LMFDB - Embedded newform 476.2.bl.a.465.4

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			465.4
Character	$\chi$	$=$	476.465
Dual form			476.2.bl.a.173.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.81862 - 0.617339i) q^{3} +(-0.0377679 + 0.576227i) q^{5} +(-2.49055 - 0.892839i) q^{7} +(0.546221 + 0.419130i) q^{9} +O(q^{10})$	\(q+(-1.81862 - 0.617339i) q^{3} +(-0.0377679 + 0.576227i) q^{5} +(-2.49055 - 0.892839i) q^{7} +(0.546221 + 0.419130i) q^{9} +(2.79943 + 2.45503i) q^{11} +(1.80971 + 1.80971i) q^{13} +(0.424413 - 1.02462i) q^{15} +(4.02948 + 0.873664i) q^{17} +(-4.67050 + 0.614884i) q^{19} +(3.97819 + 3.16125i) q^{21} +(1.83959 + 5.41926i) q^{23} +(4.62661 + 0.609105i) q^{25} +(2.46637 + 3.69118i) q^{27} +(0.603025 + 0.402928i) q^{29} +(1.62678 - 4.79234i) q^{31} +(-3.57552 - 6.19297i) q^{33} +(0.608541 - 1.40140i) q^{35} +(7.87919 + 8.98449i) q^{37} +(-2.17398 - 4.40839i) q^{39} +(-7.82180 + 5.22636i) q^{41} +(-4.23423 + 1.75388i) q^{43} +(-0.262144 + 0.298917i) q^{45} +(-0.714750 + 2.66748i) q^{47} +(5.40568 + 4.44732i) q^{49} +(-6.78876 - 4.07642i) q^{51} +(11.3681 - 8.72309i) q^{53} +(-1.52039 + 1.52039i) q^{55} +(8.87348 + 1.76504i) q^{57} +(1.40704 - 10.6875i) q^{59} +(-3.58566 + 7.27100i) q^{61} +(-0.986174 - 1.53155i) q^{63} +(-1.11115 + 0.974456i) q^{65} +(6.52209 + 3.76553i) q^{67} -10.9912i q^{69} +(-3.23897 + 0.644272i) q^{71} +(-11.7177 + 5.77855i) q^{73} +(-8.03804 - 3.96392i) q^{75} +(-4.78017 - 8.61382i) q^{77} +(-6.72981 + 2.28446i) q^{79} +(-2.74127 - 10.2306i) q^{81} +(2.41296 + 0.999482i) q^{83} +(-0.655614 + 2.28890i) q^{85} +(-0.847931 - 1.10505i) q^{87} +(-14.4607 - 3.87474i) q^{89} +(-2.89140 - 6.12296i) q^{91} +(-5.91700 + 7.71119i) q^{93} +(-0.177917 - 2.71449i) q^{95} +(4.45237 - 6.66344i) q^{97} +(0.500128 + 2.51431i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.81862	−	0.617339i	−1.04998	−	0.356421i	−0.257476	−	0.966285i	$-0.582891\pi$
$3$	−1.81862	−	0.617339i	−1.04998	−	0.356421i	−0.792506	+	0.609864i	$0.791224\pi$
$4$		0			0
$5$	−0.0377679	+	0.576227i	−0.0168903	+	0.257697i	0.981060	+	0.193704i	$0.0620501\pi$
$5$	−0.0377679	+	0.576227i	−0.0168903	+	0.257697i	−0.997950	+	0.0639927i	$0.979617\pi$
$6$		0			0
$7$	−2.49055	−	0.892839i	−0.941339	−	0.337461i
$7$	−2.49055	−	0.892839i	−0.941339	−	0.337461i
$8$		0			0
$9$	0.546221	+	0.419130i	0.182074	+	0.139710i
$10$		0			0
$11$	2.79943	+	2.45503i	0.844059	+	0.740220i	0.967699	−	0.252107i	$-0.0811235\pi$
$11$	2.79943	+	2.45503i	0.844059	+	0.740220i	−0.123640	+	0.992327i	$0.539457\pi$
$12$		0			0
$13$	1.80971	+	1.80971i	0.501924	+	0.501924i	0.912035	−	0.410112i	$-0.134510\pi$
$13$	1.80971	+	1.80971i	0.501924	+	0.501924i	−0.410112	+	0.912035i	$0.634510\pi$
$14$		0			0
$15$	0.424413	−	1.02462i	0.109583	−	0.264557i
$16$		0			0
$17$	4.02948	+	0.873664i	0.977293	+	0.211895i
$17$	4.02948	+	0.873664i	0.977293	+	0.211895i
$18$		0			0
$19$	−4.67050	+	0.614884i	−1.07149	+	0.141064i	−0.645572	−	0.763699i	$-0.723381\pi$
$19$	−4.67050	+	0.614884i	−1.07149	+	0.141064i	−0.425915	+	0.904763i	$0.640048\pi$
$20$		0			0
$21$	3.97819	+	3.16125i	0.868111	+	0.689841i
$22$		0			0
$23$	1.83959	+	5.41926i	0.383581	+	1.12999i	0.951695	+	0.307044i	$0.0993397\pi$
$23$	1.83959	+	5.41926i	0.383581	+	1.12999i	−0.568114	+	0.822950i	$0.692327\pi$
$24$		0			0
$25$	4.62661	+	0.609105i	0.925323	+	0.121821i
$26$		0			0
$27$	2.46637	+	3.69118i	0.474653	+	0.710369i
$28$		0			0
$29$	0.603025	+	0.402928i	0.111979	+	0.0748219i	0.610299	−	0.792171i	$-0.291049\pi$
$29$	0.603025	+	0.402928i	0.111979	+	0.0748219i	−0.498320	+	0.866993i	$0.666049\pi$
$30$		0			0
$31$	1.62678	−	4.79234i	0.292179	−	0.860731i	−0.697393	−	0.716689i	$-0.745657\pi$
$31$	1.62678	−	4.79234i	0.292179	−	0.860731i	0.989572	−	0.144042i	$-0.0460099\pi$
$32$		0			0
$33$	−3.57552	−	6.19297i	−0.622417	−	1.07806i
$34$		0			0
$35$	0.608541	−	1.40140i	0.102862	−	0.236880i
$36$		0			0
$37$	7.87919	+	8.98449i	1.29533	+	1.47704i	0.788556	+	0.614963i	$0.210829\pi$
$37$	7.87919	+	8.98449i	1.29533	+	1.47704i	0.506775	+	0.862078i	$0.330837\pi$
$38$		0			0
$39$	−2.17398	−	4.40839i	−0.348115	−	0.705907i
$40$		0			0
$41$	−7.82180	+	5.22636i	−1.22156	+	0.816220i	−0.987747	−	0.156062i	$-0.950120\pi$
$41$	−7.82180	+	5.22636i	−1.22156	+	0.816220i	−0.233812	+	0.972282i	$0.575120\pi$
$42$		0			0
$43$	−4.23423	+	1.75388i	−0.645714	+	0.267464i	−0.681413	−	0.731899i	$-0.738634\pi$
$43$	−4.23423	+	1.75388i	−0.645714	+	0.267464i	0.0356988	+	0.999363i	$0.488634\pi$
$44$		0			0
$45$	−0.262144	+	0.298917i	−0.0390781	+	0.0445600i
$46$		0			0
$47$	−0.714750	+	2.66748i	−0.104257	+	0.389092i	−0.998260	−	0.0589689i	$-0.981219\pi$
$47$	−0.714750	+	2.66748i	−0.104257	+	0.389092i	0.894003	+	0.448061i	$0.147885\pi$
$48$		0			0
$49$	5.40568	+	4.44732i	0.772240	+	0.635331i
$50$		0			0
$51$	−6.78876	−	4.07642i	−0.950616	−	0.570813i
$52$		0			0
$53$	11.3681	−	8.72309i	1.56154	−	1.19821i	0.672764	−	0.739858i	$-0.265107\pi$
$53$	11.3681	−	8.72309i	1.56154	−	1.19821i	0.888772	−	0.458350i	$-0.151560\pi$
$54$		0			0
$55$	−1.52039	+	1.52039i	−0.205009	+	0.205009i
$56$		0			0
$57$	8.87348	+	1.76504i	1.17532	+	0.233786i
$58$		0			0
$59$	1.40704	−	10.6875i	0.183181	−	1.39140i	−0.614786	−	0.788694i	$-0.710758\pi$
$59$	1.40704	−	10.6875i	0.183181	−	1.39140i	0.797967	−	0.602702i	$-0.205909\pi$
$60$		0			0
$61$	−3.58566	+	7.27100i	−0.459097	+	0.930957i	0.537074	+	0.843535i	$0.319529\pi$
$61$	−3.58566	+	7.27100i	−0.459097	+	0.930957i	−0.996171	+	0.0874217i	$0.972137\pi$
$62$		0			0
$63$	−0.986174	−	1.53155i	−0.124246	−	0.192957i
$64$		0			0
$65$	−1.11115	+	0.974456i	−0.137822	+	0.120866i
$66$		0			0
$67$	6.52209	+	3.76553i	0.796800	+	0.460033i	0.842351	−	0.538929i	$-0.181171\pi$
$67$	6.52209	+	3.76553i	0.796800	+	0.460033i	−0.0455509	+	0.998962i	$0.514504\pi$
$68$		0			0
$69$		−	10.9912i		−	1.32319i
$70$		0			0
$71$	−3.23897	+	0.644272i	−0.384395	+	0.0764610i	−0.383505	−	0.923539i	$-0.625283\pi$
$71$	−3.23897	+	0.644272i	−0.384395	+	0.0764610i	−0.000889917		1.00000i	$0.500283\pi$
$72$		0			0
$73$	−11.7177	+	5.77855i	−1.37146	+	0.676328i	−0.970798	−	0.239898i	$-0.922886\pi$
$73$	−11.7177	+	5.77855i	−1.37146	+	0.676328i	−0.400660	+	0.916227i	$0.631219\pi$
$74$		0			0
$75$	−8.03804	−	3.96392i	−0.928153	−	0.457714i
$76$		0			0
$77$	−4.78017	−	8.61382i	−0.544751	−	0.981636i
$78$		0			0
$79$	−6.72981	+	2.28446i	−0.757163	+	0.257022i	−0.673214	−	0.739448i	$-0.735087\pi$
$79$	−6.72981	+	2.28446i	−0.757163	+	0.257022i	−0.0839493	+	0.996470i	$0.526753\pi$
$80$		0			0
$81$	−2.74127	−	10.2306i	−0.304586	−	1.13673i
$82$		0			0
$83$	2.41296	+	0.999482i	0.264857	+	0.109707i	0.511160	−	0.859485i	$-0.329216\pi$
$83$	2.41296	+	0.999482i	0.264857	+	0.109707i	−0.246303	+	0.969193i	$0.579216\pi$
$84$		0			0
