LMFDB - Embedded newform 925.2.bb.e.151.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(151,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			151.14
Character	$\chi$	$=$	925.151
Dual form			925.2.bb.e.876.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.33394 - 1.58972i) q^{2} +(0.293922 - 0.246630i) q^{3} +(-0.400539 - 2.27157i) q^{4} -0.796243i q^{6} +(3.20026 + 1.16480i) q^{7} +(-0.551046 - 0.318147i) q^{8} +(-0.495381 + 2.80944i) q^{9} +(2.09499 - 3.62862i) q^{11} +(-0.677964 - 0.568879i) q^{12} +(-2.00538 + 0.353603i) q^{13} +(6.12066 - 3.53376i) q^{14} +(3.09419 - 1.12619i) q^{16} +(-0.729641 - 0.128655i) q^{17} +(3.80543 + 4.53514i) q^{18} +(0.966024 + 1.15126i) q^{19} +(1.22790 - 0.446919i) q^{21} +(-2.97393 - 8.17080i) q^{22} +(1.64066 - 0.947238i) q^{23} +(-0.240429 + 0.0423941i) q^{24} +(-2.11292 + 3.65969i) q^{26} +(1.12282 + 1.94478i) q^{27} +(1.36409 - 7.73616i) q^{28} +(0.664361 + 0.383569i) q^{29} -5.25639i q^{31} +(2.77237 - 7.61701i) q^{32} +(-0.279164 - 1.58322i) q^{33} +(-1.17782 + 0.988309i) q^{34} +6.58027 q^{36} +(-5.96539 + 1.18918i) q^{37} +3.11880 q^{38} +(-0.502216 + 0.598518i) q^{39} +(1.85206 + 10.5036i) q^{41} +(0.927464 - 2.54819i) q^{42} -9.93840i q^{43} +(-9.08179 - 3.30550i) q^{44} +(0.682696 - 3.87176i) q^{46} +(-1.02067 - 1.76785i) q^{47} +(0.631697 - 1.09413i) q^{48} +(3.52260 + 2.95581i) q^{49} +(-0.246188 + 0.142136i) q^{51} +(1.60647 + 4.41373i) q^{52} +(-12.4473 + 4.53045i) q^{53} +(4.58944 + 0.809242i) q^{54} +(-1.39291 - 1.66001i) q^{56} +(0.567871 + 0.100131i) q^{57} +(1.49599 - 0.544494i) q^{58} +(-0.487600 - 1.33967i) q^{59} +(2.54738 - 0.449171i) q^{61} +(-8.35621 - 7.01169i) q^{62} +(-4.85779 + 8.41393i) q^{63} +(-5.11803 - 8.86468i) q^{64} +(-2.88927 - 1.66812i) q^{66} +(-9.52005 - 3.46501i) q^{67} +1.70896i q^{68} +(0.248610 - 0.683051i) q^{69} +(-10.6121 + 8.90459i) q^{71} +(1.16679 - 1.39053i) q^{72} -3.43226 q^{73} +(-6.06698 + 11.0696i) q^{74} +(2.22824 - 2.65552i) q^{76} +(10.9311 - 9.17230i) q^{77} +(0.281554 + 1.59677i) q^{78} +(1.41012 - 3.87427i) q^{79} +(-7.23256 - 2.63244i) q^{81} +(19.1683 + 11.0668i) q^{82} +(2.48726 - 14.1059i) q^{83} +(-1.50703 - 2.61025i) q^{84} +(-15.7993 - 13.2572i) q^{86} +(0.289870 - 0.0511119i) q^{87} +(-2.30887 + 1.33303i) q^{88} +(4.49440 + 12.3483i) q^{89} +(-6.82962 - 1.20425i) q^{91} +(-2.80887 - 3.34748i) q^{92} +(-1.29638 - 1.54497i) q^{93} +(-4.17191 - 0.735620i) q^{94} +(-1.06372 - 2.92256i) q^{96} +(-2.26408 + 1.30717i) q^{97} +(9.39785 - 1.65710i) q^{98} +(9.15659 + 7.68329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$	1.33394	−	1.58972i	0.943236	−	1.12410i	−0.0488828	−	0.998805i	$-0.515566\pi$
$2$	1.33394	−	1.58972i	0.943236	−	1.12410i	0.992119	−	0.125300i	$-0.0399895\pi$
$3$	0.293922	−	0.246630i	0.169696	−	0.142392i	−0.553985	−	0.832527i	$-0.686893\pi$
$3$	0.293922	−	0.246630i	0.169696	−	0.142392i	0.723681	+	0.690135i	$0.242449\pi$
$4$	−0.400539	−	2.27157i	−0.200270	−	1.13578i
$5$		0			0
$5$		0			0
$6$		−	0.796243i		−	0.325065i
$7$	3.20026	+	1.16480i	1.20958	+	0.440253i	0.866560	−	0.499073i	$-0.166326\pi$
$7$	3.20026	+	1.16480i	1.20958	+	0.440253i	0.343025	+	0.939326i	$0.388548\pi$
$8$	−0.551046	−	0.318147i	−0.194824	−	0.112482i
$9$	−0.495381	+	2.80944i	−0.165127	+	0.936481i
$10$		0			0
$11$	2.09499	−	3.62862i	0.631662	−	1.09407i	−0.355550	−	0.934657i	$-0.615706\pi$
$11$	2.09499	−	3.62862i	0.631662	−	1.09407i	0.987212	−	0.159413i	$-0.0509603\pi$
$12$	−0.677964	−	0.568879i	−0.195711	−	0.164221i
$13$	−2.00538	+	0.353603i	−0.556193	+	0.0980718i	−0.444677	−	0.895691i	$-0.646682\pi$
$13$	−2.00538	+	0.353603i	−0.556193	+	0.0980718i	−0.111515	+	0.993763i	$0.535570\pi$
$14$	6.12066	−	3.53376i	1.63581	−	0.944438i
$15$		0			0
$16$	3.09419	−	1.12619i	0.773547	−	0.281548i
$17$	−0.729641	−	0.128655i	−0.176964	−	0.0312035i	0.0844639	−	0.996427i	$-0.473082\pi$
$17$	−0.729641	−	0.128655i	−0.176964	−	0.0312035i	−0.261428	+	0.965223i	$0.584193\pi$
$18$	3.80543	+	4.53514i	0.896949	+	1.06894i
$19$	0.966024	+	1.15126i	0.221621	+	0.264118i	0.865386	−	0.501105i	$-0.167073\pi$
$19$	0.966024	+	1.15126i	0.221621	+	0.264118i	−0.643765	+	0.765223i	$0.722629\pi$
$20$		0			0
$21$	1.22790	−	0.446919i	0.267950	−	0.0975258i
$22$	−2.97393	−	8.17080i	−0.634044	−	1.74202i
$23$	1.64066	−	0.947238i	0.342102	−	0.197513i	−0.319099	−	0.947721i	$-0.603380\pi$
$23$	1.64066	−	0.947238i	0.342102	−	0.197513i	0.661201	+	0.750209i	$0.270047\pi$
$24$	−0.240429	+	0.0423941i	−0.0490774	+	0.00865366i
$25$		0			0
$26$	−2.11292	+	3.65969i	−0.414378	+	0.717724i
$27$	1.12282	+	1.94478i	0.216087	+	0.374274i
$28$	1.36409	−	7.73616i	0.257790	−	1.46200i
$29$	0.664361	+	0.383569i	0.123369	+	0.0712270i	0.560414	−	0.828212i	$-0.310642\pi$
$29$	0.664361	+	0.383569i	0.123369	+	0.0712270i	−0.437046	+	0.899439i	$0.643975\pi$
$30$		0			0
$31$		−	5.25639i		−	0.944075i	−0.881578	−	0.472038i	$-0.843519\pi$
$31$		−	5.25639i		−	0.944075i	0.881578	−	0.472038i	$-0.156481\pi$
$32$	2.77237	−	7.61701i	0.490090	−	1.34651i
$33$	−0.279164	−	1.58322i	−0.0485962	−	0.275603i
$34$	−1.17782	+	0.988309i	−0.201995	+	0.169494i
$35$		0			0
$36$	6.58027			1.09671
$37$	−5.96539	+	1.18918i	−0.980704	+	0.195500i
$37$	−5.96539	+	1.18918i	−0.980704	+	0.195500i
$38$	3.11880			0.505937
$39$	−0.502216	+	0.598518i	−0.0804190	+	0.0958396i
$40$		0			0
$41$	1.85206	+	10.5036i	0.289244	+	1.64038i	0.689720	+	0.724076i	$0.257733\pi$
$41$	1.85206	+	10.5036i	0.289244	+	1.64038i	−0.400477	+	0.916307i	$0.631155\pi$
$42$	0.927464	−	2.54819i	0.143111	−	0.393194i
$43$		−	9.93840i		−	1.51559i	−0.652492	−	0.757796i	$-0.726276\pi$
$43$		−	9.93840i		−	1.51559i	0.652492	−	0.757796i	$-0.273724\pi$
$44$	−9.08179	−	3.30550i	−1.36913	−	0.498323i
$45$		0			0
$46$	0.682696	−	3.87176i	0.100658	−	0.570860i
$47$	−1.02067	−	1.76785i	−0.148880	−	0.257868i	0.781934	−	0.623362i	$-0.214234\pi$
$47$	−1.02067	−	1.76785i	−0.148880	−	0.257868i	−0.930814	+	0.365494i	$0.880900\pi$
$48$	0.631697	−	1.09413i	0.0911776	−	0.157924i
$49$	3.52260	+	2.95581i	0.503229	+	0.422259i
$50$		0			0
$51$	−0.246188	+	0.142136i	−0.0344732	+	0.0199031i
$52$	1.60647	+	4.41373i	0.222777	+	0.612074i
$53$	−12.4473	+	4.53045i	−1.70977	+	0.622305i	−0.996877	−	0.0789675i	$-0.974838\pi$
$53$	−12.4473	+	4.53045i	−1.70977	+	0.622305i	−0.712893	+	0.701273i	$0.752615\pi$
$54$	4.58944	+	0.809242i	0.624544	+	0.110124i
$55$		0			0
$56$	−1.39291	−	1.66001i	−0.186136	−	0.221828i
$57$	0.567871	+	0.100131i	0.0752164	+	0.0132627i
$58$	1.49599	−	0.544494i	0.196433	−	0.0714956i
$59$	−0.487600	−	1.33967i	−0.0634801	−	0.174410i	0.903897	−	0.427749i	$-0.140693\pi$
$59$	−0.487600	−	1.33967i	−0.0634801	−	0.174410i	−0.967378	+	0.253339i	$0.918471\pi$
$60$		0			0
$61$	2.54738	−	0.449171i	0.326158	−	0.0575105i	−0.00817166	−	0.999967i	$-0.502601\pi$
$61$	2.54738	−	0.449171i	0.326158	−	0.0575105i	0.334330	+	0.942456i	$0.391490\pi$
$62$	−8.35621	−	7.01169i	−1.06124	−	0.890486i
$63$	−4.85779	+	8.41393i	−0.612024	+	1.06006i
$64$	−5.11803	−	8.86468i	−0.639753	−	1.10809i
$65$		0			0
$66$	−2.88927	−	1.66812i	−0.355644	−	0.205331i
$67$	−9.52005	−	3.46501i	−1.16306	−	0.423319i	−0.312870	−	0.949796i	$-0.601290\pi$
$67$	−9.52005	−	3.46501i	−1.16306	−	0.423319i	−0.850189	+	0.526477i	$0.823512\pi$
$68$			1.70896i			0.207242i
$69$	0.248610	−	0.683051i	0.0299291	−	0.0822297i
$70$		0			0
$71$	−10.6121	+	8.90459i	−1.25942	+	1.05678i	−0.263678	+	0.964611i	$0.584936\pi$
$71$	−10.6121	+	8.90459i	−1.25942	+	1.05678i	−0.995743	+	0.0921696i	$0.970620\pi$
$72$	1.16679	−	1.39053i	0.137508	−	0.163875i
$73$	−3.43226			−0.401716			−0.200858	−	0.979620i	$-0.564373\pi$
$73$	−3.43226			−0.401716			−0.200858	+	0.979620i	$0.564373\pi$
$74$	−6.06698	+	11.0696i	−0.705272	+	1.28682i
$75$		0			0
$76$	2.22824	−	2.65552i	0.255597	−	0.304609i
$77$	10.9311	−	9.17230i	1.24572	−	1.04528i
$78$	0.281554	+	1.59677i	0.0318797	+	0.180799i
$79$	1.41012	−	3.87427i	0.158651	−	0.435889i	−0.834744	−	0.550638i	$-0.814384\pi$
$79$	1.41012	−	3.87427i	0.158651	−	0.435889i	0.993394	+	0.114749i	$0.0366065\pi$
$80$		0			0
$81$	−7.23256	−	2.63244i	−0.803617	−	0.292493i
