LMFDB - Embedded newform 460.2.x.a.33.6

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			33.6
Character	$\chi$	$=$	460.33
Dual form			460.2.x.a.237.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0980316 + 0.450644i) q^{3} +(2.20605 - 0.365176i) q^{5} +(1.83859 + 3.36712i) q^{7} +(2.53543 - 1.15789i) q^{9} +O(q^{10})$	\(q+(0.0980316 + 0.450644i) q^{3} +(2.20605 - 0.365176i) q^{5} +(1.83859 + 3.36712i) q^{7} +(2.53543 - 1.15789i) q^{9} +(-0.179116 - 0.155205i) q^{11} +(-4.88990 - 2.67009i) q^{13} +(0.380827 + 0.958343i) q^{15} +(-1.31470 + 1.75624i) q^{17} +(-0.184229 + 1.28134i) q^{19} +(-1.33713 + 1.15863i) q^{21} +(2.69233 + 3.96880i) q^{23} +(4.73329 - 1.61119i) q^{25} +(1.59948 + 2.13665i) q^{27} +(-0.986272 + 0.141805i) q^{29} +(7.10324 - 4.56498i) q^{31} +(0.0523831 - 0.0959324i) q^{33} +(5.28560 + 6.75662i) q^{35} +(1.90481 - 5.10698i) q^{37} +(0.723895 - 2.46536i) q^{39} +(-1.72046 + 3.76728i) q^{41} +(-6.06548 + 1.31946i) q^{43} +(5.17044 - 3.48024i) q^{45} +(2.92484 - 2.92484i) q^{47} +(-4.17260 + 6.49270i) q^{49} +(-0.920321 - 0.420297i) q^{51} +(-10.3521 + 5.65269i) q^{53} +(-0.451815 - 0.276980i) q^{55} +(-0.595490 + 0.0425903i) q^{57} +(-2.27261 - 7.73978i) q^{59} +(-0.294346 - 0.458011i) q^{61} +(8.56035 + 6.40820i) q^{63} +(-11.7624 - 4.10467i) q^{65} +(-0.437844 + 6.12185i) q^{67} +(-1.52458 + 1.60235i) q^{69} +(-7.22100 - 8.33348i) q^{71} +(7.73909 - 5.79341i) q^{73} +(1.19009 + 1.97508i) q^{75} +(0.193273 - 0.888462i) q^{77} +(-8.54432 + 2.50884i) q^{79} +(4.66983 - 5.38927i) q^{81} +(0.922600 + 0.344112i) q^{83} +(-2.25896 + 4.35445i) q^{85} +(-0.160589 - 0.430556i) q^{87} +(-10.6079 - 6.81727i) q^{89} -21.3741i q^{91} +(2.75352 + 2.75352i) q^{93} +(0.0614975 + 2.89398i) q^{95} +(4.97392 - 1.85518i) q^{97} +(-0.633845 - 0.186114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

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

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
$3$	0.0980316	+	0.450644i	0.0565986	+	0.260179i	0.996748	−	0.0805834i	$-0.0256783\pi$
$3$	0.0980316	+	0.450644i	0.0565986	+	0.260179i	−0.940149	+	0.340763i	$0.889315\pi$
$4$		0			0
$5$	2.20605	−	0.365176i	0.986575	−	0.163312i
$5$	2.20605	−	0.365176i	0.986575	−	0.163312i
$6$		0			0
$7$	1.83859	+	3.36712i	0.694920	+	1.27265i	0.951952	+	0.306248i	$0.0990737\pi$
$7$	1.83859	+	3.36712i	0.694920	+	1.27265i	−0.257032	+	0.966403i	$0.582744\pi$
$8$		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
$13$	−4.88990	−	2.67009i	−1.35622	−	0.740550i	−0.373844	−	0.927491i	$-0.621961\pi$
$13$	−4.88990	−	2.67009i	−1.35622	−	0.740550i	−0.982371	+	0.186942i	$0.940142\pi$
$14$		0			0
$15$	0.380827	+	0.958343i	0.0983291	+	0.247443i
$16$		0			0
$17$	−1.31470	+	1.75624i	−0.318863	+	0.425951i	−0.931123	−	0.364706i	$-0.881170\pi$
$17$	−1.31470	+	1.75624i	−0.318863	+	0.425951i	0.612260	+	0.790656i	$0.290261\pi$
$18$		0			0
$19$	−0.184229	+	1.28134i	−0.0422651	+	0.293960i	0.957715	+	0.287717i	$0.0928963\pi$
$19$	−0.184229	+	1.28134i	−0.0422651	+	0.293960i	−0.999981	+	0.00624312i	$0.998013\pi$
$20$		0			0
$21$	−1.33713	+	1.15863i	−0.291786	+	0.252834i
$22$		0			0
$23$	2.69233	+	3.96880i	0.561390	+	0.827552i
$23$	2.69233	+	3.96880i	0.561390	+	0.827552i
$24$		0			0
$25$	4.73329	−	1.61119i	0.946659	−	0.322239i
$26$		0			0
$27$	1.59948	+	2.13665i	0.307820	+	0.411199i
$28$		0			0
$29$	−0.986272	+	0.141805i	−0.183146	+	0.0263324i	−0.233278	−	0.972410i	$-0.574945\pi$
$29$	−0.986272	+	0.141805i	−0.183146	+	0.0263324i	0.0501314	+	0.998743i	$0.484036\pi$
$30$		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
$33$	0.0523831	−	0.0959324i	0.00911872	−	0.0166997i
$34$		0			0
$35$	5.28560	+	6.75662i	0.893429	+	1.14208i
$36$		0			0
$37$	1.90481	−	5.10698i	0.313148	−	0.839583i	−0.681071	−	0.732217i	$-0.738486\pi$
$37$	1.90481	−	5.10698i	0.313148	−	0.839583i	0.994220	−	0.107366i	$-0.0342416\pi$
$38$		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
$43$	−6.06548	+	1.31946i	−0.924977	+	0.201216i	−0.649737	−	0.760159i	$-0.725121\pi$
$43$	−6.06548	+	1.31946i	−0.924977	+	0.201216i	−0.275240	+	0.961376i	$0.588757\pi$
$44$		0			0
$45$	5.17044	−	3.48024i	0.770763	−	0.518803i
$46$		0			0
$47$	2.92484	−	2.92484i	0.426631	−	0.426631i	−0.460848	−	0.887479i	$-0.652455\pi$
$47$	2.92484	−	2.92484i	0.426631	−	0.426631i	0.887479	+	0.460848i	$0.152455\pi$
$48$		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
$53$	−10.3521	+	5.65269i	−1.42197	+	0.776457i	−0.991982	−	0.126376i	$-0.959665\pi$
$53$	−10.3521	+	5.65269i	−1.42197	+	0.776457i	−0.429992	+	0.902833i	$0.641484\pi$
$54$		0			0
$55$	−0.451815	−	0.276980i	−0.0609227	−	0.0373480i
$56$		0			0
$57$	−0.595490	+	0.0425903i	−0.0788746	+	0.00564122i
$58$		0			0
$59$	−2.27261	−	7.73978i	−0.295868	−	1.00763i	−0.964509	−	0.264049i	$-0.914942\pi$
$59$	−2.27261	−	7.73978i	−0.295868	−	1.00763i	0.668641	−	0.743585i	$-0.266876\pi$
$60$		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
$63$	8.56035	+	6.40820i	1.07850	+	0.807357i
$64$		0			0
$65$	−11.7624	−	4.10467i	−1.45895	−	0.509121i
$66$		0			0
$67$	−0.437844	+	6.12185i	−0.0534911	+	0.747903i	0.897955	+	0.440088i	$0.145053\pi$
$67$	−0.437844	+	6.12185i	−0.0534911	+	0.747903i	−0.951446	+	0.307816i	$0.900402\pi$
$68$		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
$73$	7.73909	−	5.79341i	0.905792	−	0.678067i	−0.0412598	−	0.999148i	$-0.513137\pi$
$73$	7.73909	−	5.79341i	0.905792	−	0.678067i	0.947052	+	0.321081i	$0.104046\pi$
$74$		0			0
$75$	1.19009	+	1.97508i	0.137419	+	0.228063i
