LMFDB - Embedded newform 460.2.x.a.17.1

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			17.1
Character	$\chi$	$=$	460.17
Dual form			460.2.x.a.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.71854 + 1.48444i) q^{3} +(1.97074 + 1.05650i) q^{5} +(2.65480 + 3.54640i) q^{7} +(3.56500 - 5.54725i) q^{9} +O(q^{10})$	\(q+(-2.71854 + 1.48444i) q^{3} +(1.97074 + 1.05650i) q^{5} +(2.65480 + 3.54640i) q^{7} +(3.56500 - 5.54725i) q^{9} +(3.12626 - 1.42772i) q^{11} +(-2.93440 - 2.19666i) q^{13} +(-6.92584 + 0.0532896i) q^{15} +(0.123611 + 1.72831i) q^{17} +(3.69125 + 4.25993i) q^{19} +(-12.4816 - 5.70016i) q^{21} +(0.448411 + 4.77482i) q^{23} +(2.76761 + 4.16417i) q^{25} +(-0.794165 + 11.1039i) q^{27} +(-2.36513 - 2.04939i) q^{29} +(-7.95628 + 2.33617i) q^{31} +(-6.37953 + 8.52205i) q^{33} +(1.48514 + 9.79384i) q^{35} +(0.932354 - 0.202821i) q^{37} +(11.2381 + 1.61579i) q^{39} +(4.88148 - 3.13714i) q^{41} +(-4.62229 - 8.46509i) q^{43} +(12.8864 - 7.16575i) q^{45} +(0.753200 + 0.753200i) q^{47} +(-3.55687 + 12.1136i) q^{49} +(-2.90160 - 4.51498i) q^{51} +(-1.09395 + 0.818922i) q^{53} +(7.66943 + 0.489248i) q^{55} +(-16.3584 - 6.10137i) q^{57} +(-9.56639 + 1.37544i) q^{59} +(-2.13110 - 7.25787i) q^{61} +(29.1372 - 2.08393i) q^{63} +(-3.46215 - 7.42924i) q^{65} +(-0.173201 - 0.464371i) q^{67} +(-8.30695 - 12.3149i) q^{69} +(-1.61678 + 3.54025i) q^{71} +(5.38240 + 0.384957i) q^{73} +(-13.7053 - 7.21215i) q^{75} +(13.3629 + 7.29668i) q^{77} +(-1.23870 - 8.61535i) q^{79} +(-6.10625 - 13.3708i) q^{81} +(0.626734 + 2.88105i) q^{83} +(-1.58235 + 3.53663i) q^{85} +(9.47189 + 2.06048i) q^{87} +(13.3133 + 3.90915i) q^{89} -16.2383i q^{91} +(18.1616 - 18.1616i) q^{93} +(2.77386 + 12.2950i) q^{95} +(-2.98325 + 13.7138i) q^{97} +(3.22523 - 22.4320i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

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
$3$	−2.71854	+	1.48444i	−1.56955	+	0.857040i	−0.570183	+	0.821518i	$0.693128\pi$
$3$	−2.71854	+	1.48444i	−1.56955	+	0.857040i	−0.999369	+	0.0355224i	$0.988690\pi$
$4$		0			0
$5$	1.97074	+	1.05650i	0.881340	+	0.472482i
$5$	1.97074	+	1.05650i	0.881340	+	0.472482i
$6$		0			0
$7$	2.65480	+	3.54640i	1.00342	+	1.34041i	0.939533	+	0.342458i	$0.111259\pi$
$7$	2.65480	+	3.54640i	1.00342	+	1.34041i	0.0638887	+	0.997957i	$0.479650\pi$
$8$		0			0
$9$	3.56500	−	5.54725i	1.18833	−	1.84908i
$10$		0			0
$11$	3.12626	−	1.42772i	0.942604	−	0.430473i	0.115995	−	0.993250i	$-0.462994\pi$
$11$	3.12626	−	1.42772i	0.942604	−	0.430473i	0.826609	+	0.562777i	$0.190267\pi$
$12$		0			0
$13$	−2.93440	−	2.19666i	−0.813855	−	0.609245i	0.109153	−	0.994025i	$-0.465186\pi$
$13$	−2.93440	−	2.19666i	−0.813855	−	0.609245i	−0.923008	+	0.384780i	$0.874277\pi$
$14$		0			0
$15$	−6.92584	+	0.0532896i	−1.78825	+	0.0137593i
$16$		0			0
$17$	0.123611	+	1.72831i	0.0299800	+	0.419176i	0.990174	+	0.139841i	$0.0446592\pi$
$17$	0.123611	+	1.72831i	0.0299800	+	0.419176i	−0.960194	+	0.279334i	$0.909886\pi$
$18$		0			0
$19$	3.69125	+	4.25993i	0.846830	+	0.977294i	0.999940	−	0.0109151i	$-0.00347446\pi$
$19$	3.69125	+	4.25993i	0.846830	+	0.977294i	−0.153110	+	0.988209i	$0.548929\pi$
$20$		0			0
$21$	−12.4816	−	5.70016i	−2.72371	−	1.24388i
$22$		0			0
$23$	0.448411	+	4.77482i	0.0935001	+	0.995619i
$23$	0.448411	+	4.77482i	0.0935001	+	0.995619i
$24$		0			0
$25$	2.76761	+	4.16417i	0.553522	+	0.832835i
$26$		0			0
$27$	−0.794165	+	11.1039i	−0.152837	+	2.13694i
$28$		0			0
$29$	−2.36513	−	2.04939i	−0.439193	−	0.380563i	0.407010	−	0.913424i	$-0.366571\pi$
$29$	−2.36513	−	2.04939i	−0.439193	−	0.380563i	−0.846203	+	0.532861i	$0.821117\pi$
$30$		0			0
$31$	−7.95628	+	2.33617i	−1.42899	+	0.419589i	−0.902536	−	0.430614i	$-0.858297\pi$
$31$	−7.95628	+	2.33617i	−1.42899	+	0.419589i	−0.526454	+	0.850204i	$0.676479\pi$
$32$		0			0
$33$	−6.37953	+	8.52205i	−1.11053	+	1.48350i
$34$		0			0
$35$	1.48514	+	9.79384i	0.251035	+	1.65546i
$36$		0			0
$37$	0.932354	−	0.202821i	0.153278	−	0.0333436i	−0.135271	−	0.990809i	$-0.543191\pi$
$37$	0.932354	−	0.202821i	0.153278	−	0.0333436i	0.288550	+	0.957465i	$0.406827\pi$
$38$		0			0
$39$	11.2381	+	1.61579i	1.79954	+	0.258734i
$40$		0			0
$41$	4.88148	−	3.13714i	0.762359	−	0.489939i	−0.100777	−	0.994909i	$-0.532133\pi$
$41$	4.88148	−	3.13714i	0.762359	−	0.489939i	0.863137	+	0.504970i	$0.168497\pi$
$42$		0			0
$43$	−4.62229	−	8.46509i	−0.704892	−	1.29091i	−0.947178	−	0.320709i	$-0.896079\pi$
$43$	−4.62229	−	8.46509i	−0.704892	−	1.29091i	0.242286	−	0.970205i	$-0.422103\pi$
$44$		0			0
$45$	12.8864	−	7.16575i	1.92099	−	1.06821i
$46$		0			0
$47$	0.753200	+	0.753200i	0.109865	+	0.109865i	0.759903	−	0.650037i	$-0.225247\pi$
$47$	0.753200	+	0.753200i	0.109865	+	0.109865i	−0.650037	+	0.759903i	$0.725247\pi$
$48$		0			0
$49$	−3.55687	+	12.1136i	−0.508124	+	1.73051i
$50$		0			0
$51$	−2.90160	−	4.51498i	−0.406306	−	0.632224i
$52$		0			0
$53$	−1.09395	+	0.818922i	−0.150266	+	0.112488i	−0.671765	−	0.740764i	$-0.734464\pi$
$53$	−1.09395	+	0.818922i	−0.150266	+	0.112488i	0.521500	+	0.853252i	$0.325373\pi$
$54$		0			0
$55$	7.66943	+	0.489248i	1.03415	+	0.0659702i
$56$		0			0
$57$	−16.3584	−	6.10137i	−2.16672	−	0.808146i
$58$		0			0
$59$	−9.56639	+	1.37544i	−1.24544	+	0.179067i	−0.733341	−	0.679861i	$-0.762040\pi$
$59$	−9.56639	+	1.37544i	−1.24544	+	0.179067i	−0.512097	+	0.858928i	$0.671131\pi$
$60$		0			0
$61$	−2.13110	−	7.25787i	−0.272860	−	0.929275i	−0.975917	−	0.218142i	$-0.930000\pi$
$61$	−2.13110	−	7.25787i	−0.272860	−	0.929275i	0.703057	−	0.711133i	$-0.251818\pi$
$62$		0			0
$63$	29.1372	−	2.08393i	3.67094	−	0.262551i
$64$		0			0
$65$	−3.46215	−	7.42924i	−0.429427	−	0.921484i
$66$		0			0
$67$	−0.173201	−	0.464371i	−0.0211599	−	0.0567320i	0.925940	−	0.377670i	$-0.123275\pi$
$67$	−0.173201	−	0.464371i	−0.0211599	−	0.0567320i	−0.947100	+	0.320938i	$0.896002\pi$
$68$		0			0
$69$	−8.30695	−	12.3149i	−1.00004	−	1.48254i
$70$		0			0
$71$	−1.61678	+	3.54025i	−0.191876	+	0.420150i	−0.980980	−	0.194110i	$-0.937818\pi$
$71$	−1.61678	+	3.54025i	−0.191876	+	0.420150i	0.789104	+	0.614260i	$0.210545\pi$
$72$		0			0
$73$	5.38240	+	0.384957i	0.629962	+	0.0450558i	0.382670	−	0.923885i	$-0.375005\pi$
$73$	5.38240	+	0.384957i	0.629962	+	0.0450558i	0.247292	+	0.968941i	$0.420459\pi$
$74$		0			0
$75$	−13.7053	−	7.21215i	−1.58255	−	0.832787i
$76$		0			0
$77$	13.3629	+	7.29668i	1.52284	+	0.831534i
$78$		0			0
$79$	−1.23870	−	8.61535i	−0.139365	−	0.969303i	−0.932735	−	0.360563i	$-0.882584\pi$
$79$	−1.23870	−	8.61535i	−0.139365	−	0.969303i	0.793370	−	0.608740i	$-0.208325\pi$
$80$		0			0
$81$	−6.10625	−	13.3708i	−0.678473	−	1.48565i
$82$		0			0
$83$	0.626734	+	2.88105i	0.0687930	+	0.316236i	0.998665	−	0.0516457i	$-0.0164466\pi$
