LMFDB - Embedded newform 476.2.bl.a.129.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(5,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 40, 15]))

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

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

chi := DirichletCharacter("476.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bl (of order $48$, degree $16$, 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:	$3.80087913621$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$12$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			129.11
Character	$\chi$	$=$	476.129
Dual form			476.2.bl.a.369.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34987 + 2.73727i) q^{3} +(2.11595 - 1.85564i) q^{5} +(-2.54468 - 0.724313i) q^{7} +(-3.84420 + 5.00986i) q^{9} +O(q^{10})$	\(q+(1.34987 + 2.73727i) q^{3} +(2.11595 - 1.85564i) q^{5} +(-2.54468 - 0.724313i) q^{7} +(-3.84420 + 5.00986i) q^{9} +(0.627584 - 0.0411340i) q^{11} +(3.98665 + 3.98665i) q^{13} +(7.93566 + 3.28706i) q^{15} +(2.65858 + 3.15150i) q^{17} +(0.833329 + 6.32976i) q^{19} +(-1.45235 - 7.94319i) q^{21} +(-2.59742 - 1.28090i) q^{23} +(0.381224 - 2.89568i) q^{25} +(-9.92242 - 1.97369i) q^{27} +(-1.73163 - 8.70549i) q^{29} +(-0.521982 + 0.257413i) q^{31} +(0.959752 + 1.66234i) q^{33} +(-6.72848 + 3.18939i) q^{35} +(0.680551 - 10.3832i) q^{37} +(-5.53106 + 16.2940i) q^{39} +(1.11325 - 5.59669i) q^{41} +(-1.27667 - 3.08216i) q^{43} +(1.16236 + 17.7341i) q^{45} +(1.45526 - 5.43109i) q^{47} +(5.95074 + 3.68628i) q^{49} +(-5.03778 + 11.5314i) q^{51} +(1.20961 + 1.57639i) q^{53} +(1.25161 - 1.25161i) q^{55} +(-16.2014 + 10.8254i) q^{57} +(-3.74505 - 0.493045i) q^{59} +(-3.93119 - 11.5809i) q^{61} +(13.4110 - 9.96407i) q^{63} +(15.8334 + 1.03777i) q^{65} +(-4.85191 - 2.80125i) q^{67} -8.83888i q^{69} +(6.06569 + 4.05296i) q^{71} +(3.86476 + 1.31191i) q^{73} +(8.44087 - 2.86529i) q^{75} +(-1.62679 - 0.349894i) q^{77} +(-2.64514 + 5.36382i) q^{79} +(-3.08830 - 11.5257i) q^{81} +(5.71488 - 13.7969i) q^{83} +(11.4735 + 1.73507i) q^{85} +(21.4918 - 16.4912i) q^{87} +(-8.63400 - 2.31347i) q^{89} +(-7.25714 - 13.0323i) q^{91} +(-1.40922 - 1.08133i) q^{93} +(13.5091 + 11.8471i) q^{95} +(3.30469 - 0.657344i) q^{97} +(-2.20648 + 3.30224i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) $ 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	1.34987	+	2.73727i	0.779349	+	1.58036i	0.813931	+	0.580961i	$0.197323\pi$
$3$	1.34987	+	2.73727i	0.779349	+	1.58036i	−0.0345824	+	0.999402i	$0.511010\pi$
$4$		0			0
$5$	2.11595	−	1.85564i	0.946284	−	0.829868i	−0.0392706	−	0.999229i	$-0.512503\pi$
$5$	2.11595	−	1.85564i	0.946284	−	0.829868i	0.985554	+	0.169360i	$0.0541701\pi$
$6$		0			0
$7$	−2.54468	−	0.724313i	−0.961797	−	0.273765i
$7$	−2.54468	−	0.724313i	−0.961797	−	0.273765i
$8$		0			0
$9$	−3.84420	+	5.00986i	−1.28140	+	1.66995i
$10$		0			0
$11$	0.627584	−	0.0411340i	0.189224	−	0.0124024i	0.0295033	−	0.999565i	$-0.490607\pi$
$11$	0.627584	−	0.0411340i	0.189224	−	0.0124024i	0.159720	+	0.987162i	$0.448941\pi$
$12$		0			0
$13$	3.98665	+	3.98665i	1.10570	+	1.10570i	0.993710	+	0.111987i	$0.0357216\pi$
$13$	3.98665	+	3.98665i	1.10570	+	1.10570i	0.111987	+	0.993710i	$0.464278\pi$
$14$		0			0
$15$	7.93566	+	3.28706i	2.04898	+	0.848715i
$16$		0			0
$17$	2.65858	+	3.15150i	0.644799	+	0.764352i
$17$	2.65858	+	3.15150i	0.644799	+	0.764352i
$18$		0			0
$19$	0.833329	+	6.32976i	0.191179	+	1.45215i	0.770704	+	0.637193i	$0.219905\pi$
$19$	0.833329	+	6.32976i	0.191179	+	1.45215i	−0.579525	+	0.814954i	$0.696762\pi$
$20$		0			0
$21$	−1.45235	−	7.94319i	−0.316928	−	1.73335i
$22$		0			0
$23$	−2.59742	−	1.28090i	−0.541599	−	0.267087i	0.150847	−	0.988557i	$-0.451800\pi$
$23$	−2.59742	−	1.28090i	−0.541599	−	0.267087i	−0.692445	+	0.721470i	$0.743467\pi$
$24$		0			0
$25$	0.381224	−	2.89568i	0.0762448	−	0.579137i
$26$		0			0
$27$	−9.92242	−	1.97369i	−1.90957	−	0.379837i
$28$		0			0
$29$	−1.73163	−	8.70549i	−0.321555	−	1.61657i	−0.716310	−	0.697782i	$-0.754170\pi$
$29$	−1.73163	−	8.70549i	−0.321555	−	1.61657i	0.394755	−	0.918786i	$-0.370830\pi$
$30$		0			0
$31$	−0.521982	+	0.257413i	−0.0937508	+	0.0462328i	−0.488560	−	0.872531i	$-0.662478\pi$
$31$	−0.521982	+	0.257413i	−0.0937508	+	0.0462328i	0.394809	+	0.918763i	$0.370811\pi$
$32$		0			0
$33$	0.959752	+	1.66234i	0.167071	+	0.289376i
$34$		0			0
$35$	−6.72848	+	3.18939i	−1.13732	+	0.539106i
$36$		0			0
$37$	0.680551	−	10.3832i	0.111882	−	1.70699i	−0.461042	−	0.887378i	$-0.652524\pi$
$37$	0.680551	−	10.3832i	0.111882	−	1.70699i	0.572924	−	0.819608i	$-0.305809\pi$
$38$		0			0
$39$	−5.53106	+	16.2940i	−0.885679	+	2.60913i
$40$		0			0
$41$	1.11325	−	5.59669i	0.173861	−	0.874056i	−0.791105	−	0.611680i	$-0.790494\pi$
$41$	1.11325	−	5.59669i	0.173861	−	0.874056i	0.964966	−	0.262376i	$-0.0845061\pi$
$42$		0			0
$43$	−1.27667	−	3.08216i	−0.194690	−	0.470024i	0.796144	−	0.605107i	$-0.206870\pi$
$43$	−1.27667	−	3.08216i	−0.194690	−	0.470024i	−0.990834	+	0.135083i	$0.956870\pi$
$44$		0			0
$45$	1.16236	+	17.7341i	0.173274	+	2.64365i
$46$		0			0
$47$	1.45526	−	5.43109i	0.212271	−	0.792206i	−0.774838	−	0.632159i	$-0.782169\pi$
$47$	1.45526	−	5.43109i	0.212271	−	0.792206i	0.987109	−	0.160047i	$-0.0511645\pi$
$48$		0			0
$49$	5.95074	+	3.68628i	0.850106	+	0.526612i
$50$		0			0
$51$	−5.03778	+	11.5314i	−0.705430	+	1.61471i
$52$		0			0
$53$	1.20961	+	1.57639i	0.166152	+	0.216534i	0.869007	−	0.494799i	$-0.164758\pi$
$53$	1.20961	+	1.57639i	0.166152	+	0.216534i	−0.702855	+	0.711333i	$0.748092\pi$
$54$		0			0
$55$	1.25161	−	1.25161i	0.168767	−	0.168767i
$56$		0			0
$57$	−16.2014	+	10.8254i	−2.14592	+	1.43386i
$58$		0			0
$59$	−3.74505	−	0.493045i	−0.487563	−	0.0641889i	−0.117263	−	0.993101i	$-0.537412\pi$
$59$	−3.74505	−	0.493045i	−0.487563	−	0.0641889i	−0.370301	+	0.928912i	$0.620745\pi$
$60$		0			0
$61$	−3.93119	−	11.5809i	−0.503338	−	1.48278i	−0.840748	−	0.541427i	$-0.817884\pi$
$61$	−3.93119	−	11.5809i	−0.503338	−	1.48278i	0.337410	−	0.941358i	$-0.390449\pi$
$62$		0			0
$63$	13.4110	−	9.96407i	1.68962	−	1.25535i
$64$		0			0
$65$	15.8334	+	1.03777i	1.96389	+	0.128720i
$66$		0			0
$67$	−4.85191	−	2.80125i	−0.592756	−	0.342228i	0.173431	−	0.984846i	$-0.444515\pi$
$67$	−4.85191	−	2.80125i	−0.592756	−	0.342228i	−0.766186	+	0.642618i	$0.777848\pi$
$68$		0			0
$69$		−	8.83888i		−	1.06408i
$70$		0			0
$71$	6.06569	+	4.05296i	0.719865	+	0.480998i	0.860750	−	0.509028i	$-0.169995\pi$
$71$	6.06569	+	4.05296i	0.719865	+	0.480998i	−0.140885	+	0.990026i	$0.544995\pi$
$72$		0			0
$73$	3.86476	+	1.31191i	0.452336	+	0.153547i	0.538305	−	0.842750i	$-0.319065\pi$
$73$	3.86476	+	1.31191i	0.452336	+	0.153547i	−0.0859682	+	0.996298i	$0.527398\pi$
$74$		0			0
$75$	8.44087	−	2.86529i	0.974668	−	0.330855i
$76$		0			0
$77$	−1.62679	−	0.349894i	−0.185390	−	0.0398741i
