LMFDB - Embedded newform 765.2.n.e.647.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [765,2,Mod(188,765)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("765.188"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(765, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.n (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.10
Character	$\chi$	$=$	765.647
Dual form			765.2.n.e.188.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34783 - 1.34783i) q^{2} -1.63327i q^{4} +(-1.47114 - 1.68397i) q^{5} +(2.83235 + 2.83235i) q^{7} +(0.494282 + 0.494282i) q^{8} +(-4.25254 - 0.286850i) q^{10} -5.95927i q^{11} +(1.43074 - 1.43074i) q^{13} +7.63505 q^{14} +4.59896 q^{16} +(-0.707107 + 0.707107i) q^{17} -3.89447i q^{19} +(-2.75038 + 2.40278i) q^{20} +(-8.03207 - 8.03207i) q^{22} +(-1.20139 - 1.20139i) q^{23} +(-0.671484 + 4.95471i) q^{25} -3.85679i q^{26} +(4.62601 - 4.62601i) q^{28} -2.03715 q^{29} +9.98051 q^{31} +(5.21004 - 5.21004i) q^{32} +1.90612i q^{34} +(0.602794 - 8.93639i) q^{35} +(-5.07077 - 5.07077i) q^{37} +(-5.24907 - 5.24907i) q^{38} +(0.105195 - 1.55951i) q^{40} +1.02348i q^{41} +(-5.74522 + 5.74522i) q^{43} -9.73313 q^{44} -3.23853 q^{46} +(-2.64170 + 2.64170i) q^{47} +9.04447i q^{49} +(5.77304 + 7.58313i) q^{50} +(-2.33680 - 2.33680i) q^{52} +(7.74013 + 7.74013i) q^{53} +(-10.0352 + 8.76694i) q^{55} +2.79997i q^{56} +(-2.74573 + 2.74573i) q^{58} -3.81699 q^{59} -0.803225 q^{61} +(13.4520 - 13.4520i) q^{62} -4.84654i q^{64} +(-4.51415 - 0.304497i) q^{65} +(-5.17596 - 5.17596i) q^{67} +(1.15490 + 1.15490i) q^{68} +(-11.2322 - 12.8572i) q^{70} -2.40278i q^{71} +(-6.90975 + 6.90975i) q^{73} -13.6690 q^{74} -6.36074 q^{76} +(16.8788 - 16.8788i) q^{77} +1.25928i q^{79} +(-6.76573 - 7.74450i) q^{80} +(1.37947 + 1.37947i) q^{82} +(12.6459 + 12.6459i) q^{83} +(2.23100 + 0.150490i) q^{85} +15.4871i q^{86} +(2.94556 - 2.94556i) q^{88} +4.48063 q^{89} +8.10474 q^{91} +(-1.96220 + 1.96220i) q^{92} +7.12111i q^{94} +(-6.55815 + 5.72931i) q^{95} +(12.1047 + 12.1047i) q^{97} +(12.1904 + 12.1904i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{7} - 20 q^{10} - 20 q^{13} - 8 q^{16} - 40 q^{22} - 24 q^{28} + 72 q^{31} + 16 q^{37} - 88 q^{40} + 36 q^{43} + 56 q^{46} + 32 q^{52} - 88 q^{55} - 80 q^{58} - 8 q^{61} + 104 q^{67} - 136 q^{70}+ \cdots + 88 q^{97}+O(q^{100}) $ 24 * q + 8 * q^7 - 20 * q^10 - 20 * q^13 - 8 * q^16 - 40 * q^22 - 24 * q^28 + 72 * q^31 + 16 * q^37 - 88 * q^40 + 36 * q^43 + 56 * q^46 + 32 * q^52 - 88 * q^55 - 80 * q^58 - 8 * q^61 + 104 * q^67 - 136 * q^70 - 136 * q^73 + 136 * q^76 + 16 * q^82 + 8 * q^85 - 64 * q^88 - 8 * q^91 + 88 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	1.34783	−	1.34783i	0.953058	−	0.953058i	−0.0458890	−	0.998947i	$-0.514612\pi$
$2$	1.34783	−	1.34783i	0.953058	−	0.953058i	0.998947	+	0.0458890i	$0.0146121\pi$
$3$		0			0
$3$		0			0
$4$		−	1.63327i		−	0.816637i
$5$	−1.47114	−	1.68397i	−0.657915	−	0.753093i
$5$	−1.47114	−	1.68397i	−0.657915	−	0.753093i
$6$		0			0
$7$	2.83235	+	2.83235i	1.07053	+	1.07053i	0.997316	+	0.0732132i	$0.0233254\pi$
$7$	2.83235	+	2.83235i	1.07053	+	1.07053i	0.0732132	+	0.997316i	$0.476675\pi$
$8$	0.494282	+	0.494282i	0.174755	+	0.174755i
$9$		0			0
$10$	−4.25254	−	0.286850i	−1.34477	−	0.0907101i
$11$		−	5.95927i		−	1.79679i	−0.439190	−	0.898394i	$-0.644734\pi$
$11$		−	5.95927i		−	1.79679i	0.439190	−	0.898394i	$-0.355266\pi$
$12$		0			0
$13$	1.43074	−	1.43074i	0.396817	−	0.396817i	−0.480292	−	0.877109i	$-0.659469\pi$
$13$	1.43074	−	1.43074i	0.396817	−	0.396817i	0.877109	+	0.480292i	$0.159469\pi$
$14$	7.63505			2.04055
$15$		0			0
$16$	4.59896			1.14974
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$18$		0			0
$19$		−	3.89447i		−	0.893452i	−0.894671	−	0.446726i	$-0.852590\pi$
$19$		−	3.89447i		−	0.893452i	0.894671	−	0.446726i	$-0.147410\pi$
$20$	−2.75038	+	2.40278i	−0.615003	+	0.537278i
$21$		0			0
$22$	−8.03207	−	8.03207i	−1.71244	−	1.71244i
$23$	−1.20139	−	1.20139i	−0.250507	−	0.250507i	0.570671	−	0.821178i	$-0.306683\pi$
$23$	−1.20139	−	1.20139i	−0.250507	−	0.250507i	−0.821178	+	0.570671i	$0.806683\pi$
$24$		0			0
$25$	−0.671484	+	4.95471i	−0.134297	+	0.990941i
$26$		−	3.85679i		−	0.756378i
$27$		0			0
$28$	4.62601	−	4.62601i	0.874234	−	0.874234i
$29$	−2.03715			−0.378290			−0.189145	−	0.981949i	$-0.560572\pi$
$29$	−2.03715			−0.378290			−0.189145	+	0.981949i	$0.560572\pi$
$30$		0			0
$31$	9.98051			1.79255			0.896277	−	0.443496i	$-0.146262\pi$
$31$	9.98051			1.79255			0.896277	+	0.443496i	$0.146262\pi$
$32$	5.21004	−	5.21004i	0.921014	−	0.921014i
$33$		0			0
$34$			1.90612i			0.326896i
$35$	0.602794	−	8.93639i	0.101891	−	1.51052i
$36$		0			0
$37$	−5.07077	−	5.07077i	−0.833629	−	0.833629i	0.154382	−	0.988011i	$-0.450661\pi$
$37$	−5.07077	−	5.07077i	−0.833629	−	0.833629i	−0.988011	+	0.154382i	$0.950661\pi$
$38$	−5.24907	−	5.24907i	−0.851511	−	0.851511i
$39$		0			0
$40$	0.105195	−	1.55951i	0.0166328	−	0.246581i
$41$			1.02348i			0.159840i	0.996801	+	0.0799201i	$0.0254665\pi$
$41$			1.02348i			0.159840i	−0.996801	+	0.0799201i	$0.974533\pi$
$42$		0			0
$43$	−5.74522	+	5.74522i	−0.876138	+	0.876138i	−0.993133	−	0.116995i	$-0.962674\pi$
$43$	−5.74522	+	5.74522i	−0.876138	+	0.876138i	0.116995	+	0.993133i	$0.462674\pi$
$44$	−9.73313			−1.46732
$45$		0			0
$46$	−3.23853			−0.477495
$47$	−2.64170	+	2.64170i	−0.385332	+	0.385332i	−0.873019	−	0.487687i	$-0.837841\pi$
$47$	−2.64170	+	2.64170i	−0.385332	+	0.385332i	0.487687	+	0.873019i	$0.337841\pi$
$48$		0			0
$49$			9.04447i			1.29207i
$50$	5.77304	+	7.58313i	0.816431	+	1.07242i
$51$		0			0
$52$	−2.33680	−	2.33680i	−0.324055	−	0.324055i
$53$	7.74013	+	7.74013i	1.06319	+	1.06319i	0.997864	+	0.0653251i	$0.0208084\pi$
$53$	7.74013	+	7.74013i	1.06319	+	1.06319i	0.0653251	+	0.997864i	$0.479192\pi$
$54$		0			0
$55$	−10.0352	+	8.76694i	−1.35315	+	1.18213i
$56$			2.79997i			0.374161i
$57$		0			0
$58$	−2.74573	+	2.74573i	−0.360532	+	0.360532i
$59$	−3.81699			−0.496930			−0.248465	−	0.968641i	$-0.579926\pi$
$59$	−3.81699			−0.496930			−0.248465	+	0.968641i	$0.579926\pi$
$60$		0			0
$61$	−0.803225			−0.102842			−0.0514212	−	0.998677i	$-0.516375\pi$
$61$	−0.803225			−0.102842			−0.0514212	+	0.998677i	$0.516375\pi$
$62$	13.4520	−	13.4520i	1.70841	−	1.70841i
$63$		0			0
$64$		−	4.84654i		−	0.605818i
$65$	−4.51415	−	0.304497i	−0.559911	−	0.0377682i
$66$		0			0
$67$	−5.17596	−	5.17596i	−0.632344	−	0.632344i	0.316311	−	0.948655i	$-0.397556\pi$
$67$	−5.17596	−	5.17596i	−0.632344	−	0.632344i	−0.948655	+	0.316311i	$0.897556\pi$
$68$	1.15490	+	1.15490i	0.140052	+	0.140052i
$69$		0			0
$70$	−11.2322	−	12.8572i	−1.34251	−	1.53672i
$71$		−	2.40278i		−	0.285157i	−0.989783	−	0.142579i	$-0.954461\pi$
$71$		−	2.40278i		−	0.285157i	0.989783	−	0.142579i	$-0.0455394\pi$
$72$		0			0
$73$	−6.90975	+	6.90975i	−0.808725	+	0.808725i	−0.984441	−	0.175716i	$-0.943776\pi$
