LMFDB - Embedded newform 975.2.m.b.443.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(443,975)] 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("975.443"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,12,0,0,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			443.5
Character	$\chi$	$=$	975.443
Dual form			975.2.m.b.482.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08900 - 1.08900i) q^{2} +(0.390653 - 1.68742i) q^{3} +0.371844i q^{4} +(-2.26302 + 1.41218i) q^{6} +(-2.02596 + 2.02596i) q^{7} +(-1.77306 + 1.77306i) q^{8} +(-2.69478 - 1.31839i) q^{9} +2.54212i q^{11} +(0.627457 + 0.145262i) q^{12} +(0.707107 + 0.707107i) q^{13} +4.41254 q^{14} +4.60542 q^{16} +(-4.99069 - 4.99069i) q^{17} +(1.49889 + 4.37035i) q^{18} +6.71590i q^{19} +(2.62720 + 4.21009i) q^{21} +(2.76837 - 2.76837i) q^{22} +(3.48619 - 3.48619i) q^{23} +(2.29925 + 3.68456i) q^{24} -1.54008i q^{26} +(-3.27740 + 4.03220i) q^{27} +(-0.753340 - 0.753340i) q^{28} +6.04496 q^{29} +6.73148 q^{31} +(-1.46918 - 1.46918i) q^{32} +(4.28962 + 0.993084i) q^{33} +10.8697i q^{34} +(0.490235 - 1.00204i) q^{36} +(-1.77436 + 1.77436i) q^{37} +(7.31362 - 7.31362i) q^{38} +(1.46942 - 0.916954i) q^{39} +2.12945i q^{41} +(1.72377 - 7.44582i) q^{42} +(7.02247 + 7.02247i) q^{43} -0.945270 q^{44} -7.59292 q^{46} +(1.22497 + 1.22497i) q^{47} +(1.79912 - 7.77128i) q^{48} -1.20902i q^{49} +(-10.3710 + 6.47177i) q^{51} +(-0.262933 + 0.262933i) q^{52} +(-4.27790 + 4.27790i) q^{53} +(7.96016 - 0.821971i) q^{54} -7.18431i q^{56} +(11.3326 + 2.62358i) q^{57} +(-6.58296 - 6.58296i) q^{58} -7.22862 q^{59} -4.44731 q^{61} +(-7.33058 - 7.33058i) q^{62} +(8.13052 - 2.78851i) q^{63} -6.01097i q^{64} +(-3.58993 - 5.75287i) q^{66} +(-10.1461 + 10.1461i) q^{67} +(1.85576 - 1.85576i) q^{68} +(-4.52078 - 7.24456i) q^{69} -7.87516i q^{71} +(7.11561 - 2.44043i) q^{72} +(4.19521 + 4.19521i) q^{73} +3.86455 q^{74} -2.49727 q^{76} +(-5.15022 - 5.15022i) q^{77} +(-2.59876 - 0.601636i) q^{78} +9.93677i q^{79} +(5.52369 + 7.10555i) q^{81} +(2.31898 - 2.31898i) q^{82} +(1.23751 - 1.23751i) q^{83} +(-1.56550 + 0.976908i) q^{84} -15.2949i q^{86} +(2.36148 - 10.2004i) q^{87} +(-4.50733 - 4.50733i) q^{88} -4.24811 q^{89} -2.86514 q^{91} +(1.29632 + 1.29632i) q^{92} +(2.62967 - 11.3588i) q^{93} -2.66799i q^{94} +(-3.05306 + 1.90518i) q^{96} +(7.82615 - 7.82615i) q^{97} +(-1.31663 + 1.31663i) q^{98} +(3.35150 - 6.85045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{6} - 32 q^{9} + 80 q^{14} - 8 q^{16} + 4 q^{21} + 16 q^{24} + 24 q^{31} - 16 q^{36} + 4 q^{39} - 16 q^{44} - 32 q^{46} + 40 q^{51} + 112 q^{54} - 72 q^{59} - 32 q^{66} - 40 q^{69} - 256 q^{74}+ \cdots - 136 q^{96}+O(q^{100}) $ 32 * q + 12 * q^6 - 32 * q^9 + 80 * q^14 - 8 * q^16 + 4 * q^21 + 16 * q^24 + 24 * q^31 - 16 * q^36 + 4 * q^39 - 16 * q^44 - 32 * q^46 + 40 * q^51 + 112 * q^54 - 72 * q^59 - 32 * q^66 - 40 * q^69 - 256 * q^74 - 56 * q^76 + 12 * q^81 + 152 * q^84 + 24 * q^89 - 8 * q^91 - 136 * q^96

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 $

$2$	−1.08900	−	1.08900i	−0.770040	−	0.770040i	0.208074	−	0.978113i	$-0.433281\pi$
$2$	−1.08900	−	1.08900i	−0.770040	−	0.770040i	−0.978113	+	0.208074i	$0.933281\pi$
$3$	0.390653	−	1.68742i	0.225543	−	0.974233i
$3$	0.390653	−	1.68742i	0.225543	−	0.974233i
$4$			0.371844i			0.185922i
$5$		0			0
$5$		0			0
$6$	−2.26302	+	1.41218i	−0.923875	+	0.576521i
$7$	−2.02596	+	2.02596i	−0.765741	+	0.765741i	−0.977354	−	0.211613i	$-0.932128\pi$
$7$	−2.02596	+	2.02596i	−0.765741	+	0.765741i	0.211613	+	0.977354i	$0.432128\pi$
$8$	−1.77306	+	1.77306i	−0.626872	+	0.626872i
$9$	−2.69478	−	1.31839i	−0.898260	−	0.439464i
$10$		0			0
$11$			2.54212i			0.766477i	0.923649	+	0.383238i	$0.125191\pi$
$11$			2.54212i			0.766477i	−0.923649	+	0.383238i	$0.874809\pi$
$12$	0.627457	+	0.145262i	0.181131	+	0.0419334i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$14$	4.41254			1.17930
$15$		0			0
$16$	4.60542			1.15135
$17$	−4.99069	−	4.99069i	−1.21042	−	1.21042i	−0.970889	−	0.239530i	$-0.923007\pi$
$17$	−4.99069	−	4.99069i	−1.21042	−	1.21042i	−0.239530	−	0.970889i	$-0.576993\pi$
$18$	1.49889	+	4.37035i	0.353292	+	1.03010i
$19$			6.71590i			1.54073i	0.637601	+	0.770367i	$0.279927\pi$
$19$			6.71590i			1.54073i	−0.637601	+	0.770367i	$0.720073\pi$
$20$		0			0
$21$	2.62720	+	4.21009i	0.573302	+	0.918718i
$22$	2.76837	−	2.76837i	0.590218	−	0.590218i
$23$	3.48619	−	3.48619i	0.726921	−	0.726921i	−0.243085	−	0.970005i	$-0.578159\pi$
$23$	3.48619	−	3.48619i	0.726921	−	0.726921i	0.970005	+	0.243085i	$0.0781593\pi$
$24$	2.29925	+	3.68456i	0.469333	+	0.752107i
$25$		0			0
$26$		−	1.54008i		−	0.302034i
$27$	−3.27740	+	4.03220i	−0.630737	+	0.775997i
$28$	−0.753340	−	0.753340i	−0.142368	−	0.142368i
$29$	6.04496			1.12252			0.561260	−	0.827639i	$-0.310317\pi$
$29$	6.04496			1.12252			0.561260	+	0.827639i	$0.310317\pi$
$30$		0			0
$31$	6.73148			1.20901			0.604505	−	0.796602i	$-0.293371\pi$
$31$	6.73148			1.20901			0.604505	+	0.796602i	$0.293371\pi$
$32$	−1.46918	−	1.46918i	−0.259716	−	0.259716i
$33$	4.28962	+	0.993084i	0.746727	+	0.172874i
$34$			10.8697i			1.86414i
$35$		0			0
$36$	0.490235	−	1.00204i	0.0817059	−	0.167006i
$37$	−1.77436	+	1.77436i	−0.291703	+	0.291703i	−0.837753	−	0.546050i	$-0.816131\pi$
$37$	−1.77436	+	1.77436i	−0.291703	+	0.291703i	0.546050	+	0.837753i	$0.316131\pi$
$38$	7.31362	−	7.31362i	1.18643	−	1.18643i
$39$	1.46942	−	0.916954i	0.235296	−	0.146830i
$40$		0			0
$41$			2.12945i			0.332565i	0.986078	+	0.166282i	$0.0531763\pi$
$41$			2.12945i			0.332565i	−0.986078	+	0.166282i	$0.946824\pi$
$42$	1.72377	−	7.44582i	0.265984	−	1.14891i
$43$	7.02247	+	7.02247i	1.07092	+	1.07092i	0.997286	+	0.0736305i	$0.0234585\pi$
$43$	7.02247	+	7.02247i	1.07092	+	1.07092i	0.0736305	+	0.997286i	$0.476541\pi$
$44$	−0.945270			−0.142505
$45$		0			0
$46$	−7.59292			−1.11952
$47$	1.22497	+	1.22497i	0.178680	+	0.178680i	0.790780	−	0.612100i	$-0.209675\pi$
$47$	1.22497	+	1.22497i	0.178680	+	0.178680i	−0.612100	+	0.790780i	$0.709675\pi$
$48$	1.79912	−	7.77128i	0.259680	−	1.12169i
$49$		−	1.20902i		−	0.172717i
$50$		0			0
$51$	−10.3710	+	6.47177i	−1.45223	+	0.906228i
$52$	−0.262933	+	0.262933i	−0.0364623	+	0.0364623i
$53$	−4.27790	+	4.27790i	−0.587615	+	0.587615i	−0.936985	−	0.349370i	$-0.886396\pi$
$53$	−4.27790	+	4.27790i	−0.587615	+	0.587615i	0.349370	+	0.936985i	$0.386396\pi$
$54$	7.96016	−	0.821971i	1.08324	−	0.111856i
$55$		0			0
$56$		−	7.18431i		−	0.960043i
$57$	11.3326	+	2.62358i	1.50103	+	0.347502i
$58$	−6.58296	−	6.58296i	−0.864385	−	0.864385i
$59$	−7.22862			−0.941087			−0.470543	−	0.882377i	$-0.655942\pi$
$59$	−7.22862			−0.941087			−0.470543	+	0.882377i	$0.655942\pi$
$60$		0			0
$61$	−4.44731			−0.569420			−0.284710	−	0.958614i	$-0.591897\pi$
$61$	−4.44731			−0.569420			−0.284710	+	0.958614i	$0.591897\pi$
$62$	−7.33058	−	7.33058i	−0.930985	−	0.930985i
$63$	8.13052	−	2.78851i	1.02435	−	0.351319i
$64$		−	6.01097i		−	0.751371i
$65$		0			0
$66$	−3.58993	−	5.75287i	−0.441890	−	0.708129i
$67$	−10.1461	+	10.1461i	−1.23954	+	1.23954i	−0.279357	+	0.960187i	$0.590121\pi$
$67$	−10.1461	+	10.1461i	−1.23954	+	1.23954i	−0.960187	+	0.279357i	$0.909879\pi$
$68$	1.85576	−	1.85576i	0.225043	−	0.225043i
$69$	−4.52078	−	7.24456i	−0.544238	−	0.872142i
$70$		0			0
$71$		−	7.87516i		−	0.934609i	−0.884096	−	0.467305i	$-0.845225\pi$
$71$		−	7.87516i		−	0.934609i	0.884096	−	0.467305i	$-0.154775\pi$
$72$	7.11561	−	2.44043i	0.838582	−	0.287607i
$73$	4.19521	+	4.19521i	0.491012	+	0.491012i	0.908625	−	0.417613i	$-0.137133\pi$
