540833i	$0.818109\pi$
$278$	−911.279	+	894.865i	−0.196600	+	0.193059i
$279$			2161.42i			0.463802i
$280$	2580.57	+	2725.26i	0.550781	+	0.581663i
$281$		−	2215.50i		−	0.470340i	−0.971954	−	0.235170i	$-0.924435\pi$
$281$		−	2215.50i		−	0.470340i	0.971954	−	0.235170i	$-0.0755647\pi$
$282$	−2440.44	−	2485.21i	−0.515342	−	0.524795i
$283$			1039.14i			0.218271i	0.994027	+	0.109135i	$0.0348082\pi$
$283$			1039.14i			0.218271i	−0.994027	+	0.109135i	$0.965192\pi$
$284$	−2510.88	−	45.6417i	−0.524624	−	0.00953640i
$285$		−	1550.26i		−	0.322208i
$286$	513.672	−	6516.69i	0.106203	−	1.34734i
$287$	−42.4589			−0.00873265
$288$	−1098.48	−	1203.14i	−0.224753	−	0.246165i
$289$	8950.17			1.82173
$290$	−8721.08	+	8564.00i	−1.76593	+	1.73412i
$291$	−1594.76			−0.321260
$292$	2034.78	+	36.9875i	0.407797	+	0.00741277i
$293$	−7130.48			−1.42173			−0.710866	−	0.703328i	$-0.751697\pi$
$293$	−7130.48			−1.42173			−0.710866	+	0.703328i	$0.751697\pi$
$294$	−1635.55	+	1606.09i	−0.324447	+	0.318603i
$295$	−6872.79			−1.35644
$296$	3166.47	−	2998.35i	0.621782	−	0.588770i
$297$		−	1331.30i		−	0.260100i
$298$	−1241.40	−	1264.17i	−0.241317	−	0.245743i
$299$	−3618.09	−	4160.12i	−0.699798	−	0.804636i
$300$	6062.62	+	110.204i	1.16675	+	0.0212087i
$301$	1571.61			0.300951
$302$	401.796	−	394.558i	0.0765587	−	0.0751797i
$303$	3582.69			0.679275
$304$	−1700.71	−	61.8500i	−0.320863	−	0.0116689i
$305$			5212.60i			0.978598i
$306$	2100.01	+	2138.53i	0.392319	+	0.399515i
$307$	5102.81			0.948641			0.474320	−	0.880352i	$-0.342694\pi$
$307$	5102.81			0.948641			0.474320	+	0.880352i	$0.342694\pi$
$308$	3366.28	+	61.1908i	0.622765	+	0.0113204i
$309$		−	1004.40i		−	0.184914i
$310$	−9418.52	+	9248.87i	−1.72560	+	1.69452i
$311$	1696.60			0.309342			0.154671	−	0.987966i	$-0.450568\pi$
$311$	1696.60			0.309342			0.154671	+	0.987966i	$0.450568\pi$
$312$	−307.634	+	3166.88i	−0.0558215	+	0.574645i
$313$	−5575.22			−1.00680			−0.503402	−	0.864052i	$-0.667919\pi$
$313$	−5575.22			−1.00680			−0.503402	+	0.864052i	$0.667919\pi$
$314$	−2787.01	+	2736.81i	−0.500891	+	0.491869i
$315$		−	1492.82i		−	0.267019i
$316$	−125.920	+	6927.19i	−0.0224162	+	1.23318i
$317$	−5150.28			−0.912519			−0.456259	−	0.889847i	$-0.650811\pi$
$317$	−5150.28			−0.912519			−0.456259	+	0.889847i	$0.650811\pi$
$318$	2982.65	+	3037.36i	0.525971	+	0.535618i
$319$			10964.7i			1.92447i
$320$	542.263	−	9935.03i	0.0947294	−	1.73558i
$321$	−1958.97			−0.340621
$322$	2026.11	−	1989.61i	0.350654	−	0.344338i
$323$	3130.89			0.539342
$324$	−11.7771	+	647.893i	−0.00201940	+	0.111093i
$325$	−7771.38	−	8935.63i	−1.32640	−	1.52511i
$326$	3134.65	+	3192.15i	0.532553	+	0.542321i
$327$			5132.95i			0.868051i
$328$	77.3927	+	81.7320i	0.0130283	+	0.0137588i
$329$	−3503.65			−0.587119
$330$	5801.23	−	5696.73i	0.967718	−	0.950287i
$331$	5006.92			0.831436			0.415718	−	0.909493i	$-0.363530\pi$
$331$	5006.92			0.831436			0.415718	+	0.909493i	$0.363530\pi$
$332$	131.097	−	7212.01i	0.0216713	−	1.19220i
$333$	−1734.50			−0.285436
$334$	7162.47	−	7033.46i	1.17339	−	1.15226i
$335$	12123.9			1.97731
$336$	−1637.70	−	59.5585i	−0.265904	−	0.00967019i
$337$	−5029.86			−0.813038			−0.406519	−	0.913642i	$-0.633258\pi$
$337$	−5029.86			−0.813038			−0.406519	+	0.913642i	$0.633258\pi$
$338$	4994.77	−	3696.85i	0.803787	−	0.594918i
$339$			121.199i			0.0194177i
$340$	−332.683	+	18301.8i	−0.0530656	+	2.91928i
$341$			11841.6i			1.88052i
$342$	474.271	+	482.970i	0.0749873	+	0.0763627i
$343$			5233.42i			0.823842i
$344$	−2864.68	−	3025.30i	−0.448992	−	0.474166i
$345$		−	6857.54i		−	1.07014i
$346$	2948.43	−	2895.32i	0.458117	−	0.449865i
$347$		−	2220.47i		−	0.343519i	−0.985139	−	0.171760i	$-0.945055\pi$
$347$		−	2220.47i		−	0.343519i	0.985139	−	0.171760i	$-0.0549452\pi$
