LMFDB - Embedded newform 476.2.bl.a.173.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [476,2,Mod(5,476)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("476.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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

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			173.6
Character	$\chi$	$=$	476.173
Dual form			476.2.bl.a.465.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0684794 - 0.0232456i) q^{3} +(-0.0410628 - 0.626497i) q^{5} +(2.51365 + 0.825556i) q^{7} +(-2.37591 + 1.82310i) q^{9} +(1.81936 - 1.59554i) q^{11} +(3.67133 - 3.67133i) q^{13} +(-0.0173753 - 0.0419476i) q^{15} +(0.282728 + 4.11340i) q^{17} +(2.90088 + 0.381908i) q^{19} +(0.191324 - 0.00189788i) q^{21} +(-0.901573 + 2.65595i) q^{23} +(4.56641 - 0.601180i) q^{25} +(-0.240854 + 0.360463i) q^{27} +(2.78844 - 1.86318i) q^{29} +(-2.44853 - 7.21314i) q^{31} +(0.0874997 - 0.151554i) q^{33} +(0.413991 - 1.60870i) q^{35} +(1.78609 - 2.03665i) q^{37} +(0.166068 - 0.336753i) q^{39} +(5.57345 + 3.72406i) q^{41} +(-7.87683 - 3.26269i) q^{43} +(1.23973 + 1.41364i) q^{45} +(1.97680 + 7.37750i) q^{47} +(5.63691 + 4.15032i) q^{49} +(0.114980 + 0.275111i) q^{51} +(-3.60948 - 2.76965i) q^{53} +(-1.07431 - 1.07431i) q^{55} +(0.207528 - 0.0412799i) q^{57} +(0.0570842 + 0.433597i) q^{59} +(4.53760 + 9.20135i) q^{61} +(-7.47729 + 2.62120i) q^{63} +(-2.45083 - 2.14932i) q^{65} +(-1.33687 + 0.771844i) q^{67} +0.202835i q^{69} +(-9.56540 - 1.90268i) q^{71} +(-5.17314 - 2.55111i) q^{73} +(0.298730 - 0.147318i) q^{75} +(5.89046 - 2.50865i) q^{77} +(-15.7351 - 5.34133i) q^{79} +(2.31720 - 8.64789i) q^{81} +(-9.91914 + 4.10864i) q^{83} +(2.56542 - 0.346036i) q^{85} +(0.147640 - 0.192408i) q^{87} +(-11.9769 + 3.20920i) q^{89} +(12.2593 - 6.19756i) q^{91} +(-0.335348 - 0.437034i) q^{93} +(0.120146 - 1.83308i) q^{95} +(-5.03836 - 7.54044i) q^{97} +(-1.41382 + 7.10774i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{6}\right)$

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
$3$	0.0684794	−	0.0232456i	0.0395366	−	0.0134209i	−0.301601	−	0.953434i	$-0.597521\pi$
$3$	0.0684794	−	0.0232456i	0.0395366	−	0.0134209i	0.341138	+	0.940013i	$0.389188\pi$
$4$		0			0
$5$	−0.0410628	−	0.626497i	−0.0183638	−	0.280178i	−0.997158	−	0.0753336i	$-0.975998\pi$
$5$	−0.0410628	−	0.626497i	−0.0183638	−	0.280178i	0.978795	−	0.204844i	$-0.0656688\pi$
$6$		0			0
$7$	2.51365	+	0.825556i	0.950072	+	0.312031i
$7$	2.51365	+	0.825556i	0.950072	+	0.312031i
$8$		0			0
$9$	−2.37591	+	1.82310i	−0.791970	+	0.607700i
$10$		0			0
$11$	1.81936	−	1.59554i	0.548559	−	0.481073i	−0.339625	−	0.940561i	$-0.610300\pi$
$11$	1.81936	−	1.59554i	0.548559	−	0.481073i	0.888184	+	0.459488i	$0.151967\pi$
$12$		0			0
$13$	3.67133	−	3.67133i	1.01824	−	1.01824i	0.0184124	−	0.999830i	$-0.494139\pi$
$13$	3.67133	−	3.67133i	1.01824	−	1.01824i	0.999830	−	0.0184124i	$-0.00586119\pi$
$14$		0			0
$15$	−0.0173753	−	0.0419476i	−0.00448628	−	0.0108308i
$16$		0			0
$17$	0.282728	+	4.11340i	0.0685717	+	0.997646i
$17$	0.282728	+	4.11340i	0.0685717	+	0.997646i
$18$		0			0
$19$	2.90088	+	0.381908i	0.665508	+	0.0876157i	0.455709	−	0.890129i	$-0.349386\pi$
$19$	2.90088	+	0.381908i	0.665508	+	0.0876157i	0.209799	+	0.977745i	$0.432719\pi$
$20$		0			0
$21$	0.191324	−	0.00189788i	0.0417503	−	0.000414151i
$22$		0			0
$23$	−0.901573	+	2.65595i	−0.187991	+	0.553803i	−0.999535	−	0.0304876i	$-0.990294\pi$
$23$	−0.901573	+	2.65595i	−0.187991	+	0.553803i	0.811544	+	0.584291i	$0.198627\pi$
$24$		0			0
$25$	4.56641	−	0.601180i	0.913282	−	0.120236i
$26$		0			0
$27$	−0.240854	+	0.360463i	−0.0463523	+	0.0693712i
$28$		0			0
$29$	2.78844	−	1.86318i	0.517800	−	0.345983i	−0.269051	−	0.963126i	$-0.586710\pi$
$29$	2.78844	−	1.86318i	0.517800	−	0.345983i	0.786851	+	0.617143i	$0.211710\pi$
$30$		0			0
$31$	−2.44853	−	7.21314i	−0.439769	−	1.29552i	−0.910598	−	0.413294i	$-0.864378\pi$
$31$	−2.44853	−	7.21314i	−0.439769	−	1.29552i	0.470828	−	0.882225i	$-0.343955\pi$
$32$		0			0
$33$	0.0874997	−	0.151554i	0.0152317	−	0.0263821i
$34$		0			0
$35$	0.413991	−	1.60870i	0.0699772	−	0.271919i
$36$		0			0
$37$	1.78609	−	2.03665i	0.293632	−	0.334823i	−0.586148	−	0.810204i	$-0.699356\pi$
$37$	1.78609	−	2.03665i	0.293632	−	0.334823i	0.879780	+	0.475381i	$0.157690\pi$
$38$		0			0
$39$	0.166068	−	0.336753i	0.0265922	−	0.0539236i
$40$		0			0
$41$	5.57345	+	3.72406i	0.870427	+	0.581601i	0.908599	−	0.417670i	$-0.137153\pi$
$41$	5.57345	+	3.72406i	0.870427	+	0.581601i	−0.0381716	+	0.999271i	$0.512153\pi$
$42$		0			0
$43$	−7.87683	−	3.26269i	−1.20120	−	0.497555i	−0.309817	−	0.950796i	$-0.600268\pi$
$43$	−7.87683	−	3.26269i	−1.20120	−	0.497555i	−0.891388	+	0.453241i	$0.850268\pi$
$44$		0			0
$45$	1.23973	+	1.41364i	0.184808	+	0.210733i
$46$		0			0
$47$	1.97680	+	7.37750i	0.288345	+	1.07612i	0.946360	+	0.323114i	$0.104730\pi$
$47$	1.97680	+	7.37750i	0.288345	+	1.07612i	−0.658015	+	0.753005i	$0.728604\pi$
$48$		0			0
$49$	5.63691	+	4.15032i	0.805273	+	0.592904i
$50$		0			0
$51$	0.114980	+	0.275111i	0.0161004	+	0.0385233i
$52$		0			0
$53$	−3.60948	−	2.76965i	−0.495800	−	0.380441i	0.330379	−	0.943848i	$-0.392823\pi$
$53$	−3.60948	−	2.76965i	−0.495800	−	0.380441i	−0.826179	+	0.563407i	$0.809490\pi$
$54$		0			0
$55$	−1.07431	−	1.07431i	−0.144860	−	0.144860i
$56$		0			0
$57$	0.207528	−	0.0412799i	0.0274878	−	0.00546766i
$58$		0			0
$59$	0.0570842	+	0.433597i	0.00743173	+	0.0564496i	0.994759	−	0.102249i	$-0.0326037\pi$
$59$	0.0570842	+	0.433597i	0.00743173	+	0.0564496i	−0.987327	+	0.158698i	$0.949270\pi$
$60$		0			0
$61$	4.53760	+	9.20135i	0.580981	+	1.17811i	0.966799	+	0.255538i	$0.0822524\pi$
$61$	4.53760	+	9.20135i	0.580981	+	1.17811i	−0.385818	+	0.922575i	$0.626081\pi$
$62$		0			0
$63$	−7.47729	+	2.62120i	−0.942050	+	0.330240i
$64$		0			0
$65$	−2.45083	−	2.14932i	−0.303988	−	0.266590i
$66$		0			0
$67$	−1.33687	+	0.771844i	−0.163325	+	0.0942957i	−0.579435	−	0.815019i	$-0.696727\pi$
$67$	−1.33687	+	0.771844i	−0.163325	+	0.0942957i	0.416110	+	0.909314i	$0.363393\pi$
$68$		0			0
$69$			0.202835i			0.0244185i
$70$		0			0
$71$	−9.56540	−	1.90268i	−1.13520	−	0.225806i	−0.408501	−	0.912758i	$-0.633948\pi$
$71$	−9.56540	−	1.90268i	−1.13520	−	0.225806i	−0.726703	+	0.686952i	$0.758948\pi$
$72$		0			0
$73$	−5.17314	−	2.55111i	−0.605470	−	0.298585i	0.113596	−	0.993527i	$-0.463763\pi$
$73$	−5.17314	−	2.55111i	−0.605470	−	0.298585i	−0.719065	+	0.694942i	$0.755430\pi$
$74$		0			0
$75$	0.298730	−	0.147318i	0.0344944	−	0.0170108i
$76$		0			0
$77$	5.89046	−	2.50865i	0.671280	−	0.285887i
$78$		0			0
$79$	−15.7351	−	5.34133i	−1.77033	−	0.600947i	−0.770977	−	0.636862i	$-0.780232\pi$
$79$	−15.7351	−	5.34133i	−1.77033	−	0.600947i	−0.999355	+	0.0359155i	$0.988565\pi$
$80$		0			0
$81$	2.31720	−	8.64789i	0.257466	−	0.960877i
$82$		0			0
