LMFDB - Embedded newform 460.2.x.a.217.12

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			217.12
Character	$\chi$	$=$	460.217
Dual form			460.2.x.a.53.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.30373 - 0.718682i) q^{3} +(-1.74600 - 1.39695i) q^{5} +(0.976498 - 0.533208i) q^{7} +(7.66923 - 3.50242i) q^{9} +O(q^{10})$	\(q+(3.30373 - 0.718682i) q^{3} +(-1.74600 - 1.39695i) q^{5} +(0.976498 - 0.533208i) q^{7} +(7.66923 - 3.50242i) q^{9} +(1.18981 + 1.03098i) q^{11} +(-2.81184 + 5.14950i) q^{13} +(-6.77228 - 3.36034i) q^{15} +(-2.58086 - 1.93201i) q^{17} +(0.413151 - 2.87353i) q^{19} +(2.84288 - 2.46337i) q^{21} +(3.78044 - 2.95098i) q^{23} +(1.09704 + 4.87817i) q^{25} +(14.7001 - 11.0043i) q^{27} +(-5.38029 + 0.773569i) q^{29} +(-1.93432 + 1.24311i) q^{31} +(4.67177 + 2.55098i) q^{33} +(-2.44983 - 0.433141i) q^{35} +(-6.69565 - 2.49735i) q^{37} +(-5.58870 + 19.0334i) q^{39} +(0.0672449 - 0.147246i) q^{41} +(1.75147 + 8.05137i) q^{43} +(-18.2832 - 4.59834i) q^{45} +(5.06547 + 5.06547i) q^{47} +(-3.11525 + 4.84742i) q^{49} +(-9.91496 - 4.52801i) q^{51} +(1.28875 + 2.36018i) q^{53} +(-0.637185 - 3.46221i) q^{55} +(-0.700215 - 9.79028i) q^{57} +(-0.348211 - 1.18590i) q^{59} +(5.81275 + 9.04482i) q^{61} +(5.62147 - 7.50941i) q^{63} +(12.1031 - 5.06302i) q^{65} +(-14.1216 - 1.01000i) q^{67} +(10.3687 - 12.4662i) q^{69} +(-0.836283 - 0.965122i) q^{71} +(9.87765 + 13.1950i) q^{73} +(7.13016 + 15.3277i) q^{75} +(1.71158 + 0.372331i) q^{77} +(2.32634 - 0.683076i) q^{79} +(24.0928 - 27.8045i) q^{81} +(1.11358 - 2.98562i) q^{83} +(1.80726 + 6.97863i) q^{85} +(-17.2191 + 6.42238i) q^{87} +(-7.38093 - 4.74344i) q^{89} +6.52777i q^{91} +(-5.49707 + 5.49707i) q^{93} +(-4.73555 + 4.44003i) q^{95} +(-1.61138 - 4.32027i) q^{97} +(12.7359 + 3.73960i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.30373	−	0.718682i	1.90741	−	0.414932i	0.907423	−	0.420217i	$-0.138046\pi$
$3$	3.30373	−	0.718682i	1.90741	−	0.414932i	0.999986	+	0.00528596i	$0.00168258\pi$
$4$		0			0
$5$	−1.74600	−	1.39695i	−0.780835	−	0.624737i
$5$	−1.74600	−	1.39695i	−0.780835	−	0.624737i
$6$		0			0
$7$	0.976498	−	0.533208i	0.369082	−	0.201534i	−0.283995	−	0.958826i	$-0.591660\pi$
$7$	0.976498	−	0.533208i	0.369082	−	0.201534i	0.653076	+	0.757292i	$0.273478\pi$
$8$		0			0
$9$	7.66923	−	3.50242i	2.55641	−	1.16747i
$10$		0			0
$11$	1.18981	+	1.03098i	0.358743	+	0.310852i	0.815520	−	0.578729i	$-0.196451\pi$
$11$	1.18981	+	1.03098i	0.358743	+	0.310852i	−0.456777	+	0.889581i	$0.650996\pi$
$12$		0			0
$13$	−2.81184	+	5.14950i	−0.779864	+	1.42821i	0.120334	+	0.992733i	$0.461603\pi$
$13$	−2.81184	+	5.14950i	−0.779864	+	1.42821i	−0.900198	+	0.435481i	$0.856578\pi$
$14$		0			0
$15$	−6.77228	−	3.36034i	−1.74860	−	0.867636i
$16$		0			0
$17$	−2.58086	−	1.93201i	−0.625950	−	0.468580i	0.238606	−	0.971116i	$-0.423310\pi$
$17$	−2.58086	−	1.93201i	−0.625950	−	0.468580i	−0.864556	+	0.502536i	$0.832400\pi$
$18$		0			0
$19$	0.413151	−	2.87353i	0.0947833	−	0.659232i	−0.885936	−	0.463808i	$-0.846483\pi$
$19$	0.413151	−	2.87353i	0.0947833	−	0.659232i	0.980719	−	0.195424i	$-0.0626082\pi$
$20$		0			0
$21$	2.84288	−	2.46337i	0.620367	−	0.537551i
$22$		0			0
$23$	3.78044	−	2.95098i	0.788276	−	0.615322i
$23$	3.78044	−	2.95098i	0.788276	−	0.615322i
$24$		0			0
$25$	1.09704	+	4.87817i	0.219407	+	0.975633i
$26$		0			0
$27$	14.7001	−	11.0043i	2.82903	−	2.11778i
$28$		0			0
$29$	−5.38029	+	0.773569i	−0.999094	+	0.143648i	−0.622408	−	0.782693i	$-0.713846\pi$
$29$	−5.38029	+	0.773569i	−0.999094	+	0.143648i	−0.376686	+	0.926341i	$0.622936\pi$
$30$		0			0
$31$	−1.93432	+	1.24311i	−0.347414	+	0.223269i	−0.702697	−	0.711489i	$-0.748021\pi$
$31$	−1.93432	+	1.24311i	−0.347414	+	0.223269i	0.355283	+	0.934759i	$0.384385\pi$
$32$		0			0
$33$	4.67177	+	2.55098i	0.813252	+	0.444069i
$34$		0			0
$35$	−2.44983	−	0.433141i	−0.414098	−	0.0732143i
$36$		0			0
$37$	−6.69565	−	2.49735i	−1.10076	−	0.410561i	−0.267562	−	0.963541i	$-0.586218\pi$
$37$	−6.69565	−	2.49735i	−1.10076	−	0.410561i	−0.833195	+	0.552979i	$0.813491\pi$
$38$		0			0
$39$	−5.58870	+	19.0334i	−0.894909	+	3.04778i
$40$		0			0
$41$	0.0672449	−	0.147246i	0.0105019	−	0.0229959i	−0.904308	−	0.426880i	$-0.859613\pi$
$41$	0.0672449	−	0.147246i	0.0105019	−	0.0229959i	0.914810	+	0.403884i	$0.132340\pi$
$42$		0			0
$43$	1.75147	+	8.05137i	0.267097	+	1.22782i	0.893764	+	0.448537i	$0.148055\pi$
$43$	1.75147	+	8.05137i	0.267097	+	1.22782i	−0.626668	+	0.779286i	$0.715582\pi$
$44$		0			0
$45$	−18.2832	−	4.59834i	−2.72550	−	0.685480i
$46$		0			0
$47$	5.06547	+	5.06547i	0.738875	+	0.738875i	0.972360	−	0.233485i	$-0.0750130\pi$
$47$	5.06547	+	5.06547i	0.738875	+	0.738875i	−0.233485	+	0.972360i	$0.575013\pi$
$48$		0			0
$49$	−3.11525	+	4.84742i	−0.445035	+	0.692489i
$50$		0			0
$51$	−9.91496	−	4.52801i	−1.38837	−	0.634048i
$52$		0			0
$53$	1.28875	+	2.36018i	0.177024	+	0.324195i	0.951092	−	0.308907i	$-0.0999631\pi$
$53$	1.28875	+	2.36018i	0.177024	+	0.324195i	−0.774068	+	0.633102i	$0.781781\pi$
$54$		0			0
$55$	−0.637185	−	3.46221i	−0.0859180	−	0.466844i
$56$		0			0
$57$	−0.700215	−	9.79028i	−0.0927457	−	1.29675i
$58$		0			0
$59$	−0.348211	−	1.18590i	−0.0453332	−	0.154391i	0.933716	−	0.358015i	$-0.116546\pi$
$59$	−0.348211	−	1.18590i	−0.0453332	−	0.154391i	−0.979049	+	0.203624i	$0.934728\pi$
$60$		0			0
$61$	5.81275	+	9.04482i	0.744246	+	1.15807i	0.982390	+	0.186840i	$0.0598247\pi$
$61$	5.81275	+	9.04482i	0.744246	+	1.15807i	−0.238144	+	0.971230i	$0.576539\pi$
$62$		0			0
$63$	5.62147	−	7.50941i	0.708239	−	0.946096i
$64$		0			0
$65$	12.1031	−	5.06302i	1.50120	−	0.627990i
$66$		0			0
$67$	−14.1216	−	1.01000i	−1.72523	−	0.123391i	−0.826796	−	0.562502i	$-0.809839\pi$
$67$	−14.1216	−	1.01000i	−1.72523	−	0.123391i	−0.898433	+	0.439111i	$0.855293\pi$
$68$		0			0
$69$	10.3687	−	12.4662i	1.24825	−	1.50075i
$70$		0			0
$71$	−0.836283	−	0.965122i	−0.0992486	−	0.114539i	0.703952	−	0.710247i	$-0.251417\pi$
$71$	−0.836283	−	0.965122i	−0.0992486	−	0.114539i	−0.803201	+	0.595708i	$0.796871\pi$
$72$		0			0
$73$	9.87765	+	13.1950i	1.15609	+	1.54436i	0.789249	+	0.614074i	$0.210470\pi$
$73$	9.87765	+	13.1950i	1.15609	+	1.54436i	0.366842	+	0.930283i	$0.380439\pi$
$74$		0			0
$75$	7.13016	+	15.3277i	0.823320	+	1.76989i
$76$		0			0
$77$	1.71158	+	0.372331i	0.195053	+	0.0424311i
$78$		0			0
$79$	2.32634	−	0.683076i	0.261734	−	0.0768520i	−0.148233	−	0.988953i	$-0.547358\pi$
$79$	2.32634	−	0.683076i	0.261734	−	0.0768520i	0.409967	+	0.912100i	$0.365540\pi$
$80$		0			0
$81$	24.0928	−	27.8045i	2.67697	−	3.08939i
$82$		0			0
$83$	1.11358	−	2.98562i	0.122231	−	0.327715i	−0.861395	−	0.507936i	$-0.830409\pi$
$83$	1.11358	−	2.98562i	0.122231	−	0.327715i	0.983626	+	0.180221i	$0.0576814\pi$
$84$		0			0
