LMFDB - Embedded newform 360.2.w.e.307.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(163,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("360.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.w (of order $4$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.4
Character	$\chi$	$=$	360.307
Dual form			360.2.w.e.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.647304 - 1.25738i) q^{2} +(-1.16200 + 1.62781i) q^{4} +(1.28903 - 1.82713i) q^{5} +(1.45533 - 1.45533i) q^{7} +(2.79894 + 0.407381i) q^{8} +O(q^{10})$	\(q+(-0.647304 - 1.25738i) q^{2} +(-1.16200 + 1.62781i) q^{4} +(1.28903 - 1.82713i) q^{5} +(1.45533 - 1.45533i) q^{7} +(2.79894 + 0.407381i) q^{8} +(-3.13178 - 0.438090i) q^{10} -0.725670 q^{11} +(4.57738 + 4.57738i) q^{13} +(-2.77193 - 0.887857i) q^{14} +(-1.29953 - 3.78302i) q^{16} +(-2.36535 - 2.36535i) q^{17} -6.41350i q^{19} +(1.47637 + 4.22141i) q^{20} +(0.469729 + 0.912441i) q^{22} +(-1.35791 - 1.35791i) q^{23} +(-1.67680 - 4.71045i) q^{25} +(2.79254 - 8.71844i) q^{26} +(0.677911 + 4.06008i) q^{28} +2.91898 q^{29} -5.71240i q^{31} +(-3.91549 + 4.08276i) q^{32} +(-1.44304 + 4.50523i) q^{34} +(-0.783110 - 4.53503i) q^{35} +(2.65700 - 2.65700i) q^{37} +(-8.06419 + 4.15148i) q^{38} +(4.35225 - 4.58889i) q^{40} -1.02625 q^{41} +(-7.38725 + 7.38725i) q^{43} +(0.843226 - 1.18125i) q^{44} +(-0.828427 + 2.58639i) q^{46} +(-1.22848 + 1.22848i) q^{47} +2.76404i q^{49} +(-4.83741 + 5.15746i) q^{50} +(-12.7700 + 2.13220i) q^{52} +(9.48969 + 9.48969i) q^{53} +(-0.935410 + 1.32589i) q^{55} +(4.66624 - 3.48050i) q^{56} +(-1.88947 - 3.67027i) q^{58} +6.43011i q^{59} +1.18105i q^{61} +(-7.18265 + 3.69766i) q^{62} +(7.66808 + 2.28046i) q^{64} +(14.2638 - 2.46308i) q^{65} +(3.02625 + 3.02625i) q^{67} +(6.59886 - 1.10181i) q^{68} +(-5.19534 + 3.92021i) q^{70} -6.55658i q^{71} +(4.38725 - 4.38725i) q^{73} +(-5.06073 - 1.62097i) q^{74} +(10.4400 + 7.45247i) q^{76} +(-1.05609 + 1.05609i) q^{77} -6.75224 q^{79} +(-8.58720 - 2.50202i) q^{80} +(0.664297 + 1.29039i) q^{82} +(-1.37207 + 1.37207i) q^{83} +(-7.37079 + 1.27279i) q^{85} +(14.0704 + 4.50677i) q^{86} +(-2.03110 - 0.295624i) q^{88} -4.63060i q^{89} +13.3232 q^{91} +(3.78831 - 0.632534i) q^{92} +(2.33986 + 0.749462i) q^{94} +(-11.7183 - 8.26720i) q^{95} +(3.27977 + 3.27977i) q^{97} +(3.47545 - 1.78918i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 8 q^{10} - 20 q^{16} - 8 q^{17} + 20 q^{20} - 28 q^{22} - 8 q^{25} + 16 q^{26} + 4 q^{28} - 20 q^{32} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 32 q^{43} + 48 q^{46} - 56 q^{50} - 48 q^{52} + 32 q^{56} - 12 q^{58} + 16 q^{62} + 8 q^{65} + 48 q^{67} - 72 q^{68} + 4 q^{70} - 40 q^{73} + 48 q^{76} - 76 q^{80} + 24 q^{82} - 80 q^{83} + 32 q^{86} + 12 q^{88} + 64 q^{91} - 16 q^{92} - 24 q^{97} + 88 q^{98}+O(q^{100}) $ 24 * q + 12 * q^8 + 8 * q^10 - 20 * q^16 - 8 * q^17 + 20 * q^20 - 28 * q^22 - 8 * q^25 + 16 * q^26 + 4 * q^28 - 20 * q^32 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 32 * q^43 + 48 * q^46 - 56 * q^50 - 48 * q^52 + 32 * q^56 - 12 * q^58 + 16 * q^62 + 8 * q^65 + 48 * q^67 - 72 * q^68 + 4 * q^70 - 40 * q^73 + 48 * q^76 - 76 * q^80 + 24 * q^82 - 80 * q^83 + 32 * q^86 + 12 * q^88 + 64 * q^91 - 16 * q^92 - 24 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.647304	−	1.25738i	−0.457713	−	0.889100i
$2$	−0.647304	−	1.25738i	−0.457713	−	0.889100i
$3$		0			0
$3$		0			0
$4$	−1.16200	+	1.62781i	−0.580998	+	0.813905i
$5$	1.28903	−	1.82713i	0.576472	−	0.817117i
$5$	1.28903	−	1.82713i	0.576472	−	0.817117i
$6$		0			0
$7$	1.45533	−	1.45533i	0.550062	−	0.550062i	−0.376397	−	0.926459i	$-0.622837\pi$
$7$	1.45533	−	1.45533i	0.550062	−	0.550062i	0.926459	+	0.376397i	$0.122837\pi$
$8$	2.79894	+	0.407381i	0.989573	+	0.144031i
$9$		0			0
$10$	−3.13178	−	0.438090i	−0.990357	−	0.138536i
$11$	−0.725670			−0.218798			−0.109399	−	0.993998i	$-0.534893\pi$
$11$	−0.725670			−0.218798			−0.109399	+	0.993998i	$0.534893\pi$
$12$		0			0
$13$	4.57738	+	4.57738i	1.26954	+	1.26954i	0.946328	+	0.323208i	$0.104761\pi$
$13$	4.57738	+	4.57738i	1.26954	+	1.26954i	0.323208	+	0.946328i	$0.395239\pi$
$14$	−2.77193	−	0.887857i	−0.740831	−	0.237290i
$15$		0			0
$16$	−1.29953	−	3.78302i	−0.324882	−	0.945754i
$17$	−2.36535	−	2.36535i	−0.573681	−	0.573681i	0.359474	−	0.933155i	$-0.382956\pi$
$17$	−2.36535	−	2.36535i	−0.573681	−	0.573681i	−0.933155	+	0.359474i	$0.882956\pi$
$18$		0			0
$19$		−	6.41350i		−	1.47136i	−0.677330	−	0.735679i	$-0.736863\pi$
$19$		−	6.41350i		−	1.47136i	0.677330	−	0.735679i	$-0.263137\pi$
$20$	1.47637	+	4.22141i	0.330126	+	0.943937i
$21$		0			0
$22$	0.469729	+	0.912441i	0.100146	+	0.194533i
$23$	−1.35791	−	1.35791i	−0.283144	−	0.283144i	0.551217	−	0.834362i	$-0.314164\pi$
$23$	−1.35791	−	1.35791i	−0.283144	−	0.283144i	−0.834362	+	0.551217i	$0.814164\pi$
$24$		0			0
$25$	−1.67680	−	4.71045i	−0.335360	−	0.942090i
$26$	2.79254	−	8.71844i	0.547662	−	1.70983i
$27$		0			0
$28$	0.677911	+	4.06008i	0.128113	+	0.767283i
$29$	2.91898			0.542042			0.271021	−	0.962573i	$-0.412639\pi$
$29$	2.91898			0.542042			0.271021	+	0.962573i	$0.412639\pi$
$30$		0			0
$31$		−	5.71240i		−	1.02598i	−0.858395	−	0.512989i	$-0.828538\pi$
$31$		−	5.71240i		−	1.02598i	0.858395	−	0.512989i	$-0.171462\pi$
$32$	−3.91549	+	4.08276i	−0.692168	+	0.721737i
$33$		0			0
$34$	−1.44304	+	4.50523i	−0.247479	+	0.772640i
$35$	−0.783110	−	4.53503i	−0.132370	−	0.766560i
$36$		0			0
$37$	2.65700	−	2.65700i	0.436808	−	0.436808i	−0.454128	−	0.890936i	$-0.650049\pi$
$37$	2.65700	−	2.65700i	0.436808	−	0.436808i	0.890936	+	0.454128i	$0.150049\pi$
$38$	−8.06419	+	4.15148i	−1.30819	+	0.673460i
$39$		0			0
$40$	4.35225	−	4.58889i	0.688151	−	0.725567i
$41$	−1.02625			−0.160274			−0.0801368	−	0.996784i	$-0.525536\pi$
$41$	−1.02625			−0.160274			−0.0801368	+	0.996784i	$0.525536\pi$
$42$		0			0
$43$	−7.38725	+	7.38725i	−1.12655	+	1.12655i	−0.135810	+	0.990735i	$0.543364\pi$
$43$	−7.38725	+	7.38725i	−1.12655	+	1.12655i	−0.990735	+	0.135810i	$0.956636\pi$
$44$	0.843226	−	1.18125i	0.127121	−	0.178081i
$45$		0			0
$46$	−0.828427	+	2.58639i	−0.122145	+	0.381342i
$47$	−1.22848	+	1.22848i	−0.179192	+	0.179192i	−0.791004	−	0.611812i	$-0.790441\pi$
$47$	−1.22848	+	1.22848i	−0.179192	+	0.179192i	0.611812	+	0.791004i	$0.290441\pi$
$48$		0			0
$49$			2.76404i			0.394864i
$50$	−4.83741	+	5.15746i	−0.684114	+	0.729376i
$51$		0			0
$52$	−12.7700	+	2.13220i	−1.77088	+	0.295684i
$53$	9.48969	+	9.48969i	1.30351	+	1.30351i	0.926010	+	0.377500i	$0.123216\pi$
$53$	9.48969	+	9.48969i	1.30351	+	1.30351i	0.377500	+	0.926010i	$0.376784\pi$
$54$		0			0
$55$	−0.935410	+	1.32589i	−0.126131	+	0.178783i
$56$	4.66624	−	3.48050i	0.623553	−	0.465101i
$57$		0			0
$58$	−1.88947	−	3.67027i	−0.248099	−	0.481929i
$59$			6.43011i			0.837129i	0.908187	+	0.418564i	$0.137467\pi$
$59$			6.43011i			0.837129i	−0.908187	+	0.418564i	$0.862533\pi$
$60$		0			0
$61$			1.18105i			0.151218i	0.997138	+	0.0756089i	$0.0240901\pi$
$61$			1.18105i			0.151218i	−0.997138	+	0.0756089i	$0.975910\pi$
$62$	−7.18265	+	3.69766i	−0.912197	+	0.469603i
$63$		0			0
$64$	7.66808	+	2.28046i	0.958510	+	0.285058i
$65$	14.2638	−	2.46308i	1.76921	−	0.305508i
$66$		0			0
$67$	3.02625	+	3.02625i	0.369716	+	0.369716i	0.867373	−	0.497658i	$-0.165806\pi$
$67$	3.02625	+	3.02625i	0.369716	+	0.369716i	−0.497658	+	0.867373i	$0.665806\pi$
$68$	6.59886	−	1.10181i	0.800229	−	0.133614i
$69$		0			0
$70$	−5.19534	+	3.92021i	−0.620962	+	0.468554i
$71$		−	6.55658i		−	0.778123i	−0.921212	−	0.389062i	$-0.872799\pi$
