LMFDB - Embedded newform 975.2.s.e.818.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(818,975)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("975.818");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.s (of order $4$, degree $2$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			818.13
Character	$\chi$	$=$	975.818
Dual form			975.2.s.e.857.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25684 - 1.25684i) q^{2} +(-1.36721 + 1.06336i) q^{3} -1.15927i q^{4} +(-0.381882 + 3.05483i) q^{6} +(-1.60133 - 1.60133i) q^{7} +(1.05665 + 1.05665i) q^{8} +(0.738515 - 2.90768i) q^{9} +2.48179 q^{11} +(1.23273 + 1.58497i) q^{12} +(-0.624771 + 3.55101i) q^{13} -4.02523 q^{14} +4.97463 q^{16} +(-1.27410 - 1.27410i) q^{17} +(-2.72628 - 4.58267i) q^{18} +1.93388 q^{19} +(3.89216 + 0.486556i) q^{21} +(3.11920 - 3.11920i) q^{22} +(5.56883 - 5.56883i) q^{23} +(-2.56827 - 0.321058i) q^{24} +(3.67780 + 5.24827i) q^{26} +(2.08222 + 4.76071i) q^{27} +(-1.85639 + 1.85639i) q^{28} +9.66063 q^{29} +6.61976i q^{31} +(4.13899 - 4.13899i) q^{32} +(-3.39312 + 2.63904i) q^{33} -3.20267 q^{34} +(-3.37080 - 0.856142i) q^{36} +(3.53521 + 3.53521i) q^{37} +(2.43057 - 2.43057i) q^{38} +(-2.92182 - 5.51933i) q^{39} -7.35052 q^{41} +(5.50332 - 4.28028i) q^{42} +(3.46312 + 3.46312i) q^{43} -2.87707i q^{44} -13.9982i q^{46} +(4.55353 - 4.55353i) q^{47} +(-6.80136 + 5.28984i) q^{48} -1.87146i q^{49} +(3.09679 + 0.387128i) q^{51} +(4.11659 + 0.724281i) q^{52} +(3.97417 - 3.97417i) q^{53} +(8.60044 + 3.36643i) q^{54} -3.38411i q^{56} +(-2.64402 + 2.05642i) q^{57} +(12.1418 - 12.1418i) q^{58} -2.79393i q^{59} -2.54520 q^{61} +(8.31996 + 8.31996i) q^{62} +(-5.83877 + 3.47355i) q^{63} -0.454797i q^{64} +(-0.947751 + 7.58144i) q^{66} +(-1.34628 - 1.34628i) q^{67} +(-1.47703 + 1.47703i) q^{68} +(-1.69206 + 13.5354i) q^{69} +6.58676 q^{71} +(3.85277 - 2.29206i) q^{72} +(2.82950 - 2.82950i) q^{73} +8.88637 q^{74} -2.24190i q^{76} +(-3.97417 - 3.97417i) q^{77} +(-10.6091 - 3.26464i) q^{78} +6.48553i q^{79} +(-7.90919 - 4.29473i) q^{81} +(-9.23840 + 9.23840i) q^{82} +(-3.17953 - 3.17953i) q^{83} +(0.564052 - 4.51208i) q^{84} +8.70515 q^{86} +(-13.2081 + 10.2728i) q^{87} +(2.62239 + 2.62239i) q^{88} +7.47217i q^{89} +(6.68682 - 4.68588i) q^{91} +(-6.45580 - 6.45580i) q^{92} +(-7.03922 - 9.05059i) q^{93} -11.4461i q^{94} +(-1.25761 + 10.0601i) q^{96} +(-9.27171 - 9.27171i) q^{97} +(-2.35212 - 2.35212i) q^{98} +(1.83284 - 7.21624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 24 q^{12} + 24 q^{16} - 24 q^{22} + 16 q^{27} - 8 q^{36} - 12 q^{42} + 64 q^{43} + 20 q^{48} + 16 q^{51} + 72 q^{52} + 8 q^{61} - 72 q^{66} - 84 q^{78} + 112 q^{81} - 48 q^{82} - 20 q^{87}+ \cdots - 40 q^{91}+O(q^{100}) $ 32 * q + 4 * q^3 + 24 * q^12 + 24 * q^16 - 24 * q^22 + 16 * q^27 - 8 * q^36 - 12 * q^42 + 64 * q^43 + 20 * q^48 + 16 * q^51 + 72 * q^52 + 8 * q^61 - 72 * q^66 - 84 * q^78 + 112 * q^81 - 48 * q^82 - 20 * q^87 + 8 * q^88 - 40 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.25684	−	1.25684i	0.888717	−	0.888717i	−0.105683	−	0.994400i	$-0.533703\pi$
$2$	1.25684	−	1.25684i	0.888717	−	0.888717i	0.994400	+	0.105683i	$0.0337027\pi$
$3$	−1.36721	+	1.06336i	−0.789358	+	0.613933i
$3$	−1.36721	+	1.06336i	−0.789358	+	0.613933i
$4$		−	1.15927i		−	0.579637i
$5$		0			0
$5$		0			0
$6$	−0.381882	+	3.05483i	−0.155903	+	1.24713i
$7$	−1.60133	−	1.60133i	−0.605247	−	0.605247i	0.336453	−	0.941700i	$-0.390773\pi$
$7$	−1.60133	−	1.60133i	−0.605247	−	0.605247i	−0.941700	+	0.336453i	$0.890773\pi$
$8$	1.05665	+	1.05665i	0.373584	+	0.373584i
$9$	0.738515	−	2.90768i	0.246172	−	0.969226i
$10$		0			0
$11$	2.48179			0.748287			0.374144	−	0.927371i	$-0.377937\pi$
$11$	2.48179			0.748287			0.374144	+	0.927371i	$0.377937\pi$
$12$	1.23273	+	1.58497i	0.355859	+	0.457541i
$13$	−0.624771	+	3.55101i	−0.173280	+	0.984873i
$13$	−0.624771	+	3.55101i	−0.173280	+	0.984873i
$14$	−4.02523			−1.07579
$15$		0			0
$16$	4.97463			1.24366
$17$	−1.27410	−	1.27410i	−0.309014	−	0.309014i	0.535513	−	0.844527i	$-0.320118\pi$
$17$	−1.27410	−	1.27410i	−0.309014	−	0.309014i	−0.844527	+	0.535513i	$0.820118\pi$
$18$	−2.72628	−	4.58267i	−0.642591	−	1.08015i
$19$	1.93388			0.443663			0.221831	−	0.975085i	$-0.428797\pi$
$19$	1.93388			0.443663			0.221831	+	0.975085i	$0.428797\pi$
$20$		0			0
$21$	3.89216	+	0.486556i	0.849338	+	0.106175i
$22$	3.11920	−	3.11920i	0.665016	−	0.665016i
$23$	5.56883	−	5.56883i	1.16118	−	1.16118i	0.176964	−	0.984217i	$-0.443372\pi$
$23$	5.56883	−	5.56883i	1.16118	−	1.16118i	0.984217	−	0.176964i	$-0.0566275\pi$
$24$	−2.56827	−	0.321058i	−0.524247	−	0.0655358i
$25$		0			0
$26$	3.67780	+	5.24827i	0.721276	+	1.02927i
$27$	2.08222	+	4.76071i	0.400723	+	0.916199i
$28$	−1.85639	+	1.85639i	−0.350824	+	0.350824i
$29$	9.66063			1.79393			0.896967	−	0.442098i	$-0.145766\pi$
$29$	9.66063			1.79393			0.896967	+	0.442098i	$0.145766\pi$
$30$		0			0
$31$			6.61976i			1.18894i	0.804116	+	0.594472i	$0.202639\pi$
$31$			6.61976i			1.18894i	−0.804116	+	0.594472i	$0.797361\pi$
$32$	4.13899	−	4.13899i	0.731677	−	0.731677i
$33$	−3.39312	+	2.63904i	−0.590667	+	0.459399i
$34$	−3.20267			−0.549253
$35$		0			0
$36$	−3.37080	−	0.856142i	−0.561800	−	0.142690i
$37$	3.53521	+	3.53521i	0.581186	+	0.581186i	0.935229	−	0.354043i	$-0.115193\pi$
$37$	3.53521	+	3.53521i	0.581186	+	0.581186i	−0.354043	+	0.935229i	$0.615193\pi$
$38$	2.43057	−	2.43057i	0.394291	−	0.394291i
$39$	−2.92182	−	5.51933i	−0.467866	−	0.883800i
$40$		0			0
$41$	−7.35052			−1.14796			−0.573979	−	0.818870i	$-0.694601\pi$
$41$	−7.35052			−1.14796			−0.573979	+	0.818870i	$0.694601\pi$
$42$	5.50332	−	4.28028i	0.849181	−	0.660462i
$43$	3.46312	+	3.46312i	0.528121	+	0.528121i	0.920012	−	0.391891i	$-0.128179\pi$
$43$	3.46312	+	3.46312i	0.528121	+	0.528121i	−0.391891	+	0.920012i	$0.628179\pi$
$44$		−	2.87707i		−	0.433735i
$45$		0			0
$46$		−	13.9982i		−	2.06392i
$47$	4.55353	−	4.55353i	0.664200	−	0.664200i	−0.292167	−	0.956367i	$-0.594376\pi$
$47$	4.55353	−	4.55353i	0.664200	−	0.664200i	0.956367	+	0.292167i	$0.0943764\pi$
$48$	−6.80136	+	5.28984i	−0.981691	+	0.763523i
$49$		−	1.87146i		−	0.267351i
$50$		0			0
$51$	3.09679	+	0.387128i	0.433637	+	0.0542087i
$52$	4.11659	+	0.724281i	0.570869	+	0.100440i
$53$	3.97417	−	3.97417i	0.545894	−	0.545894i	−0.379356	−	0.925251i	$-0.623855\pi$
$53$	3.97417	−	3.97417i	0.545894	−	0.545894i	0.925251	+	0.379356i	$0.123855\pi$
$54$	8.60044	+	3.36643i	1.17037	+	0.458113i
$55$		0			0
$56$		−	3.38411i		−	0.452221i
$57$	−2.64402	+	2.05642i	−0.350209	+	0.272379i
$58$	12.1418	−	12.1418i	1.59430	−	1.59430i
$59$		−	2.79393i		−	0.363739i	−0.983323	−	0.181869i	$-0.941785\pi$
$59$		−	2.79393i		−	0.363739i	0.983323	−	0.181869i	$-0.0582148\pi$
$60$		0			0
$61$	−2.54520			−0.325880			−0.162940	−	0.986636i	$-0.552098\pi$
$61$	−2.54520			−0.325880			−0.162940	+	0.986636i	$0.552098\pi$
$62$	8.31996	+	8.31996i	1.05664	+	1.05664i
$63$	−5.83877	+	3.47355i	−0.735616	+	0.437627i
$64$		−	0.454797i		−	0.0568496i
$65$		0			0
$66$	−0.947751	+	7.58144i	−0.116660	+	0.933211i
$67$	−1.34628	−	1.34628i	−0.164475	−	0.164475i	0.620071	−	0.784546i	$-0.287104\pi$
$67$	−1.34628	−	1.34628i	−0.164475	−	0.164475i	−0.784546	+	0.620071i	$0.787104\pi$
$68$	−1.47703	+	1.47703i	−0.179116	+	0.179116i
$69$	−1.69206	+	13.5354i	−0.203700	+	1.62948i
$70$		0			0
$71$	6.58676			0.781704			0.390852	−	0.920453i	$-0.372180\pi$
$71$	6.58676			0.781704			0.390852	+	0.920453i	$0.372180\pi$
$72$	3.85277	−	2.29206i	0.454053	−	0.270121i
$73$	2.82950	−	2.82950i	0.331168	−	0.331168i	−0.521862	−	0.853030i	$-0.674762\pi$
$73$	2.82950	−	2.82950i	0.331168	−	0.331168i	0.853030	+	0.521862i	$0.174762\pi$
$74$	8.88637			1.03302
