LMFDB - Embedded newform 476.2.bh.a.457.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(9,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 8, 3]))

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

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

chi := DirichletCharacter("476.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bh (of order $24$, degree $8$, 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:	$3.80087913621$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			457.11
Character	$\chi$	$=$	476.457
Dual form			476.2.bh.a.25.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.59278 - 2.07576i) q^{3} +(0.316063 - 2.40074i) q^{5} +(-2.64423 - 0.0897805i) q^{7} +(-0.995345 - 3.71468i) q^{9} +O(q^{10})$	\(q+(1.59278 - 2.07576i) q^{3} +(0.316063 - 2.40074i) q^{5} +(-2.64423 - 0.0897805i) q^{7} +(-0.995345 - 3.71468i) q^{9} +(-0.0980378 + 0.0129069i) q^{11} -0.710699i q^{13} +(-4.47992 - 4.47992i) q^{15} +(-2.87065 + 2.95962i) q^{17} +(6.01227 - 1.61098i) q^{19} +(-4.39804 + 5.34577i) q^{21} +(-2.94399 - 3.83668i) q^{23} +(-0.834006 - 0.223471i) q^{25} +(-2.04433 - 0.846789i) q^{27} +(8.64340 - 3.58022i) q^{29} +(-6.56213 + 8.55194i) q^{31} +(-0.129361 + 0.224060i) q^{33} +(-1.05128 + 6.31971i) q^{35} +(1.24444 + 0.163834i) q^{37} +(-1.47524 - 1.13199i) q^{39} +(-0.494155 - 0.204686i) q^{41} +(3.12025 - 3.12025i) q^{43} +(-9.23255 + 1.21549i) q^{45} +(0.634155 + 0.366129i) q^{47} +(6.98388 + 0.474800i) q^{49} +(1.57114 + 10.6728i) q^{51} +(1.56571 - 5.84330i) q^{53} +0.239442i q^{55} +(6.23224 - 15.0460i) q^{57} +(-5.39710 - 1.44615i) q^{59} +(7.45525 - 5.72062i) q^{61} +(2.29841 + 9.91182i) q^{63} +(-1.70620 - 0.224626i) q^{65} +(0.475222 + 0.823108i) q^{67} -12.6532 q^{69} +(-2.66546 - 6.43500i) q^{71} +(5.44281 + 4.17642i) q^{73} +(-1.79226 + 1.37525i) q^{75} +(0.260393 - 0.0253269i) q^{77} +(-3.97401 - 5.17903i) q^{79} +(4.97757 - 2.87380i) q^{81} +(4.47205 + 4.47205i) q^{83} +(6.19797 + 7.82709i) q^{85} +(6.33542 - 23.6441i) q^{87} +(15.1302 + 8.73541i) q^{89} +(-0.0638069 + 1.87925i) q^{91} +(7.29968 + 27.2428i) q^{93} +(-1.96729 - 14.9431i) q^{95} +(-8.65286 + 3.58413i) q^{97} +(0.145526 + 0.351332i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{5}+O(q^{10}) $ 96 * q + 4 * q^5	$ 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) $ 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{3}\right)$

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
$3$	1.59278	−	2.07576i	0.919594	−	1.19844i	−0.0601513	−	0.998189i	$-0.519158\pi$
$3$	1.59278	−	2.07576i	0.919594	−	1.19844i	0.979745	−	0.200249i	$-0.0641750\pi$
$4$		0			0
$5$	0.316063	−	2.40074i	0.141348	−	1.07364i	−0.762865	−	0.646558i	$-0.776208\pi$
$5$	0.316063	−	2.40074i	0.141348	−	1.07364i	0.904212	−	0.427083i	$-0.140459\pi$
$6$		0			0
$7$	−2.64423	−	0.0897805i	−0.999424	−	0.0339338i
$7$	−2.64423	−	0.0897805i	−0.999424	−	0.0339338i
$8$		0			0
$9$	−0.995345	−	3.71468i	−0.331782	−	1.23823i
$10$		0			0
$11$	−0.0980378	+	0.0129069i	−0.0295595	+	0.00389158i	−0.145291	−	0.989389i	$-0.546412\pi$
$11$	−0.0980378	+	0.0129069i	−0.0295595	+	0.00389158i	0.115732	+	0.993280i	$0.463079\pi$
$12$		0			0
$13$		−	0.710699i		−	0.197113i	−0.995131	−	0.0985563i	$-0.968578\pi$
$13$		−	0.710699i		−	0.197113i	0.995131	−	0.0985563i	$-0.0314225\pi$
$14$		0			0
$15$	−4.47992	−	4.47992i	−1.15671	−	1.15671i
$16$		0			0
$17$	−2.87065	+	2.95962i	−0.696234	+	0.717814i
$17$	−2.87065	+	2.95962i	−0.696234	+	0.717814i
$18$		0			0
$19$	6.01227	−	1.61098i	1.37931	−	0.369585i	0.508440	−	0.861098i	$-0.330222\pi$
$19$	6.01227	−	1.61098i	1.37931	−	0.369585i	0.870870	+	0.491513i	$0.163556\pi$
$20$		0			0
$21$	−4.39804	+	5.34577i	−0.959732	+	1.16654i
$22$		0			0
$23$	−2.94399	−	3.83668i	−0.613864	−	0.800004i	0.378201	−	0.925723i	$-0.376543\pi$
$23$	−2.94399	−	3.83668i	−0.613864	−	0.800004i	−0.992066	+	0.125720i	$0.959876\pi$
$24$		0			0
$25$	−0.834006	−	0.223471i	−0.166801	−	0.0446942i
$26$		0			0
$27$	−2.04433	−	0.846789i	−0.393431	−	0.162965i
$28$		0			0
$29$	8.64340	−	3.58022i	1.60504	−	0.664829i	0.612923	−	0.790143i	$-0.289994\pi$
$29$	8.64340	−	3.58022i	1.60504	−	0.664829i	0.992117	+	0.125314i	$0.0399937\pi$
$30$		0			0
$31$	−6.56213	+	8.55194i	−1.17859	+	1.53597i	−0.390284	+	0.920694i	$0.627623\pi$
$31$	−6.56213	+	8.55194i	−1.17859	+	1.53597i	−0.788310	+	0.615279i	$0.789043\pi$
$32$		0			0
$33$	−0.129361	+	0.224060i	−0.0225189	+	0.0390039i
$34$		0			0
$35$	−1.05128	+	6.31971i	−0.177699	+	1.06823i
$36$		0			0
$37$	1.24444	+	0.163834i	0.204585	+	0.0269342i	0.232122	−	0.972687i	$-0.425433\pi$
$37$	1.24444	+	0.163834i	0.204585	+	0.0269342i	−0.0275369	+	0.999621i	$0.508766\pi$
$38$		0			0
$39$	−1.47524	−	1.13199i	−0.236227	−	0.181263i
$40$		0			0
$41$	−0.494155	−	0.204686i	−0.0771740	−	0.0319665i	0.343763	−	0.939057i	$-0.388298\pi$
$41$	−0.494155	−	0.204686i	−0.0771740	−	0.0319665i	−0.420937	+	0.907090i	$0.638298\pi$
$42$		0			0
$43$	3.12025	−	3.12025i	0.475834	−	0.475834i	−0.427963	−	0.903796i	$-0.640768\pi$
$43$	3.12025	−	3.12025i	0.475834	−	0.475834i	0.903796	+	0.427963i	$0.140768\pi$
$44$		0			0
$45$	−9.23255	+	1.21549i	−1.37631	+	0.181194i
$46$		0			0
$47$	0.634155	+	0.366129i	0.0925010	+	0.0534055i	0.545537	−	0.838087i	$-0.316326\pi$
$47$	0.634155	+	0.366129i	0.0925010	+	0.0534055i	−0.453036	+	0.891492i	$0.649659\pi$
$48$		0			0
$49$	6.98388	+	0.474800i	0.997697	+	0.0678286i
$50$		0			0
$51$	1.57114	+	10.6728i	0.220003	+	1.49449i
$52$		0			0
$53$	1.56571	−	5.84330i	0.215067	−	0.802640i	−0.771076	−	0.636743i	$-0.780281\pi$
$53$	1.56571	−	5.84330i	0.215067	−	0.802640i	0.986143	−	0.165897i	$-0.0530519\pi$
$54$		0			0
$55$			0.239442i			0.0322864i
$56$		0			0
$57$	6.23224	−	15.0460i	0.825480	−	1.99289i
$58$		0			0
$59$	−5.39710	−	1.44615i	−0.702643	−	0.188273i	−0.110229	−	0.993906i	$-0.535158\pi$
$59$	−5.39710	−	1.44615i	−0.702643	−	0.188273i	−0.592414	+	0.805634i	$0.701825\pi$
$60$		0			0
$61$	7.45525	−	5.72062i	0.954548	−	0.732450i	−0.00900772	−	0.999959i	$-0.502867\pi$
$61$	7.45525	−	5.72062i	0.954548	−	0.732450i	0.963555	+	0.267509i	$0.0862006\pi$
$62$		0			0
$63$	2.29841	+	9.91182i	0.289573	+	1.24877i
$64$		0			0
$65$	−1.70620	−	0.224626i	−0.211628	−	0.0278614i
$66$		0			0
$67$	0.475222	+	0.823108i	0.0580576	+	0.100559i	0.893593	−	0.448877i	$-0.148176\pi$
$67$	0.475222	+	0.823108i	0.0580576	+	0.100559i	−0.835536	+	0.549436i	$0.814843\pi$
$68$		0			0
$69$	−12.6532			−1.52326
$70$		0			0
$71$	−2.66546	−	6.43500i	−0.316332	−	0.763693i	−0.999443	−	0.0333785i	$-0.989373\pi$
$71$	−2.66546	−	6.43500i	−0.316332	−	0.763693i	0.683111	−	0.730315i	$-0.260627\pi$
$72$		0			0
$73$	5.44281	+	4.17642i	0.637033	+	0.488813i	0.876061	−	0.482200i	$-0.160162\pi$
$73$	5.44281	+	4.17642i	0.637033	+	0.488813i	−0.239028	+	0.971013i	$0.576829\pi$
