LMFDB - Embedded newform 476.2.bl.a.465.7

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			465.7
Character	$\chi$	$=$	476.465
Dual form			476.2.bl.a.173.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.157228 + 0.0533716i) q^{3} +(0.226574 - 3.45685i) q^{5} +(-2.23621 + 1.41399i) q^{7} +(-2.35819 - 1.80950i) q^{9} +O(q^{10})$	\(q+(0.157228 + 0.0533716i) q^{3} +(0.226574 - 3.45685i) q^{5} +(-2.23621 + 1.41399i) q^{7} +(-2.35819 - 1.80950i) q^{9} +(-0.172000 - 0.150840i) q^{11} +(-0.727951 - 0.727951i) q^{13} +(0.220122 - 0.531420i) q^{15} +(-1.71157 - 3.75107i) q^{17} +(-4.50639 + 0.593277i) q^{19} +(-0.427061 + 0.102969i) q^{21} +(0.610492 + 1.79845i) q^{23} +(-6.94126 - 0.913834i) q^{25} +(-0.550936 - 0.824535i) q^{27} +(5.75553 + 3.84572i) q^{29} +(0.648787 - 1.91126i) q^{31} +(-0.0189927 - 0.0328962i) q^{33} +(4.38129 + 8.05061i) q^{35} +(-6.47862 - 7.38745i) q^{37} +(-0.0756022 - 0.153306i) q^{39} +(4.38589 - 2.93056i) q^{41} +(3.92951 - 1.62766i) q^{43} +(-6.78948 + 7.74192i) q^{45} +(2.88070 - 10.7509i) q^{47} +(3.00125 - 6.32396i) q^{49} +(-0.0689065 - 0.681122i) q^{51} +(-2.49024 + 1.91083i) q^{53} +(-0.560403 + 0.560403i) q^{55} +(-0.740193 - 0.147234i) q^{57} +(0.682537 - 5.18438i) q^{59} +(-0.994292 + 2.01623i) q^{61} +(7.83202 + 0.711963i) q^{63} +(-2.68135 + 2.35148i) q^{65} +(11.4486 + 6.60983i) q^{67} +0.315350i q^{69} +(-14.4752 + 2.87931i) q^{71} +(4.52180 - 2.22990i) q^{73} +(-1.04259 - 0.514146i) q^{75} +(0.597916 + 0.0941032i) q^{77} +(3.59622 - 1.22075i) q^{79} +(2.26535 + 8.45440i) q^{81} +(8.14798 + 3.37501i) q^{83} +(-13.3547 + 5.06676i) q^{85} +(0.699677 + 0.911836i) q^{87} +(12.6676 + 3.39428i) q^{89} +(2.65717 + 0.598533i) q^{91} +(0.204015 - 0.265877i) q^{93} +(1.02984 + 15.7123i) q^{95} +(-1.25638 + 1.88031i) q^{97} +(0.132664 + 0.666945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	0.157228	+	0.0533716i	0.0907755	+	0.0308141i	0.366458	−	0.930435i	$-0.380570\pi$
$3$	0.157228	+	0.0533716i	0.0907755	+	0.0308141i	−0.275682	+	0.961249i	$0.588904\pi$
$4$		0			0
$5$	0.226574	−	3.45685i	0.101327	−	1.54595i	−0.580392	−	0.814337i	$-0.697101\pi$
$5$	0.226574	−	3.45685i	0.101327	−	1.54595i	0.681719	−	0.731614i	$-0.261232\pi$
$6$		0			0
$7$	−2.23621	+	1.41399i	−0.845207	+	0.534439i
$7$	−2.23621	+	1.41399i	−0.845207	+	0.534439i
$8$		0			0
$9$	−2.35819	−	1.80950i	−0.786063	−	0.603167i
$10$		0			0
$11$	−0.172000	−	0.150840i	−0.0518601	−	0.0454801i	0.633024	−	0.774133i	$-0.281814\pi$
$11$	−0.172000	−	0.150840i	−0.0518601	−	0.0454801i	−0.684884	+	0.728652i	$0.740147\pi$
$12$		0			0
$13$	−0.727951	−	0.727951i	−0.201897	−	0.201897i	0.598915	−	0.800812i	$-0.295599\pi$
$13$	−0.727951	−	0.727951i	−0.201897	−	0.201897i	−0.800812	+	0.598915i	$0.795599\pi$
$14$		0			0
$15$	0.220122	−	0.531420i	0.0568351	−	0.137212i
$16$		0			0
$17$	−1.71157	−	3.75107i	−0.415118	−	0.909768i
$17$	−1.71157	−	3.75107i	−0.415118	−	0.909768i
$18$		0			0
$19$	−4.50639	+	0.593277i	−1.03384	+	0.136107i	−0.628299	−	0.777972i	$-0.716249\pi$
$19$	−4.50639	+	0.593277i	−1.03384	+	0.136107i	−0.405537	+	0.914079i	$0.632915\pi$
$20$		0			0
$21$	−0.427061	+	0.102969i	−0.0931924	+	0.0224696i
$22$		0			0
$23$	0.610492	+	1.79845i	0.127296	+	0.375003i	0.991829	−	0.127573i	$-0.0407188\pi$
$23$	0.610492	+	1.79845i	0.127296	+	0.375003i	−0.864533	+	0.502577i	$0.832385\pi$
$24$		0			0
$25$	−6.94126	−	0.913834i	−1.38825	−	0.182767i
$26$		0			0
$27$	−0.550936	−	0.824535i	−0.106028	−	0.158682i
$28$		0			0
$29$	5.75553	+	3.84572i	1.06877	+	0.714133i	0.960019	−	0.279936i	$-0.0903132\pi$
$29$	5.75553	+	3.84572i	1.06877	+	0.714133i	0.108756	+	0.994068i	$0.465313\pi$
$30$		0			0
$31$	0.648787	−	1.91126i	0.116526	−	0.343273i	−0.872982	−	0.487752i	$-0.837817\pi$
$31$	0.648787	−	1.91126i	0.116526	−	0.343273i	0.989508	+	0.144478i	$0.0461504\pi$
$32$		0			0
$33$	−0.0189927	−	0.0328962i	−0.00330620	−	0.00572650i
$34$		0			0
$35$	4.38129	+	8.05061i	0.740573	+	1.36080i
$36$		0			0
$37$	−6.47862	−	7.38745i	−1.06508	−	1.21449i	−0.975842	−	0.218479i	$-0.929890\pi$
$37$	−6.47862	−	7.38745i	−1.06508	−	1.21449i	−0.0892371	−	0.996010i	$-0.528443\pi$
$38$		0			0
$39$	−0.0756022	−	0.153306i	−0.0121060	−	0.0245486i
$40$		0			0
$41$	4.38589	−	2.93056i	0.684961	−	0.457677i	−0.163771	−	0.986498i	$-0.552366\pi$
$41$	4.38589	−	2.93056i	0.684961	−	0.457677i	0.848733	+	0.528822i	$0.177366\pi$
$42$		0			0
$43$	3.92951	−	1.62766i	0.599244	−	0.248215i	−0.0623778	−	0.998053i	$-0.519868\pi$
$43$	3.92951	−	1.62766i	0.599244	−	0.248215i	0.661622	+	0.749838i	$0.269868\pi$
$44$		0			0
$45$	−6.78948	+	7.74192i	−1.01212	+	1.15410i
$46$		0			0
$47$	2.88070	−	10.7509i	0.420193	−	1.56818i	−0.354009	−	0.935242i	$-0.615182\pi$
$47$	2.88070	−	10.7509i	0.420193	−	1.56818i	0.774202	−	0.632939i	$-0.218151\pi$
$48$		0			0
$49$	3.00125	−	6.32396i	0.428751	−	0.903423i
$50$		0			0
$51$	−0.0689065	−	0.681122i	−0.00964884	−	0.0953761i
$52$		0			0
$53$	−2.49024	+	1.91083i	−0.342061	+	0.262473i	−0.765478	−	0.643462i	$-0.777497\pi$
$53$	−2.49024	+	1.91083i	−0.342061	+	0.262473i	0.423417	+	0.905935i	$0.360831\pi$
$54$		0			0
$55$	−0.560403	+	0.560403i	−0.0755648	+	0.0755648i
$56$		0			0
$57$	−0.740193	−	0.147234i	−0.0980410	−	0.0195016i
$58$		0			0
$59$	0.682537	−	5.18438i	0.0888588	−	0.674949i	−0.887812	−	0.460207i	$-0.847775\pi$
$59$	0.682537	−	5.18438i	0.0888588	−	0.674949i	0.976671	−	0.214743i	$-0.0688913\pi$
$60$		0			0
$61$	−0.994292	+	2.01623i	−0.127306	+	0.258151i	−0.951189	−	0.308609i	$-0.900137\pi$
$61$	−0.994292	+	2.01623i	−0.127306	+	0.258151i	0.823883	+	0.566760i	$0.191803\pi$
$62$		0			0
$63$	7.83202	+	0.711963i	0.986742	+	0.0896990i
$64$		0			0
$65$	−2.68135	+	2.35148i	−0.332581	+	0.291666i
$66$		0			0
$67$	11.4486	+	6.60983i	1.39866	+	0.807519i	0.994253	−	0.107059i	$-0.0341432\pi$
$67$	11.4486	+	6.60983i	1.39866	+	0.807519i	0.404411	+	0.914577i	$0.367477\pi$
$68$		0			0
$69$			0.315350i			0.0379636i
$70$		0			0
$71$	−14.4752	+	2.87931i	−1.71790	+	0.341711i	−0.953122	−	0.302588i	$-0.902150\pi$
$71$	−14.4752	+	2.87931i	−1.71790	+	0.341711i	−0.764774	+	0.644298i	$0.777150\pi$
$72$		0			0
$73$	4.52180	−	2.22990i	0.529236	−	0.260991i	−0.157981	−	0.987442i	$-0.550499\pi$
$73$	4.52180	−	2.22990i	0.529236	−	0.260991i	0.687218	+	0.726452i	$0.258832\pi$
$74$		0			0
$75$	−1.04259	−	0.514146i	−0.120387	−	0.0593685i
$76$		0			0
$77$	0.597916	+	0.0941032i	0.0681388	+	0.0107241i
$78$		0			0
$79$	3.59622	−	1.22075i	0.404607	−	0.137346i	−0.111715	−	0.993740i	$-0.535634\pi$
$79$	3.59622	−	1.22075i	0.404607	−	0.137346i	0.516322	+	0.856395i	$0.327301\pi$
$80$		0			0
$81$	2.26535	+	8.45440i	0.251705	+	0.939378i
$82$		0			0
$83$	8.14798	+	3.37501i	0.894357	+	0.370455i	0.782048	−	0.623218i	$-0.214175\pi$
$83$	8.14798	+	3.37501i	0.894357	+	0.370455i	0.112309	+	0.993673i	$0.464175\pi$