$78$		0			0
$79$	−2.64514	+	5.36382i	−0.297602	+	0.603477i	−0.993392	−	0.114768i	$-0.963388\pi$
$79$	−2.64514	+	5.36382i	−0.297602	+	0.603477i	0.695790	+	0.718245i	$0.255054\pi$
$80$		0			0
$81$	−3.08830	−	11.5257i	−0.343144	−	1.28063i
$82$		0			0
$83$	5.71488	−	13.7969i	0.627289	−	1.51441i	−0.215689	−	0.976462i	$-0.569200\pi$
$83$	5.71488	−	13.7969i	0.627289	−	1.51441i	0.842978	−	0.537948i	$-0.180800\pi$
$84$		0			0
$85$	11.4735	+	1.73507i	1.24447	+	0.188195i
$86$		0			0
$87$	21.4918	−	16.4912i	2.30416	−	1.76805i
$88$		0			0
$89$	−8.63400	−	2.31347i	−0.915202	−	0.245228i	−0.229669	−	0.973269i	$-0.573764\pi$
$89$	−8.63400	−	2.31347i	−0.915202	−	0.245228i	−0.685533	+	0.728041i	$0.740431\pi$
$90$		0			0
$91$	−7.25714	−	13.0323i	−0.760755	−	1.36616i
$92$		0			0
$93$	−1.40922	−	1.08133i	−0.146129	−	0.112129i
$94$		0			0
$95$	13.5091	+	11.8471i	1.38600	+	1.21549i
$96$		0			0
$97$	3.30469	−	0.657344i	0.335541	−	0.0667432i	−0.0244446	−	0.999701i	$-0.507782\pi$
$97$	3.30469	−	0.657344i	0.335541	−	0.0667432i	0.359985	+	0.932958i	$0.382782\pi$
$98$		0			0
$99$	−2.20648	+	3.30224i	−0.221760	+	0.331887i
$100$		0			0
$101$	−5.27405	+	9.13492i	−0.524788	+	0.908959i	0.474796	+	0.880096i	$0.342522\pi$
$101$	−5.27405	+	9.13492i	−0.524788	+	0.908959i	−0.999583	+	0.0288628i	$0.990811\pi$
$102$		0			0
$103$	−7.33562	+	4.23522i	−0.722800	+	0.417309i	−0.815782	−	0.578359i	$-0.803693\pi$
$103$	−7.33562	+	4.23522i	−0.722800	+	0.417309i	0.0929824	+	0.995668i	$0.470360\pi$
$104$		0			0
$105$	−17.8128	−	14.1124i	−1.73835	−	1.37723i
$106$		0			0
$107$	3.57547	+	4.07704i	0.345653	+	0.394142i	0.898379	−	0.439221i	$-0.144746\pi$
$107$	3.57547	+	4.07704i	0.345653	+	0.394142i	−0.552726	+	0.833363i	$0.686412\pi$
$108$		0			0
$109$	−4.08781	+	4.66126i	−0.391542	+	0.446468i	−0.913705	−	0.406378i	$-0.866792\pi$
$109$	−4.08781	+	4.66126i	−0.391542	+	0.446468i	0.522164	+	0.852845i	$0.325125\pi$
$110$		0			0
$111$	29.3403	−	12.1531i	2.78485	−	1.15352i
$112$		0			0
$113$	−2.12694	−	3.18319i	−0.200086	−	0.299450i	0.717835	−	0.696213i	$-0.245133\pi$
$113$	−2.12694	−	3.18319i	−0.200086	−	0.299450i	−0.917921	+	0.396764i	$0.870133\pi$
$114$		0			0
$115$	−7.87291	+	2.10954i	−0.734153	+	0.196716i
$116$		0			0
$117$	−35.2980	+	4.64708i	−3.26331	+	0.429622i
$118$		0			0
$119$	−4.48254	−	9.94519i	−0.410913	−	0.911674i
$120$		0			0
$121$	−10.5137	+	1.38416i	−0.955793	+	0.125833i
$122$		0			0
$123$	16.8224	−	4.50755i	1.51682	−	0.406432i
$124$		0			0
$125$	3.25120	+	4.86576i	0.290796	+	0.435207i
$126$		0			0
$127$	−17.2753	+	7.15566i	−1.53293	+	0.634962i	−0.980131	−	0.198351i	$-0.936442\pi$
$127$	−17.2753	+	7.15566i	−1.53293	+	0.634962i	−0.552802	+	0.833312i	$0.686442\pi$
$128$		0			0
$129$	6.71335	−	7.65511i	0.591077	−	0.673995i
$130$		0			0
$131$	0.278634	+	0.317721i	0.0243443	+	0.0277594i	0.763884	−	0.645354i	$-0.223290\pi$
$131$	0.278634	+	0.317721i	0.0243443	+	0.0277594i	−0.739540	+	0.673113i	$0.764957\pi$
$132$		0			0
$133$	2.46418	−	16.7108i	0.213671	−	1.44901i
$134$		0			0
$135$	−24.6578	+	14.2362i	−2.12221	+	1.22526i
$136$		0			0
$137$	−1.35173	+	2.34127i	−0.115486	+	0.200028i	−0.917974	−	0.396641i	$-0.870176\pi$
$137$	−1.35173	+	2.34127i	−0.115486	+	0.200028i	0.802488	+	0.596668i	$0.203509\pi$
$138$		0			0
$139$	−0.971422	+	1.45384i	−0.0823949	+	0.123313i	−0.870378	−	0.492384i	$-0.836125\pi$
$139$	−0.971422	+	1.45384i	−0.0823949	+	0.123313i	0.787983	+	0.615697i	$0.211125\pi$
$140$		0			0
$141$	16.8308	−	3.34785i	1.41741	−	0.281940i
$142$		0			0
$143$	2.66594	+	2.33797i	0.222937	+	0.195511i
$144$		0			0
$145$	−19.8183	−	15.2071i	−1.64582	−	1.26288i
$146$		0			0
$147$	−2.05761	+	21.2648i	−0.169708	+	1.75389i
$148$		0			0
$149$	16.7562	+	4.48980i	1.37272	+	0.367819i	0.868471	−	0.495741i	$-0.165103\pi$
$149$	16.7562	+	4.48980i	1.37272	+	0.367819i	0.504247	+	0.863559i	$0.331770\pi$
$150$		0			0
$151$	13.6900	−	10.5047i	1.11408	−	0.854863i	0.123574	−	0.992335i	$-0.460564\pi$
$151$	13.6900	−	10.5047i	1.11408	−	0.854863i	0.990506	+	0.137472i	$0.0438978\pi$
$152$		0			0
$153$	−26.0087	+	1.20408i	−2.10268	+	0.0973441i
$154$		0			0
$155$	−0.626824	+	1.51329i	−0.0503477	+	0.121550i
$156$		0			0
$157$	−2.60872	−	9.73589i	−0.208199	−	0.777009i	−0.988451	−	0.151543i	$-0.951576\pi$
$157$	−2.60872	−	9.73589i	−0.208199	−	0.777009i	0.780252	−	0.625466i	$-0.215091\pi$
$158$		0			0
$159$	−2.68219	+	5.43894i	−0.212711	+	0.431336i
$160$		0			0
$161$	5.68180	+	5.14083i	0.447789	+	0.405154i
$162$		0			0
$163$	−7.96845	+	2.70493i	−0.624138	+	0.211866i	−0.615551	−	0.788097i	$-0.711067\pi$
$163$	−7.96845	+	2.70493i	−0.624138	+	0.211866i	−0.00858644	+	0.999963i	$0.502733\pi$
$164$		0			0
$165$	5.11550	+	1.73648i	0.398241	+	0.135185i
$166$		0			0
$167$	13.5896	+	9.08026i	1.05159	+	0.702651i	0.956178	−	0.292786i	$-0.0945825\pi$
$167$	13.5896	+	9.08026i	1.05159	+	0.702651i	0.0954141	+	0.995438i	$0.469582\pi$
$168$		0			0
$169$			18.7867i			1.44513i
$170$		0			0
$171$	−34.9147	−	20.1580i	−2.67000	−	1.54152i
$172$		0			0
$173$	14.0168	+	0.918709i	1.06568	+	0.0698481i	0.588136	−	0.808762i	$-0.299862\pi$
$173$	14.0168	+	0.918709i	1.06568	+	0.0698481i	0.477540	+	0.878610i	$0.341529\pi$
$174$		0			0
$175$	−3.06747	+	7.09245i	−0.231879	+	0.536139i
$176$		0			0
$177$	−3.70574	−	10.9167i	−0.278540	−	0.820553i
$178$		0			0
$179$	−1.43330	−	0.188698i	−0.107130	−	0.0141039i	0.0767705	−	0.997049i	$-0.475539\pi$
$179$	−1.43330	−	0.188698i	−0.107130	−	0.0141039i	−0.183901	+	0.982945i	$0.558872\pi$
$180$		0			0
$181$	−8.60738	+	5.75127i	−0.639782	+	0.427488i	−0.832698	−	0.553727i	$-0.813205\pi$
$181$	−8.60738	+	5.75127i	−0.639782	+	0.427488i	0.192917	+	0.981215i	$0.438205\pi$
$182$		0			0
$183$	26.3935	−	26.3935i	1.95106	−	1.95106i
$184$		0			0
$185$	−17.8275	−	23.2332i	−1.31070	−	1.70814i
$186$		0			0
$187$	1.79811	+	1.86847i	0.131491	+	0.136636i
$188$		0			0
$189$	23.8198	+	12.2093i	1.73263	+	0.888098i
$190$		0			0
$191$	−0.0806327	+	0.300925i	−0.00583437	+	0.0217742i	−0.968782	−	0.247916i	$-0.920254\pi$
$191$	−0.0806327	+	0.300925i	−0.00583437	+	0.0217742i	0.962947	+	0.269690i	$0.0869211\pi$
$192$		0			0
$193$	−1.71663	−	26.1907i	−0.123565	−	1.88524i	−0.389174	−	0.921164i	$-0.627240\pi$
$193$	−1.71663	−	26.1907i	−0.123565	−	1.88524i	0.265609	−	0.964081i	$-0.414427\pi$
$194$		0			0
$195$	18.5323	+	44.7410i	1.32713	+	3.20397i
$196$		0			0
$197$	−3.58930	+	18.0446i	−0.255727	+	1.28563i	0.612901	+	0.790160i	$0.290003\pi$
$197$	−3.58930	+	18.0446i	−0.255727	+	1.28563i	−0.868627	+	0.495466i	$0.834997\pi$
$198$		0			0
$199$	1.46331	−	4.31078i	0.103732	−	0.305583i	−0.882656	−	0.470019i	$-0.844247\pi$
$199$	1.46331	−	4.31078i	0.103732	−	0.305583i	0.986388	+	0.164436i	$0.0525803\pi$
$200$		0			0
$201$	1.11832	−	17.0623i	0.0788805	−	1.20348i
$202$		0			0
$203$	−1.89906	+	23.4069i	−0.133288	+	1.64284i