$82$	19.1683	+	11.0668i	2.11679	+	1.22213i
$83$	2.48726	−	14.1059i	0.273012	−	1.54833i	−0.472194	−	0.881494i	$-0.656538\pi$
$83$	2.48726	−	14.1059i	0.273012	−	1.54833i	0.745206	−	0.666834i	$-0.232351\pi$
$84$	−1.50703	−	2.61025i	−0.164431	−	0.284802i
$85$		0			0
$86$	−15.7993	−	13.2572i	−1.70368	−	1.42956i
$87$	0.289870	−	0.0511119i	0.0310773	−	0.00547977i
$88$	−2.30887	+	1.33303i	−0.246126	+	0.142101i
$89$	4.49440	+	12.3483i	0.476406	+	1.30891i	0.912524	+	0.409024i	$0.134131\pi$
$89$	4.49440	+	12.3483i	0.476406	+	1.30891i	−0.436118	+	0.899890i	$0.643647\pi$
$90$		0			0
$91$	−6.82962	−	1.20425i	−0.715938	−	0.126239i
$92$	−2.80887	−	3.34748i	−0.292845	−	0.348999i
$93$	−1.29638	−	1.54497i	−0.134429	−	0.160206i
$94$	−4.17191	−	0.735620i	−0.430300	−	0.0758734i
$95$		0			0
$96$	−1.06372	−	2.92256i	−0.108566	−	0.298282i
$97$	−2.26408	+	1.30717i	−0.229883	+	0.132723i	−0.610518	−	0.792002i	$-0.709039\pi$
$97$	−2.26408	+	1.30717i	−0.229883	+	0.132723i	0.380635	+	0.924725i	$0.375705\pi$
$98$	9.39785	−	1.65710i	0.949327	−	0.167392i
$99$	9.15659	+	7.68329i	0.920272	+	0.772200i
$100$		0			0
$101$	5.33462	+	9.23983i	0.530814	+	0.919397i	0.999353	+	0.0359545i	$0.0114471\pi$
$101$	5.33462	+	9.23983i	0.530814	+	0.919397i	−0.468539	+	0.883443i	$0.655220\pi$
$102$	−0.102441	+	0.580972i	−0.0101432	+	0.0575248i
$103$	14.2210	+	8.21051i	1.40124	+	0.809005i	0.994520	−	0.104548i	$-0.0333396\pi$
$103$	14.2210	+	8.21051i	1.40124	+	0.809005i	0.406719	+	0.913554i	$0.366673\pi$
$104$	1.21756	+	0.443154i	0.119391	+	0.0434548i
$105$		0			0
$106$	−9.40177	+	25.8311i	−0.913180	+	2.50894i
$107$	2.22016	+	12.5912i	0.214631	+	1.21723i	0.881546	+	0.472099i	$0.156503\pi$
$107$	2.22016	+	12.5912i	0.214631	+	1.21723i	−0.666915	+	0.745134i	$0.732385\pi$
$108$	3.96798	−	3.32953i	0.381819	−	0.320384i
$109$	2.89888	−	3.45475i	0.277662	−	0.330905i	−0.609133	−	0.793068i	$-0.708482\pi$
$109$	2.89888	−	3.45475i	0.277662	−	0.330905i	0.886795	+	0.462164i	$0.152927\pi$
$110$		0			0
$111$	−1.46007	+	1.82077i	−0.138584	+	0.172820i
$112$	11.2140			1.05962
$113$	−7.27299	+	8.66761i	−0.684185	+	0.815380i	−0.990639	−	0.136505i	$-0.956413\pi$
$113$	−7.27299	+	8.66761i	−0.684185	+	0.815380i	0.306454	+	0.951885i	$0.400857\pi$
$114$	0.916685	−	0.769190i	0.0858554	−	0.0720412i
$115$		0			0
$116$	0.605201	−	1.66278i	0.0561915	−	0.154385i
$117$		−	5.80917i		−	0.537058i
$118$	−2.78013	−	1.01189i	−0.255932	−	0.0931516i
$119$	−2.18518	−	1.26162i	−0.200315	−	0.115652i
$120$		0			0
$121$	−3.27793	−	5.67754i	−0.297994	−	0.516140i
$122$	2.68398	−	4.64879i	0.242996	−	0.420882i
$123$	3.13486	+	2.63046i	0.282661	+	0.237180i
$124$	−11.9403	+	2.10539i	−1.07227	+	0.189069i
$125$		0			0
$126$	6.89585	+	18.9462i	0.614331	+	1.68786i
$127$	−8.49119	+	3.09054i	−0.753471	+	0.274241i	−0.690066	−	0.723747i	$-0.742418\pi$
$127$	−8.49119	+	3.09054i	−0.753471	+	0.274241i	−0.0634054	+	0.997988i	$0.520196\pi$
$128$	−4.95410	−	0.873542i	−0.437885	−	0.0772109i
$129$	−2.45110	−	2.92111i	−0.215808	−	0.257190i
$130$		0			0
$131$	17.4810	+	3.08238i	1.52732	+	0.269309i	0.873307	−	0.487171i	$-0.161971\pi$
$131$	17.4810	+	3.08238i	1.52732	+	0.269309i	0.654018	+	0.756479i	$0.273082\pi$
$132$	−3.48457	+	1.26828i	−0.303293	+	0.110390i
$133$	1.75054	+	4.80956i	0.151791	+	0.417042i
$134$	−18.2076	+	10.5121i	−1.57289	+	0.908110i
$135$		0			0
$136$	0.361134	+	0.303028i	0.0309670	+	0.0259844i
$137$	6.37617	−	11.0439i	0.544753	−	0.943540i	−0.453869	−	0.891068i	$-0.649957\pi$
$137$	6.37617	−	11.0439i	0.544753	−	0.943540i	0.998622	−	0.0524719i	$-0.0167100\pi$
$138$	−0.754232	−	1.30637i	−0.0642045	−	0.111205i
$139$	2.30919	−	13.0961i	0.195863	−	1.11079i	−0.715322	−	0.698795i	$-0.753720\pi$
$139$	2.30919	−	13.0961i	0.195863	−	1.11079i	0.911185	−	0.411998i	$-0.135169\pi$
$140$		0			0
$141$	−0.736003	−	0.267883i	−0.0619826	−	0.0225598i
$142$			28.7484i			2.41252i
$143$	−2.91815	+	8.01756i	−0.244028	+	0.670462i
$144$	1.63117	+	9.25084i	0.135931	+	0.770903i
$145$		0			0
$146$	−4.57843	+	5.45636i	−0.378913	+	0.451571i
$147$	1.76436			0.145522
$148$	5.09068	+	13.0745i	0.418451	+	1.07472i
$149$	5.00022			0.409634			0.204817	−	0.978800i	$-0.434340\pi$
$149$	5.00022			0.409634			0.204817	+	0.978800i	$0.434340\pi$
$150$		0			0
$151$	5.51949	−	4.63140i	0.449170	−	0.376898i	−0.389958	−	0.920833i	$-0.627510\pi$
$151$	5.51949	−	4.63140i	0.449170	−	0.376898i	0.839128	+	0.543934i	$0.183066\pi$
$152$	−0.166053	−	0.941736i	−0.0134687	−	0.0763849i
$153$	0.722900	−	1.98615i	0.0584430	−	0.160571i
$154$		−	29.6127i		−	2.38626i
$155$		0			0
$156$	1.56073	+	0.901090i	0.124959	+	0.0721449i
$157$	−2.95184	+	16.7407i	−0.235582	+	1.33605i	0.605802	+	0.795615i	$0.292852\pi$
$157$	−2.95184	+	16.7407i	−0.235582	+	1.33605i	−0.841384	+	0.540437i	$0.818259\pi$
$158$	−4.27801	−	7.40973i	−0.340340	−	0.589486i
$159$	−2.54119	+	4.40148i	−0.201530	+	0.349060i
$160$		0			0
$161$	6.35390	−	1.12036i	0.500757	−	0.0882970i
$162$	−13.8326	+	7.98627i	−1.08679	+	0.627460i
$163$	−0.362789	−	0.996756i	−0.0284159	−	0.0780719i	0.924674	−	0.380761i	$-0.124338\pi$
$163$	−0.362789	−	0.996756i	−0.0284159	−	0.0780719i	−0.953089	+	0.302689i	$0.902116\pi$
$164$	23.1178	−	8.41418i	1.80520	−	0.657037i
$165$		0			0
$166$	−19.1067	−	22.7705i	−1.48297	−	1.76733i
$167$	−6.18886	−	7.37559i	−0.478908	−	0.570741i	0.471452	−	0.881892i	$-0.343730\pi$
$167$	−6.18886	−	7.37559i	−0.478908	−	0.570741i	−0.950360	+	0.311151i	$0.899285\pi$
$168$	−0.818816	−	0.144379i	−0.0631730	−	0.0111391i
$169$	−8.31949	+	3.02805i	−0.639961	+	0.232927i
$170$		0			0
$171$	−3.71296	+	2.14368i	−0.283937	+	0.163931i
$172$	−22.5758	+	3.98072i	−1.72139	+	0.303527i
$173$	−17.6569	−	14.8159i	−1.34243	−	1.12643i	−0.980995	−	0.194035i	$-0.937843\pi$
$173$	−17.6569	−	14.8159i	−1.34243	−	1.12643i	−0.361435	−	0.932397i	$-0.617713\pi$
$174$	0.305414	−	0.528993i	0.0231534	−	0.0401029i
$175$		0			0
$176$	2.39575	−	13.5870i	0.180587	−	1.02416i
$177$	−0.473719	−	0.273502i	−0.0356069	−	0.0205576i
$178$	25.6256	+	9.32695i	1.92072	+	0.699085i
$179$			13.3230i			0.995810i	0.867232	+	0.497905i	$0.165897\pi$
$179$			13.3230i			0.995810i	−0.867232	+	0.497905i	$0.834103\pi$
$180$		0			0
$181$	2.22773	+	12.6341i	0.165586	+	0.939083i	0.948459	+	0.316901i	$0.102642\pi$
$181$	2.22773	+	12.6341i	0.165586	+	0.939083i	−0.782873	+	0.622182i	$0.786247\pi$
$182$	−11.0247	+	9.25082i	−0.817205	+	0.685717i
$183$	0.637951	−	0.760280i	0.0471587	−	0.0562015i
$184$	−1.20544			−0.0888664
$185$		0			0
$186$	−4.18536			−0.306886
$187$	−1.99543	+	2.37806i	−0.145920	+	0.173901i
$188$	−3.60698	+	3.02662i	−0.263066	+	0.220739i
$189$	1.32804	+	7.53167i	0.0966005	+	0.547849i
$190$		0			0
$191$		−	15.3246i		−	1.10885i	−0.832233	−	0.554426i	$-0.812938\pi$
$191$		−	15.3246i		−	1.10885i	0.832233	−	0.554426i	$-0.187062\pi$
$192$	−3.69059	−	1.34327i	−0.266346	−	0.0969419i
$193$	−7.53955	−	4.35296i	−0.542709	−	0.313333i	0.203467	−	0.979082i	$-0.434779\pi$
$193$	−7.53955	−	4.35296i	−0.542709	−	0.313333i	−0.746176	+	0.665749i	$0.768112\pi$
$194$	−0.942106	+	5.34295i	−0.0676393	+	0.383601i
$195$		0			0
$196$	5.30339	−	9.18575i	0.378814	−	0.656125i
$197$	−13.7948	−	11.5752i	−0.982839	−	0.824700i	0.00167663	−	0.999999i	$-0.499466\pi$
$197$	−13.7948	−	11.5752i	−0.982839	−	0.824700i	−0.984515	+	0.175299i	$0.943911\pi$
$198$	24.4286	−	4.30743i	1.73607	−	0.306116i
$199$	1.54995	−	0.894862i	0.109873	−	0.0634351i	−0.444057	−	0.895999i	$-0.646461\pi$
$199$	1.54995	−	0.894862i	0.109873	−	0.0634351i	0.553929	+	0.832564i	$0.313128\pi$
$200$		0			0
$201$	−3.65273	+	1.32948i	−0.257643	+	0.0937745i
$202$	21.8048	+	3.84478i	1.53418	+	0.270518i
$203$	1.67935	+	2.00137i	0.117867	+	0.140469i
$204$	0.421481	+	0.502301i	0.0295095	+	0.0351681i
$205$		0			0
$206$	32.0224	−	11.6552i	2.23111	−	0.812056i
$207$	1.84846	+	5.07860i	0.128477	+	0.352987i
$208$	−5.80680	+	3.35256i	−0.402629	+	0.232458i
$209$	6.20130	−	1.09346i	0.428953	−	0.0756360i
$210$		0			0
$211$	7.50683	−	13.0022i	0.516792	−	0.895110i	−0.483018	−	0.875610i	$-0.660459\pi$
$211$	7.50683	−	13.0022i	0.516792	−	0.895110i	0.999810	−	0.0194993i	$-0.00620720\pi$
