LMFDB - Embedded newform 476.2.bl.a.465.6

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			465.6
Character	$\chi$	$=$	476.465
Dual form			476.2.bl.a.173.6

$q$-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 $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.0684794	+	0.0232456i	0.0395366	+	0.0134209i	0.341138	−	0.940013i	$-0.389188\pi$
$3$	0.0684794	+	0.0232456i	0.0395366	+	0.0134209i	−0.301601	+	0.953434i	$0.597521\pi$
$4$		0			0
$5$	−0.0410628	+	0.626497i	−0.0183638	+	0.280178i	0.978795	+	0.204844i	$0.0656688\pi$
$5$	−0.0410628	+	0.626497i	−0.0183638	+	0.280178i	−0.997158	+	0.0753336i	$0.975998\pi$
$6$		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	0.888184	−	0.459488i	$-0.151967\pi$
$11$	1.81936	+	1.59554i	0.548559	+	0.481073i	−0.339625	+	0.940561i	$0.610300\pi$
$12$		0			0
$13$	3.67133	+	3.67133i	1.01824	+	1.01824i	0.999830	+	0.0184124i	$0.00586119\pi$
$13$	3.67133	+	3.67133i	1.01824	+	1.01824i	0.0184124	+	0.999830i	$0.494139\pi$
$14$		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	0.209799	−	0.977745i	$-0.432719\pi$
$19$	2.90088	−	0.381908i	0.665508	−	0.0876157i	0.455709	+	0.890129i	$0.349386\pi$
$20$		0			0
$21$	0.191324	+	0.00189788i	0.0417503	+	0.000414151i
$22$		0			0
$23$	−0.901573	−	2.65595i	−0.187991	−	0.553803i	0.811544	−	0.584291i	$-0.198627\pi$
$23$	−0.901573	−	2.65595i	−0.187991	−	0.553803i	−0.999535	+	0.0304876i	$0.990294\pi$
$24$		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	0.786851	−	0.617143i	$-0.211710\pi$
$29$	2.78844	+	1.86318i	0.517800	+	0.345983i	−0.269051	+	0.963126i	$0.586710\pi$
$30$		0			0
$31$	−2.44853	+	7.21314i	−0.439769	+	1.29552i	0.470828	+	0.882225i	$0.343955\pi$
$31$	−2.44853	+	7.21314i	−0.439769	+	1.29552i	−0.910598	+	0.413294i	$0.864378\pi$
$32$		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	0.879780	−	0.475381i	$-0.157690\pi$
$37$	1.78609	+	2.03665i	0.293632	+	0.334823i	−0.586148	+	0.810204i	$0.699356\pi$
$38$		0			0
$39$	0.166068	+	0.336753i	0.0265922	+	0.0539236i
$40$		0			0
$41$	5.57345	−	3.72406i	0.870427	−	0.581601i	−0.0381716	−	0.999271i	$-0.512153\pi$
$41$	5.57345	−	3.72406i	0.870427	−	0.581601i	0.908599	+	0.417670i	$0.137153\pi$
$42$		0			0
$43$	−7.87683	+	3.26269i	−1.20120	+	0.497555i	−0.891388	−	0.453241i	$-0.850268\pi$
$43$	−7.87683	+	3.26269i	−1.20120	+	0.497555i	−0.309817	+	0.950796i	$0.600268\pi$
$44$		0			0
$45$	1.23973	−	1.41364i	0.184808	−	0.210733i
$46$		0			0
$47$	1.97680	−	7.37750i	0.288345	−	1.07612i	−0.658015	−	0.753005i	$-0.728604\pi$
$47$	1.97680	−	7.37750i	0.288345	−	1.07612i	0.946360	−	0.323114i	$-0.104730\pi$
$48$		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	−0.826179	−	0.563407i	$-0.809490\pi$
$53$	−3.60948	+	2.76965i	−0.495800	+	0.380441i	0.330379	+	0.943848i	$0.392823\pi$
$54$		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	−0.987327	−	0.158698i	$-0.949270\pi$
$59$	0.0570842	−	0.433597i	0.00743173	−	0.0564496i	0.994759	+	0.102249i	$0.0326037\pi$
$60$		0			0
$61$	4.53760	−	9.20135i	0.580981	−	1.17811i	−0.385818	−	0.922575i	$-0.626081\pi$
$61$	4.53760	−	9.20135i	0.580981	−	1.17811i	0.966799	−	0.255538i	$-0.0822524\pi$
$62$		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	0.416110	−	0.909314i	$-0.363393\pi$
$67$	−1.33687	−	0.771844i	−0.163325	−	0.0942957i	−0.579435	+	0.815019i	$0.696727\pi$
$68$		0			0
$69$		−	0.202835i		−	0.0244185i
$70$		0			0
$71$	−9.56540	+	1.90268i	−1.13520	+	0.225806i	−0.726703	−	0.686952i	$-0.758948\pi$
$71$	−9.56540	+	1.90268i	−1.13520	+	0.225806i	−0.408501	+	0.912758i	$0.633948\pi$
$72$		0			0
$73$	−5.17314	+	2.55111i	−0.605470	+	0.298585i	−0.719065	−	0.694942i	$-0.755430\pi$
$73$	−5.17314	+	2.55111i	−0.605470	+	0.298585i	0.113596	+	0.993527i	$0.463763\pi$
$74$		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	−0.999355	−	0.0359155i	$-0.988565\pi$
$79$	−15.7351	+	5.34133i	−1.77033	+	0.600947i	−0.770977	+	0.636862i	$0.780232\pi$
$80$		0			0
$81$	2.31720	+	8.64789i	0.257466	+	0.960877i
$82$		0			0
$83$	−9.91914	−	4.10864i	−1.08877	−	0.450982i	−0.235190	−	0.971949i	$-0.575571\pi$