$74$		0			0
$75$	−1.79226	+	1.37525i	−0.206953	+	0.158800i
$76$		0			0
$77$	0.260393	−	0.0253269i	0.0296745	−	0.00288627i
$78$		0			0
$79$	−3.97401	−	5.17903i	−0.447111	−	0.582687i	0.514366	−	0.857571i	$-0.328027\pi$
$79$	−3.97401	−	5.17903i	−0.447111	−	0.582687i	−0.961477	+	0.274884i	$0.911361\pi$
$80$		0			0
$81$	4.97757	−	2.87380i	0.553063	−	0.319311i
$82$		0			0
$83$	4.47205	+	4.47205i	0.490871	+	0.490871i	0.908581	−	0.417710i	$-0.137167\pi$
$83$	4.47205	+	4.47205i	0.490871	+	0.490871i	−0.417710	+	0.908581i	$0.637167\pi$
$84$		0			0
$85$	6.19797	+	7.82709i	0.672264	+	0.848968i
$86$		0			0
$87$	6.33542	−	23.6441i	0.679228	−	2.53491i
$88$		0			0
$89$	15.1302	+	8.73541i	1.60379	+	0.925951i	0.990719	+	0.135928i	$0.0434015\pi$
$89$	15.1302	+	8.73541i	1.60379	+	0.925951i	0.613076	+	0.790024i	$0.289932\pi$
$90$		0			0
$91$	−0.0638069	+	1.87925i	−0.00668879	+	0.196999i
$92$		0			0
$93$	7.29968	+	27.2428i	0.756941	+	2.82494i
$94$		0			0
$95$	−1.96729	−	14.9431i	−0.201840	−	1.53312i
$96$		0			0
$97$	−8.65286	+	3.58413i	−0.878565	+	0.363914i	−0.775940	−	0.630807i	$-0.782724\pi$
$97$	−8.65286	+	3.58413i	−0.878565	+	0.363914i	−0.102625	+	0.994720i	$0.532724\pi$
$98$		0			0
$99$	0.145526	+	0.351332i	0.0146260	+	0.0353102i
$100$		0			0
$101$	2.28347	+	3.95509i	0.227214	+	0.393546i	0.956981	−	0.290150i	$-0.0937051\pi$
$101$	2.28347	+	3.95509i	0.227214	+	0.393546i	−0.729768	+	0.683695i	$0.760372\pi$
$102$		0			0
$103$	−9.70842	+	16.8155i	−0.956599	+	1.65688i	−0.225934	+	0.974143i	$0.572543\pi$
$103$	−9.70842	+	16.8155i	−0.956599	+	1.65688i	−0.730665	+	0.682736i	$0.760790\pi$
$104$		0			0
$105$	11.4437	+	12.2481i	1.11679	+	1.19530i
$106$		0			0
$107$	0.610022	−	4.63358i	0.0589731	−	0.447945i	−0.936329	−	0.351124i	$-0.885799\pi$
$107$	0.610022	−	4.63358i	0.0589731	−	0.447945i	0.995302	−	0.0968204i	$-0.0308673\pi$
$108$		0			0
$109$	0.572596	+	4.34930i	0.0548448	+	0.416587i	0.996740	+	0.0806806i	$0.0257094\pi$
$109$	0.572596	+	4.34930i	0.0548448	+	0.416587i	−0.941895	+	0.335907i	$0.890957\pi$
$110$		0			0
$111$	2.32221	−	2.32221i	0.220414	−	0.220414i
$112$		0			0
$113$	−0.269382	+	0.650345i	−0.0253413	+	0.0611793i	−0.936044	−	0.351884i	$-0.885541\pi$
$113$	−0.269382	+	0.650345i	−0.0253413	+	0.0611793i	0.910702	+	0.413063i	$0.135541\pi$
$114$		0			0
$115$	−10.1413	+	5.85511i	−0.945686	+	0.545992i
$116$		0			0
$117$	−2.64002	+	0.707391i	−0.244070	+	0.0653984i
$118$		0			0
$119$	7.85636	−	7.56819i	0.720192	−	0.693775i
$120$		0			0
$121$	−10.6157	+	2.84448i	−0.965067	+	0.258589i
$122$		0			0
$123$	−1.21196	+	0.699725i	−0.109279	+	0.0630920i
$124$		0			0
$125$	3.83315	−	9.25405i	0.342848	−	0.827707i
$126$		0			0
$127$	−3.82540	+	3.82540i	−0.339450	+	0.339450i	−0.856160	−	0.516711i	$-0.827156\pi$
$127$	−3.82540	+	3.82540i	−0.339450	+	0.339450i	0.516711	+	0.856160i	$0.327156\pi$
$128$		0			0
$129$	−1.50699	−	11.4468i	−0.132684	−	1.00783i
$130$		0			0
$131$	0.227512	−	1.72812i	0.0198778	−	0.150987i	−0.978628	−	0.205641i	$-0.934072\pi$
$131$	0.227512	−	1.72812i	0.0198778	−	0.150987i	0.998505	+	0.0546538i	$0.0174055\pi$
$132$		0			0
$133$	−16.0425	+	3.72002i	−1.39106	+	0.322567i
$134$		0			0
$135$	−2.67905	+	4.64025i	−0.230576	+	0.399369i
$136$		0			0
$137$	8.84088	+	15.3128i	0.755327	+	1.30826i	0.945212	+	0.326458i	$0.105855\pi$
$137$	8.84088	+	15.3128i	0.755327	+	1.30826i	−0.189885	+	0.981806i	$0.560811\pi$
$138$		0			0
$139$	6.09667	+	14.7187i	0.517113	+	1.24842i	0.939669	+	0.342084i	$0.111133\pi$
$139$	6.09667	+	14.7187i	0.517113	+	1.24842i	−0.422557	+	0.906337i	$0.638867\pi$
$140$		0			0
$141$	1.77007	−	0.733185i	0.149066	−	0.0617453i
$142$		0			0
$143$	0.00917294	+	0.0696754i	0.000767080	+	0.00582655i
$144$		0			0
$145$	−5.86329	−	21.8821i	−0.486920	−	1.81721i
$146$		0			0
$147$	12.1094	−	13.7406i	0.998764	−	1.13330i
$148$		0			0
$149$	18.7087	+	10.8015i	1.53268	+	0.884892i	0.999237	+	0.0390555i	$0.0124349\pi$
$149$	18.7087	+	10.8015i	1.53268	+	0.884892i	0.533442	+	0.845837i	$0.320898\pi$
$150$		0			0
$151$	−2.54529	+	9.49915i	−0.207133	+	0.773030i	0.781656	+	0.623710i	$0.214375\pi$
$151$	−2.54529	+	9.49915i	−0.207133	+	0.773030i	−0.988789	+	0.149320i	$0.952291\pi$
$152$		0			0
$153$	13.8513	+	7.71769i	1.11981	+	0.623938i
$154$		0			0
$155$	18.4569	+	18.4569i	1.48249	+	1.48249i
$156$		0			0
$157$	−15.0525	+	8.69058i	−1.20132	+	0.693584i	−0.960849	−	0.277072i	$-0.910636\pi$
$157$	−15.0525	+	8.69058i	−1.20132	+	0.693584i	−0.240473	+	0.970656i	$0.577302\pi$
$158$		0			0
$159$	−9.63544	−	12.5571i	−0.764140	−	0.995846i
$160$		0			0
$161$	7.44012	+	10.4094i	0.586364	+	0.820374i
$162$		0			0
$163$	−6.94465	+	5.32882i	−0.543947	+	0.417385i	−0.843846	−	0.536586i	$-0.819714\pi$
$163$	−6.94465	+	5.32882i	−0.543947	+	0.417385i	0.299899	+	0.953971i	$0.403047\pi$
$164$		0			0
$165$	0.497023	+	0.381379i	0.0386932	+	0.0296903i
$166$		0			0
$167$	−7.66246	−	18.4988i	−0.592939	−	1.43148i	−0.880652	−	0.473764i	$-0.842895\pi$
$167$	−7.66246	−	18.4988i	−0.592939	−	1.43148i	0.287713	−	0.957717i	$-0.407105\pi$
$168$		0			0
$169$	12.4949			0.961147
$170$		0			0
$171$	−11.9686	−	20.7302i	−0.915260	−	1.58528i
$172$		0			0
$173$	−2.80220	−	0.368916i	−0.213047	−	0.0280482i	0.0232471	−	0.999730i	$-0.492600\pi$
$173$	−2.80220	−	0.368916i	−0.213047	−	0.0280482i	−0.236294	+	0.971682i	$0.575933\pi$
$174$		0			0
$175$	2.18524	+	0.665786i	0.165188	+	0.0503287i
$176$		0			0
$177$	−11.5983	+	8.89967i	−0.871779	+	0.668940i
$178$		0			0
$179$	−13.4914	−	3.61500i	−1.00839	−	0.270198i	−0.283434	−	0.958992i	$-0.591474\pi$
$179$	−13.4914	−	3.61500i	−1.00839	−	0.270198i	−0.724957	+	0.688794i	$0.758141\pi$
$180$		0			0
$181$	−4.21034	+	10.1647i	−0.312952	+	0.755534i	0.686641	+	0.726997i	$0.259085\pi$
$181$	−4.21034	+	10.1647i	−0.312952	+	0.755534i	−0.999593	+	0.0285364i	$0.990915\pi$
$182$		0			0
$183$		−	24.5870i		−	1.81752i
$184$		0			0
$185$	0.786645	−	2.93580i	0.0578353	−	0.215844i
$186$		0			0
$187$	0.243232	−	0.327206i	0.0177869	−	0.0239277i
$188$		0			0
$189$	5.32965	+	2.42264i	0.387675	+	0.176221i
$190$		0			0
$191$	16.5526	+	9.55663i	1.19770	+	0.691493i	0.960042	−	0.279855i	$-0.0902865\pi$
$191$	16.5526	+	9.55663i	1.19770	+	0.691493i	0.237659	+	0.971349i	$0.423620\pi$
$192$		0			0
$193$	−0.469461	+	0.0618058i	−0.0337926	+	0.00444888i	−0.147404	−	0.989076i	$-0.547092\pi$
$193$	−0.469461	+	0.0618058i	−0.0337926	+	0.00444888i	0.113611	+	0.993525i	$0.463758\pi$
$194$		0			0
$195$	−3.18388	+	3.18388i	−0.228002	+	0.228002i
$196$		0			0
$197$	−11.0219	−	4.56541i	−0.785277	−	0.325272i	−0.0462338	−	0.998931i	$-0.514722\pi$
$197$	−11.0219	−	4.56541i	−0.785277	−	0.325272i	−0.739043	+	0.673658i	$0.764722\pi$
$198$		0			0
$199$	−14.1629	−	10.8676i	−1.00398	−	0.770381i	−0.0305888	−	0.999532i	$-0.509738\pi$
$199$	−14.1629	−	10.8676i	−1.00398	−	0.770381i	−0.973391	+	0.229151i	$0.926405\pi$