$212$	15.2769	+	26.4603i	1.04922	+	1.81730i
$213$	−0.922985	+	5.23451i	−0.0632419	+	0.358663i
$214$	22.9780	+	13.2664i	1.57075	+	0.906870i
$215$		0			0
$216$		−	1.42889i		−	0.0972234i
$217$	6.12264	−	16.8218i	0.415632	−	1.14194i
$218$	−1.62518	−	9.21683i	−0.110071	−	0.624243i
$219$	−1.00882	+	0.846499i	−0.0681696	+	0.0572011i
$220$		0			0
$221$	1.50870			0.101486
$222$	0.946878	+	4.74990i	0.0635503	+	0.318792i
$223$	−8.60075			−0.575949			−0.287975	−	0.957638i	$-0.592982\pi$
$223$	−8.60075			−0.575949			−0.287975	+	0.957638i	$0.592982\pi$
$224$	17.7446	−	21.1472i	1.18561	−	1.41296i
$225$		0			0
$226$	4.07740	+	23.1241i	0.271225	+	1.53819i
$227$	−6.17978	+	16.9788i	−0.410166	+	1.12692i	0.546936	+	0.837174i	$0.315794\pi$
$227$	−6.17978	+	16.9788i	−0.410166	+	1.12692i	−0.957103	+	0.289749i	$0.906428\pi$
$228$		−	1.33006i		−	0.0880857i
$229$	5.74779	+	2.09202i	0.379825	+	0.138245i	0.524875	−	0.851179i	$-0.324112\pi$
$229$	5.74779	+	2.09202i	0.379825	+	0.138245i	−0.145050	+	0.989424i	$0.546334\pi$
$230$		0			0
$231$	0.950734	−	5.39188i	0.0625537	−	0.354760i
$232$	−0.244063	−	0.422729i	−0.0160235	−	0.0277535i
$233$	−7.55544	+	13.0864i	−0.494973	+	0.857319i	−0.999983	−	0.00579462i	$-0.998156\pi$
$233$	−7.55544	+	13.0864i	−0.494973	+	0.857319i	0.505010	+	0.863114i	$0.331489\pi$
$234$	−9.23498	−	7.74907i	−0.603710	−	0.506573i
$235$		0			0
$236$	−2.84785	+	1.64421i	−0.185379	+	0.107029i
$237$	−0.541045	−	1.48651i	−0.0351446	−	0.0965591i
$238$	−4.92052	+	1.79092i	−0.318950	+	0.116088i
$239$	−10.9787	−	1.93584i	−0.710153	−	0.125219i	−0.193108	−	0.981177i	$-0.561857\pi$
$239$	−10.9787	−	1.93584i	−0.710153	−	0.125219i	−0.517045	+	0.855958i	$0.672968\pi$
$240$		0			0
$241$	−10.5519	−	12.5752i	−0.679707	−	0.810043i	0.310363	−	0.950618i	$-0.399549\pi$
$241$	−10.5519	−	12.5752i	−0.679707	−	0.810043i	−0.990070	+	0.140575i	$0.955105\pi$
$242$	−13.3983	−	2.36248i	−0.861274	−	0.151866i
$243$	−9.10568	+	3.31420i	−0.584130	+	0.212606i
$244$	−2.04065	−	5.60663i	−0.130639	−	0.358928i
$245$		0			0
$246$	8.36340	−	1.47469i	0.533231	−	0.0940230i
$247$	−2.34433	−	1.96713i	−0.149166	−	0.125166i
$248$	−1.67230	+	2.89651i	−0.106191	+	0.183929i
$249$	−2.74789	−	4.75948i	−0.174140	−	0.301620i
$250$		0			0
$251$	−2.89473	−	1.67128i	−0.182714	−	0.105490i	0.405853	−	0.913938i	$-0.366974\pi$
$251$	−2.89473	−	1.67128i	−0.182714	−	0.105490i	−0.588567	+	0.808448i	$0.700308\pi$
$252$	21.0586	+	7.66469i	1.32657	+	0.482830i
$253$		−	7.93780i		−	0.499045i
$254$	−6.41360	+	17.6212i	−0.402425	+	1.10565i
$255$		0			0
$256$	7.68539	−	6.44880i	0.480337	−	0.403050i
$257$	−3.23630	+	3.85687i	−0.201875	+	0.240585i	−0.857478	−	0.514521i	$-0.827970\pi$
$257$	−3.23630	+	3.85687i	−0.201875	+	0.240585i	0.655603	+	0.755105i	$0.272414\pi$
$258$	−7.91339			−0.492666
$259$	−20.4760	−	3.14279i	−1.27231	−	0.195283i
$260$		0			0
$261$	−1.40673	+	1.67647i	−0.0870742	+	0.103771i
$262$	28.2187	−	23.6783i	1.74336	−	1.46285i
$263$	0.903888	+	5.12620i	0.0557361	+	0.316095i	0.999911	−	0.0133498i	$-0.00424949\pi$
$263$	0.903888	+	5.12620i	0.0557361	+	0.316095i	−0.944175	+	0.329445i	$0.893138\pi$
$264$	−0.349863	+	0.961241i	−0.0215326	+	0.0591603i
$265$		0			0
$266$	9.98099	+	3.63278i	0.611974	+	0.222740i
$267$	4.36645	+	2.52097i	0.267223	+	0.154281i
$268$	−4.05787	+	23.0133i	−0.247874	+	1.40576i
$269$	−11.3145	−	19.5973i	−0.689859	−	1.19487i	−0.971883	−	0.235463i	$-0.924339\pi$
$269$	−11.3145	−	19.5973i	−0.689859	−	1.19487i	0.282025	−	0.959407i	$-0.408994\pi$
$270$		0			0
$271$	10.4587	+	8.77589i	0.635321	+	0.533097i	0.902577	−	0.430528i	$-0.141673\pi$
$271$	10.4587	+	8.77589i	0.635321	+	0.533097i	−0.267257	+	0.963625i	$0.586117\pi$
$272$	−2.40253	+	0.423632i	−0.145675	+	0.0256864i
$273$	−2.30438	+	1.33043i	−0.139467	+	0.0805215i
$274$	−9.05127	−	24.8682i	−0.546807	−	1.50234i
$275$		0			0
$276$	−1.65118	−	0.291147i	−0.0993891	−	0.0175250i
$277$	−7.67915	−	9.15166i	−0.461396	−	0.549870i	0.484309	−	0.874897i	$-0.339071\pi$
$277$	−7.67915	−	9.15166i	−0.461396	−	0.549870i	−0.945705	+	0.325027i	$0.894627\pi$
$278$	−17.7388	−	21.1403i	−1.06390	−	1.26791i
$279$	14.7675	+	2.60391i	0.884109	+	0.155892i
$280$		0			0
$281$	7.10086	+	19.5095i	0.423602	+	1.16384i	0.949631	+	0.313370i	$0.101458\pi$
$281$	7.10086	+	19.5095i	0.423602	+	1.16384i	−0.526029	+	0.850466i	$0.676320\pi$
$282$	−1.40764	+	0.812702i	−0.0838238	+	0.0483957i
$283$	−17.3625	+	3.06148i	−1.03209	+	0.181986i	−0.663945	−	0.747781i	$-0.731119\pi$
$283$	−17.3625	+	3.06148i	−1.03209	+	0.181986i	−0.368148	+	0.929767i	$0.620008\pi$
$284$	24.4779	+	20.5394i	1.45250	+	1.21879i
$285$		0			0
$286$	8.85308	+	15.3340i	0.523494	+	0.906717i
$287$	−6.30747	+	35.7715i	−0.372318	+	2.11152i
$288$	20.0262	+	11.5621i	1.18005	+	0.681305i
$289$	−15.4590	−	5.62660i	−0.909350	−	0.330976i
$290$		0			0
$291$	−0.343077	+	0.942596i	−0.0201115	+	0.0552559i
$292$	1.37476	+	7.79663i	0.0804515	+	0.456263i
$293$	0.391941	−	0.328877i	0.0228974	−	0.0192132i	−0.631267	−	0.775565i	$-0.717465\pi$
$293$	0.391941	−	0.328877i	0.0228974	−	0.0192132i	0.654165	+	0.756352i	$0.273020\pi$
$294$	2.35355	−	2.80485i	0.137262	−	0.163582i
$295$		0			0
$296$	3.66554	+	1.24257i	0.213055	+	0.0722232i
$297$	9.40918			0.545976
$298$	6.66999	−	7.94898i	0.386382	−	0.460472i
$299$	−2.95521	+	2.47972i	−0.170904	+	0.143406i
$300$		0			0
$301$	11.5762	−	31.8055i	0.667244	−	1.83324i
$302$		−	14.9525i		−	0.860418i
$303$	3.84678	+	1.40011i	0.220992	+	0.0804344i
$304$	4.28560	+	2.47429i	0.245796	+	0.141910i
$305$		0			0
$306$	−2.19313	−	3.79861i	−0.125373	−	0.217152i
$307$	−4.36972	+	7.56858i	−0.249393	+	0.431962i	−0.963358	−	0.268220i	$-0.913564\pi$
$307$	−4.36972	+	7.56858i	−0.249393	+	0.431962i	0.713964	+	0.700182i	$0.246898\pi$
$308$	−25.2139	−	21.1569i	−1.43669	−	1.20553i
$309$	6.20482	−	1.09408i	0.352980	−	0.0622399i
$310$		0			0
$311$	9.83690	+	27.0267i	0.557799	+	1.53254i	0.822822	+	0.568299i	$0.192398\pi$
$311$	9.83690	+	27.0267i	0.557799	+	1.53254i	−0.265023	+	0.964242i	$0.585379\pi$
$312$	0.467161	−	0.170033i	0.0264478	−	0.00962621i
$313$	29.0257	+	5.11802i	1.64063	+	0.289288i	0.916398	−	0.400268i	$-0.131083\pi$
$313$	29.0257	+	5.11802i	1.64063	+	0.289288i	0.724233	+	0.689555i	$0.242194\pi$
$314$	22.6755	+	27.0236i	1.27965	+	1.52503i
$315$		0			0
$316$	−9.36547	−	1.65139i	−0.526849	−	0.0928977i
$317$	22.7808	−	8.29154i	1.27950	−	0.465699i	0.389232	−	0.921140i	$-0.372740\pi$
$317$	22.7808	−	8.29154i	1.27950	−	0.465699i	0.890266	+	0.455441i	$0.150518\pi$
$318$	3.60734	+	9.91109i	0.202290	+	0.555786i
$319$	2.78365	−	1.60714i	0.155855	−	0.0899828i
$320$		0			0
$321$	3.75791	+	3.15326i	0.209746	+	0.175998i
$322$	6.69463	−	11.5954i	0.373077	−	0.646189i
$323$	−0.556734	−	0.964292i	−0.0309775	−	0.0536546i
$324$	−3.08284	+	17.4836i	−0.171269	+	0.971314i
$325$		0			0
$326$	−2.06851	−	0.752874i	−0.114564	−	0.0416978i
$327$		−	1.73038i		−	0.0956900i
$328$	2.32111	−	6.37718i	0.128162	−	0.352121i
$329$	−1.20722	−	6.84647i	−0.0665560	−	0.377458i
$330$		0			0
$331$	−9.50901	+	11.3324i	−0.522663	+	0.622885i	−0.961208	−	0.275824i	$-0.911049\pi$
$331$	−9.50901	+	11.3324i	−0.522663	+	0.622885i	0.438546	+	0.898709i	$0.355494\pi$
$332$	−33.0389			−1.81324
$333$	−0.385801	−	17.3485i	−0.0211418	−	0.950693i
$334$	−19.9807			−1.09330
$335$		0			0
$336$	3.29604	−	2.76570i	0.179814	−	0.150882i
$337$	−2.64841	−	15.0199i	−0.144268	−	0.818184i	−0.967952	−	0.251135i	$-0.919196\pi$
$337$	−2.64841	−	15.0199i	−0.144268	−	0.818184i	0.823684	−	0.567049i	$-0.191915\pi$
$338$	−6.28392	+	17.2649i	−0.341800	+	0.939088i
$339$			4.34134i			0.235789i
$340$		0			0
$341$	−19.0734	−	11.0121i	−1.03288	−	0.596336i
$342$	−1.54500	+	8.76210i	−0.0835438	+	0.473800i
$343$	−4.08945	−	7.08314i	−0.220810	−	0.382454i
$344$	−3.16187	+	5.47652i	−0.170477	+	0.295274i
$345$		0			0
$346$	−47.1064	+	8.30613i	−2.53246	+	0.446540i
$347$	0.986862	−	0.569765i	0.0529775	−	0.0305866i	−0.473277	−	0.880914i	$-0.656929\pi$
$347$	0.986862	−	0.569765i	0.0529775	−	0.0305866i	0.526255	+	0.850327i	$0.323596\pi$
$348$	−0.232208	−	0.637987i	−0.0124477	−	0.0341997i