$83$	−9.91914	+	4.10864i	−1.08877	+	0.450982i	−0.853577	−	0.520967i	$-0.825571\pi$
$83$	−9.91914	+	4.10864i	−1.08877	+	0.450982i	−0.235190	+	0.971949i	$0.575571\pi$
$84$		0			0
$85$	2.56542	−	0.346036i	0.278259	−	0.0375329i
$86$		0			0
$87$	0.147640	−	0.192408i	0.0158287	−	0.0206283i
$88$		0			0
$89$	−11.9769	+	3.20920i	−1.26955	+	0.340175i	−0.829858	−	0.557974i	$-0.811579\pi$
$89$	−11.9769	+	3.20920i	−1.26955	+	0.340175i	−0.439691	+	0.898149i	$0.644912\pi$
$90$		0			0
$91$	12.2593	−	6.19756i	1.28513	−	0.649681i
$92$		0			0
$93$	−0.335348	−	0.437034i	−0.0347740	−	0.0453183i
$94$		0			0
$95$	0.120146	−	1.83308i	0.0123267	−	0.188070i
$96$		0			0
$97$	−5.03836	−	7.54044i	−0.511568	−	0.765616i	0.482322	−	0.875994i	$-0.339794\pi$
$97$	−5.03836	−	7.54044i	−0.511568	−	0.765616i	−0.993890	+	0.110379i	$0.964794\pi$
$98$		0			0
$99$	−1.41382	+	7.10774i	−0.142094	+	0.714355i
$100$		0			0
$101$	2.85907	+	4.95205i	0.284488	+	0.492748i	0.972485	−	0.232966i	$-0.0748431\pi$
$101$	2.85907	+	4.95205i	0.284488	+	0.492748i	−0.687997	+	0.725714i	$0.741510\pi$
$102$		0			0
$103$	0.144141	+	0.0832197i	0.0142026	+	0.00819988i	0.507084	−	0.861896i	$-0.330723\pi$
$103$	0.144141	+	0.0832197i	0.0142026	+	0.00819988i	−0.492882	+	0.870096i	$0.664057\pi$
$104$		0			0
$105$	−0.00904532	−	0.119786i	−0.000882733	−	0.0116899i
$106$		0			0
$107$	−3.31804	+	0.217476i	−0.320767	+	0.0210242i	−0.224936	−	0.974373i	$-0.572217\pi$
$107$	−3.31804	+	0.217476i	−0.320767	+	0.0210242i	−0.0958308	+	0.995398i	$0.530551\pi$
$108$		0			0
$109$	4.34420	+	0.284734i	0.416099	+	0.0272726i	0.272015	−	0.962293i	$-0.412310\pi$
$109$	4.34420	+	0.284734i	0.416099	+	0.0272726i	0.144084	+	0.989566i	$0.453977\pi$
$110$		0			0
$111$	0.0749675	−	0.180988i	0.00711560	−	0.0171786i
$112$		0			0
$113$	0.319206	+	1.60476i	0.0300284	+	0.150963i	0.992891	−	0.119030i	$-0.0379786\pi$
$113$	0.319206	+	1.60476i	0.0300284	+	0.150963i	−0.962862	+	0.269993i	$0.912979\pi$
$114$		0			0
$115$	1.70096	+	0.455772i	0.158616	+	0.0425010i
$116$		0			0
$117$	−2.02955	+	15.4159i	−0.187632	+	1.42520i
$118$		0			0
$119$	−2.68516	+	10.5731i	−0.246148	+	0.969232i
$120$		0			0
$121$	−0.671449	+	5.10016i	−0.0610408	+	0.463651i
$122$		0			0
$123$	0.468235	+	0.125463i	0.0422193	+	0.0113126i
$124$		0			0
$125$	−1.17658	−	5.91505i	−0.105236	−	0.529058i
$126$		0			0
$127$	4.48797	−	10.8349i	0.398243	−	0.961444i	−0.589840	−	0.807520i	$-0.700809\pi$
$127$	4.48797	−	10.8349i	0.398243	−	0.961444i	0.988083	−	0.153923i	$-0.0491909\pi$
$128$		0			0
$129$	−0.615244	−	0.0403252i	−0.0541692	−	0.00355044i
$130$		0			0
$131$	−9.56160	+	0.626700i	−0.835401	+	0.0547551i	−0.477098	−	0.878850i	$-0.658311\pi$
$131$	−9.56160	+	0.626700i	−0.835401	+	0.0547551i	−0.358303	+	0.933605i	$0.616645\pi$
$132$		0			0
$133$	6.97652	+	3.35482i	0.604941	+	0.290900i
$134$		0			0
$135$	0.235719	+	0.136093i	0.0202875	+	0.0117130i
$136$		0			0
$137$	−9.47341	−	16.4084i	−0.809368	−	1.40187i	−0.913302	−	0.407283i	$-0.866476\pi$
$137$	−9.47341	−	16.4084i	−0.809368	−	1.40187i	0.103934	−	0.994584i	$-0.466857\pi$
$138$		0			0
$139$	−1.25504	+	6.30953i	−0.106451	+	0.535167i	0.890352	+	0.455273i	$0.150458\pi$
$139$	−1.25504	+	6.30953i	−0.106451	+	0.535167i	−0.996803	+	0.0798944i	$0.974542\pi$
$140$		0			0
$141$	0.306864	+	0.459255i	0.0258426	+	0.0386763i
$142$		0			0
$143$	0.821733	−	12.5372i	0.0687168	−	1.04842i
$144$		0			0
$145$	−1.28178	−	1.67044i	−0.106446	−	0.138723i
$146$		0			0
$147$	0.482490	+	0.153178i	0.0397951	+	0.0126339i
$148$		0			0
$149$	−20.6836	+	5.54217i	−1.69447	+	0.454032i	−0.971537	−	0.236886i	$-0.923873\pi$
$149$	−20.6836	+	5.54217i	−1.69447	+	0.454032i	−0.722933	+	0.690918i	$0.757206\pi$
$150$		0			0
$151$	−5.27237	+	6.87108i	−0.429059	+	0.559161i	−0.956988	−	0.290128i	$-0.906302\pi$
$151$	−5.27237	+	6.87108i	−0.429059	+	0.559161i	0.527929	+	0.849289i	$0.322969\pi$
$152$		0			0
$153$	−8.17088	−	9.25763i	−0.660577	−	0.748435i
$154$		0			0
$155$	−4.41847	+	1.83019i	−0.354900	+	0.147004i
$156$		0			0
$157$	−0.604756	+	2.25698i	−0.0482648	+	0.180127i	−0.985850	−	0.167628i	$-0.946389\pi$
$157$	−0.604756	+	2.25698i	−0.0482648	+	0.180127i	0.937586	+	0.347755i	$0.113056\pi$
$158$		0			0
$159$	−0.311557	−	0.105759i	−0.0247081	−	0.00838727i
$160$		0			0
$161$	−4.45888	+	5.93184i	−0.351409	+	0.467494i
$162$		0			0
$163$	−12.5537	+	6.19082i	−0.983284	+	0.484902i	−0.861557	−	0.507661i	$-0.830510\pi$
$163$	−12.5537	+	6.19082i	−0.983284	+	0.484902i	−0.121728	+	0.992564i	$0.538843\pi$
$164$		0			0
$165$	−0.0985410	−	0.0485951i	−0.00767141	−	0.00378312i
$166$		0			0
$167$	22.8768	+	4.55048i	1.77026	+	0.352127i	0.969166	−	0.246410i	$-0.0792510\pi$
$167$	22.8768	+	4.55048i	1.77026	+	0.352127i	0.801095	+	0.598537i	$0.204251\pi$
$168$		0			0
$169$		−	13.9573i		−	1.07364i
$170$		0			0
$171$	−7.58849	+	4.38122i	−0.580306	+	0.335040i
$172$		0			0
$173$	16.3565	+	14.3443i	1.24356	+	1.09057i	0.992454	+	0.122614i	$0.0391276\pi$
$173$	16.3565	+	14.3443i	1.24356	+	1.09057i	0.251106	+	0.967960i	$0.419206\pi$
$174$		0			0
$175$	11.9747	+	2.25867i	0.905201	+	0.170740i
$176$		0			0
$177$	0.0139883	+	0.0283655i	0.00105143	+	0.00213208i
$178$		0			0
$179$	−3.35750	−	25.5027i	−0.250951	−	1.90616i	−0.398604	−	0.917123i	$-0.630505\pi$
$179$	−3.35750	−	25.5027i	−0.250951	−	1.90616i	0.147653	−	0.989039i	$-0.452828\pi$
$180$		0			0
$181$	19.1010	−	3.79942i	1.41976	−	0.282408i	0.575265	−	0.817967i	$-0.304899\pi$
$181$	19.1010	−	3.79942i	1.41976	−	0.282408i	0.844498	+	0.535559i	$0.179899\pi$
$182$		0			0
$183$	0.524624	+	0.524624i	0.0387813	+	0.0387813i
$184$		0			0
$185$	−1.34930	−	1.03535i	−0.0992023	−	0.0761206i
$186$		0			0
$187$	7.07748	+	7.03267i	0.517557	+	0.514280i
$188$		0			0
$189$	−0.903006	+	0.707242i	−0.0656840	+	0.0514443i
$190$		0			0
$191$	−1.43880	−	5.36969i	−0.104108	−	0.388537i	0.894134	−	0.447799i	$-0.147792\pi$
$191$	−1.43880	−	5.36969i	−0.104108	−	0.388537i	−0.998242	+	0.0592617i	$0.981125\pi$
$192$		0			0
$193$	11.0491	+	12.5991i	0.795335	+	0.906906i	0.997370	−	0.0724725i	$-0.0230890\pi$
$193$	11.0491	+	12.5991i	0.795335	+	0.906906i	−0.202035	+	0.979378i	$0.564756\pi$
$194$		0			0
$195$	−0.217794	−	0.0902131i	−0.0155965	−	0.00646030i
$196$		0			0
$197$	18.1369	+	12.1187i	1.29220	+	0.863421i	0.995792	−	0.0916398i	$-0.0292108\pi$
$197$	18.1369	+	12.1187i	1.29220	+	0.863421i	0.296409	+	0.955061i	$0.404211\pi$
$198$		0			0
$199$	−2.25736	+	4.57748i	−0.160020	+	0.324489i	−0.962086	−	0.272747i	$-0.912068\pi$
$199$	−2.25736	+	4.57748i	−0.160020	+	0.324489i	0.802066	+	0.597236i	$0.203734\pi$
$200$		0			0
$201$	−0.0736063	+	0.0839319i	−0.00519179	+	0.00592010i
$202$		0			0
$203$	8.54733	−	2.38137i	0.599905	−	0.167139i
$204$		0			0
$205$	2.10425	−	3.64467i	0.146967	−	0.254555i
$206$		0			0
$207$	−2.70000	−	7.95395i	−0.187663	−	0.552838i
$208$		0			0
$209$	5.88711	−	3.93364i	0.407220	−	0.272096i
$210$		0			0