$200$		0			0
$201$	2.46550	+	0.324589i	0.173903	+	0.0228947i
$202$		0			0
$203$	−23.1766	+	8.69089i	−1.62668	+	0.609981i
$204$		0			0
$205$	−0.647580	+	1.12164i	−0.0452289	+	0.0783388i
$206$		0			0
$207$	−11.3218	+	14.7548i	−0.786917	+	1.02553i
$208$		0			0
$209$	−0.568637	+	0.235537i	−0.0393334	+	0.0162924i
$210$		0			0
$211$	−2.53429	−	1.04974i	−0.174468	−	0.0722670i	0.293740	−	0.955885i	$-0.405100\pi$
$211$	−2.53429	−	1.04974i	−0.174468	−	0.0722670i	−0.468208	+	0.883618i	$0.655100\pi$
$212$		0			0
$213$	−17.6030	−	4.71670i	−1.20614	−	0.323183i
$214$		0			0
$215$	−6.50470	−	8.47709i	−0.443617	−	0.578133i
$216$		0			0
$217$	18.1196	−	22.0241i	1.23004	−	1.49509i
$218$		0			0
$219$	17.3384	−	4.64582i	1.17162	−	0.313936i
$220$		0			0
$221$	2.10340	+	2.04017i	0.141490	+	0.137237i
$222$		0			0
$223$	15.3029	+	15.3029i	1.02476	+	1.02476i	0.999686	+	0.0250732i	$0.00798187\pi$
$223$	15.3029	+	15.3029i	1.02476	+	1.02476i	0.0250732	+	0.999686i	$0.492018\pi$
$224$		0			0
$225$			3.32049i			0.221366i
$226$		0			0
$227$	12.3963	−	1.63200i	0.822770	−	0.108320i	0.292626	−	0.956227i	$-0.405471\pi$
$227$	12.3963	−	1.63200i	0.822770	−	0.108320i	0.530144	+	0.847907i	$0.322138\pi$
$228$		0			0
$229$	−5.42735	−	20.2552i	−0.358650	−	1.33850i	−0.875829	−	0.482622i	$-0.839685\pi$
$229$	−5.42735	−	20.2552i	−0.358650	−	1.33850i	0.517179	−	0.855877i	$-0.326982\pi$
$230$		0			0
$231$	0.362177	−	0.580852i	0.0238295	−	0.0382173i
$232$		0			0
$233$	0.643733	−	4.88964i	0.0421723	−	0.320331i	−0.957336	−	0.288977i	$-0.906685\pi$
$233$	0.643733	−	4.88964i	0.0421723	−	0.320331i	0.999508	−	0.0313537i	$-0.00998181\pi$
$234$		0			0
$235$	1.07941	−	1.40672i	0.0704131	−	0.0917641i
$236$		0			0
$237$	−17.0801			−1.10947
$238$		0			0
$239$	−13.8761			−0.897571			−0.448786	−	0.893640i	$-0.648143\pi$
$239$	−13.8761			−0.897571			−0.448786	+	0.893640i	$0.648143\pi$
$240$		0			0
$241$	4.54778	−	5.92678i	0.292948	−	0.381778i	−0.623572	−	0.781766i	$-0.714319\pi$
$241$	4.54778	−	5.92678i	0.292948	−	0.381778i	0.916520	+	0.399988i	$0.130986\pi$
$242$		0			0
$243$	2.82935	−	21.4911i	0.181503	−	1.37865i
$244$		0			0
$245$	3.34721	−	16.6164i	0.213846	−	1.06158i
$246$		0			0
$247$	−1.14493	−	4.27292i	−0.0728499	−	0.271879i
$248$		0			0
$249$	16.4059	−	2.15987i	1.03968	−	0.136876i
$250$		0			0
$251$		−	21.6968i		−	1.36949i	−0.728784	−	0.684744i	$-0.759914\pi$
$251$		−	21.6968i		−	1.36949i	0.728784	−	0.684744i	$-0.240086\pi$
$252$		0			0
$253$	0.338142	+	0.338142i	0.0212588	+	0.0212588i
$254$		0			0
$255$	26.1192	−	0.398609i	1.63565	−	0.0249619i
$256$		0			0
$257$	−9.84421	+	2.63775i	−0.614065	+	0.164538i	−0.552428	−	0.833560i	$-0.686299\pi$
$257$	−9.84421	+	2.63775i	−0.614065	+	0.164538i	−0.0616366	+	0.998099i	$0.519632\pi$
$258$		0			0
$259$	−3.27588	−	0.544942i	−0.203554	−	0.0338610i
$260$		0			0
$261$	−21.9025	−	28.5439i	−1.35573	−	1.76682i
$262$		0			0
$263$	−24.9433	−	6.68353i	−1.53807	−	0.412124i	−0.612427	−	0.790527i	$-0.709807\pi$
$263$	−24.9433	−	6.68353i	−1.53807	−	0.412124i	−0.925641	+	0.378403i	$0.876473\pi$
$264$		0			0
$265$	−13.5334	−	5.60570i	−0.831348	−	0.344356i
$266$		0			0
$267$	42.2317	−	17.4929i	2.58454	−	1.07055i
$268$		0			0
$269$	3.52016	−	4.58756i	0.214628	−	0.279709i	−0.673615	−	0.739082i	$-0.735259\pi$
$269$	3.52016	−	4.58756i	0.214628	−	0.279709i	0.888243	+	0.459374i	$0.151926\pi$
$270$		0			0
$271$	−4.48115	+	7.76158i	−0.272211	+	0.471483i	−0.969428	−	0.245378i	$-0.921088\pi$
$271$	−4.48115	+	7.76158i	−0.272211	+	0.471483i	0.697217	+	0.716860i	$0.254421\pi$
$272$		0			0
$273$	3.79924	+	3.12569i	0.229940	+	0.189175i
$274$		0			0
$275$	0.0846484	+	0.0111442i	0.00510449	+	0.000672019i
$276$		0			0
$277$	−13.1753	−	10.1098i	−0.791628	−	0.607438i	0.131770	−	0.991280i	$-0.457934\pi$
$277$	−13.1753	−	10.1098i	−0.791628	−	0.607438i	−0.923399	+	0.383843i	$0.874600\pi$
$278$		0			0
$279$	38.2993	+	15.8641i	2.29292	+	0.949758i
$280$		0			0
$281$	9.62570	−	9.62570i	0.574221	−	0.574221i	−0.359084	−	0.933305i	$-0.616911\pi$
$281$	9.62570	−	9.62570i	0.574221	−	0.574221i	0.933305	+	0.359084i	$0.116911\pi$
$282$		0			0
$283$	0.782180	−	0.102976i	0.0464958	−	0.00612129i	−0.107242	−	0.994233i	$-0.534202\pi$
$283$	0.782180	−	0.102976i	0.0464958	−	0.00612129i	0.153738	+	0.988112i	$0.450869\pi$
$284$		0			0
$285$	−34.1516	−	19.7174i	−2.02297	−	1.16796i
$286$		0			0
$287$	1.28828	+	0.585601i	0.0760448	+	0.0345669i
$288$		0			0
$289$	−0.518759	−	16.9921i	−0.0305152	−	0.999534i
$290$		0			0
$291$	−6.34235	+	23.6700i	−0.371795	+	1.38756i
$292$		0			0
$293$		−	2.14730i		−	0.125446i	−0.998031	−	0.0627232i	$-0.980021\pi$
$293$		−	2.14730i		−	0.125446i	0.998031	−	0.0627232i	$-0.0199785\pi$
$294$		0			0
$295$	−5.17765	+	12.4999i	−0.301454	+	0.727775i
$296$		0			0
$297$	0.211351	+	0.0566313i	0.0122638	+	0.00328608i
$298$		0			0
$299$	−2.72673	+	2.09229i	−0.157691	+	0.121000i
$300$		0			0
$301$	−8.53079	+	7.97052i	−0.491707	+	0.459413i
$302$		0			0
$303$	11.8469	+	1.55967i	0.680585	+	0.0896007i
$304$		0			0
$305$	−11.3774	−	19.7062i	−0.651466	−	1.12837i
$306$		0			0
$307$	−33.4998			−1.91193			−0.955967	−	0.293474i	$-0.905189\pi$
$307$	−33.4998			−1.91193			−0.955967	+	0.293474i	$0.905189\pi$
$308$		0			0
$309$	19.4414	+	46.9357i	1.10598	+	2.67008i
$310$		0			0
$311$	18.6772	+	14.3315i	1.05909	+	0.812666i	0.982847	−	0.184423i	$-0.0590416\pi$
$311$	18.6772	+	14.3315i	1.05909	+	0.812666i	0.0762406	+	0.997089i	$0.475708\pi$
$312$		0			0
$313$	−16.2193	+	12.4455i	−0.916769	+	0.703461i	−0.955251	−	0.295798i	$-0.904415\pi$
$313$	−16.2193	+	12.4455i	−0.916769	+	0.703461i	0.0384817	+	0.999259i	$0.487748\pi$
$314$		0			0
$315$	24.5221	−	2.38513i	1.38166	−	0.134387i
$316$		0			0
$317$	−3.17786	−	4.14147i	−0.178487	−	0.232608i	0.695539	−	0.718489i	$-0.255166\pi$
$317$	−3.17786	−	4.14147i	−0.178487	−	0.232608i	−0.874025	+	0.485880i	$0.838499\pi$
$318$		0			0
$319$	−0.801170	+	0.462556i	−0.0448569	+	0.0258982i
$320$		0			0
$321$	−8.64654	−	8.64654i	−0.482603	−	0.482603i
$322$		0			0
$323$	−12.4912	+	22.4186i	−0.695030	+	1.24741i
$324$		0			0
$325$	−0.158821	+	0.592727i	−0.00880979	+	0.0328786i
$326$		0			0
$327$	9.94010	+	5.73892i	0.549689	+	0.317363i
$328$		0			0
$329$	−1.64398	−	1.02506i	−0.0906354	−	0.0565136i
$330$		0			0
$331$	5.05865	+	18.8791i	0.278048	+	1.03769i	0.953771	+	0.300535i	$0.0971651\pi$
$331$	5.05865	+	18.8791i	0.278048	+	1.03769i	−0.675722	+	0.737156i	$0.736168\pi$
$332$		0			0
$333$	−0.630060	−	4.78578i	−0.0345271	−	0.262259i
$334$		0			0
$335$	2.12626	−	0.880728i	0.116170	−	0.0481193i
$336$		0			0
$337$	7.18816	+	17.3537i	0.391564	+	0.945319i	0.989600	+	0.143849i	$0.0459481\pi$
$337$	7.18816	+	17.3537i	0.391564	+	0.945319i	−0.598036	+	0.801469i	$0.704052\pi$
$338$		0			0
$339$	0.920890	+	1.59503i	0.0500159	+	0.0866301i
