LMFDB - Embedded newform 375.2.e.c.182.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,2,Mod(68,375)] 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("375.68"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			182.8
Character	$\chi$	$=$	375.182
Dual form			375.2.e.c.68.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.413570 + 0.413570i) q^{2} +(1.69938 + 0.334821i) q^{3} +1.65792i q^{4} +(-0.841285 + 0.564341i) q^{6} +(2.93422 + 2.93422i) q^{7} +(-1.51281 - 1.51281i) q^{8} +(2.77579 + 1.13798i) q^{9} -5.05566i q^{11} +(-0.555106 + 2.81744i) q^{12} +(-0.394459 + 0.394459i) q^{13} -2.42701 q^{14} -2.06454 q^{16} +(-4.21618 + 4.21618i) q^{17} +(-1.61862 + 0.677351i) q^{18} -3.72246i q^{19} +(4.00391 + 5.96879i) q^{21} +(2.09087 + 2.09087i) q^{22} +(1.85974 + 1.85974i) q^{23} +(-2.06431 - 3.07735i) q^{24} -0.326273i q^{26} +(4.33611 + 2.86325i) q^{27} +(-4.86469 + 4.86469i) q^{28} -2.32216 q^{29} +0.707221 q^{31} +(3.87944 - 3.87944i) q^{32} +(1.69274 - 8.59150i) q^{33} -3.48737i q^{34} +(-1.88667 + 4.60204i) q^{36} +(-2.33466 - 2.33466i) q^{37} +(1.53950 + 1.53950i) q^{38} +(-0.802409 + 0.538263i) q^{39} -4.45490i q^{41} +(-4.12441 - 0.812613i) q^{42} +(4.74766 - 4.74766i) q^{43} +8.38188 q^{44} -1.53826 q^{46} +(-2.25881 + 2.25881i) q^{47} +(-3.50843 - 0.691250i) q^{48} +10.2192i q^{49} +(-8.57656 + 5.75323i) q^{51} +(-0.653981 - 0.653981i) q^{52} +(5.26793 + 5.26793i) q^{53} +(-2.97744 + 0.609130i) q^{54} -8.87780i q^{56} +(1.24636 - 6.32587i) q^{57} +(0.960377 - 0.960377i) q^{58} -0.326273 q^{59} +1.14590 q^{61} +(-0.292485 + 0.292485i) q^{62} +(4.80570 + 11.4838i) q^{63} -0.920229i q^{64} +(2.85312 + 4.25325i) q^{66} +(-7.14493 - 7.14493i) q^{67} +(-6.99008 - 6.99008i) q^{68} +(2.53772 + 3.78308i) q^{69} -3.12457i q^{71} +(-2.47769 - 5.92077i) q^{72} +(1.44290 - 1.44290i) q^{73} +1.93109 q^{74} +6.17153 q^{76} +(14.8344 - 14.8344i) q^{77} +(0.109243 - 0.554462i) q^{78} -0.0493012i q^{79} +(6.41002 + 6.31757i) q^{81} +(1.84241 + 1.84241i) q^{82} +(-8.20345 - 8.20345i) q^{83} +(-9.89577 + 6.63816i) q^{84} +3.92698i q^{86} +(-3.94624 - 0.777509i) q^{87} +(-7.64824 + 7.64824i) q^{88} +5.75323 q^{89} -2.31486 q^{91} +(-3.08329 + 3.08329i) q^{92} +(1.20184 + 0.236792i) q^{93} -1.86835i q^{94} +(7.89157 - 5.29373i) q^{96} +(-9.64599 - 9.64599i) q^{97} +(-4.22637 - 4.22637i) q^{98} +(5.75323 - 14.0335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{6} - 24 q^{16} + 32 q^{21} - 56 q^{31} - 116 q^{36} - 96 q^{46} - 48 q^{51} + 144 q^{61} + 120 q^{66} + 168 q^{76} + 132 q^{81} - 56 q^{91} + 76 q^{96}+O(q^{100}) $ 32 * q + 12 * q^6 - 24 * q^16 + 32 * q^21 - 56 * q^31 - 116 * q^36 - 96 * q^46 - 48 * q^51 + 144 * q^61 + 120 * q^66 + 168 * q^76 + 132 * q^81 - 56 * q^91 + 76 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.413570	+	0.413570i	−0.292438	+	0.292438i	−0.838043	−	0.545605i	$-0.816300\pi$
$2$	−0.413570	+	0.413570i	−0.292438	+	0.292438i	0.545605	+	0.838043i	$0.316300\pi$
$3$	1.69938	+	0.334821i	0.981138	+	0.193309i
$3$	1.69938	+	0.334821i	0.981138	+	0.193309i
$4$			1.65792i			0.828960i
$5$		0			0
$5$		0			0
$6$	−0.841285	+	0.564341i	−0.343453	+	0.230391i
$7$	2.93422	+	2.93422i	1.10903	+	1.10903i	0.993278	+	0.115751i	$0.0369275\pi$
$7$	2.93422	+	2.93422i	1.10903	+	1.10903i	0.115751	+	0.993278i	$0.463073\pi$
$8$	−1.51281	−	1.51281i	−0.534858	−	0.534858i
$9$	2.77579	+	1.13798i	0.925263	+	0.379326i
$10$		0			0
$11$		−	5.05566i		−	1.52434i	−0.647377	−	0.762170i	$-0.724134\pi$
$11$		−	5.05566i		−	1.52434i	0.647377	−	0.762170i	$-0.275866\pi$
$12$	−0.555106	+	2.81744i	−0.160245	+	0.813324i
$13$	−0.394459	+	0.394459i	−0.109403	+	0.109403i	−0.759689	−	0.650286i	$-0.774649\pi$
$13$	−0.394459	+	0.394459i	−0.109403	+	0.109403i	0.650286	+	0.759689i	$0.274649\pi$
$14$	−2.42701			−0.648645
$15$		0			0
$16$	−2.06454			−0.516134
$17$	−4.21618	+	4.21618i	−1.02257	+	1.02257i	−0.0228342	+	0.999739i	$0.507269\pi$
$17$	−4.21618	+	4.21618i	−1.02257	+	1.02257i	−0.999739	+	0.0228342i	$0.992731\pi$
$18$	−1.61862	+	0.677351i	−0.381512	+	0.159653i
$19$		−	3.72246i		−	0.853990i	−0.904254	−	0.426995i	$-0.859572\pi$
$19$		−	3.72246i		−	0.853990i	0.904254	−	0.426995i	$-0.140428\pi$
$20$		0			0
$21$	4.00391	+	5.96879i	0.873725	+	1.30250i
$22$	2.09087	+	2.09087i	0.445775	+	0.445775i
$23$	1.85974	+	1.85974i	0.387782	+	0.387782i	0.873896	−	0.486114i	$-0.161586\pi$
$23$	1.85974	+	1.85974i	0.387782	+	0.387782i	−0.486114	+	0.873896i	$0.661586\pi$
$24$	−2.06431	−	3.07735i	−0.421376	−	0.628162i
$25$		0			0
$26$		−	0.326273i		−	0.0639874i
$27$	4.33611	+	2.86325i	0.834484	+	0.551032i
$28$	−4.86469	+	4.86469i	−0.919341	+	0.919341i
$29$	−2.32216			−0.431215			−0.215607	−	0.976480i	$-0.569173\pi$
$29$	−2.32216			−0.431215			−0.215607	+	0.976480i	$0.569173\pi$
$30$		0			0
$31$	0.707221			0.127021			0.0635103	−	0.997981i	$-0.479770\pi$
$31$	0.707221			0.127021			0.0635103	+	0.997981i	$0.479770\pi$
$32$	3.87944	−	3.87944i	0.685795	−	0.685795i
$33$	1.69274	−	8.59150i	0.294669	−	1.49559i
$34$		−	3.48737i		−	0.598079i
$35$		0			0
$36$	−1.88667	+	4.60204i	−0.314446	+	0.767006i
$37$	−2.33466	−	2.33466i	−0.383816	−	0.383816i	0.488659	−	0.872475i	$-0.337486\pi$
$37$	−2.33466	−	2.33466i	−0.383816	−	0.383816i	−0.872475	+	0.488659i	$0.837486\pi$
$38$	1.53950	+	1.53950i	0.249739	+	0.249739i
$39$	−0.802409	+	0.538263i	−0.128488	+	0.0861911i
$40$		0			0
$41$		−	4.45490i		−	0.695739i	−0.937543	−	0.347869i	$-0.886905\pi$
$41$		−	4.45490i		−	0.695739i	0.937543	−	0.347869i	$-0.113095\pi$
$42$	−4.12441	−	0.812613i	−0.636410	−	0.125389i
$43$	4.74766	−	4.74766i	0.724011	−	0.724011i	−0.245408	−	0.969420i	$-0.578922\pi$
$43$	4.74766	−	4.74766i	0.724011	−	0.724011i	0.969420	+	0.245408i	$0.0789220\pi$
$44$	8.38188			1.26362
$45$		0			0
$46$	−1.53826			−0.226804
$47$	−2.25881	+	2.25881i	−0.329481	+	0.329481i	−0.852389	−	0.522908i	$-0.824847\pi$
$47$	−2.25881	+	2.25881i	−0.329481	+	0.329481i	0.522908	+	0.852389i	$0.324847\pi$
$48$	−3.50843	−	0.691250i	−0.506399	−	0.0997734i
$49$			10.2192i			1.45989i
$50$		0			0
$51$	−8.57656	+	5.75323i	−1.20096	+	0.805613i
$52$	−0.653981	−	0.653981i	−0.0906909	−	0.0906909i
$53$	5.26793	+	5.26793i	0.723606	+	0.723606i	0.969338	−	0.245732i	$-0.0790284\pi$
$53$	5.26793	+	5.26793i	0.723606	+	0.723606i	−0.245732	+	0.969338i	$0.579028\pi$
$54$	−2.97744	+	0.609130i	−0.405178	+	0.0828920i
$55$		0			0
$56$		−	8.87780i		−	1.18635i
$57$	1.24636	−	6.32587i	0.165084	−	0.837882i
$58$	0.960377	−	0.960377i	0.126104	−	0.126104i
$59$	−0.326273			−0.0424771			−0.0212386	−	0.999774i	$-0.506761\pi$
$59$	−0.326273			−0.0424771			−0.0212386	+	0.999774i	$0.506761\pi$
$60$		0			0
$61$	1.14590			0.146717			0.0733586	−	0.997306i	$-0.476628\pi$
$61$	1.14590			0.146717			0.0733586	+	0.997306i	$0.476628\pi$
$62$	−0.292485	+	0.292485i	−0.0371457	+	0.0371457i
$63$	4.80570	+	11.4838i	0.605461	+	1.44683i
$64$		−	0.920229i		−	0.115029i
$65$		0			0
$66$	2.85312	+	4.25325i	0.351195	+	0.523539i
$67$	−7.14493	−	7.14493i	−0.872892	−	0.872892i	0.119895	−	0.992787i	$-0.461744\pi$
$67$	−7.14493	−	7.14493i	−0.872892	−	0.872892i	−0.992787	+	0.119895i	$0.961744\pi$
$68$	−6.99008	−	6.99008i	−0.847672	−	0.847672i
$69$	2.53772	+	3.78308i	0.305506	+	0.455429i
$70$		0			0
$71$		−	3.12457i		−	0.370818i	−0.982661	−	0.185409i	$-0.940639\pi$
$71$		−	3.12457i		−	0.370818i	0.982661	−	0.185409i	$-0.0593611\pi$
$72$	−2.47769	−	5.92077i	−0.291999	−	0.697769i
$73$	1.44290	−	1.44290i	0.168879	−	0.168879i	−0.617608	−	0.786486i	$-0.711898\pi$
$73$	1.44290	−	1.44290i	0.168879	−	0.168879i	0.786486	+	0.617608i	$0.211898\pi$
