LMFDB - Embedded newform 460.2.x.a.333.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.67311849298$
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			333.7
Character	$\chi$	$=$	460.333
Dual form			460.2.x.a.297.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0673917 + 0.0504488i) q^{3} +(2.04891 - 0.895537i) q^{5} +(0.0449089 - 0.627908i) q^{7} +(-0.843201 + 2.87168i) q^{9} +O(q^{10})$	\(q+(-0.0673917 + 0.0504488i) q^{3} +(2.04891 - 0.895537i) q^{5} +(0.0449089 - 0.627908i) q^{7} +(-0.843201 + 2.87168i) q^{9} +(0.911155 - 1.41778i) q^{11} +(4.25245 - 0.304142i) q^{13} +(-0.0929004 + 0.163716i) q^{15} +(1.60834 - 4.31212i) q^{17} +(-0.519784 + 1.13817i) q^{19} +(0.0286507 + 0.0445813i) q^{21} +(-0.0377062 + 4.79568i) q^{23} +(3.39603 - 3.66974i) q^{25} +(-0.176304 - 0.472690i) q^{27} +(-1.05485 + 0.481736i) q^{29} +(-1.42294 - 9.89674i) q^{31} +(0.0101212 + 0.141514i) q^{33} +(-0.470301 - 1.32674i) q^{35} +(4.84002 + 8.86383i) q^{37} +(-0.271236 + 0.235028i) q^{39} +(-0.171707 + 0.0504179i) q^{41} +(2.06886 + 2.76367i) q^{43} +(0.844055 + 6.63892i) q^{45} +(2.23536 - 2.23536i) q^{47} +(6.53650 + 0.939807i) q^{49} +(0.109153 + 0.371740i) q^{51} +(3.85697 + 0.275856i) q^{53} +(0.597192 - 3.72088i) q^{55} +(-0.0223901 - 0.102925i) q^{57} +(-6.23724 - 5.40460i) q^{59} +(-10.5599 + 1.51828i) q^{61} +(1.76528 + 0.658416i) q^{63} +(8.44051 - 4.43139i) q^{65} +(-6.59682 - 1.43505i) q^{67} +(-0.239395 - 0.325091i) q^{69} +(-6.12329 + 3.93520i) q^{71} +(-8.05021 + 3.00257i) q^{73} +(-0.0437301 + 0.418635i) q^{75} +(-0.849319 - 0.635792i) q^{77} +(-11.1560 + 12.8747i) q^{79} +(-7.51767 - 4.83131i) q^{81} +(-8.02787 + 4.38355i) q^{83} +(-0.566331 - 10.2755i) q^{85} +(0.0467854 - 0.0856811i) q^{87} +(0.675621 - 4.69905i) q^{89} -2.68381i q^{91} +(0.595172 + 0.595172i) q^{93} +(-0.0457168 + 2.79748i) q^{95} +(4.53191 + 2.47461i) q^{97} +(3.30314 + 3.81202i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{22}\right)$

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
$3$	−0.0673917	+	0.0504488i	−0.0389086	+	0.0291266i	−0.618555	−	0.785742i	$-0.712282\pi$
$3$	−0.0673917	+	0.0504488i	−0.0389086	+	0.0291266i	0.579646	+	0.814868i	$0.303191\pi$
$4$		0			0
$5$	2.04891	−	0.895537i	0.916298	−	0.400496i
$5$	2.04891	−	0.895537i	0.916298	−	0.400496i
$6$		0			0
$7$	0.0449089	−	0.627908i	0.0169740	−	0.237327i	−0.981881	−	0.189496i	$-0.939315\pi$
$7$	0.0449089	−	0.627908i	0.0169740	−	0.237327i	0.998855	−	0.0478309i	$-0.0152309\pi$
$8$		0			0
$9$	−0.843201	+	2.87168i	−0.281067	+	0.957226i
$10$		0			0
$11$	0.911155	−	1.41778i	0.274724	−	0.427478i	−0.676286	−	0.736639i	$-0.736412\pi$
$11$	0.911155	−	1.41778i	0.274724	−	0.427478i	0.951010	+	0.309161i	$0.100048\pi$
$12$		0			0
$13$	4.25245	−	0.304142i	1.17942	−	0.0843537i	0.532173	−	0.846635i	$-0.321375\pi$
$13$	4.25245	−	0.304142i	1.17942	−	0.0843537i	0.647245	+	0.762282i	$0.275921\pi$
$14$		0			0
$15$	−0.0929004	+	0.163716i	−0.0239868	+	0.0422714i
$16$		0			0
$17$	1.60834	−	4.31212i	0.390079	−	1.04584i	−0.582410	−	0.812895i	$-0.697890\pi$
$17$	1.60834	−	4.31212i	0.390079	−	1.04584i	0.972489	−	0.232948i	$-0.0748372\pi$
$18$		0			0
$19$	−0.519784	+	1.13817i	−0.119247	+	0.261114i	−0.959837	−	0.280557i	$-0.909481\pi$
$19$	−0.519784	+	1.13817i	−0.119247	+	0.261114i	0.840591	+	0.541671i	$0.182208\pi$
$20$		0			0
$21$	0.0286507	+	0.0445813i	0.00625209	+	0.00972845i
$22$		0			0
$23$	−0.0377062	+	4.79568i	−0.00786230	+	0.999969i
$23$	−0.0377062	+	4.79568i	−0.00786230	+	0.999969i
$24$		0			0
$25$	3.39603	−	3.66974i	0.679206	−	0.733948i
$26$		0			0
$27$	−0.176304	−	0.472690i	−0.0339298	−	0.0909693i
$28$		0			0
$29$	−1.05485	+	0.481736i	−0.195882	+	0.0894561i	−0.510941	−	0.859616i	$-0.670703\pi$
$29$	−1.05485	+	0.481736i	−0.195882	+	0.0894561i	0.315059	+	0.949072i	$0.397976\pi$
$30$		0			0
$31$	−1.42294	−	9.89674i	−0.255567	−	1.77751i	−0.563518	−	0.826104i	$-0.690552\pi$
$31$	−1.42294	−	9.89674i	−0.255567	−	1.77751i	0.307951	−	0.951402i	$-0.400357\pi$
$32$		0			0
$33$	0.0101212	+	0.141514i	0.00176188	+	0.0246343i
$34$		0			0
$35$	−0.470301	−	1.32674i	−0.0794953	−	0.224260i
$36$		0			0
$37$	4.84002	+	8.86383i	0.795694	+	1.45720i	0.887193	+	0.461399i	$0.152652\pi$
$37$	4.84002	+	8.86383i	0.795694	+	1.45720i	−0.0914989	+	0.995805i	$0.529166\pi$
$38$		0			0
$39$	−0.271236	+	0.235028i	−0.0434326	+	0.0376345i
$40$		0			0
$41$	−0.171707	+	0.0504179i	−0.0268162	+	0.00787395i	−0.295113	−	0.955462i	$-0.595357\pi$
$41$	−0.171707	+	0.0504179i	−0.0268162	+	0.00787395i	0.268297	+	0.963336i	$0.413539\pi$
$42$		0			0
$43$	2.06886	+	2.76367i	0.315498	+	0.421456i	0.930057	−	0.367414i	$-0.119757\pi$
$43$	2.06886	+	2.76367i	0.315498	+	0.421456i	−0.614559	+	0.788871i	$0.710666\pi$
$44$		0			0
$45$	0.844055	+	6.63892i	0.125824	+	0.989671i
$46$		0			0
$47$	2.23536	−	2.23536i	0.326060	−	0.326060i	−0.525026	−	0.851086i	$-0.675944\pi$
$47$	2.23536	−	2.23536i	0.326060	−	0.326060i	0.851086	+	0.525026i	$0.175944\pi$
$48$		0			0
$49$	6.53650	+	0.939807i	0.933786	+	0.134258i
$50$		0			0
$51$	0.109153	+	0.371740i	0.0152844	+	0.0520540i
$52$		0			0
$53$	3.85697	+	0.275856i	0.529796	+	0.0378918i	0.333675	−	0.942688i	$-0.391711\pi$
$53$	3.85697	+	0.275856i	0.529796	+	0.0378918i	0.196121	+	0.980580i	$0.437166\pi$
$54$		0			0
$55$	0.597192	−	3.72088i	0.0805254	−	0.501723i
$56$		0			0
$57$	−0.0223901	−	0.102925i	−0.00296564	−	0.0136328i
$58$		0			0
$59$	−6.23724	−	5.40460i	−0.812019	−	0.703619i	0.146324	−	0.989237i	$-0.453256\pi$
$59$	−6.23724	−	5.40460i	−0.812019	−	0.703619i	−0.958344	+	0.285618i	$0.907801\pi$
$60$		0			0
$61$	−10.5599	+	1.51828i	−1.35205	+	0.194396i	−0.779979	−	0.625806i	$-0.784770\pi$
$61$	−10.5599	+	1.51828i	−1.35205	+	0.194396i	−0.572074	+	0.820202i	$0.693861\pi$
$62$		0			0
$63$	1.76528	+	0.658416i	0.222405	+	0.0829527i
$64$		0			0
$65$	8.44051	−	4.43139i	1.04692	−	0.549646i
$66$		0			0
$67$	−6.59682	−	1.43505i	−0.805930	−	0.175319i	−0.209317	−	0.977848i	$-0.567124\pi$
$67$	−6.59682	−	1.43505i	−0.805930	−	0.175319i	−0.596614	+	0.802529i	$0.703488\pi$
$68$		0			0
$69$	−0.239395	−	0.325091i	−0.0288198	−	0.0391364i
$70$		0			0
$71$	−6.12329	+	3.93520i	−0.726701	+	0.467022i	−0.850962	−	0.525227i	$-0.823980\pi$
$71$	−6.12329	+	3.93520i	−0.726701	+	0.467022i	0.124261	+	0.992250i	$0.460344\pi$
$72$		0			0
$73$	−8.05021	+	3.00257i	−0.942206	+	0.351425i	−0.773180	−	0.634187i	$-0.781335\pi$
$73$	−8.05021	+	3.00257i	−0.942206	+	0.351425i	−0.169026	+	0.985612i	$0.554062\pi$
$74$		0			0
$75$	−0.0437301	+	0.418635i	−0.00504951	+	0.0483398i
$76$		0			0
$77$	−0.849319	−	0.635792i	−0.0967889	−	0.0724553i
$78$		0			0
$79$	−11.1560	+	12.8747i	−1.25515	+	1.44852i	−0.411696	+	0.911321i	$0.635063\pi$
$79$	−11.1560	+	12.8747i	−1.25515	+	1.44852i	−0.843455	+	0.537200i	$0.819482\pi$
$80$		0			0
$81$	−7.51767	−	4.83131i	−0.835297	−	0.536812i
$82$		0			0