$340$		0			0
$341$	0.532958	−	0.923110i	0.0288613	−	0.0499892i
$342$		0			0
$343$	−18.4243	−	1.88250i	−0.994821	−	0.101645i
$344$		0			0
$345$	−3.99919	+	30.3769i	−0.215309	+	1.63544i
$346$		0			0
$347$	0.929368	+	7.05925i	0.0498911	+	0.378961i	0.998116	+	0.0613600i	$0.0195438\pi$
$347$	0.929368	+	7.05925i	0.0498911	+	0.378961i	−0.948225	+	0.317601i	$0.897123\pi$
$348$		0			0
$349$	−10.8663	+	10.8663i	−0.581660	+	0.581660i	−0.935359	−	0.353699i	$-0.884924\pi$
$349$	−10.8663	+	10.8663i	−0.581660	+	0.581660i	0.353699	+	0.935359i	$0.384924\pi$
$350$		0			0
$351$	−0.601812	+	1.45290i	−0.0321224	+	0.0775503i
$352$		0			0
$353$	1.57884	−	0.911544i	0.0840332	−	0.0485166i	−0.457395	−	0.889264i	$-0.651217\pi$
$353$	1.57884	−	0.911544i	0.0840332	−	0.0485166i	0.541428	+	0.840747i	$0.317884\pi$
$354$		0			0
$355$	−16.2912	+	4.36521i	−0.864646	+	0.231681i
$356$		0			0
$357$	−3.19624	−	28.3624i	−0.169163	−	1.50110i
$358$		0			0
$359$	8.49087	−	2.27512i	0.448131	−	0.120076i	−0.0276938	−	0.999616i	$-0.508816\pi$
$359$	8.49087	−	2.27512i	0.448131	−	0.120076i	0.475825	+	0.879540i	$0.342150\pi$
$360$		0			0
$361$	17.0977	−	9.87135i	0.899878	−	0.519545i
$362$		0			0
$363$	−11.0041	+	26.5663i	−0.577567	+	1.39437i
$364$		0			0
$365$	11.7467	−	11.7467i	0.614853	−	0.614853i
$366$		0			0
$367$	2.31509	+	17.5849i	0.120847	+	0.917923i	0.939239	+	0.343263i	$0.111532\pi$
$367$	2.31509	+	17.5849i	0.120847	+	0.917923i	−0.818392	+	0.574660i	$0.805134\pi$
$368$		0			0
$369$	−0.268487	+	2.03936i	−0.0139769	+	0.106165i
$370$		0			0
$371$	−4.66471	+	15.3105i	−0.242179	+	0.794879i
$372$		0			0
$373$	13.9297	−	24.1269i	0.721251	−	1.24924i	−0.239247	−	0.970959i	$-0.576901\pi$
$373$	13.9297	−	24.1269i	0.721251	−	1.24924i	0.960498	−	0.278285i	$-0.0897661\pi$
$374$		0			0
$375$	−13.1038	−	22.6964i	−0.676675	−	1.17204i
$376$		0			0
$377$	−2.54446	−	6.14286i	−0.131046	−	0.316374i
$378$		0			0
$379$	4.63300	−	1.91905i	0.237981	−	0.0985751i	−0.260505	−	0.965472i	$-0.583889\pi$
$379$	4.63300	−	1.91905i	0.237981	−	0.0985751i	0.498487	+	0.866897i	$0.333889\pi$
$380$		0			0
$381$	1.84756	+	14.0336i	0.0946535	+	0.718965i
$382$		0			0
$383$	7.28216	+	27.1774i	0.372101	+	1.38870i	0.857534	+	0.514427i	$0.171995\pi$
$383$	7.28216	+	27.1774i	0.372101	+	1.38870i	−0.485433	+	0.874274i	$0.661338\pi$
$384$		0			0
$385$	0.0214972	−	0.633139i	0.00109560	−	0.0322678i
$386$		0			0
$387$	−14.6965	−	8.48501i	−0.747063	−	0.431317i
$388$		0			0
$389$	−3.58204	+	13.3683i	−0.181616	+	0.677802i	0.813713	+	0.581267i	$0.197443\pi$
$389$	−3.58204	+	13.3683i	−0.181616	+	0.677802i	−0.995330	+	0.0965352i	$0.969224\pi$
$390$		0			0
$391$	19.8063	+	2.30066i	1.00165	+	0.116349i
$392$		0			0
$393$	−3.22479	−	3.22479i	−0.162669	−	0.162669i
$394$		0			0
$395$	−13.6895	+	7.90365i	−0.688795	+	0.397676i
$396$		0			0
$397$	3.64074	+	4.74471i	0.182724	+	0.238130i	0.875730	−	0.482802i	$-0.160381\pi$
$397$	3.64074	+	4.74471i	0.182724	+	0.238130i	−0.693006	+	0.720932i	$0.743714\pi$
$398$		0			0
$399$	−17.8303	+	39.2254i	−0.892631	+	1.96373i
$400$		0			0
$401$	−24.4165	+	18.7354i	−1.21930	+	0.935602i	−0.999205	−	0.0398768i	$-0.987303\pi$
$401$	−24.4165	+	18.7354i	−1.21930	+	0.935602i	−0.220095	+	0.975478i	$0.570637\pi$
$402$		0			0
$403$	6.07786	+	4.66370i	0.302760	+	0.232316i
$404$		0			0
$405$	−5.32601	−	12.8581i	−0.264652	−	0.638926i
$406$		0			0
$407$	−0.124117			−0.00615226
$408$		0			0
$409$	10.6449	+	18.4375i	0.526355	+	0.911674i	0.999528	+	0.0307049i	$0.00977520\pi$
$409$	10.6449	+	18.4375i	0.526355	+	0.911674i	−0.473173	+	0.880970i	$0.656891\pi$
$410$		0			0
$411$	45.8673	+	6.03855i	2.26247	+	0.297860i
$412$		0			0
$413$	14.1413	+	4.30850i	0.695850	+	0.212008i
$414$		0			0
$415$	12.1496	−	9.32275i	0.596403	−	0.457636i
$416$		0			0
$417$	40.2630	+	10.7884i	1.97169	+	0.528312i
$418$		0			0
$419$	9.05749	−	21.8667i	0.442488	−	1.06826i	−0.532586	−	0.846376i	$-0.678780\pi$
$419$	9.05749	−	21.8667i	0.442488	−	1.06826i	0.975073	−	0.221883i	$-0.0712204\pi$
$420$		0			0
$421$		−	26.0934i		−	1.27172i	−0.771806	−	0.635858i	$-0.780647\pi$
$421$		−	26.0934i		−	1.27172i	0.771806	−	0.635858i	$-0.219353\pi$
$422$		0			0
$423$	0.728850	−	2.72011i	0.0354379	−	0.132256i
$424$		0			0
$425$	3.05553	−	1.82684i	0.148215	−	0.0886146i
$426$		0			0
$427$	−20.2270	+	14.4573i	−0.978853	+	0.699637i
$428$		0			0
$429$	0.159240	+	0.0919370i	0.00768816	+	0.00443876i
$430$		0			0
$431$	−15.8255	+	2.08346i	−0.762285	+	0.100357i	−0.501638	−	0.865077i	$-0.667269\pi$
$431$	−15.8255	+	2.08346i	−0.762285	+	0.100357i	−0.260647	+	0.965434i	$0.583936\pi$
$432$		0			0
$433$	−27.9921	+	27.9921i	−1.34521	+	1.34521i	−0.454432	+	0.890781i	$0.650158\pi$
$433$	−27.9921	+	27.9921i	−1.34521	+	1.34521i	−0.890781	+	0.454432i	$0.849842\pi$
$434$		0			0
$435$	−54.7608	−	22.6827i	−2.62558	−	1.08755i
$436$		0			0
$437$	−23.8809	−	18.3245i	−1.14238	−	0.876578i
$438$		0			0
$439$	38.0621	+	5.01098i	1.81661	+	0.239161i	0.960626	−	0.277846i	$-0.0896205\pi$
$439$	38.0621	+	5.01098i	1.81661	+	0.239161i	0.855981	+	0.517007i	$0.172954\pi$
$440$		0			0
$441$	−5.18764	−	26.4155i	−0.247031	−	1.25788i
$442$		0			0
$443$	14.6681	−	25.4059i	0.696902	−	1.20707i	−0.272633	−	0.962118i	$-0.587894\pi$
$443$	14.6681	−	25.4059i	0.696902	−	1.20707i	0.969535	−	0.244952i	$-0.0787722\pi$
$444$		0			0
$445$	25.7535	−	33.5626i	1.22083	−	1.59102i
$446$		0			0
$447$	52.2202	−	21.6303i	2.46993	−	1.02308i
$448$		0			0
$449$	−12.4359	−	5.15112i	−0.586886	−	0.243096i	0.0694240	−	0.997587i	$-0.477884\pi$
$449$	−12.4359	−	5.15112i	−0.586886	−	0.243096i	−0.656311	+	0.754491i	$0.727884\pi$
$450$		0			0
$451$	0.0510877	+	0.0136889i	0.00240562	+	0.000644585i
$452$		0			0
$453$	15.6638	+	20.4135i	0.735950	+	0.959109i
$454$		0			0
$455$	4.49142	+	0.747145i	0.210561	+	0.0350267i
$456$		0			0
$457$	23.4697	−	6.28868i	1.09786	−	0.294172i	0.335970	−	0.941873i	$-0.390936\pi$
$457$	23.4697	−	6.28868i	1.09786	−	0.294172i	0.761895	+	0.647701i	$0.224269\pi$
$458$		0			0
$459$	8.37473	−	3.61961i	0.390899	−	0.168949i
$460$		0			0
$461$	−26.3922	−	26.3922i	−1.22921	−	1.22921i	−0.964263	−	0.264945i	$-0.914646\pi$
$461$	−26.3922	−	26.3922i	−1.22921	−	1.22921i	−0.264945	−	0.964263i	$-0.585354\pi$
$462$		0			0
$463$		−	3.36049i		−	0.156175i	−0.996947	−	0.0780875i	$-0.975119\pi$
$463$		−	3.36049i		−	0.156175i	0.996947	−	0.0780875i	$-0.0248814\pi$
$464$		0			0
$465$	67.7098	−	8.91417i	3.13997	−	0.413385i
$466$		0			0
$467$	−2.96437	−	11.0632i	−0.137175	−	0.511943i	−0.999979	−	0.00640573i	$-0.997961\pi$
$467$	−2.96437	−	11.0632i	−0.137175	−	0.511943i	0.862805	−	0.505537i	$-0.168706\pi$
$468$		0			0
$469$	−1.18270	−	2.21915i	−0.0546118	−	0.102471i
$470$		0			0
$471$	−5.93589	+	45.0876i	−0.273511	+	2.07752i
$472$		0			0
$473$	−0.265630	+	0.346175i	−0.0122137	+	0.0159172i
$474$		0			0