$73$	4.19521	+	4.19521i	0.491012	+	0.491012i	−0.417613	+	0.908625i	$0.637133\pi$
$74$	3.86455			0.449245
$75$		0			0
$76$	−2.49727			−0.286456
$77$	−5.15022	−	5.15022i	−0.586923	−	0.586923i
$78$	−2.59876	−	0.601636i	−0.294252	−	0.0681218i
$79$			9.93677i			1.11797i	0.829176	+	0.558987i	$0.188810\pi$
$79$			9.93677i			1.11797i	−0.829176	+	0.558987i	$0.811190\pi$
$80$		0			0
$81$	5.52369	+	7.10555i	0.613743	+	0.789506i
$82$	2.31898	−	2.31898i	0.256088	−	0.256088i
$83$	1.23751	−	1.23751i	0.135834	−	0.135834i	−0.635920	−	0.771755i	$-0.719379\pi$
$83$	1.23751	−	1.23751i	0.135834	−	0.135834i	0.771755	+	0.635920i	$0.219379\pi$
$84$	−1.56550	+	0.976908i	−0.170810	+	0.106589i
$85$		0			0
$86$		−	15.2949i		−	1.64930i
$87$	2.36148	−	10.2004i	0.253177	−	1.09360i
$88$	−4.50733	−	4.50733i	−0.480483	−	0.480483i
$89$	−4.24811			−0.450298			−0.225149	−	0.974324i	$-0.572287\pi$
$89$	−4.24811			−0.450298			−0.225149	+	0.974324i	$0.572287\pi$
$90$		0			0
$91$	−2.86514			−0.300348
$92$	1.29632	+	1.29632i	0.135150	+	0.135150i
$93$	2.62967	−	11.3588i	0.272684	−	1.17786i
$94$		−	2.66799i		−	0.275182i
$95$		0			0
$96$	−3.05306	+	1.90518i	−0.311602	+	0.194447i
$97$	7.82615	−	7.82615i	0.794625	−	0.794625i	−0.187617	−	0.982242i	$-0.560077\pi$
$97$	7.82615	−	7.82615i	0.794625	−	0.794625i	0.982242	+	0.187617i	$0.0600765\pi$
$98$	−1.31663	+	1.31663i	−0.132999	+	0.132999i
$99$	3.35150	−	6.85045i	0.336839	−	0.688496i
$100$		0			0
$101$			10.3448i			1.02935i	0.857387	+	0.514673i	$0.172087\pi$
$101$			10.3448i			1.02935i	−0.857387	+	0.514673i	$0.827913\pi$
$102$	18.3418	+	4.24628i	1.81611	+	0.420445i
$103$	3.56412	+	3.56412i	0.351183	+	0.351183i	0.860550	−	0.509367i	$-0.170120\pi$
$103$	3.56412	+	3.56412i	0.351183	+	0.351183i	−0.509367	+	0.860550i	$0.670120\pi$
$104$	−2.50749			−0.245880
$105$		0			0
$106$	9.31728			0.904974
$107$	8.55837	+	8.55837i	0.827369	+	0.827369i	0.987152	−	0.159783i	$-0.0510794\pi$
$107$	8.55837	+	8.55837i	0.827369	+	0.827369i	−0.159783	+	0.987152i	$0.551079\pi$
$108$	−1.49935	−	1.21868i	−0.144275	−	0.117268i
$109$		−	1.26826i		−	0.121477i	−0.998154	−	0.0607386i	$-0.980654\pi$
$109$		−	1.26826i		−	0.121477i	0.998154	−	0.0607386i	$-0.0193456\pi$
$110$		0			0
$111$	2.30093	+	3.68725i	0.218395	+	0.349978i
$112$	−9.33039	+	9.33039i	−0.881639	+	0.881639i
$113$	−12.0554	+	12.0554i	−1.13407	+	1.13407i	−0.144582	+	0.989493i	$0.546184\pi$
$113$	−12.0554	+	12.0554i	−1.13407	+	1.13407i	−0.989493	+	0.144582i	$0.953816\pi$
$114$	−9.48407	−	15.1982i	−0.888265	−	1.42345i
$115$		0			0
$116$			2.24778i			0.208701i
$117$	−0.973255	−	2.83774i	−0.0899774	−	0.262349i
$118$	7.87198	+	7.87198i	0.724674	+	0.724674i
$119$	20.2219			1.85373
$120$		0			0
$121$	4.53764			0.412513
$122$	4.84312	+	4.84312i	0.438476	+	0.438476i
$123$	3.59329	+	0.831876i	0.323996	+	0.0750078i
$124$			2.50306i			0.224781i
$125$		0			0
$126$	−11.8908	−	5.81745i	−1.05932	−	0.518260i
$127$	8.17055	−	8.17055i	0.725019	−	0.725019i	−0.244604	−	0.969623i	$-0.578658\pi$
$127$	8.17055	−	8.17055i	0.725019	−	0.725019i	0.969623	+	0.244604i	$0.0786579\pi$
$128$	−9.48430	+	9.48430i	−0.838302	+	0.838302i
$129$	14.5932	−	9.10651i	1.28486	−	0.801784i
$130$		0			0
$131$		−	6.30635i		−	0.550989i	−0.961303	−	0.275494i	$-0.911158\pi$
$131$		−	6.30635i		−	0.550989i	0.961303	−	0.275494i	$-0.0888415\pi$
$132$	−0.369272	+	1.59507i	−0.0321410	+	0.138833i
$133$	−13.6061	−	13.6061i	−1.17980	−	1.17980i
$134$	22.0982			1.90900
$135$		0			0
$136$	17.6976			1.51756
$137$	3.89856	+	3.89856i	0.333076	+	0.333076i	0.853754	−	0.520677i	$-0.174320\pi$
$137$	3.89856	+	3.89856i	0.333076	+	0.333076i	−0.520677	+	0.853754i	$0.674320\pi$
$138$	−2.96619	+	12.8125i	−0.252499	+	1.09067i
$139$		−	6.91464i		−	0.586492i	−0.956037	−	0.293246i	$-0.905264\pi$
$139$		−	6.91464i		−	0.586492i	0.956037	−	0.293246i	$-0.0947355\pi$
$140$		0			0
$141$	2.54558	−	1.58850i	0.214377	−	0.133776i
$142$	−8.57605	+	8.57605i	−0.719686	+	0.719686i
$143$	−1.79755	+	1.79755i	−0.150318	+	0.150318i
$144$	−12.4106	−	6.07174i	−1.03422	−	0.505979i
$145$		0			0
$146$		−	9.13717i		−	0.756197i
$147$	−2.04013	−	0.472308i	−0.168267	−	0.0389553i
$148$	−0.659784	−	0.659784i	−0.0542339	−	0.0542339i
$149$	−15.0774			−1.23519			−0.617595	−	0.786496i	$-0.711893\pi$
$149$	−15.0774			−1.23519			−0.617595	+	0.786496i	$0.711893\pi$
$150$		0			0
$151$	−22.9527			−1.86786			−0.933931	−	0.357453i	$-0.883645\pi$
$151$	−22.9527			−1.86786			−0.933931	+	0.357453i	$0.883645\pi$
$152$	−11.9077	−	11.9077i	−0.965843	−	0.965843i
$153$	6.86913	+	20.0285i	0.555336	+	1.61921i
$154$			11.2172i			0.903907i
$155$		0			0
$156$	0.340964	+	0.546395i	0.0272989	+	0.0437466i
$157$	−14.6198	+	14.6198i	−1.16679	+	1.16679i	−0.183833	+	0.982957i	$0.558851\pi$
$157$	−14.6198	+	14.6198i	−1.16679	+	1.16679i	−0.982957	+	0.183833i	$0.941149\pi$
$158$	10.8211	−	10.8211i	0.860884	−	0.860884i
$159$	5.54745	+	8.88980i	0.439942	+	0.705007i
$160$		0			0
$161$			14.1258i			1.11327i
$162$	1.72264	−	13.7532i	0.135344	−	1.08056i
$163$	−2.98170	−	2.98170i	−0.233545	−	0.233545i	0.580626	−	0.814171i	$-0.302808\pi$
$163$	−2.98170	−	2.98170i	−0.233545	−	0.233545i	−0.814171	+	0.580626i	$0.802808\pi$
$164$	−0.791824			−0.0618311
$165$		0			0
$166$	−2.69529			−0.209195
$167$	5.47721	+	5.47721i	0.423839	+	0.423839i	0.886523	−	0.462684i	$-0.153114\pi$
$167$	5.47721	+	5.47721i	0.423839	+	0.423839i	−0.462684	+	0.886523i	$0.653114\pi$
$168$	−12.1230	−	2.80657i	−0.935306	−	0.216531i
$169$			1.00000i			0.0769231i
$170$		0			0
$171$	8.85418	−	18.0979i	0.677096	−	1.38398i
$172$	−2.61126	+	2.61126i	−0.199107	+	0.199107i
$173$	0.832834	−	0.832834i	0.0633192	−	0.0633192i	−0.674738	−	0.738057i	$-0.735743\pi$
$173$	0.832834	−	0.832834i	0.0633192	−	0.0633192i	0.738057	+	0.674738i	$0.235743\pi$
$174$	−13.6799	+	8.53658i	−1.03707	+	0.647156i
$175$		0			0
$176$			11.7075i			0.882487i
$177$	−2.82388	+	12.1977i	−0.212256	+	0.916838i
$178$	4.62619	+	4.62619i	0.346748	+	0.346748i
$179$	−13.0002			−0.971684			−0.485842	−	0.874047i	$-0.661487\pi$
$179$	−13.0002			−0.971684			−0.485842	+	0.874047i	$0.661487\pi$
$180$		0			0
$181$	−0.179054			−0.0133090			−0.00665449	−	0.999978i	$-0.502118\pi$
$181$	−0.179054			−0.0133090			−0.00665449	+	0.999978i	$0.502118\pi$
$182$	3.12014	+	3.12014i	0.231280	+	0.231280i
$183$	−1.73735	+	7.50448i	−0.128429	+	0.554747i
$184$			12.3625i			0.911373i
$185$		0			0
$186$	−15.2335	+	9.50607i	−1.11697	+	0.697019i
$187$	12.6869	−	12.6869i	0.927758	−	0.927758i
$188$	−0.455498	+	0.455498i	−0.0332206	+	0.0332206i
$189$	−1.52918	−	14.8090i	−0.111232	−	1.07719i
$190$		0			0
$191$			19.5878i			1.41732i	0.705549	+	0.708661i	$0.250701\pi$
$191$			19.5878i			1.41732i	−0.705549	+	0.708661i	$0.749299\pi$
$192$	−10.1430	−	2.34820i	−0.732011	−	0.169467i
$193$	−3.32014	−	3.32014i	−0.238989	−	0.238989i	0.577442	−	0.816431i	$-0.304051\pi$
$193$	−3.32014	−	3.32014i	−0.238989	−	0.238989i	−0.816431	+	0.577442i	$0.804051\pi$
$194$	−17.0454			−1.22379
$195$		0			0
$196$	0.449567			0.0321120
$197$	9.61128	+	9.61128i	0.684775	+	0.684775i	0.961072	−	0.276297i	$-0.0891073\pi$
$197$	9.61128	+	9.61128i	0.684775	+	0.684775i	−0.276297	+	0.961072i	$0.589107\pi$
$198$	−11.1099	+	3.81035i	−0.789548	+	0.270790i
$199$		−	2.01789i		−	0.143044i	−0.997439	−	0.0715221i	$-0.977214\pi$
$199$		−	2.01789i		−	0.143044i	0.997439	−	0.0715221i	$-0.0227856\pi$
$200$		0			0
$201$	13.1572	+	21.0844i	0.928034	+	1.48718i
$202$	11.2655	−	11.2655i	0.792637	−	0.792637i
$203$	−12.2468	+	12.2468i	−0.859559	+	0.859559i
$204$	−2.40649	−	3.85640i	−0.168488	−	0.270002i
$205$		0			0
