LMFDB - Embedded newform 460.2.s.a.9.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(9,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("460.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.s (of order $22$, degree $10$, 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:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			9.5
Character	$\chi$	$=$	460.9
Dual form			460.2.s.a.409.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.410666 + 0.355844i) q^{3} +(1.87331 + 1.22094i) q^{5} +(2.52593 + 1.15355i) q^{7} +(-0.384923 + 2.67720i) q^{9} +O(q^{10})$	\(q+(-0.410666 + 0.355844i) q^{3} +(1.87331 + 1.22094i) q^{5} +(2.52593 + 1.15355i) q^{7} +(-0.384923 + 2.67720i) q^{9} +(-2.84625 - 0.835735i) q^{11} +(-0.439869 + 0.200882i) q^{13} +(-1.20377 + 0.165208i) q^{15} +(2.00410 - 3.11844i) q^{17} +(-4.38630 + 2.81890i) q^{19} +(-1.44780 + 0.425113i) q^{21} +(4.38991 + 1.93098i) q^{23} +(2.01860 + 4.57441i) q^{25} +(-1.67593 - 2.60779i) q^{27} +(4.22734 + 2.71675i) q^{29} +(1.05483 - 1.21734i) q^{31} +(1.46625 - 0.669614i) q^{33} +(3.32344 + 5.24499i) q^{35} +(2.02003 + 0.290436i) q^{37} +(0.109157 - 0.239020i) q^{39} +(1.19168 + 8.28830i) q^{41} +(-4.09786 + 3.55082i) q^{43} +(-3.98979 + 4.54526i) q^{45} -9.54853i q^{47} +(0.465623 + 0.537357i) q^{49} +(0.286663 + 1.99378i) q^{51} +(6.61630 + 3.02156i) q^{53} +(-4.31154 - 5.04070i) q^{55} +(0.798213 - 2.71846i) q^{57} +(-4.27938 - 9.37052i) q^{59} +(3.45918 - 3.99211i) q^{61} +(-4.06058 + 6.31839i) q^{63} +(-1.06928 - 0.160741i) q^{65} +(-3.04543 - 10.3718i) q^{67} +(-2.48992 + 0.769134i) q^{69} +(7.24148 - 2.12629i) q^{71} +(-4.17561 - 6.49738i) q^{73} +(-2.45675 - 1.16025i) q^{75} +(-6.22538 - 5.39432i) q^{77} +(-2.99930 - 6.56756i) q^{79} +(-6.16929 - 1.81147i) q^{81} +(1.76268 + 0.253434i) q^{83} +(7.56174 - 3.39492i) q^{85} +(-2.70276 + 0.388599i) q^{87} +(8.38350 + 9.67507i) q^{89} -1.34281 q^{91} +0.875279i q^{93} +(-11.6586 - 0.0747303i) q^{95} +(11.4337 - 1.64392i) q^{97} +(3.33302 - 7.29829i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{9}+O(q^{10}) $ 120 * q + 20 * q^9	$ 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) $ 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.410666	+	0.355844i	−0.237098	+	0.205447i	−0.765303	−	0.643670i	$-0.777411\pi$
$3$	−0.410666	+	0.355844i	−0.237098	+	0.205447i	0.528205	+	0.849117i	$0.322865\pi$
$4$		0			0
$5$	1.87331	+	1.22094i	0.837771	+	0.546022i
$5$	1.87331	+	1.22094i	0.837771	+	0.546022i
$6$		0			0
$7$	2.52593	+	1.15355i	0.954713	+	0.436003i	0.830974	−	0.556312i	$-0.187784\pi$
$7$	2.52593	+	1.15355i	0.954713	+	0.436003i	0.123739	+	0.992315i	$0.460511\pi$
$8$		0			0
$9$	−0.384923	+	2.67720i	−0.128308	+	0.892399i
$10$		0			0
$11$	−2.84625	−	0.835735i	−0.858177	−	0.251984i	−0.177098	−	0.984193i	$-0.556671\pi$
$11$	−2.84625	−	0.835735i	−0.858177	−	0.251984i	−0.681079	+	0.732210i	$0.738489\pi$
$12$		0			0
$13$	−0.439869	+	0.200882i	−0.121998	+	0.0557145i	−0.475479	−	0.879727i	$-0.657725\pi$
$13$	−0.439869	+	0.200882i	−0.121998	+	0.0557145i	0.353481	+	0.935442i	$0.384998\pi$
$14$		0			0
$15$	−1.20377	+	0.165208i	−0.310812	+	0.0426565i
$16$		0			0
$17$	2.00410	−	3.11844i	0.486065	−	0.756332i	−0.508431	−	0.861103i	$-0.669774\pi$
$17$	2.00410	−	3.11844i	0.486065	−	0.756332i	0.994496	+	0.104770i	$0.0334107\pi$
$18$		0			0
$19$	−4.38630	+	2.81890i	−1.00629	+	0.646700i	−0.936429	−	0.350857i	$-0.885890\pi$
$19$	−4.38630	+	2.81890i	−1.00629	+	0.646700i	−0.0698563	+	0.997557i	$0.522254\pi$
$20$		0			0
$21$	−1.44780	+	0.425113i	−0.315936	+	0.0927672i
$22$		0			0
$23$	4.38991	+	1.93098i	0.915359	+	0.402638i
$23$	4.38991	+	1.93098i	0.915359	+	0.402638i
$24$		0			0
$25$	2.01860	+	4.57441i	0.403720	+	0.914883i
$26$		0			0
$27$	−1.67593	−	2.60779i	−0.322532	−	0.501869i
$28$		0			0
$29$	4.22734	+	2.71675i	0.784997	+	0.504487i	0.870689	−	0.491835i	$-0.163674\pi$
$29$	4.22734	+	2.71675i	0.784997	+	0.504487i	−0.0856915	+	0.996322i	$0.527310\pi$
$30$		0			0
$31$	1.05483	−	1.21734i	0.189454	−	0.218641i	−0.653074	−	0.757294i	$-0.726521\pi$
$31$	1.05483	−	1.21734i	0.189454	−	0.218641i	0.842528	+	0.538653i	$0.181066\pi$
$32$		0			0
$33$	1.46625	−	0.669614i	0.255241	−	0.116565i
$34$		0			0
$35$	3.32344	+	5.24499i	0.561764	+	0.886565i
$36$		0			0
$37$	2.02003	+	0.290436i	0.332090	+	0.0477474i	0.306343	−	0.951921i	$-0.400894\pi$
$37$	2.02003	+	0.290436i	0.332090	+	0.0477474i	0.0257471	+	0.999668i	$0.491804\pi$
$38$		0			0
$39$	0.109157	−	0.239020i	0.0174791	−	0.0382739i
$40$		0			0
$41$	1.19168	+	8.28830i	0.186109	+	1.29441i	0.841966	+	0.539530i	$0.181398\pi$
$41$	1.19168	+	8.28830i	0.186109	+	1.29441i	−0.655857	+	0.754885i	$0.727693\pi$
$42$		0			0
$43$	−4.09786	+	3.55082i	−0.624918	+	0.541494i	−0.908729	−	0.417386i	$-0.862946\pi$
$43$	−4.09786	+	3.55082i	−0.624918	+	0.541494i	0.283812	+	0.958880i	$0.408401\pi$
$44$		0			0
$45$	−3.98979	+	4.54526i	−0.594762	+	0.677567i
$46$		0			0
$47$		−	9.54853i		−	1.39280i	−0.717656	−	0.696398i	$-0.754785\pi$
$47$		−	9.54853i		−	1.39280i	0.717656	−	0.696398i	$-0.245215\pi$
$48$		0			0
$49$	0.465623	+	0.537357i	0.0665175	+	0.0767653i
$50$		0			0
$51$	0.286663	+	1.99378i	0.0401408	+	0.279185i
$52$		0			0
$53$	6.61630	+	3.02156i	0.908818	+	0.415043i	0.814276	−	0.580477i	$-0.197134\pi$
$53$	6.61630	+	3.02156i	0.908818	+	0.415043i	0.0945421	+	0.995521i	$0.469861\pi$
$54$		0			0
$55$	−4.31154	−	5.04070i	−0.581367	−	0.679688i
$56$		0			0
$57$	0.798213	−	2.71846i	0.105726	−	0.360069i
$58$		0			0
$59$	−4.27938	−	9.37052i	−0.557127	−	1.21994i	−0.953373	−	0.301794i	$-0.902415\pi$
$59$	−4.27938	−	9.37052i	−0.557127	−	1.21994i	0.396246	−	0.918144i	$-0.370313\pi$
$60$		0			0
$61$	3.45918	−	3.99211i	0.442903	−	0.511137i	−0.489774	−	0.871849i	$-0.662921\pi$
$61$	3.45918	−	3.99211i	0.442903	−	0.511137i	0.932677	+	0.360712i	$0.117466\pi$
$62$		0			0
$63$	−4.06058	+	6.31839i	−0.511586	+	0.796043i
$64$		0			0
$65$	−1.06928	−	0.160741i	−0.132628	−	0.0199375i
$66$		0			0
$67$	−3.04543	−	10.3718i	−0.372058	−	1.26711i	−0.906607	−	0.421977i	$-0.861336\pi$
$67$	−3.04543	−	10.3718i	−0.372058	−	1.26711i	0.534548	−	0.845138i	$-0.320482\pi$
$68$		0			0
$69$	−2.48992	+	0.769134i	−0.299751	+	0.0925928i
$70$		0			0
$71$	7.24148	−	2.12629i	0.859405	−	0.252344i	0.177802	−	0.984066i	$-0.443101\pi$
$71$	7.24148	−	2.12629i	0.859405	−	0.252344i	0.681603	+	0.731722i	$0.261283\pi$
$72$		0			0
$73$	−4.17561	−	6.49738i	−0.488718	−	0.760460i	0.506062	−	0.862497i	$-0.331101\pi$
$73$	−4.17561	−	6.49738i	−0.488718	−	0.760460i	−0.994781	+	0.102036i	$0.967464\pi$
$74$		0			0
$75$	−2.45675	−	1.16025i	−0.283681	−	0.133974i
$76$		0			0
$77$	−6.22538	−	5.39432i	−0.709447	−	0.614740i
$78$		0			0
$79$	−2.99930	−	6.56756i	−0.337448	−	0.738908i	0.662500	−	0.749061i	$-0.269495\pi$