$84$		0			0
$85$	−13.3547	+	5.06676i	−1.44852	+	0.549568i
$86$		0			0
$87$	0.699677	+	0.911836i	0.0750132	+	0.0977591i
$88$		0			0
$89$	12.6676	+	3.39428i	1.34277	+	0.359793i	0.857460	−	0.514551i	$-0.172041\pi$
$89$	12.6676	+	3.39428i	1.34277	+	0.359793i	0.485306	+	0.874344i	$0.338708\pi$
$90$		0			0
$91$	2.65717	+	0.598533i	0.278547	+	0.0627433i
$92$		0			0
$93$	0.204015	−	0.265877i	0.0211553	−	0.0275702i
$94$		0			0
$95$	1.02984	+	15.7123i	0.105659	+	1.61205i
$96$		0			0
$97$	−1.25638	+	1.88031i	−0.127567	+	0.190917i	−0.889755	−	0.456438i	$-0.849125\pi$
$97$	−1.25638	+	1.88031i	−0.127567	+	0.190917i	0.762189	+	0.647355i	$0.224125\pi$
$98$		0			0
$99$	0.132664	+	0.666945i	0.0133332	+	0.0670305i
$100$		0			0
$101$	−5.61746	+	9.72973i	−0.558958	+	0.968144i	0.438625	+	0.898670i	$0.355465\pi$
$101$	−5.61746	+	9.72973i	−0.558958	+	0.968144i	−0.997584	+	0.0694742i	$0.977868\pi$
$102$		0			0
$103$	6.09030	−	3.51623i	0.600095	−	0.346465i	−0.168984	−	0.985619i	$-0.554049\pi$
$103$	6.09030	−	3.51623i	0.600095	−	0.346465i	0.769079	+	0.639154i	$0.220715\pi$
$104$		0			0
$105$	0.259186	+	1.49962i	0.0252940	+	0.146348i
$106$		0			0
$107$	−6.68755	−	0.438325i	−0.646510	−	0.0423745i	−0.261379	−	0.965236i	$-0.584177\pi$
$107$	−6.68755	−	0.438325i	−0.646510	−	0.0423745i	−0.385131	+	0.922862i	$0.625844\pi$
$108$		0			0
$109$	−8.73672	+	0.572635i	−0.836826	+	0.0548485i	−0.477789	−	0.878475i	$-0.658562\pi$
$109$	−8.73672	+	0.572635i	−0.836826	+	0.0548485i	−0.359037	+	0.933323i	$0.616895\pi$
$110$		0			0
$111$	−0.624339	−	1.50729i	−0.0592596	−	0.143065i
$112$		0			0
$113$	−1.23644	+	6.21600i	−0.116314	+	0.584752i	0.878035	+	0.478596i	$0.158854\pi$
$113$	−1.23644	+	6.21600i	−0.116314	+	0.584752i	−0.994350	+	0.106156i	$0.966146\pi$
$114$		0			0
$115$	6.35530	−	1.70290i	0.592635	−	0.158796i
$116$		0			0
$117$	0.399417	+	3.03387i	0.0369261	+	0.280482i
$118$		0			0
$119$	9.13142	+	5.96802i	0.837076	+	0.547087i
$120$		0			0
$121$	−1.42896	−	10.8540i	−0.129905	−	0.986728i
$122$		0			0
$123$	0.845993	−	0.226683i	0.0762806	−	0.0204393i
$124$		0			0
$125$	−1.35247	+	6.79932i	−0.120968	+	0.608150i
$126$		0			0
$127$	−2.97996	−	7.19426i	−0.264429	−	0.638387i	0.734774	−	0.678312i	$-0.237288\pi$
$127$	−2.97996	−	7.19426i	−0.264429	−	0.638387i	−0.999203	+	0.0399247i	$0.987288\pi$
$128$		0			0
$129$	0.704698	−	0.0461884i	0.0620452	−	0.00406666i
$130$		0			0
$131$	14.5373	+	0.952825i	1.27013	+	0.0832487i	0.685513	−	0.728061i	$-0.259578\pi$
$131$	14.5373	+	0.952825i	1.27013	+	0.0832487i	0.584617	+	0.811309i	$0.301245\pi$
$132$		0			0
$133$	9.23833	−	7.69868i	0.801065	−	0.667560i
$134$		0			0
$135$	−2.97512	+	1.71769i	−0.256058	+	0.147835i
$136$		0			0
$137$	8.64006	−	14.9650i	0.738170	−	1.27855i	−0.215148	−	0.976581i	$-0.569023\pi$
$137$	8.64006	−	14.9650i	0.738170	−	1.27855i	0.953318	−	0.301967i	$-0.0976432\pi$
$138$		0			0
$139$	2.42014	+	12.1669i	0.205274	+	1.03198i	0.936720	+	0.350080i	$0.113846\pi$
$139$	2.42014	+	12.1669i	0.205274	+	1.03198i	−0.731446	+	0.681899i	$0.761154\pi$
$140$		0			0
$141$	1.02672	−	1.53659i	0.0864653	−	0.129405i
$142$		0			0
$143$	0.0154035	+	0.235012i	0.00128811	+	0.0196527i
$144$		0			0
$145$	14.5981	−	19.0247i	1.21231	−	1.57991i
$146$		0			0
$147$	0.809401	−	0.834120i	0.0667583	−	0.0687971i
$148$		0			0
$149$	−1.94986	−	0.522464i	−0.159739	−	0.0428019i	0.178063	−	0.984019i	$-0.443017\pi$
$149$	−1.94986	−	0.522464i	−0.159739	−	0.0428019i	−0.337802	+	0.941217i	$0.609684\pi$
$150$		0			0
$151$	8.82151	+	11.4964i	0.717885	+	0.935566i	0.999714	−	0.0238989i	$-0.00760799\pi$
$151$	8.82151	+	11.4964i	0.717885	+	0.935566i	−0.281830	+	0.959464i	$0.590941\pi$
$152$		0			0
$153$	−2.75135	+	11.9428i	−0.222433	+	0.965520i
$154$		0			0
$155$	−6.45996	−	2.67580i	−0.518876	−	0.214926i
$156$		0			0
$157$	−4.86559	−	18.1586i	−0.388316	−	1.44922i	−0.832873	−	0.553465i	$-0.813305\pi$
$157$	−4.86559	−	18.1586i	−0.388316	−	1.44922i	0.444557	−	0.895751i	$-0.353361\pi$
$158$		0			0
$159$	−0.493519	+	0.167527i	−0.0391386	+	0.0132858i
$160$		0			0
$161$	−3.90819	−	3.15848i	−0.308008	−	0.248923i
$162$		0			0
$163$	−15.7688	−	7.77630i	−1.23511	−	0.609087i	−0.296816	−	0.954935i	$-0.595925\pi$
$163$	−15.7688	−	7.77630i	−1.23511	−	0.609087i	−0.938291	+	0.345848i	$0.887591\pi$
$164$		0			0
$165$	−0.118021	+	0.0582013i	−0.00918789	+	0.00453097i
$166$		0			0
$167$	−10.4146	+	2.07160i	−0.805908	+	0.160305i	−0.580818	−	0.814033i	$-0.697267\pi$
$167$	−10.4146	+	2.07160i	−0.805908	+	0.160305i	−0.225089	+	0.974338i	$0.572267\pi$
$168$		0			0
$169$		−	11.9402i		−	0.918475i
$170$		0			0
$171$	11.7004	+	6.75525i	0.894755	+	0.516587i
$172$		0			0
$173$	3.09929	−	2.71801i	0.235635	−	0.206646i	−0.533382	−	0.845874i	$-0.679079\pi$
$173$	3.09929	−	2.71801i	0.235635	−	0.206646i	0.769017	+	0.639228i	$0.220746\pi$
$174$		0			0
$175$	16.8142	−	7.77136i	1.27104	−	0.587459i
$176$		0			0
$177$	0.384013	−	0.778701i	0.0288642	−	0.0585308i
$178$		0			0
$179$	−1.63543	+	12.4223i	−0.122238	+	0.928488i	0.814918	+	0.579576i	$0.196782\pi$
$179$	−1.63543	+	12.4223i	−0.122238	+	0.928488i	−0.937156	+	0.348911i	$0.886551\pi$
$180$		0			0
$181$	2.14316	+	0.426300i	0.159300	+	0.0316866i	0.274096	−	0.961702i	$-0.411621\pi$
$181$	2.14316	+	0.426300i	0.159300	+	0.0316866i	−0.114796	+	0.993389i	$0.536621\pi$
$182$		0			0
$183$	−0.263940	+	0.263940i	−0.0195110	+	0.0195110i
$184$		0			0
$185$	−27.0052	+	20.7218i	−1.98546	+	1.52350i
$186$		0			0
$187$	−0.271421	+	0.903360i	−0.0198483	+	0.0660602i
$188$		0			0
$189$	2.39789	+	1.06481i	0.174421	+	0.0774537i
$190$		0			0
$191$	−2.97867	+	11.1165i	−0.215529	+	0.804364i	0.770451	+	0.637499i	$0.220031\pi$
$191$	−2.97867	+	11.1165i	−0.215529	+	0.804364i	−0.985980	+	0.166865i	$0.946636\pi$
$192$		0			0
$193$	−3.15476	+	3.59731i	−0.227085	+	0.258940i	−0.854151	−	0.520026i	$-0.825922\pi$
$193$	−3.15476	+	3.59731i	−0.227085	+	0.258940i	0.627066	+	0.778966i	$0.284256\pi$
$194$		0			0
$195$	−0.547086	+	0.226610i	−0.0391776	+	0.0162279i
$196$		0			0
$197$	−7.56610	+	5.05551i	−0.539062	+	0.360190i	−0.795101	−	0.606477i	$-0.792582\pi$
$197$	−7.56610	+	5.05551i	−0.539062	+	0.360190i	0.256039	+	0.966666i	$0.417582\pi$
$198$		0			0
$199$	4.68014	+	9.49039i	0.331767	+	0.672756i	0.997286	−	0.0736245i	$-0.0234566\pi$
$199$	4.68014	+	9.49039i	0.331767	+	0.672756i	−0.665519	+	0.746380i	$0.731790\pi$
$200$		0			0
$201$	1.44725	+	1.65028i	0.102081	+	0.116402i
$202$		0			0
$203$	−18.3084	−	0.461564i	−1.28500	−	0.0323954i
$204$		0			0
$205$	−9.13678	−	15.8254i	−0.638140	−	1.10529i
$206$		0			0
$207$	1.81465	−	5.34578i	0.126127	−	0.371557i
$208$		0			0
$209$	0.864590	+	0.577701i	0.0598050	+	0.0399604i
$210$		0			0
$211$	−7.12962	−	10.6702i	−0.490823	−	0.734569i	0.500540	−	0.865713i	$-0.333135\pi$
$211$	−7.12962	−	10.6702i	−0.490823	−	0.734569i	−0.991363	+	0.131145i	$0.958135\pi$