$85$	−0.655614	+	2.28890i	−0.0711113	+	0.248266i
$86$		0			0
$87$	−0.847931	−	1.10505i	−0.0909077	−	0.118473i
$88$		0			0
$89$	−14.4607	−	3.87474i	−1.53284	−	0.410722i	−0.608893	−	0.793252i	$-0.708386\pi$
$89$	−14.4607	−	3.87474i	−1.53284	−	0.410722i	−0.923943	+	0.382530i	$0.875053\pi$
$90$		0			0
$91$	−2.89140	−	6.12296i	−0.303101	−	0.641860i
$92$		0			0
$93$	−5.91700	+	7.71119i	−0.613565	+	0.799613i
$94$		0			0
$95$	−0.177917	−	2.71449i	−0.0182539	−	0.278501i
$96$		0			0
$97$	4.45237	−	6.66344i	0.452070	−	0.676570i	−0.533508	−	0.845795i	$-0.679127\pi$
$97$	4.45237	−	6.66344i	0.452070	−	0.676570i	0.985577	+	0.169225i	$0.0541265\pi$
$98$		0			0
$99$	0.500128	+	2.51431i	0.0502647	+	0.252698i
$100$		0			0
$101$	−0.692044	+	1.19866i	−0.0688609	+	0.119271i	−0.898400	−	0.439178i	$-0.855270\pi$
$101$	−0.692044	+	1.19866i	−0.0688609	+	0.119271i	0.829539	+	0.558448i	$0.188603\pi$
$102$		0			0
$103$	4.01500	−	2.31806i	0.395609	−	0.228405i	−0.288978	−	0.957336i	$-0.593316\pi$
$103$	4.01500	−	2.31806i	0.395609	−	0.228405i	0.684588	+	0.728930i	$0.259982\pi$
$104$		0			0
$105$	−1.97185	+	2.17295i	−0.192433	+	0.212058i
$106$		0			0
$107$	−3.63932	−	0.238534i	−0.351827	−	0.0230599i	−0.111535	−	0.993761i	$-0.535577\pi$
$107$	−3.63932	−	0.238534i	−0.351827	−	0.0230599i	−0.240292	+	0.970701i	$0.577243\pi$
$108$		0			0
$109$	−9.47871	+	0.621267i	−0.907895	+	0.0595066i	−0.512191	−	0.858871i	$-0.671166\pi$
$109$	−9.47871	+	0.621267i	−0.907895	+	0.0595066i	−0.395704	+	0.918378i	$0.629499\pi$
$110$		0			0
$111$	−8.78279	−	21.2035i	−0.833626	−	2.01255i
$112$		0			0
$113$	0.420987	−	2.11644i	0.0396031	−	0.199098i	−0.955919	−	0.293632i	$-0.905136\pi$
$113$	0.420987	−	2.11644i	0.0396031	−	0.199098i	0.995522	+	0.0945337i	$0.0301360\pi$
$114$		0			0
$115$	−3.19220	+	0.855348i	−0.297674	+	0.0797616i
$116$		0			0
$117$	0.229998	+	1.74700i	0.0212633	+	0.161511i
$118$		0			0
$119$	−9.25558	−	5.77358i	−0.848458	−	0.529263i
$120$		0			0
$121$	0.373824	+	2.83948i	0.0339840	+	0.258134i
$122$		0			0
$123$	17.4513	−	4.67607i	1.57353	−	0.421627i
$124$		0			0
$125$	−1.08901	+	5.47481i	−0.0974039	+	0.489682i
$126$		0			0
$127$	1.54549	+	3.73114i	0.137140	+	0.331085i	0.977497	−	0.210947i	$-0.0676549\pi$
$127$	1.54549	+	3.73114i	0.137140	+	0.331085i	−0.840357	+	0.542033i	$0.817655\pi$
$128$		0			0
$129$	8.78321	−	0.575682i	0.773318	−	0.0506860i
$130$		0			0
$131$	6.54109	+	0.428725i	0.571497	+	0.0374579i	0.348413	−	0.937341i	$-0.386721\pi$
$131$	6.54109	+	0.428725i	0.571497	+	0.0374579i	0.223084	+	0.974799i	$0.428387\pi$
$132$		0			0
$133$	12.1811	+	2.63861i	1.05624	+	0.228796i
$134$		0			0
$135$	−2.22011	+	1.28178i	−0.191077	+	0.110318i
$136$		0			0
$137$	2.63771	−	4.56865i	0.225355	−	0.390326i	−0.731071	−	0.682301i	$-0.760979\pi$
$137$	2.63771	−	4.56865i	0.225355	−	0.390326i	0.956426	+	0.291975i	$0.0943125\pi$
$138$		0			0
$139$	1.16996	+	5.88178i	0.0992346	+	0.498886i	0.998152	+	0.0607678i	$0.0193549\pi$
$139$	1.16996	+	5.88178i	0.0992346	+	0.498886i	−0.898917	+	0.438118i	$0.855645\pi$
$140$		0			0
$141$	2.94660	−	4.40990i	0.248149	−	0.371381i
$142$		0			0
$143$	0.623256	+	9.50905i	0.0521193	+	0.795187i
$144$		0			0
$145$	−0.254953	+	0.332261i	−0.0211727	+	0.0275928i
$146$		0			0
$147$	−7.08538	−	11.4251i	−0.584393	−	0.942329i
$148$		0			0
$149$	9.90556	+	2.65419i	0.811495	+	0.217439i	0.640625	−	0.767854i	$-0.278675\pi$
$149$	9.90556	+	2.65419i	0.811495	+	0.217439i	0.170870	+	0.985294i	$0.445342\pi$
$150$		0			0
$151$	9.97806	+	13.0037i	0.812003	+	1.05822i	0.997145	+	0.0755115i	$0.0240590\pi$
$151$	9.97806	+	13.0037i	0.812003	+	1.05822i	−0.185142	+	0.982712i	$0.559274\pi$
$152$		0			0
$153$	1.83481	+	2.16609i	0.148335	+	0.175118i
$154$		0			0
$155$	2.70004	+	1.11839i	0.216872	+	0.0898315i
$156$		0			0
$157$	3.51342	+	13.1123i	0.280402	+	1.04647i	0.952134	+	0.305680i	$0.0988837\pi$
$157$	3.51342	+	13.1123i	0.280402	+	1.04647i	−0.671733	+	0.740794i	$0.734450\pi$
$158$		0			0
$159$	−26.0595	+	8.84600i	−2.06665	+	0.701533i
$160$		0			0
$161$	0.256931	−	15.1394i	0.0202490	−	1.19315i
$162$		0			0
$163$	12.2400	+	6.03611i	0.958712	+	0.472785i	0.853172	−	0.521630i	$-0.174676\pi$
$163$	12.2400	+	6.03611i	0.958712	+	0.472785i	0.105541	+	0.994415i	$0.466343\pi$
$164$		0			0
$165$	3.70360	−	1.82641i	0.288325	−	0.142186i
$166$		0			0
$167$	−2.04617	+	0.407008i	−0.158337	+	0.0314952i	−0.273622	−	0.961837i	$-0.588222\pi$
$167$	−2.04617	+	0.407008i	−0.158337	+	0.0314952i	0.115285	+	0.993332i	$0.463222\pi$
$168$		0			0
$169$		−	6.44989i		−	0.496146i
$170$		0			0
$171$	−2.80884	−	1.62169i	−0.214797	−	0.124013i
$172$		0			0
$173$	8.08071	−	7.08659i	0.614365	−	0.538784i	−0.294619	−	0.955615i	$-0.595193\pi$
$173$	8.08071	−	7.08659i	0.614365	−	0.538784i	0.908984	+	0.416831i	$0.136859\pi$
$174$		0			0
$175$	−10.9790	−	5.64783i	−0.829933	−	0.426935i
$176$		0			0
$177$	−9.15669	+	18.5679i	−0.688259	+	1.39565i
$178$		0			0
$179$	2.10718	−	16.0056i	0.157498	−	1.19632i	−0.711928	−	0.702253i	$-0.752178\pi$
$179$	2.10718	−	16.0056i	0.157498	−	1.19632i	0.869426	−	0.494064i	$-0.164489\pi$
$180$		0			0
$181$	24.1324	+	4.80023i	1.79375	+	0.356798i	0.975828	−	0.218538i	$-0.0701287\pi$
$181$	24.1324	+	4.80023i	1.79375	+	0.356798i	0.817917	+	0.575336i	$0.195129\pi$
$182$		0			0
$183$	11.0096	−	11.0096i	0.813856	−	0.813856i
$184$		0			0
$185$	−5.47469	+	4.20088i	−0.402507	+	0.308855i
$186$		0			0
$187$	9.13537	+	12.3383i	0.668044	+	0.902263i
$188$		0			0
$189$	−2.84699	−	11.3951i	−0.207088	−	0.828875i
$190$		0			0
$191$	−4.25476	+	15.8790i	−0.307864	+	1.14896i	0.622588	+	0.782549i	$0.286081\pi$
$191$	−4.25476	+	15.8790i	−0.307864	+	1.14896i	−0.930452	+	0.366413i	$0.880586\pi$
$192$		0			0
$193$	−16.4837	+	18.7961i	−1.18653	+	1.35297i	−0.265194	+	0.964195i	$0.585436\pi$
$193$	−16.4837	+	18.7961i	−1.18653	+	1.35297i	−0.921331	+	0.388778i	$0.872897\pi$
$194$		0			0
$195$	2.62234	−	1.08621i	0.187790	−	0.0777850i
$196$		0			0
$197$	−3.41614	+	2.28259i	−0.243390	+	0.162628i	−0.671282	−	0.741202i	$-0.734256\pi$
$197$	−3.41614	+	2.28259i	−0.243390	+	0.162628i	0.427892	+	0.903830i	$0.359256\pi$
$198$		0			0
$199$	−2.83497	−	5.74876i	−0.200966	−	0.407519i	0.772937	−	0.634483i	$-0.218787\pi$
$199$	−2.83497	−	5.74876i	−0.200966	−	0.407519i	−0.973903	+	0.226964i	$0.927120\pi$
$200$		0			0
$201$	−9.53661	−	10.8744i	−0.672661	−	0.767023i
$202$		0			0
$203$	−1.14211	−	1.54192i	−0.0801606	−	0.108221i
$204$		0			0
$205$	−2.71616	−	4.70452i	−0.189705	−	0.328578i
$206$		0			0
$207$	−1.26655	+	3.73114i	−0.0880313	+	0.259332i
$208$		0			0
$209$	−14.5843	−	9.74492i	−1.00882	−	0.674070i
$210$		0			0
$211$	5.99164	+	8.96713i	0.412482	+	0.617322i	0.978297	−	0.207210i	$-0.0664383\pi$
$211$	5.99164	+	8.96713i	0.412482	+	0.617322i	−0.565815	+	0.824532i	$0.691438\pi$
$212$		0			0