$73$	−6.90975	+	6.90975i	−0.808725	+	0.808725i	0.175716	+	0.984441i	$0.443776\pi$
$74$	−13.6690			−1.58899
$75$		0			0
$76$	−6.36074			−0.729626
$77$	16.8788	−	16.8788i	1.92352	−	1.92352i
$78$		0			0
$79$			1.25928i			0.141680i	0.997488	+	0.0708402i	$0.0225680\pi$
$79$			1.25928i			0.141680i	−0.997488	+	0.0708402i	$0.977432\pi$
$80$	−6.76573	−	7.74450i	−0.756431	−	0.865861i
$81$		0			0
$82$	1.37947	+	1.37947i	0.152337	+	0.152337i
$83$	12.6459	+	12.6459i	1.38807	+	1.38807i	0.829377	+	0.558690i	$0.188696\pi$
$83$	12.6459	+	12.6459i	1.38807	+	1.38807i	0.558690	+	0.829377i	$0.311304\pi$
$84$		0			0
$85$	2.23100	+	0.150490i	0.241986	+	0.0163229i
$86$			15.4871i			1.67002i
$87$		0			0
$88$	2.94556	−	2.94556i	0.313998	−	0.313998i
$89$	4.48063			0.474946			0.237473	−	0.971394i	$-0.423681\pi$
$89$	4.48063			0.474946			0.237473	+	0.971394i	$0.423681\pi$
$90$		0			0
$91$	8.10474			0.849608
$92$	−1.96220	+	1.96220i	−0.204573	+	0.204573i
$93$		0			0
$94$			7.12111i			0.734487i
$95$	−6.55815	+	5.72931i	−0.672852	+	0.587815i
$96$		0			0
$97$	12.1047	+	12.1047i	1.22905	+	1.22905i	0.964323	+	0.264727i	$0.0852817\pi$
$97$	12.1047	+	12.1047i	1.22905	+	1.22905i	0.264727	+	0.964323i	$0.414718\pi$
$98$	12.1904	+	12.1904i	1.23141	+	1.23141i
$99$		0			0
$100$	8.09239	+	1.09672i	0.809239	+	0.109672i
$101$			6.10347i			0.607318i	0.952781	+	0.303659i	$0.0982083\pi$
$101$			6.10347i			0.607318i	−0.952781	+	0.303659i	$0.901792\pi$
$102$		0			0
$103$	−4.29792	+	4.29792i	−0.423487	+	0.423487i	−0.886402	−	0.462916i	$-0.846803\pi$
$103$	−4.29792	+	4.29792i	−0.423487	+	0.423487i	0.462916	+	0.886402i	$0.346803\pi$
$104$	1.41438			0.138692
$105$		0			0
$106$	20.8647			2.02656
$107$	−5.44844	+	5.44844i	−0.526720	+	0.526720i	−0.919593	−	0.392873i	$-0.871481\pi$
$107$	−5.44844	+	5.44844i	−0.526720	+	0.526720i	0.392873	+	0.919593i	$0.371481\pi$
$108$		0			0
$109$		−	16.6290i		−	1.59276i	−0.604793	−	0.796382i	$-0.706744\pi$
$109$		−	16.6290i		−	1.59276i	0.604793	−	0.796382i	$-0.293256\pi$
$110$	−1.70942	+	25.3420i	−0.162987	+	2.41627i
$111$		0			0
$112$	13.0259	+	13.0259i	1.23083	+	1.23083i
$113$	6.58641	+	6.58641i	0.619598	+	0.619598i	0.945428	−	0.325831i	$-0.105644\pi$
$113$	6.58641	+	6.58641i	0.619598	+	0.619598i	−0.325831	+	0.945428i	$0.605644\pi$
$114$		0			0
$115$	−0.255685	+	3.79051i	−0.0238427	+	0.353467i
$116$			3.32723i			0.308926i
$117$		0			0
$118$	−5.14464	+	5.14464i	−0.473603	+	0.473603i
$119$	−4.00555			−0.367189
$120$		0			0
$121$	−24.5129			−2.22845
$122$	−1.08261	+	1.08261i	−0.0980147	+	0.0980147i
$123$		0			0
$124$		−	16.3009i		−	1.46387i
$125$	9.33140	−	6.15832i	0.834626	−	0.550817i
$126$		0			0
$127$	−2.56224	−	2.56224i	−0.227362	−	0.227362i	0.584228	−	0.811590i	$-0.301397\pi$
$127$	−2.56224	−	2.56224i	−0.227362	−	0.227362i	−0.811590	+	0.584228i	$0.801397\pi$
$128$	3.88778	+	3.88778i	0.343635	+	0.343635i
$129$		0			0
$130$	−6.49470	+	5.67388i	−0.569623	+	0.497632i
$131$		−	13.1494i		−	1.14887i	−0.818550	−	0.574435i	$-0.805222\pi$
$131$		−	13.1494i		−	1.14887i	0.818550	−	0.574435i	$-0.194778\pi$
$132$		0			0
$133$	11.0305	−	11.0305i	0.956467	−	0.956467i
$134$	−13.9526			−1.20532
$135$		0			0
$136$	−0.699021			−0.0599405
$137$	0.0775311	−	0.0775311i	0.00662393	−	0.00662393i	−0.703787	−	0.710411i	$-0.748509\pi$
$137$	0.0775311	−	0.0775311i	0.00662393	−	0.00662393i	0.710411	+	0.703787i	$0.248509\pi$
$138$		0			0
$139$			18.9107i			1.60399i	0.597332	+	0.801994i	$0.296227\pi$
$139$			18.9107i			1.60399i	−0.597332	+	0.801994i	$0.703773\pi$
$140$	−14.5956	−	0.984528i	−1.23355	−	0.0832078i
$141$		0			0
$142$	−3.23853	−	3.23853i	−0.271771	−	0.271771i
$143$	−8.52618	−	8.52618i	−0.712995	−	0.712995i
$144$		0			0
$145$	2.99694	+	3.43050i	0.248883	+	0.284887i
$146$			18.6263i			1.54152i
$147$		0			0
$148$	−8.28195	+	8.28195i	−0.680772	+	0.680772i
$149$	−17.6761			−1.44808			−0.724042	−	0.689756i	$-0.757718\pi$
$149$	−17.6761			−1.44808			−0.724042	+	0.689756i	$0.757718\pi$
$150$		0			0
$151$	−3.74113			−0.304449			−0.152225	−	0.988346i	$-0.548644\pi$
$151$	−3.74113			−0.304449			−0.152225	+	0.988346i	$0.548644\pi$
$152$	1.92497	−	1.92497i	0.156135	−	0.156135i
$153$		0			0
$154$		−	45.4993i		−	3.66644i
$155$	−14.6828	−	16.8068i	−1.17935	−	1.34996i
$156$		0			0
$157$	5.80294	+	5.80294i	0.463125	+	0.463125i	0.899678	−	0.436553i	$-0.143801\pi$
$157$	5.80294	+	5.80294i	0.463125	+	0.463125i	−0.436553	+	0.899678i	$0.643801\pi$
$158$	1.69730	+	1.69730i	0.135030	+	0.135030i
$159$		0			0
$160$	−16.4382	−	1.10882i	−1.29956	−	0.0876602i
$161$		−	6.80552i		−	0.536350i
$162$		0			0
$163$	15.4773	−	15.4773i	1.21228	−	1.21228i	0.242003	−	0.970276i	$-0.422196\pi$
$163$	15.4773	−	15.4773i	1.21228	−	1.21228i	0.970276	−	0.242003i	$-0.0778043\pi$
$164$	1.67162			0.130532
$165$		0			0
$166$	34.0889			2.64581
$167$	−12.0656	+	12.0656i	−0.933661	+	0.933661i	−0.997932	−	0.0642712i	$-0.979528\pi$
$167$	−12.0656	+	12.0656i	−0.933661	+	0.933661i	0.0642712	+	0.997932i	$0.479528\pi$
$168$		0			0
$169$			8.90595i			0.685073i
$170$	3.20983	−	2.80417i	0.246183	−	0.215070i
$171$		0			0
$172$	9.38352	+	9.38352i	0.715487	+	0.715487i
$173$	−10.8638	−	10.8638i	−0.825959	−	0.825959i	0.160996	−	0.986955i	$-0.448529\pi$
$173$	−10.8638	−	10.8638i	−0.825959	−	0.825959i	−0.986955	+	0.160996i	$0.948529\pi$
$174$		0			0
$175$	−15.9354	+	12.1316i	−1.20460	+	0.917063i
$176$		−	27.4065i		−	2.06584i
$177$		0			0
$178$	6.03911	−	6.03911i	0.452651	−	0.452651i
$179$	−19.6834			−1.47121			−0.735605	−	0.677411i	$-0.763102\pi$
$179$	−19.6834			−1.47121			−0.735605	+	0.677411i	$0.763102\pi$
$180$		0			0
$181$	2.54568			0.189219			0.0946095	−	0.995514i	$-0.469840\pi$
$181$	2.54568			0.189219			0.0946095	+	0.995514i	$0.469840\pi$
$182$	10.9238	−	10.9238i	0.809725	−	0.809725i
$183$		0			0
$184$		−	1.18765i		−	0.0875548i
$185$	−1.07918	+	15.9988i	−0.0793431	+	1.17626i
$186$		0			0
$187$	4.21384	+	4.21384i	0.308147	+	0.308147i
$188$	4.31462	+	4.31462i	0.314676	+	0.314676i
$189$		0			0
$190$	−1.11713	+	16.5614i	−0.0810451	+	1.20149i
$191$			22.5510i			1.63173i	0.578241	+	0.815866i	$0.303739\pi$
$191$			22.5510i			1.63173i	−0.578241	+	0.815866i	$0.696261\pi$
$192$		0			0
$193$	−1.54423	+	1.54423i	−0.111156	+	0.111156i	−0.760497	−	0.649341i	$-0.775045\pi$
$193$	−1.54423	+	1.54423i	−0.111156	+	0.111156i	0.649341	+	0.760497i	$0.275045\pi$
$194$	32.6302			2.34271
$195$		0			0
$196$	14.7721			1.05515
$197$	1.33287	−	1.33287i	0.0949632	−	0.0949632i	−0.658029	−	0.752992i	$-0.728610\pi$
$197$	1.33287	−	1.33287i	0.0949632	−	0.0949632i	0.752992	+	0.658029i	$0.228610\pi$
$198$		0			0
$199$		−	17.0664i		−	1.20981i	−0.796299	−	0.604904i	$-0.793212\pi$
$199$		−	17.0664i		−	1.20981i	0.796299	−	0.604904i	$-0.206788\pi$
$200$	−2.78093	+	2.11712i	−0.196641	+	0.149703i
$201$		0			0
$202$	8.22642	+	8.22642i	0.578809	+	0.578809i