$75$		0			0
$76$		−	2.24190i		−	0.257163i
$77$	−3.97417	−	3.97417i	−0.452899	−	0.452899i
$78$	−10.6091	−	3.26464i	−1.20125	−	0.369647i
$79$			6.48553i			0.729679i	0.931070	+	0.364840i	$0.118876\pi$
$79$			6.48553i			0.729679i	−0.931070	+	0.364840i	$0.881124\pi$
$80$		0			0
$81$	−7.90919	−	4.29473i	−0.878799	−	0.477192i
$82$	−9.23840	+	9.23840i	−1.02021	+	1.02021i
$83$	−3.17953	−	3.17953i	−0.348999	−	0.348999i	0.510738	−	0.859736i	$-0.329372\pi$
$83$	−3.17953	−	3.17953i	−0.348999	−	0.348999i	−0.859736	+	0.510738i	$0.829372\pi$
$84$	0.564052	−	4.51208i	0.0615431	−	0.492308i
$85$		0			0
$86$	8.70515			0.938700
$87$	−13.2081	+	10.2728i	−1.41606	+	1.10136i
$88$	2.62239	+	2.62239i	0.279548	+	0.279548i
$89$			7.47217i			0.792049i	0.918240	+	0.396024i	$0.129610\pi$
$89$			7.47217i			0.792049i	−0.918240	+	0.396024i	$0.870390\pi$
$90$		0			0
$91$	6.68682	−	4.68588i	0.700969	−	0.491214i
$92$	−6.45580	−	6.45580i	−0.673064	−	0.673064i
$93$	−7.03922	−	9.05059i	−0.729933	−	0.938503i
$94$		−	11.4461i		−	1.18057i
$95$		0			0
$96$	−1.25761	+	10.0601i	−0.128354	+	1.02676i
$97$	−9.27171	−	9.27171i	−0.941399	−	0.941399i	0.0569765	−	0.998376i	$-0.481854\pi$
$97$	−9.27171	−	9.27171i	−0.941399	−	0.941399i	−0.998376	+	0.0569765i	$0.981854\pi$
$98$	−2.35212	−	2.35212i	−0.237600	−	0.237600i
$99$	1.83284	−	7.21624i	0.184207	−	0.725260i
$100$		0			0
$101$			10.3634i			1.03120i	0.856830	+	0.515599i	$0.172430\pi$
$101$			10.3634i			1.03120i	−0.856830	+	0.515599i	$0.827570\pi$
$102$	4.37871	−	3.40560i	0.433557	−	0.337205i
$103$	−7.07081	−	7.07081i	−0.696707	−	0.696707i	0.266992	−	0.963699i	$-0.413970\pi$
$103$	−7.07081	−	7.07081i	−0.696707	−	0.696707i	−0.963699	+	0.266992i	$0.913970\pi$
$104$	−4.41236	+	3.09202i	−0.432667	+	0.303198i
$105$		0			0
$106$		−	9.98977i		−	0.970292i
$107$	2.61477	+	2.61477i	0.252779	+	0.252779i	0.822109	−	0.569330i	$-0.192797\pi$
$107$	2.61477	+	2.61477i	0.252779	+	0.252779i	−0.569330	+	0.822109i	$0.692797\pi$
$108$	5.51897	−	2.41386i	0.531063	−	0.232274i
$109$	−15.7300			−1.50666			−0.753331	−	0.657642i	$-0.771554\pi$
$109$	−15.7300			−1.50666			−0.753331	+	0.657642i	$0.771554\pi$
$110$		0			0
$111$	−8.59259	−	1.07415i	−0.815573	−	0.101954i
$112$	−7.96605	−	7.96605i	−0.752721	−	0.752721i
$113$	−4.86114	+	4.86114i	−0.457298	+	0.457298i	−0.897768	−	0.440470i	$-0.854812\pi$
$113$	−4.86114	+	4.86114i	−0.457298	+	0.457298i	0.440470	+	0.897768i	$0.354812\pi$
$114$	−0.738515	+	5.90768i	−0.0691683	+	0.553305i
$115$		0			0
$116$		−	11.1993i		−	1.03983i
$117$	9.86379	+	4.43911i	0.911908	+	0.410396i
$118$	−3.51151	−	3.51151i	−0.323261	−	0.323261i
$119$			4.08052i			0.374060i
$120$		0			0
$121$	−4.84073			−0.440066
$122$	−3.19890	+	3.19890i	−0.289615	+	0.289615i
$123$	10.0497	−	7.81628i	0.906150	−	0.704770i
$124$	7.67412			0.689156
$125$		0			0
$126$	−2.97269	+	11.7041i	−0.264828	+	1.04268i
$127$	−6.90382	+	6.90382i	−0.612615	+	0.612615i	−0.943627	−	0.331011i	$-0.892610\pi$
$127$	−6.90382	+	6.90382i	−0.612615	+	0.612615i	0.331011	+	0.943627i	$0.392610\pi$
$128$	7.70637	+	7.70637i	0.681153	+	0.681153i
$129$	−8.41736	−	1.05225i	−0.741107	−	0.0926453i
$130$		0			0
$131$		−	15.9988i		−	1.39782i	−0.715209	−	0.698911i	$-0.753668\pi$
$131$		−	15.9988i		−	1.39782i	0.715209	−	0.698911i	$-0.246332\pi$
$132$	3.05938	+	3.93356i	0.266284	+	0.342372i
$133$	−3.09679	−	3.09679i	−0.268526	−	0.268526i
$134$	−3.38411			−0.292343
$135$		0			0
$136$		−	2.69256i		−	0.230886i
$137$	−6.47173	+	6.47173i	−0.552917	+	0.552917i	−0.927282	−	0.374364i	$-0.877861\pi$
$137$	−6.47173	+	6.47173i	−0.552917	+	0.552917i	0.374364	+	0.927282i	$0.377861\pi$
$138$	14.8852	+	19.1385i	1.26711	+	1.62917i
$139$			11.9913i			1.01709i	0.861036	+	0.508543i	$0.169816\pi$
$139$			11.9913i			1.01709i	−0.861036	+	0.508543i	$0.830184\pi$
$140$		0			0
$141$	−1.38356	+	11.0677i	−0.116517	+	0.932066i
$142$	8.27848	−	8.27848i	0.694714	−	0.694714i
$143$	−1.55055	+	8.81285i	−0.129664	+	0.736968i
$144$	3.67384	−	14.4646i	0.306153	−	1.20539i
$145$		0			0
$146$		−	7.11243i		−	0.588629i
$147$	1.99004	+	2.55867i	0.164136	+	0.211036i
$148$	4.09828	−	4.09828i	0.336877	−	0.336877i
$149$		−	3.57788i		−	0.293111i	−0.989202	−	0.146556i	$-0.953181\pi$
$149$		−	3.57788i		−	0.293111i	0.989202	−	0.146556i	$-0.0468187\pi$
$150$		0			0
$151$			1.93388i			0.157377i	0.996899	+	0.0786885i	$0.0250732\pi$
$151$			1.93388i			0.157377i	−0.996899	+	0.0786885i	$0.974927\pi$
$152$	2.04344	+	2.04344i	0.165745	+	0.165745i
$153$	−4.64561	+	2.76373i	−0.375575	+	0.223434i
$154$	−9.98977			−0.804998
$155$		0			0
$156$	−6.39841	+	3.38719i	−0.512283	+	0.271192i
$157$	9.89449	−	9.89449i	0.789666	−	0.789666i	−0.191773	−	0.981439i	$-0.561424\pi$
$157$	9.89449	−	9.89449i	0.789666	−	0.789666i	0.981439	+	0.191773i	$0.0614238\pi$
$158$	8.15125	+	8.15125i	0.648479	+	0.648479i
$159$	−1.20753	+	9.65951i	−0.0957633	+	0.766049i
$160$		0			0
$161$	−17.8351			−1.40560
$162$	−15.3383	+	4.54279i	−1.20509	+	0.356915i
$163$	−3.08455	+	3.08455i	−0.241600	+	0.241600i	−0.817512	−	0.575912i	$-0.804647\pi$
$163$	−3.08455	+	3.08455i	−0.241600	+	0.241600i	0.575912	+	0.817512i	$0.304647\pi$
$164$			8.52127i			0.665400i
$165$		0			0
$166$	−7.99229			−0.620322
$167$	−0.544208	+	0.544208i	−0.0421121	+	0.0421121i	−0.727849	−	0.685737i	$-0.759480\pi$
$167$	−0.544208	+	0.544208i	−0.0421121	+	0.0421121i	0.685737	+	0.727849i	$0.259480\pi$
$168$	3.59854	+	4.62679i	0.277634	+	0.356964i
$169$	−12.2193	−	4.43714i	−0.939948	−	0.341318i
$170$		0			0
$171$	1.42820	−	5.62310i	0.109217	−	0.430010i
$172$	4.01470	−	4.01470i	0.306118	−	0.306118i
$173$	1.92582	−	1.92582i	0.146417	−	0.146417i	−0.630098	−	0.776515i	$-0.716985\pi$
$173$	1.92582	−	1.92582i	0.146417	−	0.146417i	0.776515	+	0.630098i	$0.216985\pi$
$174$	−3.68922	+	29.5116i	−0.279679	+	2.23727i
$175$		0			0
$176$	12.3460			0.930614
$177$	2.97096	+	3.81988i	0.223311	+	0.287120i
$178$	9.39129	+	9.39129i	0.703907	+	0.703907i
$179$	18.3117			1.36868			0.684342	−	0.729161i	$-0.260090\pi$
$179$	18.3117			1.36868			0.684342	+	0.729161i	$0.260090\pi$
$180$		0			0
$181$	−2.27148			−0.168838			−0.0844189	−	0.996430i	$-0.526903\pi$
$181$	−2.27148			−0.168838			−0.0844189	+	0.996430i	$0.526903\pi$
$182$	2.51485	−	14.2936i	0.186413	−	1.05951i
$183$	3.47982	−	2.70648i	0.257236	−	0.200069i
$184$	11.7687			0.867597
$185$		0			0
$186$	−20.2223	−	2.52797i	−1.48277	−	0.185360i
$187$	−3.16204	−	3.16204i	−0.231232	−	0.231232i
$188$	−5.27879	−	5.27879i	−0.384995	−	0.384995i
$189$	4.28917	−	10.9578i	0.311991	−	0.797064i
$190$		0			0
$191$			16.8964i			1.22258i	0.791407	+	0.611289i	$0.209349\pi$
$191$			16.8964i			1.22258i	−0.791407	+	0.611289i	$0.790651\pi$
$192$	0.483614	+	0.621802i	0.0349019	+	0.0448747i
$193$	−14.4083	+	14.4083i	−1.03713	+	1.03713i	−0.0378452	+	0.999284i	$0.512049\pi$
$193$	−14.4083	+	14.4083i	−1.03713	+	1.03713i	−0.999284	+	0.0378452i	$0.987951\pi$
$194$	−23.3060			−1.67328
$195$		0			0
$196$	−2.16954			−0.154967
$197$	−17.1945	+	17.1945i	−1.22506	+	1.22506i	−0.259249	+	0.965810i	$0.583475\pi$
$197$	−17.1945	+	17.1945i	−1.22506	+	1.22506i	−0.965810	+	0.259249i	$0.916525\pi$
$198$	−6.76606	−	11.3732i	−0.480843	−	0.808259i
$199$		−	18.0401i		−	1.27883i	−0.768861	−	0.639416i	$-0.779176\pi$
$199$		−	18.0401i		−	1.27883i	0.768861	−	0.639416i	$-0.220824\pi$
$200$		0			0
$201$	3.27224	+	0.409060i	0.230806	+	0.0288529i
$202$	13.0251	+	13.0251i	0.916443	+	0.916443i
$203$	−15.4699	−	15.4699i	−1.08577	−	1.08577i
$204$	0.448787	−	3.59003i	0.0314214	−	0.251352i
$205$		0			0
$206$	−17.7737			−1.23835
$207$	−12.0797	−	20.3050i	−0.839597	−	1.41130i
$208$	−3.10801	+	17.6650i	−0.215502	+	1.22484i
$209$	4.79948			0.331987
$210$		0			0
