LMFDB - Embedded newform 512.2.i.a.33.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, not 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			33.6
Character	$\chi$	$=$	512.33
Dual form			512.2.i.a.481.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06920 - 0.714416i) q^{3} +(0.330507 - 0.0657419i) q^{5} +(0.739314 + 1.78486i) q^{7} +(-0.515254 + 1.24393i) q^{9} +O(q^{10})$	\(q+(1.06920 - 0.714416i) q^{3} +(0.330507 - 0.0657419i) q^{5} +(0.739314 + 1.78486i) q^{7} +(-0.515254 + 1.24393i) q^{9} +(0.971610 - 1.45412i) q^{11} +(3.70516 + 0.737003i) q^{13} +(0.306411 - 0.306411i) q^{15} +(4.47305 + 4.47305i) q^{17} +(1.16088 - 5.83613i) q^{19} +(2.06561 + 1.38019i) q^{21} +(1.28371 + 0.531730i) q^{23} +(-4.51448 + 1.86996i) q^{25} +(1.09039 + 5.48174i) q^{27} +(-3.04996 - 4.56458i) q^{29} -10.2910i q^{31} -2.24887i q^{33} +(0.361689 + 0.541305i) q^{35} +(0.910827 + 4.57904i) q^{37} +(4.48808 - 1.85903i) q^{39} +(2.66002 + 1.10181i) q^{41} +(-5.83495 - 3.89879i) q^{43} +(-0.0885166 + 0.445003i) q^{45} +(0.0482001 + 0.0482001i) q^{47} +(2.31060 - 2.31060i) q^{49} +(7.97819 + 1.58696i) q^{51} +(-6.43049 + 9.62391i) q^{53} +(0.225527 - 0.544471i) q^{55} +(-2.92821 - 7.06933i) q^{57} +(-2.89770 + 0.576389i) q^{59} +(0.675800 - 0.451555i) q^{61} -2.60119 q^{63} +1.27304 q^{65} +(-2.41244 + 1.61194i) q^{67} +(1.75242 - 0.348577i) q^{69} +(2.88474 + 6.96439i) q^{71} +(1.92544 - 4.64843i) q^{73} +(-3.49095 + 5.22458i) q^{75} +(3.31372 + 0.659140i) q^{77} +(-10.5317 + 10.5317i) q^{79} +(2.22588 + 2.22588i) q^{81} +(-0.0104591 + 0.0525816i) q^{83} +(1.77244 + 1.18431i) q^{85} +(-6.52202 - 2.70151i) q^{87} +(-7.52277 + 3.11604i) q^{89} +(1.42383 + 7.15808i) q^{91} +(-7.35206 - 11.0031i) q^{93} -2.00520i q^{95} -12.1748i q^{97} +(1.30820 + 1.95786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	$ 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9} - 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} - 8 q^{19} + 8 q^{21} + 8 q^{23} - 8 q^{25} - 8 q^{27} + 8 q^{29} - 8 q^{35} + 8 q^{37} + 8 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{49} + 24 q^{51} + 8 q^{53} - 56 q^{55} - 8 q^{57} + 56 q^{59} + 8 q^{61} - 64 q^{63} - 16 q^{65} + 72 q^{67} + 8 q^{69} - 56 q^{71} - 8 q^{73} + 56 q^{75} + 8 q^{77} - 24 q^{79} - 8 q^{81} - 8 q^{83} + 8 q^{85} + 8 q^{87} - 8 q^{89} - 8 q^{91} - 16 q^{93} + 16 q^{99}+O(q^{100}) $ 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9 - 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 - 8 * q^19 + 8 * q^21 + 8 * q^23 - 8 * q^25 - 8 * q^27 + 8 * q^29 - 8 * q^35 + 8 * q^37 + 8 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^49 + 24 * q^51 + 8 * q^53 - 56 * q^55 - 8 * q^57 + 56 * q^59 + 8 * q^61 - 64 * q^63 - 16 * q^65 + 72 * q^67 + 8 * q^69 - 56 * q^71 - 8 * q^73 + 56 * q^75 + 8 * q^77 - 24 * q^79 - 8 * q^81 - 8 * q^83 + 8 * q^85 + 8 * q^87 - 8 * q^89 - 8 * q^91 - 16 * q^93 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{15}{16}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.06920	−	0.714416i	0.617302	−	0.412468i	−0.207223	−	0.978294i	$-0.566443\pi$
$3$	1.06920	−	0.714416i	0.617302	−	0.412468i	0.824525	+	0.565826i	$0.191443\pi$
$4$		0			0
$5$	0.330507	−	0.0657419i	0.147807	−	0.0294007i	−0.120632	−	0.992697i	$-0.538492\pi$
$5$	0.330507	−	0.0657419i	0.147807	−	0.0294007i	0.268439	+	0.963297i	$0.413492\pi$
$6$		0			0
$7$	0.739314	+	1.78486i	0.279434	+	0.674614i	0.999820	−	0.0189592i	$-0.00603527\pi$
$7$	0.739314	+	1.78486i	0.279434	+	0.674614i	−0.720386	+	0.693573i	$0.756035\pi$
$8$		0			0
$9$	−0.515254	+	1.24393i	−0.171751	+	0.414645i
$10$		0			0
$11$	0.971610	−	1.45412i	0.292951	−	0.438433i	−0.655575	−	0.755130i	$-0.727574\pi$
$11$	0.971610	−	1.45412i	0.292951	−	0.438433i	0.948527	+	0.316697i	$0.102574\pi$
$12$		0			0
$13$	3.70516	+	0.737003i	1.02763	+	0.204408i	0.679990	−	0.733221i	$-0.261984\pi$
$13$	3.70516	+	0.737003i	1.02763	+	0.204408i	0.347638	+	0.937629i	$0.386984\pi$
$14$		0			0
$15$	0.306411	−	0.306411i	0.0791149	−	0.0791149i
$16$		0			0
$17$	4.47305	+	4.47305i	1.08487	+	1.08487i	0.996047	+	0.0888265i	$0.0283117\pi$
$17$	4.47305	+	4.47305i	1.08487	+	1.08487i	0.0888265	+	0.996047i	$0.471688\pi$
$18$		0			0
$19$	1.16088	−	5.83613i	0.266324	−	1.33890i	−0.583621	−	0.812026i	$-0.698364\pi$
$19$	1.16088	−	5.83613i	0.266324	−	1.33890i	0.849944	−	0.526873i	$-0.176636\pi$
$20$		0			0
$21$	2.06561	+	1.38019i	0.450752	+	0.301183i
$22$		0			0
$23$	1.28371	+	0.531730i	0.267672	+	0.110873i	0.512483	−	0.858697i	$-0.328726\pi$
$23$	1.28371	+	0.531730i	0.267672	+	0.110873i	−0.244811	+	0.969571i	$0.578726\pi$
$24$		0			0
$25$	−4.51448	+	1.86996i	−0.902897	+	0.373992i
$26$		0			0
$27$	1.09039	+	5.48174i	0.209845	+	1.05496i
$28$		0			0
$29$	−3.04996	−	4.56458i	−0.566362	−	0.847621i	0.432169	−	0.901793i	$-0.357748\pi$
$29$	−3.04996	−	4.56458i	−0.566362	−	0.847621i	−0.998532	+	0.0541712i	$0.982748\pi$
$30$		0			0
$31$		−	10.2910i		−	1.84832i	−0.382004	−	0.924161i	$-0.624766\pi$
$31$		−	10.2910i		−	1.84832i	0.382004	−	0.924161i	$-0.375234\pi$
$32$		0			0
$33$		−	2.24887i		−	0.391478i
$34$		0			0
$35$	0.361689	+	0.541305i	0.0611366	+	0.0914973i
$36$		0			0
$37$	0.910827	+	4.57904i	0.149739	+	0.752789i	0.980555	+	0.196242i	$0.0628740\pi$
$37$	0.910827	+	4.57904i	0.149739	+	0.752789i	−0.830816	+	0.556547i	$0.812126\pi$
$38$		0			0
$39$	4.48808	−	1.85903i	0.718669	−	0.297682i
$40$		0			0
$41$	2.66002	+	1.10181i	0.415425	+	0.172074i	0.580599	−	0.814190i	$-0.302819\pi$
$41$	2.66002	+	1.10181i	0.415425	+	0.172074i	−0.165174	+	0.986264i	$0.552819\pi$
$42$		0			0
$43$	−5.83495	−	3.89879i	−0.889821	−	0.594560i	0.0244324	−	0.999701i	$-0.492222\pi$
$43$	−5.83495	−	3.89879i	−0.889821	−	0.594560i	−0.914254	+	0.405142i	$0.867222\pi$
$44$		0			0
$45$	−0.0885166	+	0.445003i	−0.0131953	+	0.0663371i
$46$		0			0
$47$	0.0482001	+	0.0482001i	0.00703071	+	0.00703071i	0.710613	−	0.703583i	$-0.248418\pi$
$47$	0.0482001	+	0.0482001i	0.00703071	+	0.00703071i	−0.703583	+	0.710613i	$0.748418\pi$
$48$		0			0
$49$	2.31060	−	2.31060i	0.330086	−	0.330086i
$50$		0			0
$51$	7.97819	+	1.58696i	1.11717	+	0.222219i
$52$		0			0
$53$	−6.43049	+	9.62391i	−0.883296	+	1.32195i	0.0627888	+	0.998027i	$0.480001\pi$
$53$	−6.43049	+	9.62391i	−0.883296	+	1.32195i	−0.946085	+	0.323919i	$0.894999\pi$
$54$		0			0
$55$	0.225527	−	0.544471i	0.0304101	−	0.0734165i
$56$		0			0
$57$	−2.92821	−	7.06933i	−0.387851	−	0.936355i
$58$		0			0
$59$	−2.89770	+	0.576389i	−0.377249	+	0.0750395i	−0.380073	−	0.924957i	$-0.624101\pi$
$59$	−2.89770	+	0.576389i	−0.377249	+	0.0750395i	0.00282397	+	0.999996i	$0.499101\pi$
$60$		0			0
$61$	0.675800	−	0.451555i	0.0865273	−	0.0578157i	−0.511554	−	0.859251i	$-0.670930\pi$
$61$	0.675800	−	0.451555i	0.0865273	−	0.0578157i	0.598081	+	0.801435i	$0.295930\pi$
$62$		0			0
$63$	−2.60119			−0.327719
$64$		0			0
$65$	1.27304			0.157901
$66$		0			0
$67$	−2.41244	+	1.61194i	−0.294727	+	0.196930i	−0.694138	−	0.719842i	$-0.744214\pi$