$204$		0			0
$205$	−8.02987	−	13.9081i	−0.560830	−	0.971387i
$206$		0			0
$207$	16.4022	−	8.08865i	1.14003	−	0.562200i
$208$		0			0
$209$	0.783352	+	3.93818i	0.0541856	+	0.272409i
$210$		0			0
$211$	7.12113	+	1.41648i	0.490239	+	0.0975145i	0.434019	−	0.900904i	$-0.357095\pi$
$211$	7.12113	+	1.41648i	0.490239	+	0.0975145i	0.0562200	+	0.998418i	$0.482095\pi$
$212$		0			0
$213$	−2.90615	+	22.0744i	−0.199126	+	1.51251i
$214$		0			0
$215$	−8.42076	−	4.15266i	−0.574291	−	0.283209i
$216$		0			0
$217$	1.51472	−	0.276955i	0.102826	−	0.0188009i
$218$		0			0
$219$	1.62588	+	12.3498i	0.109867	+	0.834523i
$220$		0			0
$221$	−1.96513	+	23.1627i	−0.132189	+	1.55809i
$222$		0			0
$223$	−18.1480	−	7.51715i	−1.21528	−	0.503386i	−0.319374	−	0.947629i	$-0.603473\pi$
$223$	−18.1480	−	7.51715i	−1.21528	−	0.503386i	−0.895906	+	0.444243i	$0.853473\pi$
$224$		0			0
$225$	13.0415	+	13.0415i	0.869432	+	0.869432i
$226$		0			0
$227$	18.9743	−	1.24364i	1.25937	−	0.0825434i	0.578948	−	0.815365i	$-0.303464\pi$
$227$	18.9743	−	1.24364i	1.25937	−	0.0825434i	0.680421	+	0.732821i	$0.261797\pi$
$228$		0			0
$229$	4.52658	−	5.89915i	0.299125	−	0.389827i	−0.619475	−	0.785016i	$-0.712654\pi$
$229$	4.52658	−	5.89915i	0.299125	−	0.389827i	0.918600	+	0.395190i	$0.129321\pi$
$230$		0			0
$231$	−1.23820	−	4.92527i	−0.0814678	−	0.324059i
$232$		0			0
$233$	4.35536	−	3.81954i	0.285329	−	0.250227i	−0.504702	−	0.863294i	$-0.668398\pi$
$233$	4.35536	−	3.81954i	0.285329	−	0.250227i	0.790031	+	0.613067i	$0.210064\pi$
$234$		0			0
$235$	−6.99891	−	14.1924i	−0.456558	−	0.925809i
$236$		0			0
$237$	−18.2528			−1.18565
$238$		0			0
$239$	−2.81756			−0.182253			−0.0911264	−	0.995839i	$-0.529047\pi$
$239$	−2.81756			−0.182253			−0.0911264	+	0.995839i	$0.529047\pi$
$240$		0			0
$241$	8.94261	+	18.1338i	0.576044	+	1.16810i	0.968658	+	0.248398i	$0.0799042\pi$
$241$	8.94261	+	18.1338i	0.576044	+	1.16810i	−0.392614	+	0.919703i	$0.628429\pi$
$242$		0			0
$243$	4.56142	−	4.00026i	0.292615	−	0.256617i
$244$		0			0
$245$	19.4319	−	3.24244i	1.24146	−	0.207152i
$246$		0			0
$247$	−21.9123	+	28.5567i	−1.39425	+	1.81702i
$248$		0			0
$249$	45.4803	−	2.98093i	2.88219	−	0.188909i
$250$		0			0
$251$	8.78785	+	8.78785i	0.554684	+	0.554684i	0.927789	−	0.373105i	$-0.121707\pi$
$251$	8.78785	+	8.78785i	0.554684	+	0.554684i	−0.373105	+	0.927789i	$0.621707\pi$
$252$		0			0
$253$	−1.68278	−	0.697032i	−0.105796	−	0.0438220i
$254$		0			0
$255$	10.7384	+	33.7482i	0.672463	+	2.11339i
$256$		0			0
$257$	−2.43804	−	18.5188i	−0.152081	−	1.15517i	−0.881869	−	0.471495i	$-0.843715\pi$
$257$	−2.43804	−	18.5188i	−0.152081	−	1.15517i	0.729788	−	0.683674i	$-0.239619\pi$
$258$		0			0
$259$	−9.25246	+	25.9289i	−0.574920	+	1.61114i
$260$		0			0
$261$	50.2700	+	24.7904i	3.11164	+	1.53449i
$262$		0			0
$263$	2.99217	−	22.7278i	0.184505	−	1.40145i	−0.609136	−	0.793066i	$-0.708483\pi$
$263$	2.99217	−	22.7278i	0.184505	−	1.40145i	0.793640	−	0.608387i	$-0.208183\pi$
$264$		0			0
$265$	5.48468	+	1.09097i	0.336921	+	0.0670179i
$266$		0			0
$267$	−5.32219	−	26.7565i	−0.325713	−	1.63747i
$268$		0			0
$269$	−15.0579	+	7.42574i	−0.918098	+	0.452756i	−0.839012	−	0.544112i	$-0.816867\pi$
$269$	−15.0579	+	7.42574i	−0.918098	+	0.452756i	−0.0790852	+	0.996868i	$0.525200\pi$
$270$		0			0
$271$	3.22721	+	5.58969i	0.196039	+	0.339550i	0.947241	−	0.320523i	$-0.103859\pi$
$271$	3.22721	+	5.58969i	0.196039	+	0.339550i	−0.751202	+	0.660073i	$0.770525\pi$
$272$		0			0
$273$	25.8767	−	37.4567i	1.56613	−	2.26698i
$274$		0			0
$275$	0.120139	−	1.83297i	0.00724465	−	0.110532i
$276$		0			0
$277$	1.20589	−	3.55244i	0.0724549	−	0.213445i	−0.904669	−	0.426114i	$-0.859882\pi$
$277$	1.20589	−	3.55244i	0.0724549	−	0.213445i	0.977124	+	0.212669i	$0.0682156\pi$
$278$		0			0
$279$	0.717002	−	3.60461i	0.0429258	−	0.215802i
$280$		0			0
$281$	11.0246	+	26.6157i	0.657670	+	1.58776i	0.801392	+	0.598139i	$0.204093\pi$
$281$	11.0246	+	26.6157i	0.657670	+	1.58776i	−0.143722	+	0.989618i	$0.545907\pi$
$282$		0			0
$283$	−1.27142	−	19.3981i	−0.0755780	−	1.15310i	−0.852230	−	0.523167i	$-0.824750\pi$
$283$	−1.27142	−	19.3981i	−0.0755780	−	1.15310i	0.776652	−	0.629930i	$-0.216916\pi$
$284$		0			0
$285$	−14.1933	+	52.9700i	−0.840737	+	3.13767i
$286$		0			0
$287$	−6.88662	+	13.4354i	−0.406504	+	0.793068i
$288$		0			0
$289$	−2.86395	+	16.7570i	−0.168468	+	0.985707i
$290$		0			0
$291$	6.26024	+	8.15850i	0.366982	+	0.478260i
$292$		0			0
$293$	−17.9975	+	17.9975i	−1.05143	+	1.05143i	−0.0528233	+	0.998604i	$0.516822\pi$
$293$	−17.9975	+	17.9975i	−1.05143	+	1.05143i	−0.998604	+	0.0528233i	$0.983178\pi$
$294$		0			0
$295$	−8.83926	+	5.90620i	−0.514642	+	0.343873i
$296$		0			0
$297$	−6.30833	−	0.830508i	−0.366047	−	0.0481909i
$298$		0			0
$299$	−5.24847	−	15.4615i	−0.303527	−	0.894161i
$300$		0			0
$301$	1.01627	+	8.76779i	0.0585767	+	0.505367i
$302$		0			0
$303$	−32.1240	−	2.10552i	−1.84548	−	0.120959i
$304$		0			0
$305$	−29.8083	−	17.2098i	−1.70682	−	0.985431i
$306$		0			0
$307$		−	16.6648i		−	0.951109i	−0.879686	−	0.475554i	$-0.842247\pi$
$307$		−	16.6648i		−	0.951109i	0.879686	−	0.475554i	$-0.157753\pi$
$308$		0			0
$309$	−21.4951	−	14.3626i	−1.22281	−	0.817057i
$310$		0			0
$311$	−14.0978	−	4.78556i	−0.799413	−	0.271364i	−0.108307	−	0.994117i	$-0.534543\pi$
$311$	−14.0978	−	4.78556i	−0.799413	−	0.271364i	−0.691106	+	0.722753i	$0.742876\pi$
$312$		0			0
$313$	−9.79956	+	3.32650i	−0.553904	+	0.188025i	−0.584336	−	0.811512i	$-0.698645\pi$
$313$	−9.79956	+	3.32650i	−0.553904	+	0.188025i	0.0304321	+	0.999537i	$0.490312\pi$
$314$		0			0
$315$	9.88723	−	45.9695i	0.557082	−	2.59009i
$316$		0			0
$317$	−5.28437	+	10.7156i	−0.296800	+	0.601851i	−0.993281	−	0.115724i	$-0.963081\pi$
$317$	−5.28437	+	10.7156i	−0.296800	+	0.601851i	0.696481	+	0.717575i	$0.254748\pi$
$318$		0			0
$319$	−1.44483	−	5.39219i	−0.0808951	−	0.301905i
$320$		0			0
$321$	−6.33353	+	15.2905i	−0.353503	+	0.853432i
$322$		0			0
$323$	−17.7328	+	19.4544i	−0.986679	+	1.08247i
$324$		0			0
$325$	13.0639	−	10.0243i	0.724654	−	0.556046i
$326$		0			0
$327$	−18.2771	−	4.89735i	−1.01073	−	0.270824i
$328$		0			0
$329$	−7.63696	+	12.7663i	−0.421039	+	0.703829i
$330$		0			0
$331$	16.4937	+	12.6561i	0.906576	+	0.695640i	0.952899	−	0.303287i	$-0.0980839\pi$
$331$	16.4937	+	12.6561i	0.906576	+	0.695640i	−0.0463238	+	0.998926i	$0.514751\pi$
$332$		0			0
$333$	49.4022	+	43.3246i	2.70723	+	2.37417i
$334$		0			0
$335$	−15.4646	+	3.07609i	−0.844919	+	0.168065i
$336$		0			0
$337$	−2.72035	+	4.07129i	−0.148187	+	0.221777i	−0.898136	−	0.439719i	$-0.855078\pi$
$337$	−2.72035	+	4.07129i	−0.148187	+	0.221777i	0.749949	+	0.661496i	$0.230078\pi$
$338$		0			0
$339$	5.84216	−	10.1189i	0.317302	−	0.549584i
$340$		0			0
$341$	−0.316999	+	0.183020i	−0.0171665	+	0.00991107i
$342$		0			0