$211$	21.6248			1.48871			0.744356	−	0.667783i	$-0.232756\pi$
$211$	21.6248			1.48871			0.744356	+	0.667783i	$0.232756\pi$
$212$	−4.60716	−	4.60716i	−0.316421	−	0.316421i
$213$	−9.00547	+	7.00412i	−0.617045	+	0.479914i
$214$	6.57267			0.449298
$215$		0			0
$216$	−2.83024	+	7.23061i	−0.192574	+	0.491981i
$217$	10.6005	−	10.6005i	0.719606	−	0.719606i
$218$	−19.7700	+	19.7700i	−1.33900	+	1.33900i
$219$	−0.859726	+	6.87730i	−0.0580949	+	0.464725i
$220$		0			0
$221$	5.32036	−	3.72832i	0.357886	−	0.250794i
$222$	−12.1495	+	9.44945i	−0.815422	+	0.634205i
$223$	16.9827	−	16.9827i	1.13725	−	1.13725i	0.148304	−	0.988942i	$-0.452619\pi$
$223$	16.9827	−	16.9827i	1.13725	−	1.13725i	0.988942	−	0.148304i	$-0.0473814\pi$
$224$	−13.2558			−0.885691
$225$		0			0
$226$			12.2193i			0.812817i
$227$	−6.28938	+	6.28938i	−0.417441	+	0.417441i	−0.884321	−	0.466880i	$-0.845378\pi$
$227$	−6.28938	+	6.28938i	−0.417441	+	0.417441i	0.466880	+	0.884321i	$0.345378\pi$
$228$	2.38395	+	3.06514i	0.157881	+	0.202994i
$229$	−12.0643			−0.797233			−0.398617	−	0.917118i	$-0.630510\pi$
$229$	−12.0643			−0.797233			−0.398617	+	0.917118i	$0.630510\pi$
$230$		0			0
$231$	9.65951	+	1.20753i	0.635549	+	0.0794496i
$232$	10.2079	+	10.2079i	0.670184	+	0.670184i
$233$	8.29631	−	8.29631i	0.543510	−	0.543510i	−0.381046	−	0.924556i	$-0.624436\pi$
$233$	8.29631	−	8.29631i	0.543510	−	0.543510i	0.924556	+	0.381046i	$0.124436\pi$
$234$	17.9764	−	6.81793i	1.17515	−	0.445702i
$235$		0			0
$236$	−3.23893			−0.210837
$237$	−6.89648	−	8.86707i	−0.447974	−	0.575978i
$238$	5.12854	+	5.12854i	0.332434	+	0.332434i
$239$		−	29.0823i		−	1.88118i	−0.339550	−	0.940588i	$-0.610275\pi$
$239$		−	29.0823i		−	1.88118i	0.339550	−	0.940588i	$-0.389725\pi$
$240$		0			0
$241$		−	4.33077i		−	0.278970i	−0.990224	−	0.139485i	$-0.955455\pi$
$241$		−	4.33077i		−	0.278970i	0.990224	−	0.139485i	$-0.0445446\pi$
$242$	−6.08400	+	6.08400i	−0.391094	+	0.391094i
$243$	15.3804	−	2.53856i	0.986651	−	0.162849i
$244$			2.95059i			0.188892i
$245$		0			0
$246$	2.80704	−	22.4546i	0.178970	−	1.43165i
$247$	−1.20823	+	6.86723i	−0.0768781	+	0.436951i
$248$	−6.99480	+	6.99480i	−0.444170	+	0.444170i
$249$	7.72807	+	0.966081i	0.489747	+	0.0612229i
$250$		0			0
$251$		−	6.63509i		−	0.418803i	−0.977830	−	0.209401i	$-0.932848\pi$
$251$		−	6.63509i		−	0.418803i	0.977830	−	0.209401i	$-0.0671515\pi$
$252$	4.02680	+	6.76874i	0.253665	+	0.426391i
$253$	13.8207	−	13.8207i	0.868897	−	0.868897i
$254$			17.3540i			1.08888i
$255$		0			0
$256$	20.2809			1.26756
$257$	−9.21184	−	9.21184i	−0.574619	−	0.574619i	0.358797	−	0.933416i	$-0.383187\pi$
$257$	−9.21184	−	9.21184i	−0.574619	−	0.574619i	−0.933416	+	0.358797i	$0.883187\pi$
$258$	−11.9017	+	9.25674i	−0.740970	+	0.576299i
$259$		−	11.3221i		−	0.703522i
$260$		0			0
$261$	7.13452	−	28.0900i	0.441616	−	1.73873i
$262$	−20.1079	−	20.1079i	−1.24227	−	1.24227i
$263$	8.70709	−	8.70709i	0.536902	−	0.536902i	−0.385716	−	0.922618i	$-0.626045\pi$
$263$	8.70709	−	8.70709i	0.536902	−	0.536902i	0.922618	+	0.385716i	$0.126045\pi$
$264$	−6.37391	−	0.796799i	−0.392287	−	0.0490396i
$265$		0			0
$266$	−7.78431			−0.477287
$267$	−7.94564	−	10.2160i	−0.486265	−	0.625210i
$268$	−1.56071	+	1.56071i	−0.0953356	+	0.0953356i
$269$	−19.9624			−1.21713			−0.608564	−	0.793505i	$-0.708254\pi$
$269$	−19.9624			−1.21713			−0.608564	+	0.793505i	$0.708254\pi$
$270$		0			0
$271$			15.4343i			0.937569i	0.883313	+	0.468784i	$0.155308\pi$
$271$			15.4343i			0.937569i	−0.883313	+	0.468784i	$0.844692\pi$
$272$	−6.33817	−	6.33817i	−0.384308	−	0.384308i
$273$	−4.15947	+	13.5171i	−0.251743	+	0.818092i
$274$			16.2678i			0.982774i
$275$		0			0
$276$	15.6913	+	1.96156i	0.944504	+	0.118072i
$277$	−8.39129	+	8.39129i	−0.504184	+	0.504184i	−0.912735	−	0.408551i	$-0.866034\pi$
$277$	−8.39129	+	8.39129i	−0.504184	+	0.504184i	0.408551	+	0.912735i	$0.366034\pi$
$278$	15.0711	+	15.0711i	0.903903	+	0.903903i
$279$	19.2481	+	4.88880i	1.15236	+	0.292685i
$280$		0			0
$281$	−20.3080			−1.21148			−0.605738	−	0.795664i	$-0.707122\pi$
$281$	−20.3080			−1.21148			−0.605738	+	0.795664i	$0.707122\pi$
$282$	12.1713	+	15.6492i	0.724793	+	0.931894i
$283$	13.2101	+	13.2101i	0.785258	+	0.785258i	0.980713	−	0.195455i	$-0.0626184\pi$
$283$	13.2101	+	13.2101i	0.785258	+	0.785258i	−0.195455	+	0.980713i	$0.562618\pi$
$284$		−	7.63586i		−	0.453105i
$285$		0			0
$286$	9.12752	+	13.0251i	0.539722	+	0.770190i
$287$	11.7706	+	11.7706i	0.694799	+	0.694799i
$288$	−8.97814	−	15.0916i	−0.529042	−	0.889278i
$289$		−	13.7533i		−	0.809020i
$290$		0			0
$291$	22.5355	+	2.81715i	1.32106	+	0.165145i
$292$	−3.28016	−	3.28016i	−0.191957	−	0.191957i
$293$	9.32896	+	9.32896i	0.545004	+	0.545004i	0.924992	−	0.379988i	$-0.124072\pi$
$293$	9.32896	+	9.32896i	0.545004	+	0.545004i	−0.379988	+	0.924992i	$0.624072\pi$
$294$	5.71699	+	0.714678i	0.333422	+	0.0416808i
$295$		0			0
$296$			7.47100i			0.434243i
$297$	5.16762	+	11.8151i	0.299856	+	0.685580i
$298$	−4.49681	−	4.49681i	−0.260493	−	0.260493i
$299$	16.2957	+	23.2542i	0.942405	+	1.34483i
$300$		0			0
$301$		−	11.0912i		−	0.639287i
$302$	2.43057	+	2.43057i	0.139864	+	0.139864i
$303$	−11.0201	−	14.1689i	−0.633086	−	0.813984i
$304$	9.62035			0.551765
$305$		0			0
$306$	−2.36522	+	9.31233i	−0.135211	+	0.532350i
$307$	16.2646	+	16.2646i	0.928272	+	0.928272i	0.997594	−	0.0693223i	$-0.0220837\pi$
$307$	16.2646	+	16.2646i	0.928272	+	0.928272i	−0.0693223	+	0.997594i	$0.522084\pi$
$308$	−4.60716	+	4.60716i	−0.262517	+	0.262517i
$309$	17.1861	+	2.14842i	0.977683	+	0.122220i
$310$		0			0
$311$		−	4.98446i		−	0.282643i	−0.989964	−	0.141321i	$-0.954865\pi$
$311$		−	4.98446i		−	0.282643i	0.989964	−	0.141321i	$-0.0451351\pi$
$312$	2.74467	−	8.91938i	0.155386	−	0.504960i
$313$	14.2484	+	14.2484i	0.805365	+	0.805365i	0.983928	−	0.178564i	$-0.0571451\pi$
$313$	14.2484	+	14.2484i	0.805365	+	0.805365i	−0.178564	+	0.983928i	$0.557145\pi$
$314$		−	24.8715i		−	1.40358i
$315$		0			0
$316$	7.51851			0.422949
$317$	14.3178	−	14.3178i	0.804168	−	0.804168i	−0.179576	−	0.983744i	$-0.557473\pi$
$317$	14.3178	−	14.3178i	0.804168	−	0.804168i	0.983744	+	0.179576i	$0.0574727\pi$
$318$	10.6228	+	13.6581i	0.595695	+	0.765908i
$319$	23.9756			1.34238
$320$		0			0
$321$	−6.35538	−	0.794482i	−0.354723	−	0.0443437i
$322$	−22.4158	+	22.4158i	−1.24918	+	1.24918i
$323$	−2.46396	−	2.46396i	−0.137098	−	0.137098i
$324$	−4.97877	+	9.16892i	−0.276598	+	0.509385i
$325$		0			0
$326$			7.75354i			0.429429i
$327$	21.5062	−	16.7267i	1.18930	−	0.924990i
$328$	−7.76696	−	7.76696i	−0.428859	−	0.428859i
$329$	−14.5834			−0.804011
$330$		0			0
$331$		−	15.6364i		−	0.859455i	−0.902959	−	0.429728i	$-0.858610\pi$
$331$		−	15.6364i		−	0.859455i	0.902959	−	0.429728i	$-0.141390\pi$
$332$	−3.68595	+	3.68595i	−0.202293	+	0.202293i
$333$	12.8901	−	7.66846i	0.706372	−	0.420229i
$334$			1.36796i			0.0748514i
$335$		0			0
$336$	19.3620	+	2.42044i	1.05629	+	0.132046i
$337$	−12.4230	+	12.4230i	−0.676726	+	0.676726i	−0.959258	−	0.282532i	$-0.908826\pi$
$337$	−12.4230	+	12.4230i	−0.676726	+	0.676726i	0.282532	+	0.959258i	$0.408826\pi$
$338$	−20.9344	+	9.78093i	−1.13868	+	0.532013i
$339$	1.47703	−	11.8154i	0.0802213	−	0.641722i
$340$		0			0
$341$			16.4289i			0.889672i
$342$	−5.27231	−	8.86234i	−0.285094	−	0.479220i
$343$	−14.2062	+	14.2062i	−0.767061	+	0.767061i
$344$			7.31864i			0.394595i
$345$		0			0
$346$		−	4.84087i		−	0.260247i
$347$	6.65873	+	6.65873i	0.357459	+	0.357459i	0.862876	−	0.505416i	$-0.168661\pi$
$347$	6.65873	+	6.65873i	0.357459	+	0.357459i	−0.505416	+	0.862876i	$0.668661\pi$
$348$	11.9089	+	15.3118i	0.638387	+	0.820798i
$349$	−3.35766			−0.179731			−0.0898657	−	0.995954i	$-0.528644\pi$