$213$	6.28820	+	0.827858i	0.430861	+	0.0567239i
$214$		0			0
$215$	−0.850713	−	2.50612i	−0.0580182	−	0.170916i
$216$		0			0
$217$	−8.33037	+	10.4831i	−0.565503	+	0.711641i
$218$		0			0
$219$	24.8775	−	3.27518i	1.68106	−	0.221316i
$220$		0			0
$221$	5.71112	+	8.87327i	0.384171	+	0.596881i
$222$		0			0
$223$	−2.97279	+	7.17695i	−0.199073	+	0.480604i	−0.991617	−	0.129210i	$-0.958756\pi$
$223$	−2.97279	+	7.17695i	−0.199073	+	0.480604i	0.792545	+	0.609814i	$0.208756\pi$
$224$		0			0
$225$	2.27186	+	2.27186i	0.151457	+	0.151457i
$226$		0			0
$227$	16.5986	+	14.5566i	1.10169	+	0.966153i	0.999590	−	0.0286216i	$-0.00911178\pi$
$227$	16.5986	+	14.5566i	1.10169	+	0.966153i	0.102096	+	0.994775i	$0.467445\pi$
$228$		0			0
$229$	−8.46944	−	6.49883i	−0.559676	−	0.429455i	0.289796	−	0.957089i	$-0.406413\pi$
$229$	−8.46944	−	6.49883i	−0.559676	−	0.429455i	−0.849472	+	0.527634i	$0.823079\pi$
$230$		0			0
$231$	3.37567	+	18.6163i	0.222103	+	1.22486i
$232$		0			0
$233$	1.61232	−	24.5992i	0.105626	−	1.61155i	−0.535787	−	0.844353i	$-0.679985\pi$
$233$	1.61232	−	24.5992i	0.105626	−	1.61155i	0.641414	−	0.767195i	$-0.278348\pi$
$234$		0			0
$235$	−1.51008	−	0.512604i	−0.0985069	−	0.0334386i
$236$		0			0
$237$	13.6493			0.886616
$238$		0			0
$239$	−6.47431			−0.418788			−0.209394	−	0.977831i	$-0.567149\pi$
$239$	−6.47431			−0.418788			−0.209394	+	0.977831i	$0.567149\pi$
$240$		0			0
$241$	4.73127	+	1.60605i	0.304768	+	0.103455i	0.469634	−	0.882861i	$-0.344386\pi$
$241$	4.73127	+	1.60605i	0.304768	+	0.103455i	−0.164866	+	0.986316i	$0.552719\pi$
$242$		0			0
$243$	−0.459348	+	7.00830i	−0.0294672	+	0.449583i
$244$		0			0
$245$	−2.76683	+	2.94693i	−0.176766	+	0.188273i
$246$		0			0
$247$	−9.56502	−	7.33950i	−0.608608	−	0.467001i
$248$		0			0
$249$	−3.77125	−	3.30730i	−0.238993	−	0.209591i
$250$		0			0
$251$	−7.01921	−	7.01921i	−0.443048	−	0.443048i	0.449987	−	0.893035i	$-0.351429\pi$
$251$	−7.01921	−	7.01921i	−0.443048	−	0.443048i	−0.893035	+	0.449987i	$0.851429\pi$
$252$		0			0
$253$	−8.15465	+	19.6871i	−0.512679	+	1.23772i
$254$		0			0
$255$	2.60534	−	3.75791i	0.163153	−	0.235329i
$256$		0			0
$257$	−4.82653	+	0.635425i	−0.301071	+	0.0396367i	−0.279548	−	0.960132i	$-0.590185\pi$
$257$	−4.82653	+	0.635425i	−0.301071	+	0.0396367i	−0.0215224	+	0.999768i	$0.506851\pi$
$258$		0			0
$259$	−11.6018	−	29.4112i	−0.720902	−	1.82752i
$260$		0			0
$261$	0.160505	+	0.472833i	0.00993503	+	0.0292676i
$262$		0			0
$263$	−10.9062	−	1.43583i	−0.672507	−	0.0885372i	−0.213463	−	0.976951i	$-0.568474\pi$
$263$	−10.9062	−	1.43583i	−0.672507	−	0.0885372i	−0.459043	+	0.888414i	$0.651808\pi$
$264$		0			0
$265$	4.59713	+	6.88009i	0.282399	+	0.422640i
$266$		0			0
$267$	23.9066	+	15.9739i	1.46306	+	0.977586i
$268$		0			0
$269$	−3.15413	+	9.29176i	−0.192311	+	0.566529i	−0.999725	−	0.0234563i	$-0.992533\pi$
$269$	−3.15413	+	9.29176i	−0.192311	+	0.566529i	0.807414	+	0.589985i	$0.200866\pi$
$270$		0			0
$271$	3.50495	+	6.07075i	0.212910	+	0.368772i	0.952624	−	0.304150i	$-0.0983724\pi$
$271$	3.50495	+	6.07075i	0.212910	+	0.368772i	−0.739714	+	0.672922i	$0.765039\pi$
$272$		0			0
$273$	1.47842	+	12.9203i	0.0894779	+	0.781973i
$274$		0			0
$275$	11.4565	+	13.0636i	0.690853	+	0.787767i
$276$		0			0
$277$	−6.86946	−	13.9299i	−0.412746	−	0.836966i	−0.999627	−	0.0272932i	$-0.991311\pi$
$277$	−6.86946	−	13.9299i	−0.412746	−	0.836966i	0.586882	−	0.809673i	$-0.300355\pi$
$278$		0			0
$279$	2.89720	−	1.93584i	0.173451	−	0.115896i
$280$		0			0
$281$	12.5498	−	5.19829i	0.748657	−	0.310104i	0.0244638	−	0.999701i	$-0.492212\pi$
$281$	12.5498	−	5.19829i	0.748657	−	0.310104i	0.724194	+	0.689597i	$0.242212\pi$
$282$		0			0
$283$	2.16997	−	2.47437i	0.128991	−	0.147086i	−0.683739	−	0.729727i	$-0.739647\pi$
$283$	2.16997	−	2.47437i	0.128991	−	0.147086i	0.812730	+	0.582641i	$0.197981\pi$
$284$		0			0
$285$	−1.35220	+	5.04648i	−0.0800974	+	0.298927i
$286$		0			0
$287$	24.1469	−	6.03290i	1.42535	−	0.356111i
$288$		0			0
$289$	15.4734	+	7.04082i	0.910201	+	0.414166i
$290$		0			0
$291$	−12.2108	+	9.36966i	−0.715809	+	0.549259i
$292$		0			0
$293$	20.5119	−	20.5119i	1.19832	−	1.19832i	0.223652	−	0.974669i	$-0.428202\pi$
$293$	20.5119	−	20.5119i	1.19832	−	1.19832i	0.974669	−	0.223652i	$-0.0717978\pi$
$294$		0			0
$295$	6.10530	+	1.21442i	0.355464	+	0.0707062i
$296$		0			0
$297$	−2.15755	+	16.3882i	−0.125194	+	0.950941i
$298$		0			0
$299$	−6.47816	+	13.1364i	−0.374642	+	0.759698i
$300$		0			0
$301$	12.1115	−	0.587631i	0.698095	−	0.0338705i
$302$		0			0
$303$	1.99854	−	1.75268i	0.114813	−	0.100689i
$304$		0			0
$305$	−4.05433	−	2.34077i	−0.232150	−	0.134032i
$306$		0			0
$307$		−	2.49268i		−	0.142265i	−0.997467	−	0.0711323i	$-0.977339\pi$
$307$		−	2.49268i		−	0.142265i	0.997467	−	0.0711323i	$-0.0226613\pi$
$308$		0			0
$309$	−8.73279	+	1.73706i	−0.496791	+	0.0988179i
$310$		0			0
$311$	28.3440	−	13.9777i	1.60724	−	0.792603i	0.607242	−	0.794517i	$-0.292276\pi$
$311$	28.3440	−	13.9777i	1.60724	−	0.792603i	0.999998	+	0.00191319i	$0.000608987\pi$
$312$		0			0
$313$	−16.2810	−	8.02891i	−0.920257	−	0.453821i	−0.0804828	−	0.996756i	$-0.525646\pi$
$313$	−16.2810	−	8.02891i	−0.920257	−	0.453821i	−0.839775	+	0.542935i	$0.817313\pi$
$314$		0			0
$315$	0.919767	−	0.510417i	0.0518230	−	0.0287587i
$316$		0			0
$317$	−24.8799	+	8.44560i	−1.39740	+	0.474352i	−0.915656	−	0.401962i	$-0.868328\pi$
$317$	−24.8799	+	8.44560i	−1.39740	+	0.474352i	−0.481740	+	0.876314i	$0.659995\pi$
$318$		0			0
$319$	0.698922	+	2.60841i	0.0391321	+	0.146043i
$320$		0			0
$321$	6.47130	+	2.68050i	0.361193	+	0.149611i
$322$		0			0
$323$	−19.3569	−	1.60279i	−1.07705	−	0.0891816i
$324$		0			0
$325$	7.27053	+	9.47514i	0.403296	+	0.525586i
$326$		0			0
$327$	17.6217	+	4.72173i	0.974484	+	0.261112i
$328$		0			0
$329$	4.16175	−	6.00534i	0.229445	−	0.331085i
$330$		0			0
$331$	−16.5242	+	21.5348i	−0.908253	+	1.18366i	0.0742179	+	0.997242i	$0.476354\pi$
$331$	−16.5242	+	21.5348i	−0.908253	+	1.18366i	−0.982471	+	0.186416i	$0.940313\pi$
$332$		0			0
$333$	0.538106	+	8.20992i	0.0294881	+	0.449901i
$334$		0			0
$335$	−2.41613	+	3.61599i	−0.132007	+	0.197563i
$336$		0			0
$337$	−5.81832	−	29.2507i	−0.316944	−	1.59339i	−0.730504	−	0.682908i	$-0.760715\pi$
$337$	−5.81832	−	29.2507i	−0.316944	−	1.59339i	0.413560	−	0.910477i	$-0.364285\pi$
$338$		0			0
$339$	−2.07218	+	3.58912i	−0.112545	+	0.194934i
$340$		0			0
$341$	16.3194	−	9.42202i	0.883746	−	0.510231i
$342$		0			0
$343$	−9.49237	−	15.9027i	−0.512540	−	0.858663i
$344$		0			0
$345$	6.33345	+	0.415116i	0.340981	+	0.0223491i
$346$		0			0
$347$	−17.2392	+	1.12992i	−0.925451	+	0.0606573i	−0.520672	−	0.853757i	$-0.674318\pi$
$347$	−17.2392	+	1.12992i	−0.925451	+	0.0606573i	−0.404780	+	0.914414i	$0.632652\pi$
$348$		0			0