$475$	−5.37428			−0.246589
$476$		0			0
$477$	−23.2644			−1.06520
$478$		0			0
$479$	−18.8492	+	24.5647i	−0.861240	+	1.12239i	0.130156	+	0.991494i	$0.458452\pi$
$479$	−18.8492	+	24.5647i	−0.861240	+	1.12239i	−0.991396	+	0.130897i	$0.958214\pi$
$480$		0			0
$481$	0.116437	−	0.884426i	0.00530906	−	0.0403264i
$482$		0			0
$483$	33.4578	+	1.13601i	1.52238	+	0.0516901i
$484$		0			0
$485$	5.86971	+	21.9060i	0.266530	+	0.994702i
$486$		0			0
$487$	20.1415	−	2.65168i	0.912699	−	0.120159i	0.340472	−	0.940255i	$-0.389413\pi$
$487$	20.1415	−	2.65168i	0.912699	−	0.120159i	0.572227	+	0.820096i	$0.306080\pi$
$488$		0			0
$489$			22.9031i			1.03571i
$490$		0			0
$491$	−6.26741	−	6.26741i	−0.282844	−	0.282844i	0.551398	−	0.834242i	$-0.314095\pi$
$491$	−6.26741	−	6.26741i	−0.282844	−	0.282844i	−0.834242	+	0.551398i	$0.814095\pi$
$492$		0			0
$493$	−14.2161	+	35.8588i	−0.640260	+	1.61500i
$494$		0			0
$495$	0.889451	−	0.238328i	0.0399778	−	0.0107120i
$496$		0			0
$497$	6.47035	+	17.2549i	0.290235	+	0.773988i
$498$		0			0
$499$	−10.3307	−	13.4632i	−0.462464	−	0.602694i	0.502661	−	0.864483i	$-0.332354\pi$
$499$	−10.3307	−	13.4632i	−0.462464	−	0.602694i	−0.965125	+	0.261789i	$0.915688\pi$
$500$		0			0
$501$	−50.6036	−	13.5592i	−2.26080	−	0.605781i
$502$		0			0
$503$	7.13161	+	2.95401i	0.317983	+	0.131713i	0.535966	−	0.844240i	$-0.319948\pi$
$503$	7.13161	+	2.95401i	0.317983	+	0.131713i	−0.217983	+	0.975953i	$0.569948\pi$
$504$		0			0
$505$	10.2168	−	4.23195i	0.454643	−	0.188319i
$506$		0			0
$507$	19.9017	−	25.9364i	0.883864	−	1.15187i
$508$		0			0
$509$	−13.1864	+	22.8395i	−0.584477	+	1.01234i	0.410464	+	0.911877i	$0.365367\pi$
$509$	−13.1864	+	22.8395i	−0.584477	+	1.01234i	−0.994940	+	0.100466i	$0.967967\pi$
$510$		0			0
$511$	−14.0171	−	11.5321i	−0.620079	−	0.510148i
$512$		0			0
$513$	−13.6552	−	1.79774i	−0.602893	−	0.0793724i
$514$		0			0
$515$	37.3010	+	28.6221i	1.64368	+	1.26124i
$516$		0			0
$517$	−0.0668967	−	0.0277095i	−0.00294211	−	0.00121866i
$518$		0			0
$519$	−5.22907	+	5.22907i	−0.229531	+	0.229531i
$520$		0			0
$521$	14.6263	−	1.92559i	0.640790	−	0.0843616i	0.196872	−	0.980429i	$-0.436922\pi$
$521$	14.6263	−	1.92559i	0.640790	−	0.0843616i	0.443918	+	0.896068i	$0.353588\pi$
$522$		0			0
$523$	19.2434	+	11.1102i	0.841456	+	0.485815i	0.857759	−	0.514052i	$-0.171856\pi$
$523$	19.2434	+	11.1102i	0.841456	+	0.485815i	−0.0163027	+	0.999867i	$0.505190\pi$
$524$		0			0
$525$	4.86262	−	3.47557i	0.212222	−	0.151686i
$526$		0			0
$527$	−6.47295	−	43.9711i	−0.281966	−	1.91541i
$528$		0			0
$529$	−0.100220	+	0.374026i	−0.00435739	+	0.0162620i
$530$		0			0
$531$			21.4879i			0.932497i
$532$		0			0
$533$	−0.145470	+	0.351196i	−0.00630100	+	0.0152120i
$534$		0			0
$535$	−10.9312	−	2.92900i	−0.472596	−	0.126632i
$536$		0			0
$537$	−28.9927	+	22.2469i	−1.25113	+	0.960023i
$538$		0			0
$539$	−0.690812	+	0.0435920i	−0.0297554	+	0.00187764i
$540$		0			0
$541$	16.1740	+	2.12934i	0.695373	+	0.0915476i	0.469924	−	0.882707i	$-0.344281\pi$
$541$	16.1740	+	2.12934i	0.695373	+	0.0915476i	0.225450	+	0.974255i	$0.427615\pi$
$542$		0			0
$543$	14.3932	+	24.9297i	0.617671	+	1.06984i
$544$		0			0
$545$	10.6225			0.455018
$546$		0			0
$547$	−12.5932	−	30.4027i	−0.538446	−	1.29992i	−0.925807	−	0.377996i	$-0.876613\pi$
$547$	−12.5932	−	30.4027i	−0.538446	−	1.29992i	0.387361	−	0.921928i	$-0.373387\pi$
$548$		0			0
$549$	−28.6708	−	21.9999i	−1.22364	−	0.938932i
$550$		0			0
$551$	46.1988	−	35.4496i	1.96814	−	1.51020i
$552$		0			0
$553$	10.0432	+	14.0513i	0.427081	+	0.597523i
$554$		0			0
$555$	−4.84105	−	6.30898i	−0.205491	−	0.267801i
$556$		0			0
$557$	6.45726	−	3.72810i	0.273603	−	0.157965i	−0.356921	−	0.934135i	$-0.616173\pi$
$557$	6.45726	−	3.72810i	0.273603	−	0.157965i	0.630524	+	0.776170i	$0.282840\pi$
$558$		0			0
$559$	−2.21756	−	2.21756i	−0.0937928	−	0.0937928i
$560$		0			0
$561$	−0.291784	−	1.02606i	−0.0123191	−	0.0433203i
$562$		0			0
$563$	9.09010	−	33.9247i	0.383102	−	1.42976i	−0.458035	−	0.888934i	$-0.651447\pi$
$563$	9.09010	−	33.9247i	0.383102	−	1.42976i	0.841137	−	0.540822i	$-0.181887\pi$
$564$		0			0
$565$	1.47616	+	0.852264i	0.0621027	+	0.0358550i
$566$		0			0
$567$	−13.4198	+	7.15210i	−0.563580	+	0.300360i
$568$		0			0
$569$	1.15860	+	4.32396i	0.0485711	+	0.181270i	0.985950	−	0.167042i	$-0.0534216\pi$
$569$	1.15860	+	4.32396i	0.0485711	+	0.181270i	−0.937379	+	0.348312i	$0.886755\pi$
$570$		0			0
$571$	3.08682	+	23.4467i	0.129179	+	0.981214i	0.926139	+	0.377182i	$0.123107\pi$
$571$	3.08682	+	23.4467i	0.129179	+	0.981214i	−0.796960	+	0.604032i	$0.793560\pi$
$572$		0			0
$573$	46.2019	−	19.1374i	1.93011	−	0.799478i
$574$		0			0
$575$	1.59792	+	3.85771i	0.0666377	+	0.160878i
$576$		0			0
$577$	−0.0109195	−	0.0189131i	−0.000454583	−	0.000787361i	0.865798	−	0.500394i	$-0.166811\pi$
$577$	−0.0109195	−	0.0189131i	−0.000454583	−	0.000787361i	−0.866253	+	0.499606i	$0.833478\pi$
$578$		0			0
$579$	−0.619457	+	1.07293i	−0.0257437	+	0.0445895i
$580$		0			0
$581$	−11.4236	−	12.2266i	−0.473931	−	0.507245i
$582$		0			0
$583$	−0.0780795	+	0.593073i	−0.00323372	+	0.0245626i
$584$		0			0
$585$	0.863847	+	6.56157i	0.0357157	+	0.271288i
$586$		0			0
$587$	−22.5174	+	22.5174i	−0.929393	+	0.929393i	−0.997667	−	0.0682734i	$-0.978251\pi$
$587$	−22.5174	+	22.5174i	−0.929393	+	0.929393i	0.0682734	+	0.997667i	$0.478251\pi$
$588$		0			0
$589$	−25.6763	+	61.9881i	−1.05797	+	2.55417i
$590$		0			0
$591$	−27.0322	+	15.6070i	−1.11195	+	0.641987i
$592$		0			0
$593$	−11.2371	+	3.01096i	−0.461451	+	0.123646i	−0.482053	−	0.876142i	$-0.660109\pi$
$593$	−11.2371	+	3.01096i	−0.461451	+	0.123646i	0.0206013	+	0.999788i	$0.493442\pi$
$594$		0			0
$595$	−15.6861	−	21.2531i	−0.643068	−	0.871291i
$596$		0			0
$597$	−45.1168	+	12.0890i	−1.84651	+	0.494770i
$598$		0			0
$599$	−16.9041	+	9.75957i	−0.690682	+	0.398765i	−0.803867	−	0.594808i	$-0.797228\pi$
$599$	−16.9041	+	9.75957i	−0.690682	+	0.398765i	0.113186	+	0.993574i	$0.463895\pi$
$600$		0			0
$601$	15.1437	−	36.5601i	0.617724	−	1.49132i	−0.236617	−	0.971603i	$-0.576039\pi$
$601$	15.1437	−	36.5601i	0.617724	−	1.49132i	0.854340	−	0.519714i	$-0.173961\pi$
$602$		0			0
$603$	2.58457	−	2.58457i	0.105252	−	0.105252i
$604$		0			0
$605$	3.47360	+	26.3846i	0.141222	+	1.07269i
$606$		0			0
$607$	1.60532	−	12.1936i	0.0651579	−	0.494924i	−0.927486	−	0.373857i	$-0.878035\pi$
$607$	1.60532	−	12.1936i	0.0651579	−	0.494924i	0.992644	−	0.121067i	$-0.0386315\pi$
$608$		0			0
$609$	−18.8751	+	61.9516i	−0.764856	+	2.51040i
$610$		0			0
$611$	0.260208	−	0.450693i	0.0105269	−	0.0182331i
$612$		0			0
$613$	−3.65753	−	6.33503i	−0.147726	−	0.255869i	0.782661	−	0.622449i	$-0.213862\pi$
$613$	−3.65753	−	6.33503i	−0.147726	−	0.255869i	−0.930387	+	0.366579i	$0.880529\pi$
$614$		0			0
$615$	1.29680	+	3.13075i	0.0522920	+	0.126244i
$616$		0			0