$79$	−2.99930	−	6.56756i	−0.337448	−	0.738908i	−0.999948	+	0.0101535i	$0.996768\pi$
$80$		0			0
$81$	−6.16929	−	1.81147i	−0.685477	−	0.201274i
$82$		0			0
$83$	1.76268	+	0.253434i	0.193479	+	0.0278180i	0.238373	−	0.971174i	$-0.423386\pi$
$83$	1.76268	+	0.253434i	0.193479	+	0.0278180i	−0.0448941	+	0.998992i	$0.514295\pi$
$84$		0			0
$85$	7.56174	−	3.39492i	0.820185	−	0.368231i
$86$		0			0
$87$	−2.70276	+	0.388599i	−0.289767	+	0.0416621i
$88$		0			0
$89$	8.38350	+	9.67507i	0.888649	+	1.02556i	0.999497	+	0.0317180i	$0.0100979\pi$
$89$	8.38350	+	9.67507i	0.888649	+	1.02556i	−0.110848	+	0.993837i	$0.535357\pi$
$90$		0			0
$91$	−1.34281			−0.140765
$92$		0			0
$93$			0.875279i			0.0907622i
$94$		0			0
$95$	−11.6586	−	0.0747303i	−1.19615	−	0.00766716i
$96$		0			0
$97$	11.4337	−	1.64392i	1.16091	−	0.166914i	0.465182	−	0.885215i	$-0.345989\pi$
$97$	11.4337	−	1.64392i	1.16091	−	0.166914i	0.695733	+	0.718301i	$0.255080\pi$
$98$		0			0
$99$	3.33302	−	7.29829i	0.334981	−	0.733505i
$100$		0			0
$101$	1.25322	−	8.71637i	0.124701	−	0.867311i	−0.827419	−	0.561585i	$-0.810192\pi$
$101$	1.25322	−	8.71637i	0.124701	−	0.867311i	0.952119	−	0.305726i	$-0.0988992\pi$
$102$		0			0
$103$	−4.61510	+	15.7176i	−0.454739	+	1.54870i	0.339208	+	0.940711i	$0.389841\pi$
$103$	−4.61510	+	15.7176i	−0.454739	+	1.54870i	−0.793947	+	0.607987i	$0.791977\pi$
$104$		0			0
$105$	−3.23122	−	0.971312i	−0.315335	−	0.0947903i
$106$		0			0
$107$	−5.18683	−	4.49442i	−0.501430	−	0.434492i	0.367061	−	0.930197i	$-0.380364\pi$
$107$	−5.18683	−	4.49442i	−0.501430	−	0.434492i	−0.868491	+	0.495705i	$0.834910\pi$
$108$		0			0
$109$	−7.80099	−	5.01339i	−0.747199	−	0.480196i	0.110802	−	0.993842i	$-0.464658\pi$
$109$	−7.80099	−	5.01339i	−0.747199	−	0.480196i	−0.858002	+	0.513646i	$0.828294\pi$
$110$		0			0
$111$	−0.932906	+	0.599542i	−0.0885475	+	0.0569061i
$112$		0			0
$113$	−5.26863	−	17.9433i	−0.495631	−	1.68796i	−0.704238	−	0.709964i	$-0.748711\pi$
$113$	−5.26863	−	17.9433i	−0.495631	−	1.68796i	0.208607	−	0.977999i	$-0.433107\pi$
$114$		0			0
$115$	5.86605	+	8.97716i	0.547012	+	0.837125i
$116$		0			0
$117$	−0.368484	−	1.25494i	−0.0340664	−	0.116019i
$118$		0			0
$119$	8.65951	−	5.56513i	0.793816	−	0.510154i
$120$		0			0
$121$	−1.85109	−	1.18962i	−0.168281	−	0.108148i
$122$		0			0
$123$	−3.43872	−	2.97967i	−0.310059	−	0.268668i
$124$		0			0
$125$	−1.80362	+	11.0339i	−0.161321	+	0.986902i
$126$		0			0
$127$	−0.171830	+	0.585199i	−0.0152474	+	0.0519280i	−0.966765	−	0.255665i	$-0.917705\pi$
$127$	−0.171830	+	0.585199i	−0.0152474	+	0.0519280i	0.951518	+	0.307593i	$0.0995236\pi$
$128$		0			0
$129$	0.419315	−	2.91640i	0.0369186	−	0.256775i
$130$		0			0
$131$	−0.943853	+	2.06675i	−0.0824648	+	0.180573i	−0.946373	−	0.323077i	$-0.895283\pi$
$131$	−0.943853	+	2.06675i	−0.0824648	+	0.180573i	0.863908	+	0.503650i	$0.168010\pi$
$132$		0			0
$133$	−14.3312	+	2.06052i	−1.24268	+	0.178670i
$134$		0			0
$135$	0.0444295	−	6.93141i	0.00382388	−	0.596561i
$136$		0			0
$137$		−	2.52713i		−	0.215908i	−0.994156	−	0.107954i	$-0.965570\pi$
$137$		−	2.52713i		−	0.215908i	0.994156	−	0.107954i	$-0.0344299\pi$
$138$		0			0
$139$	5.13901			0.435885			0.217943	−	0.975962i	$-0.430065\pi$
$139$	5.13901			0.435885			0.217943	+	0.975962i	$0.430065\pi$
$140$		0			0
$141$	3.39779	+	3.92125i	0.286145	+	0.330229i
$142$		0			0
$143$	1.41986	−	0.204146i	0.118735	−	0.0170715i
$144$		0			0
$145$	4.60214	+	10.2507i	0.382187	+	0.851270i
$146$		0			0
$147$	−0.382431	−	0.0549852i	−0.0315424	−	0.00453511i
$148$		0			0
$149$	8.66687	+	2.54482i	0.710018	+	0.208480i	0.616748	−	0.787161i	$-0.288450\pi$
$149$	8.66687	+	2.54482i	0.710018	+	0.208480i	0.0932700	+	0.995641i	$0.470268\pi$
$150$		0			0
$151$	−0.925816	−	2.02725i	−0.0753418	−	0.164976i	0.868213	−	0.496191i	$-0.165269\pi$
$151$	−0.925816	−	2.02725i	−0.0753418	−	0.164976i	−0.943555	+	0.331216i	$0.892541\pi$
$152$		0			0
$153$	7.57725	+	6.56573i	0.612585	+	0.530808i
$154$		0			0
$155$	3.46234	−	0.992574i	0.278102	−	0.0797255i
$156$		0			0
$157$	−8.35285	−	12.9973i	−0.666630	−	1.03730i	−0.995668	−	0.0929799i	$-0.970361\pi$
$157$	−8.35285	−	12.9973i	−0.666630	−	1.03730i	0.329038	−	0.944317i	$-0.393276\pi$
$158$		0			0
$159$	−3.79229	+	1.11352i	−0.300748	+	0.0883077i
$160$		0			0
$161$	8.86112	+	9.94154i	0.698354	+	0.783503i
$162$		0			0
$163$	0.0966954	+	0.329314i	0.00757376	+	0.0257939i	0.963193	−	0.268810i	$-0.0866304\pi$
$163$	0.0966954	+	0.329314i	0.00757376	+	0.0257939i	−0.955619	+	0.294604i	$0.904812\pi$
$164$		0			0
$165$	3.56431	+	0.535810i	0.277481	+	0.0417128i
$166$		0			0
$167$	11.2526	−	17.5094i	0.870752	−	1.35492i	−0.0633796	−	0.997989i	$-0.520188\pi$
$167$	11.2526	−	17.5094i	0.870752	−	1.35492i	0.934132	−	0.356928i	$-0.116176\pi$
$168$		0			0
$169$	−8.36006	+	9.64802i	−0.643081	+	0.742155i
$170$		0			0
$171$	−5.85837	−	12.8280i	−0.448001	−	0.980985i
$172$		0			0
$173$	−3.98719	+	13.5791i	−0.303140	+	1.03240i	0.657234	+	0.753687i	$0.271726\pi$
$173$	−3.98719	+	13.5791i	−0.303140	+	1.03240i	−0.960374	+	0.278714i	$0.910092\pi$
$174$		0			0
$175$	−0.177987	+	13.8832i	−0.0134545	+	1.04947i
$176$		0			0
$177$	5.09184	+	2.32537i	0.382726	+	0.174785i
$178$		0			0
$179$	0.996988	+	6.93420i	0.0745184	+	0.518287i	0.992556	+	0.121792i	$0.0388642\pi$
$179$	0.996988	+	6.93420i	0.0745184	+	0.518287i	−0.918037	+	0.396494i	$0.870227\pi$
$180$		0			0
$181$	−13.6105	−	15.7073i	−1.01166	−	1.16752i	−0.985813	−	0.167849i	$-0.946318\pi$
$181$	−13.6105	−	15.7073i	−1.01166	−	1.16752i	−0.0258449	−	0.999666i	$-0.508228\pi$
$182$		0			0
$183$			2.87035i			0.212183i
$184$		0			0
$185$	3.42954	+	3.01041i	0.252145	+	0.221330i
$186$		0			0
$187$	−8.31036	+	7.20097i	−0.607714	+	0.526587i
$188$		0			0
$189$	−1.22504	−	8.52037i	−0.0891089	−	0.619766i
$190$		0			0
$191$	1.74357	−	3.81788i	0.126160	−	0.276252i	−0.836004	−	0.548724i	$-0.815114\pi$
$191$	1.74357	−	3.81788i	0.126160	−	0.276252i	0.962164	+	0.272472i	$0.0878411\pi$
$192$		0			0
$193$	11.7299	+	1.68650i	0.844333	+	0.121397i	0.550888	−	0.834579i	$-0.314289\pi$
$193$	11.7299	+	1.68650i	0.844333	+	0.121397i	0.293445	+	0.955976i	$0.405198\pi$
$194$		0			0
$195$	0.496315	−	0.314485i	0.0355418	−	0.0225208i
$196$		0			0
$197$	12.7505	−	5.82295i	0.908434	−	0.414868i	0.0942993	−	0.995544i	$-0.469939\pi$
$197$	12.7505	−	5.82295i	0.908434	−	0.414868i	0.814135	+	0.580676i	$0.197212\pi$
$198$		0			0
$199$	−5.08862	+	5.87258i	−0.360723	+	0.416296i	−0.906882	−	0.421385i	$-0.861544\pi$
$199$	−5.08862	+	5.87258i	−0.360723	+	0.416296i	0.546159	+	0.837682i	$0.316089\pi$
$200$		0			0
$201$	4.94139	+	3.17564i	0.348539	+	0.223992i
$202$		0			0
$203$	7.54406	+	11.7388i	0.529489	+	0.823901i
$204$		0			0
$205$	−7.88715	+	16.9815i	−0.550862	+	1.18604i
$206$		0			0