$85$	1.80726	+	6.97863i	0.196024	+	0.756938i
$86$		0			0
$87$	−17.2191	+	6.42238i	−1.84608	+	0.688551i
$88$		0			0
$89$	−7.38093	−	4.74344i	−0.782377	−	0.502803i	0.0874444	−	0.996169i	$-0.472130\pi$
$89$	−7.38093	−	4.74344i	−0.782377	−	0.502803i	−0.869822	+	0.493366i	$0.835766\pi$
$90$		0			0
$91$			6.52777i			0.684297i
$92$		0			0
$93$	−5.49707	+	5.49707i	−0.570019	+	0.570019i
$94$		0			0
$95$	−4.73555	+	4.44003i	−0.485857	+	0.455537i
$96$		0			0
$97$	−1.61138	−	4.32027i	−0.163611	−	0.438657i	0.829112	−	0.559083i	$-0.188847\pi$
$97$	−1.61138	−	4.32027i	−0.163611	−	0.438657i	−0.992722	+	0.120426i	$0.961574\pi$
$98$		0			0
$99$	12.7359	+	3.73960i	1.28001	+	0.375844i
$100$		0			0
$101$	−2.15974	−	4.72918i	−0.214903	−	0.470571i	0.771225	−	0.636563i	$-0.219645\pi$
$101$	−2.15974	−	4.72918i	−0.214903	−	0.470571i	−0.986127	+	0.165992i	$0.946917\pi$
$102$		0			0
$103$	−12.0348	+	0.860748i	−1.18583	+	0.0848120i	−0.650281	−	0.759694i	$-0.725349\pi$
$103$	−12.0348	+	0.860748i	−1.18583	+	0.0848120i	−0.535546	+	0.844506i	$0.679894\pi$
$104$		0			0
$105$	−8.40488	+	0.329670i	−0.820232	+	0.0321725i
$106$		0			0
$107$	−2.09502	+	9.63067i	−0.202534	+	0.931032i	0.757867	+	0.652409i	$0.226242\pi$
$107$	−2.09502	+	9.63067i	−0.202534	+	0.931032i	−0.960401	+	0.278623i	$0.910122\pi$
$108$		0			0
$109$	−1.73427	−	12.0621i	−0.166113	−	1.15534i	−0.886824	−	0.462106i	$-0.847094\pi$
$109$	−1.73427	−	12.0621i	−0.166113	−	1.15534i	0.720711	−	0.693235i	$-0.243815\pi$
$110$		0			0
$111$	−23.9154	−	3.43852i	−2.26995	−	0.326370i
$112$		0			0
$113$	0.880815	−	12.3154i	0.0828601	−	1.15854i	−0.770580	−	0.637344i	$-0.780033\pi$
$113$	0.880815	−	12.3154i	0.0828601	−	1.15854i	0.853440	−	0.521192i	$-0.174512\pi$
$114$		0			0
$115$	−10.7230	−	0.128687i	−0.999928	−	0.0120002i
$116$		0			0
$117$	−3.52893	+	49.3410i	−0.326250	+	4.56157i
$118$		0			0
$119$	−3.55037	−	0.510465i	−0.325461	−	0.0467943i
$120$		0			0
$121$	−1.21272	−	8.43468i	−0.110248	−	0.766789i
$122$		0			0
$123$	0.116336	−	0.534788i	0.0104897	−	0.0482202i
$124$		0			0
$125$	4.89915	−	10.0498i	0.438193	−	0.898881i
$126$		0			0
$127$	6.34367	−	0.453708i	0.562909	−	0.0402601i	0.213015	−	0.977049i	$-0.431672\pi$
$127$	6.34367	−	0.453708i	0.562909	−	0.0402601i	0.349895	+	0.936789i	$0.386217\pi$
$128$		0			0
$129$	11.5728	+	25.3408i	1.01893	+	2.23113i
$130$		0			0
$131$	1.32964	+	0.390417i	0.116171	+	0.0341109i	0.339301	−	0.940678i	$-0.389809\pi$
$131$	1.32964	+	0.390417i	0.116171	+	0.0341109i	−0.223130	+	0.974789i	$0.571628\pi$
$132$		0			0
$133$	−1.12875	−	3.02629i	−0.0978748	−	0.262412i
$134$		0			0
$135$	−41.0389	−	1.32175i	−3.53206	−	0.113759i
$136$		0			0
$137$	1.53031	−	1.53031i	0.130743	−	0.130743i	−0.638707	−	0.769450i	$-0.720530\pi$
$137$	1.53031	−	1.53031i	0.130743	−	0.130743i	0.769450	+	0.638707i	$0.220530\pi$
$138$		0			0
$139$			0.0669447i			0.00567818i	0.999996	+	0.00283909i	$0.000903711\pi$
$139$			0.0669447i			0.00567818i	−0.999996	+	0.00283909i	$0.999096\pi$
$140$		0			0
$141$	20.3754	+	13.0945i	1.71592	+	1.10276i
$142$		0			0
$143$	−8.65460	+	3.22800i	−0.723734	+	0.269939i
$144$		0			0
$145$	10.4746	+	6.16537i	0.869870	+	0.512006i
$146$		0			0
$147$	−6.80818	+	18.2534i	−0.561529	+	1.50552i
$148$		0			0
$149$	8.26165	−	9.53445i	0.676821	−	0.781093i	−0.308607	−	0.951190i	$-0.599863\pi$
$149$	8.26165	−	9.53445i	0.676821	−	0.781093i	0.985427	+	0.170097i	$0.0544081\pi$
$150$		0			0
$151$	−0.885932	+	0.260133i	−0.0720961	+	0.0211693i	−0.317582	−	0.948231i	$-0.602871\pi$
$151$	−0.885932	+	0.260133i	−0.0720961	+	0.0211693i	0.245486	+	0.969400i	$0.421053\pi$
$152$		0			0
$153$	−26.5599	−	5.77775i	−2.14724	−	0.467104i
$154$		0			0
$155$	5.11389	+	0.531683i	0.410758	+	0.0427058i
$156$		0			0
$157$	11.3047	+	15.1014i	0.902217	+	1.20522i	0.978107	+	0.208105i	$0.0667295\pi$
$157$	11.3047	+	15.1014i	0.902217	+	1.20522i	−0.0758893	+	0.997116i	$0.524180\pi$
$158$		0			0
$159$	5.95392	+	6.87118i	0.472176	+	0.544920i
$160$		0			0
$161$	2.11810	−	4.89739i	0.166930	−	0.385968i
$162$		0			0
$163$	−2.53836	−	0.181547i	−0.198819	−	0.0142198i	−0.0284257	−	0.999596i	$-0.509049\pi$
$163$	−2.53836	−	0.181547i	−0.198819	−	0.0142198i	−0.170394	+	0.985376i	$0.554504\pi$
$164$		0			0
$165$	−4.59332	−	10.9803i	−0.357589	−	0.854813i
$166$		0			0
$167$	−2.03140	+	2.71363i	−0.157195	+	0.209987i	−0.872224	−	0.489107i	$-0.837323\pi$
$167$	−2.03140	+	2.71363i	−0.157195	+	0.209987i	0.715029	+	0.699095i	$0.246413\pi$
$168$		0			0
$169$	−11.5826	−	18.0228i	−0.890968	−	1.38637i
$170$		0			0
$171$	−6.89575	−	23.4848i	−0.527331	−	1.79592i
$172$		0			0
$173$	0.930431	+	13.0091i	0.0707394	+	0.989066i	0.901596	+	0.432579i	$0.142396\pi$
$173$	0.930431	+	13.0091i	0.0707394	+	0.989066i	−0.830857	+	0.556487i	$0.812149\pi$
$174$		0			0
$175$	3.67233	+	4.17857i	0.277602	+	0.315870i
$176$		0			0
$177$	−2.00268	−	3.66763i	−0.150530	−	0.275676i
$178$		0			0
$179$	−0.147641	−	0.0674254i	−0.0110352	−	0.00503961i	0.409890	−	0.912135i	$-0.365567\pi$
$179$	−0.147641	−	0.0674254i	−0.0110352	−	0.00503961i	−0.420925	+	0.907095i	$0.638294\pi$
$180$		0			0
$181$	7.83700	−	12.1946i	0.582519	−	0.906418i	−0.417478	−	0.908687i	$-0.637086\pi$
$181$	7.83700	−	12.1946i	0.582519	−	0.906418i	0.999997	+	0.00226925i	$0.000722324\pi$
$182$		0			0
$183$	25.7041	+	25.7041i	1.90010	+	1.90010i
$184$		0			0
$185$	8.20192	+	13.7139i	0.603017	+	1.00826i
$186$		0			0
$187$	−1.07888	−	4.95954i	−0.0788957	−	0.362678i
$188$		0			0
$189$	8.48698	−	18.5839i	0.617337	−	1.35178i
$190$		0			0
$191$	4.64670	−	15.8252i	0.336223	−	1.14507i	−0.601843	−	0.798615i	$-0.705567\pi$
$191$	4.64670	−	15.8252i	0.336223	−	1.14507i	0.938066	−	0.346457i	$-0.112615\pi$
$192$		0			0
$193$	−11.3157	−	4.22053i	−0.814520	−	0.303800i	−0.0925353	−	0.995709i	$-0.529497\pi$
$193$	−11.3157	−	4.22053i	−0.814520	−	0.303800i	−0.721984	+	0.691909i	$0.756770\pi$
$194$		0			0
$195$	36.3466	−	25.4251i	2.60284	−	1.82073i
$196$		0			0
$197$	−23.8363	−	13.0156i	−1.69827	−	0.927323i	−0.970366	−	0.241640i	$-0.922315\pi$
$197$	−23.8363	−	13.0156i	−1.69827	−	0.927323i	−0.727900	−	0.685683i	$-0.759504\pi$
$198$		0			0
$199$	1.05567	−	0.678440i	0.0748346	−	0.0480933i	−0.502688	−	0.864468i	$-0.667656\pi$
$199$	1.05567	−	0.678440i	0.0748346	−	0.0480933i	0.577523	+	0.816374i	$0.304019\pi$
$200$		0			0
$201$	−47.3798	+	6.81219i	−3.34192	+	0.480495i
$202$		0			0
$203$	−4.84137	+	3.62420i	−0.339797	+	0.254369i
$204$		0			0
$205$	−0.323105	+	0.163153i	−0.0225667	+	0.0113951i
$206$		0			0
$207$	18.6575	−	35.8724i	1.29678	−	2.49331i
$208$		0			0
$209$	3.45412	−	2.99301i	0.238927	−	0.207031i
$210$		0			0
$211$	−0.952521	+	6.62493i	−0.0655742	+	0.456079i	0.930408	+	0.366526i	$0.119453\pi$
$211$	−0.952521	+	6.62493i	−0.0655742	+	0.456079i	−0.995982	+	0.0895528i	$0.971456\pi$