$74$	1.93109			0.224485
$75$		0			0
$76$	6.17153			0.707923
$77$	14.8344	−	14.8344i	1.69054	−	1.69054i
$78$	0.109243	−	0.554462i	0.0123693	−	0.0627805i
$79$		−	0.0493012i		−	0.00554682i	−0.999996	−	0.00277341i	$-0.999117\pi$
$79$		−	0.0493012i		−	0.00554682i	0.999996	−	0.00277341i	$-0.000882805\pi$
$80$		0			0
$81$	6.41002	+	6.31757i	0.712224	+	0.701952i
$82$	1.84241	+	1.84241i	0.203461	+	0.203461i
$83$	−8.20345	−	8.20345i	−0.900445	−	0.900445i	0.0950292	−	0.995474i	$-0.469706\pi$
$83$	−8.20345	−	8.20345i	−0.900445	−	0.900445i	−0.995474	+	0.0950292i	$0.969706\pi$
$84$	−9.89577	+	6.63816i	−1.07972	+	0.724283i
$85$		0			0
$86$			3.92698i			0.423457i
$87$	−3.94624	−	0.777509i	−0.423081	−	0.0833577i
$88$	−7.64824	+	7.64824i	−0.815305	+	0.815305i
$89$	5.75323			0.609841			0.304920	−	0.952378i	$-0.401370\pi$
$89$	5.75323			0.609841			0.304920	+	0.952378i	$0.401370\pi$
$90$		0			0
$91$	−2.31486			−0.242663
$92$	−3.08329	+	3.08329i	−0.321456	+	0.321456i
$93$	1.20184	+	0.236792i	0.124625	+	0.0245542i
$94$		−	1.86835i		−	0.192706i
$95$		0			0
$96$	7.89157	−	5.29373i	0.805430	−	0.540289i
$97$	−9.64599	−	9.64599i	−0.979402	−	0.979402i	0.0203901	−	0.999792i	$-0.493509\pi$
$97$	−9.64599	−	9.64599i	−0.979402	−	0.979402i	−0.999792	+	0.0203901i	$0.993509\pi$
$98$	−4.22637	−	4.22637i	−0.426928	−	0.426928i
$99$	5.75323	−	14.0335i	0.578221	−	1.41042i
$100$		0			0
$101$		−	12.4137i		−	1.23521i	−0.786488	−	0.617605i	$-0.788103\pi$
$101$		−	12.4137i		−	1.23521i	0.786488	−	0.617605i	$-0.211897\pi$
$102$	1.16765	−	5.92637i	0.115614	−	0.586798i
$103$	3.87068	−	3.87068i	0.381389	−	0.381389i	−0.490213	−	0.871603i	$-0.663081\pi$
$103$	3.87068	−	3.87068i	0.381389	−	0.381389i	0.871603	+	0.490213i	$0.163081\pi$
$104$	1.19348			0.117030
$105$		0			0
$106$	−4.35732			−0.423220
$107$	−1.23052	+	1.23052i	−0.118958	+	0.118958i	−0.764080	−	0.645122i	$-0.776807\pi$
$107$	−1.23052	+	1.23052i	−0.118958	+	0.118958i	0.645122	+	0.764080i	$0.276807\pi$
$108$	−4.74704	+	7.18891i	−0.456784	+	0.691754i
$109$		−	4.43225i		−	0.424533i	−0.977212	−	0.212266i	$-0.931916\pi$
$109$		−	4.43225i		−	0.424533i	0.977212	−	0.212266i	$-0.0680844\pi$
$110$		0			0
$111$	−3.18578	−	4.74917i	−0.302381	−	0.450771i
$112$	−6.05779	−	6.05779i	−0.572408	−	0.572408i
$113$	8.78129	+	8.78129i	0.826074	+	0.826074i	0.986971	−	0.160897i	$-0.0514387\pi$
$113$	8.78129	+	8.78129i	0.826074	+	0.826074i	−0.160897	+	0.986971i	$0.551439\pi$
$114$	2.10073	+	3.13165i	0.196752	+	0.293306i
$115$		0			0
$116$		−	3.84996i		−	0.357460i
$117$	−1.54382	+	0.646050i	−0.142726	+	0.0597274i
$118$	0.134937	−	0.134937i	0.0124219	−	0.0124219i
$119$	−24.7424			−2.26813
$120$		0			0
$121$	−14.5597			−1.32361
$122$	−0.473909	+	0.473909i	−0.0429057	+	0.0429057i
$123$	1.49159	−	7.57057i	0.134493	−	0.682616i
$124$			1.17252i			0.105295i
$125$		0			0
$126$	−6.73686	−	2.76188i	−0.600167	−	0.246048i
$127$	11.2543	+	11.2543i	0.998661	+	0.998661i	0.999999	−	0.00133793i	$-0.000425876\pi$
$127$	11.2543	+	11.2543i	0.998661	+	0.998661i	−0.00133793	+	0.999999i	$0.500426\pi$
$128$	8.13946	+	8.13946i	0.719434	+	0.719434i
$129$	9.65770	−	6.47847i	0.850313	−	0.570397i
$130$		0			0
$131$			14.4294i			1.26070i	0.776311	+	0.630350i	$0.217089\pi$
$131$			14.4294i			1.26070i	−0.776311	+	0.630350i	$0.782911\pi$
$132$	14.2440	+	2.80643i	1.23978	+	0.244268i
$133$	10.9225	−	10.9225i	0.947100	−	0.947100i
$134$	5.90986			0.510534
$135$		0			0
$136$	12.7565			1.09386
$137$	2.07415	−	2.07415i	0.177207	−	0.177207i	−0.612930	−	0.790137i	$-0.710009\pi$
$137$	2.07415	−	2.07415i	0.177207	−	0.177207i	0.790137	+	0.612930i	$0.210009\pi$
$138$	−2.61409	−	0.515043i	−0.222526	−	0.0438434i
$139$		−	17.1389i		−	1.45370i	−0.686797	−	0.726850i	$-0.740984\pi$
$139$		−	17.1389i		−	1.45370i	0.686797	−	0.726850i	$-0.259016\pi$
$140$		0			0
$141$	−4.59488	+	3.08228i	−0.386959	+	0.259575i
$142$	1.29223	+	1.29223i	0.108441	+	0.108441i
$143$	1.99425	+	1.99425i	0.166768	+	0.166768i
$144$	−5.73072	−	2.34939i	−0.477560	−	0.195783i
$145$		0			0
$146$			1.19348i			0.0987731i
$147$	−3.42162	+	17.3664i	−0.282210	+	1.43236i
$148$	3.87068	−	3.87068i	0.318168	−	0.318168i
$149$	−12.8646			−1.05391			−0.526955	−	0.849893i	$-0.676666\pi$
$149$	−12.8646			−1.05391			−0.526955	+	0.849893i	$0.676666\pi$
$150$		0			0
$151$	18.4690			1.50298			0.751491	−	0.659743i	$-0.229335\pi$
$151$	18.4690			1.50298			0.751491	+	0.659743i	$0.229335\pi$
$152$	−5.63135	+	5.63135i	−0.456763	+	0.456763i
$153$	−16.5011	+	6.90531i	−1.33404	+	0.558261i
$154$			12.2701i			0.988756i
$155$		0			0
$156$	−0.892397	−	1.33033i	−0.0714489	−	0.106512i
$157$	−5.05406	−	5.05406i	−0.403358	−	0.403358i	0.476057	−	0.879414i	$-0.342066\pi$
$157$	−5.05406	−	5.05406i	−0.403358	−	0.403358i	−0.879414	+	0.476057i	$0.842066\pi$
$158$	0.0203895	+	0.0203895i	0.00162210	+	0.00162210i
$159$	7.18840	+	10.7160i	0.570077	+	0.849836i
$160$		0			0
$161$			10.9137i			0.860123i
$162$	−5.26375	+	0.0382343i	−0.413559	+	0.00300397i
$163$	1.49132	−	1.49132i	0.116809	−	0.116809i	−0.646286	−	0.763095i	$-0.723679\pi$
$163$	1.49132	−	1.49132i	0.116809	−	0.116809i	0.763095	+	0.646286i	$0.223679\pi$
$164$	7.38587			0.576739
$165$		0			0
$166$	6.78540			0.526649
$167$	−10.9448	+	10.9448i	−0.846932	+	0.846932i	−0.989749	−	0.142817i	$-0.954384\pi$
$167$	−10.9448	+	10.9448i	−0.846932	+	0.846932i	0.142817	+	0.989749i	$0.454384\pi$
$168$	2.97247	−	15.0868i	0.229331	−	1.16397i
$169$			12.6888i			0.976062i
$170$		0			0
$171$	4.23607	−	10.3328i	0.323940	−	0.790165i
$172$	7.87124	+	7.87124i	0.600176	+	0.600176i
$173$	4.06251	+	4.06251i	0.308867	+	0.308867i	0.844470	−	0.535603i	$-0.179916\pi$
$173$	4.06251	+	4.06251i	0.308867	+	0.308867i	−0.535603	+	0.844470i	$0.679916\pi$
$174$	1.95360	−	1.31049i	0.148102	−	0.0993481i
$175$		0			0
$176$			10.4376i			0.786764i
$177$	−0.554462	−	0.109243i	−0.0416759	−	0.00821121i
$178$	−2.37936	+	2.37936i	−0.178341	+	0.178341i
$179$	11.9574			0.893735			0.446867	−	0.894600i	$-0.352540\pi$
$179$	11.9574			0.893735			0.446867	+	0.894600i	$0.352540\pi$
$180$		0			0
$181$	−16.1242			−1.19851			−0.599253	−	0.800560i	$-0.704535\pi$
$181$	−16.1242			−1.19851			−0.599253	+	0.800560i	$0.704535\pi$
$182$	0.957355	−	0.957355i	0.0709639	−	0.0709639i
$183$	1.94732	+	0.383671i	0.143950	+	0.0283618i
$184$		−	5.62684i		−	0.414816i
$185$		0			0
$186$	−0.594974	+	0.399114i	−0.0436256	+	0.0292644i
$187$	21.3156	+	21.3156i	1.55875	+	1.55875i
$188$	−3.74493	−	3.74493i	−0.273127	−	0.273127i
$189$	4.32168	+	21.1245i	0.314356	+	1.53658i
$190$		0			0
$191$			16.8114i			1.21643i	0.793773	+	0.608214i	$0.208114\pi$
$191$			16.8114i			1.21643i	−0.793773	+	0.608214i	$0.791886\pi$
$192$	0.308112	−	1.56382i	0.0222361	−	0.112859i
$193$	−14.8604	+	14.8604i	−1.06968	+	1.06968i	−0.0722946	+	0.997383i	$0.523032\pi$
$193$	−14.8604	+	14.8604i	−1.06968	+	1.06968i	−0.997383	+	0.0722946i	$0.976968\pi$
$194$	7.97859			0.572829
$195$		0			0
$196$	−16.9427			−1.21019
$197$	3.43288	−	3.43288i	0.244583	−	0.244583i	−0.574160	−	0.818743i	$-0.694671\pi$
$197$	3.43288	−	3.43288i	0.244583	−	0.244583i	0.818743	+	0.574160i	$0.194671\pi$
$198$	3.42446	+	8.18318i	0.243366	+	0.581553i
$199$			17.1084i			1.21278i	0.795167	+	0.606391i	$0.207383\pi$
$199$			17.1084i			1.21278i	−0.795167	+	0.606391i	$0.792617\pi$
$200$		0			0
$201$	−9.74968	−	14.5342i	−0.687689	−	1.02517i
$202$	5.13394	+	5.13394i	0.361223	+	0.361223i
$203$	−6.81373	−	6.81373i	−0.478230	−	0.478230i
$204$	−9.53839	−	14.2192i	−0.667821	−	0.995546i
$205$		0			0
$206$			3.20159i			0.223066i
