LMFDB - Embedded newform 819.2.fm.g.370.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(370,819)] 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("819.370"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 5])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$819 = 3^{2} \cdot 7 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	819.fm (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [32,8,0,-12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			370.8
Character	$\chi$	$=$	819.370
Dual form			819.2.fm.g.622.8

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.607529 + 2.26733i) q^{2} +(-3.03963 + 1.75493i) q^{4} +(1.12678 + 1.12678i) q^{5} +(1.68394 - 2.04067i) q^{7} +(-2.50608 - 2.50608i) q^{8} +(-1.87023 + 3.23933i) q^{10} +(3.03446 - 0.813080i) q^{11} +(1.04831 + 3.44979i) q^{13} +(5.64992 + 2.57827i) q^{14} +(0.649718 - 1.12534i) q^{16} +(0.320795 + 0.555633i) q^{17} +(-2.04036 + 7.61472i) q^{19} +(-5.40242 - 1.44757i) q^{20} +(3.68704 + 6.38614i) q^{22} +(0.126569 + 0.0730744i) q^{23} -2.46074i q^{25} +(-7.18493 + 4.47270i) q^{26} +(-1.53731 + 9.15811i) q^{28} +(-1.49412 + 2.58790i) q^{29} +(-4.73334 - 4.73334i) q^{31} +(-3.90048 - 1.04513i) q^{32} +(-1.06491 + 1.06491i) q^{34} +(4.19682 - 0.401964i) q^{35} +(3.75725 - 1.00675i) q^{37} -18.5046 q^{38} -5.64759i q^{40} +(5.60356 - 1.50147i) q^{41} +(2.42713 - 1.40130i) q^{43} +(-7.79674 + 7.79674i) q^{44} +(-0.0887896 + 0.331367i) q^{46} +(-2.22937 + 2.22937i) q^{47} +(-1.32871 - 6.87274i) q^{49} +(5.57930 - 1.49497i) q^{50} +(-9.24062 - 8.64639i) q^{52} +7.32119 q^{53} +(4.33533 + 2.50300i) q^{55} +(-9.33417 + 0.894011i) q^{56} +(-6.77534 - 1.81545i) q^{58} +(-4.00631 - 1.07349i) q^{59} +(3.90292 - 2.25335i) q^{61} +(7.85639 - 13.6077i) q^{62} -12.0775i q^{64} +(-2.70594 + 5.06836i) q^{65} +(-0.366486 - 1.36775i) q^{67} +(-1.95020 - 1.12595i) q^{68} +(3.46107 + 9.27135i) q^{70} +(-13.8300 - 3.70574i) q^{71} +(-4.99083 + 4.99083i) q^{73} +(4.56527 + 7.90729i) q^{74} +(-7.16138 - 26.7267i) q^{76} +(3.45060 - 7.56152i) q^{77} -0.632916 q^{79} +(2.00010 - 0.535926i) q^{80} +(6.80865 + 11.7929i) q^{82} +(1.07813 + 1.07813i) q^{83} +(-0.264611 + 0.987541i) q^{85} +(4.65176 + 4.65176i) q^{86} +(-9.64223 - 5.56694i) q^{88} +(3.51557 + 13.1203i) q^{89} +(8.80518 + 3.66998i) q^{91} -0.512963 q^{92} +(-6.40911 - 3.70030i) q^{94} +(-10.8791 + 6.28107i) q^{95} +(-0.0487160 + 0.181811i) q^{97} +(14.7755 - 7.18800i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50}+ \cdots + 32 q^{98}+O(q^{100})$ 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8 + 4 * q^11 + 32 * q^14 + 12 * q^16 + 4 * q^22 + 12 * q^23 + 24 * q^28 - 4 * q^29 - 4 * q^32 + 20 * q^35 + 4 * q^37 - 48 * q^43 - 24 * q^44 + 84 * q^46 + 24 * q^49 + 44 * q^50 - 72 * q^53 - 60 * q^56 - 16 * q^58 - 4 * q^65 - 56 * q^67 + 56 * q^70 - 84 * q^71 + 24 * q^74 - 80 * q^79 + 36 * q^85 + 48 * q^86 - 228 * q^88 - 48 * q^91 - 24 * q^92 + 84 * q^95 + 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$ .

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.607529	+	2.26733i	0.429588	+	1.60324i	0.753696	+	0.657223i	$0.228269\pi$
$2$	0.607529	+	2.26733i	0.429588	+	1.60324i	−0.324108	+	0.946020i	$0.605064\pi$
$3$		0			0
$3$		0			0
$4$	−3.03963	+	1.75493i	−1.51982	+	0.877467i
$5$	1.12678	+	1.12678i	0.503911	+	0.503911i	0.912651	−	0.408740i	$-0.134032\pi$
$5$	1.12678	+	1.12678i	0.503911	+	0.503911i	−0.408740	+	0.912651i	$0.634032\pi$
$6$		0			0
$7$	1.68394	−	2.04067i	0.636469	−	0.771303i
$7$	1.68394	−	2.04067i	0.636469	−	0.771303i
$8$	−2.50608	−	2.50608i	−0.886032	−	0.886032i
$9$		0			0
$10$	−1.87023	+	3.23933i	−0.591418	+	1.02437i
$11$	3.03446	−	0.813080i	0.914923	−	0.245153i	0.229509	−	0.973306i	$-0.426288\pi$
$11$	3.03446	−	0.813080i	0.914923	−	0.245153i	0.685414	+	0.728154i	$0.259621\pi$
$12$		0			0
$13$	1.04831	+	3.44979i	0.290748	+	0.956800i
$13$	1.04831	+	3.44979i	0.290748	+	0.956800i
$14$	5.64992	+	2.57827i	1.51000	+	0.689072i
$15$		0			0
$16$	0.649718	−	1.12534i	0.162430	−	0.281336i
$17$	0.320795	+	0.555633i	0.0778042	+	0.134761i	0.902302	−	0.431104i	$-0.141876\pi$
$17$	0.320795	+	0.555633i	0.0778042	+	0.134761i	−0.824498	+	0.565865i	$0.808542\pi$
$18$		0			0
$19$	−2.04036	+	7.61472i	−0.468090	+	1.74694i	0.178346	+	0.983968i	$0.442925\pi$
$19$	−2.04036	+	7.61472i	−0.468090	+	1.74694i	−0.646436	+	0.762968i	$0.723741\pi$
$20$	−5.40242	−	1.44757i	−1.20802	−	0.323687i
$21$		0			0
$22$	3.68704	+	6.38614i	0.786080	+	1.36153i
$23$	0.126569	+	0.0730744i	0.0263914	+	0.0152371i	0.513138	−	0.858306i	$-0.328483\pi$
$23$	0.126569	+	0.0730744i	0.0263914	+	0.0152371i	−0.486746	+	0.873543i	$0.661816\pi$
$24$		0			0
$25$		−	2.46074i		−	0.492147i
$26$	−7.18493	+	4.47270i	−1.40908	+	0.877169i
$27$		0			0
$28$	−1.53731	+	9.15811i	−0.290523	+	1.73072i
$29$	−1.49412	+	2.58790i	−0.277452	+	0.480561i	−0.970751	−	0.240089i	$-0.922823\pi$
$29$	−1.49412	+	2.58790i	−0.277452	+	0.480561i	0.693299	+	0.720650i	$0.256157\pi$
$30$		0			0
$31$	−4.73334	−	4.73334i	−0.850132	−	0.850132i	0.140017	−	0.990149i	$-0.455284\pi$
$31$	−4.73334	−	4.73334i	−0.850132	−	0.850132i	−0.990149	+	0.140017i	$0.955284\pi$
$32$	−3.90048	−	1.04513i	−0.689514	−	0.184755i
$33$		0			0
$34$	−1.06491	+	1.06491i	−0.182631	+	0.182631i
$35$	4.19682	−	0.401964i	0.709391	−	0.0679444i
$36$		0			0
$37$	3.75725	−	1.00675i	0.617688	−	0.165509i	0.0636115	−	0.997975i	$-0.479738\pi$
$37$	3.75725	−	1.00675i	0.617688	−	0.165509i	0.554077	+	0.832466i	$0.313071\pi$
$38$	−18.5046			−3.00185
$39$		0			0
$40$		−	5.64759i		−	0.892963i
$41$	5.60356	−	1.50147i	0.875129	−	0.234490i	0.206825	−	0.978378i	$-0.433687\pi$
$41$	5.60356	−	1.50147i	0.875129	−	0.234490i	0.668305	+	0.743888i	$0.267020\pi$
$42$		0			0
$43$	2.42713	−	1.40130i	0.370133	−	0.213697i	−0.303383	−	0.952869i	$-0.598116\pi$
$43$	2.42713	−	1.40130i	0.370133	−	0.213697i	0.673517	+	0.739172i	$0.264783\pi$
$44$	−7.79674	+	7.79674i	−1.17540	+	1.17540i
$45$		0			0
$46$	−0.0887896	+	0.331367i	−0.0130913	+	0.0488574i
$47$	−2.22937	+	2.22937i	−0.325187	+	0.325187i	−0.850753	−	0.525566i	$-0.823854\pi$
$47$	−2.22937	+	2.22937i	−0.325187	+	0.325187i	0.525566	+	0.850753i	$0.323854\pi$
$48$		0			0
$49$	−1.32871	−	6.87274i	−0.189815	−	0.981820i
$50$	5.57930	−	1.49497i	0.789032	−	0.211420i
$51$		0			0
$52$	−9.24062	−	8.64639i	−1.28144	−	1.19904i
$53$	7.32119			1.00564			0.502821	−	0.864390i	$-0.332295\pi$
$53$	7.32119			1.00564			0.502821	+	0.864390i	$0.332295\pi$
$54$		0			0
$55$	4.33533	+	2.50300i	0.584575	+	0.337505i
$56$	−9.33417	+	0.894011i	−1.24733	+	0.119467i
$57$		0			0
$58$	−6.77534	−	1.81545i	−0.889646	−	0.238380i
$59$	−4.00631	−	1.07349i	−0.521578	−	0.139756i	−0.0115814	−	0.999933i	$-0.503687\pi$
$59$	−4.00631	−	1.07349i	−0.521578	−	0.139756i	−0.509996	+	0.860177i	$0.670353\pi$
$60$		0			0
$61$	3.90292	−	2.25335i	0.499718	−	0.288512i	−0.228879	−	0.973455i	$-0.573506\pi$
$61$	3.90292	−	2.25335i	0.499718	−	0.288512i	0.728597	+	0.684942i	$0.240173\pi$
$62$	7.85639	−	13.6077i	0.997763	−	1.72818i
$63$		0			0
$64$		−	12.0775i		−	1.50969i
$65$	−2.70594	+	5.06836i	−0.335631	+	0.628653i
$66$		0			0
$67$	−0.366486	−	1.36775i	−0.0447734	−	0.167097i	0.939919	−	0.341397i	$-0.110900\pi$
$67$	−0.366486	−	1.36775i	−0.0447734	−	0.167097i	−0.984692	+	0.174301i	$0.944234\pi$