$349$	−1.10394	−	2.66515i	−0.0590927	−	0.142662i	0.891575	−	0.452872i	$-0.149601\pi$
$349$	−1.10394	−	2.66515i	−0.0590927	−	0.142662i	−0.950668	+	0.310210i	$0.899601\pi$
$350$		0			0
$351$	−2.21656	+	11.1434i	−0.118311	+	0.594790i
$352$		0			0
$353$	−12.0721	+	3.23472i	−0.642535	+	0.172167i	−0.565352	−	0.824850i	$-0.691259\pi$
$353$	−12.0721	+	3.23472i	−0.642535	+	0.172167i	−0.0771838	+	0.997017i	$0.524593\pi$
$354$		0			0
$355$	−0.248918	−	1.89072i	−0.0132112	−	0.100349i
$356$		0			0
$357$	13.2682	+	16.2138i	0.702225	+	0.858125i
$358$		0			0
$359$	−0.657207	−	4.99198i	−0.0346860	−	0.263467i	−0.999997	−	0.00236445i	$-0.999247\pi$
$359$	−0.657207	−	4.99198i	−0.0346860	−	0.263467i	0.965311	−	0.261102i	$-0.0840860\pi$
$360$		0			0
$361$	3.08294	−	0.826071i	0.162260	−	0.0434774i
$362$		0			0
$363$	1.07308	−	5.39472i	0.0563219	−	0.283149i
$364$		0			0
$365$	−2.88720	−	6.97033i	−0.151123	−	0.364844i
$366$		0			0
$367$	8.88772	−	0.582532i	0.463935	−	0.0304079i	0.168356	−	0.985726i	$-0.446154\pi$
$367$	8.88772	−	0.582532i	0.463935	−	0.0304079i	0.295579	+	0.955318i	$0.404487\pi$
$368$		0			0
$369$	−6.46295	−	0.423604i	−0.336448	−	0.0220519i
$370$		0			0
$371$	−36.1012	+	11.5754i	−1.87428	+	0.600963i
$372$		0			0
$373$	13.0638	−	7.54237i	0.676416	−	0.390529i	−0.122087	−	0.992519i	$-0.538959\pi$
$373$	13.0638	−	7.54237i	0.676416	−	0.390529i	0.798503	+	0.601990i	$0.205625\pi$
$374$		0			0
$375$	5.36031	−	9.28433i	0.276805	−	0.479441i
$376$		0			0
$377$	0.362117	+	1.82048i	0.0186500	+	0.0937597i
$378$		0			0
$379$	10.7110	−	16.0301i	0.550186	−	0.823411i	−0.447292	−	0.894388i	$-0.647612\pi$
$379$	10.7110	−	16.0301i	0.550186	−	0.823411i	0.997478	+	0.0709766i	$0.0226116\pi$
$380$		0			0
$381$	−0.507282	−	7.73963i	−0.0259888	−	0.396513i
$382$		0			0
$383$	17.6802	−	23.0413i	0.903417	−	1.17736i	−0.0801443	−	0.996783i	$-0.525538\pi$
$383$	17.6802	−	23.0413i	0.903417	−	1.17736i	0.983562	−	0.180573i	$-0.0577952\pi$
$384$		0			0
$385$	5.14405	−	2.42914i	0.262165	−	0.123800i
$386$		0			0
$387$	−3.04793	−	0.816689i	−0.154935	−	0.0415147i
$388$		0			0
$389$	13.3315	+	17.3740i	0.675936	+	0.880897i	0.997828	−	0.0658796i	$-0.0209853\pi$
$389$	13.3315	+	17.3740i	0.675936	+	0.880897i	−0.321892	+	0.946777i	$0.604319\pi$
$390$		0			0
$391$	2.67798	+	23.4440i	0.135431	+	1.18561i
$392$		0			0
$393$	−11.6311	−	4.81776i	−0.586711	−	0.243024i
$394$		0			0
$395$	−1.06220	−	3.96418i	−0.0534450	−	0.199460i
$396$		0			0
$397$	5.93955	−	2.01620i	0.298097	−	0.101190i	−0.168384	−	0.985721i	$-0.553855\pi$
$397$	5.93955	−	2.01620i	0.298097	−	0.101190i	0.466481	+	0.884531i	$0.345521\pi$
$398$		0			0
$399$	−20.5239	−	12.3185i	−1.02748	−	0.616697i
$400$		0			0
$401$	−4.51750	−	2.22778i	−0.225593	−	0.111250i	0.325980	−	0.945377i	$-0.394306\pi$
$401$	−4.51750	−	2.22778i	−0.225593	−	0.111250i	−0.551573	+	0.834126i	$0.685972\pi$
$402$		0			0
$403$	11.6168	−	5.72875i	0.578672	−	0.285370i
$404$		0			0
$405$	5.99866	−	1.19321i	0.298076	−	0.0592910i
$406$		0			0
$407$			44.4951i			2.20554i
$408$		0			0
$409$	−29.9042	−	17.2652i	−1.47867	−	0.853709i	−0.478959	−	0.877837i	$-0.658986\pi$
$409$	−29.9042	−	17.2652i	−1.47867	−	0.853709i	−0.999709	+	0.0241283i	$0.992319\pi$
$410$		0			0
$411$	−7.61741	+	6.68029i	−0.375739	+	0.329514i
$412$		0			0
$413$	−13.0465	+	25.3615i	−0.641977	+	1.24796i
$414$		0			0
$415$	−0.667061	+	1.35267i	−0.0327447	+	0.0663998i
$416$		0			0
$417$	1.50334	−	11.4190i	0.0736189	−	0.559191i
$418$		0			0
$419$	−4.13904	−	0.823306i	−0.202205	−	0.0402211i	0.0929483	−	0.995671i	$-0.470371\pi$
$419$	−4.13904	−	0.823306i	−0.202205	−	0.0402211i	−0.295154	+	0.955450i	$0.595371\pi$
$420$		0			0
$421$	−3.22930	+	3.22930i	−0.157387	+	0.157387i	−0.781408	−	0.624021i	$-0.785498\pi$
$421$	−3.22930	+	3.22930i	−0.157387	+	0.157387i	0.624021	+	0.781408i	$0.285498\pi$
$422$		0			0
$423$	−1.50843	+	1.15746i	−0.0733425	+	0.0562777i
$424$		0			0
$425$	18.1107	+	6.49648i	0.878498	+	0.315126i
$426$		0			0
$427$	15.4221	−	14.9074i	0.746328	−	0.721419i
$428$		0			0
$429$	4.73684	−	17.6781i	0.228697	−	0.853509i
$430$		0			0
$431$	17.9498	−	20.4678i	0.864609	−	0.985898i	−0.135379	−	0.990794i	$-0.543225\pi$
$431$	17.9498	−	20.4678i	0.864609	−	0.985898i	0.999988	+	0.00489617i	$0.00155850\pi$
$432$		0			0
$433$	−24.9394	+	10.3303i	−1.19851	+	0.496440i	−0.890518	−	0.454948i	$-0.849658\pi$
$433$	−24.9394	+	10.3303i	−1.19851	+	0.496440i	−0.307995	+	0.951388i	$0.599658\pi$
$434$		0			0
$435$	0.668782	−	0.446866i	0.0320656	−	0.0214256i
$436$		0			0
$437$	−11.9240	−	24.1795i	−0.570403	−	1.15666i
$438$		0			0
$439$	8.61883	+	9.82789i	0.411354	+	0.469060i	0.920001	−	0.391916i	$-0.128187\pi$
$439$	8.61883	+	9.82789i	0.411354	+	0.469060i	−0.508647	+	0.860975i	$0.669854\pi$
$440$		0			0
$441$	1.08869	+	4.69490i	0.0518423	+	0.223567i
$442$		0			0
$443$	−13.1450	−	22.7678i	−0.624539	−	1.08173i	−0.988630	−	0.150369i	$-0.951954\pi$
$443$	−13.1450	−	22.7678i	−0.624539	−	1.08173i	0.364091	−	0.931363i	$-0.381380\pi$
$444$		0			0
$445$	2.77889	−	8.18633i	0.131732	−	0.388069i
$446$		0			0
$447$	−16.3759	−	10.9421i	−0.774556	−	0.517541i
$448$		0			0
$449$	−16.5823	−	24.8172i	−0.782568	−	1.17120i	−0.981552	−	0.191193i	$-0.938764\pi$
$449$	−16.5823	−	24.8172i	−0.782568	−	1.17120i	0.198984	−	0.980003i	$-0.436236\pi$
$450$		0			0
$451$	−34.7274	−	4.57195i	−1.63525	−	0.215285i
$452$		0			0
$453$	−10.1187	−	29.8086i	−0.475416	−	1.40053i
$454$		0			0
$455$	3.63742	−	1.43485i	0.170525	−	0.0672668i
$456$		0			0
$457$	−26.5340	+	3.49326i	−1.24121	+	0.163408i	−0.722395	−	0.691480i	$-0.756959\pi$
$457$	−26.5340	+	3.49326i	−1.24121	+	0.163408i	−0.518812	+	0.854888i	$0.673625\pi$
$458$		0			0
$459$	6.71334	+	17.0283i	0.313352	+	0.794814i
$460$		0			0
$461$	2.71232	−	6.54812i	0.126325	−	0.304976i	−0.848046	−	0.529923i	$-0.822221\pi$
$461$	2.71232	−	6.54812i	0.126325	−	0.304976i	0.974371	+	0.224947i	$0.0722208\pi$
$462$		0			0
$463$	12.7916	+	12.7916i	0.594478	+	0.594478i	0.938838	−	0.344360i	$-0.111904\pi$
$463$	12.7916	+	12.7916i	0.594478	+	0.594478i	−0.344360	+	0.938838i	$0.611904\pi$
$464$		0			0
$465$	−4.21992	−	3.70077i	−0.195694	−	0.171619i
$466$		0			0
$467$	−0.744940	−	0.571612i	−0.0344717	−	0.0264511i	0.591382	−	0.806392i	$-0.298583\pi$
$467$	−0.744940	−	0.571612i	−0.0344717	−	0.0264511i	−0.625854	+	0.779941i	$0.715249\pi$
$468$		0			0
$469$	−12.8816	−	15.2014i	−0.594816	−	0.701936i
$470$		0			0
$471$	1.70513	−	26.0152i	0.0785682	−	1.19872i
$472$		0			0
$473$	−16.1593	−	5.48533i	−0.743003	−	0.252216i
$474$		0			0
$475$	−21.9831			−1.00866
$476$		0			0
$477$	9.86562			0.451716
$478$		0			0
$479$	−9.70986	−	3.29605i	−0.443655	−	0.150601i	0.0906677	−	0.995881i	$-0.471100\pi$
$479$	−9.70986	−	3.29605i	−0.443655	−	0.150601i	−0.534323	+	0.845281i	$0.679433\pi$
$480$		0			0