$83$	−9.91914	−	4.10864i	−1.08877	−	0.450982i	−0.853577	+	0.520967i	$0.825571\pi$
$84$		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	−0.439691	−	0.898149i	$-0.644912\pi$
$89$	−11.9769	−	3.20920i	−1.26955	−	0.340175i	−0.829858	+	0.557974i	$0.811579\pi$
$90$		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	−0.993890	−	0.110379i	$-0.964794\pi$
$97$	−5.03836	+	7.54044i	−0.511568	+	0.765616i	0.482322	+	0.875994i	$0.339794\pi$
$98$		0			0
$99$	−1.41382	−	7.10774i	−0.142094	−	0.714355i
$100$		0			0
$101$	2.85907	−	4.95205i	0.284488	−	0.492748i	−0.687997	−	0.725714i	$-0.741510\pi$
$101$	2.85907	−	4.95205i	0.284488	−	0.492748i	0.972485	+	0.232966i	$0.0748431\pi$
$102$		0			0
$103$	0.144141	−	0.0832197i	0.0142026	−	0.00819988i	−0.492882	−	0.870096i	$-0.664057\pi$
$103$	0.144141	−	0.0832197i	0.0142026	−	0.00819988i	0.507084	+	0.861896i	$0.330723\pi$
$104$		0			0
$105$	−0.00904532	+	0.119786i	−0.000882733	+	0.0116899i
$106$		0			0
$107$	−3.31804	−	0.217476i	−0.320767	−	0.0210242i	−0.0958308	−	0.995398i	$-0.530551\pi$
$107$	−3.31804	−	0.217476i	−0.320767	−	0.0210242i	−0.224936	+	0.974373i	$0.572217\pi$
$108$		0			0
$109$	4.34420	−	0.284734i	0.416099	−	0.0272726i	0.144084	−	0.989566i	$-0.453977\pi$
$109$	4.34420	−	0.284734i	0.416099	−	0.0272726i	0.272015	+	0.962293i	$0.412310\pi$
$110$		0			0
$111$	0.0749675	+	0.180988i	0.00711560	+	0.0171786i
$112$		0			0
$113$	0.319206	−	1.60476i	0.0300284	−	0.150963i	−0.962862	−	0.269993i	$-0.912979\pi$
$113$	0.319206	−	1.60476i	0.0300284	−	0.150963i	0.992891	+	0.119030i	$0.0379786\pi$
$114$		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	0.988083	+	0.153923i	$0.0491909\pi$
$127$	4.48797	+	10.8349i	0.398243	+	0.961444i	−0.589840	+	0.807520i	$0.700809\pi$
$128$		0			0
$129$	−0.615244	+	0.0403252i	−0.0541692	+	0.00355044i
$130$		0			0
$131$	−9.56160	−	0.626700i	−0.835401	−	0.0547551i	−0.358303	−	0.933605i	$-0.616645\pi$
$131$	−9.56160	−	0.626700i	−0.835401	−	0.0547551i	−0.477098	+	0.878850i	$0.658311\pi$
$132$		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	0.103934	+	0.994584i	$0.466857\pi$
$137$	−9.47341	+	16.4084i	−0.809368	+	1.40187i	−0.913302	+	0.407283i	$0.866476\pi$
$138$		0			0
$139$	−1.25504	−	6.30953i	−0.106451	−	0.535167i	−0.996803	−	0.0798944i	$-0.974542\pi$
$139$	−1.25504	−	6.30953i	−0.106451	−	0.535167i	0.890352	−	0.455273i	$-0.150458\pi$
$140$		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	−0.722933	−	0.690918i	$-0.757206\pi$
$149$	−20.6836	−	5.54217i	−1.69447	−	0.454032i	−0.971537	+	0.236886i	$0.923873\pi$
$150$		0			0
$151$	−5.27237	−	6.87108i	−0.429059	−	0.559161i	0.527929	−	0.849289i	$-0.322969\pi$
$151$	−5.27237	−	6.87108i	−0.429059	−	0.559161i	−0.956988	+	0.290128i	$0.906302\pi$
$152$		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	0.937586	−	0.347755i	$-0.113056\pi$
$157$	−0.604756	−	2.25698i	−0.0482648	−	0.180127i	−0.985850	+	0.167628i	$0.946389\pi$
$158$		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	−0.121728	−	0.992564i	$-0.538843\pi$
$163$	−12.5537	−	6.19082i	−0.983284	−	0.484902i	−0.861557	+	0.507661i	$0.830510\pi$
$164$		0			0
$165$	−0.0985410	+	0.0485951i	−0.00767141	+	0.00378312i
$166$		0			0
$167$	22.8768	−	4.55048i	1.77026	−	0.352127i	0.801095	−	0.598537i	$-0.204251\pi$
$167$	22.8768	−	4.55048i	1.77026	−	0.352127i	0.969166	+	0.246410i	$0.0792510\pi$
$168$		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	0.251106	−	0.967960i	$-0.419206\pi$
$173$	16.3565	−	14.3443i	1.24356	−	1.09057i	0.992454	−	0.122614i	$-0.0391276\pi$
$174$		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	0.147653	+	0.989039i	$0.452828\pi$
$179$	−3.35750	+	25.5027i	−0.250951	+	1.90616i	−0.398604	+	0.917123i	$0.630505\pi$
$180$		0			0
$181$	19.1010	+	3.79942i	1.41976	+	0.282408i	0.844498	−	0.535559i	$-0.179899\pi$
$181$	19.1010	+	3.79942i	1.41976	+	0.282408i	0.575265	+	0.817967i	$0.304899\pi$
$182$		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	−0.998242	−	0.0592617i	$-0.981125\pi$
$191$	−1.43880	+	5.36969i	−0.104108	+	0.388537i	0.894134	+	0.447799i	$0.147792\pi$
$192$		0			0
$193$	11.0491	−	12.5991i	0.795335	−	0.906906i	−0.202035	−	0.979378i	$-0.564756\pi$
