LMFDB - Embedded newform 816.2.cj.c.641.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [816,2,Mod(65,816)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(816, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 0, 8, 9]))

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

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

chi := DirichletCharacter("816.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.cj (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:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			641.4
Character	$\chi$	$=$	816.641
Dual form			816.2.cj.c.401.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.69899 - 0.336782i) q^{3} +(-0.595296 + 2.99276i) q^{5} +(2.11533 - 0.420765i) q^{7} +(2.77316 - 1.14438i) q^{9} +(-1.37013 - 0.915491i) q^{11} +(3.12551 + 3.12551i) q^{13} +(-0.00349923 + 5.28516i) q^{15} +(-3.95657 + 1.15998i) q^{17} +(0.330416 + 0.797694i) q^{19} +(3.45222 - 1.42728i) q^{21} +(0.425893 - 0.637394i) q^{23} +(-3.98282 - 1.64974i) q^{25} +(4.32617 - 2.87824i) q^{27} +(7.83789 + 1.55905i) q^{29} +(-1.60475 - 2.40167i) q^{31} +(-2.63616 - 1.09398i) q^{33} +6.58114i q^{35} +(-1.98027 + 1.32318i) q^{37} +(6.36284 + 4.25761i) q^{39} +(-0.600791 - 3.02038i) q^{41} +(-4.38037 + 10.5751i) q^{43} +(1.77400 + 8.98063i) q^{45} +(-2.21238 + 2.21238i) q^{47} +(-2.16958 + 0.898671i) q^{49} +(-6.33153 + 3.30330i) q^{51} +(5.88369 - 2.43710i) q^{53} +(3.55548 - 3.55548i) q^{55} +(0.830022 + 1.24400i) q^{57} +(2.33146 - 5.62864i) q^{59} +(-1.14061 - 5.73423i) q^{61} +(5.38462 - 3.58759i) q^{63} +(-11.2145 + 7.49329i) q^{65} -7.19481i q^{67} +(0.508927 - 1.22636i) q^{69} +(1.20808 + 1.80802i) q^{71} +(12.3377 + 2.45412i) q^{73} +(-7.32238 - 1.46155i) q^{75} +(-3.28348 - 1.36006i) q^{77} +(3.31013 - 4.95397i) q^{79} +(6.38079 - 6.34708i) q^{81} +(-4.96993 - 11.9985i) q^{83} +(-1.11620 - 12.5316i) q^{85} +(13.8416 + 0.00916431i) q^{87} +(-3.42023 - 3.42023i) q^{89} +(7.92660 + 5.29638i) q^{91} +(-3.53529 - 3.53997i) q^{93} +(-2.58400 + 0.513989i) q^{95} +(-0.692072 + 3.47928i) q^{97} +(-4.84725 - 0.970853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} - 16 q^{15} + 16 q^{19} + 16 q^{21} + 16 q^{25} + 8 q^{27} - 16 q^{31} + 16 q^{37} + 24 q^{39} - 16 q^{43} - 40 q^{45} - 48 q^{49} + 40 q^{51} + 48 q^{55}+ \cdots + 64 q^{99}+O(q^{100}) $ 32 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 - 16 * q^15 + 16 * q^19 + 16 * q^21 + 16 * q^25 + 8 * q^27 - 16 * q^31 + 16 * q^37 + 24 * q^39 - 16 * q^43 - 40 * q^45 - 48 * q^49 + 40 * q^51 + 48 * q^55 + 8 * q^57 - 32 * q^61 - 64 * q^63 + 80 * q^69 + 48 * q^73 - 88 * q^75 - 16 * q^79 + 48 * q^81 + 56 * q^87 - 16 * q^91 - 72 * q^93 - 16 * q^97 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.69899	−	0.336782i	0.980914	−	0.194441i
$3$	1.69899	−	0.336782i	0.980914	−	0.194441i
$4$		0			0
$5$	−0.595296	+	2.99276i	−0.266225	+	1.33840i	0.583902	+	0.811824i	$0.301525\pi$
$5$	−0.595296	+	2.99276i	−0.266225	+	1.33840i	−0.850127	+	0.526578i	$0.823475\pi$
$6$		0			0
$7$	2.11533	−	0.420765i	0.799519	−	0.159034i	0.221610	−	0.975135i	$-0.428869\pi$
$7$	2.11533	−	0.420765i	0.799519	−	0.159034i	0.577909	+	0.816101i	$0.303869\pi$
$8$		0			0
$9$	2.77316	−	1.14438i	0.924385	−	0.381460i
$10$		0			0
$11$	−1.37013	−	0.915491i	−0.413110	−	0.276031i	0.331599	−	0.943420i	$-0.392412\pi$
$11$	−1.37013	−	0.915491i	−0.413110	−	0.276031i	−0.744709	+	0.667389i	$0.767412\pi$
$12$		0			0
$13$	3.12551	+	3.12551i	0.866861	+	0.866861i	0.992124	−	0.125262i	$-0.0399772\pi$
$13$	3.12551	+	3.12551i	0.866861	+	0.866861i	−0.125262	+	0.992124i	$0.539977\pi$
$14$		0			0
$15$	−0.00349923	+	5.28516i	−0.000903497	+	1.36462i
$16$		0			0
$17$	−3.95657	+	1.15998i	−0.959609	+	0.281336i
$17$	−3.95657	+	1.15998i	−0.959609	+	0.281336i
$18$		0			0
$19$	0.330416	+	0.797694i	0.0758025	+	0.183004i	0.957238	−	0.289300i	$-0.0934226\pi$
$19$	0.330416	+	0.797694i	0.0758025	+	0.183004i	−0.881436	+	0.472304i	$0.843423\pi$
$20$		0			0
$21$	3.45222	−	1.42728i	0.753337	−	0.311458i
$22$		0			0
$23$	0.425893	−	0.637394i	0.0888049	−	0.132906i	−0.784407	−	0.620246i	$-0.787033\pi$
$23$	0.425893	−	0.637394i	0.0888049	−	0.132906i	0.873212	+	0.487340i	$0.162033\pi$
$24$		0			0
$25$	−3.98282	−	1.64974i	−0.796563	−	0.329947i
$26$		0			0
$27$	4.32617	−	2.87824i	0.832571	−	0.553918i
$28$		0			0
$29$	7.83789	+	1.55905i	1.45546	+	0.289509i	0.858521	−	0.512778i	$-0.171384\pi$
$29$	7.83789	+	1.55905i	1.45546	+	0.289509i	0.596938	+	0.802287i	$0.296384\pi$
$30$		0			0
$31$	−1.60475	−	2.40167i	−0.288221	−	0.431353i	0.658900	−	0.752231i	$-0.271022\pi$
$31$	−1.60475	−	2.40167i	−0.288221	−	0.431353i	−0.947121	+	0.320878i	$0.896022\pi$
$32$		0			0
$33$	−2.63616	−	1.09398i	−0.458897	−	0.190437i
$34$		0			0
$35$			6.58114i			1.11242i
$36$		0			0
$37$	−1.98027	+	1.32318i	−0.325555	+	0.217529i	−0.707597	−	0.706616i	$-0.750221\pi$
$37$	−1.98027	+	1.32318i	−0.325555	+	0.217529i	0.382042	+	0.924145i	$0.375221\pi$
$38$		0			0
$39$	6.36284	+	4.25761i	1.01887	+	0.681763i
$40$		0			0
$41$	−0.600791	−	3.02038i	−0.0938278	−	0.471704i	−0.998919	−	0.0464865i	$-0.985198\pi$
$41$	−0.600791	−	3.02038i	−0.0938278	−	0.471704i	0.905091	−	0.425218i	$-0.139802\pi$
$42$		0			0
$43$	−4.38037	+	10.5751i	−0.668000	+	1.61269i	0.116952	+	0.993138i	$0.462688\pi$
$43$	−4.38037	+	10.5751i	−0.668000	+	1.61269i	−0.784952	+	0.619557i	$0.787312\pi$
$44$		0			0
$45$	1.77400	+	8.98063i	0.264452	+	1.33875i
$46$		0			0
$47$	−2.21238	+	2.21238i	−0.322708	+	0.322708i	−0.849805	−	0.527097i	$-0.823281\pi$
$47$	−2.21238	+	2.21238i	−0.322708	+	0.322708i	0.527097	+	0.849805i	$0.323281\pi$
$48$		0			0
$49$	−2.16958	+	0.898671i	−0.309940	+	0.128382i
$50$		0			0
$51$	−6.33153	+	3.30330i	−0.886591	+	0.462554i
$52$		0			0
$53$	5.88369	−	2.43710i	0.808187	−	0.334762i	0.0599567	−	0.998201i	$-0.480904\pi$
$53$	5.88369	−	2.43710i	0.808187	−	0.334762i	0.748230	+	0.663439i	$0.230904\pi$
$54$		0			0
$55$	3.55548	−	3.55548i	0.479420	−	0.479420i
$56$		0			0
$57$	0.830022	+	1.24400i	0.109939	+	0.164772i
$58$		0			0
$59$	2.33146	−	5.62864i	0.303530	−	0.732786i	−0.696356	−	0.717696i	$-0.745197\pi$
$59$	2.33146	−	5.62864i	0.303530	−	0.732786i	0.999886	−	0.0150898i	$-0.00480343\pi$
$60$		0			0
$61$	−1.14061	−	5.73423i	−0.146040	−	0.734193i	−0.982514	−	0.186187i	$-0.940387\pi$
$61$	−1.14061	−	5.73423i	−0.146040	−	0.734193i	0.836474	−	0.548006i	$-0.184613\pi$
$62$		0			0
$63$	5.38462	−	3.58759i	0.678399	−	0.451993i
$64$		0			0
$65$	−11.2145	+	7.49329i	−1.39099	+	0.929429i
$66$		0			0
$67$		−	7.19481i		−	0.878985i	−0.898246	−	0.439493i	$-0.855158\pi$
$67$		−	7.19481i		−	0.878985i	0.898246	−	0.439493i	$-0.144842\pi$
$68$		0			0
$69$	0.508927	−	1.22636i	0.0612676	−	0.147637i
$70$		0			0
$71$	1.20808	+	1.80802i	0.143373	+	0.214573i	0.896205	−	0.443639i	$-0.146313\pi$
$71$	1.20808	+	1.80802i	0.143373	+	0.214573i	−0.752832	+	0.658212i	$0.771313\pi$
$72$		0			0
$73$	12.3377	+	2.45412i	1.44402	+	0.287233i	0.854049	−	0.520193i	$-0.174140\pi$
$73$	12.3377	+	2.45412i	1.44402	+	0.287233i	0.589969	+	0.807426i	$0.299140\pi$
$74$		0			0
$75$	−7.32238	−	1.46155i	−0.845516	−	0.168766i
$76$		0			0