$348$	96.9974	−	5336.10i	0.0149414	−	0.821968i
$349$	−3444.40			−0.528294			−0.264147	−	0.964482i	$-0.585090\pi$
$349$	−3444.40			−0.528294			−0.264147	+	0.964482i	$0.585090\pi$
$350$	4351.93	−	4273.54i	0.664629	−	0.652658i
$351$	954.923	−	830.503i	0.145214	−	0.126293i
$352$	−6018.15	−	6591.52i	−0.911274	−	0.998094i
$353$			7467.79i			1.12598i	0.826464	+	0.562989i	$0.190349\pi$
$353$			7467.79i			1.12598i	−0.826464	+	0.562989i	$0.809651\pi$
$354$	2141.16	−	2102.60i	0.321473	−	0.315683i
$355$			6100.32i			0.912032i
$356$	5612.50	+	102.022i	0.835567	+	0.0151886i
$357$	3014.90			0.446961
$358$	8521.67	−	8368.17i	1.25806	−	1.23540i
$359$		−	2103.92i		−	0.309306i	−0.987969	−	0.154653i	$-0.950574\pi$
$359$		−	2103.92i		−	0.309306i	0.987969	−	0.154653i	$-0.0494260\pi$
$360$	−2873.63	+	2721.06i	−0.420705	+	0.398368i
$361$	−6151.91			−0.896911
$362$	6763.12	−	6641.30i	0.981938	−	0.964251i
$363$		−	3300.66i		−	0.477244i
$364$	2056.09	+	2452.76i	0.296067	+	0.353185i
$365$		−	4943.62i		−	0.708935i
$366$	−1594.69	−	1623.95i	−0.227749	−	0.231926i
$367$	−8045.36			−1.14432			−0.572159	−	0.820143i	$-0.693894\pi$
$367$	−8045.36			−1.14432			−0.572159	+	0.820143i	$0.693894\pi$
$368$	−7523.06	−	273.593i	−1.06567	−	0.0387555i
$369$		−	44.7705i		−	0.00631615i
$370$	−7422.06	−	7558.20i	−1.04285	−	1.06198i
$371$	4282.07			0.599229
$372$	104.754	−	5762.83i	0.0146002	−	0.803196i
$373$			320.782i			0.0445293i	0.999752	+	0.0222647i	$0.00708765\pi$
$373$			320.782i			0.0445293i	−0.999752	+	0.0222647i	$0.992912\pi$
$374$	11505.1	+	11716.1i	1.59068	+	1.61986i
$375$		−	7442.01i		−	1.02481i
$376$	6386.33	+	6744.41i	0.875931	+	0.925043i
$377$	−7864.82	+	6840.09i	−1.07443	+	0.934436i
$378$	456.700	+	465.077i	0.0621431	+	0.0632830i
$379$	7990.79			1.08301			0.541503	−	0.840699i	$-0.317855\pi$
$379$	7990.79			1.08301			0.541503	+	0.840699i	$0.317855\pi$
$380$	−75.1341	+	4133.33i	−0.0101429	+	0.557988i
$381$			6385.34i			0.858611i
$382$	4726.25	+	4812.94i	0.633026	+	0.644637i
$383$		−	1147.52i		−	0.153095i	−0.997066	−	0.0765477i	$-0.975610\pi$
$383$		−	1147.52i		−	0.153095i	0.997066	−	0.0765477i	$-0.0243897\pi$
$384$	2870.49	+	3261.08i	0.381469	+	0.433376i
$385$		−	8178.56i		−	1.08264i
$386$	3627.59	−	3562.25i	0.478340	−	0.469724i
$387$			1657.17i			0.217671i
$388$	4251.99	+	77.2910i	0.556346	+	0.0101130i
$389$			12710.1i			1.65663i	0.560263	+	0.828315i	$0.310700\pi$
$389$			12710.1i			1.65663i	−0.560263	+	0.828315i	$0.689300\pi$
$390$	7705.16	+	607.352i	1.00043	+	0.0788576i
$391$	13849.5			1.79130
$392$	4438.60	−	4202.94i	0.571895	−	0.541532i
$393$	−282.717			−0.0362880
$394$	−7349.62	−	7484.43i	−0.939768	−	0.957006i
$395$	16830.0			2.14382
$396$	−64.5222	+	3549.55i	−0.00818779	+	0.450433i
$397$	−2210.83			−0.279493			−0.139746	−	0.990187i	$-0.544629\pi$
$397$	−2210.83			−0.279493			−0.139746	+	0.990187i	$0.544629\pi$
$398$	2815.37	+	2867.01i	0.354577	+	0.361081i
$399$	680.892			0.0854316
$400$	−16159.0	−	587.657i	−2.01987	−	0.0734571i
$401$		−	4593.30i		−	0.572016i	−0.958227	−	0.286008i	$-0.907672\pi$
$401$		−	4593.30i		−	0.572016i	0.958227	−	0.286008i	$-0.0923284\pi$
$402$	−3777.11	+	3709.07i	−0.468620	+	0.460179i
$403$	−8493.78	+	7387.10i	−1.04989	+	0.913096i
$404$	−9552.27	−	173.637i	−1.17634	−	0.0213831i
$405$	1574.09			0.193129
$406$	−3761.41	−	3830.41i	−0.459792	−	0.468226i
$407$	−9502.64			−1.15732
$408$	−5495.45	−	5803.58i	−0.666827	−	0.704215i
$409$			13029.9i			1.57528i	0.616138	+	0.787638i	$0.288696\pi$
$409$			13029.9i			1.57528i	−0.616138	+	0.787638i	$0.711304\pi$
$410$	195.090	−	191.576i	0.0234996	−	0.0230763i
$411$	6441.56			0.773087
$412$	−48.6788	+	2677.96i	−0.00582096	+	0.320227i
$413$		−	3018.61i		−	0.359652i
