LMFDB - Embedded newform 460.2.m.a.261.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, 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:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			261.3
Character	$\chi$	$=$	460.261
Dual form			460.2.m.a.141.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.830167 + 1.81781i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(2.04574 + 1.31472i) q^{7} +(-0.650684 + 0.750930i) q^{9} +O(q^{10})$	\(q+(0.830167 + 1.81781i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(2.04574 + 1.31472i) q^{7} +(-0.650684 + 0.750930i) q^{9} +(0.564156 + 3.92379i) q^{11} +(-1.16364 + 0.747828i) q^{13} +(0.830167 - 1.81781i) q^{15} +(-1.96996 + 0.578433i) q^{17} +(5.29407 + 1.55448i) q^{19} +(-0.691603 + 4.81020i) q^{21} +(-2.85761 - 3.85150i) q^{23} +(-0.142315 + 0.989821i) q^{25} +(3.84714 + 1.12962i) q^{27} +(1.05491 - 0.309749i) q^{29} +(-2.31515 + 5.06948i) q^{31} +(-6.66437 + 4.28293i) q^{33} +(-0.346077 - 2.40702i) q^{35} +(-0.0422019 + 0.0487036i) q^{37} +(-2.32543 - 1.49446i) q^{39} +(2.21976 + 2.56174i) q^{41} +(-0.959509 - 2.10103i) q^{43} +0.993622 q^{45} -7.68342 q^{47} +(-0.451339 - 0.988295i) q^{49} +(-2.68688 - 3.10083i) q^{51} +(-4.52187 - 2.90603i) q^{53} +(2.59596 - 2.99590i) q^{55} +(1.56921 + 10.9141i) q^{57} +(7.86517 - 5.05464i) q^{59} +(2.66042 - 5.82552i) q^{61} +(-2.31839 + 0.680740i) q^{63} +(1.32719 + 0.389700i) q^{65} +(1.18289 - 8.22716i) q^{67} +(4.62901 - 8.39200i) q^{69} +(0.498794 - 3.46919i) q^{71} +(8.60074 + 2.52541i) q^{73} +(-1.91746 + 0.563016i) q^{75} +(-4.00455 + 8.76875i) q^{77} +(11.4618 - 7.36605i) q^{79} +(1.56455 + 10.8817i) q^{81} +(-0.379654 + 0.438144i) q^{83} +(1.72720 + 1.11001i) q^{85} +(1.43882 + 1.66048i) q^{87} +(-6.38520 - 13.9816i) q^{89} -3.36369 q^{91} -11.1373 q^{93} +(-2.29208 - 5.01896i) q^{95} +(2.97749 + 3.43621i) q^{97} +(-3.31358 - 2.12951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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
$3$	0.830167	+	1.81781i	0.479297	+	1.04951i	0.982656	+	0.185437i	$0.0593702\pi$
$3$	0.830167	+	1.81781i	0.479297	+	1.04951i	−0.503359	+	0.864078i	$0.667903\pi$
$4$		0			0
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$6$		0			0
$7$	2.04574	+	1.31472i	0.773216	+	0.496916i	0.866776	−	0.498698i	$-0.166188\pi$
$7$	2.04574	+	1.31472i	0.773216	+	0.496916i	−0.0935597	+	0.995614i	$0.529825\pi$
$8$		0			0
$9$	−0.650684	+	0.750930i	−0.216895	+	0.250310i
$10$		0			0
$11$	0.564156	+	3.92379i	0.170099	+	1.18307i	0.878671	+	0.477428i	$0.158431\pi$
$11$	0.564156	+	3.92379i	0.170099	+	1.18307i	−0.708571	+	0.705639i	$0.750660\pi$
$12$		0			0
$13$	−1.16364	+	0.747828i	−0.322736	+	0.207410i	−0.691970	−	0.721927i	$-0.743257\pi$
$13$	−1.16364	+	0.747828i	−0.322736	+	0.207410i	0.369233	+	0.929337i	$0.379620\pi$
$14$		0			0
$15$	0.830167	−	1.81781i	0.214348	−	0.469357i
$16$		0			0
$17$	−1.96996	+	0.578433i	−0.477786	+	0.140291i	−0.511754	−	0.859132i	$-0.671004\pi$
$17$	−1.96996	+	0.578433i	−0.477786	+	0.140291i	0.0339675	+	0.999423i	$0.489186\pi$
$18$		0			0
$19$	5.29407	+	1.55448i	1.21454	+	0.356622i	0.825397	−	0.564553i	$-0.190952\pi$
$19$	5.29407	+	1.55448i	1.21454	+	0.356622i	0.389147	+	0.921176i	$0.372770\pi$
$20$		0			0
$21$	−0.691603	+	4.81020i	−0.150920	+	1.04967i
$22$		0			0
$23$	−2.85761	−	3.85150i	−0.595854	−	0.803093i
$23$	−2.85761	−	3.85150i	−0.595854	−	0.803093i
$24$		0			0
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$		0			0
$27$	3.84714	+	1.12962i	0.740382	+	0.217396i
$28$		0			0
$29$	1.05491	−	0.309749i	0.195892	−	0.0575190i	−0.182315	−	0.983240i	$-0.558359\pi$
$29$	1.05491	−	0.309749i	0.195892	−	0.0575190i	0.378207	+	0.925721i	$0.376541\pi$
$30$		0			0
$31$	−2.31515	+	5.06948i	−0.415814	+	0.910505i	0.579605	+	0.814897i	$0.303207\pi$
$31$	−2.31515	+	5.06948i	−0.415814	+	0.910505i	−0.995419	+	0.0956076i	$0.969521\pi$
$32$		0			0
$33$	−6.66437	+	4.28293i	−1.16012	+	0.745563i
$34$		0			0
$35$	−0.346077	−	2.40702i	−0.0584978	−	0.406861i
$36$		0			0
$37$	−0.0422019	+	0.0487036i	−0.00693795	+	0.00800682i	−0.759208	−	0.650848i	$-0.774413\pi$
$37$	−0.0422019	+	0.0487036i	−0.00693795	+	0.00800682i	0.752270	+	0.658855i	$0.228959\pi$
$38$		0			0
$39$	−2.32543	−	1.49446i	−0.372367	−	0.239306i
$40$		0			0
$41$	2.21976	+	2.56174i	0.346669	+	0.400077i	0.902129	−	0.431466i	$-0.142004\pi$
$41$	2.21976	+	2.56174i	0.346669	+	0.400077i	−0.555461	+	0.831543i	$0.687458\pi$
$42$		0			0
$43$	−0.959509	−	2.10103i	−0.146324	−	0.320404i	0.822252	−	0.569124i	$-0.192718\pi$
$43$	−0.959509	−	2.10103i	−0.146324	−	0.320404i	−0.968576	+	0.248720i	$0.919990\pi$
$44$		0			0
$45$	0.993622			0.148120
$46$		0			0
$47$	−7.68342			−1.12074			−0.560371	−	0.828242i	$-0.689342\pi$
$47$	−7.68342			−1.12074			−0.560371	+	0.828242i	$0.689342\pi$
$48$		0			0
$49$	−0.451339	−	0.988295i	−0.0644770	−	0.141185i
$50$		0			0
$51$	−2.68688	−	3.10083i	−0.376239	−	0.434203i
$52$		0			0
$53$	−4.52187	−	2.90603i	−0.621126	−	0.399173i	0.191889	−	0.981417i	$-0.438539\pi$
$53$	−4.52187	−	2.90603i	−0.621126	−	0.399173i	−0.813015	+	0.582243i	$0.802175\pi$
$54$		0			0
$55$	2.59596	−	2.99590i	0.350039	−	0.403967i
$56$		0			0
$57$	1.56921	+	10.9141i	0.207847	+	1.44561i
$58$		0			0
$59$	7.86517	−	5.05464i	1.02396	−	0.658058i	0.0829886	−	0.996550i	$-0.473553\pi$
$59$	7.86517	−	5.05464i	1.02396	−	0.658058i	0.940969	+	0.338493i	$0.109917\pi$
$60$		0			0
$61$	2.66042	−	5.82552i	0.340632	−	0.745881i	−0.659350	−	0.751836i	$-0.729168\pi$
$61$	2.66042	−	5.82552i	0.340632	−	0.745881i	0.999982	+	0.00595521i	$0.00189561\pi$
$62$		0			0
$63$	−2.31839	+	0.680740i	−0.292089	+	0.0857652i
$64$		0			0
$65$	1.32719	+	0.389700i	0.164618	+	0.0483363i
$66$		0			0
$67$	1.18289	−	8.22716i	0.144513	−	1.00511i	−0.780496	−	0.625161i	$-0.785033\pi$
$67$	1.18289	−	8.22716i	0.144513	−	1.00511i	0.925008	−	0.379947i	$-0.124058\pi$
$68$		0			0
$69$	4.62901	−	8.39200i	0.557267	−	1.01028i
$70$		0			0
$71$	0.498794	−	3.46919i	0.0591960	−	0.411717i	−0.938580	−	0.345062i	$-0.887858\pi$
$71$	0.498794	−	3.46919i	0.0591960	−	0.411717i	0.997776	−	0.0666557i	$-0.0212329\pi$
$72$		0			0
$73$	8.60074	+	2.52541i	1.00664	+	0.295576i	0.743178	−	0.669093i	$-0.233317\pi$
$73$	8.60074	+	2.52541i	1.00664	+	0.295576i	0.263462	+	0.964670i	$0.415136\pi$
$74$		0			0
$75$	−1.91746	+	0.563016i	−0.221409	+	0.0650115i
$76$		0			0
$77$	−4.00455	+	8.76875i	−0.456361	+	0.999292i
$78$		0			0
$79$	11.4618	−	7.36605i	1.28955	−	0.828745i	0.297518	−	0.954716i	$-0.403841\pi$
$79$	11.4618	−	7.36605i	1.28955	−	0.828745i	0.992034	+	0.125971i	$0.0402047\pi$
$80$		0			0
$81$	1.56455	+	10.8817i	0.173839	+	1.20908i
$82$		0			0