$207$	−6.85940	+	11.0094i	−0.476761	+	0.765205i
$208$		0			0
$209$	14.8404	−	4.35752i	1.02653	−	0.301416i
$210$		0			0
$211$	−21.3813	+	13.7409i	−1.47195	+	0.945965i	−0.474097	+	0.880473i	$0.657225\pi$
$211$	−21.3813	+	13.7409i	−1.47195	+	0.945965i	−0.997853	+	0.0654924i	$0.979138\pi$
$212$		0			0
$213$	−2.21720	+	3.45003i	−0.151920	+	0.236392i
$214$		0			0
$215$	−12.0119	+	1.64854i	−0.819206	+	0.112429i
$216$		0			0
$217$	4.06872	−	1.85812i	0.276202	−	0.126137i
$218$		0			0
$219$	4.02683	+	1.18239i	0.272108	+	0.0798982i
$220$		0			0
$221$	−0.255105	+	1.77429i	−0.0171602	+	0.119352i
$222$		0			0
$223$	−3.93481	−	1.79697i	−0.263494	−	0.120334i	0.279288	−	0.960207i	$-0.409902\pi$
$223$	−3.93481	−	1.79697i	−0.263494	−	0.120334i	−0.542782	+	0.839874i	$0.682629\pi$
$224$		0			0
$225$	−13.0236	+	3.64340i	−0.868241	+	0.242893i
$226$		0			0
$227$	12.8830	−	11.1631i	0.855072	−	0.740924i	−0.112464	−	0.993656i	$-0.535874\pi$
$227$	12.8830	−	11.1631i	0.855072	−	0.740924i	0.967536	+	0.252732i	$0.0813290\pi$
$228$		0			0
$229$	−21.0605			−1.39172			−0.695858	−	0.718179i	$-0.744976\pi$
$229$	−21.0605			−1.39172			−0.695858	+	0.718179i	$0.744976\pi$
$230$		0			0
$231$	4.47609			0.294505
$232$		0			0
$233$	22.1699	−	19.2104i	1.45240	−	1.25851i	0.544874	−	0.838518i	$-0.316578\pi$
$233$	22.1699	−	19.2104i	1.45240	−	1.25851i	0.907527	−	0.419994i	$-0.137968\pi$
$234$		0			0
$235$	11.6582	−	17.8874i	0.760497	−	1.16684i
$236$		0			0
$237$	3.56874	+	1.62979i	0.231814	+	0.105866i
$238$		0			0
$239$	−3.02679	+	21.0518i	−0.195787	+	1.36173i	0.620558	+	0.784160i	$0.286906\pi$
$239$	−3.02679	+	21.0518i	−0.195787	+	1.36173i	−0.816345	+	0.577565i	$0.804003\pi$
$240$		0			0
$241$	21.2694	+	6.24527i	1.37009	+	0.402293i	0.882307	−	0.470674i	$-0.155989\pi$
$241$	21.2694	+	6.24527i	1.37009	+	0.402293i	0.487778	+	0.872968i	$0.337807\pi$
$242$		0			0
$243$	11.6374	−	5.31462i	0.746539	−	0.340933i
$244$		0			0
$245$	0.216175	+	1.57514i	0.0138109	+	0.100632i
$246$		0			0
$247$	1.36313	−	2.12108i	0.0867340	−	0.134961i
$248$		0			0
$249$	−0.814054	+	0.523161i	−0.0515886	+	0.0331540i
$250$		0			0
$251$	4.71048	−	1.38312i	0.297323	−	0.0873019i	−0.129669	−	0.991557i	$-0.541391\pi$
$251$	4.71048	−	1.38312i	0.297323	−	0.0873019i	0.426992	+	0.904255i	$0.359573\pi$
$252$		0			0
$253$	−10.8810	−	9.16487i	−0.684082	−	0.576190i
$254$		0			0
$255$	−1.89728	+	4.08498i	−0.118813	+	0.255811i
$256$		0			0
$257$	0.224119	+	0.348737i	0.0139802	+	0.0217536i	0.848173	−	0.529719i	$-0.177703\pi$
$257$	0.224119	+	0.348737i	0.0139802	+	0.0217536i	−0.834193	+	0.551472i	$0.814066\pi$
$258$		0			0
$259$	4.76742	+	3.06383i	0.296233	+	0.190377i
$260$		0			0
$261$	−8.90047	+	10.2717i	−0.550925	+	0.635801i
$262$		0			0
$263$	10.8686	−	4.96353i	0.670187	−	0.306064i	−0.0511069	−	0.998693i	$-0.516275\pi$
$263$	10.8686	−	4.96353i	0.670187	−	0.306064i	0.721294	+	0.692629i	$0.243548\pi$
$264$		0			0
$265$	8.70524	+	13.7384i	0.534759	+	0.843946i
$266$		0			0
$267$	−6.88563	−	0.990005i	−0.421394	−	0.0605873i
$268$		0			0
$269$	0.949596	−	2.07933i	0.0578979	−	0.126779i	−0.878472	−	0.477794i	$-0.841436\pi$
$269$	0.949596	−	2.07933i	0.0578979	−	0.126779i	0.936370	+	0.351016i	$0.114164\pi$
$270$		0			0
$271$	4.08338	+	28.4005i	0.248047	+	1.72521i	0.609473	+	0.792807i	$0.291381\pi$
$271$	4.08338	+	28.4005i	0.248047	+	1.72521i	−0.361426	+	0.932401i	$0.617710\pi$
$272$		0			0
$273$	0.551446	−	0.477831i	0.0333750	−	0.0289196i
$274$		0			0
$275$	−1.92245	−	14.7069i	−0.115928	−	0.886862i
$276$		0			0
$277$			17.5388i			1.05380i	0.849926	+	0.526902i	$0.176646\pi$
$277$			17.5388i			1.05380i	−0.849926	+	0.526902i	$0.823354\pi$
$278$		0			0
$279$	2.85304	+	3.29259i	0.170807	+	0.197122i
$280$		0			0
$281$	−0.278335	−	1.93586i	−0.0166041	−	0.115484i	0.979834	−	0.199814i	$-0.0640339\pi$
$281$	−0.278335	−	1.93586i	−0.0166041	−	0.115484i	−0.996438	+	0.0843306i	$0.973125\pi$
$282$		0			0
$283$	19.4717	+	8.89243i	1.15747	+	0.528600i	0.899228	−	0.437479i	$-0.144129\pi$
$283$	19.4717	+	8.89243i	1.15747	+	0.528600i	0.258245	+	0.966080i	$0.416856\pi$
$284$		0			0
$285$	4.81439	−	4.11796i	0.285180	−	0.243927i
$286$		0			0
$287$	−6.55091	+	22.3104i	−0.386688	+	1.31694i
$288$		0			0
$289$	1.35381	+	2.96443i	0.0796358	+	0.174378i
$290$		0			0
$291$	−4.11045	+	4.74371i	−0.240959	+	0.278081i
$292$		0			0
$293$	0.793635	−	1.23492i	0.0463646	−	0.0721448i	−0.817297	−	0.576216i	$-0.804529\pi$
$293$	0.793635	−	1.23492i	0.0463646	−	0.0721448i	0.863662	+	0.504071i	$0.168165\pi$
$294$		0			0
$295$	3.42426	−	22.7788i	0.199368	−	1.32623i
$296$		0			0
$297$	2.59068	+	8.82306i	0.150327	+	0.511966i
$298$		0			0
$299$	−2.31889	+	0.0324715i	−0.134105	+	0.00187788i
$300$		0			0
$301$	−14.4470	+	4.24202i	−0.832710	+	0.244506i
$302$		0			0
$303$	2.58701	+	4.02547i	0.148620	+	0.231257i
$304$		0			0
$305$	11.3543	−	3.25501i	0.650144	−	0.186381i
$306$		0			0
$307$	−1.39929	−	1.21249i	−0.0798618	−	0.0692006i	0.614015	−	0.789294i	$-0.289553\pi$
$307$	−1.39929	−	1.21249i	−0.0798618	−	0.0692006i	−0.693877	+	0.720094i	$0.744099\pi$
$308$		0			0
$309$	−3.69774	−	8.09693i	−0.210357	−	0.460618i
$310$		0			0
$311$	4.18356	+	1.22840i	0.237228	+	0.0696563i	0.398185	−	0.917305i	$-0.369640\pi$
$311$	4.18356	+	1.22840i	0.237228	+	0.0696563i	−0.160958	+	0.986961i	$0.551458\pi$
$312$		0			0
$313$	−22.1466	−	3.18420i	−1.25180	−	0.179982i	−0.515649	−	0.856800i	$-0.672449\pi$
$313$	−22.1466	−	3.18420i	−1.25180	−	0.179982i	−0.736150	+	0.676818i	$0.763358\pi$
$314$		0			0
$315$	−15.3211	+	6.87859i	−0.863248	+	0.387564i
$316$		0			0
$317$	−19.5608	+	2.81241i	−1.09864	+	0.157961i	−0.667708	−	0.744423i	$-0.732725\pi$
$317$	−19.5608	+	2.81241i	−1.09864	+	0.157961i	−0.430933	+	0.902384i	$0.641816\pi$
$318$		0			0
$319$	−9.76159	−	11.2655i	−0.546544	−	0.630746i
$320$		0			0
$321$	3.72937			0.208153
$322$		0			0
$323$			19.3278i			1.07542i
$324$		0			0
$325$	−1.80684	−	1.60664i	−0.100225	−	0.0891206i
$326$		0			0
$327$	4.98759	−	0.717107i	0.275814	−	0.0396561i
$328$		0			0
$329$	11.0147	−	24.1189i	0.607263	−	1.32972i
$330$		0			0
$331$	2.23808	−	15.5662i	0.123016	−	0.855594i	−0.831093	−	0.556134i	$-0.812284\pi$
$331$	2.23808	−	15.5662i	0.123016	−	0.855594i	0.954109	−	0.299460i	$-0.0968066\pi$
$332$		0			0
$333$	−1.55511	+	5.29622i	−0.0852195	+	0.290231i
$334$		0			0
$335$	6.95830	−	23.1479i	0.380173	−	1.26470i
$336$		0			0
$337$	17.4571	+	15.1266i	0.950947	+	0.824000i	0.984491	−	0.175437i	$-0.0561338\pi$
$337$	17.4571	+	15.1266i	0.950947	+	0.824000i	−0.0335435	+	0.999437i	$0.510679\pi$
$338$		0			0
$339$	8.54866	+	5.49389i	0.464300	+	0.298387i
$340$		0			0
$341$	−4.01970	+	2.58331i	−0.217679	+	0.139894i
$342$		0			0
$343$	−4.92009	−	16.7563i	−0.265660	−	0.904754i
$344$		0			0
$345$	−5.60346	−	1.59921i	−0.301680	−	0.0860988i
