LMFDB - Embedded newform 460.2.m.b.41.5

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:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			41.5
Character	$\chi$	$=$	460.41
Dual form			460.2.m.b.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.89657 - 2.18876i) q^{3} +(0.142315 - 0.989821i) q^{5} +(1.51786 + 3.32365i) q^{7} +(-0.766744 - 5.33282i) q^{9} +O(q^{10})$	\(q+(1.89657 - 2.18876i) q^{3} +(0.142315 - 0.989821i) q^{5} +(1.51786 + 3.32365i) q^{7} +(-0.766744 - 5.33282i) q^{9} +(0.489096 - 0.143611i) q^{11} +(2.48838 - 5.44878i) q^{13} +(-1.89657 - 2.18876i) q^{15} +(-3.94157 + 2.53309i) q^{17} +(6.00247 + 3.85756i) q^{19} +(10.1534 + 2.98131i) q^{21} +(-4.18151 - 2.34839i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(-5.81728 - 3.73854i) q^{27} +(-5.84609 + 3.75705i) q^{29} +(-6.23773 - 7.19872i) q^{31} +(0.613274 - 1.34288i) q^{33} +(3.50583 - 1.02941i) q^{35} +(-0.102619 - 0.713734i) q^{37} +(-7.20670 - 15.7805i) q^{39} +(-1.77104 + 12.3179i) q^{41} +(-2.54642 + 2.93873i) q^{43} -5.38766 q^{45} +8.44687 q^{47} +(-4.15873 + 4.79943i) q^{49} +(-1.93114 + 13.4313i) q^{51} +(1.80761 + 3.95812i) q^{53} +(-0.0725441 - 0.504555i) q^{55} +(19.8274 - 5.82185i) q^{57} +(1.29155 - 2.82810i) q^{59} +(0.960353 + 1.10831i) q^{61} +(16.5606 - 10.6429i) q^{63} +(-5.03919 - 3.23849i) q^{65} +(-1.34198 - 0.394041i) q^{67} +(-13.0706 + 4.69843i) q^{69} +(-2.01732 - 0.592338i) q^{71} +(13.4738 + 8.65909i) q^{73} +(-2.43639 + 1.56577i) q^{75} +(1.21969 + 1.40760i) q^{77} +(0.881489 - 1.93019i) q^{79} +(-3.70740 + 1.08859i) q^{81} +(0.539284 + 3.75080i) q^{83} +(1.94637 + 4.26195i) q^{85} +(-2.86424 + 19.9212i) q^{87} +(-5.21512 + 6.01857i) q^{89} +21.8869 q^{91} -27.5866 q^{93} +(4.67253 - 5.39239i) q^{95} +(1.22716 - 8.53510i) q^{97} +(-1.14087 - 2.49815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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
$3$	1.89657	−	2.18876i	1.09499	−	1.26368i	0.132843	−	0.991137i	$-0.457589\pi$
$3$	1.89657	−	2.18876i	1.09499	−	1.26368i	0.962143	−	0.272545i	$-0.0878653\pi$
$4$		0			0
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$6$		0			0
$7$	1.51786	+	3.32365i	0.573697	+	1.25622i	0.944805	+	0.327632i	$0.106251\pi$
$7$	1.51786	+	3.32365i	0.573697	+	1.25622i	−0.371108	+	0.928590i	$0.621022\pi$
$8$		0			0
$9$	−0.766744	−	5.33282i	−0.255581	−	1.77761i
$10$		0			0
$11$	0.489096	−	0.143611i	0.147468	−	0.0433005i	−0.207166	−	0.978306i	$-0.566424\pi$
$11$	0.489096	−	0.143611i	0.147468	−	0.0433005i	0.354633	+	0.935005i	$0.384606\pi$
$12$		0			0
$13$	2.48838	−	5.44878i	0.690151	−	1.51122i	−0.161367	−	0.986895i	$-0.551590\pi$
$13$	2.48838	−	5.44878i	0.690151	−	1.51122i	0.851518	−	0.524326i	$-0.175683\pi$
$14$		0			0
$15$	−1.89657	−	2.18876i	−0.489693	−	0.565136i
$16$		0			0
$17$	−3.94157	+	2.53309i	−0.955971	+	0.614365i	−0.922880	−	0.385087i	$-0.874171\pi$
$17$	−3.94157	+	2.53309i	−0.955971	+	0.614365i	−0.0330906	+	0.999452i	$0.510535\pi$
$18$		0			0
$19$	6.00247	+	3.85756i	1.37706	+	0.884984i	0.999165	−	0.0408635i	$-0.0130109\pi$
$19$	6.00247	+	3.85756i	1.37706	+	0.884984i	0.377897	+	0.925848i	$0.376647\pi$
$20$		0			0
$21$	10.1534	+	2.98131i	2.21566	+	0.650575i
$22$		0			0
$23$	−4.18151	−	2.34839i	−0.871906	−	0.489674i
$23$	−4.18151	−	2.34839i	−0.871906	−	0.489674i
$24$		0			0
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$		0			0
$27$	−5.81728	−	3.73854i	−1.11954	−	0.719482i
$28$		0			0
$29$	−5.84609	+	3.75705i	−1.08559	+	0.697667i	−0.955843	−	0.293879i	$-0.905054\pi$
$29$	−5.84609	+	3.75705i	−1.08559	+	0.697667i	−0.129749	+	0.991547i	$0.541417\pi$
$30$		0			0
$31$	−6.23773	−	7.19872i	−1.12033	−	1.29293i	−0.951625	−	0.307261i	$-0.900587\pi$
$31$	−6.23773	−	7.19872i	−1.12033	−	1.29293i	−0.168704	−	0.985667i	$-0.553958\pi$
$32$		0			0
$33$	0.613274	−	1.34288i	0.106757	−	0.233766i
$34$		0			0
$35$	3.50583	−	1.02941i	0.592594	−	0.174001i
$36$		0			0
$37$	−0.102619	−	0.713734i	−0.0168705	−	0.117337i	0.979646	−	0.200733i	$-0.0643324\pi$
$37$	−0.102619	−	0.713734i	−0.0168705	−	0.117337i	−0.996516	+	0.0833960i	$0.973423\pi$
$38$		0			0
$39$	−7.20670	−	15.7805i	−1.15400	−	2.52690i
$40$		0			0
$41$	−1.77104	+	12.3179i	−0.276590	+	1.92373i	0.0953009	+	0.995449i	$0.469619\pi$
$41$	−1.77104	+	12.3179i	−0.276590	+	1.92373i	−0.371891	+	0.928277i	$0.621290\pi$
$42$		0			0
$43$	−2.54642	+	2.93873i	−0.388326	+	0.448152i	−0.915930	−	0.401339i	$-0.868545\pi$
$43$	−2.54642	+	2.93873i	−0.388326	+	0.448152i	0.527604	+	0.849490i	$0.323091\pi$
$44$		0			0
$45$	−5.38766			−0.803145
$46$		0			0
$47$	8.44687			1.23210			0.616051	−	0.787706i	$-0.288731\pi$
$47$	8.44687			1.23210			0.616051	+	0.787706i	$0.288731\pi$
$48$		0			0
$49$	−4.15873	+	4.79943i	−0.594104	+	0.685633i
$50$		0			0
$51$	−1.93114	+	13.4313i	−0.270413	+	1.88076i
$52$		0			0
$53$	1.80761	+	3.95812i	0.248295	+	0.543690i	0.992209	−	0.124585i	$-0.0397601\pi$
$53$	1.80761	+	3.95812i	0.248295	+	0.543690i	−0.743914	+	0.668275i	$0.767033\pi$
$54$		0			0
$55$	−0.0725441	−	0.504555i	−0.00978185	−	0.0680342i
$56$		0			0
$57$	19.8274	−	5.82185i	2.62620	−	0.771123i
$58$		0			0
$59$	1.29155	−	2.82810i	0.168146	−	0.368187i	−0.806736	−	0.590912i	$-0.798768\pi$
$59$	1.29155	−	2.82810i	0.168146	−	0.368187i	0.974881	+	0.222725i	$0.0714952\pi$
$60$		0			0
$61$	0.960353	+	1.10831i	0.122961	+	0.141904i	0.813892	−	0.581016i	$-0.197345\pi$
$61$	0.960353	+	1.10831i	0.122961	+	0.141904i	−0.690931	+	0.722920i	$0.742799\pi$
$62$		0			0
$63$	16.5606	−	10.6429i	2.08644	−	1.34088i
$64$		0			0
$65$	−5.03919	−	3.23849i	−0.625034	−	0.401685i
$66$		0			0
$67$	−1.34198	−	0.394041i	−0.163949	−	0.0481397i	0.198728	−	0.980055i	$-0.436319\pi$
$67$	−1.34198	−	0.394041i	−0.163949	−	0.0481397i	−0.362677	+	0.931915i	$0.618137\pi$
$68$		0			0
$69$	−13.0706	+	4.69843i	−1.57352	+	0.565625i
$70$		0			0
$71$	−2.01732	−	0.592338i	−0.239412	−	0.0702976i	0.159826	−	0.987145i	$-0.448907\pi$
$71$	−2.01732	−	0.592338i	−0.239412	−	0.0702976i	−0.399237	+	0.916848i	$0.630725\pi$
$72$		0			0
$73$	13.4738	+	8.65909i	1.57699	+	1.01347i	0.976941	+	0.213507i	$0.0684887\pi$
$73$	13.4738	+	8.65909i	1.57699	+	1.01347i	0.600049	+	0.799963i	$0.295148\pi$
$74$		0			0
$75$	−2.43639	+	1.56577i	−0.281330	+	0.180800i
$76$		0			0
$77$	1.21969	+	1.40760i	0.138997	+	0.160411i
$78$		0			0
$79$	0.881489	−	1.93019i	0.0991753	−	0.217164i	−0.853540	−	0.521027i	$-0.825549\pi$
$79$	0.881489	−	1.93019i	0.0991753	−	0.217164i	0.952716	+	0.303863i	$0.0982765\pi$
$80$		0			0
$81$	−3.70740	+	1.08859i	−0.411933	+	0.120954i
$82$		0			0
$83$	0.539284	+	3.75080i	0.0591941	+	0.411704i	0.997776	+	0.0666488i	$0.0212307\pi$