$203$	−5.76994	−	5.76994i	−0.404971	−	0.404971i
$204$		0			0
$205$	1.72350	−	1.50568i	0.120375	−	0.105161i
$206$			11.5857i			0.807215i
$207$		0			0
$208$	6.57993	−	6.57993i	0.456236	−	0.456236i
$209$	−23.2082			−1.60534
$210$		0			0
$211$	−7.63136			−0.525365			−0.262682	−	0.964882i	$-0.584607\pi$
$211$	−7.63136			−0.525365			−0.262682	+	0.964882i	$0.584607\pi$
$212$	12.6418	−	12.6418i	0.868240	−	0.868240i
$213$		0			0
$214$			14.6871i			1.00399i
$215$	18.1268	+	1.22272i	1.23624	+	0.0833890i
$216$		0			0
$217$	28.2684	+	28.2684i	1.91898	+	1.91898i
$218$	−22.4129	−	22.4129i	−1.51800	−	1.51800i
$219$		0			0
$220$	14.3188	+	16.3903i	0.965374	+	1.10503i
$221$			2.02338i			0.136107i
$222$		0			0
$223$	4.63569	−	4.63569i	0.310429	−	0.310429i	−0.534647	−	0.845076i	$-0.679555\pi$
$223$	4.63569	−	4.63569i	0.310429	−	0.310429i	0.845076	+	0.534647i	$0.179555\pi$
$224$	29.5134			1.97195
$225$		0			0
$226$	17.7547			1.18102
$227$	−3.66615	+	3.66615i	−0.243331	+	0.243331i	−0.818227	−	0.574896i	$-0.805043\pi$
$227$	−3.66615	+	3.66615i	−0.243331	+	0.243331i	0.574896	+	0.818227i	$0.305043\pi$
$228$		0			0
$229$			13.6663i			0.903093i	0.892248	+	0.451546i	$0.149127\pi$
$229$			13.6663i			0.903093i	−0.892248	+	0.451546i	$0.850873\pi$
$230$	4.76434	+	5.45357i	0.314151	+	0.359598i
$231$		0			0
$232$	−1.00693	−	1.00693i	−0.0661082	−	0.0661082i
$233$	−8.38892	−	8.38892i	−0.549576	−	0.549576i	0.376742	−	0.926318i	$-0.377044\pi$
$233$	−8.38892	−	8.38892i	−0.549576	−	0.549576i	−0.926318	+	0.376742i	$0.877044\pi$
$234$		0			0
$235$	8.33485	+	0.562218i	0.543706	+	0.0366751i
$236$			6.23420i			0.405812i
$237$		0			0
$238$	−5.39879	+	5.39879i	−0.349952	+	0.349952i
$239$	−7.17220			−0.463931			−0.231966	−	0.972724i	$-0.574516\pi$
$239$	−7.17220			−0.463931			−0.231966	+	0.972724i	$0.574516\pi$
$240$		0			0
$241$	−0.542222			−0.0349276			−0.0174638	−	0.999847i	$-0.505559\pi$
$241$	−0.542222			−0.0349276			−0.0174638	+	0.999847i	$0.505559\pi$
$242$	−33.0392	+	33.0392i	−2.12384	+	2.12384i
$243$		0			0
$244$			1.31189i			0.0839850i
$245$	15.2306	−	13.3057i	0.973046	−	0.850070i
$246$		0			0
$247$	−5.57198	−	5.57198i	−0.354537	−	0.354537i
$248$	4.93319	+	4.93319i	0.313258	+	0.313258i
$249$		0			0
$250$	4.27677	−	20.8775i	0.270487	−	1.32041i
$251$			30.2271i			1.90792i	0.299940	+	0.953958i	$0.403033\pi$
$251$			30.2271i			1.90792i	−0.299940	+	0.953958i	$0.596967\pi$
$252$		0			0
$253$	−7.15941	+	7.15941i	−0.450108	+	0.450108i
$254$	−6.90690			−0.433377
$255$		0			0
$256$	20.1732			1.26083
$257$	14.2384	−	14.2384i	0.888165	−	0.888165i	−0.106182	−	0.994347i	$-0.533863\pi$
$257$	14.2384	−	14.2384i	0.888165	−	0.888165i	0.994347	+	0.106182i	$0.0338626\pi$
$258$		0			0
$259$		−	28.7244i		−	1.78485i
$260$	−0.497327	+	7.37284i	−0.0308429	+	0.457244i
$261$		0			0
$262$	−17.7231	−	17.7231i	−1.09494	−	1.09494i
$263$	2.77074	+	2.77074i	0.170851	+	0.170851i	0.787353	−	0.616502i	$-0.211451\pi$
$263$	2.77074	+	2.77074i	0.170851	+	0.170851i	−0.616502	+	0.787353i	$0.711451\pi$
$264$		0			0
$265$	1.64729	−	24.4210i	0.101192	−	1.50017i
$266$		−	29.7345i		−	1.82314i
$267$		0			0
$268$	−8.45376	+	8.45376i	−0.516396	+	0.516396i
$269$	−16.2740			−0.992242			−0.496121	−	0.868253i	$-0.665243\pi$
$269$	−16.2740			−0.992242			−0.496121	+	0.868253i	$0.665243\pi$
$270$		0			0
$271$	−2.05507			−0.124837			−0.0624184	−	0.998050i	$-0.519881\pi$
$271$	−2.05507			−0.124837			−0.0624184	+	0.998050i	$0.519881\pi$
$272$	−3.25196	+	3.25196i	−0.197179	+	0.197179i
$273$		0			0
$274$		−	0.208997i		−	0.0126260i
$275$	29.5264	+	4.00156i	1.78051	+	0.241303i
$276$		0			0
$277$	−19.8539	−	19.8539i	−1.19291	−	1.19291i	−0.976247	−	0.216659i	$-0.930484\pi$
$277$	−19.8539	−	19.8539i	−1.19291	−	1.19291i	−0.216659	−	0.976247i	$-0.569516\pi$
$278$	25.4884	+	25.4884i	1.52869	+	1.52869i
$279$		0			0
$280$	4.71505	−	4.11915i	0.281778	−	0.246166i
$281$		−	12.8292i		−	0.765327i	−0.923888	−	0.382664i	$-0.875007\pi$
$281$		−	12.8292i		−	0.765327i	0.923888	−	0.382664i	$-0.124993\pi$
$282$		0			0
$283$	11.3840	−	11.3840i	0.676707	−	0.676707i	−0.282547	−	0.959254i	$-0.591179\pi$
$283$	11.3840	−	11.3840i	0.676707	−	0.676707i	0.959254	+	0.282547i	$0.0911792\pi$
$284$	−3.92440			−0.232870
$285$		0			0
$286$	−22.9836			−1.35905
$287$	−2.89885	+	2.89885i	−0.171114	+	0.171114i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	8.66308	+	0.584359i	0.508713	+	0.0343147i
$291$		0			0
$292$	11.2855	+	11.2855i	0.660435	+	0.660435i
$293$	5.45554	+	5.45554i	0.318716	+	0.318716i	0.848274	−	0.529558i	$-0.177642\pi$
$293$	5.45554	+	5.45554i	0.318716	+	0.318716i	−0.529558	+	0.848274i	$0.677642\pi$
$294$		0			0
$295$	5.61534	+	6.42769i	0.326938	+	0.374234i
$296$		−	5.01278i		−	0.291362i
$297$		0			0
$298$	−23.8244	+	23.8244i	−1.38011	+	1.38011i
$299$	−3.43776			−0.198811
$300$		0			0
$301$	−32.5450			−1.87586
$302$	−5.04240	+	5.04240i	−0.290158	+	0.290158i
$303$		0			0
$304$		−	17.9105i		−	1.02724i
$305$	1.18166	+	1.35260i	0.0676615	+	0.0774499i
$306$		0			0
$307$	2.60964	+	2.60964i	0.148940	+	0.148940i	0.777644	−	0.628704i	$-0.216414\pi$
$307$	2.60964	+	2.60964i	0.148940	+	0.148940i	−0.628704	+	0.777644i	$0.716414\pi$
$308$	−27.5677	−	27.5677i	−1.57081	−	1.57081i
$309$		0			0
$310$	−42.4425	−	2.86291i	−2.41057	−	0.162603i
$311$		−	2.93740i		−	0.166565i	−0.996526	−	0.0832824i	$-0.973460\pi$
$311$		−	2.93740i		−	0.166565i	0.996526	−	0.0832824i	$-0.0265403\pi$
$312$		0			0
$313$	3.49597	−	3.49597i	0.197604	−	0.197604i	−0.601368	−	0.798972i	$-0.705377\pi$
$313$	3.49597	−	3.49597i	0.197604	−	0.197604i	0.798972	+	0.601368i	$0.205377\pi$
$314$	15.6427			0.882770
$315$		0			0
$316$	2.05675			0.115702
$317$	13.5894	−	13.5894i	0.763257	−	0.763257i	−0.213652	−	0.976910i	$-0.568536\pi$
$317$	13.5894	−	13.5894i	0.763257	−	0.763257i	0.976910	+	0.213652i	$0.0685360\pi$
$318$		0			0
$319$			12.1400i			0.679707i
$320$	−8.16141	+	7.12995i	−0.456237	+	0.398576i
$321$		0			0
$322$	−9.17266	−	9.17266i	−0.511173	−	0.511173i
$323$	2.75380	+	2.75380i	0.153226	+	0.153226i
$324$		0			0
$325$	6.12819	+	8.04963i	0.339931	+	0.446513i
$326$		−	41.7215i		−	2.31074i
$327$		0			0
$328$	−0.505887	+	0.505887i	−0.0279329	+	0.0279329i
$329$	−14.9645			−0.825018
$330$		0			0
$331$	10.2938			0.565797			0.282899	−	0.959150i	$-0.408704\pi$
$331$	10.2938			0.565797			0.282899	+	0.959150i	$0.408704\pi$
$332$	20.6542	−	20.6542i	1.13355	−	1.13355i
$333$		0			0
$334$			32.5246i			1.77967i
$335$	−1.10157	+	16.3307i	−0.0601852	+	0.892242i
$336$		0			0
$337$	−10.5622	−	10.5622i	−0.575358	−	0.575358i	0.358263	−	0.933621i	$-0.383369\pi$
$337$	−10.5622	−	10.5622i	−0.575358	−	0.575358i	−0.933621	+	0.358263i	$0.883369\pi$
$338$	12.0037	+	12.0037i	0.652914	+	0.652914i
$339$		0			0
$340$	0.245791	−	3.64383i	0.0133299	−	0.197615i
$341$		−	59.4766i		−	3.22084i
$342$		0			0
$343$	−5.79066	+	5.79066i	−0.312666	+	0.312666i