$349$	−3.35766			−0.179731			−0.0898657	+	0.995954i	$0.528644\pi$
$350$		0			0
$351$	−18.2062	+	4.41961i	−0.971777	+	0.235901i
$352$	10.2721	−	10.2721i	0.547504	−	0.547504i
$353$	10.8383	+	10.8383i	0.576864	+	0.576864i	0.934038	−	0.357174i	$-0.116260\pi$
$353$	10.8383	+	10.8383i	0.576864	+	0.576864i	−0.357174	+	0.934038i	$0.616260\pi$
$354$	8.53498	+	1.06695i	0.453629	+	0.0567079i
$355$		0			0
$356$	8.66230			0.459101
$357$	−4.33907	−	5.57891i	−0.229648	−	0.295267i
$358$	23.0149	−	23.0149i	1.21637	−	1.21637i
$359$		−	3.08162i		−	0.162642i	−0.996688	−	0.0813208i	$-0.974086\pi$
$359$		−	3.08162i		−	0.162642i	0.996688	−	0.0813208i	$-0.0259138\pi$
$360$		0			0
$361$	−15.2601			−0.803163
$362$	−2.85488	+	2.85488i	−0.150049	+	0.150049i
$363$	6.61828	−	5.14745i	0.347370	−	0.270171i
$364$	−5.43222	−	7.75186i	−0.284726	−	0.406308i
$365$		0			0
$366$	0.971968	−	7.77516i	0.0508056	−	0.406414i
$367$	20.0354	−	20.0354i	1.04584	−	1.04584i	0.0469411	−	0.998898i	$-0.485053\pi$
$367$	20.0354	−	20.0354i	1.04584	−	1.04584i	0.998898	−	0.0469411i	$-0.0149473\pi$
$368$	27.7029	−	27.7029i	1.44411	−	1.44411i
$369$	−5.42847	+	21.3730i	−0.282595	+	1.11263i
$370$		0			0
$371$	−12.7280			−0.660802
$372$	−10.4921	+	8.16038i	−0.543991	+	0.423096i
$373$	−25.3623	−	25.3623i	−1.31321	−	1.31321i	−0.919037	−	0.394171i	$-0.871032\pi$
$373$	−25.3623	−	25.3623i	−1.31321	−	1.31321i	−0.394171	−	0.919037i	$-0.628968\pi$
$374$	−7.94834			−0.410999
$375$		0			0
$376$	9.62301			0.496269
$377$	−6.03568	+	34.3050i	−0.310853	+	1.76680i
$378$	−8.38140	−	19.1630i	−0.431092	−	0.985636i
$379$	−17.3539			−0.891410			−0.445705	−	0.895180i	$-0.647047\pi$
$379$	−17.3539			−0.891410			−0.445705	+	0.895180i	$0.647047\pi$
$380$		0			0
$381$	2.09769	−	16.7802i	0.107468	−	0.859678i
$382$	21.2360	+	21.2360i	1.08653	+	1.08653i
$383$	−16.1283	−	16.1283i	−0.824118	−	0.824118i	0.162577	−	0.986696i	$-0.448019\pi$
$383$	−16.1283	−	16.1283i	−0.824118	−	0.824118i	−0.986696	+	0.162577i	$0.948019\pi$
$384$	−18.7309	−	2.34154i	−0.955857	−	0.119491i
$385$		0			0
$386$			36.2176i			1.84343i
$387$	12.6272	−	7.51207i	0.641877	−	0.381860i
$388$	−10.7484	+	10.7484i	−0.545670	+	0.545670i
$389$	−6.50195			−0.329662			−0.164831	−	0.986322i	$-0.552708\pi$
$389$	−6.50195			−0.329662			−0.164831	+	0.986322i	$0.552708\pi$
$390$		0			0
$391$	−14.1905			−0.717643
$392$	1.97749	−	1.97749i	0.0998782	−	0.0998782i
$393$	17.0125	+	21.8737i	0.858169	+	1.10338i
$394$			43.2214i			2.17746i
$395$		0			0
$396$	−8.36561	−	2.12476i	−0.420388	−	0.106773i
$397$	−26.0994	−	26.0994i	−1.30989	−	1.30989i	−0.921490	−	0.388402i	$-0.873027\pi$
$397$	−26.0994	−	26.0994i	−1.30989	−	1.30989i	−0.388402	−	0.921490i	$-0.626973\pi$
$398$	−22.6735	−	22.6735i	−1.13652	−	1.13652i
$399$	7.52697	+	0.940942i	0.376820	+	0.0471060i
$400$		0			0
$401$	17.6000			0.878901			0.439450	−	0.898267i	$-0.355173\pi$
$401$	17.6000			0.878901			0.439450	+	0.898267i	$0.355173\pi$
$402$	4.62679	−	3.59854i	0.230763	−	0.179479i
$403$	−23.5068	−	4.13584i	−1.17096	−	0.206021i
$404$	12.0140			0.597720
$405$		0			0
$406$	−38.8862			−1.92989
$407$	8.77366	+	8.77366i	0.434894	+	0.434894i
$408$	2.86318	+	3.68130i	0.141748	+	0.182251i
$409$	34.0937			1.68583			0.842913	−	0.538049i	$-0.180839\pi$
$409$	34.0937			1.68583			0.842913	+	0.538049i	$0.180839\pi$
$410$		0			0
$411$	1.96640	−	15.7300i	0.0969953	−	0.775904i
$412$	−8.19701	+	8.19701i	−0.403837	+	0.403837i
$413$	−4.47402	+	4.47402i	−0.220152	+	0.220152i
$414$	−40.7023	−	10.3379i	−2.00041	−	0.508080i
$415$		0			0
$416$	12.1117	+	17.2835i	0.593823	+	0.847393i
$417$	−12.7511	−	16.3946i	−0.624423	−	0.802845i
$418$	6.03216	−	6.03216i	0.295043	−	0.295043i
$419$	−14.9518			−0.730444			−0.365222	−	0.930920i	$-0.619007\pi$
$419$	−14.9518			−0.730444			−0.365222	+	0.930920i	$0.619007\pi$
$420$		0			0
$421$		−	26.9421i		−	1.31308i	−0.754293	−	0.656538i	$-0.772020\pi$
$421$		−	26.9421i		−	1.31308i	0.754293	−	0.656538i	$-0.227980\pi$
$422$	27.1788	−	27.1788i	1.32304	−	1.32304i
$423$	−9.87734	−	16.6030i	−0.480253	−	0.807267i
$424$	8.39865			0.407875
$425$		0			0
$426$	−2.51537	+	20.1214i	−0.121870	+	0.974886i
$427$	4.07572	+	4.07572i	0.197238	+	0.197238i
$428$	3.03123	−	3.03123i	0.146520	−	0.146520i
$429$	−7.25134	−	13.6978i	−0.350098	−	0.661336i
$430$		0			0
$431$	14.0679			0.677627			0.338814	−	0.940854i	$-0.389974\pi$
$431$	14.0679			0.677627			0.338814	+	0.940854i	$0.389974\pi$
$432$	10.3583	+	23.6828i	0.498362	+	1.13944i
$433$	14.6474	+	14.6474i	0.703907	+	0.703907i	0.965247	−	0.261340i	$-0.0841643\pi$
$433$	14.6474	+	14.6474i	0.703907	+	0.703907i	−0.261340	+	0.965247i	$0.584164\pi$
$434$		−	26.6461i		−	1.27905i
$435$		0			0
$436$			18.2354i			0.873317i
$437$	10.7695	−	10.7695i	0.515173	−	0.515173i
$438$	7.56310	+	9.72417i	0.361379	+	0.464639i
$439$			0.499524i			0.0238410i	0.999929	+	0.0119205i	$0.00379450\pi$
$439$			0.499524i			0.0238410i	−0.999929	+	0.0119205i	$0.996206\pi$
$440$		0			0
$441$	−5.44160	−	1.38210i	−0.259124	−	0.0658144i
$442$	2.00093	−	11.3727i	0.0951748	−	0.540944i
$443$	3.46942	−	3.46942i	0.164837	−	0.164837i	−0.619869	−	0.784706i	$-0.712814\pi$
$443$	3.46942	−	3.46942i	0.164837	−	0.164837i	0.784706	+	0.619869i	$0.212814\pi$
$444$	−1.24524	+	9.96117i	−0.0590965	+	0.472736i
$445$		0			0
$446$		−	42.6889i		−	2.02138i
$447$	3.80459	+	4.89171i	0.179951	+	0.231370i
$448$	−0.728281	+	0.728281i	−0.0344081	+	0.0344081i
$449$			14.7638i			0.696745i	0.937356	+	0.348372i	$0.113266\pi$
$449$			14.7638i			0.696745i	−0.937356	+	0.348372i	$0.886734\pi$
$450$		0			0
$451$	−18.2424			−0.859003
$452$	5.63540	+	5.63540i	0.265067	+	0.265067i
$453$	−2.05642	−	2.64402i	−0.0966190	−	0.124227i
$454$			15.8094i			0.741974i
$455$		0			0
$456$	−4.96674	−	0.620889i	−0.232589	−	0.0290758i
$457$	5.40394	+	5.40394i	0.252786	+	0.252786i	0.822112	−	0.569326i	$-0.192796\pi$
$457$	5.40394	+	5.40394i	0.252786	+	0.252786i	−0.569326	+	0.822112i	$0.692796\pi$
$458$	−15.1629	+	15.1629i	−0.708515	+	0.708515i
$459$	3.41267	−	8.71857i	0.159290	−	0.406948i
$460$		0			0
$461$	−14.9553			−0.696538			−0.348269	−	0.937395i	$-0.613230\pi$
$461$	−14.9553			−0.696538			−0.348269	+	0.937395i	$0.613230\pi$
$462$	13.6581	−	10.6228i	0.635432	−	0.494215i
$463$	−13.0006	+	13.0006i	−0.604188	+	0.604188i	−0.941421	−	0.337233i	$-0.890509\pi$
$463$	−13.0006	+	13.0006i	−0.604188	+	0.604188i	0.337233	+	0.941421i	$0.390509\pi$
$464$	48.0581			2.23104
$465$		0			0
$466$		−	20.8542i		−	0.966053i
$467$	0.156785	+	0.156785i	0.00725515	+	0.00725515i	0.710725	−	0.703470i	$-0.248367\pi$
$467$	0.156785	+	0.156785i	0.00725515	+	0.00725515i	−0.703470	+	0.710725i	$0.748367\pi$
$468$	5.14614	−	11.4348i	0.237881	−	0.528576i
$469$			4.31170i			0.199096i
$470$		0			0
$471$	−3.00638	+	24.0493i	−0.138527	+	1.10813i
$472$	2.95222	−	2.95222i	0.135887	−	0.135887i
$473$	8.59473	+	8.59473i	0.395186	+	0.395186i
$474$	−19.8122	−	2.47671i	−0.910004	−	0.113759i
$475$		0			0
$476$	4.73044			0.216819
$477$	−8.62063	−	14.4906i	−0.394711	−	0.663479i
$478$	−36.5517	−	36.5517i	−1.67183	−	1.67183i
$479$		−	26.4947i		−	1.21057i	−0.796008	−	0.605286i	$-0.793059\pi$
$479$		−	26.4947i		−	1.21057i	0.796008	−	0.605286i	$-0.206941\pi$
$480$		0			0
$481$	−14.7623	+	10.3449i	−0.673102	+	0.471686i
$482$	−5.44307	−	5.44307i	−0.247925	−	0.247925i
$483$	24.3843	−	18.9652i	1.10952	−	0.862947i
$484$			5.61173i			0.255079i
$485$		0			0
$486$	16.1401	−	22.5212i	0.732128	−	1.02158i
$487$	−4.60192	−	4.60192i	−0.208533	−	0.208533i	0.595111	−	0.803644i	$-0.297108\pi$
$487$	−4.60192	−	4.60192i	−0.208533	−	0.208533i	−0.803644	+	0.595111i	$0.797108\pi$
$488$	−2.68940	−	2.68940i	−0.121743	−	0.121743i
$489$	0.937222	−	7.49722i	0.0423827	−	0.339036i
$490$		0			0