$77$	−3.28348	−	1.36006i	−0.374187	−	0.154994i
$78$		0			0
$79$	3.31013	−	4.95397i	0.372419	−	0.557365i	−0.597166	−	0.802117i	$-0.703707\pi$
$79$	3.31013	−	4.95397i	0.372419	−	0.557365i	0.969586	+	0.244753i	$0.0787068\pi$
$80$		0			0
$81$	6.38079	−	6.34708i	0.708977	−	0.705232i
$82$		0			0
$83$	−4.96993	−	11.9985i	−0.545521	−	1.31700i	−0.920779	−	0.390084i	$-0.872446\pi$
$83$	−4.96993	−	11.9985i	−0.545521	−	1.31700i	0.375258	−	0.926920i	$-0.377554\pi$
$84$		0			0
$85$	−1.11620	−	12.5316i	−0.121069	−	1.35924i
$86$		0			0
$87$	13.8416	+	0.00916431i	1.48397	+	0.000982518i
$88$		0			0
$89$	−3.42023	−	3.42023i	−0.362544	−	0.362544i	0.502205	−	0.864749i	$-0.332522\pi$
$89$	−3.42023	−	3.42023i	−0.362544	−	0.362544i	−0.864749	+	0.502205i	$0.832522\pi$
$90$		0			0
$91$	7.92660	+	5.29638i	0.830933	+	0.555212i
$92$		0			0
$93$	−3.53529	−	3.53997i	−0.366592	−	0.367078i
$94$		0			0
$95$	−2.58400	+	0.513989i	−0.265113	+	0.0527342i
$96$		0			0
$97$	−0.692072	+	3.47928i	−0.0702692	+	0.353267i	−0.999883	−	0.0152668i	$-0.995140\pi$
$97$	−0.692072	+	3.47928i	−0.0702692	+	0.353267i	0.929614	+	0.368534i	$0.120140\pi$
$98$		0			0
$99$	−4.84725	−	0.970853i	−0.487167	−	0.0975744i
$100$		0			0
$101$	3.73948			0.372092			0.186046	−	0.982541i	$-0.440433\pi$
$101$	3.73948			0.372092			0.186046	+	0.982541i	$0.440433\pi$
$102$		0			0
$103$	−9.33404			−0.919710			−0.459855	−	0.887994i	$-0.652099\pi$
$103$	−9.33404			−0.919710			−0.459855	+	0.887994i	$0.652099\pi$
$104$		0			0
$105$	2.21641	+	11.1813i	0.216299	+	1.09119i
$106$		0			0
$107$	−0.368714	+	1.85365i	−0.0356449	+	0.179199i	−0.994506	−	0.104675i	$-0.966620\pi$
$107$	−0.368714	+	1.85365i	−0.0356449	+	0.179199i	0.958862	+	0.283874i	$0.0916198\pi$
$108$		0			0
$109$	4.12226	−	0.819969i	0.394841	−	0.0785388i	0.00632347	−	0.999980i	$-0.497987\pi$
$109$	4.12226	−	0.819969i	0.394841	−	0.0785388i	0.388518	+	0.921441i	$0.372987\pi$
$110$		0			0
$111$	−2.91885	+	2.91499i	−0.277045	+	0.276678i
$112$		0			0
$113$	−13.7072	−	9.15888i	−1.28947	−	0.861595i	−0.293917	−	0.955831i	$-0.594959\pi$
$113$	−13.7072	−	9.15888i	−1.28947	−	0.861595i	−0.995550	+	0.0942363i	$0.969959\pi$
$114$		0			0
$115$	1.65403	+	1.65403i	0.154239	+	0.154239i
$116$		0			0
$117$	12.2443	+	5.09076i	1.13199	+	0.470641i
$118$		0			0
$119$	−7.88137	+	4.11852i	−0.722484	+	0.377544i
$120$		0			0
$121$	−3.17039	−	7.65399i	−0.288217	−	0.695817i
$122$		0			0
$123$	−2.03795	−	4.92927i	−0.183756	−	0.444457i
$124$		0			0
$125$	−1.16808	+	1.74816i	−0.104477	+	0.156360i
$126$		0			0
$127$	−11.3753	−	4.71179i	−1.00939	−	0.418104i	−0.184159	−	0.982896i	$-0.558956\pi$
$127$	−11.3753	−	4.71179i	−1.00939	−	0.418104i	−0.825233	+	0.564792i	$0.808956\pi$
$128$		0			0
$129$	−3.88070	+	19.4423i	−0.341677	+	1.71180i
$130$		0			0
$131$	−3.45873	−	0.687984i	−0.302191	−	0.0601094i	0.0416661	−	0.999132i	$-0.486733\pi$
$131$	−3.45873	−	0.687984i	−0.302191	−	0.0601094i	−0.343857	+	0.939022i	$0.611733\pi$
$132$		0			0
$133$	1.03458	+	1.54836i	0.0897094	+	0.134260i
$134$		0			0
$135$	6.03852	+	14.6606i	0.519713	+	1.26178i
$136$		0			0
$137$		−	14.6484i		−	1.25150i	−0.780025	−	0.625748i	$-0.784794\pi$
$137$		−	14.6484i		−	1.25150i	0.780025	−	0.625748i	$-0.215206\pi$
$138$		0			0
$139$	4.19445	−	2.80264i	0.355768	−	0.237717i	−0.364823	−	0.931077i	$-0.618870\pi$
$139$	4.19445	−	2.80264i	0.355768	−	0.237717i	0.720591	+	0.693360i	$0.243870\pi$
$140$		0			0
$141$	−3.01373	+	4.50390i	−0.253802	+	0.379297i
$142$		0			0
$143$	−1.42098	−	7.14374i	−0.118828	−	0.597389i
$144$		0			0
$145$	−9.33173	+	22.5288i	−0.774958	+	1.87091i
$146$		0			0
$147$	−3.38345	+	2.25751i	−0.279062	+	0.186196i
$148$		0			0
$149$	−4.44785	+	4.44785i	−0.364382	+	0.364382i	−0.865423	−	0.501041i	$-0.832950\pi$
$149$	−4.44785	+	4.44785i	−0.364382	+	0.364382i	0.501041	+	0.865423i	$0.332950\pi$
$150$		0			0
$151$	14.0551	−	5.82179i	1.14378	−	0.473771i	0.271339	−	0.962484i	$-0.412533\pi$
$151$	14.0551	−	5.82179i	1.14378	−	0.473771i	0.872445	+	0.488713i	$0.162533\pi$
$152$		0			0
$153$	−9.64473	+	7.74462i	−0.779730	+	0.626115i
$154$		0			0
$155$	8.14291	−	3.37291i	0.654055	−	0.270918i
$156$		0			0
$157$	1.74527	−	1.74527i	0.139287	−	0.139287i	−0.634025	−	0.773312i	$-0.718598\pi$
$157$	1.74527	−	1.74527i	0.139287	−	0.139287i	0.773312	+	0.634025i	$0.218598\pi$
$158$		0			0
$159$	9.17558	−	6.12214i	0.727671	−	0.485518i
$160$		0			0
$161$	0.632711	−	1.52750i	0.0498646	−	0.120384i
$162$		0			0
$163$	0.216722	+	1.08953i	0.0169749	+	0.0853388i	0.988344	−	0.152236i	$-0.0486474\pi$
$163$	0.216722	+	1.08953i	0.0169749	+	0.0853388i	−0.971369	+	0.237575i	$0.923647\pi$
$164$		0			0
$165$	4.84331	−	7.23815i	0.377051	−	0.563489i
$166$		0			0
$167$	−16.5131	+	11.0337i	−1.27782	+	0.853815i	−0.994452	−	0.105195i	$-0.966453\pi$
$167$	−16.5131	+	11.0337i	−1.27782	+	0.853815i	−0.283373	+	0.959010i	$0.591453\pi$
$168$		0			0
$169$			6.53766i			0.502897i
$170$		0			0
$171$	1.82916	+	1.83401i	0.139879	+	0.140250i
$172$		0			0
$173$	−6.46476	−	9.67520i	−0.491507	−	0.735591i	0.499946	−	0.866056i	$-0.333353\pi$
$173$	−6.46476	−	9.67520i	−0.491507	−	0.735591i	−0.991453	+	0.130465i	$0.958353\pi$
$174$		0			0
$175$	−9.11912	−	1.81391i	−0.689341	−	0.137118i
$176$		0			0
$177$	2.06551	−	10.3482i	0.155253	−	0.777819i
$178$		0			0
$179$	−0.782216	−	0.324004i	−0.0584656	−	0.0242172i	0.353259	−	0.935526i	$-0.385073\pi$
$179$	−0.782216	−	0.324004i	−0.0584656	−	0.0242172i	−0.411725	+	0.911308i	$0.635073\pi$
$180$		0			0
$181$	−0.796600	+	1.19220i	−0.0592108	+	0.0886152i	−0.859894	−	0.510473i	$-0.829470\pi$
$181$	−0.796600	+	1.19220i	−0.0592108	+	0.0886152i	0.800683	+	0.599088i	$0.204470\pi$
$182$		0			0
$183$	−3.86907	−	9.35828i	−0.286010	−	0.691784i
$184$		0			0
$185$	−2.78110	−	6.71416i	−0.204470	−	0.493635i
$186$		0			0
$187$	6.48296	+	2.03288i	0.474081	+	0.148659i
$188$		0			0
$189$	7.94021	−	7.90873i	0.577565	−	0.575275i
$190$		0			0
$191$	0.509849	+	0.509849i	0.0368914	+	0.0368914i	0.725312	−	0.688420i	$-0.241696\pi$
$191$	0.509849	+	0.509849i	0.0368914	+	0.0368914i	−0.688420	+	0.725312i	$0.741696\pi$
$192$		0			0
$193$	−9.66292	−	6.45656i	−0.695552	−	0.464753i	0.156862	−	0.987621i	$-0.449862\pi$
$193$	−9.66292	−	6.45656i	−0.695552	−	0.464753i	−0.852414	+	0.522867i	$0.824862\pi$
$194$		0			0
$195$	−16.5298	+	16.5079i	−1.18372	+	1.18215i
$196$		0			0
$197$	22.8170	−	4.53858i	1.62564	−	0.323360i	0.703643	−	0.710553i	$-0.251555\pi$
$197$	22.8170	−	4.53858i	1.62564	−	0.323360i	0.921999	+	0.387193i	$0.126555\pi$
$198$		0			0
$199$	−4.70456	+	23.6514i	−0.333497	+	1.67661i	0.342357	+	0.939570i	$0.388775\pi$
$199$	−4.70456	+	23.6514i	−0.333497	+	1.67661i	−0.675854	+	0.737035i	$0.736225\pi$
$200$		0			0
$201$	−2.42308	−	12.2239i	−0.170911	−	0.862209i
$202$		0			0
$203$	17.2357			1.20971
$204$		0			0
$205$	9.39691			0.656309
$206$		0			0
$207$	0.451648	−	2.25498i	0.0313917	−	0.156732i
$208$		0			0
$209$	0.277570	−	1.39544i	0.0191999	−	0.0965244i
$210$		0			0
$211$	−15.3100	+	3.04535i	−1.05398	+	0.209651i	−0.691528	−	0.722350i	$-0.743062\pi$
$211$	−15.3100	+	3.04535i	−1.05398	+	0.209651i	−0.362457	+	0.932000i	$0.618062\pi$
$212$		0			0
$213$	2.66143	+	2.66496i	0.182358	+	0.182600i