$212$		0			0
$213$	−2.42958	−	0.319861i	−0.166472	−	0.0219165i
$214$		0			0
$215$	−4.73624	−	13.9525i	−0.323009	−	0.951553i
$216$		0			0
$217$	1.25169	+	5.19137i	0.0849702	+	0.352413i
$218$		0			0
$219$	0.829966	−	0.109267i	0.0560839	−	0.00738359i
$220$		0			0
$221$	−1.48465	+	3.97654i	−0.0998684	+	0.267491i
$222$		0			0
$223$	−0.582405	+	1.40605i	−0.0390007	+	0.0941561i	−0.942180	−	0.335108i	$-0.891227\pi$
$223$	−0.582405	+	1.40605i	−0.0390007	+	0.0941561i	0.903179	+	0.429264i	$0.141227\pi$
$224$		0			0
$225$	14.7152	+	14.7152i	0.981014	+	0.981014i
$226$		0			0
$227$	−15.0636	−	13.2104i	−0.999808	−	0.876808i	−0.00742199	−	0.999972i	$-0.502363\pi$
$227$	−15.0636	−	13.2104i	−0.999808	−	0.876808i	−0.992386	+	0.123164i	$0.960696\pi$
$228$		0			0
$229$	−14.4268	−	11.0701i	−0.953351	−	0.731532i	0.00995106	−	0.999950i	$-0.496832\pi$
$229$	−14.4268	−	11.0701i	−0.953351	−	0.731532i	−0.963302	+	0.268418i	$0.913499\pi$
$230$		0			0
$231$	0.0889866	+	0.0467074i	0.00585489	+	0.00307312i
$232$		0			0
$233$	0.225232	−	3.43637i	0.0147554	−	0.225124i	−0.984112	−	0.177548i	$-0.943184\pi$
$233$	0.225232	−	3.43637i	0.0147554	−	0.225124i	0.998868	−	0.0475765i	$-0.0151498\pi$
$234$		0			0
$235$	−36.5116	−	12.3940i	−2.38175	−	0.808496i
$236$		0			0
$237$	0.630580			0.0409606
$238$		0			0
$239$	−3.15719			−0.204221			−0.102111	−	0.994773i	$-0.532560\pi$
$239$	−3.15719			−0.204221			−0.102111	+	0.994773i	$0.532560\pi$
$240$		0			0
$241$	23.5468	+	7.99306i	1.51678	+	0.514878i	0.950871	−	0.309588i	$-0.100191\pi$
$241$	23.5468	+	7.99306i	1.51678	+	0.514878i	0.565912	+	0.824466i	$0.308524\pi$
$242$		0			0
$243$	−0.289622	+	4.41878i	−0.0185793	+	0.283465i
$244$		0			0
$245$	−21.1810	−	11.8077i	−1.35320	−	0.754368i
$246$		0			0
$247$	3.71230	+	2.84855i	0.236208	+	0.181249i
$248$		0			0
$249$	1.10096	+	0.965516i	0.0697705	+	0.0611871i
$250$		0			0
$251$	−11.4471	−	11.4471i	−0.722537	−	0.722537i	0.246584	−	0.969121i	$-0.420692\pi$
$251$	−11.4471	−	11.4471i	−0.722537	−	0.722537i	−0.969121	+	0.246584i	$0.920692\pi$
$252$		0			0
$253$	0.166274	−	0.401422i	0.0104536	−	0.0252372i
$254$		0			0
$255$	−2.37015	+	0.0838749i	−0.148424	+	0.00525245i
$256$		0			0
$257$	27.1107	−	3.56919i	1.69112	−	0.222640i	0.777404	−	0.629001i	$-0.216536\pi$
$257$	27.1107	−	3.56919i	1.69112	−	0.222640i	0.913712	+	0.406361i	$0.133203\pi$
$258$		0			0
$259$	24.9333	+	7.35916i	1.54928	+	0.457276i
$260$		0			0
$261$	−6.61378	−	19.4836i	−0.409383	−	1.20600i
$262$		0			0
$263$	10.4345	+	1.37373i	0.643421	+	0.0847080i	0.445174	−	0.895444i	$-0.353142\pi$
$263$	10.4345	+	1.37373i	0.643421	+	0.0847080i	0.198247	+	0.980152i	$0.436475\pi$
$264$		0			0
$265$	6.04123	+	9.04134i	0.371110	+	0.555405i
$266$		0			0
$267$	1.81054	+	1.20977i	0.110804	+	0.0740366i
$268$		0			0
$269$	6.86460	−	20.2225i	0.418542	−	1.23299i	−0.509487	−	0.860478i	$-0.670165\pi$
$269$	6.86460	−	20.2225i	0.418542	−	1.23299i	0.928029	−	0.372507i	$-0.121502\pi$
$270$		0			0
$271$	−15.0914	−	26.1391i	−0.916739	−	1.58784i	−0.804335	−	0.594177i	$-0.797478\pi$
$271$	−15.0914	−	26.1391i	−0.916739	−	1.58784i	−0.112405	−	0.993663i	$-0.535855\pi$
$272$		0			0
$273$	0.385836	+	0.235923i	0.0233518	+	0.0142787i
$274$		0			0
$275$	1.05606	+	1.20420i	0.0636826	+	0.0726161i
$276$		0			0
$277$	−6.03255	−	12.2328i	−0.362461	−	0.734998i	0.636892	−	0.770953i	$-0.280220\pi$
$277$	−6.03255	−	12.2328i	−0.362461	−	0.734998i	−0.999353	+	0.0359546i	$0.988553\pi$
$278$		0			0
$279$	−4.98840	+	3.33314i	−0.298648	+	0.199550i
$280$		0			0
$281$	27.5423	−	11.4084i	1.64304	−	0.680568i	0.646436	−	0.762968i	$-0.276259\pi$
$281$	27.5423	−	11.4084i	1.64304	−	0.680568i	0.996599	+	0.0824007i	$0.0262587\pi$
$282$		0			0
$283$	18.4141	−	20.9972i	1.09460	−	1.24816i	0.128029	−	0.991770i	$-0.459135\pi$
$283$	18.4141	−	20.9972i	1.09460	−	1.24816i	0.966575	−	0.256385i	$-0.0825316\pi$
$284$		0			0
$285$	−0.676673	+	2.52538i	−0.0400827	+	0.149590i
$286$		0			0
$287$	−5.66398	+	12.7550i	−0.334334	+	0.752901i
$288$		0			0
$289$	−11.1410	+	12.8405i	−0.655354	+	0.755322i
$290$		0			0
$291$	−0.297894	+	0.228582i	−0.0174629	+	0.0133997i
$292$		0			0
$293$	−6.37430	+	6.37430i	−0.372390	+	0.372390i	−0.868347	−	0.495957i	$-0.834817\pi$
$293$	−6.37430	+	6.37430i	−0.372390	+	0.372390i	0.495957	+	0.868347i	$0.334817\pi$
$294$		0			0
$295$	−17.7670	−	3.53408i	−1.03443	−	0.205762i
$296$		0			0
$297$	−0.0296118	+	0.224924i	−0.00171825	+	0.0130514i
$298$		0			0
$299$	0.864777	−	1.75359i	0.0500113	−	0.101413i
$300$		0			0
$301$	−6.48570	+	9.19607i	−0.373830	+	0.530052i
$302$		0			0
$303$	−1.40251	+	1.22997i	−0.0805723	+	0.0706600i
$304$		0			0
$305$	6.74451	+	3.89394i	0.386190	+	0.222967i
$306$		0			0
$307$		−	31.0495i		−	1.77209i	−0.463600	−	0.886044i	$-0.653443\pi$
$307$		−	31.0495i		−	1.77209i	0.463600	−	0.886044i	$-0.346557\pi$
$308$		0			0
$309$	1.14523	−	0.227801i	0.0651499	−	0.0129591i
$310$		0			0
$311$	−13.7967	+	6.80380i	−0.782341	+	0.385808i	−0.789175	−	0.614169i	$-0.789491\pi$
$311$	−13.7967	+	6.80380i	−0.782341	+	0.385808i	0.00683356	+	0.999977i	$0.497825\pi$
$312$		0			0
$313$	−24.3712	−	12.0186i	−1.37754	−	0.679329i	−0.405492	−	0.914099i	$-0.632900\pi$
$313$	−24.3712	−	12.0186i	−1.37754	−	0.679329i	−0.972051	+	0.234770i	$0.924566\pi$
$314$		0			0
$315$	4.23568	−	26.9128i	0.238654	−	1.51636i
$316$		0			0
$317$	−4.06289	+	1.37917i	−0.228195	+	0.0774617i	−0.433195	−	0.901300i	$-0.642614\pi$
$317$	−4.06289	+	1.37917i	−0.228195	+	0.0774617i	0.205000	+	0.978762i	$0.434281\pi$
$318$		0			0
$319$	−0.409864	−	1.52963i	−0.0229480	−	0.0856429i
$320$		0			0
$321$	−1.02808	−	0.425843i	−0.0573816	−	0.0237682i
$322$		0			0
$323$	9.93844	+	15.8883i	0.552990	+	0.884050i
$324$		0			0
$325$	4.38767	+	5.71812i	0.243384	+	0.317184i
$326$		0			0
$327$	−1.40422	−	0.376259i	−0.0776534	−	0.0208072i
$328$		0			0
$329$	8.75985	+	28.1145i	0.482946	+	1.55000i
$330$		0			0
$331$	−3.83347	+	4.99588i	−0.210707	+	0.274598i	−0.886736	−	0.462277i	$-0.847033\pi$
$331$	−3.83347	+	4.99588i	−0.210707	+	0.274598i	0.676029	+	0.736875i	$0.263699\pi$
$332$		0			0
$333$	1.91020	+	29.1441i	0.104678	+	1.59709i
$334$		0			0
$335$	25.4431	−	38.0783i	1.39011	−	2.08044i
$336$		0			0
$337$	5.53742	+	27.8385i	0.301643	+	1.51646i	0.772937	+	0.634483i	$0.218787\pi$
$337$	5.53742	+	27.8385i	0.301643	+	1.51646i	−0.471294	+	0.881976i	$0.656213\pi$
$338$		0			0
$339$	−0.526161	+	0.911337i	−0.0285771	+	0.0494971i
$340$		0			0
$341$	−0.399888	+	0.230875i	−0.0216551	+	0.0125026i
$342$		0			0
$343$	2.23060	+	18.3854i	0.120441	+	0.992721i
$344$		0			0
$345$	1.09012	+	0.0714500i	0.0586899	+	0.00384674i
$346$		0			0
$347$	−25.6800	+	1.68316i	−1.37857	+	0.0903566i	−0.736579	−	0.676352i	$-0.763560\pi$
$347$	−25.6800	+	1.68316i	−1.37857	+	0.0903566i	−0.641996	+	0.766708i	$0.721893\pi$