$491$			2.85195i			0.128707i	0.997927	+	0.0643533i	$0.0204985\pi$
$491$			2.85195i			0.128707i	−0.997927	+	0.0643533i	$0.979502\pi$
$492$	−9.06121	−	11.6504i	−0.408511	−	0.525238i
$493$	−12.3086	−	12.3086i	−0.554351	−	0.554351i
$494$	7.11243	+	10.1495i	0.320003	+	0.456649i
$495$		0			0
$496$			32.9309i			1.47864i
$497$	−10.5476	−	10.5476i	−0.473124	−	0.473124i
$498$	10.9271	−	8.49871i	0.489656	−	0.380836i
$499$	−16.5848			−0.742440			−0.371220	−	0.928545i	$-0.621060\pi$
$499$	−16.5848			−0.742440			−0.371220	+	0.928545i	$0.621060\pi$
$500$		0			0
$501$	0.165354	−	1.32274i	0.00738749	−	0.0590955i
$502$	−8.33922	−	8.33922i	−0.372197	−	0.372197i
$503$	−25.3184	+	25.3184i	−1.12889	+	1.12889i	−0.138536	+	0.990357i	$0.544240\pi$
$503$	−25.3184	+	25.3184i	−1.12889	+	1.12889i	−0.990357	+	0.138536i	$0.955760\pi$
$504$	−9.83991	−	2.49922i	−0.438305	−	0.111324i
$505$		0			0
$506$		−	34.7406i		−	1.54441i
$507$	21.4246	−	6.92710i	0.951502	−	0.307643i
$508$	8.00343	+	8.00343i	0.355095	+	0.355095i
$509$		−	4.71947i		−	0.209187i	−0.994515	−	0.104593i	$-0.966646\pi$
$509$		−	4.71947i		−	0.209187i	0.994515	−	0.104593i	$-0.0333541\pi$
$510$		0			0
$511$	−9.06194			−0.400877
$512$	10.0770	−	10.0770i	0.445345	−	0.445345i
$513$	4.02676	+	9.20665i	0.177786	+	0.406484i
$514$	−23.1555			−1.02135
$515$		0			0
$516$	−1.21984	+	9.75803i	−0.0537007	+	0.429573i
$517$	11.3009	−	11.3009i	0.497013	−	0.497013i
$518$	−14.2300	−	14.2300i	−0.625232	−	0.625232i
$519$	−0.585149	+	4.68084i	−0.0256852	+	0.205466i
$520$		0			0
$521$			3.26079i			0.142858i	0.997446	+	0.0714290i	$0.0227559\pi$
$521$			3.26079i			0.142858i	−0.997446	+	0.0714290i	$0.977244\pi$
$522$	−26.3376	−	44.2715i	−1.15277	−	1.93771i
$523$	−3.50662	−	3.50662i	−0.153334	−	0.153334i	0.626271	−	0.779605i	$-0.284580\pi$
$523$	−3.50662	−	3.50662i	−0.153334	−	0.153334i	−0.779605	+	0.626271i	$0.784580\pi$
$524$	−18.5470			−0.810229
$525$		0			0
$526$		−	21.8868i		−	0.954308i
$527$	8.43423	−	8.43423i	0.367401	−	0.367401i
$528$	−16.8795	+	13.1283i	−0.734587	+	0.571335i
$529$		−	39.0237i		−	1.69668i
$530$		0			0
$531$	−8.12385	−	2.06336i	−0.352545	−	0.0895422i
$532$	−3.59003	+	3.59003i	−0.155647	+	0.155647i
$533$	4.59240	−	26.1018i	0.198919	−	1.13059i
$534$	−22.8262	−	2.85349i	−0.987787	−	0.123483i
$535$		0			0
$536$		−	2.84511i		−	0.122890i
$537$	−25.0360	+	19.4720i	−1.08038	+	0.840281i
$538$	−25.0894	+	25.0894i	−1.08168	+	1.08168i
$539$		−	4.64457i		−	0.200056i
$540$		0			0
$541$			37.7594i			1.62340i	0.584072	+	0.811702i	$0.301459\pi$
$541$			37.7594i			1.62340i	−0.584072	+	0.811702i	$0.698541\pi$
$542$	19.3984	+	19.3984i	0.833234	+	0.833234i
$543$	3.10558	−	2.41541i	0.133273	−	0.103655i
$544$	−10.5470			−0.452197
$545$		0			0
$546$	11.7610	+	22.2165i	0.503324	+	0.950781i
$547$	−16.3924	+	16.3924i	−0.700888	+	0.700888i	−0.964601	−	0.263714i	$-0.915053\pi$
$547$	−16.3924	+	16.3924i	−0.700888	+	0.700888i	0.263714	+	0.964601i	$0.415053\pi$
$548$	7.50251	+	7.50251i	0.320491	+	0.320491i
$549$	−1.87967	+	7.40063i	−0.0802224	+	0.315851i
$550$		0			0
$551$	18.6825			0.795901
$552$	−16.0902	+	12.5144i	−0.684844	+	0.532647i
$553$	10.3855	−	10.3855i	0.441636	−	0.441636i
$554$			21.0930i			0.896154i
$555$		0			0
$556$	13.9012			0.589541
$557$	−9.89147	+	9.89147i	−0.419115	+	0.419115i	−0.884899	−	0.465784i	$-0.845773\pi$
$557$	−9.89147	+	9.89147i	−0.419115	+	0.419115i	0.465784	+	0.884899i	$0.345773\pi$
$558$	30.3362	−	18.0473i	1.28423	−	0.764005i
$559$	−14.4612	+	10.1339i	−0.611644	+	0.428619i
$560$		0			0
$561$	7.68558	+	0.960769i	0.324485	+	0.0405637i
$562$	−25.5239	+	25.5239i	−1.07666	+	1.07666i
$563$	1.00460	−	1.00460i	0.0423388	−	0.0423388i	−0.685620	−	0.727959i	$-0.740469\pi$
$563$	1.00460	−	1.00460i	0.0423388	−	0.0423388i	0.727959	+	0.685620i	$0.240469\pi$
$564$	12.8305	+	1.60393i	0.540260	+	0.0675376i
$565$		0			0
$566$	33.2058			1.39574
$567$	5.78796	+	19.5426i	0.243071	+	0.820710i
$568$	6.95993	+	6.95993i	0.292032	+	0.292032i
$569$	−5.08203			−0.213050			−0.106525	−	0.994310i	$-0.533972\pi$
$569$	−5.08203			−0.213050			−0.106525	+	0.994310i	$0.533972\pi$
$570$		0			0
$571$	−19.2348			−0.804953			−0.402476	−	0.915430i	$-0.631850\pi$
$571$	−19.2348			−0.804953			−0.402476	+	0.915430i	$0.631850\pi$
$572$	10.2165	+	1.79751i	0.427174	+	0.0751578i
$573$	−17.9670	−	23.1009i	−0.750582	−	0.965052i
$574$	29.5875			1.23496
$575$		0			0
$576$	−1.32240	−	0.335874i	−0.0551001	−	0.0139948i
$577$	−9.22836	−	9.22836i	−0.384182	−	0.384182i	0.488424	−	0.872606i	$-0.337572\pi$
$577$	−9.22836	−	9.22836i	−0.384182	−	0.384182i	−0.872606	+	0.488424i	$0.837572\pi$
$578$	−17.2857	−	17.2857i	−0.718990	−	0.718990i
$579$	4.37786	−	35.0203i	0.181938	−	1.45539i
$580$		0			0
$581$			10.1830i			0.422461i
$582$	31.8642	−	24.7828i	1.32081	−	1.02728i
$583$	9.86305	−	9.86305i	0.408486	−	0.408486i
$584$	5.97960			0.247438
$585$		0			0
$586$	23.4500			0.968709
$587$	1.06387	−	1.06387i	0.0439105	−	0.0439105i	−0.684811	−	0.728721i	$-0.740115\pi$
$587$	1.06387	−	1.06387i	0.0439105	−	0.0439105i	0.728721	+	0.684811i	$0.240115\pi$
$588$	2.96621	−	2.30701i	0.122324	−	0.0951393i
$589$			12.8018i			0.527490i
$590$		0			0
$591$	5.22446	−	41.7925i	0.214906	−	1.71912i
$592$	17.5864	+	17.5864i	0.722796	+	0.722796i
$593$	−2.68739	−	2.68739i	−0.110358	−	0.110358i	0.649772	−	0.760129i	$-0.274865\pi$
$593$	−2.68739	−	2.68739i	−0.110358	−	0.110358i	−0.760129	+	0.649772i	$0.774865\pi$
$594$	21.3445	+	8.35477i	0.875774	+	0.342800i
$595$		0			0
$596$	−4.14774			−0.169898
$597$	19.1832	+	24.6646i	0.785117	+	1.00946i
$598$	49.7078	+	8.74568i	2.03270	+	0.357637i
$599$	−25.8330			−1.05551			−0.527754	−	0.849397i	$-0.676966\pi$
$599$	−25.8330			−1.05551			−0.527754	+	0.849397i	$0.676966\pi$
$600$		0			0
$601$	26.5776			1.08412			0.542062	−	0.840338i	$-0.317644\pi$
$601$	26.5776			1.08412			0.542062	+	0.840338i	$0.317644\pi$
$602$	−13.9398	−	13.9398i	−0.568146	−	0.568146i
$603$	−4.90881	+	2.92031i	−0.199902	+	0.118924i
$604$	2.24190			0.0912216
$605$		0			0
$606$	−31.6584	−	3.95760i	−1.28604	−	0.160767i
$607$	−6.01113	+	6.01113i	−0.243984	+	0.243984i	−0.818496	−	0.574512i	$-0.805192\pi$
$607$	−6.01113	+	6.01113i	−0.243984	+	0.243984i	0.574512	+	0.818496i	$0.305192\pi$
$608$	8.00431	−	8.00431i	0.324618	−	0.324618i
$609$	37.6007	+	4.70044i	1.52366	+	0.190471i
$610$		0			0
$611$	13.3247	+	19.0145i	0.539060	+	0.769245i
$612$	3.20392	+	5.38554i	0.129511	+	0.217698i
$613$	3.14970	−	3.14970i	0.127215	−	0.127215i	−0.640632	−	0.767848i	$-0.721328\pi$
$613$	3.14970	−	3.14970i	0.127215	−	0.127215i	0.767848	+	0.640632i	$0.221328\pi$
$614$	40.8840			1.64994
$615$		0			0
$616$		−	8.39865i		−	0.338391i
$617$	2.15262	−	2.15262i	0.0866613	−	0.0866613i	−0.662447	−	0.749109i	$-0.730482\pi$
$617$	2.15262	−	2.15262i	0.0866613	−	0.0866613i	0.749109	+	0.662447i	$0.230482\pi$
$618$	24.3003	−	18.8999i	0.977503	−	0.760265i
$619$	12.1579			0.488668			0.244334	−	0.969691i	$-0.421431\pi$
$619$	12.1579			0.488668			0.244334	+	0.969691i	$0.421431\pi$
$620$		0			0
$621$	38.1071	+	14.9161i	1.52918	+	0.598562i
$622$	−6.26465	−	6.26465i	−0.251190	−	0.251190i
$623$	11.9654	−	11.9654i	0.479385	−	0.479385i
$624$	−14.5350	−	27.4566i	−0.581865	−	1.09914i
$625$		0			0
$626$	35.8157			1.43148
$627$	−6.56189	+	5.10360i	−0.262057	+	0.203818i
$628$	−11.4704	−	11.4704i	−0.457720	−	0.457720i
$629$		−	9.00843i		−	0.359190i
$630$		0			0
$631$			24.6040i			0.979470i	0.871871	+	0.489735i	$0.162907\pi$
$631$			24.6040i			0.979470i	−0.871871	+	0.489735i	$0.837093\pi$
$632$	−6.85297	+	6.85297i	−0.272596	+	0.272596i
$633$	−29.5656	+	22.9950i	−1.17513	+	0.913970i
$634$		−	35.9903i		−	1.42936i
$635$		0			0
$636$	11.1980	+	1.39986i	0.444030	+	0.0555080i