$83$	−0.379654	+	0.438144i	−0.0416725	+	0.0480926i	−0.776203	−	0.630483i	$-0.782857\pi$
$83$	−0.379654	+	0.438144i	−0.0416725	+	0.0480926i	0.734531	+	0.678575i	$0.237402\pi$
$84$		0			0
$85$	1.72720	+	1.11001i	0.187341	+	0.120397i
$86$		0			0
$87$	1.43882	+	1.66048i	0.154258	+	0.178023i
$88$		0			0
$89$	−6.38520	−	13.9816i	−0.676829	−	1.48205i	−0.865968	−	0.500099i	$-0.833297\pi$
$89$	−6.38520	−	13.9816i	−0.676829	−	1.48205i	0.189139	−	0.981950i	$-0.439430\pi$
$90$		0			0
$91$	−3.36369			−0.352610
$92$		0			0
$93$	−11.1373			−1.15489
$94$		0			0
$95$	−2.29208	−	5.01896i	−0.235163	−	0.514935i
$96$		0			0
$97$	2.97749	+	3.43621i	0.302318	+	0.348894i	0.886500	−	0.462729i	$-0.153130\pi$
$97$	2.97749	+	3.43621i	0.302318	+	0.348894i	−0.584181	+	0.811623i	$0.698584\pi$
$98$		0			0
$99$	−3.31358	−	2.12951i	−0.333027	−	0.214023i
$100$		0			0
$101$	2.73995	−	3.16208i	0.272636	−	0.314638i	−0.602876	−	0.797835i	$-0.705979\pi$
$101$	2.73995	−	3.16208i	0.272636	−	0.314638i	0.875512	+	0.483196i	$0.160524\pi$
$102$		0			0
$103$	−0.163176	−	1.13491i	−0.0160782	−	0.111826i	0.980202	−	0.198001i	$-0.0634449\pi$
$103$	−0.163176	−	1.13491i	−0.0160782	−	0.111826i	−0.996280	+	0.0861744i	$0.972536\pi$
$104$		0			0
$105$	4.08821	−	2.62733i	0.398969	−	0.256402i
$106$		0			0
$107$	7.73575	−	16.9389i	0.747844	−	1.63755i	−0.0223591	−	0.999750i	$-0.507118\pi$
$107$	7.73575	−	16.9389i	0.747844	−	1.63755i	0.770203	−	0.637799i	$-0.220155\pi$
$108$		0			0
$109$	10.9621	−	3.21878i	1.04998	−	0.308303i	0.289173	−	0.957277i	$-0.406620\pi$
$109$	10.9621	−	3.21878i	1.04998	−	0.308303i	0.760811	+	0.648974i	$0.224802\pi$
$110$		0			0
$111$	−0.123569	−	0.0362830i	−0.0117286	−	0.00344383i
$112$		0			0
$113$	−2.06483	+	14.3612i	−0.194243	+	1.35099i	0.626380	+	0.779518i	$0.284536\pi$
$113$	−2.06483	+	14.3612i	−0.194243	+	1.35099i	−0.820623	+	0.571470i	$0.806373\pi$
$114$		0			0
$115$	−1.03943	+	4.68184i	−0.0969272	+	0.436583i
$116$		0			0
$117$	0.195598	−	1.36041i	0.0180830	−	0.125770i
$118$		0			0
$119$	−4.79050	−	1.40662i	−0.439145	−	0.128945i
$120$		0			0
$121$	−4.52343	+	1.32820i	−0.411221	+	0.120745i
$122$		0			0
$123$	−2.81399	+	6.16179i	−0.253729	+	0.555590i
$124$		0			0
$125$	0.841254	−	0.540641i	0.0752440	−	0.0483564i
$126$		0			0
$127$	−2.50855	−	17.4474i	−0.222598	−	1.54820i	−0.728156	−	0.685412i	$-0.759622\pi$
$127$	−2.50855	−	17.4474i	−0.222598	−	1.54820i	0.505558	−	0.862793i	$-0.331287\pi$
$128$		0			0
$129$	3.02273	−	3.48842i	0.266136	−	0.307138i
$130$		0			0
$131$	−10.7424	−	6.90375i	−0.938571	−	0.603183i	−0.0205819	−	0.999788i	$-0.506552\pi$
$131$	−10.7424	−	6.90375i	−0.938571	−	0.603183i	−0.917989	+	0.396605i	$0.870188\pi$
$132$		0			0
$133$	8.78659	+	10.1403i	0.761894	+	0.879272i
$134$		0			0
$135$	−1.66563	−	3.64722i	−0.143355	−	0.313903i
$136$		0			0
$137$	−15.0353			−1.28456			−0.642278	−	0.766472i	$-0.722010\pi$
$137$	−15.0353			−1.28456			−0.642278	+	0.766472i	$0.722010\pi$
$138$		0			0
$139$	−11.3870			−0.965835			−0.482917	−	0.875666i	$-0.660423\pi$
$139$	−11.3870			−0.965835			−0.482917	+	0.875666i	$0.660423\pi$
$140$		0			0
$141$	−6.37853	−	13.9670i	−0.537169	−	1.17624i
$142$		0			0
$143$	−3.59079	−	4.14400i	−0.300277	−	0.346539i
$144$		0			0
$145$	−0.924912	−	0.594405i	−0.0768098	−	0.0493626i
$146$		0			0
$147$	1.42185	−	1.64090i	0.117272	−	0.135339i
$148$		0			0
$149$	−1.46920	−	10.2185i	−0.120361	−	0.837132i	−0.957147	−	0.289602i	$-0.906477\pi$
$149$	−1.46920	−	10.2185i	−0.120361	−	0.837132i	0.836786	−	0.547530i	$-0.184432\pi$
$150$		0			0
$151$	−14.5890	+	9.37578i	−1.18724	+	0.762990i	−0.976703	−	0.214596i	$-0.931156\pi$
$151$	−14.5890	+	9.37578i	−1.18724	+	0.762990i	−0.210533	+	0.977587i	$0.567520\pi$
$152$		0			0
$153$	0.847461	−	1.85568i	0.0685132	−	0.150023i
$154$		0			0
$155$	5.34736	−	1.57013i	0.429510	−	0.126116i
$156$		0			0
$157$	−4.54991	−	1.33597i	−0.363122	−	0.106622i	0.0950815	−	0.995469i	$-0.469689\pi$
$157$	−4.54991	−	1.33597i	−0.363122	−	0.106622i	−0.458204	+	0.888847i	$0.651507\pi$
$158$		0			0
$159$	1.52871	−	10.6324i	0.121234	−	0.843204i
$160$		0			0
$161$	−0.782304	−	11.6361i	−0.0616542	−	0.917054i
$162$		0			0
$163$	−3.17166	+	22.0594i	−0.248423	+	1.72782i	0.358907	+	0.933373i	$0.383150\pi$
$163$	−3.17166	+	22.0594i	−0.248423	+	1.72782i	−0.607330	+	0.794449i	$0.707760\pi$
$164$		0			0
$165$	7.60106	+	2.23187i	0.591742	+	0.173751i
$166$		0			0
$167$	−8.08725	+	2.37463i	−0.625810	+	0.183754i	−0.579235	−	0.815160i	$-0.696649\pi$
$167$	−8.08725	+	2.37463i	−0.625810	+	0.183754i	−0.0465748	+	0.998915i	$0.514831\pi$
$168$		0			0
$169$	−4.60558	+	10.0848i	−0.354275	+	0.775754i
$170$		0			0
$171$	−4.61207	+	2.96400i	−0.352694	+	0.226663i
$172$		0			0
$173$	0.177194	+	1.23241i	0.0134718	+	0.0936985i	0.995448	−	0.0953061i	$-0.0303830\pi$
$173$	0.177194	+	1.23241i	0.0134718	+	0.0936985i	−0.981976	+	0.189005i	$0.939474\pi$
$174$		0			0
$175$	−1.59247	+	1.83781i	−0.120380	+	0.138926i
$176$		0			0
$177$	15.7178	+	10.1012i	1.18142	+	0.759253i
$178$		0			0
$179$	16.7959	+	19.3835i	1.25539	+	1.44879i	0.843116	+	0.537731i	$0.180719\pi$
$179$	16.7959	+	19.3835i	1.25539	+	1.44879i	0.412270	+	0.911062i	$0.364736\pi$
$180$		0			0
$181$	−0.610014	−	1.33575i	−0.0453420	−	0.0992852i	0.885605	−	0.464439i	$-0.153744\pi$
$181$	−0.610014	−	1.33575i	−0.0453420	−	0.0992852i	−0.930947	+	0.365153i	$0.881017\pi$
$182$		0			0
$183$	12.7983			0.946078
$184$		0			0
$185$	0.0644441			0.00473803
$186$		0			0
$187$	−3.38102	−	7.40339i	−0.247244	−	0.541390i
$188$		0			0
$189$	6.38511	+	7.36881i	0.464448	+	0.536002i
$190$		0			0
$191$	7.03671	+	4.52222i	0.509158	+	0.327216i	0.769870	−	0.638200i	$-0.220321\pi$
$191$	7.03671	+	4.52222i	0.509158	+	0.327216i	−0.260712	+	0.965417i	$0.583957\pi$
$192$		0			0
$193$	−14.8164	+	17.0990i	−1.06651	+	1.23081i	−0.0945831	+	0.995517i	$0.530152\pi$
$193$	−14.8164	+	17.0990i	−1.06651	+	1.23081i	−0.971923	+	0.235297i	$0.924394\pi$
$194$		0			0
$195$	0.393393	+	2.73611i	0.0281714	+	0.195937i
$196$		0			0
$197$	−1.27617	+	0.820145i	−0.0909234	+	0.0584329i	−0.585313	−	0.810808i	$-0.699028\pi$
$197$	−1.27617	+	0.820145i	−0.0909234	+	0.0584329i	0.494389	+	0.869241i	$0.335392\pi$
$198$		0			0
$199$	8.88774	−	19.4614i	0.630035	−	1.37958i	−0.277956	−	0.960594i	$-0.589657\pi$
$199$	8.88774	−	19.4614i	0.630035	−	1.37958i	0.907991	−	0.418990i	$-0.137616\pi$
$200$		0			0
$201$	15.9374	−	4.67965i	1.12414	−	0.330077i
$202$		0			0
$203$	2.56530	+	0.753241i	0.180049	+	0.0528671i
$204$		0			0
$205$	0.482400	−	3.35517i	0.0336923	−	0.234335i
$206$		0			0
$207$	4.75161	+	0.360242i	0.330260	+	0.0250386i
$208$		0			0
$209$	−3.11277	+	21.6498i	−0.215315	+	1.49755i
$210$		0			0
