LMFDB - Embedded newform 460.2.x.a.217.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [460,2,Mod(17,460)] 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("460.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(460, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([0, 11, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.6
Character	$\chi$	$=$	460.217
Dual form			460.2.x.a.53.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.450644 - 0.0980316i) q^{3} +(1.16867 + 1.90636i) q^{5} +(-3.36712 + 1.83859i) q^{7} +(-2.53543 + 1.15789i) q^{9} +(-0.179116 - 0.155205i) q^{11} +(-2.67009 + 4.88990i) q^{13} +(0.713538 + 0.744522i) q^{15} +(-1.75624 - 1.31470i) q^{17} +(0.184229 - 1.28134i) q^{19} +(-1.33713 + 1.15863i) q^{21} +(3.96880 - 2.69233i) q^{23} +(-2.26841 + 4.45582i) q^{25} +(-2.13665 + 1.59948i) q^{27} +(0.986272 - 0.141805i) q^{29} +(7.10324 - 4.56498i) q^{31} +(-0.0959324 - 0.0523831i) q^{33} +(-7.44006 - 4.27023i) q^{35} +(5.10698 + 1.90481i) q^{37} +(-0.723895 + 2.46536i) q^{39} +(-1.72046 + 3.76728i) q^{41} +(1.31946 + 6.06548i) q^{43} +(-5.17044 - 3.48024i) q^{45} +(2.92484 + 2.92484i) q^{47} +(4.17260 - 6.49270i) q^{49} +(-0.920321 - 0.420297i) q^{51} +(5.65269 + 10.3521i) q^{53} +(0.0865483 - 0.522843i) q^{55} +(-0.0425903 - 0.595490i) q^{57} +(2.27261 + 7.73978i) q^{59} +(-0.294346 - 0.458011i) q^{61} +(6.40820 - 8.56035i) q^{63} +(-12.4424 + 0.624545i) q^{65} +(-6.12185 - 0.437844i) q^{67} +(1.52458 - 1.60235i) q^{69} +(-7.22100 - 8.33348i) q^{71} +(-5.79341 - 7.73909i) q^{73} +(-0.585435 + 2.23036i) q^{75} +(0.888462 + 0.193273i) q^{77} +(8.54432 - 2.50884i) q^{79} +(4.66983 - 5.38927i) q^{81} +(0.344112 - 0.922600i) q^{83} +(0.453831 - 4.88448i) q^{85} +(0.430556 - 0.160589i) q^{87} +(10.6079 + 6.81727i) q^{89} -21.3741i q^{91} +(2.75352 - 2.75352i) q^{93} +(2.65801 - 1.14626i) q^{95} +(1.85518 + 4.97392i) q^{97} +(0.633845 + 0.186114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75}+ \cdots - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.450644	−	0.0980316i	0.260179	−	0.0565986i	−0.0805834	−	0.996748i	$-0.525678\pi$
$3$	0.450644	−	0.0980316i	0.260179	−	0.0565986i	0.340763	+	0.940149i	$0.389315\pi$
$4$		0			0
$5$	1.16867	+	1.90636i	0.522646	+	0.852550i
$5$	1.16867	+	1.90636i	0.522646	+	0.852550i
$6$		0			0
$7$	−3.36712	+	1.83859i	−1.27265	+	0.694920i	−0.966403	−	0.257032i	$-0.917256\pi$
$7$	−3.36712	+	1.83859i	−1.27265	+	0.694920i	−0.306248	+	0.951952i	$0.599074\pi$
$8$		0			0
$9$	−2.53543	+	1.15789i	−0.845142	+	0.385963i
$10$		0			0
$11$	−0.179116	−	0.155205i	−0.0540055	−	0.0467960i	0.627440	−	0.778665i	$-0.284103\pi$
$11$	−0.179116	−	0.155205i	−0.0540055	−	0.0467960i	−0.681445	+	0.731869i	$0.738648\pi$
$12$		0			0
$13$	−2.67009	+	4.88990i	−0.740550	+	1.35622i	0.186942	+	0.982371i	$0.440142\pi$
$13$	−2.67009	+	4.88990i	−0.740550	+	1.35622i	−0.927491	+	0.373844i	$0.878039\pi$
$14$		0			0
$15$	0.713538	+	0.744522i	0.184235	+	0.192235i
$16$		0			0
$17$	−1.75624	−	1.31470i	−0.425951	−	0.318863i	0.364706	−	0.931123i	$-0.381170\pi$
$17$	−1.75624	−	1.31470i	−0.425951	−	0.318863i	−0.790656	+	0.612260i	$0.790261\pi$
$18$		0			0
$19$	0.184229	−	1.28134i	0.0422651	−	0.293960i	−0.957715	−	0.287717i	$-0.907104\pi$
$19$	0.184229	−	1.28134i	0.0422651	−	0.293960i	0.999981	−	0.00624312i	$-0.00198726\pi$
$20$		0			0
$21$	−1.33713	+	1.15863i	−0.291786	+	0.252834i
$22$		0			0
$23$	3.96880	−	2.69233i	0.827552	−	0.561390i
$23$	3.96880	−	2.69233i	0.827552	−	0.561390i
$24$		0			0
$25$	−2.26841	+	4.45582i	−0.453682	+	0.891164i
$26$		0			0
$27$	−2.13665	+	1.59948i	−0.411199	+	0.307820i
$28$		0			0
$29$	0.986272	−	0.141805i	0.183146	−	0.0263324i	−0.0501314	−	0.998743i	$-0.515964\pi$
$29$	0.986272	−	0.141805i	0.183146	−	0.0263324i	0.233278	+	0.972410i	$0.425055\pi$
$30$		0			0
$31$	7.10324	−	4.56498i	1.27578	−	0.819894i	0.285419	−	0.958403i	$-0.407867\pi$
$31$	7.10324	−	4.56498i	1.27578	−	0.819894i	0.990361	+	0.138509i	$0.0442310\pi$
$32$		0			0
$33$	−0.0959324	−	0.0523831i	−0.0166997	−	0.00911872i
$34$		0			0
$35$	−7.44006	−	4.27023i	−1.25760	−	0.721801i
$36$		0			0
$37$	5.10698	+	1.90481i	0.839583	+	0.313148i	0.732217	−	0.681071i	$-0.238486\pi$
$37$	5.10698	+	1.90481i	0.839583	+	0.313148i	0.107366	+	0.994220i	$0.465758\pi$
$38$		0			0
$39$	−0.723895	+	2.46536i	−0.115916	+	0.394773i
$40$		0			0
$41$	−1.72046	+	3.76728i	−0.268690	+	0.588350i	−0.995096	−	0.0989166i	$-0.968462\pi$
$41$	−1.72046	+	3.76728i	−0.268690	+	0.588350i	0.726405	+	0.687267i	$0.241190\pi$
$42$		0			0
$43$	1.31946	+	6.06548i	0.201216	+	0.924977i	0.961376	+	0.275240i	$0.0887574\pi$
$43$	1.31946	+	6.06548i	0.201216	+	0.924977i	−0.760159	+	0.649737i	$0.774879\pi$
$44$		0			0
$45$	−5.17044	−	3.48024i	−0.770763	−	0.518803i
$46$		0			0
$47$	2.92484	+	2.92484i	0.426631	+	0.426631i	0.887479	−	0.460848i	$-0.152455\pi$
$47$	2.92484	+	2.92484i	0.426631	+	0.426631i	−0.460848	+	0.887479i	$0.652455\pi$
$48$		0			0
$49$	4.17260	−	6.49270i	0.596086	−	0.927528i
$50$		0			0
$51$	−0.920321	−	0.420297i	−0.128871	−	0.0588533i
$52$		0			0
$53$	5.65269	+	10.3521i	0.776457	+	1.42197i	0.902833	+	0.429992i	$0.141484\pi$
$53$	5.65269	+	10.3521i	0.776457	+	1.42197i	−0.126376	+	0.991982i	$0.540335\pi$
$54$		0			0
$55$	0.0865483	−	0.522843i	0.0116702	−	0.0705001i
$56$		0			0
$57$	−0.0425903	−	0.595490i	−0.00564122	−	0.0788746i
$58$		0			0
$59$	2.27261	+	7.73978i	0.295868	+	1.00763i	0.964509	+	0.264049i	$0.0850580\pi$
$59$	2.27261	+	7.73978i	0.295868	+	1.00763i	−0.668641	+	0.743585i	$0.733124\pi$
$60$		0			0
$61$	−0.294346	−	0.458011i	−0.0376871	−	0.0586423i	0.821899	−	0.569633i	$-0.192915\pi$
$61$	−0.294346	−	0.458011i	−0.0376871	−	0.0586423i	−0.859586	+	0.510991i	$0.829278\pi$
$62$		0			0
$63$	6.40820	−	8.56035i	0.807357	−	1.07850i
$64$		0			0
$65$	−12.4424	+	0.624545i	−1.54329	+	0.0774652i
$66$		0			0
$67$	−6.12185	−	0.437844i	−0.747903	−	0.0534911i	−0.307816	−	0.951446i	$-0.599598\pi$
$67$	−6.12185	−	0.437844i	−0.747903	−	0.0534911i	−0.440088	+	0.897955i	$0.645053\pi$
$68$		0			0
$69$	1.52458	−	1.60235i	0.183538	−	0.192900i
$70$		0			0
$71$	−7.22100	−	8.33348i	−0.856975	−	0.989002i	0.143025	−	0.989719i	$-0.454317\pi$
$71$	−7.22100	−	8.33348i	−0.856975	−	0.989002i	−1.00000		0.000717124i	$0.999772\pi$
$72$		0			0
$73$	−5.79341	−	7.73909i	−0.678067	−	0.905792i	0.321081	−	0.947052i	$-0.395954\pi$
$73$	−5.79341	−	7.73909i	−0.678067	−	0.905792i	−0.999148	+	0.0412598i	$0.986863\pi$
$74$		0			0
$75$	−0.585435	+	2.23036i	−0.0676002	+	0.257540i
$76$		0			0
$77$	0.888462	+	0.193273i	0.101250	+	0.0220255i
$78$		0			0
$79$	8.54432	−	2.50884i	0.961311	−	0.282266i	0.236822	−	0.971553i	$-0.423894\pi$
$79$	8.54432	−	2.50884i	0.961311	−	0.282266i	0.724489	+	0.689287i	$0.242076\pi$
$80$		0			0
$81$	4.66983	−	5.38927i	0.518870	−	0.598808i
