LMFDB - Embedded newform 512.2.i.b.33.2

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			33.2
Character	$\chi$	$=$	512.33
Dual form			512.2.i.b.481.2

$q$-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	−0.824525	−	0.565826i	$-0.808557\pi$
$3$	−1.06920	+	0.714416i	−0.617302	+	0.412468i	0.207223	+	0.978294i	$0.433557\pi$
$4$		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	0.720386	−	0.693573i	$-0.243965\pi$
$7$	−0.739314	−	1.78486i	−0.279434	−	0.674614i	−0.999820	+	0.0189592i	$0.993965\pi$
$8$		0			0
$9$	−0.515254	+	1.24393i	−0.171751	+	0.414645i
$10$		0			0
$11$	−0.971610	+	1.45412i	−0.292951	+	0.438433i	−0.948527	−	0.316697i	$-0.897426\pi$
$11$	−0.971610	+	1.45412i	−0.292951	+	0.438433i	0.655575	+	0.755130i	$0.272426\pi$
$12$		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	$0.301636\pi$
$19$	−1.16088	+	5.83613i	−0.266324	+	1.33890i	−0.849944	+	0.526873i	$0.823364\pi$
$20$		0			0
$21$	2.06561	+	1.38019i	0.450752	+	0.301183i
$22$		0			0
$23$	−1.28371	−	0.531730i	−0.267672	−	0.110873i	0.244811	−	0.969571i	$-0.421274\pi$
$23$	−1.28371	−	0.531730i	−0.267672	−	0.110873i	−0.512483	+	0.858697i	$0.671274\pi$
$24$		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	$0.375234\pi$
$31$			10.2910i			1.84832i	−0.382004	+	0.924161i	$0.624766\pi$
$32$		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	0.914254	−	0.405142i	$-0.132778\pi$
$43$	5.83495	+	3.89879i	0.889821	+	0.594560i	−0.0244324	+	0.999701i	$0.507778\pi$
$44$		0			0
$45$	−0.0885166	+	0.445003i	−0.0131953	+	0.0663371i
$46$		0			0
$47$	−0.0482001	−	0.0482001i	−0.00703071	−	0.00703071i	0.703583	−	0.710613i	$-0.251582\pi$
$47$	−0.0482001	−	0.0482001i	−0.00703071	−	0.00703071i	−0.710613	+	0.703583i	$0.751582\pi$
$48$		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	−0.00282397	−	0.999996i	$-0.500899\pi$
$59$	2.89770	−	0.576389i	0.377249	−	0.0750395i	0.380073	+	0.924957i	$0.375899\pi$
$60$		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	−0.399412	−	0.916772i	$-0.630786\pi$
$67$	2.41244	−	1.61194i	0.294727	−	0.196930i	0.694138	+	0.719842i	$0.255786\pi$
$68$		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	$-0.977382\pi$
$71$	−2.88474	−	6.96439i	−0.342356	−	0.826521i	0.655121	−	0.755524i	$-0.272618\pi$
$72$		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	$-0.433810\pi$
$79$	10.5317	−	10.5317i	1.18490	−	1.18490i	0.978458	−	0.206445i	$-0.0661896\pi$
$80$		0			0
$81$	2.22588	+	2.22588i	0.247320	+	0.247320i
$82$		0			0
$83$	0.0104591	−	0.0525816i	0.00114804	−	0.00577158i	−0.980207	−	0.197975i	$-0.936563\pi$
$83$	0.0104591	−	0.0525816i	0.00114804	−	0.00577158i	0.981355	+	0.192204i	$0.0615634\pi$
$84$		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	−0.627127	−	0.778917i	$-0.715769\pi$
$103$	−5.27535	+	2.18512i	−0.519796	+	0.215306i	0.107331	+	0.994223i	$0.465769\pi$
$104$		0			0
$105$	0.773434	+	0.320367i	0.0754794	+	0.0312646i
$106$		0			0
$107$	5.94629	+	3.97318i	0.574850	+	0.384102i	0.808745	−	0.588160i	$-0.200147\pi$
$107$	5.94629	+	3.97318i	0.574850	+	0.384102i	−0.233895	+	0.972262i	$0.575147\pi$
$108$		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	$-0.493498\pi$
$127$	0.460345			0.0408490			0.0204245	+	0.999791i	$0.493498\pi$
$128$		0			0
$129$	−9.02408			−0.794526
$130$		0			0
$131$	15.2355	−	10.1801i	1.33114	−	0.889437i	0.332575	−	0.943077i	$-0.392082\pi$
$131$	15.2355	−	10.1801i	1.33114	−	0.889437i	0.998560	+	0.0536401i	$0.0170824\pi$