$68$	−1.95020	−	1.12595i	−0.236496	−	0.136541i
$69$		0			0
$70$	3.46107	+	9.27135i	0.413677	+	1.10814i
$71$	−13.8300	−	3.70574i	−1.64132	−	0.439791i	−0.684157	−	0.729335i	$-0.739830\pi$
$71$	−13.8300	−	3.70574i	−1.64132	−	0.439791i	−0.957165	+	0.289544i	$0.906496\pi$
$72$		0			0
$73$	−4.99083	+	4.99083i	−0.584133	+	0.584133i	−0.936036	−	0.351904i	$-0.885534\pi$
$73$	−4.99083	+	4.99083i	−0.584133	+	0.584133i	0.351904	+	0.936036i	$0.385534\pi$
$74$	4.56527	+	7.90729i	0.530702	+	0.919203i
$75$		0			0
$76$	−7.16138	−	26.7267i	−0.821467	−	3.06576i
$77$	3.45060	−	7.56152i	0.393233	−	0.861715i
$78$		0			0
$79$	−0.632916			−0.0712086			−0.0356043	−	0.999366i	$-0.511336\pi$
$79$	−0.632916			−0.0712086			−0.0356043	+	0.999366i	$0.511336\pi$
$80$	2.00010	−	0.535926i	0.223618	−	0.0599184i
$81$		0			0
$82$	6.80865	+	11.7929i	0.751890	+	1.30231i
$83$	1.07813	+	1.07813i	0.118340	+	0.118340i	0.763797	−	0.645457i	$-0.223333\pi$
$83$	1.07813	+	1.07813i	0.118340	+	0.118340i	−0.645457	+	0.763797i	$0.723333\pi$
$84$		0			0
$85$	−0.264611	+	0.987541i	−0.0287011	+	0.107114i
$86$	4.65176	+	4.65176i	0.501612	+	0.501612i
$87$		0			0
$88$	−9.64223	−	5.56694i	−1.02786	−	0.593438i
$89$	3.51557	+	13.1203i	0.372649	+	1.39075i	0.856749	+	0.515734i	$0.172481\pi$
$89$	3.51557	+	13.1203i	0.372649	+	1.39075i	−0.484099	+	0.875013i	$0.660853\pi$
$90$		0			0
$91$	8.80518	+	3.66998i	0.923034	+	0.384718i
$92$	−0.512963			−0.0534801
$93$		0			0
$94$	−6.40911	−	3.70030i	−0.661049	−	0.381657i
$95$	−10.8791	+	6.28107i	−1.11618	+	0.644425i
$96$		0			0
$97$	−0.0487160	+	0.181811i	−0.00494637	+	0.0184601i	−0.968355	−	0.249577i	$-0.919708\pi$
$97$	−0.0487160	+	0.181811i	−0.00494637	+	0.0184601i	0.963409	+	0.268037i	$0.0863750\pi$
$98$	14.7755	−	7.18800i	1.49255	−	0.726098i
$99$		0			0
$100$	4.31843	+	7.47974i	0.431843	+	0.747974i
$101$	−0.596904	+	1.03387i	−0.0593942	+	0.102874i	−0.894194	−	0.447680i	$-0.852250\pi$
$101$	−0.596904	+	1.03387i	−0.0593942	+	0.102874i	0.834799	+	0.550554i	$0.185584\pi$
$102$		0			0
$103$	−4.79583			−0.472548			−0.236274	−	0.971687i	$-0.575926\pi$
$103$	−4.79583			−0.472548			−0.236274	+	0.971687i	$0.575926\pi$
$104$	6.01830	−	11.2726i	0.590143	−	1.10537i
$105$		0			0
$106$	4.44783	+	16.5995i	0.432012	+	1.61229i
$107$	7.64819	−	13.2471i	0.739378	−	1.28064i	−0.213397	−	0.976966i	$-0.568453\pi$
$107$	7.64819	−	13.2471i	0.739378	−	1.28064i	0.952776	−	0.303675i	$-0.0982138\pi$
$108$		0			0
$109$	9.12415	−	9.12415i	0.873935	−	0.873935i	−0.118963	−	0.992899i	$-0.537957\pi$
$109$	9.12415	−	9.12415i	0.873935	−	0.873935i	0.992899	+	0.118963i	$0.0379571\pi$
$110$	−3.04129	+	11.3503i	−0.289976	+	1.08220i
$111$		0			0
$112$	−1.20238	−	3.22087i	−0.113614	−	0.304344i
$113$	0.770731	+	1.33494i	0.0725042	+	0.125581i	0.899998	−	0.435894i	$-0.143568\pi$
$113$	0.770731	+	1.33494i	0.0725042	+	0.125581i	−0.827494	+	0.561475i	$0.810234\pi$
$114$		0			0
$115$	0.0602761	+	0.224953i	0.00562078	+	0.0209770i
$116$		−	10.4884i		−	0.973819i
$117$		0			0
$118$		−	9.73580i		−	0.896253i
$119$	1.67407	+	0.281013i	0.153461	+	0.0257605i
$120$		0			0
$121$	−0.979449	+	0.565485i	−0.0890408	+	0.0514077i
$122$	7.48023	+	7.48023i	0.677228	+	0.677228i
$123$		0			0
$124$	22.6943	+	6.08092i	2.03801	+	0.546083i
$125$	8.40660	−	8.40660i	0.751910	−	0.751910i
$126$		0			0
$127$	2.81842	+	1.62722i	0.250095	+	0.144392i	0.619808	−	0.784754i	$-0.287211\pi$
$127$	2.81842	+	1.62722i	0.250095	+	0.144392i	−0.369713	+	0.929146i	$0.620544\pi$
$128$	19.5827	−	5.24716i	1.73088	−	0.463788i
$129$		0			0
$130$	−13.1356	−	3.05608i	−1.15207	−	0.268036i
$131$		−	16.4678i		−	1.43880i	−0.694597	−	0.719400i	$-0.744417\pi$
$131$		−	16.4678i		−	1.43880i	0.694597	−	0.719400i	$-0.255583\pi$
$132$		0			0
$133$	12.1033	+	16.9864i	1.04949	+	1.47291i
$134$	2.87848	−	1.66189i	0.248663	−	0.143565i
$135$		0			0
$136$	0.588523	−	2.19640i	0.0504654	−	0.188339i
$137$	0.0978163	−	0.365056i	0.00835701	−	0.0311888i	−0.961621	−	0.274380i	$-0.911527\pi$
$137$	0.0978163	−	0.365056i	0.00835701	−	0.0311888i	0.969978	+	0.243191i	$0.0781942\pi$
$138$		0			0
$139$	8.52132	−	4.91978i	0.722769	−	0.417291i	−0.0930022	−	0.995666i	$-0.529646\pi$
$139$	8.52132	−	4.91978i	0.722769	−	0.417291i	0.815771	+	0.578375i	$0.196313\pi$
$140$	−12.0514	+	8.58696i	−1.01853	+	0.725731i
$141$		0			0
$142$		−	33.6085i		−	2.82037i
$143$	5.98600	+	9.61588i	0.500574	+	0.804121i
$144$		0			0
$145$	−4.59954	+	1.23244i	−0.381971	+	0.102349i
$146$	−14.3479	−	8.28378i	−1.18744	−	0.685570i
$147$		0			0
$148$	−9.65388	+	9.65388i	−0.793544	+	0.793544i
$149$	5.36436	+	1.43738i	0.439465	+	0.117754i	0.471766	−	0.881724i	$-0.343617\pi$
$149$	5.36436	+	1.43738i	0.439465	+	0.117754i	−0.0323006	+	0.999478i	$0.510283\pi$
$150$		0			0
$151$	3.35521	+	3.35521i	0.273043	+	0.273043i	0.830324	−	0.557281i	$-0.188155\pi$
$151$	3.35521	+	3.35521i	0.273043	+	0.273043i	−0.557281	+	0.830324i	$0.688155\pi$
$152$	24.1964	−	13.9698i	1.96258	−	1.13310i
$153$		0			0
$154$	19.2408	+	3.22981i	1.55047	+	0.260266i
$155$		−	10.6669i		−	0.856782i
$156$		0			0
$157$		−	12.6201i		−	1.00720i	−0.863938	−	0.503598i	$-0.832009\pi$
$157$		−	12.6201i		−	1.00720i	0.863938	−	0.503598i	$-0.167991\pi$
$158$	−0.384515	−	1.43503i	−0.0305904	−	0.114165i
$159$		0			0
$160$	−3.21735	−	5.57262i	−0.254354	−	0.440554i
$161$	0.362255	−	0.135233i	0.0285497	−	0.0106578i
$162$		0			0
$163$	−3.37843	+	12.6085i	−0.264619	+	0.987571i	0.697864	+	0.716230i	$0.254134\pi$
$163$	−3.37843	+	12.6085i	−0.264619	+	0.987571i	−0.962483	+	0.271341i	$0.912533\pi$
$164$	−14.3978	+	14.3978i	−1.12428	+	1.12428i
$165$		0			0
$166$	−1.78948	+	3.09948i	−0.138891	+	0.240566i
$167$	−4.79697	−	17.9025i	−0.371201	−	1.38534i	−0.858817	−	0.512282i	$-0.828800\pi$
$167$	−4.79697	−	17.9025i	−0.371201	−	1.38534i	0.487616	−	0.873058i	$-0.337867\pi$
$168$		0			0
$169$	−10.8021	+	7.23288i	−0.830931	+	0.556375i
$170$	−2.39984			−0.184059
$171$		0			0
$172$	−4.91839	+	8.51890i	−0.375024	+	0.649560i
$173$	−2.79684	−	4.84427i	−0.212640	−	0.368303i	0.739900	−	0.672717i	$-0.234873\pi$
$173$	−2.79684	−	4.84427i	−0.212640	−	0.368303i	−0.952540	+	0.304414i	$0.901540\pi$
$174$		0			0
$175$	−5.02156	−	4.14373i	−0.379595	−	0.313236i
$176$	1.05655	−	3.94308i	0.0796402	−	0.297221i
$177$		0			0
$178$	−27.6122	+	15.9419i	−2.06962	+	1.19490i
$179$	−8.21928	−	4.74540i	−0.614338	−	0.354688i	0.160324	−	0.987065i	$-0.448746\pi$
$179$	−8.21928	−	4.74540i	−0.614338	−	0.354688i	−0.774661	+	0.632377i	$0.782080\pi$
$180$		0			0
$181$	−6.91516			−0.514000			−0.257000	−	0.966411i	$-0.582734\pi$
$181$	−6.91516			−0.514000			−0.257000	+	0.966411i	$0.582734\pi$
$182$	−2.97164	+	22.1939i	−0.220273	+	1.64512i
$183$		0			0
$184$	−0.134060	−	0.500321i	−0.00988307	−	0.0368841i
$185$	5.36798	+	3.09920i	0.394662	+	0.227858i
$186$		0			0
$187$	1.42521	+	1.42521i	0.104222	+	0.104222i
$188$	2.86407	−	10.6889i	0.208884	−	0.779565i
$189$		0			0
$190$	−20.8506	−	20.8506i	−1.51266	−	1.51266i
$191$	−1.25251	−	2.16942i	−0.0906287	−	0.156974i	0.817147	−	0.576429i	$-0.195554\pi$
$191$	−1.25251	−	2.16942i	−0.0906287	−	0.156974i	−0.907776	+	0.419456i	$0.862221\pi$
$192$		0			0
$193$	21.7882	−	5.83813i	1.56835	−	0.420238i	0.633054	−	0.774108i	$-0.281801\pi$
$193$	21.7882	−	5.83813i	1.56835	−	0.420238i	0.935295	+	0.353870i	$0.115134\pi$
$194$	−0.441821			−0.0317209