$76$		0			0
$77$	0.193273	−	0.888462i	0.0220255	−	0.101250i
$78$		0			0
$79$	−8.54432	+	2.50884i	−0.961311	+	0.282266i	−0.724489	−	0.689287i	$-0.757924\pi$
$79$	−8.54432	+	2.50884i	−0.961311	+	0.282266i	−0.236822	+	0.971553i	$0.576106\pi$
$80$		0			0
$81$	4.66983	−	5.38927i	0.518870	−	0.598808i
$82$		0			0
$83$	0.922600	+	0.344112i	0.101269	+	0.0377712i	0.399588	−	0.916695i	$-0.369153\pi$
$83$	0.922600	+	0.344112i	0.101269	+	0.0377712i	−0.298319	+	0.954466i	$0.596426\pi$
$84$		0			0
$85$	−2.25896	+	4.35445i	−0.245019	+	0.472306i
$86$		0			0
$87$	−0.160589	−	0.430556i	−0.0172170	−	0.0461605i
$88$		0			0
$89$	−10.6079	−	6.81727i	−1.12443	−	0.722630i	−0.160042	−	0.987110i	$-0.551163\pi$
$89$	−10.6079	−	6.81727i	−1.12443	−	0.722630i	−0.964391	+	0.264481i	$0.914799\pi$
$90$		0			0
$91$		−	21.3741i		−	2.24061i
$92$		0			0
$93$	2.75352	+	2.75352i	0.285527	+	0.285527i
$94$		0			0
$95$	0.0614975	+	2.89398i	0.00630951	+	0.296916i
$96$		0			0
$97$	4.97392	−	1.85518i	0.505025	−	0.188365i	−0.0840212	−	0.996464i	$-0.526776\pi$
$97$	4.97392	−	1.85518i	0.505025	−	0.188365i	0.589046	+	0.808099i	$0.299504\pi$
$98$		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
$103$	0.214604	+	3.00055i	0.0211456	+	0.295653i	0.997010	+	0.0772754i	$0.0246221\pi$
$103$	0.214604	+	3.00055i	0.0211456	+	0.295653i	−0.975864	+	0.218378i	$0.929923\pi$
$104$		0			0
$105$	−2.52667	+	3.04429i	−0.246578	+	0.297092i
$106$		0			0
$107$	−6.12296	−	1.33197i	−0.591929	−	0.128766i	−0.0933839	−	0.995630i	$-0.529768\pi$
$107$	−6.12296	−	1.33197i	−0.591929	−	0.128766i	−0.498545	+	0.866864i	$0.666132\pi$
$108$		0			0
$109$	−0.540723	−	3.76081i	−0.0517919	−	0.360221i	−0.999193	−	0.0401714i	$-0.987210\pi$
$109$	−0.540723	−	3.76081i	−0.0517919	−	0.360221i	0.947401	−	0.320049i	$-0.103699\pi$
$110$		0			0
$111$	2.48816	+	0.357744i	0.236166	+	0.0339555i
$112$		0			0
$113$	−16.1513	−	1.15516i	−1.51938	−	0.108668i	−0.713463	−	0.700693i	$-0.752874\pi$
$113$	−16.1513	−	1.15516i	−1.51938	−	0.108668i	−0.805920	+	0.592024i	$0.798329\pi$
$114$		0			0
$115$	7.38872	+	7.77218i	0.689002	+	0.724760i
$116$		0			0
$117$	−15.4897	−	1.10784i	−1.43202	−	0.102420i
$118$		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
$123$	−1.86636	−	0.406002i	−0.168284	−	0.0366080i
$124$		0			0
$125$	9.85350	−	5.28285i	0.881324	−	0.472513i
$126$		0			0
$127$	0.520642	+	7.27953i	0.0461995	+	0.645954i	0.966814	+	0.255481i	$0.0822339\pi$
$127$	0.520642	+	7.27953i	0.0461995	+	0.645954i	−0.920614	+	0.390473i	$0.872312\pi$
$128$		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
$133$	−4.65316	+	1.73554i	−0.403480	+	0.150490i
$134$		0			0
$135$	4.30878	+	4.12947i	0.370841	+	0.355408i
$136$		0			0
$137$	10.5920	+	10.5920i	0.904938	+	0.904938i	0.995858	−	0.0909203i	$-0.0289809\pi$
$137$	10.5920	+	10.5920i	0.904938	+	0.904938i	−0.0909203	+	0.995858i	$0.528981\pi$
$138$		0			0
$139$			20.2830i			1.72038i	0.509971	+	0.860192i	$0.329656\pi$
$139$			20.2830i			1.72038i	−0.509971	+	0.860192i	$0.670344\pi$
$140$		0			0
$141$	1.60479	+	1.03133i	0.135147	+	0.0868540i
$142$		0			0
$143$	0.461449	+	1.23719i	0.0385883	+	0.103459i
$144$		0			0
$145$	−2.12398	+	0.672991i	−0.176387	+	0.0558888i
$146$		0			0
$147$	−3.33494	−	1.24387i	−0.275061	−	0.102593i
$148$		0			0
$149$	6.13032	−	7.07477i	0.502216	−	0.579588i	−0.446873	−	0.894598i	$-0.647462\pi$
$149$	6.13032	−	7.07477i	0.502216	−	0.579588i	0.949088	+	0.315010i	$0.102008\pi$
$150$		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
$153$	−1.29980	+	5.97510i	−0.105083	+	0.483058i
$154$		0			0
$155$	14.0031	−	12.6645i	1.12475	−	1.01724i
$156$		0			0
$157$	2.59713	−	1.94419i	0.207274	−	0.155163i	−0.490598	−	0.871386i	$-0.663222\pi$
$157$	2.59713	−	1.94419i	0.207274	−	0.155163i	0.697871	+	0.716223i	$0.254131\pi$
$158$		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
$163$	0.241075	−	3.37067i	0.0188825	−	0.264011i	−0.979237	−	0.202717i	$-0.935023\pi$
$163$	0.241075	−	3.37067i	0.0188825	−	0.264011i	0.998120	−	0.0612940i	$-0.0195227\pi$
$164$		0			0
$165$	0.0805273	−	0.230761i	0.00626904	−	0.0179647i
$166$		0			0
$167$	−12.8821	−	9.64344i	−0.996849	−	0.746232i	−0.0294705	−	0.999566i	$-0.509382\pi$
$167$	−12.8821	−	9.64344i	−0.996849	−	0.746232i	−0.967379	+	0.253333i	$0.918473\pi$
$168$		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
$173$	−17.4395	+	1.24730i	−1.32590	+	0.0948305i	−0.716253	−	0.697840i	$-0.754144\pi$
$173$	−17.4395	+	1.24730i	−1.32590	+	0.0948305i	−0.609650	+	0.792671i	$0.708690\pi$
$174$		0			0
$175$	14.1276	+	12.9752i	1.06795	+	0.980836i
$176$		0			0
$177$	3.26510	−	1.78288i	0.245420	−	0.134009i
$178$		0			0
$179$	−7.38976	−	3.37479i	−0.552337	−	0.252244i	0.119638	−	0.992818i	$-0.461826\pi$
$179$	−7.38976	−	3.37479i	−0.552337	−	0.252244i	−0.671975	+	0.740574i	$0.734554\pi$
$180$		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
$187$	0.508061	−	0.110522i	0.0371531	−	0.00808217i
$188$		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
$193$	1.65810	−	4.44554i	0.119353	−	0.319997i	−0.863511	−	0.504330i	$-0.831740\pi$
$193$	1.65810	−	4.44554i	0.119353	−	0.319997i	0.982864	+	0.184333i	$0.0590124\pi$
$194$		0			0
$195$	0.696656	−	5.70305i	0.0498885	−	0.408404i
$196$		0			0
$197$	0.982755	−	1.79978i	0.0700184	−	0.128229i	−0.840325	−	0.542083i	$-0.817636\pi$
$197$	0.982755	−	1.79978i	0.0700184	−	0.128229i	0.910343	+	0.413854i	$0.135818\pi$
$198$		0			0
$199$	22.6474	−	14.5546i	1.60543	−	1.03175i	0.640953	−	0.767581i	$-0.278540\pi$
$199$	22.6474	−	14.5546i	1.60543	−	1.03175i	0.964477	−	0.264166i	$-0.0850968\pi$
