LMFDB - Embedded newform 312.4.m.a.181.61

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			181.61
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.62

$q$-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} +(132.332 + 8.01399i) 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} +(278.421 - 251.177i) 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} +(-24.0420 + 396.996i) 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	$-0.835289\pi$
$5$	−19.4332			−1.73816			−0.869081	+	0.494670i	$0.835289\pi$
$6$	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	$-0.263815\pi$
$11$	49.3074			1.35152			0.675761	+	0.737121i	$0.263815\pi$
$12$	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	$-0.551323\pi$
$19$	−26.5911			−0.321075			−0.160538	+	0.987030i	$0.551323\pi$
$20$	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
$26$	132.332	+	8.01399i	0.998171	+	0.0604490i
$27$		−	27.0000i		−	0.192450i
$28$	68.2713	−	1.24101i	0.460788	−	0.00837601i
$29$			222.374i			1.42392i	0.702218	+	0.711962i	$0.252193\pi$
$29$			222.374i			1.42392i	−0.702218	+	0.711962i	$0.747807\pi$
$30$	−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	$-0.640836\pi$
$37$	−192.722			−0.856307			−0.428154	+	0.903706i	$0.640836\pi$
$38$	−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	$0.105872\pi$
$43$			184.130i			0.653014i	−0.945195	+	0.326507i	$0.894128\pi$
$44$	−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
$52$	278.421	−	251.177i	0.742501	−	0.669845i
$53$			501.688i			1.30023i	0.759836	+	0.650115i	$0.225279\pi$
$53$			501.688i			1.30023i	−0.759836	+	0.650115i	$0.774721\pi$
$54$	−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	$-0.372408\pi$
$59$	353.661			0.780386			0.390193	+	0.920733i	$0.372408\pi$
$60$	−466.321	+	8.47659i	−1.00336	+	0.0182387i
$61$		−	268.231i		−	0.563008i	−0.959560	−	0.281504i	$-0.909167\pi$
$61$		−	268.231i		−	0.563008i	0.959560	−	0.281504i	$-0.0908332\pi$
$62$	−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	$-0.692590\pi$
$67$	−623.874			−1.13759			−0.568794	+	0.822480i	$0.692590\pi$
$68$	−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
$78$	−24.0420	+	396.996i	−0.0349002	+	0.576294i
$79$	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	$-0.296677\pi$
$83$	901.650			1.19240			0.596198	+	0.802837i	$0.296677\pi$
$84$	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	$-0.799809\pi$
$101$		−	1194.23i		−	1.17654i	0.808665	−	0.588269i	$-0.200191\pi$
$102$	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	$0.448805\pi$
$104$	44.8607	−	1059.65i	0.0422976	−	0.999105i
$105$	497.607			0.462490
$106$	1012.45	+	994.216i	0.927718	+	0.911008i
$107$			652.991i			0.589973i	0.955501	+	0.294986i	$0.0953151\pi$
$107$			652.991i			0.589973i	−0.955501	+	0.294986i	$0.904685\pi$
$108$	−215.964	+	3.92571i	−0.192418	+	0.00349770i
$109$	1710.98			1.50351			0.751754	−	0.659443i	$-0.229208\pi$
$109$	1710.98			1.50351			0.751754	+	0.659443i	$0.229208\pi$
$110$	−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
$130$	−2571.64	−	155.738i	−1.73498	−	0.105070i
$131$			94.2390i			0.0628527i	0.999506	+	0.0314263i	$0.0100050\pi$
$131$			94.2390i			0.0628527i	−0.999506	+	0.0314263i	$0.989995\pi$
$132$	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	$0.0439938\pi$
$139$			451.555i			0.275542i	−0.990464	+	0.137771i	$0.956006\pi$