$481$	−2.00028	+	30.5184i	−0.0912050	+	1.39152i
$482$		0			0
$483$	−9.81340	+	27.3742i	−0.446525	+	1.24557i
$484$		0			0
$485$	3.67150	+	2.81724i	0.166714	+	0.127924i
$486$		0			0
$487$	20.6084	+	18.0730i	0.933854	+	0.818968i	0.983705	−	0.179789i	$-0.0575415\pi$
$487$	20.6084	+	18.0730i	0.933854	+	0.818968i	−0.0498515	+	0.998757i	$0.515875\pi$
$488$		0			0
$489$	−18.5336	−	18.5336i	−0.838121	−	0.838121i
$490$		0			0
$491$	16.5606	−	39.9808i	0.747369	−	1.80431i	0.174510	−	0.984655i	$-0.444166\pi$
$491$	16.5606	−	39.9808i	0.747369	−	1.80431i	0.572859	−	0.819654i	$-0.305834\pi$
$492$		0			0
$493$	2.07785	+	2.15043i	0.0935818	+	0.0968506i
$494$		0			0
$495$	−1.46770	+	0.193227i	−0.0659684	+	0.00868490i
$496$		0			0
$497$	8.64205	+	1.28729i	0.387649	+	0.0577428i
$498$		0			0
$499$	−5.89623	−	17.3697i	−0.263951	−	0.777576i	−0.995411	−	0.0956910i	$-0.969494\pi$
$499$	−5.89623	−	17.3697i	−0.263951	−	0.777576i	0.731460	−	0.681885i	$-0.238839\pi$
$500$		0			0
$501$	3.97247	+	0.522985i	0.177477	+	0.0233652i
$502$		0			0
$503$	7.40218	+	11.0781i	0.330047	+	0.493950i	0.958966	−	0.283521i	$-0.0915025\pi$
$503$	7.40218	+	11.0781i	0.330047	+	0.493950i	−0.628919	+	0.777471i	$0.716502\pi$
$504$		0			0
$505$	−0.664561	−	0.444045i	−0.0295726	−	0.0197598i
$506$		0			0
$507$	−3.98177	+	11.7299i	−0.176837	+	0.520944i
$508$		0			0
$509$	−10.7010	−	18.5347i	−0.474315	−	0.821538i	0.525252	−	0.850947i	$-0.323971\pi$
$509$	−10.7010	−	18.5347i	−0.474315	−	0.821538i	−0.999567	+	0.0294084i	$0.990638\pi$
$510$		0			0
$511$	34.3429	−	3.92972i	1.51924	−	0.173840i
$512$		0			0
$513$	−13.7888	−	15.7232i	−0.608792	−	0.694194i
$514$		0			0
$515$	1.18409	+	2.40110i	0.0521773	+	0.105805i
$516$		0			0
$517$	−8.54965	+	5.71269i	−0.376013	+	0.251244i
$518$		0			0
$519$	−19.0706	+	7.89930i	−0.837106	+	0.346741i
$520$		0			0
$521$	−4.62182	+	5.27018i	−0.202486	+	0.230891i	−0.844166	−	0.536081i	$-0.819904\pi$
$521$	−4.62182	+	5.27018i	−0.202486	+	0.230891i	0.641681	+	0.766972i	$0.278237\pi$
$522$		0			0
$523$	3.43708	−	12.8274i	0.150293	−	0.560902i	−0.849169	−	0.528121i	$-0.822897\pi$
$523$	3.43708	−	12.8274i	0.150293	−	0.560902i	0.999463	−	0.0327813i	$-0.0104365\pi$
$524$		0			0
$525$	16.4800	+	17.0490i	0.719246	+	0.744080i
$526$		0			0
$527$	10.7420	−	17.8894i	0.467928	−	0.779274i
$528$		0			0
$529$	−7.73712	+	5.93690i	−0.336397	+	0.258126i
$530$		0			0
$531$	5.24801	−	5.24801i	0.227744	−	0.227744i
$532$		0			0
$533$	−23.6134	−	4.69700i	−1.02281	−	0.203449i
$534$		0			0
$535$	0.274899	−	2.08807i	0.0118849	−	0.0902751i
$536$		0			0
$537$	−13.7131	+	27.8073i	−0.591763	+	1.19998i
$538$		0			0
$539$	4.21450	+	25.7211i	0.181531	+	1.10788i
$540$		0			0
$541$	−5.17331	+	4.53687i	−0.222418	+	0.195055i	−0.763302	−	0.646042i	$-0.776423\pi$
$541$	−5.17331	+	4.53687i	−0.222418	+	0.195055i	0.540884	+	0.841097i	$0.318090\pi$
$542$		0			0
$543$	−40.9243	−	23.6277i	−1.75623	−	1.01396i
$544$		0			0
$545$		−	5.48535i		−	0.234967i
$546$		0			0
$547$	−16.5224	+	3.28651i	−0.706446	+	0.140521i	−0.535222	−	0.844711i	$-0.679772\pi$
$547$	−16.5224	+	3.28651i	−0.706446	+	0.140521i	−0.171224	+	0.985232i	$0.554772\pi$
$548$		0			0
$549$	−5.00606	+	2.46871i	−0.213653	+	0.105362i
$550$		0			0
$551$	−3.06418	−	1.51109i	−0.130539	−	0.0643745i
$552$		0			0
$553$	18.8006	+	0.319066i	0.799483	+	0.0135681i
$554$		0			0
$555$	12.5498	−	4.26007i	0.532708	−	0.180830i
$556$		0			0
$557$	−6.42922	−	23.9942i	−0.272415	−	1.01667i	−0.957554	−	0.288254i	$-0.906925\pi$
$557$	−6.42922	−	23.9942i	−0.272415	−	1.01667i	0.685139	−	0.728412i	$-0.259741\pi$
$558$		0			0
$559$	−10.8367	−	4.48873i	−0.458346	−	0.189853i
$560$		0			0
$561$	−8.99689	−	28.0783i	−0.379849	−	1.18547i
$562$		0			0
$563$	12.5437	+	16.3473i	0.528655	+	0.688956i	0.978991	−	0.203903i	$-0.0653626\pi$
$563$	12.5437	+	16.3473i	0.528655	+	0.688956i	−0.450336	+	0.892859i	$0.648696\pi$
$564$		0			0
$565$	1.20365	+	0.322518i	0.0506380	+	0.0135684i
$566$		0			0
$567$	−2.30697	+	27.9272i	−0.0968836	+	1.17283i
$568$		0			0
$569$	−18.5236	+	24.1405i	−0.776552	+	1.01202i	0.222758	+	0.974874i	$0.428494\pi$
$569$	−18.5236	+	24.1405i	−0.776552	+	1.01202i	−0.999310	+	0.0371480i	$0.988173\pi$
$570$		0			0
$571$	0.373955	+	5.70545i	0.0156495	+	0.238766i	0.998517	+	0.0544495i	$0.0173404\pi$
$571$	0.373955	+	5.70545i	0.0156495	+	0.238766i	−0.982867	+	0.184316i	$0.940993\pi$
$572$		0			0
$573$	17.5405	−	26.2512i	0.732766	−	1.09666i
$574$		0			0
$575$	5.21017	+	26.1933i	0.217279	+	1.09234i
$576$		0			0
$577$	17.1093	−	29.6341i	0.712268	−	1.23368i	−0.251736	−	0.967796i	$-0.581002\pi$
$577$	17.1093	−	29.6341i	0.712268	−	1.23368i	0.964004	−	0.265888i	$-0.0856650\pi$
$578$		0			0
$579$	41.5813	−	24.0070i	1.72806	−	0.997695i
$580$		0			0
$581$	−5.11723	−	4.64365i	−0.212298	−	0.192651i
$582$		0			0
$583$	53.2398	+	3.48952i	2.20497	+	0.144521i
$584$		0			0
$585$	−1.01536	+	0.0665501i	−0.0419799	+	0.00275151i
$586$		0			0
$587$	16.3942	+	39.5791i	0.676661	+	1.63360i	0.770057	+	0.637975i	$0.220228\pi$
$587$	16.3942	+	39.5791i	0.676661	+	1.63360i	−0.0933964	+	0.995629i	$0.529772\pi$
$588$		0			0
$589$	−4.65116	+	23.3829i	−0.191648	+	0.963478i
$590$		0			0
$591$	7.62180	−	2.04226i	0.313519	−	0.0840072i
$592$		0			0
$593$	2.21482	+	16.8232i	0.0909517	+	0.690847i	0.974801	+	0.223076i	$0.0716097\pi$
$593$	2.21482	+	16.8232i	0.0909517	+	0.690847i	−0.883849	+	0.467772i	$0.845057\pi$
$594$		0			0
$595$	3.67646	−	5.11526i	0.150720	−	0.209705i
$596$		0			0
$597$	1.60681	+	12.2050i	0.0657625	+	0.499516i
$598$		0			0
$599$	27.3153	−	7.31912i	1.11607	−	0.299051i	0.346780	−	0.937946i	$-0.387275\pi$
$599$	27.3153	−	7.31912i	1.11607	−	0.299051i	0.769294	+	0.638895i	$0.220608\pi$
$600$		0			0
$601$	−3.18251	+	15.9996i	−0.129817	+	0.652636i	0.860000	+	0.510294i	$0.170463\pi$
$601$	−3.18251	+	15.9996i	−0.129817	+	0.652636i	−0.989818	+	0.142342i	$0.954537\pi$
$602$		0			0
$603$	1.98425	+	4.79041i	0.0808051	+	0.195081i
$604$		0			0
$605$	−1.65030	+	0.108167i	−0.0670944	+	0.00439760i
$606$		0			0
$607$	41.5469	+	2.72312i	1.68633	+	0.110528i	0.878145	−	0.478394i	$-0.158781\pi$
$607$	41.5469	+	2.72312i	1.68633	+	0.110528i	0.808190	+	0.588922i	$0.200448\pi$
$608$		0			0
$609$	1.12519	+	3.50924i	0.0455949	+	0.142201i
$610$		0			0
$611$	−6.12086	+	3.53388i	−0.247624	+	0.142966i
$612$		0			0
$613$	−21.7174	+	37.6156i	−0.877156	+	1.51928i	−0.0227083	+	0.999742i	$0.507229\pi$
$613$	−21.7174	+	37.6156i	−0.877156	+	1.51928i	−0.854448	+	0.519537i	$0.826104\pi$
$614$		0			0
$615$	2.03538	+	10.2325i	0.0820744	+	0.412616i
$616$		0			0
$617$	13.8710	−	20.7595i	0.558427	−	0.835745i	−0.439622	−	0.898183i	$-0.644888\pi$
$617$	13.8710	−	20.7595i	0.558427	−	0.835745i	0.998049	+	0.0624378i	$0.0198875\pi$
$618$		0			0
$619$	−2.34123	−	35.7202i	−0.0941019	−	1.43572i	−0.740161	−	0.672430i	$-0.765251\pi$