$132$		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	−0.943175	−	0.332296i	$-0.892177\pi$
$139$	−3.24499	+	4.85647i	−0.275237	+	0.411921i	0.667939	+	0.744216i	$0.267177\pi$
$140$		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	0.884867	−	0.465844i	$-0.154249\pi$
$151$	14.5143	+	6.01204i	1.18116	+	0.489252i	0.296293	+	0.955097i	$0.404249\pi$
$152$		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	$0.0346698\pi$
$163$	9.11685	+	13.6443i	0.714087	+	1.06871i	−0.279987	+	0.960004i	$0.590330\pi$
$164$		0			0
$165$	−0.147845	−	0.743268i	−0.0115097	−	0.0578633i
$166$		0			0
$167$	1.98808	−	0.823489i	0.153842	−	0.0637235i	−0.304434	−	0.952534i	$-0.598467\pi$
$167$	1.98808	−	0.823489i	0.153842	−	0.0637235i	0.458276	+	0.888810i	$0.348467\pi$
$168$		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	0.110340	−	0.993894i	$-0.464806\pi$
$179$	−2.24858	−	0.447270i	−0.168067	−	0.0334305i	−0.278406	+	0.960463i	$0.589806\pi$
$180$		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	$-0.686672\pi$
$191$	−15.2964			−1.10681			−0.553405	+	0.832912i	$0.686672\pi$
$192$		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	0.998032	−	0.0627118i	$-0.0199749\pi$
$199$	3.49809	+	8.44513i	0.247973	+	0.598659i	−0.750059	+	0.661371i	$0.769975\pi$
$200$		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	$-0.874153\pi$
$211$	1.12050	−	5.63316i	0.0771387	−	0.387803i	0.999996	−	0.00266152i	$-0.000847190\pi$
$212$		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	$0.153384\pi$
$223$			13.8411i			0.926872i	−0.886130	+	0.463436i	$0.846616\pi$
$224$		0			0
$225$		−	6.57923i		−	0.438615i
$226$		0			0
$227$	−13.5582	−	20.2913i	−0.899890	−	1.34678i	−0.937682	−	0.347495i	$-0.887032\pi$
$227$	−13.5582	−	20.2913i	−0.899890	−	1.34678i	0.0377913	−	0.999286i	$-0.487968\pi$
$228$		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	$-0.849322\pi$
$239$	−20.8075	−	20.8075i	−1.34592	−	1.34592i	−0.455887	−	0.890038i	$-0.650678\pi$
$240$		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	−0.443402	−	0.896323i	$-0.646229\pi$
$251$	−8.08063	+	1.60734i	−0.510045	+	0.101454i	−0.0666425	+	0.997777i	$0.521229\pi$
$252$		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	$0.0248163\pi$
$263$	5.62862	+	13.5887i	0.347076	+	0.837915i	−0.649887	+	0.760031i	$0.725184\pi$
$264$		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	−0.921196	−	0.389099i	$-0.872786\pi$
$271$	−8.75941	+	8.75941i	−0.532096	+	0.532096i	0.389099	+	0.921196i	$0.372786\pi$
$272$		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	0.979175	−	0.203020i	$-0.0650756\pi$
$283$	−0.0531107	−	0.267006i	−0.00315711	−	0.0158718i	−0.982332	+	0.187148i	$0.940076\pi$
$284$		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	−0.00413726	−	0.999991i	$-0.501317\pi$
$307$	−6.84456	−	1.36147i	−0.390640	−	0.0777031i	−0.386502	+	0.922288i	$0.626317\pi$
$308$		0			0
$309$	4.07931	−	6.10512i	0.232064	−	0.347308i
$310$		0			0
$311$	−2.90025	+	7.00183i	−0.164458	+	0.397038i	−0.984528	−	0.175226i	$-0.943934\pi$
$311$	−2.90025	+	7.00183i	−0.164458	+	0.397038i	0.820070	+	0.572263i	$0.193934\pi$
$312$		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	$0.437910\pi$
$331$	−14.3128	+	21.4207i	−0.786705	+	1.17739i	−0.980533	+	0.196352i	$0.937090\pi$
$332$		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	$0.108177\pi$