$71$		−	6.55658i		−	0.778123i	0.921212	−	0.389062i	$-0.127201\pi$
$72$		0			0
$73$	4.38725	−	4.38725i	0.513489	−	0.513489i	−0.402105	−	0.915594i	$-0.631721\pi$
$73$	4.38725	−	4.38725i	0.513489	−	0.513489i	0.915594	+	0.402105i	$0.131721\pi$
$74$	−5.06073	−	1.62097i	−0.588298	−	0.188433i
$75$		0			0
$76$	10.4400	+	7.45247i	1.19755	+	0.854857i
$77$	−1.05609	+	1.05609i	−0.120352	+	0.120352i
$78$		0			0
$79$	−6.75224			−0.759686			−0.379843	−	0.925051i	$-0.624022\pi$
$79$	−6.75224			−0.759686			−0.379843	+	0.925051i	$0.624022\pi$
$80$	−8.58720	−	2.50202i	−0.960078	−	0.279734i
$81$		0			0
$82$	0.664297	+	1.29039i	0.0733593	+	0.142499i
$83$	−1.37207	+	1.37207i	−0.150604	+	0.150604i	−0.778388	−	0.627784i	$-0.783962\pi$
$83$	−1.37207	+	1.37207i	−0.150604	+	0.150604i	0.627784	+	0.778388i	$0.283962\pi$
$84$		0			0
$85$	−7.37079	+	1.27279i	−0.799475	+	0.138053i
$86$	14.0704	+	4.50677i	1.51725	+	0.485977i
$87$		0			0
$88$	−2.03110	−	0.295624i	−0.216516	−	0.0315136i
$89$		−	4.63060i		−	0.490843i	−0.969416	−	0.245421i	$-0.921074\pi$
$89$		−	4.63060i		−	0.490843i	0.969416	−	0.245421i	$-0.0789263\pi$
$90$		0			0
$91$	13.3232			1.39665
$92$	3.78831	−	0.632534i	0.394959	−	0.0659463i
$93$		0			0
$94$	2.33986	+	0.749462i	0.241338	+	0.0773011i
$95$	−11.7183	−	8.26720i	−1.20227	−	0.848197i
$96$		0			0
$97$	3.27977	+	3.27977i	0.333010	+	0.333010i	0.853728	−	0.520719i	$-0.174336\pi$
$97$	3.27977	+	3.27977i	0.333010	+	0.333010i	−0.520719	+	0.853728i	$0.674336\pi$
$98$	3.47545	−	1.78918i	0.351073	−	0.180734i
$99$		0			0
$100$	9.61615	+	2.74401i	0.961615	+	0.274401i
$101$			13.5791i			1.35117i	0.737284	+	0.675583i	$0.236108\pi$
$101$			13.5791i			1.35117i	−0.737284	+	0.675583i	$0.763892\pi$
$102$		0			0
$103$	7.90300	+	7.90300i	0.778706	+	0.778706i	0.979611	−	0.200905i	$-0.0643882\pi$
$103$	7.90300	+	7.90300i	0.778706	+	0.778706i	−0.200905	+	0.979611i	$0.564388\pi$
$104$	10.9470	+	14.6765i	1.07345	+	1.43915i
$105$		0			0
$106$	5.78941	−	18.0748i	0.562318	−	1.75558i
$107$	11.1728	+	11.1728i	1.08012	+	1.08012i	0.996498	+	0.0836196i	$0.0266481\pi$
$107$	11.1728	+	11.1728i	1.08012	+	1.08012i	0.0836196	+	0.996498i	$0.473352\pi$
$108$		0			0
$109$	12.4480			1.19230			0.596150	−	0.802873i	$-0.296696\pi$
$109$	12.4480			1.19230			0.596150	+	0.802873i	$0.296696\pi$
$110$	2.27264	+	0.317909i	0.216688	+	0.0303114i
$111$		0			0
$112$	−7.39677	−	3.61429i	−0.698929	−	0.341518i
$113$	−9.43541	+	9.43541i	−0.887609	+	0.887609i	−0.994293	−	0.106684i	$-0.965977\pi$
$113$	−9.43541	+	9.43541i	−0.887609	+	0.887609i	0.106684	+	0.994293i	$0.465977\pi$
$114$		0			0
$115$	−4.23147	+	0.730691i	−0.394587	+	0.0681373i
$116$	−3.39185	+	4.75155i	−0.314925	+	0.441171i
$117$		0			0
$118$	8.08507	−	4.16223i	0.744291	−	0.383165i
$119$	−6.88470			−0.631120
$120$		0			0
$121$	−10.4734			−0.952128
$122$	1.48502	−	0.764497i	0.134448	−	0.0692143i
$123$		0			0
$124$	9.29870	+	6.63779i	0.835048	+	0.596091i
$125$	−10.7680	−	3.00818i	−0.963124	−	0.269060i
$126$		0			0
$127$	−9.88355	+	9.88355i	−0.877024	+	0.877024i	−0.993226	−	0.116202i	$-0.962928\pi$
$127$	−9.88355	+	9.88355i	−0.877024	+	0.877024i	0.116202	+	0.993226i	$0.462928\pi$
$128$	−2.09617	−	11.1178i	−0.185277	−	0.982686i
$129$		0			0
$130$	−12.3301	−	16.3407i	−1.08142	−	1.43317i
$131$	−14.0012			−1.22329			−0.611647	−	0.791131i	$-0.709493\pi$
$131$	−14.0012			−1.22329			−0.611647	+	0.791131i	$0.709493\pi$
$132$		0			0
$133$	−9.33375	−	9.33375i	−0.809338	−	0.809338i
$134$	1.84624	−	5.76404i	0.159491	−	0.497938i
$135$		0			0
$136$	−5.65685	−	7.58405i	−0.485071	−	0.650327i
$137$	4.31776	+	4.31776i	0.368891	+	0.368891i	0.867073	−	0.498182i	$-0.165999\pi$
$137$	4.31776	+	4.31776i	0.368891	+	0.368891i	−0.498182	+	0.867073i	$0.665999\pi$
$138$		0			0
$139$		−	10.2753i		−	0.871538i	−0.900058	−	0.435769i	$-0.856476\pi$
$139$		−	10.2753i		−	0.871538i	0.900058	−	0.435769i	$-0.143524\pi$
$140$	8.29214	+	3.99494i	0.700814	+	0.337634i
$141$		0			0
$142$	−8.24410	+	4.24410i	−0.691829	+	0.356157i
$143$	−3.32166	−	3.32166i	−0.277772	−	0.277772i
$144$		0			0
$145$	3.76266	−	5.33336i	0.312472	−	0.442912i
$146$	−8.35631	−	2.67655i	−0.691574	−	0.221513i
$147$		0			0
$148$	1.23767	+	7.41251i	0.101736	+	0.609305i
$149$	3.03780			0.248867			0.124433	−	0.992228i	$-0.460289\pi$
$149$	3.03780			0.248867			0.124433	+	0.992228i	$0.460289\pi$
$150$		0			0
$151$		−	5.52994i		−	0.450020i	−0.974356	−	0.225010i	$-0.927758\pi$
$151$		−	5.52994i		−	0.450020i	0.974356	−	0.225010i	$-0.0722415\pi$
$152$	2.61274	−	17.9510i	0.211921	−	1.45602i
$153$		0			0
$154$	2.01151	+	0.644291i	0.162092	+	0.0519185i
$155$	−10.4373	−	7.36346i	−0.838344	−	0.591447i
$156$		0			0
$157$	−4.36202	+	4.36202i	−0.348127	+	0.348127i	−0.859412	−	0.511284i	$-0.829170\pi$
$157$	−4.36202	+	4.36202i	−0.348127	+	0.348127i	0.511284	+	0.859412i	$0.329170\pi$
$158$	4.37075	+	8.49011i	0.347718	+	0.675437i
$159$		0			0
$160$	2.41254	+	12.4169i	0.190728	+	0.981643i
$161$	−3.95241			−0.311494
$162$		0			0
$163$	−9.10371	+	9.10371i	−0.713058	+	0.713058i	−0.967174	−	0.254116i	$-0.918215\pi$
$163$	−9.10371	+	9.10371i	−0.713058	+	0.713058i	0.254116	+	0.967174i	$0.418215\pi$
$164$	1.19250	−	1.67054i	0.0931187	−	0.130448i
$165$		0			0
$166$	2.61335	+	0.837062i	0.202835	+	0.0649686i
$167$	15.2102	−	15.2102i	1.17700	−	1.17700i	0.196497	−	0.980504i	$-0.437043\pi$
$167$	15.2102	−	15.2102i	1.17700	−	1.17700i	0.980504	−	0.196497i	$-0.0629566\pi$
$168$		0			0
$169$			28.9048i			2.22344i
$170$	6.37152	+	8.44399i	0.488673	+	0.647624i
$171$		0			0
$172$	−3.44108	−	20.6090i	−0.262380	−	1.57142i
$173$	−5.23564	−	5.23564i	−0.398058	−	0.398058i	0.479489	−	0.877548i	$-0.340822\pi$
$173$	−5.23564	−	5.23564i	−0.398058	−	0.398058i	−0.877548	+	0.479489i	$0.840822\pi$
$174$		0			0
$175$	−9.29554	−	4.41495i	−0.702677	−	0.333739i
$176$	0.943030	+	2.74522i	0.0710835	+	0.206929i
$177$		0			0
$178$	−5.82241	+	2.99741i	−0.436408	+	0.224665i
$179$		−	16.3444i		−	1.22164i	−0.791771	−	0.610819i	$-0.790840\pi$
$179$		−	16.3444i		−	1.22164i	0.791771	−	0.610819i	$-0.209160\pi$
$180$		0			0
$181$		−	1.33892i		−	0.0995215i	−0.998761	−	0.0497608i	$-0.984154\pi$
$181$		−	1.33892i		−	0.0995215i	0.998761	−	0.0497608i	$-0.0158459\pi$
$182$	−8.62413	−	16.7522i	−0.639263	−	1.24176i
$183$		0			0
$184$	−3.24752	−	4.35390i	−0.239411	−	0.320974i
$185$	−1.42973	−	8.27963i	−0.105116	−	0.608731i
$186$		0			0
$187$	1.71646	+	1.71646i	0.125520	+	0.125520i
$188$	−0.572242	−	3.42722i	−0.0417350	−	0.249955i
$189$		0			0
$190$	−2.80969	+	20.0857i	−0.203837	+	1.45717i
$191$			18.5684i			1.34356i	0.740750	+	0.671780i	$0.234470\pi$
$191$			18.5684i			1.34356i	−0.740750	+	0.671780i	$0.765530\pi$
$192$		0			0
$193$	2.10748	−	2.10748i	0.151700	−	0.151700i	−0.627177	−	0.778877i	$-0.715790\pi$
$193$	2.10748	−	2.10748i	0.151700	−	0.151700i	0.778877	+	0.627177i	$0.215790\pi$
$194$	2.00090	−	6.24691i	0.143656	−	0.448502i
$195$		0			0
$196$	−4.49934	−	3.21181i	−0.321381	−	0.229415i
$197$	8.63291	−	8.63291i	0.615069	−	0.615069i	−0.329193	−	0.944263i	$-0.606777\pi$
$197$	8.63291	−	8.63291i	0.615069	−	0.615069i	0.944263	+	0.329193i	$0.106777\pi$
$198$		0			0
$199$	−2.36127			−0.167386			−0.0836932	−	0.996492i	$-0.526672\pi$
$199$	−2.36127			−0.167386			−0.0836932	+	0.996492i	$0.526672\pi$
$200$	−2.77431	−	13.8673i	−0.196174	−	0.980569i
$201$		0			0
$202$	17.0740	−	8.78977i	1.20132	−	0.618446i
$203$	4.24808	−	4.24808i	0.298157	−	0.298157i
$204$		0			0
$205$	−1.32287	+	1.87510i	−0.0923932	+	0.130962i
$206$	4.82142	−	15.0527i	0.335924	−	1.04877i