$346$		0			0
$347$	9.11044	+	31.0273i	0.489074	+	1.66563i	0.721027	+	0.692907i	$0.243670\pi$
$347$	9.11044	+	31.0273i	0.489074	+	1.66563i	−0.231953	+	0.972727i	$0.574512\pi$
$348$		0			0
$349$	6.33967	−	4.07426i	0.339355	−	0.218090i	−0.359852	−	0.933009i	$-0.617173\pi$
$349$	6.33967	−	4.07426i	0.339355	−	0.218090i	0.699207	+	0.714919i	$0.253537\pi$
$350$		0			0
$351$	1.26105	+	0.810425i	0.0673096	+	0.0432573i
$352$		0			0
$353$	−27.2595	−	23.6205i	−1.45088	−	1.25719i	−0.909040	−	0.416708i	$-0.863184\pi$
$353$	−27.2595	−	23.6205i	−1.45088	−	1.25719i	−0.541837	−	0.840484i	$-0.682271\pi$
$354$		0			0
$355$	16.1616	+	4.85822i	0.857770	+	0.257848i
$356$		0			0
$357$	−1.57585	+	5.36684i	−0.0834027	+	0.284043i
$358$		0			0
$359$	−2.93145	+	20.3887i	−0.154716	+	1.07607i	0.753463	+	0.657490i	$0.228382\pi$
$359$	−2.93145	+	20.3887i	−0.154716	+	1.07607i	−0.908179	+	0.418582i	$0.862527\pi$
$360$		0			0
$361$	3.40051	−	7.44607i	0.178974	−	0.391898i
$362$		0			0
$363$	1.18350	−	0.170162i	0.0621177	−	0.00893117i
$364$		0			0
$365$	0.110697	−	17.2698i	0.00579415	−	0.903942i
$366$		0			0
$367$		−	22.3239i		−	1.16530i	−0.812723	−	0.582650i	$-0.802016\pi$
$367$		−	22.3239i		−	1.16530i	0.812723	−	0.582650i	$-0.197984\pi$
$368$		0			0
$369$	−22.6481			−1.17901
$370$		0			0
$371$	13.2268	+	15.2645i	0.686701	+	0.792495i
$372$		0			0
$373$	−28.8117	+	4.14250i	−1.49181	+	0.214491i	−0.839459	−	0.543422i	$-0.817128\pi$
$373$	−28.8117	+	4.14250i	−1.49181	+	0.214491i	−0.652356	+	0.757913i	$0.726219\pi$
$374$		0			0
$375$	−3.18566	−	5.17306i	−0.164507	−	0.267135i
$376$		0			0
$377$	−2.40522	−	0.345819i	−0.123875	−	0.0178106i
$378$		0			0
$379$	12.0882	+	3.54940i	0.620927	+	0.182321i	0.577040	−	0.816716i	$-0.304208\pi$
$379$	12.0882	+	3.54940i	0.620927	+	0.182321i	0.0438869	+	0.999037i	$0.486026\pi$
$380$		0			0
$381$	−0.137675	−	0.301466i	−0.00705329	−	0.0154446i
$382$		0			0
$383$	5.65919	+	4.90371i	0.289171	+	0.250568i	0.787350	−	0.616506i	$-0.211452\pi$
$383$	5.65919	+	4.90371i	0.289171	+	0.250568i	−0.498179	+	0.867074i	$0.665998\pi$
$384$		0			0
$385$	−5.07592	−	17.7061i	−0.258693	−	0.902385i
$386$		0			0
$387$	−7.92888	−	12.3376i	−0.403048	−	0.627154i
$388$		0			0
$389$	−32.4311	+	9.52264i	−1.64432	+	0.482817i	−0.967404	−	0.253240i	$-0.918504\pi$
$389$	−32.4311	+	9.52264i	−1.64432	+	0.482817i	−0.676920	+	0.736057i	$0.736686\pi$
$390$		0			0
$391$	14.8195	−	9.81978i	0.749453	−	0.496608i
$392$		0			0
$393$	−0.347832	−	1.18461i	−0.0175458	−	0.0597556i
$394$		0			0
$395$	2.39998	−	15.9651i	0.120756	−	0.803290i
$396$		0			0
$397$	−14.9860	+	23.3187i	−0.752126	+	1.17033i	0.228329	+	0.973584i	$0.426674\pi$
$397$	−14.9860	+	23.3187i	−0.752126	+	1.17033i	−0.980454	+	0.196746i	$0.936962\pi$
$398$		0			0
$399$	5.15213	−	5.94588i	0.257929	−	0.297666i
$400$		0			0
$401$	−13.3192	−	29.1649i	−0.665127	−	1.45643i	−0.877666	−	0.479273i	$-0.840900\pi$
$401$	−13.3192	−	29.1649i	−0.665127	−	1.45643i	0.212539	−	0.977153i	$-0.431827\pi$
$402$		0			0
$403$	−0.219447	+	0.747369i	−0.0109315	+	0.0372291i
$404$		0			0
$405$	−9.34532	−	10.9258i	−0.464372	−	0.542907i
$406$		0			0
$407$	−5.50678	−	2.51486i	−0.272961	−	0.124657i
$408$		0			0
$409$	−0.567841	−	3.94942i	−0.0280779	−	0.195286i	0.970955	−	0.239264i	$-0.0769061\pi$
$409$	−0.567841	−	3.94942i	−0.0280779	−	0.195286i	−0.999033	+	0.0439775i	$0.985997\pi$
$410$		0			0
$411$	0.899266	+	1.03781i	0.0443575	+	0.0511913i
$412$		0			0
$413$		−	28.6058i		−	1.40760i
$414$		0			0
$415$	2.99261	+	2.62689i	0.146902	+	0.128949i
$416$		0			0
$417$	−2.11042	+	1.82869i	−0.103348	+	0.0895512i
$418$		0			0
$419$	−1.37576	−	9.56862i	−0.0672103	−	0.467458i	−0.995435	−	0.0954386i	$-0.969575\pi$
$419$	−1.37576	−	9.56862i	−0.0672103	−	0.467458i	0.928225	−	0.372019i	$-0.121334\pi$
$420$		0			0
$421$	9.38156	−	20.5427i	0.457229	−	1.00119i	−0.530881	−	0.847446i	$-0.678139\pi$
$421$	9.38156	−	20.5427i	0.457229	−	1.00119i	0.988110	−	0.153746i	$-0.0491337\pi$
$422$		0			0
$423$	25.5633	+	3.67545i	1.24293	+	0.178706i
$424$		0			0
$425$	18.3105	+	2.87269i	0.888190	+	0.139346i
$426$		0			0
$427$	13.3428	−	6.09345i	0.645703	−	0.294883i
$428$		0			0
$429$	−0.510446	+	0.589086i	−0.0246445	+	0.0284413i
$430$		0			0
$431$	−8.35409	−	5.36885i	−0.402402	−	0.258608i	0.323749	−	0.946143i	$-0.395057\pi$
$431$	−8.35409	−	5.36885i	−0.402402	−	0.258608i	−0.726152	+	0.687535i	$0.758693\pi$
$432$		0			0
$433$	−18.9430	−	29.4758i	−0.910340	−	1.41652i	−0.909127	−	0.416518i	$-0.863250\pi$
$433$	−18.9430	−	29.4758i	−0.910340	−	1.41652i	−0.00121308	−	0.999999i	$-0.500386\pi$
$434$		0			0
$435$	−5.53757	−	2.57195i	−0.265506	−	0.123316i
$436$		0			0
$437$	−24.6987	+	3.90486i	−1.18150	+	0.186795i
$438$		0			0
$439$	28.3041	−	8.31082i	1.35088	−	0.396654i	0.475340	−	0.879802i	$-0.342325\pi$
$439$	28.3041	−	8.31082i	1.35088	−	0.396654i	0.875539	+	0.483148i	$0.160507\pi$
$440$		0			0
$441$	−1.61784	+	1.03972i	−0.0770400	+	0.0495106i
$442$		0			0
$443$	−13.4477	+	20.9251i	−0.638921	+	0.994181i	0.359221	+	0.933253i	$0.383042\pi$
$443$	−13.4477	+	20.9251i	−0.638921	+	0.994181i	−0.998142	+	0.0609283i	$0.980594\pi$
$444$		0			0
$445$	3.89221	+	28.3602i	0.184508	+	1.34440i
$446$		0			0
$447$	−4.46475	+	2.03898i	−0.211175	+	0.0964406i
$448$		0			0
$449$	24.1081	+	7.07876i	1.13773	+	0.334068i	0.795741	−	0.605637i	$-0.207082\pi$
$449$	24.1081	+	7.07876i	1.13773	+	0.334068i	0.341988	+	0.939704i	$0.388900\pi$
$450$		0			0
$451$	3.53501	−	24.5865i	0.166457	−	1.15773i
$452$		0			0
$453$	1.10159	+	0.503078i	0.0517571	+	0.0236367i
$454$		0			0
$455$	−2.51550	−	1.63949i	−0.117928	−	0.0768606i
$456$		0			0
$457$	−14.7363	+	12.7691i	−0.689336	+	0.597313i	−0.927460	−	0.373922i	$-0.878013\pi$
$457$	−14.7363	+	12.7691i	−0.689336	+	0.597313i	0.238124	+	0.971235i	$0.423467\pi$
$458$		0			0
$459$	−11.4910			−0.536352
$460$		0			0
$461$	3.36516			0.156731			0.0783655	−	0.996925i	$-0.475030\pi$
$461$	3.36516			0.156731			0.0783655	+	0.996925i	$0.475030\pi$
$462$		0			0
$463$	−15.1023	+	13.0862i	−0.701865	+	0.608169i	−0.930911	−	0.365246i	$-0.880985\pi$
$463$	−15.1023	+	13.0862i	−0.701865	+	0.608169i	0.229046	+	0.973416i	$0.426439\pi$
$464$		0			0
$465$	−1.06866	+	1.63967i	−0.0495581	+	0.0760379i
$466$		0			0
$467$	−8.40304	−	3.83754i	−0.388846	−	0.177580i	0.211392	−	0.977401i	$-0.432200\pi$
$467$	−8.40304	−	3.83754i	−0.388846	−	0.177580i	−0.600238	+	0.799821i	$0.704928\pi$
$468$		0			0
$469$	4.27187	−	29.7115i	0.197257	−	1.37195i
$470$		0			0
$471$	8.05524	+	2.36523i	0.371166	+	0.108984i
$472$		0			0
$473$	14.6311	−	6.68179i	0.672738	−	0.307229i
$474$		0			0
$475$	−21.7490	−	14.3745i	−0.997913	−	0.659547i
$476$		0			0
$477$	−10.6361	+	16.5501i	−0.486993	+	0.757776i
$478$		0			0
$479$	−15.7004	+	10.0900i	−0.717368	+	0.461025i	−0.847720	−	0.530443i	$-0.822026\pi$