$214$		0			0
$215$	−29.0412	−	19.4047i	−1.98059	−	1.32339i
$216$		0			0
$217$	−4.40510	−	4.40510i	−0.299038	−	0.299038i
$218$		0			0
$219$	21.7882	+	0.0144256i	1.47231	+	0.000974794i
$220$		0			0
$221$	−15.9918	−	8.74079i	−1.07573	−	0.587969i
$222$		0			0
$223$	−0.930718	−	2.24695i	−0.0623255	−	0.150467i	0.889648	−	0.456646i	$-0.150949\pi$
$223$	−0.930718	−	2.24695i	−0.0623255	−	0.150467i	−0.951974	+	0.306179i	$0.900949\pi$
$224$		0			0
$225$	−12.9329	−	0.0171254i	−0.862193	−	0.00114169i
$226$		0			0
$227$	−0.780250	+	1.16773i	−0.0517870	+	0.0775048i	−0.856460	−	0.516214i	$-0.827341\pi$
$227$	−0.780250	+	1.16773i	−0.0517870	+	0.0775048i	0.804673	+	0.593719i	$0.202341\pi$
$228$		0			0
$229$	−10.0488	−	4.16234i	−0.664043	−	0.275055i	0.0250960	−	0.999685i	$-0.492011\pi$
$229$	−10.0488	−	4.16234i	−0.664043	−	0.275055i	−0.689139	+	0.724630i	$0.742011\pi$
$230$		0			0
$231$	−6.03666	−	1.20492i	−0.397183	−	0.0792780i
$232$		0			0
$233$	−14.0608	−	2.79686i	−0.921151	−	0.183228i	−0.288334	−	0.957530i	$-0.593101\pi$
$233$	−14.0608	−	2.79686i	−0.921151	−	0.183228i	−0.632817	+	0.774302i	$0.718101\pi$
$234$		0			0
$235$	−5.30409	−	7.93813i	−0.346000	−	0.517826i
$236$		0			0
$237$	3.95549	−	9.53155i	0.256937	−	0.619140i
$238$		0			0
$239$		−	23.7093i		−	1.53362i	−0.641872	−	0.766812i	$-0.721842\pi$
$239$		−	23.7093i		−	1.53362i	0.641872	−	0.766812i	$-0.278158\pi$
$240$		0			0
$241$	2.34007	−	1.56359i	0.150737	−	0.100719i	−0.477914	−	0.878406i	$-0.658607\pi$
$241$	2.34007	−	1.56359i	0.150737	−	0.100719i	0.628652	+	0.777687i	$0.283607\pi$
$242$		0			0
$243$	8.70334	−	12.9326i	0.558320	−	0.829626i
$244$		0			0
$245$	−1.39796	−	7.02801i	−0.0893123	−	0.449003i
$246$		0			0
$247$	−1.46048	+	3.52592i	−0.0929284	+	0.224349i
$248$		0			0
$249$	−12.4847	−	18.7116i	−0.791189	−	1.18580i
$250$		0			0
$251$	10.7058	−	10.7058i	0.675745	−	0.675745i	−0.283289	−	0.959034i	$-0.591426\pi$
$251$	10.7058	−	10.7058i	0.675745	−	0.675745i	0.959034	+	0.283289i	$0.0914257\pi$
$252$		0			0
$253$	−1.16706	+	0.483411i	−0.0733723	+	0.0303918i
$254$		0			0
$255$	−6.11683	−	20.9152i	−0.383050	−	1.30976i
$256$		0			0
$257$	−18.3799	+	7.61319i	−1.14650	+	0.474898i	−0.873360	−	0.487075i	$-0.838064\pi$
$257$	−18.3799	+	7.61319i	−1.14650	+	0.474898i	−0.273145	+	0.961973i	$0.588064\pi$
$258$		0			0
$259$	−3.63218	+	3.63218i	−0.225693	+	0.225693i
$260$		0			0
$261$	23.5198	−	4.64602i	1.45584	−	0.287581i
$262$		0			0
$263$	−0.0501727	+	0.121128i	−0.00309378	+	0.00746905i	−0.925419	−	0.378946i	$-0.876287\pi$
$263$	−0.0501727	+	0.121128i	−0.00309378	+	0.00746905i	0.922325	+	0.386415i	$0.126287\pi$
$264$		0			0
$265$	3.79112	+	19.0593i	0.232887	+	1.17080i
$266$		0			0
$267$	−6.96282	−	4.65908i	−0.426118	−	0.285131i
$268$		0			0
$269$	−4.94355	+	3.30317i	−0.301413	+	0.201398i	−0.697075	−	0.716999i	$-0.745515\pi$
$269$	−4.94355	+	3.30317i	−0.301413	+	0.201398i	0.395661	+	0.918396i	$0.370515\pi$
$270$		0			0
$271$			6.87483i			0.417616i	0.977957	+	0.208808i	$0.0669584\pi$
$271$			6.87483i			0.417616i	−0.977957	+	0.208808i	$0.933042\pi$
$272$		0			0
$273$	15.2510	+	6.32899i	0.923030	+	0.383048i
$274$		0			0
$275$	3.94666	+	5.90659i	0.237992	+	0.356181i
$276$		0			0
$277$	−8.13797	−	1.61874i	−0.488963	−	0.0972608i	−0.0555495	−	0.998456i	$-0.517691\pi$
$277$	−8.13797	−	1.61874i	−0.488963	−	0.0972608i	−0.433414	+	0.901195i	$0.642691\pi$
$278$		0			0
$279$	−7.19863	−	4.82377i	−0.430971	−	0.288792i
$280$		0			0
$281$	12.2411	+	5.07041i	0.730240	+	0.302475i	0.716651	−	0.697432i	$-0.245674\pi$
$281$	12.2411	+	5.07041i	0.730240	+	0.302475i	0.0135893	+	0.999908i	$0.495674\pi$
$282$		0			0
$283$	7.79633	−	11.6680i	0.463444	−	0.693593i	−0.523972	−	0.851735i	$-0.675550\pi$
$283$	7.79633	−	11.6680i	0.463444	−	0.693593i	0.987416	+	0.158142i	$0.0505505\pi$
$284$		0			0
$285$	−4.21709	+	1.74351i	−0.249799	+	0.103276i
$286$		0			0
$287$	−2.54174	−	6.13631i	−0.150034	−	0.362215i
$288$		0			0
$289$	14.3089	−	9.17907i	0.841700	−	0.539945i
$290$		0			0
$291$	−0.00406809	+	6.14435i	−0.000238475	+	0.360188i
$292$		0			0
$293$	18.6721	+	18.6721i	1.09083	+	1.09083i	0.995440	+	0.0953949i	$0.0304114\pi$
$293$	18.6721	+	18.6721i	1.09083	+	1.09083i	0.0953949	+	0.995440i	$0.469589\pi$
$294$		0			0
$295$	15.4572	+	10.3282i	0.899955	+	0.601331i
$296$		0			0
$297$	−8.56241	−	0.0170072i	−0.496842	−	0.000986857i
$298$		0			0
$299$	3.32332	−	0.661049i	0.192193	−	0.0382295i
$300$		0			0
$301$	−4.81627	+	24.2130i	−0.277605	+	1.39561i
$302$		0			0
$303$	6.35335	−	1.25939i	0.364990	−	0.0723499i
$304$		0			0
$305$	17.8402			1.02152
$306$		0			0
$307$	24.4315			1.39438			0.697189	−	0.716887i	$-0.254434\pi$
$307$	24.4315			1.39438			0.697189	+	0.716887i	$0.254434\pi$
$308$		0			0
$309$	−15.8585	+	3.14353i	−0.902157	+	0.178829i
$310$		0			0
$311$	−4.55265	+	22.8877i	−0.258157	+	1.29784i	0.606340	+	0.795206i	$0.292637\pi$
$311$	−4.55265	+	22.8877i	−0.258157	+	1.29784i	−0.864497	+	0.502638i	$0.832363\pi$
$312$		0			0
$313$	1.58360	−	0.314998i	0.0895106	−	0.0178048i	−0.150132	−	0.988666i	$-0.547970\pi$
$313$	1.58360	−	0.314998i	0.0895106	−	0.0178048i	0.239642	+	0.970861i	$0.422970\pi$
$314$		0			0
$315$	7.53133	+	18.2505i	0.424342	+	1.02830i
$316$		0			0
$317$	20.2754	+	13.5476i	1.13878	+	0.760908i	0.974251	−	0.225464i	$-0.0723900\pi$
$317$	20.2754	+	13.5476i	1.13878	+	0.760908i	0.164528	+	0.986372i	$0.447390\pi$
$318$		0			0
$319$	−9.31162	−	9.31162i	−0.521351	−	0.521351i
$320$		0			0
$321$	−0.00216735	+	3.27351i	−0.000120970	+	0.182710i
$322$		0			0
$323$	−2.23262	−	2.77286i	−0.124226	−	0.154286i
$324$		0			0
$325$	−7.29207	−	17.6046i	−0.404491	−	0.976529i
$326$		0			0
$327$	6.72755	−	2.78143i	0.372034	−	0.153813i
$328$		0			0
$329$	−3.74901	+	5.61080i	−0.206690	+	0.309333i
$330$		0			0
$331$	−28.1459	−	11.6584i	−1.54704	−	0.640804i	−0.564260	−	0.825597i	$-0.690839\pi$
$331$	−28.1459	−	11.6584i	−1.54704	−	0.640804i	−0.982777	+	0.184793i	$0.940839\pi$
$332$		0			0
$333$	−3.97739	+	5.93556i	−0.217960	+	0.325267i
$334$		0			0
$335$	21.5323	+	4.28304i	1.17644	+	0.234008i
$336$		0			0
$337$	−9.57025	−	14.3229i	−0.521325	−	0.780218i	0.473611	−	0.880734i	$-0.342950\pi$
$337$	−9.57025	−	14.3229i	−0.521325	−	0.780218i	−0.994935	+	0.100517i	$0.967950\pi$
$338$		0			0
$339$	−26.3730	−	10.9445i	−1.43239	−	0.594425i
$340$		0			0
$341$			4.75973i			0.257754i
$342$		0			0
$343$	−16.7643	+	11.2015i	−0.905186	+	0.604826i
$344$		0			0
$345$	3.36724	+	2.25314i	0.181286	+	0.121305i
$346$		0			0
$347$	3.94759	+	19.8459i	0.211918	+	1.06538i	0.929476	+	0.368884i	$0.120260\pi$
$347$	3.94759	+	19.8459i	0.211918	+	1.06538i	−0.717558	+	0.696499i	$0.754740\pi$
$348$		0			0
$349$	−2.90948	+	7.02410i	−0.155741	+	0.375992i	−0.982421	−	0.186681i	$-0.940227\pi$
$349$	−2.90948	+	7.02410i	−0.155741	+	0.375992i	0.826680	+	0.562673i	$0.190227\pi$
$350$		0			0
$351$	22.5175	+	4.52552i	1.20189	+	0.241554i
$352$		0			0
$353$	8.44344	−	8.44344i	0.449399	−	0.449399i	−0.445756	−	0.895155i	$-0.647065\pi$
$353$	8.44344	−	8.44344i	0.449399	−	0.449399i	0.895155	+	0.445756i	$0.147065\pi$
$354$		0			0
$355$	−6.13014	+	2.53919i	−0.325354	+	0.134766i
$356$		0			0