$211$	15.2178	+	4.46834i	1.04764	+	0.307613i	0.759861	−	0.650085i	$-0.225267\pi$
$211$	15.2178	+	4.46834i	1.04764	+	0.307613i	0.287774	+	0.957698i	$0.407085\pi$
$212$		0			0
$213$	6.72043	−	1.97329i	0.460476	−	0.135208i
$214$		0			0
$215$	−0.959509	+	2.10103i	−0.0654380	+	0.143289i
$216$		0			0
$217$	−11.4011	+	7.32705i	−0.773958	+	0.497393i
$218$		0			0
$219$	2.54934	+	17.7310i	0.172268	+	1.19815i
$220$		0			0
$221$	1.85976	−	2.14628i	0.125101	−	0.144375i
$222$		0			0
$223$	10.6248	+	6.82814i	0.711489	+	0.457246i	0.845667	−	0.533711i	$-0.179203\pi$
$223$	10.6248	+	6.82814i	0.711489	+	0.457246i	−0.134178	+	0.990957i	$0.542839\pi$
$224$		0			0
$225$	−0.650684	−	0.750930i	−0.0433789	−	0.0500620i
$226$		0			0
$227$	1.64545	+	3.60303i	0.109212	+	0.239141i	0.956345	−	0.292240i	$-0.0944005\pi$
$227$	1.64545	+	3.60303i	0.109212	+	0.239141i	−0.847133	+	0.531381i	$0.821673\pi$
$228$		0			0
$229$	9.63550			0.636731			0.318366	−	0.947968i	$-0.396866\pi$
$229$	9.63550			0.636731			0.318366	+	0.947968i	$0.396866\pi$
$230$		0			0
$231$	−19.2644			−1.26750
$232$		0			0
$233$	−5.41839	−	11.8646i	−0.354970	−	0.777277i	−0.999915	−	0.0130473i	$-0.995847\pi$
$233$	−5.41839	−	11.8646i	−0.354970	−	0.777277i	0.644944	−	0.764229i	$-0.276880\pi$
$234$		0			0
$235$	5.03157	+	5.80674i	0.328224	+	0.378790i
$236$		0			0
$237$	22.9053	+	14.7203i	1.48786	+	0.956189i
$238$		0			0
$239$	2.99029	−	3.45097i	0.193425	−	0.223225i	−0.650750	−	0.759292i	$-0.725545\pi$
$239$	2.99029	−	3.45097i	0.193425	−	0.223225i	0.844175	+	0.536067i	$0.180091\pi$
$240$		0			0
$241$	2.32368	+	16.1615i	0.149681	+	1.04106i	0.916741	+	0.399481i	$0.130810\pi$
$241$	2.32368	+	16.1615i	0.149681	+	1.04106i	−0.767060	+	0.641575i	$0.778281\pi$
$242$		0			0
$243$	−8.36287	+	5.37449i	−0.536478	+	0.344774i
$244$		0			0
$245$	−0.451339	+	0.988295i	−0.0288350	+	0.0631399i
$246$		0			0
$247$	−7.32289	+	2.15020i	−0.465945	+	0.136814i
$248$		0			0
$249$	−1.11164	−	0.326407i	−0.0704474	−	0.0206852i
$250$		0			0
$251$	−0.232903	+	1.61988i	−0.0147007	+	0.102246i	−0.995851	−	0.0910020i	$-0.970993\pi$
$251$	−0.232903	+	1.61988i	−0.0147007	+	0.102246i	0.981150	+	0.193248i	$0.0619021\pi$
$252$		0			0
$253$	13.5003	−	13.3855i	0.848758	−	0.841541i
$254$		0			0
$255$	−0.583915	+	4.06122i	−0.0365662	+	0.254323i
$256$		0			0
$257$	−8.58465	−	2.52068i	−0.535496	−	0.157236i	0.00279306	−	0.999996i	$-0.499111\pi$
$257$	−8.58465	−	2.52068i	−0.535496	−	0.157236i	−0.538289	+	0.842760i	$0.680929\pi$
$258$		0			0
$259$	−0.150365	+	0.0441513i	−0.00934326	+	0.00274343i
$260$		0			0
$261$	−0.453813	+	0.993712i	−0.0280903	+	0.0615092i
$262$		0			0
$263$	−16.8397	+	10.8222i	−1.03838	+	0.667327i	−0.944586	−	0.328264i	$-0.893536\pi$
$263$	−16.8397	+	10.8222i	−1.03838	+	0.667327i	−0.0937954	+	0.995591i	$0.529900\pi$
$264$		0			0
$265$	0.764964	+	5.32044i	0.0469914	+	0.326832i
$266$		0			0
$267$	20.1152	−	23.2142i	1.23103	−	1.42069i
$268$		0			0
$269$	−21.3404	−	13.7146i	−1.30115	−	0.836196i	−0.307810	−	0.951448i	$-0.599596\pi$
$269$	−21.3404	−	13.7146i	−1.30115	−	0.836196i	−0.993336	+	0.115252i	$0.963232\pi$
$270$		0			0
$271$	13.7243	+	15.8387i	0.833694	+	0.962135i	0.999712	−	0.0239882i	$-0.00763642\pi$
$271$	13.7243	+	15.8387i	0.833694	+	0.962135i	−0.166018	+	0.986123i	$0.553091\pi$
$272$		0			0
$273$	−2.79243	−	6.11456i	−0.169005	−	0.370070i
$274$		0			0
$275$	−3.96414			−0.239047
$276$		0			0
$277$	−16.6596			−1.00098			−0.500488	−	0.865744i	$-0.666846\pi$
$277$	−16.6596			−1.00098			−0.500488	+	0.865744i	$0.666846\pi$
$278$		0			0
$279$	−2.30039	−	5.03714i	−0.137721	−	0.301566i
$280$		0			0
$281$	−15.9331	−	18.3877i	−0.950486	−	1.09692i	−0.995194	−	0.0979194i	$-0.968781\pi$
$281$	−15.9331	−	18.3877i	−0.950486	−	1.09692i	0.0447082	−	0.999000i	$-0.485764\pi$
$282$		0			0
$283$	14.9035	+	9.57790i	0.885921	+	0.569347i	0.902584	−	0.430514i	$-0.141668\pi$
$283$	14.9035	+	9.57790i	0.885921	+	0.569347i	−0.0166625	+	0.999861i	$0.505304\pi$
$284$		0			0
$285$	7.22072	−	8.33316i	0.427719	−	0.493614i
$286$		0			0
$287$	1.17309	+	8.15901i	0.0692452	+	0.481611i
$288$		0			0
$289$	−10.7551	+	6.91191i	−0.632655	+	0.406583i
$290$		0			0
$291$	−3.77456	+	8.26514i	−0.221269	+	0.484511i
$292$		0			0
$293$	−4.16568	+	1.22315i	−0.243362	+	0.0714574i	−0.401139	−	0.916017i	$-0.631385\pi$
$293$	−4.16568	+	1.22315i	−0.243362	+	0.0714574i	0.157777	+	0.987475i	$0.449567\pi$
$294$		0			0
$295$	−8.97063	−	2.63401i	−0.522290	−	0.153358i
$296$		0			0
$297$	−2.26201	+	15.7327i	−0.131255	+	0.912901i
$298$		0			0
$299$	6.20550	+	2.34477i	0.358873	+	0.135601i
$300$		0			0
$301$	0.799356	−	5.55964i	0.0460741	−	0.320452i
$302$		0			0
$303$	8.02268	+	2.35567i	0.460891	+	0.135330i
$304$		0			0
$305$	−6.14484	+	1.80429i	−0.351853	+	0.103313i
$306$		0			0
$307$	0.664753	−	1.45561i	0.0379395	−	0.0830759i	−0.889713	−	0.456520i	$-0.849096\pi$
$307$	0.664753	−	1.45561i	0.0379395	−	0.0830759i	0.927653	+	0.373444i	$0.121823\pi$
$308$		0			0
$309$	1.92760	−	1.23879i	0.109657	−	0.0704724i
$310$		0			0
$311$	1.85417	+	12.8960i	0.105140	+	0.731266i	0.972385	+	0.233384i	$0.0749798\pi$
$311$	1.85417	+	12.8960i	0.105140	+	0.731266i	−0.867245	+	0.497882i	$0.834111\pi$
$312$		0			0
$313$	12.9467	−	14.9413i	0.731791	−	0.844532i	−0.260881	−	0.965371i	$-0.584013\pi$
$313$	12.9467	−	14.9413i	0.731791	−	0.844532i	0.992672	+	0.120839i	$0.0385585\pi$
$314$		0			0
$315$	2.03269	+	1.30633i	0.114529	+	0.0736034i
$316$		0			0
$317$	−4.53048	−	5.22845i	−0.254457	−	0.293659i	0.614121	−	0.789212i	$-0.289511\pi$
$317$	−4.53048	−	5.22845i	−0.254457	−	0.293659i	−0.868578	+	0.495553i	$0.834965\pi$
$318$		0			0
$319$	1.81053	+	3.96450i	0.101370	+	0.221969i
$320$		0			0
$321$	37.2138			2.07707
$322$		0			0
$323$	−11.3283			−0.630323
$324$		0			0
$325$	−0.574612	−	1.25823i	−0.0318738	−	0.0697938i
$326$		0			0
$327$	14.9516	+	17.2550i	0.826823	+	0.954204i
$328$		0			0
$329$	−15.7183	−	10.1015i	−0.866576	−	0.556915i
$330$		0			0
$331$	1.83553	−	2.11831i	0.100890	−	0.116433i	−0.703059	−	0.711131i	$-0.748183\pi$
$331$	1.83553	−	2.11831i	0.100890	−	0.116433i	0.803949	+	0.594698i	$0.202729\pi$
$332$		0			0
$333$	−0.00911286	−	0.0633813i	−0.000499382	−	0.00347328i
$334$		0			0
$335$	−6.99230	+	4.49368i	−0.382030	+	0.245516i
$336$		0			0
$337$	−2.84670	+	6.23340i	−0.155070	+	0.339555i	−0.971182	−	0.238338i	$-0.923397\pi$
$337$	−2.84670	+	6.23340i	−0.155070	+	0.339555i	0.816113	+	0.577893i	$0.196125\pi$
$338$		0			0
$339$	−27.8201	+	8.16872i	−1.51098	+	0.443664i
$340$		0			0
$341$	−21.1977	−	6.22420i	−1.14792	−	0.337059i
$342$		0			0
$343$	2.79855	−	19.4643i	0.151107	−	1.05097i
$344$		0			0
$345$	−9.37360	+	1.99722i	−0.504658	+	0.107527i
$346$		0			0