$211$	14.1614	−	21.1940i	0.974908	−	1.45905i	0.0885393	−	0.996073i	$-0.471780\pi$
$211$	14.1614	−	21.1940i	0.974908	−	1.45905i	0.886369	−	0.462980i	$-0.153220\pi$
$212$		0			0
$213$	−0.699262	+	0.0920596i	−0.0479126	+	0.00630782i
$214$		0			0
$215$	−1.72062	+	5.06878i	−0.117345	+	0.345688i
$216$		0			0
$217$	−0.199909	−	20.1527i	−0.0135707	−	1.36806i
$218$		0			0
$219$	−0.413556	−	0.0544456i	−0.0279455	−	0.00367909i
$220$		0			0
$221$	16.1396	+	14.0637i	1.08567	+	0.946023i
$222$		0			0
$223$	−0.291047	−	0.702650i	−0.0194900	−	0.0470529i	0.913835	−	0.406086i	$-0.133107\pi$
$223$	−0.291047	−	0.702650i	−0.0194900	−	0.0470529i	−0.933325	+	0.359033i	$0.883107\pi$
$224$		0			0
$225$	−9.75338	+	9.75338i	−0.650225	+	0.650225i
$226$		0			0
$227$	−4.43349	+	3.88807i	−0.294261	+	0.258060i	−0.793728	−	0.608273i	$-0.791863\pi$
$227$	−4.43349	+	3.88807i	−0.294261	+	0.258060i	0.499467	+	0.866333i	$0.333529\pi$
$228$		0			0
$229$	15.9411	−	12.2320i	1.05341	−	0.808313i	0.0714625	−	0.997443i	$-0.477233\pi$
$229$	15.9411	−	12.2320i	1.05341	−	0.808313i	0.981952	+	0.189130i	$0.0605667\pi$
$230$		0			0
$231$	0.345060	−	0.308718i	0.0227033	−	0.0203122i
$232$		0			0
$233$	0.984708	+	15.0237i	0.0645103	+	0.984238i	0.900323	+	0.435223i	$0.143330\pi$
$233$	0.984708	+	15.0237i	0.0645103	+	0.984238i	−0.835813	+	0.549015i	$0.815003\pi$
$234$		0			0
$235$	4.54081	−	1.54140i	0.296210	−	0.100550i
$236$		0			0
$237$	−1.20169			−0.0780582
$238$		0			0
$239$	−20.1344			−1.30239			−0.651193	−	0.758912i	$-0.725731\pi$
$239$	−20.1344			−1.30239			−0.651193	+	0.758912i	$0.725731\pi$
$240$		0			0
$241$	−4.35126	+	1.47705i	−0.280289	+	0.0951454i	−0.458044	−	0.888929i	$-0.651450\pi$
$241$	−4.35126	+	1.47705i	−0.280289	+	0.0951454i	0.177755	+	0.984075i	$0.443117\pi$
$242$		0			0
$243$	−0.127407	−	1.94386i	−0.00817318	−	0.124699i
$244$		0			0
$245$	2.36870	−	3.70193i	0.151331	−	0.236508i
$246$		0			0
$247$	12.0522	−	9.24797i	0.766863	−	0.588434i
$248$		0			0
$249$	−0.583749	+	0.511934i	−0.0369936	+	0.0324425i
$250$		0			0
$251$	−8.66466	+	8.66466i	−0.546908	+	0.546908i	−0.925545	−	0.378637i	$-0.876393\pi$
$251$	−8.66466	+	8.66466i	−0.546908	+	0.546908i	0.378637	+	0.925545i	$0.376393\pi$
$252$		0			0
$253$	2.59738	+	6.27063i	0.163296	+	0.394231i
$254$		0			0
$255$	0.167635	−	0.0833313i	0.0104977	−	0.00521841i
$256$		0			0
$257$	−0.971000	−	0.127835i	−0.0605693	−	0.00797410i	0.100181	−	0.994969i	$-0.468058\pi$
$257$	−0.971000	−	0.127835i	−0.0605693	−	0.00797410i	−0.160750	+	0.986995i	$0.551391\pi$
$258$		0			0
$259$	6.17099	−	3.64491i	0.383447	−	0.226484i
$260$		0			0
$261$	−3.22833	+	9.51035i	−0.199829	+	0.588676i
$262$		0			0
$263$	24.7165	−	3.25399i	1.52409	−	0.200650i	0.678545	−	0.734559i	$-0.262611\pi$
$263$	24.7165	−	3.25399i	1.52409	−	0.200650i	0.845542	+	0.533909i	$0.179277\pi$
$264$		0			0
$265$	−1.58696	+	2.37506i	−0.0974864	+	0.145899i
$266$		0			0
$267$	−0.745572	+	0.498175i	−0.0456282	+	0.0304878i
$268$		0			0
$269$	−3.68173	−	10.8460i	−0.224479	−	0.661293i	−0.999567	−	0.0294396i	$-0.990628\pi$
$269$	−3.68173	−	10.8460i	−0.224479	−	0.661293i	0.775088	−	0.631854i	$-0.217706\pi$
$270$		0			0
$271$	−6.36756	+	11.0289i	−0.386802	+	0.669961i	−0.992017	−	0.126101i	$-0.959754\pi$
$271$	−6.36756	+	11.0289i	−0.386802	+	0.669961i	0.605215	+	0.796062i	$0.293087\pi$
$272$		0			0
$273$	0.695446	−	0.709381i	0.0420903	−	0.0429337i
$274$		0			0
$275$	7.34876	−	8.37965i	0.443147	−	0.505312i
$276$		0			0
$277$	5.07519	−	10.2915i	0.304939	−	0.618354i	−0.689427	−	0.724355i	$-0.742138\pi$
$277$	5.07519	−	10.2915i	0.304939	−	0.618354i	0.994366	+	0.106000i	$0.0338045\pi$
$278$		0			0
$279$	18.9678	+	12.6739i	1.13557	+	0.758764i
$280$		0			0
$281$	−20.9857	−	8.69258i	−1.25190	−	0.518556i	−0.344489	−	0.938790i	$-0.611948\pi$
$281$	−20.9857	−	8.69258i	−1.25190	−	0.518556i	−0.907416	+	0.420234i	$0.861948\pi$
$282$		0			0
$283$	9.06187	+	10.3331i	0.538672	+	0.614238i	0.955587	−	0.294708i	$-0.0952222\pi$
$283$	9.06187	+	10.3331i	0.538672	+	0.614238i	−0.416915	+	0.908945i	$0.636889\pi$
$284$		0			0
$285$	−0.0343835	−	0.128321i	−0.00203670	−	0.00760107i
$286$		0			0
$287$	10.9353	+	13.9622i	0.645491	+	0.824163i
$288$		0			0
$289$	−16.8401	+	2.32595i	−0.990596	+	0.136821i
$290$		0			0
$291$	−0.520306	−	0.399245i	−0.0305009	−	0.0234042i
$292$		0			0
$293$	−10.9937	−	10.9937i	−0.642258	−	0.642258i	0.308852	−	0.951110i	$-0.400055\pi$
$293$	−10.9937	−	10.9937i	−0.642258	−	0.642258i	−0.951110	+	0.308852i	$0.900055\pi$
$294$		0			0
$295$	0.269303	−	0.0535678i	0.0156795	−	0.00311884i
$296$		0			0
$297$	0.136933	+	1.04011i	0.00794563	+	0.0603531i
$298$		0			0
$299$	6.44088	+	13.0608i	0.372486	+	0.755327i
$300$		0			0
$301$	−17.1061	−	14.7040i	−0.985978	−	0.847526i
$302$		0			0
$303$	0.310901	+	0.272653i	0.0178608	+	0.0156635i
$304$		0			0
$305$	5.57829	−	3.22063i	0.319412	−	0.184413i
$306$		0			0
$307$		−	1.21378i		−	0.0692742i	−0.999400	−	0.0346371i	$-0.988972\pi$
$307$		−	1.21378i		−	0.0692742i	0.999400	−	0.0346371i	$-0.0110275\pi$
$308$		0			0
$309$	0.0118052	+	0.00234819i	0.000671572	+	0.000133584i
$310$		0			0
$311$	−1.10712	−	0.545971i	−0.0627791	−	0.0309592i	0.410628	−	0.911803i	$-0.365309\pi$
$311$	−1.10712	−	0.545971i	−0.0627791	−	0.0309592i	−0.473407	+	0.880844i	$0.656976\pi$
$312$		0			0
$313$	21.5525	−	10.6285i	1.21822	−	0.600760i	0.284470	−	0.958685i	$-0.408182\pi$
$313$	21.5525	−	10.6285i	1.21822	−	0.600760i	0.933750	+	0.357925i	$0.116516\pi$
$314$		0			0
$315$	1.94921	+	4.57687i	0.109826	+	0.257877i
$316$		0			0
$317$	11.9882	+	4.06946i	0.673326	+	0.228564i	0.637101	−	0.770780i	$-0.280133\pi$
$317$	11.9882	+	4.06946i	0.673326	+	0.228564i	0.0362252	+	0.999344i	$0.488467\pi$
$318$		0			0
$319$	2.10042	−	7.83886i	0.117601	−	0.438892i
$320$		0			0
$321$	−0.222162	+	0.0920226i	−0.0123999	+	0.00513620i
$322$		0			0
$323$	−0.750780	+	12.0405i	−0.0417745	+	0.669949i
$324$		0			0
$325$	14.5577	−	18.9719i	0.807514	−	1.05237i
$326$		0			0
$327$	0.304107	−	0.0814852i	0.0168172	−	0.00450614i
$328$		0			0
$329$	−1.12156	+	20.1764i	−0.0618336	+	1.11236i
$330$		0			0
$331$	1.20168	+	1.56605i	0.0660501	+	0.0860781i	0.825210	−	0.564826i	$-0.191057\pi$
$331$	1.20168	+	1.56605i	0.0660501	+	0.0860781i	−0.759160	+	0.650904i	$0.774390\pi$
$332$		0			0
$333$	−0.530583	+	8.09513i	−0.0290758	+	0.443610i
$334$		0			0
$335$	0.538454	+	0.805853i	0.0294189	+	0.0440284i
$336$		0			0
$337$	3.79396	−	19.0735i	0.206670	−	1.03900i	−0.728566	−	0.684975i	$-0.759813\pi$
$337$	3.79396	−	19.0735i	0.206670	−	1.03900i	0.935236	−	0.354025i	$-0.115187\pi$
$338$		0			0
$339$	0.0591626	+	0.102473i	0.00321327	+	0.00556555i
$340$		0			0
$341$	−15.9636	−	9.21660i	−0.864479	−	0.499107i
$342$		0			0
$343$	10.7429	+	15.0861i	0.580064	+	0.814571i
$344$		0			0
$345$	0.127076	−	0.00832899i	0.00684153	−	0.000448418i
$346$		0			0
$347$	−1.11513	−	0.0730894i	−0.0598633	−	0.00392365i	0.0354421	−	0.999372i	$-0.488716\pi$