$83$	0.539284	+	3.75080i	0.0591941	+	0.411704i	−0.938582	+	0.345055i	$0.887860\pi$
$84$		0			0
$85$	1.94637	+	4.26195i	0.211113	+	0.462273i
$86$		0			0
$87$	−2.86424	+	19.9212i	−0.307079	+	2.13578i
$88$		0			0
$89$	−5.21512	+	6.01857i	−0.552801	+	0.637967i	−0.961533	−	0.274688i	$-0.911426\pi$
$89$	−5.21512	+	6.01857i	−0.552801	+	0.637967i	0.408732	+	0.912654i	$0.365971\pi$
$90$		0			0
$91$	21.8869			2.29437
$92$		0			0
$93$	−27.5866			−2.86059
$94$		0			0
$95$	4.67253	−	5.39239i	0.479392	−	0.553248i
$96$		0			0
$97$	1.22716	−	8.53510i	0.124599	−	0.866608i	−0.827641	−	0.561258i	$-0.810317\pi$
$97$	1.22716	−	8.53510i	0.124599	−	0.866608i	0.952240	−	0.305350i	$-0.0987735\pi$
$98$		0			0
$99$	−1.14087	−	2.49815i	−0.114661	−	0.251073i
$100$		0			0
$101$	0.000590789		0.00410903i	5.87857e−5		0.000408863i	0.989851	−	0.142110i	$-0.0453888\pi$
$101$	0.000590789		0.00410903i	5.87857e−5		0.000408863i	−0.989792	+	0.142519i	$0.954480\pi$
$102$		0			0
$103$	5.86412	−	1.72186i	0.577809	−	0.169660i	0.0202465	−	0.999795i	$-0.493555\pi$
$103$	5.86412	−	1.72186i	0.577809	−	0.169660i	0.557562	+	0.830135i	$0.311737\pi$
$104$		0			0
$105$	4.39595	−	9.62578i	0.429000	−	0.939380i
$106$		0			0
$107$	2.70420	+	3.12082i	0.261425	+	0.301701i	0.871254	−	0.490832i	$-0.163307\pi$
$107$	2.70420	+	3.12082i	0.261425	+	0.301701i	−0.609829	+	0.792533i	$0.708762\pi$
$108$		0			0
$109$	4.69578	−	3.01780i	0.449775	−	0.289053i	−0.296078	−	0.955164i	$-0.595679\pi$
$109$	4.69578	−	3.01780i	0.449775	−	0.289053i	0.745852	+	0.666111i	$0.232042\pi$
$110$		0			0
$111$	−1.75682	−	1.12904i	−0.166750	−	0.107164i
$112$		0			0
$113$	−9.79293	−	2.87546i	−0.921242	−	0.270501i	−0.213476	−	0.976948i	$-0.568479\pi$
$113$	−9.79293	−	2.87546i	−0.921242	−	0.270501i	−0.707766	+	0.706447i	$0.750297\pi$
$114$		0			0
$115$	−2.91958	+	3.80474i	−0.272252	+	0.354794i
$116$		0			0
$117$	−30.9653	−	9.09224i	−2.86275	−	0.840578i
$118$		0			0
$119$	−14.4019	−	9.25552i	−1.32022	−	0.848452i
$120$		0			0
$121$	−9.03520	+	5.80657i	−0.821382	+	0.527870i
$122$		0			0
$123$	23.6019	+	27.2381i	2.12811	+	2.45597i
$124$		0			0
$125$	−0.415415	+	0.909632i	−0.0371558	+	0.0813600i
$126$		0			0
$127$	−2.15417	+	0.632522i	−0.191152	+	0.0561273i	−0.375907	−	0.926657i	$-0.622669\pi$
$127$	−2.15417	+	0.632522i	−0.191152	+	0.0561273i	0.184755	+	0.982785i	$0.440851\pi$
$128$		0			0
$129$	1.60270	+	11.1470i	0.141110	+	0.981440i
$130$		0			0
$131$	−3.53443	−	7.73931i	−0.308804	−	0.676187i	0.690064	−	0.723748i	$-0.257582\pi$
$131$	−3.53443	−	7.73931i	−0.308804	−	0.676187i	−0.998868	+	0.0475613i	$0.984855\pi$
$132$		0			0
$133$	−3.71025	+	25.8054i	−0.321720	+	2.23761i
$134$		0			0
$135$	−4.52837	+	5.22602i	−0.389740	+	0.449784i
$136$		0			0
$137$	1.74951			0.149470			0.0747352	−	0.997203i	$-0.476189\pi$
$137$	1.74951			0.149470			0.0747352	+	0.997203i	$0.476189\pi$
$138$		0			0
$139$	−5.92395			−0.502463			−0.251232	−	0.967927i	$-0.580836\pi$
$139$	−5.92395			−0.502463			−0.251232	+	0.967927i	$0.580836\pi$
$140$		0			0
$141$	16.0201	−	18.4882i	1.34914	−	1.55699i
$142$		0			0
$143$	0.434546	−	3.02233i	0.0363386	−	0.252740i
$144$		0			0
$145$	2.88683	+	6.32127i	0.239738	+	0.524953i
$146$		0			0
$147$	2.61747	+	18.2049i	0.215886	+	1.50152i
$148$		0			0
$149$	−18.6438	+	5.47432i	−1.52736	+	0.448474i	−0.934242	−	0.356641i	$-0.883922\pi$
$149$	−18.6438	+	5.47432i	−1.52736	+	0.448474i	−0.593119	+	0.805114i	$0.702104\pi$
$150$		0			0
$151$	−4.45852	+	9.76279i	−0.362829	+	0.794484i	0.636894	+	0.770951i	$0.280219\pi$
$151$	−4.45852	+	9.76279i	−0.362829	+	0.794484i	−0.999723	+	0.0235331i	$0.992508\pi$
$152$		0			0
$153$	16.5307	+	19.0775i	1.33643	+	1.54232i
$154$		0			0
$155$	−8.01317	+	5.14975i	−0.643633	+	0.413638i
$156$		0			0
$157$	−4.39622	−	2.82528i	−0.350857	−	0.225482i	0.353327	−	0.935500i	$-0.385050\pi$
$157$	−4.39622	−	2.82528i	−0.350857	−	0.225482i	−0.704184	+	0.710018i	$0.748687\pi$
$158$		0			0
$159$	12.0917	+	3.55043i	0.958931	+	0.281567i
$160$		0			0
$161$	1.45829	−	17.4624i	0.114929	−	1.37623i
$162$		0			0
$163$	14.8057	+	4.34736i	1.15967	+	0.340511i	0.804306	−	0.594215i	$-0.202537\pi$
$163$	14.8057	+	4.34736i	1.15967	+	0.340511i	0.355368	+	0.934726i	$0.384355\pi$
$164$		0			0
$165$	−1.24194	−	0.798144i	−0.0966846	−	0.0621354i
$166$		0			0
$167$	−3.98798	+	2.56292i	−0.308599	+	0.198325i	−0.685769	−	0.727820i	$-0.740534\pi$
$167$	−3.98798	+	2.56292i	−0.308599	+	0.198325i	0.377169	+	0.926144i	$0.376897\pi$
$168$		0			0
$169$	−14.9840	−	17.2925i	−1.15262	−	1.33019i
$170$		0			0
$171$	15.9693	−	34.9679i	1.22120	−	2.67406i
$172$		0			0
$173$	9.37682	−	2.75328i	0.712906	−	0.209328i	0.0948834	−	0.995488i	$-0.469752\pi$
$173$	9.37682	−	2.75328i	0.712906	−	0.209328i	0.618023	+	0.786160i	$0.287934\pi$
$174$		0			0
$175$	−0.519996	−	3.61665i	−0.0393080	−	0.273393i
$176$		0			0
$177$	−3.74052	−	8.19059i	−0.281155	−	0.615643i
$178$		0			0
$179$	0.714491	−	4.96939i	0.0534035	−	0.371430i	−0.945541	−	0.325502i	$-0.894467\pi$
$179$	0.714491	−	4.96939i	0.0534035	−	0.371430i	0.998945	−	0.0459275i	$-0.0146243\pi$
$180$		0			0
$181$	−13.5341	+	15.6192i	−1.00598	+	1.16096i	−0.0190497	+	0.999819i	$0.506064\pi$
$181$	−13.5341	+	15.6192i	−1.00598	+	1.16096i	−0.986931	+	0.161145i	$0.948481\pi$
$182$		0			0
$183$	4.24720			0.313962
$184$		0			0
$185$	−0.721074			−0.0530144
$186$		0			0
$187$	−1.56402	+	1.80498i	−0.114373	+	0.131993i
$188$		0			0
$189$	3.59578	−	25.0092i	0.261554	−	1.81915i
$190$		0			0
$191$	−11.2503	−	24.6347i	−0.814042	−	1.78250i	−0.588959	−	0.808163i	$-0.700462\pi$
$191$	−11.2503	−	24.6347i	−0.814042	−	1.78250i	−0.225083	−	0.974340i	$-0.572265\pi$
$192$		0			0
$193$	1.73750	+	12.0846i	0.125068	+	0.869865i	0.951680	+	0.307093i	$0.0993562\pi$
$193$	1.73750	+	12.0846i	0.125068	+	0.869865i	−0.826612	+	0.562772i	$0.809735\pi$
$194$		0			0
$195$	−16.6455	+	4.88755i	−1.19201	+	0.350005i
$196$		0			0
$197$	6.29508	−	13.7843i	0.448506	−	0.982091i	−0.541453	−	0.840731i	$-0.682125\pi$
$197$	6.29508	−	13.7843i	0.448506	−	0.982091i	0.989958	−	0.141359i	$-0.0451473\pi$
$198$		0			0
$199$	0.0816220	+	0.0941968i	0.00578603	+	0.00667744i	0.758635	−	0.651516i	$-0.225867\pi$
$199$	0.0816220	+	0.0941968i	0.00578603	+	0.00667744i	−0.752849	+	0.658193i	$0.771321\pi$
$200$		0			0
$201$	−3.40762	+	2.18995i	−0.240355	+	0.154467i
$202$		0			0
$203$	−21.3607	−	13.7277i	−1.49923	−	0.963494i
$204$		0			0
$205$	11.9404	+	3.50603i	0.833956	+	0.244871i
$206$		0			0
$207$	−9.31742	+	24.0999i	−0.647605	+	1.67506i
$208$		0			0
$209$	3.48977	+	1.02469i	0.241393	+	0.0708793i
$210$		0			0
$211$	−9.72567	−	6.25031i	−0.669543	−	0.430289i	0.161218	−	0.986919i	$-0.448458\pi$