$344$	−5.67952			−0.306219
$345$		0			0
$346$	−29.2850			−1.57437
$347$	−17.3495	+	17.3495i	−0.931369	+	0.931369i	−0.997792	−	0.0664227i	$-0.978841\pi$
$347$	−17.3495	+	17.3495i	−0.931369	+	0.931369i	0.0664227	+	0.997792i	$0.478841\pi$
$348$		0			0
$349$		−	14.2017i		−	0.760202i	−0.924945	−	0.380101i	$-0.875889\pi$
$349$		−	14.2017i		−	0.760202i	0.924945	−	0.380101i	$-0.124111\pi$
$350$	−5.12681	+	37.8294i	−0.274040	+	2.02207i
$351$		0			0
$352$	−31.0481	−	31.0481i	−1.65487	−	1.65487i
$353$	2.76159	+	2.76159i	0.146984	+	0.146984i	0.776769	−	0.629785i	$-0.216857\pi$
$353$	2.76159	+	2.76159i	0.146984	+	0.146984i	−0.629785	+	0.776769i	$0.716857\pi$
$354$		0			0
$355$	−4.04620	+	3.53483i	−0.214750	+	0.187609i
$356$		−	7.31810i		−	0.387858i
$357$		0			0
$358$	−26.5299	+	26.5299i	−1.40215	+	1.40215i
$359$	27.8631			1.47056			0.735278	−	0.677766i	$-0.237052\pi$
$359$	27.8631			1.47056			0.735278	+	0.677766i	$0.237052\pi$
$360$		0			0
$361$	3.83312			0.201743
$362$	3.43114	−	3.43114i	0.180337	−	0.180337i
$363$		0			0
$364$		−	13.2373i		−	0.693821i
$365$	21.8010	+	1.47056i	1.14112	+	0.0769728i
$366$		0			0
$367$	18.8299	+	18.8299i	0.982915	+	0.982915i	0.999856	−	0.0169413i	$-0.00539285\pi$
$367$	18.8299	+	18.8299i	0.982915	+	0.982915i	−0.0169413	+	0.999856i	$0.505393\pi$
$368$	−5.52514	−	5.52514i	−0.288018	−	0.288018i
$369$		0			0
$370$	20.1091	+	23.0182i	1.04542	+	1.19666i
$371$			43.8456i			2.27635i
$372$		0			0
$373$	7.46992	−	7.46992i	0.386778	−	0.386778i	−0.486759	−	0.873536i	$-0.661821\pi$
$373$	7.46992	−	7.46992i	0.386778	−	0.386778i	0.873536	+	0.486759i	$0.161821\pi$
$374$	11.3591			0.587363
$375$		0			0
$376$	−2.61149			−0.134677
$377$	−2.91464	+	2.91464i	−0.150112	+	0.150112i
$378$		0			0
$379$		−	3.01511i		−	0.154876i	−0.996997	−	0.0774379i	$-0.975326\pi$
$379$		−	3.01511i		−	0.154876i	0.996997	−	0.0774379i	$-0.0246740\pi$
$380$	9.35754	+	10.7113i	0.480032	+	0.549476i
$381$		0			0
$382$	30.3948	+	30.3948i	1.55513	+	1.55513i
$383$	−0.519651	−	0.519651i	−0.0265529	−	0.0265529i	0.693706	−	0.720259i	$-0.255977\pi$
$383$	−0.519651	−	0.519651i	−0.0265529	−	0.0265529i	−0.720259	+	0.693706i	$0.755977\pi$
$384$		0			0
$385$	−53.2544	−	3.59221i	−2.71409	−	0.183076i
$386$			4.16272i			0.211877i
$387$		0			0
$388$	19.7704	−	19.7704i	1.00369	−	1.00369i
$389$	−13.6490			−0.692034			−0.346017	−	0.938228i	$-0.612466\pi$
$389$	−13.6490			−0.692034			−0.346017	+	0.938228i	$0.612466\pi$
$390$		0			0
$391$	1.69902			0.0859232
$392$	−4.47052	+	4.47052i	−0.225795	+	0.225795i
$393$		0			0
$394$		−	3.59296i		−	0.181011i
$395$	2.12059	−	1.85258i	0.106698	−	0.0932136i
$396$		0			0
$397$	−15.8057	−	15.8057i	−0.793263	−	0.793263i	0.188760	−	0.982023i	$-0.439553\pi$
$397$	−15.8057	−	15.8057i	−0.793263	−	0.793263i	−0.982023	+	0.188760i	$0.939553\pi$
$398$	−23.0026	−	23.0026i	−1.15302	−	1.15302i
$399$		0			0
$400$	−3.08813	+	22.7865i	−0.154406	+	1.13933i
$401$		−	18.7484i		−	0.936249i	−0.883663	−	0.468124i	$-0.844930\pi$
$401$		−	18.7484i		−	0.936249i	0.883663	−	0.468124i	$-0.155070\pi$
$402$		0			0
$403$	14.2795	−	14.2795i	0.711315	−	0.711315i
$404$	9.96864			0.495958
$405$		0			0
$406$	−15.5538			−0.771921
$407$	−30.2181	+	30.2181i	−1.49785	+	1.49785i
$408$		0			0
$409$		−	31.4769i		−	1.55643i	−0.627995	−	0.778217i	$-0.716124\pi$
$409$		−	31.4769i		−	1.55643i	0.627995	−	0.778217i	$-0.283876\pi$
$410$	0.293585	−	4.35238i	0.0144991	−	0.214949i
$411$		0			0
$412$	7.01969	+	7.01969i	0.345835	+	0.345835i
$413$	−10.8111	−	10.8111i	−0.531978	−	0.531978i
$414$		0			0
$415$	2.69135	−	39.8991i	0.132113	−	1.95857i
$416$		−	14.9085i		−	0.730947i
$417$		0			0
$418$	−31.2806	+	31.2806i	−1.52999	+	1.52999i
$419$	−11.4126			−0.557541			−0.278771	−	0.960358i	$-0.589927\pi$
$419$	−11.4126			−0.557541			−0.278771	+	0.960358i	$0.589927\pi$
$420$		0			0
$421$	−16.8519			−0.821313			−0.410656	−	0.911790i	$-0.634700\pi$
$421$	−16.8519			−0.821313			−0.410656	+	0.911790i	$0.634700\pi$
$422$	−10.2858	+	10.2858i	−0.500703	+	0.500703i
$423$		0			0
$424$			7.65162i			0.371596i
$425$	−3.02870	−	3.97832i	−0.146913	−	0.192977i
$426$		0			0
$427$	−2.27502	−	2.27502i	−0.110096	−	0.110096i
$428$	8.89879	+	8.89879i	0.430139	+	0.430139i
$429$		0			0
$430$	26.0798	−	22.7837i	1.25768	−	1.09873i
$431$		−	18.8723i		−	0.909048i	−0.890734	−	0.454524i	$-0.849809\pi$
$431$		−	18.8723i		−	0.909048i	0.890734	−	0.454524i	$-0.150191\pi$
$432$		0			0
$433$	−10.2835	+	10.2835i	−0.494194	+	0.494194i	−0.909625	−	0.415431i	$-0.863631\pi$
$433$	−10.2835	+	10.2835i	−0.494194	+	0.494194i	0.415431	+	0.909625i	$0.363631\pi$
$434$	76.2017			3.65780
$435$		0			0
$436$	−27.1596			−1.30071
$437$	−4.67877	+	4.67877i	−0.223816	+	0.223816i
$438$		0			0
$439$			34.7074i			1.65649i	0.560363	+	0.828247i	$0.310662\pi$
$439$			34.7074i			1.65649i	−0.560363	+	0.828247i	$0.689338\pi$
$440$	−9.29357	−	0.626888i	−0.443054	−	0.0298857i
$441$		0			0
$442$	2.72716	+	2.72716i	0.129718	+	0.129718i
$443$	−10.7742	−	10.7742i	−0.511898	−	0.511898i	0.403210	−	0.915108i	$-0.367895\pi$
$443$	−10.7742	−	10.7742i	−0.511898	−	0.511898i	−0.915108	+	0.403210i	$0.867895\pi$
$444$		0			0
$445$	−6.59164	−	7.54523i	−0.312474	−	0.357678i
$446$		−	12.4962i		−	0.591713i
$447$		0			0
$448$	13.7271	−	13.7271i	0.648546	−	0.648546i
$449$	0.0830944			0.00392147			0.00196073	−	0.999998i	$-0.499376\pi$
$449$	0.0830944			0.00392147			0.00196073	+	0.999998i	$0.499376\pi$
$450$		0			0
$451$	6.09918			0.287199
$452$	10.7574	−	10.7574i	0.505987	−	0.505987i
$453$		0			0
$454$			9.88268i			0.463817i
$455$	−11.9232	−	13.6481i	−0.558969	−	0.639833i
$456$		0			0
$457$	11.0377	+	11.0377i	0.516323	+	0.516323i	0.916457	−	0.400134i	$-0.131036\pi$
$457$	11.0377	+	11.0377i	0.516323	+	0.516323i	−0.400134	+	0.916457i	$0.631036\pi$
$458$	18.4198	+	18.4198i	0.860699	+	0.860699i
$459$		0			0
$460$	6.19095	+	0.417604i	0.288654	+	0.0194709i
$461$			9.79176i			0.456048i	0.973656	+	0.228024i	$0.0732264\pi$
$461$			9.79176i			0.456048i	−0.973656	+	0.228024i	$0.926774\pi$
$462$		0			0
$463$	−9.75463	+	9.75463i	−0.453336	+	0.453336i	−0.896460	−	0.443124i	$-0.853870\pi$
$463$	−9.75463	+	9.75463i	−0.453336	+	0.453336i	0.443124	+	0.896460i	$0.353870\pi$
$464$	−9.36880			−0.434936
$465$		0			0
$466$	−22.6136			−1.04756
$467$	−0.304088	+	0.304088i	−0.0140715	+	0.0140715i	−0.714108	−	0.700036i	$-0.753167\pi$
$467$	−0.304088	+	0.304088i	−0.0140715	+	0.0140715i	0.700036	+	0.714108i	$0.253167\pi$
$468$		0			0
$469$		−	29.3203i		−	1.35389i
$470$	11.9917	−	10.4762i	0.553136	−	0.483230i
$471$		0			0
$472$	−1.88667	−	1.88667i	−0.0868411	−	0.0868411i
$473$	34.2373	+	34.2373i	1.57423	+	1.57423i
$474$		0			0
$475$	19.2959	+	2.61507i	0.885359	+	0.119988i
$476$			6.54217i			0.299860i
$477$		0			0
$478$	−9.66689	+	9.66689i	−0.442153	+	0.442153i
$479$	36.0280			1.64616			0.823080	−	0.567925i	$-0.192254\pi$