$357$	−12.0034	+	9.65164i	−0.635285	+	0.510819i
$358$		0			0
$359$	−21.2469	+	8.80076i	−1.12137	+	0.464487i	−0.864839	−	0.502049i	$-0.832580\pi$
$359$	−21.2469	+	8.80076i	−1.12137	+	0.464487i	−0.256531	+	0.966536i	$0.582580\pi$
$360$		0			0
$361$	12.9079	−	12.9079i	0.679363	−	0.679363i
$362$		0			0
$363$	−7.96419	−	11.9364i	−0.418012	−	0.626496i
$364$		0			0
$365$	−14.6892	+	35.4628i	−0.768866	+	1.85621i
$366$		0			0
$367$	3.20154	+	16.0952i	0.167119	+	0.840163i	0.969828	+	0.243792i	$0.0783914\pi$
$367$	3.20154	+	16.0952i	0.167119	+	0.840163i	−0.802709	+	0.596371i	$0.796609\pi$
$368$		0			0
$369$	−5.12255	−	7.68845i	−0.266669	−	0.400245i
$370$		0			0
$371$	11.4205	−	7.63093i	0.592923	−	0.396178i
$372$		0			0
$373$			1.61824i			0.0837894i	0.999122	+	0.0418947i	$0.0133394\pi$
$373$			1.61824i			0.0837894i	−0.999122	+	0.0418947i	$0.986661\pi$
$374$		0			0
$375$	−1.39582	+	3.36351i	−0.0720798	+	0.173691i
$376$		0			0
$377$	19.6246	+	29.3703i	1.01072	+	1.51265i
$378$		0			0
$379$	15.2311	+	3.02965i	0.782368	+	0.155623i	0.570085	−	0.821586i	$-0.306910\pi$
$379$	15.2311	+	3.02965i	0.782368	+	0.155623i	0.212283	+	0.977208i	$0.431910\pi$
$380$		0			0
$381$	−20.9134	−	4.17432i	−1.07142	−	0.213857i
$382$		0			0
$383$	20.4588	+	8.47433i	1.04540	+	0.433018i	0.838247	−	0.545291i	$-0.183581\pi$
$383$	20.4588	+	8.47433i	1.04540	+	0.433018i	0.207151	+	0.978309i	$0.433581\pi$
$384$		0			0
$385$	6.02498	−	9.01702i	0.307061	−	0.459550i
$386$		0			0
$387$	−0.0454712	+	34.3393i	−0.00231143	+	1.74557i
$388$		0			0
$389$	−5.80572	−	14.0162i	−0.294362	−	0.710652i	−0.999998	−	0.00207747i	$-0.999339\pi$
$389$	−5.80572	−	14.0162i	−0.294362	−	0.710652i	0.705636	−	0.708574i	$-0.250661\pi$
$390$		0			0
$391$	−0.945713	+	3.01592i	−0.0478268	+	0.152522i
$392$		0			0
$393$	−6.10806	−	0.00404406i	−0.308111	−	0.000203996i
$394$		0			0
$395$	12.8555	+	12.8555i	0.646831	+	0.646831i
$396$		0			0
$397$	31.2942	+	20.9101i	1.57061	+	1.04945i	0.967850	+	0.251526i	$0.0809325\pi$
$397$	31.2942	+	20.9101i	1.57061	+	1.04945i	0.602760	+	0.797922i	$0.294068\pi$
$398$		0			0
$399$	2.27920	+	2.28222i	0.114103	+	0.114254i
$400$		0			0
$401$	−3.46595	+	0.689420i	−0.173081	+	0.0344280i	−0.280870	−	0.959746i	$-0.590623\pi$
$401$	−3.46595	+	0.689420i	−0.173081	+	0.0344280i	0.107789	+	0.994174i	$0.465623\pi$
$402$		0			0
$403$	2.49080	−	12.5221i	0.124076	−	0.623770i
$404$		0			0
$405$	15.1968	+	22.8746i	0.755136	+	1.13665i
$406$		0			0
$407$	3.92459			0.194535
$408$		0			0
$409$	12.2079			0.603641			0.301820	−	0.953365i	$-0.402406\pi$
$409$	12.2079			0.603641			0.301820	+	0.953365i	$0.402406\pi$
$410$		0			0
$411$	−4.93331	−	24.8875i	−0.243342	−	1.22761i
$412$		0			0
$413$	2.56347	−	12.8874i	0.126140	−	0.634148i
$414$		0			0
$415$	38.8671	−	7.73115i	1.90791	−	0.379507i
$416$		0			0
$417$	6.18246	−	6.17428i	0.302756	−	0.302356i
$418$		0			0
$419$	26.1021	+	17.4409i	1.27517	+	0.852042i	0.994187	−	0.107670i	$-0.0343389\pi$
$419$	26.1021	+	17.4409i	1.27517	+	0.852042i	0.280985	+	0.959712i	$0.409339\pi$
$420$		0			0
$421$	10.7245	+	10.7245i	0.522682	+	0.522682i	0.918380	−	0.395699i	$-0.129498\pi$
$421$	10.7245	+	10.7245i	0.522682	+	0.522682i	−0.395699	+	0.918380i	$0.629498\pi$
$422$		0			0
$423$	−3.60347	+	8.66707i	−0.175207	+	0.421407i
$424$		0			0
$425$	17.6720	+	1.90732i	0.857216	+	0.0925185i
$426$		0			0
$427$	−4.82553	−	11.6499i	−0.233524	−	0.563776i
$428$		0			0
$429$	−4.82011	−	11.6586i	−0.232717	−	0.562883i
$430$		0			0
$431$	−6.36331	+	9.52337i	−0.306510	+	0.458724i	−0.952464	−	0.304652i	$-0.901460\pi$
$431$	−6.36331	+	9.52337i	−0.306510	+	0.458724i	0.645954	+	0.763376i	$0.276460\pi$
$432$		0			0
$433$	−24.7526	−	10.2528i	−1.18953	−	0.492720i	−0.301930	−	0.953330i	$-0.597631\pi$
$433$	−24.7526	−	10.2528i	−1.18953	−	0.492720i	−0.887603	+	0.460610i	$0.847631\pi$
$434$		0			0
$435$	−8.26727	+	41.4190i	−0.396385	+	1.98589i
$436$		0			0
$437$	0.649167	+	0.129127i	0.0310539	+	0.00617700i
$438$		0			0
$439$	−4.73699	−	7.08940i	−0.226084	−	0.338359i	0.701034	−	0.713128i	$-0.252722\pi$
$439$	−4.73699	−	7.08940i	−0.226084	−	0.338359i	−0.927118	+	0.374769i	$0.877722\pi$
$440$		0			0
$441$	−4.98817	+	4.97498i	−0.237532	+	0.236904i
$442$		0			0
$443$		−	18.8773i		−	0.896886i	−0.893811	−	0.448443i	$-0.851979\pi$
$443$		−	18.8773i		−	0.896886i	0.893811	−	0.448443i	$-0.148021\pi$
$444$		0			0
$445$	12.2720	−	8.19987i	0.581747	−	0.388711i
$446$		0			0
$447$	−6.05891	+	9.05482i	−0.286577	+	0.428278i
$448$		0			0
$449$	5.31908	+	26.7408i	0.251023	+	1.26198i	0.876373	+	0.481633i	$0.159956\pi$
$449$	5.31908	+	26.7408i	0.251023	+	1.26198i	−0.625350	+	0.780345i	$0.715044\pi$
$450$		0			0
$451$	−1.94197	+	4.68833i	−0.0914438	+	0.220765i
$452$		0			0
$453$	21.9188	−	14.6247i	1.02983	−	0.687127i
$454$		0			0
$455$	−20.5695	+	20.5695i	−0.964311	+	0.964311i
$456$		0			0
$457$	9.73907	−	4.03405i	0.455574	−	0.188705i	−0.143082	−	0.989711i	$-0.545701\pi$
$457$	9.73907	−	4.03405i	0.455574	−	0.188705i	0.598657	+	0.801006i	$0.295701\pi$
$458$		0			0
$459$	−13.7781	+	16.4062i	−0.643106	+	0.765777i
$460$		0			0
$461$	9.13414	−	3.78349i	0.425419	−	0.176215i	−0.159693	−	0.987167i	$-0.551050\pi$
$461$	9.13414	−	3.78349i	0.425419	−	0.176215i	0.585112	+	0.810952i	$0.301050\pi$
$462$		0			0
$463$	16.2123	−	16.2123i	0.753448	−	0.753448i	−0.221673	−	0.975121i	$-0.571152\pi$
$463$	16.2123	−	16.2123i	0.753448	−	0.753448i	0.975121	+	0.221673i	$0.0711518\pi$
$464$		0			0
$465$	12.6988	−	8.47293i	0.588894	−	0.392923i
$466$		0			0
$467$	−9.89105	+	23.8791i	−0.457703	+	1.10499i	0.511621	+	0.859211i	$0.329045\pi$
$467$	−9.89105	+	23.8791i	−0.457703	+	1.10499i	−0.969325	+	0.245783i	$0.920955\pi$
$468$		0			0
$469$	−3.02732	−	15.2194i	−0.139789	−	0.702766i
$470$		0			0
$471$	2.37742	−	3.55297i	0.109546	−	0.163712i
$472$		0			0
$473$	15.6831	−	10.4791i	0.721111	−	0.481831i
$474$		0			0
$475$		−	3.72217i		−	0.170785i
$476$		0			0
$477$	13.5274	−	13.4916i	0.619378	−	0.617740i
$478$		0			0
$479$	4.81385	+	7.20443i	0.219950	+	0.329179i	0.924992	−	0.379987i	$-0.124072\pi$
$479$	4.81385	+	7.20443i	0.219950	+	0.329179i	−0.705041	+	0.709166i	$0.749072\pi$
$480$		0			0
$481$	−10.3250	−	2.05377i	−0.470778	−	0.0936437i
$482$		0			0
$483$	0.560538	−	2.80830i	0.0255054	−	0.127782i
$484$		0			0
$485$	−10.0006	−	4.14240i	−0.454106	−	0.188097i
$486$		0			0
$487$	21.5656	−	32.2752i	0.977229	−	1.46253i	0.0928931	−	0.995676i	$-0.470389\pi$
$487$	21.5656	−	32.2752i	0.977229	−	1.46253i	0.884336	−	0.466851i	$-0.154611\pi$
$488$		0			0
$489$	0.735143	+	1.77812i	0.0332443	+	0.0804094i
$490$		0			0
$491$	−4.84934	−	11.7073i	−0.218848	−	0.528345i	0.775882	−	0.630878i	$-0.217305\pi$
$491$	−4.84934	−	11.7073i	−0.218848	−	0.528345i	−0.994730	+	0.102533i	$0.967305\pi$
$492$		0			0
$493$	−32.8196	+	2.92328i	−1.47812	+	0.131658i
$494$		0			0
$495$	5.79108	−	13.9287i	0.260290	−	0.626049i
$496$		0			0
$497$	3.31625	+	3.31625i	0.148754	+	0.148754i
$498$		0			0
$499$	30.8610	+	20.6206i	1.38153	+	0.923106i	0.999999	−	0.00125143i	$-0.000398342\pi$
$499$	30.8610	+	20.6206i	1.38153	+	0.923106i	0.381527	+	0.924358i	$0.375398\pi$
$500$		0			0
$501$	−24.3397	+	24.3075i	−1.08742	+	1.08598i
