LMFDB - Embedded newform 512.2.i.a.33.5

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			33.5
Character	$\chi$	$=$	512.33
Dual form			512.2.i.a.481.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.306211 - 0.204603i) q^{3} +(-1.42470 + 0.283390i) q^{5} +(0.666723 + 1.60961i) q^{7} +(-1.09615 + 2.64634i) q^{9} +O(q^{10})$	\(q+(0.306211 - 0.204603i) q^{3} +(-1.42470 + 0.283390i) q^{5} +(0.666723 + 1.60961i) q^{7} +(-1.09615 + 2.64634i) q^{9} +(-1.65860 + 2.48226i) q^{11} +(-5.03569 - 1.00166i) q^{13} +(-0.378274 + 0.378274i) q^{15} +(-1.55248 - 1.55248i) q^{17} +(-0.0359002 + 0.180483i) q^{19} +(0.533490 + 0.356467i) q^{21} +(6.50946 + 2.69631i) q^{23} +(-2.66995 + 1.10593i) q^{25} +(0.421339 + 2.11821i) q^{27} +(-0.0389072 - 0.0582287i) q^{29} +6.25272i q^{31} +1.09945i q^{33} +(-1.40602 - 2.10426i) q^{35} +(1.63291 + 8.20918i) q^{37} +(-1.74693 + 0.723600i) q^{39} +(-6.98521 - 2.89337i) q^{41} +(9.23959 + 6.17369i) q^{43} +(0.811733 - 4.08086i) q^{45} +(-7.84283 - 7.84283i) q^{47} +(2.80342 - 2.80342i) q^{49} +(-0.793030 - 0.157743i) q^{51} +(1.21975 - 1.82549i) q^{53} +(1.65955 - 4.00650i) q^{55} +(0.0259343 + 0.0626110i) q^{57} +(-8.31975 + 1.65490i) q^{59} +(3.29205 - 2.19968i) q^{61} -4.99040 q^{63} +7.45818 q^{65} +(13.1855 - 8.81029i) q^{67} +(2.54494 - 0.506220i) q^{69} +(-1.13245 - 2.73397i) q^{71} +(-3.74820 + 9.04896i) q^{73} +(-0.591290 + 0.884929i) q^{75} +(-5.10131 - 1.01471i) q^{77} +(1.58284 - 1.58284i) q^{79} +(-5.51384 - 5.51384i) q^{81} +(-1.12345 + 5.64796i) q^{83} +(2.65177 + 1.77186i) q^{85} +(-0.0238276 - 0.00986972i) q^{87} +(14.5341 - 6.02023i) q^{89} +(-1.74513 - 8.77334i) q^{91} +(1.27933 + 1.91465i) q^{93} -0.267307i q^{95} +5.25588i q^{97} +(-4.75084 - 7.11013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.306211	−	0.204603i	0.176791	−	0.118128i	−0.464026	−	0.885821i	$-0.653596\pi$
$3$	0.306211	−	0.204603i	0.176791	−	0.118128i	0.640817	+	0.767694i	$0.278596\pi$
$4$		0			0
$5$	−1.42470	+	0.283390i	−0.637143	+	0.126736i	−0.503084	−	0.864238i	$-0.667801\pi$
$5$	−1.42470	+	0.283390i	−0.637143	+	0.126736i	−0.134059	+	0.990973i	$0.542801\pi$
$6$		0			0
$7$	0.666723	+	1.60961i	0.251998	+	0.608376i	0.998365	−	0.0571578i	$-0.0182038\pi$
$7$	0.666723	+	1.60961i	0.251998	+	0.608376i	−0.746367	+	0.665534i	$0.768204\pi$
$8$		0			0
$9$	−1.09615	+	2.64634i	−0.365383	+	0.882112i
$10$		0			0
$11$	−1.65860	+	2.48226i	−0.500086	+	0.748431i	−0.992542	−	0.121906i	$-0.961099\pi$
$11$	−1.65860	+	2.48226i	−0.500086	+	0.748431i	0.492456	+	0.870337i	$0.336099\pi$
$12$		0			0
$13$	−5.03569	−	1.00166i	−1.39665	−	0.277811i	−0.561337	−	0.827587i	$-0.689713\pi$
$13$	−5.03569	−	1.00166i	−1.39665	−	0.277811i	−0.835312	+	0.549776i	$0.814713\pi$
$14$		0			0
$15$	−0.378274	+	0.378274i	−0.0976700	+	0.0976700i
$16$		0			0
$17$	−1.55248	−	1.55248i	−0.376532	−	0.376532i	0.493317	−	0.869849i	$-0.335784\pi$
$17$	−1.55248	−	1.55248i	−0.376532	−	0.376532i	−0.869849	+	0.493317i	$0.835784\pi$
$18$		0			0
$19$	−0.0359002	+	0.180483i	−0.00823608	+	0.0414056i	−0.984685	−	0.174344i	$-0.944220\pi$
$19$	−0.0359002	+	0.180483i	−0.00823608	+	0.0414056i	0.976449	+	0.215750i	$0.0692195\pi$
$20$		0			0
$21$	0.533490	+	0.356467i	0.116417	+	0.0777874i
$22$		0			0
$23$	6.50946	+	2.69631i	1.35732	+	0.562219i	0.938320	−	0.345769i	$-0.112382\pi$
$23$	6.50946	+	2.69631i	1.35732	+	0.562219i	0.418997	+	0.907988i	$0.362382\pi$
$24$		0			0
$25$	−2.66995	+	1.10593i	−0.533990	+	0.221186i
$26$		0			0
$27$	0.421339	+	2.11821i	0.0810866	+	0.407650i
$28$		0			0
$29$	−0.0389072	−	0.0582287i	−0.00722489	−	0.0108128i	0.827840	−	0.560965i	$-0.189570\pi$
$29$	−0.0389072	−	0.0582287i	−0.00722489	−	0.0108128i	−0.835064	+	0.550152i	$0.814570\pi$
$30$		0			0
$31$			6.25272i			1.12302i	0.827469	+	0.561511i	$0.189780\pi$
$31$			6.25272i			1.12302i	−0.827469	+	0.561511i	$0.810220\pi$
$32$		0			0
$33$			1.09945i			0.191390i
$34$		0			0
$35$	−1.40602	−	2.10426i	−0.237662	−	0.355686i
$36$		0			0
$37$	1.63291	+	8.20918i	0.268448	+	1.34958i	0.845981	+	0.533213i	$0.179016\pi$
$37$	1.63291	+	8.20918i	0.268448	+	1.34958i	−0.577532	+	0.816368i	$0.695984\pi$
$38$		0			0
$39$	−1.74693	+	0.723600i	−0.279732	+	0.115869i
$40$		0			0
$41$	−6.98521	−	2.89337i	−1.09091	−	0.451868i	−0.236584	−	0.971611i	$-0.576028\pi$
$41$	−6.98521	−	2.89337i	−1.09091	−	0.451868i	−0.854323	+	0.519743i	$0.826028\pi$
$42$		0			0
$43$	9.23959	+	6.17369i	1.40902	+	0.941480i	0.999575	+	0.0291463i	$0.00927887\pi$
$43$	9.23959	+	6.17369i	1.40902	+	0.941480i	0.409449	+	0.912333i	$0.365721\pi$
$44$		0			0
$45$	0.811733	−	4.08086i	0.121006	−	0.608338i
$46$		0			0
$47$	−7.84283	−	7.84283i	−1.14399	−	1.14399i	−0.987713	−	0.156281i	$-0.950049\pi$
$47$	−7.84283	−	7.84283i	−1.14399	−	1.14399i	−0.156281	−	0.987713i	$-0.549951\pi$
$48$		0			0
$49$	2.80342	−	2.80342i	0.400488	−	0.400488i
$50$		0			0
$51$	−0.793030	−	0.157743i	−0.111046	−	0.0220885i
$52$		0			0
$53$	1.21975	−	1.82549i	0.167546	−	0.250750i	−0.738190	−	0.674593i	$-0.764319\pi$
$53$	1.21975	−	1.82549i	0.167546	−	0.250750i	0.905736	+	0.423843i	$0.139319\pi$
$54$		0			0
$55$	1.65955	−	4.00650i	0.223773	−	0.540236i
$56$		0			0
$57$	0.0259343	+	0.0626110i	0.00343509	+	0.00829304i
$58$		0			0
$59$	−8.31975	+	1.65490i	−1.08314	+	0.215450i	−0.704221	−	0.709981i	$-0.748704\pi$
$59$	−8.31975	+	1.65490i	−1.08314	+	0.215450i	−0.378918	+	0.925430i	$0.623704\pi$
$60$		0			0
$61$	3.29205	−	2.19968i	0.421504	−	0.281640i	−0.326675	−	0.945137i	$-0.605928\pi$
$61$	3.29205	−	2.19968i	0.421504	−	0.281640i	0.748179	+	0.663497i	$0.230928\pi$
$62$		0			0
$63$	−4.99040			−0.628731
$64$		0			0
$65$	7.45818			0.925074
$66$		0			0
$67$	13.1855	−	8.81029i	1.61087	−	1.07635i	0.667497	−	0.744612i	$-0.267366\pi$
$67$	13.1855	−	8.81029i	1.61087	−	1.07635i	0.943372	−	0.331736i	$-0.107634\pi$
$68$		0			0
$69$	2.54494	−	0.506220i	0.306375	−	0.0609417i
$70$		0			0
$71$	−1.13245	−	2.73397i	−0.134397	−	0.324462i	0.842326	−	0.538968i	$-0.181186\pi$
$71$	−1.13245	−	2.73397i	−0.134397	−	0.324462i	−0.976723	+	0.214506i	$0.931186\pi$
$72$		0			0
$73$	−3.74820	+	9.04896i	−0.438694	+	1.05910i	0.537706	+	0.843132i	$0.319291\pi$
$73$	−3.74820	+	9.04896i	−0.438694	+	1.05910i	−0.976400	+	0.215969i	$0.930709\pi$
$74$		0			0
$75$	−0.591290	+	0.884929i	−0.0682763	+	0.102183i
$76$		0			0
$77$	−5.10131	−	1.01471i	−0.581348	−	0.115637i
$78$		0			0
$79$	1.58284	−	1.58284i	0.178083	−	0.178083i	−0.612436	−	0.790520i	$-0.709810\pi$
$79$	1.58284	−	1.58284i	0.178083	−	0.178083i	0.790520	+	0.612436i	$0.209810\pi$
$80$		0			0
$81$	−5.51384	−	5.51384i	−0.612649	−	0.612649i
$82$		0			0
$83$	−1.12345	+	5.64796i	−0.123314	+	0.619944i	0.868857	+	0.495063i	$0.164855\pi$