$414$	2097.93	+	2136.41i	0.249052	+	0.253621i
$415$	−17522.0			−2.07258
$416$	973.705	−	8428.71i	0.114759	−	0.993393i
$417$	−1354.66			−0.159084
$418$	2598.34	+	2646.00i	0.304041	+	0.309618i
$419$		−	16210.3i		−	1.89003i	−0.327025	−	0.945016i	$-0.606046\pi$
$419$		−	16210.3i		−	1.89003i	0.327025	−	0.945016i	$-0.393954\pi$
$420$	−72.3504	+	3980.20i	−0.00840556	+	0.462414i
$421$	997.361			0.115459			0.0577297	−	0.998332i	$-0.481614\pi$
$421$	997.361			0.115459			0.0577297	+	0.998332i	$0.481614\pi$
$422$	−11743.0	+	11531.5i	−1.35460	+	1.33020i
$423$		−	3694.39i		−	0.424651i
$424$	−7805.21	−	8242.84i	−0.893996	−	0.944122i
$425$	29747.6			3.39523
$426$	−1866.27	−	1900.51i	−0.212257	−	0.216150i
$427$	−2289.44			−0.259470
$428$	5223.07	+	94.9428i	0.589875	+	0.0107225i
$429$	5231.64	−	4550.00i	0.588778	−	0.512065i
$430$	−7221.24	+	7091.17i	−0.809858	+	0.795271i
$431$			12985.6i			1.45127i	0.688082	+	0.725633i	$0.258453\pi$
$431$			12985.6i			1.45127i	−0.688082	+	0.725633i	$0.741547\pi$
$432$	62.8010	−	1726.86i	0.00699425	−	0.192323i
$433$	3083.02			0.342172			0.171086	−	0.985256i	$-0.445272\pi$
$433$	3083.02			0.342172			0.171086	+	0.985256i	$0.445272\pi$
$434$	−4062.22	−	4136.73i	−0.449292	−	0.457533i
$435$	−12964.3			−1.42895
$436$	248.771	−	13685.6i	0.0273257	−	1.50326i
$437$	3127.80			0.342386
$438$	1512.41	+	1540.15i	0.164990	+	0.168016i
$439$	6249.22			0.679406			0.339703	−	0.940533i	$-0.389673\pi$
$439$	6249.22			0.679406			0.339703	+	0.940533i	$0.389673\pi$
$440$	−15743.5	+	14907.6i	−1.70577	+	1.61521i
$441$	−2431.34			−0.262535
$442$	−1226.61	+	15561.3i	−0.131999	+	1.67461i
$443$			6954.31i			0.745845i	0.927863	+	0.372922i	$0.121644\pi$
$443$			6954.31i			0.745845i	−0.927863	+	0.372922i	$0.878356\pi$
$444$	4624.57	+	84.0636i	0.494307	+	0.00898532i
$445$		−	13635.9i		−	1.45259i
$446$	−11609.6	+	11400.5i	−1.23258	+	1.21038i
$447$		−	1879.26i		−	0.198850i
$448$	4363.59	+	238.168i	0.460179	+	0.0251170i
$449$			3461.92i			0.363871i	0.983310	+	0.181936i	$0.0582362\pi$
$449$			3461.92i			0.363871i	−0.983310	+	0.181936i	$0.941764\pi$
$450$	4506.20	+	4588.86i	0.472054	+	0.480713i
$451$		−	245.279i		−	0.0256092i
$452$	5.87396	−	323.143i	0.000611257	−	0.0336269i
$453$	597.290			0.0619495
$454$	3965.24	+	4037.97i	0.409907	+	0.417426i
$455$	5866.37	−	5102.02i	0.604439	−	0.525685i
$456$	−1241.11	−	1310.69i	−0.127456	−	0.134603i
$457$		−	10185.4i		−	1.04256i	−0.853385	−	0.521282i	$-0.825454\pi$
$457$		−	10185.4i		−	1.04256i	0.853385	−	0.521282i	$-0.174546\pi$
$458$	−9150.65	−	9318.49i	−0.933584	−	0.950709i
$459$			3179.03i			0.323278i
$460$	−332.355	+	18283.7i	−0.0336872	+	1.85323i
$461$	−1661.54			−0.167865			−0.0839324	−	0.996471i	$-0.526748\pi$
$461$	−1661.54			−0.167865			−0.0839324	+	0.996471i	$0.526748\pi$
$462$	2502.07	+	2547.97i	0.251963	+	0.256585i
$463$			1164.53i			0.116890i	0.998291	+	0.0584452i	$0.0186143\pi$
$463$			1164.53i			0.116890i	−0.998291	+	0.0584452i	$0.981386\pi$
$464$	−517.234	+	14222.5i	−0.0517500	+	1.42298i
$465$	−14001.1			−1.39632
$466$	−3401.55	−	3463.95i	−0.338141	−	0.344344i
$467$			17297.7i			1.71401i	0.515305	+	0.857007i	$0.327679\pi$
$467$			17297.7i			1.71401i	−0.515305	+	0.857007i	$0.672321\pi$
$468$	−2586.29	+	2168.03i	−0.255452	+	0.214139i
$469$			5324.97i			0.524273i
$470$	16098.6	−	15808.6i	1.57994	−	1.55148i
$471$	−4143.03			−0.405310
$472$	−5810.73	+	5502.23i	−0.566654	+	0.536569i
$473$			9078.99i			0.882563i
$474$	−5243.26	+	5148.81i	−0.508082	+	0.498930i
$475$	6718.27			0.648959
$476$	−8038.39	−	146.119i	−0.774032	−	0.0140700i
$477$			4515.19i			0.433410i
$478$	1879.61	−	1845.75i	0.179856	−	0.176617i
$479$		−	3869.43i		−	0.369100i	−0.982823	−	0.184550i	$-0.940917\pi$