$347$	3.71315	+	18.6673i	0.199332	+	1.00211i	−0.743472	+	0.668767i	$0.766823\pi$
$348$		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	$-0.204674\pi$
$359$	33.9190	−	14.0497i	1.79018	−	0.741516i	0.989879	−	0.141916i	$-0.0453263\pi$
$360$		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	0.453434	−	0.891290i	$-0.350199\pi$
$367$	−8.38811	−	8.38811i	−0.437856	−	0.437856i	−0.891290	+	0.453434i	$0.850199\pi$
$368$		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	0.539254	−	0.842143i	$-0.318706\pi$
$379$	26.4712	−	5.26545i	1.35973	−	0.270468i	0.820480	+	0.571676i	$0.193706\pi$
$380$		0			0
$381$	−0.492200	+	0.328877i	−0.0252162	+	0.0168489i
$382$		0			0
$383$	3.40990			0.174238			0.0871189	−	0.996198i	$-0.472234\pi$
$383$	3.40990			0.174238			0.0871189	+	0.996198i	$0.472234\pi$
$384$		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	0.560316	−	0.828279i	$-0.310680\pi$
$419$	−8.58363	−	12.8463i	−0.419338	−	0.627583i	−0.979654	+	0.200696i	$0.935680\pi$
$420$		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	0.998748	−	0.0500230i	$-0.0159295\pi$
$431$	19.6960	+	19.6960i	0.948725	+	0.948725i	−0.0500230	+	0.998748i	$0.515929\pi$
$432$		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	$-0.741381\pi$
$439$	6.53568	−	15.7785i	0.311931	−	0.753068i	0.999633	−	0.0270754i	$-0.00861943\pi$
$440$		0			0
$441$	1.68369	+	4.06478i	0.0801757	+	0.193561i
$442$		0			0
$443$	17.8876	−	3.55806i	0.849864	−	0.169048i	0.249103	−	0.968477i	$-0.419864\pi$
$443$	17.8876	−	3.55806i	0.849864	−	0.169048i	0.600761	+	0.799429i	$0.294864\pi$
$444$		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	$-0.430894\pi$
$463$	25.6472	−	25.6472i	1.19193	−	1.19193i	0.976526	−	0.215401i	$-0.0691059\pi$
$464$		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	$-0.530387\pi$
$467$	8.07541	−	40.5978i	0.373685	−	1.87864i	0.469004	−	0.883196i	$-0.344613\pi$
$468$		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	$-0.946143\pi$
$479$		−	7.37082i		−	0.336781i	0.985720	−	0.168391i	$-0.0538570\pi$
$480$		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	−0.680697	−	0.732565i	$-0.738323\pi$
$487$	−14.2123	+	5.88692i	−0.644020	+	0.266762i	0.0366766	+	0.999327i	$0.488323\pi$
$488$		0			0
$489$	−19.4955	−	8.07528i	−0.881615	−	0.365177i
$490$		0			0
$491$	−13.9347	−	9.31084i	−0.628862	−	0.420192i	0.199882	−	0.979820i	$-0.435944\pi$
$491$	−13.9347	−	9.31084i	−0.628862	−	0.420192i	−0.828744	+	0.559628i	$0.810944\pi$
$492$		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	0.642654	−	0.766156i	$-0.277833\pi$
$499$	21.0694	+	4.19096i	0.943194	+	0.187613i	0.300540	+	0.953769i	$0.402833\pi$
$500$		0			0
$501$	−1.53734	+	2.30079i	−0.0686832	+	0.102792i
$502$		0			0
$503$	3.12293	−	7.53942i	0.139245	−	0.336166i	−0.838839	−	0.544380i	$-0.816765\pi$
$503$	3.12293	−	7.53942i	0.139245	−	0.336166i	0.978083	+	0.208214i	$0.0667650\pi$
$504$		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	−0.480123	−	0.877201i	$-0.659408\pi$
$523$	11.7557	−	17.5936i	0.514040	−	0.769315i	0.994163	+	0.107886i	$0.0344081\pi$
$524$		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	0.996972	−	0.0777651i	$-0.0247784\pi$
$547$	12.7138	+	19.0275i	0.543602	+	0.813557i	−0.453370	+	0.891322i	$0.649778\pi$
$548$		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	−0.510358	−	0.859962i	$-0.670487\pi$
$563$	−31.1060	−	6.18736i	−1.31096	−	0.260766i	−0.800603	+	0.599196i	$0.795487\pi$