$83$	0.626734	+	2.88105i	0.0687930	+	0.316236i	−0.929872	+	0.367882i	$0.880083\pi$
$84$		0			0
$85$	−1.58235	+	3.53663i	−0.171630	+	0.383601i
$86$		0			0
$87$	9.47189	+	2.06048i	1.01549	+	0.220907i
$88$		0			0
$89$	13.3133	+	3.90915i	1.41121	+	0.414369i	0.896519	−	0.443006i	$-0.146088\pi$
$89$	13.3133	+	3.90915i	1.41121	+	0.414369i	0.514693	+	0.857375i	$0.327906\pi$
$90$		0			0
$91$		−	16.2383i		−	1.70223i
$92$		0			0
$93$	18.1616	−	18.1616i	1.88327	−	1.88327i
$94$		0			0
$95$	2.77386	+	12.2950i	0.284592	+	1.26144i
$96$		0			0
$97$	−2.98325	+	13.7138i	−0.302904	+	1.39243i	0.534189	+	0.845365i	$0.320617\pi$
$97$	−2.98325	+	13.7138i	−0.302904	+	1.39243i	−0.837093	+	0.547061i	$0.815747\pi$
$98$		0			0
$99$	3.22523	−	22.4320i	0.324148	−	2.25450i
$100$		0			0
$101$	12.0047	+	7.71497i	1.19452	+	0.767669i	0.977999	−	0.208610i	$-0.0668940\pi$
$101$	12.0047	+	7.71497i	1.19452	+	0.767669i	0.216517	+	0.976279i	$0.430530\pi$
$102$		0			0
$103$	1.83816	−	4.92829i	0.181119	−	0.485599i	−0.814384	−	0.580326i	$-0.802925\pi$
$103$	1.83816	−	4.92829i	0.181119	−	0.485599i	0.995503	+	0.0947271i	$0.0301979\pi$
$104$		0			0
$105$	−18.5758	−	24.4204i	−1.81281	−	2.38318i
$106$		0			0
$107$	2.72118	−	4.98347i	0.263066	−	0.481770i	−0.712442	−	0.701731i	$-0.752411\pi$
$107$	2.72118	−	4.98347i	0.263066	−	0.481770i	0.975509	+	0.219961i	$0.0705929\pi$
$108$		0			0
$109$	8.02654	−	9.26312i	0.768803	−	0.887246i	−0.227445	−	0.973791i	$-0.573037\pi$
$109$	8.02654	−	9.26312i	0.768803	−	0.887246i	0.996248	+	0.0865451i	$0.0275827\pi$
$110$		0			0
$111$	−2.23357	+	1.93540i	−0.212001	+	0.183700i
$112$		0			0
$113$	12.8101	−	4.77793i	1.20508	−	0.449470i	0.334920	−	0.942247i	$-0.391291\pi$
$113$	12.8101	−	4.77793i	1.20508	−	0.449470i	0.870156	+	0.492776i	$0.164018\pi$
$114$		0			0
$115$	−4.16091	+	9.88367i	−0.388007	+	0.921657i
$116$		0			0
$117$	−22.6466	+	8.44674i	−2.09368	+	0.780901i
$118$		0			0
$119$	−5.80111	+	5.02669i	−0.531787	+	0.460796i
$120$		0			0
$121$	0.531679	−	0.613591i	0.0483345	−	0.0557810i
$122$		0			0
$123$	−8.61364	+	15.7747i	−0.776665	+	1.42236i
$124$		0			0
$125$	1.05477	+	11.1305i	0.0943418	+	0.995540i
$126$		0			0
$127$	5.29786	−	14.2041i	0.470109	−	1.26041i	−0.458283	−	0.888806i	$-0.651535\pi$
$127$	5.29786	−	14.2041i	0.470109	−	1.26041i	0.928391	−	0.371604i	$-0.121192\pi$
$128$		0			0
$129$	25.1318	+	16.1512i	2.21273	+	1.42203i
$130$		0			0
$131$	−1.22076	+	8.49059i	−0.106659	+	0.741826i	0.864369	+	0.502858i	$0.167718\pi$
$131$	−1.22076	+	8.49059i	−0.106659	+	0.741826i	−0.971027	+	0.238968i	$0.923191\pi$
$132$		0			0
$133$	−5.30788	+	24.3999i	−0.460251	+	2.11574i
$134$		0			0
$135$	−13.2964	+	21.0438i	−1.14437	+	1.81116i
$136$		0			0
$137$	−4.64543	+	4.64543i	−0.396886	+	0.396886i	−0.877133	−	0.480247i	$-0.840547\pi$
$137$	−4.64543	+	4.64543i	−0.396886	+	0.396886i	0.480247	+	0.877133i	$0.340547\pi$
$138$		0			0
$139$		−	9.73352i		−	0.825587i	−0.910825	−	0.412793i	$-0.864553\pi$
$139$		−	9.73352i		−	0.825587i	0.910825	−	0.412793i	$-0.135447\pi$
$140$		0			0
$141$	−3.16568	−	0.929528i	−0.266599	−	0.0782804i
$142$		0			0
$143$	−12.3099	−	2.67786i	−1.02941	−	0.223934i
$144$		0			0
$145$	−2.49585	−	6.53757i	−0.207269	−	0.542916i
$146$		0			0
$147$	−8.31234	−	38.2112i	−0.685590	−	3.15161i
$148$		0			0
$149$	−7.25751	−	15.8917i	−0.594559	−	1.30190i	−0.932648	−	0.360788i	$-0.882508\pi$
$149$	−7.25751	−	15.8917i	−0.594559	−	1.30190i	0.338089	−	0.941114i	$-0.390219\pi$
$150$		0			0
$151$	1.99928	+	13.9053i	0.162699	+	1.13160i	0.893518	+	0.449027i	$0.148229\pi$
$151$	1.99928	+	13.9053i	0.162699	+	1.13160i	−0.730819	+	0.682571i	$0.760862\pi$
$152$		0			0
$153$	10.0280	+	5.47571i	0.810717	+	0.442685i
$154$		0			0
$155$	−18.1479	−	3.80184i	−1.45767	−	0.305371i
$156$		0			0
$157$	−6.92804	−	0.495503i	−0.552918	−	0.0395455i	−0.207915	−	0.978147i	$-0.566668\pi$
$157$	−6.92804	−	0.495503i	−0.552918	−	0.0395455i	−0.345003	+	0.938602i	$0.612122\pi$
$158$		0			0
$159$	1.75832	−	3.85018i	0.139444	−	0.305339i
$160$		0			0
$161$	−15.7430	+	14.2665i	−1.24072	+	1.12436i
$162$		0			0
$163$	−6.18918	−	16.5938i	−0.484774	−	1.29973i	−0.917332	−	0.398124i	$-0.869661\pi$
$163$	−6.18918	−	16.5938i	−0.484774	−	1.29973i	0.432557	−	0.901606i	$-0.357611\pi$
$164$		0			0
$165$	−21.5759	+	10.0547i	−1.67968	+	0.782760i
$166$		0			0
$167$	−1.88333	+	0.134699i	−0.145737	+	0.0104233i	−0.144017	−	0.989575i	$-0.546002\pi$
$167$	−1.88333	+	0.134699i	−0.145737	+	0.0104233i	−0.00171974	+	0.999999i	$0.500547\pi$
$168$		0			0
$169$	0.122840	+	0.418354i	0.00944921	+	0.0321810i
$170$		0			0
$171$	36.7902	−	5.28963i	2.81342	−	0.404508i
$172$		0			0
$173$	−7.07850	−	2.64014i	−0.538168	−	0.200726i	0.0656583	−	0.997842i	$-0.479085\pi$
$173$	−7.07850	−	2.64014i	−0.538168	−	0.200726i	−0.603826	+	0.797116i	$0.706358\pi$
$174$		0			0
$175$	−7.42038	+	20.8701i	−0.560928	+	1.57763i
$176$		0			0
$177$	23.9649	−	17.9399i	1.80131	−	1.34844i
$178$		0			0
$179$	11.6979	+	18.2022i	0.874339	+	1.36050i	0.932113	+	0.362168i	$0.117963\pi$
$179$	11.6979	+	18.2022i	0.874339	+	1.36050i	−0.0577741	+	0.998330i	$0.518400\pi$
$180$		0			0
$181$	4.38036	−	14.9181i	0.325590	−	1.10886i	−0.620299	−	0.784366i	$-0.712989\pi$
$181$	4.38036	−	14.9181i	0.325590	−	1.10886i	0.945889	−	0.324492i	$-0.105193\pi$
$182$		0			0
$183$	16.5673	+	16.5673i	1.22469	+	1.22469i
$184$		0			0
$185$	2.05171	+	0.585326i	0.150844	+	0.0430340i
$186$		0			0
$187$	2.85397	+	5.22666i	0.208703	+	0.382211i
$188$		0			0
$189$	−41.4872	+	26.6622i	−3.01775	+	1.93939i
$190$		0			0
$191$	15.9608	+	2.29482i	1.15489	+	0.166047i	0.693031	−	0.720908i	$-0.256275\pi$
$191$	15.9608	+	2.29482i	1.15489	+	0.166047i	0.461855	+	0.886956i	$0.347184\pi$
$192$		0			0
$193$	−3.64346	+	0.792587i	−0.262262	+	0.0570516i	−0.341774	−	0.939782i	$-0.611028\pi$
$193$	−3.64346	+	0.792587i	−0.262262	+	0.0570516i	0.0795115	+	0.996834i	$0.474664\pi$
$194$		0			0
$195$	20.4402	+	15.0574i	1.46376	+	1.07828i
$196$		0			0
$197$	−1.04376	+	1.39429i	−0.0743645	+	0.0993394i	−0.836181	−	0.548453i	$-0.815217\pi$
$197$	−1.04376	+	1.39429i	−0.0743645	+	0.0993394i	0.761817	+	0.647793i	$0.224308\pi$
$198$		0			0
$199$	−2.74816	+	0.806933i	−0.194812	+	0.0572020i	−0.377683	−	0.925935i	$-0.623279\pi$
$199$	−2.74816	+	0.806933i	−0.194812	+	0.0572020i	0.182871	+	0.983137i	$0.441461\pi$
$200$		0			0
$201$	1.16019	+	1.00531i	0.0818332	+	0.0709088i
$202$		0			0
$203$	0.989029	−	13.8284i	0.0694162	−	0.970566i
$204$		0			0
$205$	12.9345	−	1.02518i	0.903385	−	0.0716017i
$206$		0			0
$207$	28.0857	+	14.5348i	1.95209	+	1.01024i
$208$		0			0
$209$	17.6218	+	8.04760i	1.21892	+	0.556664i
$210$		0			0
$211$	−1.14516	−	1.32159i	−0.0788363	−	0.0909820i	0.714961	−	0.699164i	$-0.246444\pi$
$211$	−1.14516	−	1.32159i	−0.0788363	−	0.0909820i	−0.793797	+	0.608182i	$0.791899\pi$