$140$	−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	$-0.555090\pi$
$149$	−626.419			−0.344418			−0.172209	+	0.985060i	$0.555090\pi$
$150$	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
$156$	753.530	+	835.263i	0.386735	+	0.428683i
$157$			1381.01i			0.702017i	0.936372	+	0.351008i	$0.114161\pi$
$157$			1381.01i			0.702017i	−0.936372	+	0.351008i	$0.885839\pi$
$158$	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	$-0.375910\pi$
$163$	1581.77			0.760082			0.380041	+	0.924970i	$0.375910\pi$
$164$	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	$-0.895970\pi$
$173$		−	1461.00i		−	0.642066i	0.947068	−	0.321033i	$-0.104030\pi$
$174$	−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	$-0.656463\pi$
$179$		−	4222.63i		−	1.76321i	0.471988	−	0.881605i	$-0.343537\pi$
$180$	−25.4298	−	1398.96i	−0.0105301	−	0.579292i
$181$		−	3351.24i		−	1.37622i	−0.725606	−	0.688110i	$-0.758440\pi$
$181$		−	3351.24i		−	1.37622i	0.725606	−	0.688110i	$-0.241560\pi$
$182$	−68.4020	+	1129.50i	−0.0278587	+	0.460021i
$183$	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	$-0.733980\pi$
$197$	−3708.67			−1.34128			−0.670638	+	0.741785i	$0.733980\pi$
$198$	−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
$208$	−2049.56	−	2190.48i	−0.683229	−	0.730204i
$209$	−1311.14			−0.433940
$210$	986.128	−	1004.22i	0.324044	−	0.329988i
$211$			5818.86i			1.89852i	0.314499	+	0.949258i	$0.398163\pi$
$211$			5818.86i			1.89852i	−0.314499	+	0.949258i	$0.601837\pi$
$212$	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	$-0.405507\pi$
$227$	2000.89			0.585037			0.292519	+	0.956260i	$0.405507\pi$
$228$	−638.082	+	11.5988i	−0.185342	+	0.00336907i
$229$	−4617.48			−1.33245			−0.666226	−	0.745750i	$-0.732091\pi$
$229$	−4617.48			−1.33245			−0.666226	+	0.745750i	$0.732091\pi$
$230$	−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	$0.422425\pi$
$234$	−1190.99	−	72.1259i	−0.332724	−	0.0201497i
$235$		−	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	$0.0272517\pi$
$251$			680.070i			0.171018i	−0.996337	+	0.0855092i	$0.972748\pi$
$252$	−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
$260$	−5410.62	+	4881.18i	−1.29059	+	1.16430i
$261$		−	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	$-0.742894\pi$
$269$		−	6377.13i		−	1.44543i	0.691147	−	0.722714i	$-0.257106\pi$
$270$	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	$-0.818109\pi$
$277$		−	4986.70i		−	1.08167i	0.841130	−	0.540833i	$-0.181891\pi$
$278$	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	$-0.965192\pi$
$283$		−	1039.14i		−	0.218271i	0.994027	−	0.109135i	$-0.0348082\pi$
$284$	2510.88	−	45.6417i	0.524624	−	0.00953640i
$285$			1550.26i			0.322208i
$286$	6524.95	+	395.149i	1.34905	+	0.0816981i
$287$	−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	$-0.248303\pi$
$293$	7130.48			1.42173			0.710866	+	0.703328i	$0.248303\pi$
$294$	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	$-0.657306\pi$
$307$	−5102.81			−0.948641			−0.474320	+	0.880352i	$0.657306\pi$
$308$	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	$0.450568\pi$
$312$	3178.94	+	134.582i	0.576834	+	0.0244205i
$313$	−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	$-0.349189\pi$
$317$	5150.28			0.912519			0.456259	+	0.889847i	$0.349189\pi$
$318$	−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	$-0.636470\pi$