$211$	−9.72567	−	6.25031i	−0.669543	−	0.430289i	−0.830761	+	0.556630i	$0.812094\pi$
$212$		0			0
$213$	−5.12248	+	3.29202i	−0.350986	+	0.225565i
$214$		0			0
$215$	2.54642	+	2.93873i	0.173665	+	0.200420i
$216$		0			0
$217$	14.4580	−	31.6587i	0.981475	−	2.14913i
$218$		0			0
$219$	44.5068	−	13.0684i	3.00749	−	0.883078i
$220$		0			0
$221$	3.99417	+	27.7800i	0.268677	+	1.86869i
$222$		0			0
$223$	−5.30029	−	11.6060i	−0.354934	−	0.777197i	−0.999916	−	0.0129988i	$-0.995862\pi$
$223$	−5.30029	−	11.6060i	−0.354934	−	0.777197i	0.644982	−	0.764198i	$-0.276865\pi$
$224$		0			0
$225$	−0.766744	+	5.33282i	−0.0511163	+	0.355522i
$226$		0			0
$227$	14.3723	−	16.5865i	0.953920	−	1.10088i	−0.0408932	−	0.999164i	$-0.513020\pi$
$227$	14.3723	−	16.5865i	0.953920	−	1.10088i	0.994813	−	0.101719i	$-0.0324342\pi$
$228$		0			0
$229$	5.94303			0.392727			0.196363	−	0.980531i	$-0.437087\pi$
$229$	5.94303			0.392727			0.196363	+	0.980531i	$0.437087\pi$
$230$		0			0
$231$	5.39414			0.354908
$232$		0			0
$233$	6.16983	−	7.12036i	0.404199	−	0.466470i	−0.516760	−	0.856130i	$-0.672862\pi$
$233$	6.16983	−	7.12036i	0.404199	−	0.466470i	0.920959	+	0.389660i	$0.127407\pi$
$234$		0			0
$235$	1.20211	−	8.36089i	0.0784173	−	0.545404i
$236$		0			0
$237$	−2.55292	−	5.59012i	−0.165830	−	0.363117i
$238$		0			0
$239$	−2.17935	−	15.1577i	−0.140970	−	0.980470i	−0.930378	−	0.366601i	$-0.880521\pi$
$239$	−2.17935	−	15.1577i	−0.140970	−	0.980470i	0.789408	−	0.613869i	$-0.210388\pi$
$240$		0			0
$241$	−8.04569	+	2.36243i	−0.518268	+	0.152177i	−0.530397	−	0.847749i	$-0.677957\pi$
$241$	−8.04569	+	2.36243i	−0.518268	+	0.152177i	0.0121290	+	0.999926i	$0.496139\pi$
$242$		0			0
$243$	3.96912	−	8.69116i	0.254619	−	0.557538i
$244$		0			0
$245$	4.15873	+	4.79943i	0.265691	+	0.306624i
$246$		0			0
$247$	35.9554	−	23.1071i	2.28779	−	1.47027i
$248$		0			0
$249$	9.23240	+	5.93330i	0.585080	+	0.376008i
$250$		0			0
$251$	14.6733	+	4.30847i	0.926172	+	0.271949i	0.709833	−	0.704370i	$-0.248770\pi$
$251$	14.6733	+	4.30847i	0.926172	+	0.271949i	0.216338	+	0.976318i	$0.430589\pi$
$252$		0			0
$253$	−2.38242	−	0.548076i	−0.149781	−	0.0344572i
$254$		0			0
$255$	13.0198	+	3.82296i	0.815332	+	0.239403i
$256$		0			0
$257$	−3.32174	−	2.13475i	−0.207204	−	0.133162i	0.432923	−	0.901431i	$-0.357482\pi$
$257$	−3.32174	−	2.13475i	−0.207204	−	0.133162i	−0.640127	+	0.768269i	$0.721118\pi$
$258$		0			0
$259$	2.21644	−	1.42442i	0.137723	−	0.0885092i
$260$		0			0
$261$	24.5182	+	28.2955i	1.51764	+	1.75145i
$262$		0			0
$263$	−8.51989	+	18.6560i	−0.525359	+	1.15038i	0.442012	+	0.897009i	$0.354265\pi$
$263$	−8.51989	+	18.6560i	−0.525359	+	1.15038i	−0.967371	+	0.253366i	$0.918462\pi$
$264$		0			0
$265$	4.17508	−	1.22592i	0.256473	−	0.0753074i
$266$		0			0
$267$	3.28236	+	22.8293i	0.200877	+	1.39713i
$268$		0			0
$269$	2.53126	+	5.54269i	0.154334	+	0.337944i	0.970967	−	0.239213i	$-0.0768894\pi$
$269$	2.53126	+	5.54269i	0.154334	+	0.337944i	−0.816633	+	0.577157i	$0.804162\pi$
$270$		0			0
$271$	−0.907536	+	6.31205i	−0.0551289	+	0.383430i	0.943513	+	0.331335i	$0.107499\pi$
$271$	−0.907536	+	6.31205i	−0.0551289	+	0.383430i	−0.998642	+	0.0520949i	$0.983410\pi$
$272$		0			0
$273$	41.5100	−	47.9051i	2.51230	−	2.89935i
$274$		0			0
$275$	−0.509744			−0.0307387
$276$		0			0
$277$	20.2641			1.21755			0.608777	−	0.793341i	$-0.291660\pi$
$277$	20.2641			1.21755			0.608777	+	0.793341i	$0.291660\pi$
$278$		0			0
$279$	−33.6068	+	38.7843i	−2.01198	+	2.32195i
$280$		0			0
$281$	1.34753	−	9.37228i	0.0803870	−	0.559104i	−0.909331	−	0.416073i	$-0.863406\pi$
$281$	1.34753	−	9.37228i	0.0803870	−	0.559104i	0.989718	−	0.143031i	$-0.0456848\pi$
$282$		0			0
$283$	−4.15928	−	9.10756i	−0.247244	−	0.541388i	0.744799	−	0.667289i	$-0.232545\pi$
$283$	−4.15928	−	9.10756i	−0.247244	−	0.541388i	−0.992043	+	0.125901i	$0.959818\pi$
$284$		0			0
$285$	−2.94086	−	20.4541i	−0.174201	−	1.21160i
$286$		0			0
$287$	−43.6284	+	12.8105i	−2.57530	+	0.756178i
$288$		0			0
$289$	2.05735	−	4.50497i	0.121021	−	0.264998i
$290$		0			0
$291$	−16.3539	−	18.8734i	−0.958683	−	1.10638i
$292$		0			0
$293$	−18.3290	+	11.7793i	−1.07079	+	0.688155i	−0.952412	−	0.304814i	$-0.901406\pi$
$293$	−18.3290	+	11.7793i	−1.07079	+	0.688155i	−0.118378	+	0.992969i	$0.537769\pi$
$294$		0			0
$295$	−2.61551	−	1.68088i	−0.152281	−	0.0978649i
$296$		0			0
$297$	−3.38210	−	0.993075i	−0.196250	−	0.0576241i
$298$		0			0
$299$	−23.2011	+	16.9405i	−1.34175	+	0.979692i
$300$		0			0
$301$	−13.6324	−	4.00284i	−0.785760	−	0.230720i
$302$		0			0
$303$	0.0101142	+	0.00649997i	0.000581043	+	0.000373414i
$304$		0			0
$305$	1.23370	−	0.792850i	0.0706414	−	0.0453984i
$306$		0			0
$307$	−11.7682	−	13.5812i	−0.671645	−	0.775119i	0.312988	−	0.949757i	$-0.398670\pi$
$307$	−11.7682	−	13.5812i	−0.671645	−	0.775119i	−0.984633	+	0.174638i	$0.944125\pi$
$308$		0			0
$309$	7.35299	−	16.1008i	0.418297	−	0.915942i
$310$		0			0
$311$	−9.26590	+	2.72071i	−0.525421	+	0.154278i	−0.533677	−	0.845688i	$-0.679190\pi$
$311$	−9.26590	+	2.72071i	−0.525421	+	0.154278i	0.00825601	+	0.999966i	$0.497372\pi$
$312$		0			0
$313$	−1.29755	−	9.02466i	−0.0733419	−	0.510104i	−0.993068	−	0.117543i	$-0.962498\pi$
$313$	−1.29755	−	9.02466i	−0.0733419	−	0.510104i	0.919726	−	0.392561i	$-0.128411\pi$
$314$		0			0
$315$	−8.17772	−	17.9067i	−0.460762	−	1.00893i
$316$		0			0
$317$	1.11405	−	7.74841i	0.0625715	−	0.435194i	−0.934322	−	0.356430i	$-0.883994\pi$
$317$	1.11405	−	7.74841i	0.0625715	−	0.435194i	0.996893	−	0.0787637i	$-0.0250973\pi$
$318$		0			0
$319$	−2.31974	+	2.67712i	−0.129881	+	0.149890i
$320$		0			0
$321$	11.9594			0.667511
$322$		0			0
$323$	−33.4307			−1.86013
$324$		0			0
$325$	−3.92268	+	4.52701i	−0.217591	+	0.251113i
$326$		0			0
$327$	2.30066	−	16.0014i	0.127227	−	0.884881i
$328$		0			0
$329$	12.8212	+	28.0744i	0.706854	+	1.54779i
$330$		0			0
$331$	−0.709819	−	4.93690i	−0.0390152	−	0.271356i	0.960971	−	0.276650i	$-0.0892242\pi$
$331$	−0.709819	−	4.93690i	−0.0390152	−	0.271356i	−0.999986	+	0.00529327i	$0.998315\pi$
$332$		0			0
$333$	−3.72754	+	1.09450i	−0.204268	+	0.0599784i
$334$		0			0
$335$	−0.581014	+	1.27224i	−0.0317442	+	0.0695100i
$336$		0			0
$337$	16.1745	+	18.6664i	0.881083	+	1.01682i	0.999715	+	0.0238859i	$0.00760383\pi$
$337$	16.1745	+	18.6664i	0.881083	+	1.01682i	−0.118631	+	0.992938i	$0.537851\pi$
$338$		0			0
$339$	−24.8667	+	15.9809i	−1.35057	+	0.867961i
$340$		0			0
$341$	−4.08466	−	2.62505i	−0.221197	−	0.142155i
$342$		0			0
$343$	2.27685	+	0.668543i	0.122938	+	0.0360979i
$344$		0			0
$345$	2.79047	+	13.6062i	0.150234	+	0.732535i
$346$		0			0