$212$		0			0
$213$	−0.859997	−	12.0243i	−0.0589260	−	0.823893i
$214$		0			0
$215$	−0.165935	−	21.5659i	−0.0113167	−	1.47078i
$216$		0			0
$217$	−29.4074	−	22.0141i	−1.99630	−	1.49441i
$218$		0			0
$219$	−15.2037	+	6.94331i	−1.02737	+	0.469185i
$220$		0			0
$221$	3.43378	−	5.34307i	0.230981	−	0.359414i
$222$		0			0
$223$	−13.2998	−	17.7665i	−0.890623	−	1.18973i	−0.981035	−	0.193828i	$-0.937909\pi$
$223$	−13.2998	−	17.7665i	−0.890623	−	1.18973i	0.0904126	−	0.995904i	$-0.471181\pi$
$224$		0			0
$225$	32.9663	−	0.507335i	2.19775	−	0.0338224i
$226$		0			0
$227$	3.65823	−	1.99755i	0.242806	−	0.132582i	−0.353239	−	0.935533i	$-0.614920\pi$
$227$	3.65823	−	1.99755i	0.242806	−	0.132582i	0.596045	+	0.802951i	$0.296738\pi$
$228$		0			0
$229$	4.46018			0.294737			0.147369	−	0.989082i	$-0.452920\pi$
$229$	4.46018			0.294737			0.147369	+	0.989082i	$0.452920\pi$
$230$		0			0
$231$	−47.1590			−3.10284
$232$		0			0
$233$	1.00405	−	0.548252i	0.0657774	−	0.0359172i	−0.446024	−	0.895021i	$-0.647160\pi$
$233$	1.00405	−	0.548252i	0.0657774	−	0.0359172i	0.511801	+	0.859104i	$0.328978\pi$
$234$		0			0
$235$	0.688602	+	2.28011i	0.0449194	+	0.148738i
$236$		0			0
$237$	16.1564	+	21.5824i	1.04947	+	1.40193i
$238$		0			0
$239$	10.3372	−	16.0850i	0.668658	−	1.04045i	−0.326785	−	0.945099i	$-0.605965\pi$
$239$	10.3372	−	16.0850i	0.668658	−	1.04045i	0.995443	−	0.0953537i	$-0.0303982\pi$
$240$		0			0
$241$	−7.86992	+	3.59407i	−0.506946	+	0.231515i	−0.652434	−	0.757846i	$-0.726252\pi$
$241$	−7.86992	+	3.59407i	−0.506946	+	0.231515i	0.145488	+	0.989360i	$0.453525\pi$
$242$		0			0
$243$	9.71282	+	7.27092i	0.623078	+	0.466430i
$244$		0			0
$245$	−19.8077	+	20.1148i	−1.26546	+	1.28509i
$246$		0			0
$247$	−1.47397	−	20.6087i	−0.0937862	−	1.31130i
$248$		0			0
$249$	−5.98054	−	6.90191i	−0.379002	−	0.437391i
$250$		0			0
$251$	23.6918	+	10.8197i	1.49542	+	0.682933i	0.984288	−	0.176572i	$-0.0565007\pi$
$251$	23.6918	+	10.8197i	1.49542	+	0.682933i	0.511127	+	0.859505i	$0.329228\pi$
$252$		0			0
$253$	8.21894	+	14.2871i	0.516720	+	0.898225i
$254$		0			0
$255$	−0.948210	−	11.9634i	−0.0593792	−	0.749176i
$256$		0			0
$257$	0.829478	−	11.5976i	0.0517414	−	0.723439i	−0.903683	−	0.428203i	$-0.859147\pi$
$257$	0.829478	−	11.5976i	0.0517414	−	0.723439i	0.955424	−	0.295237i	$-0.0953985\pi$
$258$		0			0
$259$	3.19450	+	2.76805i	0.198497	+	0.171998i
$260$		0			0
$261$	−19.8002	+	5.81386i	−1.22560	+	0.359869i
$262$		0			0
$263$	7.54504	−	10.0790i	0.465247	−	0.621498i	−0.505144	−	0.863035i	$-0.668561\pi$
$263$	7.54504	−	10.0790i	0.465247	−	0.621498i	0.970392	+	0.241537i	$0.0776516\pi$
$264$		0			0
$265$	−3.02108	+	0.458118i	−0.185584	+	0.0281420i
$266$		0			0
$267$	−41.9958	+	9.13562i	−2.57010	+	0.559091i
$268$		0			0
$269$	−6.64828	−	0.955879i	−0.405353	−	0.0582810i	−0.0633770	−	0.997990i	$-0.520187\pi$
$269$	−6.64828	−	0.955879i	−0.405353	−	0.0582810i	−0.341976	+	0.939709i	$0.611096\pi$
$270$		0			0
$271$	−15.5611	+	10.0005i	−0.945268	+	0.607487i	−0.919884	−	0.392191i	$-0.871717\pi$
$271$	−15.5611	+	10.0005i	−0.945268	+	0.607487i	−0.0253840	+	0.999678i	$0.508081\pi$
$272$		0			0
$273$	24.1047	+	44.1444i	1.45888	+	2.67174i
$274$		0			0
$275$	14.5975	+	9.06694i	0.880264	+	0.546757i
$276$		0			0
$277$	−9.36324	−	9.36324i	−0.562583	−	0.562583i	0.367458	−	0.930040i	$-0.380228\pi$
$277$	−9.36324	−	9.36324i	−0.562583	−	0.562583i	−0.930040	+	0.367458i	$0.880228\pi$
$278$		0			0
$279$	−15.4048	+	52.4640i	−0.922262	+	3.14093i
$280$		0			0
$281$	5.60665	+	8.72412i	0.334465	+	0.520437i	0.967228	−	0.253908i	$-0.0817159\pi$
$281$	5.60665	+	8.72412i	0.334465	+	0.520437i	−0.632764	+	0.774345i	$0.718080\pi$
$282$		0			0
$283$	−12.8955	+	9.65344i	−0.766557	+	0.573838i	−0.909407	−	0.415907i	$-0.863464\pi$
$283$	−12.8955	+	9.65344i	−0.766557	+	0.573838i	0.142850	+	0.989744i	$0.454373\pi$
$284$		0			0
$285$	−25.7920	−	29.3069i	−1.52779	−	1.73599i
$286$		0			0
$287$	24.0849	+	8.98322i	1.42169	+	0.530262i
$288$		0			0
$289$	13.8552	−	1.99208i	0.815012	−	0.117181i
$290$		0			0
$291$	−12.2472	−	41.7100i	−0.717941	−	2.44508i
$292$		0			0
$293$	16.5113	−	1.18091i	0.964602	−	0.0689897i	0.419856	−	0.907591i	$-0.362081\pi$
$293$	16.5113	−	1.18091i	0.964602	−	0.0689897i	0.544746	+	0.838601i	$0.316626\pi$
$294$		0			0
$295$	−20.3060	−	7.39628i	−1.18226	−	0.430628i
$296$		0			0
$297$	13.3704	+	35.8475i	0.775830	+	2.08008i
$298$		0			0
$299$	9.17286	−	14.9962i	0.530480	−	0.867255i
$300$		0			0
$301$	17.7493	−	38.8656i	1.02306	−	2.24018i
$302$		0			0
$303$	−44.0878	−	3.15322i	−2.53278	−	0.181148i
$304$		0			0
$305$	3.46811	−	16.5549i	0.198583	−	0.947929i
$306$		0			0
$307$	30.1407	+	16.4581i	1.72022	+	0.939311i	0.955521	+	0.294922i	$0.0952937\pi$
$307$	30.1407	+	16.4581i	1.72022	+	0.939311i	0.764698	+	0.644389i	$0.222888\pi$
$308$		0			0
$309$	2.31863	+	16.1264i	0.131902	+	0.917399i
$310$		0			0
$311$	7.38034	+	16.1607i	0.418501	+	0.916389i	0.995055	+	0.0993295i	$0.0316698\pi$
$311$	7.38034	+	16.1607i	0.418501	+	0.916389i	−0.576554	+	0.817059i	$0.695603\pi$
$312$		0			0
$313$	−2.35444	−	10.8232i	−0.133081	−	0.611761i	−0.994577	−	0.103999i	$-0.966836\pi$
$313$	−2.35444	−	10.8232i	−0.133081	−	0.611761i	0.861497	−	0.507763i	$-0.169527\pi$
$314$		0			0
$315$	59.6234	+	26.6766i	3.35940	+	1.50306i
$316$		0			0
$317$	−5.79729	−	1.26112i	−0.325608	−	0.0708318i	0.0467900	−	0.998905i	$-0.485101\pi$
$317$	−5.79729	−	1.26112i	−0.325608	−	0.0708318i	−0.372398	+	0.928073i	$0.621464\pi$
$318$		0			0
$319$	−10.3200	−	3.03021i	−0.577807	−	0.169659i
$320$		0			0
$321$			17.5872i			0.981622i
$322$		0			0
$323$	−6.90617	+	6.90617i	−0.384270	+	0.384270i
$324$		0			0
$325$	1.02602	−	18.2988i	0.0569133	−	1.01504i
$326$		0			0
$327$	−8.06998	+	37.0971i	−0.446271	+	2.05147i
$328$		0			0
$329$	−0.671552	+	4.67075i	−0.0370239	+	0.257507i
$330$		0			0
$331$	−4.32625	−	2.78031i	−0.237792	−	0.152820i	0.416318	−	0.909219i	$-0.363320\pi$
$331$	−4.32625	−	2.78031i	−0.237792	−	0.152820i	−0.654110	+	0.756399i	$0.726957\pi$
$332$		0			0
$333$	2.19874	−	5.89506i	0.120490	−	0.323047i
$334$		0			0
$335$	0.149274	−	1.09814i	0.00815572	−	0.0599978i
$336$		0			0
$337$	−2.65259	+	4.85785i	−0.144496	+	0.264624i	−0.939896	−	0.341460i	$-0.889079\pi$
$337$	−2.65259	+	4.85785i	−0.144496	+	0.264624i	0.795401	+	0.606084i	$0.207260\pi$
$338$		0			0
$339$	−27.7324	+	32.0049i	−1.50622	+	1.73827i
$340$		0			0
$341$	−21.5380	+	18.6628i	−1.16635	+	1.01065i
$342$		0			0
$343$	−23.3475	+	8.70818i	−1.26065	+	0.470198i
$344$		0			0
$345$	−3.36007	−	33.0458i	−0.180900	−	1.77913i
$346$		0			0
$347$	−20.4543	+	7.62905i	−1.09804	+	0.409549i	−0.832204	−	0.554469i	$-0.812921\pi$
$347$	−20.4543	+	7.62905i	−1.09804	+	0.409549i	−0.265838	+	0.964018i	$0.585649\pi$