$564$		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	−0.0263699	−	0.999652i	$-0.508395\pi$
$571$	7.92899	−	1.57717i	0.331818	−	0.0660027i	0.358188	+	0.933650i	$0.383395\pi$
$572$		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	$-0.617311\pi$
$587$	15.4927	−	23.1865i	0.639452	−	0.957008i	0.999708	−	0.0241542i	$-0.00768926\pi$
$588$		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	−0.0142697	−	0.999898i	$-0.504542\pi$
$599$	−17.9005	−	7.41463i	−0.731395	−	0.302954i	−0.717125	+	0.696945i	$0.754542\pi$
$600$		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	$-0.896109\pi$
$607$		−	15.7984i		−	0.641238i	0.947208	−	0.320619i	$-0.103891\pi$
$608$		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	0.583255	−	0.812289i	$-0.301779\pi$
$619$	1.39325	+	0.930941i	0.0559995	+	0.0374177i	−0.527255	+	0.849707i	$0.676779\pi$
$620$		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	−0.983222	−	0.182414i	$-0.941609\pi$
$631$	−3.99386	+	9.64202i	−0.158993	+	0.383843i	0.824229	+	0.566257i	$0.191609\pi$
$632$		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	−0.236707	−	0.971581i	$-0.576068\pi$
$643$	14.4622	−	9.66332i	0.570332	−	0.381084i	0.807040	+	0.590497i	$0.201068\pi$
$644$		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	$0.156406\pi$
$647$	15.0550	+	36.3461i	0.591875	+	1.42891i	−0.289815	+	0.957083i	$0.593594\pi$
$648$		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	$0.143760\pi$
$659$	−2.52934	+	12.7159i	−0.0985293	+	0.495340i	−0.998264	+	0.0589024i	$0.981240\pi$
$660$		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	0.682670	−	0.730727i	$-0.260819\pi$
$683$	7.02523	+	4.69411i	0.268813	+	0.179615i	−0.413857	+	0.910342i	$0.635819\pi$
$684$		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	−0.752002	−	0.659160i	$-0.770912\pi$
$691$	−44.6617	−	8.88377i	−1.69901	−	0.337954i	−0.947009	+	0.321206i	$0.895912\pi$
$692$		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	−0.122856	−	0.992425i	$-0.539205\pi$
$719$	23.3168	−	23.3168i	0.869569	−	0.869569i	0.992425	+	0.122856i	$0.0392053\pi$
$720$		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	0.947767	−	0.318964i	$-0.103335\pi$
$727$	37.5431	+	15.5509i	1.39240	+	0.576750i	0.444630	+	0.895714i	$0.353335\pi$
$728$		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	$-0.995080\pi$
$739$	−17.1676	−	25.6932i	−0.631522	−	0.945139i	0.368359	−	0.929684i	$-0.379920\pi$
$740$		0			0
$741$	−5.63939	−	28.3511i	−0.207168	−	1.04150i
$742$		0			0
$743$	−32.9584	+	13.6518i	−1.20913	+	0.500837i	−0.893937	−	0.448192i	$-0.852068\pi$
$743$	−32.9584	+	13.6518i	−1.20913	+	0.500837i	−0.315189	+	0.949029i	$0.602068\pi$
$744$		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	$-0.871601\pi$
$751$	−35.9619	−	35.9619i	−1.31227	−	1.31227i	−0.392528	−	0.919740i	$-0.628399\pi$
$752$		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	−0.999973	−	0.00739098i	$-0.997647\pi$
$787$	−2.05604	+	10.3364i	−0.0732900	+	0.368454i	0.926683	+	0.375845i	$0.122647\pi$
$788$		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	0.776184	−	0.630506i	$-0.217153\pi$
$811$	13.9743	+	9.33736i	0.490705	+	0.327879i	−0.285479	+	0.958385i	$0.592153\pi$
$812$		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	−0.998191	−	0.0601207i	$-0.980851\pi$
$823$	−7.16774	+	17.3044i	−0.249852	+	0.603195i	0.748339	+	0.663316i	$0.230851\pi$
$824$		0			0
$825$	4.20530	+	10.1525i	0.146410	+	0.353465i