$347$	−2.79773	+	19.4587i	−0.150190	+	1.04460i	0.765709	+	0.643187i	$0.222388\pi$
$347$	−2.79773	+	19.4587i	−0.150190	+	1.04460i	−0.915899	+	0.401408i	$0.868521\pi$
$348$		0			0
$349$	−0.988890	−	0.290364i	−0.0529341	−	0.0155429i	0.255158	−	0.966899i	$-0.417872\pi$
$349$	−0.988890	−	0.290364i	−0.0529341	−	0.0155429i	−0.308092	+	0.951356i	$0.599691\pi$
$350$		0			0
$351$	−5.32146	+	1.56252i	−0.284039	+	0.0834012i
$352$		0			0
$353$	5.48906	−	12.0194i	0.292153	−	0.639726i	−0.705462	−	0.708748i	$-0.749260\pi$
$353$	5.48906	−	12.0194i	0.292153	−	0.639726i	0.997615	+	0.0690216i	$0.0219877\pi$
$354$		0			0
$355$	−2.94848	+	1.89487i	−0.156489	+	0.100569i
$356$		0			0
$357$	−1.41995	−	9.87597i	−0.0751517	−	0.522692i
$358$		0			0
$359$	−2.53650	+	2.92728i	−0.133871	+	0.154496i	−0.818727	−	0.574183i	$-0.805320\pi$
$359$	−2.53650	+	2.92728i	−0.133871	+	0.154496i	0.684856	+	0.728679i	$0.259865\pi$
$360$		0			0
$361$	9.62698	+	6.18689i	0.506683	+	0.325626i
$362$		0			0
$363$	−6.16962	−	7.12012i	−0.323821	−	0.373709i
$364$		0			0
$365$	−3.72371	−	8.15379i	−0.194908	−	0.426789i
$366$		0			0
$367$	5.49251			0.286707			0.143353	−	0.989672i	$-0.454211\pi$
$367$	5.49251			0.286707			0.143353	+	0.989672i	$0.454211\pi$
$368$		0			0
$369$	−3.36805			−0.175334
$370$		0			0
$371$	−5.42995	−	11.8899i	−0.281909	−	0.617295i
$372$		0			0
$373$	−21.5265	−	24.8430i	−1.11460	−	1.28632i	−0.954167	−	0.299273i	$-0.903256\pi$
$373$	−21.5265	−	24.8430i	−1.11460	−	1.28632i	−0.160435	−	0.987046i	$-0.551290\pi$
$374$		0			0
$375$	1.68117	+	1.08042i	0.0868150	+	0.0557926i
$376$		0			0
$377$	−0.995899	+	1.14933i	−0.0512914	+	0.0591934i
$378$		0			0
$379$	−3.72560	−	25.9121i	−0.191371	−	1.33102i	−0.828382	−	0.560163i	$-0.810739\pi$
$379$	−3.72560	−	25.9121i	−0.191371	−	1.33102i	0.637011	−	0.770855i	$-0.280171\pi$
$380$		0			0
$381$	29.6335	−	19.0443i	1.51817	−	0.975670i
$382$		0			0
$383$	9.32884	−	20.4273i	0.476682	−	1.04379i	−0.506681	−	0.862134i	$-0.669128\pi$
$383$	9.32884	−	20.4273i	0.476682	−	1.04379i	0.983363	−	0.181654i	$-0.0581449\pi$
$384$		0			0
$385$	9.24940	−	2.71587i	0.471393	−	0.138414i
$386$		0			0
$387$	2.20206	+	0.646584i	0.111937	+	0.0328677i
$388$		0			0
$389$	−0.0620187	+	0.431350i	−0.00314447	+	0.0218703i	−0.991333	−	0.131371i	$-0.958062\pi$
$389$	−0.0620187	+	0.431350i	−0.00314447	+	0.0218703i	0.988189	+	0.153241i	$0.0489712\pi$
$390$		0			0
$391$	7.85723	+	5.93437i	0.397357	+	0.300114i
$392$		0			0
$393$	3.63170	−	25.2590i	0.183195	−	1.27415i
$394$		0			0
$395$	−13.0728	−	3.83851i	−0.657762	−	0.193136i
$396$		0			0
$397$	−11.7881	+	3.46130i	−0.591629	+	0.173718i	−0.563823	−	0.825895i	$-0.690670\pi$
$397$	−11.7881	+	3.46130i	−0.591629	+	0.173718i	−0.0278055	+	0.999613i	$0.508852\pi$
$398$		0			0
$399$	−11.1388	+	24.3905i	−0.557636	+	1.22105i
$400$		0			0
$401$	−19.7574	+	12.6973i	−0.986639	+	0.634074i	−0.931246	−	0.364390i	$-0.881277\pi$
$401$	−19.7574	+	12.6973i	−0.986639	+	0.634074i	−0.0553925	+	0.998465i	$0.517641\pi$
$402$		0			0
$403$	−1.09709	−	7.63040i	−0.0546497	−	0.380097i
$404$		0			0
$405$	7.19926	−	8.30839i	0.357734	−	0.412847i
$406$		0			0
$407$	−0.214911	−	0.138115i	−0.0106528	−	0.00684611i
$408$		0			0
$409$	8.71227	+	10.0545i	0.430794	+	0.497163i	0.929095	−	0.369841i	$-0.120588\pi$
$409$	8.71227	+	10.0545i	0.430794	+	0.497163i	−0.498301	+	0.867004i	$0.666042\pi$
$410$		0			0
$411$	−12.4818	−	27.3314i	−0.615684	−	1.34816i
$412$		0			0
$413$	22.7355			1.11874
$414$		0			0
$415$	0.579748			0.0284587
$416$		0			0
$417$	−9.45313	−	20.6995i	−0.462922	−	1.01366i
$418$		0			0
$419$	25.9110	+	29.9029i	1.26584	+	1.46085i	0.826915	+	0.562327i	$0.190094\pi$
$419$	25.9110	+	29.9029i	1.26584	+	1.46085i	0.438921	+	0.898526i	$0.355361\pi$
$420$		0			0
$421$	25.8087	+	16.5863i	1.25784	+	0.808365i	0.987987	−	0.154536i	$-0.0493884\pi$
$421$	25.8087	+	16.5863i	1.25784	+	0.808365i	0.269853	+	0.962901i	$0.413025\pi$
$422$		0			0
$423$	4.99948	−	5.76971i	0.243083	−	0.280533i
$424$		0			0
$425$	−0.292191	−	2.03223i	−0.0141733	−	0.0985777i
$426$		0			0
$427$	13.1014	−	8.41978i	0.634023	−	0.407462i
$428$		0			0
$429$	4.55205	−	9.96761i	0.219775	−	0.481241i
$430$		0			0
$431$	−31.0455	+	9.11579i	−1.49541	+	0.439092i	−0.924263	−	0.381756i	$-0.875320\pi$
$431$	−31.0455	+	9.11579i	−1.49541	+	0.439092i	−0.571147	+	0.820848i	$0.693501\pi$
$432$		0			0
$433$	−9.33933	−	2.74227i	−0.448820	−	0.131785i	0.0495088	−	0.998774i	$-0.484234\pi$
$433$	−9.33933	−	2.74227i	−0.448820	−	0.131785i	−0.498328	+	0.866988i	$0.666053\pi$
$434$		0			0
$435$	0.312685	−	2.17477i	0.0149921	−	0.104272i
$436$		0			0
$437$	−9.14134	−	24.8322i	−0.437290	−	1.18789i
$438$		0			0
$439$	−4.78758	+	33.2983i	−0.228499	+	1.58924i	0.475940	+	0.879478i	$0.342108\pi$
$439$	−4.78758	+	33.2983i	−0.228499	+	1.58924i	−0.704439	+	0.709765i	$0.748801\pi$
$440$		0			0
$441$	1.03582	+	0.304144i	0.0493247	+	0.0144830i
$442$		0			0
$443$	11.5726	−	3.39801i	0.549828	−	0.161444i	0.00499356	−	0.999988i	$-0.498410\pi$
$443$	11.5726	−	3.39801i	0.549828	−	0.161444i	0.544835	+	0.838543i	$0.316592\pi$
$444$		0			0
$445$	−6.38520	+	13.9816i	−0.302687	+	0.662793i
$446$		0			0
$447$	17.3556	−	11.1538i	0.820894	−	0.527556i
$448$		0			0
$449$	2.19719	+	15.2818i	0.103692	+	0.721192i	0.973647	+	0.228061i	$0.0732386\pi$
$449$	2.19719	+	15.2818i	0.103692	+	0.721192i	−0.869955	+	0.493131i	$0.835852\pi$
$450$		0			0
$451$	−8.79944	+	10.1551i	−0.414350	+	0.478185i
$452$		0			0
$453$	−29.1547	−	18.7366i	−1.36981	−	0.880323i
$454$		0			0
$455$	2.20275	+	2.54211i	0.103266	+	0.119176i
$456$		0			0
$457$	−11.7446	−	25.7171i	−0.549390	−	1.20300i	−0.957066	−	0.289869i	$-0.906388\pi$
$457$	−11.7446	−	25.7171i	−0.549390	−	1.20300i	0.407677	−	0.913126i	$-0.366339\pi$
$458$		0			0
$459$	−8.23213			−0.384243
$460$		0			0
$461$	31.5443			1.46916			0.734582	−	0.678520i	$-0.237378\pi$
$461$	31.5443			1.46916			0.734582	+	0.678520i	$0.237378\pi$
$462$		0			0
$463$	−15.7978	−	34.5924i	−0.734186	−	1.60764i	−0.792888	−	0.609368i	$-0.791423\pi$
$463$	−15.7978	−	34.5924i	−0.734186	−	1.60764i	0.0587017	−	0.998276i	$-0.481304\pi$
$464$		0			0
$465$	7.29340	+	8.41703i	0.338223	+	0.390330i
$466$		0			0
$467$	26.7034	+	17.1613i	1.23569	+	0.794129i	0.984767	−	0.173879i	$-0.0556302\pi$
$467$	26.7034	+	17.1613i	1.23569	+	0.794129i	0.250921	+	0.968008i	$0.419267\pi$
$468$		0			0
$469$	13.2363	−	15.2755i	0.611194	−	0.705355i
$470$		0			0
$471$	−1.34864	−	9.37997i	−0.0621419	−	0.432206i
$472$		0			0
$473$	7.70269	−	4.95022i	0.354170	−	0.227611i
$474$		0			0
$475$	−2.29208	+	5.01896i	−0.105168	+	0.230286i
$476$		0			0
$477$	5.12453	−	1.50470i	0.234636	−	0.0688953i
$478$		0			0