$207$		0			0
$208$	11.3679	−	23.2647i	0.788219	−	1.61312i
$209$			4.65409i			0.321930i
$210$		0			0
$211$	−3.38157			−0.232797			−0.116398	−	0.993203i	$-0.537135\pi$
$211$	−3.38157			−0.232797			−0.116398	+	0.993203i	$0.537135\pi$
$212$	−26.4744	+	4.42043i	−1.81827	+	0.303596i
$213$		0			0
$214$	6.81625	−	21.2807i	0.465949	−	1.45472i
$215$	3.97507	+	23.0199i	0.271098	+	1.56994i
$216$		0			0
$217$	−8.31341	−	8.31341i	−0.564351	−	0.564351i
$218$	−8.05762	−	15.6518i	−0.545731	−	1.06007i
$219$		0			0
$220$	−1.07136	−	3.06335i	−0.0722309	−	0.206531i
$221$		−	21.6542i		−	1.45662i
$222$		0			0
$223$	−9.32012	−	9.32012i	−0.624122	−	0.624122i	0.322461	−	0.946583i	$-0.395490\pi$
$223$	−9.32012	−	9.32012i	−0.624122	−	0.624122i	−0.946583	+	0.322461i	$0.895490\pi$
$224$	0.243432	+	11.6401i	0.0162650	+	0.777735i
$225$		0			0
$226$	17.9714	+	5.75630i	1.19544	+	0.382903i
$227$	14.9247	+	14.9247i	0.990590	+	0.990590i	0.999956	−	0.00936616i	$-0.00298138\pi$
$227$	14.9247	+	14.9247i	0.990590	+	0.990590i	−0.00936616	+	0.999956i	$0.502981\pi$
$228$		0			0
$229$	−13.5299			−0.894082			−0.447041	−	0.894514i	$-0.647522\pi$
$229$	−13.5299			−0.894082			−0.447041	+	0.894514i	$0.647522\pi$
$230$	3.65780	+	4.84758i	0.241188	+	0.319640i
$231$		0			0
$232$	8.17005	+	1.18914i	0.536390	+	0.0780707i
$233$	−4.26526	+	4.26526i	−0.279426	+	0.279426i	−0.832880	−	0.553454i	$-0.813310\pi$
$233$	−4.26526	+	4.26526i	−0.279426	+	0.279426i	0.553454	+	0.832880i	$0.313310\pi$
$234$		0			0
$235$	0.661043	+	3.82813i	0.0431217	+	0.249720i
$236$	−10.4670	−	7.47176i	−0.681343	−	0.486370i
$237$		0			0
$238$	4.45649	+	8.65667i	0.288872	+	0.561129i
$239$	2.73939			0.177196			0.0885981	−	0.996067i	$-0.471761\pi$
$239$	2.73939			0.177196			0.0885981	+	0.996067i	$0.471761\pi$
$240$		0			0
$241$	−16.4833			−1.06178			−0.530890	−	0.847440i	$-0.678142\pi$
$241$	−16.4833			−1.06178			−0.530890	+	0.847440i	$0.678142\pi$
$242$	6.77947	+	13.1690i	0.435801	+	0.846537i
$243$		0			0
$244$	−1.92252	−	1.37237i	−0.123077	−	0.0878573i
$245$	5.05027	+	3.56294i	0.322650	+	0.227628i
$246$		0			0
$247$	29.3570	−	29.3570i	1.86794	−	1.86794i
$248$	2.32712	−	15.9886i	0.147772	−	1.01528i
$249$		0			0
$250$	3.18778	+	15.4867i	0.201613	+	0.979465i
$251$	14.0488			0.886754			0.443377	−	0.896335i	$-0.353780\pi$
$251$	14.0488			0.886754			0.443377	+	0.896335i	$0.353780\pi$
$252$		0			0
$253$	0.985396	+	0.985396i	0.0619513	+	0.0619513i
$254$	18.8250	+	6.02970i	1.18119	+	0.378337i
$255$		0			0
$256$	−12.6224	+	9.83229i	−0.788903	+	0.614518i
$257$	−4.43264	−	4.43264i	−0.276501	−	0.276501i	0.555210	−	0.831710i	$-0.312638\pi$
$257$	−4.43264	−	4.43264i	−0.276501	−	0.276501i	−0.831710	+	0.555210i	$0.812638\pi$
$258$		0			0
$259$		−	7.73360i		−	0.480543i
$260$	−12.5651	+	26.0809i	−0.779254	+	1.61747i
$261$		0			0
$262$	9.06306	+	17.6049i	0.559918	+	1.08763i
$263$	19.3432	+	19.3432i	1.19275	+	1.19275i	0.976292	+	0.216458i	$0.0694505\pi$
$263$	19.3432	+	19.3432i	1.19275	+	1.19275i	0.216458	+	0.976292i	$0.430549\pi$
$264$		0			0
$265$	29.5714	−	5.10639i	1.81656	−	0.313683i
$266$	−5.69428	+	17.7778i	−0.349138	+	1.09003i
$267$		0			0
$268$	−8.44266	+	1.40967i	−0.515717	+	0.0861093i
$269$	−24.0508			−1.46640			−0.733201	−	0.680012i	$-0.761974\pi$
$269$	−24.0508			−1.46640			−0.733201	+	0.680012i	$0.761974\pi$
$270$		0			0
$271$			24.3905i			1.48162i	0.671716	+	0.740809i	$0.265558\pi$
$271$			24.3905i			1.48162i	−0.671716	+	0.740809i	$0.734442\pi$
$272$	−5.87431	+	12.0220i	−0.356182	+	0.728940i
$273$		0			0
$274$	2.63415	−	8.22396i	0.159135	−	0.496827i
$275$	1.21680	+	3.41823i	0.0733761	+	0.206127i
$276$		0			0
$277$	−6.76755	+	6.76755i	−0.406623	+	0.406623i	−0.880559	−	0.473936i	$-0.842833\pi$
$277$	−6.76755	+	6.76755i	−0.406623	+	0.406623i	0.473936	+	0.880559i	$0.342833\pi$
$278$	−12.9199	+	6.65123i	−0.774885	+	0.398914i
$279$		0			0
$280$	−0.344390	−	13.0123i	−0.0205812	−	0.777633i
$281$	−4.79740			−0.286189			−0.143094	−	0.989709i	$-0.545705\pi$
$281$	−4.79740			−0.286189			−0.143094	+	0.989709i	$0.545705\pi$
$282$		0			0
$283$	−1.57491	+	1.57491i	−0.0936188	+	0.0936188i	−0.752365	−	0.658746i	$-0.771087\pi$
$283$	−1.57491	+	1.57491i	−0.0936188	+	0.0936188i	0.658746	+	0.752365i	$0.271087\pi$
$284$	10.6729	+	7.61872i	0.633318	+	0.452088i
$285$		0			0
$286$	−2.02646	+	6.32671i	−0.119827	+	0.374106i
$287$	−1.49353	+	1.49353i	−0.0881604	+	0.0881604i
$288$		0			0
$289$		−	5.81028i		−	0.341781i
$290$	−9.14163	−	1.27878i	−0.536815	−	0.0750925i
$291$		0			0
$292$	2.04364	+	12.2396i	0.119595	+	0.716267i
$293$	−16.8458	−	16.8458i	−0.984141	−	0.984141i	0.0157353	−	0.999876i	$-0.494991\pi$
$293$	−16.8458	−	16.8458i	−0.984141	−	0.984141i	−0.999876	+	0.0157353i	$0.994991\pi$
$294$		0			0
$295$	11.7486	+	8.28861i	0.684032	+	0.482581i
$296$	8.51918	−	6.35436i	0.495167	−	0.369340i
$297$		0			0
$298$	−1.96638	−	3.81967i	−0.113909	−	0.221267i
$299$		−	12.4314i		−	0.718924i
$300$		0			0
$301$			21.5017i			1.23934i
$302$	−6.95323	+	3.57955i	−0.400113	+	0.205980i
$303$		0			0
$304$	−24.2624	+	8.33454i	−1.39154	+	0.478019i
$305$	2.15793	+	1.52241i	0.123563	+	0.0871728i
$306$		0			0
$307$	13.5999	+	13.5999i	0.776185	+	0.776185i	0.979180	−	0.202994i	$-0.0650673\pi$
$307$	13.5999	+	13.5999i	0.776185	+	0.776185i	−0.202994	+	0.979180i	$0.565067\pi$
$308$	−0.491940	−	2.94628i	−0.0280309	−	0.167880i
$309$		0			0
$310$	−2.50255	+	17.8900i	−0.142135	+	1.01608i
$311$			6.98730i			0.396213i	0.980180	+	0.198107i	$0.0634792\pi$
$311$			6.98730i			0.396213i	−0.980180	+	0.198107i	$0.936521\pi$
$312$		0			0
$313$	13.3659	−	13.3659i	0.755486	−	0.755486i	−0.220011	−	0.975497i	$-0.570609\pi$
$313$	13.3659	−	13.3659i	0.755486	−	0.755486i	0.975497	+	0.220011i	$0.0706093\pi$
$314$	8.30826	+	2.66115i	0.468862	+	0.150178i
$315$		0			0
$316$	7.84607	−	10.9914i	0.441376	−	0.618312i
$317$	−2.24312	+	2.24312i	−0.125986	+	0.125986i	−0.767288	−	0.641302i	$-0.778395\pi$
$317$	−2.24312	+	2.24312i	−0.125986	+	0.125986i	0.641302	+	0.767288i	$0.278395\pi$
$318$		0			0
$319$	−2.11822			−0.118597
$320$	14.0511	−	11.0710i	0.785480	−	0.618887i
$321$		0			0
$322$	2.55841	+	4.96968i	0.142575	+	0.276949i
$323$	−15.1702	+	15.1702i	−0.844090	+	0.844090i
$324$		0			0
$325$	13.8861	−	29.2369i	0.770265	−	1.62177i
$326$	17.3397	+	5.55394i	0.960355	+	0.307604i
$327$		0			0
$328$	−2.87241	−	0.418075i	−0.158603	−	0.0230843i
$329$			3.57567i			0.197133i
$330$		0			0
$331$	−0.360999			−0.0198423			−0.00992116	−	0.999951i	$-0.503158\pi$
$331$	−0.360999			−0.0198423			−0.00992116	+	0.999951i	$0.503158\pi$
$332$	−0.639127	−	3.82780i	−0.0350767	−	0.210078i
$333$		0			0
$334$	−28.9706	−	9.27935i	−1.58520	−	0.507744i
$335$	9.43028	−	1.62842i	0.515231	−	0.0889702i
$336$		0			0
$337$	−0.546946	−	0.546946i	−0.0297941	−	0.0297941i	0.692053	−	0.721847i	$-0.256707\pi$
$337$	−0.546946	−	0.546946i	−0.0297941	−	0.0297941i	−0.721847	+	0.692053i	$0.756707\pi$
$338$	36.3442	−	18.7102i	1.97686	−	1.01770i
$339$		0			0
$340$	6.49297	−	13.4772i	0.352131	−	0.730905i
$341$			4.14532i			0.224482i
$342$		0			0
$343$	14.2099	+	14.2099i	0.767261	+	0.767261i
$344$	−23.6859	+	17.6670i	−1.27706	+	0.952542i
$345$		0			0
$346$	−3.19413	+	9.97223i	−0.171717	+	0.536110i
$347$	−11.5591	−	11.5591i	−0.620526	−	0.620526i	0.325140	−	0.945666i	$-0.394589\pi$
$347$	−11.5591	−	11.5591i	−0.620526	−	0.620526i	−0.945666	+	0.325140i	$0.894589\pi$
$348$		0			0
$349$	10.5842			0.566562			0.283281	−	0.959037i	$-0.408577\pi$
$349$	10.5842			0.566562			0.283281	+	0.959037i	$0.408577\pi$