$479$	−15.7004	+	10.0900i	−0.717368	+	0.461025i	0.130352	+	0.991468i	$0.458389\pi$
$480$		0			0
$481$	−0.946892	+	0.278032i	−0.0431745	+	0.0126772i
$482$		0			0
$483$	−7.17660	−	0.929473i	−0.326546	−	0.0422925i
$484$		0			0
$485$	23.4260	+	10.8803i	1.06372	+	0.494049i
$486$		0			0
$487$	17.5179	+	27.2584i	0.793813	+	1.23520i	0.968115	+	0.250505i	$0.0805968\pi$
$487$	17.5179	+	27.2584i	0.793813	+	1.23520i	−0.174302	+	0.984692i	$0.555767\pi$
$488$		0			0
$489$	−0.156894	−	0.100830i	−0.00709499	−	0.00455967i
$490$		0			0
$491$	−10.2527	+	11.8322i	−0.462696	+	0.533980i	−0.938366	−	0.345644i	$-0.887660\pi$
$491$	−10.2527	+	11.8322i	−0.462696	+	0.533980i	0.475669	+	0.879624i	$0.342206\pi$
$492$		0			0
$493$	16.9440	−	7.73807i	0.763120	−	0.348505i
$494$		0			0
$495$	15.1546	−	9.60255i	0.681147	−	0.431603i
$496$		0			0
$497$	20.7443	+	2.98258i	0.930508	+	0.133787i
$498$		0			0
$499$	−1.36699	+	2.99329i	−0.0611949	+	0.133998i	−0.937759	−	0.347288i	$-0.887103\pi$
$499$	−1.36699	+	2.99329i	−0.0611949	+	0.133998i	0.876564	+	0.481286i	$0.159830\pi$
$500$		0			0
$501$	1.60955	+	11.1947i	0.0719095	+	0.500141i
$502$		0			0
$503$	15.4260	−	13.3667i	0.687809	−	0.595990i	−0.239226	−	0.970964i	$-0.576894\pi$
$503$	15.4260	−	13.3667i	0.687809	−	0.595990i	0.927035	+	0.374974i	$0.122348\pi$
$504$		0			0
$505$	12.9899	−	14.7984i	0.578041	−	0.658519i
$506$		0			0
$507$		−	6.93699i		−	0.308083i
$508$		0			0
$509$	−3.66410	−	4.22859i	−0.162408	−	0.187429i	0.668713	−	0.743521i	$-0.266846\pi$
$509$	−3.66410	−	4.22859i	−0.162408	−	0.187429i	−0.831121	+	0.556092i	$0.812300\pi$
$510$		0			0
$511$	−3.05223	−	21.2287i	−0.135023	−	0.939104i
$512$		0			0
$513$	14.7022	+	6.71427i	0.649118	+	0.296442i
$514$		0			0
$515$	−27.8358	+	23.8092i	−1.22659	+	1.04916i
$516$		0			0
$517$	−7.98004	+	27.1775i	−0.350962	+	1.19527i
$518$		0			0
$519$	−3.19464	−	6.99529i	−0.140229	−	0.307059i
$520$		0			0
$521$	9.73484	−	11.2346i	0.426491	−	0.492197i	−0.501312	−	0.865266i	$-0.667149\pi$
$521$	9.73484	−	11.2346i	0.426491	−	0.492197i	0.927803	+	0.373069i	$0.121695\pi$
$522$		0			0
$523$	1.52958	−	2.38007i	0.0668839	−	0.104073i	−0.806201	−	0.591642i	$-0.798480\pi$
$523$	1.52958	−	2.38007i	0.0668839	−	0.104073i	0.873085	+	0.487569i	$0.162116\pi$
$524$		0			0
$525$	−4.86717	−	5.76470i	−0.212421	−	0.251592i
$526$		0			0
$527$	−1.68222	−	5.72912i	−0.0732787	−	0.249564i
$528$		0			0
$529$	15.5426	+	16.9537i	0.675765	+	0.737117i
$530$		0			0
$531$	26.7340	−	7.84981i	1.16016	−	0.340653i
$532$		0			0
$533$	−2.18915	−	3.40638i	−0.0948226	−	0.147547i
$534$		0			0
$535$	−4.22914	−	14.7523i	−0.182842	−	0.637796i
$536$		0			0
$537$	−2.87692	−	2.49287i	−0.124148	−	0.107575i
$538$		0			0
$539$	−0.876191	−	1.91859i	−0.0377402	−	0.0826396i
$540$		0			0
$541$	−30.9163	−	9.07784i	−1.32919	−	0.390287i	−0.461392	−	0.887196i	$-0.652650\pi$
$541$	−30.9163	−	9.07784i	−1.32919	−	0.390287i	−0.867802	+	0.496910i	$0.834468\pi$
$542$		0			0
$543$	11.1787	+	1.60726i	0.479724	+	0.0689739i
$544$		0			0
$545$	−8.49263	−	18.9162i	−0.363784	−	0.810282i
$546$		0			0
$547$	2.11647	−	0.304302i	0.0904936	−	0.0130110i	−0.0969193	−	0.995292i	$-0.530899\pi$
$547$	2.11647	−	0.304302i	0.0904936	−	0.0130110i	0.187413	+	0.982281i	$0.439990\pi$
$548$		0			0
$549$	9.35615	+	10.7976i	0.399311	+	0.460829i
$550$		0			0
$551$	−26.2006			−1.11618
$552$		0			0
$553$		−	20.0491i		−	0.852573i
$554$		0			0
$555$	−2.47963	−	0.0158941i	−0.105255	−	0.000674668i
$556$		0			0
$557$	−18.1844	+	2.61452i	−0.770496	+	0.110781i	−0.516341	−	0.856383i	$-0.672706\pi$
$557$	−18.1844	+	2.61452i	−0.770496	+	0.110781i	−0.254155	+	0.967164i	$0.581797\pi$
$558$		0			0
$559$	1.08923	−	2.38508i	0.0460695	−	0.100878i
$560$		0			0
$561$	0.850360	−	5.91438i	0.0359022	−	0.249705i
$562$		0			0
$563$	−1.49792	+	5.10146i	−0.0631300	+	0.215001i	−0.985017	−	0.172458i	$-0.944829\pi$
$563$	−1.49792	+	5.10146i	−0.0631300	+	0.215001i	0.921887	+	0.387459i	$0.126647\pi$
$564$		0			0
$565$	12.0379	−	40.0461i	0.506440	−	1.68475i
$566$		0			0
$567$	−13.4936	−	11.6923i	−0.566677	−	0.491029i
$568$		0			0
$569$	−4.35702	−	2.80009i	−0.182656	−	0.117386i	0.446118	−	0.894974i	$-0.352806\pi$
$569$	−4.35702	−	2.80009i	−0.182656	−	0.117386i	−0.628773	+	0.777589i	$0.716443\pi$
$570$		0			0
$571$	−39.0412	+	25.0902i	−1.63382	+	1.04999i	−0.687797	+	0.725903i	$0.741422\pi$
$571$	−39.0412	+	25.0902i	−1.63382	+	1.04999i	−0.946026	+	0.324091i	$0.894942\pi$
$572$		0			0
$573$	0.642546	+	2.18831i	0.0268428	+	0.0914180i
$574$		0			0
$575$	0.0283572	+	23.9791i	0.00118258	+	0.999999i
$576$		0			0
$577$	5.95560	+	20.2829i	0.247935	+	0.844389i	0.985581	+	0.169202i	$0.0541189\pi$
$577$	5.95560	+	20.2829i	0.247935	+	0.844389i	−0.737647	+	0.675187i	$0.764063\pi$
$578$		0			0
$579$	−5.41718	+	3.48141i	−0.225130	+	0.144683i
$580$		0			0
$581$	4.16005	+	2.67350i	0.172588	+	0.110916i
$582$		0			0
$583$	−16.3064	−	14.1296i	−0.675343	−	0.585188i
$584$		0			0
$585$	0.841925	−	2.80080i	0.0348093	−	0.115799i
$586$		0			0
$587$	−8.60605	+	29.3095i	−0.355210	+	1.20973i	0.567219	+	0.823567i	$0.308019\pi$
$587$	−8.60605	+	29.3095i	−0.355210	+	1.20973i	−0.922429	+	0.386167i	$0.873799\pi$
$588$		0			0
$589$	−1.19524	+	8.31311i	−0.0492492	+	0.342536i
$590$		0			0
$591$	−3.16413	+	6.92847i	−0.130155	+	0.284999i
$592$		0			0
$593$	−28.3871	+	4.08145i	−1.16572	+	0.167605i	−0.697884	−	0.716211i	$-0.745875\pi$
$593$	−28.3871	+	4.08145i	−1.16572	+	0.167605i	−0.467835	+	0.883816i	$0.654966\pi$
$594$		0			0
$595$	23.0167	+	0.147534i	0.943591	+	0.00604830i
$596$		0			0
$597$		−	4.22242i		−	0.172812i
$598$		0			0
$599$	−25.8895			−1.05782			−0.528909	−	0.848679i	$-0.677399\pi$
$599$	−25.8895			−1.05782			−0.528909	+	0.848679i	$0.677399\pi$
$600$		0			0
$601$	12.2013	+	14.0811i	0.497703	+	0.574380i	0.947908	−	0.318545i	$-0.103194\pi$
$601$	12.2013	+	14.0811i	0.497703	+	0.574380i	−0.450204	+	0.892926i	$0.648649\pi$
$602$		0			0
$603$	28.9396	−	4.16088i	1.17851	−	0.169444i
$604$		0			0
$605$	−2.01521	−	4.48861i	−0.0819299	−	0.182488i
$606$		0			0
$607$	33.1694	+	4.76904i	1.34630	+	0.193569i	0.777489	−	0.628896i	$-0.216493\pi$
$607$	33.1694	+	4.76904i	1.34630	+	0.193569i	0.568815	+	0.822465i	$0.307402\pi$
$608$		0			0
$609$	−7.27527	−	2.13621i	−0.294809	−	0.0865636i
$610$		0			0
$611$	1.91812	+	4.20010i	0.0775990	+	0.169918i
$612$		0			0
$613$	−1.78553	−	1.54717i	−0.0721167	−	0.0624895i	0.618057	−	0.786134i	$-0.287920\pi$
$613$	−1.78553	−	1.54717i	−0.0721167	−	0.0624895i	−0.690173	+	0.723644i	$0.742466\pi$
$614$		0			0
$615$	−2.80380	−	9.78034i	−0.113060	−	0.394381i
$616$		0			0
$617$	14.9126	+	23.2044i	0.600357	+	0.934173i	0.999848	+	0.0174364i	$0.00555047\pi$
$617$	14.9126	+	23.2044i	0.600357	+	0.934173i	−0.399491	+	0.916737i	$0.630813\pi$