$331$	−5006.92			−0.831436			−0.415718	+	0.909493i	$0.636470\pi$
$332$	−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	$0.633258\pi$
$338$	3787.02	+	4926.76i	0.609428	+	0.792842i
$339$		−	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	$0.0549452\pi$
$347$			2220.47i			0.343519i	−0.985139	+	0.171760i	$0.945055\pi$
$348$	96.9974	+	5336.10i	0.0149414	+	0.821968i
$349$	3444.40			0.528294			0.264147	−	0.964482i	$-0.414910\pi$
$349$	3444.40			0.528294			0.264147	+	0.964482i	$0.414910\pi$
$350$	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
$364$	2143.87	+	2376.41i	0.308707	+	0.342192i
$365$			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	$-0.992912\pi$
$373$		−	320.782i		−	0.0445293i	0.999752	−	0.0222647i	$-0.00708765\pi$
$374$	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	$-0.682145\pi$
$379$	−7990.79			−1.08301			−0.541503	+	0.840699i	$0.682145\pi$
$380$	−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	$-0.689300\pi$
$389$		−	12710.1i		−	1.65663i	0.560263	−	0.828315i	$-0.310700\pi$
$390$	467.213	−	7714.92i	0.0606622	−	1.00169i
$391$	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	$-0.455371\pi$
$397$	2210.83			0.279493			0.139746	+	0.990187i	$0.455371\pi$
$398$	−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
$416$	−8482.30	−	204.757i	−0.999709	−	0.0241323i
$417$	−1354.66			−0.159084
$418$	−2598.34	+	2646.00i	−0.304041	+	0.309618i
$419$			16210.3i			1.89003i	0.327025	+	0.945016i	$0.393954\pi$
$419$			16210.3i			1.89003i	−0.327025	+	0.945016i	$0.606046\pi$
$420$	−72.3504	−	3980.20i	−0.00840556	−	0.462414i
$421$	−997.361			−0.115459			−0.0577297	−	0.998332i	$-0.518386\pi$
$421$	−997.361			−0.115459			−0.0577297	+	0.998332i	$0.518386\pi$
$422$	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
$442$	15581.0	+	943.583i	1.67673	+	0.101542i
$443$		−	6954.31i		−	0.745845i	−0.927863	−	0.372922i	$-0.878356\pi$
$443$		−	6954.31i		−	0.745845i	0.927863	−	0.372922i	$-0.121644\pi$
$444$	−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	$-0.473252\pi$
$461$	1661.54			0.167865			0.0839324	+	0.996471i	$0.473252\pi$
$462$	−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	$-0.672321\pi$
$467$		−	17297.7i		−	1.71401i	0.515305	−	0.857007i	$-0.327679\pi$
$468$	−2505.79	+	2260.59i	−0.247500	+	0.223282i
$469$		−	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	$-0.779339\pi$
$491$		−	13904.9i		−	1.27804i	0.769188	−	0.639022i	$-0.220661\pi$
$492$	2.16983	+	119.368i	0.000198828	+	0.0109381i
$493$			26182.8i			2.39191i
$494$	−3518.86	−	213.101i	−0.320488	−	0.0194087i
$495$	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	$-0.598026\pi$
$499$	−6757.51			−0.606228			−0.303114	+	0.952954i	$0.598026\pi$
$500$	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	$-0.597904\pi$
$509$	−6953.24			−0.605495			−0.302747	+	0.953071i	$0.597904\pi$
$510$	−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
$520$	−871.789	+	20592.4i	−0.0735201	+	1.73661i
$521$	−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	$0.0626233\pi$
$523$			4675.88i			0.390940i	−0.980710	+	0.195470i	$0.937377\pi$
$524$	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	$-0.265915\pi$
$541$	16883.9			1.34177			0.670884	+	0.741563i	$0.265915\pi$
$542$	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
$546$	−3388.49	−	205.206i	−0.265593	−	0.0160843i