$479$		−	3869.43i		−	0.369100i	0.982823	−	0.184550i	$-0.0590828\pi$
$480$	7793.63	−	7115.70i	0.741102	−	0.676637i
$481$	−5928.02	−	6816.11i	−0.561943	−	0.646129i
$482$	−9018.74	+	8856.29i	−0.852266	+	0.836915i
$483$	3011.91			0.283741
$484$	−159.968	+	8800.30i	−0.0150233	+	0.826475i
$485$		−	10330.5i		−	0.967180i
$486$	−490.397	+	481.563i	−0.0457713	+	0.0449468i
$487$		−	6596.18i		−	0.613761i	−0.951748	−	0.306881i	$-0.900715\pi$
$487$		−	6596.18i		−	0.613761i	0.951748	−	0.306881i	$-0.0992852\pi$
$488$	4173.11	+	4407.09i	0.387106	+	0.408811i
$489$			4745.30i			0.438834i
$490$	−10403.9	−	10594.7i	−0.959181	−	0.976775i
$491$			13904.9i			1.27804i	0.769188	+	0.639022i	$0.220661\pi$
$491$			13904.9i			1.27804i	−0.769188	+	0.639022i	$0.779339\pi$
$492$	−2.16983	+	119.368i	−0.000198828	+	0.0109381i
$493$		−	26182.8i		−	2.39191i
$494$	−277.020	+	3514.41i	−0.0252302	+	0.320082i
$495$	8623.82			0.783055
$496$	−558.598	+	15359.9i	−0.0505681	+	1.39049i
$497$	−2679.33			−0.241820
$498$	5458.84	−	5360.51i	0.491198	−	0.482350i
$499$	6757.51			0.606228			0.303114	−	0.952954i	$-0.401974\pi$
$499$	6757.51			0.606228			0.303114	+	0.952954i	$0.401974\pi$
$500$	−360.681	+	19842.1i	−0.0322603	+	1.77473i
$501$	10647.4			0.949481
$502$	−1372.44	+	1347.72i	−0.122022	+	0.119824i
$503$	−9933.11			−0.880508			−0.440254	−	0.897873i	$-0.645112\pi$
$503$	−9933.11			−0.880508			−0.440254	+	0.897873i	$0.645112\pi$
$504$	−1195.12	−	1262.13i	−0.105625	−	0.111547i
$505$			23207.8i			2.04502i
$506$	11493.7	+	11704.6i	1.00980	+	1.02832i
$507$	6527.30	+	914.163i	0.571770	+	0.0800777i
$508$	309.469	−	17024.8i	0.0270285	−	1.48691i
$509$	6953.24			0.605495			0.302747	−	0.953071i	$-0.402096\pi$
$509$	6953.24			0.605495			0.302747	+	0.953071i	$0.402096\pi$
$510$	−13852.8	+	13603.3i	−1.20277	+	1.18111i
$511$	2171.30			0.187970
$512$	−7495.34	−	8833.89i	−0.646973	−	0.762513i
$513$			717.961i			0.0617909i
$514$	−15201.1	−	15480.0i	−1.30446	−	1.32839i
$515$	6506.25			0.556698
$516$	80.3158	−	4418.40i	0.00685215	−	0.376956i
$517$		−	20240.1i		−	1.72178i
$518$	3319.66	−	3259.86i	0.281578	−	0.276506i
$519$	4382.99			0.370697
$520$	−20514.3	−	1992.77i	−1.73002	−	0.168055i
$521$	−3536.95			−0.297421			−0.148711	−	0.988881i	$-0.547512\pi$
$521$	−3536.95			−0.297421			−0.148711	+	0.988881i	$0.547512\pi$
$522$	4038.94	−	3966.19i	0.338658	−	0.332558i
$523$		−	4675.88i		−	0.390940i	−0.980710	−	0.195470i	$-0.937377\pi$
$523$		−	4675.88i		−	0.390940i	0.980710	−	0.195470i	$-0.0626233\pi$
$524$	753.787	+	13.7020i	0.0628423	+	0.00114232i
$525$	6469.37			0.537802
$526$	−4280.56	−	4359.08i	−0.354832	−	0.361340i
$527$		−	28276.6i		−	2.33729i
$528$	344.062	−	9460.77i	0.0283586	−	0.779786i
$529$	1668.77			0.137156
$530$	−19675.2	+	19320.8i	−1.61252	+	1.58348i
$531$	3182.95			0.260129
$532$	−1815.41	−	32.9998i	−0.147947	−	0.00268933i
$533$	175.936	−	153.012i	0.0142976	−	0.0124347i
$534$	4171.64	+	4248.16i	0.338061	+	0.344262i
$535$		−	12689.7i		−	1.02547i
$536$	10250.4	−	9706.17i	0.826025	−	0.782169i
$537$	12667.9			1.01799
$538$	12869.6	−	12637.8i	1.03132	−	1.01274i
$539$	−13320.3			−1.06446
$540$	−4196.89	−	76.2893i	−0.334454	−	0.00607957i
$541$	−16883.9			−1.34177			−0.670884	−	0.741563i	$-0.734085\pi$
$541$	−16883.9			−1.34177			−0.670884	+	0.741563i	$0.734085\pi$
$542$	8584.80	−	8430.17i	0.680348	−	0.668094i
$543$	10053.7			0.794561
$544$	14370.8	+	15740.0i	1.13262	+	1.24053i
$545$	−33249.9			−2.61334
$546$	−266.756	+	3384.20i	−0.0209086	+	0.265257i
$547$		−	2833.26i		−	0.221465i	−0.993850	−	0.110733i	$-0.964680\pi$
$547$		−	2833.26i		−	0.221465i	0.993850	−	0.110733i	$-0.0353197\pi$
$548$	−17174.6	−	312.194i	−1.33880	−	0.0243362i
$549$		−	2414.08i		−	0.187669i
$550$	24687.7	+	25140.5i	1.91397	+	1.94908i