$83$	−1.12345	+	5.64796i	−0.123314	+	0.619944i	−0.992172	+	0.124881i	$0.960145\pi$
$84$		0			0
$85$	2.65177	+	1.77186i	0.287625	+	0.192185i
$86$		0			0
$87$	−0.0238276	−	0.00986972i	−0.00255459	−	0.00105814i
$88$		0			0
$89$	14.5341	−	6.02023i	1.54061	−	0.638143i	0.559024	−	0.829151i	$-0.311176\pi$
$89$	14.5341	−	6.02023i	1.54061	−	0.638143i	0.981588	+	0.191009i	$0.0611759\pi$
$90$		0			0
$91$	−1.74513	−	8.77334i	−0.182939	−	0.919696i
$92$		0			0
$93$	1.27933	+	1.91465i	0.132660	+	0.198540i
$94$		0			0
$95$		−	0.267307i		−	0.0274251i
$96$		0			0
$97$			5.25588i			0.533654i	0.963744	+	0.266827i	$0.0859753\pi$
$97$			5.25588i			0.533654i	−0.963744	+	0.266827i	$0.914025\pi$
$98$		0			0
$99$	−4.75084	−	7.11013i	−0.477477	−	0.714595i
$100$		0			0
$101$	0.994080	+	4.99758i	0.0989146	+	0.497278i	0.998203	+	0.0599215i	$0.0190850\pi$
$101$	0.994080	+	4.99758i	0.0989146	+	0.497278i	−0.899288	+	0.437356i	$0.855915\pi$
$102$		0			0
$103$	−0.990660	+	0.410345i	−0.0976127	+	0.0404325i	−0.430955	−	0.902373i	$-0.641823\pi$
$103$	−0.990660	+	0.410345i	−0.0976127	+	0.0404325i	0.333343	+	0.942806i	$0.391823\pi$
$104$		0			0
$105$	−0.861080	−	0.356671i	−0.0840328	−	0.0348075i
$106$		0			0
$107$	−3.35832	−	2.24396i	−0.324661	−	0.216932i	0.382549	−	0.923935i	$-0.375046\pi$
$107$	−3.35832	−	2.24396i	−0.324661	−	0.216932i	−0.707210	+	0.707004i	$0.750046\pi$
$108$		0			0
$109$	−0.692578	+	3.48183i	−0.0663370	+	0.333498i	−0.999675	−	0.0255008i	$-0.991882\pi$
$109$	−0.692578	+	3.48183i	−0.0663370	+	0.333498i	0.933338	+	0.358999i	$0.116882\pi$
$110$		0			0
$111$	2.17964	+	2.17964i	0.206882	+	0.206882i
$112$		0			0
$113$	5.12191	−	5.12191i	0.481829	−	0.481829i	−0.423886	−	0.905715i	$-0.639334\pi$
$113$	5.12191	−	5.12191i	0.481829	−	0.481829i	0.905715	+	0.423886i	$0.139334\pi$
$114$		0			0
$115$	−10.0381	−	1.99670i	−0.936058	−	0.186194i
$116$		0			0
$117$	8.17059	−	12.2282i	0.755371	−	1.13049i
$118$		0			0
$119$	1.46382	−	3.53397i	0.134188	−	0.323958i
$120$		0			0
$121$	0.798822	+	1.92853i	0.0726202	+	0.175321i
$122$		0			0
$123$	−2.73094	+	0.543217i	−0.246240	+	0.0489803i
$124$		0			0
$125$	9.52945	−	6.36737i	0.852340	−	0.569515i
$126$		0			0
$127$	2.94406			0.261243			0.130622	−	0.991432i	$-0.458303\pi$
$127$	2.94406			0.261243			0.130622	+	0.991432i	$0.458303\pi$
$128$		0			0
$129$	4.09242			0.360317
$130$		0			0
$131$	−6.41752	+	4.28805i	−0.560701	+	0.374648i	−0.803388	−	0.595456i	$-0.796971\pi$
$131$	−6.41752	+	4.28805i	−0.560701	+	0.374648i	0.242687	+	0.970105i	$0.421971\pi$
$132$		0			0
$133$	−0.314443	+	0.0625465i	−0.0272656	+	0.00542347i
$134$		0			0
$135$	−1.20056	−	2.89840i	−0.103328	−	0.249455i
$136$		0			0
$137$	1.69028	−	4.08071i	0.144411	−	0.348638i	−0.835080	−	0.550129i	$-0.814579\pi$
$137$	1.69028	−	4.08071i	0.144411	−	0.348638i	0.979490	+	0.201491i	$0.0645786\pi$
$138$		0			0
$139$	4.34787	−	6.50705i	0.368782	−	0.551921i	−0.599948	−	0.800039i	$-0.704812\pi$
$139$	4.34787	−	6.50705i	0.368782	−	0.551921i	0.968730	+	0.248118i	$0.0798121\pi$
$140$		0			0
$141$	−4.00623	−	0.796888i	−0.337385	−	0.0671101i
$142$		0			0
$143$	10.8386	−	10.8386i	0.906366	−	0.906366i
$144$		0			0
$145$	0.0719323	+	0.0719323i	0.00597365	+	0.00597365i
$146$		0			0
$147$	0.284847	−	1.43202i	0.0234938	−	0.118111i
$148$		0			0
$149$	−10.7964	−	7.21395i	−0.884479	−	0.590990i	0.0282295	−	0.999601i	$-0.491013\pi$
$149$	−10.7964	−	7.21395i	−0.884479	−	0.590990i	−0.912708	+	0.408612i	$0.866013\pi$
$150$		0			0
$151$	9.79563	+	4.05748i	0.797157	+	0.330193i	0.743817	−	0.668383i	$-0.233013\pi$
$151$	9.79563	+	4.05748i	0.797157	+	0.330193i	0.0533397	+	0.998576i	$0.483013\pi$
$152$		0			0
$153$	5.81014	−	2.40664i	0.469722	−	0.194565i
$154$		0			0
$155$	−1.77196	−	8.90823i	−0.142327	−	0.715526i
$156$		0			0
$157$	4.31959	+	6.46472i	0.344741	+	0.515941i	0.962809	−	0.270184i	$-0.0870845\pi$
$157$	4.31959	+	6.46472i	0.344741	+	0.515941i	−0.618068	+	0.786124i	$0.712084\pi$
$158$		0			0
$159$		−	0.808550i		−	0.0641222i
$160$		0			0
$161$			12.2754i			0.967437i
$162$		0			0
$163$	0.437112	+	0.654184i	0.0342372	+	0.0512396i	0.848193	−	0.529687i	$-0.177690\pi$
$163$	0.437112	+	0.654184i	0.0342372	+	0.0512396i	−0.813956	+	0.580926i	$0.802690\pi$
$164$		0			0
$165$	−0.311573	−	1.56638i	−0.0242559	−	0.121943i
$166$		0			0
$167$	−17.5845	+	7.28375i	−1.36073	+	0.563633i	−0.939259	−	0.343208i	$-0.888486\pi$
$167$	−17.5845	+	7.28375i	−1.36073	+	0.563633i	−0.421472	+	0.906841i	$0.638486\pi$
$168$		0			0
$169$	12.3444	+	5.11322i	0.949570	+	0.393325i
$170$		0			0
$171$	−0.438266	−	0.292840i	−0.0335150	−	0.0223940i
$172$		0			0
$173$	−0.285668	+	1.43615i	−0.0217189	+	0.109188i	−0.990124	−	0.140194i	$-0.955227\pi$
$173$	−0.285668	+	1.43615i	−0.0217189	+	0.109188i	0.968405	+	0.249382i	$0.0802275\pi$
$174$		0			0
$175$	−3.56024	−	3.56024i	−0.269129	−	0.269129i
$176$		0			0
$177$	−2.20900	+	2.20900i	−0.166038	+	0.166038i
$178$		0			0
$179$	9.41568	+	1.87290i	0.703761	+	0.139987i	0.533983	−	0.845496i	$-0.320695\pi$
$179$	9.41568	+	1.87290i	0.703761	+	0.139987i	0.169778	+	0.985482i	$0.445695\pi$
$180$		0			0
$181$	−1.23999	+	1.85578i	−0.0921677	+	0.137939i	−0.874688	−	0.484686i	$-0.838934\pi$
$181$	−1.23999	+	1.85578i	−0.0921677	+	0.137939i	0.782520	+	0.622625i	$0.213934\pi$
$182$		0			0
$183$	0.557999	−	1.34713i	0.0412485	−	0.0995826i
$184$		0			0
$185$	−4.65279	−	11.2328i	−0.342080	−	0.825854i
$186$		0			0
$187$	6.42861	−	1.27873i	0.470107	−	0.0935100i
$188$		0			0
$189$	−3.12858	+	2.09045i	−0.227571	+	0.152058i
$190$		0			0
$191$	13.2544			0.959054			0.479527	−	0.877527i	$-0.340808\pi$
$191$	13.2544			0.959054			0.479527	+	0.877527i	$0.340808\pi$
$192$		0			0
$193$	−9.34813			−0.672893			−0.336447	−	0.941703i	$-0.609225\pi$
$193$	−9.34813			−0.672893			−0.336447	+	0.941703i	$0.609225\pi$
$194$		0			0
$195$	2.28378	−	1.52597i	0.163545	−	0.109277i
$196$		0			0
$197$	−16.0043	+	3.18345i	−1.14026	+	0.226812i	−0.728873	−	0.684649i	$-0.759955\pi$
$197$	−16.0043	+	3.18345i	−1.14026	+	0.226812i	−0.411387	+	0.911461i	$0.634955\pi$
$198$		0			0
$199$	−2.57784	−	6.22346i	−0.182738	−	0.441170i	0.805791	−	0.592201i	$-0.201741\pi$
$199$	−2.57784	−	6.22346i	−0.182738	−	0.441170i	−0.988529	+	0.151031i	$0.951741\pi$
$200$		0			0
$201$	2.23494	−	5.39561i	0.157640	−	0.380577i
$202$		0			0
$203$	0.0677854	−	0.101448i	0.00475760	−	0.00712025i
$204$		0			0
$205$	10.7717	+	2.14263i	0.752331	+	0.149648i
$206$		0			0
$207$	−14.2707	+	14.2707i	−0.991880	+	0.991880i
$208$		0			0
$209$	−0.388462	−	0.388462i	−0.0268705	−	0.0268705i
$210$		0			0
$211$	−4.14756	+	20.8512i	−0.285530	+	1.43546i	0.525671	+	0.850688i	$0.323814\pi$
$211$	−4.14756	+	20.8512i	−0.285530	+	1.43546i	−0.811201	+	0.584768i	$0.801186\pi$
$212$		0			0