$195$		0			0
$196$	16.1000	+	18.5588i	1.15000	+	1.32563i
$197$	4.63560	+	17.3003i	0.330273	+	1.23259i	0.908904	+	0.417005i	$0.136920\pi$
$197$	4.63560	+	17.3003i	0.330273	+	1.23259i	−0.578631	+	0.815589i	$0.696413\pi$
$198$		0			0
$199$	8.20617	+	14.2135i	0.581720	+	1.00757i	0.995276	+	0.0970896i	$0.0309533\pi$
$199$	8.20617	+	14.2135i	0.581720	+	1.00757i	−0.413556	+	0.910479i	$0.635713\pi$
$200$	−6.16680	+	6.16680i	−0.436058	+	0.436058i
$201$		0			0
$202$	−2.70675	−	0.725273i	−0.190447	−	0.0510300i
$203$	2.76505	+	7.40688i	0.194068	+	0.519861i
$204$		0			0
$205$	8.00580	+	4.62215i	0.559150	+	0.322825i
$206$	−2.91361	−	10.8737i	−0.203001	−	0.757609i
$207$		0			0
$208$	4.56331	+	1.06169i	0.316408	+	0.0736146i
$209$			24.7655i			1.71307i
$210$		0			0
$211$	4.93176	−	8.54207i	0.339517	−	0.588060i	−0.644825	−	0.764330i	$-0.723070\pi$
$211$	4.93176	−	8.54207i	0.339517	−	0.588060i	0.984342	+	0.176270i	$0.0564032\pi$
$212$	−22.2537	+	12.8482i	−1.52839	+	0.882418i
$213$		0			0
$214$	34.6819	+	9.29299i	2.37081	+	0.635256i
$215$	4.31380	+	1.15588i	0.294198	+	0.0788302i
$216$		0			0
$217$	−17.6298	+	1.68856i	−1.19679	+	0.114627i
$218$	26.2306	+	15.1443i	1.77656	+	1.02570i
$219$		0			0
$220$	−17.5704			−1.18460
$221$	−1.58053	+	1.68915i	−0.106318	+	0.113624i
$222$		0			0
$223$	8.41926	−	2.25594i	0.563796	−	0.151069i	0.0343461	−	0.999410i	$-0.489065\pi$
$223$	8.41926	−	2.25594i	0.563796	−	0.151069i	0.529450	+	0.848341i	$0.322398\pi$
$224$	−8.70094	+	6.19968i	−0.581356	+	0.414234i
$225$		0			0
$226$	−2.55852	+	2.55852i	−0.170190	+	0.170190i
$227$	4.37226	−	16.3175i	0.290197	−	1.08303i	−0.654760	−	0.755837i	$-0.727230\pi$
$227$	4.37226	−	16.3175i	0.290197	−	1.08303i	0.944957	−	0.327194i	$-0.106103\pi$
$228$		0			0
$229$	−1.72909	+	1.72909i	−0.114262	+	0.114262i	−0.761926	−	0.647664i	$-0.775746\pi$
$229$	−1.72909	+	1.72909i	−0.114262	+	0.114262i	0.647664	+	0.761926i	$0.275746\pi$
$230$	−0.473424	+	0.273331i	−0.0312166	+	0.0180229i
$231$		0			0
$232$	10.2299	−	2.74108i	0.671624	−	0.179961i
$233$		−	5.37483i		−	0.352117i	−0.984380	−	0.176058i	$-0.943665\pi$
$233$		−	5.37483i		−	0.352117i	0.984380	−	0.176058i	$-0.0563348\pi$
$234$		0			0
$235$	−5.02401			−0.327730
$236$	14.0616	−	3.76780i	0.915334	−	0.245263i
$237$		0			0
$238$	0.379893	+	3.96638i	0.0246248	+	0.257102i
$239$	11.9572	−	11.9572i	0.773448	−	0.773448i	−0.205260	−	0.978708i	$-0.565804\pi$
$239$	11.9572	−	11.9572i	0.773448	−	0.773448i	0.978708	+	0.205260i	$0.0658038\pi$
$240$		0			0
$241$	−12.9893	−	3.48047i	−0.836713	−	0.224197i	−0.185073	−	0.982725i	$-0.559252\pi$
$241$	−12.9893	−	3.48047i	−0.836713	−	0.224197i	−0.651640	+	0.758528i	$0.725919\pi$
$242$	−1.87718	−	1.87718i	−0.120670	−	0.120670i
$243$		0			0
$244$	−7.90898	+	13.6987i	−0.506320	+	0.876972i
$245$	6.24690	−	9.24122i	0.399100	−	0.590400i
$246$		0			0
$247$	−28.4081	+	0.943754i	−1.80756	+	0.0600496i
$248$			23.7242i			1.50649i
$249$		0			0
$250$	24.1678	+	13.9533i	1.52850	+	0.882483i
$251$	6.40248	+	11.0894i	0.404121	+	0.699958i	0.994219	−	0.107374i	$-0.0342441\pi$
$251$	6.40248	+	11.0894i	0.404121	+	0.699958i	−0.590098	+	0.807332i	$0.700911\pi$
$252$		0			0
$253$	0.443482	+	0.118831i	0.0278815	+	0.00747082i
$254$	−1.97716	+	7.37887i	−0.124058	+	0.462992i
$255$		0			0
$256$	11.7166	+	20.2937i	0.732286	+	1.26836i
$257$	5.19036	−	8.98997i	0.323766	−	0.560779i	−0.657496	−	0.753458i	$-0.728384\pi$
$257$	5.19036	−	8.98997i	0.323766	−	0.560779i	0.981262	+	0.192679i	$0.0617176\pi$
$258$		0			0
$259$	4.27252	−	9.36263i	0.265482	−	0.581766i
$260$	−0.669566	−	20.1547i	−0.0415247	−	1.24994i
$261$		0			0
$262$	37.3379	−	10.0047i	2.30674	−	0.618090i
$263$	−2.18977	+	3.79279i	−0.135027	+	0.233873i	−0.925608	−	0.378484i	$-0.876445\pi$
$263$	−2.18977	+	3.79279i	−0.135027	+	0.233873i	0.790581	+	0.612358i	$0.209779\pi$
$264$		0			0
$265$	8.24936	+	8.24936i	0.506754	+	0.506754i
$266$	−31.1607	+	37.7620i	−1.91058	+	2.31533i
$267$		0			0
$268$	3.51429	+	3.51429i	0.214669	+	0.214669i
$269$	−10.1192	+	5.84233i	−0.616980	+	0.356213i	−0.775692	−	0.631112i	$-0.782599\pi$
$269$	−10.1192	+	5.84233i	−0.616980	+	0.356213i	0.158713	+	0.987325i	$0.449266\pi$
$270$		0			0
$271$	−7.94389	−	29.6470i	−0.482557	−	1.80093i	−0.590819	−	0.806804i	$-0.701195\pi$
$271$	−7.94389	−	29.6470i	−0.482557	−	1.80093i	0.108262	−	0.994122i	$-0.465471\pi$
$272$	0.833705			0.0505508
$273$		0			0
$274$	0.887127			0.0535933
$275$	−2.00078	−	7.46700i	−0.120651	−	0.450277i
$276$		0			0
$277$	−16.5109	+	9.53260i	−0.992047	+	0.572758i	−0.905885	−	0.423523i	$-0.860793\pi$
$277$	−16.5109	+	9.53260i	−0.992047	+	0.572758i	−0.0861613	+	0.996281i	$0.527460\pi$
$278$	16.3317	+	16.3317i	0.979511	+	0.979511i
$279$		0			0
$280$	−11.5249	−	9.51019i	−0.688745	−	0.568343i
$281$	−11.8671	−	11.8671i	−0.707931	−	0.707931i	0.258169	−	0.966100i	$-0.416881\pi$
$281$	−11.8671	−	11.8671i	−0.707931	−	0.707931i	−0.966100	+	0.258169i	$0.916881\pi$
$282$		0			0
$283$	−4.21864	+	7.30690i	−0.250772	+	0.434350i	−0.963739	−	0.266848i	$-0.914018\pi$
$283$	−4.21864	+	7.30690i	−0.250772	+	0.434350i	0.712966	+	0.701198i	$0.247351\pi$
$284$	48.5415	−	13.0067i	2.88041	−	0.771804i
$285$		0			0
$286$	−18.1657	+	19.4141i	−1.07416	+	1.14798i
$287$	6.37204	−	13.9634i	0.376129	−	0.824235i
$288$		0			0
$289$	8.29418	−	14.3659i	0.487893	−	0.845055i
$290$	−5.58870	−	9.67992i	−0.328180	−	0.568424i
$291$		0			0
$292$	6.41172	−	23.9289i	0.375218	−	1.40033i
$293$	−8.00676	−	2.14541i	−0.467760	−	0.125336i	0.0172376	−	0.999851i	$-0.494513\pi$
$293$	−8.00676	−	2.14541i	−0.467760	−	0.125336i	−0.484998	+	0.874516i	$0.661180\pi$
$294$		0			0
$295$	−3.30465	−	5.72382i	−0.192404	−	0.333253i
$296$	−11.9390	−	6.89296i	−0.693938	−	0.400645i
$297$		0			0
$298$			13.0360i			0.755156i
$299$	−0.119409	+	0.513239i	−0.00690558	+	0.0296814i
$300$		0			0
$301$	1.22753	−	7.31268i	0.0707535	−	0.421496i
$302$	−5.56897	+	9.64574i	−0.320458	+	0.555050i
$303$		0			0
$304$	7.24353	+	7.24353i	0.415445	+	0.415445i
$305$	6.93677	+	1.85870i	0.397198	+	0.106429i
$306$		0			0
$307$	17.3438	−	17.3438i	0.989863	−	0.989863i	−0.0100865	−	0.999949i	$-0.503211\pi$
$307$	17.3438	−	17.3438i	0.989863	−	0.989863i	0.999949	+	0.0100865i	$0.00321069\pi$
$308$	2.78139	+	29.0398i	0.158484	+	1.65470i
$309$		0			0
$310$	24.1853	−	6.48042i	1.37363	−	0.368063i
$311$	23.7121			1.34459			0.672294	−	0.740284i	$-0.265309\pi$
$311$	23.7121			1.34459			0.672294	+	0.740284i	$0.265309\pi$
$312$		0			0
$313$			14.0715i			0.795366i	0.917523	+	0.397683i	$0.130186\pi$
$313$			14.0715i			0.795366i	−0.917523	+	0.397683i	$0.869814\pi$
$314$	28.6140	−	7.66709i	1.61478	−	0.432679i
$315$		0			0
$316$	1.92383	−	1.11073i	0.108224	−	0.0624832i
$317$	−11.8369	+	11.8369i	−0.664828	+	0.664828i	−0.956514	−	0.291686i	$-0.905784\pi$
$317$	−11.8369	+	11.8369i	−0.664828	+	0.664828i	0.291686	+	0.956514i	$0.405784\pi$
$318$		0			0
$319$	−2.42969	+	9.06771i	−0.136036	+	0.507694i
$320$	13.6087	−	13.6087i	0.760748	−	0.760748i
$321$		0			0
$322$	0.526697	+	0.739192i	0.0293517	+	0.0411936i
$323$	−4.88553	+	1.30907i	−0.271838	+	0.0728388i
$324$		0			0
$325$	8.48903	−	2.57961i	0.470886	−	0.143091i
$326$	−30.6400			−1.69699
$327$		0			0
$328$	−17.8058	−	10.2802i	−0.983159	−	0.567627i
$329$	0.795298	+	8.30353i	0.0438462	+	0.457788i
$330$		0			0