$193$	11.0491	−	12.5991i	0.795335	−	0.906906i	0.997370	+	0.0724725i	$0.0230890\pi$
$194$		0			0
$195$	−0.217794	+	0.0902131i	−0.0155965	+	0.00646030i
$196$		0			0
$197$	18.1369	−	12.1187i	1.29220	−	0.863421i	0.296409	−	0.955061i	$-0.404211\pi$
$197$	18.1369	−	12.1187i	1.29220	−	0.863421i	0.995792	+	0.0916398i	$0.0292108\pi$
$198$		0			0
$199$	−2.25736	−	4.57748i	−0.160020	−	0.324489i	0.802066	−	0.597236i	$-0.203734\pi$
$199$	−2.25736	−	4.57748i	−0.160020	−	0.324489i	−0.962086	+	0.272747i	$0.912068\pi$
$200$		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	0.886369	+	0.462980i	$0.153220\pi$
$211$	14.1614	+	21.1940i	0.974908	+	1.45905i	0.0885393	+	0.996073i	$0.471780\pi$
$212$		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	−0.933325	−	0.359033i	$-0.883107\pi$
$223$	−0.291047	+	0.702650i	−0.0194900	+	0.0470529i	0.913835	+	0.406086i	$0.133107\pi$
$224$		0			0
$225$	−9.75338	−	9.75338i	−0.650225	−	0.650225i
$226$		0			0
$227$	−4.43349	−	3.88807i	−0.294261	−	0.258060i	0.499467	−	0.866333i	$-0.333529\pi$
$227$	−4.43349	−	3.88807i	−0.294261	−	0.258060i	−0.793728	+	0.608273i	$0.791863\pi$
$228$		0			0
$229$	15.9411	+	12.2320i	1.05341	+	0.808313i	0.981952	−	0.189130i	$-0.0605667\pi$
$229$	15.9411	+	12.2320i	1.05341	+	0.808313i	0.0714625	+	0.997443i	$0.477233\pi$
$230$		0			0
$231$	0.345060	+	0.308718i	0.0227033	+	0.0203122i
$232$		0			0
$233$	0.984708	−	15.0237i	0.0645103	−	0.984238i	−0.835813	−	0.549015i	$-0.815003\pi$
$233$	0.984708	−	15.0237i	0.0645103	−	0.984238i	0.900323	−	0.435223i	$-0.143330\pi$
$234$		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	0.177755	−	0.984075i	$-0.443117\pi$
$241$	−4.35126	−	1.47705i	−0.280289	−	0.0951454i	−0.458044	+	0.888929i	$0.651450\pi$
$242$		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	0.378637	−	0.925545i	$-0.376393\pi$
$251$	−8.66466	−	8.66466i	−0.546908	−	0.546908i	−0.925545	+	0.378637i	$0.876393\pi$
$252$		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	−0.160750	−	0.986995i	$-0.551391\pi$
$257$	−0.971000	+	0.127835i	−0.0605693	+	0.00797410i	0.100181	+	0.994969i	$0.468058\pi$
$258$		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	0.845542	−	0.533909i	$-0.179277\pi$
$263$	24.7165	+	3.25399i	1.52409	+	0.200650i	0.678545	+	0.734559i	$0.262611\pi$
$264$		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	0.775088	+	0.631854i	$0.217706\pi$
$269$	−3.68173	+	10.8460i	−0.224479	+	0.661293i	−0.999567	+	0.0294396i	$0.990628\pi$
$270$		0			0
$271$	−6.36756	−	11.0289i	−0.386802	−	0.669961i	0.605215	−	0.796062i	$-0.293087\pi$
$271$	−6.36756	−	11.0289i	−0.386802	−	0.669961i	−0.992017	+	0.126101i	$0.959754\pi$
$272$		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	0.994366	−	0.106000i	$-0.0338045\pi$
$277$	5.07519	+	10.2915i	0.304939	+	0.618354i	−0.689427	+	0.724355i	$0.742138\pi$
$278$		0			0
$279$	18.9678	−	12.6739i	1.13557	−	0.758764i
$280$		0			0
$281$	−20.9857	+	8.69258i	−1.25190	+	0.518556i	−0.907416	−	0.420234i	$-0.861948\pi$
$281$	−20.9857	+	8.69258i	−1.25190	+	0.518556i	−0.344489	+	0.938790i	$0.611948\pi$
$282$		0			0
$283$	9.06187	−	10.3331i	0.538672	−	0.614238i	−0.416915	−	0.908945i	$-0.636889\pi$
$283$	9.06187	−	10.3331i	0.538672	−	0.614238i	0.955587	+	0.294708i	$0.0952222\pi$
$284$		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	−0.951110	−	0.308852i	$-0.900055\pi$
$293$	−10.9937	+	10.9937i	−0.642258	+	0.642258i	0.308852	+	0.951110i	$0.400055\pi$
$294$		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	$0.0110275\pi$
$307$			1.21378i			0.0692742i	−0.999400	+	0.0346371i	$0.988972\pi$
$308$		0			0
$309$	0.0118052	−	0.00234819i	0.000671572	−	0.000133584i
$310$		0			0
$311$	−1.10712	+	0.545971i	−0.0627791	+	0.0309592i	−0.473407	−	0.880844i	$-0.656976\pi$
$311$	−1.10712	+	0.545971i	−0.0627791	+	0.0309592i	0.410628	+	0.911803i	$0.365309\pi$
$312$		0			0
$313$	21.5525	+	10.6285i	1.21822	+	0.600760i	0.933750	−	0.357925i	$-0.116516\pi$
$313$	21.5525	+	10.6285i	1.21822	+	0.600760i	0.284470	+	0.958685i	$0.408182\pi$
$314$		0			0
$315$	1.94921	−	4.57687i	0.109826	−	0.257877i