$347$	5.08111	+	1.49195i	0.272768	+	0.0800920i	0.415256	−	0.909705i	$-0.363692\pi$
$347$	5.08111	+	1.49195i	0.272768	+	0.0800920i	−0.142488	+	0.989797i	$0.545510\pi$
$348$		0			0
$349$	−29.1908	−	18.7598i	−1.56255	−	1.00419i	−0.981758	−	0.190133i	$-0.939108\pi$
$349$	−29.1908	−	18.7598i	−1.56255	−	1.00419i	−0.580788	−	0.814055i	$-0.697255\pi$
$350$		0			0
$351$	−34.8461	+	22.3942i	−1.85995	+	1.19531i
$352$		0			0
$353$	−16.2468	−	18.7498i	−0.864729	−	0.997951i	−0.999975	−	0.00713863i	$-0.997728\pi$
$353$	−16.2468	−	18.7498i	−0.864729	−	0.997951i	0.135245	−	0.990812i	$-0.456818\pi$
$354$		0			0
$355$	−0.873404	+	1.91249i	−0.0463555	+	0.101504i
$356$		0			0
$357$	−47.5723	+	13.9685i	−2.51779	+	0.739291i
$358$		0			0
$359$	−3.68312	−	25.6167i	−0.194388	−	1.35200i	−0.820224	−	0.572042i	$-0.806151\pi$
$359$	−3.68312	−	25.6167i	−0.194388	−	1.35200i	0.625836	−	0.779954i	$-0.284758\pi$
$360$		0			0
$361$	13.2561	+	29.0268i	0.697688	+	1.52772i
$362$		0			0
$363$	−4.42671	+	30.7885i	−0.232342	+	1.61598i
$364$		0			0
$365$	10.4885	−	12.1044i	0.548992	−	0.633571i
$366$		0			0
$367$	29.9451			1.56312			0.781561	−	0.623829i	$-0.214424\pi$
$367$	29.9451			1.56312			0.781561	+	0.623829i	$0.214424\pi$
$368$		0			0
$369$	67.0468			3.49032
$370$		0			0
$371$	−10.4117	+	12.0158i	−0.540549	+	0.623827i
$372$		0			0
$373$	3.91765	−	27.2479i	0.202848	−	1.41084i	−0.592931	−	0.805254i	$-0.702029\pi$
$373$	3.91765	−	27.2479i	0.202848	−	1.41084i	0.795779	−	0.605587i	$-0.207062\pi$
$374$		0			0
$375$	1.20310	+	2.63443i	0.0621279	+	0.136041i
$376$		0			0
$377$	5.92410	+	41.2030i	0.305107	+	2.12206i
$378$		0			0
$379$	−2.23639	+	0.656663i	−0.114875	+	0.0337305i	−0.338665	−	0.940907i	$-0.609975\pi$
$379$	−2.23639	+	0.656663i	−0.114875	+	0.0337305i	0.223790	+	0.974637i	$0.428157\pi$
$380$		0			0
$381$	−2.70110	+	5.91459i	−0.138382	+	0.303014i
$382$		0			0
$383$	1.97479	+	2.27903i	0.100907	+	0.116453i	0.803957	−	0.594688i	$-0.202724\pi$
$383$	1.97479	+	2.27903i	0.100907	+	0.116453i	−0.703050	+	0.711141i	$0.748179\pi$
$384$		0			0
$385$	1.56685	−	1.00696i	0.0798543	−	0.0513192i
$386$		0			0
$387$	17.6242	+	11.3264i	0.895887	+	0.575752i
$388$		0			0
$389$	11.8036	+	3.46586i	0.598468	+	0.175726i	0.566915	−	0.823776i	$-0.308137\pi$
$389$	11.8036	+	3.46586i	0.598468	+	0.175726i	0.0315525	+	0.999502i	$0.489955\pi$
$390$		0			0
$391$	22.4304	−	1.33580i	1.13435	−	0.0675545i
$392$		0			0
$393$	−23.6428	−	6.94215i	−1.19262	−	0.350185i
$394$		0			0
$395$	−1.78510	−	1.14721i	−0.0898179	−	0.0577225i
$396$		0			0
$397$	1.63878	−	1.05318i	0.0822479	−	0.0528575i	−0.498871	−	0.866677i	$-0.666252\pi$
$397$	1.63878	−	1.05318i	0.0822479	−	0.0528575i	0.581118	+	0.813819i	$0.302615\pi$
$398$		0			0
$399$	49.4450	+	57.0626i	2.47535	+	2.85670i
$400$		0			0
$401$	12.3346	−	27.0090i	0.615961	−	1.34877i	−0.302460	−	0.953162i	$-0.597808\pi$
$401$	12.3346	−	27.0090i	0.615961	−	1.34877i	0.918421	−	0.395605i	$-0.129465\pi$
$402$		0			0
$403$	−54.7461	+	16.0749i	−2.72710	+	0.800747i
$404$		0			0
$405$	0.549892	+	3.82458i	0.0273244	+	0.190045i
$406$		0			0
$407$	−0.152691	−	0.334347i	−0.00756862	−	0.0165730i
$408$		0			0
$409$	−3.85425	+	26.8069i	−0.190580	+	1.32551i	0.639897	+	0.768461i	$0.278977\pi$
$409$	−3.85425	+	26.8069i	−0.190580	+	1.32551i	−0.830477	+	0.557053i	$0.811932\pi$
$410$		0			0
$411$	3.31807	−	3.82925i	0.163668	−	0.188883i
$412$		0			0
$413$	11.3600			0.558990
$414$		0			0
$415$	3.78937			0.186013
$416$		0			0
$417$	−11.2352	+	12.9661i	−0.550191	+	0.634954i
$418$		0			0
$419$	−0.465179	+	3.23539i	−0.0227255	+	0.158059i	−0.998024	−	0.0628309i	$-0.979987\pi$
$419$	−0.465179	+	3.23539i	−0.0227255	+	0.158059i	0.975299	+	0.220890i	$0.0708962\pi$
$420$		0			0
$421$	−8.13772	−	17.8191i	−0.396608	−	0.868451i	−0.997603	−	0.0691981i	$-0.977956\pi$
$421$	−8.13772	−	17.8191i	−0.396608	−	0.868451i	0.600995	−	0.799253i	$-0.294771\pi$
$422$		0			0
$423$	−6.47659	−	45.0456i	−0.314902	−	2.19019i
$424$		0			0
$425$	4.49556	−	1.32002i	0.218067	−	0.0640302i
$426$		0			0
$427$	−2.22594	+	4.87413i	−0.107721	+	0.235876i
$428$		0			0
$429$	−5.79102	−	6.68319i	−0.279593	−	0.322668i
$430$		0			0
$431$	16.1383	−	10.3715i	0.777356	−	0.499576i	−0.0907993	−	0.995869i	$-0.528942\pi$
$431$	16.1383	−	10.3715i	0.777356	−	0.499576i	0.868155	+	0.496293i	$0.165306\pi$
$432$		0			0
$433$	−8.60559	−	5.53047i	−0.413558	−	0.265778i	0.317275	−	0.948333i	$-0.397232\pi$
$433$	−8.60559	−	5.53047i	−0.413558	−	0.265778i	−0.730833	+	0.682556i	$0.760868\pi$
$434$		0			0
$435$	19.3108	+	5.67017i	0.925883	+	0.271864i
$436$		0			0
$437$	−16.0404	−	30.2266i	−0.767315	−	1.44593i
$438$		0			0
$439$	−22.0525	−	6.47521i	−1.05251	−	0.309045i	−0.290679	−	0.956821i	$-0.593881\pi$
$439$	−22.0525	−	6.47521i	−1.05251	−	0.309045i	−0.761831	+	0.647775i	$0.775699\pi$
$440$		0			0
$441$	28.7832	+	18.4978i	1.37063	+	0.880849i
$442$		0			0
$443$	3.46834	−	2.22896i	0.164786	−	0.105901i	−0.455649	−	0.890160i	$-0.650593\pi$
$443$	3.46834	−	2.22896i	0.164786	−	0.105901i	0.620434	+	0.784258i	$0.286956\pi$
$444$		0			0
$445$	5.21512	+	6.01857i	0.247220	+	0.285307i
$446$		0			0
$447$	−23.3774	+	51.1893i	−1.10571	+	2.42117i
$448$		0			0
$449$	−13.2833	+	3.90033i	−0.626877	+	0.184068i	−0.579715	−	0.814819i	$-0.696836\pi$
$449$	−13.2833	+	3.90033i	−0.626877	+	0.184068i	−0.0471625	+	0.998887i	$0.515018\pi$
$450$		0			0
$451$	0.902776	+	6.27895i	0.0425101	+	0.295664i
$452$		0			0
$453$	12.9125	+	28.2745i	0.606683	+	1.32845i
$454$		0			0
$455$	3.11482	−	21.6641i	0.146025	−	1.01563i
$456$		0			0
$457$	−11.5146	+	13.2886i	−0.538631	+	0.621613i	−0.958196	−	0.286112i	$-0.907637\pi$
$457$	−11.5146	+	13.2886i	−0.538631	+	0.621613i	0.419565	+	0.907725i	$0.362183\pi$
$458$		0			0
$459$	32.3993			1.51227
$460$		0			0
$461$	−14.2648			−0.664379			−0.332190	−	0.943213i	$-0.607787\pi$
$461$	−14.2648			−0.664379			−0.332190	+	0.943213i	$0.607787\pi$
$462$		0			0
$463$	24.4575	−	28.2254i	1.13663	−	1.31175i	0.192833	−	0.981232i	$-0.438232\pi$
$463$	24.4575	−	28.2254i	1.13663	−	1.31175i	0.943801	−	0.330514i	$-0.107222\pi$
$464$		0			0
$465$	−3.92598	+	27.3058i	−0.182063	+	1.26628i
$466$		0			0
$467$	−1.18352	−	2.59154i	−0.0547667	−	0.119922i	0.880270	−	0.474473i	$-0.157361\pi$
$467$	−1.18352	−	2.59154i	−0.0547667	−	0.119922i	−0.935037	+	0.354550i	$0.884634\pi$
$468$		0			0
$469$	−0.727284	−	5.05837i	−0.0335829	−	0.233574i
$470$		0			0
$471$	−14.5216	+	4.26393i	−0.669121	+	0.196472i
$472$		0			0
$473$	−0.823409	+	1.80301i	−0.0378604	+	0.0829027i
$474$		0			0
$475$	−4.67253	−	5.39239i	−0.214391	−	0.247420i
$476$		0			0
$477$	19.7220	−	12.6746i	0.903008	−	0.580328i
$478$		0			0