$82$		0			0
$83$	0.344112	−	0.922600i	0.0377712	−	0.101269i	−0.916695	−	0.399588i	$-0.869153\pi$
$83$	0.344112	−	0.922600i	0.0377712	−	0.101269i	0.954466	+	0.298319i	$0.0964260\pi$
$84$		0			0
$85$	0.453831	−	4.88448i	0.0492249	−	0.529796i
$86$		0			0
$87$	0.430556	−	0.160589i	0.0461605	−	0.0172170i
$88$		0			0
$89$	10.6079	+	6.81727i	1.12443	+	0.722630i	0.964391	−	0.264481i	$-0.0852005\pi$
$89$	10.6079	+	6.81727i	1.12443	+	0.722630i	0.160042	+	0.987110i	$0.448837\pi$
$90$		0			0
$91$		−	21.3741i		−	2.24061i
$92$		0			0
$93$	2.75352	−	2.75352i	0.285527	−	0.285527i
$94$		0			0
$95$	2.65801	−	1.14626i	0.272706	−	0.117604i
$96$		0			0
$97$	1.85518	+	4.97392i	0.188365	+	0.505025i	0.996464	−	0.0840212i	$-0.0267763\pi$
$97$	1.85518	+	4.97392i	0.188365	+	0.505025i	−0.808099	+	0.589046i	$0.799504\pi$
$98$		0			0
$99$	0.633845	+	0.186114i	0.0637038	+	0.0187051i
$100$		0			0
$101$	−4.74868	−	10.3982i	−0.472511	−	1.03465i	−0.984455	−	0.175636i	$-0.943802\pi$
$101$	−4.74868	−	10.3982i	−0.472511	−	1.03465i	0.511944	−	0.859019i	$-0.328925\pi$
$102$		0			0
$103$	3.00055	−	0.214604i	0.295653	−	0.0211456i	0.0772754	−	0.997010i	$-0.475378\pi$
$103$	3.00055	−	0.214604i	0.295653	−	0.0211456i	0.218378	+	0.975864i	$0.429923\pi$
$104$		0			0
$105$	−3.77144	−	1.19499i	−0.368055	−	0.116619i
$106$		0			0
$107$	1.33197	−	6.12296i	0.128766	−	0.591929i	−0.866864	−	0.498545i	$-0.833868\pi$
$107$	1.33197	−	6.12296i	0.128766	−	0.591929i	0.995630	−	0.0933839i	$-0.0297684\pi$
$108$		0			0
$109$	0.540723	+	3.76081i	0.0517919	+	0.360221i	0.999193	+	0.0401714i	$0.0127904\pi$
$109$	0.540723	+	3.76081i	0.0517919	+	0.360221i	−0.947401	+	0.320049i	$0.896301\pi$
$110$		0			0
$111$	2.48816	+	0.357744i	0.236166	+	0.0339555i
$112$		0			0
$113$	−1.15516	+	16.1513i	−0.108668	+	1.51938i	0.592024	+	0.805920i	$0.298329\pi$
$113$	−1.15516	+	16.1513i	−0.108668	+	1.51938i	−0.700693	+	0.713463i	$0.747126\pi$
$114$		0			0
$115$	9.77077	+	4.41950i	0.911129	+	0.412121i
$116$		0			0
$117$	1.10784	−	15.4897i	0.102420	−	1.43202i
$118$		0			0
$119$	8.33066	+	1.19777i	0.763671	+	0.109799i
$120$		0			0
$121$	−1.55747	−	10.8324i	−0.141588	−	0.984767i
$122$		0			0
$123$	−0.406002	+	1.86636i	−0.0366080	+	0.168284i
$124$		0			0
$125$	−11.1454	+	0.882984i	−0.996876	+	0.0789765i
$126$		0			0
$127$	−7.27953	+	0.520642i	−0.645954	+	0.0461995i	−0.390473	−	0.920614i	$-0.627688\pi$
$127$	−7.27953	+	0.520642i	−0.645954	+	0.0461995i	−0.255481	+	0.966814i	$0.582234\pi$
$128$		0			0
$129$	1.18922	+	2.60402i	0.104705	+	0.229271i
$130$		0			0
$131$	12.0833	+	3.54798i	1.05572	+	0.309988i	0.763127	−	0.646248i	$-0.223663\pi$
$131$	12.0833	+	3.54798i	1.05572	+	0.309988i	0.292595	+	0.956236i	$0.405481\pi$
$132$		0			0
$133$	1.73554	+	4.65316i	0.150490	+	0.403480i
$134$		0			0
$135$	−5.54623	−	2.20396i	−0.477343	−	0.189687i
$136$		0			0
$137$	−10.5920	+	10.5920i	−0.904938	+	0.904938i	−0.995858	−	0.0909203i	$-0.971019\pi$
$137$	−10.5920	+	10.5920i	−0.904938	+	0.904938i	0.0909203	+	0.995858i	$0.471019\pi$
$138$		0			0
$139$		−	20.2830i		−	1.72038i	−0.509971	−	0.860192i	$-0.670344\pi$
$139$		−	20.2830i		−	1.72038i	0.509971	−	0.860192i	$-0.329656\pi$
$140$		0			0
$141$	1.60479	+	1.03133i	0.135147	+	0.0868540i
$142$		0			0
$143$	1.23719	−	0.461449i	0.103459	−	0.0385883i
$144$		0			0
$145$	1.42296	+	1.71447i	0.118170	+	0.142379i
$146$		0			0
$147$	1.24387	−	3.33494i	0.102593	−	0.275061i
$148$		0			0
$149$	−6.13032	+	7.07477i	−0.502216	+	0.579588i	−0.949088	−	0.315010i	$-0.897992\pi$
$149$	−6.13032	+	7.07477i	−0.502216	+	0.579588i	0.446873	+	0.894598i	$0.352538\pi$
$150$		0			0
$151$	−13.8218	+	4.05844i	−1.12480	+	0.330271i	−0.790662	−	0.612253i	$-0.790264\pi$
$151$	−13.8218	+	4.05844i	−1.12480	+	0.330271i	−0.334139	+	0.942524i	$0.608445\pi$
$152$		0			0
$153$	5.97510	+	1.29980i	0.483058	+	0.105083i
$154$		0			0
$155$	17.0038	+	8.20637i	1.36578	+	0.659151i
$156$		0			0
$157$	1.94419	+	2.59713i	0.155163	+	0.207274i	0.871386	−	0.490598i	$-0.163222\pi$
$157$	1.94419	+	2.59713i	0.155163	+	0.207274i	−0.716223	+	0.697871i	$0.754131\pi$
$158$		0			0
$159$	3.56219	+	4.11098i	0.282500	+	0.326022i
$160$		0			0
$161$	−8.41334	+	16.3624i	−0.663064	+	1.28954i
$162$		0			0
$163$	−3.37067	−	0.241075i	−0.264011	−	0.0188825i	−0.0612940	−	0.998120i	$-0.519523\pi$
$163$	−3.37067	−	0.241075i	−0.264011	−	0.0188825i	−0.202717	+	0.979237i	$0.564977\pi$
$164$		0			0
$165$	−0.0122526	−	0.244100i	−0.000953865	−	0.0190032i
$166$		0			0
$167$	9.64344	−	12.8821i	0.746232	−	0.996849i	−0.253333	−	0.967379i	$-0.581527\pi$
$167$	9.64344	−	12.8821i	0.746232	−	0.996849i	0.999566	−	0.0294705i	$-0.00938210\pi$
$168$		0			0
$169$	−9.75346	−	15.1767i	−0.750266	−	1.16744i
$170$		0			0
$171$	1.01656	+	3.46207i	0.0777379	+	0.264751i
$172$		0			0
$173$	1.24730	+	17.4395i	0.0948305	+	1.32590i	0.792671	+	0.609650i	$0.208690\pi$
$173$	1.24730	+	17.4395i	0.0948305	+	1.32590i	−0.697840	+	0.716253i	$0.745856\pi$
$174$		0			0
$175$	−0.554395	−	19.1739i	−0.0419083	−	1.44941i
$176$		0			0
$177$	1.78288	+	3.26510i	0.134009	+	0.245420i
$178$		0			0
$179$	7.38976	+	3.37479i	0.552337	+	0.252244i	0.671975	−	0.740574i	$-0.265446\pi$
$179$	7.38976	+	3.37479i	0.552337	+	0.252244i	−0.119638	+	0.992818i	$0.538174\pi$
$180$		0			0
$181$	13.1604	−	20.4780i	0.978208	−	1.52212i	0.130643	−	0.991429i	$-0.458296\pi$
$181$	13.1604	−	20.4780i	0.978208	−	1.52212i	0.847565	−	0.530692i	$-0.178068\pi$
$182$		0			0
$183$	−0.177545	−	0.177545i	−0.0131245	−	0.0131245i
$184$		0			0
$185$	2.33714	+	11.9618i	0.171830	+	0.879452i
$186$		0			0
$187$	0.110522	+	0.508061i	0.00808217	+	0.0371531i
$188$		0			0
$189$	4.25359	−	9.31406i	0.309403	−	0.677498i
$190$		0			0
$191$	1.12694	−	3.83800i	0.0815423	−	0.277708i	−0.908621	−	0.417621i	$-0.862864\pi$
$191$	1.12694	−	3.83800i	0.0815423	−	0.277708i	0.990164	+	0.139913i	$0.0446823\pi$
$192$		0			0
$193$	−4.44554	−	1.65810i	−0.319997	−	0.119353i	0.184333	−	0.982864i	$-0.440988\pi$
$193$	−4.44554	−	1.65810i	−0.319997	−	0.119353i	−0.504330	+	0.863511i	$0.668260\pi$
$194$		0			0
$195$	−5.54586	+	1.50119i	−0.397147	+	0.107503i
$196$		0			0
$197$	1.79978	+	0.982755i	0.128229	+	0.0700184i	0.542083	−	0.840325i	$-0.317636\pi$
$197$	1.79978	+	0.982755i	0.128229	+	0.0700184i	−0.413854	+	0.910343i	$0.635818\pi$
$198$		0			0
$199$	−22.6474	+	14.5546i	−1.60543	+	1.03175i	−0.640953	+	0.767581i	$0.721460\pi$
$199$	−22.6474	+	14.5546i	−1.60543	+	1.03175i	−0.964477	+	0.264166i	$0.914903\pi$
$200$		0			0
$201$	−2.80170	+	0.402823i	−0.197617	+	0.0284130i
$202$		0			0
$203$	−3.06017	+	2.29082i	−0.214782	+	0.160784i
$204$		0			0
$205$	−9.19244	+	1.12290i	−0.642028	+	0.0784268i
$206$		0			0
$207$	−6.94517	+	11.4216i	−0.482723	+	0.793859i
$208$		0			0
$209$	−0.231869	+	0.200916i	−0.0160387	+	0.0138976i