$502$		0			0
$503$	31.3353	−	6.23297i	1.39717	−	0.277914i	0.561650	−	0.827375i	$-0.310167\pi$
$503$	31.3353	−	6.23297i	1.39717	−	0.277914i	0.835520	+	0.549460i	$0.185167\pi$
$504$		0			0
$505$	−2.22610	+	11.1913i	−0.0990600	+	0.498008i
$506$		0			0
$507$	2.20176	+	11.1074i	0.0977838	+	0.493299i
$508$		0			0
$509$	−2.30289			−0.102074			−0.0510369	−	0.998697i	$-0.516253\pi$
$509$	−2.30289			−0.102074			−0.0510369	+	0.998697i	$0.516253\pi$
$510$		0			0
$511$	27.1309			1.20020
$512$		0			0
$513$	3.72539	+	2.49994i	0.164480	+	0.110375i
$514$		0			0
$515$	5.55652	−	27.9345i	0.244849	−	1.23094i
$516$		0			0
$517$	5.05666	−	1.00583i	0.222391	−	0.0442364i
$518$		0			0
$519$	−14.2420	−	14.2609i	−0.625155	−	0.625983i
$520$		0			0
$521$	−2.28875	−	1.52929i	−0.100272	−	0.0669995i	0.504423	−	0.863456i	$-0.331705\pi$
$521$	−2.28875	−	1.52929i	−0.100272	−	0.0669995i	−0.604695	+	0.796457i	$0.706705\pi$
$522$		0			0
$523$	−29.8001	−	29.8001i	−1.30307	−	1.30307i	−0.926313	−	0.376755i	$-0.877040\pi$
$523$	−29.8001	−	29.8001i	−1.30307	−	1.30307i	−0.376755	−	0.926313i	$-0.622960\pi$
$524$		0			0
$525$	−16.1042	−	0.0106624i	−0.702846	−	0.000465344i
$526$		0			0
$527$	9.13517	+	7.64091i	0.397934	+	0.332843i
$528$		0			0
$529$	8.57683	+	20.7063i	0.372906	+	0.900274i
$530$		0			0
$531$	0.0242021	−	18.2772i	0.00105028	−	0.793161i
$532$		0			0
$533$	7.56246	−	11.3180i	0.327566	−	0.490238i
$534$		0			0
$535$	−5.32803	−	2.20694i	−0.230351	−	0.0954144i
$536$		0			0
$537$	−1.43810	−	0.287045i	−0.0620585	−	0.0123869i
$538$		0			0
$539$	3.79534	+	0.754939i	0.163477	+	0.0325175i
$540$		0			0
$541$	−8.13164	−	12.1699i	−0.349606	−	0.523223i	0.614438	−	0.788965i	$-0.289383\pi$
$541$	−8.13164	−	12.1699i	−0.349606	−	0.523223i	−0.964044	+	0.265742i	$0.914383\pi$
$542$		0			0
$543$	−0.951908	+	2.29381i	−0.0408503	+	0.0984369i
$544$		0			0
$545$			12.8251i			0.549365i
$546$		0			0
$547$	−22.8049	+	15.2378i	−0.975068	+	0.651520i	−0.937577	−	0.347777i	$-0.886937\pi$
$547$	−22.8049	+	15.2378i	−0.975068	+	0.651520i	−0.0374912	+	0.999297i	$0.511937\pi$
$548$		0			0
$549$	−9.72522	−	14.5966i	−0.415062	−	0.622969i
$550$		0			0
$551$	1.34611	+	6.76737i	0.0573464	+	0.288300i
$552$		0			0
$553$	4.91757	−	11.8721i	0.209116	−	0.504851i
$554$		0			0
$555$	−6.98627	−	10.4707i	−0.296551	−	0.444456i
$556$		0			0
$557$	−31.0707	+	31.0707i	−1.31651	+	1.31651i	−0.399984	+	0.916522i	$0.630984\pi$
$557$	−31.0707	+	31.0707i	−1.31651	+	1.31651i	−0.916522	+	0.399984i	$0.869016\pi$
$558$		0			0
$559$	−46.7436	+	19.3619i	−1.97705	+	0.818919i
$560$		0			0
$561$	11.6992	+	1.27052i	0.493939	+	0.0536412i
$562$		0			0
$563$	−33.9044	+	14.0437i	−1.42890	+	0.591870i	−0.957080	−	0.289825i	$-0.906403\pi$
$563$	−33.9044	+	14.0437i	−1.42890	+	0.591870i	−0.471821	+	0.881695i	$0.656403\pi$
$564$		0			0
$565$	35.5701	−	35.5701i	1.49645	−	1.49645i
$566$		0			0
$567$	10.8268	−	16.1110i	0.454685	−	0.676598i
$568$		0			0
$569$	9.46803	−	22.8578i	0.396920	−	0.958251i	−0.591472	−	0.806326i	$-0.701453\pi$
$569$	9.46803	−	22.8578i	0.396920	−	0.958251i	0.988392	−	0.151925i	$-0.0485472\pi$
$570$		0			0
$571$	−0.384503	−	1.93303i	−0.0160910	−	0.0808947i	0.971905	−	0.235372i	$-0.0756307\pi$
$571$	−0.384503	−	1.93303i	−0.0160910	−	0.0808947i	−0.987996	+	0.154477i	$0.950631\pi$
$572$		0			0
$573$	1.03794	+	0.694522i	0.0433605	+	0.0290141i
$574$		0			0
$575$	−2.74779	+	1.83601i	−0.114591	+	0.0765671i
$576$		0			0
$577$			26.8179i			1.11645i	0.829691	+	0.558223i	$0.188517\pi$
$577$			26.8179i			1.11645i	−0.829691	+	0.558223i	$0.811483\pi$
$578$		0			0
$579$	−18.5917	−	7.71536i	−0.772644	−	0.320639i
$580$		0			0
$581$	−15.5616	−	23.2896i	−0.645603	−	0.966214i
$582$		0			0
$583$	−10.2926	−	2.04732i	−0.426275	−	0.0847913i
$584$		0			0
$585$	−22.5244	+	33.6137i	−0.931270	+	1.38976i
$586$		0			0
$587$	41.3023	+	17.1080i	1.70473	+	0.706122i	0.999994	−	0.00334911i	$-0.00106606\pi$
$587$	41.3023	+	17.1080i	1.70473	+	0.706122i	0.704735	+	0.709471i	$0.251066\pi$
$588$		0			0
$589$	1.38557	−	2.07364i	0.0570912	−	0.0854430i
$590$		0			0
$591$	37.2374	−	15.3953i	1.53174	−	0.633280i
$592$		0			0
$593$	−8.44534	−	20.3889i	−0.346809	−	0.837270i	−0.996993	−	0.0774935i	$-0.975308\pi$
$593$	−8.44534	−	20.3889i	−0.346809	−	0.837270i	0.650184	−	0.759777i	$-0.274692\pi$
$594$		0			0
$595$	−7.63399	−	26.0388i	−0.312963	−	1.06749i
$596$		0			0
$597$	−0.0276540	+	41.7680i	−0.00113180	+	1.70945i
$598$		0			0
$599$	−16.9345	−	16.9345i	−0.691926	−	0.691926i	0.270729	−	0.962655i	$-0.412735\pi$
$599$	−16.9345	−	16.9345i	−0.691926	−	0.691926i	−0.962655	+	0.270729i	$0.912735\pi$
$600$		0			0
$601$	2.19329	+	1.46551i	0.0894662	+	0.0597794i	0.599499	−	0.800376i	$-0.295367\pi$
$601$	2.19329	+	1.46551i	0.0894662	+	0.0597794i	−0.510033	+	0.860155i	$0.670367\pi$
$602$		0			0
$603$	−8.23359	−	19.9523i	−0.335298	−	0.812521i
$604$		0			0
$605$	24.7939	−	4.93180i	1.00801	−	0.200506i
$606$		0			0
$607$	−7.07635	+	35.5752i	−0.287220	+	1.44395i	0.520234	+	0.854024i	$0.325845\pi$
$607$	−7.07635	+	35.5752i	−0.287220	+	1.44395i	−0.807454	+	0.589930i	$0.799155\pi$
$608$		0			0
$609$	29.2833	−	5.80467i	1.18662	−	0.235217i
$610$		0			0
$611$	−13.8296			−0.559487
$612$		0			0
$613$	−25.0887			−1.01333			−0.506663	−	0.862144i	$-0.669121\pi$
$613$	−25.0887			−1.01333			−0.506663	+	0.862144i	$0.669121\pi$
$614$		0			0
$615$	15.9653	−	3.16471i	0.643783	−	0.127613i
$616$		0			0
$617$	−1.92552	+	9.68025i	−0.0775186	+	0.389712i	0.922475	+	0.386057i	$0.126163\pi$
$617$	−1.92552	+	9.68025i	−0.0775186	+	0.389712i	−0.999993	+	0.00365472i	$0.998837\pi$
$618$		0			0
$619$	−31.6886	+	6.30326i	−1.27367	+	0.253349i	−0.785207	−	0.619233i	$-0.787443\pi$
$619$	−31.6886	+	6.30326i	−1.27367	+	0.253349i	−0.488466	+	0.872583i	$0.662443\pi$
$620$		0			0
$621$	0.00791187	−	3.98330i	0.000317492	−	0.159844i
$622$		0			0
$623$	−8.67402	−	5.79580i	−0.347517	−	0.232204i
$624$		0			0
$625$	−19.7780	−	19.7780i	−0.791122	−	0.791122i
$626$		0			0
$627$	0.00163159	−	2.46432i	6.51594e−5	−	0.0984154i
$628$		0			0
$629$	6.30024	−	7.53232i	0.251207	−	0.300333i
$630$		0			0
$631$	1.47845	+	3.56930i	0.0588563	+	0.142092i	0.950572	−	0.310504i	$-0.100498\pi$
$631$	1.47845	+	3.56930i	0.0588563	+	0.142092i	−0.891716	+	0.452596i	$0.850498\pi$
$632$		0			0
$633$	−24.9860	+	10.3302i	−0.993104	+	0.410587i
$634$		0			0
$635$	20.8729	−	31.2385i	0.828316	−	1.23966i
$636$		0			0
$637$	−9.58987	−	3.97225i	−0.379964	−	0.157386i
$638$		0			0
$639$	5.41927	+	3.63143i	0.214383	+	0.143657i
$640$		0			0
$641$	36.7015	+	7.30038i	1.44962	+	0.288348i	0.856242	−	0.516575i	$-0.172793\pi$
$641$	36.7015	+	7.30038i	1.44962	+	0.288348i	0.593380	+	0.804922i	$0.297793\pi$
$642$		0			0
$643$	23.5997	+	35.3195i	0.930682	+	1.39286i	0.919570	+	0.392925i	$0.128537\pi$
$643$	23.5997	+	35.3195i	0.930682	+	1.39286i	0.0111111	+	0.999938i	$0.496463\pi$
$644$		0			0
$645$	−55.8760	−	23.1879i	−2.20011	−	0.913024i
$646$		0			0
$647$			48.3331i			1.90017i	0.311989	+	0.950086i	$0.399005\pi$
$647$			48.3331i			1.90017i	−0.311989	+	0.950086i	$0.600995\pi$
$648$		0			0
$649$	−8.34737	+	5.57753i	−0.327663	+	0.218937i
$650$		0			0
$651$	−8.96780	−	6.00068i	−0.351476	−	0.235185i