$316$		0			0
$317$	11.9882	−	4.06946i	0.673326	−	0.228564i	0.0362252	−	0.999344i	$-0.488467\pi$
$317$	11.9882	−	4.06946i	0.673326	−	0.228564i	0.637101	+	0.770780i	$0.280133\pi$
$318$		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	−0.759160	−	0.650904i	$-0.774390\pi$
$331$	1.20168	−	1.56605i	0.0660501	−	0.0860781i	0.825210	+	0.564826i	$0.191057\pi$
$332$		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	0.935236	+	0.354025i	$0.115187\pi$
$337$	3.79396	+	19.0735i	0.206670	+	1.03900i	−0.728566	+	0.684975i	$0.759813\pi$
$338$		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	−0.0953053	−	0.995448i	$-0.530383\pi$
$347$	−1.11513	+	0.0730894i	−0.0598633	+	0.00392365i	0.0354421	+	0.999372i	$0.488716\pi$
$348$		0			0
$349$	−5.88275	−	14.2022i	−0.314897	−	0.760228i	−0.999509	−	0.0313207i	$-0.990029\pi$
$349$	−5.88275	−	14.2022i	−0.314897	−	0.760228i	0.684613	−	0.728907i	$-0.259971\pi$
$350$		0			0
$351$	0.439125	−	2.20763i	0.0234388	−	0.117835i
$352$		0			0
$353$	−3.70446	+	0.992606i	−0.197168	+	0.0528311i	−0.356052	−	0.934466i	$-0.615877\pi$
$353$	−3.70446	+	0.992606i	−0.197168	+	0.0528311i	0.158883	+	0.987297i	$0.449211\pi$
$354$		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	0.998586	−	0.0531601i	$-0.0169294\pi$
$359$	0.384008	+	2.91683i	0.0202672	+	0.153944i	−0.978319	+	0.207104i	$0.933596\pi$
$360$		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	0.762495	−	0.646994i	$-0.223974\pi$
$367$	30.7075	−	2.01267i	1.60292	−	0.105061i	0.840422	+	0.541933i	$0.182307\pi$
$368$		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	−0.863012	−	0.505183i	$-0.831425\pi$
$373$	−16.5517	+	9.55615i	−0.857017	+	0.494799i	0.00599552	+	0.999982i	$0.498092\pi$
$374$		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	−0.974892	−	0.222679i	$-0.928520\pi$
$379$	−7.71102	+	11.5404i	−0.396089	+	0.592789i	0.578803	+	0.815467i	$0.303520\pi$
$380$		0			0
$381$	0.0554691	+	0.846295i	0.00284177	+	0.0433570i
$382$		0			0
$383$	−16.6083	+	21.6443i	−0.848643	+	1.10597i	0.144551	+	0.989497i	$0.453826\pi$
$383$	−16.6083	+	21.6443i	−0.848643	+	1.10597i	−0.993194	+	0.116476i	$0.962840\pi$
$384$		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	−0.870593	−	0.492005i	$-0.836264\pi$
$389$	−22.0998	−	28.8011i	−1.12051	−	1.46027i	−0.249914	−	0.968268i	$-0.580402\pi$
$390$		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	−0.489949	−	0.871751i	$-0.662985\pi$
$397$	−6.93312	+	2.35348i	−0.347963	+	0.118118i	0.141986	+	0.989869i	$0.454651\pi$
$398$		0			0
$399$	0.555733	−	0.0675627i	0.0278215	−	0.00338237i
$400$		0			0
$401$	−16.3379	−	8.05697i	−0.815876	−	0.402346i	−0.0140488	−	0.999901i	$-0.504472\pi$
$401$	−16.3379	−	8.05697i	−0.815876	−	0.402346i	−0.801827	+	0.597556i	$0.796139\pi$
$402$		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	0.00660812	−	0.999978i	$-0.497897\pi$
$409$	−17.3134	−	9.99592i	−0.856094	−	0.494266i	−0.862702	+	0.505712i	$0.831230\pi$
$410$		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	−0.00378943	−	0.999993i	$-0.501206\pi$
$419$	−7.98251	−	1.58782i	−0.389971	−	0.0775701i	−0.386182	+	0.922423i	$0.626206\pi$
$420$		0			0
$421$	16.5980	−	16.5980i	0.808938	−	0.808938i	−0.175535	−	0.984473i	$-0.556166\pi$
$421$	16.5980	−	16.5980i	0.808938	−	0.808938i	0.984473	+	0.175535i	$0.0561657\pi$
$422$		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	−0.716589	−	0.697496i	$-0.754298\pi$
$431$	1.42154	−	1.62096i	0.0684733	−	0.0780789i	0.785062	+	0.619417i	$0.212631\pi$
$432$		0			0
$433$	−10.1434	+	4.20152i	−0.487459	+	0.201912i	−0.612856	−	0.790194i	$-0.709980\pi$
$433$	−10.1434	+	4.20152i	−0.487459	+	0.201912i	0.125397	+	0.992107i	$0.459980\pi$
$434$		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	0.722245	−	0.691638i	$-0.243110\pi$
$439$	−1.20995	−	1.37969i	−0.0577479	−	0.0658489i	−0.779993	+	0.625789i	$0.784777\pi$
$440$		0			0
$441$	−20.9593	−	0.415860i	−0.998060	−	0.0198028i
$442$		0			0
$443$	6.02389	+	10.4337i	0.286204	+	0.495719i	0.972900	−	0.231225i	$-0.0742733\pi$
$443$	6.02389	+	10.4337i	0.286204	+	0.495719i	−0.686697	+	0.726944i	$0.740940\pi$