$350$	0.465778	+	14.5458i	0.0248969	+	0.777507i
$351$		0			0
$352$	2.84135	−	2.96274i	0.151445	−	0.157914i
$353$	16.2334	−	16.2334i	0.864016	−	0.864016i	−0.127785	−	0.991802i	$-0.540787\pi$
$353$	16.2334	−	16.2334i	0.864016	−	0.864016i	0.991802	+	0.127785i	$0.0407869\pi$
$354$		0			0
$355$	−11.9797	−	8.45163i	−0.635818	−	0.448566i
$356$	7.53774	+	5.38074i	0.399499	+	0.285179i
$357$		0			0
$358$	−20.5511	+	10.5798i	−1.08616	+	0.559159i
$359$	6.79961			0.358869			0.179435	−	0.983770i	$-0.442573\pi$
$359$	6.79961			0.358869			0.179435	+	0.983770i	$0.442573\pi$
$360$		0			0
$361$	−22.1330			−1.16490
$362$	−1.68353	+	0.866691i	−0.0884846	+	0.0455523i
$363$		0			0
$364$	−15.4815	+	21.6876i	−0.811449	+	1.13674i
$365$	−2.36078	−	13.6714i	−0.123569	−	0.715592i
$366$		0			0
$367$	−3.23043	+	3.23043i	−0.168627	+	0.168627i	−0.786376	−	0.617748i	$-0.788045\pi$
$367$	−3.23043	+	3.23043i	−0.168627	+	0.168627i	0.617748	+	0.786376i	$0.288045\pi$
$368$	−3.37236	+	6.90166i	−0.175796	+	0.359774i
$369$		0			0
$370$	−9.48515	+	7.15714i	−0.493110	+	0.372082i
$371$	27.6212			1.43402
$372$		0			0
$373$	−2.12448	−	2.12448i	−0.110001	−	0.110001i	0.649964	−	0.759965i	$-0.274784\pi$
$373$	−2.12448	−	2.12448i	−0.110001	−	0.110001i	−0.759965	+	0.649964i	$0.774784\pi$
$374$	1.04717	−	3.26931i	0.0541477	−	0.169052i
$375$		0			0
$376$	−3.93889	+	2.93797i	−0.203133	+	0.151514i
$377$	13.3613	+	13.3613i	0.688142	+	0.688142i
$378$		0			0
$379$		−	19.0820i		−	0.980175i	−0.871673	−	0.490087i	$-0.836965\pi$
$379$		−	19.0820i		−	0.980175i	0.871673	−	0.490087i	$-0.163035\pi$
$380$	27.0740	−	9.46871i	1.38887	−	0.485734i
$381$		0			0
$382$	23.3475	−	12.0194i	1.19456	−	0.614965i
$383$	−2.96986	−	2.96986i	−0.151753	−	0.151753i	0.627148	−	0.778900i	$-0.284222\pi$
$383$	−2.96986	−	2.96986i	−0.151753	−	0.151753i	−0.778900	+	0.627148i	$0.784222\pi$
$384$		0			0
$385$	0.568279	+	3.29094i	0.0289622	+	0.167722i
$386$	−4.01409	−	1.28572i	−0.204312	−	0.0654415i
$387$		0			0
$388$	−9.14991	+	1.52776i	−0.464516	+	0.0775603i
$389$	−0.831983			−0.0421832			−0.0210916	−	0.999778i	$-0.506714\pi$
$389$	−0.831983			−0.0421832			−0.0210916	+	0.999778i	$0.506714\pi$
$390$		0			0
$391$			6.42387i			0.324869i
$392$	−1.12602	+	7.73638i	−0.0568725	+	0.390746i
$393$		0			0
$394$	−16.4429	−	5.26671i	−0.828383	−	0.265333i
$395$	−8.70384	+	12.3372i	−0.437938	+	0.620752i
$396$		0			0
$397$	11.7504	−	11.7504i	0.589736	−	0.589736i	−0.347824	−	0.937560i	$-0.613079\pi$
$397$	11.7504	−	11.7504i	0.589736	−	0.589736i	0.937560	+	0.347824i	$0.113079\pi$
$398$	1.52846	+	2.96901i	0.0766149	+	0.148823i
$399$		0			0
$400$	−15.6407	+	12.4647i	−0.782033	+	0.623237i
$401$	−27.1058			−1.35360			−0.676799	−	0.736168i	$-0.736633\pi$
$401$	−27.1058			−1.35360			−0.676799	+	0.736168i	$0.736633\pi$
$402$		0			0
$403$	26.1478	−	26.1478i	1.30252	−	1.30252i
$404$	−22.1041	−	15.7788i	−1.09972	−	0.785025i
$405$		0			0
$406$	−8.09123	−	2.59164i	−0.401561	−	0.128621i
$407$	−1.92810	+	1.92810i	−0.0955725	+	0.0955725i
$408$		0			0
$409$			13.2732i			0.656319i	0.944622	+	0.328159i	$0.106428\pi$
$409$			13.2732i			0.656319i	−0.944622	+	0.328159i	$0.893572\pi$
$410$	3.21400	+	0.449591i	0.158728	+	0.0222037i
$411$		0			0
$412$	−22.0478	+	3.68133i	−1.08622	+	0.181366i
$413$	9.35791	+	9.35791i	0.460473	+	0.460473i
$414$		0			0
$415$	0.738307	+	4.27558i	0.0362421	+	0.209880i
$416$	−36.6110	+	0.765655i	−1.79500	+	0.0375393i
$417$		0			0
$418$	5.85194	−	3.01261i	0.286228	−	0.147351i
$419$		−	24.3069i		−	1.18747i	−0.804662	−	0.593734i	$-0.797653\pi$
$419$		−	24.3069i		−	1.18747i	0.804662	−	0.593734i	$-0.202347\pi$
$420$		0			0
$421$		−	1.60486i		−	0.0782162i	−0.999235	−	0.0391081i	$-0.987548\pi$
$421$		−	1.60486i		−	0.0782162i	0.999235	−	0.0391081i	$-0.0124517\pi$
$422$	2.18890	+	4.25191i	0.106554	+	0.206980i
$423$		0			0
$424$	22.6951	+	30.4270i	1.10217	+	1.47766i
$425$	−7.17563	+	15.1081i	−0.348069	+	0.732848i
$426$		0			0
$427$	1.71881	+	1.71881i	0.0831792	+	0.0831792i
$428$	−31.1700	+	5.20445i	−1.50666	+	0.251567i
$429$		0			0
$430$	26.3716	−	19.8990i	1.27175	−	0.959615i
$431$		−	16.0008i		−	0.770733i	−0.922764	−	0.385367i	$-0.874075\pi$
$431$		−	16.0008i		−	0.770733i	0.922764	−	0.385367i	$-0.125925\pi$
$432$		0			0
$433$	−17.6673	+	17.6673i	−0.849037	+	0.849037i	−0.990013	−	0.140976i	$-0.954976\pi$
$433$	−17.6673	+	17.6673i	−0.849037	+	0.849037i	0.140976	+	0.990013i	$0.454976\pi$
$434$	−5.07180	+	15.8344i	−0.243454	+	0.760076i
$435$		0			0
$436$	−14.4645	+	20.2629i	−0.692724	+	0.970419i
$437$	−8.70898	+	8.70898i	−0.416607	+	0.416607i
$438$		0			0
$439$	34.5085			1.64700			0.823500	−	0.567316i	$-0.192018\pi$
$439$	34.5085			1.64700			0.823500	+	0.567316i	$0.192018\pi$
$440$	−3.15830	+	3.33002i	−0.150566	+	0.158752i
$441$		0			0
$442$	−27.2275	+	14.0168i	−1.29508	+	0.666712i
$443$	2.03044	−	2.03044i	0.0964691	−	0.0964691i	−0.657225	−	0.753694i	$-0.728270\pi$
$443$	2.03044	−	2.03044i	0.0964691	−	0.0964691i	0.753694	+	0.657225i	$0.228270\pi$
$444$		0			0
$445$	−8.46071	−	5.96899i	−0.401076	−	0.282957i
$446$	−5.68596	+	17.7519i	−0.269238	+	0.840575i
$447$		0			0
$448$	14.4784	−	7.84075i	0.684040	−	0.370440i
$449$			19.7303i			0.931129i	0.885014	+	0.465565i	$0.154149\pi$
$449$			19.7303i			0.931129i	−0.885014	+	0.465565i	$0.845851\pi$
$450$		0			0
$451$	0.744720			0.0350675
$452$	−4.39514	−	26.3230i	−0.206730	−	1.23813i
$453$		0			0
$454$	9.10520	−	28.4269i	0.427328	−	1.33414i
$455$	17.1740	−	24.3431i	0.805128	−	1.14122i
$456$		0			0
$457$	−22.2146	−	22.2146i	−1.03915	−	1.03915i	−0.999202	−	0.0399513i	$-0.987280\pi$
$457$	−22.2146	−	22.2146i	−1.03915	−	1.03915i	−0.0399513	−	0.999202i	$-0.512720\pi$
$458$	8.75796	+	17.0122i	0.409233	+	0.794928i
$459$		0			0
$460$	3.72753	−	7.73709i	0.173797	−	0.360744i
$461$			20.6988i			0.964039i	0.876161	+	0.482019i	$0.160096\pi$
$461$			20.6988i			0.964039i	−0.876161	+	0.482019i	$0.839904\pi$
$462$		0			0
$463$	−5.67502	−	5.67502i	−0.263741	−	0.263741i	0.562831	−	0.826572i	$-0.309712\pi$
$463$	−5.67502	−	5.67502i	−0.263741	−	0.263741i	−0.826572	+	0.562831i	$0.809712\pi$
$464$	−3.79331	−	11.0426i	−0.176100	−	0.512638i
$465$		0			0
$466$	8.12395	+	2.60212i	0.376335	+	0.120541i
$467$	−3.78863	−	3.78863i	−0.175317	−	0.175317i	0.613994	−	0.789311i	$-0.289562\pi$
$467$	−3.78863	−	3.78863i	−0.175317	−	0.175317i	−0.789311	+	0.613994i	$0.789562\pi$
$468$		0			0
$469$	8.80837			0.406733
$470$	4.38551	−	3.30914i	0.202289	−	0.152639i
$471$		0			0
$472$	−2.61950	+	17.9975i	−0.120572	+	0.828400i
$473$	5.36071	−	5.36071i	0.246485	−	0.246485i
$474$		0			0
$475$	−30.2105	+	10.7542i	−1.38615	+	0.493435i
$476$	8.00000	−	11.2070i	0.366679	−	0.513672i
$477$		0			0
$478$	−1.77321	−	3.44444i	−0.0811050	−	0.157545i
$479$	−11.8931			−0.543409			−0.271705	−	0.962381i	$-0.587587\pi$
$479$	−11.8931			−0.543409			−0.271705	+	0.962381i	$0.587587\pi$
$480$		0			0
$481$	24.3242			1.10909
$482$	10.6697	+	20.7257i	0.485991	+	0.944030i
$483$		0			0
$484$	12.1701	−	17.0487i	0.553184	−	0.774941i
$485$	10.2203	−	1.76484i	0.464079	−	0.0801372i
$486$		0			0
$487$	−22.1137	+	22.1137i	−1.00207	+	1.00207i	−0.00207135	+	0.999998i	$0.500659\pi$
$487$	−22.1137	+	22.1137i	−1.00207	+	1.00207i	−0.999998	+	0.00207135i	$0.999341\pi$
$488$	−0.481137	+	3.30568i	−0.0217800	+	0.149641i
$489$		0			0
$490$	1.21090	−	8.65639i	0.0547030	−	0.391056i
$491$	−17.8731			−0.806600			−0.403300	−	0.915068i	$-0.632137\pi$
$491$	−17.8731			−0.806600			−0.403300	+	0.915068i	$0.632137\pi$
$492$		0			0
$493$	−6.90441	−	6.90441i	−0.310959	−	0.310959i