$212$		0			0
$213$	−3.45647	−	2.58748i	−0.236833	−	0.177291i
$214$		0			0
$215$	8.18934	−	16.5044i	0.558508	−	1.12559i
$216$		0			0
$217$	−1.22602	+	2.24529i	−0.0832278	+	0.152420i
$218$		0			0
$219$	42.1161	+	36.4938i	2.84594	+	2.46602i
$220$		0			0
$221$	17.2058	−	7.85764i	1.15739	−	0.528562i
$222$		0			0
$223$	1.30010	−	0.709908i	0.0870611	−	0.0475390i	−0.435129	−	0.900368i	$-0.643297\pi$
$223$	1.30010	−	0.709908i	0.0870611	−	0.0475390i	0.522190	+	0.852829i	$0.325115\pi$
$224$		0			0
$225$	25.4988	+	33.5695i	1.69992	+	2.23797i
$226$		0			0
$227$	−12.7096	+	2.76480i	−0.843563	+	0.183506i	−0.613525	−	0.789676i	$-0.710249\pi$
$227$	−12.7096	+	2.76480i	−0.843563	+	0.183506i	−0.230039	+	0.973182i	$0.573885\pi$
$228$		0			0
$229$	1.85659			0.122687			0.0613434	−	0.998117i	$-0.480462\pi$
$229$	1.85659			0.122687			0.0613434	+	0.998117i	$0.480462\pi$
$230$		0			0
$231$	5.92218			0.389651
$232$		0			0
$233$	27.9891	−	6.08866i	1.83363	−	0.398882i	0.843280	−	0.537474i	$-0.180622\pi$
$233$	27.9891	−	6.08866i	1.83363	−	0.398882i	0.990349	+	0.138593i	$0.0442579\pi$
$234$		0			0
$235$	−1.76808	−	15.9206i	−0.115337	−	1.03854i
$236$		0			0
$237$	7.19469	−	3.92860i	0.467346	−	0.255190i
$238$		0			0
$239$	−14.4340	+	6.59179i	−0.933659	+	0.426388i	−0.823365	−	0.567512i	$-0.807906\pi$
$239$	−14.4340	+	6.59179i	−0.933659	+	0.426388i	−0.110293	+	0.993899i	$0.535179\pi$
$240$		0			0
$241$	−5.23251	−	4.53399i	−0.337055	−	0.292060i	0.469844	−	0.882750i	$-0.344310\pi$
$241$	−5.23251	−	4.53399i	−0.337055	−	0.292060i	−0.806899	+	0.590690i	$0.798856\pi$
$242$		0			0
$243$	33.2125	−	60.8241i	2.13058	−	3.90187i
$244$		0			0
$245$	12.2109	−	4.11174i	0.780123	−	0.262689i
$246$		0			0
$247$	13.6355	+	10.2074i	0.867607	+	0.649482i
$248$		0			0
$249$	1.53325	−	10.6640i	0.0971659	−	0.675804i
$250$		0			0
$251$	13.3907	−	11.6031i	0.845210	−	0.732379i	−0.120302	−	0.992737i	$-0.538386\pi$
$251$	13.3907	−	11.6031i	0.845210	−	0.732379i	0.965512	+	0.260358i	$0.0838407\pi$
$252$		0			0
$253$	7.54042	+	0.386438i	0.474062	+	0.0242951i
$254$		0			0
$255$	10.9861	+	21.7567i	0.687976	+	1.36245i
$256$		0			0
$257$	14.8642	−	11.1272i	0.927206	−	0.694097i	−0.0249573	−	0.999689i	$-0.507945\pi$
$257$	14.8642	−	11.1272i	0.927206	−	0.694097i	0.952163	+	0.305591i	$0.0988541\pi$
$258$		0			0
$259$	−7.86989	+	1.13152i	−0.489011	+	0.0703092i
$260$		0			0
$261$	−38.5533	+	24.7767i	−2.38639	+	1.53364i
$262$		0			0
$263$	−16.6241	−	9.07746i	−1.02509	−	0.559740i	−0.123503	−	0.992344i	$-0.539413\pi$
$263$	−16.6241	−	9.07746i	−1.02509	−	0.559740i	−0.901584	+	0.432604i	$0.857595\pi$
$264$		0			0
$265$	1.04689	−	5.92120i	0.0643102	−	0.363737i
$266$		0			0
$267$	−27.7936	−	10.3665i	−1.70094	−	0.634419i
$268$		0			0
$269$	4.47330	−	15.2347i	0.272742	−	0.928874i	−0.703227	−	0.710965i	$-0.748258\pi$
$269$	4.47330	−	15.2347i	0.272742	−	0.928874i	0.975969	−	0.217909i	$-0.0699236\pi$
$270$		0			0
$271$	7.67372	−	16.8031i	0.466145	−	1.02072i	−0.519898	−	0.854228i	$-0.674030\pi$
$271$	7.67372	−	16.8031i	0.466145	−	1.02072i	0.986044	−	0.166488i	$-0.0532426\pi$
$272$		0			0
$273$	4.69140	+	21.5660i	0.283936	+	1.30523i
$274$		0			0
$275$	−3.72402	+	6.93514i	−0.224567	+	0.418205i
$276$		0			0
$277$	−10.1668	−	10.1668i	−0.610861	−	0.610861i	0.332309	−	0.943171i	$-0.392172\pi$
$277$	−10.1668	−	10.1668i	−0.610861	−	0.610861i	−0.943171	+	0.332309i	$0.892172\pi$
$278$		0			0
$279$	−10.4808	+	16.3085i	−0.627472	+	0.976365i
$280$		0			0
$281$	9.40826	+	4.29661i	0.561250	+	0.256314i	0.675777	−	0.737106i	$-0.263808\pi$
$281$	9.40826	+	4.29661i	0.561250	+	0.256314i	−0.114528	+	0.993420i	$0.536535\pi$
$282$		0			0
$283$	12.3329	+	22.5860i	0.733116	+	1.34260i	0.931957	+	0.362569i	$0.118100\pi$
$283$	12.3329	+	22.5860i	0.733116	+	1.34260i	−0.198841	+	0.980032i	$0.563718\pi$
$284$		0			0
$285$	−12.4540	+	18.0720i	−0.737711	+	1.07049i
$286$		0			0
$287$	−0.0128482	−	0.179641i	−0.000758403	−	0.0106039i
$288$		0			0
$289$	−1.86127	−	6.33891i	−0.109487	−	0.372877i
$290$		0			0
$291$	−8.42847	−	13.1149i	−0.494085	−	0.768812i
$292$		0			0
$293$	−6.41927	+	8.57514i	−0.375018	+	0.500965i	−0.947854	−	0.318705i	$-0.896752\pi$
$293$	−6.41927	+	8.57514i	−0.375018	+	0.500965i	0.572836	+	0.819670i	$0.305843\pi$
$294$		0			0
$295$	−1.04867	+	2.55701i	−0.0610558	+	0.148875i
$296$		0			0
$297$	28.8356	+	2.06236i	1.67321	+	0.119670i
$298$		0			0
$299$	4.56609	+	27.7651i	0.264064	+	1.60569i
$300$		0			0
$301$	6.00337	+	6.92825i	0.346028	+	0.399338i
$302$		0			0
$303$	−10.5340	−	14.0718i	−0.605162	−	0.808402i
$304$		0			0
$305$	2.48613	−	23.9124i	0.142355	−	1.36922i
$306$		0			0
$307$	17.4163	+	3.78868i	0.994000	+	0.216231i	0.680016	−	0.733197i	$-0.261973\pi$
$307$	17.4163	+	3.78868i	0.994000	+	0.216231i	0.313983	+	0.949428i	$0.398336\pi$
$308$		0			0
$309$	−39.1412	+	11.4929i	−2.22667	+	0.653808i
$310$		0			0
$311$	15.4876	−	17.8737i	0.878222	−	1.01352i	−0.121559	−	0.992584i	$-0.538789\pi$
$311$	15.4876	−	17.8737i	0.878222	−	1.01352i	0.999781	−	0.0209381i	$-0.00666529\pi$
$312$		0			0
$313$	−10.5910	+	28.3955i	−0.598637	+	1.60501i	0.184275	+	0.982875i	$0.441006\pi$
$313$	−10.5910	+	28.3955i	−0.598637	+	1.60501i	−0.782912	+	0.622132i	$0.786267\pi$
$314$		0			0
$315$	−20.3054	+	5.25849i	−1.14408	+	0.296282i
$316$		0			0
$317$	3.66154	−	1.36568i	0.205653	−	0.0767045i	−0.244527	−	0.969642i	$-0.578633\pi$
$317$	3.66154	−	1.36568i	0.205653	−	0.0767045i	0.450180	+	0.892938i	$0.351360\pi$
$318$		0			0
$319$	−7.19908	−	4.62657i	−0.403071	−	0.259038i
$320$		0			0
$321$			33.3228i			1.85990i
$322$		0			0
$323$	−6.61795	+	6.61795i	−0.368233	+	0.368233i
$324$		0			0
$325$	−28.2048	−	8.06744i	−1.56452	−	0.447501i
$326$		0			0
$327$	−14.3984	−	38.6036i	−0.796233	−	2.13478i
$328$		0			0
$329$	7.64738	+	2.24547i	0.421614	+	0.123797i
$330$		0			0
$331$	−5.28123	−	11.5643i	−0.290283	−	0.635630i	0.707164	−	0.707050i	$-0.249974\pi$
$331$	−5.28123	−	11.5643i	−0.290283	−	0.635630i	−0.997446	+	0.0714197i	$0.977247\pi$
$332$		0			0
$333$	−60.0972	+	4.29824i	−3.29331	+	0.235542i
$334$		0			0
$335$	23.2454	+	21.4907i	1.27003	+	1.17416i
$336$		0			0
$337$	−1.78902	+	8.22397i	−0.0974539	+	0.447988i	0.902400	+	0.430899i	$0.141804\pi$
$337$	−1.78902	+	8.22397i	−0.0974539	+	0.447988i	−0.999854	+	0.0170892i	$0.994560\pi$
$338$		0			0
$339$	−5.94089	−	41.3198i	−0.322665	−	2.24418i
$340$		0			0
$341$	−3.58311	−	0.515173i	−0.194036	−	0.0278982i
$342$		0			0
$343$	−1.01295	+	14.1629i	−0.0546941	+	0.764723i
$344$		0			0
$345$	−35.5185	+	7.28131i	−1.91225	+	0.392012i
$346$		0			0
$347$	−0.967585	+	13.5286i	−0.0519427	+	0.726253i	0.903033	+	0.429570i	$0.141335\pi$
$347$	−0.967585	+	13.5286i	−0.0519427	+	0.726253i	−0.954976	+	0.296683i	$0.904120\pi$
$348$		0			0