$347$	−1.11513	−	0.0730894i	−0.0598633	−	0.00392365i	−0.0953053	+	0.995448i	$0.530383\pi$
$348$		0			0
$349$	−5.88275	+	14.2022i	−0.314897	+	0.760228i	0.684613	+	0.728907i	$0.259971\pi$
$349$	−5.88275	+	14.2022i	−0.314897	+	0.760228i	−0.999509	+	0.0313207i	$0.990029\pi$
$350$		0			0
$351$	0.439125	+	2.20763i	0.0234388	+	0.117835i
$352$		0			0
$353$	−3.70446	−	0.992606i	−0.197168	−	0.0528311i	0.158883	−	0.987297i	$-0.449211\pi$
$353$	−3.70446	−	0.992606i	−0.197168	−	0.0528311i	−0.356052	+	0.934466i	$0.615877\pi$
$354$		0			0
$355$	−0.799239	+	6.07083i	−0.0424192	+	0.322206i
$356$		0			0
$357$	0.0618995	+	0.786456i	0.00327607	+	0.0416237i
$358$		0			0
$359$	0.384008	−	2.91683i	0.0202672	−	0.153944i	−0.978319	−	0.207104i	$-0.933596\pi$
$359$	0.384008	−	2.91683i	0.0202672	−	0.153944i	0.998586	+	0.0531601i	$0.0169294\pi$
$360$		0			0
$361$	−10.0833	−	2.70182i	−0.530702	−	0.142201i
$362$		0			0
$363$	0.0725760	+	0.364864i	0.00380925	+	0.0191504i
$364$		0			0
$365$	−1.38584	+	3.34571i	−0.0725381	+	0.175123i
$366$		0			0
$367$	30.7075	+	2.01267i	1.60292	+	0.105061i	0.840422	−	0.541933i	$-0.182307\pi$
$367$	30.7075	+	2.01267i	1.60292	+	0.105061i	0.762495	+	0.646994i	$0.223974\pi$
$368$		0			0
$369$	−20.0314	+	1.31293i	−1.04279	+	0.0683481i
$370$		0			0
$371$	−6.78648	−	9.94178i	−0.352337	−	0.516151i
$372$		0			0
$373$	−16.5517	−	9.55615i	−0.857017	−	0.494799i	0.00599552	−	0.999982i	$-0.498092\pi$
$373$	−16.5517	−	9.55615i	−0.857017	−	0.494799i	−0.863012	+	0.505183i	$0.831425\pi$
$374$		0			0
$375$	−0.218070	−	0.377709i	−0.0112611	−	0.0195048i
$376$		0			0
$377$	3.39695	−	17.0776i	0.174952	−	0.879542i
$378$		0			0
$379$	−7.71102	−	11.5404i	−0.396089	−	0.592789i	0.578803	−	0.815467i	$-0.303520\pi$
$379$	−7.71102	−	11.5404i	−0.396089	−	0.592789i	−0.974892	+	0.222679i	$0.928520\pi$
$380$		0			0
$381$	0.0554691	−	0.846295i	0.00284177	−	0.0433570i
$382$		0			0
$383$	−16.6083	−	21.6443i	−0.848643	−	1.10597i	−0.993194	−	0.116476i	$-0.962840\pi$
$383$	−16.6083	−	21.6443i	−0.848643	−	1.10597i	0.144551	−	0.989497i	$-0.453826\pi$
$384$		0			0
$385$	−1.81354	−	3.58734i	−0.0924265	−	0.182828i
$386$		0			0
$387$	24.6628	−	6.60839i	1.25368	−	0.335923i
$388$		0			0
$389$	−22.0998	+	28.8011i	−1.12051	+	1.46027i	−0.249914	+	0.968268i	$0.580402\pi$
$389$	−22.0998	+	28.8011i	−1.12051	+	1.46027i	−0.870593	+	0.492005i	$0.836264\pi$
$390$		0			0
$391$	−11.1799	−	2.95762i	−0.565391	−	0.149573i
$392$		0			0
$393$	−0.640205	+	0.265181i	−0.0322941	+	0.0133766i
$394$		0			0
$395$	−2.70020	+	10.0773i	−0.135862	+	0.507044i
$396$		0			0
$397$	−6.93312	−	2.35348i	−0.347963	−	0.118118i	0.141986	−	0.989869i	$-0.454651\pi$
$397$	−6.93312	−	2.35348i	−0.347963	−	0.118118i	−0.489949	+	0.871751i	$0.662985\pi$
$398$		0			0
$399$	0.555733	+	0.0675627i	0.0278215	+	0.00338237i
$400$		0			0
$401$	−16.3379	+	8.05697i	−0.815876	+	0.402346i	−0.801827	−	0.597556i	$-0.796139\pi$
$401$	−16.3379	+	8.05697i	−0.815876	+	0.402346i	−0.0140488	+	0.999901i	$0.504472\pi$
$402$		0			0
$403$	−35.4712	−	17.4924i	−1.76694	−	0.871361i
$404$		0			0
$405$	−5.51303	−	1.09661i	−0.273945	−	0.0544910i
$406$		0			0
$407$		−	6.55519i		−	0.324929i
$408$		0			0
$409$	−17.3134	+	9.99592i	−0.856094	+	0.494266i	−0.862702	−	0.505712i	$-0.831230\pi$
$409$	−17.3134	+	9.99592i	−0.856094	+	0.494266i	0.00660812	+	0.999978i	$0.497897\pi$
$410$		0			0
$411$	−1.03016	−	0.903424i	−0.0508140	−	0.0445626i
$412$		0			0
$413$	−0.214469	+	1.13704i	−0.0105533	+	0.0559501i
$414$		0			0
$415$	2.98136	+	6.04560i	0.146349	+	0.296767i
$416$		0			0
$417$	0.0607243	+	0.461247i	0.00297368	+	0.0225874i
$418$		0			0
$419$	−7.98251	+	1.58782i	−0.389971	+	0.0775701i	−0.386182	−	0.922423i	$-0.626206\pi$
$419$	−7.98251	+	1.58782i	−0.389971	+	0.0775701i	−0.00378943	+	0.999993i	$0.501206\pi$
$420$		0			0
$421$	16.5980	+	16.5980i	0.808938	+	0.808938i	0.984473	−	0.175535i	$-0.0561657\pi$
$421$	16.5980	+	16.5980i	0.808938	+	0.808938i	−0.175535	+	0.984473i	$0.556166\pi$
$422$		0			0
$423$	−18.1466	−	13.9244i	−0.882319	−	0.677027i
$424$		0			0
$425$	3.76395	+	18.6135i	0.182578	+	0.902888i
$426$		0			0
$427$	3.80974	+	26.8751i	0.184366	+	1.30058i
$428$		0			0
$429$	−0.235164	−	0.877644i	−0.0113538	−	0.0423730i
$430$		0			0
$431$	1.42154	+	1.62096i	0.0684733	+	0.0780789i	0.785062	−	0.619417i	$-0.212631\pi$
$431$	1.42154	+	1.62096i	0.0684733	+	0.0780789i	−0.716589	+	0.697496i	$0.754298\pi$
$432$		0			0
$433$	−10.1434	−	4.20152i	−0.487459	−	0.201912i	0.125397	−	0.992107i	$-0.459980\pi$
$433$	−10.1434	−	4.20152i	−0.487459	−	0.201912i	−0.612856	+	0.790194i	$0.709980\pi$
$434$		0			0
$435$	−0.126606	−	0.0845953i	−0.00607028	−	0.00405603i
$436$		0			0
$437$	−3.62968	+	7.36027i	−0.173631	+	0.352089i
$438$		0			0
$439$	−1.20995	+	1.37969i	−0.0577479	+	0.0658489i	−0.779993	−	0.625789i	$-0.784777\pi$
$439$	−1.20995	+	1.37969i	−0.0577479	+	0.0658489i	0.722245	+	0.691638i	$0.243110\pi$
$440$		0			0
$441$	−20.9593	+	0.415860i	−0.998060	+	0.0198028i
$442$		0			0
$443$	6.02389	−	10.4337i	0.286204	−	0.495719i	−0.686697	−	0.726944i	$-0.740940\pi$
$443$	6.02389	−	10.4337i	0.286204	−	0.495719i	0.972900	+	0.231225i	$0.0742733\pi$
$444$		0			0
$445$	2.50236	+	7.37172i	0.118623	+	0.349453i
$446$		0			0
$447$	−1.28757	+	0.860329i	−0.0609001	+	0.0406921i
$448$		0			0
$449$	6.14231	−	9.19262i	0.289874	−	0.433827i	−0.657740	−	0.753245i	$-0.728487\pi$
$449$	6.14231	−	9.19262i	0.289874	−	0.433827i	0.947614	+	0.319418i	$0.103487\pi$
$450$		0			0
$451$	16.0820	−	2.11724i	0.757273	−	0.0996969i
$452$		0			0
$453$	−0.201326	+	0.593087i	−0.00945912	+	0.0278657i
$454$		0			0
$455$	−4.38616	−	7.42595i	−0.205626	−	0.348134i
$456$		0			0
$457$	1.45796	+	0.191944i	0.0682005	+	0.00897877i	0.164549	−	0.986369i	$-0.447383\pi$
$457$	1.45796	+	0.191944i	0.0682005	+	0.00897877i	−0.0963487	+	0.995348i	$0.530716\pi$
$458$		0			0
$459$	−1.55083	−	0.888815i	−0.0723864	−	0.0414863i
$460$		0			0
$461$	−8.98903	−	21.7014i	−0.418661	−	1.01074i	−0.982736	−	0.185013i	$-0.940767\pi$
$461$	−8.98903	−	21.7014i	−0.418661	−	1.01074i	0.564075	−	0.825723i	$-0.309233\pi$
$462$		0			0
$463$	−25.2281	+	25.2281i	−1.17245	+	1.17245i	−0.190823	+	0.981624i	$0.561116\pi$
$463$	−25.2281	+	25.2281i	−1.17245	+	1.17245i	−0.981624	+	0.190823i	$0.938884\pi$
$464$		0			0
$465$	−0.260030	+	0.228040i	−0.0120586	+	0.0105751i
$466$		0			0
$467$	19.5644	−	15.0123i	0.905331	−	0.694685i	−0.0472781	−	0.998882i	$-0.515055\pi$
$467$	19.5644	−	15.0123i	0.905331	−	0.694685i	0.952609	+	0.304197i	$0.0983880\pi$
$468$		0			0
$469$	−3.99764	+	0.836485i	−0.184594	+	0.0386253i
$470$		0			0
$471$	0.0110516	+	0.168615i	0.000509230	+	0.00776935i
$472$		0			0
$473$	−19.5366	+	6.63177i	−0.898292	+	0.304929i
$474$		0			0
$475$	13.4762			0.618331
$476$		0			0
$477$	13.6252			0.623853
$478$		0			0