$494$	−55.9158	−	17.9100i	−2.51577	−	0.805807i
$495$		0			0
$496$	−21.6101	+	7.42344i	−0.970323	+	0.333322i
$497$	−9.54197	−	9.54197i	−0.428016	−	0.428016i
$498$		0			0
$499$		−	10.6090i		−	0.474923i	−0.971397	−	0.237461i	$-0.923685\pi$
$499$		−	10.6090i		−	0.474923i	0.971397	−	0.237461i	$-0.0763153\pi$
$500$	17.4092	−	14.0328i	0.778562	−	0.627568i
$501$		0			0
$502$	−9.09386	−	17.6647i	−0.405879	−	0.788414i
$503$	8.19221	+	8.19221i	0.365273	+	0.365273i	0.865750	−	0.500477i	$-0.166842\pi$
$503$	8.19221	+	8.19221i	0.365273	+	0.365273i	−0.500477	+	0.865750i	$0.666842\pi$
$504$		0			0
$505$	24.8107	+	17.5038i	1.10406	+	0.778909i
$506$	0.601165	−	1.87687i	0.0267250	−	0.0834369i
$507$		0			0
$508$	−4.60389	−	27.5732i	−0.204265	−	1.22336i
$509$	35.0769			1.55476			0.777379	−	0.629033i	$-0.216549\pi$
$509$	35.0769			1.55476			0.777379	+	0.629033i	$0.216549\pi$
$510$		0			0
$511$		−	12.7698i		−	0.564902i
$512$	20.5335	+	9.50670i	0.907459	+	0.420141i
$513$		0			0
$514$	−2.70424	+	8.44277i	−0.119279	+	0.372395i
$515$	24.6270	−	4.25260i	1.08520	−	0.187392i
$516$		0			0
$517$	0.891469	−	0.891469i	0.0392068	−	0.0392068i
$518$	−9.72406	+	5.00599i	−0.427251	+	0.219951i
$519$		0			0
$520$	40.9270	−	1.08320i	1.79477	−	0.0475012i
$521$	13.5092			0.591848			0.295924	−	0.955211i	$-0.404372\pi$
$521$	13.5092			0.591848			0.295924	+	0.955211i	$0.404372\pi$
$522$		0			0
$523$	3.12911	−	3.12911i	0.136827	−	0.136827i	−0.635376	−	0.772203i	$-0.719155\pi$
$523$	3.12911	−	3.12911i	0.136827	−	0.136827i	0.772203	+	0.635376i	$0.219155\pi$
$524$	16.2694	−	22.7914i	0.710732	−	0.995646i
$525$		0			0
$526$	11.8008	−	36.8425i	0.514537	−	1.60641i
$527$	−13.5118	+	13.5118i	−0.588583	+	0.588583i
$528$		0			0
$529$		−	19.3121i		−	0.839659i
$530$	−25.5623	−	33.8770i	−1.11036	−	1.47152i
$531$		0			0
$532$	26.0393	−	4.34779i	1.12895	−	0.188500i
$533$	−4.69754	−	4.69754i	−0.203473	−	0.203473i
$534$		0			0
$535$	34.8163	−	6.01208i	1.50524	−	0.259925i
$536$	7.23745	+	9.70312i	0.312610	+	0.419111i
$537$		0			0
$538$	15.5681	+	30.2409i	0.671191	+	1.30378i
$539$		−	2.00578i		−	0.0863952i
$540$		0			0
$541$		−	39.9149i		−	1.71608i	−0.513585	−	0.858038i	$-0.671683\pi$
$541$		−	39.9149i		−	1.71608i	0.513585	−	0.858038i	$-0.328317\pi$
$542$	30.6681	−	15.7881i	1.31731	−	0.678155i
$543$		0			0
$544$	18.9186	−	0.395650i	0.811130	−	0.0169633i
$545$	16.0458	−	22.7441i	0.687327	−	0.974249i
$546$		0			0
$547$	24.0087	+	24.0087i	1.02654	+	1.02654i	0.999638	+	0.0269017i	$0.00856410\pi$
$547$	24.0087	+	24.0087i	1.02654	+	1.02654i	0.0269017	+	0.999638i	$0.491436\pi$
$548$	−12.0457	+	2.01127i	−0.514567	+	0.0859173i
$549$		0			0
$550$	3.51036	−	3.74262i	0.149682	−	0.159586i
$551$		−	18.7209i		−	0.797538i
$552$		0			0
$553$	−9.82671	+	9.82671i	−0.417874	+	0.417874i
$554$	12.8900	+	4.12871i	0.547645	+	0.175412i
$555$		0			0
$556$	16.7262	+	11.9398i	0.709349	+	0.506362i
$557$	5.38621	−	5.38621i	0.228221	−	0.228221i	−0.583728	−	0.811949i	$-0.698407\pi$
$557$	5.38621	−	5.38621i	0.228221	−	0.228221i	0.811949	+	0.583728i	$0.198407\pi$
$558$		0			0
$559$	−67.6285			−2.86038
$560$	−16.1384	+	8.85593i	−0.681973	+	0.374231i
$561$		0			0
$562$	3.10537	+	6.03214i	0.130992	+	0.254451i
$563$	−11.0962	+	11.0962i	−0.467648	+	0.467648i	−0.901152	−	0.433504i	$-0.857277\pi$
$563$	−11.0962	+	11.0962i	−0.467648	+	0.467648i	0.433504	+	0.901152i	$0.357277\pi$
$564$		0			0
$565$	5.07718	+	29.4022i	0.213599	+	1.23696i
$566$	2.99971	+	0.960813i	0.126087	+	0.0403860i
$567$		0			0
$568$	2.67103	−	18.3515i	0.112074	−	0.770010i
$569$		−	13.7723i		−	0.577366i	−0.957425	−	0.288683i	$-0.906783\pi$
$569$		−	13.7723i		−	0.577366i	0.957425	−	0.288683i	$-0.0932173\pi$
$570$		0			0
$571$	−2.65223			−0.110992			−0.0554962	−	0.998459i	$-0.517674\pi$
$571$	−2.65223			−0.110992			−0.0554962	+	0.998459i	$0.517674\pi$
$572$	9.26680	−	1.54728i	0.387464	−	0.0646949i
$573$		0			0
$574$	2.84470	+	0.911165i	0.118736	+	0.0380313i
$575$	−4.11943	+	8.67333i	−0.171792	+	0.361703i
$576$		0			0
$577$	−15.4206	−	15.4206i	−0.641968	−	0.641968i	0.309071	−	0.951039i	$-0.399982\pi$
$577$	−15.4206	−	15.4206i	−0.641968	−	0.641968i	−0.951039	+	0.309071i	$0.899982\pi$
$578$	−7.30571	+	3.76101i	−0.303878	+	0.156438i
$579$		0			0
$580$	4.30950	+	12.3222i	0.178942	+	0.511653i
$581$			3.99361i			0.165683i
$582$		0			0
$583$	−6.88638	−	6.88638i	−0.285205	−	0.285205i
$584$	14.0669	−	10.4924i	0.582093	−	0.434177i
$585$		0			0
$586$	−10.2772	+	32.0858i	−0.424546	+	1.32545i
$587$	−24.4859	−	24.4859i	−1.01064	−	1.01064i	−0.999943	−	0.0107002i	$-0.996594\pi$
$587$	−24.4859	−	24.4859i	−1.01064	−	1.01064i	−0.0107002	−	0.999943i	$-0.503406\pi$
$588$		0			0
$589$	−36.6365			−1.50958
$590$	2.81697	−	20.1377i	0.115973	−	0.829057i
$591$		0			0
$592$	−13.5043	−	6.59862i	−0.555024	−	0.271202i
$593$	29.7519	−	29.7519i	1.22176	−	1.22176i	0.254759	−	0.967005i	$-0.418004\pi$
$593$	29.7519	−	29.7519i	1.22176	−	1.22176i	0.967005	−	0.254759i	$-0.0819961\pi$
$594$		0			0
$595$	−8.87459	+	12.5792i	−0.363823	+	0.515699i
$596$	−3.52992	+	4.94497i	−0.144591	+	0.202554i
$597$		0			0
$598$	−15.6309	+	8.04686i	−0.639195	+	0.329061i
$599$	2.67797			0.109419			0.0547094	−	0.998502i	$-0.482577\pi$
$599$	2.67797			0.109419			0.0547094	+	0.998502i	$0.482577\pi$
$600$		0			0
$601$	14.2758			0.582321			0.291161	−	0.956674i	$-0.405959\pi$
$601$	14.2758			0.582321			0.291161	+	0.956674i	$0.405959\pi$
$602$	27.0358	−	13.9182i	1.10190	−	0.567262i
$603$		0			0
$604$	9.00170	+	6.42577i	0.366274	+	0.261461i
$605$	−13.5005	+	19.1363i	−0.548875	+	0.778000i
$606$		0			0
$607$	4.79670	−	4.79670i	0.194692	−	0.194692i	−0.603028	−	0.797720i	$-0.706039\pi$
$607$	4.79670	−	4.79670i	0.194692	−	0.194692i	0.797720	+	0.603028i	$0.206039\pi$
$608$	26.1848	+	25.1120i	1.06193	+	1.01843i
$609$		0			0
$610$	0.517406	−	3.69879i	0.0209492	−	0.149760i
$611$	−11.2464			−0.454981
$612$		0			0
$613$	8.18940	+	8.18940i	0.330767	+	0.330767i	0.852878	−	0.522111i	$-0.174855\pi$
$613$	8.18940	+	8.18940i	0.330767	+	0.330767i	−0.522111	+	0.852878i	$0.674855\pi$
$614$	8.29692	−	25.9034i	0.334837	−	1.04538i
$615$		0			0
$616$	−3.38615	+	2.52569i	−0.136432	+	0.101763i
$617$	−19.8311	−	19.8311i	−0.798368	−	0.798368i	0.184470	−	0.982838i	$-0.440943\pi$
$617$	−19.8311	−	19.8311i	−0.798368	−	0.798368i	−0.982838	+	0.184470i	$0.940943\pi$
$618$		0			0
$619$			14.8818i			0.598149i	0.954230	+	0.299075i	$0.0966780\pi$
$619$			14.8818i			0.598149i	−0.954230	+	0.299075i	$0.903322\pi$
$620$	24.1144	−	8.43362i	0.968458	−	0.338702i
$621$		0			0
$622$	8.78567	−	4.52290i	0.352273	−	0.181352i
$623$	−6.73904	−	6.73904i	−0.269994	−	0.269994i
$624$		0			0
$625$	−19.3767	+	15.7970i	−0.775067	+	0.631879i
$626$	−25.4578	−	8.15420i	−1.01750	−	0.325907i
$627$		0			0
$628$	−2.03189	−	12.1692i	−0.0810812	−	0.485604i
$629$	−12.5694			−0.501176
$630$		0			0
$631$		−	25.6770i		−	1.02218i	−0.859526	−	0.511092i	$-0.829241\pi$
$631$		−	25.6770i		−	1.02218i	0.859526	−	0.511092i	$-0.170759\pi$
$632$	−18.8991	−	2.75073i	−0.751765	−	0.109418i
$633$		0			0
$634$	4.27243	+	1.36847i	0.169680	+	0.0543489i
$635$	5.31833	+	30.7987i	0.211051	+	1.22221i
$636$		0			0
$637$	−12.6521	+	12.6521i	−0.501293	+	0.501293i
$638$	1.37113	+	2.66340i	0.0542836	+	0.105445i
$639$		0			0
$640$	−23.0157	−	10.5012i	−0.909777	−	0.415098i
$641$	−21.1942			−0.837122			−0.418561	−	0.908189i	$-0.637465\pi$
$641$	−21.1942			−0.837122			−0.418561	+	0.908189i	$0.637465\pi$
$642$		0			0
$643$	−21.5857	+	21.5857i	−0.851256	+	0.851256i	−0.990288	−	0.139032i	$-0.955601\pi$