$617$	−18.3770	+	7.61199i	−0.739829	+	0.306447i	−0.720584	−	0.693367i	$-0.756126\pi$
$617$	−18.3770	+	7.61199i	−0.739829	+	0.306447i	−0.0192452	+	0.999815i	$0.506126\pi$
$618$		0			0
$619$	1.40411	+	10.6653i	0.0564360	+	0.428674i	0.996217	+	0.0868975i	$0.0276953\pi$
$619$	1.40411	+	10.6653i	0.0564360	+	0.428674i	−0.939781	+	0.341777i	$0.888971\pi$
$620$		0			0
$621$	2.76962	+	10.3364i	0.111141	+	0.414785i
$622$		0			0
$623$	−39.2233	−	24.4568i	−1.57145	−	0.979841i
$624$		0			0
$625$	−24.7438	−	14.2858i	−0.989750	−	0.571433i
$626$		0			0
$627$	−0.416798	+	1.55551i	−0.0166453	+	0.0621211i
$628$		0			0
$629$	−4.05725	+	3.21278i	−0.161773	+	0.128102i
$630$		0			0
$631$	25.0396	+	25.0396i	0.996810	+	0.996810i	0.999995	−	0.00318517i	$-0.00101387\pi$
$631$	25.0396	+	25.0396i	0.996810	+	0.996810i	−0.00318517	+	0.999995i	$0.501014\pi$
$632$		0			0
$633$	−6.21558	+	3.58857i	−0.247047	+	0.142633i
$634$		0			0
$635$	7.97471	+	10.3928i	0.316467	+	0.412428i
$636$		0			0
$637$	0.337440	−	4.96344i	0.0133699	−	0.196659i
$638$		0			0
$639$	−21.2509	+	16.3064i	−0.840672	+	0.645070i
$640$		0			0
$641$	−15.9082	−	12.2068i	−0.628334	−	0.482138i	0.244829	−	0.969566i	$-0.421268\pi$
$641$	−15.9082	−	12.2068i	−0.628334	−	0.482138i	−0.873163	+	0.487428i	$0.837935\pi$
$642$		0			0
$643$	−4.75333	−	11.4756i	−0.187453	−	0.452552i	0.802015	−	0.597304i	$-0.203761\pi$
$643$	−4.75333	−	11.4756i	−0.187453	−	0.452552i	−0.989468	+	0.144752i	$0.953761\pi$
$644$		0			0
$645$	−27.9570			−1.10080
$646$		0			0
$647$	1.26369	+	2.18878i	0.0496809	+	0.0860499i	0.889796	−	0.456358i	$-0.150846\pi$
$647$	1.26369	+	2.18878i	0.0496809	+	0.0860499i	−0.840116	+	0.542408i	$0.817513\pi$
$648$		0			0
$649$	0.547785	+	0.0721173i	0.0215025	+	0.00283085i
$650$		0			0
$651$	−16.8561	−	72.6914i	−0.660644	−	2.84900i
$652$		0			0
$653$	9.83628	−	7.54764i	0.384923	−	0.295362i	−0.398115	−	0.917336i	$-0.630336\pi$
$653$	9.83628	−	7.54764i	0.384923	−	0.295362i	0.783038	+	0.621973i	$0.213669\pi$
$654$		0			0
$655$	−4.07686	−	1.09239i	−0.159296	−	0.0426833i
$656$		0			0
$657$	10.0966	−	24.3753i	0.393905	−	0.950970i
$658$		0			0
$659$		−	35.4374i		−	1.38045i	−0.723596	−	0.690223i	$-0.757512\pi$
$659$		−	35.4374i		−	1.38045i	0.723596	−	0.690223i	$-0.242488\pi$
$660$		0			0
$661$	−7.69624	+	28.7228i	−0.299349	+	1.11719i	0.638353	+	0.769744i	$0.279616\pi$
$661$	−7.69624	+	28.7228i	−0.299349	+	1.11719i	−0.937702	+	0.347442i	$0.887050\pi$
$662$		0			0
$663$	7.58516	−	1.11661i	0.294583	−	0.0433654i
$664$		0			0
$665$	3.86037	+	39.6895i	0.149699	+	1.53909i
$666$		0			0
$667$	−39.1823	−	22.6219i	−1.51714	−	0.875923i
$668$		0			0
$669$	56.1393	−	7.39088i	2.17047	−	0.285748i
$670$		0			0
$671$	−0.657061	+	0.657061i	−0.0253656	+	0.0253656i
$672$		0			0
$673$	−26.1734	−	10.8414i	−1.00891	−	0.417904i	−0.183853	−	0.982954i	$-0.558857\pi$
$673$	−26.1734	−	10.8414i	−1.00891	−	0.417904i	−0.825057	+	0.565049i	$0.808857\pi$
$674$		0			0
$675$	1.51575	+	1.16308i	0.0583412	+	0.0447668i
$676$		0			0
$677$	27.5746	+	3.63026i	1.05978	+	0.139522i	0.640209	−	0.768201i	$-0.278848\pi$
$677$	27.5746	+	3.63026i	1.05978	+	0.139522i	0.419569	+	0.907723i	$0.362181\pi$
$678$		0			0
$679$	23.2019	−	8.70040i	0.890408	−	0.333891i
$680$		0			0
$681$	16.3570	−	28.3311i	0.626800	−	1.08565i
$682$		0			0
$683$	13.5708	−	17.6858i	0.519272	−	0.676728i	−0.457943	−	0.888982i	$-0.651414\pi$
$683$	13.5708	−	17.6858i	0.519272	−	0.676728i	0.977215	+	0.212253i	$0.0680802\pi$
$684$		0			0
$685$	39.5564	−	16.3848i	1.51137	−	0.626030i
$686$		0			0
$687$	−50.6894	−	20.9962i	−1.93392	−	0.801056i
$688$		0			0
$689$	−4.15283	−	1.11275i	−0.158210	−	0.0423923i
$690$		0			0
$691$	23.0315	+	30.0152i	0.876158	+	1.14183i	0.988955	+	0.148213i	$0.0473522\pi$
$691$	23.0315	+	30.0152i	0.876158	+	1.14183i	−0.112797	+	0.993618i	$0.535981\pi$
$692$		0			0
$693$	−0.353262	−	0.942067i	−0.0134193	−	0.0357862i
$694$		0			0
$695$	37.2625	−	9.98447i	1.41345	−	0.378732i
$696$		0			0
$697$	2.02434	−	0.874932i	0.0766772	−	0.0331404i
$698$		0			0
$699$	−9.12436	−	9.12436i	−0.345115	−	0.345115i
$700$		0			0
$701$			45.7392i			1.72755i	0.503880	+	0.863774i	$0.331905\pi$
$701$			45.7392i			1.72755i	−0.503880	+	0.863774i	$0.668095\pi$
$702$		0			0
$703$	7.74587	−	1.01976i	0.292141	−	0.0384611i
$704$		0			0
$705$	−1.20073	−	4.48119i	−0.0452222	−	0.168771i
$706$		0			0
$707$	−5.68292	−	10.6632i	−0.213728	−	0.401029i
$708$		0			0
$709$	1.84343	−	14.0023i	0.0692316	−	0.525866i	−0.921328	−	0.388786i	$-0.872895\pi$
$709$	1.84343	−	14.0023i	0.0692316	−	0.525866i	0.990560	−	0.137081i	$-0.0437720\pi$
$710$		0			0
$711$	−15.2829	+	19.9171i	−0.573155	+	0.746950i
$712$		0			0
$713$	52.1299			1.95228
$714$		0			0
$715$	0.170171			0.00636405
$716$		0			0
$717$	−22.1016	+	28.8034i	−0.825401	+	1.07568i
$718$		0			0
$719$	−3.57168	+	27.1296i	−0.133201	+	1.01176i	0.786070	+	0.618137i	$0.212112\pi$
$719$	−3.57168	+	27.1296i	−0.133201	+	1.01176i	−0.919271	+	0.393625i	$0.871221\pi$
$720$		0			0
$721$	27.1810	−	43.5923i	1.01227	−	1.62346i
$722$		0			0
$723$	−5.05892	−	18.8802i	−0.188143	−	0.702161i
$724$		0			0
$725$	−8.00872	+	1.05437i	−0.297436	+	0.0391583i
$726$		0			0
$727$		−	11.4379i		−	0.424207i	−0.977247	−	0.212104i	$-0.931969\pi$
$727$		−	11.4379i		−	0.424207i	0.977247	−	0.212104i	$-0.0680314\pi$
$728$		0			0
$729$	−27.9111	−	27.9111i	−1.03375	−	1.03375i
$730$		0			0
$731$	0.277630	+	18.1919i	0.0102685	+	0.672852i
$732$		0			0
$733$	5.17409	−	1.38639i	0.191110	−	0.0512076i	−0.161995	−	0.986792i	$-0.551793\pi$
$733$	5.17409	−	1.38639i	0.191110	−	0.0512076i	0.353104	+	0.935584i	$0.385126\pi$
$734$		0			0
$735$	−29.1602	−	33.4143i	−1.07559	−	1.23250i
$736$		0			0
$737$	−0.0572135	−	0.0745620i	−0.00210748	−	0.00274653i
$738$		0			0
$739$	43.6773	+	11.7033i	1.60670	+	0.430513i	0.947056	−	0.321068i	$-0.104042\pi$
$739$	43.6773	+	11.7033i	1.60670	+	0.430513i	0.659641	+	0.751581i	$0.270708\pi$
$740$		0			0
$741$	−10.6932	−	4.42925i	−0.392823	−	0.162713i
$742$		0			0
$743$	32.8694	−	13.6149i	1.20586	−	0.499484i	0.312972	−	0.949762i	$-0.398675\pi$
$743$	32.8694	−	13.6149i	1.20586	−	0.499484i	0.892888	+	0.450279i	$0.148675\pi$
$744$		0			0
$745$	31.8446	−	41.5008i	1.16670	−	1.52047i
$746$		0			0
$747$	12.1610	−	21.0634i	0.444947	−	0.770671i
$748$		0			0
$749$	−2.02904	+	12.1975i	−0.0741396	+	0.445686i
$750$		0			0
$751$	−5.81621	−	0.765719i	−0.212237	−	0.0279415i	0.0236580	−	0.999720i	$-0.492469\pi$
$751$	−5.81621	−	0.765719i	−0.212237	−	0.0279415i	−0.235895	+	0.971779i	$0.575802\pi$
$752$		0			0
$753$	−45.0372	−	34.5582i	−1.64125	−	1.25937i
$754$		0			0
$755$	22.0005	+	9.11290i	0.800679	+	0.331652i
$756$		0			0
$757$	2.78478	−	2.78478i	0.101215	−	0.101215i	−0.654686	−	0.755901i	$-0.727199\pi$
$757$	2.78478	−	2.78478i	0.101215	−	0.101215i	0.755901	+	0.654686i	$0.227199\pi$