$348$		0			0
$349$	9.18913	−	7.96243i	0.491883	−	0.426219i	−0.373273	−	0.927721i	$-0.621765\pi$
$349$	9.18913	−	7.96243i	0.491883	−	0.426219i	0.865156	+	0.501502i	$0.167219\pi$
$350$		0			0
$351$	26.7219	−	30.8387i	1.42631	−	1.64605i
$352$		0			0
$353$	4.25322	−	7.78918i	0.226376	−	0.414576i	−0.739661	−	0.672979i	$-0.765014\pi$
$353$	4.25322	−	7.78918i	0.226376	−	0.414576i	0.966037	+	0.258403i	$0.0831962\pi$
$354$		0			0
$355$	−6.92652	+	5.26877i	−0.367622	+	0.279637i
$356$		0			0
$357$	8.30876	−	22.2766i	0.439746	−	1.17901i
$358$		0			0
$359$	12.0318	+	7.73237i	0.635015	+	0.408099i	0.818163	−	0.574986i	$-0.194993\pi$
$359$	12.0318	+	7.73237i	0.635015	+	0.408099i	−0.183149	+	0.983085i	$0.558629\pi$
$360$		0			0
$361$	−1.81768	+	12.6423i	−0.0956675	+	0.665382i
$362$		0			0
$363$	−0.534557	+	2.45732i	−0.0280569	+	0.128976i
$364$		0			0
$365$	10.2006	+	6.44516i	0.533923	+	0.337355i
$366$		0			0
$367$	19.1543	−	19.1543i	0.999849	−	0.999849i	−0.000151242	−	1.00000i	$-0.500048\pi$
$367$	19.1543	−	19.1543i	0.999849	−	0.999849i	1.00000		0.000151242i	$4.81420e-5\pi$
$368$		0			0
$369$		−	38.2627i		−	1.99188i
$370$		0			0
$371$	−5.80846	−	1.70552i	−0.301560	−	0.0885460i
$372$		0			0
$373$	−27.3870	−	5.95768i	−1.41804	−	0.308477i	−0.562754	−	0.826625i	$-0.690258\pi$
$373$	−27.3870	−	5.95768i	−1.41804	−	0.308477i	−0.855291	+	0.518148i	$0.826622\pi$
$374$		0			0
$375$	−19.3899	−	28.6929i	−1.00129	−	1.48170i
$376$		0			0
$377$	2.43839	+	11.2091i	0.125584	+	0.577299i
$378$		0			0
$379$	−7.42117	−	16.2501i	−0.381200	−	0.834711i	−0.998835	−	0.0482467i	$-0.984637\pi$
$379$	−7.42117	−	16.2501i	−0.381200	−	0.834711i	0.617636	−	0.786464i	$-0.288091\pi$
$380$		0			0
$381$	6.68264	+	46.4788i	0.342362	+	2.38118i
$382$		0			0
$383$	0.737785	+	0.402861i	0.0376991	+	0.0205853i	0.497988	−	0.867184i	$-0.334072\pi$
$383$	0.737785	+	0.402861i	0.0376991	+	0.0205853i	−0.460289	+	0.887769i	$0.652254\pi$
$384$		0			0
$385$	18.6258	+	28.4977i	0.949257	+	1.45238i
$386$		0			0
$387$	−63.4364	−	4.53706i	−3.22466	−	0.230632i
$388$		0			0
$389$	5.95524	−	13.0402i	0.301943	−	0.661163i	−0.696464	−	0.717592i	$-0.745244\pi$
$389$	5.95524	−	13.0402i	0.301943	−	0.661163i	0.998407	+	0.0564294i	$0.0179716\pi$
$390$		0			0
$391$	−8.19692	+	1.36521i	−0.414536	+	0.0690416i
$392$		0			0
$393$	−9.28505	−	24.8942i	−0.468369	−	1.25575i
$394$		0			0
$395$	6.66098	−	18.2873i	0.335150	−	0.920133i
$396$		0			0
$397$	2.25773	−	0.161476i	0.113312	−	0.00810425i	−0.0145679	−	0.999894i	$-0.504637\pi$
$397$	2.25773	−	0.161476i	0.113312	−	0.00810425i	0.127880	+	0.991790i	$0.459183\pi$
$398$		0			0
$399$	−21.7905	−	74.2115i	−1.09089	−	3.71522i
$400$		0			0
$401$	10.6903	−	1.53703i	0.533847	−	0.0767556i	0.129881	−	0.991530i	$-0.458540\pi$
$401$	10.6903	−	1.53703i	0.533847	−	0.0767556i	0.403966	+	0.914774i	$0.367631\pi$
$402$		0			0
$403$	28.4787	+	10.6220i	1.41862	+	0.529119i
$404$		0			0
$405$	2.09248	−	32.8017i	0.103976	−	1.62993i
$406$		0			0
$407$	2.62521	−	1.96521i	0.130127	−	0.0974118i
$408$		0			0
$409$	1.46386	+	2.27781i	0.0723832	+	0.112630i	0.875558	−	0.483113i	$-0.160494\pi$
$409$	1.46386	+	2.27781i	0.0723832	+	0.112630i	−0.803175	+	0.595743i	$0.796858\pi$
$410$		0			0
$411$	5.73296	−	19.5247i	0.282786	−	0.963081i
$412$		0			0
$413$	−30.2748	−	30.2748i	−1.48972	−	1.48972i
$414$		0			0
$415$	−1.80871	+	6.33994i	−0.0887859	+	0.311215i
$416$		0			0
$417$	14.4488	+	26.4610i	0.707561	+	1.29580i
$418$		0			0
$419$	23.6089	−	15.1725i	1.15337	−	0.741225i	0.183062	−	0.983101i	$-0.441399\pi$
$419$	23.6089	−	15.1725i	1.15337	−	0.741225i	0.970307	+	0.241876i	$0.0777627\pi$
$420$		0			0
$421$	2.38439	+	0.342823i	0.116208	+	0.0167082i	0.200173	−	0.979760i	$-0.435849\pi$
$421$	2.38439	+	0.342823i	0.116208	+	0.0167082i	−0.0839655	+	0.996469i	$0.526759\pi$
$422$		0			0
$423$	6.86335	−	1.49303i	0.333707	−	0.0725936i
$424$		0			0
$425$	−6.85486	+	5.29801i	−0.332509	+	0.256991i
$426$		0			0
$427$	20.0817	−	26.8260i	0.971821	−	1.29820i
$428$		0			0
$429$	37.4401	−	10.9934i	1.80763	−	0.530767i
$430$		0			0
$431$	−29.3538	−	25.4353i	−1.41393	−	1.22517i	−0.938437	−	0.345451i	$-0.887726\pi$
$431$	−29.3538	−	25.4353i	−1.41393	−	1.22517i	−0.475488	−	0.879722i	$-0.657729\pi$
$432$		0			0
$433$	−1.58022	+	22.0943i	−0.0759404	+	1.06179i	0.806461	+	0.591288i	$0.201380\pi$
$433$	−1.58022	+	22.0943i	−0.0759404	+	1.06179i	−0.882401	+	0.470498i	$0.844074\pi$
$434$		0			0
$435$	16.4897	+	14.0677i	0.790621	+	0.674497i
$436$		0			0
$437$	−18.6852	+	19.5352i	−0.893834	+	0.934497i
$438$		0			0
$439$	−19.3050	−	8.81629i	−0.921377	−	0.420779i	−0.102490	−	0.994734i	$-0.532681\pi$
$439$	−19.3050	−	8.81629i	−0.921377	−	0.420779i	−0.818887	+	0.573955i	$0.805408\pi$
$440$		0			0
$441$	54.5168	+	62.9157i	2.59604	+	2.99599i
$442$		0			0
$443$	2.44538	+	34.1908i	0.116183	+	1.62446i	0.637053	+	0.770820i	$0.280153\pi$
$443$	2.44538	+	34.1908i	0.116183	+	1.62446i	−0.520870	+	0.853636i	$0.674392\pi$
$444$		0			0
$445$	22.1071	+	21.7695i	1.04798	+	1.03197i
$446$		0			0
$447$	43.3201	+	32.4291i	2.04897	+	1.53384i
$448$		0			0
$449$	9.75774	−	4.45621i	0.460496	−	0.210302i	−0.171638	−	0.985160i	$-0.554906\pi$
$449$	9.75774	−	4.45621i	0.460496	−	0.210302i	0.632135	+	0.774858i	$0.282179\pi$
$450$		0			0
$451$	10.7819	−	16.7769i	0.507698	−	0.789993i
$452$		0			0
$453$	−26.0767	−	34.8344i	−1.22519	−	1.63666i
$454$		0			0
$455$	17.1558	−	32.0014i	0.804274	−	1.50025i
$456$		0			0
$457$	16.5257	−	9.02374i	0.773042	−	0.422113i	−0.0437520	−	0.999042i	$-0.513931\pi$
$457$	16.5257	−	9.02374i	0.773042	−	0.422113i	0.816794	+	0.576930i	$0.195749\pi$
$458$		0			0
$459$	−19.2891			−0.900336
$460$		0			0
$461$	15.2685			0.711124			0.355562	−	0.934653i	$-0.384290\pi$
$461$	15.2685			0.711124			0.355562	+	0.934653i	$0.384290\pi$
$462$		0			0
$463$	8.93118	−	4.87679i	0.415067	−	0.226644i	−0.258125	−	0.966112i	$-0.583105\pi$
$463$	8.93118	−	4.87679i	0.415067	−	0.226644i	0.673192	+	0.739468i	$0.264923\pi$
$464$		0			0
$465$	54.9795	−	16.6040i	2.54961	−	0.769990i
$466$		0			0
$467$	−17.2108	−	22.9909i	−0.796421	−	1.06389i	−0.996457	−	0.0841049i	$-0.973197\pi$
$467$	−17.2108	−	22.9909i	−0.796421	−	1.06389i	0.200036	−	0.979788i	$-0.435894\pi$
$468$		0			0
$469$	1.18703	−	1.84706i	0.0548120	−	0.0852892i
$470$		0			0
$471$	19.5697	−	8.93719i	0.901725	−	0.411804i
$472$		0			0
$473$	−26.5362	−	19.8648i	−1.22014	−	0.913383i
$474$		0			0
$475$	−7.52314	+	27.1608i	−0.345185	+	1.24622i
$476$		0			0
$477$	0.642826	+	8.98789i	0.0294330	+	0.411527i
$478$		0			0
$479$	−7.30353	−	8.42872i	−0.333707	−	0.385118i	0.563953	−	0.825807i	$-0.309280\pi$
$479$	−7.30353	−	8.42872i	−0.333707	−	0.385118i	−0.897660	+	0.440689i	$0.854734\pi$
$480$		0			0