$652$		0			0
$653$	1.26227	+	6.34586i	0.0493965	+	0.248333i	0.997592	−	0.0693542i	$-0.0220939\pi$
$653$	1.26227	+	6.34586i	0.0493965	+	0.248333i	−0.948196	+	0.317687i	$0.897094\pi$
$654$		0			0
$655$	4.11794	−	9.94158i	0.160901	−	0.388450i
$656$		0			0
$657$	37.0228	−	7.31334i	1.44440	−	0.285321i
$658$		0			0
$659$	17.7005	−	17.7005i	0.689515	−	0.689515i	−0.272610	−	0.962125i	$-0.587887\pi$
$659$	17.7005	−	17.7005i	0.689515	−	0.689515i	0.962125	+	0.272610i	$0.0878869\pi$
$660$		0			0
$661$	−23.0223	+	9.53615i	−0.895464	+	0.370913i	−0.782474	−	0.622683i	$-0.786043\pi$
$661$	−23.0223	+	9.53615i	−0.895464	+	0.370913i	−0.112990	+	0.993596i	$0.536043\pi$
$662$		0			0
$663$	−30.1138	−	9.46478i	−1.16952	−	0.367582i
$664$		0			0
$665$	−5.24974	+	2.17451i	−0.203576	+	0.0843240i
$666$		0			0
$667$	4.33184	−	4.33184i	0.167729	−	0.167729i
$668$		0			0
$669$	−2.33802	−	3.50411i	−0.0903929	−	0.135477i
$670$		0			0
$671$	−3.68686	+	8.90086i	−0.142329	+	0.343614i
$672$		0			0
$673$	3.66436	+	18.4220i	0.141251	+	0.710115i	0.984887	+	0.173200i	$0.0554106\pi$
$673$	3.66436	+	18.4220i	0.141251	+	0.710115i	−0.843636	+	0.536915i	$0.819589\pi$
$674$		0			0
$675$	−21.9787	+	4.32647i	−0.845960	+	0.166526i
$676$		0			0
$677$	−8.24041	+	5.50607i	−0.316705	+	0.211615i	−0.703754	−	0.710444i	$-0.748494\pi$
$677$	−8.24041	+	5.50607i	−0.316705	+	0.211615i	0.387049	+	0.922059i	$0.373494\pi$
$678$		0			0
$679$			7.65102i			0.293619i
$680$		0			0
$681$	−0.932371	+	2.24673i	−0.0357285	+	0.0860950i
$682$		0			0
$683$	1.32660	+	1.98540i	0.0507610	+	0.0759692i	0.855982	−	0.517006i	$-0.172953\pi$
$683$	1.32660	+	1.98540i	0.0507610	+	0.0759692i	−0.805221	+	0.592975i	$0.797953\pi$
$684$		0			0
$685$	43.8391	+	8.72013i	1.67500	+	0.333179i
$686$		0			0
$687$	−18.4746	−	3.68755i	−0.704851	−	0.140689i
$688$		0			0
$689$	26.0068	+	10.7724i	0.990779	+	0.410394i
$690$		0			0
$691$	−18.1140	+	27.1095i	−0.689088	+	1.03129i	0.307722	+	0.951476i	$0.400433\pi$
$691$	−18.1140	+	27.1095i	−0.689088	+	1.03129i	−0.996810	+	0.0798165i	$0.974567\pi$
$692$		0			0
$693$	−10.6620	−	0.0141184i	−0.405017	−	0.000536313i
$694$		0			0
$695$	5.89068	+	14.2214i	0.223446	+	0.539447i
$696$		0			0
$697$	5.88065	+	11.2534i	0.222745	+	0.426254i
$698$		0			0
$699$	−24.8311	−	0.0164403i	−0.939197	−	0.000621829i
$700$		0			0
$701$	−31.7150	−	31.7150i	−1.19786	−	1.19786i	−0.974807	−	0.223051i	$-0.928398\pi$
$701$	−31.7150	−	31.7150i	−1.19786	−	1.19786i	−0.223051	−	0.974807i	$-0.571602\pi$
$702$		0			0
$703$	−1.70980	−	1.14245i	−0.0644864	−	0.0430885i
$704$		0			0
$705$	−11.6850	−	11.7005i	−0.440083	−	0.440667i
$706$		0			0
$707$	7.91022	−	1.57344i	0.297495	−	0.0591753i
$708$		0			0
$709$	−7.70314	+	38.7263i	−0.289297	+	1.45440i	0.513472	+	0.858106i	$0.328359\pi$
$709$	−7.70314	+	38.7263i	−0.289297	+	1.45440i	−0.802769	+	0.596290i	$0.796641\pi$
$710$		0			0
$711$	3.51030	−	17.5262i	0.131647	−	0.657283i
$712$		0			0
$713$	−2.21426			−0.0829248
$714$		0			0
$715$	22.2254			0.831182
$716$		0			0
$717$	−7.98484	−	40.2819i	−0.298199	−	1.50435i
$718$		0			0
$719$	8.57373	−	43.1030i	0.319746	−	1.60747i	−0.402220	−	0.915543i	$-0.631761\pi$
$719$	8.57373	−	43.1030i	0.319746	−	1.60747i	0.721966	−	0.691929i	$-0.243239\pi$
$720$		0			0
$721$	−19.7446	+	3.92744i	−0.735326	+	0.146265i
$722$		0			0
$723$	3.44918	−	3.44461i	0.128276	−	0.128107i
$724$		0			0
$725$	−28.6448	−	19.1399i	−1.06384	−	0.710837i
$726$		0			0
$727$	0.0802760	+	0.0802760i	0.00297727	+	0.00297727i	0.708594	−	0.705617i	$-0.249330\pi$
$727$	0.0802760	+	0.0802760i	0.00297727	+	0.00297727i	−0.705617	+	0.708594i	$0.749330\pi$
$728$		0			0
$729$	10.4315	−	24.9035i	0.386351	−	0.922352i
$730$		0			0
$731$	5.06429	−	46.9224i	0.187310	−	1.73549i
$732$		0			0
$733$	−3.12587	−	7.54651i	−0.115457	−	0.278737i	0.855579	−	0.517673i	$-0.173201\pi$
$733$	−3.12587	−	7.54651i	−0.115457	−	0.278737i	−0.971035	+	0.238936i	$0.923201\pi$
$734$		0			0
$735$	−4.74203	−	11.4697i	−0.174912	−	0.423068i
$736$		0			0
$737$	−6.58678	+	9.85781i	−0.242627	+	0.363117i
$738$		0			0
$739$	10.8531	+	4.49550i	0.399237	+	0.165370i	0.573263	−	0.819372i	$-0.305677\pi$
$739$	10.8531	+	4.49550i	0.399237	+	0.165370i	−0.174025	+	0.984741i	$0.555677\pi$
$740$		0			0
$741$	−1.29389	+	6.48238i	−0.0475322	+	0.238136i
$742$		0			0
$743$	−40.2557	−	8.00737i	−1.47684	−	0.293762i	−0.610021	−	0.792385i	$-0.708839\pi$
$743$	−40.2557	−	8.00737i	−1.47684	−	0.293762i	−0.866819	+	0.498623i	$0.833839\pi$
$744$		0			0
$745$	−10.6635	−	15.9591i	−0.390682	−	0.584697i
$746$		0			0
$747$	−27.5132	−	27.5862i	−1.00666	−	1.00933i
$748$		0			0
$749$			4.07622i			0.148942i
$750$		0			0
$751$	1.40436	−	0.938366i	0.0512460	−	0.0342414i	−0.529683	−	0.848195i	$-0.677689\pi$
$751$	1.40436	−	0.938366i	0.0512460	−	0.0342414i	0.580929	+	0.813954i	$0.302689\pi$
$752$		0			0
$753$	14.5836	−	21.7946i	0.531456	−	0.794241i
$754$		0			0
$755$	9.05629	+	45.5290i	0.329592	+	1.65697i
$756$		0			0
$757$	−20.8300	+	50.2881i	−0.757080	+	1.82775i	−0.242954	+	0.970038i	$0.578116\pi$
$757$	−20.8300	+	50.2881i	−0.757080	+	1.82775i	−0.514126	+	0.857715i	$0.671884\pi$
$758$		0			0
$759$	−1.82002	+	1.21436i	−0.0660625	+	0.0440783i
$760$		0			0
$761$	24.1395	−	24.1395i	0.875055	−	0.875055i	−0.117963	−	0.993018i	$-0.537636\pi$
$761$	24.1395	−	24.1395i	0.875055	−	0.875055i	0.993018	+	0.117963i	$0.0376365\pi$
$762$		0			0
$763$	8.37493	−	3.46901i	0.303193	−	0.125587i
$764$		0			0
$765$	−17.4363	−	33.4747i	−0.630410	−	1.21028i
$766$		0			0
$767$	24.8794	−	10.3054i	0.898343	−	0.372106i
$768$		0			0
$769$	31.3211	−	31.3211i	1.12947	−	1.12947i	0.139204	−	0.990264i	$-0.455546\pi$
$769$	31.3211	−	31.3211i	1.12947	−	1.12947i	0.990264	−	0.139204i	$-0.0444544\pi$
$770$		0			0
$771$	−28.6633	+	19.1248i	−1.03228	+	0.688761i
$772$		0			0
$773$	5.31114	−	12.8222i	0.191028	−	0.461184i	−0.799126	−	0.601164i	$-0.794704\pi$
$773$	5.31114	−	12.8222i	0.191028	−	0.461184i	0.990154	+	0.139980i	$0.0447039\pi$
$774$		0			0
$775$	2.42928	+	12.2128i	0.0872624	+	0.438698i
$776$		0			0
$777$	−4.94780	+	7.39431i	−0.177501	+	0.265269i
$778$		0			0
$779$	2.21083	−	1.47723i	0.0792111	−	0.0529272i
$780$		0			0
$781$		−	3.58322i		−	0.128218i
$782$		0			0
$783$	38.3954	−	15.8146i	1.37214	−	0.565168i
$784$		0			0
$785$	4.18421	+	6.26211i	0.149341	+	0.223504i
$786$		0			0
$787$	23.4782	+	4.67010i	0.836907	+	0.166471i	0.594896	−	0.803802i	$-0.297193\pi$
$787$	23.4782	+	4.67010i	0.836907	+	0.166471i	0.242011	+	0.970274i	$0.422193\pi$
$788$		0			0
$789$	−0.0444496	+	0.222692i	−0.00158245	+	0.00792806i
$790$		0			0
$791$	−32.8490	−	13.6065i	−1.16798	−	0.483792i
$792$		0			0
$793$	14.3574	−	21.4874i	0.509847	−	0.763040i
$794$		0			0
$795$	12.8599	+	31.1048i	0.456094	+	1.10317i
$796$		0			0
$797$	17.9210	+	43.2651i	0.634795	+	1.53253i	0.833529	+	0.552476i	$0.186317\pi$
$797$	17.9210	+	43.2651i	0.634795	+	1.53253i	−0.198734	+	0.980053i	$0.563683\pi$
$798$		0			0
$799$	6.18712	−	11.3197i	0.218884	−	0.400463i
$800$		0			0
$801$	−13.3989	−	5.57079i	−0.473426	−	0.196834i
$802$		0			0
$803$	−14.6575	−	14.6575i	−0.517252	−	0.517252i
$804$		0			0
$805$	4.19478	+	2.80287i	0.147847	+	0.0987880i