$206$		−	7.76265i		−	0.540850i
$207$	−13.9907	+	4.79836i	−0.972419	+	0.333509i
$208$	3.25652	+	3.25652i	0.225799	+	0.225799i
$209$	−17.0726			−1.18094
$210$		0			0
$211$	18.4845			1.27253			0.636264	−	0.771471i	$-0.280479\pi$
$211$	18.4845			1.27253			0.636264	+	0.771471i	$0.280479\pi$
$212$	−1.59071	−	1.59071i	−0.109251	−	0.109251i
$213$	−13.2887	−	3.07645i	−0.910527	−	0.210795i
$214$		−	18.6401i		−	1.27421i
$215$		0			0
$216$	−1.33830	−	12.9604i	−0.0910596	−	0.881842i
$217$	−13.6377	+	13.6377i	−0.925787	+	0.925787i
$218$	−1.38114	+	1.38114i	−0.0935423	+	0.0935423i
$219$	8.71795	−	5.44022i	0.589105	−	0.367616i
$220$		0			0
$221$		−	7.05790i		−	0.474765i
$222$	1.50970	−	6.52113i	0.101324	−	0.437670i
$223$	−13.4691	−	13.4691i	−0.901955	−	0.901955i	0.0936499	−	0.995605i	$-0.470147\pi$
$223$	−13.4691	−	13.4691i	−0.901955	−	0.901955i	−0.995605	+	0.0936499i	$0.970147\pi$
$224$	5.95299			0.397751
$225$		0			0
$226$	26.2566			1.74656
$227$	8.49517	+	8.49517i	0.563844	+	0.563844i	0.930397	−	0.366553i	$-0.119462\pi$
$227$	8.49517	+	8.49517i	0.563844	+	0.563844i	−0.366553	+	0.930397i	$0.619462\pi$
$228$	−0.975563	+	4.21394i	−0.0646083	+	0.279075i
$229$			6.37084i			0.420997i	0.977594	+	0.210499i	$0.0675088\pi$
$229$			6.37084i			0.420997i	−0.977594	+	0.210499i	$0.932491\pi$
$230$		0			0
$231$	−10.7025	+	6.67865i	−0.704176	+	0.439423i
$232$	−10.7181	+	10.7181i	−0.703677	+	0.703677i
$233$	6.75787	−	6.75787i	0.442723	−	0.442723i	−0.450203	−	0.892926i	$-0.648648\pi$
$233$	6.75787	−	6.75787i	0.442723	−	0.442723i	0.892926	+	0.450203i	$0.148648\pi$
$234$	−2.03043	+	4.15018i	−0.132733	+	0.271306i
$235$		0			0
$236$		−	2.68792i		−	0.174969i
$237$	16.7675	+	3.88183i	1.08917	+	0.252152i
$238$	−22.0216	−	22.0216i	−1.42745	−	1.42745i
$239$	−15.2007			−0.983253			−0.491627	−	0.870806i	$-0.663597\pi$
$239$	−15.2007			−0.983253			−0.491627	+	0.870806i	$0.663597\pi$
$240$		0			0
$241$	3.32408			0.214122			0.107061	−	0.994252i	$-0.465856\pi$
$241$	3.32408			0.214122			0.107061	+	0.994252i	$0.465856\pi$
$242$	−4.94150	−	4.94150i	−0.317651	−	0.317651i
$243$	14.1479	−	6.54499i	0.907588	−	0.419861i
$244$		−	1.65370i		−	0.105868i
$245$		0			0
$246$	−3.00718	−	4.81900i	−0.191730	−	0.307248i
$247$	−4.74886	+	4.74886i	−0.302163	+	0.302163i
$248$	−11.9353	+	11.9353i	−0.757894	+	0.757894i
$249$	−1.60476	−	2.57163i	−0.101698	−	0.162971i
$250$		0			0
$251$		−	13.8499i		−	0.874196i	−0.899414	−	0.437098i	$-0.856006\pi$
$251$		−	13.8499i		−	0.874196i	0.899414	−	0.437098i	$-0.143994\pi$
$252$	1.03689	+	3.02328i	0.0653179	+	0.190449i
$253$	8.86230	+	8.86230i	0.557168	+	0.557168i
$254$	−17.7955			−1.11659
$255$		0			0
$256$	8.63488			0.539680
$257$	5.07145	+	5.07145i	0.316349	+	0.316349i	0.847363	−	0.531014i	$-0.178189\pi$
$257$	5.07145	+	5.07145i	0.316349	+	0.316349i	−0.531014	+	0.847363i	$0.678189\pi$
$258$	−25.8090	−	5.97501i	−1.60680	−	0.371988i
$259$		−	7.18956i		−	0.446737i
$260$		0			0
$261$	−16.2898	−	7.96962i	−1.00832	−	0.493307i
$262$	−6.86762	+	6.86762i	−0.424283	+	0.424283i
$263$	18.8932	−	18.8932i	1.16500	−	1.16500i	0.181636	−	0.983366i	$-0.441861\pi$
$263$	18.8932	−	18.8932i	1.16500	−	1.16500i	0.983366	−	0.181636i	$-0.0581393\pi$
$264$	−9.36657	+	5.84497i	−0.576472	+	0.359733i
$265$		0			0
$266$			29.6342i			1.81699i
$267$	−1.65953	+	7.16835i	−0.101562	+	0.438696i
$268$	−3.77277	−	3.77277i	−0.230458	−	0.230458i
$269$	−11.5306			−0.703036			−0.351518	−	0.936181i	$-0.614334\pi$
$269$	−11.5306			−0.703036			−0.351518	+	0.936181i	$0.614334\pi$
$270$		0			0
$271$	25.4433			1.54557			0.772784	−	0.634669i	$-0.218864\pi$
$271$	25.4433			1.54557			0.772784	+	0.634669i	$0.218864\pi$
$272$	−22.9842	−	22.9842i	−1.39362	−	1.39362i
$273$	−1.11927	+	4.83470i	−0.0677415	+	0.292609i
$274$		−	8.49107i		−	0.512964i
$275$		0			0
$276$	2.69384	−	1.68102i	0.162150	−	0.101186i
$277$	−21.1257	+	21.1257i	−1.26932	+	1.26932i	−0.322880	+	0.946440i	$0.604651\pi$
$277$	−21.1257	+	21.1257i	−1.26932	+	1.26932i	−0.946440	+	0.322880i	$0.895349\pi$
$278$	−7.53005	+	7.53005i	−0.451622	+	0.451622i
$279$	−18.1399	−	8.87472i	−1.08600	−	0.531315i
$280$		0			0
$281$		−	3.04272i		−	0.181513i	−0.995873	−	0.0907567i	$-0.971071\pi$
$281$		−	3.04272i		−	0.181513i	0.995873	−	0.0907567i	$-0.0289286\pi$
$282$	−4.50202	−	1.04226i	−0.268091	−	0.0620655i
$283$	−12.4080	−	12.4080i	−0.737579	−	0.737579i	0.234530	−	0.972109i	$-0.424645\pi$
$283$	−12.4080	−	12.4080i	−0.737579	−	0.737579i	−0.972109	+	0.234530i	$0.924645\pi$
$284$	2.92833			0.173764
$285$		0			0
$286$	3.91506			0.231502
$287$	−4.31419	−	4.31419i	−0.254658	−	0.254658i
$288$	2.02216	+	5.89606i	0.119157	+	0.347429i
$289$			32.8139i			1.93023i
$290$		0			0
$291$	−10.1487	−	16.2633i	−0.594927	−	0.953372i
$292$	−1.55996	+	1.55996i	−0.0912899	+	0.0912899i
$293$	−13.4462	+	13.4462i	−0.785538	+	0.785538i	−0.980759	−	0.195221i	$-0.937458\pi$
$293$	−13.4462	+	13.4462i	−0.785538	+	0.785538i	0.195221	+	0.980759i	$0.437458\pi$
$294$	1.70736	+	2.73605i	0.0995752	+	0.159569i
$295$		0			0
$296$		−	6.29210i		−	0.365721i
$297$	−10.2503	−	8.33154i	−0.594784	−	0.483445i
$298$	16.4193	+	16.4193i	0.951146	+	0.951146i
$299$	4.93021			0.285122
$300$		0			0
$301$	−28.4545			−1.64009
$302$	24.9955	+	24.9955i	1.43833	+	1.43833i
$303$	17.4560	+	4.04122i	1.00282	+	0.232162i
$304$			30.9295i			1.77393i
$305$		0			0
$306$	14.3305	−	29.2915i	0.819222	−	1.67448i
$307$	−5.52040	+	5.52040i	−0.315066	+	0.315066i	−0.846868	−	0.531803i	$-0.821515\pi$
$307$	−5.52040	+	5.52040i	−0.315066	+	0.315066i	0.531803	+	0.846868i	$0.321515\pi$
$308$	1.91508	−	1.91508i	0.109122	−	0.109122i
$309$	7.40650	−	4.62184i	0.421341	−	0.262927i
$310$		0			0
$311$			6.78626i			0.384813i	0.981315	+	0.192407i	$0.0616293\pi$
$311$			6.78626i			0.384813i	−0.981315	+	0.192407i	$0.938371\pi$
$312$	−0.979557	+	4.23119i	−0.0554565	+	0.239544i
$313$	5.21708	+	5.21708i	0.294887	+	0.294887i	0.839007	−	0.544120i	$-0.183137\pi$
$313$	5.21708	+	5.21708i	0.294887	+	0.294887i	−0.544120	+	0.839007i	$0.683137\pi$
$314$	31.8420			1.79695
$315$		0			0
$316$	−3.69493			−0.207856
$317$	8.71005	+	8.71005i	0.489205	+	0.489205i	0.908055	−	0.418850i	$-0.137567\pi$
$317$	8.71005	+	8.71005i	0.489205	+	0.489205i	−0.418850	+	0.908055i	$0.637567\pi$
$318$	3.63982	−	15.7222i	0.204111	−	0.881656i
$319$			15.3670i			0.860386i
$320$		0			0
$321$	17.7849	−	11.0982i	0.992658	−	0.619443i
$322$	15.3829	−	15.3829i	0.857258	−	0.857258i
$323$	33.5170	−	33.5170i	1.86493	−	1.86493i
$324$	−2.64215	+	2.05395i	−0.146786	+	0.114108i
$325$		0			0
$326$			6.49414i			0.359677i
$327$	−2.14009	−	0.495449i	−0.118347	−	0.0273984i
$328$	−3.77565	−	3.77565i	−0.208476	−	0.208476i
$329$	−4.96349			−0.273646
$330$		0			0
$331$	−32.0566			−1.76199			−0.880994	−	0.473128i	$-0.843125\pi$
$331$	−32.0566			−1.76199			−0.880994	+	0.473128i	$0.843125\pi$
$332$	0.460160	+	0.460160i	0.0252545	+	0.0252545i
$333$	7.12081	−	2.44221i	0.390218	−	0.133832i
$334$		−	11.9294i		−	0.652746i
$335$		0			0
$336$	12.0994	+	19.3892i	0.660074	+	1.05777i
$337$	8.60740	−	8.60740i	0.468875	−	0.468875i	−0.432675	−	0.901550i	$-0.642430\pi$
$337$	8.60740	−	8.60740i	0.468875	−	0.468875i	0.901550	+	0.432675i	$0.142430\pi$
$338$	1.08900	−	1.08900i	0.0592338	−	0.0592338i
$339$	15.6330	+	25.0520i	0.849070	+	1.36064i
$340$		0			0
$341$			17.1122i			0.926678i
$342$	−29.3508	+	10.0664i	−1.58711	+	0.544328i
$343$	−11.7323	−	11.7323i	−0.633484	−	0.633484i
$344$	−24.9025			−1.34266
$345$		0			0
$346$	−1.81391			−0.0975165
$347$	22.9313	+	22.9313i	1.23102	+	1.23102i	0.963573	+	0.267445i	$0.0861794\pi$