$619$	−2.34123	−	35.7202i	−0.0941019	−	1.43572i	0.646059	−	0.763288i	$-0.276416\pi$
$620$		0			0
$621$	−15.4664	+	20.1562i	−0.620644	+	0.808839i
$622$		0			0
$623$	32.5557	+	22.5614i	1.30432	+	0.903902i
$624$		0			0
$625$	19.4240	+	5.20465i	0.776961	+	0.208186i
$626$		0			0
$627$	20.5074	+	26.7258i	0.818987	+	1.06733i
$628$		0			0
$629$	23.8996	+	43.0866i	0.952940	+	1.71798i
$630$		0			0
$631$	−3.84948	−	1.59451i	−0.153246	−	0.0634764i	0.304742	−	0.952435i	$-0.401430\pi$
$631$	−3.84948	−	1.59451i	−0.153246	−	0.0634764i	−0.457988	+	0.888958i	$0.651430\pi$
$632$		0			0
$633$	−5.36078	−	20.0067i	−0.213072	−	0.795195i
$634$		0			0
$635$	−2.20835	+	0.749635i	−0.0876359	+	0.0297484i
$636$		0			0
$637$	1.73435	+	17.8311i	0.0687176	+	0.706493i
$638$		0			0
$639$	−2.03923	−	1.00564i	−0.0806706	−	0.0397823i
$640$		0			0
$641$	−13.4862	+	6.65067i	−0.532674	+	0.262686i	−0.688674	−	0.725072i	$-0.741807\pi$
$641$	−13.4862	+	6.65067i	−0.532674	+	0.262686i	0.156000	+	0.987757i	$0.450140\pi$
$642$		0			0
$643$	−46.8777	+	9.32455i	−1.84868	+	0.367724i	−0.989567	−	0.144070i	$-0.953981\pi$
$643$	−46.8777	+	9.32455i	−1.84868	+	0.367724i	−0.859108	+	0.511794i	$0.828981\pi$
$644$		0			0
$645$			5.08287i			0.200138i
$646$		0			0
$647$	19.2081	+	11.0898i	0.755149	+	0.435986i	0.827551	−	0.561390i	$-0.189733\pi$
$647$	19.2081	+	11.0898i	0.755149	+	0.435986i	−0.0724023	+	0.997376i	$0.523067\pi$
$648$		0			0
$649$	30.1771	−	26.4646i	1.18455	−	1.03883i
$650$		0			0
$651$	21.6214	−	13.9222i	0.847411	−	0.545653i
$652$		0			0
$653$	5.25154	−	10.6491i	0.205509	−	0.416730i	−0.769579	−	0.638552i	$-0.779534\pi$
$653$	5.25154	−	10.6491i	0.205509	−	0.416730i	0.975087	+	0.221822i	$0.0712003\pi$
$654$		0			0
$655$	−0.494086	+	3.75296i	−0.0193056	+	0.146640i
$656$		0			0
$657$	−8.82244	−	1.75489i	−0.344196	−	0.0684648i
$658$		0			0
$659$	−0.994022	+	0.994022i	−0.0387216	+	0.0387216i	−0.726202	−	0.687481i	$-0.758717\pi$
$659$	−0.994022	+	0.994022i	−0.0387216	+	0.0387216i	0.687481	+	0.726202i	$0.258717\pi$
$660$		0			0
$661$	15.0961	−	11.5837i	0.587171	−	0.450552i	−0.271959	−	0.962309i	$-0.587672\pi$
$661$	15.0961	−	11.5837i	0.587171	−	0.450552i	0.859131	+	0.511756i	$0.171005\pi$
$662$		0			0
$663$	−4.90855	−	19.6628i	−0.190632	−	0.763641i
$664$		0			0
$665$	−1.98049	+	6.91944i	−0.0768002	+	0.268324i
$666$		0			0
$667$	−1.07425	+	4.00917i	−0.0415953	+	0.155236i
$668$		0			0
$669$	9.83699	−	11.2169i	0.380320	−	0.433672i
$670$		0			0
$671$	−27.8884	+	11.5517i	−1.07662	+	0.445950i
$672$		0			0
$673$	25.9436	−	17.3349i	1.00005	−	0.668213i	0.0561441	−	0.998423i	$-0.482119\pi$
$673$	25.9436	−	17.3349i	1.00005	−	0.668213i	0.943908	+	0.330209i	$0.107119\pi$
$674$		0			0
$675$	9.16262	+	18.5800i	0.352669	+	0.715143i
$676$		0			0
$677$	11.6511	+	13.2856i	0.447789	+	0.510606i	0.931060	−	0.364865i	$-0.118885\pi$
$677$	11.6511	+	13.2856i	0.447789	+	0.510606i	−0.483271	+	0.875471i	$0.660552\pi$
$678$		0			0
$679$	−17.0382	+	12.6204i	−0.653867	+	0.484326i
$680$		0			0
$681$	−21.2002	−	36.7198i	−0.812394	−	1.40711i
$682$		0			0
$683$	−1.66846	+	4.91513i	−0.0638419	+	0.188072i	−0.974170	−	0.225814i	$-0.927496\pi$
$683$	−1.66846	+	4.91513i	−0.0638419	+	0.188072i	0.910328	+	0.413887i	$0.135829\pi$
$684$		0			0
$685$	2.53296	+	1.69247i	0.0967794	+	0.0646659i
$686$		0			0
$687$	11.3907	+	17.0474i	0.434584	+	0.650400i
$688$		0			0
$689$	36.3593	+	4.78680i	1.38518	+	0.182362i
$690$		0			0
$691$	−9.68579	−	28.5334i	−0.368465	−	1.08546i	−0.960196	−	0.279327i	$-0.909889\pi$
$691$	−9.68579	−	28.5334i	−0.368465	−	1.08546i	0.591731	−	0.806135i	$-0.298445\pi$
$692$		0			0
$693$	0.999282	−	6.70855i	0.0379596	−	0.254837i
$694$		0			0
$695$	−3.43343	+	0.452019i	−0.130237	+	0.0171461i
$696$		0			0
$697$	−36.0839	+	14.2259i	−1.36677	+	0.538844i
$698$		0			0
$699$	−18.1183	+	43.7413i	−0.685295	+	1.65445i
$700$		0			0
$701$	−27.1443	−	27.1443i	−1.02523	−	1.02523i	−0.999673	−	0.0255526i	$-0.991865\pi$
$701$	−27.1443	−	27.1443i	−1.02523	−	1.02523i	−0.0255526	−	0.999673i	$-0.508135\pi$
$702$		0			0
$703$	−42.3242	−	37.1173i	−1.59629	−	1.39991i
$704$		0			0
$705$	2.42982	+	1.86447i	0.0915123	+	0.0702198i
$706$		0			0
$707$	2.79378	−	2.36743i	0.105071	−	0.0890362i
$708$		0			0
$709$	0.753856	−	11.5016i	0.0283117	−	0.431952i	−0.960050	−	0.279829i	$-0.909722\pi$
$709$	0.753856	−	11.5016i	0.0283117	−	0.431952i	0.988362	−	0.152123i	$-0.0486111\pi$
$710$		0			0
$711$	−4.63345	−	1.57284i	−0.173768	−	0.0589863i
$712$		0			0
$713$	28.9636			1.08469
$714$		0			0
$715$	−5.50291			−0.205797
$716$		0			0
$717$	11.7743	+	3.99684i	0.439720	+	0.149265i
$718$		0			0
$719$	−3.35309	+	51.1583i	−0.125049	+	1.90788i	0.230252	+	0.973131i	$0.426045\pi$
$719$	−3.35309	+	51.1583i	−0.125049	+	1.90788i	−0.355301	+	0.934752i	$0.615622\pi$
$720$		0			0
$721$	−12.0692	+	2.18850i	−0.449480	+	0.0815039i
$722$		0			0
$723$	−7.61292	−	5.84160i	−0.283128	−	0.217251i
$724$		0			0
$725$	2.54454	+	2.23150i	0.0945017	+	0.0828758i
$726$		0			0
$727$	0.557863	+	0.557863i	0.0206900	+	0.0206900i	0.717376	−	0.696686i	$-0.245343\pi$
$727$	0.557863	+	0.557863i	0.0206900	+	0.0206900i	−0.696686	+	0.717376i	$0.745343\pi$
$728$		0			0
$729$	−6.99765	+	16.8938i	−0.259172	+	0.625697i
$730$		0			0
$731$	−18.5941	+	3.36792i	−0.687726	+	0.124567i
$732$		0			0
$733$	38.7910	−	5.10693i	1.43278	−	0.188629i	0.626157	−	0.779697i	$-0.284627\pi$
$733$	38.7910	−	5.10693i	1.43278	−	0.188629i	0.806621	+	0.591069i	$0.201294\pi$
$734$		0			0
$735$	6.85107	−	3.65129i	0.252706	−	0.134680i
$736$		0			0
$737$	9.01362	+	26.5533i	0.332021	+	0.978102i
$738$		0			0
$739$	7.31649	+	0.963234i	0.269142	+	0.0354332i	0.263889	−	0.964553i	$-0.414995\pi$
$739$	7.31649	+	0.963234i	0.269142	+	0.0354332i	0.00525250	+	0.999986i	$0.498328\pi$
$740$		0			0
$741$	12.8642	+	19.2526i	0.472578	+	0.707264i
$742$		0			0
$743$	−38.6272	−	25.8099i	−1.41710	−	0.946873i	−0.999264	−	0.0383488i	$-0.987790\pi$
$743$	−38.6272	−	25.8099i	−1.41710	−	0.946873i	−0.417832	−	0.908524i	$-0.637210\pi$
$744$		0			0
$745$	−1.90353	+	5.60761i	−0.0697398	+	0.205447i
$746$		0			0
$747$	0.899097	+	1.55728i	0.0328962	+	0.0569780i
$748$		0			0
$749$	8.85094	+	3.84341i	0.323406	+	0.140435i
$750$		0			0
$751$	−16.7976	−	19.1540i	−0.612954	−	0.698940i	0.359206	−	0.933258i	$-0.383048\pi$
$751$	−16.7976	−	19.1540i	−0.612954	−	0.698940i	−0.972160	+	0.234318i	$0.924714\pi$
$752$		0			0
$753$	8.43206	+	17.0985i	0.307281	+	0.623105i
$754$		0			0
$755$	−7.86992	+	5.25851i	−0.286416	+	0.191377i
$756$		0			0
$757$	16.6733	−	6.90631i	0.606001	−	0.251014i	−0.0585164	−	0.998286i	$-0.518637\pi$
$757$	16.6733	−	6.90631i	0.606001	−	0.251014i	0.664518	+	0.747272i	$0.268637\pi$
$758$		0			0
$759$	26.9838	−	30.7692i	0.979451	−	1.11685i
$760$		0			0