$207$	3.04590	+	7.27857i	0.211705	+	0.505896i
$208$	0.814375	−	0.814375i	0.0564667	−	0.0564667i
$209$	−18.8195			−1.30177
$210$		0			0
$211$	−7.12265			−0.490343			−0.245172	−	0.969480i	$-0.578844\pi$
$211$	−7.12265			−0.490343			−0.245172	+	0.969480i	$0.578844\pi$
$212$	−8.73380	+	8.73380i	−0.599840	+	0.599840i
$213$	1.04617	−	5.30984i	0.0716825	−	0.363824i
$214$		−	1.01781i		−	0.0695760i
$215$		0			0
$216$	−2.22815	−	10.8912i	−0.151606	−	0.741054i
$217$	2.07514	+	2.07514i	0.140870	+	0.140870i
$218$	1.83305	+	1.83305i	0.124150	+	0.124150i
$219$	2.93515	−	1.96892i	0.198339	−	0.133047i
$220$		0			0
$221$		−	3.32622i		−	0.223746i
$222$	3.28166	+	0.646570i	0.220251	+	0.0433949i
$223$	−14.3937	+	14.3937i	−0.963870	+	0.963870i	−0.999370	−	0.0354995i	$-0.988698\pi$
$223$	−14.3937	+	14.3937i	−0.963870	+	0.963870i	0.0354995	+	0.999370i	$0.488698\pi$
$224$	22.7662			1.52113
$225$		0			0
$226$	−7.26336			−0.483151
$227$	−5.29262	+	5.29262i	−0.351283	+	0.351283i	−0.860587	−	0.509304i	$-0.829903\pi$
$227$	−5.29262	+	5.29262i	−0.351283	+	0.351283i	0.509304	+	0.860587i	$0.329903\pi$
$228$	10.4878	+	2.06636i	0.694570	+	0.136848i
$229$		−	12.4848i		−	0.825019i	−0.910953	−	0.412509i	$-0.864652\pi$
$229$		−	12.4848i		−	0.825019i	0.910953	−	0.412509i	$-0.135348\pi$
$230$		0			0
$231$	30.1762	−	20.2424i	1.98545	−	1.33185i
$232$	3.51298	+	3.51298i	0.230639	+	0.230639i
$233$	−8.88711	−	8.88711i	−0.582214	−	0.582214i	0.353297	−	0.935511i	$-0.385060\pi$
$233$	−8.88711	−	8.88711i	−0.582214	−	0.582214i	−0.935511	+	0.353297i	$0.885060\pi$
$234$	0.371291	−	0.905665i	0.0242721	−	0.0592052i
$235$		0			0
$236$		−	0.540934i		−	0.0352118i
$237$	0.0165071	−	0.0837815i	0.00107225	−	0.00544220i
$238$	10.2327	−	10.2327i	0.663287	−	0.663287i
$239$	−18.6949			−1.20927			−0.604635	−	0.796503i	$-0.706681\pi$
$239$	−18.6949			−1.20927			−0.604635	+	0.796503i	$0.706681\pi$
$240$		0			0
$241$	20.6840			1.33237			0.666186	−	0.745786i	$-0.267926\pi$
$241$	20.6840			1.33237			0.666186	+	0.745786i	$0.267926\pi$
$242$	6.02147	−	6.02147i	0.387075	−	0.387075i
$243$	8.77781	+	12.8822i	0.563097	+	0.826391i
$244$			1.89981i			0.121623i
$245$		0			0
$246$	2.51408	+	3.74784i	0.160292	+	0.238954i
$247$	1.46836	+	1.46836i	0.0934293	+	0.0934293i
$248$	−1.06989	−	1.06989i	−0.0679380	−	0.0679380i
$249$	−11.1941	−	16.6875i	−0.709397	−	1.05753i
$250$		0			0
$251$			26.0079i			1.64160i	0.571213	+	0.820802i	$0.306473\pi$
$251$			26.0079i			1.64160i	−0.571213	+	0.820802i	$0.693527\pi$
$252$	−19.0393	+	7.96746i	−1.19936	+	0.501903i
$253$	9.40220	−	9.40220i	0.591111	−	0.591111i
$254$	−9.30892			−0.584093
$255$		0			0
$256$	−4.89202			−0.305751
$257$	−14.1375	+	14.1375i	−0.881872	+	0.881872i	−0.993725	−	0.111853i	$-0.964321\pi$
$257$	−14.1375	+	14.1375i	−0.881872	+	0.881872i	0.111853	+	0.993725i	$0.464321\pi$
$258$	−1.31484	+	6.67344i	−0.0818581	+	0.415470i
$259$		−	13.7008i		−	0.851326i
$260$		0			0
$261$	−6.44583	−	2.64257i	−0.398987	−	0.163571i
$262$	−5.96756	−	5.96756i	−0.368677	−	0.368677i
$263$	−16.8482	−	16.8482i	−1.03891	−	1.03891i	−0.999212	−	0.0396938i	$-0.987362\pi$
$263$	−16.8482	−	16.8482i	−1.03891	−	1.03891i	−0.0396938	−	0.999212i	$-0.512638\pi$
$264$	−15.5581	+	10.4365i	−0.957532	+	0.642321i
$265$		0			0
$266$			9.03443i			0.553936i
$267$	9.77692	+	1.92630i	0.598338	+	0.117888i
$268$	11.8457	−	11.8457i	0.723592	−	0.723592i
$269$	29.3947			1.79223			0.896114	−	0.443824i	$-0.146379\pi$
$269$	29.3947			1.79223			0.896114	+	0.443824i	$0.146379\pi$
$270$		0			0
$271$	16.2670			0.988147			0.494073	−	0.869420i	$-0.335507\pi$
$271$	16.2670			0.988147			0.494073	+	0.869420i	$0.335507\pi$
$272$	8.70445	−	8.70445i	0.527785	−	0.527785i
$273$	−3.93382	−	0.775062i	−0.238086	−	0.0469089i
$274$			1.71561i			0.103644i
$275$		0			0
$276$	−6.27204	+	4.20734i	−0.377533	+	0.253252i
$277$	−15.3735	−	15.3735i	−0.923703	−	0.923703i	0.0735862	−	0.997289i	$-0.476556\pi$
$277$	−15.3735	−	15.3735i	−0.923703	−	0.923703i	−0.997289	+	0.0735862i	$0.976556\pi$
$278$	7.08812	+	7.08812i	0.425117	+	0.425117i
$279$	1.96310	+	0.804801i	0.117527	+	0.0481822i
$280$		0			0
$281$		−	9.28914i		−	0.554143i	−0.960849	−	0.277072i	$-0.910636\pi$
$281$		−	9.28914i		−	0.554143i	0.960849	−	0.277072i	$-0.0893640\pi$
$282$	0.625564	−	3.17504i	0.0372518	−	0.189071i
$283$	−13.2632	+	13.2632i	−0.788413	+	0.788413i	−0.981234	−	0.192821i	$-0.938236\pi$
$283$	−13.2632	+	13.2632i	−0.788413	+	0.788413i	0.192821	+	0.981234i	$0.438236\pi$
$284$	5.18029			0.307394
$285$		0			0
$286$	−1.64953			−0.0975385
$287$	13.0716	−	13.0716i	0.771595	−	0.771595i
$288$	15.1832	−	6.35380i	0.894681	−	0.374401i
$289$		−	18.5523i		−	1.09131i
$290$		0			0
$291$	−13.1625	−	19.6219i	−0.771601	−	1.15026i
$292$	2.39221	+	2.39221i	0.139994	+	0.139994i
$293$	3.72347	+	3.72347i	0.217528	+	0.217528i	0.807456	−	0.589928i	$-0.200844\pi$
$293$	3.72347	+	3.72347i	0.217528	+	0.217528i	−0.589928	+	0.807456i	$0.700844\pi$
$294$	−5.76714	−	8.59730i	−0.336346	−	0.501404i
$295$		0			0
$296$			7.06378i			0.410574i
$297$	14.4756	−	21.9219i	0.839961	−	1.27204i
$298$	5.32042	−	5.32042i	0.308203	−	0.308203i
$299$	−1.46718			−0.0848492
$300$		0			0
$301$	27.8613			1.60590
$302$	−7.63821	+	7.63821i	−0.439529	+	0.439529i
$303$	4.15637	−	21.0956i	0.238777	−	1.21191i
$304$			7.68514i			0.440773i
$305$		0			0
$306$	3.96855	−	9.68021i	0.226867	−	0.553381i
$307$	−6.96157	−	6.96157i	−0.397318	−	0.397318i	0.479968	−	0.877286i	$-0.340648\pi$
$307$	−6.96157	−	6.96157i	−0.397318	−	0.397318i	−0.877286	+	0.479968i	$0.840648\pi$
$308$	24.5943	+	24.5943i	1.40139	+	1.40139i
$309$	7.87374	−	5.28177i	0.447922	−	0.300470i
$310$		0			0
$311$		−	11.5915i		−	0.657295i	−0.944453	−	0.328647i	$-0.893407\pi$
$311$		−	11.5915i		−	0.657295i	0.944453	−	0.328647i	$-0.106593\pi$
$312$	2.02818	+	0.399602i	0.114823	+	0.0226230i
$313$	−12.9715	+	12.9715i	−0.733195	+	0.733195i	−0.971251	−	0.238056i	$-0.923490\pi$
$313$	−12.9715	+	12.9715i	−0.733195	+	0.733195i	0.238056	+	0.971251i	$0.423490\pi$
$314$	4.18041			0.235914
$315$		0			0
$316$	0.0817375			0.00459809
$317$	19.6531	−	19.6531i	1.10383	−	1.10383i	0.109885	−	0.993944i	$-0.464952\pi$
$317$	19.6531	−	19.6531i	1.10383	−	1.10383i	0.993944	−	0.109885i	$-0.0350481\pi$
$318$	−7.40474	−	1.45892i	−0.415237	−	0.0818122i
$319$			11.7401i			0.657318i
$320$		0			0
$321$	−2.50312	+	1.67911i	−0.139710	+	0.0937189i
$322$	−4.51360	−	4.51360i	−0.251533	−	0.251533i
$323$	15.6945	+	15.6945i	0.873267	+	0.873267i
$324$	−10.4740	+	10.6273i	−0.581890	+	0.590405i
$325$		0			0
$326$			1.23353i			0.0683188i
$327$	1.48401	−	7.53208i	0.0820660	−	0.416525i
$328$	−6.73940	+	6.73940i	−0.372121	+	0.372121i
$329$	−13.2557			−0.730809
$330$		0			0
$331$	−35.7936			−1.96739			−0.983697	−	0.179833i	$-0.942444\pi$
$331$	−35.7936			−1.96739			−0.983697	+	0.179833i	$0.942444\pi$
$332$	13.6007	−	13.6007i	0.746433	−	0.746433i
$333$	−3.82374	−	9.13732i	−0.209540	−	0.500722i
$334$		−	9.05286i		−	0.495350i
$335$		0			0
$336$	−8.26622	−	12.3228i	−0.450959	−	0.672263i
$337$	−20.6773	−	20.6773i	−1.12637	−	1.12637i	−0.990763	−	0.135603i	$-0.956703\pi$
$337$	−20.6773	−	20.6773i	−1.12637	−	1.12637i	−0.135603	−	0.990763i	$-0.543297\pi$
$338$	−5.24771	−	5.24771i	−0.285438	−	0.285438i
$339$	11.9826	+	17.8629i	0.650805	+	0.970180i
$340$		0			0
$341$		−	3.57547i		−	0.193623i
$342$	2.52141	+	6.02523i	0.136342	+	0.325807i
$343$	−9.44595	+	9.44595i	−0.510033	+	0.510033i
$344$	−14.3646			−0.774486
$345$		0			0
$346$	−3.36027			−0.180649
$347$	−15.1348	+	15.1348i	−0.812481	+	0.812481i	−0.985005	−	0.172525i	$-0.944808\pi$
