LMFDB - Embedded newform 945.2.ch.a.53.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(53,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("945.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.ch (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.14
Character	$\chi$	$=$	945.53
Dual form			945.2.ch.a.107.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.136653 + 0.509995i) q^{2} +(1.49063 + 0.860615i) q^{4} +(-1.13030 + 1.92936i) q^{5} +(0.574059 + 2.58272i) q^{7} +(-1.38929 + 1.38929i) q^{8} +O(q^{10})$	\(q+(-0.136653 + 0.509995i) q^{2} +(1.49063 + 0.860615i) q^{4} +(-1.13030 + 1.92936i) q^{5} +(0.574059 + 2.58272i) q^{7} +(-1.38929 + 1.38929i) q^{8} +(-0.829507 - 0.840098i) q^{10} +(3.52057 + 2.03260i) q^{11} +(-1.23916 - 1.23916i) q^{13} +(-1.39562 - 0.0601690i) q^{14} +(1.20255 + 2.08287i) q^{16} +(-5.70675 + 1.52912i) q^{17} +(6.15182 - 3.55176i) q^{19} +(-3.34529 + 1.90321i) q^{20} +(-1.51771 + 1.51771i) q^{22} +(1.28687 + 0.344817i) q^{23} +(-2.44487 - 4.36149i) q^{25} +(0.801303 - 0.462633i) q^{26} +(-1.36702 + 4.34393i) q^{28} -3.96150 q^{29} +(-1.17282 + 2.03139i) q^{31} +(-5.02221 + 1.34570i) q^{32} -3.11937i q^{34} +(-5.63186 - 1.81167i) q^{35} +(-4.00443 - 1.07298i) q^{37} +(0.970715 + 3.62276i) q^{38} +(-1.11014 - 4.25076i) q^{40} -6.21768i q^{41} +(6.67617 + 6.67617i) q^{43} +(3.49858 + 6.05972i) q^{44} +(-0.351710 + 0.609179i) q^{46} +(3.51049 - 13.1013i) q^{47} +(-6.34091 + 2.96527i) q^{49} +(2.55844 - 0.650859i) q^{50} +(-0.780691 - 2.91358i) q^{52} +(2.23972 + 8.35874i) q^{53} +(-7.90091 + 4.49501i) q^{55} +(-4.38570 - 2.79062i) q^{56} +(0.541350 - 2.02035i) q^{58} +(-4.03921 + 6.99612i) q^{59} +(0.0936881 + 0.162272i) q^{61} +(-0.875730 - 0.875730i) q^{62} +2.06500i q^{64} +(3.79142 - 0.990173i) q^{65} +(-0.130136 - 0.485674i) q^{67} +(-9.82263 - 2.63196i) q^{68} +(1.69355 - 2.62465i) q^{70} +12.8619i q^{71} +(-1.33454 + 0.357588i) q^{73} +(1.09443 - 1.89562i) q^{74} +12.2268 q^{76} +(-3.22864 + 10.2595i) q^{77} +(13.1890 - 7.61468i) q^{79} +(-5.37785 - 0.0341139i) q^{80} +(3.17099 + 0.849663i) q^{82} +(8.35280 - 8.35280i) q^{83} +(3.50009 - 12.7387i) q^{85} +(-4.31713 + 2.49250i) q^{86} +(-7.71499 + 2.06723i) q^{88} +(-1.12791 - 1.95360i) q^{89} +(2.48906 - 3.91177i) q^{91} +(1.62150 + 1.62150i) q^{92} +(6.20190 + 3.58067i) q^{94} +(-0.100756 + 15.8836i) q^{95} +(-7.99875 + 7.99875i) q^{97} +(-0.645770 - 3.63905i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 8 q^{7}+O(q^{10}) $ 128 * q - 8 * q^7	$ 128 q - 8 q^{7} - 8 q^{10} + 64 q^{16} - 8 q^{25} + 8 q^{28} + 16 q^{31} - 8 q^{37} + 40 q^{40} - 32 q^{43} + 80 q^{52} + 32 q^{55} + 16 q^{58} - 24 q^{61} - 16 q^{67} - 80 q^{70} + 64 q^{73} - 160 q^{76} - 40 q^{82} - 64 q^{85} - 48 q^{88} - 136 q^{91} - 208 q^{97}+O(q^{100}) $ 128 * q - 8 * q^7 - 8 * q^10 + 64 * q^16 - 8 * q^25 + 8 * q^28 + 16 * q^31 - 8 * q^37 + 40 * q^40 - 32 * q^43 + 80 * q^52 + 32 * q^55 + 16 * q^58 - 24 * q^61 - 16 * q^67 - 80 * q^70 + 64 * q^73 - 160 * q^76 - 40 * q^82 - 64 * q^85 - 48 * q^88 - 136 * q^91 - 208 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.136653	+	0.509995i	−0.0966282	+	0.360621i	−0.997261	−	0.0739591i	$-0.976437\pi$
$2$	−0.136653	+	0.509995i	−0.0966282	+	0.360621i	0.900633	+	0.434580i	$0.143103\pi$
$3$		0			0
$3$		0			0
$4$	1.49063	+	0.860615i	0.745315	+	0.430308i
$5$	−1.13030	+	1.92936i	−0.505483	+	0.862836i
$5$	−1.13030	+	1.92936i	−0.505483	+	0.862836i
$6$		0			0
$7$	0.574059	+	2.58272i	0.216974	+	0.976177i
$7$	0.574059	+	2.58272i	0.216974	+	0.976177i
$8$	−1.38929	+	1.38929i	−0.491189	+	0.491189i
$9$		0			0
$10$	−0.829507	−	0.840098i	−0.262313	−	0.265662i
$11$	3.52057	+	2.03260i	1.06149	+	0.612853i	0.925845	−	0.377904i	$-0.123355\pi$
$11$	3.52057	+	2.03260i	1.06149	+	0.612853i	0.135648	+	0.990757i	$0.456688\pi$
$12$		0			0
$13$	−1.23916	−	1.23916i	−0.343682	−	0.343682i	0.514067	−	0.857750i	$-0.328138\pi$
$13$	−1.23916	−	1.23916i	−0.343682	−	0.343682i	−0.857750	+	0.514067i	$0.828138\pi$
$14$	−1.39562	−	0.0601690i	−0.372996	−	0.0160808i
$15$		0			0
$16$	1.20255	+	2.08287i	0.300637	+	0.520719i
$17$	−5.70675	+	1.52912i	−1.38409	+	0.370866i	−0.872605	−	0.488427i	$-0.837571\pi$
$17$	−5.70675	+	1.52912i	−1.38409	+	0.370866i	−0.511484	+	0.859293i	$0.670904\pi$
$18$		0			0
$19$	6.15182	−	3.55176i	1.41133	−	0.814829i	0.415812	−	0.909451i	$-0.363497\pi$
$19$	6.15182	−	3.55176i	1.41133	−	0.814829i	0.995513	+	0.0946217i	$0.0301642\pi$
$20$	−3.34529	+	1.90321i	−0.748029	+	0.425571i
$21$		0			0
$22$	−1.51771	+	1.51771i	−0.323578	+	0.323578i
$23$	1.28687	+	0.344817i	0.268332	+	0.0718992i	0.390476	−	0.920613i	$-0.372310\pi$
$23$	1.28687	+	0.344817i	0.268332	+	0.0718992i	−0.122144	+	0.992512i	$0.538977\pi$
$24$		0			0
$25$	−2.44487	−	4.36149i	−0.488973	−	0.872299i
$26$	0.801303	−	0.462633i	0.157148	−	0.0907297i
$27$		0			0
$28$	−1.36702	+	4.34393i	−0.258343	+	0.820925i
$29$	−3.96150			−0.735632			−0.367816	−	0.929899i	$-0.619894\pi$
$29$	−3.96150			−0.735632			−0.367816	+	0.929899i	$0.619894\pi$
$30$		0			0
$31$	−1.17282	+	2.03139i	−0.210645	+	0.364849i	−0.951917	−	0.306357i	$-0.900890\pi$
$31$	−1.17282	+	2.03139i	−0.210645	+	0.364849i	0.741271	+	0.671206i	$0.234223\pi$
$32$	−5.02221	+	1.34570i	−0.887809	+	0.237888i
$33$		0			0
$34$		−	3.11937i		−	0.534968i
$35$	−5.63186	−	1.81167i	−0.951958	−	0.306229i
$36$		0			0
$37$	−4.00443	−	1.07298i	−0.658325	−	0.176398i	−0.0858348	−	0.996309i	$-0.527356\pi$
$37$	−4.00443	−	1.07298i	−0.658325	−	0.176398i	−0.572490	+	0.819912i	$0.694022\pi$
$38$	0.970715	+	3.62276i	0.157471	+	0.587689i
$39$		0			0
$40$	−1.11014	−	4.25076i	−0.175528	−	0.672104i
$41$		−	6.21768i		−	0.971038i	−0.874226	−	0.485519i	$-0.838631\pi$
$41$		−	6.21768i		−	0.971038i	0.874226	−	0.485519i	$-0.161369\pi$
$42$		0			0