$200$		0			0
$201$	−2.80170	+	0.402823i	−0.197617	+	0.0284130i
$202$		0			0
$203$	−2.29082	−	3.06017i	−0.160784	−	0.214782i
$204$		0			0
$205$	−2.41969	+	8.93907i	−0.168999	+	0.624331i
$206$		0			0
$207$	11.4216	+	6.94517i	0.793859	+	0.482723i
$208$		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
$213$	3.04755	−	4.07104i	0.208814	−	0.278943i
$214$		0			0
$215$	−12.8989	+	5.12577i	−0.879698	+	0.349575i
$216$		0			0
$217$	28.4307	+	15.5244i	1.93000	+	1.05386i
$218$		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
$223$	−0.886127	−	1.62282i	−0.0593395	−	0.108672i	0.846326	−	0.532666i	$-0.178810\pi$
$223$	−0.886127	−	1.62282i	−0.0593395	−	0.108672i	−0.905665	+	0.423994i	$0.860628\pi$
$224$		0			0
$225$	10.1353	−	9.56569i	0.675689	−	0.637713i
$226$		0			0
$227$	5.00861	+	23.0242i	0.332433	+	1.52817i	0.775307	+	0.631585i	$0.217595\pi$
$227$	5.00861	+	23.0242i	0.332433	+	1.52817i	−0.442874	+	0.896584i	$0.646041\pi$
$228$		0			0
$229$	−27.2781			−1.80259			−0.901295	−	0.433205i	$-0.857382\pi$
$229$	−27.2781			−1.80259			−0.901295	+	0.433205i	$0.857382\pi$
$230$		0			0
$231$	0.419327			0.0275897
$232$		0			0
$233$	−4.03620	−	18.5541i	−0.264420	−	1.21552i	−0.897353	−	0.441314i	$-0.854513\pi$
$233$	−4.03620	−	18.5541i	−0.264420	−	1.21552i	0.632932	−	0.774207i	$-0.281851\pi$
$234$		0			0
$235$	5.38425	−	7.52041i	0.351230	−	0.490578i
$236$		0			0
$237$	−1.96821	−	3.60450i	−0.127849	−	0.234137i
$238$		0			0
$239$	0.986603	−	0.450567i	0.0638180	−	0.0291447i	−0.383250	−	0.923645i	$-0.625195\pi$
$239$	0.986603	−	0.450567i	0.0638180	−	0.0291447i	0.447068	+	0.894500i	$0.352468\pi$
$240$		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
$243$	9.91404	+	5.41347i	0.635986	+	0.347275i
$244$		0			0
$245$	−6.83398	+	15.8469i	−0.436607	+	1.01242i
$246$		0			0
$247$	4.32217	−	5.77374i	0.275013	−	0.367374i
$248$		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
$253$	0.133738	−	1.12874i	0.00840801	−	0.0709631i
$254$		0			0
$255$	−2.18376	−	0.591115i	−0.136752	−	0.0370171i
$256$		0			0
$257$	10.0938	+	13.4837i	0.629633	+	0.841092i	0.995998	−	0.0893799i	$-0.0284885\pi$
$257$	10.0938	+	13.4837i	0.629633	+	0.841092i	−0.366364	+	0.930471i	$0.619398\pi$
$258$		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
$263$	−13.7174	+	25.1216i	−0.845853	+	1.54906i	−0.0101060	+	0.999949i	$0.503217\pi$
$263$	−13.7174	+	25.1216i	−0.845853	+	1.54906i	−0.835747	+	0.549115i	$0.814965\pi$
$264$		0			0
$265$	−20.7731	+	16.2505i	−1.27608	+	0.998258i
$266$		0			0
$267$	2.03226	−	5.44869i	0.124372	−	0.333454i
$268$		0			0
$269$	−4.23328	+	14.4172i	−0.258108	+	0.879034i	0.723854	+	0.689953i	$0.242369\pi$
$269$	−4.23328	+	14.4172i	−0.258108	+	0.879034i	−0.981962	+	0.189081i	$0.939449\pi$
$270$		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
$273$	9.63210	−	2.09533i	0.582961	−	0.126815i
$274$		0			0
$275$	−1.09787	−	0.446039i	−0.0662042	−	0.0268972i
$276$		0			0
$277$	11.1706	−	11.1706i	0.671175	−	0.671175i	−0.286812	−	0.957987i	$-0.592596\pi$
$277$	11.1706	−	11.1706i	0.671175	−	0.671175i	0.957987	+	0.286812i	$0.0925955\pi$
$278$		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
$283$	12.9760	−	7.08542i	0.771342	−	0.421185i	−0.0448293	−	0.998995i	$-0.514274\pi$
$283$	12.9760	−	7.08542i	0.771342	−	0.421185i	0.816171	+	0.577810i	$0.196093\pi$
$284$		0			0
$285$	−1.29813	+	0.311415i	−0.0768944	+	0.0184466i
$286$		0			0
$287$	−15.8481	+	1.13348i	−0.935483	+	0.0669070i
$288$		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
$293$	13.7669	+	10.3058i	0.804271	+	0.602070i	0.920317	−	0.391174i	$-0.127931\pi$
$293$	13.7669	+	10.3058i	0.804271	+	0.602070i	−0.116046	+	0.993244i	$0.537022\pi$
$294$		0			0
$295$	−7.83986	−	16.2444i	−0.456454	−	0.945787i
$296$		0			0
$297$	0.0451268	−	0.630955i	0.00261852	−	0.0366117i
$298$		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
$303$	4.22034	−	3.15931i	0.242452	−	0.181498i
$304$		0			0
$305$	−0.816595	−	0.902905i	−0.0467581	−	0.0517002i
$306$		0			0
$307$	4.56657	−	20.9922i	0.260628	−	1.19809i	−0.641672	−	0.766979i	$-0.721759\pi$
$307$	4.56657	−	20.9922i	0.260628	−	1.19809i	0.902300	−	0.431109i	$-0.141878\pi$
$308$		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
$313$	32.9867	+	12.3034i	1.86452	+	0.695429i	0.967185	+	0.254072i	$0.0817701\pi$
$313$	32.9867	+	12.3034i	1.86452	+	0.695429i	0.897332	+	0.441357i	$0.145503\pi$
$314$		0			0
$315$	21.2247	+	11.0108i	1.19587	+	0.620386i
$316$		0			0
$317$	−3.45124	−	9.25313i	−0.193841	−	0.519708i	0.803274	−	0.595609i	$-0.203089\pi$
$317$	−3.45124	−	9.25313i	−0.193841	−	0.519708i	−0.997115	+	0.0759015i	$0.975817\pi$
$318$		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
$325$	−27.4474	−	4.75974i	−1.52251	−	0.264023i
$326$		0			0
$327$	1.64178	−	0.612352i	0.0907907	−	0.0338632i
$328$		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
$333$	−1.08383	−	15.1539i	−0.0593936	−	0.830431i
$334$		0			0
$335$	1.26965	+	13.6650i	0.0693685	+	0.746598i
$336$		0			0
$337$	−3.59826	−	0.782754i	−0.196010	−	0.0426393i	0.113489	−	0.993539i	$-0.463797\pi$
$337$	−3.59826	−	0.782754i	−0.196010	−	0.0426393i	−0.309498	+	0.950900i	$0.600161\pi$
$338$		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
$343$	−2.74707	−	0.196474i	−0.148328	−	0.0106086i
$344$		0			0
$345$	−2.77816	+	4.09160i	−0.149571	+	0.220284i
$346$		0			0
$347$	−29.4339	−	2.10515i	−1.58009	−	0.113011i	−0.746499	−	0.665386i	$-0.768267\pi$
$347$	−29.4339	−	2.10515i	−1.58009	−	0.113011i	−0.833595	+	0.552376i	$0.813721\pi$