$347$	−15.1348	+	15.1348i	−0.812481	+	0.812481i	0.172525	+	0.985005i	$0.444808\pi$
$348$	1.28905	−	6.54255i	0.0691002	−	0.350717i
$349$			7.13165i			0.381748i	0.981615	+	0.190874i	$0.0611322\pi$
$349$			7.13165i			0.381748i	−0.981615	+	0.190874i	$0.938868\pi$
$350$		0			0
$351$	−2.83985	+	0.580982i	−0.151580	+	0.0310105i
$352$	−19.6132	−	19.6132i	−1.04538	−	1.04538i
$353$	−24.2562	−	24.2562i	−1.29103	−	1.29103i	−0.934153	−	0.356873i	$-0.883843\pi$
$353$	−24.2562	−	24.2562i	−1.29103	−	1.29103i	−0.356873	−	0.934153i	$-0.616157\pi$
$354$	0.274489	−	0.184129i	0.0145889	−	0.00978636i
$355$		0			0
$356$			9.53839i			0.505534i
$357$	−42.0467	−	8.28426i	−2.22535	−	0.438450i
$358$	−4.94520	+	4.94520i	−0.261362	+	0.261362i
$359$	29.7210			1.56861			0.784307	−	0.620373i	$-0.213019\pi$
$359$	29.7210			1.56861			0.784307	+	0.620373i	$0.213019\pi$
$360$		0			0
$361$	5.14332			0.270701
$362$	6.66850	−	6.66850i	0.350489	−	0.350489i
$363$	−24.7425	−	4.87490i	−1.29865	−	0.255866i
$364$		−	3.83784i		−	0.201158i
$365$		0			0
$366$	−0.964027	+	0.646677i	−0.0503905	+	0.0338024i
$367$	10.1723	+	10.1723i	0.530988	+	0.530988i	0.920866	−	0.389879i	$-0.127483\pi$
$367$	10.1723	+	10.1723i	0.530988	+	0.530988i	−0.389879	+	0.920866i	$0.627483\pi$
$368$	−3.83949	−	3.83949i	−0.200147	−	0.200147i
$369$	5.06957	−	12.3659i	0.263912	−	0.643742i
$370$		0			0
$371$			30.9145i			1.60500i
$372$	−0.392583	+	1.99255i	−0.0203545	+	0.103309i
$373$	4.69106	−	4.69106i	0.242894	−	0.242894i	−0.575152	−	0.818046i	$-0.695057\pi$
$373$	4.69106	−	4.69106i	0.242894	−	0.242894i	0.818046	+	0.575152i	$0.195057\pi$
$374$	−17.6310			−0.911676
$375$		0			0
$376$	6.83429			0.352451
$377$	0.915998	−	0.915998i	0.0471763	−	0.0471763i
$378$	−10.5238	−	6.94913i	−0.541284	−	0.357424i
$379$			31.0115i			1.59295i	0.604670	+	0.796476i	$0.293305\pi$
$379$			31.0115i			1.59295i	−0.604670	+	0.796476i	$0.706695\pi$
$380$		0			0
$381$	15.3572	+	22.8936i	0.786774	+	1.17287i
$382$	−6.95268	−	6.95268i	−0.355730	−	0.355730i
$383$	18.4939	+	18.4939i	0.944994	+	0.944994i	0.998564	−	0.0535701i	$-0.0170600\pi$
$383$	18.4939	+	18.4939i	0.944994	+	0.944994i	−0.0535701	+	0.998564i	$0.517060\pi$
$384$	11.1068	+	16.5573i	0.566791	+	0.844937i
$385$		0			0
$386$		−	12.2917i		−	0.625629i
$387$	18.5812	−	7.77578i	0.944537	−	0.395265i
$388$	15.9923	−	15.9923i	0.811885	−	0.811885i
$389$	−20.2104			−1.02471			−0.512355	−	0.858774i	$-0.671227\pi$
$389$	−20.2104			−1.02471			−0.512355	+	0.858774i	$0.671227\pi$
$390$		0			0
$391$	−15.6820			−0.793071
$392$	15.4597	−	15.4597i	0.780834	−	0.780834i
$393$	−4.83126	+	24.5210i	−0.243705	+	1.23692i
$394$			2.83947i			0.143051i
$395$		0			0
$396$	23.2663	+	9.53839i	1.16918	+	0.479322i
$397$	5.99364	+	5.99364i	0.300812	+	0.300812i	0.841332	−	0.540519i	$-0.181772\pi$
$397$	5.99364	+	5.99364i	0.300812	+	0.300812i	−0.540519	+	0.841332i	$0.681772\pi$
$398$	−7.07552	−	7.07552i	−0.354664	−	0.354664i
$399$	22.2185	−	14.9044i	1.11232	−	0.746153i
$400$		0			0
$401$		−	9.27612i		−	0.463228i	−0.972808	−	0.231614i	$-0.925599\pi$
$401$		−	9.27612i		−	0.463228i	0.972808	−	0.231614i	$-0.0744006\pi$
$402$	10.0431	+	1.97874i	0.500904	+	0.0986908i
$403$	−0.278970	+	0.278970i	−0.0138965	+	0.0138965i
$404$	20.5809			1.02394
$405$		0			0
$406$	5.63591			0.279705
$407$	−11.8033	+	11.8033i	−0.585066	+	0.585066i
$408$	21.6782	+	4.27115i	1.07323	+	0.211454i
$409$			23.9842i			1.18594i	0.805224	+	0.592970i	$0.202045\pi$
$409$			23.9842i			1.18594i	−0.805224	+	0.592970i	$0.797955\pi$
$410$		0			0
$411$	4.21924	−	2.83030i	0.208120	−	0.139609i
$412$	6.41727	+	6.41727i	0.316156	+	0.316156i
$413$	−0.957355	−	0.957355i	−0.0471084	−	0.0471084i
$414$	−4.26989	−	1.75051i	−0.209854	−	0.0860327i
$415$		0			0
$416$			3.06056i			0.150056i
$417$	5.73845	−	29.1255i	0.281013	−	1.42628i
$418$	7.78318	−	7.78318i	0.380688	−	0.380688i
$419$	−11.2278			−0.548513			−0.274257	−	0.961657i	$-0.588432\pi$
$419$	−11.2278			−0.548513			−0.274257	+	0.961657i	$0.588432\pi$
$420$		0			0
$421$	−7.29021			−0.355303			−0.177651	−	0.984093i	$-0.556850\pi$
$421$	−7.29021			−0.355303			−0.177651	+	0.984093i	$0.556850\pi$
$422$	2.94571	−	2.94571i	0.143395	−	0.143395i
$423$	−8.84046	+	3.69951i	−0.429838	+	0.179876i
$424$		−	15.9387i		−	0.774052i
$425$		0			0
$426$	1.76332	+	2.62866i	0.0854333	+	0.127359i
$427$	3.36231	+	3.36231i	0.162714	+	0.162714i
$428$	−2.04010	−	2.04010i	−0.0986118	−	0.0986118i
$429$	2.72128	+	4.05671i	0.131384	+	0.195860i
$430$		0			0
$431$		−	4.78196i		−	0.230339i	−0.993346	−	0.115170i	$-0.963259\pi$
$431$		−	4.78196i		−	0.230339i	0.993346	−	0.115170i	$-0.0367411\pi$
$432$	−8.95205	−	5.91128i	−0.430706	−	0.284407i
$433$	−19.4008	+	19.4008i	−0.932345	+	0.932345i	−0.997852	−	0.0655075i	$-0.979133\pi$
$433$	−19.4008	+	19.4008i	−0.932345	+	0.932345i	0.0655075	+	0.997852i	$0.479133\pi$
$434$	−1.71643			−0.0823913
$435$		0			0
$436$	7.34831			0.351920
$437$	6.92279	−	6.92279i	0.331162	−	0.331162i
$438$	−0.399602	+	2.02818i	−0.0190937	+	0.0969101i
$439$		−	6.83368i		−	0.326154i	−0.986613	−	0.163077i	$-0.947858\pi$
$439$		−	6.83368i		−	0.326154i	0.986613	−	0.163077i	$-0.0521419\pi$
$440$		0			0
$441$	−11.6293	+	28.3665i	−0.553774	+	1.35078i
$442$	1.37563	+	1.37563i	0.0654318	+	0.0654318i
$443$	14.7737	+	14.7737i	0.701918	+	0.701918i	0.964822	−	0.262904i	$-0.0846803\pi$
$443$	14.7737	+	14.7737i	0.701918	+	0.701918i	−0.262904	+	0.964822i	$0.584680\pi$
$444$	7.87374	−	5.28177i	0.373671	−	0.250662i
$445$		0			0
$446$		−	11.9056i		−	0.563745i
$447$	−21.8619	−	4.30734i	−1.03403	−	0.203730i
$448$	2.70015	−	2.70015i	0.127570	−	0.127570i
$449$	3.39827			0.160374			0.0801872	−	0.996780i	$-0.474448\pi$
$449$	3.39827			0.160374			0.0801872	+	0.996780i	$0.474448\pi$
$450$		0			0
$451$	−22.5225			−1.06054
$452$	−14.5587	+	14.5587i	−0.684782	+	0.684782i
$453$	31.3858	+	6.18379i	1.47463	+	0.290540i
$454$		−	4.37774i		−	0.205457i
$455$		0			0
$456$	−11.4553	+	7.68432i	−0.536444	+	0.359851i
$457$	−0.0418176	−	0.0418176i	−0.00195614	−	0.00195614i	0.706128	−	0.708084i	$-0.250440\pi$
$457$	−0.0418176	−	0.0418176i	−0.00195614	−	0.00195614i	−0.708084	+	0.706128i	$0.750440\pi$
$458$	5.16334	+	5.16334i	0.241267	+	0.241267i
$459$	−30.3538	+	6.20983i	−1.41679	+	0.289850i
$460$		0			0
$461$			10.9465i			0.509831i	0.966963	+	0.254915i	$0.0820476\pi$
$461$			10.9465i			0.509831i	−0.966963	+	0.254915i	$0.917952\pi$
$462$	−4.10830	+	20.8516i	−0.191135	+	0.970106i
$463$	25.0327	−	25.0327i	1.16337	−	1.16337i	0.179635	−	0.983733i	$-0.442508\pi$
$463$	25.0327	−	25.0327i	1.16337	−	1.16337i	0.983733	−	0.179635i	$-0.0574917\pi$
$464$	4.79419			0.222565
$465$		0			0
$466$	7.35089			0.340523
$467$	2.57209	−	2.57209i	0.119022	−	0.119022i	−0.645087	−	0.764109i	$-0.723179\pi$
$467$	2.57209	−	2.57209i	0.119022	−	0.119022i	0.764109	+	0.645087i	$0.223179\pi$
$468$	−1.07110	−	2.55953i	−0.0495116	−	0.118314i
$469$		−	41.9295i		−	1.93613i
$470$		0			0
$471$	−6.89656	−	10.2810i	−0.317777	−	0.473722i
$472$	0.493588	+	0.493588i	0.0227192	+	0.0227192i
$473$	−24.0026	−	24.0026i	−1.10364	−	1.10364i
$474$	0.0278227	+	0.0414764i	0.00127794	+	0.00190507i
$475$		0			0
$476$		−	41.0208i		−	1.88019i
$477$	8.62788	+	20.6174i	0.395044	+	0.944008i
$478$	7.73163	−	7.73163i	0.353637	−	0.353637i
$479$	−26.5358			−1.21245			−0.606226	−	0.795292i	$-0.707317\pi$
$479$	−26.5358			−1.21245			−0.606226	+	0.795292i	$0.707317\pi$
$480$		0			0
$481$	1.84186			0.0839814
$482$	−8.55427	+	8.55427i	−0.389636	+	0.389636i
$483$	−3.65415	+	18.5466i	−0.166269	+	0.843899i
$484$		−	24.1389i		−	1.09722i
$485$		0			0