$43$	6.67617	+	6.67617i	1.01811	+	1.01811i	0.999833	+	0.0182731i	$0.00581683\pi$
$43$	6.67617	+	6.67617i	1.01811	+	1.01811i	0.0182731	+	0.999833i	$0.494183\pi$
$44$	3.49858	+	6.05972i	0.527431	+	0.913537i
$45$		0			0
$46$	−0.351710	+	0.609179i	−0.0518568	+	0.0898186i
$47$	3.51049	−	13.1013i	0.512058	−	1.91103i	0.114580	−	0.993414i	$-0.463448\pi$
$47$	3.51049	−	13.1013i	0.512058	−	1.91103i	0.397478	−	0.917612i	$-0.369886\pi$
$48$		0			0
$49$	−6.34091	+	2.96527i	−0.905845	+	0.423610i
$50$	2.55844	−	0.650859i	0.361818	−	0.0920454i
$51$		0			0
$52$	−0.780691	−	2.91358i	−0.108262	−	0.404041i
$53$	2.23972	+	8.35874i	0.307649	+	1.14816i	0.930641	+	0.365933i	$0.119250\pi$
$53$	2.23972	+	8.35874i	0.307649	+	1.14816i	−0.622993	+	0.782228i	$0.714083\pi$
$54$		0			0
$55$	−7.90091	+	4.49501i	−1.06536	+	0.606107i
$56$	−4.38570	−	2.79062i	−0.586063	−	0.372913i
$57$		0			0
$58$	0.541350	−	2.02035i	0.0710827	−	0.265284i
$59$	−4.03921	+	6.99612i	−0.525860	+	0.910817i	0.473686	+	0.880694i	$0.342923\pi$
$59$	−4.03921	+	6.99612i	−0.525860	+	0.910817i	−0.999546	+	0.0301230i	$0.990410\pi$
$60$		0			0
$61$	0.0936881	+	0.162272i	0.0119955	+	0.0207769i	0.871961	−	0.489576i	$-0.162848\pi$
$61$	0.0936881	+	0.162272i	0.0119955	+	0.0207769i	−0.859965	+	0.510352i	$0.829515\pi$
$62$	−0.875730	−	0.875730i	−0.111218	−	0.111218i
$63$		0			0
$64$			2.06500i			0.258125i
$65$	3.79142	−	0.990173i	0.470267	−	0.122816i
$66$		0			0
$67$	−0.130136	−	0.485674i	−0.0158986	−	0.0593345i	0.957521	−	0.288364i	$-0.0931114\pi$
$67$	−0.130136	−	0.485674i	−0.0158986	−	0.0593345i	−0.973419	+	0.229030i	$0.926445\pi$
$68$	−9.82263	−	2.63196i	−1.19117	−	0.319173i
$69$		0			0
$70$	1.69355	−	2.62465i	0.202418	−	0.313706i
$71$			12.8619i			1.52643i	0.646147	+	0.763213i	$0.276379\pi$
$71$			12.8619i			1.52643i	−0.646147	+	0.763213i	$0.723621\pi$
$72$		0			0
$73$	−1.33454	+	0.357588i	−0.156196	+	0.0418525i	−0.336069	−	0.941837i	$-0.609098\pi$
$73$	−1.33454	+	0.357588i	−0.156196	+	0.0418525i	0.179874	+	0.983690i	$0.442431\pi$
$74$	1.09443	−	1.89562i	0.127225	−	0.220361i
$75$		0			0
$76$	12.2268			1.40251
$77$	−3.22864	+	10.2595i	−0.367937	+	1.16918i
$78$		0			0
$79$	13.1890	−	7.61468i	1.48388	−	0.856718i	0.484047	−	0.875042i	$-0.339166\pi$
$79$	13.1890	−	7.61468i	1.48388	−	0.856718i	0.999832	+	0.0183235i	$0.00583286\pi$
$80$	−5.37785	−	0.0341139i	−0.601262	−	0.00381405i
$81$		0			0
$82$	3.17099	+	0.849663i	0.350177	+	0.0938296i
$83$	8.35280	−	8.35280i	0.916839	−	0.916839i	−0.0799592	−	0.996798i	$-0.525479\pi$
$83$	8.35280	−	8.35280i	0.916839	−	0.916839i	0.996798	+	0.0799592i	$0.0254790\pi$
$84$		0			0
$85$	3.50009	−	12.7387i	0.379638	−	1.38171i
$86$	−4.31713	+	2.49250i	−0.465528	+	0.268773i
$87$		0			0
$88$	−7.71499	+	2.06723i	−0.822421	+	0.220367i
$89$	−1.12791	−	1.95360i	−0.119559	−	0.207082i	0.800034	−	0.599954i	$-0.204815\pi$
$89$	−1.12791	−	1.95360i	−0.119559	−	0.207082i	−0.919593	+	0.392873i	$0.871481\pi$
$90$		0			0
$91$	2.48906	−	3.91177i	0.260925	−	0.410065i
$92$	1.62150	+	1.62150i	0.169053	+	0.169053i
$93$		0			0
$94$	6.20190	+	3.58067i	0.639677	+	0.369318i
$95$	−0.100756	+	15.8836i	−0.0103374	+	1.62963i
$96$		0			0
$97$	−7.99875	+	7.99875i	−0.812150	+	0.812150i	−0.984956	−	0.172806i	$-0.944717\pi$
$97$	−7.99875	+	7.99875i	−0.812150	+	0.812150i	0.172806	+	0.984956i	$0.444717\pi$
$98$	−0.645770	−	3.63905i	−0.0652326	−	0.367599i
$99$		0			0
$100$	0.109180	−	8.60546i	0.0109180	−	0.860546i
$101$	10.2338	+	5.90849i	1.01830	+	0.587917i	0.913612	−	0.406588i	$-0.133281\pi$
$101$	10.2338	+	5.90849i	1.01830	+	0.587917i	0.104691	+	0.994505i	$0.466615\pi$
$102$		0			0
$103$	−2.62805	+	9.80800i	−0.258949	+	0.966411i	0.706902	+	0.707312i	$0.250092\pi$
$103$	−2.62805	+	9.80800i	−0.258949	+	0.966411i	−0.965851	+	0.259099i	$0.916574\pi$
$104$	3.44313			0.337626
$105$		0			0
$106$	−4.56898			−0.443779
$107$	1.71142	−	6.38710i	0.165449	−	0.617465i	−0.832533	−	0.553975i	$-0.813110\pi$
$107$	1.71142	−	6.38710i	0.165449	−	0.617465i	0.997982	−	0.0634897i	$-0.0202230\pi$
$108$		0			0
$109$	−9.55244	−	5.51511i	−0.914958	−	0.528251i	−0.0329351	−	0.999457i	$-0.510485\pi$
$109$	−9.55244	−	5.51511i	−0.914958	−	0.528251i	−0.882023	+	0.471206i	$0.843819\pi$
$110$	−1.21275	−	4.64369i	−0.115632	−	0.442758i
$111$		0			0
$112$	−4.68915	+	4.30154i	−0.443083	+	0.406458i
$113$	1.78157	−	1.78157i	0.167596	−	0.167596i	−0.618326	−	0.785922i	$-0.712189\pi$
$113$	1.78157	−	1.78157i	0.167596	−	0.167596i	0.785922	+	0.618326i	$0.212189\pi$
$114$		0			0
$115$	−2.11982	+	2.09310i	−0.197674	+	0.195182i
$116$	−5.90513	−	3.40933i	−0.548277	−	0.316548i
$117$		0			0
$118$	−3.01602	−	3.01602i	−0.277647	−	0.277647i
$119$	−7.22530	−	13.8611i	−0.662342	−	1.27065i
$120$		0			0
$121$	2.76296	+	4.78558i	0.251178	+	0.435053i
$122$	−0.0955609	+	0.0256055i	−0.00865168	+	0.00231821i
$123$		0			0
$124$	−3.49649	+	2.01870i	−0.313994	+	0.181285i
$125$	11.1783	+	0.212749i	0.999819	+	0.0190288i
$126$		0			0
$127$	−8.65342	+	8.65342i	−0.767867	+	0.767867i	−0.977731	−	0.209864i	$-0.932698\pi$
$127$	−8.65342	+	8.65342i	−0.767867	+	0.767867i	0.209864	+	0.977731i	$0.432698\pi$
$128$	−11.0976	−	2.97358i	−0.980895	−	0.262830i
$129$		0			0
$130$	−0.0131240	+	2.06891i	−0.00115105	+	0.181456i
$131$	−0.711094	+	0.410551i	−0.0621286	+	0.0358700i	−0.530743	−	0.847533i	$-0.678087\pi$
$131$	−0.711094	+	0.410551i	−0.0621286	+	0.0358700i	0.468614	+	0.883403i	$0.344754\pi$
$132$		0			0
$133$	12.7047	+	13.8495i	1.10164	+	1.20091i
$134$	0.265475			0.0229335
$135$		0			0
$136$	5.80395	−	10.0527i	0.497685	−	0.862015i
$137$	14.7966	−	3.96473i	1.26416	−	0.338730i	0.436367	−	0.899769i	$-0.356265\pi$
$137$	14.7966	−	3.96473i	1.26416	−	0.338730i	0.827790	+	0.561039i	$0.189598\pi$
$138$		0			0
$139$			2.92028i			0.247695i	0.992301	+	0.123847i	$0.0395233\pi$