$618$		0			0
$619$	−6.56305	+	1.92708i	−0.263791	+	0.0774560i	−0.410954	−	0.911656i	$-0.634804\pi$
$619$	−6.56305	+	1.92708i	−0.263791	+	0.0774560i	0.147162	+	0.989112i	$0.452986\pi$
$620$		0			0
$621$	−2.32156	−	14.6841i	−0.0931609	−	0.589255i
$622$		0			0
$623$	10.0154	+	34.1094i	0.401259	+	1.36656i
$624$		0			0
$625$	−16.8505	+	18.4678i	−0.674020	+	0.738713i
$626$		0			0
$627$	−4.54383	+	7.07034i	−0.181463	+	0.282362i
$628$		0			0
$629$	4.95404	−	5.71727i	0.197531	−	0.227962i
$630$		0			0
$631$	7.94511	+	17.3974i	0.316290	+	0.692578i	0.999284	−	0.0378460i	$-0.0120496\pi$
$631$	7.94511	+	17.3974i	0.316290	+	0.692578i	−0.682994	+	0.730424i	$0.739322\pi$
$632$		0			0
$633$	3.89095	−	13.2513i	0.154651	−	0.526694i
$634$		0			0
$635$	−1.03638	+	0.886466i	−0.0411277	+	0.0351783i
$636$		0			0
$637$	−0.312758	−	0.142832i	−0.0123919	−	0.00565921i
$638$		0			0
$639$	2.90509	+	20.2053i	0.114924	+	0.799311i
$640$		0			0
$641$	13.0132	+	15.0180i	0.513989	+	0.593175i	0.952116	−	0.305738i	$-0.0989033\pi$
$641$	13.0132	+	15.0180i	0.513989	+	0.593175i	−0.438127	+	0.898913i	$0.644358\pi$
$642$		0			0
$643$		−	19.0626i		−	0.751756i	−0.926669	−	0.375878i	$-0.877341\pi$
$643$		−	19.0626i		−	0.751756i	0.926669	−	0.375878i	$-0.122659\pi$
$644$		0			0
$645$	4.34626	−	4.95137i	0.171134	−	0.194960i
$646$		0			0
$647$	−33.3085	+	28.8620i	−1.30949	+	1.13468i	−0.327687	+	0.944786i	$0.606269\pi$
$647$	−33.3085	+	28.8620i	−1.30949	+	1.13468i	−0.981805	+	0.189894i	$0.939186\pi$
$648$		0			0
$649$	4.34891	+	30.2473i	0.170709	+	1.18731i
$650$		0			0
$651$	−1.00968	+	2.21089i	−0.0395726	+	0.0866518i
$652$		0			0
$653$	20.6616	+	2.97069i	0.808552	+	0.116252i	0.534179	−	0.845371i	$-0.320621\pi$
$653$	20.6616	+	2.97069i	0.808552	+	0.116252i	0.274373	+	0.961623i	$0.411530\pi$
$654$		0			0
$655$	−4.29151	+	2.71928i	−0.167683	+	0.106251i
$656$		0			0
$657$	19.0021	−	8.67795i	0.741341	−	0.338559i
$658$		0			0
$659$	19.0435	−	21.9774i	0.741830	−	0.856117i	−0.251920	−	0.967748i	$-0.581062\pi$
$659$	19.0435	−	21.9774i	0.741830	−	0.856117i	0.993750	+	0.111631i	$0.0356074\pi$
$660$		0			0
$661$	40.2156	+	25.8450i	1.56420	+	1.00525i	0.981248	+	0.192749i	$0.0617403\pi$
$661$	40.2156	+	25.8450i	1.56420	+	1.00525i	0.582956	+	0.812504i	$0.301896\pi$
$662$		0			0
$663$	−0.526609	−	0.819419i	−0.0204518	−	0.0318236i
$664$		0			0
$665$	−29.3627	−	13.6376i	−1.13864	−	0.528844i
$666$		0			0
$667$	13.3116	+	20.0892i	0.515429	+	0.777857i
$668$		0			0
$669$	2.25533	−	0.662225i	0.0871961	−	0.0256031i
$670$		0			0
$671$	−13.1821	+	8.47159i	−0.508888	+	0.327042i
$672$		0			0
$673$	−17.2153	+	26.7875i	−0.663600	+	1.03258i	0.332393	+	0.943141i	$0.392144\pi$
$673$	−17.2153	+	26.7875i	−0.663600	+	1.03258i	−0.995992	+	0.0894399i	$0.971492\pi$
$674$		0			0
$675$	8.54609	−	12.9305i	0.328939	−	0.497694i
$676$		0			0
$677$	19.5175	−	8.91333i	0.750118	−	0.342567i	−0.00340062	−	0.999994i	$-0.501082\pi$
$677$	19.5175	−	8.91333i	0.750118	−	0.342567i	0.753518	+	0.657427i	$0.228355\pi$
$678$		0			0
$679$	30.7771	+	9.03696i	1.18112	+	0.346807i
$680$		0			0
$681$	−1.31825	+	9.16865i	−0.0505156	+	0.351343i
$682$		0			0
$683$	19.6448	+	8.97146i	0.751686	+	0.343283i	0.754140	−	0.656714i	$-0.228054\pi$
$683$	19.6448	+	8.97146i	0.751686	+	0.343283i	−0.00245420	+	0.999997i	$0.500781\pi$
$684$		0			0
$685$	3.08548	−	4.73411i	0.117890	−	0.180881i
$686$		0			0
$687$	8.64883	−	7.49425i	0.329973	−	0.285924i
$688$		0			0
$689$	−3.51728			−0.133998
$690$		0			0
$691$	38.1776			1.45234			0.726172	−	0.687513i	$-0.241298\pi$
$691$	38.1776			1.45234			0.726172	+	0.687513i	$0.241298\pi$
$692$		0			0
$693$	16.8380	−	14.5902i	0.639621	−	0.554235i
$694$		0			0
$695$	9.62698	+	6.27444i	0.365172	+	0.238003i
$696$		0			0
$697$	28.2348	+	12.8944i	1.06947	+	0.488410i
$698$		0			0
$699$	−2.26855	+	15.7781i	−0.0858043	+	0.596782i
$700$		0			0
$701$	−7.76589	−	2.28027i	−0.293314	−	0.0861247i	0.131765	−	0.991281i	$-0.457935\pi$
$701$	−7.76589	−	2.28027i	−0.293314	−	0.0861247i	−0.425079	+	0.905156i	$0.639754\pi$
$702$		0			0
$703$	−9.67915	+	4.42032i	−0.365056	+	0.166715i
$704$		0			0
$705$	1.57749	+	11.4942i	0.0594118	+	0.432898i
$706$		0			0
$707$	13.2204	−	20.5713i	0.497203	−	0.773663i
$708$		0			0
$709$	5.92072	−	3.80502i	0.222357	−	0.142900i	−0.424720	−	0.905325i	$-0.639627\pi$
$709$	5.92072	−	3.80502i	0.222357	−	0.142900i	0.647077	+	0.762424i	$0.275991\pi$
$710$		0			0
$711$	18.7372	−	5.50173i	0.702698	−	0.206331i
$712$		0			0
$713$	6.98130	−	3.30716i	0.261452	−	0.123854i
$714$		0			0
$715$	2.90910	+	1.35114i	0.108794	+	0.0505299i
$716$		0			0
$717$	−6.24815	−	9.72231i	−0.233341	−	0.363086i
$718$		0			0
$719$	−17.8798	−	11.4907i	−0.666804	−	0.428529i	0.162968	−	0.986631i	$-0.447893\pi$
$719$	−17.8798	−	11.4907i	−0.666804	−	0.428529i	−0.829772	+	0.558102i	$0.811530\pi$
$720$		0			0
$721$	−29.7885	+	34.3778i	−1.10938	+	1.28030i
$722$		0			0
$723$	−10.9570	+	5.00389i	−0.407494	+	0.186096i
$724$		0			0
$725$	−3.89421	+	24.8216i	−0.144627	+	0.921852i
$726$		0			0
$727$	−19.3923	−	2.78819i	−0.719220	−	0.103408i	−0.227020	−	0.973890i	$-0.572898\pi$
$727$	−19.3923	−	2.78819i	−0.719220	−	0.103408i	−0.492200	+	0.870482i	$0.663807\pi$
$728$		0			0
$729$	5.12513	−	11.2225i	0.189820	−	0.415647i
$730$		0			0
$731$	2.86049	+	19.8951i	0.105799	+	0.735847i
$732$		0			0
$733$	6.15965	−	5.33737i	0.227512	−	0.197140i	−0.533644	−	0.845709i	$-0.679178\pi$
$733$	6.15965	−	5.33737i	0.227512	−	0.197140i	0.761156	+	0.648569i	$0.224632\pi$
$734$		0			0
$735$	−0.649279	−	0.569930i	−0.0239490	−	0.0210222i
$736$		0			0
$737$			32.0659i			1.18116i
$738$		0			0
$739$	−4.96927	−	5.73484i	−0.182798	−	0.210960i	0.656954	−	0.753931i	$-0.271845\pi$
$739$	−4.96927	−	5.73484i	−0.182798	−	0.210960i	−0.839751	+	0.542971i	$0.817299\pi$
$740$		0			0
$741$	0.194980	+	1.35612i	0.00716277	+	0.0498182i
$742$		0			0
$743$	0.956980	+	0.437038i	0.0351082	+	0.0160334i	0.432892	−	0.901446i	$-0.357493\pi$
$743$	0.956980	+	0.437038i	0.0351082	+	0.0160334i	−0.397784	+	0.917479i	$0.630221\pi$
$744$		0			0
$745$	13.1287	+	15.3490i	0.480998	+	0.562344i
$746$		0			0
$747$	−1.35699	+	4.62148i	−0.0496496	+	0.169091i
$748$		0			0
$749$	−7.91704	−	17.3359i	−0.289282	−	0.633440i
$750$		0			0
$751$	−3.79004	+	4.37394i	−0.138301	+	0.159607i	−0.820675	−	0.571396i	$-0.806402\pi$
$751$	−3.79004	+	4.37394i	−0.138301	+	0.159607i	0.682374	+	0.731003i	$0.260948\pi$
$752$		0			0
$753$	−1.44226	+	2.24420i	−0.0525588	+	0.0817831i
$754$		0			0
$755$	0.740817	−	4.92805i	0.0269611	−	0.179350i
$756$		0			0
$757$	−13.2581	−	45.1528i	−0.481872	−	1.64111i	−0.738248	−	0.674529i	$-0.764347\pi$
$757$	−13.2581	−	45.1528i	−0.481872	−	1.64111i	0.256376	−	0.966577i	$-0.417471\pi$
$758$		0			0
$759$	7.72972	−	0.108240i	0.280571	−	0.00392885i