$479$	19.5992	+	12.5956i	0.895509	+	0.575509i	0.905455	−	0.424442i	$-0.139530\pi$
$479$	19.5992	+	12.5956i	0.895509	+	0.575509i	−0.00994640	+	0.999951i	$0.503166\pi$
$480$		0			0
$481$	−4.14434	−	1.21689i	−0.188966	−	0.0554853i
$482$		0			0
$483$	−35.4553	−	36.3106i	−1.61327	−	1.65219i
$484$		0			0
$485$	−8.27358	−	2.42934i	−0.375684	−	0.110311i
$486$		0			0
$487$	11.5342	+	7.41257i	0.522664	+	0.335895i	0.775225	−	0.631685i	$-0.217637\pi$
$487$	11.5342	+	7.41257i	0.522664	+	0.335895i	−0.252561	+	0.967581i	$0.581273\pi$
$488$		0			0
$489$	37.5955	−	24.1611i	1.70013	−	1.09260i
$490$		0			0
$491$	7.04956	+	8.13563i	0.318142	+	0.367156i	0.892185	−	0.451669i	$-0.149171\pi$
$491$	7.04956	+	8.13563i	0.318142	+	0.367156i	−0.574043	+	0.818825i	$0.694626\pi$
$492$		0			0
$493$	13.5258	−	29.6174i	0.609171	−	1.33390i
$494$		0			0
$495$	−2.63508	+	0.773730i	−0.118438	+	0.0347766i
$496$		0			0
$497$	−1.09328	−	7.60395i	−0.0490405	−	0.341084i
$498$		0			0
$499$	10.1618	+	22.2513i	0.454905	+	0.996103i	0.988619	+	0.150438i	$0.0480685\pi$
$499$	10.1618	+	22.2513i	0.454905	+	0.996103i	−0.533714	+	0.845665i	$0.679204\pi$
$500$		0			0
$501$	−1.95388	+	13.5895i	−0.0872927	+	0.607134i
$502$		0			0
$503$	15.5341	−	17.9273i	0.692630	−	0.799337i	−0.295107	−	0.955464i	$-0.595355\pi$
$503$	15.5341	−	17.9273i	0.692630	−	0.799337i	0.987737	+	0.156127i	$0.0499009\pi$
$504$		0			0
$505$	0.00415128			0.000184730
$506$		0			0
$507$	−66.2674			−2.94304
$508$		0			0
$509$	5.22275	−	6.02738i	0.231494	−	0.267159i	−0.628104	−	0.778130i	$-0.716169\pi$
$509$	5.22275	−	6.02738i	0.231494	−	0.267159i	0.859598	+	0.510971i	$0.170714\pi$
$510$		0			0
$511$	−8.32844	+	57.9255i	−0.368428	+	2.56248i
$512$		0			0
$513$	−20.4965	−	44.8810i	−0.904941	−	1.98154i
$514$		0			0
$515$	−0.869784	−	6.04948i	−0.0383273	−	0.266572i
$516$		0			0
$517$	4.13133	−	1.21307i	0.181696	−	0.0533506i
$518$		0			0
$519$	11.7575	−	25.7454i	0.516098	−	1.13010i
$520$		0			0
$521$	0.801518	+	0.925002i	0.0351152	+	0.0405251i	0.773035	−	0.634363i	$-0.218737\pi$
$521$	0.801518	+	0.925002i	0.0351152	+	0.0405251i	−0.737920	+	0.674888i	$0.764192\pi$
$522$		0			0
$523$	−31.4420	+	20.2066i	−1.37486	+	0.883571i	−0.999069	−	0.0431316i	$-0.986267\pi$
$523$	−31.4420	+	20.2066i	−1.37486	+	0.883571i	−0.375795	+	0.926703i	$0.622630\pi$
$524$		0			0
$525$	−8.90219	−	5.72109i	−0.388524	−	0.249689i
$526$		0			0
$527$	42.8214	+	12.5735i	1.86533	+	0.547711i
$528$		0			0
$529$	11.9701	+	19.6397i	0.520439	+	0.853899i
$530$		0			0
$531$	−16.0720	−	4.71918i	−0.697467	−	0.204795i
$532$		0			0
$533$	62.7103	+	40.3014i	2.71628	+	1.74565i
$534$		0			0
$535$	3.47390	−	2.23254i	0.150190	−	0.0965211i
$536$		0			0
$537$	−9.52173	−	10.9887i	−0.410893	−	0.474196i
$538$		0			0
$539$	−1.34476	+	2.94462i	−0.0579231	+	0.126834i
$540$		0			0
$541$	−18.0998	+	5.31457i	−0.778170	+	0.228491i	−0.646614	−	0.762817i	$-0.723816\pi$
$541$	−18.0998	+	5.31457i	−0.778170	+	0.228491i	−0.131556	+	0.991309i	$0.541997\pi$
$542$		0			0
$543$	8.51825	+	59.2458i	0.365553	+	2.54248i
$544$		0			0
$545$	−2.31880	−	5.07747i	−0.0993265	−	0.217495i
$546$		0			0
$547$	5.35661	−	37.2560i	0.229032	−	1.59295i	−0.473168	−	0.880972i	$-0.656890\pi$
$547$	5.35661	−	37.2560i	0.229032	−	1.59295i	0.702200	−	0.711980i	$-0.252201\pi$
$548$		0			0
$549$	5.17406	−	5.97118i	0.220823	−	0.254844i
$550$		0			0
$551$	−49.5841			−2.11235
$552$		0			0
$553$	7.75326			0.329702
$554$		0			0
$555$	−1.36757	+	1.57826i	−0.0580500	+	0.0669933i
$556$		0			0
$557$	−2.30806	+	16.0529i	−0.0977958	+	0.680184i	0.880663	+	0.473743i	$0.157097\pi$
$557$	−2.30806	+	16.0529i	−0.0977958	+	0.680184i	−0.978459	+	0.206442i	$0.933812\pi$
$558$		0			0
$559$	9.67603	+	21.1876i	0.409253	+	0.896138i
$560$		0			0
$561$	0.984385	+	6.84654i	0.0415607	+	0.289061i
$562$		0			0
$563$	27.5058	−	8.07644i	1.15923	−	0.340381i	0.355098	−	0.934829i	$-0.384447\pi$
$563$	27.5058	−	8.07644i	1.15923	−	0.340381i	0.804134	+	0.594448i	$0.202629\pi$
$564$		0			0
$565$	−4.23988	+	9.28403i	−0.178373	+	0.390582i
$566$		0			0
$567$	−9.24540	−	10.6698i	−0.388270	−	0.448088i
$568$		0			0
$569$	−10.3119	+	6.62707i	−0.432298	+	0.277821i	−0.738640	−	0.674101i	$-0.764531\pi$
$569$	−10.3119	+	6.62707i	−0.432298	+	0.277821i	0.306341	+	0.951922i	$0.400895\pi$
$570$		0			0
$571$	15.4226	+	9.91152i	0.645417	+	0.414784i	0.821989	−	0.569504i	$-0.192865\pi$
$571$	15.4226	+	9.91152i	0.645417	+	0.414784i	−0.176572	+	0.984288i	$0.556501\pi$
$572$		0			0
$573$	−75.2564	−	22.0973i	−3.14388	−	0.923127i
$574$		0			0
$575$	3.35051	+	3.43134i	0.139726	+	0.143097i
$576$		0			0
$577$	−28.2970	−	8.30873i	−1.17802	−	0.345897i	−0.366608	−	0.930375i	$-0.619481\pi$
$577$	−28.2970	−	8.30873i	−1.17802	−	0.345897i	−0.811409	+	0.584478i	$0.801299\pi$
$578$		0			0
$579$	29.7455	+	19.1163i	1.23618	+	0.794445i
$580$		0			0
$581$	−11.6478	+	7.48558i	−0.483232	+	0.310554i
$582$		0			0
$583$	1.45253	+	1.67631i	0.0601575	+	0.0694255i
$584$		0			0
$585$	−13.4065	+	29.3562i	−0.554292	+	1.21373i
$586$		0			0
$587$	22.6206	−	6.64200i	0.933651	−	0.274145i	0.220687	−	0.975345i	$-0.429170\pi$
$587$	22.6206	−	6.64200i	0.933651	−	0.274145i	0.712965	+	0.701200i	$0.247352\pi$
$588$		0			0
$589$	−9.67233	−	67.2725i	−0.398541	−	2.77192i
$590$		0			0
$591$	−18.2315	−	39.9213i	−0.749942	−	1.64214i
$592$		0			0
$593$	−1.16684	+	8.11554i	−0.0479163	+	0.333265i	0.951736	+	0.306916i	$0.0992972\pi$
$593$	−1.16684	+	8.11554i	−0.0479163	+	0.333265i	−0.999653	+	0.0263490i	$0.991612\pi$
$594$		0			0
$595$	−11.2109	+	12.9381i	−0.459602	+	0.530409i
$596$		0			0
$597$	0.360976			0.0147738
$598$		0			0
$599$	−12.9965			−0.531022			−0.265511	−	0.964108i	$-0.585541\pi$
$599$	−12.9965			−0.531022			−0.265511	+	0.964108i	$0.585541\pi$
$600$		0			0
$601$	4.94281	−	5.70431i	0.201622	−	0.232684i	−0.645930	−	0.763397i	$-0.723530\pi$
$601$	4.94281	−	5.70431i	0.201622	−	0.232684i	0.847552	+	0.530713i	$0.178076\pi$
$602$		0			0
$603$	−1.07239	+	7.45867i	−0.0436713	+	0.303740i
$604$		0			0
$605$	4.46162	+	9.76959i	0.181391	+	0.397190i
$606$		0			0
$607$	−6.07773	−	42.2715i	−0.246687	−	1.71575i	−0.617104	−	0.786882i	$-0.711694\pi$
$607$	−6.07773	−	42.2715i	−0.246687	−	1.71575i	0.370417	−	0.928866i	$-0.379215\pi$
$608$		0			0
$609$	−70.5587	+	20.7179i	−2.85918	+	0.839532i
$610$		0			0
$611$	21.0190	−	46.0251i	0.850337	−	1.86198i
$612$		0			0
$613$	−22.5614	−	26.0372i	−0.911245	−	1.05163i	−0.998462	−	0.0554431i	$-0.982343\pi$
$613$	−22.5614	−	26.0372i	−0.911245	−	1.05163i	0.0872172	−	0.996189i	$-0.472203\pi$
$614$		0			0
$615$	30.3197	−	19.4853i	1.22261	−	0.785724i
$616$		0			0
$617$	23.4692	+	15.0827i	0.944835	+	0.607208i	0.919762	−	0.392477i	$-0.128382\pi$