$213$	−0.906147	−	0.605468i	−0.0620881	−	0.0414860i
$214$		0			0
$215$	−14.9132	−	6.17723i	−1.01707	−	0.421284i
$216$		0			0
$217$	−10.0645	+	4.16884i	−0.683220	+	0.282999i
$218$		0			0
$219$	0.703709	+	3.53778i	0.0475522	+	0.239061i
$220$		0			0
$221$	6.26276	+	9.37288i	0.421279	+	0.630488i
$222$		0			0
$223$			18.1448i			1.21507i	0.794294	+	0.607533i	$0.207841\pi$
$223$			18.1448i			1.21507i	−0.794294	+	0.607533i	$0.792159\pi$
$224$		0			0
$225$		−	8.27785i		−	0.551856i
$226$		0			0
$227$	13.5289	+	20.2475i	0.897946	+	1.34387i	0.938712	+	0.344703i	$0.112020\pi$
$227$	13.5289	+	20.2475i	0.897946	+	1.34387i	−0.0407657	+	0.999169i	$0.512980\pi$
$228$		0			0
$229$	−3.24498	−	16.3136i	−0.214434	−	1.07803i	−0.926607	−	0.376031i	$-0.877289\pi$
$229$	−3.24498	−	16.3136i	−0.214434	−	1.07803i	0.712173	−	0.702004i	$-0.247711\pi$
$230$		0			0
$231$	−1.76969	+	0.733029i	−0.116437	+	0.0482298i
$232$		0			0
$233$	−7.94074	−	3.28916i	−0.520215	−	0.215480i	0.107096	−	0.994249i	$-0.465845\pi$
$233$	−7.94074	−	3.28916i	−0.520215	−	0.215480i	−0.627311	+	0.778769i	$0.715845\pi$
$234$		0			0
$235$	13.3962	+	8.95106i	0.873873	+	0.583903i
$236$		0			0
$237$	0.160828	−	0.808537i	0.0104469	−	0.0525201i
$238$		0			0
$239$	10.9591	+	10.9591i	0.708886	+	0.708886i	0.966301	−	0.257415i	$-0.0828707\pi$
$239$	10.9591	+	10.9591i	0.708886	+	0.708886i	−0.257415	+	0.966301i	$0.582871\pi$
$240$		0			0
$241$	−20.9147	+	20.9147i	−1.34723	+	1.34723i	−0.458584	+	0.888651i	$0.651643\pi$
$241$	−20.9147	+	20.9147i	−1.34723	+	1.34723i	−0.888651	+	0.458584i	$0.848357\pi$
$242$		0			0
$243$	−9.17118	−	1.82426i	−0.588332	−	0.117026i
$244$		0			0
$245$	−3.19955	+	4.78847i	−0.204412	+	0.305924i
$246$		0			0
$247$	0.361565	−	0.872895i	0.0230058	−	0.0555410i
$248$		0			0
$249$	0.811579	+	1.95933i	0.0514318	+	0.124167i
$250$		0			0
$251$	5.57057	−	1.10806i	0.351611	−	0.0699398i	−0.0161250	−	0.999870i	$-0.505133\pi$
$251$	5.57057	−	1.10806i	0.351611	−	0.0699398i	0.367736	+	0.929930i	$0.380133\pi$
$252$		0			0
$253$	−17.4895	+	11.6861i	−1.09956	+	0.734700i
$254$		0			0
$255$	1.17453			0.0735518
$256$		0			0
$257$	−18.3131			−1.14234			−0.571171	−	0.820831i	$-0.693511\pi$
$257$	−18.3131			−1.14234			−0.571171	+	0.820831i	$0.693511\pi$
$258$		0			0
$259$	−12.1249	+	8.10160i	−0.753405	+	0.503409i
$260$		0			0
$261$	0.196741	−	0.0391342i	0.0121780	−	0.00242235i
$262$		0			0
$263$	5.81316	+	14.0342i	0.358455	+	0.865387i	0.995518	+	0.0945749i	$0.0301492\pi$
$263$	5.81316	+	14.0342i	0.358455	+	0.865387i	−0.637063	+	0.770812i	$0.719851\pi$
$264$		0			0
$265$	−1.22045	+	2.94643i	−0.0749718	+	0.180998i
$266$		0			0
$267$	3.21874	−	4.81719i	0.196984	−	0.294807i
$268$		0			0
$269$	13.7633	+	2.73769i	0.839162	+	0.166920i	0.595918	−	0.803045i	$-0.296788\pi$
$269$	13.7633	+	2.73769i	0.839162	+	0.166920i	0.243244	+	0.969965i	$0.421788\pi$
$270$		0			0
$271$	17.1462	−	17.1462i	1.04156	−	1.04156i	0.0424570	−	0.999098i	$-0.486481\pi$
$271$	17.1462	−	17.1462i	1.04156	−	1.04156i	0.999098	−	0.0424570i	$-0.0135186\pi$
$272$		0			0
$273$	−2.32943	−	2.32943i	−0.140984	−	0.140984i
$274$		0			0
$275$	1.68316	−	8.46181i	0.101498	−	0.510267i
$276$		0			0
$277$	5.37310	+	3.59019i	0.322838	+	0.215714i	0.706419	−	0.707794i	$-0.250309\pi$
$277$	5.37310	+	3.59019i	0.322838	+	0.215714i	−0.383581	+	0.923507i	$0.625309\pi$
$278$		0			0
$279$	−16.5468	−	6.85391i	−0.990631	−	0.410333i
$280$		0			0
$281$	2.20599	−	0.913752i	0.131598	−	0.0545099i	−0.315912	−	0.948788i	$-0.602311\pi$
$281$	2.20599	−	0.913752i	0.131598	−	0.0545099i	0.447511	+	0.894279i	$0.352311\pi$
$282$		0			0
$283$	1.14821	+	5.77245i	0.0682541	+	0.343137i	0.999790	−	0.0205138i	$-0.00653021\pi$
$283$	1.14821	+	5.77245i	0.0682541	+	0.343137i	−0.931535	+	0.363651i	$0.881530\pi$
$284$		0			0
$285$	−0.0546919	−	0.0818521i	−0.00323967	−	0.00484850i
$286$		0			0
$287$		−	13.1726i		−	0.777551i
$288$		0			0
$289$		−	12.1796i		−	0.716447i
$290$		0			0
$291$	1.07537	+	1.60941i	0.0630394	+	0.0943452i
$292$		0			0
$293$	0.402515	+	2.02358i	0.0235152	+	0.118219i	0.990760	−	0.135626i	$-0.0433047\pi$
$293$	0.402515	+	2.02358i	0.0235152	+	0.118219i	−0.967245	+	0.253845i	$0.918305\pi$
$294$		0			0
$295$	11.3841	−	4.71546i	0.662809	−	0.274545i
$296$		0			0
$297$	−5.95679	−	2.46738i	−0.345648	−	0.143172i
$298$		0			0
$299$	−30.0788	−	20.0980i	−1.73950	−	1.16230i
$300$		0			0
$301$	−3.77701	+	18.9883i	−0.217703	+	1.09447i
$302$		0			0
$303$	1.32692	+	1.32692i	0.0762295	+	0.0762295i
$304$		0			0
$305$	−4.06680	+	4.06680i	−0.232864	+	0.232864i
$306$		0			0
$307$	19.1912	+	3.81736i	1.09530	+	0.217868i	0.709493	−	0.704712i	$-0.248924\pi$
$307$	19.1912	+	3.81736i	1.09530	+	0.217868i	0.385804	+	0.922581i	$0.373924\pi$
$308$		0			0
$309$	−0.219393	+	0.328344i	−0.0124808	+	0.0186789i
$310$		0			0
$311$	−11.9287	+	28.7984i	−0.676414	+	1.63301i	0.0940829	+	0.995564i	$0.470008\pi$
$311$	−11.9287	+	28.7984i	−0.676414	+	1.63301i	−0.770497	+	0.637444i	$0.779992\pi$
$312$		0			0
$313$	3.76527	+	9.09016i	0.212825	+	0.513806i	0.993855	−	0.110688i	$-0.0353053\pi$
$313$	3.76527	+	9.09016i	0.212825	+	0.513806i	−0.781030	+	0.624494i	$0.785305\pi$
$314$		0			0
$315$	7.10980	−	1.41423i	0.400592	−	0.0796827i
$316$		0			0
$317$	6.34804	−	4.24162i	0.356541	−	0.238233i	−0.364380	−	0.931250i	$-0.618719\pi$
$317$	6.34804	−	4.24162i	0.356541	−	0.238233i	0.720921	+	0.693017i	$0.243719\pi$
$318$		0			0
$319$	0.209070			0.0117057
$320$		0			0
$321$	−1.48748			−0.0830228
$322$		0			0
$323$	0.335931	−	0.224462i	0.0186917	−	0.0124894i
$324$		0			0
$325$	14.5528	−	2.89473i	0.807245	−	0.160571i
$326$		0			0
$327$	0.500319	+	1.20788i	0.0276677	+	0.0667957i
$328$		0			0
$329$	7.39492	−	17.8529i	0.407695	−	0.984263i
$330$		0			0
$331$	−3.00110	+	4.49147i	−0.164956	+	0.246873i	−0.904734	−	0.425977i	$-0.859930\pi$
$331$	−3.00110	+	4.49147i	−0.164956	+	0.246873i	0.739778	+	0.672851i	$0.234930\pi$
$332$		0			0
$333$	−23.5142	−	4.67726i	−1.28857	−	0.256312i
$334$		0			0
$335$	−16.2886	+	16.2886i	−0.889943	+	0.889943i
$336$		0			0
$337$	9.39328	+	9.39328i	0.511684	+	0.511684i	0.915042	−	0.403358i	$-0.132157\pi$
$337$	9.39328	+	9.39328i	0.511684	+	0.511684i	−0.403358	+	0.915042i	$0.632157\pi$
$338$		0			0
$339$	0.520424	−	2.61635i	0.0282655	−	0.142100i
$340$		0			0
$341$	−15.5209	−	10.3707i	−0.840505	−	0.561607i
$342$		0			0
$343$	17.6488	+	7.31037i	0.952946	+	0.394723i
$344$		0			0
$345$	−3.48231	+	1.44242i	−0.187481	+	0.0776572i
$346$		0			0
$347$	2.30495	+	11.5878i	0.123736	+	0.622064i	0.992029	+	0.126011i	$0.0402176\pi$
$347$	2.30495	+	11.5878i	0.123736	+	0.622064i	−0.868293	+	0.496052i	$0.834782\pi$
$348$		0			0
$349$	−14.7665	−	22.0997i	−0.790435	−	1.18297i	−0.979587	−	0.201021i	$-0.935574\pi$