$479$	26.0551	+	7.65047i	1.19049	+	0.349559i	0.816209	−	0.577757i	$-0.196072\pi$
$479$	26.0551	+	7.65047i	1.19049	+	0.349559i	0.374279	+	0.927316i	$0.377890\pi$
$480$		0			0
$481$	0.0126860	−	0.0882334i	0.000578434	−	0.00402310i
$482$		0			0
$483$	20.5028	−	11.0820i	0.932911	−	0.504248i
$484$		0			0
$485$	0.647070	−	4.50047i	0.0293819	−	0.204356i
$486$		0			0
$487$	30.2572	+	8.88431i	1.37108	+	0.402587i	0.882657	−	0.470018i	$-0.155753\pi$
$487$	30.2572	+	8.88431i	1.37108	+	0.402587i	0.488427	+	0.872605i	$0.337571\pi$
$488$		0			0
$489$	−42.7328	+	12.5475i	−1.93244	+	0.567417i
$490$		0			0
$491$	6.57992	−	14.4080i	0.296948	−	0.650225i	−0.701074	−	0.713088i	$-0.747296\pi$
$491$	6.57992	−	14.4080i	0.296948	−	0.650225i	0.998022	+	0.0628632i	$0.0200232\pi$
$492$		0			0
$493$	−1.89896	+	1.22039i	−0.0855250	+	0.0549636i
$494$		0			0
$495$	0.560558	+	3.89876i	0.0251952	+	0.175236i
$496$		0			0
$497$	5.58140	−	6.44128i	0.250360	−	0.288931i
$498$		0			0
$499$	−26.2531	−	16.8719i	−1.17525	−	0.755289i	−0.200745	−	0.979644i	$-0.564336\pi$
$499$	−26.2531	−	16.8719i	−1.17525	−	0.755289i	−0.974508	+	0.224355i	$0.927973\pi$
$500$		0			0
$501$	−11.0304	−	12.7298i	−0.492802	−	0.568724i
$502$		0			0
$503$	8.82583	+	19.3259i	0.393525	+	0.861699i	0.997886	+	0.0649883i	$0.0207010\pi$
$503$	8.82583	+	19.3259i	0.393525	+	0.861699i	−0.604361	+	0.796710i	$0.706572\pi$
$504$		0			0
$505$	−4.18403			−0.186187
$506$		0			0
$507$	−22.1557			−0.983969
$508$		0			0
$509$	4.99889	+	10.9460i	0.221572	+	0.485175i	0.987474	−	0.157782i	$-0.0504345\pi$
$509$	4.99889	+	10.9460i	0.221572	+	0.485175i	−0.765902	+	0.642957i	$0.777707\pi$
$510$		0			0
$511$	14.2747	+	16.4738i	0.631474	+	0.728760i
$512$		0			0
$513$	18.6111	+	11.9606i	0.821699	+	0.528074i
$514$		0			0
$515$	−0.750853	+	0.866531i	−0.0330865	+	0.0381839i
$516$		0			0
$517$	−4.33465	−	30.1481i	−0.190638	−	1.32591i
$518$		0			0
$519$	−2.09319	+	1.34521i	−0.0918809	+	0.0590483i
$520$		0			0
$521$	17.0912	−	37.4246i	0.748780	−	1.63960i	−0.0197647	−	0.999805i	$-0.506292\pi$
$521$	17.0912	−	37.4246i	0.748780	−	1.63960i	0.768545	−	0.639796i	$-0.220981\pi$
$522$		0			0
$523$	−28.5604	+	8.38608i	−1.24886	+	0.366697i	−0.838336	−	0.545154i	$-0.816471\pi$
$523$	−28.5604	+	8.38608i	−1.24886	+	0.366697i	−0.410521	+	0.911851i	$0.634653\pi$
$524$		0			0
$525$	−4.66282	−	1.36913i	−0.203502	−	0.0597536i
$526$		0			0
$527$	1.62841	−	11.3258i	0.0709347	−	0.493361i
$528$		0			0
$529$	−6.66808	+	22.0122i	−0.289917	+	0.957052i
$530$		0			0
$531$	−1.32206	+	9.19516i	−0.0573727	+	0.399036i
$532$		0			0
$533$	−4.49875	−	1.32095i	−0.194863	−	0.0572168i
$534$		0			0
$535$	−17.8674	+	5.24635i	−0.772477	+	0.226820i
$536$		0			0
$537$	−21.2922	+	46.6234i	−0.918826	+	2.01195i
$538$		0			0
$539$	3.62324	−	2.32851i	0.156064	−	0.100296i
$540$		0			0
$541$	2.45801	+	17.0958i	0.105678	+	0.735006i	0.971908	+	0.235361i	$0.0756273\pi$
$541$	2.45801	+	17.0958i	0.105678	+	0.735006i	−0.866230	+	0.499645i	$0.833464\pi$
$542$		0			0
$543$	1.92172	−	2.21778i	0.0824689	−	0.0951742i
$544$		0			0
$545$	−9.61127	−	6.17679i	−0.411702	−	0.264585i
$546$		0			0
$547$	−17.8088	−	20.5525i	−0.761449	−	0.878759i	0.234176	−	0.972194i	$-0.424761\pi$
$547$	−17.8088	−	20.5525i	−0.761449	−	0.878759i	−0.995625	+	0.0934348i	$0.970215\pi$
$548$		0			0
$549$	2.64346	+	5.78836i	0.112820	+	0.247041i
$550$		0			0
$551$	6.06627			0.258432
$552$		0			0
$553$	33.1321			1.40892
$554$		0			0
$555$	0.0534994	+	0.117147i	0.00227092	+	0.00497263i
$556$		0			0
$557$	8.39493	+	9.68827i	0.355705	+	0.410505i	0.905196	−	0.424994i	$-0.139724\pi$
$557$	8.39493	+	9.68827i	0.355705	+	0.410505i	−0.549491	+	0.835499i	$0.685178\pi$
$558$		0			0
$559$	2.68774	+	1.72730i	0.113679	+	0.0730571i
$560$		0			0
$561$	10.6512	−	12.2921i	0.449693	−	0.518973i
$562$		0			0
$563$	−0.519286	−	3.61171i	−0.0218853	−	0.152215i	0.975948	−	0.218001i	$-0.0699537\pi$
$563$	−0.519286	−	3.61171i	−0.0218853	−	0.152215i	−0.997834	+	0.0657858i	$0.979045\pi$
$564$		0			0
$565$	12.2056	−	7.84409i	0.513495	−	0.330003i
$566$		0			0
$567$	−11.1057	+	24.3180i	−0.466394	+	1.02126i
$568$		0			0
$569$	−27.6023	+	8.10475i	−1.15715	+	0.339769i	−0.803323	−	0.595543i	$-0.796937\pi$
$569$	−27.6023	+	8.10475i	−1.15715	+	0.339769i	−0.353823	+	0.935312i	$0.615119\pi$
$570$		0			0
$571$	0.0347198	+	0.0101946i	0.00145298	+	0.000426633i	0.282459	−	0.959279i	$-0.408850\pi$
$571$	0.0347198	+	0.0101946i	0.00145298	+	0.000426633i	−0.281006	+	0.959706i	$0.590668\pi$
$572$		0			0
$573$	−2.37890	+	16.5456i	−0.0993800	+	0.691203i
$574$		0			0
$575$	4.21898	−	2.28040i	0.175943	−	0.0950994i
$576$		0			0
$577$	4.09990	−	28.5154i	0.170681	−	1.18711i	−0.706769	−	0.707444i	$-0.749848\pi$
$577$	4.09990	−	28.5154i	0.170681	−	1.18711i	0.877450	−	0.479668i	$-0.159243\pi$
$578$		0			0
$579$	−43.3829	−	12.7384i	−1.80293	−	0.529388i
$580$		0			0
$581$	−1.35271	+	0.397191i	−0.0561198	+	0.0164783i
$582$		0			0
$583$	8.85160	−	19.3823i	0.366596	−	0.802733i
$584$		0			0
$585$	−1.15622	+	0.743058i	−0.0478039	+	0.0307217i
$586$		0			0
$587$	−2.43111	−	16.9087i	−0.100343	−	0.697898i	−0.976444	−	0.215771i	$-0.930773\pi$
$587$	−2.43111	−	16.9087i	−0.100343	−	0.697898i	0.876101	−	0.482127i	$-0.160136\pi$
$588$		0			0
$589$	−20.1370	+	23.2393i	−0.829730	+	0.957559i
$590$		0			0
$591$	−2.55031	−	1.63898i	−0.104906	−	0.0674187i
$592$		0			0
$593$	21.1426	+	24.3998i	0.868221	+	1.00198i	0.999943	+	0.0106933i	$0.00340386\pi$
$593$	21.1426	+	24.3998i	0.868221	+	1.00198i	−0.131722	+	0.991287i	$0.542051\pi$
$594$		0			0
$595$	2.07406	+	4.54156i	0.0850282	+	0.186186i
$596$		0			0
$597$	42.7555			1.74987
$598$		0			0
$599$	−12.8678			−0.525763			−0.262881	−	0.964828i	$-0.584673\pi$
$599$	−12.8678			−0.525763			−0.262881	+	0.964828i	$0.584673\pi$
$600$		0			0
$601$	−4.13972	−	9.06471i	−0.168863	−	0.369757i	0.806215	−	0.591623i	$-0.201513\pi$
$601$	−4.13972	−	9.06471i	−0.168863	−	0.369757i	−0.975077	+	0.221866i	$0.928785\pi$
$602$		0			0
$603$	5.40833	+	6.24155i	0.220244	+	0.254176i
$604$		0			0
$605$	3.96600	+	2.54879i	0.161241	+	0.103623i
$606$		0			0
$607$	−15.3791	+	17.7484i	−0.624218	+	0.720386i	−0.976502	−	0.215507i	$-0.930860\pi$
$607$	−15.3791	+	17.7484i	−0.624218	+	0.720386i	0.352284	+	0.935893i	$0.385405\pi$
$608$		0			0
$609$	0.760379	+	5.28855i	0.0308121	+	0.214303i
$610$		0			0
$611$	8.94076	−	5.74588i	0.361704	−	0.232453i
$612$		0			0
$613$	−1.39823	+	3.06169i	−0.0564738	+	0.123660i	−0.935765	−	0.352624i	$-0.885289\pi$
$613$	−1.39823	+	3.06169i	−0.0564738	+	0.123660i	0.879291	+	0.476284i	$0.158017\pi$
$614$		0			0
$615$	6.49954	−	1.90844i	0.262087	−	0.0769556i
$616$		0			0
$617$	9.99059	+	2.93350i	0.402206	+	0.118098i	0.476578	−	0.879132i	$-0.341877\pi$