$139$			2.92028i			0.247695i	−0.992301	+	0.123847i	$0.960477\pi$
$140$	−6.83586	−	7.54740i	−0.577736	−	0.637871i
$141$		0			0
$142$	−6.55950	−	1.75761i	−0.550461	−	0.147496i
$143$	−1.84384	−	6.88130i	−0.154189	−	0.575443i
$144$		0			0
$145$	4.47766	−	7.64316i	0.371850	−	0.634730i
$146$		−	0.729472i		−	0.0603715i
$147$		0			0
$148$	−5.04570	−	5.04570i	−0.414754	−	0.414754i
$149$	5.13398	+	8.89231i	0.420592	+	0.728486i	0.995997	−	0.0893819i	$-0.0284892\pi$
$149$	5.13398	+	8.89231i	0.420592	+	0.728486i	−0.575406	+	0.817868i	$0.695156\pi$
$150$		0			0
$151$	2.29890	−	3.98181i	0.187082	−	0.324035i	−0.757194	−	0.653190i	$-0.773430\pi$
$151$	2.29890	−	3.98181i	0.187082	−	0.324035i	0.944276	+	0.329155i	$0.106764\pi$
$152$	−3.61226	+	13.4811i	−0.292993	+	1.09346i
$153$		0			0
$154$	−4.79109	−	3.04858i	−0.386077	−	0.245661i
$155$	−2.59365	−	4.55887i	−0.208327	−	0.366178i
$156$		0			0
$157$	−1.89268	−	7.06356i	−0.151052	−	0.563733i	−0.999411	−	0.0343125i	$-0.989076\pi$
$157$	−1.89268	−	7.06356i	−0.151052	−	0.563733i	0.848359	−	0.529421i	$-0.177591\pi$
$158$	2.08113	+	7.76690i	0.165566	+	0.617901i
$159$		0			0
$160$	3.08024	−	11.2107i	0.243515	−	0.886283i
$161$	−0.151825	+	3.52158i	−0.0119655	+	0.277539i
$162$		0			0
$163$	−3.24079	+	12.0948i	−0.253838	+	0.947336i	0.714895	+	0.699231i	$0.246474\pi$
$163$	−3.24079	+	12.0948i	−0.253838	+	0.947336i	−0.968733	+	0.248104i	$0.920192\pi$
$164$	5.35103	−	9.26825i	0.417845	−	0.723729i
$165$		0			0
$166$	3.11846	+	5.40132i	0.242039	+	0.419224i
$167$	2.32689	+	2.32689i	0.180060	+	0.180060i	0.791382	−	0.611322i	$-0.209362\pi$
$167$	2.32689	+	2.32689i	0.180060	+	0.180060i	−0.611322	+	0.791382i	$0.709362\pi$
$168$		0			0
$169$		−	9.92894i		−	0.763765i
$170$	6.01839	+	3.52581i	0.461590	+	0.270417i
$171$		0			0
$172$	4.20608	+	15.6973i	0.320711	+	1.19691i
$173$	−0.814996	−	0.218378i	−0.0619630	−	0.0166029i	0.227704	−	0.973730i	$-0.426878\pi$
$173$	−0.814996	−	0.218378i	−0.0619630	−	0.0166029i	−0.289667	+	0.957127i	$0.593545\pi$
$174$		0			0
$175$	9.86103	−	8.81816i	0.745424	−	0.666591i
$176$			9.77722i			0.736986i
$177$		0			0
$178$	1.15046	−	0.308265i	0.0862307	−	0.0231055i
$179$	7.10668	−	12.3091i	0.531179	−	0.920028i	−0.468159	−	0.883644i	$-0.655083\pi$
$179$	7.10668	−	12.3091i	0.531179	−	0.920028i	0.999338	−	0.0363841i	$-0.0115840\pi$
$180$		0			0
$181$	19.5633			1.45413			0.727065	−	0.686568i	$-0.240884\pi$
$181$	19.5633			1.45413			0.727065	+	0.686568i	$0.240884\pi$
$182$	1.65485	+	1.80397i	0.122665	+	0.133719i
$183$		0			0
$184$	−2.26690	+	1.30879i	−0.167118	+	0.0964855i
$185$	6.59636	−	6.51320i	0.484974	−	0.478860i
$186$		0			0
$187$	−23.1991	−	6.21618i	−1.69649	−	0.454572i
$188$	16.5081	−	16.5081i	1.20397	−	1.20397i
$189$		0			0
$190$	−8.08680	−	2.22193i	−0.586678	−	0.161196i
$191$	22.5713	−	13.0315i	1.63320	−	0.942929i	0.650104	−	0.759845i	$-0.274725\pi$
$191$	22.5713	−	13.0315i	1.63320	−	0.942929i	0.983097	−	0.183084i	$-0.0586079\pi$
$192$		0			0
$193$	13.0805	−	3.50492i	0.941558	−	0.252290i	0.244782	−	0.969578i	$-0.421284\pi$
$193$	13.0805	−	3.50492i	0.941558	−	0.252290i	0.696776	+	0.717288i	$0.254617\pi$
$194$	−2.98627	−	5.17238i	−0.214402	−	0.371355i
$195$		0			0
$196$	−12.0039	−	1.03697i	−0.857422	−	0.0740691i
$197$	−4.18616	−	4.18616i	−0.298252	−	0.298252i	0.542077	−	0.840329i	$-0.317638\pi$
$197$	−4.18616	−	4.18616i	−0.298252	−	0.298252i	−0.840329	+	0.542077i	$0.817638\pi$
$198$		0			0
$199$	−14.3199	−	8.26762i	−1.01511	−	0.586076i	−0.102429	−	0.994740i	$-0.532661\pi$
$199$	−14.3199	−	8.26762i	−1.01511	−	0.586076i	−0.912685	+	0.408664i	$0.865995\pi$
$200$	9.45603	+	2.66276i	0.668642	+	0.188286i
$201$		0			0
$202$	−4.41178	+	4.41178i	−0.310412	+	0.310412i
$203$	−2.27413	−	10.2315i	−0.159613	−	0.718107i
$204$		0			0
$205$	11.9961	+	7.02781i	0.837847	+	0.490844i
$206$	−4.64290	−	2.68058i	−0.323486	−	0.186765i
$207$		0			0
$208$	1.09087	−	4.07118i	0.0756382	−	0.282285i
$209$	28.8773			1.99748
$210$		0			0
$211$	3.27724			0.225614			0.112807	−	0.993617i	$-0.464016\pi$
$211$	3.27724			0.225614			0.112807	+	0.993617i	$0.464016\pi$
$212$	−3.85507	+	14.3873i	−0.264767	+	0.988125i
$213$		0			0
$214$	3.02352	+	1.74563i	0.206684	+	0.119329i
$215$	−20.4268	+	5.33470i	−1.39309	+	0.363823i
$216$		0			0
$217$	−5.91979	−	1.86294i	−0.401862	−	0.126465i
$218$	4.11805	−	4.11805i	0.278909	−	0.278909i
$219$		0			0
$220$	−15.6458	−	0.0992479i	−1.05484	−	0.00669129i
$221$	8.96642	+	5.17677i	0.603147	+	0.348227i
$222$		0			0
$223$	8.91819	+	8.91819i	0.597206	+	0.597206i	0.939568	−	0.342362i	$-0.111227\pi$
$223$	8.91819	+	8.91819i	0.597206	+	0.597206i	−0.342362	+	0.939568i	$0.611227\pi$
$224$	−6.35861	−	12.1985i	−0.424852	−	0.815044i
$225$		0			0
$226$	0.665136	+	1.15205i	0.0442442	+	0.0766332i
$227$	7.56604	−	2.02732i	0.502176	−	0.134558i	0.00116628	−	0.999999i	$-0.499629\pi$
$227$	7.56604	−	2.02732i	0.502176	−	0.134558i	0.501010	+	0.865442i	$0.332962\pi$
$228$		0			0
$229$	7.91175	−	4.56785i	0.522823	−	0.301852i	−0.215266	−	0.976555i	$-0.569062\pi$
$229$	7.91175	−	4.56785i	0.522823	−	0.301852i	0.738089	+	0.674704i	$0.235728\pi$
$230$	−0.777790	−	1.36713i	−0.0512860	−	0.0901457i
$231$		0			0
$232$	5.50368	−	5.50368i	0.361335	−	0.361335i
$233$	13.1968	+	3.53607i	0.864551	+	0.231656i	0.663730	−	0.747972i	$-0.268972\pi$
$233$	13.1968	+	3.53607i	0.864551	+	0.231656i	0.200821	+	0.979628i	$0.435639\pi$
$234$		0			0
$235$	21.3093	+	21.5814i	1.39007	+	1.40781i
$236$	−12.0419	+	6.95241i	−0.783863	+	0.452564i
$237$		0			0
$238$	8.05647	−	1.79070i	0.522224	−	0.116074i
$239$	10.5072			0.679657			0.339829	−	0.940487i	$-0.389631\pi$
$239$	10.5072			0.679657			0.339829	+	0.940487i	$0.389631\pi$
$240$		0			0
$241$	−10.3103	+	17.8580i	−0.664146	+	1.15034i	0.315370	+	0.948969i	$0.397871\pi$