$343$	−12.4727	−	13.6906i	−0.673462	−	0.739222i
$344$		0			0
$345$	−16.4018	−	18.7027i	−0.883044	−	1.00692i
$346$		0			0
$347$	−6.47405	+	7.38224i	−0.347545	+	0.396299i	−0.899031	−	0.437885i	$-0.855728\pi$
$347$	−6.47405	+	7.38224i	−0.347545	+	0.396299i	0.551486	+	0.834184i	$0.314061\pi$
$348$		0			0
$349$	3.05699	−	1.26625i	0.163637	−	0.0677806i	−0.299361	−	0.954140i	$-0.596774\pi$
$349$	3.05699	−	1.26625i	0.163637	−	0.0677806i	0.462998	+	0.886359i	$0.346774\pi$
$350$		0			0
$351$	−31.6888	−	47.4256i	−1.69142	−	2.53139i
$352$		0			0
$353$	−9.49183	+	2.54333i	−0.505199	+	0.135368i	−0.502412	−	0.864628i	$-0.667554\pi$
$353$	−9.49183	+	2.54333i	−0.505199	+	0.135368i	−0.00278732	+	0.999996i	$0.500887\pi$
$354$		0			0
$355$	20.3556	−	2.67986i	1.08036	−	0.142232i
$356$		0			0
$357$	21.1718	−	25.6946i	1.12053	−	1.35990i
$358$		0			0
$359$	2.66137	−	0.350377i	0.140462	−	0.0184922i	−0.0599673	−	0.998200i	$-0.519100\pi$
$359$	2.66137	−	0.350377i	0.140462	−	0.0184922i	0.200429	+	0.979708i	$0.435766\pi$
$360$		0			0
$361$	−21.0189	+	5.63199i	−1.10626	+	0.296420i
$362$		0			0
$363$	−17.9810	−	26.9105i	−0.943757	−	1.41243i
$364$		0			0
$365$	10.6121	−	4.39568i	0.555463	−	0.230080i
$366$		0			0
$367$	8.53526	−	9.73259i	0.445537	−	0.508037i	−0.484860	−	0.874592i	$-0.661129\pi$
$367$	8.53526	−	9.73259i	0.445537	−	0.508037i	0.930397	+	0.366555i	$0.119463\pi$
$368$		0			0
$369$	23.7591	+	27.0921i	1.23685	+	1.41036i
$370$		0			0
$371$	−1.93625	−	4.88753i	−0.100525	−	0.253748i
$372$		0			0
$373$	9.94410	−	5.74123i	0.514886	−	0.297269i	−0.219954	−	0.975510i	$-0.570591\pi$
$373$	9.94410	−	5.74123i	0.514886	−	0.297269i	0.734840	+	0.678241i	$0.237257\pi$
$374$		0			0
$375$	−8.93019	+	15.4675i	−0.461153	+	0.798741i
$376$		0			0
$377$	27.8023	−	41.6091i	1.43189	−	2.14298i
$378$		0			0
$379$	−8.99614	+	1.78944i	−0.462101	+	0.0919175i	−0.420650	−	0.907223i	$-0.638198\pi$
$379$	−8.99614	+	1.78944i	−0.462101	+	0.0919175i	−0.0414506	+	0.999141i	$0.513198\pi$
$380$		0			0
$381$	−42.9064	−	37.6279i	−2.19816	−	1.92773i
$382$		0			0
$383$	−16.3442	−	12.5413i	−0.835149	−	0.640833i	0.100039	−	0.994984i	$-0.468103\pi$
$383$	−16.3442	−	12.5413i	−0.835149	−	0.640833i	−0.935188	+	0.354151i	$0.884770\pi$
$384$		0			0
$385$	−4.09149	+	2.27838i	−0.208522	+	0.116117i
$386$		0			0
$387$	20.3490	+	5.45249i	1.03440	+	0.277166i
$388$		0			0
$389$	25.2909	−	19.4064i	1.28230	−	0.983945i	0.282607	−	0.959236i	$-0.408801\pi$
$389$	25.2909	−	19.4064i	1.28230	−	0.983945i	0.999695	−	0.0247088i	$-0.00786586\pi$
$390$		0			0
$391$	−2.86865	−	11.5911i	−0.145074	−	0.586189i
$392$		0			0
$393$	−0.493568	+	1.19158i	−0.0248972	+	0.0601072i
$394$		0			0
$395$	4.35633	+	16.2580i	0.219191	+	0.818031i
$396$		0			0
$397$	−7.06530	+	14.3270i	−0.354597	+	0.719052i	−0.998957	−	0.0456710i	$-0.985457\pi$
$397$	−7.06530	+	14.3270i	−0.354597	+	0.719052i	0.644359	+	0.764723i	$0.277124\pi$
$398$		0			0
$399$	49.0682	−	15.8123i	2.45648	−	0.791605i
$400$		0			0
$401$	−1.53534	+	0.521179i	−0.0766713	+	0.0260264i	−0.359512	−	0.933141i	$-0.617057\pi$
$401$	−1.53534	+	0.521179i	−0.0766713	+	0.0260264i	0.282840	+	0.959167i	$0.408723\pi$
$402$		0			0
$403$	−3.10718	−	1.05474i	−0.154779	−	0.0525405i
$404$		0			0
$405$	−27.9222	−	18.6570i	−1.38747	−	0.927076i
$406$		0			0
$407$		−	6.54432i		−	0.324390i
$408$		0			0
$409$	28.2345	+	16.3012i	1.39611	+	0.806043i	0.993982	−	0.109541i	$-0.0349381\pi$
$409$	28.2345	+	16.3012i	1.39611	+	0.806043i	0.402126	+	0.915584i	$0.368271\pi$
$410$		0			0
$411$	−8.23334	−	0.539641i	−0.406120	−	0.0266185i
$412$		0			0
$413$	9.17280	+	3.96722i	0.451364	+	0.195214i
$414$		0			0
$415$	−13.5098	−	39.7984i	−0.663168	−	1.95363i
$416$		0			0
$417$	−5.29083	−	0.696551i	−0.259093	−	0.0341103i
$418$		0			0
$419$	−0.593724	+	0.396714i	−0.0290053	+	0.0193807i	−0.569988	−	0.821653i	$-0.693052\pi$
$419$	−0.593724	+	0.396714i	−0.0290053	+	0.0193807i	0.540983	+	0.841033i	$0.318052\pi$
$420$		0			0
$421$	−7.20445	+	7.20445i	−0.351123	+	0.351123i	−0.860527	−	0.509404i	$-0.829866\pi$
$421$	−7.20445	+	7.20445i	−0.351123	+	0.351123i	0.509404	+	0.860527i	$0.329866\pi$
$422$		0			0
$423$	21.6147	+	28.1689i	1.05094	+	1.36962i
$424$		0			0
$425$	10.1393	−	6.49697i	0.491827	−	0.315149i
$426$		0			0
$427$	1.61540	+	32.3171i	0.0781746	+	1.56393i
$428$		0			0
$429$	−2.80097	+	10.4534i	−0.135232	+	0.504693i
$430$		0			0
$431$	0.360502	+	5.50019i	0.0173648	+	0.264935i	0.997710	+	0.0676432i	$0.0215480\pi$
$431$	0.360502	+	5.50019i	0.0173648	+	0.264935i	−0.980345	+	0.197292i	$0.936785\pi$
$432$		0			0
$433$	7.35279	+	17.7512i	0.353352	+	0.853068i	0.996202	+	0.0870755i	$0.0277521\pi$
$433$	7.35279	+	17.7512i	0.353352	+	0.853068i	−0.642849	+	0.765993i	$0.722248\pi$
$434$		0			0
$435$	14.8738	−	74.7757i	0.713145	−	3.58522i
$436$		0			0
$437$	5.94332	−	17.5084i	0.284307	−	0.837542i
$438$		0			0
$439$	−2.26739	+	34.5937i	−0.108217	+	1.65107i	0.506442	+	0.862274i	$0.330960\pi$
$439$	−2.26739	+	34.5937i	−0.108217	+	1.65107i	−0.614659	+	0.788793i	$0.710706\pi$
$440$		0			0
$441$	−41.3436	+	15.6416i	−1.96874	+	0.744838i
$442$		0			0
$443$	6.28171	+	10.8802i	0.298453	+	0.516936i	0.975782	−	0.218744i	$-0.0701961\pi$
$443$	6.28171	+	10.8802i	0.298453	+	0.516936i	−0.677329	+	0.735680i	$0.736863\pi$
$444$		0			0
$445$	−22.5621	+	11.1264i	−1.06955	+	0.527442i
$446$		0			0
$447$	10.3289	+	51.9268i	0.488539	+	2.45605i
$448$		0			0
$449$	−7.43623	−	1.47916i	−0.350938	−	0.0698058i	0.0164740	−	0.999864i	$-0.494756\pi$
$449$	−7.43623	−	1.47916i	−0.350938	−	0.0698058i	−0.367412	+	0.930058i	$0.619756\pi$
$450$		0			0
$451$	0.468444	−	3.55818i	0.0220582	−	0.167548i
$452$		0			0
$453$	47.2341	+	23.2933i	2.21925	+	1.09441i
$454$		0			0
$455$	−39.5391	−	14.1091i	−1.85362	−	0.661445i
$456$		0			0
$457$	−0.510759	−	3.87960i	−0.0238923	−	0.181480i	0.975338	−	0.220718i	$-0.0708402\pi$
$457$	−0.510759	−	3.87960i	−0.0238923	−	0.181480i	−0.999230	+	0.0392383i	$0.987507\pi$
$458$		0			0
$459$	−20.1594	−	36.5177i	−0.940960	−	1.70450i
$460$		0			0
$461$	11.7057	+	4.84866i	0.545189	+	0.225825i	0.638241	−	0.769837i	$-0.279662\pi$
$461$	11.7057	+	4.84866i	0.545189	+	0.225825i	−0.0930521	+	0.995661i	$0.529662\pi$
$462$		0			0
$463$	10.9668	+	10.9668i	0.509672	+	0.509672i	0.914426	−	0.404753i	$-0.132643\pi$
$463$	10.9668	+	10.9668i	0.509672	+	0.509672i	−0.404753	+	0.914426i	$0.632643\pi$
$464$		0			0
$465$	−4.98841	+	0.326957i	−0.231332	+	0.0151623i
$466$		0			0
$467$	4.57398	−	5.96093i	0.211659	−	0.275839i	−0.675444	−	0.737411i	$-0.736048\pi$
$467$	4.57398	−	5.96093i	0.211659	−	0.275839i	0.887103	+	0.461572i	$0.152715\pi$
$468$		0			0
$469$	10.3176	+	10.6426i	0.476421	+	0.491429i
$470$		0			0
$471$	23.1283	−	20.2830i	1.06570	−	0.934591i
$472$		0			0
$473$	−0.927999	−	1.88180i	−0.0426694	−	0.0865251i
$474$		0			0
$475$	18.6467			0.855568