$617$	9.99059	+	2.93350i	0.402206	+	0.118098i	−0.0743718	+	0.997231i	$0.523695\pi$
$618$		0			0
$619$	5.54344	−	38.5555i	0.222810	−	1.54968i	−0.504527	−	0.863396i	$-0.668333\pi$
$619$	5.54344	−	38.5555i	0.222810	−	1.54968i	0.727337	−	0.686281i	$-0.240758\pi$
$620$		0			0
$621$	−6.64290	−	18.0453i	−0.266571	−	0.724132i
$622$		0			0
$623$	5.31943	−	36.9975i	0.213119	−	1.48227i
$624$		0			0
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$		0			0
$627$	−41.9394	+	12.3145i	−1.67490	+	0.491795i
$628$		0			0
$629$	0.0549644	−	0.120355i	0.00219157	−	0.00479888i
$630$		0			0
$631$	−38.1033	+	24.4875i	−1.51687	+	0.974832i	−0.524515	+	0.851401i	$0.675753\pi$
$631$	−38.1033	+	24.4875i	−1.51687	+	0.974832i	−0.992353	+	0.123430i	$0.960610\pi$
$632$		0			0
$633$	4.51069	+	31.3725i	0.179284	+	1.24695i
$634$		0			0
$635$	−11.5431	+	13.3214i	−0.458074	+	0.528645i
$636$		0			0
$637$	1.26427	+	0.812499i	0.0500923	+	0.0321924i
$638$		0			0
$639$	2.28056	+	2.63191i	0.0902176	+	0.104117i
$640$		0			0
$641$	3.71443	+	8.13347i	0.146711	+	0.321253i	0.968693	−	0.248261i	$-0.0798590\pi$
$641$	3.71443	+	8.13347i	0.146711	+	0.321253i	−0.821982	+	0.569513i	$0.807132\pi$
$642$		0			0
$643$	−10.0281			−0.395470			−0.197735	−	0.980256i	$-0.563359\pi$
$643$	−10.0281			−0.395470			−0.197735	+	0.980256i	$0.563359\pi$
$644$		0			0
$645$	−4.61583			−0.181748
$646$		0			0
$647$	10.3949	+	22.7616i	0.408665	+	0.894851i	0.996318	+	0.0857382i	$0.0273248\pi$
$647$	10.3949	+	22.7616i	0.408665	+	0.894851i	−0.587653	+	0.809113i	$0.699948\pi$
$648$		0			0
$649$	24.2705	+	28.0097i	0.952701	+	1.09948i
$650$		0			0
$651$	−22.7840	−	14.6424i	−0.892977	−	0.573882i
$652$		0			0
$653$	−15.4884	+	17.8745i	−0.606107	+	0.699485i	−0.973007	−	0.230776i	$-0.925874\pi$
$653$	−15.4884	+	17.8745i	−0.606107	+	0.699485i	0.366900	+	0.930260i	$0.380419\pi$
$654$		0			0
$655$	1.81730	+	12.6396i	0.0710077	+	0.493869i
$656$		0			0
$657$	−7.49277	+	4.81531i	−0.292321	+	0.187863i
$658$		0			0
$659$	0.187104	−	0.409701i	0.00728855	−	0.0159597i	−0.905953	−	0.423379i	$-0.860844\pi$
$659$	0.187104	−	0.409701i	0.00728855	−	0.0159597i	0.913241	+	0.407419i	$0.133571\pi$
$660$		0			0
$661$	3.67355	−	1.07865i	0.142884	−	0.0419547i	−0.209508	−	0.977807i	$-0.567186\pi$
$661$	3.67355	−	1.07865i	0.142884	−	0.0419547i	0.352393	+	0.935852i	$0.385368\pi$
$662$		0			0
$663$	5.44546	+	1.59893i	0.211484	+	0.0620973i
$664$		0			0
$665$	1.90951	−	13.2809i	0.0740475	−	0.515012i
$666$		0			0
$667$	−4.20753	−	3.17784i	−0.162916	−	0.123046i
$668$		0			0
$669$	−3.59193	+	24.9824i	−0.138872	+	0.965875i
$670$		0			0
$671$	24.3590	+	7.15245i	0.940369	+	0.276117i
$672$		0			0
$673$	1.27743	−	0.375089i	0.0492415	−	0.0144586i	−0.257019	−	0.966406i	$-0.582740\pi$
$673$	1.27743	−	0.375089i	0.0492415	−	0.0144586i	0.306261	+	0.951948i	$0.400922\pi$
$674$		0			0
$675$	−1.66563	+	3.64722i	−0.0641101	+	0.140382i
$676$		0			0
$677$	−33.5184	+	21.5410i	−1.28822	+	0.827886i	−0.991878	−	0.127196i	$-0.959402\pi$
$677$	−33.5184	+	21.5410i	−1.28822	+	0.827886i	−0.296339	+	0.955083i	$0.595766\pi$
$678$		0			0
$679$	1.57353	+	10.9441i	0.0603865	+	0.419997i
$680$		0			0
$681$	−5.18363	+	5.98223i	−0.198637	+	0.229240i
$682$		0			0
$683$	31.4203	+	20.1926i	1.20226	+	0.772648i	0.979346	−	0.202190i	$-0.0648058\pi$
$683$	31.4203	+	20.1926i	1.20226	+	0.772648i	0.222917	+	0.974837i	$0.428442\pi$
$684$		0			0
$685$	9.84605	+	11.3630i	0.376198	+	0.434156i
$686$		0			0
$687$	7.99907	+	17.5155i	0.305184	+	0.668259i
$688$		0			0
$689$	7.43504			0.283253
$690$		0			0
$691$	4.24076			0.161326			0.0806631	−	0.996741i	$-0.474296\pi$
$691$	4.24076			0.161326			0.0806631	+	0.996741i	$0.474296\pi$
$692$		0			0
$693$	−3.97901	−	8.71282i	−0.151150	−	0.330973i
$694$		0			0
$695$	7.45691	+	8.60574i	0.282857	+	0.326434i
$696$		0			0
$697$	−5.85464	−	3.76255i	−0.221760	−	0.142517i
$698$		0			0
$699$	17.0695	−	19.6992i	0.645627	−	0.745093i
$700$		0			0
$701$	−2.98097	−	20.7331i	−0.112590	−	0.783080i	−0.965384	−	0.260833i	$-0.916003\pi$
$701$	−2.98097	−	20.7331i	−0.112590	−	0.783080i	0.852794	−	0.522247i	$-0.174906\pi$
$702$		0			0
$703$	−0.299129	+	0.192238i	−0.0112819	+	0.00725041i
$704$		0			0
$705$	−6.37853	+	13.9670i	−0.240229	+	0.526029i
$706$		0			0
$707$	9.76246	−	2.86652i	0.367155	−	0.107806i
$708$		0			0
$709$	7.66142	+	2.24960i	0.287731	+	0.0844854i	0.422413	−	0.906403i	$-0.361183\pi$
$709$	7.66142	+	2.24960i	0.287731	+	0.0844854i	−0.134682	+	0.990889i	$0.543001\pi$
$710$		0			0
$711$	−1.92662	+	13.4000i	−0.0722541	+	0.502538i
$712$		0			0
$713$	26.1409	−	5.56980i	0.978984	−	0.208591i
$714$		0			0
$715$	−0.780354	+	5.42748i	−0.0291836	+	0.202976i
$716$		0			0
$717$	8.75566	+	2.57089i	0.326986	+	0.0960118i
$718$		0			0
$719$	1.22780	−	0.360514i	0.0457891	−	0.0134449i	−0.258758	−	0.965942i	$-0.583313\pi$
$719$	1.22780	−	0.360514i	0.0457891	−	0.0134449i	0.304547	+	0.952497i	$0.401495\pi$
$720$		0			0
$721$	1.15827	−	2.53627i	0.0431364	−	0.0944555i
$722$		0			0
$723$	−27.4496	+	17.6408i	−1.02086	+	0.656068i
$724$		0			0
$725$	0.156467	+	1.08825i	0.00581105	+	0.0404168i
$726$		0			0
$727$	16.3968	−	18.9229i	0.608122	−	0.701810i	−0.365284	−	0.930896i	$-0.619028\pi$
$727$	16.3968	−	18.9229i	0.608122	−	0.701810i	0.973406	+	0.229086i	$0.0735737\pi$
$728$		0			0
$729$	11.0328	+	7.09033i	0.408621	+	0.262605i
$730$		0			0
$731$	3.10550	+	3.58394i	0.114861	+	0.132557i
$732$		0			0
$733$	11.4497	+	25.0713i	0.422903	+	0.926028i	0.994425	+	0.105442i	$0.0336256\pi$
$733$	11.4497	+	25.0713i	0.422903	+	0.926028i	−0.571523	+	0.820586i	$0.693647\pi$
$734$		0			0
$735$	−2.17122			−0.0800868
$736$		0			0
$737$	32.9490			1.21369
$738$		0			0
$739$	−18.7923	−	41.1494i	−0.691286	−	1.51371i	−0.850226	−	0.526417i	$-0.823535\pi$
$739$	−18.7923	−	41.1494i	−0.691286	−	1.51371i	0.158940	−	0.987288i	$-0.449192\pi$
$740$		0			0
$741$	−9.98788	−	11.5266i	−0.366914	−	0.423441i
$742$		0			0
$743$	28.6357	+	18.4030i	1.05054	+	0.675142i	0.947572	−	0.319543i	$-0.103529\pi$
$743$	28.6357	+	18.4030i	1.05054	+	0.675142i	0.102969	+	0.994685i	$0.467166\pi$
$744$		0			0
$745$	−6.76051	+	7.80204i	−0.247686	+	0.285845i
$746$		0			0
$747$	−0.0819806	−	0.570187i	−0.00299951	−	0.0208621i
$748$		0			0
$749$	38.0952	−	24.4823i	1.39197	−	0.894564i
$750$		0			0
$751$	−6.01594	+	13.1731i	−0.219525	+	0.480692i	−0.987067	−	0.160306i	$-0.948752\pi$
$751$	−6.01594	+	13.1731i	−0.219525	+	0.480692i	0.767543	+	0.640998i	$0.221479\pi$
$752$		0			0
$753$	−3.13798	+	0.921395i	−0.114354	+	0.0335775i
$754$		0			0
$755$	16.6395	+	4.88580i	0.605574	+	0.177812i
$756$		0			0
$757$	4.01110	−	27.8978i	0.145786	−	1.01396i	−0.777234	−	0.629211i	$-0.783378\pi$