$479$	12.8646	−	4.36694i	0.587798	−	0.199530i	−0.0116666	−	0.999932i	$-0.503714\pi$
$479$	12.8646	−	4.36694i	0.587798	−	0.199530i	0.599464	+	0.800402i	$0.295380\pi$
$480$		0			0
$481$	−0.919873	−	14.0345i	−0.0419426	−	0.639920i
$482$		0			0
$483$	−0.167452	+	0.509858i	−0.00761933	+	0.0231993i
$484$		0			0
$485$	−4.51717	+	3.46615i	−0.205114	+	0.157390i
$486$		0			0
$487$	−17.9002	+	15.6980i	−0.811135	+	0.711346i	−0.960755	−	0.277397i	$-0.910528\pi$
$487$	−17.9002	+	15.6980i	−0.811135	+	0.711346i	0.149620	+	0.988744i	$0.452195\pi$
$488$		0			0
$489$	−0.715763	+	0.715763i	−0.0323679	+	0.0323679i
$490$		0			0
$491$	13.5360	+	32.6788i	0.610871	+	1.47477i	0.862045	+	0.506831i	$0.169183\pi$
$491$	13.5360	+	32.6788i	0.610871	+	1.47477i	−0.251174	+	0.967942i	$0.580817\pi$
$492$		0			0
$493$	8.45236	+	10.9432i	0.380675	+	0.492857i
$494$		0			0
$495$	4.51104	+	0.593889i	0.202756	+	0.0266933i
$496$		0			0
$497$	−22.4733	−	12.6794i	−1.00807	−	0.568751i
$498$		0			0
$499$	7.26291	−	21.3959i	0.325133	−	0.957810i	−0.654334	−	0.756205i	$-0.727051\pi$
$499$	7.26291	−	21.3959i	0.325133	−	0.957810i	0.979467	−	0.201604i	$-0.0646156\pi$
$500$		0			0
$501$	1.67237	−	0.220172i	0.0747160	−	0.00983654i
$502$		0			0
$503$	−12.0109	+	17.9755i	−0.535538	+	0.801489i	−0.996292	−	0.0860387i	$-0.972579\pi$
$503$	−12.0109	+	17.9755i	−0.535538	+	0.801489i	0.460754	+	0.887528i	$0.347579\pi$
$504$		0			0
$505$	2.98504	−	1.99454i	0.132833	−	0.0887560i
$506$		0			0
$507$	−0.324446	−	0.955787i	−0.0144091	−	0.0424480i
$508$		0			0
$509$	−11.9230	+	20.6513i	−0.528479	+	0.915353i	0.470969	+	0.882150i	$0.343904\pi$
$509$	−11.9230	+	20.6513i	−0.528479	+	0.915353i	−0.999449	+	0.0332034i	$0.989429\pi$
$510$		0			0
$511$	−10.8974	−	10.6833i	−0.482072	−	0.472602i
$512$		0			0
$513$	−0.836352	+	0.953677i	−0.0369259	+	0.0421059i
$514$		0			0
$515$	0.0462181	−	0.0937210i	0.00203661	−	0.00412984i
$516$		0			0
$517$	15.3676	+	10.2683i	0.675866	+	0.451600i
$518$		0			0
$519$	1.45352	+	0.602069i	0.0638026	+	0.0264279i
$520$		0			0
$521$	−20.5094	−	23.3865i	−0.898535	−	1.02458i	−0.999559	−	0.0296989i	$-0.990545\pi$
$521$	−20.5094	−	23.3865i	−0.898535	−	1.02458i	0.101024	−	0.994884i	$-0.467788\pi$
$522$		0			0
$523$	−5.09815	−	19.0266i	−0.222927	−	0.831973i	−0.983225	−	0.182399i	$-0.941614\pi$
$523$	−5.09815	−	19.0266i	−0.222927	−	0.831973i	0.760298	−	0.649574i	$-0.225053\pi$
$524$		0			0
$525$	0.872524	−	0.123687i	0.0380801	−	0.00539813i
$526$		0			0
$527$	28.9783	−	12.1112i	1.26231	−	0.527570i
$528$		0			0
$529$	12.0059	+	9.21245i	0.521996	+	0.400541i
$530$		0			0
$531$	−0.926118	−	0.926118i	−0.0401901	−	0.0401901i
$532$		0			0
$533$	34.1342	−	6.78972i	1.47852	−	0.294095i
$534$		0			0
$535$	0.272496	+	2.06981i	0.0117810	+	0.0894859i
$536$		0			0
$537$	−0.822746	−	1.66836i	−0.0355041	−	0.0719952i
$538$		0			0
$539$	16.8776	−	1.44297i	0.726970	−	0.0621530i
$540$		0			0
$541$	5.79237	+	5.07977i	0.249033	+	0.218396i	0.774757	−	0.632259i	$-0.217872\pi$
$541$	5.79237	+	5.07977i	0.249033	+	0.218396i	−0.525724	+	0.850655i	$0.676205\pi$
$542$		0			0
$543$	1.21970	−	0.704195i	0.0523424	−	0.0302199i
$544$		0			0
$545$		−	2.73332i		−	0.117083i
$546$		0			0
$547$	−14.0401	−	2.79276i	−0.600313	−	0.119410i	−0.114427	−	0.993432i	$-0.536503\pi$
$547$	−14.0401	−	2.79276i	−0.600313	−	0.119410i	−0.485886	+	0.874022i	$0.661503\pi$
$548$		0			0
$549$	−27.5559	−	13.5891i	−1.17606	−	0.579968i
$550$		0			0
$551$	8.80050	−	4.33992i	0.374914	−	0.184887i
$552$		0			0
$553$	−35.1429	−	26.4164i	−1.49443	−	1.12334i
$554$		0			0
$555$	−0.116467	−	0.0395351i	−0.00494373	−	0.00167817i
$556$		0			0
$557$	0.974877	−	3.63829i	0.0413069	−	0.154159i	−0.942192	−	0.335073i	$-0.891239\pi$
$557$	0.974877	−	3.63829i	0.0413069	−	0.154159i	0.983499	+	0.180914i	$0.0579056\pi$
$558$		0			0
$559$	−40.8968	+	16.9400i	−1.72975	+	0.716486i
$560$		0			0
$561$	0.648140	+	0.317073i	0.0273645	+	0.0133868i
$562$		0			0
$563$	−16.4027	+	21.3764i	−0.691291	+	0.900908i	−0.998716	−	0.0506645i	$-0.983866\pi$
$563$	−16.4027	+	21.3764i	−0.691291	+	0.900908i	0.307425	+	0.951572i	$0.400533\pi$
$564$		0			0
$565$	0.992267	−	0.265877i	0.0417450	−	0.0111855i
$566$		0			0
$567$	12.9640	−	19.8248i	0.544435	−	0.832565i
$568$		0			0
$569$	−5.09830	−	6.64423i	−0.213732	−	0.278541i	0.674168	−	0.738578i	$-0.264503\pi$
$569$	−5.09830	−	6.64423i	−0.213732	−	0.278541i	−0.887899	+	0.460038i	$0.847836\pi$
$570$		0			0
$571$	−2.13827	+	32.6236i	−0.0894837	+	1.36526i	0.683091	+	0.730333i	$0.260635\pi$
$571$	−2.13827	+	32.6236i	−0.0894837	+	1.36526i	−0.772575	+	0.634924i	$0.781032\pi$
$572$		0			0
$573$	−0.223350	−	0.334267i	−0.00933060	−	0.0139642i
$574$		0			0
$575$	−2.52025	+	12.6702i	−0.105102	+	0.528382i
$576$		0			0
$577$	11.9261	+	20.6566i	0.496489	+	0.859945i	0.999992	−	0.00404886i	$-0.00128879\pi$
$577$	11.9261	+	20.6566i	0.496489	+	0.859945i	−0.503502	+	0.863994i	$0.667955\pi$
$578$		0			0
$579$	1.04951	+	0.605937i	0.0436163	+	0.0251819i
$580$		0			0
$581$	−28.3252	+	2.13890i	−1.17513	+	0.0887365i
$582$		0			0
$583$	−10.9860	+	0.720064i	−0.454996	+	0.0298220i
$584$		0			0
$585$	9.74138	+	0.638484i	0.402757	+	0.0263981i
$586$		0			0
$587$	11.4047	−	27.5334i	0.470722	−	1.13642i	−0.493122	−	0.869960i	$-0.664145\pi$
$587$	11.4047	−	27.5334i	0.470722	−	1.13642i	0.963845	−	0.266464i	$-0.0858554\pi$
$588$		0			0
$589$	−4.34814	−	21.8596i	−0.179162	−	0.900708i
$590$		0			0
$591$	1.52371	+	0.408277i	0.0626771	+	0.0167943i
$592$		0			0
$593$	5.44943	−	41.3926i	0.223781	−	1.69979i	−0.398641	−	0.917107i	$-0.630518\pi$
$593$	5.44943	−	41.3926i	0.223781	−	1.69979i	0.622422	−	0.782682i	$-0.286149\pi$
$594$		0			0
$595$	6.73426	+	1.24809i	0.276078	+	0.0511665i
$596$		0			0
$597$	−0.0481765	+	0.365937i	−0.00197173	+	0.0149768i
$598$		0			0
$599$	24.1246	+	6.46418i	0.985706	+	0.264119i	0.715446	−	0.698668i	$-0.246224\pi$
$599$	24.1246	+	6.46418i	0.985706	+	0.264119i	0.270260	+	0.962787i	$0.412890\pi$
$600$		0			0
$601$	2.04475	+	10.2797i	0.0834072	+	0.419316i	0.999818	+	0.0190773i	$0.00607286\pi$
$601$	2.04475	+	10.2797i	0.0834072	+	0.419316i	−0.916411	+	0.400239i	$0.868927\pi$
$602$		0			0
$603$	1.76914	−	4.27109i	0.0720450	−	0.173932i
$604$		0			0
$605$	3.22281	+	0.211234i	0.131026	+	0.00858788i
$606$		0			0
$607$	−18.2938	+	1.19904i	−0.742521	+	0.0486674i	−0.431968	−	0.901889i	$-0.642181\pi$
$607$	−18.2938	+	1.19904i	−0.742521	+	0.0486674i	−0.310553	+	0.950556i	$0.600514\pi$
$608$		0			0
$609$	0.529960	−	0.361763i	0.0214751	−	0.0146594i
$610$		0			0
$611$	34.3427	+	19.8278i	1.38936	+	0.802145i
$612$		0			0
$613$	1.20904	+	2.09411i	0.0488326	+	0.0845805i	0.889409	−	0.457113i	$-0.151117\pi$
$613$	1.20904	+	2.09411i	0.0488326	+	0.0845805i	−0.840576	+	0.541694i	$0.817783\pi$
$614$		0			0
$615$	0.0593753	−	0.298500i	0.00239424	−	0.0120367i
$616$		0			0
$617$	26.7629	+	40.0535i	1.07743	+	1.61249i	0.741963	+	0.670441i	$0.233895\pi$