$486$	−8.95792	−	1.69744i	−0.406339	−	0.0769974i
$487$	14.7208	+	14.7208i	0.667065	+	0.667065i	0.957036	−	0.289971i	$-0.0936456\pi$
$487$	14.7208	+	14.7208i	0.667065	+	0.667065i	−0.289971	+	0.957036i	$0.593646\pi$
$488$	−1.73352	−	1.73352i	−0.0784728	−	0.0784728i
$489$	3.03364	−	2.03499i	0.137186	−	0.0920254i
$490$		0			0
$491$		−	35.8455i		−	1.61769i	−0.588025	−	0.808843i	$-0.700094\pi$
$491$		−	35.8455i		−	1.61769i	0.588025	−	0.808843i	$-0.299906\pi$
$492$	12.5514	+	2.47294i	0.565861	+	0.111489i
$493$	9.79065	−	9.79065i	0.440949	−	0.440949i
$494$	−1.21454			−0.0546446
$495$		0			0
$496$	−1.46008			−0.0655597
$497$	9.16817	−	9.16817i	0.411249	−	0.411249i
$498$	11.5310	+	2.27189i	0.516716	+	0.101806i
$499$			23.6239i			1.05755i	0.848762	+	0.528774i	$0.177348\pi$
$499$			23.6239i			1.05755i	−0.848762	+	0.528774i	$0.822652\pi$
$500$		0			0
$501$	−22.2639	+	14.9348i	−0.994676	+	0.667237i
$502$	−10.7561	−	10.7561i	−0.480068	−	0.480068i
$503$	−28.1904	−	28.1904i	−1.25695	−	1.25695i	−0.952542	−	0.304406i	$-0.901542\pi$
$503$	−28.1904	−	28.1904i	−1.25695	−	1.25695i	−0.304406	−	0.952542i	$-0.598458\pi$
$504$	10.1027	−	24.6429i	0.450011	−	1.09768i
$505$		0			0
$506$			7.77694i			0.345727i
$507$	−4.24848	+	21.5631i	−0.188682	+	0.957651i
$508$	−18.6588	+	18.6588i	−0.827850	+	0.827850i
$509$	−22.2063			−0.984278			−0.492139	−	0.870517i	$-0.663785\pi$
$509$	−22.2063			−0.984278			−0.492139	+	0.870517i	$0.663785\pi$
$510$		0			0
$511$	8.46756			0.374583
$512$	−14.2557	+	14.2557i	−0.630020	+	0.630020i
$513$	10.6583	−	16.1410i	0.470576	−	0.712641i
$514$		−	11.6937i		−	0.515786i
$515$		0			0
$516$	10.7408	+	16.0117i	0.472836	+	0.704875i
$517$	11.4198	+	11.4198i	0.502242	+	0.502242i
$518$	5.66624	+	5.66624i	0.248960	+	0.248960i
$519$	5.54354	+	8.26396i	0.243334	+	0.362748i
$520$		0			0
$521$		−	23.2104i		−	1.01687i	−0.861102	−	0.508433i	$-0.830225\pi$
$521$		−	23.2104i		−	1.01687i	0.861102	−	0.508433i	$-0.169775\pi$
$522$	3.75869	−	1.57292i	0.164513	−	0.0688448i
$523$	1.61807	−	1.61807i	0.0707534	−	0.0707534i	−0.670845	−	0.741598i	$-0.734068\pi$
$523$	1.61807	−	1.61807i	0.0707534	−	0.0707534i	0.741598	+	0.670845i	$0.234068\pi$
$524$	−23.9227			−1.04507
$525$		0			0
$526$	13.9358			0.607631
$527$	−2.98177	+	2.98177i	−0.129888	+	0.129888i
$528$	−3.49473	+	17.7375i	−0.152088	+	0.771924i
$529$		−	16.0828i		−	0.699250i
$530$		0			0
$531$	−0.905665	−	0.371291i	−0.0393025	−	0.0161127i
$532$	18.1086	+	18.1086i	0.785108	+	0.785108i
$533$	1.75728	+	1.75728i	0.0761161	+	0.0761161i
$534$	−4.84010	+	3.24678i	−0.209452	+	0.140502i
$535$		0			0
$536$			21.6178i			0.933746i
$537$	20.3201	+	4.00357i	0.876877	+	0.172767i
$538$	−12.1568	+	12.1568i	−0.524116	+	0.524116i
$539$	51.6650			2.22537
$540$		0			0
$541$	18.4747			0.794290			0.397145	−	0.917756i	$-0.370001\pi$
$541$	18.4747			0.794290			0.397145	+	0.917756i	$0.370001\pi$
$542$	−6.72753	+	6.72753i	−0.288972	+	0.288972i
$543$	−27.4012	−	5.39873i	−1.17590	−	0.231682i
$544$			32.7128i			1.40255i
$545$		0			0
$546$	1.94745	−	1.30637i	0.0833433	−	0.0559074i
$547$	1.59044	+	1.59044i	0.0680025	+	0.0680025i	0.740290	−	0.672288i	$-0.234688\pi$
$547$	1.59044	+	1.59044i	0.0680025	+	0.0680025i	−0.672288	+	0.740290i	$0.734688\pi$
$548$	3.43878	+	3.43878i	0.146897	+	0.146897i
$549$	3.18077	+	1.30401i	0.135752	+	0.0556536i
$550$		0			0
$551$			8.64415i			0.368253i
$552$	1.88398	−	9.56215i	0.0801877	−	0.406992i
$553$	0.144660	−	0.144660i	0.00615159	−	0.00615159i
$554$	12.7160			0.540252
$555$		0			0
$556$	28.4149			1.20506
$557$	−10.0342	+	10.0342i	−0.425162	+	0.425162i	−0.886977	−	0.461814i	$-0.847199\pi$
$557$	−10.0342	+	10.0342i	−0.425162	+	0.425162i	0.461814	+	0.886977i	$0.347199\pi$
$558$	−1.14472	+	0.479036i	−0.0484598	+	0.0202792i
$559$			3.74552i			0.158418i
$560$		0			0
$561$	29.0864	+	43.3602i	1.22803	+	1.83067i
$562$	3.84171	+	3.84171i	0.162053	+	0.162053i
$563$	10.6833	+	10.6833i	0.450246	+	0.450246i	0.895436	−	0.445190i	$-0.146864\pi$
$563$	10.6833	+	10.6833i	0.450246	+	0.450246i	−0.445190	+	0.895436i	$0.646864\pi$
$564$	−5.11018	−	7.61794i	−0.215177	−	0.320773i
$565$		0			0
$566$		−	10.9705i		−	0.461124i
$567$	0.271266	+	37.3455i	0.0113921	+	1.56836i
$568$	−4.72687	+	4.72687i	−0.198335	+	0.198335i
$569$	13.1761			0.552370			0.276185	−	0.961105i	$-0.410930\pi$
$569$	13.1761			0.552370			0.276185	+	0.961105i	$0.410930\pi$
$570$		0			0
$571$	4.02363			0.168384			0.0841918	−	0.996450i	$-0.473169\pi$
$571$	4.02363			0.168384			0.0841918	+	0.996450i	$0.473169\pi$
$572$	−3.30631	+	3.30631i	−0.138244	+	0.138244i
$573$	−5.62880	+	28.5689i	−0.235146	+	1.19348i
$574$			10.8121i			0.451288i
$575$		0			0
$576$	1.04720	−	2.55436i	0.0436333	−	0.106432i
$577$	19.3178	+	19.3178i	0.804212	+	0.804212i	0.983751	−	0.179539i	$-0.0574607\pi$
$577$	19.3178	+	19.3178i	0.804212	+	0.804212i	−0.179539	+	0.983751i	$0.557461\pi$
$578$	7.67269	+	7.67269i	0.319142	+	0.319142i
$579$	−30.2291	+	20.2780i	−1.25628	+	0.842723i
$580$		0			0
$581$		−	48.1414i		−	1.99724i
$582$	13.5587	+	2.67140i	0.562024	+	0.110733i
$583$	26.6329	−	26.6329i	1.10302	−	1.10302i
$584$	−4.36565			−0.180652
$585$		0			0
$586$	−3.07983			−0.127227
$587$	−13.9390	+	13.9390i	−0.575325	+	0.575325i	−0.933612	−	0.358286i	$-0.883361\pi$
$587$	−13.9390	+	13.9390i	−0.575325	+	0.575325i	0.358286	+	0.933612i	$0.383361\pi$
$588$	−28.7921	−	5.67277i	−1.18736	−	0.233941i
$589$		−	2.63260i		−	0.108474i
$590$		0			0
$591$	6.98317	−	4.68437i	0.287249	−	0.192689i
$592$	4.81999	+	4.81999i	0.198100	+	0.198100i
$593$	10.6476	+	10.6476i	0.437244	+	0.437244i	0.891083	−	0.453840i	$-0.149946\pi$
$593$	10.6476	+	10.6476i	0.437244	+	0.437244i	−0.453840	+	0.891083i	$0.649946\pi$
$594$	3.07955	+	15.0529i	0.126356	+	0.617629i
$595$		0			0
$596$		−	21.3285i		−	0.873649i
$597$	−5.72825	+	29.0737i	−0.234442	+	1.18991i
$598$	0.606782	−	0.606782i	0.0248132	−	0.0248132i
$599$	32.2651			1.31832			0.659158	−	0.752005i	$-0.270913\pi$
$599$	32.2651			1.31832			0.659158	+	0.752005i	$0.270913\pi$
$600$		0			0
$601$	−19.9758			−0.814828			−0.407414	−	0.913243i	$-0.633569\pi$
$601$	−19.9758			−0.814828			−0.407414	+	0.913243i	$0.633569\pi$
$602$	−11.5226	+	11.5226i	−0.469626	+	0.469626i
$603$	−11.7021	−	27.9636i	−0.476545	−	1.13876i
$604$			30.6200i			1.24591i
$605$		0			0
$606$	7.00557	+	10.4435i	0.284582	+	0.424237i
$607$	−6.87505	−	6.87505i	−0.279050	−	0.279050i	0.553680	−	0.832730i	$-0.313223\pi$
$607$	−6.87505	−	6.87505i	−0.279050	−	0.279050i	−0.832730	+	0.553680i	$0.813223\pi$
$608$	−14.4411	−	14.4411i	−0.585662	−	0.585662i
$609$	−9.29774	−	13.8605i	−0.376763	−	0.561655i
$610$		0			0
$611$		−	1.78202i		−	0.0720927i
$612$	−11.4485	−	27.3576i	−0.462776	−	1.10586i
$613$	−10.2685	+	10.2685i	−0.414741	+	0.414741i	−0.883386	−	0.468645i	$-0.844742\pi$
$613$	−10.2685	+	10.2685i	−0.414741	+	0.414741i	0.468645	+	0.883386i	$0.344742\pi$
$614$	5.75820			0.232382
$615$		0			0
$616$	−44.8832			−1.80839
$617$	9.53217	−	9.53217i	0.383751	−	0.383751i	−0.488701	−	0.872451i	$-0.662529\pi$
$617$	9.53217	−	9.53217i	0.383751	−	0.383751i	0.872451	+	0.488701i	$0.162529\pi$
$618$	−1.07196	+	5.44073i	−0.0431206	+	0.218858i
$619$		−	1.10503i		−	0.0444149i	−0.999753	−	0.0222074i	$-0.992931\pi$
$619$		−	1.10503i		−	0.0444149i	0.999753	−	0.0222074i	$-0.00706943\pi$
$620$		0			0
$621$	2.73913	+	13.3889i	0.109917	+	0.537278i
$622$	4.79391	+	4.79391i	0.192218	+	0.192218i
$623$	16.8812	+	16.8812i	0.676331	+	0.676331i
$624$	1.65660	−	1.11126i	0.0663172	−	0.0444861i
$625$		0			0
$626$		−	10.7293i		−	0.428828i
$627$	−31.9815	−	6.30116i	−1.27722	−	0.251644i