$637$	6.64557	+	1.16923i	0.263307	+	0.0463268i
$638$	30.1334	−	30.1334i	1.19299	−	1.19299i
$639$	4.86442	−	19.1522i	0.192434	−	0.757648i
$640$		0			0
$641$			4.97308i			0.196425i	0.995165	+	0.0982124i	$0.0313124\pi$
$641$			4.97308i			0.196425i	−0.995165	+	0.0982124i	$0.968688\pi$
$642$	−8.98621	+	6.98914i	−0.354657	+	0.275839i
$643$	−19.7877	+	19.7877i	−0.780349	+	0.780349i	−0.979890	−	0.199540i	$-0.936055\pi$
$643$	−19.7877	+	19.7877i	−0.780349	+	0.780349i	0.199540	+	0.979890i	$0.436055\pi$
$644$			20.6758i			0.814740i
$645$		0			0
$646$	−6.19358			−0.243683
$647$	27.8871	+	27.8871i	1.09635	+	1.09635i	0.994833	+	0.101520i	$0.0323707\pi$
$647$	27.8871	+	27.8871i	1.09635	+	1.09635i	0.101520	+	0.994833i	$0.467629\pi$
$648$	−3.81924	−	12.8953i	−0.150034	−	0.506576i
$649$		−	6.93395i		−	0.272181i
$650$		0			0
$651$	−3.22089	+	25.7652i	−0.126236	+	1.00982i
$652$	3.57584	+	3.57584i	0.140041	+	0.140041i
$653$	−14.6549	+	14.6549i	−0.573491	+	0.573491i	−0.933102	−	0.359611i	$-0.882909\pi$
$653$	−14.6549	+	14.6549i	−0.573491	+	0.573491i	0.359611	+	0.933102i	$0.382909\pi$
$654$	6.00701	−	48.0525i	0.234893	−	1.87900i
$655$		0			0
$656$	−36.5661			−1.42767
$657$	−6.13764	−	10.3169i	−0.239452	−	0.402500i
$658$	−18.3290	+	18.3290i	−0.714538	+	0.714538i
$659$	27.9107			1.08725			0.543624	−	0.839329i	$-0.317052\pi$
$659$	27.9107			1.08725			0.543624	+	0.839329i	$0.317052\pi$
$660$		0			0
$661$			33.0735i			1.28641i	0.765693	+	0.643206i	$0.222396\pi$
$661$			33.0735i			1.28641i	−0.765693	+	0.643206i	$0.777604\pi$
$662$	−19.6524	−	19.6524i	−0.763813	−	0.763813i
$663$	−3.30948	+	10.7549i	−0.128529	+	0.417684i
$664$		−	6.71933i		−	0.260760i
$665$		0			0
$666$	6.56272	−	25.8387i	0.254300	−	1.00123i
$667$	53.7984	−	53.7984i	2.08308	−	2.08308i
$668$	0.630886	+	0.630886i	0.0244097	+	0.0244097i
$669$	−5.16010	+	41.2777i	−0.199501	+	1.59589i
$670$		0			0
$671$	−6.31666			−0.243852
$672$	18.1234	−	14.0957i	0.699127	−	0.543755i
$673$	−6.43667	−	6.43667i	−0.248115	−	0.248115i	0.572082	−	0.820197i	$-0.306136\pi$
$673$	−6.43667	−	6.43667i	−0.248115	−	0.248115i	−0.820197	+	0.572082i	$0.806136\pi$
$674$			31.2275i			1.20284i
$675$		0			0
$676$	−5.14386	+	14.1655i	−0.197841	+	0.544829i
$677$	−3.03614	−	3.03614i	−0.116688	−	0.116688i	0.646351	−	0.763040i	$-0.276294\pi$
$677$	−3.03614	−	3.03614i	−0.116688	−	0.116688i	−0.763040	+	0.646351i	$0.776294\pi$
$678$	−12.9936	−	16.7064i	−0.499016	−	0.641604i
$679$			29.6942i			1.13956i
$680$		0			0
$681$	1.91099	−	15.2868i	0.0732294	−	0.585791i
$682$	20.6484	+	20.6484i	0.790667	+	0.790667i
$683$	6.75351	+	6.75351i	0.258416	+	0.258416i	0.824410	−	0.565994i	$-0.191507\pi$
$683$	6.75351	+	6.75351i	0.258416	+	0.258416i	−0.565994	+	0.824410i	$0.691507\pi$
$684$	−6.51872	−	1.65568i	−0.249250	−	0.0633064i
$685$		0			0
$686$			35.7097i			1.36340i
$687$	16.4944	−	12.8288i	0.629302	−	0.489448i
$688$	17.2277	+	17.2277i	0.656801	+	0.656801i
$689$	11.6294	+	16.5953i	0.443044	+	0.632229i
$690$		0			0
$691$			20.7041i			0.787620i	0.919192	+	0.393810i	$0.128843\pi$
$691$			20.7041i			0.787620i	−0.919192	+	0.393810i	$0.871157\pi$
$692$	−2.23255	−	2.23255i	−0.0848688	−	0.0848688i
$693$	−14.4906	+	8.62063i	−0.550452	+	0.327471i
$694$	16.7379			0.635361
$695$		0			0
$696$	−24.8111	−	3.10163i	−0.940464	−	0.117567i
$697$	9.36529	+	9.36529i	0.354736	+	0.354736i
$698$	−4.22003	+	4.22003i	−0.159730	+	0.159730i
$699$	−2.52079	+	20.1648i	−0.0953449	+	0.762702i
$700$		0			0
$701$		−	52.1479i		−	1.96960i	−0.173691	−	0.984800i	$-0.555569\pi$
$701$		−	52.1479i		−	1.96960i	0.173691	−	0.984800i	$-0.444431\pi$
$702$	−17.3275	+	28.4370i	−0.653985	+	1.07328i
$703$	6.83669	+	6.83669i	0.257850	+	0.257850i
$704$		−	1.12871i		−	0.0425398i
$705$		0			0
$706$	27.2439			1.02534
$707$	16.5953	−	16.5953i	0.624129	−	0.624129i
$708$	4.42829	−	3.44416i	0.166425	−	0.129440i
$709$	−4.45911			−0.167465			−0.0837327	−	0.996488i	$-0.526684\pi$
$709$	−4.45911			−0.167465			−0.0837327	+	0.996488i	$0.526684\pi$
$710$		0			0
$711$	18.8578	+	4.78966i	0.707224	+	0.179626i
$712$	−7.89550	+	7.89550i	−0.295896	+	0.295896i
$713$	36.8643	+	36.8643i	1.38058	+	1.38058i
$714$	−12.4653	−	1.55828i	−0.466502	−	0.0583171i
$715$		0			0
$716$		−	21.2283i		−	0.793340i
$717$	30.9250	+	39.7615i	1.15492	+	1.48492i
$718$	−3.87309	−	3.87309i	−0.144542	−	0.144542i
$719$	6.74702			0.251621			0.125811	−	0.992054i	$-0.459847\pi$
$719$	6.74702			0.251621			0.125811	+	0.992054i	$0.459847\pi$
$720$		0			0
$721$			22.6454i			0.843360i
$722$	−19.1795	+	19.1795i	−0.713785	+	0.713785i
$723$	4.60519	+	5.92107i	0.171269	+	0.220207i
$724$			2.63327i			0.0978646i
$725$		0			0
$726$	1.84859	−	14.7876i	0.0686075	−	0.548819i
$727$	−9.42881	+	9.42881i	−0.349695	+	0.349695i	−0.859996	−	0.510301i	$-0.829534\pi$
$727$	−9.42881	+	9.42881i	−0.349695	+	0.349695i	0.510301	+	0.859996i	$0.329534\pi$
$728$	12.0170	+	2.11430i	0.445380	+	0.0783611i
$729$	−18.3288	+	19.8257i	−0.678843	+	0.734284i
$730$		0			0
$731$		−	8.82471i		−	0.326394i
$732$	−3.13755	−	4.03407i	−0.115967	−	0.149103i
$733$	−20.5774	+	20.5774i	−0.760042	+	0.760042i	−0.976330	−	0.216288i	$-0.930605\pi$
$733$	−20.5774	+	20.5774i	−0.760042	+	0.760042i	0.216288	+	0.976330i	$0.430605\pi$
$734$		−	50.3624i		−	1.85891i
$735$		0			0
$736$		−	46.0986i		−	1.69922i
$737$	−3.34119	−	3.34119i	−0.123074	−	0.123074i
$738$	20.0396	+	33.6850i	0.737668	+	1.23996i
$739$	11.6627			0.429020			0.214510	−	0.976722i	$-0.431185\pi$
$739$	11.6627			0.429020			0.214510	+	0.976722i	$0.431185\pi$
$740$		0			0
$741$	−5.65045	−	10.6737i	−0.207575	−	0.392109i
$742$	−15.9970	+	15.9970i	−0.587267	+	0.587267i
$743$	8.16248	+	8.16248i	0.299452	+	0.299452i	0.840799	−	0.541347i	$-0.182085\pi$
$743$	8.16248	+	8.16248i	0.299452	+	0.299452i	−0.541347	+	0.840799i	$0.682085\pi$
$744$	2.12533	−	17.0014i	0.0779184	−	0.623300i
$745$		0			0
$746$	−63.7524			−2.33414
$747$	−11.5932	+	6.89692i	−0.424172	+	0.252345i
$748$	−3.66568	+	3.66568i	−0.134030	+	0.134030i
$749$		−	8.37423i		−	0.305988i
$750$		0			0
$751$	−36.7121			−1.33964			−0.669822	−	0.742522i	$-0.733630\pi$
$751$	−36.7121			−1.33964			−0.669822	+	0.742522i	$0.733630\pi$
$752$	22.6521	−	22.6521i	0.826038	−	0.826038i
$753$	7.05551	+	9.07154i	0.257117	+	0.330585i
$754$	35.5299	+	50.7016i	1.29392	+	1.84644i
$755$		0			0
$756$	−12.7031	−	4.97232i	−0.462008	−	0.180842i
$757$	−5.75644	+	5.75644i	−0.209221	+	0.209221i	−0.803937	−	0.594715i	$-0.797265\pi$
$757$	−5.75644	+	5.75644i	−0.209221	+	0.209221i	0.594715	+	0.803937i	$0.297265\pi$
$758$	−21.8110	+	21.8110i	−0.792212	+	0.792212i
$759$	−4.19933	+	33.5921i	−0.152426	+	1.21932i
$760$		0			0
$761$	23.9994			0.869978			0.434989	−	0.900436i	$-0.356752\pi$
$761$	23.9994			0.869978			0.434989	+	0.900436i	$0.356752\pi$
$762$	−18.4536	−	23.7265i	−0.668502	−	0.859519i
$763$	25.1890	+	25.1890i	0.911903	+	0.911903i
$764$	19.5875			0.708652
$765$		0			0
$766$	−40.5413			−1.46482
$767$	9.92127	+	1.74557i	0.358236	+	0.0630288i
$768$	−27.7282	+	21.5660i	−1.00055	+	0.778194i
$769$	−14.2146			−0.512592			−0.256296	−	0.966598i	$-0.582502\pi$
$769$	−14.2146			−0.512592			−0.256296	+	0.966598i	$0.582502\pi$
$770$		0			0
$771$	22.3900	+	2.79896i	0.806358	+	0.100802i
$772$	16.7031	+	16.7031i	0.601158	+	0.601158i
$773$	14.3909	+	14.3909i	0.517605	+	0.517605i	0.916846	−	0.399241i	$-0.130726\pi$
$773$	14.3909	+	14.3909i	0.517605	+	0.517605i	−0.399241	+	0.916846i	$0.630726\pi$
$774$	6.42888	−	25.3118i	0.231081	−	0.909813i
$775$		0			0
$776$		−	19.5940i		−	0.703383i
$777$	12.0395	+	15.4797i	0.431916	+	0.555331i
$778$	−8.17188	+	8.17188i	−0.292976	+	0.292976i
$779$	−14.2150			−0.509307
$780$		0			0
$781$	16.3469			0.584940