$757$	4.01110	−	27.8978i	0.145786	−	1.01396i	0.923020	−	0.384752i	$-0.125713\pi$
$758$		0			0
$759$	35.5399	+	13.4289i	1.29002	+	0.487436i
$760$		0			0
$761$	2.60515	−	18.1192i	0.0944367	−	0.656822i	−0.886534	−	0.462664i	$-0.846894\pi$
$761$	2.60515	−	18.1192i	0.0944367	−	0.656822i	0.980970	−	0.194158i	$-0.0621973\pi$
$762$		0			0
$763$	26.6575	+	7.82734i	0.965065	+	0.283369i
$764$		0			0
$765$	−1.95740	+	0.574744i	−0.0707699	+	0.0207799i
$766$		0			0
$767$	−5.37225	+	11.7636i	−0.193981	+	0.424758i
$768$		0			0
$769$	−43.8623	+	28.1886i	−1.58172	+	1.01651i	−0.606547	+	0.795048i	$0.707446\pi$
$769$	−43.8623	+	28.1886i	−1.58172	+	1.01651i	−0.975169	+	0.221460i	$0.928918\pi$
$770$		0			0
$771$	−2.54457	−	17.6979i	−0.0916405	−	0.637374i
$772$		0			0
$773$	4.41755	−	5.09813i	0.158888	−	0.183367i	−0.670724	−	0.741707i	$-0.734016\pi$
$773$	4.41755	−	5.09813i	0.158888	−	0.183367i	0.829612	+	0.558341i	$0.188562\pi$
$774$		0			0
$775$	−4.68840	−	3.01305i	−0.168412	−	0.108232i
$776$		0			0
$777$	−0.205087	−	0.236683i	−0.00735747	−	0.00849097i
$778$		0			0
$779$	7.76940	+	17.0126i	0.278368	+	0.609540i
$780$		0			0
$781$	13.8938			0.497158
$782$		0			0
$783$	4.40829			0.157539
$784$		0			0
$785$	1.96990	+	4.31347i	0.0703086	+	0.153954i
$786$		0			0
$787$	15.6455	+	18.0559i	0.557702	+	0.643622i	0.962660	−	0.270713i	$-0.0872594\pi$
$787$	15.6455	+	18.0559i	0.557702	+	0.643622i	−0.404958	+	0.914335i	$0.632714\pi$
$788$		0			0
$789$	−33.6526	−	21.6272i	−1.19806	−	0.769948i
$790$		0			0
$791$	−23.1050	+	26.6646i	−0.821519	+	0.948083i
$792$		0			0
$793$	1.26070	+	8.76836i	0.0447688	+	0.311374i
$794$		0			0
$795$	−9.03652	+	5.80742i	−0.320492	+	0.205968i
$796$		0			0
$797$	−21.6368	+	47.3780i	−0.766415	+	1.67821i	−0.0320248	+	0.999487i	$0.510196\pi$
$797$	−21.6368	+	47.3780i	−0.766415	+	1.67821i	−0.734390	+	0.678728i	$0.762532\pi$
$798$		0			0
$799$	15.1361	−	4.44435i	0.535475	−	0.157230i
$800$		0			0
$801$	14.6540	+	4.30279i	0.517772	+	0.152032i
$802$		0			0
$803$	−5.05700	+	35.1722i	−0.178458	+	1.24120i
$804$		0			0
$805$	−8.28168	+	8.21126i	−0.291891	+	0.289409i
$806$		0			0
$807$	7.21454	−	50.1783i	0.253964	−	1.76636i
$808$		0			0
$809$	−46.5765	−	13.6761i	−1.63754	−	0.480826i	−0.671888	−	0.740653i	$-0.734516\pi$
$809$	−46.5765	−	13.6761i	−1.63754	−	0.480826i	−0.965655	+	0.259827i	$0.916334\pi$
$810$		0			0
$811$	26.9336	−	7.90841i	0.945765	−	0.277702i	0.227743	−	0.973721i	$-0.426866\pi$
$811$	26.9336	−	7.90841i	0.945765	−	0.277702i	0.718023	+	0.696020i	$0.245047\pi$
$812$		0			0
$813$	−17.3984	+	38.0971i	−0.610187	+	1.33612i
$814$		0			0
$815$	18.7484	−	12.0488i	0.656726	−	0.422052i
$816$		0			0
$817$	−1.81370	−	12.6145i	−0.0634533	−	0.441327i
$818$		0			0
$819$	2.18870	−	2.52589i	0.0764794	−	0.0882619i
$820$		0			0
$821$	−19.7062	−	12.6644i	−0.687750	−	0.441990i	0.149535	−	0.988756i	$-0.452222\pi$
$821$	−19.7062	−	12.6644i	−0.687750	−	0.441990i	−0.837285	+	0.546766i	$0.815859\pi$
$822$		0			0
$823$	−36.7097	−	42.3653i	−1.27962	−	1.47676i	−0.800904	−	0.598792i	$-0.795647\pi$
$823$	−36.7097	−	42.3653i	−1.27962	−	1.47676i	−0.478717	−	0.877969i	$-0.658898\pi$
$824$		0			0
$825$	−3.29090	−	7.20606i	−0.114574	−	0.250883i
$826$		0			0
$827$	45.7517			1.59094			0.795471	−	0.605991i	$-0.207223\pi$
$827$	45.7517			1.59094			0.795471	+	0.605991i	$0.207223\pi$
$828$		0			0
$829$	46.4964			1.61489			0.807444	−	0.589945i	$-0.200850\pi$
$829$	46.4964			1.61489			0.807444	+	0.589945i	$0.200850\pi$
$830$		0			0
$831$	−13.8302	−	30.2840i	−0.479765	−	1.05054i
$832$		0			0
$833$	1.46078	+	1.68583i	0.0506132	+	0.0584107i
$834$		0			0
$835$	7.09065	+	4.55688i	0.245382	+	0.157697i
$836$		0			0
$837$	−14.6333	+	16.8877i	−0.505801	+	0.583726i
$838$		0			0
$839$	−0.0105590	−	0.0734397i	−0.000364538	−	0.00253542i	0.989638	−	0.143582i	$-0.0458622\pi$
$839$	−0.0105590	−	0.0734397i	−0.000364538	−	0.00253542i	−0.990003	+	0.141047i	$0.954953\pi$
$840$		0			0
$841$	−23.3795	+	15.0251i	−0.806188	+	0.518106i
$842$		0			0
$843$	20.1983	−	44.2282i	0.695668	−	1.52330i
$844$		0			0
$845$	10.6376	−	3.12348i	0.365945	−	0.107451i
$846$		0			0
$847$	−11.0000	−	3.22988i	−0.377963	−	0.110980i
$848$		0			0
$849$	−5.03843	+	35.0430i	−0.172918	+	1.20267i
$850$		0			0
$851$	0.308179	+	0.0233645i	0.0105642	+	0.000800924i
$852$		0			0
$853$	2.57734	−	17.9258i	0.0882465	−	0.613768i	−0.896923	−	0.442186i	$-0.854203\pi$
$853$	2.57734	−	17.9258i	0.0882465	−	0.613768i	0.985170	−	0.171582i	$-0.0548878\pi$
$854$		0			0
$855$	5.26031	+	1.54457i	0.179899	+	0.0528230i
$856$		0			0
$857$	−28.3815	+	8.33355i	−0.969493	+	0.284669i	−0.727880	−	0.685704i	$-0.759494\pi$
$857$	−28.3815	+	8.33355i	−0.969493	+	0.284669i	−0.241612	+	0.970373i	$0.577676\pi$
$858$		0			0
$859$	8.14817	−	17.8420i	0.278012	−	0.608761i	−0.718189	−	0.695848i	$-0.755029\pi$
$859$	8.14817	−	17.8420i	0.278012	−	0.608761i	0.996201	+	0.0870871i	$0.0277558\pi$
$860$		0			0
$861$	−13.8577	+	8.90580i	−0.472269	+	0.303509i
$862$		0			0
$863$	−1.25316	−	8.71593i	−0.0426581	−	0.296694i	−0.999971	−	0.00763936i	$-0.997568\pi$
$863$	−1.25316	−	8.71593i	−0.0426581	−	0.296694i	0.957313	−	0.289054i	$-0.0933408\pi$
$864$		0			0
$865$	0.815357	−	0.940972i	0.0277230	−	0.0319940i
$866$		0			0
$867$	−21.4931	−	13.8128i	−0.729945	−	0.469107i
$868$		0			0
$869$	35.3691	+	40.8181i	1.19981	+	1.38466i
$870$		0			0
$871$	4.77604	+	10.4581i	0.161830	+	0.354358i
$872$		0			0
$873$	−4.51775			−0.152903
$874$		0			0
$875$	2.43177			0.0822089
$876$		0			0
$877$	−13.4364	−	29.4215i	−0.453714	−	0.993495i	−0.988876	−	0.148745i	$-0.952477\pi$
$877$	−13.4364	−	29.4215i	−0.453714	−	0.993495i	0.535162	−	0.844750i	$-0.320251\pi$
$878$		0			0
$879$	−5.68168	−	6.55700i	−0.191638	−	0.221162i
$880$		0			0
$881$	14.8976	+	9.57410i	0.501913	+	0.322560i	0.766981	−	0.641670i	$-0.221758\pi$
$881$	14.8976	+	9.57410i	0.501913	+	0.322560i	−0.265068	+	0.964230i	$0.585394\pi$
$882$		0			0
$883$	−23.5667	+	27.1974i	−0.793082	+	0.915265i	−0.997981	−	0.0635177i	$-0.979768\pi$
$883$	−23.5667	+	27.1974i	−0.793082	+	0.915265i	0.204899	+	0.978783i	$0.434314\pi$
$884$		0			0
$885$	−2.65898	−	18.4936i	−0.0893806	−	0.621655i
$886$		0			0
$887$	−1.39401	+	0.895875i	−0.0468062	+	0.0300805i	−0.563835	−	0.825888i	$-0.690674\pi$
$887$	−1.39401	+	0.895875i	−0.0468062	+	0.0300805i	0.517028	+	0.855968i	$0.327038\pi$
$888$		0			0
$889$	17.8065	−	38.9908i	0.597211	−	1.30771i
$890$		0			0
$891$	−41.8148	+	12.2779i	−1.40085	+	0.411326i
$892$		0			0
$893$	−40.6766	−	11.9437i	−1.36119	−	0.399682i
$894$		0			0
$895$	3.65010	−	25.3870i	0.122009	−	0.848595i
$896$		0			0
$897$	0.889260	+	13.2270i	0.0296915	+	0.441636i