$210$		0			0
$211$	0.442634	−	3.07859i	0.0304722	−	0.211939i	−0.968897	−	0.247466i	$-0.920402\pi$
$211$	0.442634	−	3.07859i	0.0304722	−	0.211939i	0.999369	+	0.0355276i	$0.0113112\pi$
$212$		0			0
$213$	−4.07104	−	3.04755i	−0.278943	−	0.208814i
$214$		0			0
$215$	−10.0210	+	9.60393i	−0.683424	+	0.654983i
$216$		0			0
$217$	−15.5244	+	28.4307i	−1.05386	+	1.93000i
$218$		0			0
$219$	−3.36944	−	2.91964i	−0.227686	−	0.197291i
$220$		0			0
$221$	11.1181	−	5.07747i	0.747884	−	0.341547i
$222$		0			0
$223$	−1.62282	+	0.886127i	−0.108672	+	0.0593395i	−0.532666	−	0.846326i	$-0.678810\pi$
$223$	−1.62282	+	0.886127i	−0.108672	+	0.0593395i	0.423994	+	0.905665i	$0.360628\pi$
$224$		0			0
$225$	0.592040	−	13.9240i	0.0394693	−	0.928265i
$226$		0			0
$227$	−23.0242	+	5.00861i	−1.52817	+	0.332433i	−0.896584	−	0.442874i	$-0.853959\pi$
$227$	−23.0242	+	5.00861i	−1.52817	+	0.332433i	−0.631585	+	0.775307i	$0.717595\pi$
$228$		0			0
$229$	27.2781			1.80259			0.901295	−	0.433205i	$-0.142618\pi$
$229$	27.2781			1.80259			0.901295	+	0.433205i	$0.142618\pi$
$230$		0			0
$231$	0.419327			0.0275897
$232$		0			0
$233$	−18.5541	+	4.03620i	−1.21552	+	0.264420i	−0.774207	−	0.632932i	$-0.781851\pi$
$233$	−18.5541	+	4.03620i	−1.21552	+	0.264420i	−0.441314	+	0.897353i	$0.645487\pi$
$234$		0			0
$235$	−2.15761	+	8.99397i	−0.140747	+	0.586702i
$236$		0			0
$237$	3.60450	−	1.96821i	0.234137	−	0.127849i
$238$		0			0
$239$	−0.986603	+	0.450567i	−0.0638180	+	0.0291447i	−0.447068	−	0.894500i	$-0.647532\pi$
$239$	−0.986603	+	0.450567i	−0.0638180	+	0.0291447i	0.383250	+	0.923645i	$0.374805\pi$
$240$		0			0
$241$	21.8378	+	18.9225i	1.40669	+	1.21891i	0.942948	+	0.332939i	$0.108040\pi$
$241$	21.8378	+	18.9225i	1.40669	+	1.21891i	0.463746	+	0.885968i	$0.346505\pi$
$242$		0			0
$243$	5.41347	−	9.91404i	0.347275	−	0.635986i
$244$		0			0
$245$	17.2538	+	0.366646i	1.10231	+	0.0234242i
$246$		0			0
$247$	5.77374	+	4.32217i	0.367374	+	0.275013i
$248$		0			0
$249$	0.0646281	−	0.449498i	0.00409564	−	0.0284858i
$250$		0			0
$251$	−13.8029	+	11.9603i	−0.871230	+	0.754925i	−0.970745	−	0.240111i	$-0.922816\pi$
$251$	−13.8029	+	11.9603i	−0.871230	+	0.754925i	0.0995157	+	0.995036i	$0.468271\pi$
$252$		0			0
$253$	−1.12874	−	0.133738i	−0.0709631	−	0.00840801i
$254$		0			0
$255$	−0.274317	−	2.24565i	−0.0171784	−	0.140628i
$256$		0			0
$257$	−13.4837	+	10.0938i	−0.841092	+	0.629633i	−0.930471	−	0.366364i	$-0.880602\pi$
$257$	−13.4837	+	10.0938i	−0.841092	+	0.629633i	0.0893799	+	0.995998i	$0.471511\pi$
$258$		0			0
$259$	−20.6980	+	2.97592i	−1.28611	+	0.184915i
$260$		0			0
$261$	−2.33643	+	1.50153i	−0.144621	+	0.0929424i
$262$		0			0
$263$	25.1216	+	13.7174i	1.54906	+	0.845853i	0.999949	+	0.0101060i	$0.00321688\pi$
$263$	25.1216	+	13.7174i	1.54906	+	0.845853i	0.549115	+	0.835747i	$0.314965\pi$
$264$		0			0
$265$	−13.1287	+	22.8743i	−0.806492	+	1.40516i
$266$		0			0
$267$	5.44869	+	2.03226i	0.333454	+	0.124372i
$268$		0			0
$269$	4.23328	−	14.4172i	0.258108	−	0.879034i	−0.723854	−	0.689953i	$-0.757631\pi$
$269$	4.23328	−	14.4172i	0.258108	−	0.879034i	0.981962	−	0.189081i	$-0.0605507\pi$
$270$		0			0
$271$	−6.36202	+	13.9309i	−0.386465	+	0.846241i	0.612000	+	0.790858i	$0.290365\pi$
$271$	−6.36202	+	13.9309i	−0.386465	+	0.846241i	−0.998465	+	0.0553831i	$0.982362\pi$
$272$		0			0
$273$	−2.09533	−	9.63210i	−0.126815	−	0.582961i
$274$		0			0
$275$	1.09787	−	0.446039i	0.0662042	−	0.0268972i
$276$		0			0
$277$	11.1706	+	11.1706i	0.671175	+	0.671175i	0.957987	−	0.286812i	$-0.0925955\pi$
$277$	11.1706	+	11.1706i	0.671175	+	0.671175i	−0.286812	+	0.957987i	$0.592596\pi$
$278$		0			0
$279$	−12.7240	+	19.7989i	−0.761766	+	1.18533i
$280$		0			0
$281$	10.2128	+	4.66403i	0.609245	+	0.278233i	0.696051	−	0.717992i	$-0.254939\pi$
$281$	10.2128	+	4.66403i	0.609245	+	0.278233i	−0.0868061	+	0.996225i	$0.527666\pi$
$282$		0			0
$283$	−7.08542	−	12.9760i	−0.421185	−	0.771342i	0.577810	−	0.816171i	$-0.303907\pi$
$283$	−7.08542	−	12.9760i	−0.421185	−	0.771342i	−0.998995	+	0.0448293i	$0.985726\pi$
$284$		0			0
$285$	1.08544	−	0.777125i	0.0642962	−	0.0460329i
$286$		0			0
$287$	−1.13348	−	15.8481i	−0.0669070	−	0.935483i
$288$		0			0
$289$	−3.43352	−	11.6935i	−0.201972	−	0.687853i
$290$		0			0
$291$	1.32362	+	2.05960i	0.0775923	+	0.120736i
$292$		0			0
$293$	10.3058	−	13.7669i	0.602070	−	0.804271i	−0.391174	−	0.920317i	$-0.627931\pi$
$293$	10.3058	−	13.7669i	0.602070	−	0.804271i	0.993244	+	0.116046i	$0.0370219\pi$
$294$		0			0
$295$	−12.0989	+	13.3777i	−0.704424	+	0.778878i
$296$		0			0
$297$	0.630955	+	0.0451268i	0.0366117	+	0.00261852i
$298$		0			0
$299$	2.56819	+	26.5958i	0.148522	+	1.53808i
$300$		0			0
$301$	−15.5947	−	17.9972i	−0.898864	−	1.03734i
$302$		0			0
$303$	−3.15931	−	4.22034i	−0.181498	−	0.242452i
$304$		0			0
$305$	0.529139	−	1.09639i	0.0302984	−	0.0627793i
$306$		0			0
$307$	20.9922	+	4.56657i	1.19809	+	0.260628i	0.766979	−	0.641672i	$-0.221759\pi$
$307$	20.9922	+	4.56657i	1.19809	+	0.260628i	0.431109	+	0.902300i	$0.358122\pi$
$308$		0			0
$309$	1.33114	−	0.390859i	0.0757261	−	0.0222352i
$310$		0			0
$311$	−14.3376	+	16.5465i	−0.813012	+	0.938266i	−0.999019	−	0.0442827i	$-0.985900\pi$
$311$	−14.3376	+	16.5465i	−0.813012	+	0.938266i	0.186007	+	0.982548i	$0.440445\pi$
$312$		0			0
$313$	12.3034	−	32.9867i	0.695429	−	1.86452i	0.254072	−	0.967185i	$-0.418230\pi$
$313$	12.3034	−	32.9867i	0.695429	−	1.86452i	0.441357	−	0.897332i	$-0.354497\pi$
$314$		0			0
$315$	23.8082	+	2.21208i	1.34144	+	0.124637i
$316$		0			0
$317$	9.25313	−	3.45124i	0.519708	−	0.193841i	−0.0759015	−	0.997115i	$-0.524183\pi$
$317$	9.25313	−	3.45124i	0.519708	−	0.193841i	0.595609	+	0.803274i	$0.296911\pi$
$318$		0			0
$319$	−0.198666	−	0.127675i	−0.0111231	−	0.00714841i
$320$		0			0
$321$		−	2.88985i		−	0.161296i
$322$		0			0
$323$	−2.00814	+	2.00814i	−0.111736	+	0.111736i
$324$		0			0
$325$	−15.7317	−	22.9897i	−0.872636	−	1.27524i
$326$		0			0
$327$	0.612352	+	1.64178i	0.0338632	+	0.0907907i
$328$		0			0
$329$	−15.2258	−	4.47071i	−0.839428	−	0.246478i
$330$		0			0
$331$	14.3189	+	31.3539i	0.787036	+	1.72337i	0.684948	+	0.728592i	$0.259825\pi$
$331$	14.3189	+	31.3539i	0.787036	+	1.72337i	0.102088	+	0.994775i	$0.467448\pi$
$332$		0			0
$333$	−15.1539	+	1.08383i	−0.830431	+	0.0593936i
$334$		0			0
$335$	−6.31975	−	12.1821i	−0.345285	−	0.665582i
$336$		0			0
$337$	0.782754	−	3.59826i	0.0426393	−	0.196010i	−0.950900	−	0.309498i	$-0.899839\pi$
$337$	0.782754	−	3.59826i	0.0426393	−	0.196010i	0.993539	+	0.113489i	$0.0362025\pi$
$338$		0			0
$339$	1.06277	+	7.39171i	0.0577216	+	0.401463i
$340$		0			0
$341$	−1.98081	−	0.284797i	−0.107267	−	0.0154226i
$342$		0			0
$343$	−0.196474	+	2.74707i	−0.0106086	+	0.148328i
$344$		0			0
$345$	4.83639	+	1.03378i	0.260383	+	0.0556568i
$346$		0			0