$481$	−3.18143	−	1.45291i	−0.145061	−	0.0662470i
$482$		0			0
$483$	21.6204	−	62.1535i	0.983761	−	2.82808i
$484$		0			0
$485$	−20.3679	+	23.8745i	−0.924857	+	1.08408i
$486$		0			0
$487$	2.19054	−	30.6277i	0.0992628	−	1.38788i	−0.666861	−	0.745182i	$-0.732363\pi$
$487$	2.19054	−	30.6277i	0.0992628	−	1.38788i	0.766124	−	0.642693i	$-0.222183\pi$
$488$		0			0
$489$	41.4581	+	35.9236i	1.87480	+	1.62452i
$490$		0			0
$491$	−25.3968	+	7.45716i	−1.14614	+	0.336537i	−0.799032	−	0.601288i	$-0.794654\pi$
$491$	−25.3968	+	7.45716i	−1.14614	+	0.336537i	−0.347108	+	0.937825i	$0.612836\pi$
$492$		0			0
$493$	3.24962	−	4.34099i	0.146356	−	0.195508i
$494$		0			0
$495$	30.0555	−	40.8001i	1.35089	−	1.83383i
$496$		0			0
$497$	−16.8474	+	3.66492i	−0.755708	+	0.164394i
$498$		0			0
$499$	−29.6252	−	4.25946i	−1.32621	−	0.190680i	−0.557444	−	0.830214i	$-0.688218\pi$
$499$	−29.6252	−	4.25946i	−1.32621	−	0.190680i	−0.768762	+	0.639535i	$0.779127\pi$
$500$		0			0
$501$	4.91997	−	3.16187i	0.219808	−	0.141262i
$502$		0			0
$503$	−15.4572	−	28.3077i	−0.689202	−	1.26218i	−0.954557	−	0.298028i	$-0.903671\pi$
$503$	−15.4572	−	28.3077i	−0.689202	−	1.26218i	0.265356	−	0.964151i	$-0.414511\pi$
$504$		0			0
$505$	15.5073	+	27.8872i	0.690065	+	1.24096i
$506$		0			0
$507$	−0.954965	−	0.954965i	−0.0424115	−	0.0424115i
$508$		0			0
$509$	−9.81692	+	33.4334i	−0.435127	+	1.48191i	0.392038	+	0.919949i	$0.371770\pi$
$509$	−9.81692	+	33.4334i	−0.435127	+	1.48191i	−0.827165	+	0.561959i	$0.810048\pi$
$510$		0			0
$511$	12.9240	+	20.1101i	0.571724	+	0.889620i
$512$		0			0
$513$	−50.2331	+	37.6041i	−2.21785	+	1.66026i
$514$		0			0
$515$	8.82927	−	7.77035i	0.389064	−	0.342402i
$516$		0			0
$517$	3.43006	+	1.27934i	0.150854	+	0.0562655i
$518$		0			0
$519$	23.1623	−	3.33024i	1.01671	−	0.146181i
$520$		0			0
$521$	2.18477	+	7.44063i	0.0957163	+	0.325980i	0.993406	−	0.114648i	$-0.0365740\pi$
$521$	2.18477	+	7.44063i	0.0957163	+	0.325980i	−0.897690	+	0.440628i	$0.854756\pi$
$522$		0			0
$523$	14.7331	−	1.05374i	0.644235	−	0.0460766i	0.254601	−	0.967046i	$-0.418056\pi$
$523$	14.7331	−	1.05374i	0.644235	−	0.0460766i	0.389634	+	0.920970i	$0.372601\pi$
$524$		0			0
$525$	−10.8078	−	67.7514i	−0.471689	−	2.95692i
$526$		0			0
$527$	−5.02110	−	13.4621i	−0.218723	−	0.586418i
$528$		0			0
$529$	−22.5979	+	4.28216i	−0.982515	+	0.186181i
$530$		0			0
$531$	−26.4743	+	57.9706i	−1.14889	+	2.51571i
$532$		0			0
$533$	−21.2154	−	1.51736i	−0.918943	−	0.0657241i
$534$		0			0
$535$	10.6278	−	6.94618i	0.459479	−	0.300309i
$536$		0			0
$537$	−58.8212	−	32.1188i	−2.53832	−	1.38603i
$538$		0			0
$539$	6.17505	+	42.9484i	0.265978	+	1.84992i
$540$		0			0
$541$	6.10271	+	13.3631i	0.262376	+	0.574523i	0.994270	−	0.106895i	$-0.0340908\pi$
$541$	6.10271	+	13.3631i	0.262376	+	0.574523i	−0.731894	+	0.681418i	$0.761364\pi$
$542$		0			0
$543$	10.2368	+	47.0580i	0.439305	+	2.01945i
$544$		0			0
$545$	25.6047	−	9.77512i	1.09678	−	0.418720i
$546$		0			0
$547$	27.0185	+	5.87752i	1.15523	+	0.251305i	0.749065	−	0.662496i	$-0.230503\pi$
$547$	27.0185	+	5.87752i	1.15523	+	0.251305i	0.406163	+	0.913801i	$0.366867\pi$
$548$		0			0
$549$	−47.8586	−	14.0526i	−2.04256	−	0.599749i
$550$		0			0
$551$		−	17.6401i		−	0.751493i
$552$		0			0
$553$	27.2650	−	27.2650i	1.15943	−	1.15943i
$554$		0			0
$555$	−6.44653	+	1.45439i	−0.273640	+	0.0617355i
$556$		0			0
$557$	−1.46338	+	6.72703i	−0.0620052	+	0.285033i	−0.997701	−	0.0677756i	$-0.978410\pi$
$557$	−1.46338	+	6.72703i	−0.0620052	+	0.285033i	0.935695	+	0.352809i	$0.114773\pi$
$558$		0			0
$559$	−5.03131	+	34.9935i	−0.212802	+	1.48007i
$560$		0			0
$561$	−15.5173	−	9.97235i	−0.655140	−	0.421033i
$562$		0			0
$563$	−11.2830	+	30.2508i	−0.475520	+	1.27492i	0.448914	+	0.893575i	$0.351811\pi$
$563$	−11.2830	+	30.2508i	−0.475520	+	1.27492i	−0.924434	+	0.381343i	$0.875462\pi$
$564$		0			0
$565$	30.2933	+	4.11788i	1.27445	+	0.173240i
$566$		0			0
$567$	31.2075	−	57.1522i	1.31059	−	2.40017i
$568$		0			0
$569$	−16.8005	+	19.3888i	−0.704313	+	0.812821i	−0.989329	−	0.145702i	$-0.953456\pi$
$569$	−16.8005	+	19.3888i	−0.704313	+	0.812821i	0.285015	+	0.958523i	$0.408001\pi$
$570$		0			0
$571$	0.333834	−	0.289268i	0.0139705	−	0.0121055i	−0.647848	−	0.761770i	$-0.724331\pi$
$571$	0.333834	−	0.289268i	0.0139705	−	0.0121055i	0.661818	+	0.749665i	$0.269785\pi$
$572$		0			0
$573$	−46.7967	+	17.4543i	−1.95496	+	0.729163i
$574$		0			0
$575$	−18.6422	+	15.0821i	−0.777432	+	0.628967i
$576$		0			0
$577$	8.10764	−	3.02399i	0.337525	−	0.125891i	−0.174986	−	0.984571i	$-0.555988\pi$
$577$	8.10764	−	3.02399i	0.337525	−	0.125891i	0.512511	+	0.858680i	$0.328715\pi$
$578$		0			0
$579$	8.72837	−	7.56317i	0.362738	−	0.314315i
$580$		0			0
$581$	−8.55351	+	9.87128i	−0.354860	+	0.409530i
$582$		0			0
$583$	−2.25079	+	4.12202i	−0.0932183	+	0.170717i
$584$		0			0
$585$	−53.5544	−	7.27985i	−2.21420	−	0.300985i
$586$		0			0
$587$	4.43903	−	11.9015i	0.183218	−	0.491227i	−0.812575	−	0.582857i	$-0.801935\pi$
$587$	4.43903	−	11.9015i	0.183218	−	0.491227i	0.995793	+	0.0916295i	$0.0292075\pi$
$588$		0			0
$589$	−39.3205	−	25.2698i	−1.62017	−	1.04122i
$590$		0			0
$591$	0.767753	−	5.33984i	0.0315812	−	0.219652i
$592$		0			0
$593$	6.06618	−	27.8858i	0.249108	−	1.14513i	−0.667269	−	0.744817i	$-0.732537\pi$
$593$	6.06618	−	27.8858i	0.249108	−	1.14513i	0.916377	−	0.400316i	$-0.131099\pi$
$594$		0			0
$595$	−16.7432	+	3.77740i	−0.686403	+	0.154858i
$596$		0			0
$597$	6.27316	−	6.27316i	0.256743	−	0.256743i
$598$		0			0
$599$		−	26.8992i		−	1.09907i	−0.835470	−	0.549537i	$-0.814804\pi$
$599$		−	26.8992i		−	1.09907i	0.835470	−	0.549537i	$-0.185196\pi$
$600$		0			0
$601$	2.69349	+	0.790881i	0.109870	+	0.0322607i	0.336205	−	0.941789i	$-0.390856\pi$
$601$	2.69349	+	0.790881i	0.109870	+	0.0322607i	−0.226335	+	0.974049i	$0.572675\pi$
$602$		0			0
$603$	−3.19345	−	0.694692i	−0.130047	−	0.0282900i
$604$		0			0
$605$	1.69606	−	0.647506i	0.0689546	−	0.0263249i
$606$		0			0
$607$	7.06374	+	32.4715i	0.286708	+	1.31798i	0.864846	+	0.502037i	$0.167416\pi$
$607$	7.06374	+	32.4715i	0.286708	+	1.31798i	−0.578138	+	0.815939i	$0.696220\pi$
$608$		0			0
$609$	17.8387	+	39.0613i	0.722861	+	1.58285i
$610$		0			0
$611$	−0.555662	−	3.86471i	−0.0224797	−	0.156350i
$612$		0			0
$613$	38.4057	+	20.9711i	1.55119	+	0.847015i	0.999919	+	0.0126892i	$0.00403922\pi$
$613$	38.4057	+	20.9711i	1.55119	+	0.847015i	0.551272	+	0.834325i	$0.314143\pi$
$614$		0			0
$615$	−33.6412	+	21.9875i	−1.35654	+	0.886620i
$616$		0			0
$617$	0.242274	+	0.0173278i	0.00975360	+	0.000697591i	0.0762151	−	0.997091i	$-0.475716\pi$
$617$	0.242274	+	0.0173278i	0.00975360	+	0.000697591i	−0.0664615	+	0.997789i	$0.521171\pi$
$618$		0			0
$619$	−7.71493	+	16.8933i	−0.310089	+	0.679001i	−0.998946	−	0.0458965i	$-0.985386\pi$