$331$	9.34837	+	2.50489i	0.513833	+	0.137681i	0.506413	−	0.862291i	$-0.330971\pi$
$331$	9.34837	+	2.50489i	0.513833	+	0.137681i	0.00742049	+	0.999972i	$0.497638\pi$
$332$	−5.16918	−	1.38508i	−0.283696	−	0.0760160i
$333$		0			0
$334$	37.6766	−	21.7526i	2.06157	−	1.19025i
$335$	1.12820	−	1.95410i	0.0616401	−	0.106764i
$336$		0			0
$337$			20.0838i			1.09403i	0.837122	+	0.547016i	$0.184236\pi$
$337$			20.0838i			1.09403i	−0.837122	+	0.547016i	$0.815764\pi$
$338$	−22.9619	−	20.0977i	−1.24896	−	1.09317i
$339$		0			0
$340$	−0.928749	−	3.46614i	−0.0503685	−	0.187978i
$341$	−18.2117	−	10.5145i	−0.986218	−	0.569393i
$342$		0			0
$343$	−16.2625	−	8.86180i	−0.878092	−	0.478492i
$344$	−9.59434	−	2.57080i	−0.517292	−	0.138608i
$345$		0			0
$346$	9.28440	−	9.28440i	0.499132	−	0.499132i
$347$	−11.1008	−	19.2271i	−0.595920	−	1.03216i	−0.993416	−	0.114560i	$-0.963454\pi$
$347$	−11.1008	−	19.2271i	−0.595920	−	1.03216i	0.397496	−	0.917604i	$-0.369879\pi$
$348$		0			0
$349$	1.38593	+	5.17235i	0.0741869	+	0.276869i	0.993048	−	0.117713i	$-0.0375561\pi$
$349$	1.38593	+	5.17235i	0.0741869	+	0.276869i	−0.918861	+	0.394582i	$0.870889\pi$
$350$	6.34444	−	13.9030i	0.339125	−	0.743145i
$351$		0			0
$352$	−12.6856			−0.676146
$353$	−25.2105	+	6.75514i	−1.34182	+	0.359540i	−0.857110	−	0.515134i	$-0.827742\pi$
$353$	−25.2105	+	6.75514i	−1.34182	+	0.359540i	−0.484712	+	0.874674i	$0.661075\pi$
$354$		0			0
$355$	−11.4078	−	19.7589i	−0.605465	−	1.04870i
$356$	−33.7113	−	33.7113i	−1.78669	−	1.78669i
$357$		0			0
$358$	5.76594	−	21.5188i	0.304739	−	1.13730i
$359$	16.0116	+	16.0116i	0.845061	+	0.845061i	0.989512	−	0.144451i	$-0.0461416\pi$
$359$	16.0116	+	16.0116i	0.845061	+	0.845061i	−0.144451	+	0.989512i	$0.546142\pi$
$360$		0			0
$361$	−37.3664	−	21.5735i	−1.96665	−	1.13545i
$362$	−4.20116	−	15.6789i	−0.220808	−	0.824066i
$363$		0			0
$364$	−33.2051	+	4.29712i	−1.74042	+	0.225230i
$365$	−11.2471			−0.588702
$366$		0			0
$367$	−12.2942	−	7.09806i	−0.641752	−	0.370516i	0.143537	−	0.989645i	$-0.454152\pi$
$367$	−12.2942	−	7.09806i	−0.641752	−	0.370516i	−0.785289	+	0.619129i	$0.787486\pi$
$368$	0.164468	−	0.0949555i	0.00857347	−	0.00494990i
$369$		0			0
$370$	−3.76571	+	14.0538i	−0.195770	+	0.730624i
$371$	12.3284	−	14.9402i	0.640060	−	0.775655i
$372$		0			0
$373$	−1.75321	−	3.03665i	−0.0907778	−	0.157232i	0.817061	−	0.576551i	$-0.195602\pi$
$373$	−1.75321	−	3.03665i	−0.0907778	−	0.157232i	−0.907839	+	0.419320i	$0.862269\pi$
$374$	−2.36557	+	4.09728i	−0.122321	+	0.211865i
$375$		0			0
$376$	11.1739			0.576252
$377$	−10.4940	−	2.44150i	−0.540469	−	0.125744i
$378$		0			0
$379$	6.94797	+	25.9302i	0.356893	+	1.33194i	0.878085	+	0.478504i	$0.158821\pi$
$379$	6.94797	+	25.9302i	0.356893	+	1.33194i	−0.521192	+	0.853439i	$0.674513\pi$
$380$	22.0457	−	38.1843i	1.13092	−	1.95882i
$381$		0			0
$382$	4.15784	−	4.15784i	0.212734	−	0.212734i
$383$	8.83941	−	32.9891i	0.451673	−	1.68567i	−0.246017	−	0.969266i	$-0.579122\pi$
$383$	8.83941	−	32.9891i	0.451673	−	1.68567i	0.697690	−	0.716400i	$-0.254211\pi$
$384$		0			0
$385$	12.4082	−	4.63209i	0.632382	−	0.236073i
$386$	26.4739	+	45.8542i	1.34749	+	2.33392i
$387$		0			0
$388$	−0.170987	−	0.638132i	−0.00868054	−	0.0323962i
$389$			27.4644i			1.39250i	0.717798	+	0.696251i	$0.245150\pi$
$389$			27.4644i			1.39250i	−0.717798	+	0.696251i	$0.754850\pi$
$390$		0			0
$391$			0.0937676i			0.00474203i
$392$	−13.8938	+	20.5535i	−0.701741	+	1.03811i
$393$		0			0
$394$	−36.4092	+	21.0208i	−1.83427	+	1.05901i
$395$	−0.713157	−	0.713157i	−0.0358828	−	0.0358828i
$396$		0			0
$397$	−35.8032	−	9.59343i	−1.79691	−	0.481480i	−0.803420	−	0.595412i	$-0.796989\pi$
$397$	−35.8032	−	9.59343i	−1.79691	−	0.481480i	−0.993489	+	0.113932i	$0.963655\pi$
$398$	−27.2412	+	27.2412i	−1.36548	+	1.36548i
$399$		0			0
$400$	−2.76918	−	1.59879i	−0.138459	−	0.0799393i
$401$	16.7841	−	4.49729i	0.838158	−	0.224584i	0.185888	−	0.982571i	$-0.440484\pi$
$401$	16.7841	−	4.49729i	0.838158	−	0.224584i	0.652269	+	0.757987i	$0.273817\pi$
$402$		0			0
$403$	11.3670	−	21.2910i	0.566232	−	1.06058i
$404$		−	4.19011i		−	0.208466i
$405$		0			0
$406$	−15.1140	+	10.7692i	−0.750095	+	0.534465i
$407$	10.5826	−	6.10989i	0.524562	−	0.302856i
$408$		0			0
$409$	−2.92033	+	10.8988i	−0.144401	+	0.538913i	0.855380	+	0.518001i	$0.173324\pi$
$409$	−2.92033	+	10.8988i	−0.144401	+	0.538913i	−0.999781	+	0.0209119i	$0.993343\pi$
$410$	−5.61618	+	20.9599i	−0.277363	+	1.03513i
$411$		0			0
$412$	14.5776	−	8.41637i	0.718186	−	0.414645i
$413$	−8.93702	+	6.36790i	−0.439762	+	0.313344i
$414$		0			0
$415$			2.42963i			0.119266i
$416$	−0.483418	−	14.5515i	−0.0237015	−	0.713444i
$417$		0			0
$418$	−56.1515	+	15.0458i	−2.74646	+	0.735912i
$419$	16.1248	+	9.30964i	0.787747	+	0.454806i	0.839169	−	0.543871i	$-0.183042\pi$
$419$	16.1248	+	9.30964i	0.787747	+	0.454806i	−0.0514220	+	0.998677i	$0.516375\pi$
$420$		0			0
$421$	18.9024	−	18.9024i	0.921247	−	0.921247i	−0.0758709	−	0.997118i	$-0.524174\pi$
$421$	18.9024	−	18.9024i	0.921247	−	0.921247i	0.997118	+	0.0758709i	$0.0241737\pi$
$422$	22.3639	+	5.99238i	1.08866	+	0.291704i
$423$		0			0
$424$	−18.3475	−	18.3475i	−0.891032	−	0.891032i
$425$	1.36727	−	0.789392i	0.0663222	−	0.0382911i
$426$		0			0
$427$	1.97392	−	11.7591i	0.0955245	−	0.569063i
$428$			53.6883i			2.59512i
$429$		0			0
$430$			10.4830i			0.505536i
$431$	7.64079	+	28.5158i	0.368044	+	1.37356i	0.863247	+	0.504782i	$0.168427\pi$
$431$	7.64079	+	28.5158i	0.368044	+	1.37356i	−0.495203	+	0.868777i	$0.664906\pi$
$432$		0			0
$433$	−17.9660	−	31.1180i	−0.863390	−	1.49543i	−0.868637	−	0.495449i	$-0.835004\pi$
$433$	−17.9660	−	31.1180i	−0.863390	−	1.49543i	0.00524758	−	0.999986i	$-0.498330\pi$
$434$	−14.5392	−	38.9468i	−0.697902	−	1.86951i
$435$		0			0
$436$	−11.7218	+	43.7464i	−0.561373	+	2.09507i
$437$	−0.814686	+	0.814686i	−0.0389717	+	0.0389717i
$438$		0			0
$439$	4.87991	−	8.45226i	0.232906	−	0.403404i	−0.725756	−	0.687952i	$-0.758510\pi$
$439$	4.87991	−	8.45226i	0.232906	−	0.403404i	0.958662	+	0.284548i	$0.0918434\pi$
$440$	−4.59195	−	17.1374i	−0.218912	−	0.816992i
$441$		0			0
$442$	−4.79007	−	2.55737i	−0.227840	−	0.121641i
$443$	−38.7798			−1.84248			−0.921241	−	0.388992i	$-0.872824\pi$
$443$	−38.7798			−1.84248			−0.921241	+	0.388992i	$0.872824\pi$
$444$		0			0
$445$	−10.8224	+	18.7449i	−0.513030	+	0.888595i
$446$	10.2299	+	17.7187i	0.484399	+	0.839004i
$447$		0			0
$448$	−24.6462	−	20.3377i	−1.16443	−	0.960868i
$449$	2.42216	−	9.03963i	0.114309	−	0.426606i	−0.884925	−	0.465733i	$-0.845791\pi$
$449$	2.42216	−	9.03963i	0.114309	−	0.426606i	0.999234	+	0.0391263i	$0.0124575\pi$
$450$		0			0
$451$	15.7830	−	9.11229i	0.743190	−	0.429081i
$452$	−4.68548	−	2.70516i	−0.220386	−	0.127240i
$453$		0			0
$454$	39.6534			1.86103
$455$	5.78624	+	14.0568i	0.271263	+	0.658991i
$456$		0			0
$457$	4.97477	+	18.5661i	0.232710	+	0.868485i	0.979168	+	0.203053i	$0.0650863\pi$
$457$	4.97477	+	18.5661i	0.232710	+	0.868485i	−0.746458	+	0.665433i	$0.768247\pi$
$458$	−4.97089	−	2.86995i	−0.232275	−	0.134104i
$459$		0			0
$460$	−0.577996	−	0.577996i	−0.0269492	−	0.0269492i
$461$	3.50466	−	13.0796i	0.163228	−	0.609175i	−0.835031	−	0.550202i	$-0.814551\pi$
$461$	3.50466	−	13.0796i	0.163228	−	0.609175i	0.998260	−	0.0589733i	$-0.0187827\pi$
$462$		0			0
$463$	−14.6336	−	14.6336i	−0.680081	−	0.680081i	0.279937	−	0.960018i	$-0.409686\pi$