$479$	36.0280			1.64616			0.823080	+	0.567925i	$0.192254\pi$
$480$		0			0
$481$	−14.5099			−0.661595
$482$	−0.730821	+	0.730821i	−0.0332880	+	0.0332880i
$483$		0			0
$484$			40.0364i			1.81983i
$485$	2.57618	−	38.1918i	0.116978	−	1.73420i
$486$		0			0
$487$	−0.392844	−	0.392844i	−0.0178015	−	0.0178015i	0.698150	−	0.715951i	$-0.254007\pi$
$487$	−0.392844	−	0.392844i	−0.0178015	−	0.0178015i	−0.715951	+	0.698150i	$0.754007\pi$
$488$	−0.397020	−	0.397020i	−0.0179723	−	0.0179723i
$489$		0			0
$490$	2.59441	−	38.4620i	0.117203	−	1.73753i
$491$		−	12.5111i		−	0.564617i	−0.959324	−	0.282308i	$-0.908900\pi$
$491$		−	12.5111i		−	0.564617i	0.959324	−	0.282308i	$-0.0911001\pi$
$492$		0			0
$493$	1.44049	−	1.44049i	0.0648762	−	0.0648762i
$494$	−15.0201			−0.675788
$495$		0			0
$496$	45.9000			2.06097
$497$	6.80552	−	6.80552i	0.305269	−	0.305269i
$498$		0			0
$499$			13.2427i			0.592824i	0.955060	+	0.296412i	$0.0957902\pi$
$499$			13.2427i			0.592824i	−0.955060	+	0.296412i	$0.904210\pi$
$500$	−10.0582	−	15.2407i	−0.449817	−	0.681587i
$501$		0			0
$502$	40.7409	+	40.7409i	1.81835	+	1.81835i
$503$	−20.3814	−	20.3814i	−0.908760	−	0.908760i	0.0874120	−	0.996172i	$-0.472140\pi$
$503$	−20.3814	−	20.3814i	−0.908760	−	0.908760i	−0.996172	+	0.0874120i	$0.972140\pi$
$504$		0			0
$505$	10.2780	−	8.97907i	0.457366	−	0.399563i
$506$			19.2993i			0.857958i
$507$		0			0
$508$	−4.18483	+	4.18483i	−0.185672	+	0.185672i
$509$	21.3134			0.944699			0.472350	−	0.881411i	$-0.343406\pi$
$509$	21.3134			0.944699			0.472350	+	0.881411i	$0.343406\pi$
$510$		0			0
$511$	−39.1417			−1.73153
$512$	19.4144	−	19.4144i	0.858004	−	0.858004i
$513$		0			0
$514$		−	38.3817i		−	1.69294i
$515$	13.5604	+	0.914702i	0.597543	+	0.0403066i
$516$		0			0
$517$	15.7426	+	15.7426i	0.692360	+	0.692360i
$518$	−38.7155	−	38.7155i	−1.70106	−	1.70106i
$519$		0			0
$520$	−2.08076	−	2.38177i	−0.0912472	−	0.104448i
$521$		−	8.77751i		−	0.384550i	−0.981341	−	0.192275i	$-0.938413\pi$
$521$		−	8.77751i		−	0.384550i	0.981341	−	0.192275i	$-0.0615865\pi$
$522$		0			0
$523$	3.61286	−	3.61286i	0.157979	−	0.157979i	−0.623691	−	0.781671i	$-0.714368\pi$
$523$	3.61286	−	3.61286i	0.157979	−	0.157979i	0.781671	+	0.623691i	$0.214368\pi$
$524$	−21.4766			−0.938210
$525$		0			0
$526$	7.46895			0.325662
$527$	−7.05729	+	7.05729i	−0.307420	+	0.307420i
$528$		0			0
$529$		−	20.1133i		−	0.874493i
$530$	−30.6950	−	35.1355i	−1.33330	−	1.52619i
$531$		0			0
$532$	−18.0159	−	18.0159i	−0.781087	−	0.781087i
$533$	1.46433	+	1.46433i	0.0634273	+	0.0634273i
$534$		0			0
$535$	17.1904	+	1.15956i	0.743206	+	0.0501321i
$536$		−	5.11677i		−	0.221011i
$537$		0			0
$538$	−21.9345	+	21.9345i	−0.945664	+	0.945664i
$539$	53.8985			2.32157
$540$		0			0
$541$	−12.8459			−0.552289			−0.276145	−	0.961116i	$-0.589057\pi$
$541$	−12.8459			−0.552289			−0.276145	+	0.961116i	$0.589057\pi$
$542$	−2.76988	+	2.76988i	−0.118977	+	0.118977i
$543$		0			0
$544$			7.36811i			0.315905i
$545$	−28.0026	+	24.4635i	−1.19950	+	1.04790i
$546$		0			0
$547$	24.8784	+	24.8784i	1.06372	+	1.06372i	0.997826	+	0.0658965i	$0.0209907\pi$
$547$	24.8784	+	24.8784i	1.06372	+	1.06372i	0.0658965	+	0.997826i	$0.479009\pi$
$548$	−0.126630	−	0.126630i	−0.00540935	−	0.00540935i
$549$		0			0
$550$	45.1899	−	34.4031i	1.92691	−	1.46695i
$551$			7.93363i			0.337984i
$552$		0			0
$553$	−3.56674	+	3.56674i	−0.151673	+	0.151673i
$554$	−53.5193			−2.27382
$555$		0			0
$556$	30.8864			1.30988
$557$	−9.94894	+	9.94894i	−0.421550	+	0.421550i	−0.885737	−	0.464187i	$-0.846347\pi$
$557$	−9.94894	+	9.94894i	−0.421550	+	0.421550i	0.464187	+	0.885737i	$0.346347\pi$
$558$		0			0
$559$			16.4399i			0.695332i
$560$	2.77223	−	41.0981i	0.117148	−	1.73671i
$561$		0			0
$562$	−17.2916	−	17.2916i	−0.729401	−	0.729401i
$563$	7.89353	+	7.89353i	0.332673	+	0.332673i	0.853601	−	0.520928i	$-0.174414\pi$
$563$	7.89353	+	7.89353i	0.332673	+	0.332673i	−0.520928	+	0.853601i	$0.674414\pi$
$564$		0			0
$565$	1.40175	−	20.7808i	0.0589720	−	0.874257i
$566$		−	30.6873i		−	1.28988i
$567$		0			0
$568$	1.18765	−	1.18765i	0.0498327	−	0.0498327i
$569$	16.9717			0.711490			0.355745	−	0.934583i	$-0.384227\pi$
$569$	16.9717			0.711490			0.355745	+	0.934583i	$0.384227\pi$
$570$		0			0
$571$	29.6545			1.24100			0.620500	−	0.784206i	$-0.286930\pi$
$571$	29.6545			1.24100			0.620500	+	0.784206i	$0.286930\pi$
$572$	−13.9256	+	13.9256i	−0.582259	+	0.582259i
$573$		0			0
$574$			7.81430i			0.326162i
$575$	6.75924	−	5.14582i	0.281880	−	0.214595i
$576$		0			0
$577$	−0.842451	−	0.842451i	−0.0350717	−	0.0350717i	0.689353	−	0.724425i	$-0.257895\pi$
$577$	−0.842451	−	0.842451i	−0.0350717	−	0.0350717i	−0.724425	+	0.689353i	$0.757895\pi$
$578$	−1.34783	−	1.34783i	−0.0560622	−	0.0560622i
$579$		0			0
$580$	5.60295	−	4.89483i	0.232650	−	0.203247i
$581$			71.6353i			2.97193i
$582$		0			0
$583$	46.1256	−	46.1256i	1.91033	−	1.91033i
$584$	−6.83073			−0.282658
$585$		0			0
$586$	14.7062			0.607509
$587$	10.8865	−	10.8865i	0.449336	−	0.449336i	−0.445798	−	0.895134i	$-0.647080\pi$
$587$	10.8865	−	10.8865i	0.449336	−	0.449336i	0.895134	+	0.445798i	$0.147080\pi$
$588$		0			0
$589$		−	38.8688i		−	1.60156i
$590$	16.2319	+	1.09491i	0.668257	+	0.0450766i
$591$		0			0
$592$	−23.3203	−	23.3203i	−0.958457	−	0.958457i
$593$	−10.2611	−	10.2611i	−0.421373	−	0.421373i	0.464304	−	0.885676i	$-0.346305\pi$
$593$	−10.2611	−	10.2611i	−0.421373	−	0.421373i	−0.885676	+	0.464304i	$0.846305\pi$
$594$		0			0
$595$	5.89274	+	6.74522i	0.241579	+	0.276527i
$596$			28.8700i			1.18256i
$597$		0			0
$598$	−4.63350	+	4.63350i	−0.189478	+	0.189478i
$599$	−39.6270			−1.61911			−0.809557	−	0.587042i	$-0.800292\pi$
$599$	−39.6270			−1.61911			−0.809557	+	0.587042i	$0.800292\pi$
$600$		0			0
$601$	−26.4277			−1.07801			−0.539004	−	0.842303i	$-0.681199\pi$
$601$	−26.4277			−1.07801			−0.539004	+	0.842303i	$0.681199\pi$
$602$	−43.8650	+	43.8650i	−1.78780	+	1.78780i
$603$		0			0
$604$			6.11030i			0.248625i
$605$	36.0620	+	41.2790i	1.46613	+	1.67823i
$606$		0			0
$607$	11.4082	+	11.4082i	0.463044	+	0.463044i	0.899652	−	0.436608i	$-0.143820\pi$
$607$	11.4082	+	11.4082i	0.463044	+	0.463044i	−0.436608	+	0.899652i	$0.643820\pi$
$608$	−20.2903	−	20.2903i	−0.822882	−	0.822882i
$609$		0			0
$610$	3.41575	+	0.230405i	0.138300	+	0.00932884i
$611$			7.55919i			0.305812i
$612$		0			0
$613$	−10.5234	+	10.5234i	−0.425037	+	0.425037i	−0.886934	−	0.461896i	$-0.847169\pi$
$613$	−10.5234	+	10.5234i	−0.425037	+	0.425037i	0.461896	+	0.886934i	$0.347169\pi$
$614$	7.03469			0.283897
$615$		0			0
$616$	16.6858			0.672289
$617$	29.6718	−	29.6718i	1.19454	−	1.19454i	0.218765	−	0.975777i	$-0.429797\pi$
$617$	29.6718	−	29.6718i	1.19454	−	1.19454i	0.975777	−	0.218765i	$-0.0702029\pi$
$618$		0			0
$619$			22.8080i			0.916731i	0.888764	+	0.458365i	$0.151565\pi$
$619$			22.8080i			0.916731i	−0.888764	+	0.458365i	$0.848435\pi$