$348$		0			0
$349$	1.32970	+	3.21019i	0.0711774	+	0.171837i	0.955464	−	0.295106i	$-0.0953551\pi$
$349$	1.32970	+	3.21019i	0.0711774	+	0.171837i	−0.884287	+	0.466944i	$0.845355\pi$
$350$		0			0
$351$	−0.199166	+	1.00128i	−0.0106307	+	0.0534441i
$352$		0			0
$353$	4.12634	−	1.10565i	0.219623	−	0.0588478i	−0.147330	−	0.989087i	$-0.547068\pi$
$353$	4.12634	−	1.10565i	0.219623	−	0.0588478i	0.366953	+	0.930240i	$0.380401\pi$
$354$		0			0
$355$	6.67362	+	50.6911i	0.354199	+	2.69041i
$356$		0			0
$357$	1.11719	+	1.42570i	0.0591280	+	0.0754559i
$358$		0			0
$359$	2.35578	+	17.8939i	0.124333	+	0.944405i	0.933939	+	0.357432i	$0.116347\pi$
$359$	2.35578	+	17.8939i	0.124333	+	0.944405i	−0.809606	+	0.586974i	$0.800319\pi$
$360$		0			0
$361$	1.60294	−	0.429507i	0.0843654	−	0.0226057i
$362$		0			0
$363$	0.354624	−	1.78282i	0.0186130	−	0.0935736i
$364$		0			0
$365$	−6.68392	−	16.1364i	−0.349853	−	0.844619i
$366$		0			0
$367$	−31.8888	+	2.09010i	−1.66458	+	0.109103i	−0.868371	−	0.495915i	$-0.834833\pi$
$367$	−31.8888	+	2.09010i	−1.66458	+	0.109103i	−0.796212	+	0.605018i	$0.793166\pi$
$368$		0			0
$369$	−15.6456	−	1.02547i	−0.814478	−	0.0533837i
$370$		0			0
$371$	2.86680	−	7.79419i	0.148837	−	0.404654i
$372$		0			0
$373$	26.3061	−	15.1878i	1.36208	−	0.786395i	0.372177	−	0.928162i	$-0.378612\pi$
$373$	26.3061	−	15.1878i	1.36208	−	0.786395i	0.989900	+	0.141766i	$0.0452782\pi$
$374$		0			0
$375$	−0.575536	+	0.996858i	−0.0297206	+	0.0514775i
$376$		0			0
$377$	−1.39025	−	6.98924i	−0.0716013	−	0.359964i
$378$		0			0
$379$	−6.60743	+	9.88872i	−0.339401	+	0.507949i	−0.961432	−	0.275043i	$-0.911308\pi$
$379$	−6.60743	+	9.88872i	−0.339401	+	0.507949i	0.622031	+	0.782993i	$0.286308\pi$
$380$		0			0
$381$	−0.0845631	−	1.29018i	−0.00433230	−	0.0660981i
$382$		0			0
$383$	4.26027	−	5.55209i	0.217690	−	0.283699i	−0.671724	−	0.740801i	$-0.734446\pi$
$383$	4.26027	−	5.55209i	0.217690	−	0.283699i	0.889414	+	0.457102i	$0.151113\pi$
$384$		0			0
$385$	0.460773	−	2.04558i	0.0234832	−	0.104253i
$386$		0			0
$387$	−12.2118	−	3.27213i	−0.620759	−	0.166332i
$388$		0			0
$389$	21.7354	+	28.3261i	1.10203	+	1.43619i	0.888282	+	0.459299i	$0.151899\pi$
$389$	21.7354	+	28.3261i	1.10203	+	1.43619i	0.213745	+	0.976890i	$0.431434\pi$
$390$		0			0
$391$	5.70121	−	5.36819i	0.288323	−	0.271481i
$392$		0			0
$393$	2.23481	+	0.925690i	0.112731	+	0.0466949i
$394$		0			0
$395$	−3.40515	−	12.7082i	−0.171332	−	0.639419i
$396$		0			0
$397$	−21.2687	+	7.21975i	−1.06745	+	0.362349i	−0.799240	−	0.601013i	$-0.794764\pi$
$397$	−21.2687	+	7.21975i	−1.06745	+	0.362349i	−0.268206	+	0.963362i	$0.586431\pi$
$398$		0			0
$399$	1.86341	−	0.717382i	0.0932874	−	0.0359140i
$400$		0			0
$401$	28.0546	+	13.8350i	1.40098	+	0.690887i	0.976693	−	0.214641i	$-0.0688583\pi$
$401$	28.0546	+	13.8350i	1.40098	+	0.690887i	0.424286	+	0.905528i	$0.360525\pi$
$402$		0			0
$403$	−1.86359	+	0.919022i	−0.0928322	+	0.0457798i
$404$		0			0
$405$	29.7389	−	5.91543i	1.47774	−	0.293940i
$406$		0			0
$407$			2.24788i			0.111423i
$408$		0			0
$409$	23.0233	+	13.2925i	1.13843	+	0.657274i	0.946042	−	0.324045i	$-0.105043\pi$
$409$	23.0233	+	13.2925i	1.13843	+	0.657274i	0.192390	+	0.981319i	$0.438376\pi$
$410$		0			0
$411$	2.15717	−	1.89178i	0.106405	−	0.0933148i
$412$		0			0
$413$	5.80438	+	12.5585i	0.285615	+	0.617962i
$414$		0			0
$415$	13.5130	−	27.4017i	0.663328	−	1.34510i
$416$		0			0
$417$	−0.268852	+	2.04214i	−0.0131658	+	0.100004i
$418$		0			0
$419$	12.6185	+	2.50998i	0.616455	+	0.122621i	0.493434	−	0.869783i	$-0.335742\pi$
$419$	12.6185	+	2.50998i	0.616455	+	0.122621i	0.123021	+	0.992404i	$0.460742\pi$
$420$		0			0
$421$	7.06795	−	7.06795i	0.344471	−	0.344471i	−0.513574	−	0.858045i	$-0.671679\pi$
$421$	7.06795	−	7.06795i	0.344471	−	0.344471i	0.858045	+	0.513574i	$0.171679\pi$
$422$		0			0
$423$	−26.2470	+	20.1400i	−1.27617	+	0.979242i
$424$		0			0
$425$	8.45263	+	27.6012i	0.410013	+	1.33886i
$426$		0			0
$427$	−0.627481	−	5.91462i	−0.0303660	−	0.286229i
$428$		0			0
$429$	−0.0101211	+	0.0377726i	−0.000488653	+	0.00182368i
$430$		0			0
$431$	19.5221	−	22.2607i	0.940348	−	1.07226i	−0.0569195	−	0.998379i	$-0.518128\pi$
$431$	19.5221	−	22.2607i	0.940348	−	1.07226i	0.997267	−	0.0738821i	$-0.0235388\pi$
$432$		0			0
$433$	−27.6060	+	11.4348i	−1.32666	+	0.549520i	−0.929701	−	0.368316i	$-0.879934\pi$
$433$	−27.6060	+	11.4348i	−1.32666	+	0.549520i	−0.396959	+	0.917837i	$0.629934\pi$
$434$		0			0
$435$	3.31061	−	2.21208i	0.158732	−	0.106061i
$436$		0			0
$437$	−3.81809	−	7.74233i	−0.182644	−	0.370366i
$438$		0			0
$439$	−1.81779	−	2.07279i	−0.0867584	−	0.0989290i	0.706832	−	0.707382i	$-0.250124\pi$
$439$	−1.81779	−	2.07279i	−0.0867584	−	0.0989290i	−0.793590	+	0.608453i	$0.791790\pi$
$440$		0			0
$441$	−18.5207	+	9.48231i	−0.881940	+	0.451539i
$442$		0			0
$443$	8.37862	+	14.5122i	0.398080	+	0.689495i	0.993489	−	0.113928i	$-0.0363432\pi$
$443$	8.37862	+	14.5122i	0.398080	+	0.689495i	−0.595409	+	0.803423i	$0.703010\pi$
$444$		0			0
$445$	14.6037	−	43.0210i	0.692281	−	2.03939i
$446$		0			0
$447$	−0.278688	−	0.186213i	−0.0131815	−	0.00880759i
$448$		0			0
$449$	−9.14512	−	13.6866i	−0.431585	−	0.645912i	0.550394	−	0.834905i	$-0.314478\pi$
$449$	−9.14512	−	13.6866i	−0.431585	−	0.645912i	−0.981978	+	0.188993i	$0.939478\pi$
$450$		0			0
$451$	−1.19642	−	0.157512i	−0.0563373	−	0.00741695i
$452$		0			0
$453$	0.773404	+	2.27838i	0.0363377	+	0.107047i
$454$		0			0
$455$	2.67109	−	9.04982i	0.125222	−	0.424262i
$456$		0			0
$457$	−9.62066	+	1.26658i	−0.450035	+	0.0592483i	−0.352138	−	0.935948i	$-0.614545\pi$
$457$	−9.62066	+	1.26658i	−0.450035	+	0.0592483i	−0.0978977	+	0.995196i	$0.531212\pi$
$458$		0			0
$459$	−2.14992	+	3.47785i	−0.100350	+	0.162332i
$460$		0			0
$461$	−8.43188	+	20.3564i	−0.392712	+	0.948090i	0.596635	+	0.802513i	$0.296504\pi$
$461$	−8.43188	+	20.3564i	−0.392712	+	0.948090i	−0.989347	+	0.145577i	$0.953496\pi$
$462$		0			0
$463$	15.8789	+	15.8789i	0.737956	+	0.737956i	0.972182	−	0.234226i	$-0.0752555\pi$
$463$	15.8789	+	15.8789i	0.737956	+	0.737956i	−0.234226	+	0.972182i	$0.575255\pi$
$464$		0			0
$465$	−0.872873	−	0.765489i	−0.0404785	−	0.0354987i
$466$		0			0
$467$	7.86027	+	6.03139i	0.363730	+	0.279100i	0.774416	−	0.632677i	$-0.218044\pi$
$467$	7.86027	+	6.03139i	0.363730	+	0.279100i	−0.410686	+	0.911777i	$0.634711\pi$
$468$		0			0
$469$	−34.9476	+	1.40721i	−1.61373	+	0.0649791i
$470$		0			0
$471$	0.204150	−	3.11472i	0.00940673	−	0.143519i
$472$		0			0
$473$	−0.921393	−	0.312771i	−0.0423657	−	0.0143812i
$474$		0			0
$475$	31.8221			1.46010
$476$		0			0
$477$	9.33011			0.427196
$478$		0			0
$479$	26.4275	+	8.97093i	1.20750	+	0.409892i	0.851381	−	0.524547i	$-0.175765\pi$
$479$	26.4275	+	8.97093i	1.20750	+	0.409892i	0.356122	+	0.934439i	$0.384099\pi$
$480$		0			0
$481$	−0.661584	+	10.0938i	−0.0301656	+	0.460239i