$349$	20.3776	+	2.92985i	1.09079	+	0.156831i	0.664156	−	0.747594i	$-0.268791\pi$
$349$	20.3776	+	2.92985i	1.09079	+	0.156831i	0.426631	+	0.904426i	$0.359700\pi$
$350$		0			0
$351$	15.3326	+	106.640i	0.818392	+	5.69204i
$352$		0			0
$353$	4.46159	−	20.5096i	0.237466	−	1.09162i	−0.691767	−	0.722121i	$-0.743167\pi$
$353$	4.46159	−	20.5096i	0.237466	−	1.09162i	0.929233	−	0.369494i	$-0.120469\pi$
$354$		0			0
$355$	0.111919	+	2.85335i	0.00594004	+	0.151440i
$356$		0			0
$357$	−12.0963	+	0.865145i	−0.640205	+	0.0457883i
$358$		0			0
$359$	−11.9273	−	26.1171i	−0.629498	−	1.37841i	−0.908406	−	0.418090i	$-0.862700\pi$
$359$	−11.9273	−	26.1171i	−0.629498	−	1.37841i	0.278908	−	0.960318i	$-0.410028\pi$
$360$		0			0
$361$	10.1439	+	2.97852i	0.533890	+	0.156764i
$362$		0			0
$363$	−10.0684	−	26.9944i	−0.528453	−	1.41684i
$364$		0			0
$365$	1.18643	−	36.8371i	0.0621004	−	1.92814i
$366$		0			0
$367$	8.41877	−	8.41877i	0.439456	−	0.439456i	−0.452373	−	0.891829i	$-0.649422\pi$
$367$	8.41877	−	8.41877i	0.439456	−	0.439456i	0.891829	+	0.452373i	$0.149422\pi$
$368$		0			0
$369$		−	1.36478i		−	0.0710477i
$370$		0			0
$371$	2.51693	+	1.61753i	0.130673	+	0.0839782i
$372$		0			0
$373$	12.5235	−	4.67103i	0.648443	−	0.241857i	−0.00365298	−	0.999993i	$-0.501163\pi$
$373$	12.5235	−	4.67103i	0.648443	−	0.241857i	0.652096	+	0.758137i	$0.273890\pi$
$374$		0			0
$375$	8.96287	−	36.7227i	0.462840	−	1.89635i
$376$		0			0
$377$	11.1450	−	29.8809i	0.573997	−	1.53895i
$378$		0			0
$379$	−10.1519	+	11.7159i	−0.521469	+	0.601807i	−0.953998	−	0.299813i	$-0.903076\pi$
$379$	−10.1519	+	11.7159i	−0.521469	+	0.601807i	0.432529	+	0.901620i	$0.357621\pi$
$380$		0			0
$381$	20.6317	−	6.05801i	1.05699	−	0.310361i
$382$		0			0
$383$	26.5035	+	5.76547i	1.35426	+	0.294602i	0.830385	−	0.557191i	$-0.188121\pi$
$383$	26.5035	+	5.76547i	1.35426	+	0.294602i	0.523879	+	0.851793i	$0.324484\pi$
$384$		0			0
$385$	−2.46829	−	3.04109i	−0.125796	−	0.154988i
$386$		0			0
$387$	41.6317	+	55.6135i	2.11626	+	2.82699i
$388$		0			0
$389$	−4.37580	−	5.04994i	−0.221862	−	0.256042i	0.633897	−	0.773418i	$-0.281454\pi$
$389$	−4.37580	−	5.04994i	−0.221862	−	0.256042i	−0.855758	+	0.517376i	$0.826909\pi$
$390$		0			0
$391$	−15.4581	+	0.312231i	−0.781749	+	0.0157902i
$392$		0			0
$393$	4.67336	+	0.334245i	0.235740	+	0.0168604i
$394$		0			0
$395$	−5.01602	−	2.05714i	−0.252383	−	0.103506i
$396$		0			0
$397$	−8.33463	+	11.1338i	−0.418303	+	0.558787i	−0.959355	−	0.282202i	$-0.908935\pi$
$397$	−8.33463	+	11.1338i	−0.418303	+	0.558787i	0.541052	+	0.840989i	$0.318026\pi$
$398$		0			0
$399$	−5.90402	−	9.18683i	−0.295571	−	0.459917i
$400$		0			0
$401$	8.71234	+	29.6715i	0.435074	+	1.48172i	0.827250	+	0.561835i	$0.189904\pi$
$401$	8.71234	+	29.6715i	0.435074	+	1.48172i	−0.392176	+	0.919890i	$0.628278\pi$
$402$		0			0
$403$	−0.962407	−	13.4562i	−0.0479409	−	0.670302i
$404$		0			0
$405$	−80.9076	+	14.8902i	−4.02033	+	0.739901i
$406$		0			0
$407$	−5.39186	−	9.87446i	−0.267265	−	0.489459i
$408$		0			0
$409$	−12.3230	−	5.62773i	−0.609334	−	0.278274i	0.0867542	−	0.996230i	$-0.472351\pi$
$409$	−12.3230	−	5.62773i	−0.609334	−	0.278274i	−0.696088	+	0.717956i	$0.745078\pi$
$410$		0			0
$411$	3.95592	−	6.15552i	0.195131	−	0.303630i
$412$		0			0
$413$	−0.972357	−	0.972357i	−0.0478466	−	0.0478466i
$414$		0			0
$415$	−6.11509	+	3.65728i	−0.300178	+	0.179529i
$416$		0			0
$417$	0.0481120	+	0.221167i	0.00235605	+	0.0108306i
$418$		0			0
$419$	−13.7164	+	30.0348i	−0.670092	+	1.46730i	0.202719	+	0.979237i	$0.435022\pi$
$419$	−13.7164	+	30.0348i	−0.670092	+	1.46730i	−0.872811	+	0.488059i	$0.837705\pi$
$420$		0			0
$421$	−5.29545	+	18.0347i	−0.258085	+	0.878955i	0.723886	+	0.689920i	$0.242354\pi$
$421$	−5.29545	+	18.0347i	−0.258085	+	0.878955i	−0.981970	+	0.189035i	$0.939464\pi$
$422$		0			0
$423$	56.5897	+	21.1069i	2.75149	+	1.02625i
$424$		0			0
$425$	6.59336	−	14.7093i	0.319825	−	0.713508i
$426$		0			0
$427$	10.4989	+	5.73284i	0.508078	+	0.277432i
$428$		0			0
$429$	−26.2726	+	16.8844i	−1.26845	+	0.815184i
$430$		0			0
$431$	−23.5195	+	3.38160i	−1.13290	+	0.162886i	−0.683155	−	0.730273i	$-0.739393\pi$
$431$	−23.5195	+	3.38160i	−1.13290	+	0.162886i	−0.449741	+	0.893159i	$0.648484\pi$
$432$		0			0
$433$	10.4509	−	7.82346i	0.502239	−	0.375972i	−0.317910	−	0.948121i	$-0.602981\pi$
$433$	10.4509	−	7.82346i	0.502239	−	0.375972i	0.820150	+	0.572149i	$0.193890\pi$
$434$		0			0
$435$	39.0363	+	12.8408i	1.87165	+	0.615668i
$436$		0			0
$437$	−6.91783	−	12.0824i	−0.330925	−	0.577979i
$438$		0			0
$439$	22.1158	−	19.1634i	1.05553	−	0.914620i	0.0590316	−	0.998256i	$-0.481199\pi$
$439$	22.1158	−	19.1634i	1.05553	−	0.914620i	0.996496	+	0.0836359i	$0.0266533\pi$
$440$		0			0
$441$	−6.91385	+	48.0869i	−0.329231	+	2.28985i
$442$		0			0
$443$	−27.0621	−	20.2584i	−1.28576	−	0.962506i	−0.999991	−	0.00420611i	$-0.998661\pi$
$443$	−27.0621	−	20.2584i	−1.28576	−	0.962506i	−0.285766	−	0.958299i	$-0.592248\pi$
$444$		0			0
$445$	6.26075	+	18.5929i	0.296788	+	0.881387i
$446$		0			0
$447$	20.4420	−	37.4368i	0.966874	−	1.77070i
$448$		0			0
$449$	0.0124805	+	0.0108144i	0.000588990	+	0.000510363i	0.655155	−	0.755494i	$-0.272603\pi$
$449$	0.0124805	+	0.0108144i	0.000588990	+	0.000510363i	−0.654566	+	0.756005i	$0.727149\pi$
$450$		0			0
$451$	0.231816	−	0.105867i	0.0109158	−	0.00498508i
$452$		0			0
$453$	−2.73993	+	1.49611i	−0.128733	+	0.0702935i
$454$		0			0
$455$	9.11900	−	11.3975i	0.427505	−	0.534323i
$456$		0			0
$457$	−2.92732	+	0.636799i	−0.136934	+	0.0297882i	−0.280510	−	0.959851i	$-0.590504\pi$
$457$	−2.92732	+	0.636799i	−0.136934	+	0.0297882i	0.143576	+	0.989639i	$0.454140\pi$
$458$		0			0
$459$	−59.1992			−2.76318
$460$		0			0
$461$	−25.8772			−1.20522			−0.602610	−	0.798036i	$-0.705872\pi$
$461$	−25.8772			−1.20522			−0.602610	+	0.798036i	$0.705872\pi$
$462$		0			0
$463$	−7.19331	+	1.56481i	−0.334301	+	0.0727228i	−0.376583	−	0.926383i	$-0.622901\pi$
$463$	−7.19331	+	1.56481i	−0.334301	+	0.0727228i	0.0422816	+	0.999106i	$0.486537\pi$
$464$		0			0
$465$	17.2770	−	1.91873i	0.801203	−	0.0889790i
$466$		0			0
$467$	−17.6492	+	9.63719i	−0.816708	+	0.445956i	−0.832571	−	0.553918i	$-0.813132\pi$
$467$	−17.6492	+	9.63719i	−0.816708	+	0.445956i	0.0158636	+	0.999874i	$0.494950\pi$
$468$		0			0
$469$	−14.3283	+	6.54350i	−0.661618	+	0.302151i
$470$		0			0
$471$	48.2009	+	41.7663i	2.22098	+	1.92449i
$472$		0			0
$473$	−6.21689	+	11.3854i	−0.285853	+	0.523500i
$474$		0			0
$475$	14.4708	−	1.13694i	0.663965	−	0.0521665i
$476$		0			0
$477$	18.1501	+	13.5870i	0.831036	+	0.622106i
$478$		0			0
$479$	4.03187	−	28.0423i	0.184221	−	1.28128i	−0.662425	−	0.749128i	$-0.730473\pi$
$479$	4.03187	−	28.0423i	0.184221	−	1.28128i	0.846646	−	0.532156i	$-0.178618\pi$
$480$		0			0