$241$	−10.3103	+	17.8580i	−0.664146	+	1.15034i	−0.979516	+	0.201366i	$0.935462\pi$
$242$	−2.81819	+	0.755132i	−0.181160	+	0.0485417i
$243$		0			0
$244$			0.322518i			0.0206471i
$245$	1.44603	−	15.5855i	0.0923833	−	0.995724i
$246$		0			0
$247$	−12.0243	−	3.22191i	−0.765090	−	0.205005i
$248$	−1.19280	−	4.45160i	−0.0757430	−	0.282677i
$249$		0			0
$250$	−1.63605	+	5.67182i	−0.103473	+	0.358717i
$251$		−	20.0811i		−	1.26751i	−0.773534	−	0.633755i	$-0.781513\pi$
$251$		−	20.0811i		−	1.26751i	0.773534	−	0.633755i	$-0.218487\pi$
$252$		0			0
$253$	3.82966	+	3.82966i	0.240768	+	0.240768i
$254$	−3.23069	−	5.59572i	−0.202711	−	0.351107i
$255$		0			0
$256$	0.968028	−	1.67667i	0.0605018	−	0.104792i
$257$	4.07658	−	15.2140i	0.254290	−	0.949023i	−0.714194	−	0.699947i	$-0.753207\pi$
$257$	4.07658	−	15.2140i	0.254290	−	0.949023i	0.968484	−	0.249075i	$-0.0801266\pi$
$258$		0			0
$259$	0.472441	−	10.9583i	0.0293561	−	0.680915i
$260$	6.50375	+	1.78697i	0.403346	+	0.110823i
$261$		0			0
$262$	−0.112206	−	0.418758i	−0.00693210	−	0.0258709i
$263$	3.14519	+	11.7380i	0.193941	+	0.723798i	0.992538	+	0.121932i	$0.0389090\pi$
$263$	3.14519	+	11.7380i	0.193941	+	0.723798i	−0.798597	+	0.601866i	$0.794424\pi$
$264$		0			0
$265$	−18.6586	−	5.12662i	−1.14619	−	0.314926i
$266$	−8.79933	+	4.58677i	−0.539522	+	0.281233i
$267$		0			0
$268$	0.223994	−	0.835957i	0.0136826	−	0.0510642i
$269$	−6.92183	+	11.9890i	−0.422032	+	0.730980i	−0.996138	−	0.0878004i	$-0.972016\pi$
$269$	−6.92183	+	11.9890i	−0.422032	+	0.730980i	0.574106	+	0.818781i	$0.305350\pi$
$270$		0			0
$271$	14.1377	+	24.4872i	0.858802	+	1.48749i	0.873072	+	0.487591i	$0.162124\pi$
$271$	14.1377	+	24.4872i	0.858802	+	1.48749i	−0.0142696	+	0.999898i	$0.504542\pi$
$272$	−10.0476	−	10.0476i	−0.609225	−	0.609225i
$273$		0			0
$274$			8.08798i			0.488613i
$275$	0.257863	−	20.3244i	0.0155497	−	1.22561i
$276$		0			0
$277$	1.13204	+	4.22484i	0.0680179	+	0.253846i	0.991560	−	0.129652i	$-0.0413860\pi$
$277$	1.13204	+	4.22484i	0.0680179	+	0.253846i	−0.923542	+	0.383498i	$0.874719\pi$
$278$	−1.48933	−	0.399064i	−0.0893239	−	0.0239343i
$279$		0			0
$280$	10.3413	−	5.30736i	0.618008	−	0.317176i
$281$		−	7.08103i		−	0.422419i	−0.977441	−	0.211209i	$-0.932260\pi$
$281$		−	7.08103i		−	0.422419i	0.977441	−	0.211209i	$-0.0677402\pi$
$282$		0			0
$283$	6.42019	−	1.72029i	0.381641	−	0.102260i	−0.0628979	−	0.998020i	$-0.520034\pi$
$283$	6.42019	−	1.72029i	0.381641	−	0.102260i	0.444539	+	0.895760i	$0.353368\pi$
$284$	−11.0691	+	19.1723i	−0.656833	+	1.13767i
$285$		0			0
$286$	3.76140			0.222416
$287$	16.0585	−	3.56931i	0.947905	−	0.210690i
$288$		0			0
$289$	15.5063	−	8.95258i	0.912136	−	0.526622i
$290$	3.28609	+	3.32805i	0.192966	+	0.195430i
$291$		0			0
$292$	−2.29704	−	0.615491i	−0.134424	−	0.0360189i
$293$	13.2643	−	13.2643i	0.774908	−	0.774908i	−0.204052	−	0.978960i	$-0.565411\pi$
$293$	13.2643	−	13.2643i	0.774908	−	0.774908i	0.978960	+	0.204052i	$0.0654111\pi$
$294$		0			0
$295$	−8.93253	−	15.7008i	−0.520072	−	0.914134i
$296$	7.05402	−	4.07264i	0.410007	−	0.236717i
$297$		0			0
$298$	−5.23661	+	1.40314i	−0.303349	+	0.0812820i
$299$	−1.16736	−	2.02193i	−0.0675103	−	0.116931i
$300$		0			0
$301$	−13.4102	+	21.0752i	−0.772950	+	1.21475i
$302$	1.71655	+	1.71655i	0.0987765	+	0.0987765i
$303$		0			0
$304$	14.7957	+	8.54232i	0.848593	+	0.489936i
$305$	−0.418977	−	0.00265775i	−0.0239906	−	0.000152182i
$306$		0			0
$307$	0.365522	−	0.365522i	0.0208614	−	0.0208614i	−0.696599	−	0.717461i	$-0.745304\pi$
$307$	0.365522	−	0.365522i	0.0208614	−	0.0208614i	0.717461	+	0.696599i	$0.245304\pi$
$308$	−13.6422	+	12.5145i	−0.777335	+	0.713080i
$309$		0			0
$310$	2.67943	−	0.699766i	0.152182	−	0.0397440i
$311$	−1.65255	−	0.954099i	−0.0937074	−	0.0541020i	0.452414	−	0.891808i	$-0.350563\pi$
$311$	−1.65255	−	0.954099i	−0.0937074	−	0.0541020i	−0.546121	+	0.837706i	$0.683896\pi$
$312$		0			0
$313$	6.64011	−	24.7812i	0.375321	−	1.40072i	−0.477554	−	0.878603i	$-0.658476\pi$
$313$	6.64011	−	24.7812i	0.375321	−	1.40072i	0.852875	−	0.522115i	$-0.174857\pi$
$314$	3.86102			0.217890
$315$		0			0
$316$	26.2132			1.47461
$317$	−2.42085	+	9.03474i	−0.135969	+	0.507442i	0.864023	+	0.503451i	$0.167937\pi$
$317$	−2.42085	+	9.03474i	−0.135969	+	0.507442i	−0.999992	+	0.00399004i	$0.998730\pi$
$318$		0			0
$319$	−13.9467	−	8.05216i	−0.780868	−	0.450834i
$320$	−3.98412	−	2.33406i	−0.222719	−	0.130478i
$321$		0			0
$322$	−1.77524	−	0.558664i	−0.0989304	−	0.0311331i
$323$	−29.6758	+	29.6758i	−1.65121	+	1.65121i
$324$		0			0
$325$	−2.37502	+	8.43420i	−0.131742	+	0.467845i
$326$	−5.72542	−	3.30557i	−0.317101	−	0.183079i
$327$		0			0
$328$	8.63818	+	8.63818i	0.476964	+	0.476964i
$329$	35.8523	+	1.54569i	1.97660	+	0.0852166i
$330$		0			0
$331$	3.02335	+	5.23660i	0.166179	+	0.287830i	0.937073	−	0.349133i	$-0.113524\pi$
$331$	3.02335	+	5.23660i	0.166179	+	0.287830i	−0.770895	+	0.636963i	$0.780191\pi$
$332$	19.6395	−	5.26238i	1.07786	−	0.288811i
$333$		0			0
$334$	−1.50468	+	0.868728i	−0.0823325	+	0.0475347i
$335$	1.08413	+	0.297876i	0.0592325	+	0.0162747i
$336$		0			0
$337$	−2.97450	+	2.97450i	−0.162031	+	0.162031i	−0.783466	−	0.621435i	$-0.786550\pi$
$337$	−2.97450	+	2.97450i	−0.162031	+	0.162031i	0.621435	+	0.783466i	$0.286550\pi$
$338$	5.06372	+	1.35682i	0.275430	+	0.0738012i
$339$		0			0
$340$	16.1805	−	15.9765i	0.877510	−	0.866447i
$341$	−8.25803	+	4.76778i	−0.447197	+	0.258189i
$342$		0			0
$343$	−11.2985	−	14.6746i	−0.610063	−	0.792353i
$344$	−18.5503			−1.00017
$345$		0			0
$346$	0.222743	−	0.385802i	0.0119747	−	0.0207409i
$347$	−22.2931	+	5.97342i	−1.19676	+	0.320670i	−0.801553	−	0.597924i	$-0.795993\pi$
$347$	−22.2931	+	5.97342i	−1.19676	+	0.320670i	−0.395203	+	0.918594i	$0.629326\pi$
$348$		0			0
$349$			20.7249i			1.10938i	0.832058	+	0.554689i	$0.187163\pi$