$349$	−14.7665	−	22.0997i	−0.790435	−	1.18297i	0.189152	−	0.981948i	$-0.439426\pi$
$350$		0			0
$351$		−	11.0887i		−	0.591871i
$352$		0			0
$353$			10.7979i			0.574714i	0.957824	+	0.287357i	$0.0927766\pi$
$353$			10.7979i			0.574714i	−0.957824	+	0.287357i	$0.907223\pi$
$354$		0			0
$355$	2.38817	+	3.57415i	0.126751	+	0.189696i
$356$		0			0
$357$	−0.274826	−	1.38164i	−0.0145453	−	0.0731242i
$358$		0			0
$359$	13.1862	−	5.46192i	0.695943	−	0.288269i	−0.00653056	−	0.999979i	$-0.502079\pi$
$359$	13.1862	−	5.46192i	0.695943	−	0.288269i	0.702474	+	0.711710i	$0.252079\pi$
$360$		0			0
$361$	17.5224	+	7.25803i	0.922233	+	0.382001i
$362$		0			0
$363$	0.639191	+	0.427094i	0.0335488	+	0.0224166i
$364$		0			0
$365$	2.77567	−	13.9542i	0.145285	−	0.730397i
$366$		0			0
$367$	17.9142	+	17.9142i	0.935116	+	0.935116i	0.998020	−	0.0629039i	$-0.0200362\pi$
$367$	17.9142	+	17.9142i	0.935116	+	0.935116i	−0.0629039	+	0.998020i	$0.520036\pi$
$368$		0			0
$369$	15.3136	−	15.3136i	0.797196	−	0.797196i
$370$		0			0
$371$	3.75157	+	0.746234i	0.194772	+	0.0387425i
$372$		0			0
$373$	−16.1231	+	24.1299i	−0.834820	+	1.24940i	0.131310	+	0.991341i	$0.458082\pi$
$373$	−16.1231	+	24.1299i	−0.834820	+	1.24940i	−0.966130	+	0.258056i	$0.916918\pi$
$374$		0			0
$375$	1.61523	−	3.89952i	0.0834102	−	0.201370i
$376$		0			0
$377$	0.137599	+	0.332194i	0.00708672	+	0.0171088i
$378$		0			0
$379$	−5.13105	+	1.02063i	−0.263564	+	0.0524262i	−0.325103	−	0.945678i	$-0.605399\pi$
$379$	−5.13105	+	1.02063i	−0.263564	+	0.0524262i	0.0615391	+	0.998105i	$0.480399\pi$
$380$		0			0
$381$	0.901502	−	0.602365i	0.0461854	−	0.0308601i
$382$		0			0
$383$	−8.64365			−0.441670			−0.220835	−	0.975311i	$-0.570878\pi$
$383$	−8.64365			−0.441670			−0.220835	+	0.975311i	$0.570878\pi$
$384$		0			0
$385$	7.55537			0.385057
$386$		0			0
$387$	−26.4656	+	17.6838i	−1.34532	+	0.898916i
$388$		0			0
$389$	3.11633	−	0.619876i	0.158004	−	0.0314290i	−0.115454	−	0.993313i	$-0.536832\pi$
$389$	3.11633	−	0.619876i	0.158004	−	0.0314290i	0.273458	+	0.961884i	$0.411832\pi$
$390$		0			0
$391$	−5.91985	−	14.2918i	−0.299380	−	0.722767i
$392$		0			0
$393$	−1.08776	+	2.62609i	−0.0548704	+	0.132469i
$394$		0			0
$395$	−1.80650	+	2.70362i	−0.0908950	+	0.136034i
$396$		0			0
$397$	19.5057	+	3.87993i	0.978963	+	0.194728i	0.658539	−	0.752546i	$-0.271175\pi$
$397$	19.5057	+	3.87993i	0.978963	+	0.194728i	0.320424	+	0.947274i	$0.396175\pi$
$398$		0			0
$399$	−0.0834885	+	0.0834885i	−0.00417965	+	0.00417965i
$400$		0			0
$401$	12.9963	+	12.9963i	0.649006	+	0.649006i	0.952753	−	0.303747i	$-0.0982376\pi$
$401$	12.9963	+	12.9963i	0.649006	+	0.649006i	−0.303747	+	0.952753i	$0.598238\pi$
$402$		0			0
$403$	6.26311	−	31.4868i	0.311988	−	1.56847i
$404$		0			0
$405$	9.41811	+	6.29298i	0.467989	+	0.312701i
$406$		0			0
$407$	−23.0857	−	9.56241i	−1.14432	−	0.473991i
$408$		0			0
$409$	−10.3447	+	4.28490i	−0.511510	+	0.211874i	−0.623483	−	0.781837i	$-0.714283\pi$
$409$	−10.3447	+	4.28490i	−0.511510	+	0.211874i	0.111973	+	0.993711i	$0.464283\pi$
$410$		0			0
$411$	−0.317344	−	1.59539i	−0.0156534	−	0.0786950i
$412$		0			0
$413$	−8.21072	−	12.2882i	−0.404023	−	0.604663i
$414$		0			0
$415$		−	8.36499i		−	0.410621i
$416$		0			0
$417$		−	2.88212i		−	0.141138i
$418$		0			0
$419$	−16.9150	−	25.3152i	−0.826354	−	1.23673i	−0.969027	−	0.246957i	$-0.920570\pi$
$419$	−16.9150	−	25.3152i	−0.826354	−	1.23673i	0.142672	−	0.989770i	$-0.454430\pi$
$420$		0			0
$421$	−4.45310	−	22.3872i	−0.217031	−	1.09109i	−0.923575	−	0.383418i	$-0.874747\pi$
$421$	−4.45310	−	22.3872i	−0.217031	−	1.09109i	0.706544	−	0.707669i	$-0.250253\pi$
$422$		0			0
$423$	29.3516	−	12.1579i	1.42713	−	0.591135i
$424$		0			0
$425$	5.86199	+	2.42811i	0.284348	+	0.117781i
$426$		0			0
$427$	5.73551	+	3.83235i	0.277561	+	0.185460i
$428$		0			0
$429$	1.10128	−	5.53649i	0.0531701	−	0.267304i
$430$		0			0
$431$	−9.97751	−	9.97751i	−0.480600	−	0.480600i	0.424723	−	0.905323i	$-0.360371\pi$
$431$	−9.97751	−	9.97751i	−0.480600	−	0.480600i	−0.905323	+	0.424723i	$0.860371\pi$
$432$		0			0
$433$	9.49988	−	9.49988i	0.456535	−	0.456535i	−0.440981	−	0.897516i	$-0.645369\pi$
$433$	9.49988	−	9.49988i	0.456535	−	0.456535i	0.897516	+	0.440981i	$0.145369\pi$
$434$		0			0
$435$	0.0367440	+	0.00730885i	0.00176174	+	0.000350432i
$436$		0			0
$437$	−0.720328	+	1.07805i	−0.0344580	+	0.0515700i
$438$		0			0
$439$	3.51252	−	8.47998i	0.167643	−	0.404727i	−0.817623	−	0.575754i	$-0.804709\pi$
$439$	3.51252	−	8.47998i	0.167643	−	0.404727i	0.985266	+	0.171027i	$0.0547085\pi$
$440$		0			0
$441$	4.34582	+	10.4917i	0.206944	+	0.499606i
$442$		0			0
$443$	4.35418	−	0.866101i	0.206874	−	0.0411497i	−0.0905656	−	0.995890i	$-0.528867\pi$
$443$	4.35418	−	0.866101i	0.206874	−	0.0411497i	0.297439	+	0.954741i	$0.403867\pi$
$444$		0			0
$445$	−19.0006	+	12.6958i	−0.900715	+	0.601839i
$446$		0			0
$447$	−4.78198			−0.226180
$448$		0			0
$449$	12.3670			0.583636			0.291818	−	0.956474i	$-0.405740\pi$
$449$	12.3670			0.583636			0.291818	+	0.956474i	$0.405740\pi$
$450$		0			0
$451$	18.7677	−	12.5402i	0.883738	−	0.590495i
$452$		0			0
$453$	3.82970	−	0.761775i	0.179935	−	0.0357913i
$454$		0			0
$455$	4.97254	+	12.0048i	0.233116	+	0.562793i
$456$		0			0
$457$	5.19687	−	12.5463i	0.243099	−	0.586893i	−0.754488	−	0.656314i	$-0.772115\pi$
$457$	5.19687	−	12.5463i	0.243099	−	0.586893i	0.997588	+	0.0694200i	$0.0221149\pi$
$458$		0			0
$459$	2.63437	−	3.94261i	0.122962	−	0.184025i
$460$		0			0
$461$	31.3777	+	6.24141i	1.46140	+	0.290691i	0.860836	−	0.508882i	$-0.169941\pi$
$461$	31.3777	+	6.24141i	1.46140	+	0.290691i	0.600568	+	0.799573i	$0.294941\pi$
$462$		0			0
$463$	−20.2752	+	20.2752i	−0.942266	+	0.942266i	−0.998422	−	0.0561556i	$-0.982116\pi$
$463$	−20.2752	+	20.2752i	−0.942266	+	0.942266i	0.0561556	+	0.998422i	$0.482116\pi$
$464$		0			0
$465$	−2.36525	−	2.36525i	−0.109686	−	0.109686i
$466$		0			0
$467$	1.24791	−	6.27365i	0.0577463	−	0.290310i	−0.941111	−	0.338097i	$-0.890217\pi$
$467$	1.24791	−	6.27365i	0.0577463	−	0.290310i	0.998858	+	0.0477869i	$0.0152168\pi$
$468$		0			0
$469$	22.9723	+	15.3496i	1.06076	+	0.708777i
$470$		0			0
$471$	2.64541	+	1.09576i	0.121894	+	0.0504901i
$472$		0			0
$473$	−30.6495	+	12.6954i	−1.40926	+	0.583737i
$474$		0			0
$475$	−0.103749	−	0.521583i	−0.00476035	−	0.0239319i
$476$		0			0
$477$	3.49383	+	5.22888i	0.159971	+	0.239414i
$478$		0			0
$479$		−	38.2671i		−	1.74847i	−0.485503	−	0.874235i	$-0.661364\pi$
$479$		−	38.2671i		−	1.74847i	0.485503	−	0.874235i	$-0.338636\pi$
$480$		0			0
$481$		−	42.9745i		−	1.95947i
$482$		0			0
$483$	2.51159	+	3.75886i	0.114281	+	0.171034i
$484$		0			0
$485$	−1.48946	−	7.48803i	−0.0676330	−	0.340014i
$486$		0			0