$643$	−21.5857	+	21.5857i	−0.851256	+	0.851256i	0.139032	+	0.990288i	$0.455601\pi$
$644$	4.59269	−	6.43378i	0.180977	−	0.253526i
$645$		0			0
$646$	28.8943	+	9.25491i	1.13683	+	0.364130i
$647$	4.64626	−	4.64626i	0.182663	−	0.182663i	−0.609852	−	0.792515i	$-0.708771\pi$
$647$	4.64626	−	4.64626i	0.182663	−	0.182663i	0.792515	+	0.609852i	$0.208771\pi$
$648$		0			0
$649$		−	4.66614i		−	0.183162i
$650$	−45.7503	+	1.46499i	−1.79448	+	0.0574617i
$651$		0			0
$652$	−4.24063	−	25.3976i	−0.166076	−	0.994646i
$653$	5.98212	+	5.98212i	0.234098	+	0.234098i	0.814401	−	0.580303i	$-0.197066\pi$
$653$	5.98212	+	5.98212i	0.234098	+	0.234098i	−0.580303	+	0.814401i	$0.697066\pi$
$654$		0			0
$655$	−18.0480	+	25.5821i	−0.705195	+	0.999575i
$656$	1.33365	+	3.88233i	0.0520701	+	0.151580i
$657$		0			0
$658$	4.49597	−	2.31455i	0.175271	−	0.0902304i
$659$			41.9465i			1.63400i	0.576635	+	0.817002i	$0.304365\pi$
$659$			41.9465i			1.63400i	−0.576635	+	0.817002i	$0.695635\pi$
$660$		0			0
$661$			49.8515i			1.93900i	0.245095	+	0.969499i	$0.421181\pi$
$661$			49.8515i			1.93900i	−0.245095	+	0.969499i	$0.578819\pi$
$662$	0.233676	+	0.453913i	0.00908208	+	0.0176418i
$663$		0			0
$664$	−4.39928	+	3.28137i	−0.170725	+	0.127342i
$665$	−29.0854	+	5.02248i	−1.12789	+	0.194763i
$666$		0			0
$667$	−3.96373	−	3.96373i	−0.153476	−	0.153476i
$668$	7.08512	+	42.4335i	0.274132	+	1.64180i
$669$		0			0
$670$	−8.15180	−	10.8033i	−0.314931	−	0.417370i
$671$		−	0.857052i		−	0.0330861i
$672$		0			0
$673$	14.3656	−	14.3656i	0.553754	−	0.553754i	−0.373768	−	0.927522i	$-0.621934\pi$
$673$	14.3656	−	14.3656i	0.553754	−	0.553754i	0.927522	+	0.373768i	$0.121934\pi$
$674$	−0.333678	+	1.04176i	−0.0128528	+	0.0401270i
$675$		0			0
$676$	−47.0515	−	33.5872i	−1.80967	−	1.29182i
$677$	1.59459	−	1.59459i	0.0612852	−	0.0612852i	−0.675800	−	0.737085i	$-0.736202\pi$
$677$	1.59459	−	1.59459i	0.0612852	−	0.0612852i	0.737085	+	0.675800i	$0.236202\pi$
$678$		0			0
$679$	9.54627			0.366352
$680$	−21.1489	+	0.559738i	−0.811023	+	0.0214650i
$681$		0			0
$682$	5.21223	−	2.68328i	0.199587	−	0.102748i
$683$	3.56279	−	3.56279i	0.136326	−	0.136326i	−0.635651	−	0.771977i	$-0.719268\pi$
$683$	3.56279	−	3.56279i	0.136326	−	0.136326i	0.771977	+	0.635651i	$0.219268\pi$
$684$		0			0
$685$	13.4548	−	2.32338i	0.514083	−	0.0887719i
$686$	8.66908	−	27.0653i	0.330987	−	1.03336i
$687$		0			0
$688$	37.5461	+	18.3461i	1.43143	+	0.699440i
$689$			86.8758i			3.30970i
$690$		0			0
$691$	5.67883			0.216033			0.108016	−	0.994149i	$-0.465550\pi$
$691$	5.67883			0.216033			0.108016	+	0.994149i	$0.465550\pi$
$692$	14.6064	−	2.43883i	0.555253	−	0.0927105i
$693$		0			0
$694$	−7.05192	+	22.0164i	−0.267687	+	0.835732i
$695$	−18.7743	−	13.2452i	−0.712149	−	0.502417i
$696$		0			0
$697$	2.42744	+	2.42744i	0.0919459	+	0.0919459i
$698$	−6.85122	−	13.3084i	−0.259323	−	0.503730i
$699$		0			0
$700$	17.9881	−	10.0012i	0.679886	−	0.378011i
$701$		−	14.1700i		−	0.535194i	−0.963531	−	0.267597i	$-0.913770\pi$
$701$		−	14.1700i		−	0.535194i	0.963531	−	0.267597i	$-0.0862296\pi$
$702$		0			0
$703$	−17.0407	−	17.0407i	−0.642701	−	0.642701i
$704$	−5.56450	−	1.65486i	−0.209720	−	0.0623700i
$705$		0			0
$706$	−30.9194	−	9.90357i	−1.16367	−	0.372726i
$707$	19.7620	+	19.7620i	0.743225	+	0.743225i
$708$		0			0
$709$	14.5473			0.546337			0.273168	−	0.961966i	$-0.411928\pi$
$709$	14.5473			0.546337			0.273168	+	0.961966i	$0.411928\pi$
$710$	−2.87238	+	20.5338i	−0.107798	+	0.770620i
$711$		0			0
$712$	1.88642	−	12.9608i	0.0706965	−	0.485725i
$713$	−7.75694	+	7.75694i	−0.290500	+	0.290500i
$714$		0			0
$715$	−10.3508	+	1.78738i	−0.387099	+	0.0668444i
$716$	26.6056	+	18.9921i	0.994297	+	0.709769i
$717$		0			0
$718$	−4.40141	−	8.54967i	−0.164259	−	0.319071i
$719$	−41.3534			−1.54222			−0.771110	−	0.636702i	$-0.780298\pi$
$719$	−41.3534			−1.54222			−0.771110	+	0.636702i	$0.780298\pi$
$720$		0			0
$721$	23.0029			0.856673
$722$	14.3268	+	27.8296i	0.533188	+	1.03571i
$723$		0			0
$724$	2.17952	+	1.55583i	0.0810010	+	0.0578218i
$725$	−4.89456	−	13.7497i	−0.181779	−	0.510652i
$726$		0			0
$727$	17.1262	−	17.1262i	0.635177	−	0.635177i	−0.314185	−	0.949362i	$-0.601731\pi$
$727$	17.1262	−	17.1262i	0.635177	−	0.635177i	0.949362	+	0.314185i	$0.101731\pi$
$728$	37.2907	+	5.42760i	1.38208	+	0.201160i
$729$		0			0
$730$	−15.6619	+	11.8179i	−0.579674	+	0.437401i
$731$	34.9468			1.29255
$732$		0			0
$733$	10.8014	+	10.8014i	0.398958	+	0.398958i	0.877865	−	0.478907i	$-0.158967\pi$
$733$	10.8014	+	10.8014i	0.398958	+	0.398958i	−0.478907	+	0.877865i	$0.658967\pi$
$734$	6.15295	+	1.97080i	0.227109	+	0.0727437i
$735$		0			0
$736$	10.8609	−	0.227137i	0.400339	−	0.00837239i
$737$	−2.19606	−	2.19606i	−0.0808929	−	0.0808929i
$738$		0			0
$739$			28.4640i			1.04707i	0.852006	+	0.523533i	$0.175386\pi$
$739$			28.4640i			1.04707i	−0.852006	+	0.523533i	$0.824614\pi$
$740$	15.1390	+	7.29357i	0.556521	+	0.268117i
$741$		0			0
$742$	−17.8793	−	34.7303i	−0.656370	−	1.27499i
$743$	−37.4663	−	37.4663i	−1.37451	−	1.37451i	−0.853634	−	0.520873i	$-0.825607\pi$
$743$	−37.4663	−	37.4663i	−1.37451	−	1.37451i	−0.520873	−	0.853634i	$-0.674393\pi$
$744$		0			0
$745$	3.91582	−	5.55046i	0.143465	−	0.203353i
$746$	−1.29609	+	4.04645i	−0.0474531	+	0.148151i
$747$		0			0
$748$	−4.78859	+	0.799550i	−0.175088	+	0.0292345i
$749$	32.5202			1.18826
$750$		0			0
$751$		−	33.7409i		−	1.23122i	−0.788050	−	0.615611i	$-0.788909\pi$
$751$		−	33.7409i		−	1.23122i	0.788050	−	0.615611i	$-0.211091\pi$
$752$	6.24380	+	3.05091i	0.227688	+	0.111255i
$753$		0			0
$754$	8.15138	−	25.4490i	0.296856	−	0.926798i
$755$	−10.1039	−	7.12826i	−0.367719	−	0.259424i
$756$		0			0
$757$	−3.61554	+	3.61554i	−0.131409	+	0.131409i	−0.769752	−	0.638343i	$-0.779620\pi$
$757$	−3.61554	+	3.61554i	−0.131409	+	0.131409i	0.638343	+	0.769752i	$0.279620\pi$
$758$	−23.9932	+	12.3518i	−0.871473	+	0.448638i
$759$		0			0
$760$	−29.4309	−	27.9132i	−1.06757	−	1.01252i
$761$	53.5331			1.94057			0.970286	−	0.241959i	$-0.0777901\pi$
$761$	53.5331			1.94057			0.970286	+	0.241959i	$0.0777901\pi$
$762$		0			0
$763$	18.1159	−	18.1159i	0.655839	−	0.655839i
$764$	−30.2258	−	21.5764i	−1.09353	−	0.780606i
$765$		0			0
$766$	−1.81184	+	5.65664i	−0.0654643	+	0.204383i
$767$	−29.4330	+	29.4330i	−1.06277	+	1.06277i
$768$		0			0
$769$			0.470664i			0.0169726i	0.999964	+	0.00848630i	$0.00270130\pi$
$769$			0.470664i			0.0169726i	−0.999964	+	0.00848630i	$0.997299\pi$
$770$	3.77010	−	2.84478i	0.135865	−	0.102519i
$771$		0			0
$772$	0.981695	+	5.87947i	0.0353320	+	0.211607i
$773$	−13.2975	−	13.2975i	−0.478279	−	0.478279i	0.426302	−	0.904581i	$-0.359816\pi$
$773$	−13.2975	−	13.2975i	−0.478279	−	0.478279i	−0.904581	+	0.426302i	$0.859816\pi$
$774$		0			0
$775$	−26.9080	+	9.57857i	−0.966563	+	0.344072i
$776$	7.84374	+	10.5160i	0.281574	+	0.377501i
$777$		0			0
$778$	0.538546	+	1.04612i	0.0193078	+	0.0375051i
$779$			6.58187i			0.235820i
$780$		0			0
$781$			4.75791i			0.170252i
$782$	8.07722	−	4.15819i	0.288841	−	0.148697i
$783$		0			0
$784$	10.4564	−	3.59196i	0.373444	−	0.128284i
$785$	2.34720	+	13.5928i	0.0837751	+	0.485146i
$786$		0			0
$787$	−13.2592	−	13.2592i	−0.472639	−	0.472639i	0.430128	−	0.902768i	$-0.358468\pi$
$787$	−13.2592	−	13.2592i	−0.472639	−	0.472639i	−0.902768	+	0.430128i	$0.858468\pi$
$788$	4.02133	+	24.0841i	0.143254	+	0.857962i
$789$		0			0
$790$	21.1466	+	2.95809i	0.752360	+	0.105244i
$791$			27.4632i			0.976480i
$792$		0			0
$793$	−5.40611	+	5.40611i	−0.191977	+	0.191977i