$349$			20.7249i			1.10938i	−0.832058	+	0.554689i	$0.812837\pi$
$350$	3.14968	+	6.23411i	0.168358	+	0.333227i
$351$		0			0
$352$	−20.4163	−	5.47054i	−1.08819	−	0.291581i
$353$	−0.533719	−	1.99187i	−0.0284070	−	0.106016i	0.950267	−	0.311437i	$-0.100810\pi$
$353$	−0.533719	−	1.99187i	−0.0284070	−	0.106016i	−0.978674	+	0.205421i	$0.934144\pi$
$354$		0			0
$355$	−24.8152	−	14.5377i	−1.31706	−	0.771583i
$356$		−	3.88280i		−	0.205788i
$357$		0			0
$358$	5.30645	+	5.30645i	0.280455	+	0.280455i
$359$	0.515262	+	0.892461i	0.0271945	+	0.0471023i	0.879302	−	0.476264i	$-0.158009\pi$
$359$	0.515262	+	0.892461i	0.0271945	+	0.0471023i	−0.852108	+	0.523366i	$0.824676\pi$
$360$		0			0
$361$	15.7300	−	27.2451i	0.827892	−	1.43395i
$362$	−2.67338	+	9.97720i	−0.140510	+	0.524390i
$363$		0			0
$364$	7.07680	−	3.68887i	0.370925	−	0.193350i
$365$	0.818503	−	2.97898i	0.0428424	−	0.155927i
$366$		0			0
$367$	−0.691878	−	2.58212i	−0.0361158	−	0.134786i	0.945514	−	0.325581i	$-0.105560\pi$
$367$	−0.691878	−	2.58212i	−0.0361158	−	0.134786i	−0.981630	+	0.190795i	$0.938893\pi$
$368$	0.829317	+	3.09505i	0.0432311	+	0.161341i
$369$		0			0
$370$	2.42029	+	4.25416i	0.125825	+	0.221163i
$371$	−20.3026	+	10.5830i	−1.05406	+	0.549441i
$372$		0			0
$373$	0.674038	−	2.51554i	0.0349004	−	0.130250i	−0.946278	−	0.323355i	$-0.895189\pi$
$373$	0.674038	−	2.51554i	0.0349004	−	0.130250i	0.981178	+	0.193105i	$0.0618559\pi$
$374$	6.34045	−	10.9820i	0.327857	−	0.567865i
$375$		0			0
$376$	13.3245	+	23.0787i	0.687158	+	1.19019i
$377$	4.90895	+	4.90895i	0.252824	+	0.252824i
$378$		0			0
$379$		−	4.32727i		−	0.222277i	−0.993805	−	0.111138i	$-0.964550\pi$
$379$		−	4.32727i		−	0.222277i	0.993805	−	0.111138i	$-0.0354497\pi$
$380$	−13.8199	+	23.5899i	−0.708945	+	1.21014i
$381$		0			0
$382$	3.56159	+	13.2920i	0.182227	+	0.680080i
$383$	−33.7892	−	9.05379i	−1.72655	−	0.462627i	−0.747165	−	0.664639i	$-0.768585\pi$
$383$	−33.7892	−	9.05379i	−1.72655	−	0.462627i	−0.979383	+	0.202012i	$0.935252\pi$
$384$		0			0
$385$	−16.1450	−	17.8255i	−0.822823	−	0.908470i
$386$			7.14997i			0.363924i
$387$		0			0
$388$	−18.8070	+	5.03932i	−0.954782	+	0.255833i
$389$	−11.8314	+	20.4926i	−0.599875	+	1.03901i	0.392964	+	0.919554i	$0.371450\pi$
$389$	−11.8314	+	20.4926i	−0.599875	+	1.03901i	−0.992839	+	0.119461i	$0.961883\pi$
$390$		0			0
$391$	−7.87112			−0.398060
$392$	4.68976	−	12.9290i	0.236869	−	0.653014i
$393$		0			0
$394$	2.70698	−	1.56287i	0.136375	−	0.0787364i
$395$	−0.216014	+	34.0532i	−0.0108688	+	1.71340i
$396$		0			0
$397$	−13.8047	−	3.69895i	−0.692836	−	0.185645i	−0.104816	−	0.994492i	$-0.533426\pi$
$397$	−13.8047	−	3.69895i	−0.692836	−	0.185645i	−0.588020	+	0.808847i	$0.700092\pi$
$398$	6.17331	−	6.17331i	0.309440	−	0.309440i
$399$		0			0
$400$	6.14438	−	10.3373i	0.307219	−	0.516863i
$401$	6.42551	−	3.70977i	0.320875	−	0.185257i	−0.330908	−	0.943663i	$-0.607355\pi$
$401$	6.42551	−	3.70977i	0.320875	−	0.185257i	0.651782	+	0.758406i	$0.274022\pi$
$402$		0			0
$403$	3.97055	−	1.06391i	0.197787	−	0.0529969i
$404$	10.1699	+	17.6148i	0.505971	+	0.876367i
$405$		0			0
$406$	5.52876	+	0.238359i	0.274388	+	0.0118296i
$407$	−11.9169	−	11.9169i	−0.590701	−	0.590701i
$408$		0			0
$409$	−6.09465	−	3.51875i	−0.301361	−	0.173991i	0.341693	−	0.939812i	$-0.389000\pi$
$409$	−6.09465	−	3.51875i	−0.301361	−	0.173991i	−0.643054	+	0.765821i	$0.722333\pi$
$410$	−5.22346	+	5.15761i	−0.257968	+	0.254716i
$411$		0			0
$412$	−12.3584	+	12.3584i	−0.608853	+	0.608853i
$413$	−20.3878	−	6.41598i	−1.00322	−	0.315710i
$414$		0			0
$415$	6.67443	+	25.5567i	0.327635	+	1.25453i
$416$	7.89088	+	4.55580i	0.386882	+	0.223367i
$417$		0			0
$418$	−3.94616	+	14.7273i	−0.193013	+	0.720334i
$419$	−33.0531			−1.61475			−0.807376	−	0.590037i	$-0.799113\pi$
$419$	−33.0531			−1.61475			−0.807376	+	0.590037i	$0.799113\pi$
$420$		0			0
$421$	−22.6305			−1.10295			−0.551473	−	0.834193i	$-0.685934\pi$
$421$	−22.6305			−1.10295			−0.551473	+	0.834193i	$0.685934\pi$
$422$	−0.447844	+	1.67138i	−0.0218007	+	0.0813614i
$423$		0			0
$424$	−14.7244	−	8.50111i	−0.715078	−	0.412851i
$425$	20.6215	+	21.1515i	1.00029	+	1.02600i
$426$		0			0
$427$	−0.365322	+	0.335124i	−0.0176792	+	0.0162178i
$428$	8.04793	−	8.04793i	0.389011	−	0.389011i
$429$		0			0
$430$	0.0707073	−	11.1466i	0.00340981	−	0.537535i
$431$	28.1159	+	16.2327i	1.35430	+	0.781903i	0.988848	−	0.148929i	$-0.0475827\pi$
$431$	28.1159	+	16.2327i	1.35430	+	0.781903i	0.365447	+	0.930832i	$0.380916\pi$
$432$		0			0
$433$	−3.84058	−	3.84058i	−0.184567	−	0.184567i	0.608776	−	0.793342i	$-0.291661\pi$
$433$	−3.84058	−	3.84058i	−0.184567	−	0.184567i	−0.793342	+	0.608776i	$0.791661\pi$
$434$	1.75905	−	2.76449i	0.0844370	−	0.132700i
$435$		0			0
$436$	−9.49277	−	16.4420i	−0.454621	−	0.787427i
$437$	9.14132	−	2.44941i	0.437289	−	0.117171i
$438$		0			0
$439$	−11.2595	+	6.50070i	−0.537389	+	0.310262i	−0.744020	−	0.668157i	$-0.767083\pi$
$439$	−11.2595	+	6.50070i	−0.537389	+	0.310262i	0.206631	+	0.978419i	$0.433750\pi$
$440$	4.73180	−	17.2216i	0.225579	−	0.821007i
$441$		0			0
$442$	−3.86541	+	3.86541i	−0.183859	+	0.183859i
$443$	20.5352	+	5.50239i	0.975657	+	0.261426i	0.711215	−	0.702975i	$-0.248145\pi$
$443$	20.5352	+	5.50239i	0.975657	+	0.261426i	0.264442	+	0.964402i	$0.414812\pi$
$444$		0			0
$445$	5.04408	+	0.0319967i	0.239112	+	0.00151679i
$446$	−5.76693	+	3.32954i	−0.273072	+	0.157658i
$447$		0			0
$448$	−5.33331	+	1.18543i	−0.251975	+	0.0560063i
$449$	−24.9742			−1.17860			−0.589302	−	0.807913i	$-0.700597\pi$
$449$	−24.9742			−1.17860			−0.589302	+	0.807913i	$0.700597\pi$
$450$		0			0
$451$	12.6381	−	21.8898i	0.595104	−	1.03075i
$452$	4.18891	−	1.12242i	0.197030	−	0.0527940i
$453$		0			0
$454$			4.13569i			0.194097i
$455$	4.73384	+	9.22376i	0.221926	+	0.432416i
$456$		0			0