$760$		0			0
$761$	−22.7678	+	6.68523i	−0.825332	+	0.242339i	−0.667010	−	0.745048i	$-0.732426\pi$
$761$	−22.7678	+	6.68523i	−0.825332	+	0.242339i	−0.158321	+	0.987388i	$0.550608\pi$
$762$		0			0
$763$	−13.9216	−	21.6624i	−0.503994	−	0.784230i
$764$		0			0
$765$	6.17819	+	21.5511i	0.223373	+	0.779180i
$766$		0			0
$767$	3.76473	+	3.26216i	0.135937	+	0.117790i
$768$		0			0
$769$	10.0872	+	22.0879i	0.363755	+	0.796511i	0.999693	+	0.0247717i	$0.00788589\pi$
$769$	10.0872	+	22.0879i	0.363755	+	0.796511i	−0.635939	+	0.771740i	$0.719387\pi$
$770$		0			0
$771$	−0.216134	−	0.0634627i	−0.00778388	−	0.00228555i
$772$		0			0
$773$	12.3211	+	1.77151i	0.443159	+	0.0637166i	0.360283	−	0.932843i	$-0.382680\pi$
$773$	12.3211	+	1.77151i	0.443159	+	0.0637166i	0.0828763	+	0.996560i	$0.473589\pi$
$774$		0			0
$775$	7.69792	+	2.36792i	0.276518	+	0.0850581i
$776$		0			0
$777$	−3.04806	+	0.438245i	−0.109349	+	0.0157220i
$778$		0			0
$779$	−28.5910	−	32.9957i	−1.02438	−	1.18219i
$780$		0			0
$781$	−22.3881			−0.801109
$782$		0			0
$783$		−	15.5771i		−	0.556679i
$784$		0			0
$785$	0.221438	−	34.5463i	0.00790344	−	1.23301i
$786$		0			0
$787$	13.0960	−	1.88293i	0.466823	−	0.0671191i	0.0951103	−	0.995467i	$-0.469680\pi$
$787$	13.0960	−	1.88293i	0.466823	−	0.0671191i	0.371713	+	0.928348i	$0.378771\pi$
$788$		0			0
$789$	−2.69713	+	5.90588i	−0.0960202	+	0.210255i
$790$		0			0
$791$	7.39038	−	51.4012i	0.262772	−	1.82762i
$792$		0			0
$793$	−0.719648	+	2.45089i	−0.0255554	+	0.0870338i
$794$		0			0
$795$	−8.46369	−	2.54420i	−0.300176	−	0.0902336i
$796$		0			0
$797$	−10.2766	−	8.90473i	−0.364016	−	0.315422i	0.453578	−	0.891217i	$-0.350147\pi$
$797$	−10.2766	−	8.90473i	−0.364016	−	0.315422i	−0.817594	+	0.575795i	$0.804693\pi$
$798$		0			0
$799$	−29.7765	−	19.1362i	−1.05342	−	0.676990i
$800$		0			0
$801$	−29.1291	+	18.7201i	−1.02923	+	0.661443i
$802$		0			0
$803$	6.45475	+	21.9829i	0.227783	+	0.775759i
$804$		0			0
$805$	4.46161	+	29.4425i	0.157251	+	1.03771i
$806$		0			0
$807$	0.349949	+	1.19182i	0.0123188	+	0.0419539i
$808$		0			0
$809$	−12.5160	+	8.04355i	−0.440039	+	0.282796i	−0.741843	−	0.670574i	$-0.766048\pi$
$809$	−12.5160	+	8.04355i	−0.440039	+	0.282796i	0.301803	+	0.953370i	$0.402411\pi$
$810$		0			0
$811$	−8.82291	−	5.67014i	−0.309814	−	0.199105i	0.376489	−	0.926421i	$-0.377131\pi$
$811$	−8.82291	−	5.67014i	−0.309814	−	0.199105i	−0.686303	+	0.727316i	$0.740768\pi$
$812$		0			0
$813$	−11.7831	−	10.2101i	−0.413250	−	0.358083i
$814$		0			0
$815$	−0.220933	+	0.734968i	−0.00773894	+	0.0257448i
$816$		0			0
$817$	7.96503	−	27.1264i	0.278661	−	0.949033i
$818$		0			0
$819$	0.516878	−	3.59497i	0.0180612	−	0.125618i
$820$		0			0
$821$	−14.7477	+	32.2930i	−0.514699	+	1.12703i	0.456709	+	0.889616i	$0.349028\pi$
$821$	−14.7477	+	32.2930i	−0.514699	+	1.12703i	−0.971408	+	0.237417i	$0.923699\pi$
$822$		0			0
$823$	−7.18210	+	1.03263i	−0.250352	+	0.0359952i	−0.266348	−	0.963877i	$-0.585817\pi$
$823$	−7.18210	+	1.03263i	−0.250352	+	0.0359952i	0.0159961	+	0.999872i	$0.494908\pi$
$824$		0			0
$825$	6.02286	+	5.35555i	0.209689	+	0.186456i
$826$		0			0
$827$			3.85766i			0.134144i	0.997748	+	0.0670721i	$0.0213657\pi$
$827$			3.85766i			0.134144i	−0.997748	+	0.0670721i	$0.978634\pi$
$828$		0			0
$829$	48.2278			1.67502			0.837510	−	0.546422i	$-0.184011\pi$
$829$	48.2278			1.67502			0.837510	+	0.546422i	$0.184011\pi$
$830$		0			0
$831$	−6.24107	−	7.20258i	−0.216500	−	0.249855i
$832$		0			0
$833$	2.60887	−	0.375099i	0.0903920	−	0.0129964i
$834$		0			0
$835$	42.4576	−	19.0618i	1.46931	−	0.659660i
$836$		0			0
$837$	−4.94240	−	0.710610i	−0.170834	−	0.0245623i
$838$		0			0
$839$	4.71804	+	1.38534i	0.162885	+	0.0478273i	0.362158	−	0.932117i	$-0.382040\pi$
$839$	4.71804	+	1.38534i	0.162885	+	0.0478273i	−0.199273	+	0.979944i	$0.563858\pi$
$840$		0			0
$841$	−1.55735	−	3.41012i	−0.0537017	−	0.117590i
$842$		0			0
$843$	0.803167	+	0.695948i	0.0276625	+	0.0239697i
$844$		0			0
$845$	−27.4407	+	7.86661i	−0.943988	+	0.270620i
$846$		0			0
$847$	−3.30343	−	5.14024i	−0.113507	−	0.176621i
$848$		0			0
$849$	−11.1607	+	3.27707i	−0.383034	+	0.112469i
$850$		0			0
$851$	8.30691	+	5.17563i	0.284757	+	0.177418i
$852$		0			0
$853$	−6.80525	−	23.1766i	−0.233007	−	0.793550i	−0.990115	−	0.140260i	$-0.955206\pi$
$853$	−6.80525	−	23.1766i	−0.233007	−	0.793550i	0.757107	−	0.653291i	$-0.226612\pi$
$854$		0			0
$855$	4.68774	−	31.1837i	0.160317	−	1.06646i
$856$		0			0
$857$	20.3370	−	31.6449i	0.694697	−	1.08097i	−0.297309	−	0.954781i	$-0.596089\pi$
$857$	20.3370	−	31.6449i	0.694697	−	1.08097i	0.992006	−	0.126189i	$-0.0402744\pi$
$858$		0			0
$859$	−13.1764	+	15.2064i	−0.449574	+	0.518836i	−0.934618	−	0.355654i	$-0.884258\pi$
$859$	−13.1764	+	15.2064i	−0.449574	+	0.518836i	0.485044	+	0.874490i	$0.338804\pi$
$860$		0			0
$861$	−5.24877	−	11.4932i	−0.178878	−	0.391687i
$862$		0			0
$863$	−5.24397	+	17.8593i	−0.178507	+	0.607938i	0.820818	+	0.571190i	$0.193518\pi$
$863$	−5.24397	+	17.8593i	−0.178507	+	0.607938i	−0.999325	+	0.0367482i	$0.988300\pi$
$864$		0			0
$865$	−24.0486	+	20.5698i	−0.817675	+	0.699394i
$866$		0			0
$867$	−1.61084	−	0.735645i	−0.0547069	−	0.0249838i
$868$		0			0
$869$	3.04803	+	21.1995i	0.103398	+	0.719145i
$870$		0			0
$871$	3.42309	+	3.95046i	0.115987	+	0.133856i
$872$		0			0
$873$			31.2430i			1.05742i
$874$		0			0
$875$	−17.2840	+	25.7903i	−0.584307	+	0.871872i
$876$		0			0
$877$	13.4608	−	11.6638i	0.454538	−	0.393859i	−0.397280	−	0.917697i	$-0.630046\pi$
$877$	13.4608	−	11.6638i	0.454538	−	0.393859i	0.851818	+	0.523838i	$0.175500\pi$
$878$		0			0
$879$	0.113520	+	0.789550i	0.00382894	+	0.0266309i
$880$		0			0
$881$	16.3730	−	35.8518i	0.551620	−	1.20788i	−0.404402	−	0.914581i	$-0.632520\pi$
$881$	16.3730	−	35.8518i	0.551620	−	1.20788i	0.956021	−	0.293297i	$-0.0947525\pi$
$882$		0			0
$883$	−57.4670	−	8.26251i	−1.93392	−	0.278056i	−0.936550	−	0.350534i	$-0.886000\pi$
$883$	−57.4670	−	8.26251i	−1.93392	−	0.278056i	−0.997370	+	0.0724787i	$0.976909\pi$
$884$		0			0
$885$	6.69947	+	10.5730i	0.225200	+	0.355407i
$886$		0			0
$887$	−13.0725	+	5.97002i	−0.438932	+	0.200454i	−0.622609	−	0.782533i	$-0.713927\pi$
$887$	−13.0725	+	5.97002i	−0.438932	+	0.200454i	0.183677	+	0.982987i	$0.441200\pi$
$888$		0			0
$889$	−1.10909	+	1.27996i	−0.0371977	+	0.0429284i
$890$		0			0
$891$	16.0455	+	10.3118i	0.537543	+	0.345458i
$892$		0			0
$893$	26.9164	+	41.8827i	0.900721	+	1.40155i
$894$		0			0
$895$	−6.59859	+	14.2072i	−0.220567	+	0.474894i
$896$		0			0
$897$	0.940733	−	0.838497i	0.0314102	−	0.0279966i
$898$		0			0
$899$	7.76636	−	2.28041i	0.259023	−	0.0760559i
$900$		0			0
$901$	22.6823	−	14.5770i	0.755656	−	0.485631i
$902$		0			0
$903$	4.42339	−	6.88293i	0.147201	−	0.229049i
$904$		0			0