$482$		0			0
$483$	−0.445902	−	0.705188i	−0.0202892	−	0.0320872i
$484$		0			0
$485$	6.21530	+	4.76916i	0.282222	+	0.216557i
$486$		0			0
$487$	−1.25821	−	1.10342i	−0.0570149	−	0.0500008i	0.630364	−	0.776300i	$-0.282906\pi$
$487$	−1.25821	−	1.10342i	−0.0570149	−	0.0500008i	−0.687379	+	0.726299i	$0.741239\pi$
$488$		0			0
$489$	−2.06426	−	2.06426i	−0.0933489	−	0.0933489i
$490$		0			0
$491$	1.08193	−	2.61200i	0.0488266	−	0.117878i	−0.897584	−	0.440843i	$-0.854680\pi$
$491$	1.08193	−	2.61200i	0.0488266	−	0.117878i	0.946411	+	0.322965i	$0.104680\pi$
$492$		0			0
$493$	4.57454	−	28.1716i	0.206027	−	1.26879i
$494$		0			0
$495$	2.33559	−	0.307486i	0.104977	−	0.0138205i
$496$		0			0
$497$	28.2984	−	26.9066i	1.26935	−	1.20693i
$498$		0			0
$499$	8.62471	+	25.4076i	0.386095	+	1.13740i	0.950185	+	0.311686i	$0.100894\pi$
$499$	8.62471	+	25.4076i	0.386095	+	1.13740i	−0.564090	+	0.825713i	$0.690773\pi$
$500$		0			0
$501$	−1.74803	−	0.230133i	−0.0780963	−	0.0102816i
$502$		0			0
$503$	−3.89637	−	5.83132i	−0.173730	−	0.260006i	0.734378	−	0.678740i	$-0.237474\pi$
$503$	−3.89637	−	5.83132i	−0.173730	−	0.260006i	−0.908109	+	0.418734i	$0.862474\pi$
$504$		0			0
$505$	32.3614	+	21.6232i	1.44007	+	0.962221i
$506$		0			0
$507$	0.637267	−	1.87733i	0.0283020	−	0.0833750i
$508$		0			0
$509$	6.14612	+	10.6454i	0.272422	+	0.471849i	0.969481	−	0.245165i	$-0.0788420\pi$
$509$	6.14612	+	10.6454i	0.272422	+	0.471849i	−0.697060	+	0.717013i	$0.745509\pi$
$510$		0			0
$511$	−6.95862	+	11.3803i	−0.307831	+	0.503435i
$512$		0			0
$513$	2.97191	+	3.38881i	0.131213	+	0.149620i
$514$		0			0
$515$	−10.7752	−	21.8499i	−0.474812	−	0.962823i
$516$		0			0
$517$	−2.11715	+	1.41464i	−0.0931122	+	0.0622156i
$518$		0			0
$519$	0.632359	−	0.261932i	0.0277575	−	0.0114975i
$520$		0			0
$521$	6.12235	−	6.98120i	0.268225	−	0.305852i	−0.602010	−	0.798488i	$-0.705633\pi$
$521$	6.12235	−	6.98120i	0.268225	−	0.305852i	0.870235	+	0.492636i	$0.163967\pi$
$522$		0			0
$523$	−4.27756	+	15.9641i	−0.187045	+	0.698060i	0.807139	+	0.590361i	$0.201015\pi$
$523$	−4.27756	+	15.9641i	−0.187045	+	0.698060i	−0.994184	+	0.107699i	$0.965652\pi$
$524$		0			0
$525$	3.05844	−	0.324469i	0.133481	−	0.0141610i
$526$		0			0
$527$	−8.27973	+	0.837629i	−0.360671	+	0.0364877i
$528$		0			0
$529$	15.3854	−	11.8056i	0.668930	−	0.513288i
$530$		0			0
$531$	−10.9907	+	10.9907i	−0.476956	+	0.476956i
$532$		0			0
$533$	−5.32602	−	1.05941i	−0.230696	−	0.0458882i
$534$		0			0
$535$	−3.03045	+	23.0186i	−0.131018	+	0.995179i
$536$		0			0
$537$	−0.920134	+	1.86585i	−0.0397067	+	0.0805173i
$538$		0			0
$539$	−1.47013	+	0.635014i	−0.0633228	+	0.0273520i
$540$		0			0
$541$	4.68464	−	4.10832i	0.201408	−	0.176630i	−0.552700	−	0.833380i	$-0.686403\pi$
$541$	4.68464	−	4.10832i	0.201408	−	0.176630i	0.754109	+	0.656750i	$0.228069\pi$
$542$		0			0
$543$	0.314211	+	0.181410i	0.0134841	+	0.00778505i
$544$		0			0
$545$			30.3313i			1.29925i
$546$		0			0
$547$	−45.1262	+	8.97616i	−1.92946	+	0.383793i	−0.929571	+	0.368642i	$0.879823\pi$
$547$	−45.1262	+	8.97616i	−1.92946	+	0.383793i	−0.999885	+	0.0151503i	$0.995177\pi$
$548$		0			0
$549$	5.99309	−	2.95547i	0.255779	−	0.126136i
$550$		0			0
$551$	−28.2182	−	13.9157i	−1.20214	−	0.592828i
$552$		0			0
$553$	−6.31577	+	7.81489i	−0.268574	+	0.332323i
$554$		0			0
$555$	−5.35193	+	1.81673i	−0.227177	+	0.0771161i
$556$		0			0
$557$	3.75944	+	14.0304i	0.159293	+	0.594488i	0.998699	+	0.0509845i	$0.0162359\pi$
$557$	3.75944	+	14.0304i	0.159293	+	0.594488i	−0.839407	+	0.543504i	$0.817097\pi$
$558$		0			0
$559$	−4.04534	−	1.67564i	−0.171100	−	0.0708718i
$560$		0			0
$561$	−0.0908887	+	0.127547i	−0.00383732	+	0.00538504i
$562$		0			0
$563$	16.3519	+	21.3102i	0.689149	+	0.898116i	0.998605	−	0.0527975i	$-0.0168138\pi$
$563$	16.3519	+	21.3102i	0.689149	+	0.898116i	−0.309457	+	0.950914i	$0.600147\pi$
$564$		0			0
$565$	21.2076	+	5.68257i	0.892212	+	0.239068i
$566$		0			0
$567$	−17.0202	−	15.7026i	−0.714783	−	0.659448i
$568$		0			0
$569$	14.1497	−	18.4402i	0.593185	−	0.773054i	−0.396233	−	0.918150i	$-0.629683\pi$
$569$	14.1497	−	18.4402i	0.593185	−	0.773054i	0.989417	+	0.145097i	$0.0463493\pi$
$570$		0			0
$571$	1.73077	+	26.4065i	0.0724305	+	1.10508i	0.867133	+	0.498077i	$0.165960\pi$
$571$	1.73077	+	26.4065i	0.0724305	+	1.10508i	−0.794702	+	0.606999i	$0.792373\pi$
$572$		0			0
$573$	−1.06164	+	1.58885i	−0.0443505	+	0.0663753i
$574$		0			0
$575$	−2.59410	−	13.0414i	−0.108181	−	0.543864i
$576$		0			0
$577$	12.5582	−	21.7515i	0.522805	−	0.905525i	−0.476843	−	0.878989i	$-0.658219\pi$
$577$	12.5582	−	21.7515i	0.522805	−	0.905525i	0.999648	−	0.0265364i	$-0.00844779\pi$
$578$		0			0
$579$	−0.688010	+	0.397223i	−0.0285927	+	0.0165080i
$580$		0			0
$581$	−22.9928	+	3.97397i	−0.953903	+	0.164868i
$582$		0			0
$583$	0.716553	+	0.0469654i	0.0296766	+	0.00194511i
$584$		0			0
$585$	10.5781	−	0.693328i	0.437352	−	0.0286656i
$586$		0			0
$587$	−7.01966	−	16.9470i	−0.289732	−	0.699476i	0.710258	−	0.703942i	$-0.248578\pi$
$587$	−7.01966	−	16.9470i	−0.289732	−	0.699476i	−0.999990	+	0.00446603i	$0.998578\pi$
$588$		0			0
$589$	−1.78978	+	8.99781i	−0.0737464	+	0.370748i
$590$		0			0
$591$	−1.45942	+	0.391051i	−0.0600326	+	0.0160857i
$592$		0			0
$593$	−0.870331	−	6.61082i	−0.0357402	−	0.271474i	−0.999979	−	0.00643986i	$-0.997950\pi$
$593$	−0.870331	−	6.61082i	−0.0357402	−	0.271474i	0.964239	−	0.265034i	$-0.0853832\pi$
$594$		0			0
$595$	22.6995	−	30.2137i	0.930588	−	1.23864i
$596$		0			0
$597$	0.229331	+	1.74194i	0.00938588	+	0.0712929i
$598$		0			0
$599$	−36.8514	+	9.87431i	−1.50571	+	0.403453i	−0.915007	−	0.403437i	$-0.867815\pi$
$599$	−36.8514	+	9.87431i	−1.50571	+	0.403453i	−0.590701	+	0.806890i	$0.701149\pi$
$600$		0			0
$601$	−3.79870	+	19.0974i	−0.154952	+	0.778997i	0.822652	+	0.568545i	$0.192494\pi$
$601$	−3.79870	+	19.0974i	−0.154952	+	0.778997i	−0.977604	+	0.210452i	$0.932506\pi$
$602$		0			0
$603$	−15.0374	−	36.3034i	−0.612368	−	1.47839i
$604$		0			0
$605$	−37.8444	+	2.48046i	−1.53860	+	0.100845i
$606$		0			0
$607$	15.8085	+	1.03615i	0.641648	+	0.0420559i	0.382755	−	0.923850i	$-0.374975\pi$
$607$	15.8085	+	1.03615i	0.641648	+	0.0420559i	0.258894	+	0.965906i	$0.416642\pi$
$608$		0			0
$609$	−2.85395	−	1.04972i	−0.115648	−	0.0425368i
$610$		0			0
$611$	−9.92314	+	5.72913i	−0.401447	+	0.231776i
$612$		0			0
$613$	20.2354	−	35.0487i	0.817300	−	1.41560i	−0.0903651	−	0.995909i	$-0.528803\pi$
$613$	20.2354	−	35.0487i	0.817300	−	1.41560i	0.907665	−	0.419696i	$-0.137863\pi$
$614$		0			0
$615$	−0.591930	−	2.97583i	−0.0238689	−	0.119997i
$616$		0			0
$617$	13.1105	−	19.6212i	0.527807	−	0.789920i	−0.467771	−	0.883850i	$-0.654943\pi$
$617$	13.1105	−	19.6212i	0.527807	−	0.789920i	0.995579	+	0.0939298i	$0.0299429\pi$
$618$		0			0
$619$	0.477354	+	7.28302i	0.0191865	+	0.292729i	0.996660	+	0.0816688i	$0.0260250\pi$