$444$		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	0.947614	−	0.319418i	$-0.103487\pi$
$449$	6.14231	+	9.19262i	0.289874	+	0.433827i	−0.657740	+	0.753245i	$0.728487\pi$
$450$		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	−0.0963487	−	0.995348i	$-0.530716\pi$
$457$	1.45796	−	0.191944i	0.0682005	−	0.00897877i	0.164549	+	0.986369i	$0.447383\pi$
$458$		0			0
$459$	−1.55083	+	0.888815i	−0.0723864	+	0.0414863i
$460$		0			0
$461$	−8.98903	+	21.7014i	−0.418661	+	1.01074i	0.564075	+	0.825723i	$0.309233\pi$
$461$	−8.98903	+	21.7014i	−0.418661	+	1.01074i	−0.982736	+	0.185013i	$0.940767\pi$
$462$		0			0
$463$	−25.2281	−	25.2281i	−1.17245	−	1.17245i	−0.981624	−	0.190823i	$-0.938884\pi$
$463$	−25.2281	−	25.2281i	−1.17245	−	1.17245i	−0.190823	−	0.981624i	$-0.561116\pi$
$464$		0			0
$465$	−0.260030	−	0.228040i	−0.0120586	−	0.0105751i
$466$		0			0
$467$	19.5644	+	15.0123i	0.905331	+	0.694685i	0.952609	−	0.304197i	$-0.0983880\pi$
$467$	19.5644	+	15.0123i	0.905331	+	0.694685i	−0.0472781	+	0.998882i	$0.515055\pi$
$468$		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	0.599464	−	0.800402i	$-0.295380\pi$
$479$	12.8646	+	4.36694i	0.587798	+	0.199530i	−0.0116666	+	0.999932i	$0.503714\pi$
$480$		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	0.149620	−	0.988744i	$-0.452195\pi$
$487$	−17.9002	−	15.6980i	−0.811135	−	0.711346i	−0.960755	+	0.277397i	$0.910528\pi$
$488$		0			0
$489$	−0.715763	−	0.715763i	−0.0323679	−	0.0323679i
$490$		0			0
$491$	13.5360	−	32.6788i	0.610871	−	1.47477i	−0.251174	−	0.967942i	$-0.580817\pi$
$491$	13.5360	−	32.6788i	0.610871	−	1.47477i	0.862045	−	0.506831i	$-0.169183\pi$
$492$		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	0.979467	+	0.201604i	$0.0646156\pi$
$499$	7.26291	+	21.3959i	0.325133	+	0.957810i	−0.654334	+	0.756205i	$0.727051\pi$
$500$		0			0
$501$	1.67237	+	0.220172i	0.0747160	+	0.00983654i
$502$		0			0
$503$	−12.0109	−	17.9755i	−0.535538	−	0.801489i	0.460754	−	0.887528i	$-0.347579\pi$
$503$	−12.0109	−	17.9755i	−0.535538	−	0.801489i	−0.996292	+	0.0860387i	$0.972579\pi$
$504$		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	−0.999449	−	0.0332034i	$-0.989429\pi$
$509$	−11.9230	−	20.6513i	−0.528479	−	0.915353i	0.470969	−	0.882150i	$-0.343904\pi$
$510$		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	0.101024	+	0.994884i	$0.467788\pi$
$521$	−20.5094	+	23.3865i	−0.898535	+	1.02458i	−0.999559	+	0.0296989i	$0.990545\pi$
$522$		0			0
$523$	−5.09815	+	19.0266i	−0.222927	+	0.831973i	0.760298	+	0.649574i	$0.225053\pi$
$523$	−5.09815	+	19.0266i	−0.222927	+	0.831973i	−0.983225	+	0.182399i	$0.941614\pi$
$524$		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	−0.525724	−	0.850655i	$-0.676205\pi$
$541$	5.79237	−	5.07977i	0.249033	−	0.218396i	0.774757	+	0.632259i	$0.217872\pi$
$542$		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	−0.485886	−	0.874022i	$-0.661503\pi$
$547$	−14.0401	+	2.79276i	−0.600313	+	0.119410i	−0.114427	+	0.993432i	$0.536503\pi$
$548$		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	0.983499	−	0.180914i	$-0.0579056\pi$
$557$	0.974877	+	3.63829i	0.0413069	+	0.154159i	−0.942192	+	0.335073i	$0.891239\pi$
$558$		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	0.307425	−	0.951572i	$-0.400533\pi$
$563$	−16.4027	−	21.3764i	−0.691291	−	0.900908i	−0.998716	+	0.0506645i	$0.983866\pi$
$564$		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	−0.887899	−	0.460038i	$-0.847836\pi$
$569$	−5.09830	+	6.64423i	−0.213732	+	0.278541i	0.674168	+	0.738578i	$0.264503\pi$
$570$		0			0
$571$	−2.13827	−	32.6236i	−0.0894837	−	1.36526i	−0.772575	−	0.634924i	$-0.781032\pi$
$571$	−2.13827	−	32.6236i	−0.0894837	−	1.36526i	0.683091	−	0.730333i	$-0.260635\pi$
$572$		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	−0.503502	−	0.863994i	$-0.667955\pi$
$577$	11.9261	−	20.6566i	0.496489	−	0.859945i	0.999992	+	0.00404886i	$0.00128879\pi$
$578$		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	0.963845	+	0.266464i	$0.0858554\pi$
$587$	11.4047	+	27.5334i	0.470722	+	1.13642i	−0.493122	+	0.869960i	$0.664145\pi$