$476$		0			0
$477$	−12.5475			−0.574509
$478$		0			0
$479$	2.30658	+	4.67727i	0.105390	+	0.213710i	0.943180	−	0.332283i	$-0.107819\pi$
$479$	2.30658	+	4.67727i	0.105390	+	0.213710i	−0.837789	+	0.545993i	$0.816152\pi$
$480$		0			0
$481$	44.1072	−	38.6810i	2.01112	−	1.76370i
$482$		0			0
$483$	−6.40212	+	22.4921i	−0.291306	+	1.02343i
$484$		0			0
$485$	5.77278	−	7.52324i	0.262129	−	0.341613i
$486$		0			0
$487$	−29.8311	+	1.95523i	−1.35178	+	0.0886001i	−0.724004	−	0.689796i	$-0.757700\pi$
$487$	−29.8311	+	1.95523i	−1.35178	+	0.0886001i	−0.627773	+	0.778396i	$0.716033\pi$
$488$		0			0
$489$	−18.1605	−	18.1605i	−0.821246	−	0.821246i
$490$		0			0
$491$	11.2061	+	4.64170i	0.505722	+	0.209477i	0.620932	−	0.783864i	$-0.286754\pi$
$491$	11.2061	+	4.64170i	0.505722	+	0.209477i	−0.115210	+	0.993341i	$0.536754\pi$
$492$		0			0
$493$	22.8317	−	28.6014i	1.02829	−	1.28814i
$494$		0			0
$495$	1.45895	+	11.0818i	0.0655749	+	0.498091i
$496$		0			0
$497$	−12.4996	−	14.7069i	−0.560683	−	0.659696i
$498$		0			0
$499$	−25.4276	−	12.5395i	−1.13829	−	0.561345i	−0.227325	−	0.973819i	$-0.572998\pi$
$499$	−25.4276	−	12.5395i	−1.13829	−	0.561345i	−0.910969	+	0.412474i	$0.864665\pi$
$500$		0			0
$501$	−6.51094	+	49.4555i	−0.290887	+	2.20951i
$502$		0			0
$503$	26.6193	+	5.29490i	1.18689	+	0.236088i	0.748772	−	0.662828i	$-0.230644\pi$
$503$	26.6193	+	5.29490i	1.18689	+	0.236088i	0.438122	+	0.898915i	$0.355644\pi$
$504$		0			0
$505$	5.79150	+	29.1158i	0.257718	+	1.29564i
$506$		0			0
$507$	−51.4243	+	25.3596i	−2.28383	+	1.12626i
$508$		0			0
$509$	−19.9426	−	34.5416i	−0.883939	−	1.53103i	−0.846925	−	0.531713i	$-0.821549\pi$
$509$	−19.9426	−	34.5416i	−0.883939	−	1.53103i	−0.0370145	−	0.999315i	$-0.511785\pi$
$510$		0			0
$511$	−8.88433	−	6.13768i	−0.393020	−	0.271515i
$512$		0			0
$513$	4.22436	−	64.4513i	0.186510	−	2.84559i
$514$		0			0
$515$	−7.66278	+	22.5738i	−0.337662	+	0.994721i
$516$		0			0
$517$	0.689893	−	3.46832i	0.0303414	−	0.152537i
$518$		0			0
$519$	16.4061	+	39.6078i	0.720148	+	1.73859i
$520$		0			0
$521$	−0.414408	−	6.32265i	−0.0181556	−	0.277000i	−0.997278	−	0.0737301i	$-0.976510\pi$
$521$	−0.414408	−	6.32265i	−0.0181556	−	0.277000i	0.979123	−	0.203270i	$-0.0651570\pi$
$522$		0			0
$523$	−3.15521	+	11.7754i	−0.137968	+	0.514903i	0.862000	+	0.506908i	$0.169212\pi$
$523$	−3.15521	+	11.7754i	−0.137968	+	0.514903i	−0.999968	+	0.00799511i	$0.997455\pi$
$524$		0			0
$525$	−23.5546	+	1.17740i	−1.02801	+	0.0513860i
$526$		0			0
$527$	−2.19897	−	0.960677i	−0.0957886	−	0.0418477i
$528$		0			0
$529$	−8.89566	−	11.5930i	−0.386768	−	0.504045i
$530$		0			0
$531$	16.8668	−	16.8668i	0.731957	−	0.731957i
$532$		0			0
$533$	26.7502	−	17.8739i	1.15868	−	0.774204i
$534$		0			0
$535$	15.1310	+	1.99204i	0.654172	+	0.0861234i
$536$		0			0
$537$	−1.41826	−	4.17805i	−0.0612024	−	0.180296i
$538$		0			0
$539$	3.88622	+	2.06867i	0.167391	+	0.0891040i
$540$		0			0
$541$	−27.1820	−	1.78160i	−1.16864	−	0.0765969i	−0.531305	−	0.847181i	$-0.678298\pi$
$541$	−27.1820	−	1.78160i	−1.16864	−	0.0765969i	−0.637339	+	0.770584i	$0.719965\pi$
$542$		0			0
$543$	−27.3616	−	15.7972i	−1.17420	−	0.677925i
$544$		0			0
$545$			17.4485i			0.747413i
$546$		0			0
$547$	5.06303	+	3.38301i	0.216480	+	0.144647i	0.659082	−	0.752071i	$-0.270945\pi$
$547$	5.06303	+	3.38301i	0.216480	+	0.144647i	−0.442603	+	0.896718i	$0.645945\pi$
$548$		0			0
$549$	73.1312	+	24.8247i	3.12116	+	1.05949i
$550$		0			0
$551$	53.6606	−	18.2153i	2.28602	−	0.775999i
$552$		0			0
$553$	10.6161	−	11.7333i	0.451443	−	0.498950i
$554$		0			0
$555$	39.5308	−	80.1605i	1.67799	−	3.40262i
$556$		0			0
$557$	−8.05242	−	30.0521i	−0.341192	−	1.27335i	−0.896998	−	0.442034i	$-0.854257\pi$
$557$	−8.05242	−	30.0521i	−0.341192	−	1.27335i	0.555806	−	0.831312i	$-0.312410\pi$
$558$		0			0
$559$	7.19783	−	17.3771i	0.304436	−	0.734973i
$560$		0			0
$561$	−2.68730	+	7.44412i	−0.113458	+	0.314291i
$562$		0			0
$563$	13.5104	−	10.3669i	0.569396	−	0.436913i	−0.283516	−	0.958968i	$-0.591501\pi$
$563$	13.5104	−	10.3669i	0.569396	−	0.436913i	0.852912	+	0.522054i	$0.174834\pi$
$564$		0			0
$565$	−10.4074	−	2.78865i	−0.437842	−	0.117319i
$566$		0			0
$567$	−0.489486	+	31.5660i	−0.0205565	+	1.32565i
$568$		0			0
$569$	3.01040	+	2.30996i	0.126203	+	0.0968387i	0.669934	−	0.742421i	$-0.266322\pi$
$569$	3.01040	+	2.30996i	0.126203	+	0.0968387i	−0.543731	+	0.839259i	$0.682989\pi$
$570$		0			0
$571$	−8.06292	−	7.07100i	−0.337423	−	0.295912i	0.473819	−	0.880622i	$-0.342875\pi$
$571$	−8.06292	−	7.07100i	−0.337423	−	0.295912i	−0.811242	+	0.584710i	$0.801208\pi$
$572$		0			0
$573$	−0.932557	+	0.185497i	−0.0389581	+	0.00774925i
$574$		0			0
$575$	−4.69929	+	7.03299i	−0.195974	+	0.293296i
$576$		0			0
$577$	−0.262901	+	0.455359i	−0.0109447	+	0.0189568i	−0.871446	−	0.490492i	$-0.836817\pi$
$577$	−0.262901	+	0.455359i	−0.0109447	+	0.0189568i	0.860501	+	0.509448i	$0.170151\pi$
$578$		0			0
$579$	69.3737	−	40.0529i	2.88307	−	1.66454i
$580$		0			0
$581$	−24.5358	+	30.9693i	−1.01792	+	1.28482i
$582$		0			0
$583$	0.823972	+	0.939560i	0.0341254	+	0.0389126i
$584$		0			0
$585$	−66.0657	+	75.3335i	−2.73148	+	3.11466i
$586$		0			0
$587$	−39.2912	+	16.2750i	−1.62172	+	0.671739i	−0.994268	−	0.106915i	$-0.965903\pi$
$587$	−39.2912	+	16.2750i	−1.62172	+	0.671739i	−0.627454	+	0.778654i	$0.715903\pi$
$588$		0			0
$589$	−2.06435	−	3.08952i	−0.0850600	−	0.127301i
$590$		0			0
$591$	−54.2381	+	14.5330i	−2.23106	+	0.597810i
$592$		0			0
$593$	−41.7137	+	5.49172i	−1.71298	+	0.225518i	−0.922235	−	0.386630i	$-0.873639\pi$
$593$	−41.7137	+	5.49172i	−1.71298	+	0.225518i	−0.790743	+	0.612148i	$0.790306\pi$
$594$		0			0
$595$	−27.9396	−	12.7256i	−1.14541	−	0.521698i
$596$		0			0
$597$	13.7751	−	1.81352i	0.563776	−	0.0742225i
$598$		0			0
$599$	8.62727	−	2.31167i	0.352501	−	0.0944523i	−0.0782235	−	0.996936i	$-0.524925\pi$
$599$	8.62727	−	2.31167i	0.352501	−	0.0944523i	0.430724	+	0.902484i	$0.358258\pi$
$600$		0			0
$601$	−5.74135	−	8.59253i	−0.234194	−	0.350497i	0.695694	−	0.718338i	$-0.255097\pi$
$601$	−5.74135	−	8.59253i	−0.234194	−	0.350497i	−0.929889	+	0.367841i	$0.880097\pi$
$602$		0			0
$603$	32.6857	−	13.5388i	1.33106	−	0.551344i
$604$		0			0
$605$	−19.6781	+	22.4385i	−0.800027	+	0.912256i
$606$		0			0
$607$	−22.5058	−	25.6630i	−0.913483	−	1.04163i	−0.998974	−	0.0452886i	$-0.985579\pi$
$607$	−22.5058	−	25.6630i	−0.913483	−	1.04163i	0.0854912	−	0.996339i	$-0.472754\pi$
$608$		0			0
$609$	−66.6344	+	26.3980i	−2.70016	+	1.06970i
$610$		0			0
$611$	27.4534	−	15.8502i	1.11065	−	0.641232i
$612$		0			0
$613$	−4.33149	+	7.50237i	−0.174947	+	0.303018i	−0.940143	−	0.340780i	$-0.889309\pi$
$613$	−4.33149	+	7.50237i	−0.174947	+	0.303018i	0.765196	+	0.643798i	$0.222642\pi$
$614$		0			0
$615$	27.2310	−	40.7541i	1.09806	−	1.64336i
$616$		0			0