$761$	−10.0503	+	37.5084i	−0.364325	+	1.35968i	0.504009	+	0.863698i	$0.331858\pi$
$761$	−10.0503	+	37.5084i	−0.364325	+	1.35968i	−0.868334	+	0.495980i	$0.834809\pi$
$762$		0			0
$763$	24.1619	+	6.91566i	0.874719	+	0.250364i
$764$		0			0
$765$	−1.31746	+	0.975457i	−0.0476327	+	0.0352677i
$766$		0			0
$767$	21.8876	−	16.7950i	0.790317	−	0.606432i
$768$		0			0
$769$	17.2534	−	17.2534i	0.622174	−	0.622174i	−0.323913	−	0.946087i	$-0.604999\pi$
$769$	17.2534	−	17.2534i	0.622174	−	0.622174i	0.946087	+	0.323913i	$0.104999\pi$
$770$		0			0
$771$	9.16991	+	1.82401i	0.330246	+	0.0656900i
$772$		0			0
$773$	−2.26983	+	17.2411i	−0.0816401	+	0.620118i	0.900895	+	0.434038i	$0.142912\pi$
$773$	−2.26983	+	17.2411i	−0.0816401	+	0.620118i	−0.982535	+	0.186080i	$0.940422\pi$
$774$		0			0
$775$	10.4455	−	21.1814i	0.375215	−	0.760860i
$776$		0			0
$777$	2.94265	+	60.6501i	0.105567	+	2.17581i
$778$		0			0
$779$	33.3181	−	29.2192i	1.19375	−	1.04689i
$780$		0			0
$781$	−10.6490	−	6.14819i	−0.381050	−	0.220000i
$782$		0			0
$783$			3.21965i			0.115061i
$784$		0			0
$785$	−7.68834	+	1.52931i	−0.274409	+	0.0545833i
$786$		0			0
$787$	−15.4024	+	7.59560i	−0.549035	+	0.270754i	−0.695578	−	0.718450i	$-0.744852\pi$
$787$	−15.4024	+	7.59560i	−0.549035	+	0.270754i	0.146544	+	0.989204i	$0.453185\pi$
$788$		0			0
$789$	18.9479	+	9.34407i	0.674563	+	0.332658i
$790$		0			0
$791$	−2.93813	+	4.89523i	−0.104468	+	0.174054i
$792$		0			0
$793$	−19.6474	+	6.66940i	−0.697701	+	0.236837i
$794$		0			0
$795$	−4.11309	−	15.3503i	−0.145876	−	0.544418i
$796$		0			0
$797$	−9.17186	−	3.79911i	−0.324884	−	0.134571i	0.214280	−	0.976772i	$-0.431260\pi$
$797$	−9.17186	−	3.79911i	−0.324884	−	0.134571i	−0.539164	+	0.842201i	$0.681260\pi$
$798$		0			0
$799$	−5.21055	+	10.1241i	−0.184336	+	0.358166i
$800$		0			0
$801$	−6.27473	−	8.17739i	−0.221707	−	0.288934i
$802$		0			0
$803$	−46.9895	−	12.5908i	−1.65822	−	0.444320i
$804$		0			0
$805$	8.71402	+	0.719834i	0.307129	+	0.0253708i
$806$		0			0
$807$	11.4723	−	14.9510i	0.403845	−	0.526301i
$808$		0			0
$809$	−0.305577	−	4.66220i	−0.0107435	−	0.163914i	−0.999859	−	0.0167750i	$-0.994660\pi$
$809$	−0.305577	−	4.66220i	−0.0107435	−	0.163914i	0.989116	−	0.147139i	$-0.0470066\pi$
$810$		0			0
$811$	15.7419	−	23.5594i	0.552772	−	0.827281i	−0.444893	−	0.895584i	$-0.646758\pi$
$811$	15.7419	−	23.5594i	0.552772	−	0.827281i	0.997665	+	0.0683025i	$0.0217583\pi$
$812$		0			0
$813$	−2.62647	−	13.2041i	−0.0921142	−	0.463090i
$814$		0			0
$815$	−3.94045	+	6.82506i	−0.138028	+	0.239071i
$816$		0			0
$817$	18.6976	−	10.7950i	0.654145	−	0.377671i
$818$		0			0
$819$	0.986973	−	4.55635i	0.0344876	−	0.159212i
$820$		0			0
$821$	−6.96339	−	0.456404i	−0.243024	−	0.0159286i	−0.0565955	−	0.998397i	$-0.518025\pi$
$821$	−6.96339	−	0.456404i	−0.243024	−	0.0159286i	−0.186428	+	0.982469i	$0.559691\pi$
$822$		0			0
$823$	−27.3781	+	1.79445i	−0.954340	+	0.0625508i	−0.534611	−	0.845098i	$-0.679542\pi$
$823$	−27.3781	+	1.79445i	−0.954340	+	0.0625508i	−0.419730	+	0.907649i	$0.637875\pi$
$824$		0			0
$825$	−12.7704	−	30.8304i	−0.444607	−	1.07338i
$826$		0			0
$827$	−4.63314	+	23.2924i	−0.161110	+	0.809955i	0.812716	+	0.582660i	$0.197988\pi$
$827$	−4.63314	+	23.2924i	−0.161110	+	0.809955i	−0.973826	+	0.227295i	$0.927012\pi$
$828$		0			0
$829$	−5.68451	+	1.52316i	−0.197431	+	0.0529015i	−0.356179	−	0.934418i	$-0.615921\pi$
$829$	−5.68451	+	1.52316i	−0.197431	+	0.0529015i	0.158748	+	0.987319i	$0.449254\pi$
$830$		0			0
$831$	3.89349	+	29.5740i	0.135064	+	1.02591i
$832$		0			0
$833$	17.8966	+	22.6431i	0.620081	+	0.784538i
$834$		0			0
$835$	−0.157249	−	1.19443i	−0.00544184	−	0.0413349i
$836$		0			0
$837$	21.7017	−	5.81495i	0.750120	−	0.200994i
$838$		0			0
$839$	8.03308	−	40.3850i	0.277333	−	1.39425i	−0.551232	−	0.834352i	$-0.685842\pi$
$839$	8.03308	−	40.3850i	0.277333	−	1.39425i	0.828565	−	0.559893i	$-0.189158\pi$
$840$		0			0
$841$	−10.8965	−	26.3066i	−0.375742	−	0.907123i
$842$		0			0
$843$	−26.0324	+	1.70626i	−0.896605	+	0.0587666i
$844$		0			0
$845$	3.71660	+	0.243599i	0.127855	+	0.00838006i
$846$		0			0
$847$	1.60417	−	7.40563i	0.0551199	−	0.254460i
$848$		0			0
$849$	−5.47388	+	3.16035i	−0.187863	+	0.108463i
$850$		0			0
$851$	−34.1948	+	59.2271i	−1.17218	+	2.03028i
$852$		0			0
$853$	11.1168	+	55.8879i	0.380632	+	1.91357i	0.405967	+	0.913888i	$0.366935\pi$
$853$	11.1168	+	55.8879i	0.380632	+	1.91357i	−0.0253351	+	0.999679i	$0.508065\pi$
$854$		0			0
$855$	1.04054	−	1.55728i	0.0355858	−	0.0532580i
$856$		0			0
$857$	0.233777	+	3.56675i	0.00798567	+	0.121838i	0.999990	−	0.00436224i	$-0.00138855\pi$
$857$	0.233777	+	3.56675i	0.00798567	+	0.121838i	−0.992005	+	0.126200i	$0.959722\pi$
$858$		0			0
$859$	−4.30752	+	5.61367i	−0.146971	+	0.191536i	−0.861037	−	0.508542i	$-0.830185\pi$
$859$	−4.30752	+	5.61367i	−0.146971	+	0.191536i	0.714067	+	0.700078i	$0.246851\pi$
$860$		0			0
$861$	−47.6384	−	3.93524i	−1.62351	−	0.134113i
$862$		0			0
$863$	10.9097	+	2.92325i	0.371371	+	0.0995086i	0.439677	−	0.898156i	$-0.355093\pi$
$863$	10.9097	+	2.92325i	0.371371	+	0.0995086i	−0.0683062	+	0.997664i	$0.521759\pi$
$864$		0			0
$865$	3.77830	+	4.92397i	0.128466	+	0.167420i
$866$		0			0
$867$	−23.7937	−	22.3569i	−0.808078	−	0.759282i
$868$		0			0
$869$	−24.4481	−	10.1267i	−0.829344	−	0.343525i
$870$		0			0
$871$	4.98858	+	18.6176i	0.169031	+	0.630834i
$872$		0			0
$873$	5.22482	−	1.77359i	0.176833	−	0.0600269i
$874$		0			0
$875$	7.60036	−	12.6630i	0.256939	−	0.428087i
$876$		0			0
$877$	30.0249	+	14.8067i	1.01387	+	0.499986i	0.871795	−	0.489870i	$-0.162956\pi$
$877$	30.0249	+	14.8067i	1.01387	+	0.499986i	0.142075	+	0.989856i	$0.454623\pi$
$878$		0			0
$879$	−49.9663	+	24.6407i	−1.68532	+	0.831109i
$880$		0			0
$881$	26.5811	−	5.28731i	0.895540	−	0.178134i	0.274198	−	0.961673i	$-0.411588\pi$
$881$	26.5811	−	5.28731i	0.895540	−	0.178134i	0.621342	+	0.783539i	$0.286588\pi$
$882$		0			0
$883$		−	12.6667i		−	0.426268i	−0.977023	−	0.213134i	$-0.931633\pi$
$883$		−	12.6667i		−	0.426268i	0.977023	−	0.213134i	$-0.0683672\pi$
$884$		0			0
$885$	−10.3535	−	5.97761i	−0.348030	−	0.200935i
$886$		0			0
$887$	22.4111	−	19.6540i	0.752491	−	0.659917i	−0.194600	−	0.980883i	$-0.562341\pi$
$887$	22.4111	−	19.6540i	0.752491	−	0.659917i	0.947091	+	0.320966i	$0.104008\pi$
$888$		0			0
$889$	−0.517811	−	10.6725i	−0.0173668	−	0.357943i
$890$		0			0
$891$	17.4424	−	35.3696i	0.584342	−	1.18493i
$892$		0			0
$893$	1.69805	−	12.8980i	0.0568231	−	0.431614i
$894$		0			0
$895$	9.14329	+	1.81871i	0.305627	+	0.0607929i
$896$		0			0
$897$	19.8910	−	19.8910i	0.664140	−	0.664140i
$898$		0			0
$899$	2.91196	−	2.23443i	0.0971193	−	0.0745223i
$900$		0			0
$901$	53.4288	−	25.2176i	1.77997	−	0.840119i
$902$		0			0
$903$	−22.3890	−	6.40822i	−0.745060	−	0.213252i
$904$		0			0