$794$	−22.3808	−	7.16862i	−0.794265	−	0.254405i
$795$		0			0
$796$	2.74379	−	3.84371i	0.0972511	−	0.136237i
$797$	−17.1774	+	17.1774i	−0.608453	+	0.608453i	−0.942542	−	0.334089i	$-0.891572\pi$
$797$	−17.1774	+	17.1774i	−0.608453	+	0.608453i	0.334089	+	0.942542i	$0.391572\pi$
$798$		0			0
$799$	5.81155			0.205598
$800$	25.7971	+	11.5977i	0.912067	+	0.410042i
$801$		0			0
$802$	17.5457	+	34.0822i	0.619559	+	1.20348i
$803$	−3.18370	+	3.18370i	−0.112350	+	0.112350i
$804$		0			0
$805$	−5.09478	+	7.22157i	−0.179567	+	0.254527i
$806$	−49.8033	−	15.9521i	−1.75424	−	0.561889i
$807$		0			0
$808$	−5.53184	+	38.0069i	−0.194610	+	1.33708i
$809$		−	41.7364i		−	1.46737i	−0.679488	−	0.733686i	$-0.737798\pi$
$809$		−	41.7364i		−	1.46737i	0.679488	−	0.733686i	$-0.262202\pi$
$810$		0			0
$811$	34.4392			1.20932			0.604661	−	0.796483i	$-0.293308\pi$
$811$	34.4392			1.20932			0.604661	+	0.796483i	$0.293308\pi$
$812$	1.97881	+	11.8513i	0.0694427	+	0.415900i
$813$		0			0
$814$	3.67242	+	1.17629i	0.128718	+	0.0412288i
$815$	4.89870	+	28.3686i	0.171594	+	0.993709i
$816$		0			0
$817$	47.3782	+	47.3782i	1.65755	+	1.65755i
$818$	16.6895	−	8.59181i	0.583533	−	0.300405i
$819$		0			0
$820$	−1.51513	−	4.33223i	−0.0529106	−	0.151288i
$821$		−	12.0902i		−	0.421952i	−0.977491	−	0.210976i	$-0.932336\pi$
$821$		−	12.0902i		−	0.421952i	0.977491	−	0.210976i	$-0.0676642\pi$
$822$		0			0
$823$	−10.0784	−	10.0784i	−0.351310	−	0.351310i	0.509287	−	0.860597i	$-0.329909\pi$
$823$	−10.0784	−	10.0784i	−0.351310	−	0.351310i	−0.860597	+	0.509287i	$0.829909\pi$
$824$	18.9005	+	25.3395i	0.658429	+	0.882744i
$825$		0			0
$826$	5.70902	−	17.8238i	0.198642	−	0.620171i
$827$	−22.1941	−	22.1941i	−0.771763	−	0.771763i	0.206652	−	0.978415i	$-0.433743\pi$
$827$	−22.1941	−	22.1941i	−0.771763	−	0.771763i	−0.978415	+	0.206652i	$0.933743\pi$
$828$		0			0
$829$	−2.71154			−0.0941755			−0.0470878	−	0.998891i	$-0.514994\pi$
$829$	−2.71154			−0.0941755			−0.0470878	+	0.998891i	$0.514994\pi$
$830$	4.89810	−	3.69593i	0.170016	−	0.128287i
$831$		0			0
$832$	24.6612	+	45.5382i	0.854972	+	1.57875i
$833$	6.53792	−	6.53792i	0.226526	−	0.226526i
$834$		0			0
$835$	−8.18460	−	47.3974i	−0.283240	−	1.64026i
$836$	−7.57597	−	5.40803i	−0.262020	−	0.187041i
$837$		0			0
$838$	−30.5629	+	15.7339i	−1.05578	+	0.543519i
$839$	53.2192			1.83733			0.918666	−	0.395036i	$-0.129268\pi$
$839$	53.2192			1.83733			0.918666	+	0.395036i	$0.129268\pi$
$840$		0			0
$841$	−20.4795			−0.706191
$842$	−2.01792	+	1.03883i	−0.0695420	+	0.0358005i
$843$		0			0
$844$	3.92937	−	5.50455i	0.135255	−	0.189475i
$845$	52.8127	+	37.2591i	1.81681	+	1.28175i
$846$		0			0
$847$	−15.2422	+	15.2422i	−0.523729	+	0.523729i
$848$	23.5675	−	48.2318i	0.809313	−	1.65629i
$849$		0			0
$850$	23.6413	−	0.757030i	0.810891	−	0.0259659i
$851$	−7.21594			−0.247359
$852$		0			0
$853$	18.5528	+	18.5528i	0.635236	+	0.635236i	0.949376	−	0.314141i	$-0.101716\pi$
$853$	18.5528	+	18.5528i	0.635236	+	0.635236i	−0.314141	+	0.949376i	$0.601716\pi$
$854$	1.04860	−	3.27379i	0.0358825	−	0.112027i
$855$		0			0
$856$	26.7204	+	35.8236i	0.913285	+	1.22443i
$857$	12.8811	+	12.8811i	0.440009	+	0.440009i	0.892015	−	0.452006i	$-0.149291\pi$
$857$	12.8811	+	12.8811i	0.440009	+	0.440009i	−0.452006	+	0.892015i	$0.649291\pi$
$858$		0			0
$859$			3.82914i			0.130648i	0.997864	+	0.0653242i	$0.0208082\pi$
$859$			3.82914i			0.130648i	−0.997864	+	0.0653242i	$0.979192\pi$
$860$	−42.0910	−	20.2783i	−1.43529	−	0.691485i
$861$		0			0
$862$	−20.1191	+	10.3574i	−0.685259	+	0.352774i
$863$	−16.5089	−	16.5089i	−0.561970	−	0.561970i	0.367897	−	0.929867i	$-0.380078\pi$
$863$	−16.5089	−	16.5089i	−0.561970	−	0.561970i	−0.929867	+	0.367897i	$0.880078\pi$
$864$		0			0
$865$	−16.3151	+	2.81729i	−0.554730	+	0.0957908i
$866$	33.6506	+	10.7784i	1.14349	+	0.366264i
$867$		0			0
$868$	23.1928	−	3.87250i	0.787215	−	0.131441i
$869$	4.89989			0.166218
$870$		0			0
$871$			27.7046i			0.938734i
$872$	34.8411	+	5.07107i	1.17987	+	0.171728i
$873$		0			0
$874$	16.5878	+	5.31312i	0.561092	+	0.179719i
$875$	−20.0489	+	11.2932i	−0.677777	+	0.381778i
$876$		0			0
$877$	−27.6423	+	27.6423i	−0.933416	+	0.933416i	−0.997918	−	0.0645020i	$-0.979454\pi$
$877$	−27.6423	+	27.6423i	−0.933416	+	0.933416i	0.0645020	+	0.997918i	$0.479454\pi$
$878$	−22.3375	−	43.3902i	−0.753853	−	1.46435i
$879$		0			0
$880$	6.23147	+	1.81564i	0.210063	+	0.0612051i
$881$	14.6973			0.495165			0.247582	−	0.968867i	$-0.420364\pi$
$881$	14.6973			0.495165			0.247582	+	0.968867i	$0.420364\pi$
$882$		0			0
$883$	−31.5345	+	31.5345i	−1.06122	+	1.06122i	−0.0632202	+	0.998000i	$0.520137\pi$
$883$	−31.5345	+	31.5345i	−1.06122	+	1.06122i	−0.998000	+	0.0632202i	$0.979863\pi$
$884$	35.2489	+	25.1620i	1.18555	+	0.846291i
$885$		0			0
$886$	−3.86734	−	1.23872i	−0.129926	−	0.0416156i
$887$	−18.5981	+	18.5981i	−0.624464	+	0.624464i	−0.946670	−	0.322206i	$-0.895576\pi$
$887$	−18.5981	+	18.5981i	−0.624464	+	0.624464i	0.322206	+	0.946670i	$0.395576\pi$
$888$		0			0
$889$			28.7676i			0.964835i
$890$	−2.02862	+	14.5021i	−0.0679996	+	0.486110i
$891$		0			0
$892$	26.0013	−	4.34144i	0.870589	−	0.145362i
$893$	7.87885	+	7.87885i	0.263656	+	0.263656i
$894$		0			0
$895$	−29.8633	−	21.0684i	−0.998221	−	0.704240i
$896$	−19.2307	−	13.1295i	−0.642452	−	0.438624i
$897$		0			0
$898$	24.8084	−	12.7715i	0.827867	−	0.426190i
$899$		−	16.6744i		−	0.556123i
$900$		0			0
$901$		−	44.8928i		−	1.49560i
$902$	−0.482060	−	0.936394i	−0.0160508	−	0.0311785i
$903$		0			0
$904$	−30.2529	+	22.5653i	−1.00620	+	0.750511i
$905$	−2.44639	−	1.72591i	−0.0813207	−	0.0573713i
$906$		0			0
$907$	−15.1848	−	15.1848i	−0.504203	−	0.504203i	0.408538	−	0.912741i	$-0.366039\pi$
$907$	−15.1848	−	15.1848i	−0.504203	−	0.504203i	−0.912741	+	0.408538i	$0.866039\pi$
$908$	−41.6371	+	6.95215i	−1.38178	+	0.230715i
$909$		0			0
$910$	−41.7253	−	5.83675i	−1.38318	−	0.193486i
$911$		−	51.3671i		−	1.70187i	−0.525272	−	0.850934i	$-0.676036\pi$
$911$		−	51.3671i		−	1.70187i	0.525272	−	0.850934i	$-0.323964\pi$
$912$		0			0
$913$	0.995667	−	0.995667i	0.0329518	−	0.0329518i
$914$	−13.5525	+	42.3116i	−0.448277	+	1.39954i
$915$		0			0
$916$	15.7217	−	22.0241i	0.519460	−	0.727697i
$917$	−20.3764	+	20.3764i	−0.672888	+	0.672888i
$918$		0			0
$919$	31.4287			1.03674			0.518369	−	0.855157i	$-0.326539\pi$
$919$	31.4287			1.03674			0.518369	+	0.855157i	$0.326539\pi$
$920$	−12.1413	+	0.321338i	−0.400286	+	0.0105942i
$921$		0			0
$922$	26.0262	−	13.3984i	0.857127	−	0.441253i
$923$	30.0120	−	30.0120i	0.987855	−	0.987855i
$924$		0			0
$925$	−16.9709	−	8.06040i	−0.558000	−	0.265024i
$926$	−3.46218	+	10.8091i	−0.113774	+	0.355209i
$927$		0			0
$928$	−11.4293	+	11.9175i	−0.375184	+	0.391212i
$929$		−	17.2221i		−	0.565038i	−0.959262	−	0.282519i	$-0.908830\pi$
$929$		−	17.2221i		−	0.565038i	0.959262	−	0.282519i	$-0.0911700\pi$
$930$		0			0
$931$	17.7272			0.580986
$932$	−1.98681	−	11.8992i	−0.0650803	−	0.389773i
$933$		0			0
$934$	−2.31135	+	7.21614i	−0.0756295	+	0.236119i
$935$	5.34876	−	0.923625i	0.174923	−	0.0302058i
$936$		0			0
$937$	−29.3915	−	29.3915i	−0.960177	−	0.960177i	0.0390597	−	0.999237i	$-0.487564\pi$
$937$	−29.3915	−	29.3915i	−0.960177	−	0.960177i	−0.999237	+	0.0390597i	$0.987564\pi$
$938$	−5.70169	−	11.0755i	−0.186167	−	0.361626i
$939$		0			0
$940$	−6.99960	−	3.37222i	−0.228302	−	0.109990i
$941$			40.1614i			1.30922i	0.755966	+	0.654611i	$0.227168\pi$
$941$			40.1614i			1.30922i	−0.755966	+	0.654611i	$0.772832\pi$
$942$		0			0
$943$	1.39356	+	1.39356i	0.0453806	+	0.0453806i