$617$	23.4692	+	15.0827i	0.944835	+	0.607208i	0.0250729	+	0.999686i	$0.492018\pi$
$618$		0			0
$619$	31.1176	+	9.13696i	1.25072	+	0.367246i	0.839034	−	0.544079i	$-0.183121\pi$
$619$	31.1176	+	9.13696i	1.25072	+	0.367246i	0.411689	+	0.911324i	$0.364939\pi$
$620$		0			0
$621$	15.5455	+	29.2940i	0.623818	+	1.17553i
$622$		0			0
$623$	−27.9194	−	8.19788i	−1.11857	−	0.328441i
$624$		0			0
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$		0			0
$627$	8.86141	−	5.69488i	0.353891	−	0.227432i
$628$		0			0
$629$	2.21244	+	2.55329i	0.0882156	+	0.101806i
$630$		0			0
$631$	−6.64881	+	14.5589i	−0.264685	+	0.579579i	−0.994579	−	0.103981i	$-0.966842\pi$
$631$	−6.64881	+	14.5589i	−0.264685	+	0.579579i	0.729894	+	0.683560i	$0.239569\pi$
$632$		0			0
$633$	−32.1259	+	9.43301i	−1.27689	+	0.374928i
$634$		0			0
$635$	0.319513	+	2.22226i	0.0126795	+	0.0881879i
$636$		0			0
$637$	15.8026	+	34.6028i	0.626120	+	1.37101i
$638$		0			0
$639$	−1.61207	+	11.2122i	−0.0637724	+	0.443547i
$640$		0			0
$641$	16.8812	−	19.4820i	0.666769	−	0.769492i	−0.317098	−	0.948393i	$-0.602709\pi$
$641$	16.8812	−	19.4820i	0.666769	−	0.769492i	0.983867	+	0.178900i	$0.0572540\pi$
$642$		0			0
$643$	−17.0614			−0.672837			−0.336419	−	0.941713i	$-0.609216\pi$
$643$	−17.0614			−0.672837			−0.336419	+	0.941713i	$0.609216\pi$
$644$		0			0
$645$	11.2616			0.443427
$646$		0			0
$647$	−8.46082	+	9.76430i	−0.332629	+	0.383874i	−0.897285	−	0.441452i	$-0.854463\pi$
$647$	−8.46082	+	9.76430i	−0.332629	+	0.383874i	0.564656	+	0.825326i	$0.309009\pi$
$648$		0			0
$649$	0.225544	−	1.56869i	0.00885338	−	0.0615766i
$650$		0			0
$651$	−41.8726	−	91.6881i	−1.64112	−	3.59354i
$652$		0			0
$653$	−1.40052	−	9.74083i	−0.0548066	−	0.381188i	−0.998702	−	0.0509424i	$-0.983778\pi$
$653$	−1.40052	−	9.74083i	−0.0548066	−	0.381188i	0.943895	−	0.330246i	$-0.107132\pi$
$654$		0			0
$655$	−8.16354	+	2.39703i	−0.318976	+	0.0936598i
$656$		0			0
$657$	35.8464	−	78.4928i	1.39850	−	3.06229i
$658$		0			0
$659$	−4.32768	−	4.99441i	−0.168582	−	0.194554i	0.665172	−	0.746690i	$-0.268358\pi$
$659$	−4.32768	−	4.99441i	−0.168582	−	0.194554i	−0.833754	+	0.552136i	$0.813813\pi$
$660$		0			0
$661$	−31.4278	+	20.1974i	−1.22240	+	0.785588i	−0.982690	−	0.185256i	$-0.940688\pi$
$661$	−31.4278	+	20.1974i	−1.22240	+	0.785588i	−0.239709	+	0.970845i	$0.577052\pi$
$662$		0			0
$663$	68.3791	+	43.9446i	2.65562	+	1.70667i
$664$		0			0
$665$	25.0147	+	7.34497i	0.970027	+	0.284826i
$666$		0			0
$667$	33.2685	−	1.98125i	1.28816	−	0.0767143i
$668$		0			0
$669$	−35.4552	−	10.4106i	−1.37078	−	0.402497i
$670$		0			0
$671$	0.628870	+	0.404150i	0.0242773	+	0.0156020i
$672$		0			0
$673$	−16.9358	+	10.8840i	−0.652828	+	0.419547i	−0.824699	−	0.565573i	$-0.808655\pi$
$673$	−16.9358	+	10.8840i	−0.652828	+	0.419547i	0.171871	+	0.985119i	$0.445019\pi$
$674$		0			0
$675$	4.52837	+	5.22602i	0.174297	+	0.201150i
$676$		0			0
$677$	−18.1463	+	39.7350i	−0.697421	+	1.52714i	0.145650	+	0.989336i	$0.453473\pi$
$677$	−18.1463	+	39.7350i	−0.697421	+	1.52714i	−0.843071	+	0.537802i	$0.819255\pi$
$678$		0			0
$679$	30.2304	−	8.87644i	1.16013	−	0.340646i
$680$		0			0
$681$	−9.04579	−	62.9149i	−0.346635	−	2.41090i
$682$		0			0
$683$	16.5988	+	36.3462i	0.635134	+	1.39075i	0.903983	+	0.427567i	$0.140629\pi$
$683$	16.5988	+	36.3462i	0.635134	+	1.39075i	−0.268849	+	0.963182i	$0.586643\pi$
$684$		0			0
$685$	0.248981	−	1.73170i	0.00951307	−	0.0661648i
$686$		0			0
$687$	11.2714	−	13.0079i	0.430030	−	0.496282i
$688$		0			0
$689$	26.0650			0.992996
$690$		0			0
$691$	14.9022			0.566907			0.283454	−	0.958986i	$-0.408520\pi$
$691$	14.9022			0.566907			0.283454	+	0.958986i	$0.408520\pi$
$692$		0			0
$693$	6.57129	−	7.58368i	0.249623	−	0.288080i
$694$		0			0
$695$	−0.843067	+	5.86366i	−0.0319793	+	0.222421i
$696$		0			0
$697$	−24.2216	−	53.0379i	−0.917458	−	2.00895i
$698$		0			0
$699$	−3.88324	−	27.0086i	−0.146878	−	1.02156i
$700$		0			0
$701$	33.8243	−	9.93171i	1.27753	−	0.375115i	0.428536	−	0.903525i	$-0.359029\pi$
$701$	33.8243	−	9.93171i	1.27753	−	0.375115i	0.848990	+	0.528409i	$0.177211\pi$
$702$		0			0
$703$	2.13730	−	4.68003i	0.0806098	−	0.176511i
$704$		0			0
$705$	−16.0201	−	18.4882i	−0.603352	−	0.696305i
$706$		0			0
$707$	−0.0127602	+	0.00820050i	−0.000479898	+	0.000308412i
$708$		0			0
$709$	43.1567	+	27.7351i	1.62078	+	1.04161i	0.955486	+	0.295036i	$0.0953316\pi$
$709$	43.1567	+	27.7351i	1.62078	+	1.04161i	0.665297	+	0.746578i	$0.268305\pi$
$710$		0			0
$711$	−10.9692	−	3.22086i	−0.411379	−	0.120792i
$712$		0			0
$713$	9.17770	+	44.7502i	0.343708	+	1.67591i
$714$		0			0
$715$	−2.92973	−	0.860246i	−0.109566	−	0.0321714i
$716$		0			0
$717$	−37.3099	−	23.9776i	−1.39336	−	0.895459i
$718$		0			0
$719$	41.8538	−	26.8978i	1.56089	−	1.00312i	0.578626	−	0.815593i	$-0.303589\pi$
$719$	41.8538	−	26.8978i	1.56089	−	1.00312i	0.982260	−	0.187527i	$-0.0600471\pi$
$720$		0			0
$721$	14.6238	+	16.8767i	0.544618	+	0.628523i
$722$		0			0
$723$	−10.0884	+	22.0906i	−0.375193	+	0.821559i
$724$		0			0
$725$	6.66777	−	1.95783i	0.247635	−	0.0727121i
$726$		0			0
$727$	4.71999	+	32.8282i	0.175055	+	1.21753i	0.868008	+	0.496550i	$0.165400\pi$
$727$	4.71999	+	32.8282i	0.175055	+	1.21753i	−0.692953	+	0.720982i	$0.743691\pi$
$728$		0			0
$729$	−16.3105	−	35.7151i	−0.604094	−	1.32278i
$730$		0			0
$731$	2.59283	−	18.0335i	0.0958992	−	0.666994i
$732$		0			0
$733$	−28.4838	+	32.8721i	−1.05207	+	1.21416i	−0.0759129	+	0.997114i	$0.524187\pi$
$733$	−28.4838	+	32.8721i	−1.05207	+	1.21416i	−0.976162	+	0.217044i	$0.930358\pi$
$734$		0			0
$735$	18.3921			0.678404
$736$		0			0
$737$	−0.712945			−0.0262617
$738$		0			0
$739$	−25.0741	+	28.9370i	−0.922365	+	1.06447i	0.0753671	+	0.997156i	$0.475987\pi$
$739$	−25.0741	+	28.9370i	−0.922365	+	1.06447i	−0.997732	+	0.0673101i	$0.978558\pi$
$740$		0			0
$741$	17.6160	−	122.522i	0.647141	−	4.50096i
$742$		0			0
$743$	−14.1464	−	30.9763i	−0.518982	−	1.13641i	−0.969824	−	0.243808i	$-0.921603\pi$
$743$	−14.1464	−	30.9763i	−0.518982	−	1.13641i	0.450842	−	0.892604i	$-0.351124\pi$
$744$		0			0
$745$	2.76531	+	19.2331i	0.101313	+	0.704647i
$746$		0			0
$747$	19.5889	−	5.75181i	0.716719	−	0.210448i
$748$		0			0
$749$	−6.26790	+	13.7248i	−0.229024	+	0.501493i
$750$		0			0
$751$	15.1803	+	17.5191i	0.553939	+	0.639279i	0.961796	−	0.273766i	$-0.0882694\pi$
$751$	15.1803	+	17.5191i	0.553939	+	0.639279i	−0.407858	+	0.913046i	$0.633724\pi$
$752$		0			0
$753$	37.2592	−	23.9451i	1.35780	−	0.872606i
$754$		0			0
$755$	9.02890	+	5.80252i	0.328595	+	0.211175i
$756$		0			0
$757$	8.24191	+	2.42004i	0.299557	+	0.0879580i	0.428057	−	0.903752i	$-0.359198\pi$