$347$	22.9313	+	22.9313i	1.23102	+	1.23102i	0.267445	+	0.963573i	$0.413821\pi$
$348$	3.79295	+	0.878101i	0.203323	+	0.0470711i
$349$		−	14.9443i		−	0.799950i	−0.916526	−	0.399975i	$-0.869019\pi$
$349$		−	14.9443i		−	0.799950i	0.916526	−	0.399975i	$-0.130981\pi$
$350$		0			0
$351$	−5.16867	+	0.533720i	−0.275883	+	0.0284879i
$352$	3.73482	−	3.73482i	0.199067	−	0.199067i
$353$	−25.1633	+	25.1633i	−1.33931	+	1.33931i	−0.442580	+	0.896729i	$0.645937\pi$
$353$	−25.1633	+	25.1633i	−1.33931	+	1.33931i	−0.896729	+	0.442580i	$0.854063\pi$
$354$	16.3585	−	10.2081i	0.869447	−	0.542556i
$355$		0			0
$356$		−	1.57963i		−	0.0837203i
$357$	7.89972	−	34.1228i	0.418097	−	1.80597i
$358$	14.1573	+	14.1573i	0.748235	+	0.748235i
$359$	20.9144			1.10382			0.551909	−	0.833904i	$-0.313900\pi$
$359$	20.9144			1.10382			0.551909	+	0.833904i	$0.313900\pi$
$360$		0			0
$361$	−26.1033			−1.37386
$362$	0.194990	+	0.194990i	0.0102484	+	0.0102484i
$363$	1.77264	−	7.65692i	0.0930396	−	0.401884i
$364$		−	1.06538i		−	0.0558413i
$365$		0			0
$366$	10.0644	−	6.28041i	0.526073	−	0.328282i
$367$	22.4440	−	22.4440i	1.17157	−	1.17157i	0.189733	−	0.981836i	$-0.439238\pi$
$367$	22.4440	−	22.4440i	1.17157	−	1.17157i	0.981836	−	0.189733i	$-0.0607622\pi$
$368$	16.0554	−	16.0554i	0.836944	−	0.836944i
$369$	2.80745	−	5.73841i	0.146150	−	0.298730i
$370$		0			0
$371$		−	17.3337i		−	0.899922i
$372$	4.22371	+	0.977826i	0.218989	+	0.0506979i
$373$	5.54286	+	5.54286i	0.286998	+	0.286998i	0.835892	−	0.548894i	$-0.184951\pi$
$373$	5.54286	+	5.54286i	0.286998	+	0.286998i	−0.548894	+	0.835892i	$0.684951\pi$
$374$	−27.6321			−1.42882
$375$		0			0
$376$	−4.34390			−0.224020
$377$	4.27443	+	4.27443i	0.220144	+	0.220144i
$378$	−14.4617	+	17.7922i	−0.743829	+	0.915134i
$379$		−	6.81554i		−	0.350091i	−0.984560	−	0.175045i	$-0.943993\pi$
$379$		−	6.81554i		−	0.350091i	0.984560	−	0.175045i	$-0.0560072\pi$
$380$		0			0
$381$	−10.5953	−	16.9790i	−0.542815	−	0.869861i
$382$	21.3311	−	21.3311i	1.09139	−	1.09139i
$383$	5.15570	−	5.15570i	0.263444	−	0.263444i	−0.563008	−	0.826452i	$-0.690356\pi$
$383$	5.15570	−	5.15570i	0.263444	−	0.263444i	0.826452	+	0.563008i	$0.190356\pi$
$384$	12.2989	+	19.7091i	0.627628	+	1.00577i
$385$		0			0
$386$			7.23127i			0.368062i
$387$	−9.66565	−	28.1824i	−0.491333	−	1.43259i
$388$	2.91010	+	2.91010i	0.147738	+	0.147738i
$389$	−8.44117			−0.427985			−0.213992	−	0.976835i	$-0.568647\pi$
$389$	−8.44117			−0.427985			−0.213992	+	0.976835i	$0.568647\pi$
$390$		0			0
$391$	−34.7969			−1.75976
$392$	2.14367	+	2.14367i	0.108272	+	0.108272i
$393$	−10.6415	−	2.46359i	−0.536791	−	0.124272i
$394$		−	20.9334i		−	1.05461i
$395$		0			0
$396$	2.54730	+	1.24624i	0.128006	+	0.0626257i
$397$	−18.7419	+	18.7419i	−0.940630	+	0.940630i	−0.998334	−	0.0577040i	$-0.981622\pi$
$397$	−18.7419	+	18.7419i	−0.940630	+	0.940630i	0.0577040	+	0.998334i	$0.481622\pi$
$398$	−2.19748	+	2.19748i	−0.110150	+	0.110150i
$399$	−28.2746	+	17.6440i	−1.41550	+	0.883306i
$400$		0			0
$401$		−	33.3203i		−	1.66394i	−0.554824	−	0.831968i	$-0.687214\pi$
$401$		−	33.3203i		−	1.66394i	0.554824	−	0.831968i	$-0.312786\pi$
$402$	8.63273	−	37.2890i	0.430561	−	1.85981i
$403$	4.75987	+	4.75987i	0.237106	+	0.237106i
$404$	−3.84665			−0.191378
$405$		0			0
$406$	26.6736			1.32379
$407$	−4.51063	−	4.51063i	−0.223583	−	0.223583i
$408$	6.91361	−	29.8633i	0.342275	−	1.47845i
$409$		−	17.8239i		−	0.881337i	−0.897670	−	0.440668i	$-0.854741\pi$
$409$		−	17.8239i		−	0.881337i	0.897670	−	0.440668i	$-0.145259\pi$
$410$		0			0
$411$	8.10150	−	5.05553i	0.399617	−	0.249371i
$412$	−1.32529	+	1.32529i	−0.0652926	+	0.0652926i
$413$	14.6449	−	14.6449i	0.720628	−	0.720628i
$414$	20.4613	+	10.0104i	1.00562	+	0.491986i
$415$		0			0
$416$		−	2.07773i		−	0.101869i
$417$	−11.6679	−	2.70122i	−0.571380	−	0.132279i
$418$	18.5921	+	18.5921i	0.909368	+	0.909368i
$419$	8.51083			0.415781			0.207891	−	0.978152i	$-0.433340\pi$
$419$	8.51083			0.415781			0.207891	+	0.978152i	$0.433340\pi$
$420$		0			0
$421$	24.8993			1.21352			0.606760	−	0.794885i	$-0.292469\pi$
$421$	24.8993			1.21352			0.606760	+	0.794885i	$0.292469\pi$
$422$	−20.1297	−	20.1297i	−0.979897	−	0.979897i
$423$	−1.68604	−	4.91602i	−0.0819780	−	0.239025i
$424$		−	15.1700i		−	0.736720i
$425$		0			0
$426$	11.1212	+	17.8217i	0.538822	+	0.863462i
$427$	9.01007	−	9.01007i	0.436028	−	0.436028i
$428$	−3.18238	+	3.18238i	−0.153826	+	0.153826i
$429$	2.33100	+	3.73544i	0.112542	+	0.180349i
$430$		0			0
$431$			21.5217i			1.03666i	0.855180	+	0.518332i	$0.173447\pi$
$431$			21.5217i			1.03666i	−0.855180	+	0.518332i	$0.826553\pi$
$432$	−15.0938	+	18.5700i	−0.726202	+	0.893448i
$433$	9.81142	+	9.81142i	0.471507	+	0.471507i	0.902402	−	0.430895i	$-0.141802\pi$
$433$	9.81142	+	9.81142i	0.471507	+	0.471507i	−0.430895	+	0.902402i	$0.641802\pi$
$434$	29.7029			1.42579
$435$		0			0
$436$	0.471594			0.0225853
$437$	23.4129	+	23.4129i	1.11999	+	1.11999i
$438$	−15.4183	−	3.56946i	−0.736713	−	0.170555i
$439$			7.91746i			0.377880i	0.981989	+	0.188940i	$0.0605051\pi$
$439$			7.91746i			0.377880i	−0.981989	+	0.188940i	$0.939495\pi$
$440$		0			0
$441$	−1.59396	+	3.25805i	−0.0759031	+	0.155145i
$442$	−7.68605	+	7.68605i	−0.365588	+	0.365588i
$443$	14.0065	−	14.0065i	0.665467	−	0.665467i	−0.291196	−	0.956663i	$-0.594053\pi$
$443$	14.0065	−	14.0065i	0.665467	−	0.665467i	0.956663	+	0.291196i	$0.0940533\pi$
$444$	−1.37108	+	0.855587i	−0.0650686	+	0.0406044i
$445$		0			0
$446$			29.3356i			1.38908i
$447$	−5.89004	+	25.4420i	−0.278589	+	1.20336i
$448$	12.1780	+	12.1780i	0.575355	+	0.575355i
$449$	37.1012			1.75091			0.875457	−	0.483296i	$-0.160560\pi$
$449$	37.1012			1.75091			0.875457	+	0.483296i	$0.160560\pi$
$450$		0			0
$451$	−5.41332			−0.254903
$452$	−4.48272	−	4.48272i	−0.210849	−	0.210849i
$453$	−8.96652	+	38.7308i	−0.421284	+	1.81973i
$454$		−	18.5025i		−	0.868364i
$455$		0			0
$456$	−24.7451	+	15.4416i	−1.15880	+	0.723117i
$457$	11.3050	−	11.3050i	0.528826	−	0.528826i	−0.391396	−	0.920222i	$-0.628008\pi$
$457$	11.3050	−	11.3050i	0.528826	−	0.528826i	0.920222	+	0.391396i	$0.128008\pi$
$458$	6.93785	−	6.93785i	0.324185	−	0.324185i
$459$	36.4799	−	3.76694i	1.70274	−	0.175826i
$460$		0			0
$461$			31.2905i			1.45734i	0.684864	+	0.728671i	$0.259862\pi$
$461$			31.2905i			1.45734i	−0.684864	+	0.728671i	$0.740138\pi$
$462$	18.9281	+	4.38203i	0.880616	+	0.203870i
$463$	−2.74013	−	2.74013i	−0.127345	−	0.127345i	0.640562	−	0.767907i	$-0.278701\pi$
$463$	−2.74013	−	2.74013i	−0.127345	−	0.127345i	−0.767907	+	0.640562i	$0.778701\pi$
$464$	27.8396			1.29242
$465$		0			0
$466$	−14.7186			−0.681828
$467$	−26.1266	−	26.1266i	−1.20899	−	1.20899i	−0.971353	−	0.237641i	$-0.923626\pi$
$467$	−26.1266	−	26.1266i	−1.20899	−	1.20899i	−0.237641	−	0.971353i	$-0.576374\pi$
$468$	1.05520	−	0.361899i	0.0487765	−	0.0167288i
$469$		−	41.1112i		−	1.89834i
$470$		0			0
$471$	18.9586	+	30.3811i	0.873564	+	1.39989i
$472$	12.8168	−	12.8168i	0.589941	−	0.589941i
$473$	−17.8519	+	17.8519i	−0.820833	+	0.820833i
$474$	−14.0325	−	22.4871i	−0.644535	−	1.03287i
$475$		0			0
$476$			7.51937i			0.344650i
$477$	17.1680	−	5.88807i	0.786067	−	0.269596i
$478$	16.5536	+	16.5536i	0.757144	+	0.757144i
$479$	19.8159			0.905412			0.452706	−	0.891660i	$-0.350459\pi$
$479$	19.8159			0.905412			0.452706	+	0.891660i	$0.350459\pi$
$480$		0			0
$481$	−2.50932			−0.114415
$482$	−3.61992	−	3.61992i	−0.164883	−	0.164883i
$483$	23.8361	+	5.51826i	1.08458	+	0.251090i
$484$			1.68729i			0.0766952i
$485$		0			0
$486$	−22.5346	−	8.27957i	−1.02219	−	0.375569i
$487$	20.8051	−	20.8051i	0.942768	−	0.942768i	−0.0556804	−	0.998449i	$-0.517733\pi$