$619$	0.477354	+	7.28302i	0.0191865	+	0.292729i	−0.977473	+	0.211060i	$0.932308\pi$
$620$		0			0
$621$	1.14654	−	1.49421i	0.0460092	−	0.0599604i
$622$		0			0
$623$	−33.1269	+	10.3216i	−1.32720	+	0.413526i
$624$		0			0
$625$	−10.6152	−	2.84433i	−0.424607	−	0.113773i
$626$		0			0
$627$	0.105105	+	0.136975i	0.00419748	+	0.00547026i
$628$		0			0
$629$	−16.6222	+	36.9459i	−0.662770	+	1.47313i
$630$		0			0
$631$	−29.5055	−	12.2216i	−1.17460	−	0.486534i	−0.291887	−	0.956453i	$-0.594283\pi$
$631$	−29.5055	−	12.2216i	−1.17460	−	0.486534i	−0.882710	+	0.469919i	$0.844283\pi$
$632$		0			0
$633$	−0.551486	−	2.05818i	−0.0219196	−	0.0818051i
$634$		0			0
$635$	−25.5447	+	8.67124i	−1.01371	+	0.344108i
$636$		0			0
$637$	−6.78830	+	2.41877i	−0.268962	+	0.0958350i
$638$		0			0
$639$	39.3455	+	19.4030i	1.55648	+	0.767572i
$640$		0			0
$641$	32.7683	−	16.1595i	1.29427	−	0.638263i	0.340909	−	0.940096i	$-0.389265\pi$
$641$	32.7683	−	16.1595i	1.29427	−	0.638263i	0.953361	+	0.301833i	$0.0975985\pi$
$642$		0			0
$643$	−19.7662	+	3.93175i	−0.779504	+	0.155053i	−0.568777	−	0.822492i	$-0.692583\pi$
$643$	−19.7662	+	3.93175i	−0.779504	+	0.155053i	−0.210727	+	0.977545i	$0.567583\pi$
$644$		0			0
$645$		−	2.44650i		−	0.0963309i
$646$		0			0
$647$	5.30581	+	3.06331i	0.208593	+	0.120431i	0.600657	−	0.799507i	$-0.294906\pi$
$647$	5.30581	+	3.06331i	0.208593	+	0.120431i	−0.392064	+	0.919938i	$0.628239\pi$
$648$		0			0
$649$	−0.899411	+	0.788762i	−0.0353050	+	0.0309616i
$650$		0			0
$651$	−0.0802713	+	0.883032i	−0.00314608	+	0.0346087i
$652$		0			0
$653$	−7.25935	+	14.7205i	−0.284080	+	0.576058i	−0.991405	−	0.130831i	$-0.958235\pi$
$653$	−7.25935	+	14.7205i	−0.284080	+	0.576058i	0.707324	+	0.706889i	$0.249902\pi$
$654$		0			0
$655$	6.58755	−	50.0374i	0.257397	−	1.95512i
$656$		0			0
$657$	−14.6983	−	2.92367i	−0.573434	−	0.114063i
$658$		0			0
$659$	31.4824	−	31.4824i	1.22638	−	1.22638i	0.261055	−	0.965324i	$-0.415930\pi$
$659$	31.4824	−	31.4824i	1.22638	−	1.22638i	0.965324	−	0.261055i	$-0.0840704\pi$
$660$		0			0
$661$	−2.54166	+	1.95028i	−0.0988591	+	0.0758573i	−0.657008	−	0.753883i	$-0.728178\pi$
$661$	−2.54166	+	1.95028i	−0.0988591	+	0.0758573i	0.558149	+	0.829741i	$0.311512\pi$
$662$		0			0
$663$	−0.445663	+	0.545984i	−0.0173081	+	0.0212043i
$664$		0			0
$665$	−24.5200	−	33.6798i	−0.950846	−	1.30605i
$666$		0			0
$667$	−3.40264	+	12.6988i	−0.131751	+	0.491701i
$668$		0			0
$669$	−0.166613	+	0.189986i	−0.00644165	+	0.00734529i
$670$		0			0
$671$	0.475147	−	0.196812i	0.0183428	−	0.00759785i
$672$		0			0
$673$	26.1647	−	17.4827i	1.00857	−	0.673908i	0.0625633	−	0.998041i	$-0.480072\pi$
$673$	26.1647	−	17.4827i	1.00857	−	0.673908i	0.946012	+	0.324133i	$0.105072\pi$
$674$		0			0
$675$	3.07070	+	6.22677i	0.118191	+	0.239669i
$676$		0			0
$677$	−3.05172	−	3.47982i	−0.117287	−	0.133740i	0.690217	−	0.723603i	$-0.257515\pi$
$677$	−3.05172	−	3.47982i	−0.117287	−	0.133740i	−0.807504	+	0.589863i	$0.799182\pi$
$678$		0			0
$679$	0.150791	−	5.98129i	0.00578684	−	0.229541i
$680$		0			0
$681$	−1.66336	−	2.88102i	−0.0637400	−	0.110401i
$682$		0			0
$683$	4.41300	−	13.0003i	0.168859	−	0.497442i	−0.829252	−	0.558874i	$-0.811233\pi$
$683$	4.41300	−	13.0003i	0.168859	−	0.497442i	0.998111	+	0.0614321i	$0.0195668\pi$
$684$		0			0
$685$	−49.7742	−	33.2581i	−1.90178	−	1.27073i
$686$		0			0
$687$	−1.67747	−	2.51051i	−0.0639994	−	0.0957819i
$688$		0			0
$689$	3.20376	+	0.421784i	0.122054	+	0.0160687i
$690$		0			0
$691$	12.9669	+	38.1991i	0.493282	+	1.45316i	0.853894	+	0.520447i	$0.174235\pi$
$691$	12.9669	+	38.1991i	0.493282	+	1.45316i	−0.360611	+	0.932716i	$0.617432\pi$
$692$		0			0
$693$	−1.23972	−	1.30384i	−0.0470930	−	0.0495289i
$694$		0			0
$695$	42.6074	−	5.60937i	1.61619	−	0.212775i
$696$		0			0
$697$	−18.4995	−	11.4359i	−0.700719	−	0.433166i
$698$		0			0
$699$	0.218818	−	0.528273i	0.00827644	−	0.0199811i
$700$		0			0
$701$	10.1158	+	10.1158i	0.382067	+	0.382067i	0.871846	−	0.489779i	$-0.162923\pi$
$701$	10.1158	+	10.1158i	0.382067	+	0.382067i	−0.489779	+	0.871846i	$0.662923\pi$
$702$		0			0
$703$	33.5780	+	29.4471i	1.26642	+	1.11062i
$704$		0			0
$705$	−5.07915	−	3.89737i	−0.191292	−	0.146783i
$706$		0			0
$707$	−1.19594	−	29.7007i	−0.0449780	−	1.11701i
$708$		0			0
$709$	−2.68572	+	40.9761i	−0.100864	+	1.53889i	0.584923	+	0.811089i	$0.301125\pi$
$709$	−2.68572	+	40.9761i	−0.100864	+	1.53889i	−0.685787	+	0.727802i	$0.740542\pi$
$710$		0			0
$711$	−10.6895	−	3.62861i	−0.400889	−	0.136083i
$712$		0			0
$713$	3.83340			0.143562
$714$		0			0
$715$	0.815892			0.0305126
$716$		0			0
$717$	−0.496397	−	0.168504i	−0.0185383	−	0.00629290i
$718$		0			0
$719$	−0.839544	+	12.8090i	−0.0313097	+	0.477694i	0.953197	+	0.302349i	$0.0977708\pi$
$719$	−0.839544	+	12.8090i	−0.0313097	+	0.477694i	−0.984507	+	0.175345i	$0.943896\pi$
$720$		0			0
$721$	−8.64725	+	16.4747i	−0.322040	+	0.613548i
$722$		0			0
$723$	3.27561	+	2.51346i	0.121821	+	0.0934767i
$724$		0			0
$725$	−36.4362	−	31.9537i	−1.35321	−	1.18673i
$726$		0			0
$727$	−8.39967	−	8.39967i	−0.311526	−	0.311526i	0.533974	−	0.845501i	$-0.320698\pi$
$727$	−8.39967	−	8.39967i	−0.311526	−	0.311526i	−0.845501	+	0.533974i	$0.820698\pi$
$728$		0			0
$729$	9.76709	−	23.5799i	0.361744	−	0.873328i
$730$		0			0
$731$	−12.8311	−	11.9540i	−0.474575	−	0.442134i
$732$		0			0
$733$	−1.45737	+	0.191866i	−0.0538292	+	0.00708675i	−0.157393	−	0.987536i	$-0.550309\pi$
$733$	−1.45737	+	0.191866i	−0.0538292	+	0.00708675i	0.103563	+	0.994623i	$0.466976\pi$
$734$		0			0
$735$	−2.70004	−	2.98697i	−0.0995925	−	0.110176i
$736$		0			0
$737$	−0.972128	−	2.86380i	−0.0358088	−	0.105489i
$738$		0			0
$739$	−19.4319	−	2.55826i	−0.714814	−	0.0941070i	−0.235657	−	0.971836i	$-0.575724\pi$
$739$	−19.4319	−	2.55826i	−0.714814	−	0.0941070i	−0.479157	+	0.877729i	$0.659057\pi$
$740$		0			0
$741$	0.431646	+	0.646003i	0.0158569	+	0.0237315i
$742$		0			0
$743$	11.0831	+	7.40546i	0.406598	+	0.271680i	0.742007	−	0.670393i	$-0.233874\pi$
$743$	11.0831	+	7.40546i	0.406598	+	0.271680i	−0.335408	+	0.942073i	$0.608874\pi$
$744$		0			0
$745$	−2.24787	+	6.62201i	−0.0823556	+	0.242612i
$746$		0			0
$747$	−13.1074	−	22.7027i	−0.479575	−	0.830648i
$748$		0			0
$749$	15.5746	−	8.47596i	0.569082	−	0.309705i
$750$		0			0
$751$	−5.41255	−	6.17183i	−0.197507	−	0.225213i	0.644606	−	0.764515i	$-0.277022\pi$
$751$	−5.41255	−	6.17183i	−0.197507	−	0.225213i	−0.842113	+	0.539302i	$0.818688\pi$
$752$		0			0
$753$	−1.18886	−	2.41076i	−0.0433243	−	0.0878531i
$754$		0			0
$755$	41.7401	−	27.8899i	1.51908	−	1.01502i
$756$		0			0
$757$	8.03455	−	3.32802i	0.292021	−	0.120959i	−0.231864	−	0.972748i	$-0.574482\pi$
$757$	8.03455	−	3.32802i	0.292021	−	0.120959i	0.523884	+	0.851789i	$0.324482\pi$
$758$		0			0
$759$	0.0475675	−	0.0542403i	0.00172659	−	0.00196880i