$547$			2833.26i			0.221465i	0.993850	+	0.110733i	$0.0353197\pi$
$547$			2833.26i			0.221465i	−0.993850	+	0.110733i	$0.964680\pi$
$548$	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	$-0.436592\pi$
$557$	5202.74			0.395776			0.197888	+	0.980225i	$0.436592\pi$
$558$	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	$0.249310\pi$
$563$			18851.0i			1.41114i	−0.708638	+	0.705572i	$0.750690\pi$
$564$	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	$0.0696161\pi$
$571$			5920.74i			0.433932i	−0.976179	+	0.216966i	$0.930384\pi$
$572$	13728.2	−	12384.9i	1.00351	−	0.905310i
$573$		−	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	$-0.659548\pi$
$587$	−13667.5			−0.961016			−0.480508	+	0.876990i	$0.659548\pi$
$588$	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
$598$	15565.6	+	942.650i	1.06442	+	0.0644613i
$599$	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	$-0.456157\pi$
$613$	4167.72			0.274605			0.137302	+	0.990529i	$0.456157\pi$
$614$	−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	$-0.863047\pi$
$619$	−27993.9			−1.81772			−0.908861	+	0.417098i	$0.863047\pi$
$620$	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
$624$	6571.44	−	6148.69i	0.421584	−	0.394463i
$625$	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	$-0.448680\pi$
$643$	5234.84			0.321060			0.160530	+	0.987031i	$0.448680\pi$
$644$	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
$650$	33433.8	+	2024.74i	2.01751	+	0.122180i
$651$			6149.47i			0.370225i
$652$	−229.984	−	12652.0i	−0.0138142	−	0.759957i
$653$		−	12855.0i		−	0.770374i	−0.922839	−	0.385187i	$-0.874137\pi$
$653$		−	12855.0i		−	0.770374i	0.922839	−	0.385187i	$-0.125863\pi$
$654$	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	$-0.848959\pi$
$659$		−	15459.0i		−	0.913805i	0.889517	−	0.456902i	$-0.151041\pi$
$660$	−22993.1	+	417.959i	−1.35607	+	0.0246500i
$661$	31286.3			1.84100			0.920498	−	0.390748i	$-0.127784\pi$
$661$	31286.3			1.84100			0.920498	+	0.390748i	$0.127784\pi$
$662$	−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
$676$	17447.6	+	2121.02i	0.992692	+	0.120677i
$677$			14036.5i			0.796846i	0.917202	+	0.398423i	$0.130442\pi$
$677$			14036.5i			0.796846i	−0.917202	+	0.398423i	$0.869558\pi$
$678$	−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	$-0.592686\pi$
$683$	−10248.8			−0.574170			−0.287085	+	0.957905i	$0.592686\pi$
$684$	−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	$-0.393834\pi$
$691$	11893.3			0.654763			0.327381	+	0.944892i	$0.393834\pi$
$692$	−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	$0.231513\pi$
$701$			24679.9i			1.32974i	−0.746959	+	0.664870i	$0.768487\pi$
$702$	216.378	−	3572.97i	0.0116334	−	0.192098i
$703$	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	$-0.542473\pi$
$709$	−5023.16			−0.266077			−0.133039	+	0.991111i	$0.542473\pi$
$710$	−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	$0.289820\pi$
$728$	9044.42	+	382.900i	0.460451	+	0.0194934i
$729$	−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	$-0.495141\pi$
$733$	605.906			0.0305316			0.0152658	+	0.999883i	$0.495141\pi$
$734$	−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	$-0.632425\pi$
$739$	−16237.4			−0.808256			−0.404128	+	0.914703i	$0.632425\pi$
$740$	−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