$487$	20.8051	−	20.8051i	0.942768	−	0.942768i	0.998449	+	0.0556804i	$0.0177328\pi$
$488$	7.88536	−	7.88536i	0.356953	−	0.356953i
$489$	−6.19619	+	3.86657i	−0.280201	+	0.174853i
$490$		0			0
$491$		−	10.4305i		−	0.470722i	−0.971908	−	0.235361i	$-0.924373\pi$
$491$		−	10.4305i		−	0.470722i	0.971908	−	0.235361i	$-0.0756273\pi$
$492$	−0.309328	+	1.33614i	−0.0139456	+	0.0602379i
$493$	−30.1685	−	30.1685i	−1.35872	−	1.35872i
$494$	10.3430			0.465355
$495$		0			0
$496$	31.0013			1.39200
$497$	15.9547	+	15.9547i	0.715668	+	0.715668i
$498$	−1.05292	+	4.54810i	−0.0471826	+	0.203805i
$499$		−	0.867019i		−	0.0388131i	−0.999812	−	0.0194066i	$-0.993822\pi$
$499$		−	0.867019i		−	0.0388131i	0.999812	−	0.0194066i	$-0.00617768\pi$
$500$		0			0
$501$	11.3820	−	7.10268i	0.508512	−	0.317324i
$502$	−15.0825	+	15.0825i	−0.673166	+	0.673166i
$503$	4.83819	−	4.83819i	0.215724	−	0.215724i	−0.590969	−	0.806694i	$-0.701255\pi$
$503$	4.83819	−	4.83819i	0.215724	−	0.215724i	0.806694	+	0.590969i	$0.201255\pi$
$504$	−9.47172	+	19.3601i	−0.421904	+	0.862369i
$505$		0			0
$506$		−	19.3021i		−	0.858083i
$507$	1.68742	+	0.390653i	0.0749410	+	0.0173495i
$508$	3.03817	+	3.03817i	0.134797	+	0.134797i
$509$	0.634330			0.0281162			0.0140581	−	0.999901i	$-0.495525\pi$
$509$	0.634330			0.0281162			0.0140581	+	0.999901i	$0.495525\pi$
$510$		0			0
$511$	−16.9986			−0.751976
$512$	9.56522	+	9.56522i	0.422727	+	0.422727i
$513$	−27.0798	−	22.0107i	−1.19560	−	0.971797i
$514$		−	11.0456i		−	0.487202i
$515$		0			0
$516$	3.38620	+	5.42639i	0.149069	+	0.238884i
$517$	−3.11402	+	3.11402i	−0.136954	+	0.136954i
$518$	−7.82943	+	7.82943i	−0.344005	+	0.344005i
$519$	−1.07999	−	1.73069i	−0.0474064	−	0.0759688i
$520$		0			0
$521$		−	35.1991i		−	1.54210i	−0.636774	−	0.771050i	$-0.719732\pi$
$521$		−	35.1991i		−	1.54210i	0.636774	−	0.771050i	$-0.280268\pi$
$522$	9.06072	+	26.4186i	0.396577	+	1.15631i
$523$	21.0711	+	21.0711i	0.921374	+	0.921374i	0.997127	−	0.0757527i	$-0.0241359\pi$
$523$	21.0711	+	21.0711i	0.921374	+	0.921374i	−0.0757527	+	0.997127i	$0.524136\pi$
$524$	2.34498			0.102441
$525$		0			0
$526$	−41.1493			−1.79419
$527$	−33.5947	−	33.5947i	−1.46341	−	1.46341i
$528$	19.7555	+	4.57357i	0.859748	+	0.199039i
$529$		−	1.30702i		−	0.0568269i
$530$		0			0
$531$	19.4796	+	9.53015i	0.845341	+	0.413573i
$532$	5.05936	−	5.05936i	0.219351	−	0.219351i
$533$	−1.50575	+	1.50575i	−0.0652213	+	0.0652213i
$534$	9.61357	−	5.99910i	0.416020	−	0.259606i
$535$		0			0
$536$		−	35.9794i		−	1.55407i
$537$	−5.07858	+	21.9369i	−0.219157	+	0.946647i
$538$	12.5569	+	12.5569i	0.541365	+	0.541365i
$539$	3.07348			0.132384
$540$		0			0
$541$	19.2852			0.829135			0.414568	−	0.910019i	$-0.363933\pi$
$541$	19.2852			0.829135			0.414568	+	0.910019i	$0.363933\pi$
$542$	−27.7077	−	27.7077i	−1.19015	−	1.19015i
$543$	−0.0699479	+	0.302139i	−0.00300175	+	0.0129660i
$544$			14.6644i			0.628732i
$545$		0			0
$546$	6.48388	−	4.04610i	0.277484	−	0.173157i
$547$	25.7799	−	25.7799i	1.10227	−	1.10227i	0.108134	−	0.994136i	$-0.465512\pi$
$547$	25.7799	−	25.7799i	1.10227	−	1.10227i	0.994136	−	0.108134i	$-0.0344876\pi$
$548$	−1.44965	+	1.44965i	−0.0619262	+	0.0619262i
$549$	11.9845	+	5.86329i	0.511487	+	0.250239i
$550$		0			0
$551$			40.5973i			1.72950i
$552$	20.8607	+	4.82943i	0.887890	+	0.205554i
$553$	−20.1315	−	20.1315i	−0.856078	−	0.856078i
$554$	46.0118			1.95485
$555$		0			0
$556$	2.57117			0.109042
$557$	23.4547	+	23.4547i	0.993810	+	0.993810i	0.999981	−	0.00617141i	$-0.00196443\pi$
$557$	23.4547	+	23.4547i	0.993810	+	0.993810i	−0.00617141	+	0.999981i	$0.501964\pi$
$558$	10.0897	+	29.4189i	0.427133	+	1.24540i
$559$			9.93127i			0.420048i
$560$		0			0
$561$	−16.4520	−	26.3643i	−0.694603	−	1.11310i
$562$	−3.31352	+	3.31352i	−0.139772	+	0.139772i
$563$	−25.5031	+	25.5031i	−1.07483	+	1.07483i	−0.0778645	+	0.996964i	$0.524810\pi$
$563$	−25.5031	+	25.5031i	−1.07483	+	1.07483i	−0.996964	+	0.0778645i	$0.975190\pi$
$564$	0.590675	+	0.946558i	0.0248719	+	0.0398573i
$565$		0			0
$566$			27.0246i			1.13593i
$567$	−25.5863	−	3.20478i	−1.07452	−	0.134588i
$568$	13.9631	+	13.9631i	0.585881	+	0.585881i
$569$	−25.9087			−1.08615			−0.543074	−	0.839685i	$-0.682740\pi$
$569$	−25.9087			−1.08615			−0.543074	+	0.839685i	$0.682740\pi$
$570$		0			0
$571$	−31.2937			−1.30960			−0.654801	−	0.755801i	$-0.727248\pi$
$571$	−31.2937			−1.30960			−0.654801	+	0.755801i	$0.727248\pi$
$572$	−0.668407	−	0.668407i	−0.0279475	−	0.0279475i
$573$	33.0529	+	7.65202i	1.38080	+	0.319668i
$574$			9.39630i			0.392194i
$575$		0			0
$576$	−7.92481	+	16.1982i	−0.330200	+	0.674927i
$577$	17.5221	−	17.5221i	0.729455	−	0.729455i	−0.241056	−	0.970511i	$-0.577494\pi$
$577$	17.5221	−	17.5221i	0.729455	−	0.729455i	0.970511	+	0.241056i	$0.0774937\pi$
$578$	35.7343	−	35.7343i	1.48635	−	1.48635i
$579$	−6.89950	+	4.30546i	−0.286733	+	0.178929i
$580$		0			0
$581$			5.01428i			0.208027i
$582$	−6.65881	+	28.7627i	−0.276017	+	1.19225i
$583$	−10.8749	−	10.8749i	−0.450394	−	0.450394i
$584$	−14.8767			−0.615604
$585$		0			0
$586$	29.2859			1.20979
$587$	−10.1437	−	10.1437i	−0.418675	−	0.418675i	0.466072	−	0.884747i	$-0.345669\pi$
$587$	−10.1437	−	10.1437i	−0.418675	−	0.418675i	−0.884747	+	0.466072i	$0.845669\pi$
$588$	0.175625	−	0.758610i	0.00724264	−	0.0312845i
$589$			45.2079i			1.86276i
$590$		0			0
$591$	19.9729	−	12.4636i	0.821577	−	0.512684i
$592$	−8.17167	+	8.17167i	−0.335853	+	0.335853i
$593$	2.99449	−	2.99449i	0.122969	−	0.122969i	−0.642944	−	0.765913i	$-0.722287\pi$
$593$	2.99449	−	2.99449i	0.122969	−	0.122969i	0.765913	+	0.642944i	$0.222287\pi$
$594$	2.08955	+	20.2357i	0.0857352	+	0.830279i
$595$		0			0
$596$		−	5.60645i		−	0.229649i
$597$	−3.40503	−	0.788293i	−0.139358	−	0.0322627i
$598$	−5.36901	−	5.36901i	−0.219555	−	0.219555i
$599$	−26.7949			−1.09481			−0.547405	−	0.836868i	$-0.684384\pi$
$599$	−26.7949			−1.09481			−0.547405	+	0.836868i	$0.684384\pi$
$600$		0			0
$601$	−6.10748			−0.249129			−0.124565	−	0.992211i	$-0.539753\pi$
$601$	−6.10748			−0.249129			−0.124565	+	0.992211i	$0.539753\pi$
$602$	30.9869	+	30.9869i	1.26293	+	1.26293i
$603$	40.7181	−	13.9650i	1.65817	−	0.568699i
$604$		−	8.53481i		−	0.347276i
$605$		0			0
$606$	−14.6087	−	23.4105i	−0.593439	−	0.950987i
$607$	−2.31847	+	2.31847i	−0.0941037	+	0.0941037i	−0.752591	−	0.658488i	$-0.771196\pi$
$607$	−2.31847	+	2.31847i	−0.0941037	+	0.0941037i	0.658488	+	0.752591i	$0.271196\pi$
$608$	9.86686	−	9.86686i	0.400154	−	0.400154i
$609$	15.8813	+	25.4498i	0.643543	+	1.03128i
$610$		0			0
$611$			1.73237i			0.0700842i
$612$	−7.44746	+	2.55424i	−0.301046	+	0.103249i
$613$	−10.4936	−	10.4936i	−0.423832	−	0.423832i	0.462688	−	0.886521i	$-0.346885\pi$
$613$	−10.4936	−	10.4936i	−0.423832	−	0.423832i	−0.886521	+	0.462688i	$0.846885\pi$
$614$	12.0234			0.485226
$615$		0			0
$616$	18.2633			0.735851
$617$	−33.0048	−	33.0048i	−1.32872	−	1.32872i	−0.906487	−	0.422235i	$-0.861246\pi$
$617$	−33.0048	−	33.0048i	−1.32872	−	1.32872i	−0.422235	−	0.906487i	$-0.638754\pi$
$618$	−13.0989	−	3.03250i	−0.526914	−	0.121985i
$619$			13.2296i			0.531741i	0.964009	+	0.265871i	$0.0856594\pi$
$619$			13.2296i			0.531741i	−0.964009	+	0.265871i	$0.914341\pi$
$620$		0			0
$621$	2.63136	+	25.4826i	0.105593	+	1.02258i
$622$	7.39024	−	7.39024i	0.296322	−	0.296322i
$623$	8.60649	−	8.60649i	0.344812	−	0.344812i
$624$	6.76730	−	4.22296i	0.270909	−	0.169054i
$625$		0			0
$626$		−	11.3628i		−	0.454149i
$627$	−6.66946	+	28.8087i	−0.266352	+	1.15051i
$628$	−5.43630	−	5.43630i	−0.216932	−	0.216932i
$629$	17.7105			0.706165