$588$		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	0.622422	+	0.782682i	$0.286149\pi$
$593$	5.44943	+	41.3926i	0.223781	+	1.69979i	−0.398641	+	0.917107i	$0.630518\pi$
$594$		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	0.270260	−	0.962787i	$-0.412890\pi$
$599$	24.1246	−	6.46418i	0.985706	−	0.264119i	0.715446	+	0.698668i	$0.246224\pi$
$600$		0			0
$601$	2.04475	−	10.2797i	0.0834072	−	0.419316i	−0.916411	−	0.400239i	$-0.868927\pi$
$601$	2.04475	−	10.2797i	0.0834072	−	0.419316i	0.999818	−	0.0190773i	$-0.00607286\pi$
$602$		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	−0.310553	−	0.950556i	$-0.600514\pi$
$607$	−18.2938	−	1.19904i	−0.742521	−	0.0486674i	−0.431968	+	0.901889i	$0.642181\pi$
$608$		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	−0.840576	−	0.541694i	$-0.817783\pi$
$613$	1.20904	−	2.09411i	0.0488326	−	0.0845805i	0.889409	+	0.457113i	$0.151117\pi$
$614$		0			0
$615$	0.0593753	+	0.298500i	0.00239424	+	0.0120367i
$616$		0			0
$617$	26.7629	−	40.0535i	1.07743	−	1.61249i	0.335469	−	0.942051i	$-0.391105\pi$
$617$	26.7629	−	40.0535i	1.07743	−	1.61249i	0.741963	−	0.670441i	$-0.233895\pi$
$618$		0			0
$619$	−0.683337	−	10.4257i	−0.0274656	−	0.419045i	−0.989347	−	0.145577i	$-0.953496\pi$
$619$	−0.683337	−	10.4257i	−0.0274656	−	0.419045i	0.961881	−	0.273467i	$-0.0881706\pi$
$620$		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	0.117752	−	0.993043i	$-0.462431\pi$
$631$	−12.5893	−	5.21467i	−0.501173	−	0.207593i	−0.618925	+	0.785450i	$0.712431\pi$
$632$		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	−0.498804	−	0.866715i	$-0.666227\pi$
$641$	−2.90764	+	1.43389i	−0.114845	+	0.0566353i	0.383959	+	0.923350i	$0.374560\pi$
$642$		0			0
$643$	2.18821	−	0.435261i	0.0862944	−	0.0171650i	−0.151754	−	0.988418i	$-0.548492\pi$
$643$	2.18821	−	0.435261i	0.0862944	−	0.0171650i	0.238049	+	0.971253i	$0.423492\pi$
$644$		0			0
$645$		−	0.387104i		−	0.0152422i
$646$		0			0
$647$	24.6477	+	14.2304i	0.969001	+	0.559453i	0.898932	−	0.438089i	$-0.144345\pi$
$647$	24.6477	+	14.2304i	0.969001	+	0.559453i	0.0700694	+	0.997542i	$0.477678\pi$
$648$		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	−0.686043	−	0.727561i	$-0.740654\pi$
$653$	7.89121	−	16.0018i	0.308807	−	0.626198i	0.994850	+	0.101363i	$0.0323204\pi$
$654$		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	−0.947256	−	0.320477i	$-0.896157\pi$
$659$	−16.0901	+	16.0901i	−0.626780	+	0.626780i	0.320477	+	0.947256i	$0.396157\pi$
$660$		0			0
$661$	30.6867	−	23.5467i	1.19357	−	0.915862i	0.195677	−	0.980668i	$-0.437310\pi$
$661$	30.6867	−	23.5467i	1.19357	−	0.915862i	0.997898	+	0.0648063i	$0.0206429\pi$
$662$		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	−0.751685	−	0.659522i	$-0.770759\pi$
$673$	−11.1558	+	7.45405i	−0.430024	+	0.287333i	0.321662	+	0.946855i	$0.395759\pi$
$674$		0			0
$675$	−0.883135	−	1.79082i	−0.0339919	−	0.0689287i
$676$		0			0
$677$	19.0158	+	21.6833i	0.730836	+	0.833359i	0.991231	−	0.132143i	$-0.0421860\pi$
$677$	19.0158	+	21.6833i	0.730836	+	0.833359i	−0.260395	+	0.965502i	$0.583853\pi$
$678$		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	−0.752750	−	0.658307i	$-0.771273\pi$
$683$	6.40809	−	18.8776i	0.245199	−	0.722332i	0.997948	−	0.0640250i	$-0.0203937\pi$
$684$		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	0.980955	−	0.194237i	$-0.0622230\pi$
$691$	2.22038	+	6.54102i	0.0844671	+	0.248832i	−0.896488	+	0.443069i	$0.853890\pi$
$692$		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	0.998923	−	0.0463917i	$-0.0147722\pi$
$701$	25.2196	+	25.2196i	0.952532	+	0.952532i	−0.0463917	+	0.998923i	$0.514772\pi$
$702$		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	−0.999752	−	0.0222786i	$-0.992908\pi$
$709$	−0.150312	+	2.29331i	−0.00564507	+	0.0861271i	0.994107	+	0.108406i	$0.0345746\pi$
$710$		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	0.515662	+	0.856792i	$0.327546\pi$
$719$	−2.88044	+	43.9470i	−0.107422	+	1.63895i	−0.623084	+	0.782155i	$0.714121\pi$
$720$		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	0.260297	−	0.965529i	$-0.416179\pi$