$905$	−3.67745	+	13.7244i	−0.122243	+	0.456216i
$906$		0			0
$907$	−16.6948	+	19.0368i	−0.554341	+	0.632105i	−0.959354	−	0.282206i	$-0.908934\pi$
$907$	−16.6948	+	19.0368i	−0.554341	+	0.632105i	0.405013	+	0.914311i	$0.367267\pi$
$908$		0			0
$909$	−0.880401	+	0.364674i	−0.0292010	+	0.0120955i
$910$		0			0
$911$	−18.6646	+	12.4713i	−0.618386	+	0.413192i	−0.824922	−	0.565247i	$-0.808781\pi$
$911$	−18.6646	+	12.4713i	−0.618386	+	0.413192i	0.206536	+	0.978439i	$0.433781\pi$
$912$		0			0
$913$	4.30115	+	8.72188i	0.142347	+	0.288652i
$914$		0			0
$915$	5.92824	+	6.75987i	0.195982	+	0.223474i
$916$		0			0
$917$	−15.9081	−	6.90790i	−0.525332	−	0.228119i
$918$		0			0
$919$	1.78461	+	3.09104i	0.0588689	+	0.101964i	0.893958	−	0.448151i	$-0.147917\pi$
$919$	1.78461	+	3.09104i	0.0588689	+	0.101964i	−0.835089	+	0.550115i	$0.814584\pi$
$920$		0			0
$921$	−1.53883	+	4.53324i	−0.0507061	+	0.149375i
$922$		0			0
$923$	−7.02755	−	4.69566i	−0.231315	−	0.154560i
$924$		0			0
$925$	30.9815	+	46.3670i	1.01866	+	1.52454i
$926$		0			0
$927$	3.16464	+	0.416633i	0.103940	+	0.0136840i
$928$		0			0
$929$	−0.0951841	−	0.280403i	−0.00312289	−	0.00919974i	0.945358	−	0.326036i	$-0.105713\pi$
$929$	−0.0951841	−	0.280403i	−0.00312289	−	0.00919974i	−0.948480	+	0.316836i	$0.897380\pi$
$930$		0			0
$931$	−27.9818	−	17.4474i	−0.917067	−	0.571814i
$932$		0			0
$933$	−60.1760	+	7.92232i	−1.97007	+	0.259365i
$934$		0			0
$935$	−7.45467	+	4.79806i	−0.243794	+	0.156913i
$936$		0			0
$937$	2.05827	−	4.96910i	0.0672408	−	0.162334i	−0.886687	−	0.462370i	$-0.846999\pi$
$937$	2.05827	−	4.96910i	0.0672408	−	0.162334i	0.953928	+	0.300037i	$0.0969990\pi$
$938$		0			0
$939$	24.6525	+	24.6525i	0.804503	+	0.804503i
$940$		0			0
$941$	27.4124	+	24.0401i	0.893620	+	0.783684i	0.977090	−	0.212827i	$-0.0682669\pi$
$941$	27.4124	+	24.0401i	0.893620	+	0.783684i	−0.0834700	+	0.996510i	$0.526600\pi$
$942$		0			0
$943$	−42.7119	−	32.7740i	−1.39089	−	1.06727i
$944$		0			0
$945$	6.67372	−	1.21014i	0.217096	−	0.0393659i
$946$		0			0
$947$	2.72960	−	41.6457i	0.0887002	−	1.35330i	−0.689043	−	0.724721i	$-0.741969\pi$
$947$	2.72960	−	41.6457i	0.0887002	−	1.35330i	0.777743	−	0.628583i	$-0.216365\pi$
$948$		0			0
$949$	−31.6632	−	10.7482i	−1.02783	−	0.348902i
$950$		0			0
$951$	50.4610			1.63631
$952$		0			0
$953$	6.60890			0.214083			0.107042	−	0.994255i	$-0.465862\pi$
$953$	6.60890			0.214083			0.107042	+	0.994255i	$0.465862\pi$
$954$		0			0
$955$	−8.98921	−	3.05143i	−0.290884	−	0.0987418i
$956$		0			0
$957$	0.339200	−	5.17519i	0.0109648	−	0.167290i
$958$		0			0
$959$	−10.6484	+	9.02340i	−0.343855	+	0.291381i
$960$		0			0
$961$	4.27380	+	3.27940i	0.137865	+	0.105787i
$962$		0			0
$963$	−1.88790	−	1.65564i	−0.0608366	−	0.0533523i
$964$		0			0
$965$	−10.2083	−	10.2083i	−0.328616	−	0.328616i
$966$		0			0
$967$	17.0120	−	41.0706i	0.547069	−	1.32074i	−0.372580	−	0.928000i	$-0.621527\pi$
$967$	17.0120	−	41.0706i	0.547069	−	1.32074i	0.919649	−	0.392741i	$-0.128473\pi$
$968$		0			0
$969$	34.2134	+	14.8646i	1.09909	+	0.477521i
$970$		0			0
$971$	43.6710	−	5.74940i	1.40147	−	0.184507i	0.608397	−	0.793633i	$-0.291813\pi$
$971$	43.6710	−	5.74940i	1.40147	−	0.184507i	0.793073	+	0.609126i	$0.208480\pi$
$972$		0			0
$973$	2.33764	−	15.6935i	0.0749413	−	0.503109i
$974$		0			0
$975$	−7.37297	−	21.7201i	−0.236124	−	0.695599i
$976$		0			0
$977$	25.7706	+	3.39277i	0.824475	+	0.108544i	0.530946	−	0.847406i	$-0.321837\pi$
$977$	25.7706	+	3.39277i	0.824475	+	0.108544i	0.293529	+	0.955950i	$0.405170\pi$
$978$		0			0
$979$	−30.9692	−	46.3487i	−0.989779	−	1.48131i
$980$		0			0
$981$	−5.43786	−	3.63346i	−0.173617	−	0.116007i
$982$		0			0
$983$	−2.58296	+	7.60914i	−0.0823835	+	0.242694i	−0.980315	−	0.197442i	$-0.936737\pi$
$983$	−2.58296	+	7.60914i	−0.0823835	+	0.242694i	0.897931	+	0.440136i	$0.145070\pi$
$984$		0			0
$985$	−1.18627	−	2.05468i	−0.0377977	−	0.0654676i
$986$		0			0
$987$	−11.2760	+	8.35224i	−0.358919	+	0.265855i
$988$		0			0
$989$	−17.2940	−	19.7200i	−0.549916	−	0.627059i
$990$		0			0
$991$	−23.4045	−	47.4597i	−0.743469	−	1.50761i	−0.857699	−	0.514152i	$-0.828107\pi$
$991$	−23.4045	−	47.4597i	−0.743469	−	1.50761i	0.114230	−	0.993454i	$-0.463560\pi$
$992$		0			0
$993$	43.3456	−	28.9626i	1.37553	−	0.919100i
$994$		0			0
$995$	3.41966	−	1.41647i	0.108411	−	0.0449051i
$996$		0			0
$997$	−17.3449	+	19.7780i	−0.549317	+	0.626376i	−0.958162	−	0.286228i	$-0.907599\pi$
$997$	−17.3449	+	19.7780i	−0.549317	+	0.626376i	0.408844	+	0.912604i	$0.365932\pi$
$998$		0			0
$999$	−13.7304	+	51.2426i	−0.434411	+	1.62124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.465.4	yes	192
7.5	odd	6	inner	476.2.bl.a.397.4	yes	192
17.3	odd	16	inner	476.2.bl.a.241.4	yes	192
119.54	even	48	inner	476.2.bl.a.173.4	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.173.4	✓	192	119.54	even	48	inner
476.2.bl.a.241.4	yes	192	17.3	odd	16	inner
476.2.bl.a.397.4	yes	192	7.5	odd	6	inner
476.2.bl.a.465.4	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)

\(f(q)\)	\(=\)	\(q+(-1.81862 - 0.617339i) q^{3} +(-0.0377679 + 0.576227i) q^{5} +(-2.49055 - 0.892839i) q^{7} +(0.546221 + 0.419130i) q^{9} +O(q^{10})\)	\(q+(-1.81862 - 0.617339i) q^{3} +(-0.0377679 + 0.576227i) q^{5} +(-2.49055 - 0.892839i) q^{7} +(0.546221 + 0.419130i) q^{9} +(2.79943 + 2.45503i) q^{11} +(1.80971 + 1.80971i) q^{13} +(0.424413 - 1.02462i) q^{15} +(4.02948 + 0.873664i) q^{17} +(-4.67050 + 0.614884i) q^{19} +(3.97819 + 3.16125i) q^{21} +(1.83959 + 5.41926i) q^{23} +(4.62661 + 0.609105i) q^{25} +(2.46637 + 3.69118i) q^{27} +(0.603025 + 0.402928i) q^{29} +(1.62678 - 4.79234i) q^{31} +(-3.57552 - 6.19297i) q^{33} +(0.608541 - 1.40140i) q^{35} +(7.87919 + 8.98449i) q^{37} +(-2.17398 - 4.40839i) q^{39} +(-7.82180 + 5.22636i) q^{41} +(-4.23423 + 1.75388i) q^{43} +(-0.262144 + 0.298917i) q^{45} +(-0.714750 + 2.66748i) q^{47} +(5.40568 + 4.44732i) q^{49} +(-6.78876 - 4.07642i) q^{51} +(11.3681 - 8.72309i) q^{53} +(-1.52039 + 1.52039i) q^{55} +(8.87348 + 1.76504i) q^{57} +(1.40704 - 10.6875i) q^{59} +(-3.58566 + 7.27100i) q^{61} +(-0.986174 - 1.53155i) q^{63} +(-1.11115 + 0.974456i) q^{65} +(6.52209 + 3.76553i) q^{67} -10.9912i q^{69} +(-3.23897 + 0.644272i) q^{71} +(-11.7177 + 5.77855i) q^{73} +(-8.03804 - 3.96392i) q^{75} +(-4.78017 - 8.61382i) q^{77} +(-6.72981 + 2.28446i) q^{79} +(-2.74127 - 10.2306i) q^{81} +(2.41296 + 0.999482i) q^{83} +(-0.655614 + 2.28890i) q^{85} +(-0.847931 - 1.10505i) q^{87} +(-14.4607 - 3.87474i) q^{89} +(-2.89140 - 6.12296i) q^{91} +(-5.91700 + 7.71119i) q^{93} +(-0.177917 - 2.71449i) q^{95} +(4.45237 - 6.66344i) q^{97} +(0.500128 + 2.51431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 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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