$754$	−1782.10	+	29427.2i	−0.0860748	+	1.42132i
$755$		−	3869.09i		−	0.186504i
$756$	−33.5072	−	1843.32i	−0.00161196	−	0.0886786i
$757$		−	21350.2i		−	1.02508i	−0.858663	−	0.512541i	$-0.828704\pi$
$757$		−	21350.2i		−	1.02508i	0.858663	−	0.512541i	$-0.171296\pi$
$758$	−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	$-0.319658\pi$
$773$	23070.5			1.07346			0.536732	+	0.843752i	$0.319658\pi$
$774$	−3344.33	−	3284.09i	−0.155309	−	0.152512i
$775$		−	60676.1i		−	2.81232i
$776$	−8270.38	+	8734.09i	−0.382589	+	0.404041i
$777$	4934.84			0.227846
$778$	−25650.2	−	25188.2i	−1.18201	−	1.16072i
$779$		−	132.278i		−	0.00608387i
$780$	−14643.5	−	16231.9i	−0.672208	−	0.745121i
$781$			15478.2i			0.709158i
$782$	27446.1	−	27949.5i	1.25508	−	1.27810i
$783$	6004.10			0.274034
$784$	−17278.1	+	628.355i	−0.787084	+	0.0286241i
$785$		−	26837.5i		−	1.22022i
$786$	−560.272	+	570.549i	−0.0254252	+	0.0258916i
$787$	−19690.9			−0.891873			−0.445936	−	0.895065i	$-0.647129\pi$
$787$	−19690.9			−0.891873			−0.445936	+	0.895065i	$0.647129\pi$
$788$	539.228	+	29664.4i	0.0243772	+	1.34106i
$789$			6480.00i			0.292388i
$790$	−33352.7	+	33964.5i	−1.50207	+	1.52962i
$791$		−	344.823i		−	0.0155000i
$792$	7291.18	+	6904.07i	0.327122	+	0.309755i
$793$	9486.66	−	8250.62i	0.424819	−	0.369468i
$794$	4381.30	−	4461.67i	0.195827	−	0.199419i
$795$	29248.3			1.30482
$796$	206.558	+	11363.3i	0.00919757	+	0.505984i
$797$		−	41083.0i		−	1.82589i	−0.408080	−	0.912946i	$-0.633802\pi$
$797$		−	41083.0i		−	1.82589i	0.408080	−	0.912946i	$-0.366198\pi$
$798$	1349.35	−	1374.10i	0.0598578	−	0.0609558i
$799$			48331.7i			2.13999i
$800$	−30837.0	+	33774.9i	−1.36281	+	1.49265i
$801$			6315.11i			0.278568i
$802$	−9269.71	−	9102.74i	−0.408136	−	0.400784i
$803$		−	12543.3i		−	0.551238i
$804$	−14970.5	+	272.128i	−0.656678	+	0.0119368i
$805$		−	19510.4i		−	0.854226i
$806$	1924.62	−	31780.6i	0.0841091	−	1.38886i
$807$	19131.4			0.834519
$808$	−18579.7	+	19621.5i	−0.808951	+	0.854308i
$809$	−1696.39			−0.0737230			−0.0368615	−	0.999320i	$-0.511736\pi$
$809$	−1696.39			−0.0737230			−0.0368615	+	0.999320i	$0.511736\pi$
$810$	−3119.45	+	3176.66i	−0.135316	+	0.137798i
$811$	−15395.7			−0.666603			−0.333301	−	0.942820i	$-0.608163\pi$
$811$	−15395.7			−0.666603			−0.333301	+	0.942820i	$0.608163\pi$
$812$	275.968	+	15181.8i	0.0119268	+	0.656127i
$813$	−12761.8			−0.550522
$814$	−18831.8	+	19177.2i	−0.810877	+	0.825750i
$815$	−30738.8			−1.32115
$816$	−821.591	−	22591.5i	−0.0352468	−	0.969193i
$817$		−	4896.23i		−	0.209667i
$818$	26295.6	+	25821.9i	1.12397	+	1.10372i
$819$	2716.86	−	2362.87i	0.115915	−	0.100812i
$820$	−773.237	+	14.0556i	−0.0329300	+	0.000598588i
$821$	14236.0			0.605164			0.302582	−	0.953123i	$-0.402151\pi$
$821$	14236.0			0.605164			0.302582	+	0.953123i	$0.402151\pi$
$822$	−12765.5	+	12999.7i	−0.541664	+	0.551600i
$823$	7665.68			0.324677			0.162338	−	0.986735i	$-0.448096\pi$
$823$	7665.68			0.324677			0.162338	+	0.986735i	$0.448096\pi$
$824$	−5500.84	−	5208.78i	−0.232562	−	0.220214i
$825$			37372.7i			1.57715i
$826$	6091.84	+	5982.11i	0.256613	+	0.251991i
$827$	32596.1			1.37059			0.685295	−	0.728266i	$-0.259673\pi$
$827$	32596.1			1.37059			0.685295	+	0.728266i	$0.259673\pi$
$828$	153.921	+	8467.64i	0.00646031	+	0.355400i
$829$		−	39242.2i		−	1.64407i	−0.569434	−	0.822037i	$-0.692837\pi$