$347$	2.10515	−	29.4339i	0.113011	−	1.58009i	−0.552376	−	0.833595i	$-0.686279\pi$
$347$	2.10515	−	29.4339i	0.113011	−	1.58009i	0.665386	−	0.746499i	$-0.268267\pi$
$348$		0			0
$349$	7.02613	+	1.01020i	0.376100	+	0.0540750i	0.327773	−	0.944757i	$-0.393702\pi$
$349$	7.02613	+	1.01020i	0.376100	+	0.0540750i	0.0483271	+	0.998832i	$0.484611\pi$
$350$		0			0
$351$	−2.11624	−	14.7188i	−0.112957	−	0.785631i
$352$		0			0
$353$	−1.55140	+	7.13168i	−0.0825728	+	0.379581i	−0.999825	−	0.0187268i	$-0.994039\pi$
$353$	−1.55140	+	7.13168i	−0.0825728	+	0.379581i	0.917252	+	0.398308i	$0.130402\pi$
$354$		0			0
$355$	7.44762	−	23.5049i	0.395279	−	1.24751i
$356$		0			0
$357$	3.87158	−	0.276901i	0.204906	−	0.0146552i
$358$		0			0
$359$	8.33160	+	18.2437i	0.439725	+	0.962863i	0.991649	+	0.128969i	$0.0411666\pi$
$359$	8.33160	+	18.2437i	0.439725	+	0.962863i	−0.551924	+	0.833894i	$0.686106\pi$
$360$		0			0
$361$	16.6225	+	4.88080i	0.874867	+	0.256884i
$362$		0			0
$363$	−1.76379	−	4.72889i	−0.0925747	−	0.248202i
$364$		0			0
$365$	7.98289	−	20.0888i	0.417843	−	1.05149i
$366$		0			0
$367$	17.5734	−	17.5734i	0.917324	−	0.917324i	−0.0795098	−	0.996834i	$-0.525336\pi$
$367$	17.5734	−	17.5734i	0.917324	−	0.917324i	0.996834	+	0.0795098i	$0.0253355\pi$
$368$		0			0
$369$		−	11.5438i		−	0.600944i
$370$		0			0
$371$	−38.0666	−	24.4639i	−1.97632	−	1.27010i
$372$		0			0
$373$	2.28764	−	0.853247i	0.118450	−	0.0441795i	−0.289540	−	0.957166i	$-0.593502\pi$
$373$	2.28764	−	0.853247i	0.118450	−	0.0441795i	0.407990	+	0.912986i	$0.366230\pi$
$374$		0			0
$375$	−4.93605	+	1.49051i	−0.254897	+	0.0769698i
$376$		0			0
$377$	−1.94002	+	5.20141i	−0.0999163	+	0.267886i
$378$		0			0
$379$	12.3052	−	14.2010i	0.632078	−	0.729457i	−0.345875	−	0.938281i	$-0.612418\pi$
$379$	12.3052	−	14.2010i	0.632078	−	0.729457i	0.977953	+	0.208823i	$0.0669634\pi$
$380$		0			0
$381$	−3.22944	+	0.948248i	−0.165449	+	0.0485802i
$382$		0			0
$383$	16.7395	+	3.64145i	0.855347	+	0.186069i	0.618798	−	0.785550i	$-0.287620\pi$
$383$	16.7395	+	3.64145i	0.855347	+	0.186069i	0.236549	+	0.971620i	$0.423984\pi$
$384$		0			0
$385$	0.669873	+	1.91960i	0.0341399	+	0.0978319i
$386$		0			0
$387$	−10.3686	−	13.8508i	−0.527064	−	0.704075i
$388$		0			0
$389$	−6.72218	−	7.75781i	−0.340828	−	0.393337i	0.559298	−	0.828967i	$-0.311071\pi$
$389$	−6.72218	−	7.75781i	−0.340828	−	0.393337i	−0.900126	+	0.435630i	$0.856525\pi$
$390$		0			0
$391$	−10.5098	−	0.489421i	−0.531502	−	0.0247511i
$392$		0			0
$393$	5.79308	+	0.414329i	0.292222	+	0.0209001i
$394$		0			0
$395$	14.7683	+	13.3565i	0.743071	+	0.672040i
$396$		0			0
$397$	15.0622	−	20.1208i	0.755951	−	1.00983i	−0.243254	−	0.969963i	$-0.578215\pi$
$397$	15.0622	−	20.1208i	0.755951	−	1.00983i	0.999205	−	0.0398692i	$-0.0126941\pi$
$398$		0			0
$399$	1.23827	+	1.92678i	0.0619908	+	0.0964596i
$400$		0			0
$401$	9.35848	+	31.8721i	0.467340	+	1.59161i	0.769690	+	0.638418i	$0.220411\pi$
$401$	9.35848	+	31.8721i	0.467340	+	1.59161i	−0.302350	+	0.953197i	$0.597771\pi$
$402$		0			0
$403$	3.35600	+	46.9231i	0.167174	+	2.33740i
$404$		0			0
$405$	15.7314	+	2.60408i	0.781699	+	0.129398i
$406$		0			0
$407$	−0.619107	−	1.13381i	−0.0306880	−	0.0562008i
$408$		0			0
$409$	−31.9481	−	14.5902i	−1.57973	−	0.721440i	−0.583831	−	0.811875i	$-0.698447\pi$
$409$	−31.9481	−	14.5902i	−1.57973	−	0.721440i	−0.995902	+	0.0904353i	$0.971174\pi$
$410$		0			0
$411$	−3.73488	+	5.81159i	−0.184228	+	0.286664i
$412$		0			0
$413$	−21.8824	−	21.8824i	−1.07676	−	1.07676i
$414$		0			0
$415$	2.16096	−	0.422216i	0.106077	−	0.0207258i
$416$		0			0
$417$	−1.98838	−	9.14042i	−0.0973712	−	0.447608i
$418$		0			0
$419$	−3.05029	+	6.67920i	−0.149016	+	0.326300i	−0.969389	−	0.245528i	$-0.921039\pi$
$419$	−3.05029	+	6.67920i	−0.149016	+	0.326300i	0.820373	+	0.571829i	$0.193766\pi$
$420$		0			0
$421$	5.49139	−	18.7019i	0.267634	−	0.911477i	−0.710534	−	0.703662i	$-0.751547\pi$
$421$	5.49139	−	18.7019i	0.267634	−	0.911477i	0.978168	−	0.207815i	$-0.0666351\pi$
$422$		0			0
$423$	−10.8024	−	4.02907i	−0.525228	−	0.195900i
$424$		0			0
$425$	9.84196	−	4.84319i	0.477405	−	0.234929i
$426$		0			0
$427$	1.83319	+	1.00100i	0.0887142	+	0.0484416i
$428$		0			0
$429$	0.512296	−	0.329233i	0.0247339	−	0.0158955i
$430$		0			0
$431$	−13.8710	+	1.99435i	−0.668143	+	0.0960645i	−0.468036	−	0.883710i	$-0.655038\pi$
$431$	−13.8710	+	1.99435i	−0.668143	+	0.0960645i	−0.200107	+	0.979774i	$0.564129\pi$
$432$		0			0
$433$	6.60035	−	4.94096i	0.317193	−	0.237448i	−0.428803	−	0.903398i	$-0.641065\pi$
$433$	6.60035	−	4.94096i	0.317193	−	0.237448i	0.745996	+	0.665950i	$0.231974\pi$
$434$		0			0
$435$	0.809320	+	0.633119i	0.0388039	+	0.0303557i
$436$		0			0
$437$	−2.71863	−	5.58140i	−0.130050	−	0.266995i
$438$		0			0
$439$	−23.3928	+	20.2700i	−1.11648	+	0.967434i	−0.999669	−	0.0257207i	$-0.991812\pi$
$439$	−23.3928	+	20.2700i	−1.11648	+	0.967434i	−0.116809	+	0.993154i	$0.537267\pi$
$440$		0			0
$441$	−3.06150	+	21.2932i	−0.145786	+	1.01396i
$442$		0			0
$443$	−20.9519	−	15.6844i	−0.995456	−	0.745189i	−0.0283595	−	0.999598i	$-0.509028\pi$
$443$	−20.9519	−	15.6844i	−0.995456	−	0.745189i	−0.967097	+	0.254408i	$0.918119\pi$
$444$		0			0
$445$	−0.599033	+	28.1896i	−0.0283969	+	1.33631i
$446$		0			0
$447$	−2.06904	+	3.78917i	−0.0978623	+	0.179221i
$448$		0			0
$449$	−4.29583	−	3.72235i	−0.202733	−	0.175669i	0.547577	−	0.836755i	$-0.315550\pi$
$449$	−4.29583	−	3.72235i	−0.202733	−	0.175669i	−0.750310	+	0.661086i	$0.770096\pi$
$450$		0			0
$451$	0.892861	−	0.407756i	0.0420432	−	0.0192005i
$452$		0			0
$453$	−5.83085	+	3.18388i	−0.273957	+	0.149592i
$454$		0			0
$455$	40.7467	−	24.9793i	1.91023	−	1.17105i
$456$		0			0
$457$	15.5573	−	3.38428i	0.727740	−	0.158310i	0.166592	−	0.986026i	$-0.446724\pi$
$457$	15.5573	−	3.38428i	0.727740	−	0.158310i	0.561148	+	0.827716i	$0.310360\pi$
$458$		0			0
$459$	5.85532			0.273303
$460$		0			0
$461$	36.7438			1.71133			0.855664	−	0.517532i	$-0.173149\pi$
$461$	36.7438			1.71133			0.855664	+	0.517532i	$0.173149\pi$
$462$		0			0
$463$	−0.864334	+	0.188024i	−0.0401690	+	0.00873823i	−0.232605	−	0.972571i	$-0.574725\pi$
$463$	−0.864334	+	0.188024i	−0.0401690	+	0.00873823i	0.192436	+	0.981310i	$0.438361\pi$
$464$		0			0
$465$	8.46716	+	2.03124i	0.392655	+	0.0941964i
$466$		0			0
$467$	4.25299	−	2.32231i	0.196805	−	0.107464i	−0.377825	−	0.925877i	$-0.623328\pi$
$467$	4.25299	−	2.32231i	0.196805	−	0.107464i	0.574630	+	0.818413i	$0.305146\pi$
$468$		0			0
$469$	21.4180	−	9.78128i	0.988992	−	0.451658i
$470$		0			0
$471$	1.13074	+	0.979789i	0.0521016	+	0.0451463i
$472$		0			0
$473$	0.705055	−	1.29121i	0.0324184	−	0.0593699i
$474$		0			0
$475$	5.29153	+	3.72751i	0.242792	+	0.171030i
$476$		0			0
$477$	−26.3186	−	19.7019i	−1.20505	−	0.902086i
$478$		0			0
$479$	3.73327	−	25.9655i	0.170578	−	1.18639i	−0.707090	−	0.707123i	$-0.749993\pi$