$83$	−8.02787	+	4.38355i	−0.881174	+	0.481157i	−0.855076	−	0.518502i	$-0.826490\pi$
$83$	−8.02787	+	4.38355i	−0.881174	+	0.481157i	−0.0260973	+	0.999659i	$0.508308\pi$
$84$		0			0
$85$	−0.566331	−	10.2755i	−0.0614272	−	1.11453i
$86$		0			0
$87$	0.0467854	−	0.0856811i	0.00501592	−	0.00918598i
$88$		0			0
$89$	0.675621	−	4.69905i	0.0716157	−	0.498098i	−0.922170	−	0.386786i	$-0.873585\pi$
$89$	0.675621	−	4.69905i	0.0716157	−	0.498098i	0.993785	−	0.111313i	$-0.0355055\pi$
$90$		0			0
$91$		−	2.68381i		−	0.281340i
$92$		0			0
$93$	0.595172	+	0.595172i	0.0617165	+	0.0617165i
$94$		0			0
$95$	−0.0457168	+	2.79748i	−0.00469045	+	0.287016i
$96$		0			0
$97$	4.53191	+	2.47461i	0.460146	+	0.251259i	0.692563	−	0.721358i	$-0.256482\pi$
$97$	4.53191	+	2.47461i	0.460146	+	0.251259i	−0.232417	+	0.972616i	$0.574663\pi$
$98$		0			0
$99$	3.30314	+	3.81202i	0.331978	+	0.383123i
$100$		0			0
$101$	−9.00640	−	2.64452i	−0.896170	−	0.263139i	−0.198961	−	0.980007i	$-0.563757\pi$
$101$	−9.00640	−	2.64452i	−0.896170	−	0.263139i	−0.697209	+	0.716868i	$0.745575\pi$
$102$		0			0
$103$	−14.7927	+	3.21795i	−1.45757	+	0.317074i	−0.870382	−	0.492378i	$-0.836128\pi$
$103$	−14.7927	+	3.21795i	−1.45757	+	0.317074i	−0.587186	+	0.809452i	$0.699764\pi$
$104$		0			0
$105$	0.0986268	+	0.0656852i	0.00962499	+	0.00641022i
$106$		0			0
$107$	5.30055	−	7.08071i	0.512424	−	0.684518i	−0.467477	−	0.884005i	$-0.654837\pi$
$107$	5.30055	−	7.08071i	0.512424	−	0.684518i	0.979900	+	0.199487i	$0.0639277\pi$
$108$		0			0
$109$	−0.954794	−	2.09071i	−0.0914526	−	0.200253i	0.858378	−	0.513017i	$-0.171472\pi$
$109$	−0.954794	−	2.09071i	−0.0914526	−	0.200253i	−0.949831	+	0.312764i	$0.898745\pi$
$110$		0			0
$111$	−0.773346	−	0.353175i	−0.0734027	−	0.0335219i
$112$		0			0
$113$	−1.53809	+	7.07049i	−0.144691	+	0.665135i	0.846466	+	0.532443i	$0.178726\pi$
$113$	−1.53809	+	7.07049i	−0.144691	+	0.665135i	−0.991157	+	0.132693i	$0.957638\pi$
$114$		0			0
$115$	4.21745	+	9.85967i	0.393280	+	0.919419i
$116$		0			0
$117$	−2.71228	+	12.4681i	−0.250750	+	1.15268i
$118$		0			0
$119$	−2.63539	−	1.20354i	−0.241586	−	0.110328i
$120$		0			0
$121$	3.38965	+	7.42231i	0.308150	+	0.674755i
$122$		0			0
$123$	0.00902813	−	0.0120602i	0.000814039	−	0.00108743i
$124$		0			0
$125$	3.67175	−	10.5602i	0.328412	−	0.944535i
$126$		0			0
$127$	10.2598	−	2.23188i	0.910410	−	0.198047i	0.267114	−	0.963665i	$-0.413930\pi$
$127$	10.2598	−	2.23188i	0.910410	−	0.198047i	0.643296	+	0.765618i	$0.277566\pi$
$128$		0			0
$129$	−0.278848	−	0.0818771i	−0.0245512	−	0.00720888i
$130$		0			0
$131$	−8.88383	−	10.2525i	−0.776183	−	0.895763i	0.220644	−	0.975354i	$-0.429184\pi$
$131$	−8.88383	−	10.2525i	−0.776183	−	0.895763i	−0.996828	+	0.0795909i	$0.974639\pi$
$132$		0			0
$133$	0.691322	+	0.377490i	0.0599452	+	0.0327325i
$134$		0			0
$135$	−0.784543	−	0.810611i	−0.0675227	−	0.0697663i
$136$		0			0
$137$	3.40367	+	3.40367i	0.290795	+	0.290795i	0.837394	−	0.546599i	$-0.184078\pi$
$137$	3.40367	+	3.40367i	0.290795	+	0.290795i	−0.546599	+	0.837394i	$0.684078\pi$
$138$		0			0
$139$			15.3309i			1.30035i	0.759783	+	0.650176i	$0.225305\pi$
$139$			15.3309i			1.30035i	−0.759783	+	0.650176i	$0.774695\pi$
$140$		0			0
$141$	−0.0378734	+	0.263415i	−0.00318951	+	0.0221836i
$142$		0			0
$143$	3.44344	−	6.30619i	0.287955	−	0.527350i
$144$		0			0
$145$	−1.72989	+	1.93169i	−0.143659	+	0.160418i
$146$		0			0
$147$	−0.487918	+	0.266423i	−0.0402428	+	0.0219742i
$148$		0			0
$149$	−13.4410	−	8.63802i	−1.10113	−	0.707654i	−0.141789	−	0.989897i	$-0.545285\pi$
$149$	−13.4410	−	8.63802i	−1.10113	−	0.707654i	−0.959343	+	0.282243i	$0.908922\pi$
$150$		0			0
$151$	−2.00085	+	2.30910i	−0.162827	+	0.187912i	−0.831300	−	0.555824i	$-0.812403\pi$
$151$	−2.00085	+	2.30910i	−0.162827	+	0.187912i	0.668473	+	0.743736i	$0.266948\pi$
$152$		0			0
$153$	11.0269	+	8.25462i	0.891471	+	0.667346i
$154$		0			0
$155$	−11.7784	−	19.0032i	−0.946060	−	1.52637i
$156$		0			0
$157$	7.96871	−	2.97218i	0.635973	−	0.237206i	−0.0107363	−	0.999942i	$-0.503418\pi$
$157$	7.96871	−	2.97218i	0.635973	−	0.237206i	0.646709	+	0.762737i	$0.276145\pi$
$158$		0			0
$159$	−0.273844	+	0.175989i	−0.0217173	+	0.0139568i
$160$		0			0
$161$	3.00955	+	0.239045i	0.237186	+	0.0188394i
$162$		0			0
$163$	3.16924	+	0.689427i	0.248234	+	0.0540001i	0.334961	−	0.942232i	$-0.391277\pi$
$163$	3.16924	+	0.689427i	0.248234	+	0.0540001i	−0.0867263	+	0.996232i	$0.527641\pi$
$164$		0			0
$165$	0.147468	+	0.280884i	0.0114804	+	0.0218668i
$166$		0			0
$167$	0.186595	+	0.0695964i	0.0144392	+	0.00538553i	0.356673	−	0.934229i	$-0.383911\pi$
$167$	0.186595	+	0.0695964i	0.0144392	+	0.00538553i	−0.342234	+	0.939615i	$0.611184\pi$
$168$		0			0
$169$	5.12319	−	0.736604i	0.394092	−	0.0566618i
$170$		0			0
$171$	−2.83017	−	2.45236i	−0.216429	−	0.187536i
$172$		0			0
$173$	−3.52161	−	16.1886i	−0.267743	−	1.23079i	−0.892886	−	0.450283i	$-0.851323\pi$
$173$	−3.52161	−	16.1886i	−0.267743	−	1.23079i	0.625143	−	0.780510i	$-0.285041\pi$
$174$		0			0
$175$	−2.15175	−	2.29720i	−0.162657	−	0.173652i
$176$		0			0
$177$	0.692993	+	0.0495638i	0.0520886	+	0.00372545i
$178$		0			0
$179$	2.06711	+	7.03994i	0.154503	+	0.526190i	0.999969	−	0.00783953i	$-0.00249543\pi$
$179$	2.06711	+	7.03994i	0.154503	+	0.526190i	−0.845466	+	0.534029i	$0.820677\pi$
$180$		0			0
$181$	−3.42582	−	0.492559i	−0.254640	−	0.0366116i	0.0138128	−	0.999905i	$-0.495603\pi$
$181$	−3.42582	−	0.492559i	−0.254640	−	0.0366116i	−0.268452	+	0.963293i	$0.586512\pi$
$182$		0			0
$183$	0.635052	−	0.635052i	0.0469444	−	0.0469444i
$184$		0			0
$185$	17.8546	+	13.8267i	1.31270	+	1.01656i
$186$		0			0
$187$	−4.64822	−	6.20929i	−0.339911	−	0.454068i
$188$		0			0
$189$	−0.304724	+	0.0894749i	−0.0221654	+	0.00650834i
$190$		0			0
$191$	14.3356	−	12.4218i	1.03728	−	0.898812i	0.0423267	−	0.999104i	$-0.486523\pi$
$191$	14.3356	−	12.4218i	1.03728	−	0.898812i	0.994958	+	0.100291i	$0.0319775\pi$
$192$		0			0
$193$	12.5805	+	23.0395i	0.905564	+	1.65842i	0.740417	+	0.672148i	$0.234628\pi$
$193$	12.5805	+	23.0395i	0.905564	+	1.65842i	0.165147	+	0.986269i	$0.447190\pi$
$194$		0			0
$195$	−0.345262	+	0.724452i	−0.0247247	+	0.0518791i
$196$		0			0
$197$	0.125489	+	1.75456i	0.00894072	+	0.125008i	0.999962	−	0.00869520i	$-0.00276780\pi$
$197$	0.125489	+	1.75456i	0.00894072	+	0.125008i	−0.991021	+	0.133703i	$0.957313\pi$
$198$		0			0
$199$	2.19370	+	15.2575i	0.155507	+	1.08158i	0.906786	+	0.421592i	$0.138528\pi$
$199$	2.19370	+	15.2575i	0.155507	+	1.08158i	−0.751278	+	0.659985i	$0.770562\pi$
$200$		0			0
$201$	0.516967	−	0.236091i	0.0364641	−	0.0166526i
$202$		0			0
$203$	0.255114	+	0.683986i	0.0179055	+	0.0480064i
$204$		0			0
$205$	−0.306661	+	0.257072i	−0.0214182	+	0.0179547i
$206$		0			0
$207$	−13.7399	−	4.15201i	−0.954987	−	0.288584i
$208$		0			0
$209$	1.14007	+	1.77399i	0.0788605	+	0.122709i
$210$		0			0