$551$		−	5913.18i		−	0.457187i
$552$	−5490.02	−	5797.84i	−0.423316	−	0.447052i
$553$			7391.94i			0.568422i
$554$	10063.6	−	9882.35i	0.771773	−	0.757871i
$555$		−	11235.7i		−	0.859328i
$556$	3611.84	+	65.6546i	0.275497	+	0.00500787i
$557$	−5202.74			−0.395776			−0.197888	−	0.980225i	$-0.563408\pi$
$557$	−5202.74			−0.395776			−0.197888	+	0.980225i	$0.563408\pi$
$558$	4361.94	−	4283.38i	0.330924	−	0.324964i
$559$	−6512.23	+	5663.73i	−0.492733	+	0.428534i
$560$	385.805	−	10608.6i	0.0291129	−	0.800527i
$561$			17416.7i			1.31075i
$562$	−4471.08	+	4390.54i	−0.335589	+	0.329544i
$563$		−	18851.0i		−	1.41114i	−0.708638	−	0.705572i	$-0.750690\pi$
$563$		−	18851.0i		−	1.41114i	0.708638	−	0.705572i	$-0.249310\pi$
$564$	−179.051	+	9850.09i	−0.0133677	+	0.735396i
$565$	−785.094			−0.0584587
$566$	2097.09	−	2059.31i	0.155737	−	0.152932i
$567$			691.361i			0.0512071i
$568$	4883.80	+	5157.63i	0.360774	+	0.381003i
$569$	−11997.1			−0.883906			−0.441953	−	0.897038i	$-0.645714\pi$
$569$	−11997.1			−0.883906			−0.441953	+	0.897038i	$0.645714\pi$
$570$	−3128.56	+	3072.21i	−0.229896	+	0.225755i
$571$		−	5920.74i		−	0.433932i	−0.976179	−	0.216966i	$-0.930384\pi$
$571$		−	5920.74i		−	0.433932i	0.976179	−	0.216966i	$-0.0696161\pi$
$572$	−14169.3	+	11877.8i	−1.03575	+	0.868242i
$573$			7154.69i			0.521625i
$574$	84.1426	+	85.6860i	0.00611854	+	0.00623078i
$575$	29718.2			2.15536
$576$	−251.135	+	4601.15i	−0.0181666	+	0.332838i
$577$		−	11759.5i		−	0.848446i	−0.905558	−	0.424223i	$-0.860547\pi$
$577$		−	11759.5i		−	0.848446i	0.905558	−	0.424223i	$-0.139453\pi$
$578$	−17736.9	−	18062.3i	−1.27640	−	1.29981i
$579$	5392.60			0.387062
$580$	34565.9	+	628.324i	2.47460	+	0.0449823i
$581$		−	7695.87i		−	0.549533i
$582$	3160.41	+	3218.38i	0.225091	+	0.229220i
$583$			24736.9i			1.75729i
$584$	−3957.77	−	4179.68i	−0.280435	−	0.296159i
$585$	5379.79	+	6185.75i	0.380217	+	0.437178i
$586$	14130.8	+	14390.0i	0.996138	+	1.01441i
$587$	13667.5			0.961016			0.480508	−	0.876990i	$-0.340452\pi$
$587$	13667.5			0.961016			0.480508	+	0.876990i	$0.340452\pi$
$588$	6482.49	+	117.836i	0.454649	+	0.00826442i
$589$		−	6386.07i		−	0.446746i
$590$	13620.1	+	13869.9i	0.950390	+	0.967823i
$591$		−	11126.0i		−	0.774386i
$592$	−12326.1	−	448.265i	−0.855741	−	0.0311209i
$593$		−	15113.2i		−	1.04659i	−0.852152	−	0.523294i	$-0.824703\pi$
$593$		−	15113.2i		−	1.04659i	0.852152	−	0.523294i	$-0.175297\pi$
$594$	−2686.69	+	2638.29i	−0.185583	+	0.182240i
$595$			19529.7i			1.34561i
$596$	−91.0793	+	5010.52i	−0.00625965	+	0.344361i
$597$			4261.96i			0.292178i
$598$	−1225.39	+	15545.9i	−0.0837961	+	1.06308i
$599$	5927.32			0.404314			0.202157	−	0.979353i	$-0.435205\pi$
$599$	5927.32			0.404314			0.202157	+	0.979353i	$0.435205\pi$
$600$	−11792.1	−	12453.3i	−0.802354	−	0.847341i
$601$	16427.9			1.11499			0.557493	−	0.830182i	$-0.311764\pi$
$601$	16427.9			1.11499			0.557493	+	0.830182i	$0.311764\pi$
$602$	−3114.53	−	3171.66i	−0.210862	−	0.214729i
$603$	−5614.87			−0.379196
$604$	−1592.51	−	28.9480i	−0.107282	−	0.00195013i
$605$	21380.8			1.43678
$606$	−7099.97	−	7230.21i	−0.475935	−	0.484665i
$607$	−23279.8			−1.55667			−0.778333	−	0.627851i	$-0.783935\pi$
$607$	−23279.8			−1.55667			−0.778333	+	0.627851i	$0.783935\pi$
$608$	3245.55	+	3554.76i	0.216487	+	0.237113i
$609$		−	5694.10i		−	0.378878i
$610$	10519.5	−	10330.0i	0.698233	−	0.685657i
$611$	14517.9	−	12626.4i	0.961265	−	0.836019i
$612$	154.074	−	8476.02i	0.0101766	−	0.559841i
$613$	−4167.72			−0.274605			−0.137302	−	0.990529i	$-0.543843\pi$
$613$	−4167.72			−0.274605			−0.137302	+	0.990529i	$0.543843\pi$
$614$	−10112.5	−	10297.9i	−0.664667	−	0.676858i
$615$	290.012			0.0190153
$616$	−6547.61	−	6914.73i	−0.428264	−	0.452276i