$630$		0			0
$631$	−7.59160			−0.302217			−0.151108	−	0.988517i	$-0.548284\pi$
$631$	−7.59160			−0.302217			−0.151108	+	0.988517i	$0.548284\pi$
$632$	−17.6185	−	17.6185i	−0.700827	−	0.700827i
$633$	7.22103	−	31.1912i	0.287010	−	1.23974i
$634$		−	18.9705i		−	0.753415i
$635$		0			0
$636$	−3.30562	+	2.06279i	−0.131076	+	0.0817948i
$637$	0.854908	−	0.854908i	0.0338727	−	0.0338727i
$638$	16.7347	−	16.7347i	0.662531	−	0.662531i
$639$	−10.3825	+	21.2218i	−0.410727	+	0.839522i
$640$		0			0
$641$		−	24.9790i		−	0.986611i	−0.869856	−	0.493306i	$-0.835788\pi$
$641$		−	24.9790i		−	0.986611i	0.869856	−	0.493306i	$-0.164212\pi$
$642$	−31.4538	−	7.28182i	−1.24138	−	0.287391i
$643$	15.6201	+	15.6201i	0.615995	+	0.615995i	0.944502	−	0.328506i	$-0.106545\pi$
$643$	15.6201	+	15.6201i	0.615995	+	0.615995i	−0.328506	+	0.944502i	$0.606545\pi$
$644$	−5.25257			−0.206980
$645$		0			0
$646$	−73.0000			−2.87215
$647$	−31.8586	−	31.8586i	−1.25249	−	1.25249i	−0.954601	−	0.297889i	$-0.903717\pi$
$647$	−31.8586	−	31.8586i	−1.25249	−	1.25249i	−0.297889	−	0.954601i	$-0.596283\pi$
$648$	−22.3924	−	2.80473i	−0.879658	−	0.110180i
$649$		−	18.3760i		−	0.721321i
$650$		0			0
$651$	17.6849	+	28.3401i	0.693128	+	1.11074i
$652$	1.10873	−	1.10873i	0.0434211	−	0.0434211i
$653$	−11.1691	+	11.1691i	−0.437079	+	0.437079i	−0.891028	−	0.453949i	$-0.850015\pi$
$653$	−11.1691	+	11.1691i	−0.437079	+	0.437079i	0.453949	+	0.891028i	$0.350015\pi$
$654$	1.79101	+	2.87010i	0.0700342	+	0.112230i
$655$		0			0
$656$			9.80703i			0.382900i
$657$	−5.77424	−	16.8361i	−0.225275	−	0.656839i
$658$	5.40524	+	5.40524i	0.210718	+	0.210718i
$659$	12.8172			0.499288			0.249644	−	0.968338i	$-0.419686\pi$
$659$	12.8172			0.499288			0.249644	+	0.968338i	$0.419686\pi$
$660$		0			0
$661$	−2.25434			−0.0876835			−0.0438417	−	0.999038i	$-0.513960\pi$
$661$	−2.25434			−0.0876835			−0.0438417	+	0.999038i	$0.513960\pi$
$662$	34.9096	+	34.9096i	1.35680	+	1.35680i
$663$	−11.9096	−	2.75719i	−0.462532	−	0.107080i
$664$			4.38836i			0.170301i
$665$		0			0
$666$	−10.4141	−	5.09499i	−0.403539	−	0.197427i
$667$	21.0739	−	21.0739i	0.815983	−	0.815983i
$668$	−2.03667	+	2.03667i	−0.0788010	+	0.0788010i
$669$	−27.9897	+	17.4663i	−1.08214	+	0.675285i
$670$		0			0
$671$		−	11.3056i		−	0.436447i
$672$	2.32555	−	10.0452i	0.0897101	−	0.387502i
$673$	−10.4216	−	10.4216i	−0.401721	−	0.401721i	0.477118	−	0.878839i	$-0.341681\pi$
$673$	−10.4216	−	10.4216i	−0.401721	−	0.401721i	−0.878839	+	0.477118i	$0.841681\pi$
$674$	−18.7469			−0.722105
$675$		0			0
$676$	−0.371844			−0.0143017
$677$	−19.5211	−	19.5211i	−0.750257	−	0.750257i	0.224270	−	0.974527i	$-0.428000\pi$
$677$	−19.5211	−	19.5211i	−0.750257	−	0.750257i	−0.974527	+	0.224270i	$0.928000\pi$
$678$	10.2572	−	44.3060i	0.393926	−	1.70156i
$679$			31.7109i			1.21695i
$680$		0			0
$681$	17.6536	−	11.0163i	0.676487	−	0.422144i
$682$	18.6352	−	18.6352i	0.713578	−	0.713578i
$683$	−2.77487	+	2.77487i	−0.106177	+	0.106177i	−0.758200	−	0.652022i	$-0.773921\pi$
$683$	−2.77487	+	2.77487i	−0.106177	+	0.106177i	0.652022	+	0.758200i	$0.273921\pi$
$684$	6.72959	+	3.29237i	0.257312	+	0.125887i
$685$		0			0
$686$			25.5529i			0.975615i
$687$	10.7503	+	2.48879i	0.410149	+	0.0949531i
$688$	32.3414	+	32.3414i	1.23300	+	1.23300i
$689$	−6.04987			−0.230482
$690$		0			0
$691$	18.6443			0.709264			0.354632	−	0.935006i	$-0.384606\pi$
$691$	18.6443			0.709264			0.354632	+	0.935006i	$0.384606\pi$
$692$	0.309684	+	0.309684i	0.0117724	+	0.0117724i
$693$	7.08872	+	20.6687i	0.269278	+	0.785140i
$694$		−	49.9445i		−	1.89587i
$695$		0			0
$696$	13.8989	+	22.2730i	0.526836	+	0.844255i
$697$	10.6274	−	10.6274i	0.402543	−	0.402543i
$698$	−16.2743	+	16.2743i	−0.615993	+	0.615993i
$699$	−8.76340	−	14.0434i	−0.331462	−	0.531168i
$700$		0			0
$701$			15.5485i			0.587260i	0.955919	+	0.293630i	$0.0948634\pi$
$701$			15.5485i			0.587260i	−0.955919	+	0.293630i	$0.905137\pi$
$702$	6.20990	+	5.04746i	0.234378	+	0.190504i
$703$	−11.9164	−	11.9164i	−0.449436	−	0.449436i
$704$	15.2806			0.575909
$705$		0			0
$706$	54.8057			2.06264
$707$	−20.9581	−	20.9581i	−0.788212	−	0.788212i
$708$	−4.53565	−	1.05004i	−0.170460	−	0.0394630i
$709$			12.6610i			0.475495i	0.971327	+	0.237748i	$0.0764091\pi$
$709$			12.6610i			0.475495i	−0.971327	+	0.237748i	$0.923591\pi$
$710$		0			0
$711$	13.1006	−	26.7774i	0.491309	−	1.00423i
$712$	7.53216	−	7.53216i	0.282280	−	0.282280i
$713$	23.4672	−	23.4672i	0.878853	−	0.878853i
$714$	−45.7625	+	28.5569i	−1.71262	+	1.06872i
$715$		0			0
$716$		−	4.83406i		−	0.180657i
$717$	−5.93820	+	25.6500i	−0.221766	+	0.957918i
$718$	−22.7758	−	22.7758i	−0.849984	−	0.849984i
$719$	−32.8944			−1.22675			−0.613377	−	0.789790i	$-0.710190\pi$
$719$	−32.8944			−1.22675			−0.613377	+	0.789790i	$0.710190\pi$
$720$		0			0
$721$	−14.4415			−0.537830
$722$	28.4265	+	28.4265i	1.05793	+	1.05793i
$723$	1.29856	−	5.60911i	0.0482939	−	0.208605i
$724$		−	0.0665801i		−	0.00247443i
$725$		0			0
$726$	−10.2688	+	6.40798i	−0.381111	+	0.237822i
$727$	−10.4144	+	10.4144i	−0.386247	+	0.386247i	−0.873346	−	0.487100i	$-0.838055\pi$
$727$	−10.4144	+	10.4144i	−0.386247	+	0.386247i	0.487100	+	0.873346i	$0.338055\pi$
$728$	5.08007	−	5.08007i	0.188280	−	0.188280i
$729$	−5.51725	−	26.4303i	−0.204342	−	0.978899i
$730$		0			0
$731$		−	70.0938i		−	2.59251i
$732$	−2.79050	−	0.646024i	−0.103140	−	0.0238777i
$733$	−24.7309	−	24.7309i	−0.913458	−	0.913458i	0.0830846	−	0.996543i	$-0.473523\pi$
$733$	−24.7309	−	24.7309i	−0.913458	−	0.913458i	−0.996543	+	0.0830846i	$0.973523\pi$
$734$	−48.8831			−1.80431
$735$		0			0
$736$	−10.2437			−0.377586
$737$	−25.7926	−	25.7926i	−0.950082	−	0.950082i
$738$	−9.30645	+	3.19182i	−0.342575	+	0.117492i
$739$		−	18.4069i		−	0.677108i	−0.940947	−	0.338554i	$-0.890062\pi$
$739$		−	18.4069i		−	0.677108i	0.940947	−	0.338554i	$-0.109938\pi$
$740$		0			0
$741$	6.15817	+	9.86848i	0.226226	+	0.362528i
$742$	−18.8764	+	18.8764i	−0.692976	+	0.692976i
$743$	−29.4392	+	29.4392i	−1.08002	+	1.08002i	−0.0835140	+	0.996507i	$0.526614\pi$
$743$	−29.4392	+	29.4392i	−1.08002	+	1.08002i	−0.996507	+	0.0835140i	$0.973386\pi$
$744$	15.4774	+	24.8025i	0.567428	+	0.909304i
$745$		0			0
$746$		−	12.0723i		−	0.442000i
$747$	−4.96633	+	1.70329i	−0.181709	+	0.0623203i
$748$	4.71755	+	4.71755i	0.172491	+	0.172491i
$749$	−34.6778			−1.26710
$750$		0			0
$751$	33.9016			1.23709			0.618544	−	0.785750i	$-0.287723\pi$
$751$	33.9016			1.23709			0.618544	+	0.785750i	$0.287723\pi$
$752$	5.64151	+	5.64151i	0.205725	+	0.205725i
$753$	−23.3706	−	5.41049i	−0.851671	−	0.197169i
$754$		−	9.30971i		−	0.339040i
$755$		0			0
$756$	5.50662	−	0.568617i	0.200274	−	0.0206804i
$757$	−6.24285	+	6.24285i	−0.226900	+	0.226900i	−0.811396	−	0.584496i	$-0.801292\pi$
$757$	−6.24285	+	6.24285i	−0.226900	+	0.226900i	0.584496	+	0.811396i	$0.301292\pi$
$758$	−7.42212	+	7.42212i	−0.269584	+	0.269584i
$759$	18.4165	−	11.4923i	0.668477	−	0.417146i
$760$		0			0
$761$			12.8530i			0.465920i	0.972486	+	0.232960i	$0.0748411\pi$
$761$			12.8530i			0.465920i	−0.972486	+	0.232960i	$0.925159\pi$
$762$	−6.95185	+	30.0285i	−0.251839	+	1.08782i
$763$	2.56944	+	2.56944i	0.0930201	+	0.0930201i
$764$	−7.28360			−0.263511
$765$		0			0
$766$	−11.2291			−0.405724
$767$	−5.11141	−	5.11141i	−0.184562	−	0.184562i
$768$	3.37324	−	14.5707i	0.121721	−	0.525774i
$769$			31.2909i			1.12838i	0.825646	+	0.564189i	$0.190811\pi$
$769$			31.2909i			1.12838i	−0.825646	+	0.564189i	$0.809189\pi$
$770$		0			0
$771$	10.5389	−	6.57650i	0.379548	−	0.236847i
$772$	1.23457	−	1.23457i	0.0444333	−	0.0444333i