$727$	−19.0151	−	19.0151i	−0.705231	−	0.705231i	−0.965529	+	0.260297i	$0.916179\pi$
$728$		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	−0.139758	−	0.990186i	$-0.544633\pi$
$733$	−0.500212	+	0.0658541i	−0.0184757	+	0.00243238i	0.121283	+	0.992618i	$0.461299\pi$
$734$		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	−0.810293	−	0.586025i	$-0.800692\pi$
$739$	−47.4275	−	6.24395i	−1.74465	−	0.229688i	−0.934357	+	0.356338i	$0.884025\pi$
$740$		0			0
$741$	0.610352	+	0.913456i	0.0224218	+	0.0335567i
$742$		0			0
$743$	18.7633	+	12.5372i	0.688358	+	0.459946i	0.849917	−	0.526917i	$-0.176652\pi$
$743$	18.7633	+	12.5372i	0.688358	+	0.459946i	−0.161559	+	0.986863i	$0.551652\pi$
$744$		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	0.593237	−	0.805028i	$-0.297850\pi$
$751$	−7.73727	−	8.82266i	−0.282337	−	0.321944i	−0.875574	+	0.483084i	$0.839516\pi$
$752$		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	0.127552	−	0.991832i	$-0.459288\pi$
$757$	25.2871	−	10.4743i	0.919076	−	0.380694i	0.791524	+	0.611138i	$0.209288\pi$
$758$		0			0
$759$	0.323632	−	0.369031i	0.0117471	−	0.0133950i
$760$		0			0
$761$	−3.11390	+	11.6212i	−0.112879	+	0.421269i	−0.999119	−	0.0419558i	$-0.986641\pi$
$761$	−3.11390	+	11.6212i	−0.112879	+	0.421269i	0.886241	+	0.463225i	$0.153308\pi$
$762$		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	−0.687460	−	0.726222i	$-0.741274\pi$
$769$	1.07491	−	1.07491i	0.0387624	−	0.0387624i	0.726222	+	0.687460i	$0.241274\pi$
$770$		0			0
$771$	−0.0694651	−	0.0138175i	−0.00250173	−	0.000497624i
$772$		0			0
$773$	−1.97936	+	15.0347i	−0.0711925	+	0.540760i	0.918268	+	0.395959i	$0.129588\pi$
$773$	−1.97936	+	15.0347i	−0.0711925	+	0.540760i	−0.989461	+	0.144802i	$0.953746\pi$
$774$		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	−0.336822	−	0.941568i	$-0.609352\pi$
$787$	5.75464	−	2.83788i	0.205131	−	0.101159i	0.541952	+	0.840409i	$0.317685\pi$
$788$		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	0.196212	−	0.980561i	$-0.437136\pi$
$797$	−10.1182	−	4.19111i	−0.358406	−	0.148457i	−0.554619	+	0.832105i	$0.687136\pi$
$798$		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	0.995583	+	0.0938908i	$0.0299305\pi$
$809$	0.590832	+	9.01436i	0.0207726	+	0.316928i	−0.974810	+	0.223037i	$0.928403\pi$
$810$		0			0
$811$	24.7423	−	37.0295i	0.868819	−	1.30028i	−0.0839144	−	0.996473i	$-0.526742\pi$
$811$	24.7423	−	37.0295i	0.868819	−	1.30028i	0.952734	−	0.303807i	$-0.0982578\pi$
$812$		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	0.765076	−	0.643940i	$-0.222701\pi$
$821$	41.2477	+	2.70352i	1.43956	+	0.0943535i	0.674480	+	0.738293i	$0.264368\pi$
$822$		0			0
$823$	−5.56054	+	0.364457i	−0.193828	+	0.0127042i	−0.162008	−	0.986789i	$-0.551797\pi$
$823$	−5.56054	+	0.364457i	−0.193828	+	0.0127042i	−0.0318202	+	0.999494i	$0.510130\pi$
$824$		0			0
$825$	0.308448	+	0.744660i	0.0107388	+	0.0259257i
$826$		0			0
$827$	−3.00896	+	15.1271i	−0.104632	+	0.526019i	0.892547	+	0.450954i	$0.148916\pi$
$827$	−3.00896	+	15.1271i	−0.104632	+	0.526019i	−0.997179	+	0.0750647i	$0.976084\pi$
$828$		0			0
$829$	8.56943	−	2.29617i	0.297628	−	0.0797493i	−0.106915	−	0.994268i	$-0.534097\pi$
$829$	8.56943	−	2.29617i	0.297628	−	0.0797493i	0.404543	+	0.914519i	$0.367431\pi$
$830$		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	−0.771203	−	0.636589i	$-0.780345\pi$
$839$	5.35595	−	26.9262i	0.184908	−	0.929594i	0.956111	−	0.293005i	$-0.0946553\pi$
$840$		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	0.652671	+	0.757642i	$0.273649\pi$
$853$	9.91896	+	49.8660i	0.339619	+	1.70738i	−0.313052	+	0.949736i	$0.601351\pi$
$854$		0			0
$855$	3.05642	−	4.57426i	0.104528	−	0.156436i
$856$		0			0
$857$	−0.257568	−	3.92973i	−0.00879835	−	0.134237i	−0.999998	−	0.00186345i	$-0.999407\pi$
$857$	−0.257568	−	3.92973i	−0.00879835	−	0.134237i	0.991200	−	0.132373i	$-0.0422598\pi$
$858$		0			0
$859$	−3.71729	+	4.84447i	−0.126832	+	0.165291i	−0.852453	−	0.522804i	$-0.824886\pi$
$859$	−3.71729	+	4.84447i	−0.126832	+	0.165291i	0.725621	+	0.688095i	$0.241553\pi$
$860$		0			0