$619$	−7.71493	+	16.8933i	−0.310089	+	0.679001i	0.688857	+	0.724897i	$0.258113\pi$
$620$		0			0
$621$	−53.3751	+	1.18710i	−2.14187	+	0.0476366i
$622$		0			0
$623$	21.4809	+	57.5925i	0.860614	+	2.30740i
$624$		0			0
$625$	−9.68068	+	23.0496i	−0.387227	+	0.921984i
$626$		0			0
$627$	−59.8517	+	4.28068i	−2.39025	+	0.170954i
$628$		0			0
$629$	0.465786	+	1.58632i	0.0185721	+	0.0632508i
$630$		0			0
$631$	−5.67665	+	0.816179i	−0.225984	+	0.0324916i	−0.254377	−	0.967105i	$-0.581870\pi$
$631$	−5.67665	+	0.816179i	−0.225984	+	0.0324916i	0.0283926	+	0.999597i	$0.490961\pi$
$632$		0			0
$633$	5.07499	+	1.89287i	0.201713	+	0.0752350i
$634$		0			0
$635$	25.4473	−	22.3954i	1.00985	−	0.888732i
$636$		0			0
$637$	37.0467	−	27.7328i	1.46784	−	1.09881i
$638$		0			0
$639$	13.8748	+	21.5897i	0.548880	+	0.854074i
$640$		0			0
$641$	11.5370	−	39.2915i	0.455685	−	1.55192i	−0.336527	−	0.941674i	$-0.609252\pi$
$641$	11.5370	−	39.2915i	0.455685	−	1.55192i	0.792212	−	0.610246i	$-0.208930\pi$
$642$		0			0
$643$	−18.4995	−	18.4995i	−0.729550	−	0.729550i	0.240980	−	0.970530i	$-0.422531\pi$
$643$	−18.4995	−	18.4995i	−0.729550	−	0.729550i	−0.970530	+	0.240980i	$0.922531\pi$
$644$		0			0
$645$	32.4643	+	58.3816i	1.27828	+	2.29877i
$646$		0			0
$647$	−16.1252	−	29.5312i	−0.633949	−	1.16099i	−0.975264	−	0.221041i	$-0.929054\pi$
$647$	−16.1252	−	29.5312i	−0.633949	−	1.16099i	0.341316	−	0.939949i	$-0.389127\pi$
$648$		0			0
$649$	−27.9433	+	17.9581i	−1.09687	+	0.704916i
$650$		0			0
$651$	112.624	+	16.1929i	4.41407	+	0.634648i
$652$		0			0
$653$	−10.6209	+	2.31043i	−0.415627	+	0.0904141i	−0.415516	−	0.909586i	$-0.636399\pi$
$653$	−10.6209	+	2.31043i	−0.415627	+	0.0904141i	−0.000110893		1.00000i	$0.500035\pi$
$654$		0			0
$655$	−11.3761	+	15.4430i	−0.444502	+	0.603407i
$656$		0			0
$657$	21.3237	−	28.4851i	0.831917	−	1.11131i
$658$		0			0
$659$	23.3102	−	6.84450i	0.908037	−	0.266624i	0.205823	−	0.978589i	$-0.434013\pi$
$659$	23.3102	−	6.84450i	0.908037	−	0.266624i	0.702214	+	0.711966i	$0.252195\pi$
$660$		0			0
$661$	31.0550	+	26.9093i	1.20790	+	1.04665i	0.997616	+	0.0690091i	$0.0219838\pi$
$661$	31.0550	+	26.9093i	1.20790	+	1.04665i	0.210282	+	0.977641i	$0.432562\pi$
$662$		0			0
$663$	−1.40344	+	19.6226i	−0.0545049	+	0.762078i
$664$		0			0
$665$	−36.2390	+	42.4780i	−1.40529	+	1.64723i
$666$		0			0
$667$	8.72494	−	12.2120i	0.337831	−	0.472852i
$668$		0			0
$669$	62.5294	+	28.5562i	2.41753	+	1.10405i
$670$		0			0
$671$	−17.0246	−	19.6474i	−0.657226	−	0.758480i
$672$		0			0
$673$	1.65219	+	23.1007i	0.0636873	+	0.890465i	0.924412	+	0.381395i	$0.124556\pi$
$673$	1.65219	+	23.1007i	0.0636873	+	0.890465i	−0.860725	+	0.509070i	$0.829989\pi$
$674$		0			0
$675$	−48.4364	+	27.4241i	−1.86432	+	1.05556i
$676$		0			0
$677$	−2.87656	−	2.15337i	−0.110555	−	0.0827605i	0.542570	−	0.840011i	$-0.317451\pi$
$677$	−2.87656	−	2.15337i	−0.110555	−	0.0827605i	−0.653125	+	0.757250i	$0.726542\pi$
$678$		0			0
$679$	−56.5546	+	25.8276i	−2.17037	+	0.991174i
$680$		0			0
$681$	−6.97984	+	10.8608i	−0.267468	+	0.416188i
$682$		0			0
$683$	20.9027	+	27.9228i	0.799821	+	1.06844i	0.996130	+	0.0878935i	$0.0280135\pi$
$683$	20.9027	+	27.9228i	0.799821	+	1.06844i	−0.196309	+	0.980542i	$0.562896\pi$
$684$		0			0
$685$	−14.0628	+	4.24702i	−0.537313	+	0.162270i
$686$		0			0
$687$	−12.1252	+	6.62086i	−0.462605	+	0.252601i
$688$		0			0
$689$	5.00898			0.190827
$690$		0			0
$691$	−30.2540			−1.15092			−0.575458	−	0.817831i	$-0.695176\pi$
$691$	−30.2540			−1.15092			−0.575458	+	0.817831i	$0.695176\pi$
$692$		0			0
$693$	88.1153	−	48.1146i	3.34722	−	1.82772i
$694$		0			0
$695$	10.2835	−	19.1822i	0.390075	−	0.727623i
$696$		0			0
$697$	6.02533	+	8.04891i	0.228226	+	0.304874i
$698$		0			0
$699$	−1.91570	+	2.98089i	−0.0724586	+	0.112748i
$700$		0			0
$701$	−33.7017	+	15.3911i	−1.27290	+	0.581313i	−0.933246	−	0.359239i	$-0.883036\pi$
$701$	−33.7017	+	15.3911i	−1.27290	+	0.581313i	−0.339652	+	0.940551i	$0.610309\pi$
$702$		0			0
$703$	4.30555	+	3.22310i	0.162387	+	0.121561i
$704$		0			0
$705$	−5.25668	−	5.17641i	−0.197978	−	0.194955i
$706$		0			0
$707$	4.50981	+	63.0554i	0.169609	+	2.37144i
$708$		0			0
$709$	−0.615911	−	0.710800i	−0.0231310	−	0.0266946i	0.744066	−	0.668106i	$-0.232895\pi$
$709$	−0.615911	−	0.710800i	−0.0231310	−	0.0266946i	−0.767197	+	0.641411i	$0.778349\pi$
$710$		0			0
$711$	−52.2075	−	23.8424i	−1.95794	−	0.894159i
$712$		0			0
$713$	−14.7225	−	36.9422i	−0.551362	−	1.38350i
$714$		0			0
$715$	−21.4304	−	18.2828i	−0.801453	−	0.683738i
$716$		0			0
$717$	−4.22496	+	59.0727i	−0.157784	+	2.20611i
$718$		0			0
$719$	−6.39288	−	5.53946i	−0.238414	−	0.206587i	0.527456	−	0.849582i	$-0.323146\pi$
$719$	−6.39288	−	5.53946i	−0.238414	−	0.206587i	−0.765870	+	0.642995i	$0.777691\pi$
$720$		0			0
$721$	22.3577	−	6.56480i	0.832643	−	0.244486i
$722$		0			0
$723$	16.0595	−	21.4530i	0.597261	−	0.797847i
$724$		0			0
$725$	1.98829	−	15.5207i	0.0738431	−	0.576425i
$726$		0			0
$727$	−38.4304	+	8.36002i	−1.42530	+	0.310056i	−0.858083	−	0.513510i	$-0.828345\pi$
$727$	−38.4304	+	8.36002i	−1.42530	+	0.310056i	−0.567220	+	0.823566i	$0.691981\pi$
$728$		0			0
$729$	6.45069	+	0.927470i	0.238915	+	0.0343507i
$730$		0			0
$731$	14.0589	−	9.03510i	0.519987	−	0.334175i
$732$		0			0
$733$	4.50436	+	8.24913i	0.166373	+	0.304689i	0.947542	−	0.319630i	$-0.103559\pi$
$733$	4.50436	+	8.24913i	0.166373	+	0.304689i	−0.781170	+	0.624318i	$0.785377\pi$
$734$		0			0
$735$	23.9888	−	84.0862i	0.884839	−	3.10157i
$736$		0			0
$737$	−1.20446	−	1.20446i	−0.0443670	−	0.0443670i
$738$		0			0
$739$	3.80157	−	12.9470i	0.139843	−	0.476261i	−0.859552	−	0.511049i	$-0.829257\pi$
$739$	3.80157	−	12.9470i	0.139843	−	0.476261i	0.999395	+	0.0347873i	$0.0110754\pi$
$740$		0			0
$741$	34.5994	+	53.8377i	1.27104	+	1.97778i
$742$		0			0
$743$	−28.1229	+	21.0525i	−1.03173	+	0.772343i	−0.974128	−	0.225997i	$-0.927436\pi$
$743$	−28.1229	+	21.0525i	−1.03173	+	0.772343i	−0.0576011	+	0.998340i	$0.518345\pi$
$744$		0			0
$745$	2.48699	−	38.9860i	0.0911164	−	1.42834i
$746$		0			0
$747$	18.2162	+	6.79430i	0.666497	+	0.248590i
$748$		0			0
$749$	24.8976	−	3.57973i	0.909738	−	0.130801i
$750$		0			0
$751$	7.51634	+	25.5983i	0.274275	+	0.934095i	0.975286	+	0.220945i	$0.0709140\pi$
$751$	7.51634	+	25.5983i	0.274275	+	0.934095i	−0.701011	+	0.713150i	$0.747268\pi$
$752$		0			0
$753$	−80.4684	+	5.75522i	−2.93243	+	0.209732i
$754$		0			0
$755$	−10.7509	+	29.5160i	−0.391266	+	1.07420i
$756$		0			0
$757$	−4.89844	−	13.1332i	−0.178037	−	0.477335i	0.817024	−	0.576604i	$-0.195622\pi$
$757$	−4.89844	−	13.1332i	−0.178037	−	0.477335i	−0.995061	+	0.0992688i	$0.968350\pi$
$758$		0			0
$759$	−43.5519	−	26.6397i	−1.58083	−	0.966961i
$760$		0			0