$457$	−9.91943	−	2.65790i	−0.464011	−	0.124331i	0.0192367	−	0.999815i	$-0.493876\pi$
$457$	−9.91943	−	2.65790i	−0.464011	−	0.124331i	−0.483248	+	0.875484i	$0.660543\pi$
$458$	1.24842	+	4.65916i	0.0583348	+	0.217708i
$459$		0			0
$460$	−4.96122	+	1.29568i	−0.231318	+	0.0604115i
$461$		−	6.32388i		−	0.294532i	−0.989097	−	0.147266i	$-0.952953\pi$
$461$		−	6.32388i		−	0.294532i	0.989097	−	0.147266i	$-0.0470474\pi$
$462$		0			0
$463$	15.6998	+	15.6998i	0.729631	+	0.729631i	0.970546	−	0.240915i	$-0.0774477\pi$
$463$	15.6998	+	15.6998i	0.729631	+	0.729631i	−0.240915	+	0.970546i	$0.577448\pi$
$464$	−4.76389	−	8.25130i	−0.221158	−	0.383057i
$465$		0			0
$466$	−3.60676	+	6.24709i	−0.167080	+	0.289391i
$467$	−3.68733	+	13.7613i	−0.170629	+	0.636797i	0.826626	+	0.562752i	$0.190257\pi$
$467$	−3.68733	+	13.7613i	−0.170629	+	0.636797i	−0.997255	+	0.0740447i	$0.976409\pi$
$468$		0			0
$469$	1.17966	−	0.614911i	0.0544714	−	0.0283939i
$470$	−13.9184	+	7.91849i	−0.642007	+	0.365253i
$471$		0			0
$472$	−4.10801	−	15.3313i	−0.189087	−	0.705681i
$473$	9.93393	+	37.0739i	0.456763	+	1.70466i
$474$		0			0
$475$	−30.5313	−	18.1476i	−1.40087	−	0.832668i
$476$	1.15887	−	26.8800i	0.0531167	−	1.23204i
$477$		0			0
$478$	−1.43585	+	5.35865i	−0.0656740	+	0.245099i
$479$	−20.9002	+	36.2003i	−0.954956	+	1.65403i	−0.220489	+	0.975390i	$0.570765\pi$
$479$	−20.9002	+	36.2003i	−0.954956	+	1.65403i	−0.734468	+	0.678644i	$0.762568\pi$
$480$		0			0
$481$	3.63254	+	6.29175i	0.165630	+	0.286879i
$482$	−7.69856	−	7.69856i	−0.350660	−	0.350660i
$483$		0			0
$484$			9.51137i			0.432335i
$485$	−6.39152	−	24.4734i	−0.290224	−	1.11128i
$486$		0			0
$487$	1.35537	+	5.05832i	0.0614178	+	0.229214i	0.989812	−	0.142384i	$-0.0454766\pi$
$487$	1.35537	+	5.05832i	0.0614178	+	0.229214i	−0.928394	+	0.371598i	$0.878810\pi$
$488$	−0.355604	−	0.0952839i	−0.0160975	−	0.00431330i
$489$		0			0
$490$	7.75095	+	2.86728i	0.350152	+	0.129530i
$491$		−	34.3210i		−	1.54888i	−0.632645	−	0.774442i	$-0.718031\pi$
$491$		−	34.3210i		−	1.54888i	0.632645	−	0.774442i	$-0.281969\pi$
$492$		0			0
$493$	22.6073	−	6.05760i	1.01818	−	0.272820i
$494$	3.28632	−	5.69207i	0.147858	−	0.256098i
$495$		0			0
$496$	−5.64151			−0.253311
$497$	−33.2187	+	7.38348i	−1.49006	+	0.331194i
$498$		0			0
$499$	19.2364	−	11.1061i	0.861138	−	0.497178i	−0.00325539	−	0.999995i	$-0.501036\pi$
$499$	19.2364	−	11.1061i	0.861138	−	0.497178i	0.864393	+	0.502817i	$0.167703\pi$
$500$	16.4796	+	9.93736i	0.736992	+	0.444412i
$501$		0			0
$502$	10.2413	+	2.74414i	0.457091	+	0.122477i
$503$	−4.58828	+	4.58828i	−0.204581	+	0.204581i	−0.801960	−	0.597378i	$-0.796209\pi$
$503$	−4.58828	+	4.58828i	−0.204581	+	0.204581i	0.597378	+	0.801960i	$0.296209\pi$
$504$		0			0
$505$	−22.9668	+	13.0664i	−1.02201	+	0.581446i
$506$	−2.47644	+	1.42977i	−0.110091	+	0.0635612i
$507$		0			0
$508$	−20.3463	+	5.45178i	−0.902721	+	0.241883i
$509$	−13.7026	−	23.7337i	−0.607359	−	1.05198i	−0.991674	−	0.128774i	$-0.958896\pi$
$509$	−13.7026	−	23.7337i	−0.607359	−	1.05198i	0.384315	−	0.923202i	$-0.374438\pi$
$510$		0			0
$511$	−1.68965	−	3.24146i	−0.0747458	−	0.143394i
$512$	−15.5251	−	15.5251i	−0.686121	−	0.686121i
$513$		0			0
$514$	7.20199	+	4.15807i	0.317666	+	0.183405i
$515$	−15.9527	−	16.1564i	−0.702960	−	0.711935i
$516$		0			0
$517$	38.9888	−	38.9888i	1.71472	−	1.71472i
$518$	5.52412	+	1.73842i	0.242716	+	0.0763820i
$519$		0			0
$520$	−3.89175	+	6.64303i	−0.170664	+	0.291316i
$521$	−33.4233	−	19.2970i	−1.46430	−	0.845416i	−0.465098	−	0.885259i	$-0.653981\pi$
$521$	−33.4233	−	19.2970i	−1.46430	−	0.845416i	−0.999206	+	0.0398434i	$0.987314\pi$
$522$		0			0
$523$	3.23694	−	12.0804i	0.141541	−	0.528240i	−0.858344	−	0.513075i	$-0.828506\pi$
$523$	3.23694	−	12.0804i	0.141541	−	0.528240i	0.999885	−	0.0151644i	$-0.00482718\pi$
$524$	−1.41330			−0.0617405
$525$		0			0
$526$	−6.41614			−0.279757
$527$	3.58677	−	13.3860i	0.156242	−	0.583104i
$528$		0			0
$529$	−18.3814	−	10.6125i	−0.799193	−	0.461414i
$530$	5.16430	−	8.81521i	0.224323	−	0.382908i
$531$		0			0
$532$	7.01890	+	31.5784i	0.304308	+	1.36910i
$533$	−7.70472	+	7.70472i	−0.333729	+	0.333729i
$534$		0			0
$535$	10.3886	+	10.5213i	0.449139	+	0.454874i
$536$	0.855541	+	0.493947i	0.0369537	+	0.0213352i
$537$		0			0
$538$	−5.16843	−	5.16843i	−0.222827	−	0.222827i
$539$	−28.3509	−	2.44911i	−1.22116	−	0.105491i
$540$		0			0
$541$	−16.2300	−	28.1111i	−0.697780	−	1.20859i	−0.969234	−	0.246140i	$-0.920838\pi$
$541$	−16.2300	−	28.1111i	−0.697780	−	1.20859i	0.271454	−	0.962451i	$-0.412496\pi$
$542$	−14.4203	+	3.86391i	−0.619405	+	0.165969i
$543$		0			0
$544$	26.6027	−	15.3591i	1.14058	−	0.658516i
$545$	21.4377	−	12.1964i	0.918291	−	0.522437i
$546$		0			0
$547$	22.7139	−	22.7139i	0.971174	−	0.971174i	−0.0284219	−	0.999596i	$-0.509048\pi$
$547$	22.7139	−	22.7139i	0.971174	−	0.971174i	0.999596	+	0.0284219i	$0.00904818\pi$
$548$	25.4683	+	6.82422i	1.08795	+	0.291516i
$549$		0			0
$550$	10.3301	+	2.90890i	0.440478	+	0.124036i
$551$	−24.3704	+	14.0703i	−1.03822	+	0.599414i
$552$		0			0
$553$	27.2379	+	29.6923i	1.15827	+	1.26264i
$554$	−2.30935			−0.0981148
$555$		0			0
$556$	−2.51324	+	4.35305i	−0.106585	+	0.184610i
$557$	19.0413	−	5.10209i	0.806804	−	0.216182i	0.168235	−	0.985747i	$-0.446193\pi$
$557$	19.0413	−	5.10209i	0.806804	−	0.216182i	0.638569	+	0.769564i	$0.279527\pi$
$558$		0			0
$559$		−	16.5457i		−	0.699810i
$560$	−2.99910	−	13.9091i	−0.126735	−	0.587766i
$561$		0			0
$562$	3.61129	+	0.967643i	0.152333	+	0.0408175i
$563$	0.537331	+	2.00535i	0.0226458	+	0.0845154i	0.976324	−	0.216314i	$-0.0694033\pi$
$563$	0.537331	+	2.00535i	0.0226458	+	0.0845154i	−0.953678	+	0.300829i	$0.902737\pi$
$564$		0			0
$565$	1.42359	+	5.45099i	0.0598910	+	0.229325i
$566$			3.50935i			0.147509i
$567$		0			0
$568$	−17.8689	−	17.8689i	−0.749764	−	0.749764i