$620$	−27.4502	+	23.9810i	−1.10243	+	0.963099i
$621$		0			0
$622$	−3.95911	−	3.95911i	−0.158746	−	0.158746i
$623$	12.6907	+	12.6907i	0.508443	+	0.508443i
$624$		0			0
$625$	−24.0982	−	6.65401i	−0.963929	−	0.266160i
$626$		−	9.42393i		−	0.376656i
$627$		0			0
$628$	9.47780	−	9.47780i	0.378205	−	0.378205i
$629$	7.17115			0.285932
$630$		0			0
$631$	41.2154			1.64076			0.820379	−	0.571820i	$-0.193762\pi$
$631$	41.2154			1.64076			0.820379	+	0.571820i	$0.193762\pi$
$632$	−0.622441	+	0.622441i	−0.0247594	+	0.0247594i
$633$		0			0
$634$		−	36.6323i		−	1.45486i
$635$	−0.545306	+	8.08413i	−0.0216398	+	0.320809i
$636$		0			0
$637$	12.9403	+	12.9403i	0.512713	+	0.512713i
$638$	16.3626	+	16.3626i	0.647800	+	0.647800i
$639$		0			0
$640$	0.827415	−	12.2664i	0.0327065	−	0.484871i
$641$		−	12.2797i		−	0.485018i	−0.970149	−	0.242509i	$-0.922030\pi$
$641$		−	12.2797i		−	0.485018i	0.970149	−	0.242509i	$-0.0779704\pi$
$642$		0			0
$643$	16.0366	−	16.0366i	0.632420	−	0.632420i	−0.316254	−	0.948674i	$-0.602425\pi$
$643$	16.0366	−	16.0366i	0.632420	−	0.632420i	0.948674	+	0.316254i	$0.102425\pi$
$644$	−11.1153			−0.438004
$645$		0			0
$646$	7.42330			0.292066
$647$	−20.3237	+	20.3237i	−0.799008	+	0.799008i	−0.982939	−	0.183931i	$-0.941118\pi$
$647$	−20.3237	+	20.3237i	−0.799008	+	0.799008i	0.183931	+	0.982939i	$0.441118\pi$
$648$		0			0
$649$			22.7465i			0.892878i
$650$	19.1092	+	2.58977i	0.749526	+	0.101579i
$651$		0			0
$652$	−25.2787	−	25.2787i	−0.989992	−	0.989992i
$653$	−7.23170	−	7.23170i	−0.282998	−	0.282998i	0.551305	−	0.834304i	$-0.314130\pi$
$653$	−7.23170	−	7.23170i	−0.282998	−	0.282998i	−0.834304	+	0.551305i	$0.814130\pi$
$654$		0			0
$655$	−22.1432	+	19.3447i	−0.865206	+	0.755859i
$656$			4.70693i			0.183775i
$657$		0			0
$658$	−20.1695	+	20.1695i	−0.786290	+	0.786290i
$659$	46.4581			1.80975			0.904875	−	0.425677i	$-0.139964\pi$
$659$	46.4581			1.80975			0.904875	+	0.425677i	$0.139964\pi$
$660$		0			0
$661$	37.2982			1.45073			0.725366	−	0.688364i	$-0.241671\pi$
$661$	37.2982			1.45073			0.725366	+	0.688364i	$0.241671\pi$
$662$	13.8742	−	13.8742i	0.539237	−	0.539237i
$663$		0			0
$664$			12.5013i			0.485144i
$665$	−34.8025	−	2.34756i	−1.34958	−	0.0910346i
$666$		0			0
$667$	2.44742	+	2.44742i	0.0947643	+	0.0947643i
$668$	19.7064	+	19.7064i	0.762463	+	0.762463i
$669$		0			0
$670$	20.5262	+	23.4957i	0.792998	+	0.907718i
$671$			4.78664i			0.184786i
$672$		0			0
$673$	21.8962	−	21.8962i	0.844035	−	0.844035i	−0.145346	−	0.989381i	$-0.546430\pi$
$673$	21.8962	−	21.8962i	0.844035	−	0.844035i	0.989381	+	0.145346i	$0.0464296\pi$
$674$	−28.4719			−1.09670
$675$		0			0
$676$	14.5459			0.559456
$677$	10.5006	−	10.5006i	0.403571	−	0.403571i	−0.475918	−	0.879490i	$-0.657884\pi$
$677$	10.5006	−	10.5006i	0.403571	−	0.403571i	0.879490	+	0.475918i	$0.157884\pi$
$678$		0			0
$679$			68.5698i			2.63147i
$680$	1.02836	+	1.17713i	0.0394358	+	0.0451408i
$681$		0			0
$682$	−80.1642	−	80.1642i	−3.06964	−	3.06964i
$683$	−13.0770	−	13.0770i	−0.500376	−	0.500376i	0.411179	−	0.911555i	$-0.365117\pi$
$683$	−13.0770	−	13.0770i	−0.500376	−	0.500376i	−0.911555	+	0.411179i	$0.865117\pi$
$684$		0			0
$685$	−0.244619	−	0.0165005i	−0.00934641	−	0.000630452i
$686$			15.6096i			0.595978i
$687$		0			0
$688$	−26.4220	+	26.4220i	−1.00733	+	1.00733i
$689$	22.1483			0.843782
$690$		0			0
$691$	−3.36760			−0.128110			−0.0640548	−	0.997946i	$-0.520403\pi$
$691$	−3.36760			−0.128110			−0.0640548	+	0.997946i	$0.520403\pi$
$692$	−17.7436	+	17.7436i	−0.674509	+	0.674509i
$693$		0			0
$694$			46.7682i			1.77530i
$695$	31.8450	−	27.8204i	1.20795	−	1.05529i
$696$		0			0
$697$	−0.723708	−	0.723708i	−0.0274124	−	0.0274124i
$698$	−19.1415	−	19.1415i	−0.724516	−	0.724516i
$699$		0			0
$700$	19.8142	+	26.0268i	0.748908	+	0.983722i
$701$		−	4.90728i		−	0.185345i	−0.995697	−	0.0926726i	$-0.970459\pi$
$701$		−	4.90728i		−	0.185345i	0.995697	−	0.0926726i	$-0.0295410\pi$
$702$		0			0
$703$	−19.7479	+	19.7479i	−0.744807	+	0.744807i
$704$	−28.8819			−1.08853
$705$		0			0
$706$	7.44428			0.280169
$707$	−17.2872	+	17.2872i	−0.650152	+	0.650152i
$708$		0			0
$709$			47.8742i			1.79795i	0.437995	+	0.898977i	$0.355689\pi$
$709$			47.8742i			1.79795i	−0.437995	+	0.898977i	$0.644311\pi$
$710$	−0.689238	+	10.2179i	−0.0258666	+	0.383471i
$711$		0			0
$712$	2.21470	+	2.21470i	0.0829993	+	0.0829993i
$713$	−11.9905	−	11.9905i	−0.449047	−	0.449047i
$714$		0			0
$715$	−1.81458	+	26.9010i	−0.0678614	+	1.00604i
$716$			32.1485i			1.20144i
$717$		0			0
$718$	37.5546	−	37.5546i	1.40152	−	1.40152i
$719$	−39.7225			−1.48140			−0.740699	−	0.671837i	$-0.765505\pi$
$719$	−39.7225			−1.48140			−0.740699	+	0.671837i	$0.765505\pi$
$720$		0			0
$721$	−24.3465			−0.906710
$722$	5.16638	−	5.16638i	0.192273	−	0.192273i
$723$		0			0
$724$		−	4.15780i		−	0.154523i
$725$	1.36792	−	10.0935i	0.0508031	−	0.374863i
$726$		0			0
$727$	5.66609	+	5.66609i	0.210144	+	0.210144i	0.804328	−	0.594185i	$-0.202525\pi$
$727$	5.66609	+	5.66609i	0.210144	+	0.210144i	−0.594185	+	0.804328i	$0.702525\pi$
$728$	4.00603	+	4.00603i	0.148473	+	0.148473i
$729$		0			0
$730$	31.3660	−	27.4019i	1.16091	−	1.01419i
$731$		−	8.12497i		−	0.300513i
$732$		0			0
$733$	28.0671	−	28.0671i	1.03668	−	1.03668i	0.0373826	−	0.999301i	$-0.488098\pi$
$733$	28.0671	−	28.0671i	1.03668	−	1.03668i	0.999301	−	0.0373826i	$-0.0119020\pi$
$734$	50.7590			1.87355
$735$		0			0
$736$	−12.5186			−0.461441
$737$	−30.8450	+	30.8450i	−1.13619	+	1.13619i
$738$		0			0
$739$		−	50.7412i		−	1.86654i	−0.359171	−	0.933272i	$-0.616940\pi$
$739$		−	50.7412i		−	1.86654i	0.359171	−	0.933272i	$-0.383060\pi$
$740$	26.1305	+	1.76260i	0.960575	+	0.0647945i
$741$		0			0
$742$	59.0963	+	59.0963i	2.16949	+	2.16949i
$743$	20.7995	+	20.7995i	0.763059	+	0.763059i	0.976874	−	0.213815i	$-0.0685890\pi$
$743$	20.7995	+	20.7995i	0.763059	+	0.763059i	−0.213815	+	0.976874i	$0.568589\pi$
$744$		0			0
$745$	26.0041	+	29.7660i	0.952716	+	1.09054i
$746$		−	20.1363i		−	0.737243i
$747$		0			0
$748$	6.88236	−	6.88236i	0.251644	−	0.251644i
$749$	−30.8638			−1.12774
$750$		0			0
$751$	−45.9138			−1.67542			−0.837708	−	0.546118i	$-0.816105\pi$
$751$	−45.9138			−1.67542			−0.837708	+	0.546118i	$0.816105\pi$
$752$	−12.1491	+	12.1491i	−0.443032	+	0.443032i
$753$		0			0
$754$			7.85687i			0.286130i
$755$	5.50374	+	6.29994i	0.200302	+	0.229278i
$756$		0			0
$757$	11.5524	+	11.5524i	0.419880	+	0.419880i	0.885162	−	0.465282i	$-0.154047\pi$
$757$	11.5524	+	11.5524i	0.419880	+	0.419880i	−0.465282	+	0.885162i	$0.654047\pi$
$758$	−4.06385	−	4.06385i	−0.147606	−	0.147606i
$759$		0			0
$760$	−6.07348	−	0.409680i	−0.220308	−	0.0148607i
$761$		−	21.4014i		−	0.775799i	−0.921702	−	0.387900i	$-0.873201\pi$
$761$		−	21.4014i		−	0.775799i	0.921702	−	0.387900i	$-0.126799\pi$
$762$		0			0
$763$	47.0991	−	47.0991i	1.70510	−	1.70510i
$764$	36.8320			1.33253
$765$		0			0