$617$	−37.5627	+	7.47168i	−1.51222	+	0.300799i	−0.880367	−	0.474293i	$-0.842704\pi$
$617$	−37.5627	+	7.47168i	−1.51222	+	0.300799i	−0.631849	+	0.775091i	$0.717704\pi$
$618$		0			0
$619$	−19.1341	−	16.7801i	−0.769063	−	0.674450i	0.182051	−	0.983289i	$-0.441726\pi$
$619$	−19.1341	−	16.7801i	−0.769063	−	0.674450i	−0.951114	+	0.308839i	$0.900060\pi$
$620$		0			0
$621$	23.2445	+	17.8362i	0.932771	+	0.715740i
$622$		0			0
$623$	20.2950	+	12.1408i	0.813104	+	0.486409i
$624$		0			0
$625$	30.0142	+	8.04229i	1.20057	+	0.321692i
$626$		0			0
$627$	−9.72243	+	7.46028i	−0.388276	+	0.297935i
$628$		0			0
$629$	34.5320	−	25.4598i	1.37688	−	1.01515i
$630$		0			0
$631$	−8.09982	+	19.5547i	−0.322449	+	0.778460i	0.676662	+	0.736294i	$0.263426\pi$
$631$	−8.09982	+	19.5547i	−0.322449	+	0.778460i	−0.999111	+	0.0421662i	$0.986574\pi$
$632$		0			0
$633$	5.73532	+	21.4045i	0.227959	+	0.850753i
$634$		0			0
$635$	−23.2754	+	47.1978i	−0.923655	+	1.87299i
$636$		0			0
$637$	9.02760	+	38.4194i	0.357687	+	1.52223i
$638$		0			0
$639$	−43.6225	+	14.8079i	−1.72568	+	0.585790i
$640$		0			0
$641$	34.4168	+	11.6829i	1.35938	+	0.461448i	0.903499	−	0.428590i	$-0.140990\pi$
$641$	34.4168	+	11.6829i	1.35938	+	0.461448i	0.455885	+	0.890039i	$0.349323\pi$
$642$		0			0
$643$	30.0969	+	20.1101i	1.18691	+	0.793066i	0.982581	−	0.185837i	$-0.0594998\pi$
$643$	30.0969	+	20.1101i	1.18691	+	0.793066i	0.204326	+	0.978903i	$0.434500\pi$
$644$		0			0
$645$		−	28.6554i		−	1.12831i
$646$		0			0
$647$	−7.01912	−	4.05249i	−0.275950	−	0.159320i	0.355638	−	0.934624i	$-0.384263\pi$
$647$	−7.01912	−	4.05249i	−0.275950	−	0.159320i	−0.631589	+	0.775304i	$0.717597\pi$
$648$		0			0
$649$	−2.37061	−	0.155378i	−0.0930546	−	0.00609912i
$650$		0			0
$651$	2.80278	+	3.77235i	0.109850	+	0.147850i
$652$		0			0
$653$	−12.2788	−	36.1721i	−0.480506	−	1.41552i	−0.869339	−	0.494216i	$-0.835455\pi$
$653$	−12.2788	−	36.1721i	−0.480506	−	1.41552i	0.388834	−	0.921308i	$-0.372878\pi$
$654$		0			0
$655$	1.17915	+	0.155238i	0.0460733	+	0.00606567i
$656$		0			0
$657$	−21.4294	+	14.3187i	−0.836042	+	0.558625i
$658$		0			0
$659$	3.19469	−	3.19469i	0.124447	−	0.124447i	−0.642140	−	0.766587i	$-0.721953\pi$
$659$	3.19469	−	3.19469i	0.124447	−	0.124447i	0.766587	+	0.642140i	$0.221953\pi$
$660$		0			0
$661$	13.5828	+	17.7015i	0.528311	+	0.688508i	0.978927	−	0.204210i	$-0.0654624\pi$
$661$	13.5828	+	17.7015i	0.528311	+	0.688508i	−0.450616	+	0.892718i	$0.648796\pi$
$662$		0			0
$663$	−66.0553	+	25.8876i	−2.56538	+	1.00539i
$664$		0			0
$665$	−25.7951	−	39.9319i	−1.00029	−	1.54849i
$666$		0			0
$667$	−6.65313	+	24.8298i	−0.257610	+	0.961415i
$668$		0			0
$669$	−3.92102	−	59.8232i	−0.151595	−	2.31290i
$670$		0			0
$671$	−2.94352	−	7.10629i	−0.113633	−	0.274335i
$672$		0			0
$673$	−4.02746	+	20.2474i	−0.155247	+	0.780481i	0.822183	+	0.569223i	$0.192756\pi$
$673$	−4.02746	+	20.2474i	−0.155247	+	0.780481i	−0.977430	+	0.211258i	$0.932244\pi$
$674$		0			0
$675$	−9.49785	+	27.9798i	−0.365572	+	1.07694i
$676$		0			0
$677$	−1.90239	+	29.0249i	−0.0731148	+	1.11552i	0.790865	+	0.611990i	$0.209631\pi$
$677$	−1.90239	+	29.0249i	−0.0731148	+	1.11552i	−0.863980	+	0.503526i	$0.832036\pi$
$678$		0			0
$679$	−8.88549	−	0.720904i	−0.340994	−	0.0276657i
$680$		0			0
$681$	29.0171	+	50.2590i	1.11194	+	1.92593i
$682$		0			0
$683$	−27.0082	+	13.3190i	−1.03344	+	0.509636i	−0.878227	−	0.478245i	$-0.841273\pi$
$683$	−27.0082	+	13.3190i	−1.03344	+	0.509636i	−0.155213	+	0.987881i	$0.549607\pi$
$684$		0			0
$685$	1.48435	+	7.46234i	0.0567142	+	0.285121i
$686$		0			0
$687$	22.2579	+	4.42736i	0.849191	+	0.168915i
$688$		0			0
$689$	−1.46223	+	11.1068i	−0.0557067	+	0.423134i
$690$		0			0
$691$	0.514230	+	0.253590i	0.0195622	+	0.00964702i	0.452044	−	0.891996i	$-0.350695\pi$
$691$	0.514230	+	0.253590i	0.0195622	+	0.00964702i	−0.432481	+	0.901643i	$0.642362\pi$
$692$		0			0
$693$	8.00664	−	6.80493i	0.304147	−	0.258498i
$694$		0			0
$695$	0.642314	+	4.87886i	0.0243644	+	0.185066i
$696$		0			0
$697$	20.5977	−	11.3708i	0.780192	−	0.430700i
$698$		0			0
$699$	16.3343	+	6.76589i	0.617820	+	0.255909i
$700$		0			0
$701$	23.6563	+	23.6563i	0.893486	+	0.893486i	0.994849	−	0.101364i	$-0.0323206\pi$
$701$	23.6563	+	23.6563i	0.893486	+	0.893486i	−0.101364	+	0.994849i	$0.532321\pi$
$702$		0			0
$703$	66.2903	−	4.34489i	2.50019	−	0.163871i
$704$		0			0
$705$	29.4007	−	38.3158i	1.10730	−	1.44306i
$706$		0			0
$707$	20.0373	−	19.4253i	0.753580	−	0.730565i
$708$		0			0
$709$	3.05914	−	2.68279i	0.114888	−	0.100754i	−0.599974	−	0.800019i	$-0.704823\pi$
$709$	3.05914	−	2.68279i	0.114888	−	0.100754i	0.714863	+	0.699265i	$0.246489\pi$
$710$		0			0
$711$	−16.7035	−	33.8714i	−0.626432	−	1.27028i
$712$		0			0
$713$	1.68553			0.0631235
$714$		0			0
$715$	9.97944			0.373210
$716$		0			0
$717$	−3.80335	−	7.71242i	−0.142039	−	0.288026i
$718$		0			0
$719$	32.8674	−	28.8239i	1.22575	−	1.07495i	0.230962	−	0.972963i	$-0.425813\pi$
$719$	32.8674	−	28.8239i	1.22575	−	1.07495i	0.994786	−	0.101989i	$-0.0325207\pi$
$720$		0			0
$721$	21.7344	−	5.46398i	0.809431	−	0.203489i
$722$		0			0
$723$	−37.5658	+	48.9566i	−1.39709	+	1.82072i
$724$		0			0
$725$	−25.8685	+	1.69551i	−0.960731	+	0.0629697i
$726$		0			0
$727$	−22.9966	−	22.9966i	−0.852897	−	0.852897i	0.137592	−	0.990489i	$-0.456064\pi$
$727$	−22.9966	−	22.9966i	−0.852897	−	0.852897i	−0.990489	+	0.137592i	$0.956064\pi$
$728$		0			0
$729$	−15.9648	−	6.61283i	−0.591288	−	0.244920i
$730$		0			0
$731$	6.31930	−	12.2176i	0.233728	−	0.451883i
$732$		0			0
$733$	4.29611	+	32.6322i	0.158681	+	1.20530i	0.866599	+	0.499004i	$0.166301\pi$
$733$	4.29611	+	32.6322i	0.158681	+	1.20530i	−0.707919	+	0.706294i	$0.750366\pi$
$734$		0			0
$735$	35.1060	+	48.8135i	1.29491	+	1.80051i
$736$		0			0
$737$	−3.16021	−	1.55844i	−0.116408	−	0.0574060i
$738$		0			0
$739$	−5.72253	+	43.4669i	−0.210507	+	1.59896i	0.481088	+	0.876672i	$0.340242\pi$
$739$	−5.72253	+	43.4669i	−0.210507	+	1.59896i	−0.691595	+	0.722285i	$0.743092\pi$
$740$		0			0
$741$	−107.746	−	21.4321i	−3.95816	−	0.787326i
$742$		0			0
$743$	4.79739	+	24.1181i	0.175999	+	0.884807i	0.963339	+	0.268288i	$0.0864578\pi$
$743$	4.79739	+	24.1181i	0.175999	+	0.884807i	−0.787340	+	0.616519i	$0.788542\pi$
$744$		0			0
$745$	43.7867	−	21.5932i	1.60422	−	0.791115i
$746$		0			0
$747$	47.1516	+	81.6690i	1.72519	+	2.98811i
$748$		0			0
$749$	−6.14535	−	12.9645i	−0.224546	−	0.473712i
$750$		0			0
$751$	−0.0109046	+	0.166373i	−0.000397916	+	0.00607102i	−0.998053	−	0.0623673i	$-0.980135\pi$
$751$	−0.0109046	+	0.166373i	−0.000397916	+	0.00607102i	0.997655	+	0.0684383i	$0.0218016\pi$
$752$		0			0
$753$	−12.1922	+	35.9172i	−0.444310	+	1.30889i
$754$		0			0
$755$	9.47446	−	47.6313i	0.344811	−	1.73348i
$756$		0			0
$757$	−3.04810	−	7.35876i	−0.110785	−	0.267459i	0.858757	−	0.512383i	$-0.171237\pi$