$905$	−6.31893	−	46.0423i	−0.210048	−	1.53050i
$906$		0			0
$907$	3.25108	−	1.48472i	0.107950	−	0.0492993i	−0.360708	−	0.932679i	$-0.617465\pi$
$907$	3.25108	−	1.48472i	0.107950	−	0.0492993i	0.468658	+	0.883380i	$0.344738\pi$
$908$		0			0
$909$	22.8531	+	6.71026i	0.757988	+	0.222565i
$910$		0			0
$911$	5.63457	−	39.1893i	0.186682	−	1.29840i	−0.653844	−	0.756629i	$-0.726845\pi$
$911$	5.63457	−	39.1893i	0.186682	−	1.29840i	0.840526	−	0.541771i	$-0.182246\pi$
$912$		0			0
$913$	−4.80521	−	2.19447i	−0.159029	−	0.0726263i
$914$		0			0
$915$	−3.50454	+	5.37707i	−0.115856	+	0.177760i
$916$		0			0
$917$	−4.76822	+	4.13169i	−0.157460	+	0.136440i
$918$		0			0
$919$	45.6466			1.50574			0.752872	−	0.658167i	$-0.228668\pi$
$919$	45.6466			1.50574			0.752872	+	0.658167i	$0.228668\pi$
$920$		0			0
$921$	1.00610			0.0331521
$922$		0			0
$923$	−2.75817	+	2.38997i	−0.0907864	+	0.0786668i
$924$		0			0
$925$	2.74905	+	9.82671i	0.0903883	+	0.323100i
$926$		0			0
$927$	−40.3026	−	18.4056i	−1.32371	−	0.604519i
$928$		0			0
$929$	1.93174	−	13.4355i	0.0633783	−	0.440806i	−0.933282	−	0.359145i	$-0.883068\pi$
$929$	1.93174	−	13.4355i	0.0633783	−	0.440806i	0.996660	−	0.0816610i	$-0.0260225\pi$
$930$		0			0
$931$	−3.55712	−	1.04446i	−0.116580	−	0.0342309i
$932$		0			0
$933$	−2.15516	+	0.984230i	−0.0705569	+	0.0322223i
$934$		0			0
$935$	−24.3599	+	3.34319i	−0.796653	+	0.109334i
$936$		0			0
$937$	−8.77219	+	13.6498i	−0.286575	+	0.445919i	−0.954457	−	0.298347i	$-0.903565\pi$
$937$	−8.77219	+	13.6498i	−0.286575	+	0.445919i	0.667882	+	0.744267i	$0.267201\pi$
$938$		0			0
$939$	10.2279	−	6.57309i	0.333776	−	0.214505i
$940$		0			0
$941$	41.0251	−	12.0461i	1.33738	−	0.392690i	0.466646	−	0.884444i	$-0.345462\pi$
$941$	41.0251	−	12.0461i	1.33738	−	0.392690i	0.870734	+	0.491754i	$0.163644\pi$
$942$		0			0
$943$	−10.7732	+	38.6860i	−0.350824	+	1.25979i
$944$		0			0
$945$	8.10799	−	17.4570i	0.263753	−	0.567877i
$946$		0			0
$947$	−13.7547	−	21.4028i	−0.446969	−	0.695497i	0.542530	−	0.840036i	$-0.317466\pi$
$947$	−13.7547	−	21.4028i	−0.446969	−	0.695497i	−0.989499	+	0.144539i	$0.953830\pi$
$948$		0			0
$949$	3.14193	+	2.01919i	0.101991	+	0.0655458i
$950$		0			0
$951$	7.03216	−	8.11554i	0.228033	−	0.263165i
$952$		0			0
$953$	−8.87320	+	4.05226i	−0.287431	+	0.131265i	−0.553913	−	0.832574i	$-0.686866\pi$
$953$	−8.87320	+	4.05226i	−0.287431	+	0.131265i	0.266482	+	0.963840i	$0.414139\pi$
$954$		0			0
$955$	7.92766	−	5.02329i	0.256533	−	0.162550i
$956$		0			0
$957$	8.01751	+	1.15274i	0.259169	+	0.0372629i
$958$		0			0
$959$	2.91519	−	6.38337i	0.0941363	−	0.206130i
$960$		0			0
$961$	4.04251	+	28.1163i	0.130404	+	0.906976i
$962$		0			0
$963$	14.0290	−	12.1562i	0.452077	−	0.391727i
$964$		0			0
$965$	19.9146	+	17.4808i	0.641073	+	0.562727i
$966$		0			0
$967$		−	43.1538i		−	1.38773i	−0.720104	−	0.693866i	$-0.755906\pi$
$967$		−	43.1538i		−	1.38773i	0.720104	−	0.693866i	$-0.244094\pi$
$968$		0			0
$969$	−6.87767	−	7.93725i	−0.220942	−	0.254981i
$970$		0			0
$971$	−6.98392	−	48.5743i	−0.224125	−	1.55882i	−0.722198	−	0.691687i	$-0.756868\pi$
$971$	−6.98392	−	48.5743i	−0.224125	−	1.55882i	0.498073	−	0.867135i	$-0.334041\pi$
$972$		0			0
$973$	12.9808	+	5.92813i	0.416145	+	0.190047i
$974$		0			0
$975$	1.31372	+	0.0168423i	0.0420727	+	0.000539384i
$976$		0			0
$977$	−2.13679	+	7.27724i	−0.0683620	+	0.232819i	−0.986586	−	0.163242i	$-0.947805\pi$
$977$	−2.13679	+	7.27724i	−0.0683620	+	0.232819i	0.918224	+	0.396061i	$0.129623\pi$
$978$		0			0
$979$	−15.7757	−	34.5441i	−0.504195	−	1.10403i
$980$		0			0
$981$	16.4246	−	18.9550i	0.524398	−	0.605188i
$982$		0			0
$983$	13.9474	−	21.7026i	0.444853	−	0.692206i	−0.544333	−	0.838869i	$-0.683217\pi$
$983$	13.9474	−	21.7026i	0.444853	−	0.692206i	0.989186	+	0.146664i	$0.0468535\pi$
$984$		0			0
$985$	30.9951	+	4.65939i	0.987587	+	0.148461i
$986$		0			0
$987$	4.05920	+	13.8244i	0.129206	+	0.440034i
$988$		0			0
$989$	−24.8458	+	7.67486i	−0.790051	+	0.244046i
$990$		0			0
$991$	−29.9284	+	8.78779i	−0.950708	+	0.279153i	−0.720082	−	0.693889i	$-0.755896\pi$
$991$	−29.9284	+	8.78779i	−0.950708	+	0.279153i	−0.230627	+	0.973042i	$0.574078\pi$
$992$		0			0
$993$	4.62003	+	7.18890i	0.146612	+	0.228133i
$994$		0			0
$995$	−16.7027	+	4.78827i	−0.529510	+	0.151798i
$996$		0			0
$997$	−33.9106	−	29.3837i	−1.07396	−	0.930592i	−0.0761738	−	0.997095i	$-0.524270\pi$
$997$	−33.9106	−	29.3837i	−1.07396	−	0.930592i	−0.997786	+	0.0665029i	$0.978816\pi$
$998$		0			0
$999$	−2.62802	−	5.75456i	−0.0831468	−	0.182066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.s.a.9.5	✓	120
5.4	even	2	inner	460.2.s.a.9.8	yes	120
23.18	even	11	inner	460.2.s.a.409.8	yes	120
115.64	even	22	inner	460.2.s.a.409.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.s.a.9.5	✓	120	1.1	even	1	trivial
460.2.s.a.9.8	yes	120	5.4	even	2	inner
460.2.s.a.409.5	yes	120	115.64	even	22	inner
460.2.s.a.409.8	yes	120	23.18	even	11	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.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.410666 + 0.355844i) q^{3} +(1.87331 + 1.22094i) q^{5} +(2.52593 + 1.15355i) q^{7} +(-0.384923 + 2.67720i) q^{9} +O(q^{10})\)	\(q+(-0.410666 + 0.355844i) q^{3} +(1.87331 + 1.22094i) q^{5} +(2.52593 + 1.15355i) q^{7} +(-0.384923 + 2.67720i) q^{9} +(-2.84625 - 0.835735i) q^{11} +(-0.439869 + 0.200882i) q^{13} +(-1.20377 + 0.165208i) q^{15} +(2.00410 - 3.11844i) q^{17} +(-4.38630 + 2.81890i) q^{19} +(-1.44780 + 0.425113i) q^{21} +(4.38991 + 1.93098i) q^{23} +(2.01860 + 4.57441i) q^{25} +(-1.67593 - 2.60779i) q^{27} +(4.22734 + 2.71675i) q^{29} +(1.05483 - 1.21734i) q^{31} +(1.46625 - 0.669614i) q^{33} +(3.32344 + 5.24499i) q^{35} +(2.02003 + 0.290436i) q^{37} +(0.109157 - 0.239020i) q^{39} +(1.19168 + 8.28830i) q^{41} +(-4.09786 + 3.55082i) q^{43} +(-3.98979 + 4.54526i) q^{45} -9.54853i q^{47} +(0.465623 + 0.537357i) q^{49} +(0.286663 + 1.99378i) q^{51} +(6.61630 + 3.02156i) q^{53} +(-4.31154 - 5.04070i) q^{55} +(0.798213 - 2.71846i) q^{57} +(-4.27938 - 9.37052i) q^{59} +(3.45918 - 3.99211i) q^{61} +(-4.06058 + 6.31839i) q^{63} +(-1.06928 - 0.160741i) q^{65} +(-3.04543 - 10.3718i) q^{67} +(-2.48992 + 0.769134i) q^{69} +(7.24148 - 2.12629i) q^{71} +(-4.17561 - 6.49738i) q^{73} +(-2.45675 - 1.16025i) q^{75} +(-6.22538 - 5.39432i) q^{77} +(-2.99930 - 6.56756i) q^{79} +(-6.16929 - 1.81147i) q^{81} +(1.76268 + 0.253434i) q^{83} +(7.56174 - 3.39492i) q^{85} +(-2.70276 + 0.388599i) q^{87} +(8.38350 + 9.67507i) q^{89} -1.34281 q^{91} +0.875279i q^{93} +(-11.6586 - 0.0747303i) q^{95} +(11.4337 - 1.64392i) q^{97} +(3.33302 - 7.29829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{9}+O(q^{10}) \) 120 * q + 20 * q^9	\( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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