$944$	24.3252	−	8.35612i	0.791718	−	0.271968i
$945$		0			0
$946$	−10.2104	−	3.27043i	−0.331970	−	0.106331i
$947$	−20.5497	−	20.5497i	−0.667777	−	0.667777i	0.289424	−	0.957201i	$-0.406536\pi$
$947$	−20.5497	−	20.5497i	−0.667777	−	0.667777i	−0.957201	+	0.289424i	$0.906536\pi$
$948$		0			0
$949$	40.1642			1.30379
$950$	33.0774	+	31.0248i	1.07317	+	1.00658i
$951$		0			0
$952$	−19.2698	−	2.80470i	−0.624539	−	0.0909007i
$953$	−14.0425	+	14.0425i	−0.454882	+	0.454882i	−0.896971	−	0.442089i	$-0.854238\pi$
$953$	−14.0425	+	14.0425i	−0.454882	+	0.454882i	0.442089	+	0.896971i	$0.354238\pi$
$954$		0			0
$955$	33.9268	+	23.9352i	1.09785	+	0.774525i
$956$	−3.18316	+	4.45920i	−0.102951	+	0.144221i
$957$		0			0
$958$	7.69844	+	14.9541i	0.248725	+	0.483145i
$959$	12.5675			0.405826
$960$		0			0
$961$	−1.63154			−0.0526302
$962$	−15.7451	−	30.5847i	−0.507643	−	0.986089i
$963$		0			0
$964$	19.1535	−	26.8316i	0.616893	−	0.864189i
$965$	−1.13404	−	6.56726i	−0.0365059	−	0.211408i
$966$		0			0
$967$	0.168063	−	0.168063i	0.00540454	−	0.00540454i	−0.704399	−	0.709804i	$-0.748784\pi$
$967$	0.168063	−	0.168063i	0.00540454	−	0.00540454i	0.709804	+	0.704399i	$0.248784\pi$
$968$	−29.3144	−	4.26666i	−0.942200	−	0.137136i
$969$		0			0
$970$	−8.83469	−	11.7084i	−0.283665	−	0.375933i
$971$	45.2762			1.45298			0.726492	−	0.687175i	$-0.241149\pi$
$971$	45.2762			1.45298			0.726492	+	0.687175i	$0.241149\pi$
$972$		0			0
$973$	−14.9539	−	14.9539i	−0.479400	−	0.479400i
$974$	42.1196	+	13.4910i	1.34960	+	0.432280i
$975$		0			0
$976$	4.46793	−	1.53481i	0.143015	−	0.0491280i
$977$	−33.1509	−	33.1509i	−1.06059	−	1.06059i	−0.998042	−	0.0625482i	$-0.980077\pi$
$977$	−33.1509	−	33.1509i	−1.06059	−	1.06059i	−0.0625482	−	0.998042i	$-0.519923\pi$
$978$		0			0
$979$			3.36029i			0.107395i
$980$	−11.6682	+	4.08075i	−0.372726	+	0.130355i
$981$		0			0
$982$	11.5693	+	22.4732i	0.369191	+	0.717149i
$983$	−3.16720	−	3.16720i	−0.101018	−	0.101018i	0.654792	−	0.755809i	$-0.272756\pi$
$983$	−3.16720	−	3.16720i	−0.101018	−	0.101018i	−0.755809	+	0.654792i	$0.772756\pi$
$984$		0			0
$985$	−4.64536	−	26.9015i	−0.148013	−	0.857154i
$986$	−4.21220	+	13.1507i	−0.134144	+	0.418803i
$987$		0			0
$988$	13.6749	+	81.9004i	0.435057	+	2.60560i
$989$	20.0625			0.637950
$990$		0			0
$991$			28.3462i			0.900447i	0.892916	+	0.450224i	$0.148656\pi$
$991$			28.3462i			0.900447i	−0.892916	+	0.450224i	$0.851344\pi$
$992$	23.3224	+	22.3669i	0.740486	+	0.710148i
$993$		0			0
$994$	−5.82131	+	18.1744i	−0.184641	+	0.576457i
$995$	−3.04375	+	4.31435i	−0.0964935	+	0.136774i
$996$		0			0
$997$	28.3453	−	28.3453i	0.897705	−	0.897705i	−0.0975279	−	0.995233i	$-0.531094\pi$
$997$	28.3453	−	28.3453i	0.897705	−	0.897705i	0.995233	+	0.0975279i	$0.0310935\pi$
$998$	−13.3395	+	6.86723i	−0.422254	+	0.217378i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.w.e.307.4		24
3.2	odd	2		120.2.v.a.67.9	yes	24
4.3	odd	2		1440.2.bi.e.847.9		24
5.3	odd	4	inner	360.2.w.e.163.2		24
8.3	odd	2	inner	360.2.w.e.307.2		24
8.5	even	2		1440.2.bi.e.847.4		24
12.11	even	2		480.2.bh.a.367.9		24
15.2	even	4		600.2.v.b.43.2		24
15.8	even	4		120.2.v.a.43.11	yes	24
15.14	odd	2		600.2.v.b.307.4		24
20.3	even	4		1440.2.bi.e.1423.4		24
24.5	odd	2		480.2.bh.a.367.10		24
24.11	even	2		120.2.v.a.67.11	yes	24
40.3	even	4	inner	360.2.w.e.163.4		24
40.13	odd	4		1440.2.bi.e.1423.9		24
60.23	odd	4		480.2.bh.a.463.10		24
60.47	odd	4		2400.2.bh.b.943.1		24
60.59	even	2		2400.2.bh.b.1807.2		24
120.29	odd	2		2400.2.bh.b.1807.1		24
120.53	even	4		480.2.bh.a.463.9		24
120.59	even	2		600.2.v.b.307.2		24
120.77	even	4		2400.2.bh.b.943.2		24
120.83	odd	4		120.2.v.a.43.9	✓	24
120.107	odd	4		600.2.v.b.43.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.v.a.43.9	✓	24	120.83	odd	4
120.2.v.a.43.11	yes	24	15.8	even	4
120.2.v.a.67.9	yes	24	3.2	odd	2
120.2.v.a.67.11	yes	24	24.11	even	2
360.2.w.e.163.2		24	5.3	odd	4	inner
360.2.w.e.163.4		24	40.3	even	4	inner
360.2.w.e.307.2		24	8.3	odd	2	inner
360.2.w.e.307.4		24	1.1	even	1	trivial
480.2.bh.a.367.9		24	12.11	even	2
480.2.bh.a.367.10		24	24.5	odd	2
480.2.bh.a.463.9		24	120.53	even	4
480.2.bh.a.463.10		24	60.23	odd	4
600.2.v.b.43.2		24	15.2	even	4
600.2.v.b.43.4		24	120.107	odd	4
600.2.v.b.307.2		24	120.59	even	2
600.2.v.b.307.4		24	15.14	odd	2
1440.2.bi.e.847.4		24	8.5	even	2
1440.2.bi.e.847.9		24	4.3	odd	2
1440.2.bi.e.1423.4		24	20.3	even	4
1440.2.bi.e.1423.9		24	40.13	odd	4
2400.2.bh.b.943.1		24	60.47	odd	4
2400.2.bh.b.943.2		24	120.77	even	4
2400.2.bh.b.1807.1		24	120.29	odd	2
2400.2.bh.b.1807.2		24	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.647304 - 1.25738i) q^{2} +(-1.16200 + 1.62781i) q^{4} +(1.28903 - 1.82713i) q^{5} +(1.45533 - 1.45533i) q^{7} +(2.79894 + 0.407381i) q^{8} +O(q^{10})\)	\(q+(-0.647304 - 1.25738i) q^{2} +(-1.16200 + 1.62781i) q^{4} +(1.28903 - 1.82713i) q^{5} +(1.45533 - 1.45533i) q^{7} +(2.79894 + 0.407381i) q^{8} +(-3.13178 - 0.438090i) q^{10} -0.725670 q^{11} +(4.57738 + 4.57738i) q^{13} +(-2.77193 - 0.887857i) q^{14} +(-1.29953 - 3.78302i) q^{16} +(-2.36535 - 2.36535i) q^{17} -6.41350i q^{19} +(1.47637 + 4.22141i) q^{20} +(0.469729 + 0.912441i) q^{22} +(-1.35791 - 1.35791i) q^{23} +(-1.67680 - 4.71045i) q^{25} +(2.79254 - 8.71844i) q^{26} +(0.677911 + 4.06008i) q^{28} +2.91898 q^{29} -5.71240i q^{31} +(-3.91549 + 4.08276i) q^{32} +(-1.44304 + 4.50523i) q^{34} +(-0.783110 - 4.53503i) q^{35} +(2.65700 - 2.65700i) q^{37} +(-8.06419 + 4.15148i) q^{38} +(4.35225 - 4.58889i) q^{40} -1.02625 q^{41} +(-7.38725 + 7.38725i) q^{43} +(0.843226 - 1.18125i) q^{44} +(-0.828427 + 2.58639i) q^{46} +(-1.22848 + 1.22848i) q^{47} +2.76404i q^{49} +(-4.83741 + 5.15746i) q^{50} +(-12.7700 + 2.13220i) q^{52} +(9.48969 + 9.48969i) q^{53} +(-0.935410 + 1.32589i) q^{55} +(4.66624 - 3.48050i) q^{56} +(-1.88947 - 3.67027i) q^{58} +6.43011i q^{59} +1.18105i q^{61} +(-7.18265 + 3.69766i) q^{62} +(7.66808 + 2.28046i) q^{64} +(14.2638 - 2.46308i) q^{65} +(3.02625 + 3.02625i) q^{67} +(6.59886 - 1.10181i) q^{68} +(-5.19534 + 3.92021i) q^{70} -6.55658i q^{71} +(4.38725 - 4.38725i) q^{73} +(-5.06073 - 1.62097i) q^{74} +(10.4400 + 7.45247i) q^{76} +(-1.05609 + 1.05609i) q^{77} -6.75224 q^{79} +(-8.58720 - 2.50202i) q^{80} +(0.664297 + 1.29039i) q^{82} +(-1.37207 + 1.37207i) q^{83} +(-7.37079 + 1.27279i) q^{85} +(14.0704 + 4.50677i) q^{86} +(-2.03110 - 0.295624i) q^{88} -4.63060i q^{89} +13.3232 q^{91} +(3.78831 - 0.632534i) q^{92} +(2.33986 + 0.749462i) q^{94} +(-11.7183 - 8.26720i) q^{95} +(3.27977 + 3.27977i) q^{97} +(3.47545 - 1.78918i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 8 q^{10} - 20 q^{16} - 8 q^{17} + 20 q^{20} - 28 q^{22} - 8 q^{25} + 16 q^{26} + 4 q^{28} - 20 q^{32} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 32 q^{43} + 48 q^{46} - 56 q^{50} - 48 q^{52} + 32 q^{56} - 12 q^{58} + 16 q^{62} + 8 q^{65} + 48 q^{67} - 72 q^{68} + 4 q^{70} - 40 q^{73} + 48 q^{76} - 76 q^{80} + 24 q^{82} - 80 q^{83} + 32 q^{86} + 12 q^{88} + 64 q^{91} - 16 q^{92} - 24 q^{97} + 88 q^{98}+O(q^{100}) \) 24 * q + 12 * q^8 + 8 * q^10 - 20 * q^16 - 8 * q^17 + 20 * q^20 - 28 * q^22 - 8 * q^25 + 16 * q^26 + 4 * q^28 - 20 * q^32 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 32 * q^43 + 48 * q^46 - 56 * q^50 - 48 * q^52 + 32 * q^56 - 12 * q^58 + 16 * q^62 + 8 * q^65 + 48 * q^67 - 72 * q^68 + 4 * q^70 - 40 * q^73 + 48 * q^76 - 76 * q^80 + 24 * q^82 - 80 * q^83 + 32 * q^86 + 12 * q^88 + 64 * q^91 - 16 * q^92 - 24 * q^97 + 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more