$349$	29.6988	−	10.8095i	1.58974	−	0.578618i	0.612447	−	0.790512i	$-0.290185\pi$
$349$	29.6988	−	10.8095i	1.58974	−	0.578618i	0.977293	+	0.211894i	$0.0679632\pi$
$350$		0			0
$351$	−2.93936	−	3.50300i	−0.156892	−	0.186976i
$352$	−21.8312	−	26.0174i	−1.16361	−	1.38673i
$353$	28.6822	+	5.05745i	1.52660	+	0.269181i	0.873023	−	0.487678i	$-0.162156\pi$
$353$	28.6822	+	5.05745i	1.52660	+	0.269181i	0.653578	+	0.756859i	$0.273267\pi$
$354$	−1.06670	+	0.388248i	−0.0566946	+	0.0206352i
$355$		0			0
$356$	26.2498	−	15.1553i	1.39123	−	0.803230i
$357$	−0.953425	+	0.168115i	−0.0504606	+	0.00889757i
$358$	21.1800	+	17.7721i	1.11940	+	0.939284i
$359$	−0.0422360	+	0.0731549i	−0.00222913	+	0.00386097i	−0.867138	−	0.498068i	$-0.834043\pi$
$359$	−0.0422360	+	0.0731549i	−0.00222913	+	0.00386097i	0.864909	+	0.501929i	$0.167376\pi$
$360$		0			0
$361$	2.90711	−	16.4871i	0.153006	−	0.867740i
$362$	23.0563	+	13.3116i	1.21181	+	0.699641i
$363$	−2.36371	−	0.860319i	−0.124062	−	0.0451550i
$364$			15.9963i			0.838434i
$365$		0			0
$366$	−0.357650	−	2.02833i	−0.0186947	−	0.106023i
$367$	−9.80964	+	8.23127i	−0.512059	+	0.429669i	−0.861853	−	0.507158i	$-0.830696\pi$
$367$	−9.80964	+	8.23127i	−0.512059	+	0.429669i	0.349794	+	0.936827i	$0.386252\pi$
$368$	4.00975	−	4.77863i	0.209023	−	0.249104i
$369$	−30.4267			−1.58395
$370$		0			0
$371$	−45.1117			−2.34208
$372$	−2.99025	+	3.56364i	−0.155037	+	0.184766i
$373$	9.92150	−	8.32512i	0.513716	−	0.431059i	−0.348719	−	0.937227i	$-0.613383\pi$
$373$	9.92150	−	8.32512i	0.513716	−	0.431059i	0.862434	+	0.506169i	$0.168939\pi$
$374$	1.11868	+	6.34436i	0.0578457	+	0.328059i
$375$		0			0
$376$			1.29889i			0.0669852i
$377$	−1.46793	−	0.534282i	−0.0756022	−	0.0275169i
$378$	13.7448	+	7.93557i	0.706956	+	0.408161i
$379$	4.68752	−	26.5842i	0.240782	−	1.36554i	−0.589307	−	0.807909i	$-0.700599\pi$
$379$	4.68752	−	26.5842i	0.240782	−	1.36554i	0.830089	−	0.557631i	$-0.188290\pi$
$380$		0			0
$381$	−1.73353	+	3.00256i	−0.0888113	+	0.153826i
$382$	−24.3620	−	20.4421i	−1.24647	−	1.04591i
$383$	−10.9977	+	1.93918i	−0.561954	+	0.0990877i	−0.447407	−	0.894330i	$-0.647653\pi$
$383$	−10.9977	+	1.93918i	−0.561954	+	0.0990877i	−0.114547	+	0.993418i	$0.536542\pi$
$384$	−1.67156	+	0.965076i	−0.0853015	+	0.0492488i
$385$		0			0
$386$	−16.9773	+	6.17923i	−0.864122	+	0.314515i
$387$	27.9214	+	4.92329i	1.41932	+	0.250265i
$388$	3.87618	+	4.61945i	0.196783	+	0.234517i
$389$	2.79684	+	3.33314i	0.141805	+	0.168997i	0.832273	−	0.554367i	$-0.187039\pi$
$389$	2.79684	+	3.33314i	0.141805	+	0.168997i	−0.690467	+	0.723364i	$0.742595\pi$
$390$		0			0
$391$	−1.31896	+	0.480063i	−0.0667028	+	0.0242778i
$392$	−1.00073	−	2.74949i	−0.0505447	−	0.138870i
$393$	5.89826	−	3.40536i	0.297528	−	0.171778i
$394$	−36.8028	+	6.48932i	−1.85410	+	0.326927i
$395$		0			0
$396$	13.7856	−	23.8773i	0.692751	−	1.19988i
$397$	−3.05525	−	5.29185i	−0.153339	−	0.265591i	0.779114	−	0.626882i	$-0.215669\pi$
$397$	−3.05525	−	5.29185i	−0.153339	−	0.265591i	−0.932453	+	0.361292i	$0.882336\pi$
$398$	0.644948	−	3.65768i	0.0323283	−	0.183343i
$399$	1.70070	+	0.981901i	0.0851416	+	0.0491565i
$400$		0			0
$401$			9.95090i			0.496924i	0.968642	+	0.248462i	$0.0799251\pi$
$401$			9.95090i			0.496924i	−0.968642	+	0.248462i	$0.920075\pi$
$402$	−2.75899	+	7.58027i	−0.137606	+	0.378070i
$403$	1.85867	+	10.5411i	0.0925871	+	0.525088i
$404$	18.8522	−	15.8189i	0.937931	−	0.787018i
$405$		0			0
$406$	5.42177			0.269078
$407$	−8.18231	+	24.1375i	−0.405582	+	1.19645i
$408$	0.180881			0.00895494
$409$	−12.9702	+	15.4573i	−0.641336	+	0.764315i	−0.984581	−	0.174931i	$-0.944030\pi$
$409$	−12.9702	+	15.4573i	−0.641336	+	0.764315i	0.343244	+	0.939246i	$0.388474\pi$
$410$		0			0
$411$	−0.849647	−	4.81858i	−0.0419100	−	0.237683i
$412$	12.9547	−	35.5927i	0.638231	−	1.75352i
$413$		−	4.85525i		−	0.238911i
$414$	10.5393	+	3.83599i	0.517978	+	0.188529i
$415$		0			0
$416$	−2.86625	+	16.2553i	−0.140530	+	0.796983i
$417$	−2.55116	−	4.41873i	−0.124931	−	0.216386i
$418$	6.53385	−	11.3170i	0.319581	−	0.553531i
$419$	−9.44859	−	7.92831i	−0.461594	−	0.387323i	0.382123	−	0.924111i	$-0.375193\pi$
$419$	−9.44859	−	7.92831i	−0.461594	−	0.387323i	−0.843717	+	0.536788i	$0.819637\pi$
$420$		0			0
$421$	−2.81356	+	1.62441i	−0.137124	+	0.0791688i	−0.566993	−	0.823723i	$-0.691893\pi$
$421$	−2.81356	+	1.62441i	−0.137124	+	0.0791688i	0.429868	+	0.902892i	$0.358560\pi$
$422$	−10.6563	−	29.2779i	−0.518741	−	1.42523i
$423$	5.47230	−	1.99176i	0.266073	−	0.0968425i
$424$	8.30039	+	1.46358i	0.403103	+	0.0710779i
$425$		0			0
$426$	7.09022	+	8.44980i	0.343522	+	0.409394i
$427$	8.67547	+	1.52972i	0.419835	+	0.0740283i
$428$	27.7124	−	10.0865i	1.33953	−	0.487549i
$429$	1.11966	+	3.07624i	0.0540577	+	0.148522i
$430$		0			0
$431$	−7.23039	+	1.27491i	−0.348276	+	0.0614104i	−0.345050	−	0.938584i	$-0.612138\pi$
$431$	−7.23039	+	1.27491i	−0.348276	+	0.0614104i	−0.00322596	+	0.999995i	$0.501027\pi$
$432$	5.66442	+	4.75301i	0.272529	+	0.228679i
$433$	6.26226	−	10.8466i	0.300945	−	0.521252i	−0.675405	−	0.737447i	$-0.736031\pi$
$433$	6.26226	−	10.8466i	0.300945	−	0.521252i	0.976350	+	0.216195i	$0.0693646\pi$
$434$	−18.5748	−	32.1726i	−0.891620	−	1.54433i
$435$		0			0
$436$	−9.00881	−	5.20124i	−0.431444	−	0.249094i
$437$	2.67544	+	0.973781i	0.127984	+	0.0465822i
$438$			2.73292i			0.130584i
$439$	11.4814	−	31.5448i	0.547975	−	1.50555i	−0.288465	−	0.957491i	$-0.593145\pi$
$439$	11.4814	−	31.5448i	0.547975	−	1.50555i	0.836440	−	0.548059i	$-0.184633\pi$
$440$		0			0
$441$	−10.0492	+	8.43229i	−0.478534	+	0.401538i
$442$	2.01251	−	2.39842i	0.0957254	−	0.114081i
$443$	−31.5728			−1.50007			−0.750034	−	0.661400i	$-0.769963\pi$
$443$	−31.5728			−1.50007			−0.750034	+	0.661400i	$0.769963\pi$
$444$	4.72082	+	2.58736i	0.224040	+	0.122791i
$445$		0			0
$446$	−11.4729	+	13.6728i	−0.543256	+	0.647427i
$447$	1.46968	−	1.23320i	0.0695133	−	0.0583286i
$448$	−6.05344	−	34.3308i	−0.285998	−	1.62198i
$449$	−6.68188	+	18.3583i	−0.315338	+	0.866383i	0.676218	+	0.736701i	$0.263618\pi$
$449$	−6.68188	+	18.3583i	−0.315338	+	0.866383i	−0.991556	+	0.129681i	$0.958605\pi$
$450$		0			0
$451$	41.9936	+	15.2844i	1.97740	+	0.719714i
$452$	22.6022	+	13.0494i	1.06312	+	0.613792i
$453$	0.480058	−	2.72254i	0.0225551	−	0.127916i
$454$	18.7482	+	32.4728i	0.879896	+	1.52402i
$455$		0			0
$456$	−0.281067	−	0.235843i	−0.0131622	−	0.0110444i
$457$	29.3811	−	5.18068i	1.37439	−	0.242342i	0.562812	−	0.826585i	$-0.309720\pi$
$457$	29.3811	−	5.18068i	1.37439	−	0.242342i	0.811579	+	0.584243i	$0.198608\pi$
$458$	10.9929	−	6.34677i	0.513666	−	0.296565i
$459$	−0.569049	−	1.56345i	−0.0265609	−	0.0729756i
$460$		0			0
$461$	−30.4547	−	5.36999i	−1.41842	−	0.250105i	−0.588728	−	0.808331i	$-0.700371\pi$
$461$	−30.4547	−	5.36999i	−1.41842	−	0.250105i	−0.829689	+	0.558226i	$0.811482\pi$
$462$	−7.30338	−	8.70383i	−0.339784	−	0.404939i
$463$	11.1860	+	13.3309i	0.519857	+	0.619541i	0.960547	−	0.278118i	$-0.0897107\pi$
$463$	11.1860	+	13.3309i	0.519857	+	0.619541i	−0.440690	+	0.897659i	$0.645266\pi$
$464$	2.48763	+	0.438636i	0.115485	+	0.0203632i
$465$		0			0
$466$	10.7253	+	29.4675i	0.496840	+	1.36506i
$467$	12.3845	−	7.15022i	0.573089	−	0.330873i	−0.185293	−	0.982683i	$-0.559324\pi$
$467$	12.3845	−	7.15022i	0.573089	−	0.330873i	0.758382	+	0.651810i	$0.225990\pi$
$468$	−13.1959	+	2.32680i	−0.609982	+	0.107556i
$469$	−26.4306	−	22.1779i	−1.22045	−	1.02408i
$470$		0			0
$471$	3.26114	+	5.64847i	0.150266	+	0.260268i
$472$	−0.157521	+	0.893348i	−0.00725051	+	0.0411197i
$473$	−36.0627	−	20.8208i	−1.65816	−	0.957342i
$474$	−3.08486	−	1.12280i	−0.141692	−	0.0515718i
$475$		0			0
$476$	−1.99060	+	5.46912i	−0.0912389	+	0.250677i
$477$	−6.56189	−	37.2143i	−0.300448	−	1.70393i
$478$	−17.7224	+	14.8708i	−0.810602	+	0.680176i
$479$	−12.3159	+	14.6775i	−0.562728	+	0.670633i	−0.970121	−	0.242620i	$-0.921993\pi$
$479$	−12.3159	+	14.6775i	−0.562728	+	0.670633i	0.407394	+	0.913253i	$0.366438\pi$
$480$		0			0
$481$	11.5424	−	4.49414i	0.526287	−	0.204915i
$482$	−34.0667			−1.55170
$483$	1.59123	−	1.89636i	0.0724037	−	0.0862874i
$484$	−11.5840	+	9.72013i	−0.526545	+	0.441824i