$758$		0			0
$759$	1.24049	−	0.163313i	0.0450268	−	0.00592789i
$760$		0			0
$761$	−46.9070	−	27.0817i	−1.70038	−	0.981713i	−0.945373	−	0.325991i	$-0.894302\pi$
$761$	−46.9070	−	27.0817i	−1.70038	−	0.981713i	−0.755003	−	0.655721i	$-0.772365\pi$
$762$		0			0
$763$	−1.12359	−	11.5519i	−0.0406768	−	0.418209i
$764$		0			0
$765$	22.9060	−	30.8141i	0.828169	−	1.11409i
$766$		0			0
$767$	−1.02778	+	3.83572i	−0.0371109	+	0.138500i
$768$		0			0
$769$		−	6.35912i		−	0.229316i	−0.993405	−	0.114658i	$-0.963423\pi$
$769$		−	6.35912i		−	0.229316i	0.993405	−	0.114658i	$-0.0365772\pi$
$770$		0			0
$771$	−10.2044	+	24.6355i	−0.367501	+	0.887227i
$772$		0			0
$773$	24.6393	+	6.60208i	0.886214	+	0.237460i	0.673086	−	0.739564i	$-0.264968\pi$
$773$	24.6393	+	6.60208i	0.886214	+	0.237460i	0.213128	+	0.977024i	$0.431635\pi$
$774$		0			0
$775$	7.38397	−	5.66592i	0.265240	−	0.203526i
$776$		0			0
$777$	−6.34894	+	5.93196i	−0.227767	+	0.212808i
$778$		0			0
$779$	−3.30074	−	0.434550i	−0.118261	−	0.0155694i
$780$		0			0
$781$	0.344372	+	0.596470i	0.0123226	+	0.0213434i
$782$		0			0
$783$	−20.7016			−0.739816
$784$		0			0
$785$	16.1062	+	38.8839i	0.574856	+	1.38783i
$786$		0			0
$787$	0.868293	+	0.666265i	0.0309513	+	0.0237498i	0.624121	−	0.781327i	$-0.285457\pi$
$787$	0.868293	+	0.666265i	0.0309513	+	0.0237498i	−0.593170	+	0.805077i	$0.702124\pi$
$788$		0			0
$789$	−53.6026	+	41.1307i	−1.90830	+	1.46429i
$790$		0			0
$791$	0.770695	−	1.69547i	0.0274028	−	0.0602841i
$792$		0			0
$793$	−4.06564	−	5.29845i	−0.144375	−	0.188153i
$794$		0			0
$795$	−33.1918	+	19.1633i	−1.17719	+	0.679652i
$796$		0			0
$797$	−28.7159	−	28.7159i	−1.01717	−	1.01717i	−0.999850	−	0.0173180i	$-0.994487\pi$
$797$	−28.7159	−	28.7159i	−1.01717	−	1.01717i	−0.0173180	−	0.999850i	$-0.505513\pi$
$798$		0			0
$799$	−2.90404	+	0.825831i	−0.102738	+	0.0292158i
$800$		0			0
$801$	17.3895	−	64.8985i	0.614428	−	2.29307i
$802$		0			0
$803$	−0.587506	−	0.339197i	−0.0207326	−	0.0119700i
$804$		0			0
$805$	27.3417	−	14.5717i	0.963668	−	0.513587i
$806$		0			0
$807$	−3.91580	−	14.6140i	−0.137843	−	0.514437i
$808$		0			0
$809$	−4.41371	−	33.5255i	−0.155178	−	1.17869i	−0.874855	−	0.484384i	$-0.839044\pi$
$809$	−4.41371	−	33.5255i	−0.155178	−	1.17869i	0.719678	−	0.694308i	$-0.244290\pi$
$810$		0			0
$811$	−36.8070	+	15.2460i	−1.29247	+	0.535358i	−0.919720	−	0.392574i	$-0.871585\pi$
$811$	−36.8070	+	15.2460i	−1.29247	+	0.535358i	−0.372749	+	0.927932i	$0.621585\pi$
$812$		0			0
$813$	8.97365	+	21.6643i	0.314719	+	0.759800i
$814$		0			0
$815$	10.5981	+	18.3565i	0.371237	+	0.643001i
$816$		0			0
$817$	13.7331	−	23.7865i	0.480461	−	0.832184i
$818$		0			0
$819$	7.04432	−	1.63348i	0.246149	−	0.0570785i
$820$		0			0
$821$	−4.16106	+	31.6064i	−0.145222	+	1.10307i	0.751265	+	0.660000i	$0.229444\pi$
$821$	−4.16106	+	31.6064i	−0.145222	+	1.10307i	−0.896487	+	0.443070i	$0.853889\pi$
$822$		0			0
$823$	−6.38735	−	48.5167i	−0.222649	−	1.69119i	−0.628949	−	0.777447i	$-0.716514\pi$
$823$	−6.38735	−	48.5167i	−0.222649	−	1.69119i	0.406300	−	0.913740i	$-0.366819\pi$
$824$		0			0
$825$	0.157959	−	0.157959i	0.00549943	−	0.00549943i
$826$		0			0
$827$	15.0460	−	36.3242i	0.523201	−	1.26312i	−0.412704	−	0.910865i	$-0.635416\pi$
$827$	15.0460	−	36.3242i	0.523201	−	1.26312i	0.935905	−	0.352253i	$-0.114584\pi$
$828$		0			0
$829$	−0.977007	+	0.564075i	−0.0339329	+	0.0195911i	−0.516870	−	0.856064i	$-0.672903\pi$
$829$	−0.977007	+	0.564075i	−0.0339329	+	0.0195911i	0.482938	+	0.875655i	$0.339570\pi$
$830$		0			0
$831$	−41.9708	+	11.2461i	−1.45595	+	0.390121i
$832$		0			0
$833$	−21.4535	+	19.3067i	−0.743319	+	0.668937i
$834$		0			0
$835$	−46.8326	+	12.5487i	−1.62071	+	0.434267i
$836$		0			0
$837$	20.6568	−	11.9262i	0.714005	−	0.412231i
$838$		0			0
$839$	−7.37460	+	17.8039i	−0.254600	+	0.614658i	−0.998565	−	0.0535609i	$-0.982943\pi$
$839$	−7.37460	+	17.8039i	−0.254600	+	0.614658i	0.743965	+	0.668219i	$0.232943\pi$
$840$		0			0
$841$	41.3844	−	41.3844i	1.42705	−	1.42705i
$842$		0			0
$843$	−4.64895	−	35.3122i	−0.160118	−	1.21622i
$844$		0			0
$845$	3.94918	−	29.9970i	0.135856	−	1.03193i
$846$		0			0
$847$	28.3258	−	6.56836i	0.973286	−	0.225692i
$848$		0			0
$849$	1.03209	−	1.78763i	0.0354213	−	0.0613514i
$850$		0			0
$851$	−3.03505	−	5.25687i	−0.104040	−	0.180203i
$852$		0			0
$853$	11.7303	+	28.3195i	0.401639	+	0.969642i	0.987268	+	0.159063i	$0.0508473\pi$
$853$	11.7303	+	28.3195i	0.401639	+	0.969642i	−0.585630	+	0.810579i	$0.699153\pi$
$854$		0			0
$855$	−53.5505	+	22.1813i	−1.83139	+	0.758586i
$856$		0			0
$857$	−0.788056	−	5.98588i	−0.0269195	−	0.204474i	0.972700	−	0.232067i	$-0.0745489\pi$
$857$	−0.788056	−	5.98588i	−0.0269195	−	0.204474i	−0.999619	+	0.0275935i	$0.991216\pi$
$858$		0			0
$859$	3.27322	+	12.2158i	0.111681	+	0.416799i	0.999017	−	0.0443241i	$-0.0141134\pi$
$859$	3.27322	+	12.2158i	0.111681	+	0.416799i	−0.887336	+	0.461123i	$0.847447\pi$
$860$		0			0
$861$	3.26752	−	1.74142i	0.111357	−	0.0593475i
$862$		0			0
$863$	29.3365	+	16.9375i	0.998627	+	0.576558i	0.907842	−	0.419313i	$-0.137729\pi$
$863$	29.3365	+	16.9375i	0.998627	+	0.576558i	0.0907853	+	0.995870i	$0.471062\pi$
$864$		0			0
$865$	−1.77134	+	6.61073i	−0.0602274	+	0.224772i
$866$		0			0
$867$	−36.0977	−	25.9879i	−1.22594	−	0.882595i
$868$		0			0
$869$	0.456448	+	0.456448i	0.0154840	+	0.0154840i
$870$		0			0
$871$	0.584982	−	0.337740i	0.0198214	−	0.0114439i
$872$		0			0
$873$	21.9265	+	28.5752i	0.742099	+	0.967122i
$874$		0			0
$875$	−10.9666	+	24.1257i	−0.370737	+	0.815597i
$876$		0			0
$877$	20.2678	−	15.5521i	0.684396	−	0.525156i	−0.207022	−	0.978336i	$-0.566377\pi$
$877$	20.2678	−	15.5521i	0.684396	−	0.525156i	0.891419	+	0.453180i	$0.149711\pi$
$878$		0			0
$879$	−4.45726	−	3.42018i	−0.150340	−	0.115360i
$880$		0			0
$881$	10.5467	+	25.4619i	0.355326	+	0.857833i	0.995944	+	0.0899731i	$0.0286781\pi$
$881$	10.5467	+	25.4619i	0.355326	+	0.857833i	−0.640618	+	0.767859i	$0.721322\pi$
$882$		0			0
$883$	−18.5772			−0.625171			−0.312586	−	0.949890i	$-0.601195\pi$
$883$	−18.5772			−0.625171			−0.312586	+	0.949890i	$0.601195\pi$
$884$		0			0
$885$	17.7000	+	30.6572i	0.594978	+	1.03053i
$886$		0			0
$887$	−10.6182	−	1.39792i	−0.356525	−	0.0469374i	−0.0498636	−	0.998756i	$-0.515879\pi$
$887$	−10.6182	−	1.39792i	−0.356525	−	0.0469374i	−0.306662	+	0.951819i	$0.599212\pi$
$888$		0			0
$889$	10.4587	−	9.77179i	0.350773	−	0.327735i
$890$		0			0
$891$	−0.450898	+	0.345986i	−0.0151057	+	0.0115910i
$892$		0			0
$893$	4.40254	+	1.17966i	0.147325	+	0.0394757i
$894$		0			0
$895$	−12.9428	+	31.2466i	−0.432629	+	1.04446i
$896$		0			0
$897$			8.99259i			0.300254i
$898$		0			0
$899$	−26.1014	+	97.4117i	−0.870530	+	3.24886i
$900$		0			0
$901$	12.7994	+	21.4080i	0.426410	+	0.713203i
$902$		0			0
$903$	2.95714	+	30.4031i	0.0984075	+	1.01175i