$569$	6.36146	+	11.0184i	0.266686	+	0.461914i	0.968004	−	0.250935i	$-0.0807379\pi$
$569$	6.36146	+	11.0184i	0.266686	+	0.461914i	−0.701318	+	0.712849i	$0.747405\pi$
$570$		0			0
$571$	−5.14582	+	8.91283i	−0.215346	+	0.372990i	−0.953380	−	0.301774i	$-0.902421\pi$
$571$	−5.14582	+	8.91283i	−0.215346	+	0.372990i	0.738034	+	0.674764i	$0.235755\pi$
$572$	3.17367	−	11.8443i	0.132698	−	0.495235i
$573$		0			0
$574$	−0.374111	+	8.67753i	−0.0156151	+	0.362193i
$575$	−1.64232	−	6.45572i	−0.0684893	−	0.269222i
$576$		0			0
$577$	8.96671	+	33.4642i	0.373289	+	1.39313i	0.855828	+	0.517260i	$0.173048\pi$
$577$	8.96671	+	33.4642i	0.373289	+	1.39313i	−0.482539	+	0.875874i	$0.660285\pi$
$578$	2.44679	+	9.13154i	0.101773	+	0.379822i
$579$		0			0
$580$	13.2524	−	7.53957i	0.550274	−	0.313064i
$581$	26.3680	+	16.7780i	1.09393	+	0.696067i
$582$		0			0
$583$	−9.10491	+	33.9800i	−0.377087	+	1.40731i
$584$	1.35727	−	2.35086i	0.0561641	−	0.0972791i
$585$		0			0
$586$	4.95212	+	8.57733i	0.204570	+	0.354326i
$587$	11.5448	+	11.5448i	0.476505	+	0.476505i	0.904012	−	0.427507i	$-0.140608\pi$
$587$	11.5448	+	11.5448i	0.476505	+	0.476505i	−0.427507	+	0.904012i	$0.640608\pi$
$588$		0			0
$589$			16.6623i			0.686560i
$590$	9.22798	−	2.41000i	0.379910	−	0.0992179i
$591$		0			0
$592$	−2.58063	−	9.63105i	−0.106063	−	0.395834i
$593$	33.4698	+	8.96820i	1.37444	+	0.368280i	0.869098	−	0.494640i	$-0.164700\pi$
$593$	33.4698	+	8.96820i	1.37444	+	0.368280i	0.505341	+	0.862920i	$0.331367\pi$
$594$		0			0
$595$	34.9099	+	1.72698i	1.43116	+	0.0707991i
$596$			17.6735i			0.723935i
$597$		0			0
$598$	1.19070	−	0.319047i	0.0486913	−	0.0130468i
$599$	−20.7668	+	35.9692i	−0.848510	+	1.46966i	0.0340274	+	0.999421i	$0.489167\pi$
$599$	−20.7668	+	35.9692i	−0.848510	+	1.46966i	−0.882538	+	0.470242i	$0.844167\pi$
$600$		0			0
$601$	11.8307			0.482583			0.241291	−	0.970453i	$-0.422429\pi$
$601$	11.8307			0.482583			0.241291	+	0.970453i	$0.422429\pi$
$602$	−8.91572	−	9.71911i	−0.363378	−	0.396122i
$603$		0			0
$604$	6.85361	−	3.95693i	0.278869	−	0.161005i
$605$	−12.3561	−	0.0783797i	−0.502346	−	0.00318659i
$606$		0			0
$607$	13.2559	+	3.55190i	0.538039	+	0.144167i	0.517598	−	0.855624i	$-0.326826\pi$
$607$	13.2559	+	3.55190i	0.538039	+	0.144167i	0.0204409	+	0.999791i	$0.493493\pi$
$608$	−26.1162	+	26.1162i	−1.05915	+	1.05915i
$609$		0			0
$610$	0.0586099	−	0.213313i	0.00237304	−	0.00863680i
$611$	−20.5848	+	11.8846i	−0.832771	+	0.480801i
$612$		0			0
$613$	−18.3007	+	4.90365i	−0.739158	+	0.198057i	−0.608704	−	0.793398i	$-0.708310\pi$
$613$	−18.3007	+	4.90365i	−0.739158	+	0.198057i	−0.130454	+	0.991454i	$0.541644\pi$
$614$	0.136465	+	0.236364i	0.00550727	+	0.00953887i
$615$		0			0
$616$	−9.76793	−	18.7390i	−0.393561	−	0.755015i
$617$	15.2683	+	15.2683i	0.614680	+	0.614680i	0.944162	−	0.329482i	$-0.106874\pi$
$617$	15.2683	+	15.2683i	0.614680	+	0.614680i	−0.329482	+	0.944162i	$0.606874\pi$
$618$		0			0
$619$	24.7039	+	14.2628i	0.992933	+	0.573270i	0.906150	−	0.422957i	$-0.139008\pi$
$619$	24.7039	+	14.2628i	0.992933	+	0.573270i	0.0867832	+	0.996227i	$0.472341\pi$
$620$	0.0572666	−	9.02773i	0.00229988	−	0.362562i
$621$		0			0
$622$	0.712411	−	0.712411i	0.0285651	−	0.0285651i
$623$	4.39813	−	4.03457i	0.176207	−	0.161642i
$624$		0			0
$625$	−13.0453	+	21.3265i	−0.521811	+	0.853061i
$626$	11.7309	+	6.77285i	0.468862	+	0.270698i
$627$		0			0
$628$	3.25773	−	12.1580i	0.129998	−	0.485158i
$629$	24.4930			0.976600
$630$		0			0
$631$	2.15298			0.0857088			0.0428544	−	0.999081i	$-0.486355\pi$
$631$	2.15298			0.0857088			0.0428544	+	0.999081i	$0.486355\pi$
$632$	−7.74438	+	28.9024i	−0.308055	+	1.14968i
$633$		0			0
$634$	−4.27686	−	2.46925i	−0.169856	−	0.0980663i
$635$	−6.91465	−	26.4765i	−0.274399	−	1.05069i
$636$		0			0
$637$	11.5319	+	4.18298i	0.456910	+	0.165736i
$638$	6.01242	−	6.01242i	0.238034	−	0.238034i
$639$		0			0
$640$	18.2806	−	18.0502i	0.722605	−	0.713495i
$641$	−1.15758	−	0.668330i	−0.0457217	−	0.0263974i	0.476965	−	0.878922i	$-0.341737\pi$
$641$	−1.15758	−	0.668330i	−0.0457217	−	0.0263974i	−0.522687	+	0.852525i	$0.675070\pi$
$642$		0			0
$643$	−28.8832	−	28.8832i	−1.13904	−	1.13904i	−0.988622	−	0.150421i	$-0.951937\pi$
$643$	−28.8832	−	28.8832i	−1.13904	−	1.13904i	−0.150421	−	0.988622i	$-0.548063\pi$
$644$	−3.25704	+	5.11871i	−0.128345	+	0.201705i
$645$		0			0
$646$	−11.0793	−	19.1898i	−0.435907	−	0.755014i
$647$	4.54879	−	1.21884i	0.178831	−	0.0479177i	−0.168292	−	0.985737i	$-0.553825\pi$
$647$	4.54879	−	1.21884i	0.178831	−	0.0479177i	0.347123	+	0.937819i	$0.387159\pi$
$648$		0			0
$649$	−28.4407	+	16.4202i	−1.11639	+	0.644550i
$650$	−3.97685	−	2.36380i	−0.155985	−	0.0927161i
$651$		0			0
$652$	−15.2398	+	15.2398i	−0.596835	+	0.596835i
$653$	−10.7491	−	2.88020i	−0.420643	−	0.112711i	0.0422873	−	0.999105i	$-0.486536\pi$
$653$	−10.7491	−	2.88020i	−0.420643	−	0.112711i	−0.462931	+	0.886394i	$0.653202\pi$
$654$		0			0
$655$	0.0116465	−	1.83600i	0.000455067	−	0.0717385i
$656$	12.9506	−	7.47706i	0.505638	−	0.291930i
$657$		0			0
$658$	−5.68762	+	18.0733i	−0.221726	+	0.704571i
$659$	17.5188			0.682434			0.341217	−	0.939985i	$-0.389161\pi$
$659$	17.5188			0.682434			0.341217	+	0.939985i	$0.389161\pi$
$660$		0			0
$661$	−4.84733	+	8.39582i	−0.188539	+	0.326560i	−0.944763	−	0.327753i	$-0.893709\pi$
$661$	−4.84733	+	8.39582i	−0.188539	+	0.326560i	0.756224	+	0.654313i	$0.227042\pi$
$662$	−3.08379	+	0.826300i	−0.119855	+	0.0321151i
$663$		0			0
$664$			23.2090i			0.900683i
$665$	−41.0808	+	8.85791i	−1.59305	+	0.343495i
$666$		0			0
$667$	−5.09794	−	1.36599i	−0.197393	−	0.0528914i
$668$	1.46598	+	5.47110i	0.0567203	+	0.211683i
$669$		0			0
$670$	−0.300065	+	0.512197i	−0.0115925	+	0.0197879i
$671$			0.761723i			0.0294060i
$672$		0			0