$67$	−2.41244	+	1.61194i	−0.294727	+	0.196930i	0.399412	+	0.916772i	$0.369214\pi$
$68$		0			0
$69$	1.75242	−	0.348577i	0.210966	−	0.0419638i
$70$		0			0
$71$	2.88474	+	6.96439i	0.342356	+	0.826521i	0.997477	+	0.0709962i	$0.0226178\pi$
$71$	2.88474	+	6.96439i	0.342356	+	0.826521i	−0.655121	+	0.755524i	$0.727382\pi$
$72$		0			0
$73$	1.92544	−	4.64843i	0.225356	−	0.544057i	−0.770246	−	0.637747i	$-0.779866\pi$
$73$	1.92544	−	4.64843i	0.225356	−	0.544057i	0.995601	+	0.0936903i	$0.0298663\pi$
$74$		0			0
$75$	−3.49095	+	5.22458i	−0.403100	+	0.603282i
$76$		0			0
$77$	3.31372	+	0.659140i	0.377634	+	0.0751160i
$78$		0			0
$79$	−10.5317	+	10.5317i	−1.18490	+	1.18490i	−0.206445	+	0.978458i	$0.566190\pi$
$79$	−10.5317	+	10.5317i	−1.18490	+	1.18490i	−0.978458	+	0.206445i	$0.933810\pi$
$80$		0			0
$81$	2.22588	+	2.22588i	0.247320	+	0.247320i
$82$		0			0
$83$	−0.0104591	+	0.0525816i	−0.00114804	+	0.00577158i	−0.981355	−	0.192204i	$-0.938437\pi$
$83$	−0.0104591	+	0.0525816i	−0.00114804	+	0.00577158i	0.980207	+	0.197975i	$0.0634366\pi$
$84$		0			0
$85$	1.77244	+	1.18431i	0.192248	+	0.128456i
$86$		0			0
$87$	−6.52202	−	2.70151i	−0.699233	−	0.289632i
$88$		0			0
$89$	−7.52277	+	3.11604i	−0.797413	+	0.330299i	−0.743920	−	0.668269i	$-0.767035\pi$
$89$	−7.52277	+	3.11604i	−0.797413	+	0.330299i	−0.0534930	+	0.998568i	$0.517035\pi$
$90$		0			0
$91$	1.42383	+	7.15808i	0.149258	+	0.750371i
$92$		0			0
$93$	−7.35206	−	11.0031i	−0.762373	−	1.14097i
$94$		0			0
$95$		−	2.00520i		−	0.205729i
$96$		0			0
$97$		−	12.1748i		−	1.23616i	−0.786115	−	0.618081i	$-0.787910\pi$
$97$		−	12.1748i		−	1.23616i	0.786115	−	0.618081i	$-0.212090\pi$
$98$		0			0
$99$	1.30820	+	1.95786i	0.131479	+	0.196772i
$100$		0			0
$101$	−3.22333	−	16.2048i	−0.320733	−	1.61244i	−0.718894	−	0.695120i	$-0.755351\pi$
$101$	−3.22333	−	16.2048i	−0.320733	−	1.61244i	0.398160	−	0.917316i	$-0.369649\pi$
$102$		0			0
$103$	5.27535	−	2.18512i	0.519796	−	0.215306i	−0.107331	−	0.994223i	$-0.534231\pi$
$103$	5.27535	−	2.18512i	0.519796	−	0.215306i	0.627127	+	0.778917i	$0.284231\pi$
$104$		0			0
$105$	0.773434	+	0.320367i	0.0754794	+	0.0312646i
$106$		0			0
$107$	−5.94629	−	3.97318i	−0.574850	−	0.384102i	0.233895	−	0.972262i	$-0.424853\pi$
$107$	−5.94629	−	3.97318i	−0.574850	−	0.384102i	−0.808745	+	0.588160i	$0.799853\pi$
$108$		0			0
$109$	0.986910	−	4.96153i	0.0945288	−	0.475229i	−0.904302	−	0.426893i	$-0.859608\pi$
$109$	0.986910	−	4.96153i	0.0945288	−	0.475229i	0.998831	−	0.0483359i	$-0.0153918\pi$
$110$		0			0
$111$	4.24519	+	4.24519i	0.402936	+	0.402936i
$112$		0			0
$113$	−9.81440	+	9.81440i	−0.923261	+	0.923261i	−0.997258	−	0.0739972i	$-0.976424\pi$
$113$	−9.81440	+	9.81440i	−0.923261	+	0.923261i	0.0739972	+	0.997258i	$0.476424\pi$
$114$		0			0
$115$	0.459232	+	0.0913470i	0.0428236	+	0.00851815i
$116$		0			0
$117$	−2.82589	+	4.22924i	−0.261253	+	0.390993i
$118$		0			0
$119$	−4.67679	+	11.2908i	−0.428720	+	1.03502i
$120$		0			0
$121$	3.03909	+	7.33701i	0.276281	+	0.667001i
$122$		0			0
$123$	3.63124	−	0.722298i	0.327418	−	0.0651274i
$124$		0			0
$125$	−2.77009	+	1.85091i	−0.247764	+	0.165551i
$126$		0			0
$127$	−0.460345			−0.0408490			−0.0204245	−	0.999791i	$-0.506502\pi$
$127$	−0.460345			−0.0408490			−0.0204245	+	0.999791i	$0.506502\pi$
$128$		0			0
$129$	−9.02408			−0.794526
$130$		0			0
$131$	−15.2355	+	10.1801i	−1.33114	+	0.889437i	−0.998560	−	0.0536401i	$-0.982918\pi$
$131$	−15.2355	+	10.1801i	−1.33114	+	0.889437i	−0.332575	+	0.943077i	$0.607918\pi$
$132$		0			0
$133$	11.2749	−	2.24272i	0.977660	−	0.194469i
$134$		0			0
$135$	0.720760	+	1.74007i	0.0620331	+	0.149761i
$136$		0			0
$137$	3.64275	−	8.79438i	0.311221	−	0.751355i	−0.688439	−	0.725294i	$-0.741704\pi$
$137$	3.64275	−	8.79438i	0.311221	−	0.751355i	0.999660	−	0.0260607i	$-0.00829631\pi$
$138$		0			0
$139$	3.24499	−	4.85647i	0.275237	−	0.411921i	−0.667939	−	0.744216i	$-0.732823\pi$
$139$	3.24499	−	4.85647i	0.275237	−	0.411921i	0.943175	+	0.332296i	$0.107823\pi$
$140$		0			0
$141$	0.0859705	+	0.0171006i	0.00724002	+	0.00144013i
$142$		0			0
$143$	4.67166	−	4.67166i	0.390664	−	0.390664i
$144$		0			0
$145$	−1.30812	−	1.30812i	−0.108633	−	0.108633i
$146$		0			0
$147$	0.819762	−	4.12122i	0.0676128	−	0.339913i
$148$		0			0
$149$	−15.1308	−	10.1101i	−1.23957	−	0.828252i	−0.249435	−	0.968392i	$-0.580245\pi$
$149$	−15.1308	−	10.1101i	−1.23957	−	0.828252i	−0.990132	+	0.140140i	$0.955245\pi$
$150$		0			0
$151$	−14.5143	−	6.01204i	−1.18116	−	0.489252i	−0.296293	−	0.955097i	$-0.595751\pi$
$151$	−14.5143	−	6.01204i	−1.18116	−	0.489252i	−0.884867	+	0.465844i	$0.845751\pi$
$152$		0			0
$153$	−7.86894	+	3.25942i	−0.636166	+	0.263509i
$154$		0			0
$155$	−0.676551	−	3.40125i	−0.0543419	−	0.273195i
$156$		0			0
$157$	3.85444	+	5.76858i	0.307618	+	0.460383i	0.952779	−	0.303663i	$-0.0982099\pi$
$157$	3.85444	+	5.76858i	0.307618	+	0.460383i	−0.645161	+	0.764046i	$0.723210\pi$
$158$		0			0
$159$			14.8839i			1.18037i
$160$		0			0
$161$			2.68436i			0.211557i
$162$		0			0
$163$	−9.11685	−	13.6443i	−0.714087	−	1.06871i	−0.994074	−	0.108703i	$-0.965330\pi$
$163$	−9.11685	−	13.6443i	−0.714087	−	1.06871i	0.279987	−	0.960004i	$-0.409670\pi$
$164$		0			0
$165$	−0.147845	−	0.743268i	−0.0115097	−	0.0578633i
$166$		0			0
$167$	−1.98808	+	0.823489i	−0.153842	+	0.0637235i	−0.458276	−	0.888810i	$-0.651533\pi$
$167$	−1.98808	+	0.823489i	−0.153842	+	0.0637235i	0.304434	+	0.952534i	$0.401533\pi$
$168$		0			0
$169$	1.17464	+	0.486552i	0.0903569	+	0.0374270i
$170$		0			0
$171$	6.66161	+	4.45114i	0.509426	+	0.340388i
$172$		0			0
$173$	−1.79167	+	9.00732i	−0.136218	+	0.684814i	0.850965	+	0.525222i	$0.176018\pi$
$173$	−1.79167	+	9.00732i	−0.136218	+	0.684814i	−0.987183	+	0.159592i	$0.948982\pi$
$174$		0			0
$175$	−6.67524	−	6.67524i	−0.504601	−	0.504601i
$176$		0			0
$177$	−2.68644	+	2.68644i	−0.201925	+	0.201925i
$178$		0			0
$179$	2.24858	+	0.447270i	0.168067	+	0.0334305i	0.278406	−	0.960463i	$-0.410194\pi$
$179$	2.24858	+	0.447270i	0.168067	+	0.0334305i	−0.110340	+	0.993894i	$0.535194\pi$
$180$		0			0
$181$	5.64020	−	8.44116i	0.419233	−	0.627426i	−0.560400	−	0.828222i	$-0.689353\pi$
$181$	5.64020	−	8.44116i	0.419233	−	0.627426i	0.979633	+	0.200796i	$0.0643527\pi$
$182$		0			0
$183$	0.399966	−	0.965604i	0.0295663	−	0.0713795i
$184$		0			0
$185$	0.602070	+	1.45352i	0.0442650	+	0.106865i
$186$		0			0
$187$	10.8504	−	2.15828i	0.793459	−	0.157829i
$188$		0			0
$189$	−8.97800	+	5.99891i	−0.653054	+	0.436356i
$190$		0			0
$191$	15.2964			1.10681			0.553405	−	0.832912i	$-0.313328\pi$
$191$	15.2964			1.10681			0.553405	+	0.832912i	$0.313328\pi$
$192$		0			0
$193$	13.0208			0.937258			0.468629	−	0.883395i	$-0.344748\pi$
$193$	13.0208			0.937258			0.468629	+	0.883395i	$0.344748\pi$
$194$		0			0
$195$	1.36113	−	0.909476i	0.0974724	−	0.0651289i
$196$		0			0
$197$	−4.45565	+	0.886285i	−0.317452	+	0.0631452i	−0.351245	−	0.936284i	$-0.614241\pi$
$197$	−4.45565	+	0.886285i	−0.317452	+	0.0631452i	0.0337925	+	0.999429i	$0.489241\pi$