$479$	3.73327	−	25.9655i	0.170578	−	1.18639i	0.877668	−	0.479269i	$-0.159098\pi$
$480$		0			0
$481$	−22.9504	+	19.8867i	−1.04645	+	0.906754i
$482$		0			0
$483$	−2.18739	+	8.19838i	−0.0995297	+	0.373039i
$484$		0			0
$485$	−7.31398	+	9.34951i	−0.332111	+	0.424539i
$486$		0			0
$487$	21.8881	−	16.3852i	0.991845	−	0.742486i	0.0254840	−	0.999675i	$-0.491887\pi$
$487$	21.8881	−	16.3852i	0.991845	−	0.742486i	0.966361	+	0.257189i	$0.0827964\pi$
$488$		0			0
$489$	−1.54261	+	0.221793i	−0.0697590	+	0.0100298i
$490$		0			0
$491$	12.1514	−	7.80922i	0.548384	−	0.352425i	−0.236926	−	0.971528i	$-0.576140\pi$
$491$	12.1514	−	7.80922i	0.548384	−	0.352425i	0.785310	+	0.619103i	$0.212504\pi$
$492$		0			0
$493$	−1.91856	−	1.04761i	−0.0864076	−	0.0471821i
$494$		0			0
$495$	0.385958	+	1.42584i	0.0173475	+	0.0640868i
$496$		0			0
$497$	39.6358	+	14.7834i	1.77791	+	0.663125i
$498$		0			0
$499$	0.207165	−	0.705540i	0.00927399	−	0.0315843i	−0.954726	−	0.297487i	$-0.903852\pi$
$499$	0.207165	−	0.705540i	0.00927399	−	0.0315843i	0.964000	+	0.265902i	$0.0856698\pi$
$500$		0			0
$501$	3.08290	−	6.75062i	0.137734	−	0.301595i
$502$		0			0
$503$	−4.79817	−	22.0568i	−0.213940	−	0.983465i	−0.951372	−	0.308044i	$-0.900326\pi$
$503$	−4.79817	−	22.0568i	−0.213940	−	0.983465i	0.737432	−	0.675421i	$-0.236038\pi$
$504$		0			0
$505$	14.2730	−	21.2047i	0.635139	−	0.943597i
$506$		0			0
$507$	−5.88313	−	5.88313i	−0.261279	−	0.261279i
$508$		0			0
$509$	3.70988	−	5.77268i	0.164437	−	0.255870i	−0.749250	−	0.662287i	$-0.769586\pi$
$509$	3.70988	−	5.77268i	0.164437	−	0.255870i	0.913687	+	0.406418i	$0.133222\pi$
$510$		0			0
$511$	33.7361	+	15.4067i	1.49240	+	0.681554i
$512$		0			0
$513$	1.65585	+	3.03246i	0.0731075	+	0.133886i
$514$		0			0
$515$	3.91578	+	5.46933i	0.172550	+	0.241008i
$516$		0			0
$517$	−0.0699360	−	0.977833i	−0.00307578	−	0.0430051i
$518$		0			0
$519$	2.27171	+	7.73674i	0.0997171	+	0.339605i
$520$		0			0
$521$	1.77970	+	2.76927i	0.0779703	+	0.121324i	0.878049	−	0.478571i	$-0.158845\pi$
$521$	1.77970	+	2.76927i	0.0779703	+	0.121324i	−0.800078	+	0.599895i	$0.795209\pi$
$522$		0			0
$523$	−2.00717	+	2.68127i	−0.0877676	+	0.117244i	−0.842276	−	0.539047i	$-0.818785\pi$
$523$	−2.00717	+	2.68127i	−0.0877676	+	0.117244i	0.754508	+	0.656291i	$0.227875\pi$
$524$		0			0
$525$	−2.12949	−	8.58627i	−0.0929384	−	0.374736i
$526$		0			0
$527$	−18.4766	−	1.32147i	−0.804853	−	0.0575642i
$528$		0			0
$529$	8.50272	−	21.3706i	0.369684	−	0.929158i
$530$		0			0
$531$	−14.7238	−	16.9922i	−0.638960	−	0.737400i
$532$		0			0
$533$	−13.8279	−	18.4718i	−0.598951	−	0.800105i
$534$		0			0
$535$	13.2292	−	4.61652i	0.571948	−	0.199590i
$536$		0			0
$537$	3.66099	+	0.796399i	0.157983	+	0.0343672i
$538$		0			0
$539$	−1.75508	+	0.515337i	−0.0755965	+	0.0221971i
$540$		0			0
$541$	−13.3316	+	15.3855i	−0.573170	+	0.661473i	−0.966122	−	0.258086i	$-0.916908\pi$
$541$	−13.3316	+	15.3855i	−0.573170	+	0.661473i	0.392952	+	0.919559i	$0.371454\pi$
$542$		0			0
$543$	3.92318	−	10.5184i	0.168360	−	0.451390i
$544$		0			0
$545$	−6.53753	+	5.42597i	−0.280037	+	0.232423i
$546$		0			0
$547$	−34.7896	+	12.9758i	−1.48749	+	0.554807i	−0.956286	−	0.292434i	$-0.905535\pi$
$547$	−34.7896	+	12.9758i	−1.48749	+	0.554807i	−0.531209	+	0.847241i	$0.678262\pi$
$548$		0			0
$549$	1.27662	+	0.820432i	0.0544847	+	0.0350152i
$550$		0			0
$551$		−	1.28988i		−	0.0549507i
$552$		0			0
$553$	−24.1570	+	24.1570i	−1.02726	+	1.02726i
$554$		0			0
$555$	2.22586	+	5.16142i	0.0944824	+	0.219090i
$556$		0			0
$557$	2.38960	+	6.40675i	0.101250	+	0.271463i	0.977691	−	0.210046i	$-0.0673615\pi$
$557$	2.38960	+	6.40675i	0.101250	+	0.271463i	−0.876441	+	0.481509i	$0.840089\pi$
$558$		0			0
$559$	−33.1827	−	9.74332i	−1.40348	−	0.412099i
$560$		0			0
$561$	0.0996121	+	0.218120i	0.00420563	+	0.00920904i
$562$		0			0
$563$	−21.9589	+	1.57053i	−0.925456	+	0.0661899i	−0.525926	−	0.850530i	$-0.676281\pi$
$563$	−21.9589	+	1.57053i	−0.925456	+	0.0661899i	−0.399530	+	0.916720i	$0.630827\pi$
$564$		0			0
$565$	−32.1401	+	16.6734i	−1.35214	+	0.701454i
$566$		0			0
$567$	−5.81523	+	26.7322i	−0.244217	+	1.12265i
$568$		0			0
$569$	1.15072	+	8.00345i	0.0482408	+	0.335522i	0.999622	+	0.0275051i	$0.00875624\pi$
$569$	1.15072	+	8.00345i	0.0482408	+	0.335522i	−0.951381	+	0.308017i	$0.900335\pi$
$570$		0			0
$571$	4.51900	+	0.649734i	0.189114	+	0.0271905i	0.236221	−	0.971699i	$-0.424091\pi$
$571$	4.51900	+	0.649734i	0.189114	+	0.0271905i	−0.0471068	+	0.998890i	$0.515000\pi$
$572$		0			0
$573$	0.131603	−	1.84005i	0.00549778	−	0.0768690i
$574$		0			0
$575$	2.99366	+	23.7916i	0.124844	+	0.992176i
$576$		0			0
$577$	2.18226	−	30.5120i	0.0908486	−	1.27023i	−0.723692	−	0.690123i	$-0.757556\pi$
$577$	2.18226	−	30.5120i	0.0908486	−	1.27023i	0.814541	−	0.580106i	$-0.196989\pi$
$578$		0			0
$579$	−2.16590	−	0.311410i	−0.0900118	−	0.0129417i
$580$		0			0
$581$	0.537614	+	3.73918i	0.0223040	+	0.155128i
$582$		0			0
$583$	0.594213	−	2.73155i	0.0246098	−	0.113129i
$584$		0			0
$585$	30.8236	−	15.9904i	1.27440	−	0.661121i
$586$		0			0
$587$	−25.0888	+	1.79439i	−1.03553	+	0.0740622i	−0.578738	−	0.815514i	$-0.696455\pi$
$587$	−25.0888	+	1.79439i	−1.03553	+	0.0740622i	−0.456787	+	0.889576i	$0.651000\pi$
$588$		0			0
$589$	−4.54068	−	9.94270i	−0.187095	−	0.409682i
$590$		0			0
$591$	0.907402	+	0.266437i	0.0373255	+	0.0109598i
$592$		0			0
$593$	−2.59676	−	6.96219i	−0.106636	−	0.285903i	0.872662	−	0.488324i	$-0.162392\pi$
$593$	−2.59676	−	6.96219i	−0.106636	−	0.285903i	−0.979299	+	0.202421i	$0.935119\pi$
$594$		0			0
$595$	7.45244	+	17.2810i	0.305520	+	0.708453i
$596$		0			0
$597$	−8.77909	+	8.77909i	−0.359304	+	0.359304i
$598$		0			0
$599$			10.5868i			0.432564i	0.976331	+	0.216282i	$0.0693931\pi$
$599$			10.5868i			0.432564i	−0.976331	+	0.216282i	$0.930607\pi$
$600$		0			0
$601$	4.36855	+	2.80749i	0.178197	+	0.114520i	0.626698	−	0.779262i	$-0.284406\pi$
$601$	4.36855	+	2.80749i	0.178197	+	0.114520i	−0.448502	+	0.893782i	$0.648042\pi$
$602$		0			0
$603$	16.0285	−	5.97831i	0.652730	−	0.243456i
$604$		0			0
$605$	18.8303	−	15.6287i	0.765562	−	0.635395i
$606$		0			0
$607$	6.88291	−	18.4538i	0.279369	−	0.749016i	−0.719163	−	0.694842i	$-0.755474\pi$
$607$	6.88291	−	18.4538i	0.279369	−	0.749016i	0.998531	−	0.0541748i	$-0.0172528\pi$
$608$		0			0
$609$	−1.15448	+	1.33234i	−0.0467818	+	0.0539890i
$610$		0			0
$611$	−22.1118	+	6.49260i	−0.894546	+	0.262662i
$612$		0			0
$613$	34.5648	+	7.51911i	1.39606	+	0.303694i	0.846779	−	0.531945i	$-0.178539\pi$
$613$	34.5648	+	7.51911i	1.39606	+	0.303694i	0.549279	+	0.835639i	$0.314902\pi$
$614$		0			0
$615$	−4.03244	+	1.40718i	−0.162604	+	0.0567429i
$616$		0			0
$617$	4.14989	+	5.54361i	0.167068	+	0.223177i	0.876260	−	0.481838i	$-0.160031\pi$