$463$	−14.6336	−	14.6336i	−0.680081	−	0.680081i	−0.960018	+	0.279937i	$0.909686\pi$
$464$	1.94152	+	3.36281i	0.0901328	+	0.156115i
$465$		0			0
$466$	12.1865	−	3.26536i	0.564529	−	0.151265i
$467$	−30.9732			−1.43327			−0.716634	−	0.697449i	$-0.754318\pi$
$467$	−30.9732			−1.43327			−0.716634	+	0.697449i	$0.754318\pi$
$468$		0			0
$469$	−3.40826	−	1.55532i	−0.157379	−	0.0718179i
$470$	−3.05223	−	11.3911i	−0.140789	−	0.525431i
$471$		0			0
$472$	7.34989	+	12.7304i	0.338306	+	0.585963i
$473$	6.22564	−	6.22564i	0.286255	−	0.286255i
$474$		0			0
$475$	18.7378	+	5.02078i	0.859750	+	0.230369i
$476$	−5.58171	+	2.08370i	−0.255837	+	0.0955061i
$477$		0			0
$478$	34.3753	+	19.8466i	1.57229	+	0.907761i
$479$	−1.90105	−	7.09483i	−0.0868613	−	0.324171i	0.908799	−	0.417235i	$-0.137001\pi$
$479$	−1.90105	−	7.09483i	−0.0868613	−	0.324171i	−0.995660	+	0.0930636i	$0.970334\pi$
$480$		0			0
$481$	7.41183	+	11.9063i	0.337951	+	0.542882i
$482$		−	31.5654i		−	1.43777i
$483$		0			0
$484$	1.98478	−	3.43773i	0.0902171	−	0.156261i
$485$	−0.259753	+	0.149968i	−0.0117948	+	0.00680971i
$486$		0			0
$487$	9.52611	+	2.55251i	0.431669	+	0.115665i	0.468110	−	0.883670i	$-0.344935\pi$
$487$	9.52611	+	2.55251i	0.431669	+	0.115665i	−0.0364405	+	0.999336i	$0.511602\pi$
$488$	−15.4281	−	4.13395i	−0.698398	−	0.187135i
$489$		0			0
$490$	24.7480	+	8.54946i	1.11800	+	0.386225i
$491$	−33.1372	−	19.1318i	−1.49546	−	0.863404i	−0.495473	−	0.868623i	$-0.665005\pi$
$491$	−33.1372	−	19.1318i	−1.49546	−	0.863404i	−0.999986	+	0.00521946i	$0.998339\pi$
$492$		0			0
$493$	−1.91723			−0.0863477
$494$	−19.3985	−	63.8371i	−0.872781	−	2.87217i
$495$		0			0
$496$	−8.40197	+	2.25130i	−0.377260	+	0.101086i
$497$	−30.8511	+	21.9823i	−1.38386	+	0.986042i
$498$		0			0
$499$	0.00102712	−	0.00102712i	4.59801e−5	−	4.59801e-5i	−0.707084	−	0.707130i	$-0.749990\pi$
$499$	0.00102712	−	0.00102712i	4.59801e−5	−	4.59801e-5i	0.707130	+	0.707084i	$0.249990\pi$
$500$	−10.8000	+	40.3060i	−0.482989	+	1.80254i
$501$		0			0
$502$	−21.2537	+	21.2537i	−0.948598	+	0.948598i
$503$	−21.6205	+	12.4826i	−0.964012	+	0.556573i	−0.897406	−	0.441206i	$-0.854551\pi$
$503$	−21.6205	+	12.4826i	−0.964012	+	0.556573i	−0.0666068	+	0.997779i	$0.521217\pi$
$504$		0			0
$505$	−1.83752	+	0.492362i	−0.0817686	+	0.0219098i
$506$			1.07771i			0.0479102i
$507$		0			0
$508$	−11.4226			−0.506798
$509$	2.53176	−	0.678383i	0.112218	−	0.0300688i	−0.202273	−	0.979329i	$-0.564833\pi$
$509$	2.53176	−	0.678383i	0.112218	−	0.0300688i	0.314491	+	0.949260i	$0.398166\pi$
$510$		0			0
$511$	1.78042	+	18.5889i	0.0787610	+	0.822325i
$512$	−10.2233	+	10.2233i	−0.451811	+	0.451811i
$513$		0			0
$514$	23.5365	+	6.30659i	1.03815	+	0.278172i
$515$	−5.40385	−	5.40385i	−0.238122	−	0.238122i
$516$		0			0
$517$	−4.95226	+	8.57757i	−0.217800	+	0.377241i
$518$	23.8238	+	3.99914i	1.04676	+	0.175712i
$519$		0			0
$520$	19.4830	−	5.92041i	0.854387	−	0.259627i
$521$			29.8603i			1.30820i	0.756406	+	0.654102i	$0.226953\pi$
$521$			29.8603i			1.30820i	−0.756406	+	0.654102i	$0.773047\pi$
$522$		0			0
$523$	−13.9268	−	8.04062i	−0.608975	−	0.351592i	0.163589	−	0.986529i	$-0.447693\pi$
$523$	−13.9268	−	8.04062i	−0.608975	−	0.351592i	−0.772564	+	0.634937i	$0.781026\pi$
$524$	28.8999	+	50.0561i	1.26250	+	2.18671i
$525$		0			0
$526$	−9.92985	−	2.66069i	−0.432962	−	0.116012i
$527$	1.11157	−	4.14843i	0.0484207	−	0.180708i
$528$		0			0
$529$	−11.4893	−	19.9001i	−0.499536	−	0.865221i
$530$	−13.6923	+	23.7157i	−0.594755	+	1.03015i
$531$		0			0
$532$	−66.5997	−	30.3920i	−2.88746	−	1.31766i
$533$	11.0540	+	17.7571i	0.478802	+	0.769146i
$534$		0			0
$535$	23.5443	−	6.30868i	1.01791	−	0.272748i
$536$	−2.50923	+	4.34612i	−0.108382	+	0.187724i
$537$		0			0
$538$	−19.3942	−	19.3942i	−0.836143	−	0.836143i
$539$	−9.62000	−	19.7747i	−0.414363	−	0.851756i
$540$		0			0
$541$	12.4465	+	12.4465i	0.535115	+	0.535115i	0.922090	−	0.386975i	$-0.126480\pi$
$541$	12.4465	+	12.4465i	0.535115	+	0.535115i	−0.386975	+	0.922090i	$0.626480\pi$
$542$	62.3933	−	36.0228i	2.68002	−	1.54731i
$543$		0			0
$544$	−0.670546	−	2.50251i	−0.0287494	−	0.107294i
$545$	20.5618			0.880771
$546$		0			0
$547$	−15.8734			−0.678698			−0.339349	−	0.940661i	$-0.610207\pi$
$547$	−15.8734			−0.678698			−0.339349	+	0.940661i	$0.610207\pi$
$548$	0.343322	+	1.28130i	0.0146660	+	0.0547343i
$549$		0			0
$550$	15.7146	−	9.07284i	0.670073	−	0.386867i
$551$	−16.6576	−	16.6576i	−0.709636	−	0.709636i
$552$		0			0
$553$	−1.06579	+	1.29158i	−0.0453221	+	0.0549234i
$554$	−31.6444	−	31.6444i	−1.34444	−	1.34444i
$555$		0			0
$556$	−17.2678	+	29.9087i	−0.732318	+	1.26841i
$557$	2.44666	−	0.655582i	0.103668	−	0.0277779i	−0.206612	−	0.978423i	$-0.566244\pi$
$557$	2.44666	−	0.655582i	0.103668	−	0.0277779i	0.310280	+	0.950645i	$0.399577\pi$
$558$		0			0
$559$	7.37857	+	6.90409i	0.312080	+	0.292012i
$560$	2.27440	−	4.98403i	0.0961109	−	0.210614i
$561$		0			0
$562$	19.6970	−	34.1162i	0.830867	−	1.43910i
$563$	10.1159	+	17.5213i	0.426336	+	0.738436i	0.996544	−	0.0830642i	$-0.0264707\pi$
$563$	10.1159	+	17.5213i	0.426336	+	0.738436i	−0.570208	+	0.821500i	$0.693137\pi$
$564$		0			0
$565$	−0.635745	+	2.37263i	−0.0267460	+	0.0998174i
$566$	−19.1301	−	5.12589i	−0.804098	−	0.215457i
$567$		0			0
$568$	25.3722	+	43.9460i	1.06459	+	1.84393i
$569$	12.8801	+	7.43632i	0.539961	+	0.311747i	0.745063	−	0.666994i	$-0.232419\pi$
$569$	12.8801	+	7.43632i	0.539961	+	0.311747i	−0.205102	+	0.978741i	$0.565753\pi$
$570$		0			0
$571$			36.9235i			1.54520i	0.634893	+	0.772600i	$0.281044\pi$
$571$			36.9235i			1.54520i	−0.634893	+	0.772600i	$0.718956\pi$
$572$	−35.0705	−	18.7237i	−1.46637	−	0.782879i
$573$		0			0
$574$	35.5309	+	5.96431i	1.48303	+	0.248946i
$575$	0.179817	−	0.311452i	0.00749888	−	0.0129884i
$576$		0			0
$577$	14.5105	+	14.5105i	0.604080	+	0.604080i	0.941393	−	0.337312i	$-0.109518\pi$
$577$	14.5105	+	14.5105i	0.604080	+	0.604080i	−0.337312	+	0.941393i	$0.609518\pi$
$578$	37.6113	+	10.0779i	1.56442	+	0.419186i
$579$		0			0
$580$	11.8181	−	11.8181i	0.490718	−	0.490718i
$581$	4.01563	−	0.384610i	0.166596	−	0.0159563i
$582$		0			0
$583$	22.2158	−	5.95271i	0.920086	−	0.246536i
$584$	25.0148			1.03512
$585$		0			0
$586$		−	19.4573i		−	0.803776i
$587$	19.8321	−	5.31399i	0.818557	−	0.219332i	0.174842	−	0.984597i	$-0.444059\pi$
$587$	19.8321	−	5.31399i	0.818557	−	0.219332i	0.643715	+	0.765265i	$0.277392\pi$
$588$		0			0
$589$	45.7007	−	26.3853i	1.88307	−	1.08719i
$590$	10.9701	−	10.9701i	0.451632	−	0.451632i
$591$		0			0
$592$	1.30821	−	4.88231i	0.0537671	−	0.200662i
$593$	−29.4133	+	29.4133i	−1.20786	+	1.20786i	−0.236140	+	0.971719i	$0.575882\pi$
$593$	−29.4133	+	29.4133i	−1.20786	+	1.20786i	−0.971719	+	0.236140i	$0.924118\pi$
$594$		0			0
$595$	1.56966	+	2.20294i	0.0643499	+	0.0903118i
$596$	−18.8282	+	5.04500i	−0.771233	+	0.206651i
$597$		0			0
$598$	−1.23623	+	0.0410690i	−0.0505530	+	0.00167944i
$599$	4.33998			0.177327			0.0886634	−	0.996062i	$-0.471740\pi$
$599$	4.33998			0.177327			0.0886634	+	0.996062i	$0.471740\pi$
$600$		0			0
$601$	5.72067	+	3.30283i	0.233351	+	0.134725i	0.612117	−	0.790767i	$-0.290318\pi$
$601$	5.72067	+	3.30283i	0.233351	+	0.134725i	−0.378766	+	0.925492i	$0.623652\pi$
$602$	17.3260	−	1.65946i	0.706156	−	0.0676344i
$603$		0			0