$757$	−3.04810	−	7.35876i	−0.110785	−	0.267459i	−0.969542	+	0.244924i	$0.921237\pi$
$758$		0			0
$759$	−0.363579	−	5.54714i	−0.0131971	−	0.201348i
$760$		0			0
$761$	−3.90447	+	14.5717i	−0.141537	+	0.528222i	0.858348	+	0.513067i	$0.171491\pi$
$761$	−3.90447	+	14.5717i	−0.141537	+	0.528222i	−0.999885	+	0.0151551i	$0.995176\pi$
$762$		0			0
$763$	13.7784	−	8.90053i	0.498810	−	0.322221i
$764$		0			0
$765$	−52.7989	+	50.8106i	−1.90895	+	1.83706i
$766$		0			0
$767$	−12.9646	−	16.8958i	−0.468124	−	0.610071i
$768$		0			0
$769$	30.8411	−	30.8411i	1.11216	−	1.11216i	0.119300	−	0.992858i	$-0.461935\pi$
$769$	30.8411	−	30.8411i	1.11216	−	1.11216i	0.992858	−	0.119300i	$-0.0380651\pi$
$770$		0			0
$771$	47.3998	−	31.6715i	1.70706	−	1.14062i
$772$		0			0
$773$	16.4684	+	2.16810i	0.592326	+	0.0779812i	0.420729	−	0.907186i	$-0.361774\pi$
$773$	16.4684	+	2.16810i	0.592326	+	0.0779812i	0.171596	+	0.985167i	$0.445108\pi$
$774$		0			0
$775$	0.546395	+	1.60963i	0.0196271	+	0.0578196i
$776$		0			0
$777$	−83.4641	+	9.67425i	−2.99426	+	0.347062i
$778$		0			0
$779$	36.3534	+	2.38273i	1.30250	+	0.0853702i
$780$		0			0
$781$	3.97344	+	2.29407i	0.142181	+	0.0820882i
$782$		0			0
$783$			89.7972i			3.20909i
$784$		0			0
$785$	−23.5863	−	15.7598i	−0.841830	−	0.562493i
$786$		0			0
$787$	−3.25301	−	1.10425i	−0.115957	−	0.0393622i	0.262858	−	0.964835i	$-0.415335\pi$
$787$	−3.25301	−	1.10425i	−0.115957	−	0.0393622i	−0.378815	+	0.925472i	$0.623668\pi$
$788$		0			0
$789$	66.2510	−	22.4892i	2.35860	−	0.800636i
$790$		0			0
$791$	3.10675	+	9.64076i	0.110463	+	0.342786i
$792$		0			0
$793$	30.4968	−	61.8413i	1.08297	−	2.19605i
$794$		0			0
$795$	4.41734	+	16.4857i	0.156667	+	0.584689i
$796$		0			0
$797$	−2.58592	+	6.24297i	−0.0915981	+	0.221137i	−0.963038	−	0.269364i	$-0.913186\pi$
$797$	−2.58592	+	6.24297i	−0.0915981	+	0.221137i	0.871440	+	0.490502i	$0.163186\pi$
$798$		0			0
$799$	20.9850	−	9.85272i	0.742396	−	0.348564i
$800$		0			0
$801$	44.7810	−	34.3617i	1.58226	−	1.21411i
$802$		0			0
$803$	2.47943	+	0.664360i	0.0874971	+	0.0234448i
$804$		0			0
$805$	21.5620	+	0.334356i	0.759960	+	0.0117845i
$806$		0			0
$807$	−40.6525	−	31.1938i	−1.43104	−	1.09807i
$808$		0			0
$809$	17.2441	+	15.1227i	0.606271	+	0.531686i	0.906513	−	0.422177i	$-0.138734\pi$
$809$	17.2441	+	15.1227i	0.606271	+	0.531686i	−0.300242	+	0.953863i	$0.597067\pi$
$810$		0			0
$811$	46.0451	−	9.15895i	1.61686	−	0.321614i	0.697972	−	0.716125i	$-0.254086\pi$
$811$	46.0451	−	9.15895i	1.61686	−	0.321614i	0.918891	+	0.394511i	$0.129086\pi$
$812$		0			0
$813$	−10.9442	+	16.3791i	−0.383829	+	0.574441i
$814$		0			0
$815$	−11.8415	+	20.5101i	−0.414790	+	0.718437i
$816$		0			0
$817$	18.4454	−	10.6495i	0.645324	−	0.372578i
$818$		0			0
$819$	93.1880	+	13.7415i	3.25625	+	0.480168i
$820$		0			0
$821$	−4.85125	−	5.53179i	−0.169310	−	0.193061i	0.660962	−	0.750419i	$-0.270148\pi$
$821$	−4.85125	−	5.53179i	−0.169310	−	0.193061i	−0.830272	+	0.557358i	$0.811815\pi$
$822$		0			0
$823$	8.48857	−	9.67936i	0.295893	−	0.337401i	−0.584722	−	0.811234i	$-0.698796\pi$
$823$	8.48857	−	9.67936i	0.295893	−	0.337401i	0.880615	+	0.473832i	$0.157130\pi$
$824$		0			0
$825$	5.17949	−	2.14542i	0.180327	−	0.0746938i
$826$		0			0
$827$	−19.7720	−	29.5909i	−0.687541	−	1.02898i	−0.996950	−	0.0780481i	$-0.975131\pi$
$827$	−19.7720	−	29.5909i	−0.687541	−	1.02898i	0.309409	−	0.950929i	$-0.399869\pi$
$828$		0			0
$829$	8.67063	−	2.32329i	0.301143	−	0.0806911i	−0.105083	−	0.994463i	$-0.533511\pi$
$829$	8.67063	−	2.32329i	0.301143	−	0.0806911i	0.406227	+	0.913772i	$0.366844\pi$
$830$		0			0
$831$	11.3518	−	1.49449i	0.393788	−	0.0518432i
$832$		0			0
$833$	4.20317	+	28.5540i	0.145631	+	0.989339i
$834$		0			0
$835$	45.6046	−	6.00396i	1.57821	−	0.207776i
$836$		0			0
$837$	5.68738	−	1.52393i	0.196585	−	0.0526747i
$838$		0			0
$839$	22.1885	+	33.2075i	0.766033	+	1.14645i	0.985308	+	0.170787i	$0.0546310\pi$
$839$	22.1885	+	33.2075i	0.766033	+	1.14645i	−0.219275	+	0.975663i	$0.570369\pi$
$840$		0			0
$841$	−45.9945	+	19.0515i	−1.58602	+	0.656949i
$842$		0			0
$843$	−57.9725	+	66.1049i	−1.99668	+	2.27677i
$844$		0			0
$845$	34.8614	+	39.7518i	1.19927	+	1.36750i
$846$		0			0
$847$	27.7566	+	4.09299i	0.953727	+	0.140637i
$848$		0			0
$849$	51.3816	−	29.6652i	1.76341	−	1.01811i
$850$		0			0
$851$	−15.0675	+	26.0978i	−0.516509	+	0.894620i
$852$		0			0
$853$	−24.3433	+	36.4324i	−0.833500	+	1.24742i	0.133093	+	0.991104i	$0.457509\pi$
$853$	−24.3433	+	36.4324i	−0.833500	+	1.24742i	−0.966593	+	0.256317i	$0.917491\pi$
$854$		0			0
$855$	−111.284	+	22.1358i	−3.80584	+	0.757028i
$856$		0			0
$857$	−22.6415	−	19.8561i	−0.773420	−	0.678271i	0.178731	−	0.983898i	$-0.442801\pi$
$857$	−22.6415	−	19.8561i	−0.773420	−	0.678271i	−0.952151	+	0.305627i	$0.901134\pi$
$858$		0			0
$859$	−36.2146	−	27.7885i	−1.23563	−	0.948130i	−0.235907	−	0.971776i	$-0.575806\pi$
$859$	−36.2146	−	27.7885i	−1.23563	−	0.948130i	−0.999720	+	0.0236458i	$0.992473\pi$
$860$		0			0
$861$	−46.0724	−	0.714434i	−1.57014	−	0.0243478i
$862$		0			0
$863$	21.6792	+	5.80892i	0.737968	+	0.197738i	0.608175	−	0.793803i	$-0.291902\pi$
$863$	21.6792	+	5.80892i	0.737968	+	0.197738i	0.129793	+	0.991541i	$0.458569\pi$
$864$		0			0
$865$	31.3637	−	24.0662i	1.06640	−	0.818275i
$866$		0			0
$867$	−49.7344	+	14.7804i	−1.68907	+	0.501970i
$868$		0			0
$869$	−1.43941	+	3.47505i	−0.0488288	+	0.117883i
$870$		0			0
$871$	−8.17526	−	30.5105i	−0.277008	−	1.03381i
$872$		0			0
$873$	−9.41071	+	19.0830i	−0.318504	+	0.645863i
$874$		0			0
$875$	−4.74890	−	14.7367i	−0.160542	−	0.498190i
$876$		0			0
$877$	20.9744	−	7.11985i	0.708255	−	0.240420i	0.0560121	−	0.998430i	$-0.482161\pi$
$877$	20.9744	−	7.11985i	0.708255	−	0.240420i	0.652243	+	0.758010i	$0.273828\pi$
$878$		0			0
$879$	−73.5585	−	24.9697i	−2.48107	−	0.842208i
$880$		0			0
$881$	−7.56708	−	5.05616i	−0.254941	−	0.170346i	0.421532	−	0.906814i	$-0.361493\pi$
$881$	−7.56708	−	5.05616i	−0.254941	−	0.170346i	−0.676473	+	0.736467i	$0.736493\pi$
$882$		0			0
$883$			40.4772i			1.36217i	0.732206	+	0.681083i	$0.238491\pi$
$883$			40.4772i			1.36217i	−0.732206	+	0.681083i	$0.761509\pi$
$884$		0			0
$885$	−28.0987	−	16.2228i	−0.944529	−	0.545324i
$886$		0			0
$887$	0.824367	+	0.0540319i	0.0276795	+	0.00181421i	0.0792366	−	0.996856i	$-0.474752\pi$
$887$	0.824367	+	0.0540319i	0.0276795	+	0.00181421i	−0.0515571	+	0.998670i	$0.516418\pi$
$888$		0			0
$889$	49.1429	−	5.69611i	1.64820	−	0.191041i
$890$		0			0
$891$	−2.41226	−	7.10629i	−0.0808138	−	0.238070i
$892$		0			0
$893$	35.5902	+	4.68554i	1.19098	+	0.156796i
$894$		0			0
$895$	−3.38296	+	2.26042i	−0.113080	+	0.0755576i
$896$		0			0
$897$	35.2375	−	35.2375i	1.17655	−	1.17655i
$898$		0			0
$899$	3.14479	+	4.09837i	0.104885	+	0.136688i
$900$		0			0
$901$	−1.75217	+	8.00303i	−0.0583731	+	0.266619i
$902$		0			0