$766$	−1.40080			−0.0506129
$767$	−5.46113	+	5.46113i	−0.197190	+	0.197190i
$768$		0			0
$769$		−	21.8053i		−	0.786320i	−0.919470	−	0.393160i	$-0.871382\pi$
$769$		−	21.8053i		−	0.786320i	0.919470	−	0.393160i	$-0.128618\pi$
$770$	−76.6193	+	66.9360i	−2.76117	+	2.41221i
$771$		0			0
$772$	2.52216	+	2.52216i	0.0907745	+	0.0907745i
$773$	13.6880	+	13.6880i	0.492323	+	0.492323i	0.909037	−	0.416715i	$-0.136819\pi$
$773$	13.6880	+	13.6880i	0.492323	+	0.492323i	−0.416715	+	0.909037i	$0.636819\pi$
$774$		0			0
$775$	−6.70175	+	49.4505i	−0.240734	+	1.77631i
$776$			11.9663i			0.429566i
$777$		0			0
$778$	−18.3965	+	18.3965i	−0.659548	+	0.659548i
$779$	3.98590			0.142810
$780$		0			0
$781$	−14.3188			−0.512367
$782$	2.28999	−	2.28999i	0.0818897	−	0.0818897i
$783$		0			0
$784$			41.5952i			1.48554i
$785$	1.23501	−	18.3089i	0.0440793	−	0.653473i
$786$		0			0
$787$	−4.49629	−	4.49629i	−0.160275	−	0.160275i	0.622413	−	0.782689i	$-0.286152\pi$
$787$	−4.49629	−	4.49629i	−0.160275	−	0.160275i	−0.782689	+	0.622413i	$0.786152\pi$
$788$	−2.17695	−	2.17695i	−0.0775505	−	0.0775505i
$789$		0			0
$790$	0.361226	−	5.35515i	0.0128518	−	0.190528i
$791$			37.3101i			1.32660i
$792$		0			0
$793$	−1.14921	+	1.14921i	−0.0408096	+	0.0408096i
$794$	−42.6066			−1.51205
$795$		0			0
$796$	−27.8742			−0.987974
$797$	9.29986	−	9.29986i	0.329418	−	0.329418i	−0.522947	−	0.852365i	$-0.675168\pi$
$797$	9.29986	−	9.29986i	0.329418	−	0.329418i	0.852365	+	0.522947i	$0.175168\pi$
$798$		0			0
$799$		−	3.73593i		−	0.132168i
$800$	22.3158	+	29.3127i	0.788981	+	1.03636i
$801$		0			0
$802$	−25.2696	−	25.2696i	−0.892299	−	0.892299i
$803$	41.1771	+	41.1771i	1.45311	+	1.45311i
$804$		0			0
$805$	−11.4603	+	10.0119i	−0.403921	+	0.352873i
$806$		−	38.4927i		−	1.35585i
$807$		0			0
$808$	−3.01684	+	3.01684i	−0.106132	+	0.106132i
$809$	35.0967			1.23393			0.616967	−	0.786989i	$-0.288361\pi$
$809$	35.0967			1.23393			0.616967	+	0.786989i	$0.288361\pi$
$810$		0			0
$811$	−45.8292			−1.60928			−0.804641	−	0.593762i	$-0.797642\pi$
$811$	−45.8292			−1.60928			−0.804641	+	0.593762i	$0.797642\pi$
$812$	−9.42390	+	9.42390i	−0.330714	+	0.330714i
$813$		0			0
$814$			81.4575i			2.85508i
$815$	−48.8327	−	3.29395i	−1.71053	−	0.115382i
$816$		0			0
$817$	22.3746	+	22.3746i	0.782787	+	0.782787i
$818$	−42.4255	−	42.4255i	−1.48337	−	1.48337i
$819$		0			0
$820$	−2.45919	−	2.81495i	−0.0858786	−	0.0983023i
$821$			32.4166i			1.13135i	0.824629	+	0.565674i	$0.191384\pi$
$821$			32.4166i			1.13135i	−0.824629	+	0.565674i	$0.808616\pi$
$822$		0			0
$823$	0.636529	−	0.636529i	0.0221880	−	0.0221880i	−0.695926	−	0.718114i	$-0.745006\pi$
$823$	0.636529	−	0.636529i	0.0221880	−	0.0221880i	0.718114	+	0.695926i	$0.245006\pi$
$824$	−4.24877			−0.148013
$825$		0			0
$826$	−29.1429			−1.01401
$827$	31.3800	−	31.3800i	1.09119	−	1.09119i	0.0957859	−	0.995402i	$-0.469464\pi$
$827$	31.3800	−	31.3800i	1.09119	−	1.09119i	0.995402	−	0.0957859i	$-0.0305364\pi$
$828$		0			0
$829$		−	24.1035i		−	0.837150i	−0.908182	−	0.418575i	$-0.862530\pi$
$829$		−	24.1035i		−	0.837150i	0.908182	−	0.418575i	$-0.137470\pi$
$830$	−50.1497	−	57.4046i	−1.74072	−	1.99254i
$831$		0			0
$832$	−6.93415	−	6.93415i	−0.240398	−	0.240398i
$833$	−6.39540	−	6.39540i	−0.221588	−	0.221588i
$834$		0			0
$835$	38.0682	+	2.56785i	1.31740	+	0.0888640i
$836$			37.9054i			1.31098i
$837$		0			0
$838$	−15.3822	+	15.3822i	−0.531369	+	0.531369i
$839$	−16.2856			−0.562240			−0.281120	−	0.959673i	$-0.590706\pi$
$839$	−16.2856			−0.562240			−0.281120	+	0.959673i	$0.590706\pi$
$840$		0			0
$841$	−24.8500			−0.856897
$842$	−22.7135	+	22.7135i	−0.782758	+	0.782758i
$843$		0			0
$844$			12.4641i			0.429032i
$845$	14.9973	−	13.1019i	0.515924	−	0.450720i
$846$		0			0
$847$	−69.4293	−	69.4293i	−2.38562	−	2.38562i
$848$	35.5966	+	35.5966i	1.22239	+	1.22239i
$849$		0			0
$850$	−9.44424	−	1.27993i	−0.323935	−	0.0439011i
$851$			12.1839i			0.417660i
$852$		0			0
$853$	−30.9846	+	30.9846i	−1.06089	+	1.06089i	−0.0628692	+	0.998022i	$0.520025\pi$
$853$	−30.9846	+	30.9846i	−1.06089	+	1.06089i	−0.998022	+	0.0628692i	$0.979975\pi$
$854$	−6.13266			−0.209855
$855$		0			0
$856$	−5.38613			−0.184094
$857$	17.6625	−	17.6625i	0.603340	−	0.603340i	−0.337857	−	0.941197i	$-0.609702\pi$
$857$	17.6625	−	17.6625i	0.603340	−	0.603340i	0.941197	+	0.337857i	$0.109702\pi$
$858$		0			0
$859$			18.8491i			0.643122i	0.946889	+	0.321561i	$0.104208\pi$
$859$			18.8491i			0.643122i	−0.946889	+	0.321561i	$0.895792\pi$
$860$	1.99704	−	29.6060i	0.0680985	−	1.00956i
$861$		0			0
$862$	−25.4366	−	25.4366i	−0.866375	−	0.866375i
$863$	−3.20650	−	3.20650i	−0.109150	−	0.109150i	0.650422	−	0.759573i	$-0.274592\pi$
$863$	−3.20650	−	3.20650i	−0.109150	−	0.109150i	−0.759573	+	0.650422i	$0.774592\pi$
$864$		0			0
$865$	−2.31208	+	34.2765i	−0.0786131	+	1.16543i
$866$			27.7208i			0.941991i
$867$		0			0
$868$	46.1700	−	46.1700i	1.56711	−	1.56711i
$869$	7.50441			0.254570
$870$		0			0
$871$	−14.8109			−0.501849
$872$	8.21940	−	8.21940i	0.278344	−	0.278344i
$873$		0			0
$874$			12.6123i			0.426619i
$875$	43.8724	+	8.98731i	1.48316	+	0.303826i
$876$		0			0
$877$	−39.6600	−	39.6600i	−1.33922	−	1.33922i	−0.896813	−	0.442410i	$-0.854124\pi$
$877$	−39.6600	−	39.6600i	−1.33922	−	1.33922i	−0.442410	−	0.896813i	$-0.645876\pi$
$878$	46.7796	+	46.7796i	1.57873	+	1.57873i
$879$		0			0
$880$	−46.1516	+	40.3188i	−1.55577	+	1.35915i
$881$			22.1777i			0.747187i	0.927593	+	0.373593i	$0.121874\pi$
$881$			22.1777i			0.747187i	−0.927593	+	0.373593i	$0.878126\pi$
$882$		0			0
$883$	−14.5160	+	14.5160i	−0.488502	+	0.488502i	−0.907833	−	0.419331i	$-0.862265\pi$
$883$	−14.5160	+	14.5160i	−0.488502	+	0.488502i	0.419331	+	0.907833i	$0.362265\pi$
$884$	3.30473			0.111150
$885$		0			0
$886$	−29.0435			−0.975736
$887$	11.7038	−	11.7038i	0.392974	−	0.392974i	−0.482772	−	0.875746i	$-0.660370\pi$
$887$	11.7038	−	11.7038i	0.392974	−	0.392974i	0.875746	+	0.482772i	$0.160370\pi$
$888$		0			0
$889$		−	14.5143i		−	0.486795i
$890$	−19.0541	−	1.28527i	−0.638693	−	0.0430824i
$891$		0			0
$892$	−7.57136	−	7.57136i	−0.253508	−	0.253508i
$893$	10.2880	+	10.2880i	0.344276	+	0.344276i
$894$		0			0
$895$	28.9571	+	33.1463i	0.967930	+	1.10796i
$896$			22.0232i			0.735742i
$897$		0			0
$898$	0.111997	−	0.111997i	0.00373739	−	0.00373739i
$899$	−20.3318			−0.678105
$900$		0			0
$901$	−10.9462			−0.364671
$902$	8.22064	−	8.22064i	0.273717	−	0.273717i
$903$		0			0
$904$			6.51110i			0.216556i
$905$	−3.74506	−	4.28684i	−0.124490	−	0.142499i
$906$		0			0
$907$	1.74394	+	1.74394i	0.0579066	+	0.0579066i	0.735467	−	0.677560i	$-0.236963\pi$
$907$	1.74394	+	1.74394i	0.0579066	+	0.0579066i	−0.677560	+	0.735467i	$0.736963\pi$
$908$	5.98783	+	5.98783i	0.198713	+	0.198713i
$909$		0			0
$910$	−34.4657	−	2.32485i	−1.14253	−	0.0770680i
$911$		−	6.81654i		−	0.225842i	−0.993604	−	0.112921i	$-0.963979\pi$