$617$			19433.5i			1.26801i	0.773328	+	0.634006i	$0.218591\pi$
$617$			19433.5i			1.26801i	−0.773328	+	0.634006i	$0.781409\pi$
$618$	−2026.97	+	1990.46i	−0.131937	+	0.129560i
$619$	27993.9			1.81772			0.908861	−	0.417098i	$-0.136953\pi$
$619$	27993.9			1.81772			0.908861	+	0.417098i	$0.136953\pi$
$620$	37330.2	+	678.573i	2.41809	+	0.0439551i
$621$			3175.89i			0.205224i
$622$	−3362.22	−	3423.90i	−0.216741	−	0.220717i
$623$	5989.05			0.385146
$624$	7000.71	−	5655.11i	0.449123	−	0.362797i
$625$	16626.1			1.06407
$626$	11048.6	+	11251.3i	0.705420	+	0.718359i
$627$			3933.42i			0.250535i
$628$	11046.3	+	200.794i	0.701901	+	0.0127589i
$629$	22691.5			1.43843
$630$	−3012.65	+	2958.38i	−0.190519	+	0.187087i
$631$		−	5978.76i		−	0.377196i	−0.982054	−	0.188598i	$-0.939606\pi$
$631$		−	5978.76i		−	0.377196i	0.982054	−	0.188598i	$-0.0603943\pi$
$632$	14229.3	−	13473.8i	0.895584	−	0.848035i
$633$	−17456.6			−1.09611
$634$	10206.5	+	10393.7i	0.639358	+	0.651085i
$635$	−41362.6			−2.58492
$636$	218.831	−	12038.5i	0.0136434	−	0.750564i
$637$	−8309.60	−	9554.47i	−0.516857	−	0.594289i
$638$	22127.8	−	21729.2i	1.37311	−	1.34838i
$639$		−	2825.20i		−	0.174903i
$640$	−21124.4	+	18594.3i	−1.30471	+	1.14845i
$641$	−10474.7			−0.645437			−0.322719	−	0.946495i	$-0.604597\pi$
$641$	−10474.7			−0.645437			−0.322719	+	0.946495i	$0.604597\pi$
$642$	3882.18	+	3953.39i	0.238657	+	0.243034i
$643$	−5234.84			−0.321060			−0.160530	−	0.987031i	$-0.551320\pi$
$643$	−5234.84			−0.321060			−0.160530	+	0.987031i	$0.551320\pi$
$644$	−8030.45	−	145.974i	−0.491373	−	0.00893197i
$645$	−10734.7			−0.655318
$646$	−6204.62	−	6318.43i	−0.377891	−	0.384823i
$647$	18120.4			1.10106			0.550531	−	0.834814i	$-0.314425\pi$
$647$	18120.4			1.10106			0.550531	+	0.834814i	$0.314425\pi$
$648$	1330.85	−	1260.19i	0.0806800	−	0.0763965i
$649$	17438.1			1.05471
$650$	−2632.05	+	33391.5i	−0.158827	+	2.01496i
$651$		−	6149.47i		−	0.370225i
$652$	229.984	−	12652.0i	0.0138142	−	0.759957i
$653$			12855.0i			0.770374i	0.922839	+	0.385187i	$0.125863\pi$
$653$			12855.0i			0.770374i	−0.922839	+	0.385187i	$0.874137\pi$
$654$	10358.8	−	10172.2i	0.619358	−	0.608201i
$655$		−	1831.37i		−	0.109248i
$656$	11.5705	−	318.157i	0.000688646	−	0.0189359i
$657$			2289.51i			0.135955i
$658$	6943.32	+	7070.68i	0.411366	+	0.418912i
$659$			15459.0i			0.913805i	0.889517	+	0.456902i	$0.151041\pi$
$659$			15459.0i			0.913805i	−0.889517	+	0.456902i	$0.848959\pi$
$660$	−22993.1	−	417.959i	−1.35607	−	0.0246500i
$661$	−31286.3			−1.84100			−0.920498	−	0.390748i	$-0.872216\pi$
$661$	−31286.3			−1.84100			−0.920498	+	0.390748i	$0.872216\pi$
$662$	−9922.43	−	10104.4i	−0.582547	−	0.593233i
$663$	−12492.7	+	10865.0i	−0.731790	+	0.636443i
$664$	−14814.3	+	14027.8i	−0.865823	+	0.819854i
$665$			4410.64i			0.257199i
$666$	3437.33	+	3500.38i	0.199991	+	0.203659i
$667$		−	26156.9i		−	1.51844i
$668$	−28388.3	−	516.032i	−1.64428	−	0.0298890i
$669$	−17258.3			−0.997376
$670$	−24026.4	−	24467.2i	−1.38541	−	1.41082i
$671$		−	13225.8i		−	0.760917i
$672$	3125.30	+	3423.06i	0.179406	+	0.196499i
$673$	−18362.9			−1.05176			−0.525881	−	0.850558i	$-0.676264\pi$
$673$	−18362.9			−1.05176			−0.525881	+	0.850558i	$0.676264\pi$
$674$	9967.88	+	10150.7i	0.569657	+	0.580106i
$675$			6821.57i			0.388981i
$676$	−17358.9	−	2753.71i	−0.987650	−	0.156675i
$677$		−	14036.5i		−	0.796846i	−0.917202	−	0.398423i	$-0.869558\pi$
$677$		−	14036.5i		−	0.796846i	0.917202	−	0.398423i	$-0.130442\pi$
$678$	244.590	−	240.185i	0.0138546	−	0.0136051i
$679$	4537.27			0.256442
$680$	37594.1	−	35598.1i	2.12010	−	2.00754i
$681$			6002.66i			0.337771i
$682$	23897.4	−	23466.9i	1.34175	−	1.31759i
$683$	10248.8			0.574170			0.287085	−	0.957905i	$-0.407314\pi$