$617$	4.14989	+	5.54361i	0.167068	+	0.223177i	−0.709192	+	0.705016i	$0.750940\pi$
$618$		0			0
$619$	4.31757	+	4.98274i	0.173538	+	0.200273i	0.835855	−	0.548950i	$-0.184972\pi$
$619$	4.31757	+	4.98274i	0.173538	+	0.200273i	−0.662317	+	0.749223i	$0.730427\pi$
$620$		0			0
$621$	−4.17362	+	12.1006i	−0.167482	+	0.485580i
$622$		0			0
$623$	−48.2521	−	3.45106i	−1.93318	−	0.138264i
$624$		0			0
$625$	−14.7086	−	20.2153i	−0.588345	−	0.808610i
$626$		0			0
$627$	−0.0847943	+	0.113272i	−0.00338636	+	0.00452365i
$628$		0			0
$629$	−6.46483	−	10.0595i	−0.257770	−	0.401097i
$630$		0			0
$631$	5.42840	+	18.4874i	0.216101	+	0.735974i	0.994173	+	0.107798i	$0.0343799\pi$
$631$	5.42840	+	18.4874i	0.216101	+	0.735974i	−0.778071	+	0.628176i	$0.783802\pi$
$632$		0			0
$633$	−0.102328	−	1.43074i	−0.00406719	−	0.0568667i
$634$		0			0
$635$	−9.49992	−	13.2689i	−0.376993	−	0.526562i
$636$		0			0
$637$	20.6074	+	37.7397i	0.816497	+	1.49530i
$638$		0			0
$639$	27.9576	+	12.7678i	1.10598	+	0.505086i
$640$		0			0
$641$	−27.0532	+	42.0956i	−1.06854	+	1.66268i	−0.405484	+	0.914102i	$0.632897\pi$
$641$	−27.0532	+	42.0956i	−1.06854	+	1.66268i	−0.663052	+	0.748573i	$0.730739\pi$
$642$		0			0
$643$	−13.9341	−	13.9341i	−0.549508	−	0.549508i	0.376790	−	0.926299i	$-0.377028\pi$
$643$	−13.9341	−	13.9341i	−0.549508	−	0.549508i	−0.926299	+	0.376790i	$0.877028\pi$
$644$		0			0
$645$	−3.57440	+	5.31033i	−0.140742	+	0.209094i
$646$		0			0
$647$	3.92385	+	18.0376i	0.154262	+	0.709132i	0.987680	+	0.156488i	$0.0500174\pi$
$647$	3.92385	+	18.0376i	0.154262	+	0.709132i	−0.833418	+	0.552644i	$0.813619\pi$
$648$		0			0
$649$	0.794192	−	1.73904i	0.0311748	−	0.0682632i
$650$		0			0
$651$	−4.20885	+	14.3340i	−0.164958	+	0.561794i
$652$		0			0
$653$	36.5296	+	13.6249i	1.42952	+	0.533182i	0.940710	−	0.339211i	$-0.110160\pi$
$653$	36.5296	+	13.6249i	1.42952	+	0.533182i	0.488805	+	0.872393i	$0.337433\pi$
$654$		0			0
$655$	7.35770	+	27.1815i	0.287489	+	1.06207i
$656$		0			0
$657$	23.6498	+	12.9138i	0.922666	+	0.503814i
$658$		0			0
$659$	−23.5469	+	15.1327i	−0.917258	+	0.589486i	−0.911861	−	0.410499i	$-0.865354\pi$
$659$	−23.5469	+	15.1327i	−0.917258	+	0.589486i	−0.00539743	+	0.999985i	$0.501718\pi$
$660$		0			0
$661$	41.9082	−	6.02549i	1.63004	−	0.234364i	0.734262	−	0.678867i	$-0.237529\pi$
$661$	41.9082	−	6.02549i	1.63004	−	0.234364i	0.895778	+	0.444502i	$0.146619\pi$
$662$		0			0
$663$	4.51255	−	3.37805i	0.175253	−	0.131193i
$664$		0			0
$665$	−6.84231	+	8.74657i	−0.265334	+	0.339178i
$666$		0			0
$667$	3.53253	−	3.21816i	0.136780	−	0.124608i
$668$		0			0
$669$	−0.644446	+	0.558416i	−0.0249157	+	0.0215896i
$670$		0			0
$671$	−0.0183635	+	0.127721i	−0.000708914	+	0.00493061i
$672$		0			0
$673$	−15.0400	−	11.2588i	−0.579748	−	0.433994i	0.268737	−	0.963214i	$-0.413394\pi$
$673$	−15.0400	−	11.2588i	−0.579748	−	0.433994i	−0.848485	+	0.529220i	$0.822485\pi$
$674$		0			0
$675$	−2.28018	−	13.1488i	−0.0877641	−	0.506098i
$676$		0			0
$677$	−11.5755	+	21.1989i	−0.444881	+	0.814739i	−0.999853	−	0.0171298i	$-0.994547\pi$
$677$	−11.5755	+	21.1989i	−0.444881	+	0.814739i	0.554972	+	0.831869i	$0.312729\pi$
$678$		0			0
$679$	−15.3916	−	13.3369i	−0.590674	−	0.511822i
$680$		0			0
$681$	−9.88471	+	4.51420i	−0.378783	+	0.172984i
$682$		0			0
$683$	28.9807	−	15.8246i	1.10891	−	0.605513i	0.182949	−	0.983122i	$-0.441436\pi$
$683$	28.9807	−	15.8246i	1.10891	−	0.605513i	0.925965	+	0.377610i	$0.123254\pi$
$684$		0			0
$685$	−32.5708	−	7.81360i	−1.24447	−	0.298542i
$686$		0			0
$687$	12.2927	−	2.67412i	0.468997	−	0.102024i
$688$		0			0
$689$	−65.7141			−2.50351
$690$		0			0
$691$	22.8941			0.870934			0.435467	−	0.900205i	$-0.356583\pi$
$691$	22.8941			0.870934			0.435467	+	0.900205i	$0.356583\pi$
$692$		0			0
$693$	−2.47642	+	0.538712i	−0.0940713	+	0.0204640i
$694$		0			0
$695$	38.6667	−	23.7042i	1.46671	−	0.899152i
$696$		0			0
$697$	7.97439	−	4.35435i	0.302052	−	0.164933i
$698$		0			0
$699$	−7.96563	+	3.63778i	−0.301288	+	0.137593i
$700$		0			0
$701$	3.88850	+	3.36940i	0.146867	+	0.127261i	0.725195	−	0.688543i	$-0.241749\pi$
$701$	3.88850	+	3.36940i	0.146867	+	0.127261i	−0.578329	+	0.815804i	$0.696295\pi$
$702$		0			0
$703$	3.38157	−	6.19288i	0.127538	−	0.233569i
$704$		0			0
$705$	−0.0906232	+	4.26459i	−0.00341307	+	0.160614i
$706$		0			0
$707$	35.1073	+	26.2810i	1.32034	+	0.988397i
$708$		0			0
$709$	−5.36626	+	37.3232i	−0.201534	+	1.40170i	0.598200	+	0.801347i	$0.295883\pi$
$709$	−5.36626	+	37.3232i	−0.201534	+	1.40170i	−0.799734	+	0.600355i	$0.795026\pi$
$710$		0			0
$711$	−18.7585	+	16.2544i	−0.703500	+	0.609586i
$712$		0			0
$713$	15.9009	−	37.2417i	0.595494	−	1.39471i
$714$		0			0
$715$	2.32556	+	1.81925i	0.0869710	+	0.0680361i
$716$		0			0
$717$	−0.400437	+	0.299763i	−0.0149546	+	0.0111949i
$718$		0			0
$719$	13.3152	−	1.91444i	0.496573	−	0.0713964i	0.110522	−	0.993874i	$-0.464748\pi$
$719$	13.3152	−	1.91444i	0.496573	−	0.0713964i	0.386051	+	0.922477i	$0.373839\pi$
$720$		0			0
$721$	−9.70866	+	6.23937i	−0.361569	+	0.232366i
$722$		0			0
$723$	11.6961	+	6.38653i	0.434981	+	0.237518i
$724$		0			0
$725$	−1.60542	+	4.71632i	−0.0596236	+	0.175160i
$726$		0			0
$727$	−17.3415	−	6.46805i	−0.643161	−	0.239887i	0.00665558	−	0.999978i	$-0.497881\pi$
$727$	−17.3415	−	6.46805i	−0.643161	−	0.239887i	−0.649816	+	0.760091i	$0.725154\pi$
$728$		0			0
$729$	−4.55947	+	15.5281i	−0.168869	+	0.575115i
$730$		0			0
$731$	5.65702	−	12.3871i	0.209232	−	0.458155i
$732$		0			0
$733$	6.98390	+	32.1045i	0.257956	+	1.18581i	0.905690	+	0.423940i	$0.139353\pi$
$733$	6.98390	+	32.1045i	0.257956	+	1.18581i	−0.647734	+	0.761867i	$0.724283\pi$
$734$		0			0
$735$	7.81127	−	1.52619i	0.288123	−	0.0562945i
$736$		0			0
$737$	1.02857	+	1.02857i	0.0378877	+	0.0378877i
$738$		0			0
$739$	6.46485	−	10.0595i	0.237813	−	0.370045i	−0.701748	−	0.712425i	$-0.747597\pi$
$739$	6.46485	−	10.0595i	0.237813	−	0.370045i	0.939561	+	0.342380i	$0.111233\pi$
$740$		0			0
$741$	3.02561	+	1.38175i	0.111149	+	0.0507598i
$742$		0			0
$743$	7.52859	+	13.7876i	0.276197	+	0.505817i	0.978549	−	0.206012i	$-0.0660487\pi$
$743$	7.52859	+	13.7876i	0.276197	+	0.505817i	−0.702352	+	0.711829i	$0.747867\pi$
$744$		0			0
$745$	−20.6514	−	3.41851i	−0.756608	−	0.125245i
$746$		0			0
$747$	0.195799	+	2.73763i	0.00716391	+	0.100165i
$748$		0			0
$749$	6.77269	+	23.0657i	0.247469	+	0.842801i
$750$		0			0
$751$	3.75625	+	5.84483i	0.137067	+	0.213281i	0.903001	−	0.429639i	$-0.141359\pi$
$751$	3.75625	+	5.84483i	0.137067	+	0.213281i	−0.765933	+	0.642920i	$0.777723\pi$
$752$		0			0
$753$	−5.04770	+	6.74294i	−0.183948	+	0.245726i
$754$		0			0
$755$	−23.8900	−	21.6063i	−0.869446	−	0.786334i
$756$		0			0
$757$	−16.0005	−	1.14438i	−0.581547	−	0.0415931i	−0.222533	−	0.974925i	$-0.571432\pi$