$487$	0.702848	−	0.291129i	0.0318491	−	0.0131923i	−0.366702	−	0.930338i	$-0.619513\pi$
$487$	0.702848	−	0.291129i	0.0318491	−	0.0131923i	0.398551	+	0.917146i	$0.369513\pi$
$488$		0			0
$489$	0.267696	+	0.110884i	0.0121057	+	0.00501433i
$490$		0			0
$491$	−16.0938	−	10.7535i	−0.726303	−	0.485300i	0.136628	−	0.990622i	$-0.456374\pi$
$491$	−16.0938	−	10.7535i	−0.726303	−	0.485300i	−0.862931	+	0.505322i	$0.831374\pi$
$492$		0			0
$493$	−0.0299963	+	0.150802i	−0.00135097	+	0.00679177i
$494$		0			0
$495$	8.78343	+	8.78343i	0.394786	+	0.394786i
$496$		0			0
$497$	3.64560	−	3.64560i	0.163528	−	0.163528i
$498$		0			0
$499$	−27.5562	−	5.48127i	−1.23359	−	0.245376i	−0.465109	−	0.885253i	$-0.653985\pi$
$499$	−27.5562	−	5.48127i	−1.23359	−	0.245376i	−0.768477	+	0.639878i	$0.778985\pi$
$500$		0			0
$501$	−3.89429	+	5.82822i	−0.173984	+	0.260386i
$502$		0			0
$503$	−0.279297	+	0.674282i	−0.0124532	+	0.0300647i	−0.929984	−	0.367600i	$-0.880179\pi$
$503$	−0.279297	+	0.674282i	−0.0124532	+	0.0300647i	0.917531	+	0.397665i	$0.130179\pi$
$504$		0			0
$505$	−2.83252	−	6.83831i	−0.126046	−	0.304301i
$506$		0			0
$507$	4.82617	−	0.959986i	0.214338	−	0.0426345i
$508$		0			0
$509$	14.6162	−	9.76623i	0.647851	−	0.432880i	−0.187750	−	0.982217i	$-0.560119\pi$
$509$	14.6162	−	9.76623i	0.647851	−	0.432880i	0.835601	+	0.549336i	$0.185119\pi$
$510$		0			0
$511$	−17.0643			−0.754882
$512$		0			0
$513$	−0.397427			−0.0175468
$514$		0			0
$515$	1.29510	−	0.865359i	0.0570690	−	0.0381323i
$516$		0			0
$517$	32.4761	−	6.45989i	1.42830	−	0.284106i
$518$		0			0
$519$	0.206366	+	0.498212i	0.00905848	+	0.0218691i
$520$		0			0
$521$	0.465084	−	1.12281i	0.0203757	−	0.0491913i	−0.913364	−	0.407143i	$-0.866525\pi$
$521$	0.465084	−	1.12281i	0.0203757	−	0.0491913i	0.933740	+	0.357952i	$0.116525\pi$
$522$		0			0
$523$	−16.7116	+	25.0106i	−0.730746	+	1.09364i	0.260990	+	0.965341i	$0.415951\pi$
$523$	−16.7116	+	25.0106i	−0.730746	+	1.09364i	−0.991736	+	0.128297i	$0.959049\pi$
$524$		0			0
$525$	−1.81862	−	0.361746i	−0.0793710	−	0.0157879i
$526$		0			0
$527$	9.70724	−	9.70724i	0.422854	−	0.422854i
$528$		0			0
$529$	18.8396	+	18.8396i	0.819111	+	0.819111i
$530$		0			0
$531$	4.74025	−	23.8308i	0.205709	−	1.03417i
$532$		0			0
$533$	32.2772	+	21.5669i	1.39808	+	0.934167i
$534$		0			0
$535$	5.42050	+	2.24524i	0.234349	+	0.0970704i
$536$		0			0
$537$	3.26638	−	1.35298i	0.140955	−	0.0583854i
$538$		0			0
$539$	2.30908	+	11.6086i	0.0994593	+	0.500016i
$540$		0			0
$541$	−12.6138	−	18.8780i	−0.542312	−	0.811627i	0.454556	−	0.890718i	$-0.349798\pi$
$541$	−12.6138	−	18.8780i	−0.542312	−	0.811627i	−0.996867	+	0.0790916i	$0.974798\pi$
$542$		0			0
$543$			0.821964i			0.0352739i
$544$		0			0
$545$		−	5.15681i		−	0.220893i
$546$		0			0
$547$	−17.7222	−	26.5232i	−0.757748	−	1.13405i	−0.987006	−	0.160684i	$-0.948630\pi$
$547$	−17.7222	−	26.5232i	−0.757748	−	1.13405i	0.229258	−	0.973366i	$-0.426370\pi$
$548$		0			0
$549$	2.21251	+	11.1230i	0.0944276	+	0.474720i
$550$		0			0
$551$	0.0119061	−	0.00493165i	0.000507215	−	0.000210095i
$552$		0			0
$553$	3.60307	+	1.49244i	0.153218	+	0.0634651i
$554$		0			0
$555$	−3.72301	−	2.48764i	−0.158033	−	0.105594i
$556$		0			0
$557$	5.25641	−	26.4258i	0.222721	−	1.11970i	−0.693940	−	0.720032i	$-0.744127\pi$
$557$	5.25641	−	26.4258i	0.222721	−	1.11970i	0.916662	−	0.399664i	$-0.130873\pi$
$558$		0			0
$559$	−40.3437	−	40.3437i	−1.70636	−	1.70636i
$560$		0			0
$561$	1.70688	−	1.70688i	0.0720644	−	0.0720644i
$562$		0			0
$563$	37.9592	+	7.55055i	1.59979	+	0.318218i	0.912786	−	0.408437i	$-0.133926\pi$
$563$	37.9592	+	7.55055i	1.59979	+	0.318218i	0.687002	+	0.726655i	$0.258926\pi$
$564$		0			0
$565$	−5.84567	+	8.74866i	−0.245929	+	0.368059i
$566$		0			0
$567$	5.19894	−	12.5514i	0.218335	−	0.527107i
$568$		0			0
$569$	−2.03813	−	4.92049i	−0.0854431	−	0.206278i	0.875383	−	0.483430i	$-0.160609\pi$
$569$	−2.03813	−	4.92049i	−0.0854431	−	0.206278i	−0.960826	+	0.277152i	$0.910609\pi$
$570$		0			0
$571$	14.3880	−	2.86195i	0.602118	−	0.119769i	0.115387	−	0.993321i	$-0.463189\pi$
$571$	14.3880	−	2.86195i	0.602118	−	0.119769i	0.486731	+	0.873552i	$0.338189\pi$
$572$		0			0
$573$	4.05864	−	2.71189i	0.169552	−	0.113291i
$574$		0			0
$575$	−20.3619			−0.849149
$576$		0			0
$577$	−10.2313			−0.425936			−0.212968	−	0.977059i	$-0.568313\pi$
$577$	−10.2313			−0.425936			−0.212968	+	0.977059i	$0.568313\pi$
$578$		0			0
$579$	−2.86250	+	1.91266i	−0.118961	+	0.0794874i
$580$		0			0
$581$	−9.84005	+	1.95731i	−0.408234	+	0.0812028i
$582$		0			0
$583$	2.50827	+	6.05550i	0.103882	+	0.250793i
$584$		0			0
$585$	−8.17527	+	19.7369i	−0.338006	+	0.816018i
$586$		0			0
$587$	15.0588	−	22.5371i	0.621543	−	0.930206i	−0.378446	−	0.925623i	$-0.623541\pi$
$587$	15.0588	−	22.5371i	0.621543	−	0.930206i	0.999990	−	0.00458217i	$-0.00145855\pi$
$588$		0			0
$589$	−1.12851	−	0.224474i	−0.0464994	−	0.00924930i
$590$		0			0
$591$	−4.24934	+	4.24934i	−0.174795	+	0.174795i
$592$		0			0
$593$	9.24907	+	9.24907i	0.379814	+	0.379814i	0.871035	−	0.491221i	$-0.163449\pi$
$593$	9.24907	+	9.24907i	0.379814	+	0.379814i	−0.491221	+	0.871035i	$0.663449\pi$
$594$		0			0
$595$	−1.08400	+	5.44966i	−0.0444399	+	0.223414i
$596$		0			0
$597$	−2.06270	−	1.37826i	−0.0844209	−	0.0564082i
$598$		0			0
$599$	−5.52517	−	2.28860i	−0.225752	−	0.0935097i	0.266940	−	0.963713i	$-0.413987\pi$
$599$	−5.52517	−	2.28860i	−0.225752	−	0.0935097i	−0.492693	+	0.870203i	$0.663987\pi$
$600$		0			0
$601$	−16.7410	+	6.93436i	−0.682880	+	0.282858i	−0.697030	−	0.717042i	$-0.745496\pi$
$601$	−16.7410	+	6.93436i	−0.682880	+	0.282858i	0.0141501	+	0.999900i	$0.495496\pi$
$602$		0			0
$603$	8.86169	+	44.5507i	0.360876	+	1.81425i
$604$		0			0
$605$	−1.68460	−	2.52119i	−0.0684888	−	0.102501i
$606$		0			0
$607$			7.72029i			0.313357i	0.987650	+	0.156679i	$0.0500787\pi$
$607$			7.72029i			0.313357i	−0.987650	+	0.156679i	$0.949921\pi$
$608$		0			0
$609$		−	0.0449336i		−	0.00182080i
$610$		0			0
$611$	31.6382	+	47.3499i	1.27994	+	1.91557i
$612$		0			0
$613$	5.99511	+	30.1394i	0.242140	+	1.21732i	0.890143	+	0.455682i	$0.150605\pi$
$613$	5.99511	+	30.1394i	0.242140	+	1.21732i	−0.648003	+	0.761638i	$0.724395\pi$
$614$		0			0
$615$	3.73681	−	1.54784i	0.150683	−	0.0624149i
$616$		0			0
$617$	−17.6517	−	7.31159i	−0.710632	−	0.294353i	−0.00206586	−	0.999998i	$-0.500658\pi$
$617$	−17.6517	−	7.31159i	−0.710632	−	0.294353i	−0.708566	+	0.705644i	$0.750658\pi$
$618$		0			0
$619$	−9.76932	−	6.52765i	−0.392662	−	0.262368i	0.343529	−	0.939142i	$-0.388378\pi$
$619$	−9.76932	−	6.52765i	−0.392662	−	0.262368i	−0.736191	+	0.676774i	$0.763378\pi$
$620$		0			0
$621$	−2.96866	+	14.9245i	−0.119128	+	0.598899i
$622$		0			0
$623$	19.3805	+	19.3805i	0.776462	+	0.776462i