$782$	−17.8351	+	17.8351i	−0.637782	+	0.637782i
$783$	20.1155	+	45.9915i	0.718870	+	1.64360i
$784$		−	9.30982i		−	0.332494i
$785$		0			0
$786$	48.8736	+	6.10966i	1.74326	+	0.217924i
$787$	−16.3053	−	16.3053i	−0.581220	−	0.581220i	0.354019	−	0.935238i	$-0.384815\pi$
$787$	−16.3053	−	16.3053i	−0.581220	−	0.581220i	−0.935238	+	0.354019i	$0.884815\pi$
$788$	19.9332	+	19.9332i	0.710090	+	0.710090i
$789$	−2.64560	+	21.1632i	−0.0941858	+	0.753430i
$790$		0			0
$791$	15.5686			0.553557
$792$	9.56175	−	5.68840i	0.339762	−	0.202128i
$793$	1.59017	−	9.03804i	0.0564686	−	0.320950i
$794$	−65.6054			−2.32825
$795$		0			0
$796$	−20.9135			−0.741258
$797$	−32.3953	−	32.3953i	−1.14750	−	1.14750i	−0.987042	−	0.160459i	$-0.948703\pi$
$797$	−32.3953	−	32.3953i	−1.14750	−	1.14750i	−0.160459	−	0.987042i	$-0.551297\pi$
$798$	10.6428	−	8.27756i	0.376750	−	0.293022i
$799$	−11.6033			−0.410495
$800$		0			0
$801$	21.7267	+	5.51831i	0.767674	+	0.194980i
$802$	22.1203	−	22.1203i	0.781094	−	0.781094i
$803$	7.02221	−	7.02221i	0.247809	−	0.247809i
$804$	0.474213	−	3.79342i	0.0167242	−	0.133784i
$805$		0			0
$806$	−34.7423	+	24.3462i	−1.22375	+	0.857557i
$807$	27.2927	−	21.2273i	0.960749	−	0.747235i
$808$	−10.9505	+	10.9505i	−0.385238	+	0.385238i
$809$	−9.15265			−0.321790			−0.160895	−	0.986972i	$-0.551438\pi$
$809$	−9.15265			−0.321790			−0.160895	+	0.986972i	$0.551438\pi$
$810$		0			0
$811$		−	5.06477i		−	0.177848i	−0.996038	−	0.0889240i	$-0.971657\pi$
$811$		−	5.06477i		−	0.177848i	0.996038	−	0.0889240i	$-0.0283428\pi$
$812$	−17.9338	+	17.9338i	−0.629355	+	0.629355i
$813$	−16.4123	−	21.1019i	−0.575605	−	0.740077i
$814$	22.0541			0.772996
$815$		0			0
$816$	15.4054	+	1.92582i	0.539296	+	0.0674171i
$817$	6.69726	+	6.69726i	0.234307	+	0.234307i
$818$	42.8502	−	42.8502i	1.49822	−	1.49822i
$819$	−8.68672	−	22.9037i	−0.303539	−	0.800320i
$820$		0			0
$821$	−25.6728			−0.895986			−0.447993	−	0.894037i	$-0.647861\pi$
$821$	−25.6728			−0.895986			−0.447993	+	0.894037i	$0.647861\pi$
$822$	−17.2986	−	22.2415i	−0.603358	−	0.775761i
$823$	−18.2052	−	18.2052i	−0.634593	−	0.634593i	0.314624	−	0.949216i	$-0.398122\pi$
$823$	−18.2052	−	18.2052i	−0.634593	−	0.634593i	−0.949216	+	0.314624i	$0.898122\pi$
$824$		−	14.9428i		−	0.520557i
$825$		0			0
$826$			11.2462i			0.391306i
$827$	37.3547	−	37.3547i	1.29895	−	1.29895i	0.369865	−	0.929086i	$-0.379404\pi$
$827$	37.3547	−	37.3547i	1.29895	−	1.29895i	0.929086	−	0.369865i	$-0.120596\pi$
$828$	−23.5391	+	14.0037i	−0.818040	+	0.486662i
$829$		−	13.2807i		−	0.461257i	−0.973042	−	0.230628i	$-0.925922\pi$
$829$		−	13.2807i		−	0.461257i	0.973042	−	0.230628i	$-0.0740782\pi$
$830$		0			0
$831$	2.54965	−	20.3956i	0.0884463	−	0.707517i
$832$	1.61499	+	0.284144i	0.0559896	+	0.00985092i
$833$	−2.38443	+	2.38443i	−0.0826154	+	0.0826154i
$834$	−36.6313	−	4.57926i	−1.26844	−	0.158567i
$835$		0			0
$836$		−	5.56392i		−	0.192432i
$837$	−31.5148	+	13.7838i	−1.08931	+	0.476437i
$838$	−18.7920	+	18.7920i	−0.649159	+	0.649159i
$839$			41.5203i			1.43344i	0.697362	+	0.716719i	$0.254357\pi$
$839$			41.5203i			1.43344i	−0.697362	+	0.716719i	$0.745643\pi$
$840$		0			0
$841$	64.3277			2.21820
$842$	−33.8618	−	33.8618i	−1.16695	−	1.16695i
$843$	27.7653	−	21.5948i	0.956288	−	0.743765i
$844$		−	25.0691i		−	0.862913i
$845$		0			0
$846$	−33.2815	−	8.45310i	−1.14424	−	0.290623i
$847$	7.75162	+	7.75162i	0.266349	+	0.266349i
$848$	19.7700	−	19.7700i	0.678906	−	0.678906i
$849$	−32.1080	−	4.01381i	−1.10195	−	0.137753i
$850$		0			0
$851$	39.3740			1.34972
$852$	8.11970	+	10.4398i	0.278176	+	0.357662i
$853$	28.1269	−	28.1269i	0.963046	−	0.963046i	−0.0362950	−	0.999341i	$-0.511556\pi$
$853$	28.1269	−	28.1269i	0.963046	−	0.963046i	0.999341	+	0.0362950i	$0.0115556\pi$
$854$	10.2450			0.350578
$855$		0			0
$856$			5.52581i			0.188868i
$857$	1.93395	+	1.93395i	0.0660625	+	0.0660625i	0.739366	−	0.673304i	$-0.235125\pi$
$857$	1.93395	+	1.93395i	0.0660625	+	0.0660625i	−0.673304	+	0.739366i	$0.735125\pi$
$858$	−26.3296	−	8.10214i	−0.898879	−	0.276603i
$859$			17.6240i			0.601324i	0.953731	+	0.300662i	$0.0972076\pi$
$859$			17.6240i			0.601324i	−0.953731	+	0.300662i	$0.902792\pi$
$860$		0			0
$861$	−28.6094	−	3.57644i	−0.975005	−	0.121885i
$862$	17.6810	−	17.6810i	0.602219	−	0.602219i
$863$	−18.9188	−	18.9188i	−0.644003	−	0.644003i	0.307534	−	0.951537i	$-0.400496\pi$
$863$	−18.9188	−	18.9188i	−0.644003	−	0.644003i	−0.951537	+	0.307534i	$0.900496\pi$
$864$	28.3228	+	11.0863i	0.963561	+	0.377162i
$865$		0			0
$866$	36.8187			1.25115
$867$	14.6248	+	18.8037i	0.496684	+	0.638606i
$868$	−12.2888	−	12.2888i	−0.417110	−	0.417110i
$869$			16.0957i			0.546010i
$870$		0			0
$871$	5.62178	−	3.93954i	0.190487	−	0.133486i
$872$	−16.6212	−	16.6212i	−0.562864	−	0.562864i
$873$	−33.8064	+	20.1118i	−1.14417	+	0.680683i
$874$		−	27.0709i		−	0.915686i
$875$		0			0
$876$	7.97267	+	0.996659i	0.269372	+	0.0336740i
$877$	7.67412	+	7.67412i	0.259137	+	0.259137i	0.824703	−	0.565566i	$-0.191342\pi$
$877$	7.67412	+	7.67412i	0.259137	+	0.259137i	−0.565566	+	0.824703i	$0.691342\pi$
$878$	0.627820	+	0.627820i	0.0211879	+	0.0211879i
$879$	−22.6747	−	2.83455i	−0.764799	−	0.0956070i
$880$		0			0
$881$		−	22.3843i		−	0.754145i	−0.926184	−	0.377073i	$-0.876931\pi$
$881$		−	22.3843i		−	0.754145i	0.926184	−	0.377073i	$-0.123069\pi$
$882$	−8.57628	+	5.10213i	−0.288778	+	0.171798i
$883$	−25.3525	−	25.3525i	−0.853181	−	0.853181i	0.137342	−	0.990524i	$-0.456144\pi$
$883$	−25.3525	−	25.3525i	−0.853181	−	0.853181i	−0.990524	+	0.137342i	$0.956144\pi$
$884$	−4.32214	−	6.16775i	−0.145369	−	0.207444i
$885$		0			0
$886$		−	8.72098i		−	0.292987i
$887$	−16.1083	−	16.1083i	−0.540864	−	0.540864i	0.382919	−	0.923782i	$-0.374919\pi$
$887$	−16.1083	−	16.1083i	−0.540864	−	0.540864i	−0.923782	+	0.382919i	$0.874919\pi$
$888$	−7.94439	−	10.2144i	−0.266596	−	0.342773i
$889$	22.1107			0.741568
$890$		0			0
$891$	−19.6289	−	10.6586i	−0.657594	−	0.357077i
$892$	−19.6876	−	19.6876i	−0.659190	−	0.659190i
$893$	8.80598	−	8.80598i	0.294681	−	0.294681i
$894$	10.9298	+	1.36633i	0.365548	+	0.0456969i
$895$		0			0
$896$		−	24.6809i		−	0.824533i
$897$	−47.0073	−	14.4651i	−1.56953	−	0.482974i
$898$	18.5556	+	18.5556i	0.619209	+	0.619209i
$899$			63.9511i			2.13289i
$900$		0			0
$901$	−10.1270			−0.337379
$902$	−22.9278	+	22.9278i	−0.763411	+	0.763411i
$903$	11.7940	+	15.1640i	0.392480	+	0.504626i
$904$	−10.2731			−0.341678
$905$		0			0
$906$	−5.90768	−	0.738515i	−0.196269	−	0.0245355i
$907$	−7.78524	+	7.78524i	−0.258505	+	0.258505i	−0.824446	−	0.565941i	$-0.808513\pi$
$907$	−7.78524	+	7.78524i	−0.258505	+	0.258505i	0.565941	+	0.824446i	$0.308513\pi$
$908$	7.29112	+	7.29112i	0.241964	+	0.241964i
$909$	30.1334	+	7.65353i	0.999463	+	0.253852i
$910$		0			0
$911$			13.2800i			0.439986i	0.975501	+	0.219993i	$0.0706034\pi$
$911$			13.2800i			0.439986i	−0.975501	+	0.219993i	$0.929397\pi$
$912$	−13.1530	+	10.2299i	−0.435540	+	0.338747i
$913$	−7.89092	−	7.89092i	−0.261151	−	0.261151i
$914$	13.5837			0.449310
$915$		0			0
$916$			13.9859i			0.462106i
$917$	−25.6194	+	25.6194i	−0.846028	+	0.846028i
$918$	−6.66865	−	15.2470i	−0.220098	−	0.503225i
$919$		−	17.0532i		−	0.562534i	−0.959630	−	0.281267i	$-0.909245\pi$
$919$		−	17.0532i		−	0.562534i	0.959630	−	0.281267i	$-0.0907546\pi$
$920$		0			0
$921$	−39.5324	−	4.94192i	−1.30264	−	0.162842i
$922$	−18.7964	+	18.7964i	−0.619026	+	0.619026i
$923$	−4.11522	+	23.3896i	−0.135454	+	0.769879i
$924$	1.39986	−	11.1980i	0.0460519	−	0.368388i
$925$		0			0
$926$			32.6792i			1.07390i
$927$	−25.7815	+	15.3377i	−0.846777	+	0.503757i
$928$	39.9852	−	39.9852i	1.31258	−	1.31258i
$929$		−	17.0211i		−	0.558445i	−0.960226	−	0.279223i	$-0.909923\pi$