$806$		0			0
$807$	−7.28661	+	7.27696i	−0.256501	+	0.256161i
$808$		0			0
$809$	−11.4907	+	2.28565i	−0.403993	+	0.0803592i	−0.392904	−	0.919579i	$-0.628530\pi$
$809$	−11.4907	+	2.28565i	−0.403993	+	0.0803592i	−0.0110886	+	0.999939i	$0.503530\pi$
$810$		0			0
$811$	−3.67314	+	18.4661i	−0.128982	+	0.648434i	0.861157	+	0.508340i	$0.169741\pi$
$811$	−3.67314	+	18.4661i	−0.128982	+	0.648434i	−0.990138	+	0.140094i	$0.955259\pi$
$812$		0			0
$813$	2.31531	+	11.6803i	0.0812016	+	0.409645i
$814$		0			0
$815$	−3.38972			−0.118737
$816$		0			0
$817$	−9.88307			−0.345765
$818$		0			0
$819$	28.0428	+	5.61666i	0.979893	+	0.196262i
$820$		0			0
$821$	5.91006	−	29.7119i	0.206263	−	1.03695i	−0.729408	−	0.684079i	$-0.760205\pi$
$821$	5.91006	−	29.7119i	0.206263	−	1.03695i	0.935671	−	0.352874i	$-0.114795\pi$
$822$		0			0
$823$	−22.5083	+	4.47717i	−0.784589	+	0.156064i	−0.571099	−	0.820881i	$-0.693483\pi$
$823$	−22.5083	+	4.47717i	−0.784589	+	0.156064i	−0.213489	+	0.976945i	$0.568483\pi$
$824$		0			0
$825$	8.69457	+	8.70609i	0.302706	+	0.303107i
$826$		0			0
$827$	14.5585	+	9.72768i	0.506249	+	0.338265i	0.782324	−	0.622871i	$-0.214034\pi$
$827$	14.5585	+	9.72768i	0.506249	+	0.338265i	−0.276076	+	0.961136i	$0.589034\pi$
$828$		0			0
$829$	−31.1358	−	31.1358i	−1.08139	−	1.08139i	−0.996380	−	0.0850121i	$-0.972907\pi$
$829$	−31.1358	−	31.1358i	−1.08139	−	1.08139i	−0.0850121	−	0.996380i	$-0.527093\pi$
$830$		0			0
$831$	−14.3715	−	0.00951518i	−0.498542	−	0.000330078i
$832$		0			0
$833$	7.54167	−	6.07232i	0.261303	−	0.210394i
$834$		0			0
$835$	−23.1910	−	55.9881i	−0.802559	−	1.93755i
$836$		0			0
$837$	−13.8550	−	5.77119i	−0.478898	−	0.199481i
$838$		0			0
$839$	−10.9879	+	16.4446i	−0.379346	+	0.567731i	−0.971186	−	0.238325i	$-0.923402\pi$
$839$	−10.9879	+	16.4446i	−0.379346	+	0.567731i	0.591840	+	0.806056i	$0.298402\pi$
$840$		0			0
$841$	32.2093	+	13.3415i	1.11067	+	0.460053i
$842$		0			0
$843$	22.5051	+	4.49203i	0.775116	+	0.154714i
$844$		0			0
$845$	−19.5656	−	3.89185i	−0.673078	−	0.133884i
$846$		0			0
$847$	−9.92694	−	14.8567i	−0.341094	−	0.510483i
$848$		0			0
$849$	9.31634	−	22.4496i	0.319736	−	0.770468i
$850$		0			0
$851$			1.82575i			0.0625858i
$852$		0			0
$853$	−5.13456	+	3.43080i	−0.175804	+	0.117469i	−0.640359	−	0.768076i	$-0.721214\pi$
$853$	−5.13456	+	3.43080i	−0.175804	+	0.117469i	0.464555	+	0.885544i	$0.346214\pi$
$854$		0			0
$855$	−6.57763	+	4.38245i	−0.224950	+	0.149877i
$856$		0			0
$857$	5.07296	+	25.5035i	0.173289	+	0.871184i	0.965393	+	0.260798i	$0.0839856\pi$
$857$	5.07296	+	25.5035i	0.173289	+	0.871184i	−0.792104	+	0.610386i	$0.791014\pi$
$858$		0			0
$859$	1.25664	−	3.03380i	0.0428761	−	0.103512i	−0.900991	−	0.433838i	$-0.857159\pi$
$859$	1.25664	−	3.03380i	0.0428761	−	0.103512i	0.943867	+	0.330326i	$0.107159\pi$
$860$		0			0
$861$	−6.38500	−	9.56953i	−0.217600	−	0.326129i
$862$		0			0
$863$	−10.3922	+	10.3922i	−0.353754	+	0.353754i	−0.861504	−	0.507750i	$-0.830477\pi$
$863$	−10.3922	+	10.3922i	−0.353754	+	0.353754i	0.507750	+	0.861504i	$0.330477\pi$
$864$		0			0
$865$	32.8040	−	13.5878i	1.11537	−	0.462000i
$866$		0			0
$867$	21.2194	−	20.4142i	0.720648	−	0.693301i
$868$		0			0
$869$	−9.07062	+	3.75718i	−0.307700	+	0.127453i
$870$		0			0
$871$	22.4875	−	22.4875i	0.761958	−	0.761958i
$872$		0			0
$873$	2.06239	+	10.4406i	0.0698014	+	0.353360i
$874$		0			0
$875$	−1.73532	+	4.18943i	−0.0586644	+	0.141629i
$876$		0			0
$877$	2.60180	+	13.0801i	0.0878565	+	0.441684i	0.999527	+	0.0307618i	$0.00979334\pi$
$877$	2.60180	+	13.0801i	0.0878565	+	0.441684i	−0.911670	+	0.410923i	$0.865207\pi$
$878$		0			0
$879$	38.0121	+	25.4353i	1.28212	+	0.857912i
$880$		0			0
$881$	−16.3958	+	10.9553i	−0.552389	+	0.369094i	−0.800218	−	0.599709i	$-0.795283\pi$
$881$	−16.3958	+	10.9553i	−0.552389	+	0.369094i	0.247829	+	0.968804i	$0.420283\pi$
$882$		0			0
$883$			44.5932i			1.50068i	0.661051	+	0.750341i	$0.270111\pi$
$883$			44.5932i			1.50068i	−0.661051	+	0.750341i	$0.729889\pi$
$884$		0			0
$885$	29.7401	+	12.3418i	0.999702	+	0.414866i
$886$		0			0
$887$	−9.28722	−	13.8993i	−0.311834	−	0.466693i	0.642137	−	0.766590i	$-0.278048\pi$
$887$	−9.28722	−	13.8993i	−0.311834	−	0.466693i	−0.953972	+	0.299896i	$0.903048\pi$
$888$		0			0
$889$	−26.0450	−	5.18067i	−0.873522	−	0.173754i
$890$		0			0
$891$	−14.5532	+	2.85477i	−0.487551	+	0.0956383i
$892$		0			0
$893$	−2.49580	−	1.03380i	−0.0835189	−	0.0345947i
$894$		0			0
$895$	1.43532	−	2.14810i	0.0479773	−	0.0718032i
$896$		0			0
$897$	5.42367	−	2.24235i	0.181091	−	0.0748699i
$898$		0			0
$899$	−8.83348	−	21.3259i	−0.294613	−	0.711259i
$900$		0			0
$901$	−20.4523	+	16.4675i	−0.681363	+	0.548613i
$902$		0			0
$903$	−0.0283106	+	42.7598i	−0.000942119	+	1.42296i
$904$		0			0
$905$	−3.09374	−	3.09374i	−0.102839	−	0.102839i
$906$		0			0
$907$	−7.66078	−	5.11877i	−0.254372	−	0.169966i	0.421846	−	0.906668i	$-0.361382\pi$
$907$	−7.66078	−	5.11877i	−0.254372	−	0.169966i	−0.676218	+	0.736702i	$0.736382\pi$
$908$		0			0
$909$	10.3702	−	4.27938i	0.343956	−	0.141938i
$910$		0			0
$911$	−1.96677	+	0.391215i	−0.0651621	+	0.0129615i	−0.227564	−	0.973763i	$-0.573076\pi$
$911$	−1.96677	+	0.391215i	−0.0651621	+	0.0129615i	0.162402	+	0.986725i	$0.448076\pi$
$912$		0			0
$913$	−4.17505	+	20.9894i	−0.138174	+	0.694648i
$914$		0			0
$915$	30.3103	−	6.00824i	1.00203	−	0.198626i
$916$		0			0
$917$	−7.60583			−0.251167
$918$		0			0
$919$	−4.18774			−0.138141			−0.0690703	−	0.997612i	$-0.522003\pi$
$919$	−4.18774			−0.138141			−0.0690703	+	0.997612i	$0.522003\pi$
$920$		0			0
$921$	41.5089	−	8.22807i	1.36777	−	0.271124i
$922$		0			0
$923$	−1.87512	+	9.42688i	−0.0617204	+	0.310290i
$924$		0			0
$925$	10.0700	−	2.00304i	0.331098	−	0.0658595i
$926$		0			0
$927$	−25.8847	+	10.6817i	−0.850166	+	0.350832i
$928$		0			0
$929$	−20.3321	−	13.5854i	−0.667073	−	0.445724i	0.175375	−	0.984502i	$-0.443886\pi$
$929$	−20.3321	−	13.5854i	−0.667073	−	0.445724i	−0.842448	+	0.538778i	$0.818886\pi$
$930$		0			0
$931$	−1.43373	−	1.43373i	−0.0469885	−	0.0469885i
$932$		0			0
$933$	−0.0267611	+	40.4193i	−0.000876118	+	1.32327i
$934$		0			0
$935$	−9.94321	+	18.1918i	−0.325178	+	0.594934i
$936$		0			0
$937$	−19.3663	−	46.7545i	−0.632671	−	1.52740i	−0.836252	−	0.548345i	$-0.815258\pi$
$937$	−19.3663	−	46.7545i	−0.632671	−	1.52740i	0.203582	−	0.979058i	$-0.434742\pi$
$938$		0			0
$939$	2.58445	−	1.06851i	0.0843403	−	0.0348695i
$940$		0			0
$941$	−2.00221	+	2.99651i	−0.0652701	+	0.0976836i	−0.862669	−	0.505769i	$-0.831209\pi$
$941$	−2.00221	+	2.99651i	−0.0652701	+	0.0976836i	0.797399	+	0.603453i	$0.206209\pi$
$942$		0			0
$943$	−2.18105	−	0.903419i	−0.0710246	−	0.0294194i
$944$		0			0
$945$	18.9421	+	28.4711i	0.616187	+	0.926166i
$946$		0			0
$947$	26.2908	+	5.22957i	0.854336	+	0.169938i	0.602783	−	0.797905i	$-0.294059\pi$
$947$	26.2908	+	5.22957i	0.854336	+	0.169938i	0.251554	+	0.967843i	$0.419059\pi$
$948$		0			0
$949$	30.8912	+	46.2320i	1.00277	+	1.50075i
$950$		0			0
$951$	39.0103	+	16.1889i	1.26500	+	0.524960i
$952$		0			0
$953$		−	24.2594i		−	0.785838i	−0.919573	−	0.392919i	$-0.871465\pi$
$953$		−	24.2594i		−	0.785838i	0.919573	−	0.392919i	$-0.128535\pi$