$624$		0			0
$625$	−1.55466	+	1.55466i	−0.0621862	+	0.0621862i
$626$		0			0
$627$	−0.198432	−	0.0394705i	−0.00792460	−	0.00157630i
$628$		0			0
$629$	10.2095	−	15.2797i	0.407081	−	0.609240i
$630$		0			0
$631$	−4.61559	+	11.1430i	−0.183744	+	0.443596i	−0.988732	−	0.149694i	$-0.952171\pi$
$631$	−4.61559	+	11.1430i	−0.183744	+	0.443596i	0.804989	+	0.593290i	$0.202171\pi$
$632$		0			0
$633$	2.99620	+	7.23347i	0.119088	+	0.287504i
$634$		0			0
$635$	−4.19439	+	0.834315i	−0.166449	+	0.0331088i
$636$		0			0
$637$	−16.9252	+	11.3091i	−0.670601	+	0.448081i
$638$		0			0
$639$	8.47633			0.335318
$640$		0			0
$641$	6.70997			0.265028			0.132514	−	0.991181i	$-0.457695\pi$
$641$	6.70997			0.265028			0.132514	+	0.991181i	$0.457695\pi$
$642$		0			0
$643$	0.990370	−	0.661744i	0.0390564	−	0.0260966i	−0.535889	−	0.844289i	$-0.680023\pi$
$643$	0.990370	−	0.661744i	0.0390564	−	0.0260966i	0.574945	+	0.818192i	$0.305023\pi$
$644$		0			0
$645$	−5.83045	+	1.15975i	−0.229574	+	0.0456651i
$646$		0			0
$647$	3.48816	+	8.42116i	0.137134	+	0.331070i	0.977496	−	0.210956i	$-0.0676576\pi$
$647$	3.48816	+	8.42116i	0.137134	+	0.331070i	−0.840362	+	0.542026i	$0.817658\pi$
$648$		0			0
$649$	9.69120	−	23.3966i	0.380413	−	0.918398i
$650$		0			0
$651$	−2.22889	+	3.33577i	−0.0873570	+	0.130739i
$652$		0			0
$653$	−32.8825	−	6.54074i	−1.28679	−	0.255959i	−0.496150	−	0.868237i	$-0.665253\pi$
$653$	−32.8825	−	6.54074i	−1.28679	−	0.255959i	−0.790643	+	0.612278i	$0.790253\pi$
$654$		0			0
$655$	7.92782	−	7.92782i	0.309765	−	0.309765i
$656$		0			0
$657$	−19.8380	−	19.8380i	−0.773954	−	0.773954i
$658$		0			0
$659$	5.99601	−	30.1440i	0.233571	−	1.17424i	−0.668853	−	0.743395i	$-0.733214\pi$
$659$	5.99601	−	30.1440i	0.233571	−	1.17424i	0.902424	−	0.430848i	$-0.141786\pi$
$660$		0			0
$661$	−37.6753	−	25.1739i	−1.46540	−	0.979149i	−0.995331	−	0.0965199i	$-0.969229\pi$
$661$	−37.6753	−	25.1739i	−1.46540	−	0.979149i	−0.470069	−	0.882629i	$-0.655771\pi$
$662$		0			0
$663$	3.83545	+	1.58869i	0.148956	+	0.0616997i
$664$		0			0
$665$	0.430260	−	0.178220i	0.0166848	−	0.00691106i
$666$		0			0
$667$	−0.0962624	−	0.483944i	−0.00372729	−	0.0187384i
$668$		0			0
$669$	3.71249	+	5.55614i	0.143533	+	0.214813i
$670$		0			0
$671$			11.8201i			0.456310i
$672$		0			0
$673$		−	32.2882i		−	1.24462i	−0.782771	−	0.622310i	$-0.786194\pi$
$673$		−	32.2882i		−	1.24462i	0.782771	−	0.622310i	$-0.213806\pi$
$674$		0			0
$675$	−3.46755	−	5.18955i	−0.133466	−	0.199746i
$676$		0			0
$677$	−1.07518	−	5.40530i	−0.0413225	−	0.207742i	0.954608	−	0.297864i	$-0.0962743\pi$
$677$	−1.07518	−	5.40530i	−0.0413225	−	0.207742i	−0.995931	+	0.0901220i	$0.971274\pi$
$678$		0			0
$679$	−8.45994	+	3.50422i	−0.324663	+	0.134480i
$680$		0			0
$681$	8.28540	+	3.43193i	0.317497	+	0.131512i
$682$		0			0
$683$	16.8416	+	11.2532i	0.644427	+	0.430592i	0.834371	−	0.551203i	$-0.185831\pi$
$683$	16.8416	+	11.2532i	0.644427	+	0.430592i	−0.189945	+	0.981795i	$0.560831\pi$
$684$		0			0
$685$	−1.25171	+	6.29277i	−0.0478254	+	0.240435i
$686$		0			0
$687$	−4.33147	−	4.33147i	−0.165256	−	0.165256i
$688$		0			0
$689$	−7.97082	+	7.97082i	−0.303664	+	0.303664i
$690$		0			0
$691$	−17.9592	−	3.57231i	−0.683201	−	0.135897i	−0.158726	−	0.987323i	$-0.550739\pi$
$691$	−17.9592	−	3.57231i	−0.683201	−	0.135897i	−0.524476	+	0.851425i	$0.675739\pi$
$692$		0			0
$693$	8.27706	−	12.3875i	0.314419	−	0.470562i
$694$		0			0
$695$	−4.35036	+	10.5027i	−0.165019	+	0.398390i
$696$		0			0
$697$	6.35251	+	15.3363i	0.240618	+	0.580904i
$698$		0			0
$699$	−3.10451	+	0.617526i	−0.117423	+	0.0233570i
$700$		0			0
$701$	−11.9298	+	7.97124i	−0.450583	+	0.301070i	−0.760079	−	0.649831i	$-0.774840\pi$
$701$	−11.9298	+	7.97124i	−0.450583	+	0.301070i	0.309496	+	0.950901i	$0.399840\pi$
$702$		0			0
$703$	−1.54024			−0.0580911
$704$		0			0
$705$	5.93348			0.223468
$706$		0			0
$707$	−7.38139	+	4.93208i	−0.277606	+	0.185490i
$708$		0			0
$709$	−8.17031	+	1.62518i	−0.306843	+	0.0610348i	−0.346110	−	0.938194i	$-0.612498\pi$
$709$	−8.17031	+	1.62518i	−0.306843	+	0.0610348i	0.0392674	+	0.999229i	$0.487498\pi$
$710$		0			0
$711$	2.45370	+	5.92375i	0.0920208	+	0.222158i
$712$		0			0
$713$	−16.8593	+	40.7019i	−0.631385	+	1.52430i
$714$		0			0
$715$	−12.3701	+	18.5132i	−0.462616	+	0.692354i
$716$		0			0
$717$	5.59807	+	1.11353i	0.209064	+	0.0415854i
$718$		0			0
$719$	−14.9481	+	14.9481i	−0.557471	+	0.557471i	−0.928587	−	0.371116i	$-0.878975\pi$
$719$	−14.9481	+	14.9481i	−0.557471	+	0.557471i	0.371116	+	0.928587i	$0.378975\pi$
$720$		0			0
$721$	−1.32099	−	1.32099i	−0.0491963	−	0.0491963i
$722$		0			0
$723$	−2.12509	+	10.6835i	−0.0790328	+	0.397325i
$724$		0			0
$725$	0.168277	+	0.112439i	0.00624966	+	0.00417589i
$726$		0			0
$727$	12.1904	+	5.04943i	0.452117	+	0.187273i	0.597110	−	0.802160i	$-0.296316\pi$
$727$	12.1904	+	5.04943i	0.452117	+	0.187273i	−0.144992	+	0.989433i	$0.546316\pi$
$728$		0			0
$729$	18.4310	−	7.63436i	0.682629	−	0.282754i
$730$		0			0
$731$	−4.75974	−	23.9288i	−0.176045	−	0.885040i
$732$		0			0
$733$	−8.53401	−	12.7721i	−0.315211	−	0.471746i	0.639706	−	0.768620i	$-0.279056\pi$
$733$	−8.53401	−	12.7721i	−0.315211	−	0.471746i	−0.954917	+	0.296873i	$0.904056\pi$
$734$		0			0
$735$			2.12092i			0.0782313i
$736$		0			0
$737$			47.3427i			1.74389i
$738$		0			0
$739$	8.82990	+	13.2149i	0.324813	+	0.486117i	0.957557	−	0.288244i	$-0.0930714\pi$
$739$	8.82990	+	13.2149i	0.324813	+	0.486117i	−0.632744	+	0.774361i	$0.718071\pi$
$740$		0			0
$741$	−0.0678823	−	0.341267i	−0.00249372	−	0.0125368i
$742$		0			0
$743$	19.6016	−	8.11923i	0.719112	−	0.297866i	0.00704260	−	0.999975i	$-0.497758\pi$
$743$	19.6016	−	8.11923i	0.719112	−	0.297866i	0.712069	+	0.702109i	$0.247758\pi$
$744$		0			0
$745$	17.4260	+	7.21808i	0.638439	+	0.264450i
$746$		0			0
$747$	−13.7149	−	9.16402i	−0.501803	−	0.335294i
$748$		0			0
$749$	1.37283	−	6.90170i	0.0501622	−	0.252183i
$750$		0			0
$751$	35.0649	+	35.0649i	1.27954	+	1.27954i	0.940928	+	0.338608i	$0.109956\pi$
$751$	35.0649	+	35.0649i	1.27954	+	1.27954i	0.338608	+	0.940928i	$0.390044\pi$
$752$		0			0
$753$	1.47906	−	1.47906i	0.0538998	−	0.0538998i
$754$		0			0
$755$	−15.1056	−	3.00470i	−0.549750	−	0.109352i
$756$		0			0
$757$	−4.47197	+	6.69277i	−0.162536	+	0.243253i	−0.903794	−	0.427968i	$-0.859230\pi$
$757$	−4.47197	+	6.69277i	−0.162536	+	0.243253i	0.741258	+	0.671221i	$0.234230\pi$
$758$		0			0
$759$	−2.96446	+	7.15683i	−0.107603	+	0.259776i
$760$		0			0
$761$	−14.8692	−	35.8975i	−0.539009	−	1.30128i	−0.925415	−	0.378955i	$-0.876284\pi$
$761$	−14.8692	−	35.8975i	−0.539009	−	1.30128i	0.386406	−	0.922329i	$-0.373716\pi$
$762$		0			0
$763$	−6.06615	+	1.20663i	−0.219609	+	0.0436830i
$764$		0			0
$765$	−7.59566	+	5.07526i	−0.274622	+	0.183496i