$481$	31.6872	−	27.4571i	1.44481	−	1.25194i
$482$		0			0
$483$	3.47798	−	17.7019i	0.158253	−	0.805464i
$484$		0			0
$485$	−3.22176	+	9.79422i	−0.146292	+	0.444733i
$486$		0			0
$487$	19.8328	−	14.8466i	0.898709	−	0.672765i	−0.0466095	−	0.998913i	$-0.514842\pi$
$487$	19.8328	−	14.8466i	0.898709	−	0.672765i	0.945319	+	0.326148i	$0.105751\pi$
$488$		0			0
$489$	−8.51652	+	1.22449i	−0.385130	+	0.0553734i
$490$		0			0
$491$	−18.6766	+	12.0028i	−0.842865	+	0.541677i	−0.889342	−	0.457243i	$-0.848837\pi$
$491$	−18.6766	+	12.0028i	−0.842865	+	0.541677i	0.0464767	+	0.998919i	$0.485201\pi$
$492$		0			0
$493$	15.3803	+	8.39828i	0.692694	+	0.378239i
$494$		0			0
$495$	−17.0128	−	24.3208i	−0.764670	−	1.09314i
$496$		0			0
$497$	−1.33124	−	0.496527i	−0.0597143	−	0.0222723i
$498$		0			0
$499$	2.56990	−	8.75227i	0.115044	−	0.391805i	−0.881759	−	0.471701i	$-0.843640\pi$
$499$	2.56990	−	8.75227i	0.115044	−	0.391805i	0.996803	+	0.0798951i	$0.0254585\pi$
$500$		0			0
$501$	−4.76096	+	10.4250i	−0.212704	+	0.465757i
$502$		0			0
$503$	2.22993	+	10.2508i	0.0994276	+	0.457061i	0.999761	+	0.0218605i	$0.00695896\pi$
$503$	2.22993	+	10.2508i	0.0994276	+	0.457061i	−0.900333	+	0.435201i	$0.856677\pi$
$504$		0			0
$505$	−2.83553	+	11.2742i	−0.126180	+	0.501696i
$506$		0			0
$507$	−51.2184	−	51.2184i	−2.27469	−	2.27469i
$508$		0			0
$509$	−1.37985	+	2.14709i	−0.0611609	+	0.0951682i	−0.870487	−	0.492191i	$-0.836196\pi$
$509$	−1.37985	+	2.14709i	−0.0611609	+	0.0951682i	0.809326	+	0.587359i	$0.199832\pi$
$510$		0			0
$511$	16.6812	+	7.61804i	0.737932	+	0.337002i
$512$		0			0
$513$	−25.5479	−	46.7875i	−1.12797	−	2.06572i
$514$		0			0
$515$	22.2152	+	15.3092i	0.978920	+	0.674606i
$516$		0			0
$517$	0.804572	+	11.2494i	0.0353850	+	0.494747i
$518$		0			0
$519$	12.4233	+	42.3100i	0.545324	+	1.85720i
$520$		0			0
$521$	−9.97717	−	15.5248i	−0.437108	−	0.680153i	0.550898	−	0.834573i	$-0.314286\pi$
$521$	−9.97717	−	15.5248i	−0.437108	−	0.680153i	−0.988005	+	0.154420i	$0.950649\pi$
$522$		0			0
$523$	−17.0308	+	22.7505i	−0.744706	+	0.994810i	0.254907	+	0.966966i	$0.417955\pi$
$523$	−17.0308	+	22.7505i	−0.744706	+	0.994810i	−0.999612	+	0.0278446i	$0.991136\pi$
$524$		0			0
$525$	15.1355	+	11.1656i	0.660566	+	0.487308i
$526$		0			0
$527$	7.39391	+	0.528823i	0.322084	+	0.0230359i
$528$		0			0
$529$	5.58343	−	22.3120i	0.242758	−	0.970087i
$530$		0			0
$531$	−6.82402	−	7.87534i	−0.296137	−	0.341760i
$532$		0			0
$533$	0.569160	+	0.760309i	0.0246531	+	0.0329326i
$534$		0			0
$535$	17.1115	−	13.8885i	0.739795	−	0.600452i
$536$		0			0
$537$	−0.536224	−	0.116648i	−0.0231398	−	0.00503375i
$538$		0			0
$539$	−8.70416	+	2.55577i	−0.374915	+	0.110085i
$540$		0			0
$541$	11.6481	−	13.4427i	0.500793	−	0.577946i	−0.447925	−	0.894071i	$-0.647837\pi$
$541$	11.6481	−	13.4427i	0.500793	−	0.577946i	0.948717	+	0.316126i	$0.102382\pi$
$542$		0			0
$543$	17.1273	−	45.9200i	0.735002	−	1.97062i
$544$		0			0
$545$	−13.8222	+	23.4832i	−0.592078	+	1.00591i
$546$		0			0
$547$	−3.27933	+	1.22313i	−0.140214	+	0.0522971i	−0.418591	−	0.908175i	$-0.637476\pi$
$547$	−3.27933	+	1.22313i	−0.140214	+	0.0522971i	0.278378	+	0.960472i	$0.410203\pi$
$548$		0			0
$549$	76.2581	+	49.0081i	3.25462	+	2.09161i
$550$		0			0
$551$			15.7800i			0.672250i
$552$		0			0
$553$	1.90745	−	1.90745i	0.0811129	−	0.0811129i
$554$		0			0
$555$	36.9529	+	39.4124i	1.56856	+	1.67296i
$556$		0			0
$557$	6.31573	+	16.9331i	0.267606	+	0.717480i	0.999355	+	0.0359055i	$0.0114315\pi$
$557$	6.31573	+	16.9331i	0.267606	+	0.717480i	−0.731749	+	0.681574i	$0.761296\pi$
$558$		0			0
$559$	−46.3854	−	13.6200i	−1.96189	−	0.576064i
$560$		0			0
$561$	−7.12868	−	15.6096i	−0.300973	−	0.659039i
$562$		0			0
$563$	14.2242	−	1.01733i	0.599478	−	0.0428755i	0.231697	−	0.972788i	$-0.425572\pi$
$563$	14.2242	−	1.01733i	0.599478	−	0.0428755i	0.367781	+	0.929913i	$0.380118\pi$
$564$		0			0
$565$	−18.7420	+	20.2722i	−0.788480	+	0.852860i
$566$		0			0
$567$	8.70093	−	39.9975i	0.365405	−	1.67974i
$568$		0			0
$569$	4.20808	+	29.2678i	0.176412	+	1.22697i	0.864983	+	0.501802i	$0.167329\pi$
$569$	4.20808	+	29.2678i	0.176412	+	1.22697i	−0.688571	+	0.725169i	$0.741762\pi$
$570$		0			0
$571$	−8.25719	−	1.18720i	−0.345552	−	0.0496829i	−0.0326462	−	0.999467i	$-0.510393\pi$
$571$	−8.25719	−	1.18720i	−0.345552	−	0.0496829i	−0.312906	+	0.949784i	$0.601303\pi$
$572$		0			0
$573$	3.97814	−	55.6217i	0.166189	−	2.32363i
$574$		0			0
$575$	18.5427	+	15.2043i	0.773282	+	0.634062i
$576$		0			0
$577$	−0.388837	+	5.43665i	−0.0161875	+	0.226331i	0.982918	+	0.184044i	$0.0589189\pi$
$577$	−0.388837	+	5.43665i	−0.0161875	+	0.226331i	−0.999106	+	0.0422868i	$0.986536\pi$
$578$		0			0
$579$	−40.4171	−	5.81111i	−1.67968	−	0.241501i
$580$		0			0
$581$	−0.504550	−	3.50922i	−0.0209323	−	0.145587i
$582$		0			0
$583$	−0.899918	+	4.13686i	−0.0372708	+	0.171331i
$584$		0			0
$585$	75.0886	−	81.2196i	3.10453	−	3.35802i
$586$		0			0
$587$	−41.0782	+	2.93797i	−1.69548	+	0.121263i	−0.885330	−	0.464964i	$-0.846067\pi$
$587$	−41.0782	+	2.93797i	−1.69548	+	0.121263i	−0.810147	+	0.586227i	$0.800613\pi$
$588$		0			0
$589$	2.77295	+	6.07191i	0.114257	+	0.250189i
$590$		0			0
$591$	−88.1028	−	25.8693i	−3.62406	−	1.06412i
$592$		0			0
$593$	7.70930	+	20.6694i	0.316583	+	0.848792i	0.993614	+	0.112837i	$0.0359938\pi$
$593$	7.70930	+	20.6694i	0.316583	+	0.848792i	−0.677030	+	0.735955i	$0.736733\pi$
$594$		0			0
$595$	5.48584	+	5.85097i	0.224898	+	0.239866i
$596$		0			0
$597$	3.00007	−	3.00007i	0.122785	−	0.122785i
$598$		0			0
$599$			24.1695i			0.987539i	0.869593	+	0.493769i	$0.164381\pi$
$599$			24.1695i			0.987539i	−0.869593	+	0.493769i	$0.835619\pi$
$600$		0			0
$601$	−3.09215	−	1.98720i	−0.126131	−	0.0810598i	0.476054	−	0.879416i	$-0.342067\pi$
$601$	−3.09215	−	1.98720i	−0.126131	−	0.0810598i	−0.602185	+	0.798356i	$0.705703\pi$
$602$		0			0
$603$	−111.839	+	41.7139i	−4.55445	+	1.69872i
$604$		0			0
$605$	−9.66545	+	16.4211i	−0.392957	+	0.667612i
$606$		0			0
$607$	−9.70960	+	26.0324i	−0.394100	+	1.05662i	0.576746	+	0.816923i	$0.304322\pi$
$607$	−9.70960	+	26.0324i	−0.394100	+	1.05662i	−0.970847	+	0.239701i	$0.922951\pi$
$608$		0			0
$609$	−13.3899	+	15.4528i	−0.542587	+	0.626179i
$610$		0			0
$611$	−40.3280	+	11.8414i	−1.63149	+	0.479050i
$612$		0			0
$613$	5.40926	+	1.17671i	0.218478	+	0.0475270i	0.320472	−	0.947258i	$-0.396159\pi$
$613$	5.40926	+	1.17671i	0.218478	+	0.0475270i	−0.101994	+	0.994785i	$0.532522\pi$
$614$		0			0
$615$	−0.950197	+	0.771224i	−0.0383157	+	0.0310988i
$616$		0			0
$617$	0.714693	+	0.954719i	0.0287725	+	0.0384355i	0.814697	−	0.579887i	$-0.196903\pi$
$617$	0.714693	+	0.954719i	0.0287725	+	0.0384355i	−0.785924	+	0.618323i	$0.787812\pi$
$618$		0			0
$619$	−24.6834	−	28.4862i	−0.992110	−	1.14496i	−0.989438	−	0.144960i	$-0.953695\pi$