$829$		−	39242.2i		−	1.64407i	0.569434	−	0.822037i	$-0.307163\pi$
$830$	−34724.0	+	35361.0i	−1.45216	+	1.47879i
$831$	14960.1			0.624500
$832$	−17222.9	+	16712.3i	−0.717666	+	0.696387i
$833$	31807.8			1.32302
$834$	−2684.60	+	2733.84i	−0.111463	+	0.113507i
$835$		−	68971.1i		−	2.85849i
$836$	190.635	+	10487.4i	0.00788668	+	0.433868i
$837$	−6484.26			−0.267776
$838$	32713.8	+	32124.6i	1.34854	+	1.32425i
$839$			10837.1i			0.445935i	0.974826	+	0.222967i	$0.0715744\pi$
$839$			10837.1i			0.445935i	−0.974826	+	0.222967i	$0.928426\pi$
$840$	−8175.78	−	7741.71i	−0.335823	−	0.317993i
$841$	−25061.2			−1.02756
$842$	−1976.51	+	2012.77i	−0.0808968	+	0.0823807i
$843$	6646.49			0.271551
$844$	46543.2	−	846.043i	1.89820	−	0.0345047i
$845$	5921.72	−	42282.2i	0.241081	−	1.72136i
$846$	−7455.63	−	7321.33i	−0.302990	−	0.297533i
$847$			9390.72i			0.380955i
$848$	−1166.91	−	32086.8i	−0.0472545	−	1.29937i
$849$	3117.43			0.126019
$850$	58952.1	−	60033.4i	2.37887	−	2.42251i
$851$	−22669.1			−0.913145
$852$	136.925	+	7532.63i	0.00550584	+	0.302892i
$853$	−1992.41			−0.0799751			−0.0399875	−	0.999200i	$-0.512732\pi$
$853$	−1992.41			−0.0799751			−0.0399875	+	0.999200i	$0.512732\pi$
$854$	4537.07	−	4620.30i	0.181798	−	0.185133i
$855$	−4650.77			−0.186027
$856$	10159.2	−	10728.8i	0.405646	−	0.428391i
$857$	−37337.6			−1.48825			−0.744123	−	0.668042i	$-0.767132\pi$
$857$	−37337.6			−1.48825			−0.744123	+	0.668042i	$0.767132\pi$
$858$	−1185.45	+	19574.9i	−0.0471684	+	0.778875i
$859$		−	11756.6i		−	0.466974i	−0.972360	−	0.233487i	$-0.924986\pi$
$859$		−	11756.6i		−	0.466974i	0.972360	−	0.233487i	$-0.0750136\pi$
$860$	−28621.3	+	520.266i	−1.13486	+	0.0206290i
$861$		−	127.377i		−	0.00504180i
$862$	26206.2	+	25734.2i	1.03548	+	1.01683i
$863$		−	16911.3i		−	0.667052i	−0.942741	−	0.333526i	$-0.891761\pi$
$863$		−	16911.3i		−	0.667052i	0.942741	−	0.333526i	$-0.108239\pi$
$864$	3609.42	+	3295.45i	0.142124	+	0.129761i
$865$			28391.9i			1.11602i
$866$	6109.74	−	6221.81i	0.239743	−	0.244141i
$867$			26850.5i			1.05178i
$868$	−298.037	−	16395.9i	−0.0116544	−	0.641143i
$869$	42702.3			1.66694
$870$	25692.0	−	26163.3i	1.00120	−	1.01956i
$871$	−19190.0	−	22064.9i	−0.746530	−	0.858369i
$872$	−28111.8	−	26619.3i	−1.09173	−	1.03376i
$873$			4784.28i			0.185479i
$874$	−6198.49	+	6312.19i	−0.239894	+	0.244294i
$875$		−	21173.3i		−	0.818044i
$876$	−110.962	−	6104.35i	−0.00427977	−	0.235442i
$877$	−18720.3			−0.720797			−0.360399	−	0.932798i	$-0.617359\pi$
$877$	−18720.3			−0.720797			−0.360399	+	0.932798i	$0.617359\pi$
$878$	12384.3	−	12611.5i	0.476027	−	0.484758i
$879$			21391.4i			0.820837i
$880$	61284.5	−	2228.74i	2.34761	−	0.0853761i
$881$	12882.9			0.492664			0.246332	−	0.969186i	$-0.420775\pi$
$881$	12882.9			0.492664			0.246332	+	0.969186i	$0.420775\pi$
$882$	−4818.28	+	4906.66i	−0.183945	+	0.187320i
$883$		−	15385.2i		−	0.586359i	−0.956057	−	0.293179i	$-0.905287\pi$
$883$		−	15385.2i		−	0.586359i	0.956057	−	0.293179i	$-0.0947133\pi$
$884$	32781.8	−	29574.0i	1.24725	−	1.12521i
$885$		−	20618.4i		−	0.783140i
$886$	−14034.4	−	13781.6i	−0.532163	−	0.522577i
$887$	10431.2			0.394866			0.197433	−	0.980316i	$-0.436740\pi$
$887$	10431.2			0.394866			0.197433	+	0.980316i	$0.436740\pi$
$888$	−8995.06	+	9499.41i	−0.339926	+	0.358986i
$889$		−	18167.0i		−	0.685377i
$890$	27518.5	+	27022.8i	1.03643	+	1.01776i
$891$	3993.90			0.150169