$348$		0			0
$349$	−7.02613	−	1.01020i	−0.376100	−	0.0540750i	−0.0483271	−	0.998832i	$-0.515389\pi$
$349$	−7.02613	−	1.01020i	−0.376100	−	0.0540750i	−0.327773	+	0.944757i	$0.606298\pi$
$350$		0			0
$351$	−2.11624	−	14.7188i	−0.112957	−	0.785631i
$352$		0			0
$353$	−7.13168	−	1.55140i	−0.379581	−	0.0825728i	0.0187268	−	0.999825i	$-0.494039\pi$
$353$	−7.13168	−	1.55140i	−0.379581	−	0.0825728i	−0.398308	+	0.917252i	$0.630402\pi$
$354$		0			0
$355$	−18.9731	−	15.7471i	−1.00699	−	0.835770i
$356$		0			0
$357$	−0.276901	−	3.87158i	−0.0146552	−	0.204906i
$358$		0			0
$359$	−8.33160	−	18.2437i	−0.439725	−	0.962863i	−0.991649	−	0.128969i	$-0.958833\pi$
$359$	−8.33160	−	18.2437i	−0.439725	−	0.962863i	0.551924	−	0.833894i	$-0.313894\pi$
$360$		0			0
$361$	16.6225	+	4.88080i	0.874867	+	0.256884i
$362$		0			0
$363$	4.72889	−	1.76379i	0.248202	−	0.0925747i
$364$		0			0
$365$	14.9572	−	15.6067i	0.782895	−	0.816890i
$366$		0			0
$367$	−17.5734	−	17.5734i	−0.917324	−	0.917324i	0.0795098	−	0.996834i	$-0.474664\pi$
$367$	−17.5734	−	17.5734i	−0.917324	−	0.917324i	−0.996834	+	0.0795098i	$0.974664\pi$
$368$		0			0
$369$			11.5438i			0.600944i
$370$		0			0
$371$	−38.0666	−	24.4639i	−1.97632	−	1.27010i
$372$		0			0
$373$	0.853247	+	2.28764i	0.0441795	+	0.118450i	0.957166	−	0.289540i	$-0.0935025\pi$
$373$	0.853247	+	2.28764i	0.0441795	+	0.118450i	−0.912986	+	0.407990i	$0.866230\pi$
$374$		0			0
$375$	3.34664	+	3.92253i	0.172820	+	0.202559i
$376$		0			0
$377$	5.20141	+	1.94002i	0.267886	+	0.0999163i
$378$		0			0
$379$	−12.3052	+	14.2010i	−0.632078	+	0.729457i	−0.977953	−	0.208823i	$-0.933037\pi$
$379$	−12.3052	+	14.2010i	−0.632078	+	0.729457i	0.345875	+	0.938281i	$0.387582\pi$
$380$		0			0
$381$	−3.22944	+	0.948248i	−0.165449	+	0.0485802i
$382$		0			0
$383$	−3.64145	+	16.7395i	−0.186069	+	0.855347i	0.785550	+	0.618798i	$0.212380\pi$
$383$	−3.64145	+	16.7395i	−0.186069	+	0.855347i	−0.971620	+	0.236549i	$0.923984\pi$
$384$		0			0
$385$	0.101924	−	2.03057i	0.00519454	−	0.103487i
$386$		0			0
$387$	−13.8508	+	10.3686i	−0.704075	+	0.527064i
$388$		0			0
$389$	6.72218	+	7.75781i	0.340828	+	0.393337i	0.900126	−	0.435630i	$-0.143475\pi$
$389$	6.72218	+	7.75781i	0.340828	+	0.393337i	−0.559298	+	0.828967i	$0.688929\pi$
$390$		0			0
$391$	−10.5098	−	0.489421i	−0.531502	−	0.0247511i
$392$		0			0
$393$	−0.414329	+	5.79308i	−0.0209001	+	0.292222i
$394$		0			0
$395$	−17.9330	+	8.65480i	−0.902307	+	0.435470i
$396$		0			0
$397$	−20.1208	−	15.0622i	−1.00983	−	0.755951i	−0.0398692	−	0.999205i	$-0.512694\pi$
$397$	−20.1208	−	15.0622i	−1.00983	−	0.755951i	−0.969963	+	0.243254i	$0.921785\pi$
$398$		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
$403$	−46.9231	+	3.35600i	−2.33740	+	0.167174i
$404$		0			0
$405$	8.33383	−	13.5943i	0.414111	−	0.675506i
$406$		0			0
$407$	−1.13381	+	0.619107i	−0.0562008	+	0.0306880i
$408$		0			0
$409$	31.9481	+	14.5902i	1.57973	+	0.721440i	0.995902	−	0.0904353i	$-0.0288258\pi$
$409$	31.9481	+	14.5902i	1.57973	+	0.721440i	0.583831	+	0.811875i	$0.301553\pi$
$410$		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
$417$	−9.14042	+	1.98838i	−0.447608	+	0.0973712i
$418$		0			0
$419$	3.05029	−	6.67920i	0.149016	−	0.326300i	−0.820373	−	0.571829i	$-0.806234\pi$
$419$	3.05029	−	6.67920i	0.149016	−	0.326300i	0.969389	+	0.245528i	$0.0789615\pi$
$420$		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
$423$	4.02907	−	10.8024i	0.195900	−	0.525228i
$424$		0			0
$425$	−3.39324	+	10.4310i	−0.164596	+	0.505980i
$426$		0			0
$427$	1.00100	−	1.83319i	0.0484416	−	0.0887142i
$428$		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
$433$	4.94096	+	6.60035i	0.237448	+	0.317193i	0.903398	−	0.428803i	$-0.141065\pi$
$433$	4.94096	+	6.60035i	0.237448	+	0.317193i	−0.665950	+	0.745996i	$0.731974\pi$
$434$		0			0
$435$	−0.511496	−	0.891184i	−0.0245244	−	0.0427290i
$436$		0			0
$437$	−5.58140	+	2.71863i	−0.266995	+	0.130050i
$438$		0			0
$439$	23.3928	−	20.2700i	1.11648	−	0.967434i	0.116809	−	0.993154i	$-0.462733\pi$
$439$	23.3928	−	20.2700i	1.11648	−	0.967434i	0.999669	+	0.0257207i	$0.00818804\pi$
$440$		0			0
$441$	−3.06150	+	21.2932i	−0.145786	+	1.01396i
$442$		0			0
$443$	15.6844	−	20.9519i	0.745189	−	0.995456i	−0.254408	−	0.967097i	$-0.581881\pi$
$443$	15.6844	−	20.9519i	0.745189	−	0.995456i	0.999598	−	0.0283595i	$-0.00902832\pi$
$444$		0			0
$445$	−25.8910	−	11.1655i	−1.22735	−	0.529295i
$446$		0			0
$447$	3.78917	+	2.06904i	0.179221	+	0.0978623i
$448$		0			0
$449$	4.29583	+	3.72235i	0.202733	+	0.175669i	0.750310	−	0.661086i	$-0.229904\pi$
$449$	4.29583	+	3.72235i	0.202733	+	0.175669i	−0.547577	+	0.836755i	$0.684450\pi$
$450$		0			0
$451$	0.892861	−	0.407756i	0.0420432	−	0.0192005i
$452$		0			0
$453$	−3.18388	−	5.83085i	−0.149592	−	0.273957i
$454$		0			0
$455$	−7.80531	−	47.1522i	−0.365918	−	2.21053i
$456$		0			0
$457$	−3.38428	−	15.5573i	−0.158310	−	0.727740i	−0.986026	−	0.166592i	$-0.946724\pi$
$457$	−3.38428	−	15.5573i	−0.158310	−	0.727740i	0.827716	−	0.561148i	$-0.189640\pi$
$458$		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
$463$	−0.188024	−	0.864334i	−0.00873823	−	0.0401690i	0.972571	−	0.232605i	$-0.0747249\pi$
$463$	−0.188024	−	0.864334i	−0.00873823	−	0.0401690i	−0.981310	+	0.192436i	$0.938361\pi$
$464$		0			0
$465$	7.07992	+	5.06888i	0.328323	+	0.235064i
$466$		0			0
$467$	−2.32231	−	4.25299i	−0.107464	−	0.196805i	0.818413	−	0.574630i	$-0.194854\pi$
$467$	−2.32231	−	4.25299i	−0.107464	−	0.196805i	−0.925877	+	0.377825i	$0.876672\pi$