$617$	26.7629	+	40.0535i	1.07743	+	1.61249i	0.335469	+	0.942051i	$0.391105\pi$
$618$		0			0
$619$	−0.683337	+	10.4257i	−0.0274656	+	0.419045i	0.961881	+	0.273467i	$0.0881706\pi$
$619$	−0.683337	+	10.4257i	−0.0274656	+	0.419045i	−0.989347	+	0.145577i	$0.953496\pi$
$620$		0			0
$621$	−0.740224	−	0.964679i	−0.0297042	−	0.0387112i
$622$		0			0
$623$	−32.7552	−	1.82078i	−1.31231	−	0.0729481i
$624$		0			0
$625$	18.5869	−	4.98035i	0.743477	−	0.199214i
$626$		0			0
$627$	0.311706	−	0.406223i	0.0124483	−	0.0162230i
$628$		0			0
$629$	8.88254	+	6.77110i	0.354170	+	0.269982i
$630$		0			0
$631$	−12.5893	+	5.21467i	−0.501173	+	0.207593i	−0.618925	−	0.785450i	$-0.712431\pi$
$631$	−12.5893	+	5.21467i	−0.501173	+	0.207593i	0.117752	+	0.993043i	$0.462431\pi$
$632$		0			0
$633$	0.477094	−	1.78054i	0.0189628	−	0.0707701i
$634$		0			0
$635$	−6.97233	−	2.36679i	−0.276689	−	0.0939231i
$636$		0			0
$637$	35.9322	−	5.45776i	1.42368	−	0.216244i
$638$		0			0
$639$	26.1953	−	12.9181i	1.03627	−	0.511032i
$640$		0			0
$641$	−2.90764	−	1.43389i	−0.114845	−	0.0566353i	0.383959	−	0.923350i	$-0.374560\pi$
$641$	−2.90764	−	1.43389i	−0.114845	−	0.0566353i	−0.498804	+	0.866715i	$0.666227\pi$
$642$		0			0
$643$	2.18821	+	0.435261i	0.0862944	+	0.0171650i	0.238049	−	0.971253i	$-0.423492\pi$
$643$	2.18821	+	0.435261i	0.0862944	+	0.0171650i	−0.151754	+	0.988418i	$0.548492\pi$
$644$		0			0
$645$			0.387104i			0.0152422i
$646$		0			0
$647$	24.6477	−	14.2304i	0.969001	−	0.559453i	0.0700694	−	0.997542i	$-0.477678\pi$
$647$	24.6477	−	14.2304i	0.969001	−	0.559453i	0.898932	+	0.438089i	$0.144345\pi$
$648$		0			0
$649$	0.795679	+	0.697791i	0.0312331	+	0.0273907i
$650$		0			0
$651$	−0.482153	−	1.37540i	−0.0188971	−	0.0539062i
$652$		0			0
$653$	7.89121	+	16.0018i	0.308807	+	0.626198i	0.994850	−	0.101363i	$-0.0323204\pi$
$653$	7.89121	+	16.0018i	0.308807	+	0.626198i	−0.686043	+	0.727561i	$0.740654\pi$
$654$		0			0
$655$	0.785252	+	5.96458i	0.0306823	+	0.233055i
$656$		0			0
$657$	16.9418	−	3.36994i	0.660964	−	0.131474i
$658$		0			0
$659$	−16.0901	−	16.0901i	−0.626780	−	0.626780i	0.320477	−	0.947256i	$-0.396157\pi$
$659$	−16.0901	−	16.0901i	−0.626780	−	0.626780i	−0.947256	+	0.320477i	$0.896157\pi$
$660$		0			0
$661$	30.6867	+	23.5467i	1.19357	+	0.915862i	0.997898	−	0.0648063i	$-0.0206429\pi$
$661$	30.6867	+	23.5467i	1.19357	+	0.915862i	0.195677	+	0.980668i	$0.437310\pi$
$662$		0			0
$663$	1.43215	+	0.587895i	0.0556201	+	0.0228319i
$664$		0			0
$665$	1.81531	−	4.50853i	0.0703948	−	0.174833i
$666$		0			0
$667$	2.43452	+	9.08574i	0.0942649	+	0.351801i
$668$		0			0
$669$	−0.0362643	−	0.0413515i	−0.00140206	−	0.00159874i
$670$		0			0
$671$	22.9367	+	9.50068i	0.885460	+	0.366770i
$672$		0			0
$673$	−11.1558	−	7.45405i	−0.430024	−	0.287333i	0.321662	−	0.946855i	$-0.395759\pi$
$673$	−11.1558	−	7.45405i	−0.430024	−	0.287333i	−0.751685	+	0.659522i	$0.770759\pi$
$674$		0			0
$675$	−0.883135	+	1.79082i	−0.0339919	+	0.0689287i
$676$		0			0
$677$	19.0158	−	21.6833i	0.730836	−	0.833359i	−0.260395	−	0.965502i	$-0.583853\pi$
$677$	19.0158	−	21.6833i	0.730836	−	0.833359i	0.991231	+	0.132143i	$0.0421860\pi$
$678$		0			0
$679$	−6.43964	−	23.1135i	−0.247131	−	0.887015i
$680$		0			0
$681$	−0.213222	+	0.369312i	−0.00817070	+	0.0141521i
$682$		0			0
$683$	6.40809	+	18.8776i	0.245199	+	0.722332i	0.997948	+	0.0640250i	$0.0203937\pi$
$683$	6.40809	+	18.8776i	0.245199	+	0.722332i	−0.752750	+	0.658307i	$0.771273\pi$
$684$		0			0
$685$	−9.89083	+	6.60884i	−0.377909	+	0.252511i
$686$		0			0
$687$	0.807294	−	1.20820i	0.0308002	−	0.0460957i
$688$		0			0
$689$	−23.4199	+	3.08329i	−0.892226	+	0.117464i
$690$		0			0
$691$	2.22038	−	6.54102i	0.0844671	−	0.248832i	−0.896488	−	0.443069i	$-0.853890\pi$
$691$	2.22038	−	6.54102i	0.0844671	−	0.248832i	0.980955	+	0.194237i	$0.0622230\pi$
$692$		0			0
$693$	−9.42169	+	16.6992i	−0.357900	+	0.634351i
$694$		0			0
$695$	4.00444	+	0.527194i	0.151897	+	0.0199976i
$696$		0			0
$697$	−13.7428	+	23.9787i	−0.520545	+	0.908260i
$698$		0			0
$699$	0.416668	+	1.00593i	0.0157598	+	0.0380476i
$700$		0			0
$701$	25.2196	−	25.2196i	0.952532	−	0.952532i	−0.0463917	−	0.998923i	$-0.514772\pi$
$701$	25.2196	−	25.2196i	0.952532	−	0.952532i	0.998923	+	0.0463917i	$0.0147722\pi$
$702$		0			0
$703$	5.95906	−	5.22596i	0.224750	−	0.197101i
$704$		0			0
$705$	0.275121	−	0.211108i	0.0103617	−	0.00795079i
$706$		0			0
$707$	3.09851	+	14.8081i	0.116532	+	0.556915i
$708$		0			0
$709$	−0.150312	−	2.29331i	−0.00564507	−	0.0861271i	0.994107	−	0.108406i	$-0.0345746\pi$
$709$	−0.150312	−	2.29331i	−0.00564507	−	0.0861271i	−0.999752	+	0.0222786i	$0.992908\pi$
$710$		0			0
$711$	47.1229	−	15.9961i	1.76725	−	0.599899i
$712$		0			0
$713$	21.3653			0.800135
$714$		0			0
$715$	−7.88828			−0.295005
$716$		0			0
$717$	−1.37879	+	0.468037i	−0.0514919	+	0.0174792i
$718$		0			0
$719$	−2.88044	−	43.9470i	−0.107422	−	1.63895i	−0.623084	−	0.782155i	$-0.714121\pi$
$719$	−2.88044	−	43.9470i	−0.107422	−	1.63895i	0.515662	−	0.856792i	$-0.327546\pi$
$720$		0			0
$721$	0.293617	+	0.328182i	0.0109349	+	0.0122221i
$722$		0			0
$723$	−0.263637	+	0.202296i	−0.00980475	+	0.00752345i
$724$		0			0
$725$	11.6131	−	10.1844i	0.431298	−	0.378239i
$726$		0			0
$727$	−19.0151	+	19.0151i	−0.705231	+	0.705231i	−0.965529	−	0.260297i	$-0.916179\pi$
$727$	−19.0151	+	19.0151i	−0.705231	+	0.705231i	0.260297	+	0.965529i	$0.416179\pi$
$728$		0			0
$729$	10.2245	+	24.6842i	0.378687	+	0.914230i
$730$		0			0
$731$	11.1937	−	33.3230i	0.414016	−	1.23250i
$732$		0			0
$733$	−0.500212	−	0.0658541i	−0.0184757	−	0.00243238i	0.121283	−	0.992618i	$-0.461299\pi$
$733$	−0.500212	−	0.0658541i	−0.0184757	−	0.00243238i	−0.139758	+	0.990186i	$0.544633\pi$
$734$		0			0
$735$	0.0761533	−	0.308568i	0.00280896	−	0.0113817i
$736$		0			0
$737$	−1.20075	+	3.53730i	−0.0442302	+	0.130298i
$738$		0			0
$739$	−47.4275	+	6.24395i	−1.74465	+	0.229688i	−0.934357	−	0.356338i	$-0.884025\pi$
$739$	−47.4275	+	6.24395i	−1.74465	+	0.229688i	−0.810293	+	0.586025i	$0.800692\pi$
$740$		0			0
$741$	0.610352	−	0.913456i	0.0224218	−	0.0335567i
$742$		0			0
$743$	18.7633	−	12.5372i	0.688358	−	0.459946i	−0.161559	−	0.986863i	$-0.551652\pi$
$743$	18.7633	−	12.5372i	0.688358	−	0.459946i	0.849917	+	0.526917i	$0.176652\pi$
$744$		0			0
$745$	4.32148	+	12.7307i	0.158327	+	0.466416i
$746$		0			0
$747$	16.0765	−	27.8454i	0.588209	−	1.01881i
$748$		0			0
$749$	−8.51995	−	2.19257i	−0.311312	−	0.0801148i
$750$		0			0
$751$	−7.73727	+	8.82266i	−0.282337	+	0.321944i	−0.875574	−	0.483084i	$-0.839516\pi$
$751$	−7.73727	+	8.82266i	−0.282337	+	0.321944i	0.593237	+	0.805028i	$0.297850\pi$
$752$		0			0
$753$	−0.391935	+	0.794766i	−0.0142829	+	0.0289629i
$754$		0			0
$755$	4.52121	+	3.02098i	0.164544	+	0.109945i
$756$		0			0
$757$	25.2871	+	10.4743i	0.919076	+	0.380694i	0.791524	−	0.611138i	$-0.209288\pi$