$766$		0			0
$767$	43.5533			1.57262
$768$		0			0
$769$	−8.75459			−0.315699			−0.157849	−	0.987463i	$-0.550456\pi$
$769$	−8.75459			−0.315699			−0.157849	+	0.987463i	$0.550456\pi$
$770$		0			0
$771$	−5.60768	+	3.74693i	−0.201956	+	0.134942i
$772$		0			0
$773$	−22.8691	+	4.54895i	−0.822544	+	0.163614i	−0.588382	−	0.808583i	$-0.700235\pi$
$773$	−22.8691	+	4.54895i	−0.822544	+	0.163614i	−0.234162	+	0.972197i	$0.575235\pi$
$774$		0			0
$775$	−6.91507	−	16.6945i	−0.248397	−	0.599683i
$776$		0			0
$777$	−2.05516	+	4.96159i	−0.0737284	+	0.177996i
$778$		0			0
$779$	0.772974	−	1.15684i	0.0276947	−	0.0414480i
$780$		0			0
$781$	8.66470	+	1.72352i	0.310048	+	0.0616723i
$782$		0			0
$783$	0.106948	−	0.106948i	0.00382200	−	0.00382200i
$784$		0			0
$785$	−7.98613	−	7.98613i	−0.285037	−	0.285037i
$786$		0			0
$787$	−7.15249	+	35.9580i	−0.254959	+	1.28176i	0.614956	+	0.788561i	$0.289174\pi$
$787$	−7.15249	+	35.9580i	−0.254959	+	1.28176i	−0.869915	+	0.493202i	$0.835826\pi$
$788$		0			0
$789$	4.65150	+	3.10803i	0.165598	+	0.110649i
$790$		0			0
$791$	11.6592	+	4.82940i	0.414553	+	0.171714i
$792$		0			0
$793$	−18.7811	+	7.77937i	−0.666935	+	0.276254i
$794$		0			0
$795$	0.229135	+	1.15194i	0.00812657	+	0.0408550i
$796$		0			0
$797$	22.6473	+	33.8941i	0.802209	+	1.20059i	0.976419	+	0.215882i	$0.0692627\pi$
$797$	22.6473	+	33.8941i	0.802209	+	1.20059i	−0.174210	+	0.984708i	$0.555737\pi$
$798$		0			0
$799$			24.3517i			0.861501i
$800$		0			0
$801$			45.0612i			1.59216i
$802$		0			0
$803$	−16.2452	−	24.3126i	−0.573279	−	0.857973i
$804$		0			0
$805$	−3.47872	−	17.4887i	−0.122609	−	0.616396i
$806$		0			0
$807$	4.77460	−	1.97771i	0.168074	−	0.0696185i
$808$		0			0
$809$	−20.5884	−	8.52801i	−0.723851	−	0.299829i	−0.00982829	−	0.999952i	$-0.503128\pi$
$809$	−20.5884	−	8.52801i	−0.723851	−	0.299829i	−0.714022	+	0.700123i	$0.753128\pi$
$810$		0			0
$811$	28.5660	+	19.0872i	1.00309	+	0.670241i	0.944660	−	0.328050i	$-0.106392\pi$
$811$	28.5660	+	19.0872i	1.00309	+	0.670241i	0.0584267	+	0.998292i	$0.481392\pi$
$812$		0			0
$813$	1.74217	−	8.75850i	0.0611007	−	0.307174i
$814$		0			0
$815$	−0.808140	−	0.808140i	−0.0283079	−	0.0283079i
$816$		0			0
$817$	−1.44595	+	1.44595i	−0.0505873	+	0.0505873i
$818$		0			0
$819$	25.1301	+	4.99869i	0.878117	+	0.174668i
$820$		0			0
$821$	−18.1775	+	27.2045i	−0.634398	+	0.949444i	0.365429	+	0.930839i	$0.380922\pi$
$821$	−18.1775	+	27.2045i	−0.634398	+	0.949444i	−0.999827	+	0.0186046i	$0.994078\pi$
$822$		0			0
$823$	13.8958	−	33.5474i	0.484377	−	1.16939i	−0.473134	−	0.880991i	$-0.656877\pi$
$823$	13.8958	−	33.5474i	0.484377	−	1.16939i	0.957511	−	0.288398i	$-0.0931227\pi$
$824$		0			0
$825$	−1.21591	−	2.93548i	−0.0423327	−	0.102200i
$826$		0			0
$827$	−31.3707	+	6.24001i	−1.09087	+	0.216987i	−0.707573	−	0.706641i	$-0.750210\pi$
$827$	−31.3707	+	6.24001i	−1.09087	+	0.216987i	−0.383292	+	0.923627i	$0.625210\pi$
$828$		0			0
$829$	28.9138	−	19.3196i	1.00422	−	0.670997i	0.0592783	−	0.998241i	$-0.481120\pi$
$829$	28.9138	−	19.3196i	1.00422	−	0.670997i	0.944940	+	0.327244i	$0.106120\pi$
$830$		0			0
$831$	2.37987			0.0825567
$832$		0			0
$833$	−8.70450			−0.301593
$834$		0			0
$835$	22.9885	−	15.3604i	0.795548	−	0.531568i
$836$		0			0
$837$	−13.2446	+	2.63451i	−0.457800	+	0.0910621i
$838$		0			0
$839$	4.77355	+	11.5244i	0.164801	+	0.397865i	0.984609	−	0.174774i	$-0.0559195\pi$
$839$	4.77355	+	11.5244i	0.164801	+	0.397865i	−0.819807	+	0.572639i	$0.805920\pi$
$840$		0			0
$841$	11.0959	−	26.7880i	0.382619	−	0.923723i
$842$		0			0
$843$	0.488541	−	0.731154i	0.0168263	−	0.0251823i
$844$		0			0
$845$	−19.0361	−	3.78651i	−0.654860	−	0.130260i
$846$		0			0
$847$	−2.57159	+	2.57159i	−0.0883608	+	0.0883608i
$848$		0			0
$849$	1.53266	+	1.53266i	0.0526007	+	0.0526007i
$850$		0			0
$851$	−11.5051	+	57.8402i	−0.394391	+	1.98274i
$852$		0			0
$853$	−15.0593	−	10.0623i	−0.515620	−	0.344526i	0.270379	−	0.962754i	$-0.412851\pi$
$853$	−15.0593	−	10.0623i	−0.515620	−	0.344526i	−0.785999	+	0.618228i	$0.787851\pi$
$854$		0			0
$855$	0.707383	+	0.293008i	0.0241920	+	0.0100206i
$856$		0			0
$857$	45.1567	−	18.7045i	1.54252	−	0.638933i	0.560577	−	0.828102i	$-0.310579\pi$
$857$	45.1567	−	18.7045i	1.54252	−	0.638933i	0.981945	+	0.189169i	$0.0605793\pi$
$858$		0			0
$859$	−10.5662	−	53.1197i	−0.360513	−	1.81242i	−0.555385	−	0.831593i	$-0.687429\pi$
$859$	−10.5662	−	53.1197i	−0.360513	−	1.81242i	0.194872	−	0.980829i	$-0.437571\pi$
$860$		0			0
$861$	−2.69515	−	4.03358i	−0.0918505	−	0.137464i
$862$		0			0
$863$			9.30109i			0.316613i	0.987390	+	0.158306i	$0.0506034\pi$
$863$			9.30109i			0.316613i	−0.987390	+	0.158306i	$0.949397\pi$
$864$		0			0
$865$		−	2.12703i		−	0.0723211i
$866$		0			0
$867$	−2.49199	−	3.72952i	−0.0846324	−	0.126661i
$868$		0			0
$869$	1.30373	+	6.55432i	0.0442262	+	0.222340i
$870$		0			0
$871$	−75.2232	+	31.1585i	−2.54884	+	1.05576i
$872$		0			0
$873$	−13.9088	−	5.76123i	−0.470743	−	0.194988i
$874$		0			0
$875$	16.6025	+	11.0934i	0.561267	+	0.375027i
$876$		0			0
$877$	−4.03688	+	20.2948i	−0.136316	+	0.685306i	0.850824	+	0.525450i	$0.176103\pi$
$877$	−4.03688	+	20.2948i	−0.136316	+	0.685306i	−0.987140	+	0.159856i	$0.948897\pi$
$878$		0			0
$879$	0.537286	+	0.537286i	0.0181222	+	0.0181222i
$880$		0			0
$881$	−21.4492	+	21.4492i	−0.722643	+	0.722643i	−0.969143	−	0.246500i	$-0.920719\pi$
$881$	−21.4492	+	21.4492i	−0.722643	+	0.722643i	0.246500	+	0.969143i	$0.420719\pi$
$882$		0			0
$883$	−34.4043	−	6.84345i	−1.15780	−	0.230300i	−0.421417	−	0.906867i	$-0.638467\pi$
$883$	−34.4043	−	6.84345i	−1.15780	−	0.230300i	−0.736381	+	0.676567i	$0.763467\pi$
$884$		0			0
$885$	2.52114	−	3.77315i	0.0847472	−	0.126833i
$886$		0			0
$887$	−8.28163	+	19.9936i	−0.278070	+	0.671320i	−0.999782	−	0.0208730i	$-0.993355\pi$
$887$	−8.28163	+	19.9936i	−0.278070	+	0.671320i	0.721712	+	0.692193i	$0.243355\pi$
$888$		0			0
$889$	1.96287	+	4.73879i	0.0658326	+	0.158934i
$890$		0			0
$891$	22.8320	−	4.54158i	0.764902	−	0.152148i
$892$		0			0
$893$	1.69705	−	1.13394i	0.0567898	−	0.0379457i
$894$		0			0
$895$	−13.9452			−0.466138
$896$		0			0
$897$	−13.3226			−0.444828
$898$		0			0
$899$	0.364088	−	0.243276i	0.0121430	−	0.00811371i
$900$		0			0
$901$	−4.72769	+	0.940395i	−0.157502	+	0.0313291i
$902$		0			0
$903$	2.72851	+	6.58721i	0.0907992	+	0.219209i
$904$		0			0
$905$	1.24070	−	2.99531i	0.0412423	−	0.0995676i
$906$		0			0
$907$	18.4680	−	27.6393i	0.613220	−	0.917748i	−0.386771	−	0.922176i	$-0.626409\pi$
$907$	18.4680	−	27.6393i	0.613220	−	0.917748i	0.999990	+	0.00442801i	$0.00140948\pi$
$908$		0			0
$909$	−14.3149	−	2.84742i	−0.474796	−	0.0944428i
$910$		0			0
$911$	38.1083	−	38.1083i	1.26258	−	1.26258i	0.312748	−	0.949836i	$-0.398751\pi$