$911$		−	6.81654i		−	0.225842i	0.993604	−	0.112921i	$-0.0360207\pi$
$912$		0			0
$913$	75.3603	−	75.3603i	2.49406	−	2.49406i
$914$	29.7539			0.984171
$915$		0			0
$916$	22.3208			0.737499
$917$	37.2438	−	37.2438i	1.22990	−	1.22990i
$918$		0			0
$919$		−	22.8968i		−	0.755296i	−0.925949	−	0.377648i	$-0.876733\pi$
$919$		−	22.8968i		−	0.755296i	0.925949	−	0.377648i	$-0.123267\pi$
$920$	−1.99996	+	1.74720i	−0.0659369	+	0.0576036i
$921$		0			0
$922$	13.1976	+	13.1976i	0.434640	+	0.434640i
$923$	−3.43776	−	3.43776i	−0.113155	−	0.113155i
$924$		0			0
$925$	28.5291	−	21.7192i	0.938031	−	0.714123i
$926$			26.2951i			0.864110i
$927$		0			0
$928$	−10.6137	+	10.6137i	−0.348410	+	0.348410i
$929$	25.7176			0.843767			0.421883	−	0.906650i	$-0.361369\pi$
$929$	25.7176			0.843767			0.421883	+	0.906650i	$0.361369\pi$
$930$		0			0
$931$	35.2234			1.15440
$932$	−13.7014	+	13.7014i	−0.448804	+	0.448804i
$933$		0			0
$934$			0.819717i			0.0268220i
$935$	0.896808	−	13.2951i	0.0293288	−	0.434797i
$936$		0			0
$937$	−22.2367	−	22.2367i	−0.726443	−	0.726443i	0.243466	−	0.969909i	$-0.421715\pi$
$937$	−22.2367	−	22.2367i	−0.726443	−	0.726443i	−0.969909	+	0.243466i	$0.921715\pi$
$938$	−39.5187	−	39.5187i	−1.29033	−	1.29033i
$939$		0			0
$940$	0.918257	−	13.6131i	0.0299502	−	0.444011i
$941$			40.0183i			1.30456i	0.757978	+	0.652280i	$0.226187\pi$
$941$			40.0183i			1.30456i	−0.757978	+	0.652280i	$0.773813\pi$
$942$		0			0
$943$	1.22959	−	1.22959i	0.0400411	−	0.0400411i
$944$	−17.5542			−0.571341
$945$		0			0
$946$	92.2920			3.00067
$947$	−24.3013	+	24.3013i	−0.789686	+	0.789686i	−0.981443	−	0.191756i	$-0.938582\pi$
$947$	−24.3013	+	24.3013i	−0.789686	+	0.789686i	0.191756	+	0.981443i	$0.438582\pi$
$948$		0			0
$949$			19.7721i			0.641831i
$950$	29.5323	−	22.4829i	0.958153	−	0.729442i
$951$		0			0
$952$	−1.97988	−	1.97988i	−0.0641681	−	0.0641681i
$953$	−4.96771	−	4.96771i	−0.160920	−	0.160920i	0.622054	−	0.782974i	$-0.286298\pi$
$953$	−4.96771	−	4.96771i	−0.160920	−	0.160920i	−0.782974	+	0.622054i	$0.786298\pi$
$954$		0			0
$955$	37.9751	−	33.1757i	1.22885	−	1.07354i
$956$			11.7142i			0.378864i
$957$		0			0
$958$	48.5595	−	48.5595i	1.56889	−	1.56889i
$959$	0.439191			0.0141822
$960$		0			0
$961$	68.6106			2.21325
$962$	−19.5569	+	19.5569i	−0.630538	+	0.630538i
$963$		0			0
$964$			0.885598i			0.0285232i
$965$	4.87223	+	0.328651i	0.156843	+	0.0105796i
$966$		0			0
$967$	−4.88064	−	4.88064i	−0.156951	−	0.156951i	0.624263	−	0.781214i	$-0.285399\pi$
$967$	−4.88064	−	4.88064i	−0.156951	−	0.156951i	−0.781214	+	0.624263i	$0.785399\pi$
$968$	−12.1163	−	12.1163i	−0.389433	−	0.389433i
$969$		0			0
$970$	−48.0036	−	54.9481i	−1.54130	−	1.76428i
$971$			1.08498i			0.0348186i	0.999848	+	0.0174093i	$0.00554184\pi$
$971$			1.08498i			0.0348186i	−0.999848	+	0.0174093i	$0.994458\pi$
$972$		0			0
$973$	−53.5619	+	53.5619i	−1.71712	+	1.71712i
$974$	−1.05897			−0.0339316
$975$		0			0
$976$	−3.69400			−0.118242
$977$	−19.2257	+	19.2257i	−0.615085	+	0.615085i	−0.944267	−	0.329181i	$-0.893227\pi$
$977$	−19.2257	+	19.2257i	−0.615085	+	0.615085i	0.329181	+	0.944267i	$0.393227\pi$
$978$		0			0
$979$		−	26.7013i		−	0.853377i
$980$	−21.7319	−	24.8757i	−0.694199	−	0.794626i
$981$		0			0
$982$	−16.8628	−	16.8628i	−0.538112	−	0.538112i
$983$	−10.2136	−	10.2136i	−0.325764	−	0.325764i	0.525209	−	0.850973i	$-0.323987\pi$
$983$	−10.2136	−	10.2136i	−0.325764	−	0.325764i	−0.850973	+	0.525209i	$0.823987\pi$
$984$		0			0
$985$	−4.20536	−	0.283668i	−0.133994	−	0.00903840i
$986$		−	3.88305i		−	0.123662i
$987$		0			0
$988$	−9.10057	+	9.10057i	−0.289528	+	0.289528i
$989$	13.8045			0.438957
$990$		0			0
$991$	−5.55365			−0.176418			−0.0882088	−	0.996102i	$-0.528114\pi$
$991$	−5.55365			−0.176418			−0.0882088	+	0.996102i	$0.528114\pi$
$992$	51.9989	−	51.9989i	1.65097	−	1.65097i
$993$		0			0
$994$		−	18.3453i		−	0.581878i
$995$	−28.7393	+	25.1071i	−0.911097	+	0.795950i
$996$		0			0
$997$	34.3812	+	34.3812i	1.08886	+	1.08886i	0.995646	+	0.0932188i	$0.0297156\pi$
$997$	34.3812	+	34.3812i	1.08886	+	1.08886i	0.0932188	+	0.995646i	$0.470284\pi$
$998$	17.8489	+	17.8489i	0.564996	+	0.564996i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.n.e.647.10	yes	24
3.2	odd	2	inner	765.2.n.e.647.3	yes	24
5.3	odd	4	inner	765.2.n.e.188.3	✓	24
15.8	even	4	inner	765.2.n.e.188.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
765.2.n.e.188.3	✓	24	5.3	odd	4	inner
765.2.n.e.188.10	yes	24	15.8	even	4	inner
765.2.n.e.647.3	yes	24	3.2	odd	2	inner
765.2.n.e.647.10	yes	24	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34783 - 1.34783i) q^{2} -1.63327i q^{4} +(-1.47114 - 1.68397i) q^{5} +(2.83235 + 2.83235i) q^{7} +(0.494282 + 0.494282i) q^{8} +(-4.25254 - 0.286850i) q^{10} -5.95927i q^{11} +(1.43074 - 1.43074i) q^{13} +7.63505 q^{14} +4.59896 q^{16} +(-0.707107 + 0.707107i) q^{17} -3.89447i q^{19} +(-2.75038 + 2.40278i) q^{20} +(-8.03207 - 8.03207i) q^{22} +(-1.20139 - 1.20139i) q^{23} +(-0.671484 + 4.95471i) q^{25} -3.85679i q^{26} +(4.62601 - 4.62601i) q^{28} -2.03715 q^{29} +9.98051 q^{31} +(5.21004 - 5.21004i) q^{32} +1.90612i q^{34} +(0.602794 - 8.93639i) q^{35} +(-5.07077 - 5.07077i) q^{37} +(-5.24907 - 5.24907i) q^{38} +(0.105195 - 1.55951i) q^{40} +1.02348i q^{41} +(-5.74522 + 5.74522i) q^{43} -9.73313 q^{44} -3.23853 q^{46} +(-2.64170 + 2.64170i) q^{47} +9.04447i q^{49} +(5.77304 + 7.58313i) q^{50} +(-2.33680 - 2.33680i) q^{52} +(7.74013 + 7.74013i) q^{53} +(-10.0352 + 8.76694i) q^{55} +2.79997i q^{56} +(-2.74573 + 2.74573i) q^{58} -3.81699 q^{59} -0.803225 q^{61} +(13.4520 - 13.4520i) q^{62} -4.84654i q^{64} +(-4.51415 - 0.304497i) q^{65} +(-5.17596 - 5.17596i) q^{67} +(1.15490 + 1.15490i) q^{68} +(-11.2322 - 12.8572i) q^{70} -2.40278i q^{71} +(-6.90975 + 6.90975i) q^{73} -13.6690 q^{74} -6.36074 q^{76} +(16.8788 - 16.8788i) q^{77} +1.25928i q^{79} +(-6.76573 - 7.74450i) q^{80} +(1.37947 + 1.37947i) q^{82} +(12.6459 + 12.6459i) q^{83} +(2.23100 + 0.150490i) q^{85} +15.4871i q^{86} +(2.94556 - 2.94556i) q^{88} +4.48063 q^{89} +8.10474 q^{91} +(-1.96220 + 1.96220i) q^{92} +7.12111i q^{94} +(-6.55815 + 5.72931i) q^{95} +(12.1047 + 12.1047i) q^{97} +(12.1904 + 12.1904i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{7} - 20 q^{10} - 20 q^{13} - 8 q^{16} - 40 q^{22} - 24 q^{28} + 72 q^{31} + 16 q^{37} - 88 q^{40} + 36 q^{43} + 56 q^{46} + 32 q^{52} - 88 q^{55} - 80 q^{58} - 8 q^{61} + 104 q^{67} - 136 q^{70}+ \cdots + 88 q^{97}+O(q^{100}) \) 24 * q + 8 * q^7 - 20 * q^10 - 20 * q^13 - 8 * q^16 - 40 * q^22 - 24 * q^28 + 72 * q^31 + 16 * q^37 - 88 * q^40 + 36 * q^43 + 56 * q^46 + 32 * q^52 - 88 * q^55 - 80 * q^58 - 8 * q^61 + 104 * q^67 - 136 * q^70 - 136 * q^73 + 136 * q^76 + 16 * q^82 + 8 * q^85 - 64 * q^88 - 8 * q^91 + 88 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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