$954$		0			0
$955$	−1.82937	+	1.22234i	−0.0591969	+	0.0395541i
$956$		0			0
$957$	−18.9564	−	12.6844i	−0.612772	−	0.410028i
$958$		0			0
$959$	−6.16353	−	30.9862i	−0.199031	−	1.00060i
$960$		0			0
$961$	8.67037	−	20.9321i	0.279689	−	0.675230i
$962$		0			0
$963$	1.09878	+	5.56241i	0.0354076	+	0.179246i
$964$		0			0
$965$	25.0752	−	25.0752i	0.807200	−	0.807200i
$966$		0			0
$967$	12.2636	−	5.07976i	0.394372	−	0.163354i	−0.176680	−	0.984268i	$-0.556536\pi$
$967$	12.2636	−	5.07976i	0.394372	−	0.163354i	0.571051	+	0.820914i	$0.306536\pi$
$968$		0			0
$969$	−4.72705	−	3.95916i	−0.151855	−	0.127187i
$970$		0			0
$971$	−14.2905	+	5.91933i	−0.458605	+	0.189960i	−0.600012	−	0.799991i	$-0.704837\pi$
$971$	−14.2905	+	5.91933i	−0.458605	+	0.189960i	0.141407	+	0.989952i	$0.454837\pi$
$972$		0			0
$973$	7.69338	−	7.69338i	0.246638	−	0.246638i
$974$		0			0
$975$	−18.3181	−	27.4543i	−0.586649	−	0.879241i
$976$		0			0
$977$	−7.72995	+	18.6618i	−0.247303	+	0.597042i	−0.997973	−	0.0636347i	$-0.979731\pi$
$977$	−7.72995	+	18.6618i	−0.247303	+	0.597042i	0.750670	+	0.660677i	$0.229731\pi$
$978$		0			0
$979$	1.55497	+	7.81735i	0.0496970	+	0.249844i
$980$		0			0
$981$	10.4933	−	6.99134i	0.335026	−	0.223216i
$982$		0			0
$983$	21.6898	−	14.4927i	0.691797	−	0.462244i	−0.159315	−	0.987228i	$-0.550929\pi$
$983$	21.6898	−	14.4927i	0.691797	−	0.462244i	0.851112	+	0.524984i	$0.175929\pi$
$984$		0			0
$985$			70.9874i			2.26185i
$986$		0			0
$987$	−4.47994	+	10.7953i	−0.142598	+	0.343618i
$988$		0			0
$989$	4.87497	+	7.29590i	0.155015	+	0.231996i
$990$		0			0
$991$	−35.4161	−	7.04470i	−1.12503	−	0.223782i	−0.402701	−	0.915332i	$-0.631928\pi$
$991$	−35.4161	−	7.04470i	−1.12503	−	0.223782i	−0.722329	+	0.691549i	$0.756928\pi$
$992$		0			0
$993$	−51.7460	−	10.3285i	−1.64211	−	0.327766i
$994$		0			0
$995$	−67.9824	−	28.1592i	−2.15519	−	0.892707i
$996$		0			0
$997$	8.20777	−	12.2838i	0.259943	−	0.389032i	−0.678425	−	0.734669i	$-0.737337\pi$
$997$	8.20777	−	12.2838i	0.259943	−	0.389032i	0.938368	+	0.345638i	$0.112337\pi$
$998$		0			0
$999$	−4.75858	+	11.4240i	−0.150555	+	0.361439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.cj.c.641.4		32
3.2	odd	2	inner	816.2.cj.c.641.3		32
4.3	odd	2		51.2.i.a.29.1	✓	32
12.11	even	2		51.2.i.a.29.4	yes	32
17.10	odd	16	inner	816.2.cj.c.401.3		32
51.44	even	16	inner	816.2.cj.c.401.4		32
68.3	even	16		867.2.i.g.329.1		32
68.7	even	16		867.2.i.h.503.4		32
68.11	even	16		867.2.i.d.653.1		32
68.15	odd	8		867.2.i.b.65.1		32
68.19	odd	8		867.2.i.i.65.1		32
68.23	even	16		867.2.i.c.653.1		32
68.27	even	16		51.2.i.a.44.4	yes	32
68.31	even	16		867.2.i.f.329.1		32
68.39	even	16		867.2.i.i.827.4		32
68.43	odd	8		867.2.i.g.224.4		32
68.47	odd	4		867.2.i.c.158.4		32
68.55	odd	4		867.2.i.d.158.4		32
68.59	odd	8		867.2.i.f.224.4		32
68.63	even	16		867.2.i.b.827.4		32
68.67	odd	2		867.2.i.h.131.1		32
204.11	odd	16		867.2.i.d.653.4		32
204.23	odd	16		867.2.i.c.653.4		32
204.47	even	4		867.2.i.c.158.1		32
204.59	even	8		867.2.i.f.224.1		32
204.71	odd	16		867.2.i.g.329.4		32
204.83	even	8		867.2.i.b.65.4		32
204.95	odd	16		51.2.i.a.44.1	yes	32
204.107	odd	16		867.2.i.i.827.1		32
204.131	odd	16		867.2.i.b.827.1		32
204.143	odd	16		867.2.i.h.503.1		32
204.155	even	8		867.2.i.i.65.4		32
204.167	odd	16		867.2.i.f.329.4		32
204.179	even	8		867.2.i.g.224.1		32
204.191	even	4		867.2.i.d.158.1		32
204.203	even	2		867.2.i.h.131.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.1	✓	32	4.3	odd	2
51.2.i.a.29.4	yes	32	12.11	even	2
51.2.i.a.44.1	yes	32	204.95	odd	16
51.2.i.a.44.4	yes	32	68.27	even	16
816.2.cj.c.401.3		32	17.10	odd	16	inner
816.2.cj.c.401.4		32	51.44	even	16	inner
816.2.cj.c.641.3		32	3.2	odd	2	inner
816.2.cj.c.641.4		32	1.1	even	1	trivial
867.2.i.b.65.1		32	68.15	odd	8
867.2.i.b.65.4		32	204.83	even	8
867.2.i.b.827.1		32	204.131	odd	16
867.2.i.b.827.4		32	68.63	even	16
867.2.i.c.158.1		32	204.47	even	4
867.2.i.c.158.4		32	68.47	odd	4
867.2.i.c.653.1		32	68.23	even	16
867.2.i.c.653.4		32	204.23	odd	16
867.2.i.d.158.1		32	204.191	even	4
867.2.i.d.158.4		32	68.55	odd	4
867.2.i.d.653.1		32	68.11	even	16
867.2.i.d.653.4		32	204.11	odd	16
867.2.i.f.224.1		32	204.59	even	8
867.2.i.f.224.4		32	68.59	odd	8
867.2.i.f.329.1		32	68.31	even	16
867.2.i.f.329.4		32	204.167	odd	16
867.2.i.g.224.1		32	204.179	even	8
867.2.i.g.224.4		32	68.43	odd	8
867.2.i.g.329.1		32	68.3	even	16
867.2.i.g.329.4		32	204.71	odd	16
867.2.i.h.131.1		32	68.67	odd	2
867.2.i.h.131.4		32	204.203	even	2
867.2.i.h.503.1		32	204.143	odd	16
867.2.i.h.503.4		32	68.7	even	16
867.2.i.i.65.1		32	68.19	odd	8
867.2.i.i.65.4		32	204.155	even	8
867.2.i.i.827.1		32	204.107	odd	16
867.2.i.i.827.4		32	68.39	even	16

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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.cj (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.69899 - 0.336782i) q^{3} +(-0.595296 + 2.99276i) q^{5} +(2.11533 - 0.420765i) q^{7} +(2.77316 - 1.14438i) q^{9} +(-1.37013 - 0.915491i) q^{11} +(3.12551 + 3.12551i) q^{13} +(-0.00349923 + 5.28516i) q^{15} +(-3.95657 + 1.15998i) q^{17} +(0.330416 + 0.797694i) q^{19} +(3.45222 - 1.42728i) q^{21} +(0.425893 - 0.637394i) q^{23} +(-3.98282 - 1.64974i) q^{25} +(4.32617 - 2.87824i) q^{27} +(7.83789 + 1.55905i) q^{29} +(-1.60475 - 2.40167i) q^{31} +(-2.63616 - 1.09398i) q^{33} +6.58114i q^{35} +(-1.98027 + 1.32318i) q^{37} +(6.36284 + 4.25761i) q^{39} +(-0.600791 - 3.02038i) q^{41} +(-4.38037 + 10.5751i) q^{43} +(1.77400 + 8.98063i) q^{45} +(-2.21238 + 2.21238i) q^{47} +(-2.16958 + 0.898671i) q^{49} +(-6.33153 + 3.30330i) q^{51} +(5.88369 - 2.43710i) q^{53} +(3.55548 - 3.55548i) q^{55} +(0.830022 + 1.24400i) q^{57} +(2.33146 - 5.62864i) q^{59} +(-1.14061 - 5.73423i) q^{61} +(5.38462 - 3.58759i) q^{63} +(-11.2145 + 7.49329i) q^{65} -7.19481i q^{67} +(0.508927 - 1.22636i) q^{69} +(1.20808 + 1.80802i) q^{71} +(12.3377 + 2.45412i) q^{73} +(-7.32238 - 1.46155i) q^{75} +(-3.28348 - 1.36006i) q^{77} +(3.31013 - 4.95397i) q^{79} +(6.38079 - 6.34708i) q^{81} +(-4.96993 - 11.9985i) q^{83} +(-1.11620 - 12.5316i) q^{85} +(13.8416 + 0.00916431i) q^{87} +(-3.42023 - 3.42023i) q^{89} +(7.92660 + 5.29638i) q^{91} +(-3.53529 - 3.53997i) q^{93} +(-2.58400 + 0.513989i) q^{95} +(-0.692072 + 3.47928i) q^{97} +(-4.84725 - 0.970853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} - 16 q^{15} + 16 q^{19} + 16 q^{21} + 16 q^{25} + 8 q^{27} - 16 q^{31} + 16 q^{37} + 24 q^{39} - 16 q^{43} - 40 q^{45} - 48 q^{49} + 40 q^{51} + 48 q^{55}+ \cdots + 64 q^{99}+O(q^{100}) \) 32 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 - 16 * q^15 + 16 * q^19 + 16 * q^21 + 16 * q^25 + 8 * q^27 - 16 * q^31 + 16 * q^37 + 24 * q^39 - 16 * q^43 - 40 * q^45 - 48 * q^49 + 40 * q^51 + 48 * q^55 + 8 * q^57 - 32 * q^61 - 64 * q^63 + 80 * q^69 + 48 * q^73 - 88 * q^75 - 16 * q^79 + 48 * q^81 + 56 * q^87 - 16 * q^91 - 72 * q^93 - 16 * q^97 + 64 * q^99

Introduction

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Varieties

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Representations

Groups

Database

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