$468$		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
$473$	1.29121	+	0.705055i	0.0593699	+	0.0324184i
$474$		0			0
$475$	1.19248	+	6.36180i	0.0547147	+	0.291900i
$476$		0			0
$477$	−19.7019	+	26.3186i	−0.902086	+	1.20505i
$478$		0			0
$479$	−3.73327	+	25.9655i	−0.170578	+	1.18639i	0.707090	+	0.707123i	$0.250007\pi$
$479$	−3.73327	+	25.9655i	−0.170578	+	1.18639i	−0.877668	+	0.479269i	$0.840902\pi$
$480$		0			0
$481$	−22.9504	+	19.8867i	−1.04645	+	0.906754i
$482$		0			0
$483$	−8.19838	−	2.18739i	−0.373039	−	0.0995297i
$484$		0			0
$485$	10.2952	−	5.90896i	0.467483	−	0.268312i
$486$		0			0
$487$	−16.3852	−	21.8881i	−0.742486	−	0.991845i	−0.999675	−	0.0254840i	$-0.991887\pi$
$487$	−16.3852	−	21.8881i	−0.742486	−	0.991845i	0.257189	−	0.966361i	$-0.417204\pi$
$488$		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
$493$	1.04761	−	1.91856i	0.0471821	−	0.0864076i
$494$		0			0
$495$	−1.46626	−	0.179110i	−0.0659033	−	0.00805042i
$496$		0			0
$497$	14.7834	−	39.6358i	0.663125	−	1.77791i
$498$		0			0
$499$	−0.207165	+	0.705540i	−0.00927399	+	0.0315843i	−0.964000	−	0.265902i	$-0.914330\pi$
$499$	−0.207165	+	0.705540i	−0.00927399	+	0.0315843i	0.954726	+	0.297487i	$0.0961483\pi$
$500$		0			0
$501$	3.08290	−	6.75062i	0.137734	−	0.301595i
$502$		0			0
$503$	22.0568	−	4.79817i	0.983465	−	0.213940i	0.308044	−	0.951372i	$-0.400326\pi$
$503$	22.0568	−	4.79817i	0.983465	−	0.213940i	0.675421	+	0.737432i	$0.263962\pi$
$504$		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	−0.913687	−	0.406418i	$-0.866778\pi$
$509$	−3.70988	+	5.77268i	−0.164437	+	0.255870i	0.749250	+	0.662287i	$0.230414\pi$
$510$		0			0
$511$	33.7361	+	15.4067i	1.49240	+	0.681554i
$512$		0			0
$513$	−3.03246	+	1.65585i	−0.133886	+	0.0731075i
$514$		0			0
$515$	1.56916	+	6.54100i	0.0691454	+	0.288231i
$516$		0			0
$517$	−0.977833	+	0.0699360i	−0.0430051	+	0.00307578i
$518$		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
$523$	−2.68127	−	2.00717i	−0.117244	−	0.0877676i	0.539047	−	0.842276i	$-0.318785\pi$
$523$	−2.68127	−	2.00717i	−0.117244	−	0.0877676i	−0.656291	+	0.754508i	$0.727875\pi$
$524$		0			0
$525$	−4.46226	+	7.63852i	−0.194749	+	0.333372i
$526$		0			0
$527$	−1.32147	+	18.4766i	−0.0575642	+	0.804853i
$528$		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
$533$	18.4718	−	13.8279i	0.800105	−	0.598951i
$534$		0			0
$535$	−13.9939	−	0.702425i	−0.605011	−	0.0303685i
$536$		0			0
$537$	0.796399	−	3.66099i	0.0343672	−	0.157983i
$538$		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
$543$	10.5184	+	3.92318i	0.451390	+	0.168360i
$544$		0			0
$545$	−2.56622	−	8.09908i	−0.109925	−	0.346926i
$546$		0			0
$547$	12.9758	+	34.7896i	0.554807	+	1.48749i	0.847241	+	0.531209i	$0.178262\pi$
$547$	12.9758	+	34.7896i	0.554807	+	1.48749i	−0.292434	+	0.956286i	$0.594465\pi$
$548$		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
$555$	5.61965	−	0.119418i	0.238541	−	0.00506902i
$556$		0			0
$557$	6.40675	−	2.38960i	0.271463	−	0.101250i	−0.210046	−	0.977691i	$-0.567361\pi$
$557$	6.40675	−	2.38960i	0.271463	−	0.101250i	0.481509	+	0.876441i	$0.340089\pi$
$558$		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
$563$	−1.57053	−	21.9589i	−0.0661899	−	0.925456i	−0.916720	−	0.399530i	$-0.869173\pi$
$563$	−1.57053	−	21.9589i	−0.0661899	−	0.925456i	0.850530	−	0.525926i	$-0.176281\pi$
$564$		0			0
$565$	−36.0523	+	3.34972i	−1.51673	+	0.140924i
$566$		0			0
$567$	26.7322	+	5.81523i	1.12265	+	0.244217i
$568$		0			0
$569$	−1.15072	−	8.00345i	−0.0482408	−	0.335522i	−0.999622	−	0.0275051i	$-0.991244\pi$
$569$	−1.15072	−	8.00345i	−0.0482408	−	0.335522i	0.951381	−	0.308017i	$-0.0996653\pi$
$570$		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
$573$	1.84005	+	0.131603i	0.0768690	+	0.00549778i
$574$		0			0
$575$	19.1381	+	14.4476i	0.798113	+	0.602507i
$576$		0			0
$577$	−30.5120	−	2.18226i	−1.27023	−	0.0908486i	−0.580106	−	0.814541i	$-0.696989\pi$
$577$	−30.5120	−	2.18226i	−1.27023	−	0.0908486i	−0.690123	+	0.723692i	$0.742444\pi$
$578$		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
$583$	2.73155	+	0.594213i	0.113129	+	0.0246098i
$584$		0			0
$585$	−34.5755	+	3.21250i	−1.42952	+	0.132821i
$586$		0			0
$587$	1.79439	+	25.0888i	0.0740622	+	1.03553i	0.889576	+	0.456787i	$0.151000\pi$
$587$	1.79439	+	25.0888i	0.0740622	+	1.03553i	−0.815514	+	0.578738i	$0.803545\pi$
$588$		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
$593$	6.96219	−	2.59676i	0.285903	−	0.106636i	−0.202421	−	0.979299i	$-0.564881\pi$
$593$	6.96219	−	2.59676i	0.285903	−	0.106636i	0.488324	+	0.872662i	$0.337608\pi$
$594$		0			0
$595$	−18.8152	+	0.399827i	−0.771350	+	0.0163913i
$596$		0			0
$597$	8.77909	+	8.77909i	0.359304	+	0.359304i
$598$		0			0
$599$		−	10.5868i		−	0.432564i	−0.976331	−	0.216282i	$-0.930607\pi$
$599$		−	10.5868i		−	0.432564i	0.976331	−	0.216282i	$-0.0693931\pi$
$600$		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
$603$	5.97831	+	16.0285i	0.243456	+	0.652730i
$604$		0			0
$605$	−7.39160	−	23.3281i	−0.300511	−	0.948423i
$606$		0			0
$607$	−18.4538	−	6.88291i	−0.749016	−	0.279369i	−0.0541748	−	0.998531i	$-0.517253\pi$
$607$	−18.4538	−	6.88291i	−0.749016	−	0.279369i	−0.694842	+	0.719163i	$0.744526\pi$
$608$		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
$613$	−7.51911	+	34.5648i	−0.303694	+	1.39606i	0.531945	+	0.846779i	$0.321461\pi$
$613$	−7.51911	+	34.5648i	−0.303694	+	1.39606i	−0.835639	+	0.549279i	$0.814902\pi$
$614$		0			0
$615$	−4.26554	−	0.214109i	−0.172003	−	0.00863370i
$616$		0			0