$619$	−24.6834	−	28.4862i	−0.992110	−	1.14496i	−0.00267268	−	0.999996i	$-0.500851\pi$
$620$		0			0
$621$	23.0991	−	84.9808i	0.926936	−	3.41016i
$622$		0			0
$623$	−9.73671	−	0.696383i	−0.390093	−	0.0279000i
$624$		0			0
$625$	−22.5930	+	10.7030i	−0.903721	+	0.428122i
$626$		0			0
$627$	9.26046	−	12.3705i	0.369827	−	0.494031i
$628$		0			0
$629$	12.4556	+	19.3813i	0.496638	+	0.772784i
$630$		0			0
$631$	3.34091	+	11.3781i	0.133000	+	0.452955i	0.998881	−	0.0472944i	$-0.0150599\pi$
$631$	3.34091	+	11.3781i	0.133000	+	0.452955i	−0.865881	+	0.500249i	$0.833242\pi$
$632$		0			0
$633$	1.61435	+	22.5715i	0.0641645	+	0.897138i
$634$		0			0
$635$	−11.7099	−	8.06964i	−0.464691	−	0.320234i
$636$		0			0
$637$	−16.2022	−	29.6721i	−0.641955	−	1.17565i
$638$		0			0
$639$	−9.79391	−	4.47273i	−0.387441	−	0.176938i
$640$		0			0
$641$	−0.248509	+	0.386687i	−0.00981550	+	0.0152732i	−0.846127	−	0.532982i	$-0.821071\pi$
$641$	−0.248509	+	0.386687i	−0.00981550	+	0.0152732i	0.836311	+	0.548255i	$0.184708\pi$
$642$		0			0
$643$	−6.04499	−	6.04499i	−0.238391	−	0.238391i	0.577793	−	0.816184i	$-0.303914\pi$
$643$	−6.04499	−	6.04499i	−0.238391	−	0.238391i	−0.816184	+	0.577793i	$0.803914\pi$
$644$		0			0
$645$	15.1939	−	60.4117i	0.598260	−	2.37871i
$646$		0			0
$647$	6.45478	+	29.6722i	0.253764	+	1.16653i	0.910856	+	0.412723i	$0.135422\pi$
$647$	6.45478	+	29.6722i	0.253764	+	1.16653i	−0.657093	+	0.753810i	$0.728214\pi$
$648$		0			0
$649$	0.808330	−	1.77000i	0.0317297	−	0.0694784i
$650$		0			0
$651$	−2.43679	+	8.29896i	−0.0955055	+	0.325262i
$652$		0			0
$653$	9.35814	+	3.49041i	0.366212	+	0.136590i	0.525832	−	0.850588i	$-0.323754\pi$
$653$	9.35814	+	3.49041i	0.366212	+	0.136590i	−0.159620	+	0.987179i	$0.551027\pi$
$654$		0			0
$655$	−1.77616	−	2.53912i	−0.0694002	−	0.0992115i
$656$		0			0
$657$	121.968	+	66.5998i	4.75844	+	2.59830i
$658$		0			0
$659$	23.0375	−	14.8053i	0.897414	−	0.576733i	−0.00860854	−	0.999963i	$-0.502740\pi$
$659$	23.0375	−	14.8053i	0.897414	−	0.576733i	0.906022	+	0.423230i	$0.139104\pi$
$660$		0			0
$661$	13.0065	−	1.87006i	0.505896	−	0.0727368i	0.115358	−	0.993324i	$-0.463198\pi$
$661$	13.0065	−	1.87006i	0.505896	−	0.0727368i	0.390537	+	0.920587i	$0.372289\pi$
$662$		0			0
$663$	51.1963	−	38.3250i	1.98830	−	1.48842i
$664$		0			0
$665$	−2.25679	+	6.86071i	−0.0875147	+	0.266047i
$666$		0			0
$667$	−18.0571	+	18.8015i	−0.699172	+	0.727999i
$668$		0			0
$669$	3.78498	−	3.27970i	0.146336	−	0.126801i
$670$		0			0
$671$	−2.40893	+	16.7545i	−0.0929958	+	0.646800i
$672$		0			0
$673$	−21.9125	−	16.4035i	−0.844667	−	0.632310i	0.0867638	−	0.996229i	$-0.472347\pi$
$673$	−21.9125	−	16.4035i	−0.844667	−	0.632310i	−0.931430	+	0.363919i	$0.881438\pi$
$674$		0			0
$675$	69.8074	+	59.6372i	2.68689	+	2.29544i
$676$		0			0
$677$	0.853003	−	1.56216i	0.0327836	−	0.0600386i	−0.860774	−	0.508988i	$-0.830020\pi$
$677$	0.853003	−	1.56216i	0.0327836	−	0.0600386i	0.893557	+	0.448949i	$0.148202\pi$
$678$		0			0
$679$	−3.87711	−	3.35954i	−0.148790	−	0.128927i
$680$		0			0
$681$	−40.0019	+	18.2683i	−1.53288	+	0.700042i
$682$		0			0
$683$	−1.88018	+	1.02666i	−0.0719433	+	0.0392840i	−0.514818	−	0.857300i	$-0.672140\pi$
$683$	−1.88018	+	1.02666i	−0.0719433	+	0.0392840i	0.442875	+	0.896584i	$0.353959\pi$
$684$		0			0
$685$	−4.80969	+	0.534147i	−0.183769	+	0.0204087i
$686$		0			0
$687$	6.13366	−	1.33430i	0.234014	−	0.0509066i
$688$		0			0
$689$	−15.7775			−0.601075
$690$		0			0
$691$	29.5289			1.12333			0.561667	−	0.827364i	$-0.310160\pi$
$691$	29.5289			1.12333			0.561667	+	0.827364i	$0.310160\pi$
$692$		0			0
$693$	14.4306	−	3.13918i	0.548172	−	0.119247i
$694$		0			0
$695$	0.0935187	−	0.116886i	0.00354737	−	0.00443372i
$696$		0			0
$697$	−0.458029	+	0.250103i	−0.0173491	+	0.00947332i
$698$		0			0
$699$	88.0927	−	40.2306i	3.33197	−	1.52166i
$700$		0			0
$701$	15.4143	+	13.3566i	0.582192	+	0.504472i	0.895430	−	0.445203i	$-0.146868\pi$
$701$	15.4143	+	13.3566i	0.582192	+	0.504472i	−0.313238	+	0.949675i	$0.601414\pi$
$702$		0			0
$703$	−9.94250	+	18.2083i	−0.374989	+	0.686740i
$704$		0			0
$705$	−17.2831	−	51.3265i	−0.650919	−	1.93307i
$706$		0			0
$707$	−4.63062	−	3.46644i	−0.174153	−	0.130369i
$708$		0			0
$709$	0.898270	−	6.24761i	0.0337353	−	0.234634i	−0.965977	−	0.258629i	$-0.916729\pi$
$709$	0.898270	−	6.24761i	0.0337353	−	0.234634i	0.999712	+	0.0239948i	$0.00763851\pi$
$710$		0			0
$711$	15.4488	−	13.3865i	0.579377	−	0.502033i
$712$		0			0
$713$	−3.64418	+	10.4076i	−0.136476	+	0.389769i
$714$		0			0
$715$	19.6203	+	6.45400i	0.733758	+	0.241366i
$716$		0			0
$717$	−42.9487	+	32.1510i	−1.60395	+	1.20070i
$718$		0			0
$719$	38.2210	−	5.49535i	1.42540	−	0.204942i	0.613943	−	0.789351i	$-0.289583\pi$
$719$	38.2210	−	5.49535i	1.42540	−	0.204942i	0.811460	+	0.584409i	$0.198673\pi$
$720$		0			0
$721$	−11.2930	+	7.25759i	−0.420574	+	0.270287i
$722$		0			0
$723$	−20.5453	−	11.2186i	−0.764087	−	0.417223i
$724$		0			0
$725$	−9.67596	−	25.3973i	−0.359356	−	0.943232i
$726$		0			0
$727$	−7.54083	−	2.81259i	−0.279674	−	0.104313i	0.205713	−	0.978612i	$-0.434049\pi$
$727$	−7.54083	−	2.81259i	−0.279674	−	0.104313i	−0.485387	+	0.874299i	$0.661321\pi$
$728$		0			0
$729$	34.9165	−	118.915i	1.29320	−	4.40425i
$730$		0			0
$731$	11.0350	−	24.1633i	0.408145	−	0.893712i
$732$		0			0
$733$	3.74803	+	17.2294i	0.138437	+	0.636384i	0.993107	+	0.117212i	$0.0373958\pi$
$733$	3.74803	+	17.2294i	0.138437	+	0.636384i	−0.854670	+	0.519171i	$0.826241\pi$
$734$		0			0
$735$	37.3863	−	22.3598i	1.37902	−	0.824754i
$736$		0			0
$737$	−15.7608	−	15.7608i	−0.580557	−	0.580557i
$738$		0			0
$739$	17.8434	−	27.7648i	0.656379	−	1.02135i	−0.340332	−	0.940305i	$-0.610540\pi$
$739$	17.8434	−	27.7648i	0.656379	−	1.02135i	0.996711	−	0.0810399i	$-0.0258241\pi$
$740$		0			0
$741$	52.3839	+	23.9229i	1.92437	+	0.878831i
$742$		0			0
$743$	19.3615	+	35.4580i	0.710305	+	1.30083i	0.944460	+	0.328628i	$0.106586\pi$
$743$	19.3615	+	35.4580i	0.710305	+	1.30083i	−0.234154	+	0.972200i	$0.575232\pi$
$744$		0			0
$745$	−27.7440	+	5.10601i	−1.01646	+	0.187070i
$746$		0			0
$747$	−1.91661	−	26.7977i	−0.0701250	−	0.980475i
$748$		0			0
$749$	3.08937	+	10.5214i	0.112883	+	0.384444i
$750$		0			0
$751$	16.8284	+	26.1855i	0.614076	+	0.955521i	0.999463	+	0.0327657i	$0.0104315\pi$
$751$	16.8284	+	26.1855i	0.614076	+	0.955521i	−0.385387	+	0.922755i	$0.625932\pi$
$752$		0			0
$753$	35.9002	−	47.9570i	1.30828	−	1.74765i
$754$		0			0
$755$	1.91023	+	0.783414i	0.0695204	+	0.0285114i
$756$		0			0
$757$	16.4646	+	1.17757i	0.598416	+	0.0427996i	0.367262	−	0.930117i	$-0.380295\pi$
$757$	16.4646	+	1.17757i	0.598416	+	0.0427996i	0.231154	+	0.972917i	$0.425750\pi$
$758$		0			0
$759$	25.1893	−	4.14248i	0.914312	−	0.150363i
$760$		0			0