$898$		0			0
$899$	−0.872009	+	6.06496i	−0.0290831	+	0.202278i
$900$		0			0
$901$	10.5888	+	3.10917i	0.352766	+	0.103581i
$902$		0			0
$903$	10.7700	−	3.16235i	0.358403	−	0.105237i
$904$		0			0
$905$	−0.610014	+	1.33575i	−0.0202776	+	0.0444017i
$906$		0			0
$907$	−1.56788	+	1.00762i	−0.0520608	+	0.0334574i	−0.566412	−	0.824122i	$-0.691669\pi$
$907$	−1.56788	+	1.00762i	−0.0520608	+	0.0334574i	0.514352	+	0.857579i	$0.328033\pi$
$908$		0			0
$909$	0.591651	+	4.11503i	0.0196238	+	0.136487i
$910$		0			0
$911$	39.2178	−	45.2598i	1.29934	−	1.49952i	0.554723	−	0.832035i	$-0.312824\pi$
$911$	39.2178	−	45.2598i	1.29934	−	1.49952i	0.744621	−	0.667488i	$-0.232630\pi$
$912$		0			0
$913$	−1.93337	−	1.24250i	−0.0639852	−	0.0411208i
$914$		0			0
$915$	−8.38110	−	9.67231i	−0.277071	−	0.319757i
$916$		0			0
$917$	−12.8997	−	28.2465i	−0.425987	−	0.932782i
$918$		0			0
$919$	−58.5807			−1.93240			−0.966200	−	0.257795i	$-0.917004\pi$
$919$	−58.5807			−1.93240			−0.966200	+	0.257795i	$0.917004\pi$
$920$		0			0
$921$	3.19788			0.105374
$922$		0			0
$923$	2.01394	+	4.40991i	0.0662896	+	0.145154i
$924$		0			0
$925$	−0.0422019	−	0.0487036i	−0.00138759	−	0.00160136i
$926$		0			0
$927$	0.958416	+	0.615937i	0.0314785	+	0.0202300i
$928$		0			0
$929$	18.1957	−	20.9989i	0.596981	−	0.688953i	−0.374186	−	0.927354i	$-0.622078\pi$
$929$	18.1957	−	20.9989i	0.596981	−	0.688953i	0.971167	+	0.238401i	$0.0766233\pi$
$930$		0			0
$931$	−0.853138	−	5.93370i	−0.0279605	−	0.194469i
$932$		0			0
$933$	−21.9033	+	14.0764i	−0.717081	+	0.460840i
$934$		0			0
$935$	−3.38102	+	7.40339i	−0.110571	+	0.242117i
$936$		0			0
$937$	20.0237	−	5.87950i	0.654146	−	0.192075i	0.0622147	−	0.998063i	$-0.480184\pi$
$937$	20.0237	−	5.87950i	0.654146	−	0.192075i	0.591932	+	0.805988i	$0.298365\pi$
$938$		0			0
$939$	37.9084	+	11.1309i	1.23709	+	0.363244i
$940$		0			0
$941$	3.07349	−	21.3766i	0.100193	−	0.696857i	−0.876372	−	0.481634i	$-0.840043\pi$
$941$	3.07349	−	21.3766i	0.100193	−	0.696857i	0.976565	−	0.215222i	$-0.0690476\pi$
$942$		0			0
$943$	3.52332	−	15.8699i	0.114735	−	0.516794i
$944$		0			0
$945$	1.38762	−	9.65109i	0.0451392	−	0.313950i
$946$		0			0
$947$	38.1855	+	11.2123i	1.24086	+	0.364350i	0.835339	−	0.549735i	$-0.185271\pi$
$947$	38.1855	+	11.2123i	1.24086	+	0.364350i	0.405523	+	0.914085i	$0.367090\pi$
$948$		0			0
$949$	−11.8968	+	3.49320i	−0.386185	+	0.113394i
$950$		0			0
$951$	5.74329	−	12.5760i	0.186239	−	0.407806i
$952$		0			0
$953$	−36.2268	+	23.2816i	−1.17350	+	0.754164i	−0.974180	−	0.225771i	$-0.927510\pi$
$953$	−36.2268	+	23.2816i	−1.17350	+	0.754164i	−0.199321	+	0.979934i	$0.563874\pi$
$954$		0			0
$955$	−1.19040	−	8.27941i	−0.0385204	−	0.267916i
$956$		0			0
$957$	−5.70368	+	6.58239i	−0.184374	+	0.212779i
$958$		0			0
$959$	−30.7584	−	19.7672i	−0.993239	−	0.638316i
$960$		0			0
$961$	−0.0389772	−	0.0449821i	−0.00125733	−	0.00145103i
$962$		0			0
$963$	7.68642	+	16.8309i	0.247691	+	0.542368i
$964$		0			0
$965$	22.6252			0.728332
$966$		0			0
$967$	−40.8900			−1.31493			−0.657467	−	0.753483i	$-0.728372\pi$
$967$	−40.8900			−1.31493			−0.657467	+	0.753483i	$0.728372\pi$
$968$		0			0
$969$	−9.40438	−	20.5927i	−0.302112	−	0.661533i
$970$		0			0
$971$	3.60821	+	4.16409i	0.115793	+	0.133632i	0.810687	−	0.585480i	$-0.199094\pi$
$971$	3.60821	+	4.16409i	0.115793	+	0.133632i	−0.694894	+	0.719112i	$0.744549\pi$
$972$		0			0
$973$	−23.2949	−	14.9707i	−0.746799	−	0.479939i
$974$		0			0
$975$	1.81019	−	2.08908i	0.0579726	−	0.0669040i
$976$		0			0
$977$	1.44822	+	10.0726i	0.0463328	+	0.322251i	0.999786	+	0.0207091i	$0.00659238\pi$
$977$	1.44822	+	10.0726i	0.0463328	+	0.322251i	−0.953453	+	0.301542i	$0.902499\pi$
$978$		0			0
$979$	51.2587	−	32.9420i	1.63824	−	1.05283i
$980$		0			0
$981$	−4.71582	+	10.3262i	−0.150565	+	0.329690i
$982$		0			0
$983$	−33.4294	+	9.81574i	−1.06623	+	0.313074i	−0.767358	−	0.641219i	$-0.778429\pi$
$983$	−33.4294	+	9.81574i	−1.06623	+	0.313074i	−0.298873	+	0.954293i	$0.596611\pi$
$984$		0			0
$985$	1.45554	+	0.427385i	0.0463773	+	0.0136176i
$986$		0			0
$987$	5.31388	−	36.9588i	0.169143	−	1.17641i
$988$		0			0
$989$	−5.35021	+	9.69948i	−0.170127	+	0.308426i
$990$		0			0
$991$	−1.05370	+	7.32867i	−0.0334720	+	0.232803i	−0.999689	−	0.0249258i	$-0.992065\pi$
$991$	−1.05370	+	7.32867i	−0.0334720	+	0.232803i	0.966217	+	0.257729i	$0.0829741\pi$
$992$		0			0
$993$	5.37449	+	1.57809i	0.170554	+	0.0500793i
$994$		0			0
$995$	−20.5282	+	6.02762i	−0.650788	+	0.191088i
$996$		0			0
$997$	17.7193	−	38.7999i	0.561176	−	1.22880i	−0.390188	−	0.920735i	$-0.627590\pi$
$997$	17.7193	−	38.7999i	0.561176	−	1.22880i	0.951364	−	0.308069i	$-0.0996827\pi$
$998$		0			0
$999$	−0.217373	+	0.139697i	−0.00687739	+	0.00441983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.a.261.3	yes	30
23.3	even	11	inner	460.2.m.a.141.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.141.3	✓	30	23.3	even	11	inner
460.2.m.a.261.3	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.830167 + 1.81781i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(2.04574 + 1.31472i) q^{7} +(-0.650684 + 0.750930i) q^{9} +O(q^{10})\)	\(q+(0.830167 + 1.81781i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(2.04574 + 1.31472i) q^{7} +(-0.650684 + 0.750930i) q^{9} +(0.564156 + 3.92379i) q^{11} +(-1.16364 + 0.747828i) q^{13} +(0.830167 - 1.81781i) q^{15} +(-1.96996 + 0.578433i) q^{17} +(5.29407 + 1.55448i) q^{19} +(-0.691603 + 4.81020i) q^{21} +(-2.85761 - 3.85150i) q^{23} +(-0.142315 + 0.989821i) q^{25} +(3.84714 + 1.12962i) q^{27} +(1.05491 - 0.309749i) q^{29} +(-2.31515 + 5.06948i) q^{31} +(-6.66437 + 4.28293i) q^{33} +(-0.346077 - 2.40702i) q^{35} +(-0.0422019 + 0.0487036i) q^{37} +(-2.32543 - 1.49446i) q^{39} +(2.21976 + 2.56174i) q^{41} +(-0.959509 - 2.10103i) q^{43} +0.993622 q^{45} -7.68342 q^{47} +(-0.451339 - 0.988295i) q^{49} +(-2.68688 - 3.10083i) q^{51} +(-4.52187 - 2.90603i) q^{53} +(2.59596 - 2.99590i) q^{55} +(1.56921 + 10.9141i) q^{57} +(7.86517 - 5.05464i) q^{59} +(2.66042 - 5.82552i) q^{61} +(-2.31839 + 0.680740i) q^{63} +(1.32719 + 0.389700i) q^{65} +(1.18289 - 8.22716i) q^{67} +(4.62901 - 8.39200i) q^{69} +(0.498794 - 3.46919i) q^{71} +(8.60074 + 2.52541i) q^{73} +(-1.91746 + 0.563016i) q^{75} +(-4.00455 + 8.76875i) q^{77} +(11.4618 - 7.36605i) q^{79} +(1.56455 + 10.8817i) q^{81} +(-0.379654 + 0.438144i) q^{83} +(1.72720 + 1.11001i) q^{85} +(1.43882 + 1.66048i) q^{87} +(-6.38520 - 13.9816i) q^{89} -3.36369 q^{91} -11.1373 q^{93} +(-2.29208 - 5.01896i) q^{95} +(2.97749 + 3.43621i) q^{97} +(-3.31358 - 2.12951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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