$773$	−18.8605	+	18.8605i	−0.678365	+	0.678365i	−0.959630	−	0.281265i	$-0.909246\pi$
$773$	−18.8605	+	18.8605i	−0.678365	+	0.678365i	0.281265	+	0.959630i	$0.409246\pi$
$774$	−20.1647	+	41.2165i	−0.724805	+	1.48150i
$775$		0			0
$776$			27.7525i			0.996257i
$777$	−12.1318	−	2.80862i	−0.435226	−	0.100759i
$778$	9.19244	+	9.19244i	0.329565	+	0.329565i
$779$	−14.3012			−0.512394
$780$		0			0
$781$	20.0196			0.716356
$782$	37.8939	+	37.8939i	1.35508	+	1.35508i
$783$	−19.8118	+	24.3745i	−0.708015	+	0.871072i
$784$		−	5.56806i		−	0.198859i
$785$		0			0
$786$	8.90572	+	14.2714i	0.317656	+	0.509045i
$787$	6.49071	−	6.49071i	0.231369	−	0.231369i	−0.581895	−	0.813264i	$-0.697689\pi$
$787$	6.49071	−	6.49071i	0.231369	−	0.231369i	0.813264	+	0.581895i	$0.197689\pi$
$788$	−3.57389	+	3.57389i	−0.127315	+	0.127315i
$789$	−24.5001	−	39.2614i	−0.872225	−	1.39774i
$790$		0			0
$791$		−	48.8474i		−	1.73681i
$792$	6.20385	+	18.0887i	0.220444	+	0.642754i
$793$	−3.14472	−	3.14472i	−0.111672	−	0.111672i
$794$	40.8199			1.44864
$795$		0			0
$796$	0.750338			0.0265950
$797$	−2.88338	−	2.88338i	−0.102135	−	0.102135i	0.654193	−	0.756328i	$-0.273008\pi$
$797$	−2.88338	−	2.88338i	−0.102135	−	0.102135i	−0.756328	+	0.654193i	$0.773008\pi$
$798$	50.0054	+	11.5767i	1.77017	+	0.409810i
$799$		−	12.2269i		−	0.432557i
$800$		0			0
$801$	11.4477	+	5.60067i	0.404485	+	0.197890i
$802$	−36.2858	+	36.2858i	−1.28130	+	1.28130i
$803$	−10.6647	+	10.6647i	−0.376349	+	0.376349i
$804$	−7.84008	+	4.89240i	−0.276498	+	0.172542i
$805$		0			0
$806$		−	10.3670i		−	0.365162i
$807$	−4.50448	+	19.4571i	−0.158565	+	0.684921i
$808$	−18.3420	−	18.3420i	−0.645268	−	0.645268i
$809$	−26.4145			−0.928685			−0.464343	−	0.885656i	$-0.653709\pi$
$809$	−26.4145			−0.928685			−0.464343	+	0.885656i	$0.653709\pi$
$810$		0			0
$811$	−8.96380			−0.314762			−0.157381	−	0.987538i	$-0.550305\pi$
$811$	−8.96380			−0.314762			−0.157381	+	0.987538i	$0.550305\pi$
$812$	−4.55391	−	4.55391i	−0.159811	−	0.159811i
$813$	9.93948	−	42.9335i	0.348593	−	1.50574i
$814$			9.82415i			0.344336i
$815$		0			0
$816$	−47.7629	+	29.8052i	−1.67203	+	1.04339i
$817$	−47.1622	+	47.1622i	−1.65000	+	1.65000i
$818$	−19.4103	+	19.4103i	−0.678664	+	0.678664i
$819$	7.72092	+	3.77737i	0.269791	+	0.131992i
$820$		0			0
$821$		−	27.0937i		−	0.945578i	−0.881176	−	0.472789i	$-0.843247\pi$
$821$		−	27.0937i		−	0.945578i	0.881176	−	0.472789i	$-0.156753\pi$
$822$	−14.3280	−	3.31706i	−0.499747	−	0.115696i
$823$	13.3278	+	13.3278i	0.464578	+	0.464578i	0.900153	−	0.435574i	$-0.143455\pi$
$823$	13.3278	+	13.3278i	0.464578	+	0.464578i	−0.435574	+	0.900153i	$0.643455\pi$
$824$	−12.6388			−0.440294
$825$		0			0
$826$	−31.8966			−1.10982
$827$	9.54808	+	9.54808i	0.332019	+	0.332019i	0.853353	−	0.521334i	$-0.174565\pi$
$827$	9.54808	+	9.54808i	0.332019	+	0.332019i	−0.521334	+	0.853353i	$0.674565\pi$
$828$	−1.78424	−	5.20234i	−0.0620066	−	0.180794i
$829$		−	46.0936i		−	1.60090i	−0.599401	−	0.800449i	$-0.704594\pi$
$829$		−	46.0936i		−	1.60090i	0.599401	−	0.800449i	$-0.295406\pi$
$830$		0			0
$831$	27.3951	+	43.9008i	0.950327	+	1.52290i
$832$	4.25040	−	4.25040i	0.147356	−	0.147356i
$833$	−6.03385	+	6.03385i	−0.209061	+	0.209061i
$834$	9.76473	+	15.6480i	0.338125	+	0.541846i
$835$		0			0
$836$		−	6.34834i		−	0.219562i
$837$	−22.0618	+	27.1427i	−0.762566	+	0.938187i
$838$	−9.26830	−	9.26830i	−0.320168	−	0.320168i
$839$	49.7092			1.71615			0.858075	−	0.513524i	$-0.171660\pi$
$839$	49.7092			1.71615			0.858075	+	0.513524i	$0.171660\pi$
$840$		0			0
$841$	7.54150			0.260052
$842$	−27.1154	−	27.1154i	−0.934458	−	0.934458i
$843$	−5.13435	−	1.18865i	−0.176836	−	0.0409391i
$844$			6.87336i			0.236591i
$845$		0			0
$846$	−3.51745	+	7.18965i	−0.120933	+	0.247185i
$847$	−9.19308	+	9.19308i	−0.315878	+	0.315878i
$848$	−19.7015	+	19.7015i	−0.676554	+	0.676554i
$849$	−25.7847	+	16.0903i	−0.884930	+	0.552218i
$850$		0			0
$851$			12.3715i			0.424089i
$852$	1.14396	−	4.94132i	0.0391914	−	0.169287i
$853$	2.33952	+	2.33952i	0.0801037	+	0.0801037i	0.746023	−	0.665920i	$-0.231961\pi$
$853$	2.33952	+	2.33952i	0.0801037	+	0.0801037i	−0.665920	+	0.746023i	$0.731961\pi$
$854$	−19.6239			−0.671517
$855$		0			0
$856$	−30.3491			−1.03731
$857$	2.58902	+	2.58902i	0.0884391	+	0.0884391i	0.749942	−	0.661503i	$-0.230081\pi$
$857$	2.58902	+	2.58902i	0.0884391	+	0.0884391i	−0.661503	+	0.749942i	$0.730081\pi$
$858$	1.52943	−	6.60636i	0.0522138	−	0.225537i
$859$		−	15.0346i		−	0.512974i	−0.966548	−	0.256487i	$-0.917435\pi$
$859$		−	15.0346i		−	0.512974i	0.966548	−	0.256487i	$-0.0825651\pi$
$860$		0			0
$861$	−8.96520	+	5.59450i	−0.305533	+	0.190660i
$862$	23.4371	−	23.4371i	0.798272	−	0.798272i
$863$	0.333239	−	0.333239i	0.0113436	−	0.0113436i	−0.701412	−	0.712756i	$-0.747447\pi$
$863$	0.333239	−	0.333239i	0.0113436	−	0.0113436i	0.712756	+	0.701412i	$0.247447\pi$
$864$	10.7391	−	1.10893i	0.365352	−	0.0377265i
$865$		0			0
$866$		−	21.3693i		−	0.726158i
$867$	55.3709	+	12.8188i	1.88049	+	0.435350i
$868$	−5.07109	−	5.07109i	−0.172124	−	0.172124i
$869$	−25.2604			−0.856902
$870$		0			0
$871$	−14.3488			−0.486189
$872$	2.24870	+	2.24870i	0.0761507	+	0.0761507i
$873$	−31.4077	+	10.7718i	−1.06299	+	0.364571i
$874$		−	50.9933i		−	1.72487i
$875$		0			0
$876$	2.02291	+	3.24172i	0.0683478	+	0.109527i
$877$	−38.0820	+	38.0820i	−1.28594	+	1.28594i	−0.348704	+	0.937233i	$0.613378\pi$
$877$	−38.0820	+	38.0820i	−1.28594	+	1.28594i	−0.937233	+	0.348704i	$0.886622\pi$
$878$	8.62212	−	8.62212i	0.290982	−	0.290982i
$879$	17.4367	+	27.9423i	0.588124	+	0.942470i
$880$		0			0
$881$		−	28.6553i		−	0.965420i	−0.875780	−	0.482710i	$-0.839652\pi$
$881$		−	28.6553i		−	0.965420i	0.875780	−	0.482710i	$-0.160348\pi$
$882$	5.28385	−	1.81219i	0.177916	−	0.0610197i
$883$	23.6027	+	23.6027i	0.794294	+	0.794294i	0.982189	−	0.187895i	$-0.0601666\pi$
$883$	23.6027	+	23.6027i	0.794294	+	0.794294i	−0.187895	+	0.982189i	$0.560167\pi$
$884$	2.62443			0.0882693
$885$		0			0
$886$	−30.5061			−1.02487
$887$	0.423510	+	0.423510i	0.0142201	+	0.0142201i	0.714181	−	0.699961i	$-0.246799\pi$
$887$	0.423510	+	0.423510i	0.0142201	+	0.0142201i	−0.699961	+	0.714181i	$0.746799\pi$
$888$	−10.6174	−	2.45802i	−0.356297	−	0.0824859i
$889$			33.1064i			1.11035i
$890$		0			0
$891$	−18.0631	+	14.0419i	−0.605138	+	0.470420i
$892$	5.00839	−	5.00839i	0.167693	−	0.167693i
$893$	−8.22679	+	8.22679i	−0.275299	+	0.275299i
$894$	34.1206	−	21.2921i	1.14116	−	0.712113i
$895$		0			0
$896$		−	38.4296i		−	1.28384i
$897$	1.92600	−	8.31935i	0.0643073	−	0.277775i
$898$	−40.4032	−	40.4032i	−1.34827	−	1.34827i
$899$	40.6915			1.35714
$900$		0			0
$901$	42.6994			1.42252
$902$	5.89511	+	5.89511i	0.196286	+	0.196286i
$903$	−11.1158	+	48.0147i	−0.369911	+	1.59783i
$904$		−	42.7499i		−	1.42184i
$905$		0			0
$906$	51.9424	−	32.4133i	1.72567	−	1.07686i
$907$	25.5002	−	25.5002i	0.846719	−	0.846719i	−0.143004	−	0.989722i	$-0.545676\pi$
$907$	25.5002	−	25.5002i	0.846719	−	0.846719i	0.989722	+	0.143004i	$0.0456760\pi$
$908$	−3.15887	+	3.15887i	−0.104831	+	0.104831i
$909$	13.6385	−	27.8770i	0.452360	−	0.924620i
$910$		0			0
$911$			27.4361i			0.909000i	0.890747	+	0.454500i	$0.150182\pi$
$911$			27.4361i			0.909000i	−0.890747	+	0.454500i	$0.849818\pi$
$912$	52.1912	+	12.0827i	1.72822	+	0.400098i
$913$	3.14589	+	3.14589i	0.104114	+	0.104114i
$914$	−24.6223			−0.814434
$915$		0			0
$916$	−2.36896			−0.0782726
$917$	12.7764	+	12.7764i	0.421914	+	0.421914i
$918$	−43.8289	−	35.6245i	−1.44657	−	1.17578i
$919$		−	7.41415i		−	0.244570i	−0.992495	−	0.122285i	$-0.960978\pi$