$198$		0			0
$199$	−3.49809	−	8.44513i	−0.247973	−	0.598659i	0.750059	−	0.661371i	$-0.230025\pi$
$199$	−3.49809	−	8.44513i	−0.247973	−	0.598659i	−0.998032	+	0.0627118i	$0.980025\pi$
$200$		0			0
$201$	−1.42778	+	3.44697i	−0.100708	+	0.243131i
$202$		0			0
$203$	5.89227	−	8.81841i	0.413556	−	0.618931i
$204$		0			0
$205$	0.951589	+	0.189283i	0.0664619	+	0.0132201i
$206$		0			0
$207$	−1.32287	+	1.32287i	−0.0919461	+	0.0919461i
$208$		0			0
$209$	−7.35849	−	7.35849i	−0.508997	−	0.508997i
$210$		0			0
$211$	−1.12050	+	5.63316i	−0.0771387	+	0.387803i	0.922858	+	0.385141i	$0.125847\pi$
$211$	−1.12050	+	5.63316i	−0.0771387	+	0.387803i	−0.999996	+	0.00266152i	$0.999153\pi$
$212$		0			0
$213$	8.05983	+	5.38541i	0.552250	+	0.369002i
$214$		0			0
$215$	−2.18481	−	0.904976i	−0.149003	−	0.0617189i
$216$		0			0
$217$	18.3680	−	7.60829i	1.24690	−	0.516484i
$218$		0			0
$219$	−1.26223	−	6.34566i	−0.0852936	−	0.428800i
$220$		0			0
$221$	13.2767	+	19.8700i	0.893090	+	1.33660i
$222$		0			0
$223$		−	13.8411i		−	0.926872i	−0.886130	−	0.463436i	$-0.846616\pi$
$223$		−	13.8411i		−	0.926872i	0.886130	−	0.463436i	$-0.153384\pi$
$224$		0			0
$225$		−	6.57923i		−	0.438615i
$226$		0			0
$227$	13.5582	+	20.2913i	0.899890	+	1.34678i	0.937682	+	0.347495i	$0.112968\pi$
$227$	13.5582	+	20.2913i	0.899890	+	1.34678i	−0.0377913	+	0.999286i	$0.512032\pi$
$228$		0			0
$229$	−1.91748	−	9.63980i	−0.126710	−	0.637016i	−0.990982	−	0.133991i	$-0.957221\pi$
$229$	−1.91748	−	9.63980i	−0.126710	−	0.637016i	0.864272	−	0.503025i	$-0.167779\pi$
$230$		0			0
$231$	4.01393	−	1.66262i	0.264097	−	0.109393i
$232$		0			0
$233$	13.0360	+	5.39971i	0.854020	+	0.353747i	0.766366	−	0.642404i	$-0.222063\pi$
$233$	13.0360	+	5.39971i	0.854020	+	0.353747i	0.0876541	+	0.996151i	$0.472063\pi$
$234$		0			0
$235$	0.0190993	+	0.0127617i	0.00124590	+	0.000832483i
$236$		0			0
$237$	−3.73645	+	18.7844i	−0.242709	+	1.22018i
$238$		0			0
$239$	20.8075	+	20.8075i	1.34592	+	1.34592i	0.890038	+	0.455887i	$0.150678\pi$
$239$	20.8075	+	20.8075i	1.34592	+	1.34592i	0.455887	+	0.890038i	$0.349322\pi$
$240$		0			0
$241$	5.88520	−	5.88520i	0.379099	−	0.379099i	−0.491678	−	0.870777i	$-0.663616\pi$
$241$	5.88520	−	5.88520i	0.379099	−	0.379099i	0.870777	+	0.491678i	$0.163616\pi$
$242$		0			0
$243$	−12.4751	−	2.48145i	−0.800278	−	0.159185i
$244$		0			0
$245$	0.611767	−	0.915574i	0.0390843	−	0.0584938i
$246$		0			0
$247$	8.60249	−	20.7682i	0.547363	−	1.32145i
$248$		0			0
$249$	0.0263822	+	0.0636924i	0.00167191	+	0.00403634i
$250$		0			0
$251$	8.08063	−	1.60734i	0.510045	−	0.101454i	0.0666425	−	0.997777i	$-0.478771\pi$
$251$	8.08063	−	1.60734i	0.510045	−	0.101454i	0.443402	+	0.896323i	$0.353771\pi$
$252$		0			0
$253$	2.02046	−	1.35003i	0.127025	−	0.0848757i
$254$		0			0
$255$	2.74118			0.171659
$256$		0			0
$257$	−14.0980			−0.879412			−0.439706	−	0.898142i	$-0.644917\pi$
$257$	−14.0980			−0.879412			−0.439706	+	0.898142i	$0.644917\pi$
$258$		0			0
$259$	−7.49956	+	5.01105i	−0.466000	+	0.311371i
$260$		0			0
$261$	7.24954	−	1.44202i	0.448735	−	0.0892590i
$262$		0			0
$263$	−5.62862	−	13.5887i	−0.347076	−	0.837915i	−0.996962	−	0.0778837i	$-0.975184\pi$
$263$	−5.62862	−	13.5887i	−0.347076	−	0.837915i	0.649887	−	0.760031i	$-0.274816\pi$
$264$		0			0
$265$	−1.49263	+	3.60352i	−0.0916914	+	0.221363i
$266$		0			0
$267$	−5.81720	+	8.70605i	−0.356007	+	0.532802i
$268$		0			0
$269$	4.35266	+	0.865799i	0.265387	+	0.0527887i	0.325990	−	0.945373i	$-0.394302\pi$
$269$	4.35266	+	0.865799i	0.265387	+	0.0527887i	−0.0606033	+	0.998162i	$0.519302\pi$
$270$		0			0
$271$	8.75941	−	8.75941i	0.532096	−	0.532096i	−0.389099	−	0.921196i	$-0.627214\pi$
$271$	8.75941	−	8.75941i	0.532096	−	0.532096i	0.921196	+	0.389099i	$0.127214\pi$
$272$		0			0
$273$	6.63620	+	6.63620i	0.401641	+	0.401641i
$274$		0			0
$275$	−1.66718	+	8.38146i	−0.100534	+	0.505421i
$276$		0			0
$277$	15.3547	+	10.2597i	0.922572	+	0.616443i	0.923517	−	0.383557i	$-0.125301\pi$
$277$	15.3547	+	10.2597i	0.922572	+	0.616443i	−0.000945275		1.00000i	$0.500301\pi$
$278$		0			0
$279$	12.8013	+	5.30249i	0.766397	+	0.317452i
$280$		0			0
$281$	14.0773	−	5.83101i	0.839781	−	0.347849i	0.0790137	−	0.996874i	$-0.474823\pi$
$281$	14.0773	−	5.83101i	0.839781	−	0.347849i	0.760767	+	0.649025i	$0.224823\pi$
$282$		0			0
$283$	0.0531107	+	0.267006i	0.00315711	+	0.0158718i	0.982332	−	0.187148i	$-0.0599244\pi$
$283$	0.0531107	+	0.267006i	0.00315711	+	0.0158718i	−0.979175	+	0.203020i	$0.934924\pi$
$284$		0			0
$285$	−1.43255	−	2.14396i	−0.0848567	−	0.126997i
$286$		0			0
$287$			5.56235i			0.328335i
$288$		0			0
$289$			23.0163i			1.35390i
$290$		0			0
$291$	−8.69785	−	13.0173i	−0.509877	−	0.763085i
$292$		0			0
$293$	3.24074	+	16.2923i	0.189326	+	0.951807i	0.952250	+	0.305319i	$0.0987631\pi$
$293$	3.24074	+	16.2923i	0.189326	+	0.951807i	−0.762924	+	0.646488i	$0.776237\pi$
$294$		0			0
$295$	−0.919819	+	0.381001i	−0.0535539	+	0.0221828i
$296$		0			0
$297$	9.03051	+	3.74056i	0.524003	+	0.217049i
$298$		0			0
$299$	4.36447	+	2.91625i	0.252404	+	0.168651i
$300$		0			0
$301$	2.64494	−	13.2970i	0.152452	−	0.766427i
$302$		0			0
$303$	−15.0233	−	15.0233i	−0.863068	−	0.863068i
$304$		0			0
$305$	0.193670	−	0.193670i	0.0110895	−	0.0110895i
$306$		0			0
$307$	6.84456	+	1.36147i	0.390640	+	0.0777031i	0.386502	−	0.922288i	$-0.373683\pi$
$307$	6.84456	+	1.36147i	0.390640	+	0.0777031i	0.00413726	+	0.999991i	$0.498683\pi$
$308$		0			0
$309$	4.07931	−	6.10512i	0.232064	−	0.347308i
$310$		0			0
$311$	2.90025	−	7.00183i	0.164458	−	0.397038i	−0.820070	−	0.572263i	$-0.806066\pi$
$311$	2.90025	−	7.00183i	0.164458	−	0.397038i	0.984528	+	0.175226i	$0.0560655\pi$
$312$		0			0
$313$	5.70821	+	13.7808i	0.322647	+	0.778938i	0.999099	+	0.0424514i	$0.0135167\pi$
$313$	5.70821	+	13.7808i	0.322647	+	0.778938i	−0.676452	+	0.736487i	$0.736483\pi$
$314$		0			0
$315$	−0.859710	+	0.171007i	−0.0484392	+	0.00963515i
$316$		0			0
$317$	12.0391	−	8.04424i	0.676181	−	0.451809i	−0.169478	−	0.985534i	$-0.554208\pi$
$317$	12.0391	−	8.04424i	0.676181	−	0.451809i	0.845658	+	0.533725i	$0.179208\pi$
$318$		0			0
$319$	−9.60080			−0.537541
$320$		0			0
$321$	−9.19627			−0.513286
$322$		0			0
$323$	31.2979	−	20.9126i	1.74146	−	1.16361i
$324$		0			0
$325$	−18.1051	+	3.60132i	−1.00429	+	0.199766i
$326$		0			0
$327$	−2.48939	−	6.00993i	−0.137664	−	0.332350i
$328$		0			0
$329$	−0.0503956	+	0.121666i	−0.00277840	+	0.00670764i
$330$		0			0
$331$	14.3128	−	21.4207i	0.786705	−	1.17739i	−0.193828	−	0.981035i	$-0.562090\pi$
$331$	14.3128	−	21.4207i	0.786705	−	1.17739i	0.980533	−	0.196352i	$-0.0629095\pi$
$332$		0			0
$333$	−6.16533	−	1.22636i	−0.337858	−	0.0672041i
$334$		0			0
$335$	−0.691356	+	0.691356i	−0.0377728	+	0.0377728i
$336$		0			0
$337$	−10.9026	−	10.9026i	−0.593904	−	0.593904i	0.344780	−	0.938684i	$-0.387954\pi$
$337$	−10.9026	−	10.9026i	−0.593904	−	0.593904i	−0.938684	+	0.344780i	$0.887954\pi$
$338$		0			0
$339$	−3.48198	+	17.5051i	−0.189115	+	0.950747i