$211$	−2.49156	+	5.45576i	−0.171526	+	0.375590i	−0.975799	−	0.218671i	$-0.929828\pi$
$211$	−2.49156	+	5.45576i	−0.171526	+	0.375590i	0.804273	+	0.594261i	$0.202555\pi$
$212$		0			0
$213$	0.214133	−	0.574112i	0.0146721	−	0.0393375i
$214$		0			0
$215$	6.71387	+	3.80977i	0.457882	+	0.259824i
$216$		0			0
$217$	−6.27814	+	0.449021i	−0.426188	+	0.0304816i
$218$		0			0
$219$	0.391041	−	0.608472i	0.0264241	−	0.0411167i
$220$		0			0
$221$	5.52789	−	18.8263i	0.371846	−	1.26639i
$222$		0			0
$223$	1.22757	−	17.1637i	0.0822043	−	1.14937i	−0.774159	−	0.632992i	$-0.781827\pi$
$223$	1.22757	−	17.1637i	0.0822043	−	1.14937i	0.856363	−	0.516374i	$-0.172719\pi$
$224$		0			0
$225$	7.67478	+	12.8466i	0.511652	+	0.856442i
$226$		0			0
$227$	10.6774	−	7.99302i	0.708686	−	0.530516i	−0.183032	−	0.983107i	$-0.558591\pi$
$227$	10.6774	−	7.99302i	0.708686	−	0.530516i	0.891718	+	0.452591i	$0.149500\pi$
$228$		0			0
$229$	−19.4355			−1.28434			−0.642168	−	0.766564i	$-0.721965\pi$
$229$	−19.4355			−1.28434			−0.642168	+	0.766564i	$0.721965\pi$
$230$		0			0
$231$	0.0893120			0.00587630
$232$		0			0
$233$	7.04595	−	5.27453i	0.461595	−	0.345546i	−0.343034	−	0.939323i	$-0.611455\pi$
$233$	7.04595	−	5.27453i	0.461595	−	0.345546i	0.804630	+	0.593777i	$0.202364\pi$
$234$		0			0
$235$	2.57819	−	6.58188i	0.168183	−	0.429354i
$236$		0			0
$237$	0.102308	−	1.43046i	0.00664564	−	0.0929182i
$238$		0			0
$239$	6.21132	−	21.1538i	0.401777	−	1.36833i	−0.471829	−	0.881690i	$-0.656406\pi$
$239$	6.21132	−	21.1538i	0.401777	−	1.36833i	0.873605	−	0.486635i	$-0.161776\pi$
$240$		0			0
$241$	−4.87195	+	7.58091i	−0.313830	+	0.488329i	−0.961956	−	0.273204i	$-0.911917\pi$
$241$	−4.87195	+	7.58091i	−0.313830	+	0.488329i	0.648126	+	0.761533i	$0.275553\pi$
$242$		0			0
$243$	2.26000	−	0.161639i	0.144979	−	0.0103691i
$244$		0			0
$245$	14.2343	−	3.92810i	0.909396	−	0.250957i
$246$		0			0
$247$	−1.86419	+	4.99809i	−0.118616	+	0.318021i
$248$		0			0
$249$	0.319867	−	0.700411i	0.0202707	−	0.0443867i
$250$		0			0
$251$	9.03427	+	14.0576i	0.570238	+	0.887307i	0.999877	−	0.0156934i	$-0.00499558\pi$
$251$	9.03427	+	14.0576i	0.570238	+	0.887307i	−0.429639	+	0.903001i	$0.641359\pi$
$252$		0			0
$253$	6.76489	+	4.42307i	0.425305	+	0.278076i
$254$		0			0
$255$	0.556550	+	0.663910i	0.0348525	+	0.0415756i
$256$		0			0
$257$	−7.17831	−	19.2458i	−0.447771	−	1.20052i	−0.943304	−	0.331931i	$-0.892300\pi$
$257$	−7.17831	−	19.2458i	−0.447771	−	1.20052i	0.495533	−	0.868589i	$-0.334973\pi$
$258$		0			0
$259$	5.78303	−	2.64102i	0.359340	−	0.164105i
$260$		0			0
$261$	−0.493937	−	3.43541i	−0.0305739	−	0.212646i
$262$		0			0
$263$	2.08381	+	29.1355i	0.128493	+	1.79657i	0.497828	+	0.867276i	$0.334131\pi$
$263$	2.08381	+	29.1355i	0.128493	+	1.79657i	−0.369334	+	0.929297i	$0.620414\pi$
$264$		0			0
$265$	8.14961	−	2.88886i	0.500627	−	0.177461i
$266$		0			0
$267$	0.191530	+	0.350761i	0.0117214	+	0.0214662i
$268$		0			0
$269$	17.4138	−	15.0892i	1.06174	−	0.920002i	0.0647777	−	0.997900i	$-0.479366\pi$
$269$	17.4138	−	15.0892i	1.06174	−	0.920002i	0.996961	+	0.0778976i	$0.0248207\pi$
$270$		0			0
$271$	11.7169	−	3.44040i	0.711753	−	0.208990i	0.0942393	−	0.995550i	$-0.469958\pi$
$271$	11.7169	−	3.44040i	0.711753	−	0.208990i	0.617514	+	0.786560i	$0.288140\pi$
$272$		0			0
$273$	0.135395	+	0.180866i	0.00819447	+	0.0109465i
$274$		0			0
$275$	−2.10859	−	8.15854i	−0.127153	−	0.491978i
$276$		0			0
$277$	−3.50196	+	3.50196i	−0.210412	+	0.210412i	−0.804443	−	0.594030i	$-0.797536\pi$
$277$	−3.50196	+	3.50196i	−0.210412	+	0.210412i	0.594030	+	0.804443i	$0.297536\pi$
$278$		0			0
$279$	29.6201	+	4.25872i	1.77331	+	0.254963i
$280$		0			0
$281$	−1.39110	−	4.73763i	−0.0829858	−	0.282624i	0.907537	−	0.419972i	$-0.137960\pi$
$281$	−1.39110	−	4.73763i	−0.0829858	−	0.282624i	−0.990523	+	0.137349i	$0.956142\pi$
$282$		0			0
$283$	14.0298	+	1.00343i	0.833987	+	0.0596479i	0.481799	−	0.876282i	$-0.339983\pi$
$283$	14.0298	+	1.00343i	0.833987	+	0.0596479i	0.352188	+	0.935929i	$0.385438\pi$
$284$		0			0
$285$	−0.138049	−	0.190833i	−0.00817730	−	0.0113040i
$286$		0			0
$287$	0.0239466	+	0.110081i	0.00141352	+	0.00649786i
$288$		0			0
$289$	−3.15991	−	2.73808i	−0.185877	−	0.161063i
$290$		0			0
$291$	−0.430254	+	0.0618612i	−0.0252219	+	0.00362637i
$292$		0			0
$293$	−21.2909	−	7.94111i	−1.24383	−	0.463925i	−0.360537	−	0.932745i	$-0.617406\pi$
$293$	−21.2909	−	7.94111i	−1.24383	−	0.463925i	−0.883294	+	0.468820i	$0.844679\pi$
$294$		0			0
$295$	−17.6195	−	5.48783i	−1.02585	−	0.319514i
$296$		0			0
$297$	−0.830814	−	0.180732i	−0.0482087	−	0.0104872i
$298$		0			0
$299$	1.29822	+	20.4049i	0.0750781	+	1.18005i
$300$		0			0
$301$	1.82824	−	1.17494i	0.105378	−	0.0677225i
$302$		0			0
$303$	0.740368	−	0.276143i	0.0425331	−	0.0158640i
$304$		0			0
$305$	−20.2765	+	12.5676i	−1.16103	+	0.719617i
$306$		0			0
$307$	18.5704	+	13.9017i	1.05987	+	0.793410i	0.979111	−	0.203324i	$-0.0651745\pi$
$307$	18.5704	+	13.9017i	1.05987	+	0.793410i	0.0807596	+	0.996734i	$0.474265\pi$
$308$		0			0
$309$	0.834562	−	0.963136i	0.0474766	−	0.0547909i
$310$		0			0
$311$	14.8653	+	9.55333i	0.842932	+	0.541720i	0.889363	−	0.457202i	$-0.151148\pi$
$311$	14.8653	+	9.55333i	0.842932	+	0.541720i	−0.0464308	+	0.998922i	$0.514785\pi$
$312$		0			0
$313$	3.95418	−	2.15914i	0.223503	−	0.122042i	−0.363597	−	0.931556i	$-0.618451\pi$
$313$	3.95418	−	2.15914i	0.223503	−	0.122042i	0.587100	+	0.809514i	$0.300270\pi$
$314$		0			0
$315$	4.20653	−	0.231843i	0.237011	−	0.0130628i
$316$		0			0
$317$	−10.6807	+	19.5603i	−0.599890	+	1.09862i	0.384585	+	0.923090i	$0.374345\pi$
$317$	−10.6807	+	19.5603i	−0.599890	+	1.09862i	−0.984475	+	0.175527i	$0.943837\pi$
$318$		0			0
$319$	−0.278138	+	1.93449i	−0.0155727	+	0.108311i
$320$		0			0
$321$			0.744587i			0.0415588i
$322$		0			0
$323$	4.07193	+	4.07193i	0.226568	+	0.226568i
$324$		0			0
$325$	13.3253	−	16.6383i	0.739157	−	0.922926i
$326$		0			0
$327$	0.169819	+	0.0927280i	0.00939099	+	0.00512787i
$328$		0			0
$329$	−1.30321	−	1.50398i	−0.0718483	−	0.0829174i
$330$		0			0
$331$	3.72649	+	1.09420i	0.204827	+	0.0601425i	0.382536	−	0.923940i	$-0.375051\pi$
$331$	3.72649	+	1.09420i	0.204827	+	0.0601425i	−0.177710	+	0.984083i	$0.556869\pi$
$332$		0			0
$333$	−29.5352	+	6.42498i	−1.61852	+	0.352087i
$334$		0			0
$335$	−14.8014	+	2.96741i	−0.808687	+	0.162127i
$336$		0			0
$337$	−5.03627	+	6.72766i	−0.274343	+	0.366479i	−0.916459	−	0.400128i	$-0.868966\pi$
$337$	−5.03627	+	6.72766i	−0.274343	+	0.366479i	0.642116	+	0.766607i	$0.278057\pi$
$338$		0			0
$339$	−0.253043	−	0.554087i	−0.0137434	−	0.0300939i
$340$		0			0
$341$	−15.3280	−	7.00004i	−0.830055	−	0.379074i
$342$		0			0
$343$	1.82035	−	8.36799i	0.0982894	−	0.451829i
$344$		0			0
$345$	−0.781629	−	0.451694i	−0.0420815	−	0.0243184i
$346$		0			0
$347$	5.80420	−	26.6815i	0.311586	−	1.43234i	−0.508976	−	0.860781i	$-0.669976\pi$