$757$	25.2871	+	10.4743i	0.919076	+	0.380694i	0.127552	+	0.991832i	$0.459288\pi$
$758$		0			0
$759$	0.323632	+	0.369031i	0.0117471	+	0.0133950i
$760$		0			0
$761$	−3.11390	−	11.6212i	−0.112879	−	0.421269i	0.886241	−	0.463225i	$-0.153308\pi$
$761$	−3.11390	−	11.6212i	−0.112879	−	0.421269i	−0.999119	+	0.0419558i	$0.986641\pi$
$762$		0			0
$763$	10.6848	+	4.30210i	0.386814	+	0.155747i
$764$		0			0
$765$	−5.46436	+	5.49918i	−0.197564	+	0.198823i
$766$		0			0
$767$	1.80145	+	1.38230i	0.0650467	+	0.0499121i
$768$		0			0
$769$	1.07491	+	1.07491i	0.0387624	+	0.0387624i	0.726222	−	0.687460i	$-0.241274\pi$
$769$	1.07491	+	1.07491i	0.0387624	+	0.0387624i	−0.687460	+	0.726222i	$0.741274\pi$
$770$		0			0
$771$	−0.0694651	+	0.0138175i	−0.00250173	+	0.000497624i
$772$		0			0
$773$	−1.97936	−	15.0347i	−0.0711925	−	0.540760i	−0.989461	−	0.144802i	$-0.953746\pi$
$773$	−1.97936	−	15.0347i	−0.0711925	−	0.540760i	0.918268	−	0.395959i	$-0.129588\pi$
$774$		0			0
$775$	−15.5174	−	31.4662i	−0.557401	−	1.13030i
$776$		0			0
$777$	0.337858	−	0.393050i	0.0121206	−	0.0141006i
$778$		0			0
$779$	14.7457	+	12.9316i	0.528318	+	0.463323i
$780$		0			0
$781$	−20.4387	+	11.8003i	−0.731356	+	0.422248i
$782$		0			0
$783$			1.45388i			0.0519576i
$784$		0			0
$785$	1.43882	+	0.286200i	0.0513538	+	0.0102149i
$786$		0			0
$787$	5.75464	+	2.83788i	0.205131	+	0.101159i	0.541952	−	0.840409i	$-0.317685\pi$
$787$	5.75464	+	2.83788i	0.205131	+	0.101159i	−0.336822	+	0.941568i	$0.609352\pi$
$788$		0			0
$789$	1.61693	−	0.797383i	0.0575644	−	0.0283876i
$790$		0			0
$791$	−0.522443	+	4.29732i	−0.0185759	+	0.152795i
$792$		0			0
$793$	50.4402	+	17.1221i	1.79118	+	0.608025i
$794$		0			0
$795$	−0.0534646	+	0.199533i	−0.00189619	+	0.00707669i
$796$		0			0
$797$	−10.1182	+	4.19111i	−0.358406	+	0.148457i	−0.554619	−	0.832105i	$-0.687136\pi$
$797$	−10.1182	+	4.19111i	−0.358406	+	0.148457i	0.196212	+	0.980561i	$0.437136\pi$
$798$		0			0
$799$	−29.7877	+	10.2172i	−1.05381	+	0.361458i
$800$		0			0
$801$	22.6054	−	29.4599i	0.798721	−	1.04091i
$802$		0			0
$803$	−13.4822	+	3.61255i	−0.475777	+	0.127484i
$804$		0			0
$805$	3.89937	+	2.54990i	0.137435	+	0.0898720i
$806$		0			0
$807$	−0.504245	−	0.657145i	−0.0177503	−	0.0231326i
$808$		0			0
$809$	0.590832	−	9.01436i	0.0207726	−	0.316928i	−0.974810	−	0.223037i	$-0.928403\pi$
$809$	0.590832	−	9.01436i	0.0207726	−	0.316928i	0.995583	−	0.0938908i	$-0.0299305\pi$
$810$		0			0
$811$	24.7423	+	37.0295i	0.868819	+	1.30028i	0.952734	+	0.303807i	$0.0982578\pi$
$811$	24.7423	+	37.0295i	0.868819	+	1.30028i	−0.0839144	+	0.996473i	$0.526742\pi$
$812$		0			0
$813$	−0.179672	+	0.903274i	−0.00630138	+	0.0316792i
$814$		0			0
$815$	4.39402	+	7.61067i	0.153916	+	0.266590i
$816$		0			0
$817$	−21.6037	−	12.4729i	−0.755817	−	0.436371i
$818$		0			0
$819$	−17.8283	+	37.0748i	−0.622971	+	1.29550i
$820$		0			0
$821$	41.2477	−	2.70352i	1.43956	−	0.0943535i	0.674480	−	0.738293i	$-0.264368\pi$
$821$	41.2477	−	2.70352i	1.43956	−	0.0943535i	0.765076	+	0.643940i	$0.222701\pi$
$822$		0			0
$823$	−5.56054	−	0.364457i	−0.193828	−	0.0127042i	−0.0318202	−	0.999494i	$-0.510130\pi$
$823$	−5.56054	−	0.364457i	−0.193828	−	0.0127042i	−0.162008	+	0.986789i	$0.551797\pi$
$824$		0			0
$825$	0.308448	−	0.744660i	0.0107388	−	0.0259257i
$826$		0			0
$827$	−3.00896	−	15.1271i	−0.104632	−	0.526019i	−0.997179	−	0.0750647i	$-0.976084\pi$
$827$	−3.00896	−	15.1271i	−0.104632	−	0.526019i	0.892547	−	0.450954i	$-0.148916\pi$
$828$		0			0
$829$	8.56943	+	2.29617i	0.297628	+	0.0797493i	0.404543	−	0.914519i	$-0.367431\pi$
$829$	8.56943	+	2.29617i	0.297628	+	0.0797493i	−0.106915	+	0.994268i	$0.534097\pi$
$830$		0			0
$831$	0.108314	−	0.822730i	0.00375739	−	0.0285402i
$832$		0			0
$833$	−15.4782	+	24.3603i	−0.536289	+	0.844034i
$834$		0			0
$835$	1.91148	−	14.5191i	0.0661494	−	0.502455i
$836$		0			0
$837$	3.18981	+	0.854707i	0.110256	+	0.0295430i
$838$		0			0
$839$	5.35595	+	26.9262i	0.184908	+	0.929594i	0.956111	+	0.293005i	$0.0946553\pi$
$839$	5.35595	+	26.9262i	0.184908	+	0.929594i	−0.771203	+	0.636589i	$0.780345\pi$
$840$		0			0
$841$	−6.79384	+	16.4018i	−0.234271	+	0.565579i
$842$		0			0
$843$	−1.63916	−	0.107436i	−0.0564555	−	0.00370029i
$844$		0			0
$845$	−8.74420	+	0.573125i	−0.300810	+	0.0197161i
$846$		0			0
$847$	−5.89826	+	12.2657i	−0.202667	+	0.421455i
$848$		0			0
$849$	0.860750	+	0.496954i	0.0295409	+	0.0170554i
$850$		0			0
$851$	3.79894	+	6.57996i	0.130226	+	0.225558i
$852$		0			0
$853$	9.91896	−	49.8660i	0.339619	−	1.70738i	−0.313052	−	0.949736i	$-0.601351\pi$
$853$	9.91896	−	49.8660i	0.339619	−	1.70738i	0.652671	−	0.757642i	$-0.273649\pi$
$854$		0			0
$855$	3.05642	+	4.57426i	0.104528	+	0.156436i
$856$		0			0
$857$	−0.257568	+	3.92973i	−0.00879835	+	0.134237i	0.991200	+	0.132373i	$0.0422598\pi$
$857$	−0.257568	+	3.92973i	−0.00879835	+	0.134237i	−0.999998	+	0.00186345i	$0.999407\pi$
$858$		0			0
$859$	−3.71729	−	4.84447i	−0.126832	−	0.165291i	0.725621	−	0.688095i	$-0.241553\pi$
$859$	−3.71729	−	4.84447i	−0.126832	−	0.165291i	−0.852453	+	0.522804i	$0.824886\pi$
$860$		0			0
$861$	1.07340	+	0.701925i	0.0365815	+	0.0239215i
$862$		0			0
$863$	−21.7747	+	5.83450i	−0.741218	+	0.198609i	−0.609619	−	0.792694i	$-0.708678\pi$
$863$	−21.7747	+	5.83450i	−0.741218	+	0.198609i	−0.131599	+	0.991303i	$0.542011\pi$
$864$		0			0
$865$	8.31499	−	10.8363i	0.282718	−	0.368445i
$866$		0			0
$867$	−1.09913	+	0.550739i	−0.0373285	+	0.0187041i
$868$		0			0
$869$	−37.1501	+	15.3881i	−1.26023	+	0.522005i
$870$		0			0
$871$	−2.07441	+	7.74179i	−0.0702886	+	0.262320i
$872$		0			0
$873$	25.7177	+	8.72997i	0.870411	+	0.295465i
$874$		0			0
$875$	1.92570	−	15.8397i	0.0651005	−	0.535480i
$876$		0			0
$877$	27.5267	−	13.5747i	0.929512	−	0.458384i	0.0864831	−	0.996253i	$-0.472437\pi$
$877$	27.5267	−	13.5747i	0.929512	−	0.458384i	0.843028	+	0.537869i	$0.180770\pi$
$878$		0			0
$879$	−1.00840	−	0.497286i	−0.0340124	−	0.0167730i
$880$		0			0
$881$	−41.3305	−	8.22114i	−1.39246	−	0.276977i	−0.558821	−	0.829288i	$-0.688746\pi$
$881$	−41.3305	−	8.22114i	−1.39246	−	0.276977i	−0.833638	+	0.552311i	$0.813746\pi$
$882$		0			0
$883$		−	25.4892i		−	0.857780i	−0.903357	−	0.428890i	$-0.858905\pi$
$883$		−	25.4892i		−	0.857780i	0.903357	−	0.428890i	$-0.141095\pi$
$884$		0			0
$885$	0.0171965	−	0.00992842i	0.000578055	−	0.000333740i
$886$		0			0
$887$	8.73722	+	7.66234i	0.293367	+	0.257276i	0.793359	−	0.608754i	$-0.208330\pi$
$887$	8.73722	+	7.66234i	0.293367	+	0.257276i	−0.499992	+	0.866030i	$0.666664\pi$
$888$		0			0
$889$	20.2260	−	23.5302i	0.678360	−	0.789176i
$890$		0			0
$891$	−9.58223	−	19.4308i	−0.321017	−	0.650958i
$892$		0			0
$893$	2.91692	+	22.1562i	0.0976110	+	0.741429i
$894$		0			0
$895$	−15.8395	+	3.15067i	−0.529456	+	0.105315i
$896$		0			0
$897$	0.744675	+	0.744675i	0.0248640	+	0.0248640i
$898$		0			0
$899$	−20.2669	−	15.5514i	−0.675940	−	0.518667i
$900$		0			0