$761$	14.7262	+	16.9949i	0.533824	+	0.616065i	0.957037	−	0.289964i	$-0.0936435\pi$
$761$	14.7262	+	16.9949i	0.533824	+	0.616065i	−0.423214	+	0.906030i	$0.639098\pi$
$762$		0			0
$763$	−8.12514	−	10.8539i	−0.294150	−	0.392938i
$764$		0			0
$765$	38.3023	+	47.1909i	1.38482	+	1.70619i
$766$		0			0
$767$	7.08589	+	1.54144i	0.255857	+	0.0556582i
$768$		0			0
$769$	40.3215	−	11.8395i	1.45403	−	0.426942i	0.543159	−	0.839630i	$-0.317228\pi$
$769$	40.3215	−	11.8395i	1.45403	−	0.426942i	0.910872	+	0.412688i	$0.135410\pi$
$770$		0			0
$771$	41.1105	−	47.4440i	1.48056	−	1.70865i
$772$		0			0
$773$	−6.58373	+	17.6517i	−0.236800	+	0.634886i	−0.999936	−	0.0113525i	$-0.996386\pi$
$773$	−6.58373	+	17.6517i	−0.236800	+	0.634886i	0.763135	+	0.646239i	$0.223659\pi$
$774$		0			0
$775$	−8.18613	−	8.07220i	−0.294054	−	0.289962i
$776$		0			0
$777$	−25.1868	+	9.39419i	−0.903571	+	0.337015i
$778$		0			0
$779$	−0.395332	−	0.254065i	−0.0141642	−	0.00910281i
$780$		0			0
$781$		−	2.01051i		−	0.0719416i
$782$		0			0
$783$	−70.5780	+	70.5780i	−2.52225	+	2.52225i
$784$		0			0
$785$	1.35784	−	42.1592i	0.0484633	−	1.50473i
$786$		0			0
$787$	10.1544	+	27.2251i	0.361967	+	0.970470i	0.982496	+	0.186286i	$0.0596452\pi$
$787$	10.1544	+	27.2251i	0.361967	+	0.970470i	−0.620529	+	0.784184i	$0.713082\pi$
$788$		0			0
$789$	−61.4454	−	18.0420i	−2.18751	−	0.642312i
$790$		0			0
$791$	−5.70656	−	12.4956i	−0.202902	−	0.444293i
$792$		0			0
$793$	−62.9208	+	4.50018i	−2.23438	+	0.159806i
$794$		0			0
$795$	−0.796807	−	20.3144i	−0.0282598	−	0.720479i
$796$		0			0
$797$	6.23466	−	28.6603i	0.220843	−	1.01520i	−0.724539	−	0.689234i	$-0.757947\pi$
$797$	6.23466	−	28.6603i	0.220843	−	1.01520i	0.945382	−	0.325965i	$-0.105689\pi$
$798$		0			0
$799$	−3.28674	−	22.8598i	−0.116277	−	0.808722i
$800$		0			0
$801$	−73.2196	−	10.5274i	−2.58709	−	0.371967i
$802$		0			0
$803$	−1.85121	+	25.8833i	−0.0653277	+	0.913400i
$804$		0			0
$805$	−10.5396	+	5.59195i	−0.371473	+	0.197090i
$806$		0			0
$807$	3.82969	−	53.5461i	0.134812	−	1.88491i
$808$		0			0
$809$	−12.1908	−	1.75278i	−0.428607	−	0.0616244i	−0.0753643	−	0.997156i	$-0.524012\pi$
$809$	−12.1908	−	1.75278i	−0.428607	−	0.0616244i	−0.353243	+	0.935532i	$0.614921\pi$
$810$		0			0
$811$	−1.75450	−	12.2028i	−0.0616089	−	0.428499i	−0.997160	−	0.0753087i	$-0.976006\pi$
$811$	−1.75450	−	12.2028i	−0.0616089	−	0.428499i	0.935551	−	0.353191i	$-0.114903\pi$
$812$		0			0
$813$	13.2758	−	61.0279i	0.465603	−	2.14034i
$814$		0			0
$815$	4.17836	+	3.86295i	0.146362	+	0.135313i
$816$		0			0
$817$	23.8595	−	1.70646i	0.834737	−	0.0597015i
$818$		0			0
$819$	22.8630	+	50.0630i	0.798898	+	1.74934i
$820$		0			0
$821$	−19.1769	−	5.63085i	−0.669279	−	0.196518i	−0.0705970	−	0.997505i	$-0.522490\pi$
$821$	−19.1769	−	5.63085i	−0.669279	−	0.196518i	−0.598682	+	0.800987i	$0.704309\pi$
$822$		0			0
$823$	−7.28606	−	19.5347i	−0.253976	−	0.680936i	−0.999889	−	0.0148930i	$-0.995259\pi$
$823$	−7.28606	−	19.5347i	−0.253976	−	0.680936i	0.745913	−	0.666043i	$-0.232013\pi$
$824$		0			0
$825$	−7.31901	+	25.5882i	−0.254815	+	0.890867i
$826$		0			0
$827$	−28.7693	+	28.7693i	−1.00041	+	1.00041i	−0.000405360		1.00000i	$0.500129\pi$
$827$	−28.7693	+	28.7693i	−1.00041	+	1.00041i	−1.00000		0.000405360i	$0.999871\pi$
$828$		0			0
$829$		−	28.6031i		−	0.993427i	−0.867915	−	0.496713i	$-0.834540\pi$
$829$		−	28.6031i		−	0.993427i	0.867915	−	0.496713i	$-0.165460\pi$
$830$		0			0
$831$	−40.8949	−	26.2816i	−1.41863	−	0.911697i
$832$		0			0
$833$	17.4053	−	6.49183i	0.603057	−	0.224928i
$834$		0			0
$835$	7.33765	−	1.90023i	0.253930	−	0.0657602i
$836$		0			0
$837$	−14.7550	+	39.5597i	−0.510008	+	1.36738i
$838$		0			0
$839$	−35.6894	+	41.1878i	−1.23213	+	1.42196i	−0.359815	+	0.933024i	$0.617160\pi$
$839$	−35.6894	+	41.1878i	−1.23213	+	1.42196i	−0.872320	+	0.488935i	$0.837385\pi$
$840$		0			0
$841$	0.523785	−	0.153797i	0.0180615	−	0.00530335i
$842$		0			0
$843$	34.1702	+	7.43328i	1.17689	+	0.256016i
$844$		0			0
$845$	−4.95390	+	47.6482i	−0.170420	+	1.63915i
$846$		0			0
$847$	−5.68167	−	7.58982i	−0.195224	−	0.260789i
$848$		0			0
$849$	56.9768	+	65.7547i	1.95544	+	2.25670i
$850$		0			0
$851$	−32.6821	+	10.3177i	−1.12033	+	0.353685i
$852$		0			0
$853$	25.1114	+	1.79600i	0.859798	+	0.0614940i	0.494272	−	0.869307i	$-0.335435\pi$
$853$	25.1114	+	1.79600i	0.859798	+	0.0614940i	0.365526	+	0.930801i	$0.380889\pi$
$854$		0			0
$855$	−20.7672	+	50.6375i	−0.710222	+	1.73176i
$856$		0			0
$857$	−17.6490	+	23.5763i	−0.602878	+	0.805351i	−0.993334	−	0.115271i	$-0.963226\pi$
$857$	−17.6490	+	23.5763i	−0.602878	+	0.805351i	0.390456	+	0.920622i	$0.372317\pi$
$858$		0			0
$859$	1.50344	+	2.33940i	0.0512967	+	0.0798193i	0.865955	−	0.500122i	$-0.166712\pi$
$859$	1.50344	+	2.33940i	0.0512967	+	0.0798193i	−0.814658	+	0.579942i	$0.803075\pi$
$860$		0			0
$861$	−0.171552	−	0.584251i	−0.00584646	−	0.0199112i
$862$		0			0
$863$	−0.558047	−	7.80252i	−0.0189961	−	0.265601i	−0.998070	−	0.0620963i	$-0.980221\pi$
$863$	−0.558047	−	7.80252i	−0.0189961	−	0.265601i	0.979074	−	0.203504i	$-0.0652331\pi$
$864$		0			0
$865$	16.5486	−	24.0137i	0.562670	−	0.816491i
$866$		0			0
$867$	−10.7048	−	19.6044i	−0.363554	−	0.665800i
$868$		0			0
$869$	3.47216	+	1.58568i	0.117785	+	0.0537905i
$870$		0			0
$871$	44.9087	−	69.8793i	1.52167	−	2.36777i
$872$		0			0
$873$	−27.4895	−	27.4895i	−0.930377	−	0.930377i
$874$		0			0
$875$	−0.574620	−	12.4259i	−0.0194257	−	0.420071i
$876$		0			0
$877$	9.58709	+	44.0711i	0.323733	+	1.48818i	0.795229	+	0.606309i	$0.207350\pi$
$877$	9.58709	+	44.0711i	0.323733	+	1.48818i	−0.471496	+	0.881868i	$0.656286\pi$
$878$		0			0
$879$	−15.0447	+	32.9434i	−0.507446	+	1.11115i
$880$		0			0
$881$	−8.77362	+	29.8802i	−0.295591	+	1.00669i	0.669071	+	0.743198i	$0.266692\pi$
$881$	−8.77362	+	29.8802i	−0.295591	+	1.00669i	−0.964662	+	0.263491i	$0.915126\pi$
$882$		0			0
$883$	−35.8261	−	13.3624i	−1.20564	−	0.449682i	−0.335293	−	0.942114i	$-0.608835\pi$
$883$	−35.8261	−	13.3624i	−1.20564	−	0.449682i	−0.870351	+	0.492432i	$0.836108\pi$
$884$		0			0
$885$	−1.62684	+	9.20133i	−0.0546855	+	0.309299i
$886$		0			0
$887$	−2.79618	−	1.52683i	−0.0938865	−	0.0512659i	0.431620	−	0.902056i	$-0.357942\pi$
$887$	−2.79618	−	1.52683i	−0.0938865	−	0.0512659i	−0.525506	+	0.850790i	$0.676124\pi$
$888$		0			0
$889$	5.95266	−	3.82554i	0.199646	−	0.128305i
$890$		0			0
$891$	57.3318	−	8.24307i	1.92069	−	0.276153i
$892$		0			0
$893$	16.6486	−	12.4630i	0.557123	−	0.417057i
$894$		0			0
$895$	0.163591	+	0.323973i	0.00546825	+	0.0108292i
$896$		0			0
$897$	35.0394	+	88.4467i	1.16993	+	2.95315i
$898$		0			0
$899$	9.44556	−	8.18463i	0.315027	−	0.272973i
$900$		0			0
$901$	1.23379	−	8.58117i	0.0411034	−	0.285880i
$902$		0			0
$903$	24.8127	+	18.5746i	0.825716	+	0.618123i