$892$	−46014.5	+	836.433i	−1.72722	+	0.0313967i
$893$		−	10915.3i		−	0.409035i
$894$	−3792.51	−	3724.20i	−0.141880	−	0.139324i
$895$			82059.5i			3.06474i
$896$	−8166.86	+	9278.11i	−0.304504	+	0.345938i
$897$	−12480.4	+	10854.3i	−0.464557	+	0.404028i
$898$	6986.48	+	6860.63i	0.259623	+	0.254947i
$899$	53404.8			1.98126
$900$	330.611	+	18187.9i	0.0122449	+	0.673624i
$901$			59069.7i			2.18413i
$902$	494.997	+	486.081i	0.0182723	+	0.0179431i
$903$		−	4714.83i		−	0.173754i
$904$	663.773	+	628.532i	0.0244212	+	0.0231246i
$905$			65125.5i			2.39209i
$906$	−1183.67	+	1205.39i	−0.0434050	+	0.0442012i
$907$			15331.1i			0.561259i	0.959816	+	0.280630i	$0.0905433\pi$
$907$			15331.1i			0.561259i	−0.959816	+	0.280630i	$0.909457\pi$
$908$	−290.922	−	16004.4i	−0.0106328	−	0.584940i
$909$			10748.1i			0.392180i
$910$	1329.27	−	21949.8i	0.0484230	−	0.799591i
$911$	−21761.7			−0.791435			−0.395717	−	0.918372i	$-0.629504\pi$
$911$	−21761.7			−0.791435			−0.395717	+	0.918372i	$0.629504\pi$
$912$	185.550	+	5102.13i	0.00673704	+	0.185250i
$913$	44458.0			1.61155
$914$	−20555.0	−	20184.8i	−0.743873	−	0.730474i
$915$	−15637.8			−0.564994
$916$	671.366	+	36933.7i	0.0242168	+	1.33223i
$917$	−804.360			−0.0289665
$918$	−6415.58	−	6300.02i	−0.230660	−	0.226505i
$919$	1163.74			0.0417716			0.0208858	−	0.999782i	$-0.493351\pi$
$919$	1163.74			0.0417716			0.0208858	+	0.999782i	$0.493351\pi$
$920$	37556.9	+	35562.9i	1.34589	+	1.27443i
$921$		−	15308.4i		−	0.547698i
$922$	3292.75	−	3353.14i	0.117615	−	0.119772i
$923$	−11102.3	+	9655.72i	−0.395922	+	0.344336i
$924$	183.573	+	10098.8i	0.00653581	+	0.359553i
$925$	−48691.5			−1.73077
$926$	2350.13	+	2307.79i	0.0834017	+	0.0818994i
$927$	−3013.20			−0.106760
$928$	−29727.4	−	27141.6i	−1.05156	−	0.960092i
$929$			9553.67i			0.337401i	0.985667	+	0.168701i	$0.0539571\pi$
$929$			9553.67i			0.337401i	−0.985667	+	0.168701i	$0.946043\pi$
$930$	−27746.6	+	28255.6i	−0.978331	+	0.996276i
$931$	−7183.55			−0.252880
$932$	−249.566	−	13729.3i	−0.00877124	−	0.482530i
$933$			5089.80i			0.178599i
$934$	−34908.5	−	34279.7i	−1.22295	−	1.20093i
$935$	−112821.			−3.94613
$936$	−403.746	+	9536.82i	−0.0140992	+	0.333035i
$937$	27671.4			0.964766			0.482383	−	0.875960i	$-0.339771\pi$
$937$	27671.4			0.964766			0.482383	+	0.875960i	$0.339771\pi$
$938$	−10746.3	−	10552.7i	−0.374071	−	0.367333i
$939$		−	16725.7i		−	0.581279i
$940$	−63806.4	+	1159.85i	−2.21397	+	0.0402447i
$941$	−34867.0			−1.20790			−0.603948	−	0.797024i	$-0.706407\pi$
$941$	−34867.0			−1.20790			−0.603948	+	0.797024i	$0.706407\pi$
$942$	−8210.42	+	8361.02i	−0.283981	+	0.289190i
$943$			585.128i			0.0202061i
$944$	−22619.4	+	822.603i	−0.779871	+	0.0283617i
$945$	−4478.46			−0.154163
$946$	18322.2	+	17992.2i	0.629712	+	0.618369i
$947$	−14400.4			−0.494139			−0.247070	−	0.968998i	$-0.579468\pi$
$947$	−14400.4			−0.494139			−0.247070	+	0.968998i	$0.579468\pi$
$948$	20781.6	−	377.759i	0.711977	−	0.0129420i
$949$	8997.14	−	7824.88i	0.307755	−	0.267657i
$950$	−13313.9	+	13558.1i	−0.454694	+	0.463035i
$951$			15450.8i			0.526843i
$952$	15635.1	−	16511.8i	0.532288	−	0.562133i
$953$	5233.88			0.177903			0.0889517	−	0.996036i	$-0.471648\pi$
$953$	5233.88			0.177903			0.0889517	+	0.996036i	$0.471648\pi$
$954$	−9112.08	−	8947.95i	−0.309239	−	0.303669i
$955$	46346.3			1.57040
$956$	7449.79	−	135.419i	0.252033	−	0.00458135i