$683$	10248.8			0.574170			0.287085	+	0.957905i	$0.407314\pi$
$684$	34.7964	−	1914.25i	0.00194514	−	0.107007i
$685$			41726.8i			2.32744i
$686$	10561.5	−	10371.3i	0.587814	−	0.577226i
$687$		−	13852.4i		−	0.769291i
$688$	−428.280	+	11776.6i	−0.0237326	+	0.652583i
$689$	−17743.5	+	15431.6i	−0.981091	+	0.853262i
$690$	−13839.1	+	13589.9i	−0.763547	+	0.749794i
$691$	−11893.3			−0.654763			−0.327381	−	0.944892i	$-0.606166\pi$
$691$	−11893.3			−0.654763			−0.327381	+	0.944892i	$0.606166\pi$
$692$	−11686.0	−	212.424i	−0.641960	−	0.0116693i
$693$			3787.69i			0.207623i
$694$	−4481.12	+	4400.40i	−0.245102	+	0.240687i
$695$		−	8775.17i		−	0.478937i
$696$	−10961.0	+	10379.0i	−0.596946	+	0.565252i
$697$			585.707i			0.0318296i
$698$	6825.91	+	6951.12i	0.370150	+	0.376940i
$699$		−	5149.34i		−	0.278635i
$700$	−17248.8	−	313.542i	−0.931347	−	0.0169297i
$701$		−	24679.9i		−	1.32974i	−0.746959	−	0.664870i	$-0.768487\pi$
$701$		−	24679.9i		−	1.32974i	0.746959	−	0.664870i	$-0.231513\pi$
$702$	−3568.44	−	281.279i	−0.191855	−	0.0151228i
$703$	5124.71			0.274939
$704$	−1375.87	+	25207.9i	−0.0736576	+	1.34951i
$705$	23931.3			1.27845
$706$	15070.7	−	14799.2i	0.803389	−	0.788918i
$707$	−10193.1			−0.542224
$708$	−8486.47	−	154.264i	−0.450482	−	0.00818868i
$709$	5023.16			0.266077			0.133039	−	0.991111i	$-0.457527\pi$
$709$	5023.16			0.266077			0.133039	+	0.991111i	$0.457527\pi$
$710$	12311.0	−	12089.3i	0.650738	−	0.639016i
$711$	−7794.38			−0.411128
$712$	−10916.6	−	11528.7i	−0.574605	−	0.606822i
$713$		−	28248.7i		−	1.48376i
$714$	−5974.75	−	6084.34i	−0.313164	−	0.318908i
$715$	29473.7	+	33889.2i	1.54161	+	1.77257i
$716$	−33775.5	−	613.957i	−1.76292	−	0.0320456i
$717$	2794.13			0.145535
$718$	−4245.91	+	4169.43i	−0.220691	+	0.216716i
$719$	−15982.2			−0.828978			−0.414489	−	0.910054i	$-0.636040\pi$
$719$	−15982.2			−0.828978			−0.414489	+	0.910054i	$0.636040\pi$
$720$	11186.2	+	406.809i	0.579005	+	0.0210568i
$721$			2857.63i			0.147605i
$722$	12191.5	+	12415.1i	0.628422	+	0.639949i
$723$	−13406.8			−0.689633
$724$	−26805.5	−	487.260i	−1.37599	−	0.0250122i
$725$		−	56183.0i		−	2.87805i
$726$	−6661.04	+	6541.05i	−0.340515	+	0.334382i
$727$	24046.0			1.22671			0.613353	−	0.789809i	$-0.289820\pi$
$727$	24046.0			1.22671			0.613353	+	0.789809i	$0.289820\pi$
$728$	875.250	−	9010.11i	0.0445590	−	0.458705i
$729$	−729.000			−0.0370370
$730$	−9976.69	+	9796.99i	−0.505827	+	0.496716i
$731$		−	21679.9i		−	1.09693i
$732$	−117.000	+	6436.48i	−0.00590770	+	0.324999i
$733$	−605.906			−0.0305316			−0.0152658	−	0.999883i	$-0.504859\pi$
$733$	−605.906			−0.0305316			−0.0152658	+	0.999883i	$0.504859\pi$
$734$	15943.8	+	16236.3i	0.801768	+	0.816474i
$735$		−	15749.6i		−	0.790383i
$736$	14356.6	+	15724.4i	0.719012	+	0.787514i
$737$	−30761.6			−1.53747
$738$	−90.3510	+	88.7235i	−0.00450659	+	0.00442542i
$739$	16237.4			0.808256			0.404128	−	0.914703i	$-0.367575\pi$
$739$	16237.4			0.808256			0.404128	+	0.914703i	$0.367575\pi$
$740$	−544.543	+	29956.8i	−0.0270511	+	1.48815i
$741$	−2821.39	+	2453.78i	−0.139873	+	0.121649i
$742$	−8485.95	−	8641.61i	−0.419850	−	0.427552i
$743$			25041.0i			1.23643i	0.786011	+	0.618213i	$0.212143\pi$
$743$			25041.0i			1.23643i	−0.786011	+	0.618213i	$0.787857\pi$
$744$	−11837.5	+	11209.0i	−0.583313	+	0.552343i
$745$	12173.4			0.598654
$746$	647.367	−	635.707i	0.0317718	−	0.0311996i
$747$	8114.85			0.397466
$748$	844.108	−	46436.7i	0.0412616	−	2.26991i
$749$	5573.49			0.271897
$750$	−15018.7	+	14748.1i	−0.731205	+	0.718035i
$751$	12977.4			0.630562			0.315281	−	0.948998i	$-0.397901\pi$
$751$	12977.4			0.630562			0.315281	+	0.948998i	$0.397901\pi$
$752$	954.780	−	26253.9i	0.0462995	−	1.27311i
$753$	−2040.21			−0.0987376