$911$	38.1083	−	38.1083i	1.26258	−	1.26258i	0.949836	−	0.312748i	$-0.101249\pi$
$912$		0			0
$913$	−12.1564	−	12.1564i	−0.402317	−	0.402317i
$914$		0			0
$915$	−0.413216	+	2.07738i	−0.0136605	+	0.0686760i
$916$		0			0
$917$	−11.1808	−	7.47077i	−0.369223	−	0.246707i
$918$		0			0
$919$	−4.18590	−	1.73385i	−0.138080	−	0.0571946i	0.312573	−	0.949894i	$-0.398809\pi$
$919$	−4.18590	−	1.73385i	−0.138080	−	0.0571946i	−0.450653	+	0.892699i	$0.648809\pi$
$920$		0			0
$921$	6.65758	−	2.75766i	0.219375	−	0.0908680i
$922$		0			0
$923$	2.96414	+	14.9017i	0.0975659	+	0.490497i
$924$		0			0
$925$	−13.4386	−	20.1122i	−0.441857	−	0.661286i
$926$		0			0
$927$		−	3.07142i		−	0.100879i
$928$		0			0
$929$			6.50934i			0.213564i	0.994282	+	0.106782i	$0.0340548\pi$
$929$			6.50934i			0.213564i	−0.994282	+	0.106782i	$0.965945\pi$
$930$		0			0
$931$	0.405325	+	0.606611i	0.0132840	+	0.0198809i
$932$		0			0
$933$	2.23956	+	11.2590i	0.0733199	+	0.368604i
$934$		0			0
$935$	−8.79643	+	3.64360i	−0.287674	+	0.119159i
$936$		0			0
$937$	−19.5113	−	8.08185i	−0.637407	−	0.264023i	0.0404894	−	0.999180i	$-0.487108\pi$
$937$	−19.5113	−	8.08185i	−0.637407	−	0.264023i	−0.677897	+	0.735157i	$0.737108\pi$
$938$		0			0
$939$	3.01284	+	2.01312i	0.0983204	+	0.0656956i
$940$		0			0
$941$	−10.7030	+	53.8075i	−0.348907	+	1.75408i	0.264573	+	0.964366i	$0.414769\pi$
$941$	−10.7030	+	53.8075i	−0.348907	+	1.75408i	−0.613480	+	0.789710i	$0.710231\pi$
$942$		0			0
$943$	−37.6685	−	37.6685i	−1.22666	−	1.22666i
$944$		0			0
$945$	3.86487	−	3.86487i	0.125724	−	0.125724i
$946$		0			0
$947$	42.5123	+	8.45622i	1.38146	+	0.274790i	0.829234	−	0.558901i	$-0.188777\pi$
$947$	42.5123	+	8.45622i	1.38146	+	0.274790i	0.552230	+	0.833692i	$0.313777\pi$
$948$		0			0
$949$	27.9388	−	41.8133i	0.906931	−	1.35732i
$950$		0			0
$951$	1.07599	−	2.59766i	0.0348913	−	0.0842349i
$952$		0			0
$953$	11.3628	+	27.4322i	0.368077	+	0.888616i	0.994065	+	0.108784i	$0.0346956\pi$
$953$	11.3628	+	27.4322i	0.368077	+	0.888616i	−0.625989	+	0.779832i	$0.715304\pi$
$954$		0			0
$955$	−18.8835	+	3.75616i	−0.611055	+	0.121546i
$956$		0			0
$957$	0.0640196	−	0.0427765i	0.00206946	−	0.00138277i
$958$		0			0
$959$	7.69531			0.248494
$960$		0			0
$961$	−8.09657			−0.261180
$962$		0			0
$963$	9.61949	−	6.42754i	0.309984	−	0.207124i
$964$		0			0
$965$	13.3182	−	2.64916i	0.428729	−	0.0852795i
$966$		0			0
$967$	−12.7234	−	30.7169i	−0.409155	−	0.987788i	−0.985361	−	0.170483i	$-0.945467\pi$
$967$	−12.7234	−	30.7169i	−0.409155	−	0.987788i	0.576205	−	0.817305i	$-0.304533\pi$
$968$		0			0
$969$	0.0569399	−	0.137465i	0.00182917	−	0.00441602i
$970$		0			0
$971$	1.52250	−	2.27858i	0.0488594	−	0.0731232i	−0.806236	−	0.591594i	$-0.798499\pi$
$971$	1.52250	−	2.27858i	0.0488594	−	0.0731232i	0.855095	+	0.518471i	$0.173499\pi$
$972$		0			0
$973$	13.3727	+	2.65999i	0.428708	+	0.0852753i
$974$		0			0
$975$	3.86395	−	3.86395i	0.123746	−	0.123746i
$976$		0			0
$977$	−24.7249	−	24.7249i	−0.791018	−	0.791018i	0.190642	−	0.981660i	$-0.438943\pi$
$977$	−24.7249	−	24.7249i	−0.791018	−	0.791018i	−0.981660	+	0.190642i	$0.938943\pi$
$978$		0			0
$979$	−9.16243	+	46.0626i	−0.292832	+	1.47217i
$980$		0			0
$981$	−8.45491	−	5.64939i	−0.269944	−	0.180371i
$982$		0			0
$983$	−8.66961	−	3.59107i	−0.276517	−	0.114537i	0.240115	−	0.970744i	$-0.422815\pi$
$983$	−8.66961	−	3.59107i	−0.276517	−	0.114537i	−0.516633	+	0.856207i	$0.672815\pi$
$984$		0			0
$985$	21.8991	−	9.07090i	0.697763	−	0.289023i
$986$		0			0
$987$	−1.38836	−	6.97978i	−0.0441921	−	0.222169i
$988$		0			0
$989$	43.4986	+	65.1002i	1.38317	+	2.07007i
$990$		0			0
$991$			39.1011i			1.24209i	0.783776	+	0.621044i	$0.213291\pi$
$991$			39.1011i			1.24209i	−0.783776	+	0.621044i	$0.786709\pi$
$992$		0			0
$993$			1.98937i			0.0631308i
$994$		0			0
$995$	5.43630	+	8.13600i	0.172342	+	0.257929i
$996$		0			0
$997$	−7.93159	−	39.8748i	−0.251196	−	1.26285i	−0.876094	−	0.482140i	$-0.839860\pi$
$997$	−7.93159	−	39.8748i	−0.251196	−	1.26285i	0.624898	−	0.780706i	$-0.285140\pi$
$998$		0			0
$999$	−16.7008	+	6.91769i	−0.528389	+	0.218866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.a.33.5		56
4.3	odd	2		512.2.i.b.33.3		56
8.3	odd	2		64.2.i.a.13.4	yes	56
8.5	even	2		256.2.i.a.145.3		56
24.11	even	2		576.2.bd.a.397.4		56
64.5	even	16	inner	512.2.i.a.481.5		56
64.27	odd	16		64.2.i.a.5.4	✓	56
64.37	even	16		256.2.i.a.113.3		56
64.59	odd	16		512.2.i.b.481.3		56
192.155	even	16		576.2.bd.a.325.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.4	✓	56	64.27	odd	16
64.2.i.a.13.4	yes	56	8.3	odd	2
256.2.i.a.113.3		56	64.37	even	16
256.2.i.a.145.3		56	8.5	even	2
512.2.i.a.33.5		56	1.1	even	1	trivial
512.2.i.a.481.5		56	64.5	even	16	inner
512.2.i.b.33.3		56	4.3	odd	2
512.2.i.b.481.3		56	64.59	odd	16
576.2.bd.a.325.4		56	192.155	even	16
576.2.bd.a.397.4		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)

\(f(q)\)	\(=\)	\(q+(0.306211 - 0.204603i) q^{3} +(-1.42470 + 0.283390i) q^{5} +(0.666723 + 1.60961i) q^{7} +(-1.09615 + 2.64634i) q^{9} +O(q^{10})\)	\(q+(0.306211 - 0.204603i) q^{3} +(-1.42470 + 0.283390i) q^{5} +(0.666723 + 1.60961i) q^{7} +(-1.09615 + 2.64634i) q^{9} +(-1.65860 + 2.48226i) q^{11} +(-5.03569 - 1.00166i) q^{13} +(-0.378274 + 0.378274i) q^{15} +(-1.55248 - 1.55248i) q^{17} +(-0.0359002 + 0.180483i) q^{19} +(0.533490 + 0.356467i) q^{21} +(6.50946 + 2.69631i) q^{23} +(-2.66995 + 1.10593i) q^{25} +(0.421339 + 2.11821i) q^{27} +(-0.0389072 - 0.0582287i) q^{29} +6.25272i q^{31} +1.09945i q^{33} +(-1.40602 - 2.10426i) q^{35} +(1.63291 + 8.20918i) q^{37} +(-1.74693 + 0.723600i) q^{39} +(-6.98521 - 2.89337i) q^{41} +(9.23959 + 6.17369i) q^{43} +(0.811733 - 4.08086i) q^{45} +(-7.84283 - 7.84283i) q^{47} +(2.80342 - 2.80342i) q^{49} +(-0.793030 - 0.157743i) q^{51} +(1.21975 - 1.82549i) q^{53} +(1.65955 - 4.00650i) q^{55} +(0.0259343 + 0.0626110i) q^{57} +(-8.31975 + 1.65490i) q^{59} +(3.29205 - 2.19968i) q^{61} -4.99040 q^{63} +7.45818 q^{65} +(13.1855 - 8.81029i) q^{67} +(2.54494 - 0.506220i) q^{69} +(-1.13245 - 2.73397i) q^{71} +(-3.74820 + 9.04896i) q^{73} +(-0.591290 + 0.884929i) q^{75} +(-5.10131 - 1.01471i) q^{77} +(1.58284 - 1.58284i) q^{79} +(-5.51384 - 5.51384i) q^{81} +(-1.12345 + 5.64796i) q^{83} +(2.65177 + 1.77186i) q^{85} +(-0.0238276 - 0.00986972i) q^{87} +(14.5341 - 6.02023i) q^{89} +(-1.74513 - 8.77334i) q^{91} +(1.27933 + 1.91465i) q^{93} -0.267307i q^{95} +5.25588i q^{97} +(-4.75084 - 7.11013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 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

Varieties

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Groups

Database

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