$617$	5.54361	−	4.14989i	0.223177	−	0.167068i	−0.481838	−	0.876260i	$-0.660031\pi$
$617$	5.54361	−	4.14989i	0.223177	−	0.167068i	0.705016	+	0.709192i	$0.250940\pi$
$618$		0			0
$619$	−4.31757	−	4.98274i	−0.173538	−	0.200273i	0.662317	−	0.749223i	$-0.269573\pi$
$619$	−4.31757	−	4.98274i	−0.173538	−	0.200273i	−0.835855	+	0.548950i	$0.815028\pi$
$620$		0			0
$621$	−4.17362	+	12.1006i	−0.167482	+	0.485580i
$622$		0			0
$623$	3.45106	−	48.2521i	0.138264	−	1.93318i
$624$		0			0
$625$	19.8081	−	15.2525i	0.792325	−	0.610100i
$626$		0			0
$627$	0.113272	+	0.0847943i	0.00452365	+	0.00338636i
$628$		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
$633$	1.43074	−	0.102328i	0.0568667	−	0.00406719i
$634$		0			0
$635$	3.80687	+	15.8689i	0.151071	+	0.629737i
$636$		0			0
$637$	37.7397	−	20.6074i	1.49530	−	0.816497i
$638$		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	$-0.622972\pi$
$643$	13.9341	−	13.9341i	0.549508	−	0.549508i	0.926299	+	0.376790i	$0.122972\pi$
$644$		0			0
$645$	−3.57440	−	5.31033i	−0.140742	−	0.209094i
$646$		0			0
$647$	18.0376	−	3.92385i	0.709132	−	0.154262i	0.156488	−	0.987680i	$-0.449983\pi$
$647$	18.0376	−	3.92385i	0.709132	−	0.154262i	0.552644	+	0.833418i	$0.313619\pi$
$648$		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
$653$	−13.6249	+	36.5296i	−0.533182	+	1.42952i	0.339211	+	0.940710i	$0.389840\pi$
$653$	−13.6249	+	36.5296i	−0.533182	+	1.42952i	−0.872393	+	0.488805i	$0.837433\pi$
$654$		0			0
$655$	27.9520	+	3.41447i	1.09217	+	0.133414i
$656$		0			0
$657$	12.9138	−	23.6498i	0.503814	−	0.922666i
$658$		0			0
$659$	23.5469	−	15.1327i	0.917258	−	0.589486i	0.00539743	−	0.999985i	$-0.498282\pi$
$659$	23.5469	−	15.1327i	0.917258	−	0.589486i	0.911861	+	0.410499i	$0.134646\pi$
$660$		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
$663$	3.37805	+	4.51255i	0.131193	+	0.175253i
$664$		0			0
$665$	−9.63131	+	5.52790i	−0.373486	+	0.214363i
$666$		0			0
$667$	−3.21816	−	3.53253i	−0.124608	−	0.136780i
$668$		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
$673$	11.2588	−	15.0400i	0.433994	−	0.579748i	−0.529220	−	0.848485i	$-0.677515\pi$
$673$	11.2588	−	15.0400i	0.433994	−	0.579748i	0.963214	+	0.268737i	$0.0866062\pi$
$674$		0			0
$675$	11.0134	+	7.53634i	0.423905	+	0.290074i
$676$		0			0
$677$	21.1989	+	11.5755i	0.814739	+	0.444881i	0.831869	−	0.554972i	$-0.187271\pi$
$677$	21.1989	+	11.5755i	0.814739	+	0.444881i	−0.0171298	+	0.999853i	$0.505453\pi$
$678$		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
$683$	15.8246	+	28.9807i	0.605513	+	1.10891i	0.983122	+	0.182949i	$0.0585643\pi$
$683$	15.8246	+	28.9807i	0.605513	+	1.10891i	−0.377610	+	0.925965i	$0.623254\pi$
$684$		0			0
$685$	27.2345	+	19.4986i	1.04058	+	0.745002i
$686$		0			0
$687$	−2.67412	−	12.2927i	−0.102024	−	0.468997i
$688$		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
$693$	−0.538712	−	2.47642i	−0.0204640	−	0.0940713i
$694$		0			0
$695$	7.40688	+	44.7453i	0.280959	+	1.69729i
$696$		0			0
$697$	−4.35435	−	7.97439i	−0.164933	−	0.302052i
$698$		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
$703$	6.19288	+	3.38157i	0.233569	+	0.127538i
$704$		0			0
$705$	3.91685	+	1.68914i	0.147517	+	0.0636167i
$706$		0			0
$707$	26.2810	−	35.1073i	0.988397	−	1.32034i
$708$		0			0
$709$	5.36626	−	37.3232i	0.201534	−	1.40170i	−0.598200	−	0.801347i	$-0.704117\pi$
$709$	5.36626	−	37.3232i	0.201534	−	1.40170i	0.799734	−	0.600355i	$-0.204974\pi$
$710$		0			0
$711$	−18.7585	+	16.2544i	−0.703500	+	0.609586i
$712$		0			0
$713$	37.2417	+	15.9009i	1.39471	+	0.595494i
$714$		0			0
$715$	1.46977	+	2.56079i	0.0549663	+	0.0957683i
$716$		0			0
$717$	0.299763	+	0.400437i	0.0111949	+	0.0149546i
$718$		0			0
$719$	−13.3152	+	1.91444i	−0.496573	+	0.0713964i	−0.386051	−	0.922477i	$-0.626161\pi$
$719$	−13.3152	+	1.91444i	−0.496573	+	0.0713964i	−0.110522	+	0.993874i	$0.535252\pi$
$720$		0			0
$721$	−9.70866	+	6.23937i	−0.361569	+	0.232366i
$722$		0			0
$723$	−6.38653	+	11.6961i	−0.237518	+	0.434981i
$724$		0			0
$725$	−4.43984	+	2.26028i	−0.164892	+	0.0839446i
$726$		0			0
$727$	−6.46805	+	17.3415i	−0.239887	+	0.643161i	−0.999978	−	0.00665558i	$-0.997881\pi$
$727$	−6.46805	+	17.3415i	−0.239887	+	0.643161i	0.760091	+	0.649816i	$0.225154\pi$
$728$		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
$733$	−32.1045	+	6.98390i	−1.18581	+	0.257956i	−0.761867	−	0.647734i	$-0.775717\pi$
$733$	−32.1045	+	6.98390i	−1.18581	+	0.257956i	−0.423940	+	0.905690i	$0.639353\pi$
$734$		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	−0.939561	−	0.342380i	$-0.888767\pi$
$739$	−6.46485	+	10.0595i	−0.237813	+	0.370045i	0.701748	+	0.712425i	$0.252403\pi$
$740$		0			0
$741$	3.02561	+	1.38175i	0.111149	+	0.0507598i
$742$		0			0
$743$	−13.7876	+	7.52859i	−0.505817	+	0.276197i	−0.711829	−	0.702352i	$-0.752133\pi$
$743$	−13.7876	+	7.52859i	−0.505817	+	0.276197i	0.206012	+	0.978549i	$0.433951\pi$
$744$		0			0
$745$	10.9402	−	17.8459i	0.400820	−	0.653824i
$746$		0			0
$747$	2.73763	−	0.195799i	0.100165	−	0.00716391i
$748$		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
$753$	−6.74294	−	5.04770i	−0.245726	−	0.183948i
$754$		0			0
$755$	−29.0095	+	14.0005i	−1.05576	+	0.509531i
$756$		0			0
$757$	−1.14438	+	16.0005i	−0.0415931	+	0.581547i	0.933332	+	0.359014i	$0.116887\pi$
$757$	−1.14438	+	16.0005i	−0.0415931	+	0.581547i	−0.974925	+	0.222533i	$0.928568\pi$
$758$		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
$763$	11.6689	−	8.73526i	0.422444	−	0.316238i
$764$		0			0