$861$	1.07340	−	0.701925i	0.0365815	−	0.0239215i
$862$		0			0
$863$	−21.7747	−	5.83450i	−0.741218	−	0.198609i	−0.131599	−	0.991303i	$-0.542011\pi$
$863$	−21.7747	−	5.83450i	−0.741218	−	0.198609i	−0.609619	+	0.792694i	$0.708678\pi$
$864$		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	0.843028	−	0.537869i	$-0.180770\pi$
$877$	27.5267	+	13.5747i	0.929512	+	0.458384i	0.0864831	+	0.996253i	$0.472437\pi$
$878$		0			0
$879$	−1.00840	+	0.497286i	−0.0340124	+	0.0167730i
$880$		0			0
$881$	−41.3305	+	8.22114i	−1.39246	+	0.276977i	−0.833638	−	0.552311i	$-0.813746\pi$
$881$	−41.3305	+	8.22114i	−1.39246	+	0.276977i	−0.558821	+	0.829288i	$0.688746\pi$
$882$		0			0
$883$			25.4892i			0.857780i	0.903357	+	0.428890i	$0.141095\pi$
$883$			25.4892i			0.857780i	−0.903357	+	0.428890i	$0.858905\pi$
$884$		0			0
$885$	0.0171965	+	0.00992842i	0.000578055	+	0.000333740i
$886$		0			0
$887$	8.73722	−	7.66234i	0.293367	−	0.257276i	−0.499992	−	0.866030i	$-0.666664\pi$
$887$	8.73722	−	7.66234i	0.293367	−	0.257276i	0.793359	+	0.608754i	$0.208330\pi$
$888$		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	−0.969687	−	0.244350i	$-0.921426\pi$
$907$	−18.0957	+	20.6342i	−0.600858	+	0.685148i	0.368829	+	0.929497i	$0.379759\pi$
$908$		0			0
$909$	−15.8210	+	6.55326i	−0.524749	+	0.217358i
$910$		0			0
$911$	−7.92486	+	5.29522i	−0.262562	+	0.175439i	−0.679883	−	0.733321i	$-0.737969\pi$
$911$	−7.92486	+	5.29522i	−0.262562	+	0.175439i	0.417320	+	0.908759i	$0.362969\pi$
$912$		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	0.863176	−	0.504902i	$-0.168471\pi$
$919$	−0.171885	−	0.297714i	−0.00566997	−	0.00982068i	−0.868846	+	0.495082i	$0.835138\pi$
$920$		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	−0.992298	−	0.123872i	$-0.960469\pi$
$929$	−8.54839	−	25.1828i	−0.280464	−	0.826219i	0.711835	−	0.702347i	$-0.247865\pi$
$930$		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	0.290373	+	0.956914i	$0.406221\pi$
$937$	−18.1089	+	43.7187i	−0.591592	+	1.42823i	−0.881965	+	0.471316i	$0.843779\pi$
$938$		0			0
$939$	1.22884	+	1.22884i	0.0401016	+	0.0401016i
$940$		0			0
$941$	−34.6208	−	30.3617i	−1.12861	−	0.989762i	−0.128609	−	0.991695i	$-0.541051\pi$
$941$	−34.6208	−	30.3617i	−1.12861	−	0.989762i	−0.999998	+	0.00193359i	$0.999385\pi$
$942$		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	0.311286	+	0.950316i	$0.399240\pi$
$947$	−3.73521	+	56.9883i	−0.121378	+	1.85187i	−0.432664	+	0.901555i	$0.642426\pi$
$948$		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	−0.542208	−	0.840244i	$-0.682412\pi$
$967$	13.5374	−	32.6821i	0.435333	−	1.05099i	0.977542	−	0.210743i	$-0.0675883\pi$
$968$		0			0
$969$	0.228475	−	0.841976i	0.00733968	−	0.0270482i
$970$		0			0
$971$	49.5136	−	6.51859i	1.58897	−	0.209192i	0.716402	−	0.697688i	$-0.245788\pi$
$971$	49.5136	−	6.51859i	1.58897	−	0.209192i	0.872566	+	0.488496i	$0.162454\pi$
$972$		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	0.437906	−	0.899021i	$-0.355720\pi$
$977$	19.6358	+	2.58511i	0.628206	+	0.0827049i	0.190300	+	0.981726i	$0.439054\pi$
$978$		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	−0.879191	−	0.476470i	$-0.841916\pi$
$983$	3.39785	−	10.0098i	0.108375	−	0.319262i	0.987565	+	0.157208i	$0.0502494\pi$
$984$		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	−0.980989	−	0.194061i	$-0.937834\pi$
$991$	−16.9288	−	34.3281i	−0.537760	−	1.09047i	0.443229	−	0.896408i	$-0.353833\pi$
$992$		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	0.414049	−	0.910255i	$-0.364114\pi$
$997$	39.8629	−	45.4550i	1.26247	−	1.43957i	0.848423	−	0.529318i	$-0.177552\pi$
$998$		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.465.6	yes	192
7.5	odd	6	inner	476.2.bl.a.397.6	yes	192
17.3	odd	16	inner	476.2.bl.a.241.6	yes	192
119.54	even	48	inner	476.2.bl.a.173.6	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.173.6	✓	192	119.54	even	48	inner
476.2.bl.a.241.6	yes	192	17.3	odd	16	inner
476.2.bl.a.397.6	yes	192	7.5	odd	6	inner
476.2.bl.a.465.6	yes	192	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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