$903$	−22.6280	+	14.6172i	−0.753012	+	0.486430i
$904$		0			0
$905$	−7.54053	+	28.1416i	−0.250656	+	0.935460i
$906$		0			0
$907$	−1.15647	−	17.6443i	−0.0384000	−	0.585870i	−0.973093	−	0.230414i	$-0.925992\pi$
$907$	−1.15647	−	17.6443i	−0.0384000	−	0.585870i	0.934693	−	0.355456i	$-0.115675\pi$
$908$		0			0
$909$	−25.4902	−	61.5388i	−0.845457	−	2.04111i
$910$		0			0
$911$	8.56758	−	43.0721i	0.283857	−	1.42704i	−0.530995	−	0.847375i	$-0.678182\pi$
$911$	8.56758	−	43.0721i	0.283857	−	1.42704i	0.814852	−	0.579669i	$-0.196818\pi$
$912$		0			0
$913$	3.01904	−	8.89380i	0.0999156	−	0.294342i
$914$		0			0
$915$	6.87055	−	104.824i	0.227133	−	3.46538i
$916$		0			0
$917$	−0.478903	−	1.01031i	−0.0158148	−	0.0333635i
$918$		0			0
$919$	−23.0399	−	39.9062i	−0.760015	−	1.31638i	−0.942842	−	0.333239i	$-0.891858\pi$
$919$	−23.0399	−	39.9062i	−0.760015	−	1.31638i	0.182828	−	0.983145i	$-0.441475\pi$
$920$		0			0
$921$	45.6160	−	22.4953i	1.50310	−	0.741246i
$922$		0			0
$923$	8.02402	+	40.3395i	0.264114	+	1.32779i
$924$		0			0
$925$	−29.8070	−	5.92898i	−0.980049	−	0.194944i
$926$		0			0
$927$	6.98173	−	53.0315i	0.229310	−	1.74178i
$928$		0			0
$929$	−27.9426	−	13.7798i	−0.916768	−	0.452100i	−0.0782253	−	0.996936i	$-0.524925\pi$
$929$	−27.9426	−	13.7798i	−0.916768	−	0.452100i	−0.838543	+	0.544836i	$0.816592\pi$
$930$		0			0
$931$	−18.3744	+	40.7387i	−0.602195	+	1.33516i
$932$		0			0
$933$	−5.93086	−	45.0494i	−0.194168	−	1.47485i
$934$		0			0
$935$	7.27194	+	0.616953i	0.237818	+	0.0201765i
$936$		0			0
$937$	42.0182	+	17.4045i	1.37267	+	0.568580i	0.942512	−	0.334171i	$-0.108456\pi$
$937$	42.0182	+	17.4045i	1.37267	+	0.568580i	0.430162	+	0.902752i	$0.358456\pi$
$938$		0			0
$939$	−22.3337	−	22.3337i	−0.728832	−	0.728832i
$940$		0			0
$941$	−54.4317	+	3.56764i	−1.77442	+	0.116302i	−0.917146	−	0.398552i	$-0.869513\pi$
$941$	−54.4317	+	3.56764i	−1.77442	+	0.116302i	−0.857278	+	0.514854i	$0.827846\pi$
$942$		0			0
$943$	−10.0604	+	13.1110i	−0.327612	+	0.426952i
$944$		0			0
$945$	73.0577	−	18.3665i	2.37657	−	0.597464i
$946$		0			0
$947$	22.3733	−	19.6209i	0.727036	−	0.637593i	−0.213635	−	0.976914i	$-0.568530\pi$
$947$	22.3733	−	19.6209i	0.727036	−	0.637593i	0.940671	+	0.339320i	$0.110197\pi$
$948$		0			0
$949$	10.1773	+	20.6376i	0.330370	+	0.669924i
$950$		0			0
$951$	−36.4648			−1.18245
$952$		0			0
$953$	2.31129			0.0748701			0.0374350	−	0.999299i	$-0.488081\pi$
$953$	2.31129			0.0748701			0.0374350	+	0.999299i	$0.488081\pi$
$954$		0			0
$955$	0.387794	+	0.786369i	0.0125487	+	0.0254463i
$956$		0			0
$957$	12.8095	−	11.2337i	0.414074	−	0.363133i
$958$		0			0
$959$	5.13552	−	4.97868i	0.165835	−	0.160770i
$960$		0			0
$961$	−18.6654	+	24.3252i	−0.602110	+	0.784685i
$962$		0			0
$963$	−34.1702	+	2.23963i	−1.10112	+	0.0721712i
$964$		0			0
$965$	−52.2328	−	52.2328i	−1.68143	−	1.68143i
$966$		0			0
$967$	−49.7537	−	20.6086i	−1.59997	−	0.662729i	−0.608558	−	0.793509i	$-0.708252\pi$
$967$	−49.7537	−	20.6086i	−1.59997	−	0.662729i	−0.991411	+	0.130780i	$0.958252\pi$
$968$		0			0
$969$	−77.1889	−	22.2785i	−2.47967	−	0.715689i
$970$		0			0
$971$	−4.52109	−	34.3411i	−0.145089	−	1.10206i	−0.896759	−	0.442519i	$-0.854085\pi$
$971$	−4.52109	−	34.3411i	−0.145089	−	1.10206i	0.751670	−	0.659539i	$-0.229249\pi$
$972$		0			0
$973$	3.52498	−	2.99592i	0.113006	−	0.0960449i
$974$		0			0
$975$	45.0737	+	22.2279i	1.44351	+	0.711862i
$976$		0			0
$977$	−5.00747	+	38.0355i	−0.160203	+	1.21686i	0.702697	+	0.711489i	$0.251979\pi$
$977$	−5.00747	+	38.0355i	−0.160203	+	1.21686i	−0.862900	+	0.505375i	$0.831354\pi$
$978$		0			0
$979$	−5.51372	−	1.09675i	−0.176219	−	0.0350522i
$980$		0			0
$981$	−7.63788	−	38.3982i	−0.243859	−	1.22596i
$982$		0			0
$983$	30.9901	−	15.2826i	0.988431	−	0.487440i	0.125136	−	0.992140i	$-0.460063\pi$
$983$	30.9901	−	15.2826i	0.988431	−	0.487440i	0.863295	+	0.504700i	$0.168397\pi$
$984$		0			0
$985$	25.8896	+	44.8420i	0.824910	+	1.42879i
$986$		0			0
$987$	−45.2537	−	3.67156i	−1.44044	−	0.116867i
$988$		0			0
$989$	−0.631900	+	9.64093i	−0.0200933	+	0.306564i
$990$		0			0
$991$	11.7208	−	34.5283i	0.372323	−	1.09683i	−0.585797	−	0.810458i	$-0.699218\pi$
$991$	11.7208	−	34.5283i	0.372323	−	1.09683i	0.958119	−	0.286369i	$-0.0924484\pi$
$992$		0			0
$993$	−12.3787	+	62.2317i	−0.392825	+	1.97486i
$994$		0			0
$995$	−4.90297	−	11.8368i	−0.155434	−	0.375252i
$996$		0			0
$997$	−0.601115	−	9.17125i	−0.0190375	−	0.290456i	−0.996753	−	0.0805214i	$-0.974341\pi$
$997$	−0.601115	−	9.17125i	−0.0190375	−	0.290456i	0.977715	−	0.209935i	$-0.0673252\pi$
$998$		0			0
$999$	−27.2459	+	101.683i	−0.862023	+	3.21711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.129.11	yes	192
7.5	odd	6	inner	476.2.bl.a.61.11	✓	192
17.12	odd	16	inner	476.2.bl.a.437.11	yes	192
119.12	even	48	inner	476.2.bl.a.369.11	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.61.11	✓	192	7.5	odd	6	inner
476.2.bl.a.129.11	yes	192	1.1	even	1	trivial
476.2.bl.a.369.11	yes	192	119.12	even	48	inner
476.2.bl.a.437.11	yes	192	17.12	odd	16	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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34987 + 2.73727i) q^{3} +(2.11595 - 1.85564i) q^{5} +(-2.54468 - 0.724313i) q^{7} +(-3.84420 + 5.00986i) q^{9} +O(q^{10})\)	\(q+(1.34987 + 2.73727i) q^{3} +(2.11595 - 1.85564i) q^{5} +(-2.54468 - 0.724313i) q^{7} +(-3.84420 + 5.00986i) q^{9} +(0.627584 - 0.0411340i) q^{11} +(3.98665 + 3.98665i) q^{13} +(7.93566 + 3.28706i) q^{15} +(2.65858 + 3.15150i) q^{17} +(0.833329 + 6.32976i) q^{19} +(-1.45235 - 7.94319i) q^{21} +(-2.59742 - 1.28090i) q^{23} +(0.381224 - 2.89568i) q^{25} +(-9.92242 - 1.97369i) q^{27} +(-1.73163 - 8.70549i) q^{29} +(-0.521982 + 0.257413i) q^{31} +(0.959752 + 1.66234i) q^{33} +(-6.72848 + 3.18939i) q^{35} +(0.680551 - 10.3832i) q^{37} +(-5.53106 + 16.2940i) q^{39} +(1.11325 - 5.59669i) q^{41} +(-1.27667 - 3.08216i) q^{43} +(1.16236 + 17.7341i) q^{45} +(1.45526 - 5.43109i) q^{47} +(5.95074 + 3.68628i) q^{49} +(-5.03778 + 11.5314i) q^{51} +(1.20961 + 1.57639i) q^{53} +(1.25161 - 1.25161i) q^{55} +(-16.2014 + 10.8254i) q^{57} +(-3.74505 - 0.493045i) q^{59} +(-3.93119 - 11.5809i) q^{61} +(13.4110 - 9.96407i) q^{63} +(15.8334 + 1.03777i) q^{65} +(-4.85191 - 2.80125i) q^{67} -8.83888i q^{69} +(6.06569 + 4.05296i) q^{71} +(3.86476 + 1.31191i) q^{73} +(8.44087 - 2.86529i) q^{75} +(-1.62679 - 0.349894i) q^{77} +(-2.64514 + 5.36382i) q^{79} +(-3.08830 - 11.5257i) q^{81} +(5.71488 - 13.7969i) q^{83} +(11.4735 + 1.73507i) q^{85} +(21.4918 - 16.4912i) q^{87} +(-8.63400 - 2.31347i) q^{89} +(-7.25714 - 13.0323i) q^{91} +(-1.40922 - 1.08133i) q^{93} +(13.5091 + 11.8471i) q^{95} +(3.30469 - 0.657344i) q^{97} +(-2.20648 + 3.30224i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) \) 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more