$340$		0			0
$341$	−14.9643	−	9.99885i	−0.810364	−	0.541468i
$342$		0			0
$343$	18.3264	+	7.59104i	0.989532	+	0.409878i
$344$		0			0
$345$	0.556270	−	0.230415i	0.0299486	−	0.0124051i
$346$		0			0
$347$	−3.71315	−	18.6673i	−0.199332	−	1.00211i	−0.942805	−	0.333345i	$-0.891823\pi$
$347$	−3.71315	−	18.6673i	−0.199332	−	1.00211i	0.743472	−	0.668767i	$-0.233177\pi$
$348$		0			0
$349$	0.0981410	+	0.146878i	0.00525337	+	0.00786222i	0.834087	−	0.551633i	$-0.185995\pi$
$349$	0.0981410	+	0.146878i	0.00525337	+	0.00786222i	−0.828834	+	0.559495i	$0.810995\pi$
$350$		0			0
$351$			21.1144i			1.12700i
$352$		0			0
$353$			12.0283i			0.640199i	0.947384	+	0.320100i	$0.103716\pi$
$353$			12.0283i			0.640199i	−0.947384	+	0.320100i	$0.896284\pi$
$354$		0			0
$355$	1.41128	+	2.11213i	0.0749030	+	0.112100i
$356$		0			0
$357$	3.06588	+	15.4132i	0.162264	+	0.815755i
$358$		0			0
$359$	−33.9190	+	14.0497i	−1.79018	+	0.741516i	−0.800300	+	0.599600i	$0.795326\pi$
$359$	−33.9190	+	14.0497i	−1.79018	+	0.741516i	−0.989879	+	0.141916i	$0.954674\pi$
$360$		0			0
$361$	−15.1590	−	6.27907i	−0.797843	−	0.330477i
$362$		0			0
$363$	8.49106	+	5.67355i	0.445665	+	0.297784i
$364$		0			0
$365$	0.330775	−	1.66292i	0.0173136	−	0.0870412i
$366$		0			0
$367$	8.38811	+	8.38811i	0.437856	+	0.437856i	0.891290	−	0.453434i	$-0.149801\pi$
$367$	8.38811	+	8.38811i	0.437856	+	0.437856i	−0.453434	+	0.891290i	$0.649801\pi$
$368$		0			0
$369$	−2.74117	+	2.74117i	−0.142700	+	0.142700i
$370$		0			0
$371$	−21.9315	−	4.36245i	−1.13863	−	0.226487i
$372$		0			0
$373$	12.9524	−	19.3846i	0.670647	−	1.00369i	−0.327617	−	0.944810i	$-0.606246\pi$
$373$	12.9524	−	19.3846i	0.670647	−	1.00369i	0.998265	−	0.0588843i	$-0.0187543\pi$
$374$		0			0
$375$	−1.63945	+	3.95799i	−0.0846609	+	0.204389i
$376$		0			0
$377$	−7.93648	−	19.1604i	−0.408749	−	0.986808i
$378$		0			0
$379$	−26.4712	+	5.26545i	−1.35973	+	0.270468i	−0.820480	−	0.571676i	$-0.806294\pi$
$379$	−26.4712	+	5.26545i	−1.35973	+	0.270468i	−0.539254	+	0.842143i	$0.681294\pi$
$380$		0			0
$381$	−0.492200	+	0.328877i	−0.0252162	+	0.0168489i
$382$		0			0
$383$	−3.40990			−0.174238			−0.0871189	−	0.996198i	$-0.527766\pi$
$383$	−3.40990			−0.174238			−0.0871189	+	0.996198i	$0.527766\pi$
$384$		0			0
$385$	1.13854			0.0580254
$386$		0			0
$387$	7.85632	−	5.24943i	0.399359	−	0.266843i
$388$		0			0
$389$	−6.70403	+	1.33351i	−0.339908	+	0.0676119i	−0.362093	−	0.932142i	$-0.617938\pi$
$389$	−6.70403	+	1.33351i	−0.339908	+	0.0676119i	0.0221851	+	0.999754i	$0.492938\pi$
$390$		0			0
$391$	3.36364	+	8.12055i	0.170107	+	0.410674i
$392$		0			0
$393$	−9.01703	+	21.7690i	−0.454849	+	1.09810i
$394$		0			0
$395$	−2.78841	+	4.17316i	−0.140300	+	0.209974i
$396$		0			0
$397$	−25.0619	−	4.98511i	−1.25782	−	0.250196i	−0.479207	−	0.877702i	$-0.659076\pi$
$397$	−25.0619	−	4.98511i	−1.25782	−	0.250196i	−0.778611	+	0.627506i	$0.784076\pi$
$398$		0			0
$399$	10.4529	−	10.4529i	0.523300	−	0.523300i
$400$		0			0
$401$	2.21860	+	2.21860i	0.110791	+	0.110791i	0.760329	−	0.649538i	$-0.225038\pi$
$401$	2.21860	+	2.21860i	0.110791	+	0.110791i	−0.649538	+	0.760329i	$0.725038\pi$
$402$		0			0
$403$	7.58451	−	38.1299i	0.377811	−	1.89939i
$404$		0			0
$405$	0.882002	+	0.589335i	0.0438270	+	0.0292843i
$406$		0			0
$407$	7.54342	+	3.12459i	0.373914	+	0.154880i
$408$		0			0
$409$	10.6896	−	4.42777i	0.528566	−	0.218939i	−0.102409	−	0.994742i	$-0.532655\pi$
$409$	10.6896	−	4.42777i	0.528566	−	0.218939i	0.630975	+	0.775803i	$0.282655\pi$
$410$		0			0
$411$	−2.38802	−	12.0054i	−0.117792	−	0.592182i
$412$		0			0
$413$	−3.17109	−	4.74587i	−0.156039	−	0.233529i
$414$		0			0
$415$			0.0180662i			0.000886835i
$416$		0			0
$417$		−	7.51080i		−	0.367806i
$418$		0			0
$419$	8.58363	+	12.8463i	0.419338	+	0.627583i	0.979654	−	0.200696i	$-0.0643203\pi$
$419$	8.58363	+	12.8463i	0.419338	+	0.627583i	−0.560316	+	0.828279i	$0.689320\pi$
$420$		0			0
$421$	1.91938	+	9.64937i	0.0935448	+	0.470281i	0.998953	+	0.0457401i	$0.0145646\pi$
$421$	1.91938	+	9.64937i	0.0935448	+	0.470281i	−0.905409	+	0.424541i	$0.860435\pi$
$422$		0			0
$423$	−0.0847932	+	0.0351225i	−0.00412278	+	0.00170771i
$424$		0			0
$425$	−28.5579	−	11.8291i	−1.38526	−	0.573795i
$426$		0			0
$427$	1.30559	+	0.872368i	0.0631820	+	0.0422168i
$428$		0			0
$429$	1.65743	−	8.33244i	0.0800213	−	0.402294i
$430$		0			0
$431$	−19.6960	−	19.6960i	−0.948725	−	0.948725i	0.0500230	−	0.998748i	$-0.484071\pi$
$431$	−19.6960	−	19.6960i	−0.948725	−	0.948725i	−0.998748	+	0.0500230i	$0.984071\pi$
$432$		0			0
$433$	28.0515	−	28.0515i	1.34807	−	1.34807i	0.460312	−	0.887757i	$-0.347738\pi$
$433$	28.0515	−	28.0515i	1.34807	−	1.34807i	0.887757	−	0.460312i	$-0.152262\pi$
$434$		0			0
$435$	−2.33317	−	0.464097i	−0.111867	−	0.0222518i
$436$		0			0
$437$	4.59347	−	6.87462i	0.219736	−	0.328858i
$438$		0			0
$439$	−6.53568	+	15.7785i	−0.311931	+	0.753068i	0.687702	+	0.725993i	$0.258619\pi$
$439$	−6.53568	+	15.7785i	−0.311931	+	0.753068i	−0.999633	+	0.0270754i	$0.991381\pi$
$440$		0			0
$441$	1.68369	+	4.06478i	0.0801757	+	0.193561i
$442$		0			0
$443$	−17.8876	+	3.55806i	−0.849864	+	0.169048i	−0.600761	−	0.799429i	$-0.705136\pi$
$443$	−17.8876	+	3.55806i	−0.849864	+	0.169048i	−0.249103	+	0.968477i	$0.580136\pi$
$444$		0			0
$445$	−2.28148	+	1.52443i	−0.108152	+	0.0722651i
$446$		0			0
$447$	−23.4007			−1.10681
$448$		0			0
$449$	7.49157			0.353549			0.176775	−	0.984251i	$-0.443434\pi$
$449$	7.49157			0.353549			0.176775	+	0.984251i	$0.443434\pi$
$450$		0			0
$451$	4.18666	−	2.79744i	0.197142	−	0.131726i
$452$		0			0
$453$	−19.8138	+	3.94121i	−0.930934	+	0.185174i
$454$		0			0
$455$	0.941173	+	2.27219i	0.0441228	+	0.106522i
$456$		0			0
$457$	−6.33038	+	15.2829i	−0.296123	+	0.714904i	0.703867	+	0.710332i	$0.251455\pi$
$457$	−6.33038	+	15.2829i	−0.296123	+	0.714904i	−0.999990	+	0.00457167i	$0.998545\pi$
$458$		0			0
$459$	−19.6427	+	29.3974i	−0.916844	+	1.37215i
$460$		0			0
$461$	16.1652	+	3.21545i	0.752886	+	0.149758i	0.556591	−	0.830786i	$-0.312109\pi$
$461$	16.1652	+	3.21545i	0.752886	+	0.149758i	0.196295	+	0.980545i	$0.437109\pi$
$462$		0			0
$463$	−25.6472	+	25.6472i	−1.19193	+	1.19193i	−0.215401	+	0.976526i	$0.569106\pi$
$463$	−25.6472	+	25.6472i	−1.19193	+	1.19193i	−0.976526	+	0.215401i	$0.930894\pi$
$464$		0			0
$465$	−3.15328	−	3.15328i	−0.146230	−	0.146230i
$466$		0			0
$467$	−8.07541	+	40.5978i	−0.373685	+	1.87864i	0.0953188	+	0.995447i	$0.469613\pi$
$467$	−8.07541	+	40.5978i	−0.373685	+	1.87864i	−0.469004	+	0.883196i	$0.655387\pi$
$468$		0			0
$469$	−4.66064	−	3.11414i	−0.215208	−	0.143798i
$470$		0			0
$471$	8.24233	+	3.41408i	0.379786	+	0.157313i
$472$		0			0
$473$	−11.3386	+	4.69660i	−0.521349	+	0.215950i
$474$		0			0
$475$	5.67256	+	28.5179i	0.260275	+	1.30849i
$476$		0			0
$477$	−8.65817	−	12.9579i	−0.396431	−	0.593300i
$478$		0			0
$479$			7.37082i			0.336781i	0.985720	+	0.168391i	$0.0538570\pi$
$479$			7.37082i			0.336781i	−0.985720	+	0.168391i	$0.946143\pi$