$604$	−16.0868	−	4.31044i	−0.654561	−	0.175389i
$605$	−1.74080	−	0.466446i	−0.0707735	−	0.0189637i
$606$		0			0
$607$	−39.8777	+	23.0234i	−1.61859	+	0.934492i	−0.631301	+	0.775538i	$0.717479\pi$
$607$	−39.8777	+	23.0234i	−1.61859	+	0.934492i	−0.987286	+	0.158954i	$0.949188\pi$
$608$	15.9168	−	27.5686i	0.645510	−	1.11806i
$609$		0			0
$610$			16.8571i			0.682526i
$611$	−10.0279	−	5.35379i	−0.405686	−	0.216591i
$612$		0			0
$613$	7.42773	+	27.7207i	0.300003	+	1.11963i	0.937162	+	0.348895i	$0.113443\pi$
$613$	7.42773	+	27.7207i	0.300003	+	1.11963i	−0.637159	+	0.770733i	$0.719890\pi$
$614$	49.8609	+	28.7872i	2.01222	+	1.16176i
$615$		0			0
$616$	−27.5972	+	10.3023i	−1.11192	+	0.415090i
$617$	−0.0947548	−	0.0253895i	−0.00381469	−	0.00102214i	0.256911	−	0.966435i	$-0.417295\pi$
$617$	−0.0947548	−	0.0253895i	−0.00381469	−	0.00102214i	−0.260726	+	0.965413i	$0.583962\pi$
$618$		0			0
$619$	−29.9073	+	29.9073i	−1.20208	+	1.20208i	−0.228543	+	0.973534i	$0.573396\pi$
$619$	−29.9073	+	29.9073i	−1.20208	+	1.20208i	−0.973534	+	0.228543i	$0.926604\pi$
$620$	18.7196	+	32.4233i	0.751798	+	1.30215i
$621$		0			0
$622$	14.4058	+	53.7630i	0.577619	+	2.15570i
$623$	32.6942	+	14.9196i	1.30987	+	0.597741i
$624$		0			0
$625$	6.64109			0.265644
$626$	−31.9046	+	8.54882i	−1.27517	+	0.341680i
$627$		0			0
$628$	22.1475	+	38.3606i	0.883781	+	1.53075i
$629$	1.76469	+	1.76469i	0.0703629	+	0.0703629i
$630$		0			0
$631$	2.02584	−	7.56053i	0.0806473	−	0.300980i	−0.913807	−	0.406148i	$-0.866872\pi$
$631$	2.02584	−	7.56053i	0.0806473	−	0.300980i	0.994454	+	0.105169i	$0.0335383\pi$
$632$	1.58614	+	1.58614i	0.0630931	+	0.0630931i
$633$		0			0
$634$	−34.0295	−	19.6469i	−1.35148	−	0.780279i
$635$	1.34223	+	5.00926i	0.0532646	+	0.198786i
$636$		0			0
$637$	22.3166	−	11.7885i	0.884216	−	0.467077i
$638$	−22.0356			−0.872397
$639$		0			0
$640$	27.9777	+	16.1530i	1.10592	+	0.638502i
$641$	28.9275	−	16.7013i	1.14257	−	0.659661i	0.195502	−	0.980703i	$-0.437366\pi$
$641$	28.9275	−	16.7013i	1.14257	−	0.659661i	0.947065	+	0.321042i	$0.104033\pi$
$642$		0			0
$643$	−4.94009	+	18.4367i	−0.194818	+	0.727071i	0.797496	+	0.603324i	$0.206158\pi$
$643$	−4.94009	+	18.4367i	−0.194818	+	0.727071i	−0.992314	+	0.123746i	$0.960509\pi$
$644$	−0.863797	+	1.04679i	−0.0340384	+	0.0412493i
$645$		0			0
$646$	−5.93619	−	10.2818i	−0.233556	−	0.404532i
$647$	−16.4522	+	28.4961i	−0.646804	+	1.12030i	0.337078	+	0.941477i	$0.390561\pi$
$647$	−16.4522	+	28.4961i	−0.646804	+	1.12030i	−0.983882	+	0.178821i	$0.942772\pi$
$648$		0			0
$649$	−13.0298			−0.511465
$650$	11.0061	+	17.6802i	0.431696	+	0.693475i
$651$		0			0
$652$	−11.8578	−	44.2541i	−0.464389	−	1.73312i
$653$	13.9982	−	24.2457i	0.547793	−	0.948806i	−0.450632	−	0.892710i	$-0.648801\pi$
$653$	13.9982	−	24.2457i	0.547793	−	0.948806i	0.998425	−	0.0560961i	$-0.0178653\pi$
$654$		0			0
$655$	18.5556	−	18.5556i	0.725027	−	0.725027i
$656$	1.95106	−	7.28147i	0.0761763	−	0.284294i
$657$		0			0
$658$	−18.3437	+	6.84783i	−0.715110	+	0.266956i
$659$	5.35203	+	9.27000i	0.208486	+	0.361108i	0.951238	−	0.308459i	$-0.0998132\pi$
$659$	5.35203	+	9.27000i	0.208486	+	0.361108i	−0.742752	+	0.669567i	$0.766480\pi$
$660$		0			0
$661$	6.21818	+	23.2066i	0.241859	+	0.902631i	0.974936	+	0.222485i	$0.0714169\pi$
$661$	6.21818	+	23.2066i	0.241859	+	0.902631i	−0.733077	+	0.680146i	$0.761916\pi$
$662$			22.7176i			0.882945i
$663$		0			0
$664$		−	5.40377i		−	0.209707i
$665$	−5.50216	+	32.7777i	−0.213365	+	1.27107i
$666$		0			0
$667$	−0.378218	+	0.218364i	−0.0146447	+	0.00845510i
$668$	45.9988	+	45.9988i	1.77975	+	1.77975i
$669$		0			0
$670$	5.11599	+	1.37083i	0.197648	+	0.0529596i
$671$	10.0111	−	10.0111i	0.386474	−	0.386474i
$672$		0			0
$673$	4.79792	+	2.77008i	0.184946	+	0.106779i	0.589615	−	0.807685i	$-0.299280\pi$
$673$	4.79792	+	2.77008i	0.184946	+	0.106779i	−0.404668	+	0.914464i	$0.632613\pi$
$674$	−45.5365	+	12.2015i	−1.75400	+	0.469983i
$675$		0			0
$676$	20.1412	−	40.9423i	0.774663	−	1.57470i
$677$			44.0680i			1.69367i	0.531855	+	0.846835i	$0.321495\pi$
$677$			44.0680i			1.69367i	−0.531855	+	0.846835i	$0.678505\pi$
$678$		0			0
$679$	0.288982	+	0.405572i	0.0110901	+	0.0155644i
$680$	3.13799	−	1.81172i	0.120336	−	0.0694763i
$681$		0			0
$682$	12.7758	−	47.6798i	0.489209	−	1.82575i
$683$	−1.33328	+	4.97587i	−0.0510166	+	0.190396i	−0.986731	−	0.162361i	$-0.948089\pi$
$683$	−1.33328	+	4.97587i	−0.0510166	+	0.190396i	0.935715	+	0.352757i	$0.114756\pi$
$684$		0			0
$685$	0.521554	−	0.301120i	0.0199276	−	0.0115052i
$686$	10.2127	−	42.2562i	0.389922	−	1.61335i
$687$		0			0
$688$		−	3.64181i		−	0.138843i
$689$	7.67485	+	25.2566i	0.292388	+	0.962198i
$690$		0			0
$691$	2.95186	−	0.790947i	0.112294	−	0.0300891i	−0.202234	−	0.979337i	$-0.564820\pi$
$691$	2.95186	−	0.790947i	0.112294	−	0.0300891i	0.314528	+	0.949248i	$0.398154\pi$
$692$	17.0028	+	9.81655i	0.646348	+	0.373169i
$693$		0			0
$694$	36.8501	−	36.8501i	1.39881	−	1.39881i
$695$	15.1452	+	4.05813i	0.574489	+	0.153934i
$696$		0			0
$697$	2.63186	+	2.63186i	0.0996888	+	0.0996888i
$698$	−10.8854	+	6.28470i	−0.412019	+	0.237879i
$699$		0			0
$700$	22.5357	+	3.78290i	0.851769	+	0.142980i
$701$			11.0158i			0.416061i	0.978122	+	0.208031i	$0.0667054\pi$
$701$			11.0158i			0.416061i	−0.978122	+	0.208031i	$0.933295\pi$
$702$		0			0
$703$			30.6645i			1.15653i
$704$	−9.81997	−	36.6486i	−0.370104	−	1.38125i
$705$		0			0
$706$	−30.6322	−	53.0566i	−1.15286	−	1.99681i
$707$	1.10464	+	2.95906i	0.0415443	+	0.111287i
$708$		0			0
$709$	7.29113	−	27.2109i	0.273824	−	1.02192i	−0.682801	−	0.730604i	$-0.739239\pi$
$709$	7.29113	−	27.2109i	0.273824	−	1.02192i	0.956625	−	0.291321i	$-0.0940948\pi$
$710$	37.8694	−	37.8694i	1.42121	−	1.42121i
$711$		0			0
$712$	24.0702	−	41.6907i	0.902067	−	1.56243i
$713$	−0.253206	−	0.944977i	−0.00948263	−	0.0353897i
$714$		0			0
$715$	−4.09008	+	17.5799i	−0.152960	+	0.657450i
$716$	33.3115			1.24491
$717$		0			0
$718$	−26.5761	+	46.0311i	−0.991811	+	1.71787i
$719$	−21.0559	−	36.4699i	−0.785252	−	1.36010i	−0.928848	−	0.370460i	$-0.879200\pi$
$719$	−21.0559	−	36.4699i	−0.785252	−	1.36010i	0.143596	−	0.989636i	$-0.454133\pi$
$720$		0			0
$721$	−8.07589	+	9.78674i	−0.300762	+	0.364477i
$722$	26.2130	−	97.8284i	0.975548	−	3.64079i
$723$		0			0
$724$	21.0195	−	12.1356i	0.781185	−	0.451018i
$725$	6.36814	+	3.67665i	0.236507	+	0.136547i
$726$		0			0
$727$	10.0901			0.374223			0.187111	−	0.982339i	$-0.440087\pi$
$727$	10.0901			0.374223			0.187111	+	0.982339i	$0.440087\pi$
$728$	−12.8692	−	31.2637i	−0.476965	−	1.15871i
$729$		0			0
$730$	−6.83295	−	25.5009i	−0.252899	−	0.943832i
$731$	1.55722	+	0.899062i	0.0575959	+	0.0332530i
$732$		0			0
$733$	−18.7908	−	18.7908i	−0.694053	−	0.694053i	0.269068	−	0.963121i	$-0.413284\pi$
$733$	−18.7908	−	18.7908i	−0.694053	−	0.694053i	−0.963121	+	0.269068i	$0.913284\pi$
$734$	8.62455	−	32.1873i	0.318338	−	1.18805i
$735$		0			0
$736$	−0.417306	−	0.417306i	−0.0153821	−	0.0153821i
$737$	−2.22417	−	3.85238i	−0.0819285	−	0.141904i
$738$		0			0
$739$	−24.3011	+	6.51146i	−0.893930	+	0.239528i	−0.676407	−	0.736528i	$-0.736464\pi$
$739$	−24.3011	+	6.51146i	−0.893930	+	0.239528i	−0.217522	+	0.976055i	$0.569797\pi$
$740$	−21.7556			−0.799751
$741$		0			0
$742$	41.3641	+	18.8760i	1.51852	+	0.692960i
$743$	2.81817	+	10.5175i	0.103388	+	0.385851i	0.998157	−	0.0606785i	$-0.0193264\pi$