$901$	10.3722	−	15.6303i	0.345548	−	0.520721i
$902$		0			0
$903$	−1.51322	−	0.609282i	−0.0503568	−	0.0202756i
$904$		0			0
$905$	−3.16466	−	11.8107i	−0.105197	−	0.392600i
$906$		0			0
$907$	−18.0957	−	20.6342i	−0.600858	−	0.685148i	0.368829	−	0.929497i	$-0.379759\pi$
$907$	−18.0957	−	20.6342i	−0.600858	−	0.685148i	−0.969687	+	0.244350i	$0.921426\pi$
$908$		0			0
$909$	−15.8210	−	6.55326i	−0.524749	−	0.217358i
$910$		0			0
$911$	−7.92486	−	5.29522i	−0.262562	−	0.175439i	0.417320	−	0.908759i	$-0.362969\pi$
$911$	−7.92486	−	5.29522i	−0.262562	−	0.175439i	−0.679883	+	0.733321i	$0.737969\pi$
$912$		0			0
$913$	−11.4910	+	23.3015i	−0.380297	+	0.771167i
$914$		0			0
$915$	0.307133	−	0.350218i	0.0101535	−	0.0115778i
$916$		0			0
$917$	−24.5519	−	6.31833i	−0.810776	−	0.208650i
$918$		0			0
$919$	−0.171885	+	0.297714i	−0.00566997	+	0.00982068i	−0.868846	−	0.495082i	$-0.835138\pi$
$919$	−0.171885	+	0.297714i	−0.00566997	+	0.00982068i	0.863176	+	0.504902i	$0.168471\pi$
$920$		0			0
$921$	−0.0282151	−	0.0831190i	−0.000929720	−	0.00273887i
$922$		0			0
$923$	−42.1031	+	28.1324i	−1.38584	+	0.925988i
$924$		0			0
$925$	6.93165	−	10.3739i	0.227911	−	0.341093i
$926$		0			0
$927$	−0.494183	+	0.0650605i	−0.0162311	+	0.00213687i
$928$		0			0
$929$	−8.54839	+	25.1828i	−0.280464	+	0.826219i	0.711835	+	0.702347i	$0.247865\pi$
$929$	−8.54839	+	25.1828i	−0.280464	+	0.826219i	−0.992298	+	0.123872i	$0.960469\pi$
$930$		0			0
$931$	14.7670	+	14.1924i	0.483968	+	0.465136i
$932$		0			0
$933$	−0.0885064	−	0.0116521i	−0.00289757	−	0.000381472i
$934$		0			0
$935$	4.11533	−	4.72280i	0.134586	−	0.154452i
$936$		0			0
$937$	−18.1089	−	43.7187i	−0.591592	−	1.42823i	−0.881965	−	0.471316i	$-0.843779\pi$
$937$	−18.1089	−	43.7187i	−0.591592	−	1.42823i	0.290373	−	0.956914i	$-0.406221\pi$
$938$		0			0
$939$	1.22884	−	1.22884i	0.0401016	−	0.0401016i
$940$		0			0
$941$	−34.6208	+	30.3617i	−1.12861	+	0.989762i	−0.999998	−	0.00193359i	$-0.999385\pi$
$941$	−34.6208	+	30.3617i	−1.12861	+	0.989762i	−0.128609	+	0.991695i	$0.541051\pi$
$942$		0			0
$943$	−14.9158	+	11.4453i	−0.485725	+	0.372710i
$944$		0			0
$945$	0.480165	+	0.536689i	0.0156198	+	0.0174585i
$946$		0			0
$947$	−3.73521	−	56.9883i	−0.121378	−	1.85187i	−0.432664	−	0.901555i	$-0.642426\pi$
$947$	−3.73521	−	56.9883i	−0.121378	−	1.85187i	0.311286	−	0.950316i	$-0.399240\pi$
$948$		0			0
$949$	−28.3582	+	9.62632i	−0.920547	+	0.312484i
$950$		0			0
$951$	0.915545			0.0296886
$952$		0			0
$953$	61.5184			1.99278			0.996388	−	0.0849160i	$-0.0270622\pi$
$953$	61.5184			1.99278			0.996388	+	0.0849160i	$0.0270622\pi$
$954$		0			0
$955$	−3.30502	+	1.12190i	−0.106948	+	0.0363039i
$956$		0			0
$957$	−0.0383840	−	0.585626i	−0.00124078	−	0.0189306i
$958$		0			0
$959$	−10.2668	−	49.0660i	−0.331532	−	1.58442i
$960$		0			0
$961$	−21.4402	+	16.4516i	−0.691618	+	0.530697i
$962$		0			0
$963$	7.48689	−	6.56583i	0.241262	−	0.211581i
$964$		0			0
$965$	7.43961	−	7.43961i	0.239490	−	0.239490i
$966$		0			0
$967$	13.5374	+	32.6821i	0.435333	+	1.05099i	0.977542	+	0.210743i	$0.0675883\pi$
$967$	13.5374	+	32.6821i	0.435333	+	1.05099i	−0.542208	+	0.840244i	$0.682412\pi$
$968$		0			0
$969$	0.228475	+	0.841976i	0.00733968	+	0.0270482i
$970$		0			0
$971$	49.5136	+	6.51859i	1.58897	+	0.209192i	0.872566	−	0.488496i	$-0.162454\pi$
$971$	49.5136	+	6.51859i	1.58897	+	0.209192i	0.716402	+	0.697688i	$0.245788\pi$
$972$		0			0
$973$	−8.36362	+	14.8239i	−0.268125	+	0.475231i
$974$		0			0
$975$	0.555886	−	1.63759i	0.0178026	−	0.0524448i
$976$		0			0
$977$	19.6358	−	2.58511i	0.628206	−	0.0827049i	0.190300	−	0.981726i	$-0.439054\pi$
$977$	19.6358	−	2.58511i	0.628206	−	0.0827049i	0.437906	+	0.899021i	$0.355720\pi$
$978$		0			0
$979$	−16.6699	+	24.9483i	−0.532774	+	0.797352i
$980$		0			0
$981$	−10.8405	+	7.24341i	−0.346111	+	0.231264i
$982$		0			0
$983$	3.39785	+	10.0098i	0.108375	+	0.319262i	0.987565	−	0.157208i	$-0.0502494\pi$
$983$	3.39785	+	10.0098i	0.108375	+	0.319262i	−0.879191	+	0.476470i	$0.841916\pi$
$984$		0			0
$985$	6.84758	−	11.8603i	0.218182	−	0.377902i
$986$		0			0
$987$	0.392210	+	1.40774i	0.0124842	+	0.0448089i
$988$		0			0
$989$	15.7671	−	17.9789i	0.501363	−	0.571695i
$990$		0			0
$991$	−16.9288	+	34.3281i	−0.537760	+	1.09047i	0.443229	+	0.896408i	$0.353833\pi$
$991$	−16.9288	+	34.3281i	−0.537760	+	1.09047i	−0.980989	+	0.194061i	$0.937834\pi$
$992$		0			0
$993$	0.118694	+	0.0793088i	0.00376664	+	0.00251679i
$994$		0			0
$995$	2.96047	+	1.22627i	0.0938532	+	0.0388753i
$996$		0			0
$997$	39.8629	+	45.4550i	1.26247	+	1.43957i	0.848423	+	0.529318i	$0.177552\pi$
$997$	39.8629	+	45.4550i	1.26247	+	1.43957i	0.414049	+	0.910255i	$0.364114\pi$
$998$		0			0
$999$	0.303950	+	1.13436i	0.00961655	+	0.0358895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.173.6	✓	192
7.3	odd	6	inner	476.2.bl.a.241.6	yes	192
17.6	odd	16	inner	476.2.bl.a.397.6	yes	192
119.108	even	48	inner	476.2.bl.a.465.6	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.173.6	✓	192	1.1	even	1	trivial
476.2.bl.a.241.6	yes	192	7.3	odd	6	inner
476.2.bl.a.397.6	yes	192	17.6	odd	16	inner
476.2.bl.a.465.6	yes	192	119.108	even	48	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.0684794 - 0.0232456i) q^{3} +(-0.0410628 - 0.626497i) q^{5} +(2.51365 + 0.825556i) q^{7} +(-2.37591 + 1.82310i) q^{9} +(1.81936 - 1.59554i) q^{11} +(3.67133 - 3.67133i) q^{13} +(-0.0173753 - 0.0419476i) q^{15} +(0.282728 + 4.11340i) q^{17} +(2.90088 + 0.381908i) q^{19} +(0.191324 - 0.00189788i) q^{21} +(-0.901573 + 2.65595i) q^{23} +(4.56641 - 0.601180i) q^{25} +(-0.240854 + 0.360463i) q^{27} +(2.78844 - 1.86318i) q^{29} +(-2.44853 - 7.21314i) q^{31} +(0.0874997 - 0.151554i) q^{33} +(0.413991 - 1.60870i) q^{35} +(1.78609 - 2.03665i) q^{37} +(0.166068 - 0.336753i) q^{39} +(5.57345 + 3.72406i) q^{41} +(-7.87683 - 3.26269i) q^{43} +(1.23973 + 1.41364i) q^{45} +(1.97680 + 7.37750i) q^{47} +(5.63691 + 4.15032i) q^{49} +(0.114980 + 0.275111i) q^{51} +(-3.60948 - 2.76965i) q^{53} +(-1.07431 - 1.07431i) q^{55} +(0.207528 - 0.0412799i) q^{57} +(0.0570842 + 0.433597i) q^{59} +(4.53760 + 9.20135i) q^{61} +(-7.47729 + 2.62120i) q^{63} +(-2.45083 - 2.14932i) q^{65} +(-1.33687 + 0.771844i) q^{67} +0.202835i q^{69} +(-9.56540 - 1.90268i) q^{71} +(-5.17314 - 2.55111i) q^{73} +(0.298730 - 0.147318i) q^{75} +(5.89046 - 2.50865i) q^{77} +(-15.7351 - 5.34133i) q^{79} +(2.31720 - 8.64789i) q^{81} +(-9.91914 + 4.10864i) q^{83} +(2.56542 - 0.346036i) q^{85} +(0.147640 - 0.192408i) q^{87} +(-11.9769 + 3.20920i) q^{89} +(12.2593 - 6.19756i) q^{91} +(-0.335348 - 0.437034i) q^{93} +(0.120146 - 1.83308i) q^{95} +(-5.03836 - 7.54044i) q^{97} +(-1.41382 + 7.10774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77}+ \cdots - 368 q^{99}+O(q^{100}) \) 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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