$919$		−	7.41415i		−	0.244570i	0.992495	−	0.122285i	$-0.0390222\pi$
$920$		0			0
$921$	7.15868	+	11.4718i	0.235887	+	0.378009i
$922$	34.0753	−	34.0753i	1.12221	−	1.12221i
$923$	5.56858	−	5.56858i	0.183292	−	0.183292i
$924$	−2.48341	−	3.97967i	−0.0816983	−	0.130922i
$925$		0			0
$926$			5.96800i			0.196121i
$927$	−4.90562	−	14.3034i	−0.161122	−	0.469786i
$928$	−8.88112	−	8.88112i	−0.291537	−	0.291537i
$929$	18.8254			0.617643			0.308821	−	0.951120i	$-0.400066\pi$
$929$	18.8254			0.617643			0.308821	+	0.951120i	$0.400066\pi$
$930$		0			0
$931$	8.11968			0.266112
$932$	2.51287	+	2.51287i	0.0823118	+	0.0823118i
$933$	11.4513	+	2.65107i	0.374898	+	0.0867921i
$934$			56.9037i			1.86195i
$935$		0			0
$936$	6.75714	+	3.30585i	0.220864	+	0.108055i
$937$	20.2784	−	20.2784i	0.662467	−	0.662467i	−0.293494	−	0.955961i	$-0.594818\pi$
$937$	20.2784	−	20.2784i	0.662467	−	0.662467i	0.955961	+	0.293494i	$0.0948180\pi$
$938$	−44.7701	+	44.7701i	−1.46180	+	1.46180i
$939$	10.8415	−	6.76535i	0.353798	−	0.220779i
$940$		0			0
$941$			8.10981i			0.264372i	0.991225	+	0.132186i	$0.0421997\pi$
$941$			8.10981i			0.264372i	−0.991225	+	0.132186i	$0.957800\pi$
$942$	12.4392	−	53.7309i	0.405290	−	1.75065i
$943$	7.42368	+	7.42368i	0.241748	+	0.241748i
$944$	−33.2909			−1.08352
$945$		0			0
$946$	38.8815			1.26415
$947$	5.56915	+	5.56915i	0.180973	+	0.180973i	0.791780	−	0.610807i	$-0.209155\pi$
$947$	5.56915	+	5.56915i	0.180973	+	0.180973i	−0.610807	+	0.791780i	$0.709155\pi$
$948$	−1.44343	+	6.23490i	−0.0468805	+	0.202500i
$949$			5.93292i			0.192591i
$950$		0			0
$951$	18.1001	−	11.2949i	0.586937	−	0.366263i
$952$	−35.8546	+	35.8546i	−1.16205	+	1.16205i
$953$	−20.1301	+	20.1301i	−0.652078	+	0.652078i	−0.953493	−	0.301415i	$-0.902541\pi$
$953$	−20.1301	+	20.1301i	−0.652078	+	0.652078i	0.301415	+	0.953493i	$0.402541\pi$
$954$	−25.1080	−	12.2838i	−0.812903	−	0.397703i
$955$		0			0
$956$		−	5.65229i		−	0.182808i
$957$	25.9306	+	6.00315i	0.838216	+	0.194054i
$958$	−21.5795	−	21.5795i	−0.697203	−	0.697203i
$959$	−15.7966			−0.510100
$960$		0			0
$961$	14.3128			0.461703
$962$	2.73265	+	2.73265i	0.0881043	+	0.0881043i
$963$	−11.7797	−	34.3462i	−0.379594	−	1.10679i
$964$			1.23604i			0.0398100i
$965$		0			0
$966$	−19.9481	−	31.9669i	−0.641820	−	1.02852i
$967$	−16.8281	+	16.8281i	−0.541154	+	0.541154i	−0.923867	−	0.382713i	$-0.874990\pi$
$967$	−16.8281	+	16.8281i	−0.541154	+	0.541154i	0.382713	+	0.923867i	$0.374990\pi$
$968$	−8.04553	+	8.04553i	−0.258593	+	0.258593i
$969$	−43.4637	−	69.6507i	−1.39626	−	2.23750i
$970$		0			0
$971$			31.1570i			0.999876i	0.866061	+	0.499938i	$0.166644\pi$
$971$			31.1570i			0.999876i	−0.866061	+	0.499938i	$0.833356\pi$
$972$	2.43371	+	5.26081i	0.0780614	+	0.168740i
$973$	14.0088	+	14.0088i	0.449101	+	0.449101i
$974$	−45.3135			−1.45194
$975$		0			0
$976$	−20.4817			−0.655604
$977$	14.2012	+	14.2012i	0.454336	+	0.454336i	0.896791	−	0.442455i	$-0.145892\pi$
$977$	14.2012	+	14.2012i	0.454336	+	0.454336i	−0.442455	+	0.896791i	$0.645892\pi$
$978$	10.9584	+	2.53695i	0.350410	+	0.0811228i
$979$		−	10.7992i		−	0.345143i
$980$		0			0
$981$	−1.67206	+	3.41768i	−0.0533848	+	0.109118i
$982$	−11.3588	+	11.3588i	−0.362475	+	0.362475i
$983$	8.30773	−	8.30773i	0.264975	−	0.264975i	−0.562096	−	0.827072i	$-0.690005\pi$
$983$	8.30773	−	8.30773i	0.264975	−	0.264975i	0.827072	+	0.562096i	$0.190005\pi$
$984$	−7.84609	+	4.89615i	−0.250124	+	0.156084i
$985$		0			0
$986$			65.7070i			2.09254i
$987$	−1.93900	+	8.37549i	−0.0617190	+	0.266595i
$988$	−1.76583	−	1.76583i	−0.0561787	−	0.0561787i
$989$	48.9633			1.55694
$990$		0			0
$991$	−14.6031			−0.463883			−0.231941	−	0.972730i	$-0.574508\pi$
$991$	−14.6031			−0.463883			−0.231941	+	0.972730i	$0.574508\pi$
$992$	−9.88974	−	9.88974i	−0.314000	−	0.314000i
$993$	−12.5230	+	54.0929i	−0.397405	+	1.71659i
$994$		−	34.7494i		−	1.10219i
$995$		0			0
$996$	0.956246	−	0.596721i	0.0302998	−	0.0189078i
$997$	38.9943	−	38.9943i	1.23496	−	1.23496i	0.272925	−	0.962035i	$-0.412009\pi$
$997$	38.9943	−	38.9943i	1.23496	−	1.23496i	0.962035	−	0.272925i	$-0.0879912\pi$
$998$	−0.944184	+	0.944184i	−0.0298876	+	0.0298876i
$999$	−1.33928	−	12.9699i	−0.0423728	−	0.410348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.m.b.443.5	✓	32
3.2	odd	2		975.2.m.c.443.12	yes	32
5.2	odd	4		975.2.m.c.482.12	yes	32
5.3	odd	4		975.2.m.c.482.5	yes	32
5.4	even	2	inner	975.2.m.b.443.12	yes	32
15.2	even	4	inner	975.2.m.b.482.5	yes	32
15.8	even	4	inner	975.2.m.b.482.12	yes	32
15.14	odd	2		975.2.m.c.443.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.m.b.443.5	✓	32	1.1	even	1	trivial
975.2.m.b.443.12	yes	32	5.4	even	2	inner
975.2.m.b.482.5	yes	32	15.2	even	4	inner
975.2.m.b.482.12	yes	32	15.8	even	4	inner
975.2.m.c.443.5	yes	32	15.14	odd	2
975.2.m.c.443.12	yes	32	3.2	odd	2
975.2.m.c.482.5	yes	32	5.3	odd	4
975.2.m.c.482.12	yes	32	5.2	odd	4

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

\(f(q)\)	\(=\)	\(q+(-1.08900 - 1.08900i) q^{2} +(0.390653 - 1.68742i) q^{3} +0.371844i q^{4} +(-2.26302 + 1.41218i) q^{6} +(-2.02596 + 2.02596i) q^{7} +(-1.77306 + 1.77306i) q^{8} +(-2.69478 - 1.31839i) q^{9} +2.54212i q^{11} +(0.627457 + 0.145262i) q^{12} +(0.707107 + 0.707107i) q^{13} +4.41254 q^{14} +4.60542 q^{16} +(-4.99069 - 4.99069i) q^{17} +(1.49889 + 4.37035i) q^{18} +6.71590i q^{19} +(2.62720 + 4.21009i) q^{21} +(2.76837 - 2.76837i) q^{22} +(3.48619 - 3.48619i) q^{23} +(2.29925 + 3.68456i) q^{24} -1.54008i q^{26} +(-3.27740 + 4.03220i) q^{27} +(-0.753340 - 0.753340i) q^{28} +6.04496 q^{29} +6.73148 q^{31} +(-1.46918 - 1.46918i) q^{32} +(4.28962 + 0.993084i) q^{33} +10.8697i q^{34} +(0.490235 - 1.00204i) q^{36} +(-1.77436 + 1.77436i) q^{37} +(7.31362 - 7.31362i) q^{38} +(1.46942 - 0.916954i) q^{39} +2.12945i q^{41} +(1.72377 - 7.44582i) q^{42} +(7.02247 + 7.02247i) q^{43} -0.945270 q^{44} -7.59292 q^{46} +(1.22497 + 1.22497i) q^{47} +(1.79912 - 7.77128i) q^{48} -1.20902i q^{49} +(-10.3710 + 6.47177i) q^{51} +(-0.262933 + 0.262933i) q^{52} +(-4.27790 + 4.27790i) q^{53} +(7.96016 - 0.821971i) q^{54} -7.18431i q^{56} +(11.3326 + 2.62358i) q^{57} +(-6.58296 - 6.58296i) q^{58} -7.22862 q^{59} -4.44731 q^{61} +(-7.33058 - 7.33058i) q^{62} +(8.13052 - 2.78851i) q^{63} -6.01097i q^{64} +(-3.58993 - 5.75287i) q^{66} +(-10.1461 + 10.1461i) q^{67} +(1.85576 - 1.85576i) q^{68} +(-4.52078 - 7.24456i) q^{69} -7.87516i q^{71} +(7.11561 - 2.44043i) q^{72} +(4.19521 + 4.19521i) q^{73} +3.86455 q^{74} -2.49727 q^{76} +(-5.15022 - 5.15022i) q^{77} +(-2.59876 - 0.601636i) q^{78} +9.93677i q^{79} +(5.52369 + 7.10555i) q^{81} +(2.31898 - 2.31898i) q^{82} +(1.23751 - 1.23751i) q^{83} +(-1.56550 + 0.976908i) q^{84} -15.2949i q^{86} +(2.36148 - 10.2004i) q^{87} +(-4.50733 - 4.50733i) q^{88} -4.24811 q^{89} -2.86514 q^{91} +(1.29632 + 1.29632i) q^{92} +(2.62967 - 11.3588i) q^{93} -2.66799i q^{94} +(-3.05306 + 1.90518i) q^{96} +(7.82615 - 7.82615i) q^{97} +(-1.31663 + 1.31663i) q^{98} +(3.35150 - 6.85045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{6} - 32 q^{9} + 80 q^{14} - 8 q^{16} + 4 q^{21} + 16 q^{24} + 24 q^{31} - 16 q^{36} + 4 q^{39} - 16 q^{44} - 32 q^{46} + 40 q^{51} + 112 q^{54} - 72 q^{59} - 32 q^{66} - 40 q^{69} - 256 q^{74}+ \cdots - 136 q^{96}+O(q^{100}) \) 32 * q + 12 * q^6 - 32 * q^9 + 80 * q^14 - 8 * q^16 + 4 * q^21 + 16 * q^24 + 24 * q^31 - 16 * q^36 + 4 * q^39 - 16 * q^44 - 32 * q^46 + 40 * q^51 + 112 * q^54 - 72 * q^59 - 32 * q^66 - 40 * q^69 - 256 * q^74 - 56 * q^76 + 12 * q^81 + 152 * q^84 + 24 * q^89 - 8 * q^91 - 136 * q^96

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