$757$	−16.0005	−	1.14438i	−0.581547	−	0.0415931i	−0.359014	+	0.933332i	$0.616887\pi$
$758$		0			0
$759$	−0.521769	+	0.0503839i	−0.0189390	+	0.00182882i
$760$		0			0
$761$	−7.97187	−	9.20003i	−0.288980	−	0.333501i	0.592634	−	0.805472i	$-0.298088\pi$
$761$	−7.97187	−	9.20003i	−0.288980	−	0.333501i	−0.881614	+	0.471971i	$0.843543\pi$
$762$		0			0
$763$	−8.73526	−	11.6689i	−0.316238	−	0.422444i
$764$		0			0
$765$	4.50504	+	12.9097i	0.162880	+	0.466752i
$766$		0			0
$767$	−43.9149	−	9.55309i	−1.58567	−	0.344942i
$768$		0			0
$769$	−40.0976	+	11.7737i	−1.44596	+	0.424571i	−0.908202	−	0.418531i	$-0.862545\pi$
$769$	−40.0976	+	11.7737i	−1.44596	+	0.424571i	−0.537754	+	0.843102i	$0.680727\pi$
$770$		0			0
$771$	−5.08685	+	5.87054i	−0.183198	+	0.211422i
$772$		0			0
$773$	6.66627	−	17.8730i	0.239769	−	0.642846i	−0.760208	−	0.649680i	$-0.774903\pi$
$773$	6.66627	−	17.8730i	0.239769	−	0.642846i	0.999977	+	0.00683443i	$0.00217548\pi$
$774$		0			0
$775$	4.22763	+	42.0060i	0.151861	+	1.50890i
$776$		0			0
$777$	−9.03568	+	3.37014i	−0.324153	+	0.120903i
$778$		0			0
$779$	4.51022	+	2.89854i	0.161595	+	0.103851i
$780$		0			0
$781$			2.61339i			0.0935145i
$782$		0			0
$783$	−1.88051	+	1.88051i	−0.0672039	+	0.0672039i
$784$		0			0
$785$	−2.67895	+	6.74151i	−0.0956157	+	0.240615i
$786$		0			0
$787$	−2.57481	−	6.90333i	−0.0917821	−	0.246077i	0.882945	−	0.469477i	$-0.155557\pi$
$787$	−2.57481	−	6.90333i	−0.0917821	−	0.246077i	−0.974727	+	0.223399i	$0.928285\pi$
$788$		0			0
$789$	12.6656	+	3.71897i	0.450909	+	0.132399i
$790$		0			0
$791$	−25.8059	−	56.5071i	−0.917553	−	2.00916i
$792$		0			0
$793$	3.02556	−	0.216392i	0.107441	−	0.00768431i
$794$		0			0
$795$	−3.67398	+	11.5952i	−0.130303	+	0.411239i
$796$		0			0
$797$	4.05149	−	18.6244i	0.143511	−	0.659710i	−0.848033	−	0.529943i	$-0.822213\pi$
$797$	4.05149	−	18.6244i	0.143511	−	0.659710i	0.991544	−	0.129767i	$-0.0414231\pi$
$798$		0			0
$799$	−1.29142	−	8.98201i	−0.0456871	−	0.317761i
$800$		0			0
$801$	−34.7892	−	5.00193i	−1.22921	−	0.176734i
$802$		0			0
$803$	−0.163452	+	2.28536i	−0.00576810	+	0.0806485i
$804$		0			0
$805$	−41.0250	+	3.08341i	−1.44594	+	0.108676i
$806$		0			0
$807$	0.494358	−	6.91203i	0.0174022	−	0.243315i
$808$		0			0
$809$	42.7075	+	6.14041i	1.50151	+	0.215885i	0.843504	−	0.537123i	$-0.180489\pi$
$809$	42.7075	+	6.14041i	1.50151	+	0.215885i	0.658011	+	0.753008i	$0.271398\pi$
$810$		0			0
$811$	1.77326	+	12.3333i	0.0622677	+	0.433081i	0.996979	+	0.0776730i	$0.0247490\pi$
$811$	1.77326	+	12.3333i	0.0622677	+	0.433081i	−0.934711	+	0.355408i	$0.884342\pi$
$812$		0			0
$813$	−1.50134	+	6.90155i	−0.0526543	+	0.242048i
$814$		0			0
$815$	−3.47963	−	6.70745i	−0.121886	−	0.234952i
$816$		0			0
$817$	8.01505	−	0.573248i	0.280411	−	0.0200554i
$818$		0			0
$819$	24.7488	+	54.1924i	0.864794	+	1.89364i
$820$		0			0
$821$	3.78553	+	1.11153i	0.132116	+	0.0387928i	0.347122	−	0.937820i	$-0.387159\pi$
$821$	3.78553	+	1.11153i	0.132116	+	0.0387928i	−0.215006	+	0.976613i	$0.568977\pi$
$822$		0			0
$823$	12.8463	+	34.4422i	0.447793	+	1.20058i	0.943290	+	0.331970i	$0.107713\pi$
$823$	12.8463	+	34.4422i	0.447793	+	1.20058i	−0.495497	+	0.868610i	$0.665014\pi$
$824$		0			0
$825$	0.451024	−	0.308631i	0.0157026	−	0.0107452i
$826$		0			0
$827$	7.70901	−	7.70901i	0.268069	−	0.268069i	−0.560253	−	0.828322i	$-0.689296\pi$
$827$	7.70901	−	7.70901i	0.268069	−	0.268069i	0.828322	+	0.560253i	$0.189296\pi$
$828$		0			0
$829$		−	28.4563i		−	0.988327i	−0.869369	−	0.494164i	$-0.835474\pi$
$829$		−	28.4563i		−	0.988327i	0.869369	−	0.494164i	$-0.164526\pi$
$830$		0			0
$831$	6.12902	+	3.93888i	0.212613	+	0.136638i
$832$		0			0
$833$	−15.8641	+	5.91699i	−0.549657	+	0.205012i
$834$		0			0
$835$	35.8280	+	3.32888i	1.23988	+	0.115201i
$836$		0			0
$837$	−7.87558	+	21.1153i	−0.272220	+	0.729850i
$838$		0			0
$839$	13.2472	−	15.2881i	0.457346	−	0.527805i	−0.479503	−	0.877540i	$-0.659183\pi$
$839$	13.2472	−	15.2881i	0.457346	−	0.527805i	0.936849	+	0.349735i	$0.113728\pi$
$840$		0			0
$841$	−26.8727	+	7.89053i	−0.926644	+	0.272087i
$842$		0			0
$843$	5.05956	+	1.10064i	0.174261	+	0.0379081i
$844$		0			0
$845$	17.5336	−	36.3301i	0.603174	−	1.24979i
$846$		0			0
$847$	25.1605	+	33.6106i	0.864527	+	1.15487i
$848$		0			0
$849$	−4.46506	−	5.15295i	−0.153240	−	0.176849i
$850$		0			0
$851$	25.3970	−	6.18989i	0.870597	−	0.212187i
$852$		0			0
$853$	−54.2301	−	3.87862i	−1.85680	−	0.132801i	−0.902321	−	0.431065i	$-0.858138\pi$
$853$	−54.2301	−	3.87862i	−1.85680	−	0.132801i	−0.954484	+	0.298263i	$0.903593\pi$
$854$		0			0
$855$	−5.41193	+	5.98394i	−0.185084	+	0.204647i
$856$		0			0
$857$	5.81704	−	7.77065i	0.198706	−	0.265441i	−0.690110	−	0.723705i	$-0.742438\pi$
$857$	5.81704	−	7.77065i	0.198706	−	0.265441i	0.888816	+	0.458264i	$0.151529\pi$
$858$		0			0
$859$	−24.8725	−	38.7023i	−0.848637	−	1.32051i	−0.945638	−	0.325221i	$-0.894561\pi$
$859$	−24.8725	−	38.7023i	−0.848637	−	1.32051i	0.0970009	−	0.995284i	$-0.469075\pi$
$860$		0			0
$861$	−2.06441	−	7.03073i	−0.0703548	−	0.239606i
$862$		0			0
$863$	−3.10852	−	43.4627i	−0.105815	−	1.47949i	−0.722003	−	0.691889i	$-0.756779\pi$
$863$	−3.10852	−	43.4627i	−0.105815	−	1.47949i	0.616188	−	0.787599i	$-0.288676\pi$
$864$		0			0
$865$	−31.7883	+	22.7589i	−1.08084	+	0.773826i
$866$		0			0
$867$	−2.69363	−	4.93301i	−0.0914805	−	0.167534i
$868$		0			0
$869$	−1.91981	−	0.876746i	−0.0651250	−	0.0297416i
$870$		0			0
$871$	18.4869	−	28.7662i	0.626405	−	0.974705i
$872$		0			0
$873$	−10.4629	−	10.4629i	−0.354116	−	0.354116i
$874$		0			0
$875$	35.9045	−	23.4649i	1.21379	−	0.793259i
$876$		0			0
$877$	−2.99519	−	13.7687i	−0.101140	−	0.464935i	−0.999662	−	0.0260050i	$-0.991721\pi$
$877$	−2.99519	−	13.7687i	−0.101140	−	0.464935i	0.898522	−	0.438930i	$-0.144642\pi$
$878$		0			0
$879$	3.29464	−	7.21426i	0.111126	−	0.243331i
$880$		0			0
$881$	5.98857	−	20.3952i	0.201760	−	0.687131i	−0.794994	−	0.606618i	$-0.792526\pi$
$881$	5.98857	−	20.3952i	0.201760	−	0.687131i	0.996754	−	0.0805134i	$-0.0256560\pi$
$882$		0			0
$883$	−14.9557	−	5.57819i	−0.503299	−	0.187721i	0.0849739	−	0.996383i	$-0.472919\pi$
$883$	−14.9557	−	5.57819i	−0.503299	−	0.187721i	−0.588273	+	0.808662i	$0.700192\pi$
$884$		0			0
$885$	−4.14085	+	7.21464i	−0.139193	+	0.242517i
$886$		0			0
$887$	−23.4544	−	12.8071i	−0.787522	−	0.430020i	0.0345498	−	0.999403i	$-0.489000\pi$
$887$	−23.4544	−	12.8071i	−0.787522	−	0.430020i	−0.822072	+	0.569383i	$0.807182\pi$
$888$		0			0
$889$	23.5538	−	15.1371i	0.789969	−	0.507682i
$890$		0			0
$891$	−1.67288	+	0.240524i	−0.0560436	+	0.00805785i
$892$		0			0
$893$	4.28656	−	3.20888i	0.143444	−	0.107381i
$894$		0			0
$895$	2.20264	+	18.0316i	0.0736263	+	0.602729i
$896$		0			0
$897$	3.76457	+	11.7335i	0.125695	+	0.391769i
$898$		0			0
$899$	6.35839	−	5.50958i	0.212064	−	0.183755i
$900$		0			0