$485$		0			0
$486$	−6.87775	+	18.8965i	−0.311981	+	0.857161i
$487$		−	30.8326i		−	1.39716i	−0.715533	−	0.698579i	$-0.753816\pi$
$487$		−	30.8326i		−	1.39716i	0.715533	−	0.698579i	$-0.246184\pi$
$488$	−1.54662	−	0.562925i	−0.0700124	−	0.0254824i
$489$	−0.352461	−	0.203494i	−0.0159389	−	0.00920230i
$490$		0			0
$491$	−2.74684	−	4.75767i	−0.123963	−	0.214711i	0.797364	−	0.603499i	$-0.206227\pi$
$491$	−2.74684	−	4.75767i	−0.123963	−	0.214711i	−0.921327	+	0.388788i	$0.872894\pi$
$492$	4.71963	−	8.17465i	0.212778	−	0.368541i
$493$	−0.435397	−	0.365341i	−0.0196093	−	0.0164541i
$494$	−6.25439	+	1.10282i	−0.281398	+	0.0496181i
$495$		0			0
$496$	−5.91970	−	16.2642i	−0.265802	−	0.730286i
$497$	−44.3335	+	16.1361i	−1.98863	+	0.723801i
$498$	−11.2318	−	1.98046i	−0.503307	−	0.0887467i
$499$	15.0046	+	17.8817i	0.671697	+	0.800497i	0.989014	−	0.147822i	$-0.0472264\pi$
$499$	15.0046	+	17.8817i	0.671697	+	0.800497i	−0.317317	+	0.948319i	$0.602782\pi$
$500$		0			0
$501$	−3.63808	−	0.641492i	−0.162538	−	0.0286597i
$502$	−6.51826	+	2.37245i	−0.290924	+	0.105888i
$503$	−1.57928	−	4.33903i	−0.0704164	−	0.193468i	0.899492	−	0.436937i	$-0.143937\pi$
$503$	−1.57928	−	4.33903i	−0.0704164	−	0.193468i	−0.969909	+	0.243469i	$0.921714\pi$
$504$	5.35373	−	3.09098i	0.238474	−	0.137683i
$505$		0			0
$506$	−12.6189	−	10.5885i	−0.560979	−	0.470718i
$507$	−1.69847	+	2.94184i	−0.0754319	+	0.130652i
$508$	10.4214	+	18.0504i	0.462376	+	0.800859i
$509$	2.83264	−	16.0647i	0.125554	−	0.712055i	−0.855423	−	0.517931i	$-0.826702\pi$
$509$	2.83264	−	16.0647i	0.125554	−	0.712055i	0.980977	−	0.194124i	$-0.0621864\pi$
$510$		0			0
$511$	−10.9841	−	3.99790i	−0.485910	−	0.176857i
$512$		−	30.8810i		−	1.36476i
$513$	−1.15428	+	3.17137i	−0.0509629	+	0.140019i
$514$	1.81434	+	10.2896i	0.0800271	+	0.453856i
$515$		0			0
$516$	−5.65375	+	6.73788i	−0.248892	+	0.296618i
$517$	−8.55316			−0.376168
$518$	−32.3098	+	28.3588i	−1.41961	+	1.24602i
$519$	−8.84379			−0.388199
$520$		0			0
$521$	2.75136	−	2.30866i	0.120539	−	0.101144i	−0.580526	−	0.814242i	$-0.697153\pi$
$521$	2.75136	−	2.30866i	0.120539	−	0.101144i	0.701065	+	0.713098i	$0.252708\pi$
$522$	0.788643	+	4.47262i	0.0345180	+	0.195761i
$523$	7.77856	−	21.3714i	0.340132	−	0.934506i	−0.645223	−	0.763994i	$-0.723236\pi$
$523$	7.77856	−	21.3714i	0.340132	−	0.934506i	0.985356	−	0.170512i	$-0.0545422\pi$
$524$		−	40.9440i		−	1.78865i
$525$		0			0
$526$	9.35498	+	5.40110i	0.407897	+	0.235499i
$527$	−0.676262	+	3.83527i	−0.0294585	+	0.167067i
$528$	−2.64679	−	4.58438i	−0.115187	−	0.199509i
$529$	−9.70548	+	16.8104i	−0.421977	+	0.730886i
$530$		0			0
$531$	4.00527	−	0.706238i	0.173814	−	0.0306481i
$532$	10.2241	−	5.90289i	0.443271	−	0.255923i
$533$	−7.42819	−	20.4088i	−0.321750	−	0.884002i
$534$	9.83223	−	3.57864i	0.425482	−	0.154863i
$535$		0			0
$536$	4.14360	+	4.93815i	0.178976	+	0.213296i
$537$	3.28586	+	3.91593i	0.141795	+	0.168985i
$538$	−46.2472	−	8.15463i	−1.99386	−	0.351571i
$539$	18.1053	−	6.58980i	0.779851	−	0.283843i
$540$		0			0
$541$	−16.9754	+	9.80077i	−0.729831	+	0.421368i	−0.818360	−	0.574706i	$-0.805117\pi$
$541$	−16.9754	+	9.80077i	−0.729831	+	0.421368i	0.0885296	+	0.996074i	$0.471783\pi$
$542$	27.9025	−	4.91996i	1.19851	−	0.211330i
$543$	3.77071	+	3.16401i	0.161817	+	0.135780i
$544$	−3.00280	+	5.20100i	−0.128744	+	0.222991i
$545$		0			0
$546$	−0.958873	+	5.43804i	−0.0410360	+	0.232727i
$547$	19.2326	+	11.1039i	0.822326	+	0.474770i	0.851218	−	0.524812i	$-0.175864\pi$
$547$	19.2326	+	11.1039i	0.822326	+	0.474770i	−0.0288917	+	0.999583i	$0.509198\pi$
$548$	−27.6408	−	10.0604i	−1.18076	−	0.429760i
$549$			7.37922i			0.314938i
$550$		0			0
$551$	0.200200	+	1.13539i	0.00852881	+	0.0483693i
$552$	−0.354306	+	0.297298i	−0.0150803	+	0.0126538i
$553$	9.02549	−	10.7562i	0.383803	−	0.457398i
$554$	−24.7921			−1.05332
$555$		0			0
$556$	−30.6735			−1.30085
$557$	−10.7814	+	12.8488i	−0.456824	+	0.544422i	−0.944461	−	0.328625i	$-0.893415\pi$
$557$	−10.7814	+	12.8488i	−0.456824	+	0.544422i	0.487636	+	0.873047i	$0.337859\pi$
$558$	23.8385	−	20.0028i	1.00916	−	0.846788i
$559$	3.51424	+	19.9303i	0.148637	+	0.842961i
$560$		0			0
$561$			1.19110i			0.0502881i
$562$	40.4868	+	14.7360i	1.70783	+	0.621600i
$563$	6.03170	+	3.48240i	0.254206	+	0.146766i	0.621688	−	0.783265i	$-0.286447\pi$
$563$	6.03170	+	3.48240i	0.254206	+	0.146766i	−0.367483	+	0.930030i	$0.619780\pi$
$564$	−0.313717	+	1.77918i	−0.0132099	+	0.0749169i
$565$		0			0
$566$	−18.2936	+	31.6854i	−0.768936	+	1.33184i
$567$	−20.0798	−	16.8490i	−0.843273	−	0.707590i
$568$	8.68071	−	1.53064i	0.364235	−	0.0642244i
$569$	17.2559	−	9.96269i	0.723404	−	0.417658i	−0.0926002	−	0.995703i	$-0.529518\pi$
$569$	17.2559	−	9.96269i	0.723404	−	0.417658i	0.816004	+	0.578046i	$0.196185\pi$
$570$		0			0
$571$	24.6512	−	8.97230i	1.03162	−	0.375479i	0.229923	−	0.973209i	$-0.426153\pi$
$571$	24.6512	−	8.97230i	1.03162	−	0.375479i	0.801698	+	0.597730i	$0.203930\pi$
$572$	19.3813	+	3.41744i	0.810372	+	0.142890i
$573$	−3.77951	−	4.50425i	−0.157891	−	0.188168i
$574$	48.4530	+	57.7440i	2.02239	+	2.41019i
$575$		0			0
$576$	27.4402	−	9.98741i	1.14334	−	0.416142i
$577$	11.4106	+	31.3503i	0.475029	+	1.30513i	0.913666	+	0.406466i	$0.133239\pi$
$577$	11.4106	+	31.3503i	0.475029	+	1.30513i	−0.438637	+	0.898664i	$0.644539\pi$
$578$	−29.5660	+	17.0699i	−1.22978	+	0.710016i
$579$	−3.28961	+	0.580047i	−0.136711	+	0.0241059i
$580$		0			0
$581$	24.3905	−	42.2455i	1.01189	−	1.75264i
$582$	1.04082	+	1.80276i	0.0431436	+	0.0747269i
$583$	−9.63765	+	54.6578i	−0.399151	+	2.26370i
$584$	1.89134	+	1.09196i	0.0782641	+	0.0451858i
$585$		0			0
$586$		−	1.06178i		−	0.0438617i
$587$	10.5014	−	28.8524i	0.433439	−	1.19086i	−0.510248	−	0.860027i	$-0.670447\pi$
$587$	10.5014	−	28.8524i	0.433439	−	1.19086i	0.943688	−	0.330838i	$-0.107331\pi$
$588$	−0.706695	−	4.00787i	−0.0291436	−	0.165282i
$589$	6.05148	−	5.07780i	0.249347	−	0.209227i
$590$		0			0
$591$	−6.90938			−0.284214
$592$	−17.1188	+	10.3977i	−0.703577	+	0.427344i
$593$	8.45396			0.347163			0.173581	−	0.984820i	$-0.444466\pi$
$593$	8.45396			0.347163			0.173581	+	0.984820i	$0.444466\pi$
$594$	12.5512	−	14.9580i	0.514984	−	0.613734i
$595$		0			0
$596$	−2.00279	−	11.3584i	−0.0820373	−	0.465257i
$597$	0.234864	−	0.645283i	0.00961233	−	0.0264097i
$598$			8.00576i			0.327380i
$599$	2.98441	+	1.08624i	0.121940	+	0.0443824i	0.402269	−	0.915521i	$-0.368222\pi$
$599$	2.98441	+	1.08624i	0.121940	+	0.0443824i	−0.280330	+	0.959904i	$0.590444\pi$
$600$		0			0
$601$	2.16502	−	12.2784i	0.0883129	−	0.500847i	−0.908280	−	0.418364i	$-0.862604\pi$
$601$	2.16502	−	12.2784i	0.0883129	−	0.500847i	0.996592	−	0.0824834i	$-0.0262852\pi$
$602$	−35.1199	−	60.8295i	−1.43138	−	2.47923i
$603$	14.4508	−	25.0295i	0.588482	−	1.01928i
$604$	−12.7313	−	10.6829i	−0.518030	−	0.434679i
$605$		0			0
$606$	7.35715	−	4.24765i	0.298864	−	0.172549i
$607$	−5.59413	−	15.3698i	−0.227059	−	0.623839i	0.772884	−	0.634548i	$-0.218814\pi$
$607$	−5.59413	−	15.3698i	−0.227059	−	0.623839i	−0.999943	+	0.0107084i	$0.996591\pi$
$608$	11.4474	−	4.16649i	0.464251	−	0.168974i
$609$	0.987194	+	0.174069i	0.0400031	+	0.00705363i
$610$		0			0
$611$	2.67195	+	3.18431i	0.108096	+	0.128823i
$612$	−4.80123	−	0.846586i	−0.194078	−	0.0342212i
$613$	−11.6594	+	4.24366i	−0.470917	+	0.171400i	−0.566568	−	0.824015i	$-0.691729\pi$
$613$	−11.6594	+	4.24366i	−0.470917	+	0.171400i	0.0956506	+	0.995415i	$0.469507\pi$
$614$	6.20302	+	17.0427i	0.250334	+	0.687786i
$615$		0			0
$616$	−8.94169	+	1.57666i	−0.360271	+	0.0635255i
$617$	−23.9113	−	20.0640i	−0.962634	−	0.807745i	0.0187459	−	0.999824i	$-0.494033\pi$
$617$	−23.9113	−	20.0640i	−0.962634	−	0.807745i	−0.981380	+	0.192079i	$0.938477\pi$
$618$	6.53756	−	11.3234i	0.262979	−	0.455494i
$619$	13.9396	+	24.1441i	0.560280	+	0.970433i	0.997472	+	0.0710650i	$0.0226398\pi$
$619$	13.9396	+	24.1441i	0.560280	+	0.970433i	−0.437192	+	0.899368i	$0.644027\pi$
$620$		0			0
$621$	3.68434	+	2.12716i	0.147848	+	0.0853599i
$622$	56.0867	+	20.4139i	2.24887	+	0.818523i
$623$			44.7528i			1.79298i
$624$	−0.879905	+	2.41752i	−0.0352244	+	0.0967782i