$757$	8.24191	+	2.42004i	0.299557	+	0.0879580i	−0.128500	+	0.991709i	$0.541016\pi$
$758$		0			0
$759$	−5.71803	+	4.17507i	−0.207551	+	0.151546i
$760$		0			0
$761$	32.1981	+	9.45421i	1.16718	+	0.342715i	0.807219	−	0.590253i	$-0.200972\pi$
$761$	32.1981	+	9.45421i	1.16718	+	0.342715i	0.359961	+	0.932967i	$0.382790\pi$
$762$		0			0
$763$	17.1577	+	11.0266i	0.621149	+	0.399188i
$764$		0			0
$765$	21.2358	−	13.6474i	0.767783	−	0.493424i
$766$		0			0
$767$	−12.1958	−	14.0748i	−0.440366	−	0.508210i
$768$		0			0
$769$	20.5025	−	44.8942i	0.739339	−	1.61893i	−0.0452998	−	0.998973i	$-0.514424\pi$
$769$	20.5025	−	44.8942i	0.739339	−	1.61893i	0.784639	−	0.619953i	$-0.212848\pi$
$770$		0			0
$771$	−10.9724	+	3.22178i	−0.395160	+	0.116030i
$772$		0			0
$773$	4.17509	+	29.0384i	0.150168	+	1.04444i	0.915936	+	0.401323i	$0.131450\pi$
$773$	4.17509	+	29.0384i	0.150168	+	1.04444i	−0.765769	+	0.643116i	$0.777641\pi$
$774$		0			0
$775$	3.95694	+	8.66449i	0.142138	+	0.311238i
$776$		0			0
$777$	1.08593	−	7.55278i	0.0389574	−	0.270954i
$778$		0			0
$779$	−58.1474	+	67.1057i	−2.08335	+	2.40431i
$780$		0			0
$781$	−1.07173			−0.0383495
$782$		0			0
$783$	48.0543			1.71732
$784$		0			0
$785$	−3.42217	+	3.94940i	−0.122143	+	0.140960i
$786$		0			0
$787$	3.23174	−	22.4773i	0.115199	−	0.801228i	−0.847527	−	0.530752i	$-0.821910\pi$
$787$	3.23174	−	22.4773i	0.115199	−	0.801228i	0.962727	−	0.270477i	$-0.0871813\pi$
$788$		0			0
$789$	24.6748	+	54.0304i	0.878447	+	1.92353i
$790$		0			0
$791$	−5.30727	−	36.9128i	−0.188705	−	1.31247i
$792$		0			0
$793$	8.42864	−	2.47487i	0.299310	−	0.0878853i
$794$		0			0
$795$	5.23511	−	11.4633i	0.185670	−	0.406561i
$796$		0			0
$797$	9.00581	+	10.3933i	0.319002	+	0.368148i	0.892491	−	0.451065i	$-0.148956\pi$
$797$	9.00581	+	10.3933i	0.319002	+	0.368148i	−0.573489	+	0.819213i	$0.694410\pi$
$798$		0			0
$799$	−33.2939	+	21.3967i	−1.17785	+	0.756961i
$800$		0			0
$801$	36.0946	+	23.1966i	1.27534	+	0.819611i
$802$		0			0
$803$	7.83353	+	2.30013i	0.276439	+	0.0811699i
$804$		0			0
$805$	−17.0771	−	3.92861i	−0.601890	−	0.138465i
$806$		0			0
$807$	16.9323	+	4.97178i	0.596047	+	0.175015i
$808$		0			0
$809$	8.92670	+	5.73684i	0.313846	+	0.201697i	0.688075	−	0.725640i	$-0.258456\pi$
$809$	8.92670	+	5.73684i	0.313846	+	0.201697i	−0.374229	+	0.927336i	$0.622092\pi$
$810$		0			0
$811$	−2.55805	+	1.64396i	−0.0898254	+	0.0577273i	−0.584782	−	0.811190i	$-0.698820\pi$
$811$	−2.55805	+	1.64396i	−0.0898254	+	0.0577273i	0.494957	+	0.868917i	$0.335184\pi$
$812$		0			0
$813$	12.0944	+	13.9576i	0.424168	+	0.489516i
$814$		0			0
$815$	6.41018	−	14.0363i	0.224539	−	0.491671i
$816$		0			0
$817$	−26.6211	+	7.81667i	−0.931356	+	0.273471i
$818$		0			0
$819$	−16.7816	−	116.719i	−0.586397	−	4.07848i
$820$		0			0
$821$	8.14905	+	17.8439i	0.284404	+	0.622757i	0.996879	−	0.0789395i	$-0.0251534\pi$
$821$	8.14905	+	17.8439i	0.284404	+	0.622757i	−0.712476	+	0.701697i	$0.752426\pi$
$822$		0			0
$823$	2.88526	−	20.0675i	0.100574	−	0.699507i	−0.875682	−	0.482888i	$-0.839588\pi$
$823$	2.88526	−	20.0675i	0.100574	−	0.699507i	0.976256	−	0.216619i	$-0.0695031\pi$
$824$		0			0
$825$	−0.966766	+	1.11571i	−0.0336585	+	0.0388439i
$826$		0			0
$827$	−40.3092			−1.40169			−0.700845	−	0.713314i	$-0.747194\pi$
$827$	−40.3092			−1.40169			−0.700845	+	0.713314i	$0.747194\pi$
$828$		0			0
$829$	−7.25537			−0.251990			−0.125995	−	0.992031i	$-0.540212\pi$
$829$	−7.25537			−0.251990			−0.125995	+	0.992031i	$0.540212\pi$
$830$		0			0
$831$	38.4324	−	44.3534i	1.33321	−	1.53860i
$832$		0			0
$833$	4.23452	−	29.4517i	0.146717	−	1.02044i
$834$		0			0
$835$	1.96928	+	4.31213i	0.0681499	+	0.149227i
$836$		0			0
$837$	9.37391	+	65.1970i	0.324010	+	2.25354i
$838$		0			0
$839$	−21.4407	+	6.29556i	−0.740216	+	0.217347i	−0.630037	−	0.776565i	$-0.716960\pi$
$839$	−21.4407	+	6.29556i	−0.740216	+	0.217347i	−0.110178	+	0.993912i	$0.535142\pi$
$840$		0			0
$841$	8.01428	−	17.5488i	0.276355	−	0.605132i
$842$		0			0
$843$	−17.9580	−	20.7246i	−0.618506	−	0.713794i
$844$		0			0
$845$	−19.2489	+	12.3705i	−0.662183	+	0.425559i
$846$		0			0
$847$	−33.0132	−	21.2163i	−1.13435	−	0.729000i
$848$		0			0
$849$	−27.8226	−	8.16947i	−0.954871	−	0.280375i
$850$		0			0
$851$	−1.24702	+	3.22548i	−0.0427474	+	0.110568i
$852$		0			0
$853$	5.65554	+	1.66062i	0.193642	+	0.0568584i	0.377115	−	0.926166i	$-0.376916\pi$
$853$	5.65554	+	1.66062i	0.193642	+	0.0568584i	−0.183474	+	0.983025i	$0.558734\pi$
$854$		0			0
$855$	−32.3393	−	20.7832i	−1.10598	−	0.710771i
$856$		0			0
$857$	32.7978	−	21.0779i	1.12035	−	0.720006i	0.156827	−	0.987626i	$-0.449873\pi$
$857$	32.7978	−	21.0779i	1.12035	−	0.720006i	0.963525	+	0.267620i	$0.0862370\pi$
$858$		0			0
$859$	−6.34042	−	7.31723i	−0.216332	−	0.249661i	0.637203	−	0.770696i	$-0.280091\pi$
$859$	−6.34042	−	7.31723i	−0.216332	−	0.249661i	−0.853535	+	0.521035i	$0.825546\pi$
$860$		0			0
$861$	−54.7054	+	119.788i	−1.86436	+	4.08237i
$862$		0			0
$863$	−16.7381	+	4.91474i	−0.569770	+	0.167300i	−0.553913	−	0.832575i	$-0.686866\pi$
$863$	−16.7381	+	4.91474i	−0.569770	+	0.167300i	−0.0158574	+	0.999874i	$0.505048\pi$
$864$		0			0
$865$	−1.39080	−	9.67321i	−0.0472885	−	0.328899i
$866$		0			0
$867$	−5.95839	−	13.0470i	−0.202357	−	0.443101i
$868$		0			0
$869$	0.153935	−	1.07064i	0.00522188	−	0.0363190i
$870$		0			0
$871$	−5.48639	+	6.33163i	−0.185899	+	0.214539i
$872$		0			0
$873$	−46.4571			−1.57234
$874$		0			0
$875$	−3.65384			−0.123522
$876$		0			0
$877$	8.39208	−	9.68498i	0.283380	−	0.327038i	−0.596157	−	0.802868i	$-0.703307\pi$
$877$	8.39208	−	9.68498i	0.283380	−	0.327038i	0.879538	+	0.475829i	$0.157852\pi$
$878$		0			0
$879$	−8.98011	+	62.4580i	−0.302892	+	2.10666i
$880$		0			0
$881$	14.1260	+	30.9316i	0.475917	+	1.04211i	0.983566	+	0.180549i	$0.0577874\pi$
$881$	14.1260	+	30.9316i	0.475917	+	1.04211i	−0.507649	+	0.861564i	$0.669485\pi$
$882$		0			0
$883$	4.16597	+	28.9749i	0.140196	+	0.975085i	0.931521	+	0.363688i	$0.118483\pi$
$883$	4.16597	+	28.9749i	0.140196	+	0.975085i	−0.791325	+	0.611396i	$0.790608\pi$
$884$		0			0
$885$	−8.63955	+	2.53680i	−0.290415	+	0.0852737i
$886$		0			0
$887$	1.59947	−	3.50235i	0.0537049	−	0.117597i	−0.880877	−	0.473345i	$-0.843046\pi$
$887$	1.59947	−	3.50235i	0.0537049	−	0.117597i	0.934582	+	0.355748i	$0.115774\pi$
$888$		0			0
$889$	−5.37202	−	6.19964i	−0.180172	−	0.207929i
$890$		0			0
$891$	−1.65694	+	1.06485i	−0.0555095	+	0.0356738i
$892$		0			0
$893$	50.7021	+	32.5843i	1.69668	+	1.09039i
$894$		0			0
$895$	−4.81713	−	1.41444i	−0.161019	−	0.0472794i
$896$		0			0
$897$	−6.92385	+	82.9104i	−0.231181	+	2.76830i
$898$		0			0
$899$	63.5123	+	18.6489i	2.11825	+	0.621975i