$480$		0			0
$481$			17.6374i			0.804195i
$482$		0			0
$483$	1.91775	+	2.87011i	0.0872606	+	0.130595i
$484$		0			0
$485$	−0.800394	−	4.02385i	−0.0363440	−	0.182714i
$486$		0			0
$487$	14.2123	−	5.88692i	0.644020	−	0.266762i	−0.0366766	−	0.999327i	$-0.511677\pi$
$487$	14.2123	−	5.88692i	0.644020	−	0.266762i	0.680697	+	0.732565i	$0.261677\pi$
$488$		0			0
$489$	−19.4955	−	8.07528i	−0.881615	−	0.365177i
$490$		0			0
$491$	13.9347	+	9.31084i	0.628862	+	0.420192i	0.828744	−	0.559628i	$-0.189056\pi$
$491$	13.9347	+	9.31084i	0.628862	+	0.420192i	−0.199882	+	0.979820i	$0.564056\pi$
$492$		0			0
$493$	6.77499	−	34.0602i	0.305130	−	1.53399i
$494$		0			0
$495$	0.561082	+	0.561082i	0.0252188	+	0.0252188i
$496$		0			0
$497$	−10.2977	+	10.2977i	−0.461917	+	0.461917i
$498$		0			0
$499$	−21.0694	−	4.19096i	−0.943194	−	0.187613i	−0.300540	−	0.953769i	$-0.597167\pi$
$499$	−21.0694	−	4.19096i	−0.943194	−	0.187613i	−0.642654	+	0.766156i	$0.722167\pi$
$500$		0			0
$501$	−1.53734	+	2.30079i	−0.0686832	+	0.102792i
$502$		0			0
$503$	−3.12293	+	7.53942i	−0.139245	+	0.336166i	−0.978083	−	0.208214i	$-0.933235\pi$
$503$	−3.12293	+	7.53942i	−0.139245	+	0.336166i	0.838839	+	0.544380i	$0.183235\pi$
$504$		0			0
$505$	−2.13067	−	5.14389i	−0.0948135	−	0.228900i
$506$		0			0
$507$	1.60352	−	0.318961i	0.0712149	−	0.0141655i
$508$		0			0
$509$	5.05284	−	3.37620i	0.223963	−	0.149647i	−0.438527	−	0.898718i	$-0.644500\pi$
$509$	5.05284	−	3.37620i	0.223963	−	0.149647i	0.662490	+	0.749071i	$0.269500\pi$
$510$		0			0
$511$	9.72030			0.430001
$512$		0			0
$513$	33.2579			1.46837
$514$		0			0
$515$	1.59989	−	1.06901i	0.0704994	−	0.0471062i
$516$		0			0
$517$	0.116920	−	0.0232569i	0.00514215	−	0.00102284i
$518$		0			0
$519$	4.51932	+	10.9106i	0.198376	+	0.478923i
$520$		0			0
$521$	9.28701	−	22.4208i	0.406871	−	0.982274i	−0.579085	−	0.815267i	$-0.696590\pi$
$521$	9.28701	−	22.4208i	0.406871	−	0.982274i	0.985956	−	0.167006i	$-0.0534100\pi$
$522$		0			0
$523$	−11.7557	+	17.5936i	−0.514040	+	0.769315i	−0.994163	−	0.107886i	$-0.965592\pi$
$523$	−11.7557	+	17.5936i	−0.514040	+	0.769315i	0.480123	+	0.877201i	$0.340592\pi$
$524$		0			0
$525$	−11.9061	−	2.36826i	−0.519623	−	0.103359i
$526$		0			0
$527$	46.0322	−	46.0322i	2.00519	−	2.00519i
$528$		0			0
$529$	−14.8983	−	14.8983i	−0.647751	−	0.647751i
$530$		0			0
$531$	0.776065	−	3.90154i	0.0336783	−	0.169312i
$532$		0			0
$533$	9.04375	+	6.04284i	0.391728	+	0.261745i
$534$		0			0
$535$	−2.22650	−	0.922245i	−0.0962598	−	0.0398721i
$536$		0			0
$537$	2.72371	−	1.12820i	0.117537	−	0.0486854i
$538$		0			0
$539$	−1.11488	−	5.60489i	−0.0480213	−	0.241420i
$540$		0			0
$541$	21.5427	+	32.2410i	0.926195	+	1.38615i	0.922434	+	0.386156i	$0.126197\pi$
$541$	21.5427	+	32.2410i	0.926195	+	1.38615i	0.00376128	+	0.999993i	$0.498803\pi$
$542$		0			0
$543$		−	13.0547i		−	0.560232i
$544$		0			0
$545$		−	1.70470i		−	0.0730214i
$546$		0			0
$547$	−12.7138	−	19.0275i	−0.543602	−	0.813557i	0.453370	−	0.891322i	$-0.350222\pi$
$547$	−12.7138	−	19.0275i	−0.543602	−	0.813557i	−0.996972	+	0.0777651i	$0.975222\pi$
$548$		0			0
$549$	0.213496	+	1.07332i	0.00911178	+	0.0458080i
$550$		0			0
$551$	−30.1801	+	12.5010i	−1.28572	+	0.532561i
$552$		0			0
$553$	−26.5837	−	11.0113i	−1.13046	−	0.468250i
$554$		0			0
$555$	1.68215	+	1.12398i	0.0714034	+	0.0477102i
$556$		0			0
$557$	−1.11280	+	5.59444i	−0.0471510	+	0.237044i	−0.997173	−	0.0751386i	$-0.976060\pi$
$557$	−1.11280	+	5.59444i	−0.0471510	+	0.237044i	0.950022	+	0.312183i	$0.101060\pi$
$558$		0			0
$559$	−18.7460	−	18.7460i	−0.792873	−	0.792873i
$560$		0			0
$561$	10.0593	−	10.0593i	0.424705	−	0.424705i
$562$		0			0
$563$	31.1060	+	6.18736i	1.31096	+	0.260766i	0.800603	−	0.599196i	$-0.204513\pi$
$563$	31.1060	+	6.18736i	1.31096	+	0.260766i	0.510358	+	0.859962i	$0.329513\pi$
$564$		0			0
$565$	−2.59851	+	3.88895i	−0.109320	+	0.163609i
$566$		0			0
$567$	−2.32726	+	5.61851i	−0.0977358	+	0.235955i
$568$		0			0
$569$	−6.06734	−	14.6478i	−0.254356	−	0.614070i	0.744190	−	0.667967i	$-0.232835\pi$
$569$	−6.06734	−	14.6478i	−0.254356	−	0.614070i	−0.998546	+	0.0538978i	$0.982835\pi$
$570$		0			0
$571$	−7.92899	+	1.57717i	−0.331818	+	0.0660027i	−0.358188	−	0.933650i	$-0.616605\pi$
$571$	−7.92899	+	1.57717i	−0.331818	+	0.0660027i	0.0263699	+	0.999652i	$0.491605\pi$
$572$		0			0
$573$	16.3549	−	10.9280i	0.683236	−	0.456524i
$574$		0			0
$575$	−6.78960			−0.283146
$576$		0			0
$577$	7.30913			0.304283			0.152142	−	0.988359i	$-0.451383\pi$
$577$	7.30913			0.304283			0.152142	+	0.988359i	$0.451383\pi$
$578$		0			0
$579$	13.9218	−	9.30227i	0.578571	−	0.386589i
$580$		0			0
$581$	−0.101584	+	0.0202062i	−0.00421439	+	0.000838295i
$582$		0			0
$583$	7.74636	+	18.7014i	0.320821	+	0.774532i
$584$		0			0
$585$	−0.655937	+	1.58357i	−0.0271197	+	0.0654726i
$586$		0			0
$587$	−15.4927	+	23.1865i	−0.639452	+	0.957008i	0.360256	+	0.932853i	$0.382689\pi$
$587$	−15.4927	+	23.1865i	−0.639452	+	0.957008i	−0.999708	+	0.0241542i	$0.992311\pi$
$588$		0			0
$589$	−60.0597	−	11.9466i	−2.47472	−	0.492251i
$590$		0			0
$591$	−4.13080	+	4.13080i	−0.169919	+	0.169919i
$592$		0			0
$593$	3.85403	+	3.85403i	0.158266	+	0.158266i	0.781798	−	0.623532i	$-0.214303\pi$
$593$	3.85403	+	3.85403i	0.158266	+	0.158266i	−0.623532	+	0.781798i	$0.714303\pi$
$594$		0			0
$595$	−0.803434	+	4.03914i	−0.0329376	+	0.165588i
$596$		0			0
$597$	−9.77348	−	6.53043i	−0.400002	−	0.267273i
$598$		0			0
$599$	17.9005	+	7.41463i	0.731395	+	0.302954i	0.717125	−	0.696945i	$-0.245458\pi$
$599$	17.9005	+	7.41463i	0.731395	+	0.302954i	0.0142697	+	0.999898i	$0.495458\pi$
$600$		0			0
$601$	−4.00096	+	1.65725i	−0.163203	+	0.0676007i	−0.462789	−	0.886468i	$-0.653151\pi$
$601$	−4.00096	+	1.65725i	−0.163203	+	0.0676007i	0.299586	+	0.954069i	$0.403151\pi$
$602$		0			0
$603$	−0.762128	−	3.83148i	−0.0310363	−	0.156030i
$604$		0			0
$605$	1.48679	+	2.22514i	0.0604466	+	0.0904647i
$606$		0			0
$607$			15.7984i			0.641238i	0.947208	+	0.320619i	$0.103891\pi$
$607$			15.7984i			0.641238i	−0.947208	+	0.320619i	$0.896109\pi$
$608$		0			0
$609$		−	13.6382i		−	0.552646i
$610$		0			0
$611$	0.143066	+	0.214113i	0.00578782	+	0.00866209i
$612$		0			0
$613$	8.55301	+	42.9989i	0.345453	+	1.73671i	0.628688	+	0.777657i	$0.283592\pi$
$613$	8.55301	+	42.9989i	0.345453	+	1.73671i	−0.283236	+	0.959050i	$0.591408\pi$
$614$		0			0
$615$	1.15266	−	0.477449i	0.0464799	−	0.0192526i
$616$		0			0
$617$	8.53227	+	3.53418i	0.343496	+	0.142281i	0.547761	−	0.836635i	$-0.315480\pi$
$617$	8.53227	+	3.53418i	0.343496	+	0.142281i	−0.204265	+	0.978916i	$0.565480\pi$
$618$		0			0
$619$	−1.39325	−	0.930941i	−0.0559995	−	0.0374177i	0.527255	−	0.849707i	$-0.323221\pi$
$619$	−1.39325	−	0.930941i	−0.0559995	−	0.0374177i	−0.583255	+	0.812289i	$0.698221\pi$
$620$		0			0
$621$	−1.51507	+	7.61675i	−0.0607975	+	0.305650i
$622$		0			0
$623$	−11.1234	−	11.1234i	−0.445649	−	0.445649i
$624$		0			0
$625$	16.4823	−	16.4823i	0.659293	−	0.659293i
$626$		0			0