$743$	2.81817	+	10.5175i	0.103388	+	0.385851i	−0.894769	+	0.446530i	$0.852660\pi$
$744$		0			0
$745$	4.42484	+	7.66405i	0.162114	+	0.280789i
$746$	5.81996	−	5.81996i	0.213084	−	0.213084i
$747$		0			0
$748$	−6.83328	−	1.83097i	−0.249850	−	0.0669470i
$749$	−14.1539	−	37.9147i	−0.517171	−	1.38537i
$750$		0			0
$751$	−27.9154	−	16.1170i	−1.01865	−	0.588117i	−0.104936	−	0.994479i	$-0.533464\pi$
$751$	−27.9154	−	16.1170i	−1.01865	−	0.588117i	−0.913712	+	0.406362i	$0.866797\pi$
$752$	1.06035	+	3.95727i	0.0386669	+	0.144307i
$753$		0			0
$754$	−0.839723	−	25.2766i	−0.0305809	−	0.920521i
$755$			7.56115i			0.275179i
$756$		0			0
$757$	−16.9609	+	29.3771i	−0.616453	+	1.06773i	0.373675	+	0.927560i	$0.378098\pi$
$757$	−16.9609	+	29.3771i	−0.616453	+	1.06773i	−0.990128	+	0.140168i	$0.955236\pi$
$758$	−54.5711	+	31.5066i	−1.98211	+	1.14437i
$759$		0			0
$760$	43.0048	+	11.5231i	1.55995	+	0.417987i
$761$	−9.36045	−	2.50812i	−0.339316	−	0.0909194i	0.0851375	−	0.996369i	$-0.472867\pi$
$761$	−9.36045	−	2.50812i	−0.339316	−	0.0909194i	−0.424453	+	0.905450i	$0.639534\pi$
$762$		0			0
$763$	−3.25493	−	33.9839i	−0.117836	−	1.23030i
$764$	7.61437	+	4.39616i	0.275478	+	0.159047i
$765$		0			0
$766$	80.1674			2.89656
$767$	−0.496535	−	14.9463i	−0.0179288	−	0.539679i
$768$		0			0
$769$	−14.6001	+	3.91210i	−0.526495	+	0.141074i	−0.512269	−	0.858825i	$-0.671195\pi$
$769$	−14.6001	+	3.91210i	−0.526495	+	0.141074i	−0.0142256	+	0.999899i	$0.504528\pi$
$770$	18.0408	+	25.3194i	0.650146	+	0.912448i
$771$		0			0
$772$	−55.9826	+	55.9826i	−2.01486	+	2.01486i
$773$	−10.1225	+	37.7776i	−0.364081	+	1.35877i	0.504582	+	0.863364i	$0.331647\pi$
$773$	−10.1225	+	37.7776i	−0.364081	+	1.35877i	−0.868663	+	0.495404i	$0.835020\pi$
$774$		0			0
$775$	−11.6475	+	11.6475i	−0.418390	+	0.418390i
$776$	0.577718	−	0.333546i	0.0207389	−	0.0119736i
$777$		0			0
$778$	−62.2709	+	16.6854i	−2.23252	+	0.598202i
$779$			45.7331i			1.63856i
$780$		0			0
$781$	−44.9797			−1.60950
$782$	−0.212602	+	0.0569665i	−0.00760263	+	0.00203712i
$783$		0			0
$784$	−8.59749	−	2.97009i	−0.307053	−	0.106075i
$785$	14.2201	−	14.2201i	0.507537	−	0.507537i
$786$		0			0
$787$	1.68505	+	0.451508i	0.0600656	+	0.0160945i	0.288727	−	0.957412i	$-0.406768\pi$
$787$	1.68505	+	0.451508i	0.0600656	+	0.0160945i	−0.228661	+	0.973506i	$0.573435\pi$
$788$	−44.4514	−	44.4514i	−1.58352	−	1.58352i
$789$		0			0
$790$	1.18370	−	2.05022i	0.0421141	−	0.0729437i
$791$	4.02205	+	0.675153i	0.143008	+	0.0240057i
$792$		0			0
$793$	11.8651	+	11.1021i	0.421341	+	0.394246i
$794$		−	87.0058i		−	3.08772i
$795$		0			0
$796$	−49.8875	−	28.8026i	−1.76822	−	1.02088i
$797$	−12.2921	−	21.2905i	−0.435407	−	0.754148i	0.561921	−	0.827191i	$-0.310062\pi$
$797$	−12.2921	−	21.2905i	−0.435407	−	0.754148i	−0.997329	+	0.0730430i	$0.976729\pi$
$798$		0			0
$799$	−1.95388	−	0.523540i	−0.0691233	−	0.0185215i
$800$	−2.57179	+	9.59806i	−0.0909266	+	0.339343i
$801$		0			0
$802$	20.3936	+	35.3228i	0.720125	+	1.24729i
$803$	−11.0865	+	19.2024i	−0.391235	+	0.677638i
$804$		0			0
$805$	0.560558	+	0.255804i	0.0197571	+	0.00901590i
$806$	55.1795	+	12.8379i	1.94362	+	0.452195i
$807$		0			0
$808$	4.08684	−	1.09507i	0.143775	−	0.0385243i
$809$	−1.41467	+	2.45029i	−0.0497373	+	0.0861475i	−0.889822	−	0.456307i	$-0.849172\pi$
$809$	−1.41467	+	2.45029i	−0.0497373	+	0.0861475i	0.840085	+	0.542455i	$0.182505\pi$
$810$		0			0
$811$	6.39483	+	6.39483i	0.224553	+	0.224553i	0.810412	−	0.585860i	$-0.199243\pi$
$811$	6.39483	+	6.39483i	0.224553	+	0.224553i	−0.585860	+	0.810412i	$0.699243\pi$
$812$	−21.4033	−	17.6617i	−0.751110	−	0.619806i
$813$		0			0
$814$	20.2824	+	20.2824i	0.710897	+	0.710897i
$815$	−18.0137	+	10.4002i	−0.630993	+	0.364304i
$816$		0			0
$817$	5.71832	+	21.3410i	0.200059	+	0.746629i
$818$	−26.4854			−0.926041
$819$		0			0
$820$	−32.4463			−1.13307
$821$	−9.65789	−	36.0437i	−0.337063	−	1.25793i	−0.901616	−	0.432538i	$-0.857618\pi$
$821$	−9.65789	−	36.0437i	−0.337063	−	1.25793i	0.564553	−	0.825397i	$-0.309049\pi$
$822$		0			0
$823$	34.1966	−	19.7434i	1.19202	−	0.688212i	0.233254	−	0.972416i	$-0.425063\pi$
$823$	34.1966	−	19.7434i	1.19202	−	0.688212i	0.958764	+	0.284204i	$0.0917293\pi$
$824$	12.0187	+	12.0187i	0.418692	+	0.418692i
$825$		0			0
$826$	−19.8676	−	16.3945i	−0.691283	−	0.570437i
$827$	24.4804	+	24.4804i	0.851267	+	0.851267i	0.990289	−	0.139022i	$-0.0443958\pi$
$827$	24.4804	+	24.4804i	0.851267	+	0.851267i	−0.139022	+	0.990289i	$0.544396\pi$
$828$		0			0
$829$	6.73903	−	11.6723i	0.234056	−	0.405397i	−0.724942	−	0.688810i	$-0.758133\pi$
$829$	6.73903	−	11.6723i	0.234056	−	0.405397i	0.958998	+	0.283413i	$0.0914667\pi$
$830$	−5.50878	+	1.47607i	−0.191212	+	0.0512352i
$831$		0			0
$832$	41.6648	−	12.6609i	1.44447	−	0.438938i
$833$	3.39248	−	2.94301i	0.117542	−	0.101969i
$834$		0			0
$835$	14.7671	−	25.5773i	0.511036	−	0.885141i
$836$	−43.4618	−	75.2781i	−1.50316	−	2.60355i
$837$		0			0
$838$	−11.3118	+	42.2160i	−0.390758	+	1.45833i
$839$	48.1190	+	12.8935i	1.66125	+	0.445132i	0.962732	−	0.270457i	$-0.0871749\pi$
$839$	48.1190	+	12.8935i	1.66125	+	0.445132i	0.698522	+	0.715589i	$0.253842\pi$
$840$		0			0
$841$	10.0352	+	17.3815i	0.346041	+	0.599360i
$842$	54.3417	+	31.3742i	1.87274	+	1.08123i
$843$		0			0
$844$			34.6197i			1.19166i
$845$	−20.3214	−	4.02173i	−0.699079	−	0.138352i
$846$		0			0
$847$	−0.495359	+	2.95098i	−0.0170208	+	0.101397i
$848$	4.75671	−	8.23886i	0.163346	−	0.282924i
$849$		0			0
$850$	2.62046	+	2.62046i	0.0898812	+	0.0898812i
$851$	0.549117	+	0.147136i	0.0188235	+	0.00504374i
$852$		0			0
$853$	15.4604	−	15.4604i	0.529355	−	0.529355i	−0.391025	−	0.920380i	$-0.627879\pi$
$853$	15.4604	−	15.4604i	0.529355	−	0.529355i	0.920380	+	0.391025i	$0.127879\pi$
$854$	27.8610	−	2.66848i	0.953383	−	0.0913134i
$855$		0			0
$856$	−52.3651	+	14.0312i	−1.78980	+	0.479576i
$857$	25.0101			0.854328			0.427164	−	0.904174i	$-0.359513\pi$
$857$	25.0101			0.854328			0.427164	+	0.904174i	$0.359513\pi$
$858$		0			0
$859$		−	35.7674i		−	1.22037i	−0.792260	−	0.610183i	$-0.791096\pi$
$859$		−	35.7674i		−	1.22037i	0.792260	−	0.610183i	$-0.208904\pi$
$860$	−15.1409	+	4.05698i	−0.516299	+	0.138342i
$861$		0			0
$862$	−60.0127	+	34.6484i	−2.04404	+	1.18013i
$863$	−29.2685	+	29.2685i	−0.996311	+	0.996311i	−0.999993	−	0.00368256i	$-0.998828\pi$
$863$	−29.2685	+	29.2685i	−0.996311	+	0.996311i	0.00368256	+	0.999993i	$0.498828\pi$
$864$		0			0
$865$	2.30700	−	8.60985i	0.0784405	−	0.292744i
$866$	59.6398	−	59.6398i	2.02664	−	2.02664i
$867$		0			0
$868$	50.6250	−	36.0718i	1.71832	−	1.22436i
$869$	−1.92056	+	0.514612i	−0.0651504	+	0.0174570i
$870$		0			0
$871$	4.33425	−	2.69812i	0.146860	−	0.0914222i
$872$	−45.7317			−1.54867
$873$		0			0
$874$	−2.34210	−	1.35221i	−0.0792229	−	0.0457393i
$875$	−2.99895	−	31.3113i	−0.101383	−	1.05852i
$876$		0			0
$877$	−24.2371	−	6.49432i	−0.818430	−	0.219298i	−0.174770	−	0.984609i	$-0.555918\pi$
$877$	−24.2371	−	6.49432i	−0.818430	−	0.219298i	−0.643660	+	0.765312i	$0.722585\pi$
$878$	22.1287	+	5.92937i	0.746808	+	0.200107i
$879$		0			0
$880$	5.63348	−	3.25249i	0.189905	−	0.109641i
$881$	−18.7477	+	32.4719i	−0.631624	+	1.09401i	0.355595	+	0.934640i	$0.384278\pi$
$881$	−18.7477	+	32.4719i	−0.631624	+	1.09401i	−0.987220	+	0.159365i	$0.949055\pi$
$882$		0			0