$904$		0			0
$905$	−30.7187	+	10.3439i	−1.02112	+	0.343841i
$906$		0			0
$907$	3.97816	−	7.28546i	0.132093	−	0.241910i	−0.803258	−	0.595631i	$-0.796902\pi$
$907$	3.97816	−	7.28546i	0.132093	−	0.241910i	0.935351	+	0.353721i	$0.115084\pi$
$908$		0			0
$909$	−33.1272	−	28.7048i	−1.09876	−	0.952079i
$910$		0			0
$911$	−9.17625	+	4.19065i	−0.304023	+	0.138843i	−0.561585	−	0.827419i	$-0.689808\pi$
$911$	−9.17625	+	4.19065i	−0.304023	+	0.138843i	0.257562	+	0.966262i	$0.417081\pi$
$912$		0			0
$913$	4.40307	−	2.40426i	0.145720	−	0.0795694i
$914$		0			0
$915$	−8.97192	−	80.7869i	−0.296602	−	2.67073i
$916$		0			0
$917$	1.50656	−	0.327733i	0.0497511	−	0.0108227i
$918$		0			0
$919$	45.6371			1.50543			0.752714	−	0.658348i	$-0.228744\pi$
$919$	45.6371			1.50543			0.752714	+	0.658348i	$0.228744\pi$
$920$		0			0
$921$	60.2616			1.98569
$922$		0			0
$923$	7.32139	−	1.59267i	0.240987	−	0.0524234i
$924$		0			0
$925$	4.83711	−	35.4022i	0.159043	−	1.16402i
$926$		0			0
$927$	−89.2832	+	48.7523i	−2.93244	+	1.60124i
$928$		0			0
$929$	4.88086	−	2.22901i	0.160136	−	0.0731316i	−0.333735	−	0.942667i	$-0.608309\pi$
$929$	4.88086	−	2.22901i	0.160136	−	0.0731316i	0.493870	+	0.869535i	$0.335582\pi$
$930$		0			0
$931$	12.6421	+	10.9545i	0.414329	+	0.359018i
$932$		0			0
$933$	38.3214	−	70.1804i	1.25459	−	2.29760i
$934$		0			0
$935$	−5.04453	+	10.1665i	−0.164974	+	0.332481i
$936$		0			0
$937$	−26.8315	−	20.0858i	−0.876549	−	0.656176i	0.0632155	−	0.998000i	$-0.479864\pi$
$937$	−26.8315	−	20.0858i	−0.876549	−	0.656176i	−0.939764	+	0.341824i	$0.888955\pi$
$938$		0			0
$939$	−14.5824	+	101.423i	−0.475877	+	3.30980i
$940$		0			0
$941$	−41.7825	+	36.2048i	−1.36207	+	1.18024i	−0.397135	+	0.917760i	$0.629996\pi$
$941$	−41.7825	+	36.2048i	−1.36207	+	1.18024i	−0.964937	+	0.262482i	$0.915459\pi$
$942$		0			0
$943$	−0.180304	−	0.755092i	−0.00587151	−	0.0245892i
$944$		0			0
$945$	−40.7791	+	20.5916i	−1.32655	+	0.669844i
$946$		0			0
$947$	−17.4860	+	13.0898i	−0.568217	+	0.425362i	−0.844377	−	0.535750i	$-0.820029\pi$
$947$	−17.4860	+	13.0898i	−0.568217	+	0.425362i	0.276160	+	0.961112i	$0.410938\pi$
$948$		0			0
$949$	−95.7220	+	13.7627i	−3.10727	+	0.446757i
$950$		0			0
$951$	11.1153	−	7.14334i	0.360437	−	0.231639i
$952$		0			0
$953$	−20.9081	−	11.4167i	−0.677279	−	0.369822i	0.103500	−	0.994629i	$-0.466996\pi$
$953$	−20.9081	−	11.4167i	−0.677279	−	0.369822i	−0.780779	+	0.624807i	$0.785178\pi$
$954$		0			0
$955$	−30.2202	+	21.1396i	−0.977904	+	0.684061i
$956$		0			0
$957$	−27.1088	−	10.1111i	−0.876305	−	0.326845i
$958$		0			0
$959$	0.678369	−	2.31031i	0.0219057	−	0.0746039i
$960$		0			0
$961$	−10.6816	+	23.3894i	−0.344568	+	0.754498i
$962$		0			0
$963$	17.6634	+	81.1975i	0.569196	+	2.61655i
$964$		0			0
$965$	13.8613	+	23.1765i	0.446210	+	0.746079i
$966$		0			0
$967$	14.6392	+	14.6392i	0.470766	+	0.470766i	0.902163	−	0.431396i	$-0.141979\pi$
$967$	14.6392	+	14.6392i	0.470766	+	0.470766i	−0.431396	+	0.902163i	$0.641979\pi$
$968$		0			0
$969$	−17.1077	+	26.6201i	−0.549579	+	0.855162i
$970$		0			0
$971$	−22.6763	−	10.3559i	−0.727718	−	0.332338i	0.0168741	−	0.999858i	$-0.494629\pi$
$971$	−22.6763	−	10.3559i	−0.727718	−	0.332338i	−0.744592	+	0.667520i	$0.767356\pi$
$972$		0			0
$973$	0.0356955	+	0.0653714i	0.00114434	+	0.00209571i
$974$		0			0
$975$	−98.9790	−	6.38233i	−3.16987	−	0.204398i
$976$		0			0
$977$	−3.89344	−	54.4374i	−0.124562	−	1.74161i	−0.548708	−	0.836014i	$-0.684880\pi$
$977$	−3.89344	−	54.4374i	−0.124562	−	1.74161i	0.424146	−	0.905594i	$-0.360574\pi$
$978$		0			0
$979$	−3.89155	−	13.2534i	−0.124375	−	0.423581i
$980$		0			0
$981$	−55.5472	−	86.4331i	−1.77348	−	2.75960i
$982$		0			0
$983$	−27.6440	+	36.9281i	−0.881708	+	1.17782i	0.101409	+	0.994845i	$0.467665\pi$
$983$	−27.6440	+	36.9281i	−0.881708	+	1.17782i	−0.983117	+	0.182979i	$0.941426\pi$
$984$		0			0
$985$	23.4360	+	56.0235i	0.746733	+	1.78506i
$986$		0			0
$987$	26.8787	+	1.92240i	0.855557	+	0.0611906i
$988$		0			0
$989$	30.3808	+	25.2692i	0.966052	+	0.803513i
$990$		0			0
$991$	17.9537	+	20.7196i	0.570317	+	0.658181i	0.965494	−	0.260424i	$-0.0838624\pi$
$991$	17.9537	+	20.7196i	0.570317	+	0.658181i	−0.395177	+	0.918605i	$0.629317\pi$
$992$		0			0
$993$	−25.7588	−	34.4097i	−0.817431	−	1.09196i
$994$		0			0
$995$	−2.79095	−	0.290171i	−0.0884792	−	0.00919903i
$996$		0			0
$997$	49.6371	+	10.7979i	1.57202	+	0.341972i	0.912295	−	0.409534i	$-0.134309\pi$
$997$	49.6371	+	10.7979i	1.57202	+	0.341972i	0.659726	+	0.751506i	$0.270672\pi$
$998$		0			0
$999$	−125.908	+	36.9699i	−3.98355	+	1.16968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.217.12	yes	240
5.3	odd	4	inner	460.2.x.a.33.12	✓	240
23.7	odd	22	inner	460.2.x.a.237.12	yes	240
115.53	even	44	inner	460.2.x.a.53.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.33.12	✓	240	5.3	odd	4	inner
460.2.x.a.53.12	yes	240	115.53	even	44	inner
460.2.x.a.217.12	yes	240	1.1	even	1	trivial
460.2.x.a.237.12	yes	240	23.7	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(3.30373 - 0.718682i) q^{3} +(-1.74600 - 1.39695i) q^{5} +(0.976498 - 0.533208i) q^{7} +(7.66923 - 3.50242i) q^{9} +O(q^{10})\)	\(q+(3.30373 - 0.718682i) q^{3} +(-1.74600 - 1.39695i) q^{5} +(0.976498 - 0.533208i) q^{7} +(7.66923 - 3.50242i) q^{9} +(1.18981 + 1.03098i) q^{11} +(-2.81184 + 5.14950i) q^{13} +(-6.77228 - 3.36034i) q^{15} +(-2.58086 - 1.93201i) q^{17} +(0.413151 - 2.87353i) q^{19} +(2.84288 - 2.46337i) q^{21} +(3.78044 - 2.95098i) q^{23} +(1.09704 + 4.87817i) q^{25} +(14.7001 - 11.0043i) q^{27} +(-5.38029 + 0.773569i) q^{29} +(-1.93432 + 1.24311i) q^{31} +(4.67177 + 2.55098i) q^{33} +(-2.44983 - 0.433141i) q^{35} +(-6.69565 - 2.49735i) q^{37} +(-5.58870 + 19.0334i) q^{39} +(0.0672449 - 0.147246i) q^{41} +(1.75147 + 8.05137i) q^{43} +(-18.2832 - 4.59834i) q^{45} +(5.06547 + 5.06547i) q^{47} +(-3.11525 + 4.84742i) q^{49} +(-9.91496 - 4.52801i) q^{51} +(1.28875 + 2.36018i) q^{53} +(-0.637185 - 3.46221i) q^{55} +(-0.700215 - 9.79028i) q^{57} +(-0.348211 - 1.18590i) q^{59} +(5.81275 + 9.04482i) q^{61} +(5.62147 - 7.50941i) q^{63} +(12.1031 - 5.06302i) q^{65} +(-14.1216 - 1.01000i) q^{67} +(10.3687 - 12.4662i) q^{69} +(-0.836283 - 0.965122i) q^{71} +(9.87765 + 13.1950i) q^{73} +(7.13016 + 15.3277i) q^{75} +(1.71158 + 0.372331i) q^{77} +(2.32634 - 0.683076i) q^{79} +(24.0928 - 27.8045i) q^{81} +(1.11358 - 2.98562i) q^{83} +(1.80726 + 6.97863i) q^{85} +(-17.2191 + 6.42238i) q^{87} +(-7.38093 - 4.74344i) q^{89} +6.52777i q^{91} +(-5.49707 + 5.49707i) q^{93} +(-4.73555 + 4.44003i) q^{95} +(-1.61138 - 4.32027i) q^{97} +(12.7359 + 3.73960i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 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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