$904$		0			0
$905$	23.0719	+	13.3206i	0.766937	+	0.442791i
$906$		0			0
$907$	15.1831	−	1.99889i	0.504146	−	0.0663721i	0.125836	−	0.992051i	$-0.459839\pi$
$907$	15.1831	−	1.99889i	0.504146	−	0.0663721i	0.378310	+	0.925679i	$0.376505\pi$
$908$		0			0
$909$	12.4190	−	12.4190i	0.411913	−	0.411913i
$910$		0			0
$911$	33.1949	+	13.7498i	1.09980	+	0.455550i	0.857412	−	0.514630i	$-0.172071\pi$
$911$	33.1949	+	13.7498i	1.09980	+	0.455550i	0.242383	+	0.970181i	$0.422071\pi$
$912$		0			0
$913$	−0.496150	−	0.380709i	−0.0164202	−	0.0125996i
$914$		0			0
$915$	−59.0269	−	7.77103i	−1.95137	−	0.256902i
$916$		0			0
$917$	−0.756745	+	4.54913i	−0.0249899	+	0.150225i
$918$		0			0
$919$	−9.89943	+	17.1463i	−0.326552	+	0.565605i	−0.981825	−	0.189787i	$-0.939220\pi$
$919$	−9.89943	+	17.1463i	−0.326552	+	0.565605i	0.655273	+	0.755392i	$0.272553\pi$
$920$		0			0
$921$	−53.3579	+	69.5374i	−1.75820	+	2.29133i
$922$		0			0
$923$	−4.57335	+	1.89434i	−0.150534	+	0.0623531i
$924$		0			0
$925$	−1.00126	−	0.414736i	−0.0329213	−	0.0136364i
$926$		0			0
$927$	72.1273	+	19.3265i	2.36897	+	0.634764i
$928$		0			0
$929$	−25.8210	−	33.6506i	−0.847159	−	1.10404i	−0.993390	−	0.114789i	$-0.963381\pi$
$929$	−25.8210	−	33.6506i	−0.847159	−	1.10404i	0.146231	−	0.989250i	$-0.453286\pi$
$930$		0			0
$931$	42.7539	−	8.39629i	1.40120	−	0.275177i
$932$		0			0
$933$	59.4975	−	15.9423i	1.94786	−	0.521928i
$934$		0			0
$935$	−0.708659	−	0.687354i	−0.0231756	−	0.0224789i
$936$		0			0
$937$	18.3610	+	18.3610i	0.599828	+	0.599828i	0.940267	−	0.340439i	$-0.110576\pi$
$937$	18.3610	+	18.3610i	0.599828	+	0.599828i	−0.340439	+	0.940267i	$0.610576\pi$
$938$		0			0
$939$			53.4903i			1.74559i
$940$		0			0
$941$	10.8426	−	1.42746i	0.353459	−	0.0465338i	0.0482940	−	0.998833i	$-0.484622\pi$
$941$	10.8426	−	1.42746i	0.353459	−	0.0465338i	0.305165	+	0.952299i	$0.401288\pi$
$942$		0			0
$943$	0.669473	+	2.49851i	0.0218010	+	0.0813626i
$944$		0			0
$945$	7.50063	−	12.0294i	0.243995	−	0.391315i
$946$		0			0
$947$	−3.57616	+	27.1636i	−0.116210	+	0.882699i	0.829687	+	0.558230i	$0.188519\pi$
$947$	−3.57616	+	27.1636i	−0.116210	+	0.882699i	−0.945896	+	0.324470i	$0.894814\pi$
$948$		0			0
$949$	2.96818	−	3.86820i	0.0963511	−	0.125567i
$950$		0			0
$951$	−13.6583			−0.442902
$952$		0			0
$953$	24.4996			0.793620			0.396810	−	0.917901i	$-0.370117\pi$
$953$	24.4996			0.793620			0.396810	+	0.917901i	$0.370117\pi$
$954$		0			0
$955$	28.1746	−	36.7178i	0.911708	−	1.18816i
$956$		0			0
$957$	−0.315938	+	2.39979i	−0.0102128	+	0.0775740i
$958$		0			0
$959$	−22.0025	−	41.2844i	−0.710497	−	1.33314i
$960$		0			0
$961$	−22.0507	−	82.2942i	−0.711312	−	2.65465i
$962$		0			0
$963$	−17.8194	+	2.34597i	−0.574223	+	0.0755979i
$964$		0			0
$965$			1.14659i			0.0369099i
$966$		0			0
$967$	−5.10604	−	5.10604i	−0.164199	−	0.164199i	0.620225	−	0.784424i	$-0.287041\pi$
$967$	−5.10604	−	5.10604i	−0.164199	−	0.164199i	−0.784424	+	0.620225i	$0.787041\pi$
$968$		0			0
$969$	26.6398	+	61.6367i	0.855794	+	1.98006i
$970$		0			0
$971$	10.7051	−	2.86843i	0.343544	−	0.0920522i	−0.0829219	−	0.996556i	$-0.526425\pi$
$971$	10.7051	−	2.86843i	0.343544	−	0.0920522i	0.426466	+	0.904504i	$0.359759\pi$
$972$		0			0
$973$	−14.7995	−	39.4669i	−0.474451	−	1.26525i
$974$		0			0
$975$	0.977390	+	1.27376i	0.0313015	+	0.0407929i
$976$		0			0
$977$	−9.03592	−	2.42117i	−0.289085	−	0.0774600i	0.111363	−	0.993780i	$-0.464479\pi$
$977$	−9.03592	−	2.42117i	−0.289085	−	0.0774600i	−0.400447	+	0.916320i	$0.631145\pi$
$978$		0			0
$979$	−1.59608	−	0.661116i	−0.0510108	−	0.0211294i
$980$		0			0
$981$	15.5863	−	6.45607i	0.497633	−	0.206126i
$982$		0			0
$983$	17.7531	−	23.1362i	0.566234	−	0.737931i	−0.419217	−	0.907886i	$-0.637695\pi$
$983$	17.7531	−	23.1362i	0.566234	−	0.737931i	0.985452	+	0.169955i	$0.0543622\pi$
$984$		0			0
$985$	−14.4440	+	25.0177i	−0.460223	+	0.797129i
$986$		0			0
$987$	−4.74628	+	1.77979i	−0.151076	+	0.0566514i
$988$		0			0
$989$	−21.1574	−	2.78543i	−0.672766	−	0.0885714i
$990$		0			0
$991$	39.8771	+	30.5988i	1.26674	+	0.972003i	0.999966	+	0.00824358i	$0.00262404\pi$
$991$	39.8771	+	30.5988i	1.26674	+	0.972003i	0.266773	+	0.963759i	$0.414043\pi$
$992$		0			0
$993$	47.2458	+	19.5698i	1.49930	+	0.621030i
$994$		0			0
$995$	−30.5665	+	30.5665i	−0.969023	+	0.969023i
$996$		0			0
$997$	−42.5245	+	5.59846i	−1.34676	+	0.177305i	−0.769183	−	0.639028i	$-0.779337\pi$
$997$	−42.5245	+	5.59846i	−1.34676	+	0.177305i	−0.577581	+	0.816333i	$0.696003\pi$
$998$		0			0
$999$	−2.40532	−	1.38871i	−0.0761010	−	0.0439369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bh.a.457.11	yes	96
7.4	even	3	inner	476.2.bh.a.389.2	yes	96
17.8	even	8	inner	476.2.bh.a.93.2	yes	96
119.25	even	24	inner	476.2.bh.a.25.11	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bh.a.25.11	✓	96	119.25	even	24	inner
476.2.bh.a.93.2	yes	96	17.8	even	8	inner
476.2.bh.a.389.2	yes	96	7.4	even	3	inner
476.2.bh.a.457.11	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.59278 - 2.07576i) q^{3} +(0.316063 - 2.40074i) q^{5} +(-2.64423 - 0.0897805i) q^{7} +(-0.995345 - 3.71468i) q^{9} +O(q^{10})\)	\(q+(1.59278 - 2.07576i) q^{3} +(0.316063 - 2.40074i) q^{5} +(-2.64423 - 0.0897805i) q^{7} +(-0.995345 - 3.71468i) q^{9} +(-0.0980378 + 0.0129069i) q^{11} -0.710699i q^{13} +(-4.47992 - 4.47992i) q^{15} +(-2.87065 + 2.95962i) q^{17} +(6.01227 - 1.61098i) q^{19} +(-4.39804 + 5.34577i) q^{21} +(-2.94399 - 3.83668i) q^{23} +(-0.834006 - 0.223471i) q^{25} +(-2.04433 - 0.846789i) q^{27} +(8.64340 - 3.58022i) q^{29} +(-6.56213 + 8.55194i) q^{31} +(-0.129361 + 0.224060i) q^{33} +(-1.05128 + 6.31971i) q^{35} +(1.24444 + 0.163834i) q^{37} +(-1.47524 - 1.13199i) q^{39} +(-0.494155 - 0.204686i) q^{41} +(3.12025 - 3.12025i) q^{43} +(-9.23255 + 1.21549i) q^{45} +(0.634155 + 0.366129i) q^{47} +(6.98388 + 0.474800i) q^{49} +(1.57114 + 10.6728i) q^{51} +(1.56571 - 5.84330i) q^{53} +0.239442i q^{55} +(6.23224 - 15.0460i) q^{57} +(-5.39710 - 1.44615i) q^{59} +(7.45525 - 5.72062i) q^{61} +(2.29841 + 9.91182i) q^{63} +(-1.70620 - 0.224626i) q^{65} +(0.475222 + 0.823108i) q^{67} -12.6532 q^{69} +(-2.66546 - 6.43500i) q^{71} +(5.44281 + 4.17642i) q^{73} +(-1.79226 + 1.37525i) q^{75} +(0.260393 - 0.0253269i) q^{77} +(-3.97401 - 5.17903i) q^{79} +(4.97757 - 2.87380i) q^{81} +(4.47205 + 4.47205i) q^{83} +(6.19797 + 7.82709i) q^{85} +(6.33542 - 23.6441i) q^{87} +(15.1302 + 8.73541i) q^{89} +(-0.0638069 + 1.87925i) q^{91} +(7.29968 + 27.2428i) q^{93} +(-1.96729 - 14.9431i) q^{95} +(-8.65286 + 3.58413i) q^{97} +(0.145526 + 0.351332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{5}+O(q^{10}) \) 96 * q + 4 * q^5	\( 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) \) 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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