$760$		0			0
$761$	0.0999157	−	0.372891i	0.00362194	−	0.0135173i	−0.964091	−	0.265571i	$-0.914439\pi$
$761$	0.0999157	−	0.372891i	0.00362194	−	0.0135173i	0.967713	+	0.252054i	$0.0811061\pi$
$762$		0			0
$763$	18.7274	−	13.6342i	0.677978	−	0.493591i
$764$		0			0
$765$	40.6612	+	12.2169i	1.47011	+	0.441704i
$766$		0			0
$767$	−4.27083	+	3.27712i	−0.154211	+	0.118330i
$768$		0			0
$769$	8.89287	−	8.89287i	0.320685	−	0.320685i	−0.528345	−	0.849030i	$-0.677187\pi$
$769$	8.89287	−	8.89287i	0.320685	−	0.320685i	0.849030	+	0.528345i	$0.177187\pi$
$770$		0			0
$771$	4.45304	+	0.885765i	0.160372	+	0.0319001i
$772$		0			0
$773$	0.902374	−	6.85421i	0.0324561	−	0.246529i	−0.967524	−	0.252778i	$-0.918656\pi$
$773$	0.902374	−	6.85421i	0.0324561	−	0.246529i	0.999980	+	0.00624905i	$0.00198915\pi$
$774$		0			0
$775$	−6.24997	+	12.6737i	−0.224506	+	0.455253i
$776$		0			0
$777$	3.52744	+	2.48780i	0.126546	+	0.0892493i
$778$		0			0
$779$	−18.0259	+	15.8083i	−0.645845	+	0.566391i
$780$		0			0
$781$	2.92406	+	1.68821i	0.104631	+	0.0604089i
$782$		0			0
$783$		−	6.86438i		−	0.245313i
$784$		0			0
$785$	−63.8740	+	12.7053i	−2.27976	+	0.453473i
$786$		0			0
$787$	46.4641	−	22.9136i	1.65627	−	0.816781i	0.658321	−	0.752738i	$-0.271267\pi$
$787$	46.4641	−	22.9136i	1.65627	−	0.816781i	0.997947	−	0.0640432i	$-0.0203995\pi$
$788$		0			0
$789$	1.56728	+	0.772898i	0.0557967	+	0.0275159i
$790$		0			0
$791$	−6.02444	−	15.6486i	−0.214204	−	0.556400i
$792$		0			0
$793$	2.19151	−	0.743917i	0.0778228	−	0.0264173i
$794$		0			0
$795$	0.467298	+	1.74398i	0.0165734	+	0.0618526i
$796$		0			0
$797$	−30.2375	−	12.5248i	−1.07107	−	0.443650i	−0.223699	−	0.974658i	$-0.571813\pi$
$797$	−30.2375	−	12.5248i	−1.07107	−	0.443650i	−0.847367	+	0.531008i	$0.821813\pi$
$798$		0			0
$799$	−45.2579	+	7.59529i	−1.60111	+	0.268702i
$800$		0			0
$801$	−23.7307	−	30.9264i	−0.838483	−	1.09273i
$802$		0			0
$803$	−1.11411	−	0.298525i	−0.0393161	−	0.0105347i
$804$		0			0
$805$	−11.8039	+	12.7944i	−0.416033	+	0.450943i
$806$		0			0
$807$	2.15861	−	2.81316i	0.0759867	−	0.0990279i
$808$		0			0
$809$	−0.000136964	−	0.00208967i	−4.81541e−6	−	7.34689e-5i	0.997857	−	0.0654399i	$-0.0208451\pi$
$809$	−0.000136964	−	0.00208967i	−4.81541e−6	−	7.34689e-5i	−0.997861	+	0.0653664i	$0.979178\pi$
$810$		0			0
$811$	−10.7563	+	16.0980i	−0.377706	+	0.565277i	−0.970810	−	0.239849i	$-0.922902\pi$
$811$	−10.7563	+	16.0980i	−0.377706	+	0.565277i	0.593105	+	0.805125i	$0.297902\pi$
$812$		0			0
$813$	−0.977705	−	4.91525i	−0.0342896	−	0.172385i
$814$		0			0
$815$	−30.4543	+	52.7484i	−1.06677	+	1.84770i
$816$		0			0
$817$	−16.7422	+	9.66613i	−0.585736	+	0.338175i
$818$		0			0
$819$	−5.18305	−	6.21960i	−0.181110	−	0.217330i
$820$		0			0
$821$	−9.91010	−	0.649542i	−0.345865	−	0.0226692i	−0.108519	−	0.994094i	$-0.534611\pi$
$821$	−9.91010	−	0.649542i	−0.345865	−	0.0226692i	−0.237346	+	0.971425i	$0.576277\pi$
$822$		0			0
$823$	5.95433	−	0.390268i	0.207555	−	0.0136039i	0.0387291	−	0.999250i	$-0.487669\pi$
$823$	5.95433	−	0.390268i	0.207555	−	0.0136039i	0.168826	+	0.985646i	$0.446002\pi$
$824$		0			0
$825$	0.101771	+	0.245697i	0.00354322	+	0.00855408i
$826$		0			0
$827$	−5.05431	+	25.4097i	−0.175756	+	0.883583i	0.787770	+	0.615969i	$0.211235\pi$
$827$	−5.05431	+	25.4097i	−0.175756	+	0.883583i	−0.963526	+	0.267614i	$0.913765\pi$
$828$		0			0
$829$	4.53874	−	1.21615i	0.157637	−	0.0422387i	−0.179138	−	0.983824i	$-0.557331\pi$
$829$	4.53874	−	1.21615i	0.157637	−	0.0422387i	0.336774	+	0.941585i	$0.390664\pi$
$830$		0			0
$831$	−0.295600	−	2.24530i	−0.0102542	−	0.0778887i
$832$		0			0
$833$	−28.8585	−	0.433980i	−0.999887	−	0.0150365i
$834$		0			0
$835$	4.80152	+	36.4712i	0.166163	+	1.26214i
$836$		0			0
$837$	−1.93334	+	0.518038i	−0.0668262	+	0.0179060i
$838$		0			0
$839$	10.5492	−	53.0344i	0.364198	−	1.83095i	−0.169818	−	0.985475i	$-0.554318\pi$
$839$	10.5492	−	53.0344i	0.364198	−	1.83095i	0.534017	−	0.845474i	$-0.320682\pi$
$840$		0			0
$841$	7.23872	+	17.4758i	0.249611	+	0.602614i
$842$		0			0
$843$	4.93930	−	0.323739i	0.170118	−	0.0111502i
$844$		0			0
$845$	−41.2754	−	2.70533i	−1.41992	−	0.0930663i
$846$		0			0
$847$	18.5429	+	22.2513i	0.637142	+	0.764563i
$848$		0			0
$849$	4.01586	−	2.31856i	0.137824	−	0.0795727i
$850$		0			0
$851$	9.33083	−	16.1615i	0.319857	−	0.554008i
$852$		0			0
$853$	6.34332	+	31.8900i	0.217191	+	1.09189i	0.923385	+	0.383875i	$0.125411\pi$
$853$	6.34332	+	31.8900i	0.217191	+	1.09189i	−0.706194	+	0.708018i	$0.749589\pi$
$854$		0			0
$855$	26.0029	−	38.9161i	0.889281	−	1.33090i
$856$		0			0
$857$	−1.24590	−	19.0088i	−0.0425592	−	0.649328i	−0.964845	−	0.262819i	$-0.915348\pi$
$857$	−1.24590	−	19.0088i	−0.0425592	−	0.649328i	0.922286	−	0.386508i	$-0.126319\pi$
$858$		0			0
$859$	−15.1164	+	19.7001i	−0.515766	+	0.672160i	−0.976535	−	0.215361i	$-0.930907\pi$
$859$	−15.1164	+	19.7001i	−0.515766	+	0.672160i	0.460768	+	0.887520i	$0.347574\pi$
$860$		0			0
$861$	−1.57129	+	1.70314i	−0.0535494	+	0.0580428i
$862$		0			0
$863$	51.6853	+	13.8490i	1.75939	+	0.471426i	0.986589	−	0.163225i	$-0.0521896\pi$
$863$	51.6853	+	13.8490i	1.75939	+	0.471426i	0.772799	+	0.634651i	$0.218856\pi$
$864$		0			0
$865$	−8.69352	−	11.3296i	−0.295589	−	0.385219i
$866$		0			0
$867$	−2.43700	+	1.42426i	−0.0827647	+	0.0483705i
$868$		0			0
$869$	−0.802691	−	0.332486i	−0.0272294	−	0.0112788i
$870$		0			0
$871$	−3.52236	−	13.1456i	−0.119351	−	0.445422i
$872$		0			0
$873$	6.36522	−	2.16070i	0.215430	−	0.0731286i
$874$		0			0
$875$	−6.58978	−	17.1171i	−0.222775	−	0.578663i
$876$		0			0
$877$	−44.2798	−	21.8364i	−1.49522	−	0.737362i	−0.503288	−	0.864119i	$-0.667877\pi$
$877$	−44.2798	−	21.8364i	−1.49522	−	0.737362i	−0.991934	+	0.126757i	$0.959543\pi$
$878$		0			0
$879$	−1.34242	+	0.662010i	−0.0452788	+	0.0223290i
$880$		0			0
$881$	−23.1291	+	4.60067i	−0.779240	+	0.155000i	−0.568656	−	0.822575i	$-0.692537\pi$
$881$	−23.1291	+	4.60067i	−0.779240	+	0.155000i	−0.210584	+	0.977576i	$0.567537\pi$
$882$		0			0
$883$			47.7307i			1.60627i	0.595799	+	0.803133i	$0.296835\pi$
$883$			47.7307i			1.60627i	−0.595799	+	0.803133i	$0.703165\pi$
$884$		0			0
$885$	−2.60485	−	1.50391i	−0.0875610	−	0.0505533i
$886$		0			0
$887$	−16.6787	+	14.6268i	−0.560016	+	0.491121i	−0.891921	−	0.452192i	$-0.850642\pi$
$887$	−16.6787	+	14.6268i	−0.560016	+	0.491121i	0.331905	+	0.943313i	$0.392309\pi$
$888$		0			0
$889$	16.8364	+	11.8742i	0.564676	+	0.398249i
$890$		0			0
$891$	0.885623	−	1.79587i	0.0296695	−	0.0601638i
$892$		0			0
$893$	−6.60326	+	50.1568i	−0.220970	+	1.67843i
$894$		0			0
$895$	42.5715	+	8.46801i	1.42301	+	0.283054i
$896$		0			0
$897$	0.229559	−	0.229559i	0.00766476	−	0.00766476i
$898$		0			0
$899$	11.0843	−	8.50529i	0.369682	−	0.283667i
$900$		0			0
$901$	11.4299	+	6.07054i	0.380785	+	0.202239i
$902$		0			0