$883$			19.9652i			0.671881i	0.941883	+	0.335941i	$0.109054\pi$
$883$			19.9652i			0.671881i	−0.941883	+	0.335941i	$0.890946\pi$
$884$	1.83988	−	7.90812i	0.0618818	−	0.265979i
$885$		0			0
$886$	−23.5598	−	87.9265i	−0.791508	−	2.95395i
$887$	−44.5877	−	25.7427i	−1.49711	−	0.864355i	−0.497113	−	0.867686i	$-0.665606\pi$
$887$	−44.5877	−	25.7427i	−1.49711	−	0.864355i	−0.999994	+	0.00333069i	$0.998940\pi$
$888$		0			0
$889$	8.06667	−	3.01135i	0.270547	−	0.100998i
$890$	−49.0758	−	13.1498i	−1.64502	−	0.440783i
$891$		0			0
$892$	−21.6325	+	21.6325i	−0.724309	+	0.724309i
$893$	−12.4273	−	21.5247i	−0.415863	−	0.720297i
$894$		0			0
$895$	−3.91429	−	14.6083i	−0.130840	−	0.488303i
$896$	22.2683	−	48.7978i	0.743930	−	1.63022i
$897$		0			0
$898$	21.9673			0.733059
$899$	19.3216	−	5.17720i	0.644411	−	0.172669i
$900$		0			0
$901$	2.34860	+	4.06789i	0.0782432	+	0.135521i
$902$	30.2492	+	30.2492i	1.00719	+	1.00719i
$903$		0			0
$904$	1.41396	−	5.27699i	0.0470277	−	0.175510i
$905$	−7.79185	−	7.79185i	−0.259010	−	0.259010i
$906$		0			0
$907$	25.0770	+	14.4782i	0.832669	+	0.480742i	0.854766	−	0.519014i	$-0.173701\pi$
$907$	25.0770	+	14.4782i	0.832669	+	0.480742i	−0.0220968	+	0.999756i	$0.507034\pi$
$908$	15.3461	+	57.2723i	0.509277	+	1.90065i
$909$		0			0
$910$	−28.3560	+	21.6592i	−0.939991	+	0.717995i
$911$	−3.65299			−0.121029			−0.0605144	−	0.998167i	$-0.519274\pi$
$911$	−3.65299			−0.121029			−0.0605144	+	0.998167i	$0.519274\pi$
$912$		0			0
$913$	4.14815	+	2.39494i	0.137284	+	0.0792609i
$914$	−39.0731	+	22.5589i	−1.29242	+	0.746181i
$915$		0			0
$916$	2.22137	−	8.29025i	0.0733960	−	0.273918i
$917$	−33.6054	−	27.7308i	−1.10975	−	0.915750i
$918$		0			0
$919$	−21.3670	−	37.0087i	−0.704831	−	1.22080i	−0.966753	−	0.255714i	$-0.917690\pi$
$919$	−21.3670	−	37.0087i	−0.704831	−	1.22080i	0.261922	−	0.965089i	$-0.415644\pi$
$920$	0.412694	−	0.714807i	0.0136061	−	0.0235665i
$921$		0			0
$922$	31.7848			1.04678
$923$	−1.71407	−	51.5954i	−0.0564192	−	1.69828i
$924$		0			0
$925$	−2.47735	−	9.24560i	−0.0814548	−	0.303994i
$926$	24.2888	−	42.0695i	0.798181	−	1.38249i
$927$		0			0
$928$	8.53250	−	8.53250i	0.280093	−	0.280093i
$929$	−4.38107	+	16.3504i	−0.143738	+	0.536438i	0.856070	+	0.516860i	$0.172899\pi$
$929$	−4.38107	+	16.3504i	−0.143738	+	0.536438i	−0.999808	+	0.0195786i	$0.993768\pi$
$930$		0			0
$931$	55.0450	+	3.90510i	1.80403	+	0.127985i
$932$	9.43247	+	16.3375i	0.308971	+	0.535153i
$933$		0			0
$934$	−18.8171	−	70.2264i	−0.615714	−	2.29788i
$935$			3.21180i			0.105037i
$936$		0			0
$937$			46.5686i			1.52133i	0.649145	+	0.760665i	$0.275127\pi$
$937$			46.5686i			1.52133i	−0.649145	+	0.760665i	$0.724873\pi$
$938$	1.45580	−	8.67255i	0.0475335	−	0.283169i
$939$		0			0
$940$	15.2712	−	8.81680i	0.498090	−	0.287572i
$941$	8.41532	+	8.41532i	0.274331	+	0.274331i	0.830841	−	0.556510i	$-0.187860\pi$
$941$	8.41532	+	8.41532i	0.274331	+	0.274331i	−0.556510	+	0.830841i	$0.687860\pi$
$942$		0			0
$943$	0.818954	+	0.219438i	0.0266688	+	0.00714588i
$944$	−3.81102	+	3.81102i	−0.124038	+	0.124038i
$945$		0			0
$946$	17.8978	+	10.3333i	0.581909	+	0.335965i
$947$	41.7309	−	11.1818i	1.35607	−	0.363358i	0.493699	−	0.869633i	$-0.335644\pi$
$947$	41.7309	−	11.1818i	1.35607	−	0.363358i	0.862373	+	0.506274i	$0.168978\pi$
$948$		0			0
$949$	−22.4492	−	11.9854i	−0.728733	−	0.389063i
$950$			45.5350i			1.47735i
$951$		0			0
$952$	−3.49110	−	4.89958i	−0.113147	−	0.158796i
$953$	50.8066	−	29.3332i	1.64579	−	0.950195i	0.667066	−	0.744999i	$-0.267550\pi$
$953$	50.8066	−	29.3332i	1.64579	−	0.950195i	0.978721	−	0.205196i	$-0.0657832\pi$
$954$		0			0
$955$	1.03315	−	3.85576i	0.0334319	−	0.124770i
$956$	−15.3614	+	57.3297i	−0.496825	+	1.85417i
$957$		0			0
$958$	14.9314	−	8.62062i	0.482410	−	0.278520i
$959$	−0.580243	−	0.814342i	−0.0187370	−	0.0262965i
$960$		0			0
$961$			13.8090i			0.445450i
$962$	−22.4927	+	24.0385i	−0.725193	+	0.775032i
$963$		0			0
$964$	45.5907	−	12.2160i	1.46838	−	0.393450i
$965$	31.1288	+	17.9722i	1.00207	+	0.578546i
$966$		0			0
$967$	−7.53769	+	7.53769i	−0.242396	+	0.242396i	−0.817841	−	0.575445i	$-0.804829\pi$
$967$	−7.53769	+	7.53769i	−0.242396	+	0.242396i	0.575445	+	0.817841i	$0.304829\pi$
$968$	3.87172	+	1.03743i	0.124442	+	0.0333441i
$969$		0			0
$970$	−0.497835	−	0.497835i	−0.0159845	−	0.0159845i
$971$	27.3314	−	15.7798i	0.877107	−	0.506398i	0.00740334	−	0.999973i	$-0.497643\pi$
$971$	27.3314	−	15.7798i	0.877107	−	0.506398i	0.869703	+	0.493575i	$0.164310\pi$
$972$		0			0
$973$	4.30969	−	25.6738i	0.138162	−	0.823066i
$974$			23.1495i			0.741759i
$975$		0			0
$976$		−	5.85618i		−	0.187452i
$977$	0.295580	+	1.10312i	0.00945644	+	0.0352919i	0.970493	−	0.241130i	$-0.0775180\pi$
$977$	0.295580	+	1.10312i	0.00945644	+	0.0352919i	−0.961036	+	0.276422i	$0.910851\pi$
$978$		0			0
$979$	21.3357	+	36.9545i	0.681891	+	1.18107i
$980$	−2.77056	+	39.0528i	−0.0885022	+	1.24750i
$981$		0			0
$982$	23.2462	−	86.7559i	0.741815	−	2.76849i
$983$	20.8611	−	20.8611i	0.665366	−	0.665366i	−0.291274	−	0.956640i	$-0.594079\pi$
$983$	20.8611	−	20.8611i	0.665366	−	0.665366i	0.956640	+	0.291274i	$0.0940791\pi$
$984$		0			0
$985$	−14.2703	+	24.7169i	−0.454690	+	0.787546i
$986$	−1.16477	−	4.34699i	−0.0370939	−	0.138436i
$987$		0			0
$988$	84.6940	−	52.7230i	2.69448	−	1.67734i
$989$	0.409597			0.0130244
$990$		0			0
$991$	22.8046	−	39.4987i	0.724412	−	1.25472i	−0.234804	−	0.972043i	$-0.575445\pi$
$991$	22.8046	−	39.4987i	0.724412	−	1.25472i	0.959216	−	0.282675i	$-0.0912219\pi$
$992$	13.5153	+	23.4093i	0.429113	+	0.743245i
$993$		0			0
$994$	−68.5841	−	56.5947i	−2.17536	−	1.79507i
$995$	−6.76894	+	25.2620i	−0.214590	+	0.800860i
$996$		0			0
$997$	−22.5784	+	13.0357i	−0.715065	+	0.412843i	−0.812934	−	0.582356i	$-0.802131\pi$
$997$	−22.5784	+	13.0357i	−0.715065	+	0.412843i	0.0978683	+	0.995199i	$0.468798\pi$
$998$	0.00295282	+	0.00170481i	9.34698e−5	+	5.39648e-5i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.g.370.8		32
3.2	odd	2		91.2.bc.a.6.2	yes	32
7.6	odd	2	inner	819.2.fm.g.370.7		32
13.11	odd	12	inner	819.2.fm.g.622.7		32
21.2	odd	6		637.2.bb.b.227.1		32
21.5	even	6		637.2.bb.b.227.2		32
21.11	odd	6		637.2.x.b.19.7		32
21.17	even	6		637.2.x.b.19.8		32
21.20	even	2		91.2.bc.a.6.1	✓	32
39.11	even	12		91.2.bc.a.76.1	yes	32
91.76	even	12	inner	819.2.fm.g.622.8		32
273.11	even	12		637.2.bb.b.362.2		32
273.89	odd	12		637.2.x.b.570.8		32
273.128	even	12		637.2.x.b.570.7		32
273.167	odd	12		91.2.bc.a.76.2	yes	32
273.206	odd	12		637.2.bb.b.362.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.1	✓	32	21.20	even	2
91.2.bc.a.6.2	yes	32	3.2	odd	2
91.2.bc.a.76.1	yes	32	39.11	even	12
91.2.bc.a.76.2	yes	32	273.167	odd	12
637.2.x.b.19.7		32	21.11	odd	6
637.2.x.b.19.8		32	21.17	even	6
637.2.x.b.570.7		32	273.128	even	12
637.2.x.b.570.8		32	273.89	odd	12
637.2.bb.b.227.1		32	21.2	odd	6
637.2.bb.b.227.2		32	21.5	even	6
637.2.bb.b.362.1		32	273.206	odd	12
637.2.bb.b.362.2		32	273.11	even	12
819.2.fm.g.370.7		32	7.6	odd	2	inner
819.2.fm.g.370.8		32	1.1	even	1	trivial
819.2.fm.g.622.7		32	13.11	odd	12	inner
819.2.fm.g.622.8		32	91.76	even	12	inner

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	819.2.fm.g.370.8

Level	$819$
Weight	$2$
Character	819.370
Analytic conductor	$6.540$
Analytic rank	$0$
Dimension	$32$
Inner twists	$4$