$625$		0			0
$626$	46.8547	−	39.3158i	1.87269	−	1.57138i
$627$	1.55302	−	1.85082i	0.0620216	−	0.0739145i
$628$	39.2100			1.56465
$629$	4.50558	−	0.100196i	0.179649	−	0.00399509i
$630$		0			0
$631$	9.04455	−	10.7789i	0.360058	−	0.429100i	−0.555357	−	0.831612i	$-0.687418\pi$
$631$	9.04455	−	10.7789i	0.360058	−	0.429100i	0.915415	+	0.402512i	$0.131863\pi$
$632$	−2.00962	+	1.68628i	−0.0799386	+	0.0670764i
$633$	−1.00031	−	5.67305i	−0.0397588	−	0.225483i
$634$	17.2069	−	47.2756i	0.683374	−	1.87755i
$635$		0			0
$636$	11.0161	+	4.00954i	0.436817	+	0.158988i
$637$	−8.10934	−	4.68193i	−0.321304	−	0.185505i
$638$	1.15830	−	6.56907i	0.0458577	−	0.260072i
$639$	−19.7599	−	34.2252i	−0.781690	−	1.35393i
$640$		0			0
$641$	−10.6093	−	8.90229i	−0.419044	−	0.351619i	0.408756	−	0.912644i	$-0.365963\pi$
$641$	−10.6093	−	8.90229i	−0.419044	−	0.351619i	−0.827799	+	0.561025i	$0.810407\pi$
$642$	10.0256	−	1.76779i	0.395680	−	0.0697690i
$643$	5.53814	−	3.19744i	0.218403	−	0.126095i	−0.386808	−	0.922160i	$-0.626422\pi$
$643$	5.53814	−	3.19744i	0.218403	−	0.126095i	0.605210	+	0.796065i	$0.293089\pi$
$644$	−5.08997	−	13.9846i	−0.200573	−	0.551069i
$645$		0			0
$646$	−2.27561	−	0.401251i	−0.0895325	−	0.0157870i
$647$	30.3864	+	36.2131i	1.19461	+	1.42368i	0.880335	+	0.474352i	$0.157317\pi$
$647$	30.3864	+	36.2131i	1.19461	+	1.42368i	0.314276	+	0.949332i	$0.398238\pi$
$648$	3.14797	+	3.75161i	0.123664	+	0.147377i
$649$	−5.88267	−	1.03727i	−0.230915	−	0.0407165i
$650$		0			0
$651$	−2.34918	−	6.45432i	−0.0920717	−	0.252965i
$652$	−2.11889	+	1.22334i	−0.0829821	+	0.0479097i
$653$	38.5315	−	6.79414i	1.50785	−	0.265875i	0.642207	−	0.766531i	$-0.278019\pi$
$653$	38.5315	−	6.79414i	1.50785	−	0.265875i	0.865646	+	0.500656i	$0.166908\pi$
$654$	−2.75082	−	2.30821i	−0.107566	−	0.0902582i
$655$		0			0
$656$	17.5597	+	30.4142i	0.685590	+	1.18748i
$657$	1.70028	−	9.64275i	0.0663342	−	0.376200i
$658$	−12.4943	−	7.21362i	−0.487080	−	0.281216i
$659$	−20.9382	−	7.62088i	−0.815636	−	0.296867i	−0.0996862	−	0.995019i	$-0.531784\pi$
$659$	−20.9382	−	7.62088i	−0.815636	−	0.296867i	−0.715950	+	0.698152i	$0.754006\pi$
$660$		0			0
$661$	1.44341	−	3.96574i	0.0561422	−	0.154249i	−0.908451	−	0.417991i	$-0.862734\pi$
$661$	1.44341	−	3.96574i	0.0561422	−	0.154249i	0.964593	+	0.263742i	$0.0849566\pi$
$662$	5.33097	+	30.2334i	0.207194	+	1.17506i
$663$	0.443440	−	0.372090i	0.0172218	−	0.0144508i
$664$	−5.85835	+	6.98171i	−0.227348	+	0.270943i
$665$		0			0
$666$	−28.0940	−	22.5285i	−1.08862	−	0.872962i
$667$	1.45333			0.0562730
$668$	−14.2753	+	17.0126i	−0.552328	+	0.658239i
$669$	−2.52795	+	2.12120i	−0.0977362	+	0.0820104i
$670$		0			0
$671$	3.70685	−	10.1845i	0.143101	−	0.393167i
$672$		−	10.5920i		−	0.408594i
$673$	39.3918	+	14.3375i	1.51844	+	0.552668i	0.960759	−	0.277385i	$-0.0894676\pi$
$673$	39.3918	+	14.3375i	1.51844	+	0.552668i	0.557685	+	0.830053i	$0.311690\pi$
$674$	−27.4102	−	15.8253i	−1.05580	−	0.609568i
$675$		0			0
$676$	10.2107	+	17.6854i	0.392719	+	0.680209i
$677$	15.5199	−	26.8813i	0.596479	−	1.03313i	−0.396857	−	0.917880i	$-0.629899\pi$
$677$	15.5199	−	26.8813i	0.596479	−	1.03313i	0.993336	−	0.115252i	$-0.0367676\pi$
$678$	6.90153	+	5.79107i	0.265052	+	0.222405i
$679$	−8.76825	+	1.54608i	−0.336494	+	0.0593330i
$680$		0			0
$681$	2.37111	+	6.51456i	0.0908610	+	0.249638i
$682$	−42.9489	+	15.6321i	−1.64460	+	0.598585i
$683$	49.3165	+	8.69583i	1.88704	+	0.332737i	0.993274	−	0.115790i	$-0.0369398\pi$
$683$	49.3165	+	8.69583i	1.88704	+	0.332737i	0.893770	+	0.448526i	$0.148051\pi$
$684$	6.35669	+	7.57561i	0.243054	+	0.289661i
$685$		0			0
$686$	−16.7153	−	2.94736i	−0.638194	−	0.112531i
$687$	2.20536	−	0.802684i	0.0841396	−	0.0306243i
$688$	−11.1925	−	30.7513i	−0.426712	−	1.17238i
$689$	23.3596	−	13.4867i	0.889931	−	0.513802i
$690$		0			0
$691$	−6.59295	−	5.53214i	−0.250808	−	0.210453i	0.508712	−	0.860937i	$-0.330122\pi$
$691$	−6.59295	−	5.53214i	−0.250808	−	0.210453i	−0.759520	+	0.650484i	$0.774566\pi$
$692$	−26.5831	+	46.0432i	−1.01054	+	1.75030i
$693$	20.3540	+	35.2541i	0.773184	+	1.33919i
$694$	0.410643	−	2.32887i	0.0155878	−	0.0884027i
$695$		0			0
$696$	−0.175993	−	0.0640561i	−0.00667099	−	0.00242804i
$697$		−	7.90211i		−	0.299314i
$698$	22.4322	−	61.6320i	0.849072	−	2.33281i
$699$	1.00679	+	5.70978i	0.0380802	+	0.215964i
$700$		0			0
$701$	14.7334	−	17.5586i	0.556474	−	0.663180i	−0.412322	−	0.911038i	$-0.635282\pi$
$701$	14.7334	−	17.5586i	0.556474	−	0.663180i	0.968796	+	0.247858i	$0.0797267\pi$
$702$	−9.48973			−0.358167
$703$	−7.13177	−	5.71895i	−0.268980	−	0.215694i
$704$	−42.8888			−1.61643
$705$		0			0
$706$	46.3002	−	38.8505i	1.74253	−	1.46216i
$707$	6.30962	+	35.7836i	0.237298	+	1.34578i
$708$	−0.431535	+	1.18563i	−0.0162181	+	0.0445588i
$709$		−	39.3083i		−	1.47625i	−0.674661	−	0.738127i	$-0.735710\pi$
$709$		−	39.3083i		−	1.47625i	0.674661	−	0.738127i	$-0.264290\pi$
$710$		0			0
$711$	10.1860	+	5.88088i	0.382004	+	0.220550i
$712$	1.45194	−	8.23434i	0.0544136	−	0.308595i
$713$	−4.97905	−	8.62397i	−0.186467	−	0.322970i
$714$	−1.00455	+	1.73994i	−0.0375945	+	0.0651155i
$715$		0			0
$716$	30.2642	−	5.33639i	1.13103	−	0.199430i
$717$	−3.70432	+	2.13869i	−0.138340	+	0.0798708i
$718$	0.0599559	+	0.164728i	0.00223754	+	0.00614758i
$719$	−23.3678	+	8.50517i	−0.871470	+	0.317189i	−0.738762	−	0.673966i	$-0.764589\pi$
$719$	−23.3678	+	8.50517i	−0.871470	+	0.317189i	−0.132708	+	0.991155i	$0.542367\pi$
$720$		0			0
$721$	35.9474	+	42.8404i	1.33875	+	1.59546i
$722$	−22.3320	−	26.6142i	−0.831110	−	0.990478i
$723$	−6.20286	−	1.09373i	−0.230687	−	0.0406763i
$724$	27.8069	−	10.1209i	1.03343	−	0.376139i
$725$		0			0
$726$	−4.52071	+	2.61003i	−0.167779	+	0.0968674i
$727$	40.6160	−	7.16170i	1.50637	−	0.265613i	0.641307	−	0.767284i	$-0.278393\pi$
$727$	40.6160	−	7.16170i	1.50637	−	0.265613i	0.865058	+	0.501672i	$0.167281\pi$
$728$	3.38031	+	2.83642i	0.125283	+	0.105125i
$729$	9.68611	−	16.7768i	0.358745	−	0.621364i
$730$		0			0
$731$	−1.27863	+	7.25146i	−0.0472918	+	0.268205i
$732$	−1.98255	−	1.14463i	−0.0732773	−	0.0423067i
$733$	−2.66602	−	0.970351i	−0.0984716	−	0.0358407i	0.292315	−	0.956322i	$-0.405575\pi$
$733$	−2.66602	−	0.970351i	−0.0984716	−	0.0358407i	−0.390786	+	0.920482i	$0.627797\pi$
$734$			26.5746i			0.980887i
$735$		0			0
$736$	−2.66660	−	15.1231i	−0.0982923	−	0.557443i
$737$	−32.5176	+	27.2855i	−1.19780	+	1.00507i
$738$	−40.5873	+	48.3700i	−1.49404	+	1.78053i
$739$	32.4466			1.19357			0.596784	−	0.802402i	$-0.296445\pi$
$739$	32.4466			1.19357			0.596784	+	0.802402i	$0.296445\pi$
$740$		0			0
$741$	−1.17420			−0.0431355
$742$	−60.1762	+	71.7152i	−2.20914	+	2.63275i
$743$	8.21025	−	6.88922i	0.301205	−	0.252741i	−0.479641	−	0.877465i	$-0.659233\pi$
$743$	8.21025	−	6.88922i	0.301205	−	0.252741i	0.780846	+	0.624724i	$0.214789\pi$
$744$	0.222840	+	1.26379i	0.00816971	+	0.0463327i
$745$		0			0
$746$		−	26.8776i		−	0.984060i
$747$	38.3977	+	13.9756i	1.40490	+	0.511341i
$748$	6.20117	+	3.58025i	0.226737	+	0.130907i
$749$	−7.56108	+	42.8810i	−0.276276	+	1.56684i
$750$		0			0
$751$	2.83062	−	4.90277i	0.103291	−	0.178905i	−0.809748	−	0.586778i	$-0.800396\pi$
$751$	2.83062	−	4.90277i	0.103291	−	0.178905i	0.913039	+	0.407873i	$0.133729\pi$
$752$	−5.14909	−	4.32060i	−0.187768	−	0.157556i
$753$	−1.26301	+	0.222703i	−0.0460267	+	0.00811575i
$754$	−2.80749	+	1.62090i	−0.102243	+	0.0590298i
$755$		0			0
$756$	16.5768	−	6.03346i	0.602892	−	0.219435i
$757$	−19.6719	−	3.46869i	−0.714987	−	0.126072i	−0.195691	−	0.980666i	$-0.562695\pi$
$757$	−19.6719	−	3.46869i	−0.714987	−	0.126072i	−0.519297	+	0.854594i	$0.673806\pi$
$758$	−36.0087	−	42.9135i	−1.30790	−	1.55869i
$759$	−1.95770	−	2.33309i	−0.0710599	−	0.0846859i
$760$		0			0
$761$	11.9305	−	4.34234i	0.432480	−	0.157410i	−0.116601	−	0.993179i	$-0.537200\pi$
$761$	11.9305	−	4.34234i	0.432480	−	0.157410i	0.549081	+	0.835769i	$0.314978\pi$
$762$	2.46082	+	6.76105i	0.0891462	+	0.244927i
$763$	13.3013	−	7.67948i	0.481538	−	0.278016i
$764$	−34.8110	+	6.13812i	−1.25942	+	0.222069i
$765$		0			0
$766$	−11.5874	+	20.0700i	−0.418670	+	0.725158i