$761$	11.3838	−	24.9270i	0.412662	−	0.903604i	−0.583166	−	0.812353i	$-0.698186\pi$
$761$	11.3838	−	24.9270i	0.412662	−	0.903604i	0.995828	−	0.0912508i	$-0.0290865\pi$
$762$		0			0
$763$	54.1597	+	3.87357i	1.96071	+	0.140233i
$764$		0			0
$765$	13.9775	+	21.3858i	0.505357	+	0.773206i
$766$		0			0
$767$	31.0930	+	16.9780i	1.12270	+	0.613042i
$768$		0			0
$769$	−1.05609	−	7.34529i	−0.0380837	−	0.264878i	0.961879	−	0.273474i	$-0.0881728\pi$
$769$	−1.05609	−	7.34529i	−0.0380837	−	0.264878i	−0.999963	+	0.00859621i	$0.997264\pi$
$770$		0			0
$771$	14.9610	+	32.7599i	0.538806	+	1.17982i
$772$		0			0
$773$	−9.13377	−	41.9873i	−0.328519	−	1.51018i	−0.784467	−	0.620171i	$-0.787063\pi$
$773$	−9.13377	−	41.9873i	−0.328519	−	1.51018i	0.455948	−	0.890006i	$-0.349300\pi$
$774$		0			0
$775$	−31.7481	−	26.6657i	−1.14043	−	0.957860i
$776$		0			0
$777$	−12.7934	−	2.78303i	−0.458961	−	0.0998408i
$778$		0			0
$779$	31.3827	+	9.21480i	1.12440	+	0.330154i
$780$		0			0
$781$			13.3760i			0.478633i
$782$		0			0
$783$	24.6345	−	24.6345i	0.880365	−	0.880365i
$784$		0			0
$785$	−13.1298	−	8.29599i	−0.468624	−	0.296097i
$786$		0			0
$787$	1.61780	−	7.43693i	0.0576685	−	0.265098i	−0.939281	−	0.343149i	$-0.888506\pi$
$787$	1.61780	−	7.43693i	0.0576685	−	0.265098i	0.996949	+	0.0780516i	$0.0248699\pi$
$788$		0			0
$789$	−5.54989	+	38.6003i	−0.197581	+	1.37421i
$790$		0			0
$791$	50.9529	+	32.7454i	1.81168	+	1.16429i
$792$		0			0
$793$	−9.68959	+	25.9788i	−0.344087	+	0.922534i
$794$		0			0
$795$	7.53290	−	5.73002i	0.267164	−	0.203223i
$796$		0			0
$797$	−2.53870	+	4.64927i	−0.0899252	+	0.164686i	−0.918770	−	0.394792i	$-0.870817\pi$
$797$	−2.53870	+	4.64927i	−0.0899252	+	0.164686i	0.828845	+	0.559478i	$0.188998\pi$
$798$		0			0
$799$	−1.20866	+	1.39486i	−0.0427591	+	0.0493467i
$800$		0			0
$801$	69.1471	−	59.9163i	2.44319	−	2.11704i
$802$		0			0
$803$	17.3764	−	6.48106i	0.613200	−	0.228712i
$804$		0			0
$805$	−46.0979	+	11.4829i	−1.62474	+	0.404721i
$806$		0			0
$807$	19.4926	−	7.27036i	0.686172	−	0.255929i
$808$		0			0
$809$	−4.11633	+	3.56682i	−0.144722	+	0.125403i	−0.724213	−	0.689576i	$-0.757797\pi$
$809$	−4.11633	+	3.56682i	−0.144722	+	0.125403i	0.579491	+	0.814979i	$0.303251\pi$
$810$		0			0
$811$	25.8390	−	29.8198i	0.907329	−	1.04711i	−0.0913543	−	0.995818i	$-0.529120\pi$
$811$	25.8390	−	29.8198i	0.907329	−	1.04711i	0.998684	−	0.0512953i	$-0.0163350\pi$
$812$		0			0
$813$	27.4583	−	50.2862i	0.963006	−	1.76361i
$814$		0			0
$815$	5.33417	−	39.2410i	0.186848	−	1.37455i
$816$		0			0
$817$	18.9986	−	50.9373i	0.664678	−	1.78207i
$818$		0			0
$819$	−90.0778	−	57.8895i	−3.14757	−	2.02282i
$820$		0			0
$821$	−6.39532	+	44.4804i	−0.223198	+	1.55238i	0.502630	+	0.864502i	$0.332366\pi$
$821$	−6.39532	+	44.4804i	−0.223198	+	1.55238i	−0.725828	+	0.687876i	$0.758543\pi$
$822$		0			0
$823$	0.988372	−	4.54348i	0.0344525	−	0.158376i	−0.956707	−	0.291054i	$-0.905994\pi$
$823$	0.988372	−	4.54348i	0.0344525	−	0.158376i	0.991159	+	0.132678i	$0.0423577\pi$
$824$		0			0
$825$	−53.1433	−	2.97976i	−1.85021	−	0.103742i
$826$		0			0
$827$	36.8913	−	36.8913i	1.28284	−	1.28284i	0.343790	−	0.939046i	$-0.388289\pi$
$827$	36.8913	−	36.8913i	1.28284	−	1.28284i	0.939046	−	0.343790i	$-0.111711\pi$
$828$		0			0
$829$			37.7806i			1.31218i	0.754685	+	0.656088i	$0.227790\pi$
$829$			37.7806i			1.31218i	−0.754685	+	0.656088i	$0.772210\pi$
$830$		0			0
$831$	39.3535	+	11.5552i	1.36516	+	0.400847i
$832$		0			0
$833$	−21.3756	−	4.64998i	−0.740621	−	0.161112i
$834$		0			0
$835$	−3.85386	−	1.72429i	−0.133368	−	0.0596714i
$836$		0			0
$837$	−19.6220	−	90.2008i	−0.678235	−	3.11780i
$838$		0			0
$839$	−8.57559	−	18.7779i	−0.296062	−	0.648286i	0.701888	−	0.712288i	$-0.252341\pi$
$839$	−8.57559	−	18.7779i	−0.296062	−	0.648286i	−0.997950	+	0.0640019i	$0.979614\pi$
$840$		0			0
$841$	−2.73332	−	19.0107i	−0.0942525	−	0.655541i
$842$		0			0
$843$	−28.1923	−	15.3942i	−0.970995	−	0.530204i
$844$		0			0
$845$	−0.199906	+	0.954245i	−0.00687699	+	0.0328270i
$846$		0			0
$847$	3.58755	+	0.256586i	0.123270	+	0.00881641i
$848$		0			0
$849$	20.7270	−	45.3858i	0.711350	−	1.55764i
$850$		0			0
$851$	1.38651	+	4.36088i	0.0475290	+	0.149489i
$852$		0			0
$853$	−3.92897	−	10.5340i	−0.134525	−	0.360677i	0.852168	−	0.523268i	$-0.175287\pi$
$853$	−3.92897	−	10.5340i	−0.134525	−	0.360677i	−0.986693	+	0.162592i	$0.948015\pi$
$854$		0			0
$855$	78.0923	+	28.4444i	2.67070	+	0.972779i
$856$		0			0
$857$	12.2654	−	0.877240i	0.418979	−	0.0299659i	0.139741	−	0.990188i	$-0.455373\pi$
$857$	12.2654	−	0.877240i	0.418979	−	0.0299659i	0.279237	+	0.960222i	$0.409918\pi$
$858$		0			0
$859$	9.02164	+	30.7249i	0.307814	+	1.04832i	0.957576	+	0.288181i	$0.0930506\pi$
$859$	9.02164	+	30.7249i	0.307814	+	1.04832i	−0.649761	+	0.760138i	$0.725131\pi$
$860$		0			0
$861$	−78.8110	+	11.3313i	−2.68587	+	0.386170i
$862$		0			0
$863$	−16.6538	−	6.21155i	−0.566902	−	0.211444i	0.0496375	−	0.998767i	$-0.484193\pi$
$863$	−16.6538	−	6.21155i	−0.566902	−	0.211444i	−0.616540	+	0.787324i	$0.711466\pi$
$864$		0			0
$865$	−11.1605	−	12.6815i	−0.379470	−	0.431183i
$866$		0			0
$867$	−34.7089	+	25.9827i	−1.17877	+	0.882420i
$868$		0			0
$869$	−16.1728	−	25.1654i	−0.548624	−	0.853676i
$870$		0			0
$871$	−0.511825	+	1.74311i	−0.0173425	+	0.0590632i
$872$		0			0
$873$	65.4386	+	65.4386i	2.21476	+	2.21476i
$874$		0			0
$875$	−36.6729	+	33.2899i	−1.23977	+	1.12540i
$876$		0			0
$877$	1.37937	+	2.52613i	0.0465781	+	0.0853014i	0.899931	−	0.436032i	$-0.143617\pi$
$877$	1.37937	+	2.52613i	0.0465781	+	0.0853014i	−0.853353	+	0.521333i	$0.825435\pi$
$878$		0			0
$879$	−43.1338	+	27.7204i	−1.45487	+	0.934985i
$880$		0			0
$881$	1.22252	+	0.175771i	0.0411876	+	0.00592189i	0.162878	−	0.986646i	$-0.447922\pi$
$881$	1.22252	+	0.175771i	0.0411876	+	0.00592189i	−0.121690	+	0.992568i	$0.538831\pi$
$882$		0			0
$883$	−35.8383	+	7.79615i	−1.20606	+	0.262361i	−0.770287	−	0.637697i	$-0.779887\pi$
$883$	−35.8383	+	7.79615i	−1.20606	+	0.262361i	−0.435769	+	0.900059i	$0.643524\pi$
$884$		0			0
$885$	66.1820	−	10.0359i	2.22468	−	0.337352i
$886$		0			0
$887$	−1.29007	+	1.72333i	−0.0433164	+	0.0578639i	−0.821676	−	0.569954i	$-0.806961\pi$
$887$	−1.29007	+	1.72333i	−0.0433164	+	0.0578639i	0.778360	+	0.627818i	$0.216052\pi$
$888$		0			0
$889$	64.4382	−	18.9208i	2.16119	−	0.634582i
$890$		0			0
$891$	−38.1795	−	33.0827i	−1.27906	−	1.10831i
$892$		0			0
$893$	−0.428329	+	5.98882i	−0.0143335	+	0.200408i
$894$		0			0
$895$	3.82272	+	48.2306i	0.127780	+	1.61217i
$896$		0			0
$897$	−2.67585	+	54.3844i	−0.0893440	+	1.81584i
$898$		0			0
$899$	23.6053	+	10.7802i	0.787282	+	0.359540i
$900$		0			0
$901$	−1.55057	−	1.78946i	−0.0516570	−	0.0596154i
$902$		0			0
$903$	9.44124	+	132.006i	0.314185	+	4.39288i