$347$	5.80420	−	26.6815i	0.311586	−	1.43234i	0.820562	−	0.571557i	$-0.193660\pi$
$348$		0			0
$349$	−32.2125	−	14.7109i	−1.72429	−	0.787459i	−0.994611	−	0.103672i	$-0.966941\pi$
$349$	−32.2125	−	14.7109i	−1.72429	−	0.787459i	−0.729682	−	0.683786i	$-0.760332\pi$
$350$		0			0
$351$	−0.893491	−	1.95647i	−0.0476910	−	0.104429i
$352$		0			0
$353$	10.2408	−	13.6801i	0.545063	−	0.728119i	−0.440439	−	0.897783i	$-0.645177\pi$
$353$	10.2408	−	13.6801i	0.545063	−	0.728119i	0.985502	+	0.169663i	$0.0542680\pi$
$354$		0			0
$355$	−9.02192	+	13.5465i	−0.478834	+	0.718972i
$356$		0			0
$357$	0.238320	−	0.0518434i	0.0126132	−	0.00274384i
$358$		0			0
$359$	−0.223340	−	0.0655787i	−0.0117875	−	0.00346111i	0.275834	−	0.961205i	$-0.411046\pi$
$359$	−0.223340	−	0.0655787i	−0.0117875	−	0.00346111i	−0.287621	+	0.957744i	$0.592864\pi$
$360$		0			0
$361$	11.4171	+	13.1760i	0.600900	+	0.693476i
$362$		0			0
$363$	−0.602881	−	0.329198i	−0.0316430	−	0.0172784i
$364$		0			0
$365$	−13.8052	+	13.3612i	−0.722597	+	0.699360i
$366$		0			0
$367$	4.11814	+	4.11814i	0.214965	+	0.214965i	0.806373	−	0.591408i	$-0.201428\pi$
$367$	4.11814	+	4.11814i	0.214965	+	0.214965i	−0.591408	+	0.806373i	$0.701428\pi$
$368$		0			0
$369$		−	0.535601i		−	0.0278823i
$370$		0			0
$371$	0.346425	−	2.40944i	0.0179855	−	0.125092i
$372$		0			0
$373$	7.84961	−	14.3755i	0.406437	−	0.744335i	−0.591647	−	0.806197i	$-0.701522\pi$
$373$	7.84961	−	14.3755i	0.406437	−	0.744335i	0.998085	+	0.0618624i	$0.0197040\pi$
$374$		0			0
$375$	0.285304	+	0.896906i	0.0147331	+	0.0463160i
$376$		0			0
$377$	−4.33921	+	2.36939i	−0.223481	+	0.122030i
$378$		0			0
$379$	−14.1572	−	9.09831i	−0.727209	−	0.467349i	0.123929	−	0.992291i	$-0.460450\pi$
$379$	−14.1572	−	9.09831i	−0.727209	−	0.467349i	−0.851138	+	0.524942i	$0.824087\pi$
$380$		0			0
$381$	−0.578829	+	0.668004i	−0.0296543	+	0.0342229i
$382$		0			0
$383$	−28.7972	−	21.5573i	−1.47147	−	1.10153i	−0.971940	−	0.235231i	$-0.924415\pi$
$383$	−28.7972	−	21.5573i	−1.47147	−	1.10153i	−0.499529	−	0.866297i	$-0.666494\pi$
$384$		0			0
$385$	−2.30955	−	0.542082i	−0.117706	−	0.0276271i
$386$		0			0
$387$	−9.68085	+	3.61077i	−0.492105	+	0.183546i
$388$		0			0
$389$	−12.4071	+	7.97357i	−0.629066	+	0.404276i	−0.815964	−	0.578103i	$-0.803793\pi$
$389$	−12.4071	+	7.97357i	−0.629066	+	0.404276i	0.186898	+	0.982379i	$0.440157\pi$
$390$		0			0
$391$	20.6189	+	7.87568i	1.04274	+	0.398290i
$392$		0			0
$393$	1.11592	+	0.242754i	0.0562908	+	0.0122453i
$394$		0			0
$395$	−11.3278	+	36.3698i	−0.569965	+	1.82996i
$396$		0			0
$397$	−12.1378	−	4.52718i	−0.609181	−	0.227213i	0.0258922	−	0.999665i	$-0.491757\pi$
$397$	−12.1378	−	4.52718i	−0.609181	−	0.227213i	−0.635073	+	0.772452i	$0.719030\pi$
$398$		0			0
$399$	−0.0656332	+	0.00943663i	−0.00328577	+	0.000472422i
$400$		0			0
$401$	17.5808	+	15.2339i	0.877945	+	0.760744i	0.972039	−	0.234820i	$-0.0754499\pi$
$401$	17.5808	+	15.2339i	0.877945	+	0.760744i	−0.0940939	+	0.995563i	$0.529995\pi$
$402$		0			0
$403$	−9.06098	−	41.6526i	−0.451359	−	2.07487i
$404$		0			0
$405$	−19.7296	−	3.16655i	−0.980372	−	0.157347i
$406$		0			0
$407$	16.9770	+	1.21422i	0.841519	+	0.0601866i
$408$		0			0
$409$	1.77853	+	6.05713i	0.0879428	+	0.299506i	0.991706	−	0.128527i	$-0.0410249\pi$
$409$	1.77853	+	6.05713i	0.0879428	+	0.299506i	−0.903763	+	0.428033i	$0.859207\pi$
$410$		0			0
$411$	−0.401090	−	0.0576681i	−0.0197843	−	0.00284456i
$412$		0			0
$413$	−3.67370	+	3.67370i	−0.180771	+	0.180771i
$414$		0			0
$415$	−12.5227	+	16.1707i	−0.614716	+	0.793790i
$416$		0			0
$417$	−0.773426	−	1.03318i	−0.0378749	−	0.0505949i
$418$		0			0
$419$	30.1534	−	8.85385i	1.47309	−	0.432539i	0.555989	−	0.831190i	$-0.312340\pi$
$419$	30.1534	−	8.85385i	1.47309	−	0.432539i	0.917103	+	0.398651i	$0.130522\pi$
$420$		0			0
$421$	−17.9307	+	15.5370i	−0.873889	+	0.757229i	−0.971261	−	0.238019i	$-0.923502\pi$
$421$	−17.9307	+	15.5370i	−0.873889	+	0.757229i	0.0973714	+	0.995248i	$0.468957\pi$
$422$		0			0
$423$	4.53437	+	8.30408i	0.220469	+	0.403758i
$424$		0			0
$425$	−10.3624	−	20.5463i	−0.502651	−	0.996641i
$426$		0			0
$427$	0.479108	+	6.69881i	0.0231857	+	0.324178i
$428$		0			0
$429$	0.0860803	+	0.598701i	0.00415600	+	0.0289056i
$430$		0			0
$431$	−20.9714	+	9.57733i	−1.01016	+	0.461324i	−0.850571	−	0.525860i	$-0.823744\pi$
$431$	−20.9714	+	9.57733i	−1.01016	+	0.461324i	−0.159587	+	0.987184i	$0.551016\pi$
$432$		0			0
$433$	−7.44279	−	19.9549i	−0.357678	−	0.958971i	−0.983804	−	0.179249i	$-0.942633\pi$
$433$	−7.44279	−	19.9549i	−0.357678	−	0.958971i	0.626126	−	0.779722i	$-0.284640\pi$
$434$		0			0
$435$	0.0191283	−	0.217451i	0.000917134	−	0.0104260i
$436$		0			0
$437$	−5.43869	−	2.53563i	−0.260168	−	0.121296i
$438$		0			0
$439$	7.79096	+	12.1230i	0.371842	+	0.578598i	0.975866	−	0.218368i	$-0.0700734\pi$
$439$	7.79096	+	12.1230i	0.371842	+	0.578598i	−0.604024	+	0.796966i	$0.706437\pi$
$440$		0			0
$441$	−8.21041	+	17.9783i	−0.390972	+	0.856109i
$442$		0			0
$443$	−4.75637	+	12.7523i	−0.225982	+	0.605881i	−0.999615	−	0.0277532i	$-0.991165\pi$
$443$	−4.75637	+	12.7523i	−0.225982	+	0.605881i	0.773633	+	0.633634i	$0.218437\pi$
$444$		0			0
$445$	−2.82389	−	10.2330i	−0.133865	−	0.485089i
$446$		0			0
$447$	1.34159	−	0.0959524i	0.0634550	−	0.00453839i
$448$		0			0
$449$	12.7165	−	19.7872i	0.600127	−	0.933816i	−0.399725	−	0.916635i	$-0.630895\pi$
$449$	12.7165	−	19.7872i	0.600127	−	0.933816i	0.999852	−	0.0171808i	$-0.00546909\pi$
$450$		0			0
$451$	−0.0849704	+	0.289383i	−0.00400110	+	0.0136265i
$452$		0			0
$453$	0.0183492	−	0.256555i	0.000862119	−	0.0120540i
$454$		0			0
$455$	−2.40345	−	5.49887i	−0.112675	−	0.257791i
$456$		0			0
$457$	−7.47680	+	5.59706i	−0.349750	+	0.261820i	−0.759680	−	0.650298i	$-0.774644\pi$
$457$	−7.47680	+	5.59706i	−0.349750	+	0.261820i	0.409930	+	0.912117i	$0.365553\pi$
$458$		0			0
$459$	−2.32186			−0.108375
$460$		0			0
$461$	−5.13368			−0.239099			−0.119550	−	0.992828i	$-0.538145\pi$
$461$	−5.13368			−0.239099			−0.119550	+	0.992828i	$0.538145\pi$
$462$		0			0
$463$	7.08790	−	5.30594i	0.329403	−	0.246588i	−0.421756	−	0.906709i	$-0.638586\pi$
$463$	7.08790	−	5.30594i	0.329403	−	0.246588i	0.751159	+	0.660121i	$0.229495\pi$
$464$		0			0
$465$	1.75245	+	0.686453i	0.0812679	+	0.0318335i
$466$		0			0
$467$	−2.27136	+	31.7577i	−0.105106	+	1.46957i	0.621984	+	0.783030i	$0.286327\pi$
$467$	−2.27136	+	31.7577i	−0.105106	+	1.46957i	−0.727090	+	0.686543i	$0.759128\pi$
$468$		0			0
$469$	−1.19734	+	4.07775i	−0.0552878	+	0.188293i
$470$		0			0
$471$	−0.387082	+	0.602312i	−0.0178358	+	0.0277531i
$472$		0			0
$473$	5.80335	−	0.415064i	0.266838	−	0.0190846i
$474$		0			0
$475$	2.41158	+	5.77272i	0.110651	+	0.264871i
$476$		0			0
$477$	−4.04437	+	10.8434i	−0.185179	+	0.496485i
$478$		0			0
$479$	12.1288	−	26.5583i	0.554177	−	1.21348i	−0.400627	−	0.916241i	$-0.631208\pi$