$767$	1.45153	+	2.51413i	0.0524119	+	0.0907800i
$768$	0.668436	−	3.79089i	0.0241201	−	0.136792i
$769$	26.2274	+	15.1424i	0.945786	+	0.546050i	0.891769	−	0.452490i	$-0.149464\pi$
$769$	26.2274	+	15.1424i	0.945786	+	0.546050i	0.0540164	+	0.998540i	$0.482798\pi$
$770$		0			0
$771$			1.93178i			0.0695715i
$772$	−6.86817	+	18.8701i	−0.247191	+	0.679151i
$773$	6.71175	+	38.0642i	0.241405	+	1.36907i	0.828696	+	0.559699i	$0.189083\pi$
$773$	6.71175	+	38.0642i	0.241405	+	1.36907i	−0.587291	+	0.809376i	$0.699806\pi$
$774$	45.0720	−	37.8199i	1.62008	−	1.35941i
$775$		0			0
$776$	1.66349			0.0597157
$777$	−6.79344	+	4.12625i	−0.243713	+	0.148028i
$778$	9.02959			0.323726
$779$	−10.3032	+	12.2789i	−0.369152	+	0.439938i
$780$		0			0
$781$	10.0792	+	57.1622i	0.360663	+	2.04542i
$782$	−0.996245	+	2.73716i	−0.0356257	+	0.0978807i
$783$			1.72272i			0.0615649i
$784$	14.2284	+	5.17871i	0.508157	+	0.184954i
$785$		0			0
$786$	2.45432	−	13.9192i	0.0875428	−	0.496480i
$787$	2.41252	+	4.17861i	0.0859971	+	0.148951i	0.905816	−	0.423672i	$-0.139259\pi$
$787$	2.41252	+	4.17861i	0.0859971	+	0.148951i	−0.819819	+	0.572623i	$0.805926\pi$
$788$	−20.7685	+	35.9722i	−0.739849	+	1.28146i
$789$	1.52995	+	1.28378i	0.0544675	+	0.0457037i
$790$		0			0
$791$	−33.3715	+	19.2670i	−1.18655	+	0.685057i
$792$	−2.60129	−	7.14699i	−0.0924329	−	0.253957i
$793$	−4.94963	+	1.80152i	−0.175767	+	0.0639738i
$794$	−12.4881	−	2.20199i	−0.443186	−	0.0781457i
$795$		0			0
$796$	−2.65356	−	3.16239i	−0.0940528	−	0.112088i
$797$	−27.6718	−	4.87928i	−0.980185	−	0.172833i	−0.339474	−	0.940615i	$-0.610249\pi$
$797$	−27.6718	−	4.87928i	−0.980185	−	0.172833i	−0.640711	+	0.767782i	$0.721360\pi$
$798$	3.82958	−	1.39385i	0.135566	−	0.0493419i
$799$	0.517279	+	1.42121i	0.0183000	+	0.0502789i
$800$		0			0
$801$	−36.9182	+	6.50967i	−1.30444	+	0.230008i
$802$	15.8192	+	13.2739i	0.558595	+	0.468717i
$803$	−7.19055	+	12.4544i	−0.253749	+	0.439506i
$804$	4.48307	+	7.76491i	0.158106	+	0.273847i
$805$		0			0
$806$	19.2367	+	11.1063i	0.677585	+	0.391204i
$807$	−8.15887	−	2.96959i	−0.287206	−	0.104534i
$808$		−	6.78876i		−	0.238828i
$809$	2.11555	−	5.81242i	0.0743786	−	0.204354i	−0.896932	−	0.442169i	$-0.854209\pi$
$809$	2.11555	−	5.81242i	0.0743786	−	0.204354i	0.971310	+	0.237815i	$0.0764313\pi$
$810$		0			0
$811$	−4.28857	+	3.59854i	−0.150592	+	0.126362i	−0.714971	−	0.699154i	$-0.753560\pi$
$811$	−4.28857	+	3.59854i	−0.150592	+	0.126362i	0.564379	+	0.825516i	$0.309116\pi$
$812$	3.87360	−	4.61638i	0.135937	−	0.162003i
$813$	5.23843			0.183720
$814$	27.4572	+	45.2055i	0.962375	+	1.58445i
$815$		0			0
$816$	−0.601677	+	0.717051i	−0.0210629	+	0.0251018i
$817$	11.4417	−	9.60073i	0.400294	−	0.335887i
$818$	7.27140	+	41.2382i	0.254239	+	1.44186i
$819$	6.76652	−	18.5909i	0.236441	−	0.649617i
$820$		0			0
$821$	−16.4320	−	5.98077i	−0.573482	−	0.208730i	0.0389669	−	0.999241i	$-0.487593\pi$
$821$	−16.4320	−	5.98077i	−0.573482	−	0.208730i	−0.612449	+	0.790510i	$0.709816\pi$
$822$	−8.79360	−	5.07699i	−0.306712	−	0.177080i
$823$	−5.18271	+	29.3926i	−0.180658	+	1.02456i	0.750751	+	0.660586i	$0.229692\pi$
$823$	−5.18271	+	29.3926i	−0.180658	+	1.02456i	−0.931408	+	0.363976i	$0.881419\pi$
$824$	−5.22429	−	9.04874i	−0.181997	−	0.315228i
$825$		0			0
$826$	−7.71851	−	6.47660i	−0.268561	−	0.225350i
$827$	38.1522	−	6.72726i	1.32668	−	0.233930i	0.534994	−	0.844856i	$-0.320314\pi$
$827$	38.1522	−	6.72726i	1.32668	−	0.233930i	0.791688	+	0.610926i	$0.209203\pi$
$828$	10.7960	−	6.23308i	0.375187	−	0.216614i
$829$	17.0126	+	46.7418i	0.590873	+	1.62341i	0.768889	+	0.639382i	$0.220810\pi$
$829$	17.0126	+	46.7418i	0.590873	+	1.62341i	−0.178016	+	0.984028i	$0.556968\pi$
$830$		0			0
$831$	−4.51414	−	0.795965i	−0.156594	−	0.0276117i
$832$	13.3982	+	15.9673i	0.464498	+	0.553567i
$833$	−2.18995	−	2.60988i	−0.0758773	−	0.0904271i
$834$	−10.4276	−	1.83868i	−0.361080	−	0.0636681i
$835$		0			0
$836$	−4.96773	−	13.6487i	−0.171812	−	0.472051i
$837$	10.2225	−	5.90198i	0.353342	−	0.204002i
$838$	−25.2077	+	4.44479i	−0.870784	+	0.153543i
$839$	36.1751	+	30.3545i	1.24890	+	1.04795i	0.996774	+	0.0802593i	$0.0255749\pi$
$839$	36.1751	+	30.3545i	1.24890	+	1.04795i	0.252128	+	0.967694i	$0.418870\pi$
$840$		0			0
$841$	−14.2057	−	24.6051i	−0.489853	−	0.848451i
$842$	−1.17075	+	6.63964i	−0.0403466	+	0.228817i
$843$	6.89871	+	3.98297i	0.237604	+	0.137181i
$844$	−32.5422	−	11.8444i	−1.12015	−	0.407701i
$845$		0			0
$846$	4.13337	−	11.3563i	0.142108	−	0.390439i
$847$	−3.87703	−	21.9878i	−0.133216	−	0.755508i
$848$	−33.4122	+	28.0361i	−1.14738	+	0.962764i
$849$	−4.34817	+	5.18194i	−0.149229	+	0.177844i
$850$		0			0
$851$	−8.66076	+	7.60169i	−0.296887	+	0.260583i
$852$	12.2602			0.420029
$853$	8.13453	−	9.69436i	0.278521	−	0.331928i	−0.608590	−	0.793485i	$-0.708264\pi$
$853$	8.13453	−	9.69436i	0.278521	−	0.331928i	0.887111	+	0.461557i	$0.152709\pi$
$854$	14.0044	−	11.7511i	0.479219	−	0.402113i
$855$		0			0
$856$	2.78242	−	7.64464i	0.0951013	−	0.261289i
$857$		−	39.0532i		−	1.33403i	−0.745043	−	0.667016i	$-0.767571\pi$
$857$		−	39.0532i		−	1.33403i	0.745043	−	0.667016i	$-0.232429\pi$
$858$	6.38393	+	2.32356i	0.217944	+	0.0793251i
$859$	−25.4718	−	14.7062i	−0.869088	−	0.501768i	−0.00204271	−	0.999998i	$-0.500650\pi$
$859$	−25.4718	−	14.7062i	−0.869088	−	0.501768i	−0.867045	+	0.498230i	$0.833984\pi$
$860$		0			0
$861$	6.96840	+	12.0696i	0.237483	+	0.411332i
$862$	−7.61813	+	13.1950i	−0.259474	+	0.449423i
$863$	−4.82785	−	4.05105i	−0.164342	−	0.137899i	0.556908	−	0.830574i	$-0.311988\pi$
$863$	−4.82785	−	4.05105i	−0.164342	−	0.137899i	−0.721250	+	0.692675i	$0.756432\pi$
$864$	17.9263	−	3.16089i	0.609865	−	0.107536i
$865$		0			0
$866$	−8.88957	−	24.4239i	−0.302080	−	0.829957i
$867$	−5.93141	+	2.15886i	−0.201441	+	0.0733186i
$868$	−40.6643	−	7.17021i	−1.38024	−	0.243373i
$869$	−11.1041	−	13.2333i	−0.376680	−	0.448909i
$870$		0			0
$871$	20.3166	+	3.58236i	0.688400	+	0.121384i
$872$	−2.69653	+	0.981457i	−0.0913161	+	0.0332363i
$873$	−2.55083	−	7.00836i	−0.0863326	−	0.237197i
$874$	5.11691	−	2.95425i	0.173082	−	0.0999290i
$875$		0			0
$876$	2.32695	+	1.95254i	0.0786204	+	0.0659704i
$877$	−25.7571	+	44.6125i	−0.869754	+	1.50646i	−0.00750624	+	0.999972i	$0.502389\pi$
$877$	−25.7571	+	44.6125i	−0.869754	+	1.50646i	−0.862248	+	0.506487i	$0.830944\pi$
$878$	−34.8321	−	60.3309i	−1.17553	−	2.03607i
$879$	0.0340890	−	0.193328i	0.00114979	−	0.00652081i
$880$		0			0
$881$	−2.52115	−	0.917625i	−0.0849398	−	0.0309156i	0.299201	−	0.954190i	$-0.403280\pi$
$881$	−2.52115	−	0.917625i	−0.0849398	−	0.0309156i	−0.384141	+	0.923275i	$0.625502\pi$
$882$			27.2236i			0.916667i
$883$	11.4063	−	31.3387i	0.383854	−	1.05463i	−0.585865	−	0.810408i	$-0.699245\pi$
$883$	11.4063	−	31.3387i	0.383854	−	1.05463i	0.969719	−	0.244222i	$-0.0785325\pi$
$884$	−0.604293	−	3.42712i	−0.0203246	−	0.115266i
$885$		0			0
$886$	−42.1161	+	50.1920i	−1.41492	+	1.68623i
$887$	−2.81693			−0.0945833			−0.0472916	−	0.998881i	$-0.515059\pi$
$887$	−2.81693			−0.0945833			−0.0472916	+	0.998881i	$0.515059\pi$
$888$	1.38384	−	0.538811i	0.0464386	−	0.0180813i
$889$	−30.7739			−1.03212
$890$		0			0
$891$	−24.7042	+	20.7293i	−0.827622	+	0.694458i
$892$	3.44494	+	19.5372i	0.115345	+	0.654154i
$893$	1.04927	−	2.88285i	0.0351125	−	0.0964708i
$894$		−	3.98140i		−	0.133158i
$895$		0			0
$896$	−14.8369	−	8.56610i	−0.495667	−	0.286173i
$897$	−0.257029	+	1.45769i	−0.00858196	+	0.0486707i
$898$	20.2715	+	35.1112i	0.676467	+	1.17168i
$899$	2.01619	−	3.49214i	0.0672436	−	0.116469i
$900$		0			0
$901$	9.66493	−	1.70419i	0.321986	−	0.0567747i
$902$	80.3148	−	46.3697i	2.67419	−	1.54394i
$903$	−4.44166	−	12.2034i	−0.147809	−	0.406103i
$904$	6.76533	−	2.46238i	0.225011	−	0.0818975i
$905$		0			0
$906$	−3.68773	−	4.39486i	−0.122516	−	0.146009i
$907$	−10.2726	−	12.2424i	−0.341096	−	0.406502i	0.568041	−	0.823000i	$-0.307702\pi$
$907$	−10.2726	−	12.2424i	−0.341096	−	0.406502i	−0.909136	+	0.416498i	$0.863257\pi$
$908$	41.0438	+	7.23713i	1.36209	+	0.240172i
$909$	−28.6014	+	10.4101i	−0.948650	+	0.345280i
$910$		0			0
$911$	7.26052	−	4.19186i	0.240552	−	0.138883i	−0.374879	−	0.927074i	$-0.622316\pi$