$900$		0			0
$901$	−17.1511	−	11.0224i	−0.571387	−	0.367208i
$902$		0			0
$903$	−34.6161	+	22.2464i	−1.15195	+	0.740315i
$904$		0			0
$905$	13.5341	+	15.6192i	0.449888	+	0.519199i
$906$		0			0
$907$	7.90264	−	17.3044i	0.262403	−	0.574582i	−0.731871	−	0.681443i	$-0.761353\pi$
$907$	7.90264	−	17.3044i	0.262403	−	0.574582i	0.994274	+	0.106861i	$0.0340800\pi$
$908$		0			0
$909$	0.0214597	−	0.00630114i	0.000711774	−	0.000208996i
$910$		0			0
$911$	4.51169	+	31.3795i	0.149479	+	1.03965i	0.917075	+	0.398715i	$0.130544\pi$
$911$	4.51169	+	31.3795i	0.149479	+	1.03965i	−0.767596	+	0.640934i	$0.778547\pi$
$912$		0			0
$913$	0.802419	+	1.75705i	0.0265562	+	0.0581500i
$914$		0			0
$915$	0.604439	−	4.20397i	0.0199821	−	0.138979i
$916$		0			0
$917$	20.3580	−	23.4944i	0.672281	−	0.775853i
$918$		0			0
$919$	−18.7401			−0.618178			−0.309089	−	0.951033i	$-0.600024\pi$
$919$	−18.7401			−0.618178			−0.309089	+	0.951033i	$0.600024\pi$
$920$		0			0
$921$	−52.0452			−1.71495
$922$		0			0
$923$	−8.24737	+	9.51797i	−0.271466	+	0.313288i
$924$		0			0
$925$	−0.102619	+	0.713734i	−0.00337411	+	0.0234674i
$926$		0			0
$927$	−13.6787	−	29.9521i	−0.449266	−	0.983756i
$928$		0			0
$929$	−8.60779	−	59.8685i	−0.282412	−	1.96422i	−0.264517	−	0.964381i	$-0.585213\pi$
$929$	−8.60779	−	59.8685i	−0.282412	−	1.96422i	−0.0178952	−	0.999840i	$-0.505697\pi$
$930$		0			0
$931$	−43.4767	+	12.7659i	−1.42489	+	0.418386i
$932$		0			0
$933$	−11.6185	+	25.4409i	−0.380371	+	0.832897i
$934$		0			0
$935$	1.56402	+	1.80498i	0.0511490	+	0.0590291i
$936$		0			0
$937$	−32.3206	+	20.7712i	−1.05587	+	0.678566i	−0.948862	−	0.315692i	$-0.897763\pi$
$937$	−32.3206	+	20.7712i	−1.05587	+	0.678566i	−0.107008	+	0.994258i	$0.534127\pi$
$938$		0			0
$939$	−22.2137	−	14.2759i	−0.724917	−	0.465876i
$940$		0			0
$941$	−40.4341	−	11.8725i	−1.31811	−	0.387033i	−0.454302	−	0.890848i	$-0.650111\pi$
$941$	−40.4341	−	11.8725i	−1.31811	−	0.387033i	−0.863812	+	0.503815i	$0.831929\pi$
$942$		0			0
$943$	36.3328	−	47.3481i	1.18316	−	1.54187i
$944$		0			0
$945$	−24.2429	−	7.11836i	−0.788622	−	0.231560i
$946$		0			0
$947$	32.5191	+	20.8988i	1.05673	+	0.679119i	0.949069	−	0.315069i	$-0.102028\pi$
$947$	32.5191	+	20.8988i	1.05673	+	0.679119i	0.107661	+	0.994188i	$0.465664\pi$
$948$		0			0
$949$	80.7094	−	51.8688i	2.61994	−	1.68373i
$950$		0			0
$951$	−14.8465	−	17.1338i	−0.481432	−	0.555602i
$952$		0			0
$953$	17.8177	−	39.0154i	0.577173	−	1.26383i	−0.365716	−	0.930726i	$-0.619176\pi$
$953$	17.8177	−	39.0154i	0.577173	−	1.26383i	0.942889	−	0.333106i	$-0.108097\pi$
$954$		0			0
$955$	−25.9850	+	7.62989i	−0.840855	+	0.246897i
$956$		0			0
$957$	1.46003	+	10.1547i	0.0471960	+	0.328255i
$958$		0			0
$959$	2.65551	+	5.81475i	0.0857508	+	0.187768i
$960$		0			0
$961$	−8.50058	+	59.1228i	−0.274212	+	1.90719i
$962$		0			0
$963$	14.5693	−	16.8139i	0.469490	−	0.541820i
$964$		0			0
$965$	12.2088			0.393016
$966$		0			0
$967$	−19.0722			−0.613320			−0.306660	−	0.951819i	$-0.599211\pi$
$967$	−19.0722			−0.613320			−0.306660	+	0.951819i	$0.599211\pi$
$968$		0			0
$969$	−63.4038	+	73.1718i	−2.03682	+	2.35062i
$970$		0			0
$971$	−5.72362	+	39.8086i	−0.183680	+	1.27752i	0.664290	+	0.747475i	$0.268734\pi$
$971$	−5.72362	+	39.8086i	−0.183680	+	1.27752i	−0.847970	+	0.530045i	$0.822175\pi$
$972$		0			0
$973$	−8.99174	−	19.6892i	−0.288262	−	0.631205i
$974$		0			0
$975$	2.46890	+	17.1716i	0.0790682	+	0.549932i
$976$		0			0
$977$	−36.6039	+	10.7479i	−1.17106	+	0.343855i	−0.808723	−	0.588190i	$-0.799841\pi$
$977$	−36.6039	+	10.7479i	−1.17106	+	0.343855i	−0.362341	+	0.932045i	$0.618023\pi$
$978$		0			0
$979$	−1.68636	+	3.69260i	−0.0538962	+	0.118016i
$980$		0			0
$981$	−19.6938	−	22.7279i	−0.628776	−	0.725646i
$982$		0			0
$983$	3.06853	−	1.97203i	0.0978710	−	0.0628979i	−0.490790	−	0.871278i	$-0.663292\pi$
$983$	3.06853	−	1.97203i	0.0978710	−	0.0628979i	0.588661	+	0.808380i	$0.299655\pi$
$984$		0			0
$985$	−12.7481	−	8.19271i	−0.406189	−	0.261042i
$986$		0			0
$987$	85.7645	+	25.1827i	2.72991	+	0.801575i
$988$		0			0
$989$	17.5492	−	6.30833i	0.558032	−	0.200593i
$990$		0			0
$991$	28.6584	+	8.41486i	0.910363	+	0.267307i	0.703194	−	0.710998i	$-0.251757\pi$
$991$	28.6584	+	8.41486i	0.910363	+	0.267307i	0.207169	+	0.978305i	$0.433575\pi$
$992$		0			0
$993$	−12.1519	−	7.80956i	−0.385629	−	0.247829i
$994$		0			0
$995$	0.104854	−	0.0673856i	0.00332410	−	0.00213627i
$996$		0			0
$997$	23.0887	+	26.6458i	0.731226	+	0.843880i	0.992609	−	0.121355i	$-0.0387239\pi$
$997$	23.0887	+	26.6458i	0.731226	+	0.843880i	−0.261383	+	0.965235i	$0.584178\pi$
$998$		0			0
$999$	−2.07136	+	4.53564i	−0.0655349	+	0.143501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.b.41.5	✓	50
23.9	even	11	inner	460.2.m.b.101.5	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.b.41.5	✓	50	1.1	even	1	trivial
460.2.m.b.101.5	yes	50	23.9	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.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.89657 - 2.18876i) q^{3} +(0.142315 - 0.989821i) q^{5} +(1.51786 + 3.32365i) q^{7} +(-0.766744 - 5.33282i) q^{9} +O(q^{10})\)	\(q+(1.89657 - 2.18876i) q^{3} +(0.142315 - 0.989821i) q^{5} +(1.51786 + 3.32365i) q^{7} +(-0.766744 - 5.33282i) q^{9} +(0.489096 - 0.143611i) q^{11} +(2.48838 - 5.44878i) q^{13} +(-1.89657 - 2.18876i) q^{15} +(-3.94157 + 2.53309i) q^{17} +(6.00247 + 3.85756i) q^{19} +(10.1534 + 2.98131i) q^{21} +(-4.18151 - 2.34839i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(-5.81728 - 3.73854i) q^{27} +(-5.84609 + 3.75705i) q^{29} +(-6.23773 - 7.19872i) q^{31} +(0.613274 - 1.34288i) q^{33} +(3.50583 - 1.02941i) q^{35} +(-0.102619 - 0.713734i) q^{37} +(-7.20670 - 15.7805i) q^{39} +(-1.77104 + 12.3179i) q^{41} +(-2.54642 + 2.93873i) q^{43} -5.38766 q^{45} +8.44687 q^{47} +(-4.15873 + 4.79943i) q^{49} +(-1.93114 + 13.4313i) q^{51} +(1.80761 + 3.95812i) q^{53} +(-0.0725441 - 0.504555i) q^{55} +(19.8274 - 5.82185i) q^{57} +(1.29155 - 2.82810i) q^{59} +(0.960353 + 1.10831i) q^{61} +(16.5606 - 10.6429i) q^{63} +(-5.03919 - 3.23849i) q^{65} +(-1.34198 - 0.394041i) q^{67} +(-13.0706 + 4.69843i) q^{69} +(-2.01732 - 0.592338i) q^{71} +(13.4738 + 8.65909i) q^{73} +(-2.43639 + 1.56577i) q^{75} +(1.21969 + 1.40760i) q^{77} +(0.881489 - 1.93019i) q^{79} +(-3.70740 + 1.08859i) q^{81} +(0.539284 + 3.75080i) q^{83} +(1.94637 + 4.26195i) q^{85} +(-2.86424 + 19.9212i) q^{87} +(-5.21512 + 6.01857i) q^{89} +21.8869 q^{91} -27.5866 q^{93} +(4.67253 - 5.39239i) q^{95} +(1.22716 - 8.53510i) q^{97} +(-1.14087 - 2.49815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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