$627$	−13.1247	−	2.61067i	−0.524150	−	0.104260i
$628$		0			0
$629$	−16.4081	+	24.5564i	−0.654233	+	0.979129i
$630$		0			0
$631$	3.99386	−	9.64202i	0.158993	−	0.383843i	−0.824229	−	0.566257i	$-0.808391\pi$
$631$	3.99386	−	9.64202i	0.158993	−	0.383843i	0.983222	+	0.182414i	$0.0583911\pi$
$632$		0			0
$633$	2.82637	+	6.82347i	0.112338	+	0.271209i
$634$		0			0
$635$	−0.152147	+	0.0302640i	−0.00603778	+	0.00120099i
$636$		0			0
$637$	10.2641	−	6.85824i	0.406678	−	0.271733i
$638$		0			0
$639$	−10.1496			−0.401513
$640$		0			0
$641$	−3.82056			−0.150903			−0.0754515	−	0.997149i	$-0.524040\pi$
$641$	−3.82056			−0.150903			−0.0754515	+	0.997149i	$0.524040\pi$
$642$		0			0
$643$	−14.4622	+	9.66332i	−0.570332	+	0.381084i	−0.807040	−	0.590497i	$-0.798932\pi$
$643$	−14.4622	+	9.66332i	−0.570332	+	0.381084i	0.236707	+	0.971581i	$0.423932\pi$
$644$		0			0
$645$	−2.98252	+	0.593260i	−0.117437	+	0.0233596i
$646$		0			0
$647$	−15.0550	−	36.3461i	−0.591875	−	1.42891i	−0.881690	−	0.471829i	$-0.843594\pi$
$647$	−15.0550	−	36.3461i	−0.591875	−	1.42891i	0.289815	−	0.957083i	$-0.406406\pi$
$648$		0			0
$649$	−1.97730	+	4.77362i	−0.0776158	+	0.187381i
$650$		0			0
$651$	14.2036	−	21.2572i	0.556683	−	0.833135i
$652$		0			0
$653$	18.2191	+	3.62400i	0.712968	+	0.141818i	0.538232	−	0.842797i	$-0.319093\pi$
$653$	18.2191	+	3.62400i	0.712968	+	0.141818i	0.174737	+	0.984615i	$0.444093\pi$
$654$		0			0
$655$	−4.36620	+	4.36620i	−0.170601	+	0.170601i
$656$		0			0
$657$	4.79024	+	4.79024i	0.186885	+	0.186885i
$658$		0			0
$659$	2.52934	−	12.7159i	0.0985293	−	0.495340i	−0.899734	−	0.436438i	$-0.856240\pi$
$659$	2.52934	−	12.7159i	0.0985293	−	0.495340i	0.998264	−	0.0589024i	$-0.0187601\pi$
$660$		0			0
$661$	10.3862	+	6.93980i	0.403974	+	0.269927i	0.740915	−	0.671599i	$-0.234392\pi$
$661$	10.3862	+	6.93980i	0.403974	+	0.269927i	−0.336941	+	0.941526i	$0.609392\pi$
$662$		0			0
$663$	28.3909	+	11.7599i	1.10261	+	0.456717i
$664$		0			0
$665$	3.57900	−	1.48247i	0.138788	−	0.0574878i
$666$		0			0
$667$	−1.48813	−	7.48135i	−0.0576208	−	0.289679i
$668$		0			0
$669$	−9.88833	−	14.7989i	−0.382305	−	0.572160i
$670$		0			0
$671$		−	1.42143i		−	0.0548736i
$672$		0			0
$673$			24.6534i			0.950320i	0.879899	+	0.475160i	$0.157610\pi$
$673$			24.6534i			0.950320i	−0.879899	+	0.475160i	$0.842390\pi$
$674$		0			0
$675$	−15.1732	−	22.7082i	−0.584015	−	0.874040i
$676$		0			0
$677$	−5.08875	−	25.5829i	−0.195576	−	0.983229i	−0.946467	−	0.322802i	$-0.895375\pi$
$677$	−5.08875	−	25.5829i	−0.195576	−	0.983229i	0.750890	−	0.660427i	$-0.229625\pi$
$678$		0			0
$679$	21.7303	−	9.00098i	0.833932	−	0.345426i
$680$		0			0
$681$	28.9928	+	12.0092i	1.11101	+	0.460195i
$682$		0			0
$683$	−7.02523	−	4.69411i	−0.268813	−	0.179615i	0.413857	−	0.910342i	$-0.364181\pi$
$683$	−7.02523	−	4.69411i	−0.268813	−	0.179615i	−0.682670	+	0.730727i	$0.739181\pi$
$684$		0			0
$685$	0.625796	−	3.14609i	0.0239104	−	0.120206i
$686$		0			0
$687$	−8.93699	−	8.93699i	−0.340967	−	0.340967i
$688$		0			0
$689$	−30.9189	+	30.9189i	−1.17792	+	1.17792i
$690$		0			0
$691$	44.6617	+	8.88377i	1.69901	+	0.337954i	0.947009	−	0.321206i	$-0.104088\pi$
$691$	44.6617	+	8.88377i	1.69901	+	0.337954i	0.752002	+	0.659160i	$0.229088\pi$
$692$		0			0
$693$	−2.52734	+	3.78243i	−0.0960056	+	0.143682i
$694$		0			0
$695$	0.753218	−	1.81843i	0.0285712	−	0.0689770i
$696$		0			0
$697$	6.96991	+	16.8268i	0.264004	+	0.637362i
$698$		0			0
$699$	17.7958	−	3.53980i	0.673098	−	0.133887i
$700$		0			0
$701$	−16.3596	+	10.9311i	−0.617894	+	0.412863i	−0.824742	−	0.565510i	$-0.808679\pi$
$701$	−16.3596	+	10.9311i	−0.617894	+	0.412863i	0.206848	+	0.978373i	$0.433679\pi$
$702$		0			0
$703$	27.7812			1.04779
$704$		0			0
$705$	0.0295381			0.00111247
$706$		0			0
$707$	26.5402	−	17.7336i	0.998148	−	0.666941i
$708$		0			0
$709$	−2.20271	+	0.438146i	−0.0827245	+	0.0164549i	−0.236279	−	0.971685i	$-0.575928\pi$
$709$	−2.20271	+	0.438146i	−0.0827245	+	0.0164549i	0.153555	+	0.988140i	$0.450928\pi$
$710$		0			0
$711$	−7.67420	−	18.5272i	−0.287805	−	0.694823i
$712$		0			0
$713$	5.47204	−	13.2107i	0.204930	−	0.494744i
$714$		0			0
$715$	1.23689	−	1.85114i	0.0462572	−	0.0692288i
$716$		0			0
$717$	37.1125	+	7.38214i	1.38599	+	0.275691i
$718$		0			0
$719$	−23.3168	+	23.3168i	−0.869569	+	0.869569i	−0.992425	−	0.122856i	$-0.960795\pi$
$719$	−23.3168	+	23.3168i	−0.869569	+	0.869569i	0.122856	+	0.992425i	$0.460795\pi$
$720$		0			0
$721$	7.80028	+	7.80028i	0.290498	+	0.290498i
$722$		0			0
$723$	2.08797	−	10.4969i	0.0776523	−	0.390385i
$724$		0			0
$725$	22.3046	+	14.9034i	0.828371	+	0.553500i
$726$		0			0
$727$	−37.5431	−	15.5509i	−1.39240	−	0.576750i	−0.444630	−	0.895714i	$-0.646665\pi$
$727$	−37.5431	−	15.5509i	−1.39240	−	0.576750i	−0.947767	+	0.318964i	$0.896665\pi$
$728$		0			0
$729$	−23.8359	+	9.87315i	−0.882811	+	0.365672i
$730$		0			0
$731$	−8.66054	−	43.5395i	−0.320322	−	1.61037i
$732$		0			0
$733$	9.59637	+	14.3620i	0.354450	+	0.530472i	0.965255	−	0.261309i	$-0.0841542\pi$
$733$	9.59637	+	14.3620i	0.354450	+	0.530472i	−0.610805	+	0.791781i	$0.709154\pi$
$734$		0			0
$735$		−	1.41599i		−	0.0522294i
$736$		0			0
$737$			5.07415i			0.186909i
$738$		0			0
$739$	17.1676	+	25.6932i	0.631522	+	0.945139i	0.999881	+	0.0154555i	$0.00491984\pi$
$739$	17.1676	+	25.6932i	0.631522	+	0.945139i	−0.368359	+	0.929684i	$0.620080\pi$
$740$		0			0
$741$	−5.63939	−	28.3511i	−0.207168	−	1.04150i
$742$		0			0
$743$	32.9584	−	13.6518i	1.20913	−	0.500837i	0.315189	−	0.949029i	$-0.397932\pi$
$743$	32.9584	−	13.6518i	1.20913	−	0.500837i	0.893937	+	0.448192i	$0.147932\pi$
$744$		0			0
$745$	−5.66551	−	2.34673i	−0.207568	−	0.0859775i
$746$		0			0
$747$	−0.0600190	−	0.0401034i	−0.00219598	−	0.00146731i
$748$		0			0
$749$	2.69541	−	13.5507i	0.0984881	−	0.495133i
$750$		0			0
$751$	35.9619	+	35.9619i	1.31227	+	1.31227i	0.919740	+	0.392528i	$0.128399\pi$
$751$	35.9619	+	35.9619i	1.31227	+	1.31227i	0.392528	+	0.919740i	$0.371601\pi$
$752$		0			0
$753$	7.49149	−	7.49149i	0.273005	−	0.273005i
$754$		0			0
$755$	−5.19233	−	1.03282i	−0.188968	−	0.0375881i
$756$		0			0
$757$	0.770529	−	1.15318i	0.0280054	−	0.0419130i	−0.817203	−	0.576350i	$-0.804476\pi$
$757$	0.770529	−	1.15318i	0.0280054	−	0.0419130i	0.845208	+	0.534437i	$0.179476\pi$
$758$		0			0
$759$	1.19579	−	2.88690i	0.0434045	−	0.104788i
$760$		0			0
$761$	7.73362	+	18.6706i	0.280344	+	0.676809i	0.999844	−	0.0176832i	$-0.00562903\pi$
$761$	7.73362	+	18.6706i	0.280344	+	0.676809i	−0.719500	+	0.694492i	$0.755629\pi$
$762$		0			0
$763$	9.58528	−	1.90663i	0.347011	−	0.0690247i
$764$		0			0
$765$	−2.38646	+	1.59458i	−0.0862826	+	0.0576522i
$766$		0			0
$767$	−11.1613			−0.403010
$768$		0			0
$769$	−19.0515			−0.687015			−0.343508	−	0.939150i	$-0.611615\pi$
$769$	−19.0515			−0.687015			−0.343508	+	0.939150i	$0.611615\pi$
$770$		0			0
$771$	−15.0736	+	10.0719i	−0.542863	+	0.362729i
$772$		0			0
$773$	37.2271	−	7.40493i	1.33896	−	0.266337i	0.526912	−	0.849920i	$-0.323350\pi$