$901$	3.68251	−	25.6124i	0.122682	−	0.853274i
$902$		0			0
$903$	−8.79196	−	6.58158i	−0.292578	−	0.219021i
$904$		0			0
$905$	54.4188	+	1.15641i	1.80894	+	0.0384402i
$906$		0			0
$907$	0.0833377	−	0.152622i	0.00276718	−	0.00506772i	−0.876292	−	0.481781i	$-0.839990\pi$
$907$	0.0833377	−	0.152622i	0.00276718	−	0.00506772i	0.879059	+	0.476713i	$0.158172\pi$
$908$		0			0
$909$	24.0798	+	20.8653i	0.798678	+	0.692058i
$910$		0			0
$911$	25.6474	−	11.7128i	0.849738	−	0.388062i	0.0575521	−	0.998343i	$-0.481670\pi$
$911$	25.6474	−	11.7128i	0.849738	−	0.388062i	0.792186	+	0.610280i	$0.208943\pi$
$912$		0			0
$913$	−0.204828	+	0.111844i	−0.00677881	+	0.00370151i
$914$		0			0
$915$	0.130972	−	0.545955i	0.00432981	−	0.0180487i
$916$		0			0
$917$	−47.2091	+	10.2697i	−1.55898	+	0.339136i
$918$		0			0
$919$	6.39970			0.211107			0.105553	−	0.994414i	$-0.466339\pi$
$919$	6.39970			0.211107			0.105553	+	0.994414i	$0.466339\pi$
$920$		0			0
$921$	9.90768			0.326469
$922$		0			0
$923$	60.0306	−	13.0589i	1.97593	−	0.429838i
$924$		0			0
$925$	−20.0722	+	18.4349i	−0.659970	+	0.606136i
$926$		0			0
$927$	−7.35920	+	4.01843i	−0.241708	+	0.131982i
$928$		0			0
$929$	−3.01153	+	1.37532i	−0.0988051	+	0.0451228i	−0.464204	−	0.885728i	$-0.653660\pi$
$929$	−3.01153	+	1.37532i	−0.0988051	+	0.0451228i	0.365399	+	0.930851i	$0.380932\pi$
$930$		0			0
$931$	−7.55066	−	6.54268i	−0.247463	−	0.214428i
$932$		0			0
$933$	−4.83908	+	8.86212i	−0.158424	+	0.290133i
$934$		0			0
$935$	−0.839383	+	0.804451i	−0.0274508	+	0.0263084i
$936$		0			0
$937$	−3.62975	−	2.71720i	−0.118579	−	0.0887669i	0.538342	−	0.842726i	$-0.319051\pi$
$937$	−3.62975	−	2.71720i	−0.118579	−	0.0887669i	−0.656921	+	0.753959i	$0.728142\pi$
$938$		0			0
$939$	2.31071	−	16.0714i	0.0754073	−	0.524469i
$940$		0			0
$941$	26.6137	−	23.0609i	0.867582	−	0.751764i	−0.102451	−	0.994738i	$-0.532668\pi$
$941$	26.6137	−	23.0609i	0.867582	−	0.751764i	0.970033	+	0.242974i	$0.0781229\pi$
$942$		0			0
$943$	3.31460	+	19.5836i	0.107938	+	0.637730i
$944$		0			0
$945$	22.7270	−	2.77621i	0.739309	−	0.0903102i
$946$		0			0
$947$	23.8323	−	17.8406i	0.774444	−	0.579742i	−0.137286	−	0.990531i	$-0.543838\pi$
$947$	23.8323	−	17.8406i	0.774444	−	0.579742i	0.911730	+	0.410790i	$0.134747\pi$
$948$		0			0
$949$	53.3123	−	7.66516i	1.73059	−	0.248821i
$950$		0			0
$951$	3.83154	−	2.46238i	0.124246	−	0.0798481i
$952$		0			0
$953$	3.22753	+	1.76237i	0.104550	+	0.0570886i	0.530673	−	0.847577i	$-0.321939\pi$
$953$	3.22753	+	1.76237i	0.104550	+	0.0570886i	−0.426123	+	0.904665i	$0.640121\pi$
$954$		0			0
$955$	8.63362	−	2.33701i	0.279377	−	0.0756239i
$956$		0			0
$957$	−0.102044	−	0.0380603i	−0.00329860	−	0.00123032i
$958$		0			0
$959$	16.1903	−	55.1390i	0.522811	−	1.78053i
$960$		0			0
$961$	16.7392	−	36.6537i	0.539973	−	1.18238i
$962$		0			0
$963$	3.71261	+	17.0666i	0.119637	+	0.549963i
$964$		0			0
$965$	−2.03444	−	10.4126i	−0.0654911	−	0.335193i
$966$		0			0
$967$	−27.0045	−	27.0045i	−0.868407	−	0.868407i	0.123889	−	0.992296i	$-0.460463\pi$
$967$	−27.0045	−	27.0045i	−0.868407	−	0.868407i	−0.992296	+	0.123889i	$0.960463\pi$
$968$		0			0
$969$	−0.708095	+	1.10182i	−0.0227473	+	0.0353955i
$970$		0			0
$971$	16.5576	+	7.56161i	0.531359	+	0.242664i	0.662981	−	0.748636i	$-0.269291\pi$
$971$	16.5576	+	7.56161i	0.531359	+	0.242664i	−0.131621	+	0.991300i	$0.542018\pi$
$972$		0			0
$973$	37.2921	+	68.2953i	1.19553	+	2.18945i
$974$		0			0
$975$	−9.34310	−	8.81799i	−0.299219	−	0.282402i
$976$		0			0
$977$	−1.55320	−	21.7165i	−0.0496911	−	0.694773i	−0.959850	−	0.280514i	$-0.909495\pi$
$977$	−1.55320	−	21.7165i	−0.0496911	−	0.694773i	0.910159	−	0.414259i	$-0.135959\pi$
$978$		0			0
$979$	−0.841967	−	2.86748i	−0.0269094	−	0.0916449i
$980$		0			0
$981$	−5.72558	−	8.90917i	−0.182804	−	0.284448i
$982$		0			0
$983$	−16.7690	+	22.4008i	−0.534848	+	0.714473i	−0.983837	−	0.179064i	$-0.942693\pi$
$983$	−16.7690	+	22.4008i	−0.534848	+	0.714473i	0.448990	+	0.893537i	$0.351784\pi$
$984$		0			0
$985$	0.229870	+	4.57955i	0.00732428	+	0.145917i
$986$		0			0
$987$	−7.29970	−	0.522085i	−0.232352	−	0.0166182i
$988$		0			0
$989$	21.5670	+	20.5202i	0.685790	+	0.652506i
$990$		0			0
$991$	24.5436	+	28.3248i	0.779652	+	0.899767i	0.997084	−	0.0763088i	$-0.0243135\pi$
$991$	24.5436	+	28.3248i	0.779652	+	0.899767i	−0.217432	+	0.976075i	$0.569768\pi$
$992$		0			0
$993$	9.52638	+	12.7258i	0.302311	+	0.403840i
$994$		0			0
$995$	−54.2136	−	26.1645i	−1.71869	−	0.829470i
$996$		0			0
$997$	38.1845	+	8.30652i	1.20931	+	0.263070i	0.771638	−	0.636062i	$-0.219438\pi$
$997$	38.1845	+	8.30652i	1.20931	+	0.263070i	0.437676	+	0.899133i	$0.355802\pi$
$998$		0			0
$999$	−13.9586	+	4.09860i	−0.441629	+	0.129674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.217.6	yes	240
5.3	odd	4	inner	460.2.x.a.33.6	✓	240
23.7	odd	22	inner	460.2.x.a.237.6	yes	240
115.53	even	44	inner	460.2.x.a.53.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.33.6	✓	240	5.3	odd	4	inner
460.2.x.a.53.6	yes	240	115.53	even	44	inner
460.2.x.a.217.6	yes	240	1.1	even	1	trivial
460.2.x.a.237.6	yes	240	23.7	odd	22	inner

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.450644 - 0.0980316i) q^{3} +(1.16867 + 1.90636i) q^{5} +(-3.36712 + 1.83859i) q^{7} +(-2.53543 + 1.15789i) q^{9} +(-0.179116 - 0.155205i) q^{11} +(-2.67009 + 4.88990i) q^{13} +(0.713538 + 0.744522i) q^{15} +(-1.75624 - 1.31470i) q^{17} +(0.184229 - 1.28134i) q^{19} +(-1.33713 + 1.15863i) q^{21} +(3.96880 - 2.69233i) q^{23} +(-2.26841 + 4.45582i) q^{25} +(-2.13665 + 1.59948i) q^{27} +(0.986272 - 0.141805i) q^{29} +(7.10324 - 4.56498i) q^{31} +(-0.0959324 - 0.0523831i) q^{33} +(-7.44006 - 4.27023i) q^{35} +(5.10698 + 1.90481i) q^{37} +(-0.723895 + 2.46536i) q^{39} +(-1.72046 + 3.76728i) q^{41} +(1.31946 + 6.06548i) q^{43} +(-5.17044 - 3.48024i) q^{45} +(2.92484 + 2.92484i) q^{47} +(4.17260 - 6.49270i) q^{49} +(-0.920321 - 0.420297i) q^{51} +(5.65269 + 10.3521i) q^{53} +(0.0865483 - 0.522843i) q^{55} +(-0.0425903 - 0.595490i) q^{57} +(2.27261 + 7.73978i) q^{59} +(-0.294346 - 0.458011i) q^{61} +(6.40820 - 8.56035i) q^{63} +(-12.4424 + 0.624545i) q^{65} +(-6.12185 - 0.437844i) q^{67} +(1.52458 - 1.60235i) q^{69} +(-7.22100 - 8.33348i) q^{71} +(-5.79341 - 7.73909i) q^{73} +(-0.585435 + 2.23036i) q^{75} +(0.888462 + 0.193273i) q^{77} +(8.54432 - 2.50884i) q^{79} +(4.66983 - 5.38927i) q^{81} +(0.344112 - 0.922600i) q^{83} +(0.453831 - 4.88448i) q^{85} +(0.430556 - 0.160589i) q^{87} +(10.6079 + 6.81727i) q^{89} -21.3741i q^{91} +(2.75352 - 2.75352i) q^{93} +(2.65801 - 1.14626i) q^{95} +(1.85518 + 4.97392i) q^{97} +(0.633845 + 0.186114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75}+ \cdots - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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