$479$	12.1288	−	26.5583i	0.554177	−	1.21348i	0.954804	−	0.297237i	$-0.0960652\pi$
$480$		0			0
$481$	23.2778	+	36.2210i	1.06138	+	1.65153i
$482$		0			0
$483$	−0.214878	+	0.135719i	−0.00977730	+	0.00617541i
$484$		0			0
$485$	11.5016	+	1.01175i	0.522259	+	0.0459412i
$486$		0			0
$487$	−6.26462	−	16.7961i	−0.283877	−	0.761103i	−0.998125	−	0.0612107i	$-0.980504\pi$
$487$	−6.26462	−	16.7961i	−0.283877	−	0.761103i	0.714248	−	0.699893i	$-0.246769\pi$
$488$		0			0
$489$	−0.248361	+	0.113423i	−0.0112313	+	0.00512916i
$490$		0			0
$491$	1.47388	+	10.2510i	0.0665151	+	0.462623i	0.995672	+	0.0929371i	$0.0296256\pi$
$491$	1.47388	+	10.2510i	0.0665151	+	0.462623i	−0.929157	+	0.369686i	$0.879465\pi$
$492$		0			0
$493$	0.380741	+	5.32346i	0.0171477	+	0.239757i
$494$		0			0
$495$	10.1816	+	4.85239i	0.457630	+	0.218099i
$496$		0			0
$497$	2.19595	+	4.02159i	0.0985019	+	0.180393i
$498$		0			0
$499$	19.8177	−	17.1721i	0.887163	−	0.768731i	−0.0866126	−	0.996242i	$-0.527604\pi$
$499$	19.8177	−	17.1721i	0.887163	−	0.768731i	0.973775	+	0.227511i	$0.0730588\pi$
$500$		0			0
$501$	−0.0160860	+	0.00472328i	−0.000718669	+	0.000211020i
$502$		0			0
$503$	−2.04658	−	2.73392i	−0.0912527	−	0.121899i	0.752591	−	0.658488i	$-0.228804\pi$
$503$	−2.04658	−	2.73392i	−0.0912527	−	0.121899i	−0.843844	+	0.536589i	$0.819713\pi$
$504$		0			0
$505$	−20.8215	+	2.64719i	−0.926545	+	0.117799i
$506$		0			0
$507$	−0.308100	+	0.308100i	−0.0136832	+	0.0136832i
$508$		0			0
$509$	−4.50351	−	0.647506i	−0.199614	−	0.0287002i	0.0417823	−	0.999127i	$-0.486696\pi$
$509$	−4.50351	−	0.647506i	−0.199614	−	0.0287002i	−0.241397	+	0.970427i	$0.577605\pi$
$510$		0			0
$511$	1.52381	+	5.18963i	0.0674095	+	0.229576i
$512$		0			0
$513$	0.629641	+	0.0450328i	0.0277993	+	0.00198825i
$514$		0			0
$515$	−27.4270	+	19.8407i	−1.20858	+	0.874285i
$516$		0			0
$517$	−1.13250	−	5.20601i	−0.0498072	−	0.228960i
$518$		0			0
$519$	1.05402	+	0.913313i	0.0462663	+	0.0400900i
$520$		0			0
$521$	19.5994	−	2.81797i	0.858667	−	0.123458i	0.301103	−	0.953592i	$-0.402645\pi$
$521$	19.5994	−	2.81797i	0.858667	−	0.123458i	0.557564	+	0.830134i	$0.311736\pi$
$522$		0			0
$523$	−30.5732	−	11.4032i	−1.33687	−	0.498628i	−0.423553	−	0.905871i	$-0.639217\pi$
$523$	−30.5732	−	11.4032i	−1.33687	−	0.498628i	−0.913320	+	0.407243i	$0.866490\pi$
$524$		0			0
$525$	0.260901	+	0.0462589i	0.0113866	+	0.00201890i
$526$		0			0
$527$	−44.9645	−	9.78143i	−1.95868	−	0.426086i
$528$		0			0
$529$	−22.9972	−	0.361654i	−0.999876	−	0.0157241i
$530$		0			0
$531$	20.7795	−	13.3542i	0.901754	−	0.579522i
$532$		0			0
$533$	−0.714844	+	0.266623i	−0.0309633	+	0.0115487i
$534$		0			0
$535$	4.51930	−	19.2545i	0.195386	−	0.832447i
$536$		0			0
$537$	−0.494462	−	0.370150i	−0.0213376	−	0.0159731i
$538$		0			0
$539$	7.28821	−	8.41104i	0.313925	−	0.362289i
$540$		0			0
$541$	−30.4412	−	19.5634i	−1.30877	−	0.841095i	−0.314631	−	0.949214i	$-0.601881\pi$
$541$	−30.4412	−	19.5634i	−1.30877	−	0.841095i	−0.994138	+	0.108119i	$0.965517\pi$
$542$		0			0
$543$	0.255721	−	0.139634i	0.0109740	−	0.00599228i
$544$		0			0
$545$	−3.82859	−	3.42861i	−0.163999	−	0.146865i
$546$		0			0
$547$	11.7630	−	21.5424i	0.502950	−	0.921084i	−0.495667	−	0.868513i	$-0.665076\pi$
$547$	11.7630	−	21.5424i	0.502950	−	0.921084i	0.998617	−	0.0525718i	$-0.0167418\pi$
$548$		0			0
$549$	4.54408	−	31.6048i	0.193937	−	1.34886i
$550$		0			0
$551$		−	1.45100i		−	0.0618147i
$552$		0			0
$553$	7.58314	+	7.58314i	0.322468	+	0.322468i
$554$		0			0
$555$	−1.90079	−	0.0310630i	−0.0806842	−	0.00131855i
$556$		0			0
$557$	−27.3679	−	14.9440i	−1.15962	−	0.633198i	−0.220023	−	0.975495i	$-0.570613\pi$
$557$	−27.3679	−	14.9440i	−1.15962	−	0.633198i	−0.939592	+	0.342297i	$0.888795\pi$
$558$		0			0
$559$	9.63829	+	11.1232i	0.407656	+	0.470460i
$560$		0			0
$561$	0.626502	+	0.183958i	0.0264509	+	0.00776670i
$562$		0			0
$563$	−22.0787	+	4.80292i	−0.930506	+	0.202419i	−0.652177	−	0.758067i	$-0.726144\pi$
$563$	−22.0787	+	4.80292i	−0.930506	+	0.202419i	−0.278329	+	0.960486i	$0.589780\pi$
$564$		0			0
$565$	3.18048	+	15.8642i	0.133804	+	0.667411i
$566$		0			0
$567$	−3.37123	+	4.50343i	−0.141578	+	0.189126i
$568$		0			0
$569$	−9.89795	−	21.6735i	−0.414944	−	0.908600i	−0.995534	−	0.0944042i	$-0.969905\pi$
$569$	−9.89795	−	21.6735i	−0.414944	−	0.908600i	0.580590	−	0.814196i	$-0.302822\pi$
$570$		0			0
$571$	20.4554	+	9.34167i	0.856032	+	0.390937i	0.794570	−	0.607173i	$-0.207696\pi$
$571$	20.4554	+	9.34167i	0.856032	+	0.390937i	0.0614619	+	0.998109i	$0.480424\pi$
$572$		0			0
$573$	−0.339431	+	1.56034i	−0.0141799	+	0.0651841i
$574$		0			0
$575$	17.4709	+	16.4246i	0.728585	+	0.684955i
$576$		0			0
$577$	−4.75550	+	21.8607i	−0.197974	+	0.910072i	0.765743	+	0.643147i	$0.222371\pi$
$577$	−4.75550	+	21.8607i	−0.197974	+	0.910072i	−0.963717	+	0.266926i	$0.913992\pi$
$578$		0			0
$579$	−2.01013	−	0.917997i	−0.0835383	−	0.0381506i
$580$		0			0
$581$	2.39194	+	5.23763i	0.0992345	+	0.217293i
$582$		0			0
$583$	3.90541	−	5.21701i	0.161745	−	0.216066i
$584$		0			0
$585$	5.60848	+	27.9750i	0.231882	+	1.15662i
$586$		0			0
$587$	−12.1216	+	2.63688i	−0.500310	+	0.108836i	−0.455637	−	0.890166i	$-0.650588\pi$
$587$	−12.1216	+	2.63688i	−0.500310	+	0.108836i	−0.0446736	+	0.999002i	$0.514225\pi$
$588$		0			0
$589$	12.0038	+	3.52462i	0.494606	+	0.145230i
$590$		0			0
$591$	−0.0969725	−	0.111912i	−0.00398892	−	0.00460346i
$592$		0			0
$593$	38.7924	+	21.1823i	1.59301	+	0.869851i	0.997801	+	0.0662833i	$0.0211141\pi$
$593$	38.7924	+	21.1823i	1.59301	+	0.869851i	0.595213	+	0.803568i	$0.297068\pi$
$594$		0			0
$595$	−6.47748	−	0.105856i	−0.265551	−	0.00433966i
$596$		0			0
$597$	−0.917560	−	0.917560i	−0.0375532	−	0.0375532i
$598$		0			0
$599$			41.5560i			1.69793i	0.528446	+	0.848967i	$0.322775\pi$
$599$			41.5560i			1.69793i	−0.528446	+	0.848967i	$0.677225\pi$
$600$		0			0
$601$	1.24483	−	8.65795i	0.0507775	−	0.353165i	−0.948554	−	0.316615i	$-0.897454\pi$
$601$	1.24483	−	8.65795i	0.0507775	−	0.353165i	0.999332	−	0.0365508i	$-0.0116371\pi$
$602$		0			0
$603$	9.68346	−	17.7339i	0.394341	−	0.722181i
$604$		0			0
$605$	13.5920	+	12.1720i	0.552595	+	0.494864i
$606$		0			0
$607$	33.5316	−	18.3096i	1.36101	−	0.743165i	0.377838	−	0.925872i	$-0.376668\pi$
$607$	33.5316	−	18.3096i	1.36101	−	0.743165i	0.983167	+	0.182707i	$0.0584858\pi$
$608$		0			0
$609$	−0.0516988	−	0.0332248i	−0.00209494	−	0.00134634i
$610$		0			0
$611$	8.82588	−	10.1856i	0.357057	−	0.412066i
$612$		0			0
$613$	−0.313263	−	0.234506i	−0.0126526	−	0.00947160i	0.592933	−	0.805252i	$-0.297970\pi$
$613$	−0.313263	−	0.234506i	−0.0126526	−	0.00947160i	−0.605585	+	0.795780i	$0.707061\pi$
$614$		0			0
$615$	0.00769746	−	0.0327952i	0.000310392	−	0.00132243i
$616$		0			0
$617$	−0.609414	+	0.227300i	−0.0245341	+	0.00915074i	−0.361701	−	0.932294i	$-0.617804\pi$
$617$	−0.609414	+	0.227300i	−0.0245341	+	0.00915074i	0.337167	+	0.941445i	$0.390531\pi$