$957$	−32894.1			−1.11109
$958$	−7808.87	−	7668.22i	−0.263354	−	0.258610i
$959$	−18326.9			−0.617108
$960$	29805.1	−	1626.79i	1.00204	−	0.0546921i
$961$	−27884.7			−0.936012
$962$	−25503.4	−	1544.48i	−0.854741	−	0.0517629i
$963$		−	5876.92i		−	0.196658i
$964$	−35745.6	+	649.769i	−1.19428	+	0.0217092i
$965$		−	34931.9i		−	1.16528i
$966$	−5968.84	+	6078.32i	−0.198804	+	0.202450i
$967$			9071.26i			0.301667i	0.988559	+	0.150834i	$0.0481958\pi$
$967$			9071.26i			0.301667i	−0.988559	+	0.150834i	$0.951804\pi$
$968$	−18076.8	−	17117.1i	−0.600219	−	0.568352i
$969$		−	9392.68i		−	0.311389i
$970$	20847.8	+	20472.3i	0.690086	+	0.677656i
$971$		−	25453.9i		−	0.841250i	−0.907235	−	0.420625i	$-0.861811\pi$
$971$		−	25453.9i		−	0.841250i	0.907235	−	0.420625i	$-0.138189\pi$
$972$	1943.68	−	35.3314i	0.0641394	−	0.00116590i
$973$	−3854.16			−0.126987
$974$	−13311.7	−	13071.9i	−0.437921	−	0.430033i
$975$	−26806.9	+	23314.2i	−0.880521	+	0.765795i
$976$	623.896	+	17155.4i	0.0204615	+	0.562636i
$977$		−	27836.1i		−	0.911522i	−0.890102	−	0.455761i	$-0.849367\pi$
$977$		−	27836.1i		−	0.911522i	0.890102	−	0.455761i	$-0.150633\pi$
$978$	9576.45	+	9403.95i	0.313109	+	0.307470i
$979$		−	34597.9i		−	1.12947i
$980$	763.312	+	41991.9i	0.0248807	+	1.36876i
$981$	−15398.8			−0.501170
$982$	−28061.4	−	27556.0i	−0.911889	−	0.895464i
$983$		−	16318.3i		−	0.529475i	−0.964321	−	0.264737i	$-0.914715\pi$
$983$		−	16318.3i		−	0.529475i	0.964321	−	0.264737i	$-0.0852852\pi$
$984$	245.196	+	232.178i	0.00794367	+	0.00752192i
$985$	72071.4			2.33136
$986$	52839.2	+	51887.5i	1.70664	+	1.67590i
$987$		−	10510.9i		−	0.338974i
$988$	−7403.53	+	6679.08i	−0.238399	+	0.215071i
$989$			21658.4i			0.696358i
$990$	17090.2	−	17403.7i	0.548648	−	0.558712i
$991$	−3221.51			−0.103264			−0.0516321	−	0.998666i	$-0.516442\pi$
$991$	−3221.51			−0.103264			−0.0516321	+	0.998666i	$0.516442\pi$
$992$	32104.8	+	29312.1i	1.02755	+	0.938167i
$993$		−	15020.8i		−	0.480030i
$994$	−5309.75	+	5407.15i	−0.169432	+	0.172539i
$995$	27607.9			0.879627
$996$	21636.0	−	393.291i	0.688317	−	0.0125119i
$997$			43681.6i			1.38757i	0.720180	+	0.693787i	$0.244059\pi$
$997$			43681.6i			1.38757i	−0.720180	+	0.693787i	$0.755941\pi$
$998$	−13391.6	+	13637.3i	−0.424754	+	0.432546i
$999$			5203.50i			0.164796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.4.m.a.181.61	yes	84
4.3	odd	2		1248.4.m.a.337.13		84
8.3	odd	2		1248.4.m.a.337.16		84
8.5	even	2	inner	312.4.m.a.181.23	✓	84
13.12	even	2	inner	312.4.m.a.181.24	yes	84
52.51	odd	2		1248.4.m.a.337.14		84
104.51	odd	2		1248.4.m.a.337.15		84
104.77	even	2	inner	312.4.m.a.181.62	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.4.m.a.181.23	✓	84	8.5	even	2	inner
312.4.m.a.181.24	yes	84	13.12	even	2	inner
312.4.m.a.181.61	yes	84	1.1	even	1	trivial
312.4.m.a.181.62	yes	84	104.77	even	2	inner
1248.4.m.a.337.13		84	4.3	odd	2
1248.4.m.a.337.14		84	52.51	odd	2
1248.4.m.a.337.15		84	104.51	odd	2
1248.4.m.a.337.16		84	8.3	odd	2

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} +(132.332 + 8.01399i) 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} +(278.421 - 251.177i) 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} +(-24.0420 + 396.996i) 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

Introduction

L-functions

Modular forms

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