$826$		0			0
$827$	−13.2520	+	2.63599i	−0.460818	+	0.0916624i	−0.420040	−	0.907506i	$-0.637984\pi$
$827$	−13.2520	+	2.63599i	−0.460818	+	0.0916624i	−0.0407786	+	0.999168i	$0.512984\pi$
$828$		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	0.964279	−	0.264888i	$-0.0853351\pi$
$839$	2.75538	+	6.65208i	0.0951264	+	0.229655i	−0.869153	+	0.494544i	$0.835335\pi$
$840$		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	$-0.826696\pi$
$859$	−7.71770	−	38.7995i	−0.263325	−	1.32382i	0.592087	−	0.805874i	$-0.298304\pi$
$860$		0			0
$861$	3.97383	+	5.94725i	0.135428	+	0.202682i
$862$		0			0
$863$			15.7292i			0.535427i	0.963499	+	0.267713i	$0.0862681\pi$
$863$			15.7292i			0.535427i	−0.963499	+	0.267713i	$0.913732\pi$
$864$		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	0.000942833	−	1.00000i	$-0.499700\pi$
$883$	−11.3177	−	2.25122i	−0.380869	−	0.0757596i	−0.381812	+	0.924240i	$0.624700\pi$
$884$		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	$-0.743574\pi$
$887$	9.14647	−	22.0815i	0.307109	−	0.741426i	0.999796	−	0.0201879i	$-0.00642646\pi$
$888$		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	−0.962961	−	0.269640i	$-0.913095\pi$
$907$	−10.4003	+	15.5652i	−0.345337	+	0.516833i	0.617624	+	0.786473i	$0.288095\pi$
$908$		0			0
$909$	21.8185	+	4.33997i	0.723675	+	0.143948i
$910$		0			0
$911$	0.953962	−	0.953962i	0.0316062	−	0.0316062i	−0.691127	−	0.722733i	$-0.742886\pi$
$911$	0.953962	−	0.953962i	0.0316062	−	0.0316062i	0.722733	+	0.691127i	$0.242886\pi$
$912$		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	0.762305	−	0.647218i	$-0.224068\pi$
$919$	25.5763	+	10.5941i	0.843685	+	0.349466i	0.0813793	+	0.996683i	$0.474068\pi$
$920$		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	0.681699	−	0.731632i	$-0.261241\pi$
$947$	31.7435	+	6.31417i	1.03152	+	0.205183i	0.349824	+	0.936815i	$0.386241\pi$
$948$		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	0.947561	−	0.319576i	$-0.103540\pi$
$967$	1.60334	+	3.87079i	0.0515598	+	0.124476i	−0.896001	+	0.444052i	$0.853540\pi$
$968$		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	$0.422742\pi$
$971$	−23.3219	+	34.9037i	−0.748435	+	1.12011i	−0.988773	+	0.149423i	$0.952258\pi$
$972$		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	0.728380	−	0.685174i	$-0.240274\pi$
$983$	23.7946	+	9.85606i	0.758931	+	0.314359i	0.0305512	+	0.999533i	$0.490274\pi$
$984$		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	$0.251544\pi$
$991$			44.7350i			1.42105i	−0.703670	+	0.710527i	$0.748456\pi$
$992$		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.b.33.2		56
4.3	odd	2		512.2.i.a.33.6		56
8.3	odd	2		256.2.i.a.145.2		56
8.5	even	2		64.2.i.a.13.5	yes	56
24.5	odd	2		576.2.bd.a.397.3		56
64.5	even	16	inner	512.2.i.b.481.2		56
64.27	odd	16		256.2.i.a.113.2		56
64.37	even	16		64.2.i.a.5.5	✓	56
64.59	odd	16		512.2.i.a.481.6		56
192.101	odd	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	64.37	even	16
64.2.i.a.13.5	yes	56	8.5	even	2
256.2.i.a.113.2		56	64.27	odd	16
256.2.i.a.145.2		56	8.3	odd	2
512.2.i.a.33.6		56	4.3	odd	2
512.2.i.a.481.6		56	64.59	odd	16
512.2.i.b.33.2		56	1.1	even	1	trivial
512.2.i.b.481.2		56	64.5	even	16	inner
576.2.bd.a.325.3		56	192.101	odd	16
576.2.bd.a.397.3		56	24.5	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
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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