$765$	−0.685463	+	13.6560i	−0.0247830	+	0.493734i
$766$		0			0
$767$	−9.55309	+	43.9149i	−0.344942	+	1.58567i
$768$		0			0
$769$	40.0976	−	11.7737i	1.44596	−	0.424571i	0.537754	−	0.843102i	$-0.319273\pi$
$769$	40.0976	−	11.7737i	1.44596	−	0.424571i	0.908202	+	0.418531i	$0.137455\pi$
$770$		0			0
$771$	−5.08685	+	5.87054i	−0.183198	+	0.211422i
$772$		0			0
$773$	17.8730	+	6.66627i	0.642846	+	0.239769i	0.649680	−	0.760208i	$-0.274903\pi$
$773$	17.8730	+	6.66627i	0.642846	+	0.239769i	−0.00683443	+	0.999977i	$0.502175\pi$
$774$		0			0
$775$	26.2667	−	33.0521i	0.943526	−	1.18727i
$776$		0			0
$777$	3.37014	+	9.03568i	0.120903	+	0.324153i
$778$		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
$785$	5.01942	−	5.23738i	0.179151	−	0.186930i
$786$		0			0
$787$	−6.90333	+	2.57481i	−0.246077	+	0.0917821i	−0.469477	−	0.882945i	$-0.655557\pi$
$787$	−6.90333	+	2.57481i	−0.246077	+	0.0917821i	0.223399	+	0.974727i	$0.428285\pi$
$788$		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
$793$	0.216392	+	3.02556i	0.00768431	+	0.107441i
$794$		0			0
$795$	−9.35959	−	7.76820i	−0.331950	−	0.275510i
$796$		0			0
$797$	−18.6244	−	4.05149i	−0.659710	−	0.143511i	−0.129767	−	0.991544i	$-0.541423\pi$
$797$	−18.6244	−	4.05149i	−0.659710	−	0.143511i	−0.529943	+	0.848033i	$0.677787\pi$
$798$		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
$803$	−2.28536	−	0.163452i	−0.0806485	−	0.00576810i
$804$		0			0
$805$	−12.5851	+	39.1685i	−0.443565	+	1.38051i
$806$		0			0
$807$	−6.91203	−	0.494358i	−0.243315	−	0.0174022i
$808$		0			0
$809$	−42.7075	−	6.14041i	−1.50151	−	0.215885i	−0.658011	−	0.753008i	$-0.728602\pi$
$809$	−42.7075	−	6.14041i	−1.50151	−	0.215885i	−0.843504	+	0.537123i	$0.819511\pi$
$810$		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
$813$	−6.90155	−	1.50134i	−0.242048	−	0.0526543i
$814$		0			0
$815$	−0.699066	−	7.52390i	−0.0244872	−	0.263551i
$816$		0			0
$817$	−0.573248	−	8.01505i	−0.0200554	−	0.280411i
$818$		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
$823$	−34.4422	+	12.8463i	−1.20058	+	0.447793i	−0.868610	−	0.495497i	$-0.834986\pi$
$823$	−34.4422	+	12.8463i	−1.20058	+	0.447793i	−0.331970	+	0.943290i	$0.607713\pi$
$824$		0			0
$825$	0.0933788	−	0.538476i	0.00325103	−	0.0187473i
$826$		0			0
$827$	−7.70901	−	7.70901i	−0.268069	−	0.268069i	0.560253	−	0.828322i	$-0.310704\pi$
$827$	−7.70901	−	7.70901i	−0.268069	−	0.268069i	−0.828322	+	0.560253i	$0.810704\pi$
$828$		0			0
$829$			28.4563i			0.988327i	0.869369	+	0.494164i	$0.164526\pi$
$829$			28.4563i			0.988327i	−0.869369	+	0.494164i	$0.835474\pi$
$830$		0			0
$831$	6.12902	+	3.93888i	0.212613	+	0.136638i
$832$		0			0
$833$	−5.91699	−	15.8641i	−0.205012	−	0.549657i
$834$		0			0
$835$	−31.9402	−	16.5696i	−1.10533	−	0.573416i
$836$		0			0
$837$	21.1153	+	7.87558i	0.729850	+	0.272220i
$838$		0			0
$839$	−13.2472	+	15.2881i	−0.457346	+	0.527805i	−0.936849	−	0.349735i	$-0.886272\pi$
$839$	−13.2472	+	15.2881i	−0.457346	+	0.527805i	0.479503	+	0.877540i	$0.340817\pi$
$840$		0			0
$841$	−26.8727	+	7.89053i	−0.926644	+	0.272087i
$842$		0			0
$843$	−1.10064	+	5.05956i	−0.0379081	+	0.174261i
$844$		0			0
$845$	27.0587	+	29.9187i	0.930849	+	1.02924i
$846$		0			0
$847$	33.6106	−	25.1605i	1.15487	−	0.864527i
$848$		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
$853$	3.87862	−	54.2301i	0.132801	−	1.85680i	−0.298263	−	0.954484i	$-0.596407\pi$
$853$	3.87862	−	54.2301i	0.132801	−	1.85680i	0.431065	−	0.902321i	$-0.358138\pi$
$854$		0			0
$855$	3.50684	+	7.26627i	0.119931	+	0.248501i
$856$		0			0
$857$	−7.77065	−	5.81704i	−0.265441	−	0.198706i	0.458264	−	0.888816i	$-0.348471\pi$
$857$	−7.77065	−	5.81704i	−0.265441	−	0.198706i	−0.723705	+	0.690110i	$0.757562\pi$
$858$		0			0
$859$	24.8725	+	38.7023i	0.848637	+	1.32051i	0.945638	+	0.325221i	$0.105439\pi$
$859$	24.8725	+	38.7023i	0.848637	+	1.32051i	−0.0970009	+	0.995284i	$0.530925\pi$
$860$		0			0
$861$	−2.06441	−	7.03073i	−0.0703548	−	0.239606i
$862$		0			0
$863$	43.4627	−	3.10852i	1.47949	−	0.105815i	0.691889	−	0.722003i	$-0.256779\pi$
$863$	43.4627	−	3.10852i	1.47949	−	0.105815i	0.787599	+	0.616188i	$0.211324\pi$
$864$		0			0
$865$	−38.0170	+	9.12011i	−1.29262	+	0.310093i
$866$		0			0
$867$	−4.93301	+	2.69363i	−0.167534	+	0.0914805i
$868$		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
$877$	−13.7687	+	2.99519i	−0.464935	+	0.101140i	−0.438930	−	0.898522i	$-0.644642\pi$
$877$	−13.7687	+	2.99519i	−0.464935	+	0.101140i	−0.0260050	+	0.999662i	$0.508279\pi$
$878$		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
$883$	5.57819	−	14.9557i	0.187721	−	0.503299i	−0.808662	−	0.588273i	$-0.799808\pi$
$883$	5.57819	−	14.9557i	0.187721	−	0.503299i	0.996383	+	0.0849739i	$0.0270807\pi$
$884$		0			0
$885$	6.55190	−	5.12545i	0.220240	−	0.172290i
$886$		0			0
$887$	−12.8071	+	23.4544i	−0.430020	+	0.787522i	−0.999403	−	0.0345498i	$-0.989000\pi$
$887$	−12.8071	+	23.4544i	−0.430020	+	0.787522i	0.569383	+	0.822072i	$0.307182\pi$
$888$		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
$893$	3.20888	+	4.28656i	0.107381	+	0.143444i
$894$		0			0
$895$	−17.5346	−	4.74638i	−0.586116	−	0.158654i
$896$		0			0
$897$	11.7335	−	3.76457i	0.391769	−	0.125695i
$898$		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
$903$	6.58158	−	8.79196i	0.219021	−	0.292578i
$904$		0			0
$905$	21.5545	−	49.9814i	0.716495	−	1.66144i
$906$		0			0
$907$	−0.152622	−	0.0833377i	−0.00506772	−	0.00276718i	0.476713	−	0.879059i	$-0.341828\pi$
$907$	−0.152622	−	0.0833377i	−0.00506772	−	0.00276718i	−0.481781	+	0.876292i	$0.660010\pi$