$904$		0			0
$905$	24.3936	−	24.7719i	0.810870	−	0.823445i
$906$		0			0
$907$	12.0813	+	9.04397i	0.401154	+	0.300300i	0.780740	−	0.624857i	$-0.214843\pi$
$907$	12.0813	+	9.04397i	0.401154	+	0.300300i	−0.379586	+	0.925157i	$0.623933\pi$
$908$		0			0
$909$	85.5938	−	39.0894i	2.83897	−	1.29651i
$910$		0			0
$911$	−12.0940	+	18.8186i	−0.400692	+	0.623489i	−0.981706	−	0.190405i	$-0.939020\pi$
$911$	−12.0940	+	18.8186i	−0.400692	+	0.623489i	0.581013	+	0.813894i	$0.302656\pi$
$912$		0			0
$913$	6.07266	+	8.11212i	0.200976	+	0.268472i
$914$		0			0
$915$	15.1465	+	50.1533i	0.500726	+	1.65802i
$916$		0			0
$917$	−33.3519	+	18.2115i	−1.10138	+	0.601398i
$918$		0			0
$919$	−42.3231			−1.39611			−0.698055	−	0.716044i	$-0.745951\pi$
$919$	−42.3231			−1.39611			−0.698055	+	0.716044i	$0.745951\pi$
$920$		0			0
$921$	−106.370			−3.50500
$922$		0			0
$923$	12.5210	−	6.83698i	0.412134	−	0.225042i
$924$		0			0
$925$	3.42497	+	3.32115i	0.112612	+	0.109199i
$926$		0			0
$927$	−20.7854	−	27.7661i	−0.682683	−	0.911958i
$928$		0			0
$929$	−8.49353	+	13.2162i	−0.278664	+	0.433609i	−0.952168	−	0.305574i	$-0.901152\pi$
$929$	−8.49353	+	13.2162i	−0.278664	+	0.433609i	0.673505	+	0.739183i	$0.264788\pi$
$930$		0			0
$931$	−64.7322	+	29.5622i	−2.12151	+	0.968862i
$932$		0			0
$933$	−44.0533	−	32.9779i	−1.44224	−	1.07965i
$934$		0			0
$935$	0.102454	+	13.3156i	0.00335061	+	0.435466i
$936$		0			0
$937$	2.74721	+	38.4110i	0.0897475	+	1.25483i	0.820283	+	0.571958i	$0.193816\pi$
$937$	2.74721	+	38.4110i	0.0897475	+	1.25483i	−0.730535	+	0.682875i	$0.760729\pi$
$938$		0			0
$939$	22.4669	+	25.9282i	0.733181	+	0.846136i
$940$		0			0
$941$	2.45738	+	1.12225i	0.0801082	+	0.0365842i	0.455066	−	0.890458i	$-0.349616\pi$
$941$	2.45738	+	1.12225i	0.0801082	+	0.0365842i	−0.374958	+	0.927042i	$0.622343\pi$
$942$		0			0
$943$	17.1682	+	21.9015i	0.559073	+	0.713210i
$944$		0			0
$945$	−109.929	+	8.71290i	−3.57599	+	0.283431i
$946$		0			0
$947$	1.43389	−	20.0485i	0.0465953	−	0.651487i	−0.919465	−	0.393171i	$-0.871378\pi$
$947$	1.43389	−	20.0485i	0.0465953	−	0.651487i	0.966060	−	0.258316i	$-0.0831676\pi$
$948$		0			0
$949$	−14.9485	−	12.9529i	−0.485248	−	0.420470i
$950$		0			0
$951$	17.6322	−	5.17730i	0.571765	−	0.167885i
$952$		0			0
$953$	−15.0628	+	20.1215i	−0.487932	+	0.651801i	−0.975167	−	0.221470i	$-0.928915\pi$
$953$	−15.0628	+	20.1215i	−0.487932	+	0.651801i	0.487235	+	0.873271i	$0.338005\pi$
$954$		0			0
$955$	29.0301	+	21.3851i	0.939393	+	0.692007i
$956$		0			0
$957$	32.5534	−	7.08156i	1.05230	−	0.228914i
$958$		0			0
$959$	−28.8073	−	4.14186i	−0.930236	−	0.133748i
$960$		0			0
$961$	31.7658	−	20.4146i	1.02470	−	0.658537i
$962$		0			0
$963$	−17.9435	−	32.8611i	−0.578223	−	1.05894i
$964$		0			0
$965$	−8.01767	−	2.28734i	−0.258098	−	0.0736322i
$966$		0			0
$967$	31.3708	+	31.3708i	1.00882	+	1.00882i	0.999961	+	0.00885645i	$0.00281913\pi$
$967$	31.3708	+	31.3708i	1.00882	+	1.00882i	0.00885645	+	0.999961i	$0.497181\pi$
$968$		0			0
$969$	8.52295	−	29.0265i	0.273797	−	0.932466i
$970$		0			0
$971$	−1.41235	−	2.19765i	−0.0453244	−	0.0705261i	0.817852	−	0.575429i	$-0.195165\pi$
$971$	−1.41235	−	2.19765i	−0.0453244	−	0.0705261i	−0.863176	+	0.504903i	$0.831528\pi$
$972$		0			0
$973$	34.5190	−	25.8406i	1.10663	−	0.828412i
$974$		0			0
$975$	24.3742	+	51.2693i	0.780599	+	1.64193i
$976$		0			0
$977$	−56.4107	−	21.0401i	−1.80474	−	0.673133i	−0.996435	−	0.0843689i	$-0.973113\pi$
$977$	−56.4107	−	21.0401i	−1.80474	−	0.673133i	−0.808305	−	0.588764i	$-0.799615\pi$
$978$		0			0
$979$	47.2022	−	6.78665i	1.50859	−	0.216902i
$980$		0			0
$981$	−22.7702	−	77.5483i	−0.726997	−	2.47593i
$982$		0			0
$983$	7.77850	−	0.556329i	0.248096	−	0.0177442i	0.0532625	−	0.998581i	$-0.483038\pi$
$983$	7.77850	−	0.556329i	0.248096	−	0.0177442i	0.194833	+	0.980836i	$0.437583\pi$
$984$		0			0
$985$	−3.53004	+	1.64506i	−0.112477	+	0.0524159i
$986$		0			0
$987$	−5.10779	−	13.6945i	−0.162583	−	0.435901i
$988$		0			0
$989$	38.3466	−	25.8664i	1.21935	−	0.822505i
$990$		0			0
$991$	3.79617	−	8.31246i	0.120589	−	0.264054i	−0.839705	−	0.543043i	$-0.817272\pi$
$991$	3.79617	−	8.31246i	0.120589	−	0.264054i	0.960294	+	0.278989i	$0.0899993\pi$
$992$		0			0
$993$	15.8883	+	1.13635i	0.504200	+	0.0360611i
$994$		0			0
$995$	−6.26843	−	1.31318i	−0.198723	−	0.0416307i
$996$		0			0
$997$	−18.8941	−	10.3169i	−0.598381	−	0.326741i	0.151353	−	0.988480i	$-0.451637\pi$
$997$	−18.8941	−	10.3169i	−0.598381	−	0.326741i	−0.749734	+	0.661739i	$0.769819\pi$
$998$		0			0
$999$	1.51166	+	10.5138i	0.0478268	+	0.332642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.17.1	✓	240
5.3	odd	4	inner	460.2.x.a.293.1	yes	240
23.19	odd	22	inner	460.2.x.a.157.1	yes	240
115.88	even	44	inner	460.2.x.a.433.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.17.1	✓	240	1.1	even	1	trivial
460.2.x.a.157.1	yes	240	23.19	odd	22	inner
460.2.x.a.293.1	yes	240	5.3	odd	4	inner
460.2.x.a.433.1	yes	240	115.88	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)

\(f(q)\)	\(=\)	\(q+(-2.71854 + 1.48444i) q^{3} +(1.97074 + 1.05650i) q^{5} +(2.65480 + 3.54640i) q^{7} +(3.56500 - 5.54725i) q^{9} +O(q^{10})\)	\(q+(-2.71854 + 1.48444i) q^{3} +(1.97074 + 1.05650i) q^{5} +(2.65480 + 3.54640i) q^{7} +(3.56500 - 5.54725i) q^{9} +(3.12626 - 1.42772i) q^{11} +(-2.93440 - 2.19666i) q^{13} +(-6.92584 + 0.0532896i) q^{15} +(0.123611 + 1.72831i) q^{17} +(3.69125 + 4.25993i) q^{19} +(-12.4816 - 5.70016i) q^{21} +(0.448411 + 4.77482i) q^{23} +(2.76761 + 4.16417i) q^{25} +(-0.794165 + 11.1039i) q^{27} +(-2.36513 - 2.04939i) q^{29} +(-7.95628 + 2.33617i) q^{31} +(-6.37953 + 8.52205i) q^{33} +(1.48514 + 9.79384i) q^{35} +(0.932354 - 0.202821i) q^{37} +(11.2381 + 1.61579i) q^{39} +(4.88148 - 3.13714i) q^{41} +(-4.62229 - 8.46509i) q^{43} +(12.8864 - 7.16575i) q^{45} +(0.753200 + 0.753200i) q^{47} +(-3.55687 + 12.1136i) q^{49} +(-2.90160 - 4.51498i) q^{51} +(-1.09395 + 0.818922i) q^{53} +(7.66943 + 0.489248i) q^{55} +(-16.3584 - 6.10137i) q^{57} +(-9.56639 + 1.37544i) q^{59} +(-2.13110 - 7.25787i) q^{61} +(29.1372 - 2.08393i) q^{63} +(-3.46215 - 7.42924i) q^{65} +(-0.173201 - 0.464371i) q^{67} +(-8.30695 - 12.3149i) q^{69} +(-1.61678 + 3.54025i) q^{71} +(5.38240 + 0.384957i) q^{73} +(-13.7053 - 7.21215i) q^{75} +(13.3629 + 7.29668i) q^{77} +(-1.23870 - 8.61535i) q^{79} +(-6.10625 - 13.3708i) q^{81} +(0.626734 + 2.88105i) q^{83} +(-1.58235 + 3.53663i) q^{85} +(9.47189 + 2.06048i) q^{87} +(13.3133 + 3.90915i) q^{89} -16.2383i q^{91} +(18.1616 - 18.1616i) q^{93} +(2.77386 + 12.2950i) q^{95} +(-2.98325 + 13.7138i) q^{97} +(3.22523 - 22.4320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 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

Related objects

Downloads

Learn more