$628$	8.37922	−	8.37922i	0.334367	−	0.334367i
$629$	19.6867			0.784960
$630$		0			0
$631$	2.54536			0.101329			0.0506646	−	0.998716i	$-0.483866\pi$
$631$	2.54536			0.101329			0.0506646	+	0.998716i	$0.483866\pi$
$632$	−0.0745832	+	0.0745832i	−0.00296676	+	0.00296676i
$633$	−12.1041	−	2.38481i	−0.481094	−	0.0947877i
$634$			16.2559i			0.645604i
$635$		0			0
$636$	−17.7663	+	11.9178i	−0.704480	+	0.472571i
$637$	−4.03107	−	4.03107i	−0.159717	−	0.159717i
$638$	−4.85534	−	4.85534i	−0.192225	−	0.192225i
$639$	3.55569	−	8.67315i	0.140661	−	0.343105i
$640$		0			0
$641$		−	15.4810i		−	0.611464i	−0.952118	−	0.305732i	$-0.901099\pi$
$641$		−	15.4810i		−	0.611464i	0.952118	−	0.305732i	$-0.0989012\pi$
$642$	0.340784	−	1.72964i	0.0134497	−	0.0682636i
$643$	−9.51828	+	9.51828i	−0.375364	+	0.375364i	−0.869427	−	0.494062i	$-0.835512\pi$
$643$	−9.51828	+	9.51828i	−0.375364	+	0.375364i	0.494062	+	0.869427i	$0.335512\pi$
$644$	−18.0941			−0.713007
$645$		0			0
$646$	−12.9816			−0.510754
$647$	0.268453	−	0.268453i	0.0105540	−	0.0105540i	−0.701810	−	0.712364i	$-0.747624\pi$
$647$	0.268453	−	0.268453i	0.0105540	−	0.0105540i	0.712364	+	0.701810i	$0.247624\pi$
$648$	−0.139858	−	19.2544i	−0.00549414	−	0.756383i
$649$			1.64953i			0.0647496i
$650$		0			0
$651$	2.83165	+	4.22125i	0.110981	+	0.165444i
$652$	2.47248	+	2.47248i	0.0968299	+	0.0968299i
$653$	30.6239	+	30.6239i	1.19841	+	1.19841i	0.974644	+	0.223763i	$0.0718341\pi$
$653$	30.6239	+	30.6239i	1.19841	+	1.19841i	0.223763	+	0.974644i	$0.428166\pi$
$654$	2.50130	+	3.72879i	0.0978086	+	0.145807i
$655$		0			0
$656$			9.19731i			0.359094i
$657$	5.64717	−	2.36320i	0.220317	−	0.0921972i
$658$	5.48215	−	5.48215i	0.213717	−	0.213717i
$659$	−21.7554			−0.847471			−0.423735	−	0.905786i	$-0.639281\pi$
$659$	−21.7554			−0.847471			−0.423735	+	0.905786i	$0.639281\pi$
$660$		0			0
$661$	−18.9468			−0.736947			−0.368473	−	0.929638i	$-0.620119\pi$
$661$	−18.9468			−0.736947			−0.368473	+	0.929638i	$0.620119\pi$
$662$	14.8032	−	14.8032i	0.575341	−	0.575341i
$663$	1.11369	−	5.65251i	0.0432521	−	0.219525i
$664$			24.8205i			0.963220i
$665$		0			0
$666$	5.36030	+	2.19754i	0.207708	+	0.0851528i
$667$	−4.31861	−	4.31861i	−0.167217	−	0.167217i
$668$	−18.1455	−	18.1455i	−0.702072	−	0.702072i
$669$	−29.2796	+	19.6410i	−1.13201	+	0.759365i
$670$		0			0
$671$		−	5.79327i		−	0.223647i
$672$	38.6885	+	7.62262i	1.49244	+	0.294049i
$673$	9.85460	−	9.85460i	0.379867	−	0.379867i	−0.491187	−	0.871054i	$-0.663437\pi$
$673$	9.85460	−	9.85460i	0.379867	−	0.379867i	0.871054	+	0.491187i	$0.163437\pi$
$674$	17.1031			0.658785
$675$		0			0
$676$	−21.0370			−0.809116
$677$	3.21474	−	3.21474i	0.123553	−	0.123553i	−0.642627	−	0.766179i	$-0.722155\pi$
$677$	3.21474	−	3.21474i	0.123553	−	0.123553i	0.766179	+	0.642627i	$0.222155\pi$
$678$	−12.3432	−	2.43192i	−0.474038	−	0.0933975i
$679$		−	56.6068i		−	2.17237i
$680$		0			0
$681$	−10.7663	+	7.22209i	−0.412564	+	0.276751i
$682$	1.47871	+	1.47871i	0.0566226	+	0.0566226i
$683$	7.28232	+	7.28232i	0.278650	+	0.278650i	0.832570	−	0.553920i	$-0.186869\pi$
$683$	7.28232	+	7.28232i	0.278650	+	0.278650i	−0.553920	+	0.832570i	$0.686869\pi$
$684$	17.1309	+	7.02306i	0.655015	+	0.268533i
$685$		0			0
$686$		−	7.81313i		−	0.298307i
$687$	4.18017	−	21.2164i	0.159484	−	0.809457i
$688$	−9.80172	+	9.80172i	−0.373687	+	0.373687i
$689$	−4.15596			−0.158330
$690$		0			0
$691$	16.9029			0.643015			0.321508	−	0.946907i	$-0.395810\pi$
$691$	16.9029			0.643015			0.321508	+	0.946907i	$0.395810\pi$
$692$	−6.73531	+	6.73531i	−0.256038	+	0.256038i
$693$	58.0584	−	24.2960i	2.20546	−	0.922928i
$694$		−	12.5186i		−	0.475201i
$695$		0			0
$696$	4.79367	+	7.14611i	0.181704	+	0.270873i
$697$	18.7827	+	18.7827i	0.711444	+	0.711444i
$698$	−2.94944	−	2.94944i	−0.111638	−	0.111638i
$699$	−12.1270	−	18.0782i	−0.458685	−	0.683780i
$700$		0			0
$701$		−	8.63610i		−	0.326181i	−0.986611	−	0.163091i	$-0.947854\pi$
$701$		−	8.63610i		−	0.326181i	0.986611	−	0.163091i	$-0.0521463\pi$
$702$	0.934201	−	1.41475i	0.0352591	−	0.0533964i
$703$	−8.69067	+	8.69067i	−0.327775	+	0.327775i
$704$	−4.65237			−0.175343
$705$		0			0
$706$	20.0633			0.755091
$707$	36.4245	−	36.4245i	1.36988	−	1.36988i
$708$	0.181116	−	0.919253i	0.00680676	−	0.0345477i
$709$			9.14503i			0.343449i	0.985145	+	0.171724i	$0.0549339\pi$
$709$			9.14503i			0.343449i	−0.985145	+	0.171724i	$0.945066\pi$
$710$		0			0
$711$	0.0561036	−	0.136850i	0.00210405	−	0.00513227i
$712$	−8.70352	−	8.70352i	−0.326178	−	0.326178i
$713$	1.31524	+	1.31524i	0.0492563	+	0.0492563i
$714$	20.8154	−	13.9631i	0.778996	−	0.522557i
$715$		0			0
$716$			19.8243i			0.740870i
$717$	−31.7697	−	6.25943i	−1.18646	−	0.233763i
$718$	−12.2917	+	12.2917i	−0.458723	+	0.458723i
$719$	7.96557			0.297066			0.148533	−	0.988907i	$-0.452545\pi$
$719$	7.96557			0.297066			0.148533	+	0.988907i	$0.452545\pi$
$720$		0			0
$721$	22.7148			0.845944
$722$	−2.12713	+	2.12713i	−0.0791634	+	0.0791634i
$723$	35.1499	+	6.92543i	1.30724	+	0.257559i
$724$		−	26.7327i		−	0.993512i
$725$		0			0
$726$	12.2489	−	8.21666i	0.454599	−	0.304949i
$727$	−2.95813	−	2.95813i	−0.109711	−	0.109711i	0.650120	−	0.759831i	$-0.274718\pi$
$727$	−2.95813	−	2.95813i	−0.109711	−	0.109711i	−0.759831	+	0.650120i	$0.774718\pi$
$728$	3.50193	+	3.50193i	0.129790	+	0.129790i
$729$	10.6036	+	24.8307i	0.392727	+	0.919655i
$730$		0			0
$731$			40.0340i			1.48071i
$732$	−0.636095	+	3.22849i	−0.0235108	+	0.119329i
$733$	36.7526	−	36.7526i	1.35749	−	1.35749i	0.480487	−	0.877002i	$-0.340460\pi$
$733$	36.7526	−	36.7526i	1.35749	−	1.35749i	0.877002	−	0.480487i	$-0.159540\pi$
$734$	−8.41389			−0.310562
$735$		0			0
$736$	14.4295			0.531878
$737$	−36.1223	+	36.1223i	−1.33058	+	1.33058i
$738$	3.01753	+	7.21078i	0.111077	+	0.265432i
$739$			25.2371i			0.928362i	0.885740	+	0.464181i	$0.153651\pi$
$739$			25.2371i			0.928362i	−0.885740	+	0.464181i	$0.846349\pi$
$740$		0			0
$741$	2.00366	+	2.98693i	0.0736063	+	0.109728i
$742$	−12.7853	−	12.7853i	−0.469363	−	0.469363i
$743$	−9.19220	−	9.19220i	−0.337229	−	0.337229i	0.518094	−	0.855323i	$-0.326642\pi$
$743$	−9.19220	−	9.19220i	−0.337229	−	0.337229i	−0.855323	+	0.518094i	$0.826642\pi$
$744$	−1.45993	−	2.17637i	−0.0535235	−	0.0797895i
$745$		0			0
$746$			3.88017i			0.142063i
$747$	−13.4357	−	32.1064i	−0.491587	−	1.17471i
$748$	−35.3395	+	35.3395i	−1.29214	+	1.29214i
$749$	−7.22120			−0.263857
$750$		0			0
$751$	51.7120			1.88700			0.943500	−	0.331373i	$-0.107512\pi$
$751$	51.7120			1.88700			0.943500	+	0.331373i	$0.107512\pi$
$752$	4.66340	−	4.66340i	0.170057	−	0.170057i
$753$	−8.70799	+	44.1973i	−0.317337	+	1.61064i
$754$			0.757659i			0.0275923i
$755$		0			0
$756$	−35.0226	+	7.16500i	−1.27376	+	0.260588i
$757$	−31.2767	−	31.2767i	−1.13677	−	1.13677i	−0.989025	−	0.147747i	$-0.952798\pi$
$757$	−31.2767	−	31.2767i	−1.13677	−	1.13677i	−0.147747	−	0.989025i	$-0.547202\pi$
$758$	−12.8254	−	12.8254i	−0.465840	−	0.465840i
$759$	19.1260	−	12.8299i	0.694229	−	0.465695i
$760$		0			0
$761$		−	34.2727i		−	1.24238i	−0.783658	−	0.621192i	$-0.786649\pi$
$761$		−	34.2727i		−	1.24238i	0.783658	−	0.621192i	$-0.213351\pi$
$762$	−15.8194	−	3.11682i	−0.573076	−	0.112911i
$763$	13.0052	−	13.0052i	0.470819	−	0.470819i
$764$	−27.8719			−1.00837
$765$		0			0
$766$	−15.2970			−0.552705
$767$	0.128701	−	0.128701i	0.00464714	−	0.00464714i
$768$	−8.31341	−	1.63795i	−0.299984	−	0.0591045i
$769$		−	18.2156i		−	0.656873i	−0.944526	−	0.328436i	$-0.893478\pi$
$769$		−	18.2156i		−	0.656873i	0.944526	−	0.328436i	$-0.106522\pi$
$770$		0			0