$618$		0			0
$619$	−18.3405	+	11.7867i	−0.737167	+	0.473749i	−0.854570	−	0.519336i	$-0.826179\pi$
$619$	−18.3405	+	11.7867i	−0.737167	+	0.473749i	0.117403	+	0.993084i	$0.462543\pi$
$620$		0			0
$621$	2.27352	−	0.827677i	0.0912332	−	0.0332135i
$622$		0			0
$623$	−2.92023	−	0.635257i	−0.116997	−	0.0254510i
$624$		0			0
$625$	−1.93399	−	24.9251i	−0.0773596	−	0.997003i
$626$		0			0
$627$	−0.166327	−	0.0620367i	−0.00664246	−	0.00247751i
$628$		0			0
$629$	46.0063	−	6.61471i	1.83439	−	0.263746i
$630$		0			0
$631$	13.5393	+	11.7318i	0.538989	+	0.467037i	0.881305	−	0.472548i	$-0.156666\pi$
$631$	13.5393	+	11.7318i	0.538989	+	0.467037i	−0.342316	+	0.939585i	$0.611211\pi$
$632$		0			0
$633$	−0.107326	−	0.493369i	−0.00426582	−	0.0196096i
$634$		0			0
$635$	19.0226	−	13.7609i	0.754890	−	0.546086i
$636$		0			0
$637$	28.0820	+	2.00846i	1.11265	+	0.0795782i
$638$		0			0
$639$	−6.13746	−	20.9023i	−0.242794	−	0.826882i
$640$		0			0
$641$	−6.68376	−	0.960980i	−0.263993	−	0.0379564i	0.00904740	−	0.999959i	$-0.497120\pi$
$641$	−6.68376	−	0.960980i	−0.263993	−	0.0379564i	−0.273040	+	0.962003i	$0.588029\pi$
$642$		0			0
$643$	18.5823	−	18.5823i	0.732816	−	0.732816i	−0.238361	−	0.971177i	$-0.576610\pi$
$643$	18.5823	−	18.5823i	0.732816	−	0.732816i	0.971177	+	0.238361i	$0.0766101\pi$
$644$		0			0
$645$	−0.644657	+	0.0819600i	−0.0253833	+	0.00322717i
$646$		0			0
$647$	20.0532	+	26.7879i	0.788371	+	1.05314i	0.997170	+	0.0751817i	$0.0239537\pi$
$647$	20.0532	+	26.7879i	0.788371	+	1.05314i	−0.208799	+	0.977959i	$0.566955\pi$
$648$		0			0
$649$	−13.3456	+	3.91864i	−0.523863	+	0.153820i
$650$		0			0
$651$	0.400442	−	0.346985i	0.0156945	−	0.0135994i
$652$		0			0
$653$	−3.26498	−	5.97936i	−0.127768	−	0.233990i	0.805962	−	0.591967i	$-0.201649\pi$
$653$	−3.26498	−	5.97936i	−0.127768	−	0.233990i	−0.933730	+	0.357977i	$0.883467\pi$
$654$		0			0
$655$	−27.3836	−	13.0506i	−1.06997	−	0.509928i
$656$		0			0
$657$	−1.83448	−	25.6494i	−0.0715699	−	1.00068i
$658$		0			0
$659$	3.64491	+	25.3509i	0.141985	+	0.987531i	0.928863	+	0.370422i	$0.120787\pi$
$659$	3.64491	+	25.3509i	0.141985	+	0.987531i	−0.786878	+	0.617109i	$0.788304\pi$
$660$		0			0
$661$	31.1310	−	14.2170i	1.21085	−	0.552978i	0.295389	−	0.955377i	$-0.404551\pi$
$661$	31.1310	−	14.2170i	1.21085	−	0.552978i	0.915465	+	0.402398i	$0.131823\pi$
$662$		0			0
$663$	0.577228	+	1.54761i	0.0224177	+	0.0601041i
$664$		0			0
$665$	1.75451	+	0.154338i	0.0680369	+	0.00598496i
$666$		0			0
$667$	−2.27048	−	5.07691i	−0.0879133	−	0.196579i
$668$		0			0
$669$	0.783159	+	1.21862i	0.0302787	+	0.0471145i
$670$		0			0
$671$	−7.46908	+	16.3550i	−0.288341	+	0.631378i
$672$		0			0
$673$	7.28574	−	19.5338i	0.280845	−	0.752974i	−0.717559	−	0.696497i	$-0.754741\pi$
$673$	7.28574	−	19.5338i	0.280845	−	0.752974i	0.998404	−	0.0564762i	$-0.0179865\pi$
$674$		0			0
$675$	−2.33339	−	0.958278i	−0.0898120	−	0.0368841i
$676$		0			0
$677$	−20.5865	+	1.47238i	−0.791205	+	0.0565881i	−0.461091	−	0.887353i	$-0.652542\pi$
$677$	−20.5865	+	1.47238i	−0.791205	+	0.0565881i	−0.330114	+	0.943941i	$0.607087\pi$
$678$		0			0
$679$	1.75735	−	2.73449i	0.0674409	−	0.104940i
$680$		0			0
$681$	−0.316331	+	1.07733i	−0.0121218	+	0.0412832i
$682$		0			0
$683$	0.182186	−	2.54730i	0.00697117	−	0.0974697i	−0.992775	−	0.119989i	$-0.961714\pi$
$683$	0.182186	−	2.54730i	0.00697117	−	0.0974697i	0.999746	+	0.0225191i	$0.00716866\pi$
$684$		0			0
$685$	10.0219	+	3.92569i	0.382918	+	0.149993i
$686$		0			0
$687$	1.30979	−	0.980498i	0.0499717	−	0.0374083i
$688$		0			0
$689$	16.4855			0.628048
$690$		0			0
$691$	37.9606			1.44409			0.722044	−	0.691847i	$-0.243203\pi$
$691$	37.9606			1.44409			0.722044	+	0.691847i	$0.243203\pi$
$692$		0			0
$693$	2.54194	−	1.90287i	0.0965603	−	0.0722841i
$694$		0			0
$695$	13.7294	+	31.4116i	0.520786	+	1.19151i
$696$		0			0
$697$	−0.0587557	+	0.821513i	−0.00222553	+	0.0311170i
$698$		0			0
$699$	−0.208745	+	0.710919i	−0.00789544	+	0.0268894i
$700$		0			0
$701$	−0.844992	+	1.31483i	−0.0319149	+	0.0496606i	−0.856844	−	0.515575i	$-0.827578\pi$
$701$	−0.844992	+	1.31483i	−0.0319149	+	0.0496606i	0.824930	+	0.565236i	$0.191215\pi$
$702$		0			0
$703$	−12.6043	+	0.901476i	−0.475380	+	0.0339998i
$704$		0			0
$705$	0.158299	+	0.573630i	0.00596189	+	0.0216042i
$706$		0			0
$707$	−2.06498	+	5.53642i	−0.0776615	+	0.208219i
$708$		0			0
$709$	2.01588	−	4.41416i	0.0757079	−	0.165777i	−0.867994	−	0.496575i	$-0.834591\pi$
$709$	2.01588	−	4.41416i	0.0757079	−	0.165777i	0.943702	+	0.330798i	$0.107318\pi$
$710$		0			0
$711$	−27.5653	−	42.8925i	−1.03378	−	1.60859i
$712$		0			0
$713$	47.5153	−	6.45078i	1.77946	−	0.241584i
$714$		0			0
$715$	1.40786	−	16.0045i	0.0526509	−	0.598535i
$716$		0			0
$717$	0.648592	+	1.73894i	0.0242221	+	0.0649420i
$718$		0			0
$719$	−42.4538	+	19.3880i	−1.58326	+	0.723050i	−0.996249	−	0.0865303i	$-0.972422\pi$
$719$	−42.4538	+	19.3880i	−1.58326	+	0.723050i	−0.587009	+	0.809580i	$0.699695\pi$
$720$		0			0
$721$	1.35626	+	9.43296i	0.0505096	+	0.351302i
$722$		0			0
$723$	−0.0541184	−	0.756674i	−0.00201268	−	0.0281410i
$724$		0			0
$725$	−1.81447	+	5.50703i	−0.0673877	+	0.204526i
$726$		0			0
$727$	6.94325	+	12.7156i	0.257511	+	0.471596i	0.974166	−	0.225832i	$-0.0725099\pi$
$727$	6.94325	+	12.7156i	0.257511	+	0.471596i	−0.716656	+	0.697427i	$0.754328\pi$
$728$		0			0
$729$	20.1166	−	17.4311i	0.745059	−	0.645597i
$730$		0			0
$731$	15.2447	−	4.47626i	0.563847	−	0.165560i
$732$		0			0
$733$	14.0344	+	18.7477i	0.518371	+	0.692463i	0.980982	−	0.194098i	$-0.0621781\pi$
$733$	14.0344	+	18.7477i	0.518371	+	0.692463i	−0.462611	+	0.886562i	$0.653087\pi$
$734$		0			0
$735$	−0.761105	+	0.982824i	−0.0280738	+	0.0362520i
$736$		0			0
$737$	−8.04532	+	8.04532i	−0.296353	+	0.296353i
$738$		0			0
$739$	6.34416	+	0.912153i	0.233374	+	0.0335541i	0.258009	−	0.966142i	$-0.416933\pi$
$739$	6.34416	+	0.912153i	0.233374	+	0.0335541i	−0.0246356	+	0.999696i	$0.507843\pi$
$740$		0			0
$741$	−0.126517	−	0.430876i	−0.00464770	−	0.0158286i
$742$		0			0
$743$	30.1062	+	2.15324i	1.10449	+	0.0789947i	0.611652	−	0.791127i	$-0.290505\pi$
$743$	30.1062	+	2.15324i	1.10449	+	0.0789947i	0.492838	+	0.870121i	$0.335960\pi$
$744$		0			0
$745$	−35.2751	−	5.66156i	−1.29238	−	0.207423i
$746$		0			0
$747$	−5.81904	−	26.7497i	−0.212908	−	0.978720i
$748$		0			0
$749$	−4.20799	−	3.64625i	−0.153757	−	0.133231i
$750$		0			0
$751$	40.0029	−	5.75155i	1.45973	−	0.209877i	0.633732	−	0.773553i	$-0.281522\pi$
$751$	40.0029	−	5.75155i	1.45973	−	0.209877i	0.825996	+	0.563676i	$0.190613\pi$
$752$		0			0
$753$	−1.31802	−	0.491597i	−0.0480314	−	0.0179148i
$754$		0			0
$755$	−2.03167	+	6.52297i	−0.0739399	+	0.237395i
$756$		0			0
$757$	50.9157	+	11.0760i	1.85056	+	0.402566i	0.993614	−	0.112834i	$-0.0359929\pi$
$757$	50.9157	+	11.0760i	1.85056	+	0.402566i	0.856950	+	0.515400i	$0.172357\pi$
$758$		0			0