$773$	37.2271	−	7.40493i	1.33896	−	0.266337i	0.812053	+	0.583583i	$0.198350\pi$
$774$		0			0
$775$	19.2438	+	46.4586i	0.691258	+	1.66884i
$776$		0			0
$777$	−4.43855	+	10.7156i	−0.159232	+	0.384420i
$778$		0			0
$779$	9.51828	−	14.2451i	0.341028	−	0.510384i
$780$		0			0
$781$	12.9299	+	2.57191i	0.462667	+	0.0920302i
$782$		0			0
$783$	21.6962	−	21.6962i	0.775359	−	0.775359i
$784$		0			0
$785$	1.65316	+	1.65316i	0.0590037	+	0.0590037i
$786$		0			0
$787$	2.05604	−	10.3364i	0.0732900	−	0.368454i	−0.926683	−	0.375845i	$-0.877353\pi$
$787$	2.05604	−	10.3364i	0.0732900	−	0.368454i	0.999973	+	0.00739098i	$0.00235264\pi$
$788$		0			0
$789$	−15.7261	−	10.5078i	−0.559864	−	0.374089i
$790$		0			0
$791$	−24.7733	−	10.2614i	−0.880836	−	0.364854i
$792$		0			0
$793$	2.83675	−	1.17502i	0.100736	−	0.0417261i
$794$		0			0
$795$	0.978497	+	4.91924i	0.0347037	+	0.174467i
$796$		0			0
$797$	−5.97698	−	8.94519i	−0.211716	−	0.316855i	0.710379	−	0.703819i	$-0.248524\pi$
$797$	−5.97698	−	8.94519i	−0.211716	−	0.316855i	−0.922095	+	0.386965i	$0.873524\pi$
$798$		0			0
$799$			0.431203i			0.0152549i
$800$		0			0
$801$		−	10.9634i		−	0.387372i
$802$		0			0
$803$	−4.88858	−	7.31627i	−0.172514	−	0.258186i
$804$		0			0
$805$	0.176475	+	0.887200i	0.00621993	+	0.0312697i
$806$		0			0
$807$	5.27240	−	2.18390i	0.185597	−	0.0768769i
$808$		0			0
$809$	35.5966	+	14.7446i	1.25151	+	0.518393i	0.907294	−	0.420497i	$-0.138144\pi$
$809$	35.5966	+	14.7446i	1.25151	+	0.518393i	0.344217	+	0.938890i	$0.388144\pi$
$810$		0			0
$811$	−13.9743	−	9.33736i	−0.490705	−	0.327879i	0.285479	−	0.958385i	$-0.407847\pi$
$811$	−13.9743	−	9.33736i	−0.490705	−	0.327879i	−0.776184	+	0.630506i	$0.782847\pi$
$812$		0			0
$813$	3.10769	−	15.6234i	0.108991	−	0.547937i
$814$		0			0
$815$	−3.91019	−	3.91019i	−0.136968	−	0.136968i
$816$		0			0
$817$	−29.5275	+	29.5275i	−1.03304	+	1.03304i
$818$		0			0
$819$	−9.63782	−	1.91708i	−0.336773	−	0.0669883i
$820$		0			0
$821$	6.39270	−	9.56735i	0.223107	−	0.333903i	−0.702983	−	0.711207i	$-0.748149\pi$
$821$	6.39270	−	9.56735i	0.223107	−	0.333903i	0.926089	+	0.377304i	$0.123149\pi$
$822$		0			0
$823$	7.16774	−	17.3044i	0.249852	−	0.603195i	−0.748339	−	0.663316i	$-0.769149\pi$
$823$	7.16774	−	17.3044i	0.249852	−	0.603195i	0.998191	+	0.0601207i	$0.0191486\pi$
$824$		0			0
$825$	4.20530	+	10.1525i	0.146410	+	0.353465i
$826$		0			0
$827$	13.2520	−	2.63599i	0.460818	−	0.0916624i	0.0407786	−	0.999168i	$-0.487016\pi$
$827$	13.2520	−	2.63599i	0.460818	−	0.0916624i	0.420040	+	0.907506i	$0.362016\pi$
$828$		0			0
$829$	−2.19833	+	1.46888i	−0.0763512	+	0.0510162i	−0.593160	−	0.805085i	$-0.702120\pi$
$829$	−2.19833	+	1.46888i	−0.0763512	+	0.0510162i	0.516809	+	0.856101i	$0.327120\pi$
$830$		0			0
$831$	23.7468			0.823769
$832$		0			0
$833$	20.6709			0.716203
$834$		0			0
$835$	−0.602936	+	0.402869i	−0.0208655	+	0.0139419i
$836$		0			0
$837$	56.4126	−	11.2212i	1.94991	−	0.387860i
$838$		0			0
$839$	−2.75538	−	6.65208i	−0.0951264	−	0.229655i	0.869153	−	0.494544i	$-0.164665\pi$
$839$	−2.75538	−	6.65208i	−0.0951264	−	0.229655i	−0.964279	+	0.264888i	$0.914665\pi$
$840$		0			0
$841$	−0.435350	+	1.05103i	−0.0150121	+	0.0362423i
$842$		0			0
$843$	10.8857	−	16.2915i	0.374922	−	0.561110i
$844$		0			0
$845$	0.420213	+	0.0835857i	0.0144558	+	0.00287543i
$846$		0			0
$847$	−10.8487	+	10.8487i	−0.372766	+	0.372766i
$848$		0			0
$849$	0.247539	+	0.247539i	0.00849551	+	0.00849551i
$850$		0			0
$851$	−1.26557	+	6.36247i	−0.0433833	+	0.218103i
$852$		0			0
$853$	9.12898	+	6.09979i	0.312570	+	0.208853i	0.701953	−	0.712223i	$-0.252312\pi$
$853$	9.12898	+	6.09979i	0.312570	+	0.208853i	−0.389383	+	0.921076i	$0.627312\pi$
$854$		0			0
$855$	2.49434	+	1.03319i	0.0853045	+	0.0353343i
$856$		0			0
$857$	32.3059	−	13.3815i	1.10355	−	0.457105i	0.244837	−	0.969564i	$-0.421266\pi$
$857$	32.3059	−	13.3815i	1.10355	−	0.457105i	0.858711	+	0.512460i	$0.171266\pi$
$858$		0			0
$859$	7.71770	+	38.7995i	0.263325	+	1.32382i	0.855412	+	0.517949i	$0.173304\pi$
$859$	7.71770	+	38.7995i	0.263325	+	1.32382i	−0.592087	+	0.805874i	$0.701696\pi$
$860$		0			0
$861$	3.97383	+	5.94725i	0.135428	+	0.202682i
$862$		0			0
$863$		−	15.7292i		−	0.535427i	−0.963499	−	0.267713i	$-0.913732\pi$
$863$		−	15.7292i		−	0.535427i	0.963499	−	0.267713i	$-0.0862681\pi$
$864$		0			0
$865$			3.09477i			0.105225i
$866$		0			0
$867$	16.4432	+	24.6090i	0.558441	+	0.835766i
$868$		0			0
$869$	5.08160	+	25.5469i	0.172381	+	0.866619i
$870$		0			0
$871$	−10.1265	+	4.19453i	−0.343123	+	0.142126i
$872$		0			0
$873$	15.1446	+	6.27311i	0.512568	+	0.212313i
$874$		0			0
$875$	−5.35159	−	3.57581i	−0.180917	−	0.120885i
$876$		0			0
$877$	−10.1260	+	50.9066i	−0.341929	+	1.71899i	0.301480	+	0.953472i	$0.402519\pi$
$877$	−10.1260	+	50.9066i	−0.341929	+	1.71899i	−0.643410	+	0.765522i	$0.722481\pi$
$878$		0			0
$879$	15.1045	+	15.1045i	0.509462	+	0.509462i
$880$		0			0
$881$	4.72269	−	4.72269i	0.159112	−	0.159112i	−0.623061	−	0.782173i	$-0.714111\pi$
$881$	4.72269	−	4.72269i	0.159112	−	0.159112i	0.782173	+	0.623061i	$0.214111\pi$
$882$		0			0
$883$	11.3177	+	2.25122i	0.380869	+	0.0757596i	0.381812	−	0.924240i	$-0.375300\pi$
$883$	11.3177	+	2.25122i	0.380869	+	0.0757596i	−0.000942833		1.00000i	$0.500300\pi$
$884$		0			0
$885$	−0.711275	+	1.06450i	−0.0239093	+	0.0357827i
$886$		0			0
$887$	−9.14647	+	22.0815i	−0.307109	+	0.741426i	0.692688	+	0.721238i	$0.256426\pi$
$887$	−9.14647	+	22.0815i	−0.307109	+	0.741426i	−0.999796	+	0.0201879i	$0.993574\pi$
$888$		0			0
$889$	−0.340339	−	0.821652i	−0.0114146	−	0.0275573i
$890$		0			0
$891$	5.39937	−	1.07400i	0.180886	−	0.0359804i
$892$		0			0
$893$	0.337257	−	0.225348i	0.0112859	−	0.00754097i
$894$		0			0
$895$	0.772576			0.0258244
$896$		0			0
$897$	6.74990			0.225373
$898$		0			0
$899$	−46.9742	+	31.3871i	−1.56668	+	1.04682i
$900$		0			0
$901$	−71.8121	+	14.2843i	−2.39241	+	0.475880i
$902$		0			0
$903$	−6.67162	−	16.1067i	−0.222018	−	0.535998i
$904$		0			0
$905$	1.30919	−	3.16066i	0.0435189	−	0.105064i
$906$		0			0
$907$	10.4003	−	15.5652i	0.345337	−	0.516833i	−0.617624	−	0.786473i	$-0.711905\pi$
$907$	10.4003	−	15.5652i	0.345337	−	0.516833i	0.962961	+	0.269640i	$0.0869048\pi$
$908$		0			0
$909$	21.8185	+	4.33997i	0.723675	+	0.143948i
$910$		0			0
$911$	−0.953962	+	0.953962i	−0.0316062	+	0.0316062i	−0.722733	−	0.691127i	$-0.757114\pi$
$911$	−0.953962	+	0.953962i	−0.0316062	+	0.0316062i	0.691127	+	0.722733i	$0.257114\pi$
$912$		0			0
$913$	0.0662976	+	0.0662976i	0.00219413	+	0.00219413i
$914$		0			0
$915$	0.0687110	−	0.345433i	0.00227151	−	0.0114197i
$916$		0			0
$917$	−29.4339	−	19.6671i	−0.971992	−	0.649464i
$918$		0			0
$919$	−25.5763	−	10.5941i	−0.843685	−	0.349466i	−0.0813793	−	0.996683i	$-0.525932\pi$
$919$	−25.5763	−	10.5941i	−0.843685	−	0.349466i	−0.762305	+	0.647218i	$0.775932\pi$
$920$		0			0
$921$	8.29085	−	3.43418i	0.273193	−	0.113160i
$922$		0			0
$923$	5.55567	+	27.9303i	0.182867	+	0.919336i
$924$		0			0
$925$	−12.6745	−	18.9688i	−0.416736	−	0.623690i