$771$	−28.7585	+	19.2914i	−1.03571	+	0.694764i
$772$	−24.6374	−	24.6374i	−0.886720	−	0.886720i
$773$	−5.91299	−	5.91299i	−0.212675	−	0.212675i	0.592728	−	0.805403i	$-0.298051\pi$
$773$	−5.91299	−	5.91299i	−0.212675	−	0.212675i	−0.805403	+	0.592728i	$0.798051\pi$
$774$	−4.46881	+	10.9005i	−0.160628	+	0.391809i
$775$		0			0
$776$			29.1850i			1.04768i
$777$	4.58731	−	23.2829i	0.164569	−	0.835268i
$778$	8.35843	−	8.35843i	0.299664	−	0.299664i
$779$	−16.5832			−0.594154
$780$		0			0
$781$	−15.7968			−0.565253
$782$	6.48559	−	6.48559i	0.231924	−	0.231924i
$783$	−10.0691	−	6.64893i	−0.359842	−	0.237613i
$784$		−	21.0980i		−	0.753500i
$785$		0			0
$786$	−8.14309	−	12.1392i	−0.290454	−	0.432992i
$787$	12.0178	+	12.0178i	0.428388	+	0.428388i	0.888079	−	0.459691i	$-0.152040\pi$
$787$	12.0178	+	12.0178i	0.428388	+	0.428388i	−0.459691	+	0.888079i	$0.652040\pi$
$788$	5.69144	+	5.69144i	0.202749	+	0.202749i
$789$	−22.9904	−	34.2727i	−0.818480	−	1.22014i
$790$		0			0
$791$			51.5324i			1.83228i
$792$	−29.9334	+	12.5264i	−1.06364	+	0.445106i
$793$	−0.452010	+	0.452010i	−0.0160513	+	0.0160513i
$794$	−4.95758			−0.175938
$795$		0			0
$796$	−28.3643			−1.00535
$797$	22.2558	−	22.2558i	0.788341	−	0.788341i	−0.192881	−	0.981222i	$-0.561783\pi$
$797$	22.2558	−	22.2558i	0.788341	−	0.788341i	0.981222	+	0.192881i	$0.0617833\pi$
$798$	−3.02492	+	15.3529i	−0.107081	+	0.543488i
$799$		−	19.0471i		−	0.673838i
$800$		0			0
$801$	15.9697	+	6.54704i	0.564263	+	0.231328i
$802$	3.83633	+	3.83633i	0.135465	+	0.135465i
$803$	−7.29481	−	7.29481i	−0.257428	−	0.257428i
$804$	24.0966	−	16.1642i	0.849821	−	0.570067i
$805$		0			0
$806$		−	0.230747i		−	0.00812772i
$807$	49.9528	+	9.84197i	1.75842	+	0.346454i
$808$	−18.7795	+	18.7795i	−0.660662	+	0.660662i
$809$	40.6465			1.42905			0.714527	−	0.699608i	$-0.246642\pi$
$809$	40.6465			1.42905			0.714527	+	0.699608i	$0.246642\pi$
$810$		0			0
$811$	6.04647			0.212320			0.106160	−	0.994349i	$-0.466144\pi$
$811$	6.04647			0.212320			0.106160	+	0.994349i	$0.466144\pi$
$812$	11.2966	−	11.2966i	0.396433	−	0.396433i
$813$	27.6437	+	5.44652i	0.969508	+	0.191018i
$814$		−	9.76295i		−	0.342191i
$815$		0			0
$816$	17.7066	−	11.8777i	0.619855	−	0.415804i
$817$	−17.6730	−	17.6730i	−0.618298	−	0.618298i
$818$	−9.91913	−	9.91913i	−0.346814	−	0.346814i
$819$	−6.42555	−	2.63425i	−0.224527	−	0.0920482i
$820$		0			0
$821$		−	34.7316i		−	1.21214i	−0.795410	−	0.606071i	$-0.792745\pi$
$821$		−	34.7316i		−	1.21214i	0.795410	−	0.606071i	$-0.207255\pi$
$822$	−0.574424	+	2.91548i	−0.0200353	+	0.101689i
$823$	−11.9810	+	11.9810i	−0.417633	+	0.417633i	−0.884387	−	0.466754i	$-0.845423\pi$
$823$	−11.9810	+	11.9810i	−0.417633	+	0.417633i	0.466754	+	0.884387i	$0.345423\pi$
$824$	−11.7112			−0.407978
$825$		0			0
$826$	0.791867			0.0275526
$827$	34.6408	−	34.6408i	1.20458	−	1.20458i	0.231821	−	0.972758i	$-0.425531\pi$
$827$	34.6408	−	34.6408i	1.20458	−	1.20458i	0.972758	−	0.231821i	$-0.0744685\pi$
$828$	−12.0673	+	5.04986i	−0.419367	+	0.175495i
$829$			29.4830i			1.02399i	0.858989	+	0.511994i	$0.171093\pi$
$829$			29.4830i			1.02399i	−0.858989	+	0.511994i	$0.828907\pi$
$830$		0			0
$831$	−20.9780	−	31.2728i	−0.727720	−	1.08484i
$832$	0.362993	+	0.362993i	0.0125845	+	0.0125845i
$833$	−43.0861	−	43.0861i	−1.49285	−	1.49285i
$834$	9.67217	+	14.4187i	0.334920	+	0.499278i
$835$		0			0
$836$		−	31.2012i		−	1.07912i
$837$	3.06658	+	2.02495i	0.105997	+	0.0699925i
$838$	4.64348	−	4.64348i	0.160406	−	0.160406i
$839$	−44.7027			−1.54331			−0.771655	−	0.636041i	$-0.780571\pi$
$839$	−44.7027			−1.54331			−0.771655	+	0.636041i	$0.780571\pi$
$840$		0			0
$841$	−23.6076			−0.814054
$842$	3.01501	−	3.01501i	0.103904	−	0.103904i
$843$	3.11020	−	15.7858i	0.107121	−	0.543691i
$844$		−	11.8088i		−	0.406475i
$845$		0			0
$846$	2.12614	−	5.18616i	0.0730983	−	0.178304i
$847$	−42.7214	−	42.7214i	−1.46792	−	1.46792i
$848$	−10.8758	−	10.8758i	−0.373477	−	0.373477i
$849$	−26.9799	+	18.0984i	−0.925949	+	0.621134i
$850$		0			0
$851$		−	8.68371i		−	0.297674i
$852$	8.80328	+	1.73447i	0.301595	+	0.0594219i
$853$	−9.76148	+	9.76148i	−0.334227	+	0.334227i	−0.854189	−	0.519962i	$-0.825946\pi$
$853$	−9.76148	+	9.76148i	−0.334227	+	0.334227i	0.519962	+	0.854189i	$0.325946\pi$
$854$	−2.78110			−0.0951674
$855$		0			0
$856$	3.72306			0.127252
$857$	−1.82209	+	1.82209i	−0.0622413	+	0.0622413i	−0.737542	−	0.675301i	$-0.764014\pi$
$857$	−1.82209	+	1.82209i	−0.0622413	+	0.0622413i	0.675301	+	0.737542i	$0.264014\pi$
$858$	−2.80317	−	0.552296i	−0.0956988	−	0.0188551i
$859$			17.6971i			0.603818i	0.953337	+	0.301909i	$0.0976239\pi$
$859$			17.6971i			0.603818i	−0.953337	+	0.301909i	$0.902376\pi$
$860$		0			0
$861$	26.5904	−	17.8370i	0.906197	−	0.607885i
$862$	1.97768	+	1.97768i	0.0673600	+	0.0673600i
$863$	27.9161	+	27.9161i	0.950274	+	0.950274i	0.998821	−	0.0485468i	$-0.0154590\pi$
$863$	27.9161	+	27.9161i	0.950274	+	0.950274i	−0.0485468	+	0.998821i	$0.515459\pi$
$864$	27.9295	−	5.71386i	0.950180	−	0.194390i
$865$		0			0
$866$		−	16.0472i		−	0.545306i
$867$	6.21171	−	31.5275i	0.210961	−	1.07073i
$868$	−3.44041	+	3.44041i	−0.116775	+	0.116775i
$869$	−0.249250			−0.00845524
$870$		0			0
$871$	5.63676			0.190994
$872$	−6.70514	+	6.70514i	−0.227065	+	0.227065i
$873$	−15.7983	−	37.7522i	−0.534692	−	1.27772i
$874$			5.72612i			0.193689i
$875$		0			0
$876$	3.26432	+	4.86624i	0.110291	+	0.164415i
$877$	5.52180	+	5.52180i	0.186458	+	0.186458i	0.794163	−	0.607705i	$-0.207910\pi$
$877$	5.52180	+	5.52180i	0.186458	+	0.186458i	−0.607705	+	0.794163i	$0.707910\pi$
$878$	2.82621	+	2.82621i	0.0953798	+	0.0953798i
$879$	5.08090	+	7.57430i	0.171375	+	0.255475i
$880$		0			0
$881$		−	10.4696i		−	0.352730i	−0.984325	−	0.176365i	$-0.943566\pi$
$881$		−	10.4696i		−	0.352730i	0.984325	−	0.176365i	$-0.0564339\pi$
$882$	−6.92201	−	16.5410i	−0.233076	−	0.556966i
$883$	8.41420	−	8.41420i	0.283160	−	0.283160i	−0.551208	−	0.834368i	$-0.685833\pi$
$883$	8.41420	−	8.41420i	0.283160	−	0.283160i	0.834368	+	0.551208i	$0.185833\pi$
$884$	5.51460			0.185476
$885$		0			0
$886$	−12.2199			−0.410535
$887$	10.9900	−	10.9900i	0.369007	−	0.369007i	−0.498108	−	0.867115i	$-0.665972\pi$
$887$	10.9900	−	10.9900i	0.369007	−	0.369007i	0.867115	+	0.498108i	$0.165972\pi$
$888$	−2.36510	+	12.0040i	−0.0793676	+	0.402829i
$889$			66.0453i			2.21509i
$890$		0			0
$891$	31.9395	−	32.4069i	1.07001	−	1.08567i
$892$	−23.8635	−	23.8635i	−0.799010	−	0.799010i
$893$	8.40832	+	8.40832i	0.281374	+	0.281374i
$894$	10.8228	−	7.26003i	0.361969	−	0.242812i
$895$		0			0
$896$			47.7659i			1.59575i
$897$	−2.49330	−	0.491243i	−0.0832488	−	0.0164021i
$898$	−1.40542	+	1.40542i	−0.0468996	+	0.0468996i
$899$	−1.64228			−0.0547732
$900$		0			0
$901$	−44.4211			−1.47988
$902$	9.31463	−	9.31463i	0.310143	−	0.310143i
$903$	47.3470	+	9.32856i	1.57561	+	0.310435i
$904$		−	26.5688i		−	0.883664i
$905$		0			0
$906$	−15.5377	+	10.4228i	−0.516204	+	0.346274i
$907$	10.2557	+	10.2557i	0.340534	+	0.340534i	0.856568	−	0.516034i	$-0.172592\pi$
$907$	10.2557	+	10.2557i	0.340534	+	0.340534i	−0.516034	+	0.856568i	$0.672592\pi$
$908$	−8.77474	−	8.77474i	−0.291200	−	0.291200i
$909$	14.1265	−	34.4578i	0.468547	−	1.14289i
$910$		0			0
$911$			30.4901i			1.01018i	0.863066	+	0.505091i	$0.168541\pi$
$911$			30.4901i			1.01018i	−0.863066	+	0.505091i	$0.831459\pi$
$912$	−2.57315	+	13.0600i	−0.0852054	+	0.432459i
$913$	−41.4739	+	41.4739i	−1.37258	+	1.37258i
$914$	0.0345890			0.00114410
$915$		0			0
$916$	20.6988			0.683907
$917$	−42.3389	+	42.3389i	−1.39815	+	1.39815i
$918$	9.98521	−	15.1216i	0.329561	−	0.499087i