$903$	−1.51054	+	1.09972i	−0.0502677	+	0.0365965i
$904$		0			0
$905$	1.95924	−	7.31198i	0.0651273	−	0.243058i
$906$		0			0
$907$	16.0501	−	18.3016i	0.532934	−	0.607695i	−0.421239	−	0.906950i	$-0.638405\pi$
$907$	16.0501	−	18.3016i	0.532934	−	0.607695i	0.954173	+	0.299255i	$0.0967380\pi$
$908$		0			0
$909$	30.8530	−	12.7797i	1.02333	−	0.423877i
$910$		0			0
$911$	16.2217	−	10.8390i	0.537448	−	0.359111i	−0.257031	−	0.966403i	$-0.582744\pi$
$911$	16.2217	−	10.8390i	0.537448	−	0.359111i	0.794479	+	0.607292i	$0.207744\pi$
$912$		0			0
$913$	−0.892370	−	1.80955i	−0.0295331	−	0.0598873i
$914$		0			0
$915$	0.852598	+	0.972202i	0.0281860	+	0.0321400i
$916$		0			0
$917$	−33.8557	+	18.4249i	−1.11801	+	0.608444i
$918$		0			0
$919$	7.41205	+	12.8380i	0.244501	+	0.423488i	0.961991	−	0.273081i	$-0.0880426\pi$
$919$	7.41205	+	12.8380i	0.244501	+	0.423488i	−0.717490	+	0.696569i	$0.754709\pi$
$920$		0			0
$921$	1.65716	−	4.88185i	0.0546054	−	0.160862i
$922$		0			0
$923$	12.6333	+	8.44128i	0.415829	+	0.277848i
$924$		0			0
$925$	38.2189	+	57.1986i	1.25663	+	1.88068i
$926$		0			0
$927$	−20.7247	−	2.72846i	−0.680688	−	0.0896143i
$928$		0			0
$929$	−11.3562	−	33.4542i	−0.372584	−	1.09760i	−0.957976	−	0.286847i	$-0.907393\pi$
$929$	−11.3562	−	33.4542i	−0.372584	−	1.09760i	0.585392	−	0.810750i	$-0.300940\pi$
$930$		0			0
$931$	−9.77295	+	30.2788i	−0.320296	+	0.992347i
$932$		0			0
$933$	−2.53236	+	0.333392i	−0.0829058	+	0.0109148i
$934$		0			0
$935$	3.06128	+	1.14294i	0.100115	+	0.0373781i
$936$		0			0
$937$	10.2874	−	24.8359i	0.336074	−	0.811354i	−0.662011	−	0.749494i	$-0.730297\pi$
$937$	10.2874	−	24.8359i	0.336074	−	0.811354i	0.998085	−	0.0618601i	$-0.0197032\pi$
$938$		0			0
$939$	−3.19038	−	3.19038i	−0.104114	−	0.104114i
$940$		0			0
$941$	15.6003	+	13.6811i	0.508556	+	0.445992i	0.874770	−	0.484539i	$-0.161013\pi$
$941$	15.6003	+	13.6811i	0.508556	+	0.445992i	−0.366214	+	0.930531i	$0.619346\pi$
$942$		0			0
$943$	7.94803	+	6.09874i	0.258823	+	0.198602i
$944$		0			0
$945$	4.22420	−	8.04790i	0.137413	−	0.261798i
$946$		0			0
$947$	2.85010	−	43.4841i	0.0926158	−	1.41304i	−0.658355	−	0.752708i	$-0.728747\pi$
$947$	2.85010	−	43.4841i	0.0926158	−	1.41304i	0.750970	−	0.660336i	$-0.229586\pi$
$948$		0			0
$949$	−4.91491	−	1.66839i	−0.159545	−	0.0541581i
$950$		0			0
$951$	−0.712408			−0.0231014
$952$		0			0
$953$	27.4368			0.888765			0.444382	−	0.895837i	$-0.353423\pi$
$953$	27.4368			0.888765			0.444382	+	0.895837i	$0.353423\pi$
$954$		0			0
$955$	37.7533	+	12.8155i	1.22167	+	0.414701i
$956$		0			0
$957$	0.0171970	−	0.262376i	0.000555901	−	0.00848140i
$958$		0			0
$959$	1.83944	+	45.6819i	0.0593988	+	1.47514i
$960$		0			0
$961$	21.3619	+	16.3916i	0.689095	+	0.528761i
$962$		0			0
$963$	14.9774	+	13.1348i	0.482639	+	0.423263i
$964$		0			0
$965$	11.7206	+	11.7206i	0.377299	+	0.377299i
$966$		0			0
$967$	18.9878	−	45.8407i	0.610607	−	1.47414i	−0.251727	−	0.967798i	$-0.580999\pi$
$967$	18.9878	−	45.8407i	0.610607	−	1.47414i	0.862335	−	0.506338i	$-0.169001\pi$
$968$		0			0
$969$	0.714613	+	3.02852i	0.0229567	+	0.0972900i
$970$		0			0
$971$	−10.0667	+	1.32530i	−0.323055	+	0.0425311i	−0.290310	−	0.956933i	$-0.593758\pi$
$971$	−10.0667	+	1.32530i	−0.323055	+	0.0425311i	−0.0327455	+	0.999464i	$0.510425\pi$
$972$		0			0
$973$	−22.6158	−	23.7856i	−0.725029	−	0.762531i
$974$		0			0
$975$	0.384678	+	1.13322i	0.0123196	+	0.0362922i
$976$		0			0
$977$	32.8928	+	4.33042i	1.05233	+	0.138542i	0.636795	−	0.771033i	$-0.280260\pi$
$977$	32.8928	+	4.33042i	1.05233	+	0.138542i	0.415539	+	0.909576i	$0.363593\pi$
$978$		0			0
$979$	−1.66684	−	2.49461i	−0.0532725	−	0.0797280i
$980$		0			0
$981$	21.6390	+	14.4587i	0.690881	+	0.461632i
$982$		0			0
$983$	11.9199	−	35.1149i	0.380186	−	1.11999i	−0.573505	−	0.819202i	$-0.694417\pi$
$983$	11.9199	−	35.1149i	0.380186	−	1.11999i	0.953691	−	0.300789i	$-0.0972500\pi$
$984$		0			0
$985$	15.7618	+	27.3003i	0.502214	+	0.869861i
$986$		0			0
$987$	−0.123227	+	4.88792i	−0.00392236	+	0.155584i
$988$		0			0
$989$	5.32619	+	6.07336i	0.169363	+	0.193122i
$990$		0			0
$991$	25.7356	+	52.1866i	0.817517	+	1.65776i	0.751305	+	0.659955i	$0.229425\pi$
$991$	25.7356	+	52.1866i	0.817517	+	1.65776i	0.0662126	+	0.997806i	$0.478908\pi$
$992$		0			0
$993$	−0.869367	+	0.580893i	−0.0275885	+	0.0184341i
$994$		0			0
$995$	33.8673	−	14.0283i	1.07366	−	0.444726i
$996$		0			0
$997$	−14.1214	+	16.1024i	−0.447230	+	0.509968i	−0.930896	−	0.365285i	$-0.880972\pi$
$997$	−14.1214	+	16.1024i	−0.447230	+	0.509968i	0.483666	+	0.875253i	$0.339305\pi$
$998$		0			0
$999$	−2.52190	+	9.41186i	−0.0797894	+	0.297778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.465.7	yes	192
7.5	odd	6	inner	476.2.bl.a.397.7	yes	192
17.3	odd	16	inner	476.2.bl.a.241.7	yes	192
119.54	even	48	inner	476.2.bl.a.173.7	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.173.7	✓	192	119.54	even	48	inner
476.2.bl.a.241.7	yes	192	17.3	odd	16	inner
476.2.bl.a.397.7	yes	192	7.5	odd	6	inner
476.2.bl.a.465.7	yes	192	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.157228 + 0.0533716i) q^{3} +(0.226574 - 3.45685i) q^{5} +(-2.23621 + 1.41399i) q^{7} +(-2.35819 - 1.80950i) q^{9} +O(q^{10})\)	\(q+(0.157228 + 0.0533716i) q^{3} +(0.226574 - 3.45685i) q^{5} +(-2.23621 + 1.41399i) q^{7} +(-2.35819 - 1.80950i) q^{9} +(-0.172000 - 0.150840i) q^{11} +(-0.727951 - 0.727951i) q^{13} +(0.220122 - 0.531420i) q^{15} +(-1.71157 - 3.75107i) q^{17} +(-4.50639 + 0.593277i) q^{19} +(-0.427061 + 0.102969i) q^{21} +(0.610492 + 1.79845i) q^{23} +(-6.94126 - 0.913834i) q^{25} +(-0.550936 - 0.824535i) q^{27} +(5.75553 + 3.84572i) q^{29} +(0.648787 - 1.91126i) q^{31} +(-0.0189927 - 0.0328962i) q^{33} +(4.38129 + 8.05061i) q^{35} +(-6.47862 - 7.38745i) q^{37} +(-0.0756022 - 0.153306i) q^{39} +(4.38589 - 2.93056i) q^{41} +(3.92951 - 1.62766i) q^{43} +(-6.78948 + 7.74192i) q^{45} +(2.88070 - 10.7509i) q^{47} +(3.00125 - 6.32396i) q^{49} +(-0.0689065 - 0.681122i) q^{51} +(-2.49024 + 1.91083i) q^{53} +(-0.560403 + 0.560403i) q^{55} +(-0.740193 - 0.147234i) q^{57} +(0.682537 - 5.18438i) q^{59} +(-0.994292 + 2.01623i) q^{61} +(7.83202 + 0.711963i) q^{63} +(-2.68135 + 2.35148i) q^{65} +(11.4486 + 6.60983i) q^{67} +0.315350i q^{69} +(-14.4752 + 2.87931i) q^{71} +(4.52180 - 2.22990i) q^{73} +(-1.04259 - 0.514146i) q^{75} +(0.597916 + 0.0941032i) q^{77} +(3.59622 - 1.22075i) q^{79} +(2.26535 + 8.45440i) q^{81} +(8.14798 + 3.37501i) q^{83} +(-13.3547 + 5.06676i) q^{85} +(0.699677 + 0.911836i) q^{87} +(12.6676 + 3.39428i) q^{89} +(2.65717 + 0.598533i) q^{91} +(0.204015 - 0.265877i) q^{93} +(1.02984 + 15.7123i) q^{95} +(-1.25638 + 1.88031i) q^{97} +(0.132664 + 0.666945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 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

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