$911$	7.26052	−	4.19186i	0.240552	−	0.138883i	0.615430	+	0.788191i	$0.288982\pi$
$912$	1.86987	−	0.329708i	0.0619174	−	0.0109177i
$913$	−45.9744	−	38.5771i	−1.52153	−	1.27671i
$914$	30.9567	−	53.6186i	1.02396	−	1.77355i
$915$		0			0
$916$	2.44997	−	13.8944i	0.0809491	−	0.459085i
$917$	52.3535	+	30.2263i	1.72887	+	0.998161i
$918$	−3.24453	−	1.18091i	−0.107085	−	0.0389759i
$919$			31.3634i			1.03458i	0.855809	+	0.517291i	$0.173060\pi$
$919$			31.3634i			1.03458i	−0.855809	+	0.517291i	$0.826940\pi$
$920$		0			0
$921$	0.582280	+	3.30227i	0.0191868	+	0.108814i
$922$	−49.1615	+	41.2514i	−1.61905	+	1.35854i
$923$	18.1326	−	21.6096i	0.596841	−	0.711287i
$924$	−12.6288			−0.415458
$925$		0			0
$926$	36.1139			1.18678
$927$	−30.1118	+	35.8858i	−0.989000	+	1.17864i
$928$	4.76350	−	3.99705i	0.156370	−	0.131210i
$929$	5.33172	+	30.2377i	0.174928	+	0.992067i	0.938227	+	0.346021i	$0.112467\pi$
$929$	5.33172	+	30.2377i	0.174928	+	0.992067i	−0.763299	+	0.646046i	$0.776421\pi$
$930$		0			0
$931$			6.91082i			0.226493i
$932$	32.7529	+	11.9211i	1.07286	+	0.390488i
$933$	9.55686	+	5.51765i	0.312878	+	0.180640i
$934$	5.15333	−	29.2260i	0.168622	−	0.956303i
$935$		0			0
$936$	−1.84817	+	3.20112i	−0.0604093	+	0.104632i
$937$	−20.2885	−	17.0241i	−0.662796	−	0.556152i	0.248127	−	0.968727i	$-0.420185\pi$
$937$	−20.2885	−	17.0241i	−0.662796	−	0.556152i	−0.910923	+	0.412575i	$0.864629\pi$
$938$	−70.5135	+	12.4334i	−2.30235	+	0.405966i
$939$	9.79355	−	5.65431i	0.319601	−	0.184521i
$940$		0			0
$941$	33.7169	−	12.2720i	1.09914	−	0.400054i	0.272141	−	0.962257i	$-0.412268\pi$
$941$	33.7169	−	12.2720i	1.09914	−	0.400054i	0.826999	+	0.562203i	$0.190046\pi$
$942$	13.3297	+	2.35038i	0.434304	+	0.0765795i
$943$	12.9880	+	15.4785i	0.422948	+	0.504049i
$944$	−3.01745	−	3.59606i	−0.0982096	−	0.117042i
$945$		0			0
$946$	−81.2047	+	29.5561i	−2.64019	+	0.960952i
$947$	16.2849	+	44.7424i	0.529189	+	1.45393i	0.860028	+	0.510247i	$0.170446\pi$
$947$	16.2849	+	44.7424i	0.529189	+	1.45393i	−0.330839	+	0.943687i	$0.607332\pi$
$948$	−3.16000	+	1.82443i	−0.102632	+	0.0592546i
$949$	6.88300	−	1.21366i	0.223432	−	0.0393970i
$950$		0			0
$951$	4.65084	−	8.05549i	0.150814	−	0.261217i
$952$	0.802758	+	1.39042i	0.0260175	+	0.0450637i
$953$	−0.244254	+	1.38523i	−0.00791217	+	0.0448721i	−0.988508	−	0.151167i	$-0.951697\pi$
$953$	−0.244254	+	1.38523i	−0.00791217	+	0.0448721i	0.980596	+	0.196039i	$0.0628080\pi$
$954$	−67.9137	−	39.2100i	−2.19879	−	1.26947i
$955$		0			0
$956$			25.7143i			0.831659i
$957$	0.421808	−	1.15891i	0.0136351	−	0.0374621i
$958$	6.90457	+	39.1578i	0.223077	+	1.26513i
$959$	33.2693	−	27.9163i	1.07432	−	0.901463i
$960$		0			0
$961$	3.37038			0.108722
$962$	8.25236	−	24.3441i	0.266067	−	0.784885i
$963$	−36.4740			−1.17536
$964$	−24.3391	+	29.0062i	−0.783910	+	0.934227i
$965$		0			0
$966$	−0.892082	−	5.05925i	−0.0287023	−	0.162779i
$967$	−1.69636	+	4.66071i	−0.0545513	+	0.149878i	−0.963975	−	0.265992i	$-0.914301\pi$
$967$	−1.69636	+	4.66071i	−0.0545513	+	0.149878i	0.909424	+	0.415870i	$0.136523\pi$
$968$			4.17145i			0.134076i
$969$	−0.401459	−	0.146119i	−0.0128967	−	0.00469403i
$970$		0			0
$971$	0.351984	−	1.99620i	0.0112957	−	0.0640611i	−0.978639	−	0.205587i	$-0.934090\pi$
$971$	0.351984	−	1.99620i	0.0112957	−	0.0640611i	0.989935	+	0.141526i	$0.0452008\pi$
$972$	11.1756	+	19.3567i	0.358458	+	0.620867i
$973$	22.6443	−	39.2210i	0.725942	−	1.25737i
$974$	−49.0153	−	41.1288i	−1.57055	−	1.31785i
$975$		0			0
$976$	7.37621	−	4.25865i	0.236107	−	0.136316i
$977$	−7.82344	−	21.4947i	−0.250294	−	0.687677i	−0.999674	−	0.0255366i	$-0.991871\pi$
$977$	−7.82344	−	21.4947i	−0.250294	−	0.687677i	0.749380	−	0.662140i	$-0.230352\pi$
$978$	−0.793660	+	0.288869i	−0.0253785	+	0.00923700i
$979$	54.2229	+	9.56096i	1.73297	+	0.305570i
$980$		0			0
$981$	8.26987	+	9.85565i	0.264037	+	0.314667i
$982$	−11.2275	−	1.97971i	−0.358284	−	0.0631751i
$983$	−21.8025	+	7.93548i	−0.695393	+	0.253102i	−0.665443	−	0.746449i	$-0.731757\pi$
$983$	−21.8025	+	7.93548i	−0.695393	+	0.253102i	−0.0299504	+	0.999551i	$0.509535\pi$
$984$	−0.890580	−	2.44685i	−0.0283906	−	0.0780027i
$985$		0			0
$986$	−1.16158	+	0.204819i	−0.0369924	+	0.00652275i
$987$	−2.04337	−	1.71459i	−0.0650412	−	0.0545760i
$988$	−3.52948	+	6.11323i	−0.112288	+	0.194488i
$989$	−9.41403	−	16.3056i	−0.299349	−	0.518487i
$990$		0			0
$991$	−9.93175	−	5.73410i	−0.315492	−	0.182150i	0.333889	−	0.942612i	$-0.391639\pi$
$991$	−9.93175	−	5.73410i	−0.315492	−	0.182150i	−0.649382	+	0.760463i	$0.724972\pi$
$992$	−40.0380	−	14.5726i	−1.27121	−	0.462682i
$993$			5.67605i			0.180124i
$994$	−33.4862	+	92.0025i	−1.06212	+	2.91814i
$995$		0			0
$996$	−9.71085	+	8.14837i	−0.307700	+	0.258191i
$997$	13.2157	−	15.7498i	0.418545	−	0.498802i	−0.515036	−	0.857168i	$-0.672222\pi$
$997$	13.2157	−	15.7498i	0.418545	−	0.498802i	0.933581	+	0.358366i	$0.116666\pi$
$998$	48.4422			1.53341
$999$	−9.01076	−	10.2661i	−0.285088	−	0.324806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bb.e.151.14		96
5.2	odd	4		185.2.v.a.114.14	yes	96
5.3	odd	4		185.2.v.a.114.3	yes	96
5.4	even	2	inner	925.2.bb.e.151.3		96
37.25	even	18	inner	925.2.bb.e.876.14		96
185.62	odd	36		185.2.v.a.99.3	✓	96
185.99	even	18	inner	925.2.bb.e.876.3		96
185.173	odd	36		185.2.v.a.99.14	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.99.3	✓	96	185.62	odd	36
185.2.v.a.99.14	yes	96	185.173	odd	36
185.2.v.a.114.3	yes	96	5.3	odd	4
185.2.v.a.114.14	yes	96	5.2	odd	4
925.2.bb.e.151.3		96	5.4	even	2	inner
925.2.bb.e.151.14		96	1.1	even	1	trivial
925.2.bb.e.876.3		96	185.99	even	18	inner
925.2.bb.e.876.14		96	37.25	even	18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33394 - 1.58972i) q^{2} +(0.293922 - 0.246630i) q^{3} +(-0.400539 - 2.27157i) q^{4} -0.796243i q^{6} +(3.20026 + 1.16480i) q^{7} +(-0.551046 - 0.318147i) q^{8} +(-0.495381 + 2.80944i) q^{9} +(2.09499 - 3.62862i) q^{11} +(-0.677964 - 0.568879i) q^{12} +(-2.00538 + 0.353603i) q^{13} +(6.12066 - 3.53376i) q^{14} +(3.09419 - 1.12619i) q^{16} +(-0.729641 - 0.128655i) q^{17} +(3.80543 + 4.53514i) q^{18} +(0.966024 + 1.15126i) q^{19} +(1.22790 - 0.446919i) q^{21} +(-2.97393 - 8.17080i) q^{22} +(1.64066 - 0.947238i) q^{23} +(-0.240429 + 0.0423941i) q^{24} +(-2.11292 + 3.65969i) q^{26} +(1.12282 + 1.94478i) q^{27} +(1.36409 - 7.73616i) q^{28} +(0.664361 + 0.383569i) q^{29} -5.25639i q^{31} +(2.77237 - 7.61701i) q^{32} +(-0.279164 - 1.58322i) q^{33} +(-1.17782 + 0.988309i) q^{34} +6.58027 q^{36} +(-5.96539 + 1.18918i) q^{37} +3.11880 q^{38} +(-0.502216 + 0.598518i) q^{39} +(1.85206 + 10.5036i) q^{41} +(0.927464 - 2.54819i) q^{42} -9.93840i q^{43} +(-9.08179 - 3.30550i) q^{44} +(0.682696 - 3.87176i) q^{46} +(-1.02067 - 1.76785i) q^{47} +(0.631697 - 1.09413i) q^{48} +(3.52260 + 2.95581i) q^{49} +(-0.246188 + 0.142136i) q^{51} +(1.60647 + 4.41373i) q^{52} +(-12.4473 + 4.53045i) q^{53} +(4.58944 + 0.809242i) q^{54} +(-1.39291 - 1.66001i) q^{56} +(0.567871 + 0.100131i) q^{57} +(1.49599 - 0.544494i) q^{58} +(-0.487600 - 1.33967i) q^{59} +(2.54738 - 0.449171i) q^{61} +(-8.35621 - 7.01169i) q^{62} +(-4.85779 + 8.41393i) q^{63} +(-5.11803 - 8.86468i) q^{64} +(-2.88927 - 1.66812i) q^{66} +(-9.52005 - 3.46501i) q^{67} +1.70896i q^{68} +(0.248610 - 0.683051i) q^{69} +(-10.6121 + 8.90459i) q^{71} +(1.16679 - 1.39053i) q^{72} -3.43226 q^{73} +(-6.06698 + 11.0696i) q^{74} +(2.22824 - 2.65552i) q^{76} +(10.9311 - 9.17230i) q^{77} +(0.281554 + 1.59677i) q^{78} +(1.41012 - 3.87427i) q^{79} +(-7.23256 - 2.63244i) q^{81} +(19.1683 + 11.0668i) q^{82} +(2.48726 - 14.1059i) q^{83} +(-1.50703 - 2.61025i) q^{84} +(-15.7993 - 13.2572i) q^{86} +(0.289870 - 0.0511119i) q^{87} +(-2.30887 + 1.33303i) q^{88} +(4.49440 + 12.3483i) q^{89} +(-6.82962 - 1.20425i) q^{91} +(-2.80887 - 3.34748i) q^{92} +(-1.29638 - 1.54497i) q^{93} +(-4.17191 - 0.735620i) q^{94} +(-1.06372 - 2.92256i) q^{96} +(-2.26408 + 1.30717i) q^{97} +(9.39785 - 1.65710i) q^{98} +(9.15659 + 7.68329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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