$759$	−0.679036	+	0.0432023i	−0.0246474	+	0.00156815i
$760$		0			0
$761$	2.23185	−	1.43432i	0.0809045	−	0.0519941i	−0.499563	−	0.866277i	$-0.666506\pi$
$761$	2.23185	−	1.43432i	0.0809045	−	0.0519941i	0.580468	+	0.814283i	$0.302870\pi$
$762$		0			0
$763$	−1.35565	+	0.505631i	−0.0490778	+	0.0183051i
$764$		0			0
$765$	29.9854	+	7.03796i	1.08412	+	0.254458i
$766$		0			0
$767$	−28.1673	−	21.0858i	−1.01706	−	0.761364i
$768$		0			0
$769$	−21.1044	+	24.3558i	−0.761044	+	0.878291i	−0.995590	−	0.0938138i	$-0.970094\pi$
$769$	−21.1044	+	24.3558i	−0.761044	+	0.878291i	0.234546	+	0.972105i	$0.424640\pi$
$770$		0			0
$771$	1.45468	+	0.934869i	0.0523892	+	0.0336685i
$772$		0			0
$773$	−24.2397	+	13.2359i	−0.871841	+	0.476061i	−0.851878	−	0.523740i	$-0.824536\pi$
$773$	−24.2397	+	13.2359i	−0.871841	+	0.476061i	−0.0199623	+	0.999801i	$0.506355\pi$
$774$		0			0
$775$	−41.1508	−	28.3878i	−1.47818	−	1.01972i
$776$		0			0
$777$	−0.256492	+	0.469729i	−0.00920158	+	0.0168514i
$778$		0			0
$779$	0.0318668	−	0.221638i	0.00114175	−	0.00794101i
$780$		0			0
$781$			12.2671i			0.438951i
$782$		0			0
$783$	0.413688	+	0.413688i	0.0147840	+	0.0147840i
$784$		0			0
$785$	13.6655	−	13.2260i	0.487741	−	0.472056i
$786$		0			0
$787$	8.13392	+	4.44146i	0.289943	+	0.158321i	0.617638	−	0.786463i	$-0.288090\pi$
$787$	8.13392	+	4.44146i	0.289943	+	0.158321i	−0.327695	+	0.944784i	$0.606272\pi$
$788$		0			0
$789$	−1.61028	−	1.85836i	−0.0573276	−	0.0661595i
$790$		0			0
$791$	4.37054	+	1.28331i	0.155399	+	0.0456291i
$792$		0			0
$793$	−44.4436	+	9.66811i	−1.57824	+	0.343325i
$794$		0			0
$795$	−0.403477	+	0.605823i	−0.0143098	+	0.0214863i
$796$		0			0
$797$	4.07222	−	5.43985i	0.144245	−	0.192689i	−0.722600	−	0.691267i	$-0.757053\pi$
$797$	4.07222	−	5.43985i	0.144245	−	0.192689i	0.866845	+	0.498577i	$0.166144\pi$
$798$		0			0
$799$	−6.04392	−	13.2343i	−0.213818	−	0.468197i
$800$		0			0
$801$	12.9245	+	5.90241i	0.456664	+	0.208552i
$802$		0			0
$803$	−3.07799	+	14.1493i	−0.108620	+	0.499317i
$804$		0			0
$805$	6.38037	−	2.20539i	0.224878	−	0.0777297i
$806$		0			0
$807$	−0.412317	+	1.89539i	−0.0145142	+	0.0667208i
$808$		0			0
$809$	7.10057	+	3.24272i	0.249643	+	0.114008i	0.536307	−	0.844023i	$-0.319819\pi$
$809$	7.10057	+	3.24272i	0.249643	+	0.114008i	−0.286664	+	0.958031i	$0.592546\pi$
$810$		0			0
$811$	−4.58437	−	10.0384i	−0.160979	−	0.352495i	0.811904	−	0.583790i	$-0.198431\pi$
$811$	−4.58437	−	10.0384i	−0.160979	−	0.352495i	−0.972884	+	0.231295i	$0.925704\pi$
$812$		0			0
$813$	−0.616060	+	0.822959i	−0.0216062	+	0.0288624i
$814$		0			0
$815$	7.11089	−	1.42560i	0.249084	−	0.0499367i
$816$		0			0
$817$	−4.22089	+	0.918197i	−0.147670	+	0.0321237i
$818$		0			0
$819$	7.70704	+	2.26299i	0.269306	+	0.0790753i
$820$		0			0
$821$	−22.8001	−	26.3127i	−0.795729	−	0.918320i	0.202410	−	0.979301i	$-0.435123\pi$
$821$	−22.8001	−	26.3127i	−0.795729	−	0.918320i	−0.998139	+	0.0609808i	$0.980577\pi$
$822$		0			0
$823$	19.0697	+	10.4129i	0.664729	+	0.362970i	0.775922	−	0.630829i	$-0.217285\pi$
$823$	19.0697	+	10.4129i	0.664729	+	0.362970i	−0.111192	+	0.993799i	$0.535467\pi$
$824$		0			0
$825$	0.553690	+	0.443441i	0.0192770	+	0.0154386i
$826$		0			0
$827$	−22.7686	−	22.7686i	−0.791742	−	0.791742i	0.190035	−	0.981777i	$-0.439140\pi$
$827$	−22.7686	−	22.7686i	−0.791742	−	0.791742i	−0.981777	+	0.190035i	$0.939140\pi$
$828$		0			0
$829$		−	4.05817i		−	0.140946i	−0.997514	−	0.0704730i	$-0.977549\pi$
$829$		−	4.05817i		−	0.140946i	0.997514	−	0.0704730i	$-0.0224509\pi$
$830$		0			0
$831$	0.0593333	−	0.412672i	0.00205825	−	0.0143154i
$832$		0			0
$833$	14.5655	−	26.6747i	0.504663	−	0.924222i
$834$		0			0
$835$	0.444642	−	0.0245064i	0.0153875	−	0.000848078i
$836$		0			0
$837$	−4.42722	+	2.41745i	−0.153027	+	0.0835591i
$838$		0			0
$839$	34.8988	+	22.4281i	1.20484	+	0.774303i	0.979787	−	0.200043i	$-0.0641083\pi$
$839$	34.8988	+	22.4281i	1.20484	+	0.774303i	0.225052	+	0.974347i	$0.427745\pi$
$840$		0			0
$841$	−18.1103	+	20.9004i	−0.624494	+	0.720704i
$842$		0			0
$843$	0.332756	+	0.249098i	0.0114607	+	0.00857939i
$844$		0			0
$845$	9.83728	−	6.09724i	0.338413	−	0.209751i
$846$		0			0
$847$	4.81275	−	1.79506i	0.165368	−	0.0616791i
$848$		0			0
$849$	−0.996116	+	0.640165i	−0.0341866	+	0.0219704i
$850$		0			0
$851$	−42.6906	+	22.8770i	−1.46342	+	0.784212i
$852$		0			0
$853$	−48.9290	−	10.6439i	−1.67530	−	0.364439i	−0.728196	−	0.685369i	$-0.759641\pi$
$853$	−48.9290	−	10.6439i	−1.67530	−	0.364439i	−0.947103	+	0.320930i	$0.896004\pi$
$854$		0			0
$855$	−7.99493	−	2.49013i	−0.273421	−	0.0851605i
$856$		0			0
$857$	14.7718	+	5.50958i	0.504594	+	0.188204i	0.588853	−	0.808240i	$-0.299580\pi$
$857$	14.7718	+	5.50958i	0.504594	+	0.188204i	−0.0842592	+	0.996444i	$0.526852\pi$
$858$		0			0
$859$	−29.1760	+	4.19487i	−0.995471	+	0.143127i	−0.620749	−	0.784010i	$-0.713171\pi$
$859$	−29.1760	+	4.19487i	−0.995471	+	0.143127i	−0.374723	+	0.927137i	$0.622262\pi$
$860$		0			0
$861$	−0.00716723	−	0.00621044i	−0.000244259	−	0.000211651i
$862$		0			0
$863$	−0.406509	−	1.86869i	−0.0138377	−	0.0636111i	0.969710	−	0.244258i	$-0.0785444\pi$
$863$	−0.406509	−	1.86869i	−0.0138377	−	0.0636111i	−0.983548	+	0.180647i	$0.942181\pi$
$864$		0			0
$865$	−21.7129	−	30.0151i	−0.738260	−	1.02054i
$866$		0			0
$867$	0.351084	+	0.0251100i	0.0119234	+	0.000852781i
$868$		0			0
$869$	8.08874	+	27.5477i	0.274392	+	0.934492i
$870$		0			0
$871$	−28.4892	−	4.09612i	−0.965318	−	0.138792i
$872$		0			0
$873$	−10.9276	+	10.9276i	−0.369843	+	0.369843i
$874$		0			0
$875$	−6.46595	−	2.77977i	−0.218589	−	0.0939734i
$876$		0			0
$877$	14.4104	+	19.2500i	0.486604	+	0.650027i	0.974898	−	0.222652i	$-0.0714715\pi$
$877$	14.4104	+	19.2500i	0.486604	+	0.650027i	−0.488294	+	0.872679i	$0.662381\pi$
$878$		0			0
$879$	1.83545	−	0.538937i	0.0619082	−	0.0181779i
$880$		0			0
$881$	−0.00758884	+	0.00657576i	−0.000255674	+	0.000221543i	−0.654989	−	0.755639i	$-0.727327\pi$
$881$	−0.00758884	+	0.00657576i	−0.000255674	+	0.000221543i	0.654733	+	0.755860i	$0.272781\pi$
$882$		0			0
$883$	12.6363	+	23.1416i	0.425245	+	0.778777i	0.999195	−	0.0401126i	$-0.0127717\pi$
$883$	12.6363	+	23.1416i	0.425245	+	0.778777i	−0.573951	+	0.818890i	$0.694590\pi$
$884$		0			0
$885$	1.46426	−	0.519049i	0.0492207	−	0.0174476i
$886$		0			0
$887$	0.122938	+	1.71890i	0.00412785	+	0.0577149i	0.999099	−	0.0424519i	$-0.0135169\pi$
$887$	0.122938	+	1.71890i	0.00412785	+	0.0577149i	−0.994971	+	0.100167i	$0.968062\pi$
$888$		0			0
$889$	−0.940661	−	6.54244i	−0.0315487	−	0.219426i
$890$		0			0
$891$	−13.6995	+	6.25636i	−0.458951	+	0.209596i
$892$		0			0
$893$	1.38231	+	3.70611i	0.0462572	+	0.124020i
$894$		0			0
$895$	10.5398	+	12.5730i	0.352308	+	0.420269i
$896$		0			0
$897$	−1.11689	−	1.30963i	−0.0372919	−	0.0437271i
$898$		0			0
$899$	6.26861	+	9.75414i	0.209070	+	0.325319i
$900$		0			0
$901$	7.39285	−	16.1881i	0.246291	−	0.539303i