$929$		−	17.0211i		−	0.558445i	0.960226	−	0.279223i	$-0.0900768\pi$
$930$		0			0
$931$		−	3.61918i		−	0.118614i
$932$	−9.61770	−	9.61770i	−0.315038	−	0.315038i
$933$	5.30030	+	6.81480i	0.173524	+	0.223106i
$934$	0.394106			0.0128955
$935$		0			0
$936$	5.73201	+	15.1132i	0.187357	+	0.493991i
$937$	−10.5008	+	10.5008i	−0.343048	+	0.343048i	−0.857512	−	0.514464i	$-0.827991\pi$
$937$	−10.5008	+	10.5008i	−0.343048	+	0.343048i	0.514464	+	0.857512i	$0.327991\pi$
$938$	5.41909	+	5.41909i	0.176940	+	0.176940i
$939$	−34.6316	−	4.32928i	−1.13016	−	0.141281i
$940$		0			0
$941$	−49.0451			−1.59882			−0.799412	−	0.600783i	$-0.794856\pi$
$941$	−49.0451			−1.59882			−0.799412	+	0.600783i	$0.794856\pi$
$942$	26.4474	+	34.0045i	0.861704	+	1.10793i
$943$	−40.9338	+	40.9338i	−1.33299	+	1.33299i
$944$		−	13.8988i		−	0.452367i
$945$		0			0
$946$	21.6043			0.702417
$947$	−10.6955	+	10.6955i	−0.347558	+	0.347558i	−0.859199	−	0.511641i	$-0.829038\pi$
$947$	−10.6955	+	10.6955i	−0.347558	+	0.347558i	0.511641	+	0.859199i	$0.329038\pi$
$948$	−10.2794	+	7.99491i	−0.333858	+	0.259663i
$949$	8.27978	+	11.8154i	0.268773	+	0.383543i
$950$		0			0
$951$	−4.35038	+	34.8004i	−0.141071	+	1.12848i
$952$	−4.31170	+	4.31170i	−0.139743	+	0.139743i
$953$	15.7057	−	15.7057i	0.508756	−	0.508756i	−0.405388	−	0.914145i	$-0.632864\pi$
$953$	15.7057	−	15.7057i	0.508756	−	0.508756i	0.914145	+	0.405388i	$0.132864\pi$
$954$	−29.0470	−	7.37759i	−0.940432	−	0.238858i
$955$		0			0
$956$	−33.7143			−1.09040
$957$	−32.7797	+	25.4948i	−1.05962	+	0.824130i
$958$	−33.2995	−	33.2995i	−1.07586	−	1.07586i
$959$	20.7268			0.669303
$960$		0			0
$961$	−12.8213			−0.413589
$962$	−5.55195	+	31.5556i	−0.179002	+	1.01739i
$963$	9.53395	−	5.67186i	0.307227	−	0.182773i
$964$	−5.02055			−0.161701
$965$		0			0
$966$	6.81091	−	54.4832i	0.219138	−	1.75297i
$967$	−31.6460	−	31.6460i	−1.01767	−	1.01767i	−0.999841	−	0.0178258i	$-0.994326\pi$
$967$	−31.6460	−	31.6460i	−1.01767	−	1.01767i	−0.0178258	−	0.999841i	$-0.505674\pi$
$968$	−5.11497	−	5.11497i	−0.164402	−	0.164402i
$969$	5.98882	+	0.748659i	0.192389	+	0.0240504i
$970$		0			0
$971$			35.7161i			1.14618i	0.819491	+	0.573092i	$0.194256\pi$
$971$			35.7161i			1.14618i	−0.819491	+	0.573092i	$0.805744\pi$
$972$	−2.94288	−	17.8301i	−0.0943931	−	0.571900i
$973$	19.2020	−	19.2020i	0.615589	−	0.615589i
$974$	−11.5677			−0.370653
$975$		0			0
$976$	−12.6614			−0.405283
$977$	−3.00427	+	3.00427i	−0.0961151	+	0.0961151i	−0.753529	−	0.657414i	$-0.771650\pi$
$977$	−3.00427	+	3.00427i	−0.0961151	+	0.0961151i	0.657414	+	0.753529i	$0.271650\pi$
$978$	−8.24484	−	10.6007i	−0.263641	−	0.338973i
$979$			18.5443i			0.592680i
$980$		0			0
$981$	−11.6168	+	45.7378i	−0.370897	+	1.46030i
$982$	3.58443	+	3.58443i	0.114384	+	0.114384i
$983$	41.1733	+	41.1733i	1.31322	+	1.31322i	0.919025	+	0.394198i	$0.128978\pi$
$983$	41.1733	+	41.1733i	1.31322	+	1.31322i	0.394198	+	0.919025i	$0.371022\pi$
$984$	18.8782	+	2.35995i	0.601814	+	0.0752324i
$985$		0			0
$986$	−30.9398			−0.985323
$987$	19.9386	−	15.5075i	0.634652	−	0.493609i
$988$	7.96100	+	1.40067i	0.253273	+	0.0445614i
$989$	38.5710			1.22649
$990$		0			0
$991$	−30.2659			−0.961429			−0.480715	−	0.876877i	$-0.659623\pi$
$991$	−30.2659			−0.961429			−0.480715	+	0.876877i	$0.659623\pi$
$992$	27.3991	+	27.3991i	0.869923	+	0.869923i
$993$	16.6272	+	21.3782i	0.527648	+	0.678418i
$994$	−26.5132			−0.840948
$995$		0			0
$996$	1.11995	−	8.95895i	0.0354871	−	0.283875i
$997$	−15.8921	+	15.8921i	−0.503309	+	0.503309i	−0.912465	−	0.409155i	$-0.865823\pi$
$997$	−15.8921	+	15.8921i	−0.503309	+	0.503309i	0.409155	+	0.912465i	$0.365823\pi$
$998$	−20.8444	+	20.8444i	−0.659819	+	0.659819i
$999$	−9.46906	+	24.1912i	−0.299588	+	0.765376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.s.e.818.13		32
3.2	odd	2	inner	975.2.s.e.818.4		32
5.2	odd	4	inner	975.2.s.e.857.14		32
5.3	odd	4		195.2.s.b.77.3	yes	32
5.4	even	2		195.2.s.b.38.4	yes	32
13.12	even	2	inner	975.2.s.e.818.3		32
15.2	even	4	inner	975.2.s.e.857.3		32
15.8	even	4		195.2.s.b.77.14	yes	32
15.14	odd	2		195.2.s.b.38.13	yes	32
39.38	odd	2	inner	975.2.s.e.818.14		32
65.12	odd	4	inner	975.2.s.e.857.4		32
65.38	odd	4		195.2.s.b.77.13	yes	32
65.64	even	2		195.2.s.b.38.14	yes	32
195.38	even	4		195.2.s.b.77.4	yes	32
195.77	even	4	inner	975.2.s.e.857.13		32
195.194	odd	2		195.2.s.b.38.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.s.b.38.3	✓	32	195.194	odd	2
195.2.s.b.38.4	yes	32	5.4	even	2
195.2.s.b.38.13	yes	32	15.14	odd	2
195.2.s.b.38.14	yes	32	65.64	even	2
195.2.s.b.77.3	yes	32	5.3	odd	4
195.2.s.b.77.4	yes	32	195.38	even	4
195.2.s.b.77.13	yes	32	65.38	odd	4
195.2.s.b.77.14	yes	32	15.8	even	4
975.2.s.e.818.3		32	13.12	even	2	inner
975.2.s.e.818.4		32	3.2	odd	2	inner
975.2.s.e.818.13		32	1.1	even	1	trivial
975.2.s.e.818.14		32	39.38	odd	2	inner
975.2.s.e.857.3		32	15.2	even	4	inner
975.2.s.e.857.4		32	65.12	odd	4	inner
975.2.s.e.857.13		32	195.77	even	4	inner
975.2.s.e.857.14		32	5.2	odd	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25684 - 1.25684i) q^{2} +(-1.36721 + 1.06336i) q^{3} -1.15927i q^{4} +(-0.381882 + 3.05483i) q^{6} +(-1.60133 - 1.60133i) q^{7} +(1.05665 + 1.05665i) q^{8} +(0.738515 - 2.90768i) q^{9} +2.48179 q^{11} +(1.23273 + 1.58497i) q^{12} +(-0.624771 + 3.55101i) q^{13} -4.02523 q^{14} +4.97463 q^{16} +(-1.27410 - 1.27410i) q^{17} +(-2.72628 - 4.58267i) q^{18} +1.93388 q^{19} +(3.89216 + 0.486556i) q^{21} +(3.11920 - 3.11920i) q^{22} +(5.56883 - 5.56883i) q^{23} +(-2.56827 - 0.321058i) q^{24} +(3.67780 + 5.24827i) q^{26} +(2.08222 + 4.76071i) q^{27} +(-1.85639 + 1.85639i) q^{28} +9.66063 q^{29} +6.61976i q^{31} +(4.13899 - 4.13899i) q^{32} +(-3.39312 + 2.63904i) q^{33} -3.20267 q^{34} +(-3.37080 - 0.856142i) q^{36} +(3.53521 + 3.53521i) q^{37} +(2.43057 - 2.43057i) q^{38} +(-2.92182 - 5.51933i) q^{39} -7.35052 q^{41} +(5.50332 - 4.28028i) q^{42} +(3.46312 + 3.46312i) q^{43} -2.87707i q^{44} -13.9982i q^{46} +(4.55353 - 4.55353i) q^{47} +(-6.80136 + 5.28984i) q^{48} -1.87146i q^{49} +(3.09679 + 0.387128i) q^{51} +(4.11659 + 0.724281i) q^{52} +(3.97417 - 3.97417i) q^{53} +(8.60044 + 3.36643i) q^{54} -3.38411i q^{56} +(-2.64402 + 2.05642i) q^{57} +(12.1418 - 12.1418i) q^{58} -2.79393i q^{59} -2.54520 q^{61} +(8.31996 + 8.31996i) q^{62} +(-5.83877 + 3.47355i) q^{63} -0.454797i q^{64} +(-0.947751 + 7.58144i) q^{66} +(-1.34628 - 1.34628i) q^{67} +(-1.47703 + 1.47703i) q^{68} +(-1.69206 + 13.5354i) q^{69} +6.58676 q^{71} +(3.85277 - 2.29206i) q^{72} +(2.82950 - 2.82950i) q^{73} +8.88637 q^{74} -2.24190i q^{76} +(-3.97417 - 3.97417i) q^{77} +(-10.6091 - 3.26464i) q^{78} +6.48553i q^{79} +(-7.90919 - 4.29473i) q^{81} +(-9.23840 + 9.23840i) q^{82} +(-3.17953 - 3.17953i) q^{83} +(0.564052 - 4.51208i) q^{84} +8.70515 q^{86} +(-13.2081 + 10.2728i) q^{87} +(2.62239 + 2.62239i) q^{88} +7.47217i q^{89} +(6.68682 - 4.68588i) q^{91} +(-6.45580 - 6.45580i) q^{92} +(-7.03922 - 9.05059i) q^{93} -11.4461i q^{94} +(-1.25761 + 10.0601i) q^{96} +(-9.27171 - 9.27171i) q^{97} +(-2.35212 - 2.35212i) q^{98} +(1.83284 - 7.21624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 24 q^{12} + 24 q^{16} - 24 q^{22} + 16 q^{27} - 8 q^{36} - 12 q^{42} + 64 q^{43} + 20 q^{48} + 16 q^{51} + 72 q^{52} + 8 q^{61} - 72 q^{66} - 84 q^{78} + 112 q^{81} - 48 q^{82} - 20 q^{87}+ \cdots - 40 q^{91}+O(q^{100}) \) 32 * q + 4 * q^3 + 24 * q^12 + 24 * q^16 - 24 * q^22 + 16 * q^27 - 8 * q^36 - 12 * q^42 + 64 * q^43 + 20 * q^48 + 16 * q^51 + 72 * q^52 + 8 * q^61 - 72 * q^66 - 84 * q^78 + 112 * q^81 - 48 * q^82 - 20 * q^87 + 8 * q^88 - 40 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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