$754$	29390.0	+	2316.64i	1.41952	+	0.111892i
$755$			3869.09i			0.186504i
$756$	33.5072	−	1843.32i	0.00161196	−	0.0886786i
$757$			21350.2i			1.02508i	0.858663	+	0.512541i	$0.171296\pi$
$757$			21350.2i			1.02508i	−0.858663	+	0.512541i	$0.828704\pi$
$758$	−15835.7	−	16126.2i	−0.758810	−	0.772729i
$759$			17399.4i			0.832094i
$760$	8490.35	−	8039.57i	0.405233	−	0.383718i
$761$		−	32649.8i		−	1.55526i	−0.628722	−	0.777630i	$-0.716422\pi$
$761$		−	32649.8i		−	1.55526i	0.628722	−	0.777630i	$-0.283578\pi$
$762$	12886.2	−	12654.1i	0.612622	−	0.601587i
$763$		−	14603.8i		−	0.692913i
$764$	346.756	−	19076.0i	0.0164204	−	0.903332i
$765$	−20593.0			−0.973256
$766$	−2315.80	+	2274.09i	−0.109234	+	0.107266i
$767$	10878.4	+	12508.1i	0.512121	+	0.588842i
$768$	892.580	−	12255.5i	0.0419378	−	0.575825i
$769$		−	27941.7i		−	1.31028i	−0.755508	−	0.655139i	$-0.772610\pi$
$769$		−	27941.7i		−	1.31028i	0.755508	−	0.655139i	$-0.227390\pi$
$770$	−16505.1	+	16207.8i	−0.772471	+	0.758557i
$771$		−	23011.8i		−	1.07490i
$772$	−14377.9	−	261.355i	−0.670300	−	0.0121844i
$773$	−23070.5			−1.07346			−0.536732	−	0.843752i	$-0.680342\pi$
$773$	−23070.5			−1.07346			−0.536732	+	0.843752i	$0.680342\pi$
$774$	3344.33	−	3284.09i	0.155309	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98174 - 2.01809i) q^{2} -3.00000i q^{3} +(-0.145397 + 7.99868i) q^{4} +19.4332 q^{5} +(-6.05428 + 5.94523i) q^{6} +8.53532i q^{7} +(16.4302 - 15.5579i) q^{8} -9.00000 q^{9} +(-38.5117 - 39.2181i) q^{10} -49.3074 q^{11} +(23.9960 + 0.436190i) q^{12} +(-30.7594 - 35.3675i) q^{13} +(17.2251 - 16.9148i) q^{14} -58.2997i q^{15} +(-63.9577 - 2.32596i) q^{16} +117.742 q^{17} +(17.8357 + 18.1628i) q^{18} +26.5911 q^{19} +(-2.82553 + 155.440i) q^{20} +25.6060 q^{21} +(97.7145 + 99.5069i) q^{22} +117.626 q^{23} +(-46.6737 - 49.2906i) q^{24} +252.651 q^{25} +(-10.4177 + 132.165i) q^{26} +27.0000i q^{27} +(-68.2713 - 1.24101i) q^{28} -222.374i q^{29} +(-117.654 + 115.535i) q^{30} -240.158i q^{31} +(122.054 + 133.682i) q^{32} +147.922i q^{33} +(-233.334 - 237.614i) q^{34} +165.869i q^{35} +(1.30857 - 71.9881i) q^{36} +192.722 q^{37} +(-52.6968 - 53.6634i) q^{38} +(-106.103 + 92.2781i) q^{39} +(319.292 - 302.340i) q^{40} +4.97450i q^{41} +(-50.7444 - 51.6752i) q^{42} -184.130i q^{43} +(7.16913 - 394.394i) q^{44} -174.899 q^{45} +(-233.104 - 237.379i) q^{46} +410.488i q^{47} +(-6.97789 + 191.873i) q^{48} +270.148 q^{49} +(-500.689 - 509.873i) q^{50} -353.226i q^{51} +(287.366 - 240.892i) q^{52} -501.688i q^{53} +(54.4885 - 53.5070i) q^{54} -958.203 q^{55} +(132.792 + 140.237i) q^{56} -79.7734i q^{57} +(-448.771 + 440.688i) q^{58} -353.661 q^{59} +(466.321 + 8.47659i) q^{60} +268.231i q^{61} +(-484.661 + 475.931i) q^{62} -76.8179i q^{63} +(27.9039 - 511.239i) q^{64} +(-597.754 - 687.305i) q^{65} +(298.521 - 293.144i) q^{66} +623.874 q^{67} +(-17.1193 + 941.780i) q^{68} -352.877i q^{69} +(334.739 - 328.709i) q^{70} +313.912i q^{71} +(-147.872 + 140.021i) q^{72} -254.390i q^{73} +(-381.926 - 388.932i) q^{74} -757.953i q^{75} +(-3.86626 + 212.694i) q^{76} -420.854i q^{77} +(396.494 + 31.2532i) q^{78} +866.042 q^{79} +(-1242.91 - 45.2010i) q^{80} +81.0000 q^{81} +(10.0390 - 9.85817i) q^{82} -901.650 q^{83} +(-3.72302 + 204.814i) q^{84} +2288.11 q^{85} +(-371.592 + 364.899i) q^{86} -667.122 q^{87} +(-810.131 + 767.119i) q^{88} -701.679i q^{89} +(346.605 + 352.963i) q^{90} +(301.873 - 262.541i) q^{91} +(-17.1024 + 940.849i) q^{92} -720.473 q^{93} +(828.403 - 813.482i) q^{94} +516.752 q^{95} +(401.046 - 366.161i) q^{96} -531.587i q^{97} +(-535.364 - 545.184i) q^{98} +443.767 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

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