$902$		0			0
$903$	−0.0639340	+	0.171414i	−0.00212759	+	0.00570429i
$904$		0			0
$905$	−7.46030	+	2.05874i	−0.247989	+	0.0684350i
$906$		0			0
$907$	−27.1639	+	1.94280i	−0.901964	+	0.0645097i	−0.514613	−	0.857423i	$-0.672064\pi$
$907$	−27.1639	+	1.94280i	−0.901964	+	0.0645097i	−0.387351	+	0.921932i	$0.626610\pi$
$908$		0			0
$909$	15.1884	−	23.6336i	0.503768	−	0.783878i
$910$		0			0
$911$	−3.87640	+	13.2018i	−0.128431	+	0.437396i	−0.998452	−	0.0556188i	$-0.982287\pi$
$911$	−3.87640	+	13.2018i	−0.128431	+	0.437396i	0.870021	+	0.493014i	$0.164105\pi$
$912$		0			0
$913$	−1.09971	+	15.3759i	−0.0363949	+	0.508868i
$914$		0			0
$915$	0.732449	−	1.86987i	0.0242140	−	0.0618161i
$916$		0			0
$917$	−6.83658	+	5.11780i	−0.225764	+	0.169005i
$918$		0			0
$919$	−17.3908			−0.573669			−0.286835	−	0.957980i	$-0.592603\pi$
$919$	−17.3908			−0.573669			−0.286835	+	0.957980i	$0.592603\pi$
$920$		0			0
$921$	−1.95281			−0.0643474
$922$		0			0
$923$	−24.8421	+	18.5966i	−0.817689	+	0.612114i
$924$		0			0
$925$	48.9648	+	12.3402i	1.60995	+	0.405743i
$926$		0			0
$927$	3.23228	−	45.1932i	0.106162	−	1.48434i
$928$		0			0
$929$	7.89219	−	26.8783i	0.258934	−	0.881850i	−0.722714	−	0.691148i	$-0.757105\pi$
$929$	7.89219	−	26.8783i	0.258934	−	0.881850i	0.981648	−	0.190702i	$-0.0610764\pi$
$930$		0			0
$931$	−4.46722	+	6.95113i	−0.146407	+	0.227814i
$932$		0			0
$933$	−1.48375	+	0.106120i	−0.0485757	+	0.00347421i
$934$		0			0
$935$	−15.0844	−	8.55960i	−0.493313	−	0.279929i
$936$		0			0
$937$	9.43493	−	25.2960i	0.308226	−	0.826385i	−0.686807	−	0.726839i	$-0.740988\pi$
$937$	9.43493	−	25.2960i	0.308226	−	0.826385i	0.995033	−	0.0995455i	$-0.0317389\pi$
$938$		0			0
$939$	−0.157552	+	0.344992i	−0.00514153	+	0.0112584i
$940$		0			0
$941$	−2.01246	−	3.13145i	−0.0656044	−	0.102082i	0.806901	−	0.590686i	$-0.201143\pi$
$941$	−2.01246	−	3.13145i	−0.0656044	−	0.102082i	−0.872506	+	0.488604i	$0.837506\pi$
$942$		0			0
$943$	−0.235314	−	0.825356i	−0.00766287	−	0.0268773i
$944$		0			0
$945$	−0.544222	+	0.456217i	−0.0177035	+	0.0148407i
$946$		0			0
$947$	6.70921	+	17.9881i	0.218020	+	0.584534i	0.999209	−	0.0397600i	$-0.0126593\pi$
$947$	6.70921	+	17.9881i	0.218020	+	0.584534i	−0.781189	+	0.624294i	$0.785387\pi$
$948$		0			0
$949$	−33.3199	+	15.2167i	−1.08161	+	0.493955i
$950$		0			0
$951$	−0.267001	−	1.85703i	−0.00865810	−	0.0602184i
$952$		0			0
$953$	−3.35665	−	46.9321i	−0.108732	−	1.52028i	−0.700198	−	0.713949i	$-0.746905\pi$
$953$	−3.35665	−	46.9321i	−0.108732	−	1.52028i	0.591466	−	0.806330i	$-0.298550\pi$
$954$		0			0
$955$	18.2480	−	38.2892i	0.590491	−	1.23901i
$956$		0			0
$957$	−0.0788486	−	0.144400i	−0.00254881	−	0.00466780i
$958$		0			0
$959$	2.29005	−	1.98434i	0.0739495	−	0.0640776i
$960$		0			0
$961$	−66.1763	+	19.4311i	−2.13472	+	0.626811i
$962$		0			0
$963$	15.8641	+	21.1920i	0.511213	+	0.682901i
$964$		0			0
$965$	46.4089	+	35.9394i	1.49396	+	1.15693i
$966$		0			0
$967$	15.5685	−	15.5685i	0.500649	−	0.500649i	−0.410991	−	0.911640i	$-0.634817\pi$
$967$	15.5685	−	15.5685i	0.500649	−	0.500649i	0.911640	+	0.410991i	$0.134817\pi$
$968$		0			0
$969$	−0.479838	−	0.0689903i	−0.0154146	−	0.00221629i
$970$		0			0
$971$	3.46217	+	11.7911i	0.111106	+	0.378394i	0.996208	−	0.0870043i	$-0.0277294\pi$
$971$	3.46217	+	11.7911i	0.111106	+	0.378394i	−0.885102	+	0.465398i	$0.845911\pi$
$972$		0			0
$973$	9.62641	+	0.688495i	0.308609	+	0.0220721i
$974$		0			0
$975$	−0.0586358	+	1.79353i	−0.00187785	+	0.0574389i
$976$		0			0
$977$	9.70348	+	44.6062i	0.310442	+	1.42708i	0.822812	+	0.568313i	$0.192404\pi$
$977$	9.70348	+	44.6062i	0.310442	+	1.42708i	−0.512371	+	0.858764i	$0.671233\pi$
$978$		0			0
$979$	−6.04665	−	5.23945i	−0.193252	−	0.167454i
$980$		0			0
$981$	6.80892	−	0.978975i	0.217392	−	0.0312563i
$982$		0			0
$983$	−28.8539	−	10.7620i	−0.920297	−	0.343253i	−0.155732	−	0.987799i	$-0.549774\pi$
$983$	−28.8539	−	10.7620i	−0.920297	−	0.343253i	−0.764565	+	0.644546i	$0.777046\pi$
$984$		0			0
$985$	1.82839	+	3.48256i	0.0582574	+	0.110964i
$986$		0			0
$987$	0.163700	+	0.0356107i	0.00521062	+	0.00113350i
$988$		0			0
$989$	−13.3317	+	9.81739i	−0.423924	+	0.312175i
$990$		0			0
$991$	6.06714	−	3.89911i	0.192729	−	0.123859i	−0.440718	−	0.897646i	$-0.645276\pi$
$991$	6.06714	−	3.89911i	0.192729	−	0.123859i	0.633447	+	0.773786i	$0.281640\pi$
$992$		0			0
$993$	−0.306336	+	0.114257i	−0.00972126	+	0.00362584i
$994$		0			0
$995$	18.1584	+	29.2967i	0.575659	+	0.928767i
$996$		0			0
$997$	24.6518	+	18.4541i	0.780732	+	0.584449i	0.913566	−	0.406690i	$-0.133317\pi$
$997$	24.6518	+	18.4541i	0.780732	+	0.584449i	−0.132834	+	0.991138i	$0.542408\pi$
$998$		0			0
$999$	3.33653	−	3.85056i	0.105563	−	0.121826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.333.7	yes	240
5.2	odd	4	inner	460.2.x.a.57.6	✓	240
23.21	odd	22	inner	460.2.x.a.113.6	yes	240
115.67	even	44	inner	460.2.x.a.297.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.57.6	✓	240	5.2	odd	4	inner
460.2.x.a.113.6	yes	240	23.21	odd	22	inner
460.2.x.a.297.7	yes	240	115.67	even	44	inner
460.2.x.a.333.7	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0673917 + 0.0504488i) q^{3} +(2.04891 - 0.895537i) q^{5} +(0.0449089 - 0.627908i) q^{7} +(-0.843201 + 2.87168i) q^{9} +O(q^{10})\)	\(q+(-0.0673917 + 0.0504488i) q^{3} +(2.04891 - 0.895537i) q^{5} +(0.0449089 - 0.627908i) q^{7} +(-0.843201 + 2.87168i) q^{9} +(0.911155 - 1.41778i) q^{11} +(4.25245 - 0.304142i) q^{13} +(-0.0929004 + 0.163716i) q^{15} +(1.60834 - 4.31212i) q^{17} +(-0.519784 + 1.13817i) q^{19} +(0.0286507 + 0.0445813i) q^{21} +(-0.0377062 + 4.79568i) q^{23} +(3.39603 - 3.66974i) q^{25} +(-0.176304 - 0.472690i) q^{27} +(-1.05485 + 0.481736i) q^{29} +(-1.42294 - 9.89674i) q^{31} +(0.0101212 + 0.141514i) q^{33} +(-0.470301 - 1.32674i) q^{35} +(4.84002 + 8.86383i) q^{37} +(-0.271236 + 0.235028i) q^{39} +(-0.171707 + 0.0504179i) q^{41} +(2.06886 + 2.76367i) q^{43} +(0.844055 + 6.63892i) q^{45} +(2.23536 - 2.23536i) q^{47} +(6.53650 + 0.939807i) q^{49} +(0.109153 + 0.371740i) q^{51} +(3.85697 + 0.275856i) q^{53} +(0.597192 - 3.72088i) q^{55} +(-0.0223901 - 0.102925i) q^{57} +(-6.23724 - 5.40460i) q^{59} +(-10.5599 + 1.51828i) q^{61} +(1.76528 + 0.658416i) q^{63} +(8.44051 - 4.43139i) q^{65} +(-6.59682 - 1.43505i) q^{67} +(-0.239395 - 0.325091i) q^{69} +(-6.12329 + 3.93520i) q^{71} +(-8.05021 + 3.00257i) q^{73} +(-0.0437301 + 0.418635i) q^{75} +(-0.849319 - 0.635792i) q^{77} +(-11.1560 + 12.8747i) q^{79} +(-7.51767 - 4.83131i) q^{81} +(-8.02787 + 4.38355i) q^{83} +(-0.566331 - 10.2755i) q^{85} +(0.0467854 - 0.0856811i) q^{87} +(0.675621 - 4.69905i) q^{89} -2.68381i q^{91} +(0.595172 + 0.595172i) q^{93} +(-0.0457168 + 2.79748i) q^{95} +(4.53191 + 2.47461i) q^{97} +(3.30314 + 3.81202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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