$926$		0			0
$927$			7.68808i			0.252510i
$928$		0			0
$929$		−	40.9562i		−	1.34373i	−0.740673	−	0.671865i	$-0.765493\pi$
$929$		−	40.9562i		−	1.34373i	0.740673	−	0.671865i	$-0.234507\pi$
$930$		0			0
$931$	−10.8026	−	16.1673i	−0.354042	−	0.529861i
$932$		0			0
$933$	−1.90127	−	9.55834i	−0.0622448	−	0.312926i
$934$		0			0
$935$	3.44424	−	1.42665i	0.112639	−	0.0466565i
$936$		0			0
$937$	−1.45370	−	0.602142i	−0.0474903	−	0.0196711i	0.358812	−	0.933410i	$-0.383182\pi$
$937$	−1.45370	−	0.602142i	−0.0474903	−	0.0196711i	−0.406302	+	0.913739i	$0.633182\pi$
$938$		0			0
$939$	15.9484	+	10.6564i	0.520458	+	0.347759i
$940$		0			0
$941$	−11.6410	+	58.5231i	−0.379485	+	1.90780i	0.0383299	+	0.999265i	$0.487796\pi$
$941$	−11.6410	+	58.5231i	−0.379485	+	1.90780i	−0.417814	+	0.908532i	$0.637204\pi$
$942$		0			0
$943$	2.82882	+	2.82882i	0.0921191	+	0.0921191i
$944$		0			0
$945$	−2.57291	+	2.57291i	−0.0836969	+	0.0836969i
$946$		0			0
$947$	−31.7435	−	6.31417i	−1.03152	−	0.205183i	−0.349824	−	0.936815i	$-0.613759\pi$
$947$	−31.7435	−	6.31417i	−1.03152	−	0.205183i	−0.681699	+	0.731632i	$0.738759\pi$
$948$		0			0
$949$	10.5600	−	15.8041i	0.342792	−	0.513024i
$950$		0			0
$951$	7.12521	−	17.2018i	0.231051	−	0.557806i
$952$		0			0
$953$	−11.5018	−	27.7677i	−0.372579	−	0.899484i	−0.993312	−	0.115462i	$-0.963165\pi$
$953$	−11.5018	−	27.7677i	−0.372579	−	0.899484i	0.620733	−	0.784022i	$-0.286835\pi$
$954$		0			0
$955$	5.05558	−	1.00562i	0.163595	−	0.0325410i
$956$		0			0
$957$	−10.2652	+	6.85896i	−0.331825	+	0.221719i
$958$		0			0
$959$	18.3899			0.593841
$960$		0			0
$961$	−74.9050			−2.41629
$962$		0			0
$963$	8.00623	−	5.34959i	0.257997	−	0.172388i
$964$		0			0
$965$	4.30347	−	0.856013i	0.138534	−	0.0275560i
$966$		0			0
$967$	−1.60334	−	3.87079i	−0.0515598	−	0.124476i	0.896001	−	0.444052i	$-0.146460\pi$
$967$	−1.60334	−	3.87079i	−0.0515598	−	0.124476i	−0.947561	+	0.319576i	$0.896460\pi$
$968$		0			0
$969$	18.5234	−	44.7195i	0.595058	−	1.43660i
$970$		0			0
$971$	23.3219	−	34.9037i	0.748435	−	1.12011i	−0.240339	−	0.970689i	$-0.577258\pi$
$971$	23.3219	−	34.9037i	0.748435	−	1.12011i	0.988773	−	0.149423i	$-0.0477415\pi$
$972$		0			0
$973$	11.0672	+	2.20140i	0.354798	+	0.0705737i
$974$		0			0
$975$	−16.7851	+	16.7851i	−0.537553	+	0.537553i
$976$		0			0
$977$	25.9305	+	25.9305i	0.829590	+	0.829590i	0.987460	−	0.157870i	$-0.0504627\pi$
$977$	25.9305	+	25.9305i	0.829590	+	0.829590i	−0.157870	+	0.987460i	$0.550463\pi$
$978$		0			0
$979$	−2.77812	+	13.9666i	−0.0887892	+	0.446373i
$980$		0			0
$981$	5.66331	+	3.78410i	0.180816	+	0.120817i
$982$		0			0
$983$	−23.7946	−	9.85606i	−0.758931	−	0.314359i	−0.0305512	−	0.999533i	$-0.509726\pi$
$983$	−23.7946	−	9.85606i	−0.758931	−	0.314359i	−0.728380	+	0.685174i	$0.759726\pi$
$984$		0			0
$985$	−1.41436	+	0.585847i	−0.0450652	+	0.0186666i
$986$		0			0
$987$	0.0330370	+	0.166088i	0.00105158	+	0.00528664i
$988$		0			0
$989$	−5.41728	−	8.10753i	−0.172259	−	0.257805i
$990$		0			0
$991$		−	44.7350i		−	1.42105i	−0.703670	−	0.710527i	$-0.748456\pi$
$991$		−	44.7350i		−	1.42105i	0.703670	−	0.710527i	$-0.251544\pi$
$992$		0			0
$993$		−	33.1283i		−	1.05129i
$994$		0			0
$995$	−1.71134	−	2.56120i	−0.0542532	−	0.0811956i
$996$		0			0
$997$	−8.79997	−	44.2404i	−0.278698	−	1.40111i	−0.825762	−	0.564018i	$-0.809255\pi$
$997$	−8.79997	−	44.2404i	−0.278698	−	1.40111i	0.547064	−	0.837091i	$-0.315745\pi$
$998$		0			0
$999$	−24.1079	+	9.98583i	−0.762741	+	0.315938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.a.33.6		56
4.3	odd	2		512.2.i.b.33.2		56
8.3	odd	2		64.2.i.a.13.5	yes	56
8.5	even	2		256.2.i.a.145.2		56
24.11	even	2		576.2.bd.a.397.3		56
64.5	even	16	inner	512.2.i.a.481.6		56
64.27	odd	16		64.2.i.a.5.5	✓	56
64.37	even	16		256.2.i.a.113.2		56
64.59	odd	16		512.2.i.b.481.2		56
192.155	even	16		576.2.bd.a.325.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.5	✓	56	64.27	odd	16
64.2.i.a.13.5	yes	56	8.3	odd	2
256.2.i.a.113.2		56	64.37	even	16
256.2.i.a.145.2		56	8.5	even	2
512.2.i.a.33.6		56	1.1	even	1	trivial
512.2.i.a.481.6		56	64.5	even	16	inner
512.2.i.b.33.2		56	4.3	odd	2
512.2.i.b.481.2		56	64.59	odd	16
576.2.bd.a.325.3		56	192.155	even	16
576.2.bd.a.397.3		56	24.11	even	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.06920 - 0.714416i) q^{3} +(0.330507 - 0.0657419i) q^{5} +(0.739314 + 1.78486i) q^{7} +(-0.515254 + 1.24393i) q^{9} +O(q^{10})\)	\(q+(1.06920 - 0.714416i) q^{3} +(0.330507 - 0.0657419i) q^{5} +(0.739314 + 1.78486i) q^{7} +(-0.515254 + 1.24393i) q^{9} +(0.971610 - 1.45412i) q^{11} +(3.70516 + 0.737003i) q^{13} +(0.306411 - 0.306411i) q^{15} +(4.47305 + 4.47305i) q^{17} +(1.16088 - 5.83613i) q^{19} +(2.06561 + 1.38019i) q^{21} +(1.28371 + 0.531730i) q^{23} +(-4.51448 + 1.86996i) q^{25} +(1.09039 + 5.48174i) q^{27} +(-3.04996 - 4.56458i) q^{29} -10.2910i q^{31} -2.24887i q^{33} +(0.361689 + 0.541305i) q^{35} +(0.910827 + 4.57904i) q^{37} +(4.48808 - 1.85903i) q^{39} +(2.66002 + 1.10181i) q^{41} +(-5.83495 - 3.89879i) q^{43} +(-0.0885166 + 0.445003i) q^{45} +(0.0482001 + 0.0482001i) q^{47} +(2.31060 - 2.31060i) q^{49} +(7.97819 + 1.58696i) q^{51} +(-6.43049 + 9.62391i) q^{53} +(0.225527 - 0.544471i) q^{55} +(-2.92821 - 7.06933i) q^{57} +(-2.89770 + 0.576389i) q^{59} +(0.675800 - 0.451555i) q^{61} -2.60119 q^{63} +1.27304 q^{65} +(-2.41244 + 1.61194i) q^{67} +(1.75242 - 0.348577i) q^{69} +(2.88474 + 6.96439i) q^{71} +(1.92544 - 4.64843i) q^{73} +(-3.49095 + 5.22458i) q^{75} +(3.31372 + 0.659140i) q^{77} +(-10.5317 + 10.5317i) q^{79} +(2.22588 + 2.22588i) q^{81} +(-0.0104591 + 0.0525816i) q^{83} +(1.77244 + 1.18431i) q^{85} +(-6.52202 - 2.70151i) q^{87} +(-7.52277 + 3.11604i) q^{89} +(1.42383 + 7.15808i) q^{91} +(-7.35206 - 11.0031i) q^{93} -2.00520i q^{95} -12.1748i q^{97} +(1.30820 + 1.95786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9} - 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} - 8 q^{19} + 8 q^{21} + 8 q^{23} - 8 q^{25} - 8 q^{27} + 8 q^{29} - 8 q^{35} + 8 q^{37} + 8 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{49} + 24 q^{51} + 8 q^{53} - 56 q^{55} - 8 q^{57} + 56 q^{59} + 8 q^{61} - 64 q^{63} - 16 q^{65} + 72 q^{67} + 8 q^{69} - 56 q^{71} - 8 q^{73} + 56 q^{75} + 8 q^{77} - 24 q^{79} - 8 q^{81} - 8 q^{83} + 8 q^{85} + 8 q^{87} - 8 q^{89} - 8 q^{91} - 16 q^{93} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9 - 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 - 8 * q^19 + 8 * q^21 + 8 * q^23 - 8 * q^25 - 8 * q^27 + 8 * q^29 - 8 * q^35 + 8 * q^37 + 8 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^49 + 24 * q^51 + 8 * q^53 - 56 * q^55 - 8 * q^57 + 56 * q^59 + 8 * q^61 - 64 * q^63 - 16 * q^65 + 72 * q^67 + 8 * q^69 - 56 * q^71 - 8 * q^73 + 56 * q^75 + 8 * q^77 - 24 * q^79 - 8 * q^81 - 8 * q^83 + 8 * q^85 + 8 * q^87 - 8 * q^89 - 8 * q^91 - 16 * q^93 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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