$908$		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
$913$	−0.111844	−	0.204828i	−0.00370151	−	0.00677881i
$914$		0			0
$915$	0.326837	−	0.456507i	0.0108049	−	0.0150916i
$916$		0			0
$917$	10.2697	+	47.2091i	0.339136	+	1.55898i
$918$		0			0
$919$	−6.39970			−0.211107			−0.105553	−	0.994414i	$-0.533661\pi$
$919$	−6.39970			−0.211107			−0.105553	+	0.994414i	$0.533661\pi$
$920$		0			0
$921$	9.90768			0.326469
$922$		0			0
$923$	13.0589	+	60.0306i	0.429838	+	1.97593i
$924$		0			0
$925$	0.787671	−	27.2419i	0.0258985	−	0.895707i
$926$		0			0
$927$	4.01843	+	7.35920i	0.131982	+	0.241708i
$928$		0			0
$929$	3.01153	−	1.37532i	0.0988051	−	0.0451228i	−0.365399	−	0.930851i	$-0.619068\pi$
$929$	3.01153	−	1.37532i	0.0988051	−	0.0451228i	0.464204	+	0.885728i	$0.346340\pi$
$930$		0			0
$931$	−7.55066	−	6.54268i	−0.247463	−	0.214428i
$932$		0			0
$933$	−8.86212	−	4.83908i	−0.290133	−	0.158424i
$934$		0			0
$935$	1.08045	−	0.429349i	0.0353344	−	0.0140412i
$936$		0			0
$937$	−2.71720	+	3.62975i	−0.0887669	+	0.118579i	−0.842726	−	0.538342i	$-0.819051\pi$
$937$	−2.71720	+	3.62975i	−0.0887669	+	0.118579i	0.753959	+	0.656921i	$0.228142\pi$
$938$		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
$943$	−19.5836	+	3.31460i	−0.637730	+	0.107938i
$944$		0			0
$945$	−5.98234	+	22.1006i	−0.194606	+	0.718931i
$946$		0			0
$947$	−17.8406	−	23.8323i	−0.579742	−	0.774444i	0.410790	−	0.911730i	$-0.365253\pi$
$947$	−17.8406	−	23.8323i	−0.579742	−	0.774444i	−0.990531	+	0.137286i	$0.956162\pi$
$948$		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
$953$	−1.76237	+	3.22753i	−0.0570886	+	0.104550i	−0.904665	−	0.426123i	$-0.859879\pi$
$953$	−1.76237	+	3.22753i	−0.0570886	+	0.104550i	0.847577	+	0.530673i	$0.178061\pi$
$954$		0			0
$955$	1.08453	−	8.87833i	0.0350946	−	0.287296i
$956$		0			0
$957$	−0.0380603	+	0.102044i	−0.00123032	+	0.00329860i
$958$		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
$963$	−17.0666	+	3.71261i	−0.549963	+	0.119637i
$964$		0			0
$965$	2.03444	−	10.4126i	0.0654911	−	0.335193i
$966$		0			0
$967$	−27.0045	+	27.0045i	−0.868407	+	0.868407i	−0.992296	−	0.123889i	$-0.960463\pi$
$967$	−27.0045	+	27.0045i	−0.868407	+	0.868407i	0.123889	+	0.992296i	$0.460463\pi$
$968$		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
$973$	−68.2953	+	37.2921i	−2.18945	+	1.19553i
$974$		0			0
$975$	−0.545763	−	12.8356i	−0.0174784	−	0.411068i
$976$		0			0
$977$	−21.7165	+	1.55320i	−0.694773	+	0.0496911i	−0.414259	−	0.910159i	$-0.635959\pi$
$977$	−21.7165	+	1.55320i	−0.694773	+	0.0496911i	−0.280514	+	0.959850i	$0.590505\pi$
$978$		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
$983$	−22.4008	−	16.7690i	−0.714473	−	0.534848i	0.179064	−	0.983837i	$-0.442693\pi$
$983$	−22.4008	−	16.7690i	−0.714473	−	0.534848i	−0.893537	+	0.448990i	$0.851784\pi$
$984$		0			0
$985$	1.51077	−	4.32928i	0.0481370	−	0.137942i
$986$		0			0
$987$	−0.522085	+	7.29970i	−0.0166182	+	0.232352i
$988$		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
$993$	−12.7258	+	9.52638i	−0.403840	+	0.302311i
$994$		0			0
$995$	44.6462	−	40.3784i	1.41538	−	1.28008i
$996$		0			0
$997$	8.30652	−	38.1845i	0.263070	−	1.20931i	−0.636062	−	0.771638i	$-0.719438\pi$
$997$	8.30652	−	38.1845i	0.263070	−	1.20931i	0.899133	−	0.437676i	$-0.144198\pi$
$998$		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.33.6	✓	240
5.2	odd	4	inner	460.2.x.a.217.6	yes	240
23.7	odd	22	inner	460.2.x.a.53.6	yes	240
115.7	even	44	inner	460.2.x.a.237.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.33.6	✓	240	1.1	even	1	trivial
460.2.x.a.53.6	yes	240	23.7	odd	22	inner
460.2.x.a.217.6	yes	240	5.2	odd	4	inner
460.2.x.a.237.6	yes	240	115.7	even	44	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.0980316 + 0.450644i) q^{3} +(2.20605 - 0.365176i) q^{5} +(1.83859 + 3.36712i) q^{7} +(2.53543 - 1.15789i) q^{9} +O(q^{10})\)	\(q+(0.0980316 + 0.450644i) q^{3} +(2.20605 - 0.365176i) q^{5} +(1.83859 + 3.36712i) q^{7} +(2.53543 - 1.15789i) q^{9} +(-0.179116 - 0.155205i) q^{11} +(-4.88990 - 2.67009i) q^{13} +(0.380827 + 0.958343i) q^{15} +(-1.31470 + 1.75624i) q^{17} +(-0.184229 + 1.28134i) q^{19} +(-1.33713 + 1.15863i) q^{21} +(2.69233 + 3.96880i) q^{23} +(4.73329 - 1.61119i) q^{25} +(1.59948 + 2.13665i) q^{27} +(-0.986272 + 0.141805i) q^{29} +(7.10324 - 4.56498i) q^{31} +(0.0523831 - 0.0959324i) q^{33} +(5.28560 + 6.75662i) q^{35} +(1.90481 - 5.10698i) q^{37} +(0.723895 - 2.46536i) q^{39} +(-1.72046 + 3.76728i) q^{41} +(-6.06548 + 1.31946i) q^{43} +(5.17044 - 3.48024i) q^{45} +(2.92484 - 2.92484i) q^{47} +(-4.17260 + 6.49270i) q^{49} +(-0.920321 - 0.420297i) q^{51} +(-10.3521 + 5.65269i) q^{53} +(-0.451815 - 0.276980i) q^{55} +(-0.595490 + 0.0425903i) q^{57} +(-2.27261 - 7.73978i) q^{59} +(-0.294346 - 0.458011i) q^{61} +(8.56035 + 6.40820i) q^{63} +(-11.7624 - 4.10467i) q^{65} +(-0.437844 + 6.12185i) q^{67} +(-1.52458 + 1.60235i) q^{69} +(-7.22100 - 8.33348i) q^{71} +(7.73909 - 5.79341i) q^{73} +(1.19009 + 1.97508i) q^{75} +(0.193273 - 0.888462i) q^{77} +(-8.54432 + 2.50884i) q^{79} +(4.66983 - 5.38927i) q^{81} +(0.922600 + 0.344112i) q^{83} +(-2.25896 + 4.35445i) q^{85} +(-0.160589 - 0.430556i) q^{87} +(-10.6079 - 6.81727i) q^{89} -21.3741i q^{91} +(2.75352 + 2.75352i) q^{93} +(0.0614975 + 2.89398i) q^{95} +(4.97392 - 1.85518i) q^{97} +(-0.633845 - 0.186114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 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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