$919$			9.67738i			0.319227i	0.987180	+	0.159614i	$0.0510249\pi$
$919$			9.67738i			0.319227i	−0.987180	+	0.159614i	$0.948975\pi$
$920$		0			0
$921$	−9.49948	−	14.1612i	−0.313019	−	0.466629i
$922$	−4.52716	−	4.52716i	−0.149094	−	0.149094i
$923$	1.23252	+	1.23252i	0.0405687	+	0.0405687i
$924$	33.5603	+	50.0297i	1.10405	+	1.64586i
$925$		0			0
$926$			20.7056i			0.680427i
$927$	15.1489	−	6.33945i	0.497556	−	0.208215i
$928$	−9.00870	+	9.00870i	−0.295725	+	0.295725i
$929$	36.4054			1.19442			0.597212	−	0.802084i	$-0.296275\pi$
$929$	36.4054			1.19442			0.597212	+	0.802084i	$0.296275\pi$
$930$		0			0
$931$	38.0407			1.24673
$932$	14.7341	−	14.7341i	0.482632	−	0.482632i
$933$	3.88108	−	19.6984i	0.127061	−	0.644897i
$934$			2.12748i			0.0696133i
$935$		0			0
$936$	3.31285	+	1.35815i	0.108284	+	0.0443926i
$937$	−21.5242	−	21.5242i	−0.703165	−	0.703165i	0.261924	−	0.965089i	$-0.415643\pi$
$937$	−21.5242	−	21.5242i	−0.703165	−	0.703165i	−0.965089	+	0.261924i	$0.915643\pi$
$938$	17.3408	+	17.3408i	0.566197	+	0.566197i
$939$	−26.3867	+	17.7004i	−0.861098	+	0.577632i
$940$		0			0
$941$			32.4342i			1.05733i	0.848832	+	0.528663i	$0.177306\pi$
$941$			32.4342i			1.05733i	−0.848832	+	0.528663i	$0.822694\pi$
$942$	7.10411	+	1.39969i	0.231465	+	0.0456044i
$943$	8.28494	−	8.28494i	0.269795	−	0.269795i
$944$	0.673602			0.0219239
$945$		0			0
$946$	19.8535			0.645493
$947$	−28.8440	+	28.8440i	−0.937305	+	0.937305i	−0.998147	−	0.0608424i	$-0.980621\pi$
$947$	−28.8440	+	28.8440i	−0.937305	+	0.937305i	0.0608424	+	0.998147i	$0.480621\pi$
$948$	0.138903	+	0.0273674i	0.00451136	+	0.000888852i
$949$			1.13833i			0.0369517i
$950$		0			0
$951$	39.9784	−	26.8178i	1.29639	−	0.869628i
$952$	37.4304	+	37.4304i	1.21313	+	1.21313i
$953$	28.3783	+	28.3783i	0.919264	+	0.919264i	0.996976	−	0.0777121i	$-0.0247615\pi$
$953$	28.3783	+	28.3783i	0.919264	+	0.919264i	−0.0777121	+	0.996976i	$0.524761\pi$
$954$	−12.0950	−	4.95852i	−0.391590	−	0.160538i
$955$		0			0
$956$		−	30.9946i		−	1.00244i
$957$	−3.93082	+	19.9509i	−0.127065	+	0.644919i
$958$	10.9744	−	10.9744i	0.354567	−	0.354567i
$959$	12.1720			0.393055
$960$		0			0
$961$	−30.4998			−0.983866
$962$	−0.761737	+	0.761737i	−0.0245594	+	0.0245594i
$963$	−4.81595	+	2.01535i	−0.155192	+	0.0649439i
$964$			34.2924i			1.10448i
$965$		0			0
$966$	−6.15907	−	9.18156i	−0.198165	−	0.295412i
$967$	−11.9954	−	11.9954i	−0.385747	−	0.385747i	0.487420	−	0.873167i	$-0.337938\pi$
$967$	−11.9954	−	11.9954i	−0.385747	−	0.385747i	−0.873167	+	0.487420i	$0.837938\pi$
$968$	22.0261	+	22.0261i	0.707944	+	0.707944i
$969$	21.4161	+	31.9259i	0.687985	+	1.02561i
$970$		0			0
$971$			52.7584i			1.69310i	0.532312	+	0.846548i	$0.321323\pi$
$971$			52.7584i			1.69310i	−0.532312	+	0.846548i	$0.678677\pi$
$972$	−21.3576	+	14.5529i	−0.685045	+	0.466784i
$973$	50.2891	−	50.2891i	1.61220	−	1.61220i
$974$	−12.1762			−0.390150
$975$		0			0
$976$	−2.36575			−0.0757257
$977$	−2.24479	+	2.24479i	−0.0718171	+	0.0718171i	−0.742103	−	0.670286i	$-0.766171\pi$
$977$	−2.24479	+	2.24479i	−0.0718171	+	0.0718171i	0.670286	+	0.742103i	$0.266171\pi$
$978$	−0.413011	+	2.09623i	−0.0132066	+	0.0670301i
$979$		−	29.0864i		−	0.929605i
$980$		0			0
$981$	5.04380	−	12.3030i	0.161036	−	0.392804i
$982$	14.8246	+	14.8246i	0.473073	+	0.473073i
$983$	33.5271	+	33.5271i	1.06935	+	1.06935i	0.997409	+	0.0719395i	$0.0229188\pi$
$983$	33.5271	+	33.5271i	1.06935	+	1.06935i	0.0719395	+	0.997409i	$0.477081\pi$
$984$	−13.7093	+	9.19632i	−0.437037	+	0.293168i
$985$		0			0
$986$			8.09824i			0.257901i
$987$	−22.5264	−	4.43828i	−0.717025	−	0.141272i
$988$	−2.43442	+	2.43442i	−0.0774491	+	0.0774491i
$989$	17.6588			0.561517
$990$		0			0
$991$	11.5062			0.365507			0.182753	−	0.983159i	$-0.441499\pi$
$991$	11.5062			0.365507			0.182753	+	0.983159i	$0.441499\pi$
$992$	2.74362	−	2.74362i	0.0871101	−	0.0871101i
$993$	−60.8270	−	11.9844i	−1.93029	−	0.380315i
$994$			7.58336i			0.240530i
$995$		0			0
$996$	27.6665	−	18.5589i	0.876646	−	0.588061i
$997$	36.3683	+	36.3683i	1.15179	+	1.15179i	0.986193	+	0.165602i	$0.0529567\pi$
$997$	36.3683	+	36.3683i	1.15179	+	1.15179i	0.165602	+	0.986193i	$0.447043\pi$
$998$	−9.77012	−	9.77012i	−0.309268	−	0.309268i
$999$	−3.43862	−	16.8080i	−0.108793	−	0.531783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.e.c.182.8	yes	32
3.2	odd	2	inner	375.2.e.c.182.10	yes	32
5.2	odd	4	inner	375.2.e.c.68.7	✓	32
5.3	odd	4	inner	375.2.e.c.68.10	yes	32
5.4	even	2	inner	375.2.e.c.182.9	yes	32
15.2	even	4	inner	375.2.e.c.68.9	yes	32
15.8	even	4	inner	375.2.e.c.68.8	yes	32
15.14	odd	2	inner	375.2.e.c.182.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
375.2.e.c.68.7	✓	32	5.2	odd	4	inner
375.2.e.c.68.8	yes	32	15.8	even	4	inner
375.2.e.c.68.9	yes	32	15.2	even	4	inner
375.2.e.c.68.10	yes	32	5.3	odd	4	inner
375.2.e.c.182.7	yes	32	15.14	odd	2	inner
375.2.e.c.182.8	yes	32	1.1	even	1	trivial
375.2.e.c.182.9	yes	32	5.4	even	2	inner
375.2.e.c.182.10	yes	32	3.2	odd	2	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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.413570 + 0.413570i) q^{2} +(1.69938 + 0.334821i) q^{3} +1.65792i q^{4} +(-0.841285 + 0.564341i) q^{6} +(2.93422 + 2.93422i) q^{7} +(-1.51281 - 1.51281i) q^{8} +(2.77579 + 1.13798i) q^{9} -5.05566i q^{11} +(-0.555106 + 2.81744i) q^{12} +(-0.394459 + 0.394459i) q^{13} -2.42701 q^{14} -2.06454 q^{16} +(-4.21618 + 4.21618i) q^{17} +(-1.61862 + 0.677351i) q^{18} -3.72246i q^{19} +(4.00391 + 5.96879i) q^{21} +(2.09087 + 2.09087i) q^{22} +(1.85974 + 1.85974i) q^{23} +(-2.06431 - 3.07735i) q^{24} -0.326273i q^{26} +(4.33611 + 2.86325i) q^{27} +(-4.86469 + 4.86469i) q^{28} -2.32216 q^{29} +0.707221 q^{31} +(3.87944 - 3.87944i) q^{32} +(1.69274 - 8.59150i) q^{33} -3.48737i q^{34} +(-1.88667 + 4.60204i) q^{36} +(-2.33466 - 2.33466i) q^{37} +(1.53950 + 1.53950i) q^{38} +(-0.802409 + 0.538263i) q^{39} -4.45490i q^{41} +(-4.12441 - 0.812613i) q^{42} +(4.74766 - 4.74766i) q^{43} +8.38188 q^{44} -1.53826 q^{46} +(-2.25881 + 2.25881i) q^{47} +(-3.50843 - 0.691250i) q^{48} +10.2192i q^{49} +(-8.57656 + 5.75323i) q^{51} +(-0.653981 - 0.653981i) q^{52} +(5.26793 + 5.26793i) q^{53} +(-2.97744 + 0.609130i) q^{54} -8.87780i q^{56} +(1.24636 - 6.32587i) q^{57} +(0.960377 - 0.960377i) q^{58} -0.326273 q^{59} +1.14590 q^{61} +(-0.292485 + 0.292485i) q^{62} +(4.80570 + 11.4838i) q^{63} -0.920229i q^{64} +(2.85312 + 4.25325i) q^{66} +(-7.14493 - 7.14493i) q^{67} +(-6.99008 - 6.99008i) q^{68} +(2.53772 + 3.78308i) q^{69} -3.12457i q^{71} +(-2.47769 - 5.92077i) q^{72} +(1.44290 - 1.44290i) q^{73} +1.93109 q^{74} +6.17153 q^{76} +(14.8344 - 14.8344i) q^{77} +(0.109243 - 0.554462i) q^{78} -0.0493012i q^{79} +(6.41002 + 6.31757i) q^{81} +(1.84241 + 1.84241i) q^{82} +(-8.20345 - 8.20345i) q^{83} +(-9.89577 + 6.63816i) q^{84} +3.92698i q^{86} +(-3.94624 - 0.777509i) q^{87} +(-7.64824 + 7.64824i) q^{88} +5.75323 q^{89} -2.31486 q^{91} +(-3.08329 + 3.08329i) q^{92} +(1.20184 + 0.236792i) q^{93} -1.86835i q^{94} +(7.89157 - 5.29373i) q^{96} +(-9.64599 - 9.64599i) q^{97} +(-4.22637 - 4.22637i) q^{98} +(5.75323 - 14.0335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{6} - 24 q^{16} + 32 q^{21} - 56 q^{31} - 116 q^{36} - 96 q^{46} - 48 q^{51} + 144 q^{61} + 120 q^{66} + 168 q^{76} + 132 q^{81} - 56 q^{91} + 76 q^{96}+O(q^{100}) \) 32 * q + 12 * q^6 - 24 * q^16 + 32 * q^21 - 56 * q^31 - 116 * q^36 - 96 * q^46 - 48 * q^51 + 144 * q^61 + 120 * q^66 + 168 * q^76 + 132 * q^81 - 56 * q^91 + 76 * q^96

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