$673$	7.82584	+	7.82584i	0.301664	+	0.301664i	0.841665	−	0.540001i	$-0.181576\pi$
$673$	7.82584	+	7.82584i	0.301664	+	0.301664i	−0.540001	+	0.841665i	$0.681576\pi$
$674$	−1.11051	−	1.92345i	−0.0427751	−	0.0740886i
$675$		0			0
$676$	8.54500	−	14.8004i	0.328654	−	0.569245i
$677$	−7.68337	+	28.6747i	−0.295296	+	1.10206i	0.645686	+	0.763603i	$0.276572\pi$
$677$	−7.68337	+	28.6747i	−0.295296	+	1.10206i	−0.940982	+	0.338457i	$0.890095\pi$
$678$		0			0
$679$	−25.2503	−	16.0668i	−0.969018	−	0.616587i
$680$	12.8352	+	22.5605i	0.492207	+	0.865155i
$681$		0			0
$682$	−1.30306	−	4.86309i	−0.0498967	−	0.186217i
$683$	−11.5065	−	42.9428i	−0.440284	−	1.64316i	−0.728096	−	0.685475i	$-0.759594\pi$
$683$	−11.5065	−	42.9428i	−0.440284	−	1.64316i	0.287812	−	0.957687i	$-0.407072\pi$
$684$		0			0
$685$	−9.07510	+	33.0293i	−0.346742	+	1.26198i
$686$	9.02794	−	3.75687i	0.344688	−	0.143438i
$687$		0			0
$688$	−5.87721	+	21.9340i	−0.224066	+	0.836227i
$689$	7.58247	−	13.1332i	0.288869	−	0.500336i
$690$		0			0
$691$	−9.88097	−	17.1143i	−0.375890	−	0.651060i	0.614570	−	0.788862i	$-0.289330\pi$
$691$	−9.88097	−	17.1143i	−0.375890	−	0.651060i	−0.990460	+	0.137802i	$0.955996\pi$
$692$	−1.02692	−	1.02692i	−0.0390376	−	0.0390376i
$693$		0			0
$694$		−	12.1857i		−	0.462561i
$695$	−5.63427	−	3.30077i	−0.213720	−	0.125206i
$696$		0			0
$697$	9.50756	+	35.4827i	0.360125	+	1.34400i
$698$	−10.5696	−	2.83211i	−0.400065	−	0.107197i
$699$		0			0
$700$	22.2882	−	4.65806i	0.842415	−	0.176058i
$701$			18.8019i			0.710139i	0.934840	+	0.355069i	$0.115543\pi$
$701$			18.8019i			0.710139i	−0.934840	+	0.355069i	$0.884457\pi$
$702$		0			0
$703$	−28.4455	+	7.62196i	−1.07284	+	0.287468i
$704$	−4.19732	+	7.26997i	−0.158192	+	0.273997i
$705$		0			0
$706$	1.08878			0.0409766
$707$	−9.38519	+	29.8229i	−0.352966	+	1.12161i
$708$		0			0
$709$	24.2520	−	14.0019i	0.910802	−	0.525852i	0.0301132	−	0.999546i	$-0.490413\pi$
$709$	24.2520	−	14.0019i	0.910802	−	0.525852i	0.880689	+	0.473694i	$0.157080\pi$
$710$	10.8052	−	10.6690i	0.405514	−	0.400401i
$711$		0			0
$712$	4.28113	+	1.14713i	0.160442	+	0.0429904i
$713$	−2.20973	+	2.20973i	−0.0827552	+	0.0827552i
$714$		0			0
$715$	15.3606	+	4.22047i	0.574453	+	0.157837i
$716$	21.1869	−	12.2322i	0.791790	−	0.457140i
$717$		0			0
$718$	−0.525563	+	0.140824i	−0.0196138	+	0.00525551i
$719$	−15.0626	−	26.0892i	−0.561741	−	0.972965i	−0.997345	−	0.0728260i	$-0.976798\pi$
$719$	−15.0626	−	26.0892i	−0.561741	−	0.972965i	0.435603	−	0.900139i	$-0.356535\pi$
$720$		0			0
$721$	−26.8400	−	1.15714i	−0.999574	−	0.0430943i
$722$	11.7453	+	11.7453i	0.437116	+	0.437116i
$723$		0			0
$724$	29.1617	+	16.8365i	1.08378	+	0.625723i
$725$	9.68533	+	17.2781i	0.359704	+	0.641691i
$726$		0			0
$727$	23.1929	−	23.1929i	0.860177	−	0.860177i	−0.131182	−	0.991358i	$-0.541877\pi$
$727$	23.1929	−	23.1929i	0.860177	−	0.860177i	0.991358	+	0.131182i	$0.0418771\pi$
$728$	1.97656	+	8.89264i	0.0732561	+	0.329583i
$729$		0			0
$730$	1.40741	+	0.824519i	0.0520908	+	0.0305168i
$731$	−48.3078	−	27.8905i	−1.78673	−	1.03157i
$732$		0			0
$733$	3.20069	−	11.9451i	0.118220	−	0.441203i	−0.881288	−	0.472580i	$-0.843323\pi$
$733$	3.20069	−	11.9451i	0.118220	−	0.441203i	0.999508	+	0.0313771i	$0.00998929\pi$
$734$	1.41142			0.0520964
$735$		0			0
$736$	−6.92696			−0.255331
$737$	0.529030	−	1.97437i	0.0194871	−	0.0727267i
$738$		0			0
$739$	−41.6927	−	24.0713i	−1.53369	−	0.885477i	−0.999187	−	0.0403112i	$-0.987165\pi$
$739$	−41.6927	−	24.0713i	−1.53369	−	0.885477i	−0.534504	−	0.845166i	$-0.679502\pi$
$740$	15.4381	−	4.03184i	0.567516	−	0.148214i
$741$		0			0
$742$	−2.62286	−	11.8004i	−0.0962884	−	0.433207i
$743$	−8.27857	+	8.27857i	−0.303711	+	0.303711i	−0.842464	−	0.538753i	$-0.818896\pi$
$743$	−8.27857	+	8.27857i	−0.303711	+	0.303711i	0.538753	+	0.842464i	$0.318896\pi$
$744$		0			0
$745$	−22.9594	−	0.145641i	−0.841166	−	0.00533587i
$746$	1.19081	+	0.687512i	0.0435985	+	0.0251716i
$747$		0			0
$748$	−29.2315	−	29.2315i	−1.06881	−	1.06881i
$749$	17.4786	+	0.753547i	0.638653	+	0.0275340i
$750$		0			0
$751$	−5.17319	−	8.96023i	−0.188772	−	0.326963i	0.756069	−	0.654492i	$-0.227118\pi$
$751$	−5.17319	−	8.96023i	−0.188772	−	0.326963i	−0.944841	+	0.327529i	$0.893784\pi$
$752$	31.5100	−	8.44307i	1.14905	−	0.307887i
$753$		0			0
$754$	−3.17436	+	1.83272i	−0.115603	+	0.0667437i
$755$	5.08391	+	8.93602i	0.185022	+	0.325215i
$756$		0			0
$757$	36.0548	−	36.0548i	1.31043	−	1.31043i	0.389341	−	0.921094i	$-0.372703\pi$
$757$	36.0548	−	36.0548i	1.31043	−	1.31043i	0.921094	−	0.389341i	$-0.127297\pi$
$758$	2.20689	+	0.591334i	0.0801578	+	0.0214782i
$759$		0			0
$760$	−21.9270	−	22.2070i	−0.795377	−	0.805532i
$761$	11.9872	−	6.92083i	0.434537	−	0.250880i	−0.266741	−	0.963768i	$-0.585947\pi$
$761$	11.9872	−	6.92083i	0.434537	−	0.250880i	0.701278	+	0.712888i	$0.252613\pi$
$762$		0			0
$763$	8.76032	−	27.8373i	0.317145	−	1.00778i
$764$	44.8606			1.62300
$765$		0			0
$766$	9.23478	−	15.9951i	0.333666	−	0.577927i
$767$	13.6746	−	3.66409i	0.493761	−	0.132303i
$768$		0			0
$769$			25.5104i			0.919928i	0.887937	+	0.459964i	$0.152138\pi$
$769$			25.5104i			0.919928i	−0.887937	+	0.459964i	$0.847862\pi$
$770$	11.2972	−	5.79796i	0.407121	−	0.208944i
$771$		0			0
$772$	22.5146	+	6.03278i	0.810319	+	0.217124i
$773$	1.03391	+	3.85860i	0.0371872	+	0.138784i	0.982024	−	0.188758i	$-0.0604462\pi$
$773$	1.03391	+	3.85860i	0.0371872	+	0.138784i	−0.944836	+	0.327542i	$0.893780\pi$
$774$		0			0
$775$	11.7273	+	0.148788i	0.421257	+	0.00534463i
$776$		−	22.2252i		−	0.797839i
$777$		0			0
$778$	−8.83432	−	8.83432i	−0.316726	−	0.316726i
$779$	−22.0837	−	38.2500i	−0.791230	−	1.37045i
$780$		0			0
$781$	−26.1431	+	45.2812i	−0.935475	+	1.62029i
$782$	1.07561	−	4.01424i	0.0384638	−	0.143549i
$783$		0			0
$784$	−13.8015	−	9.64145i	−0.492912	−	0.344337i
$785$	15.7674	+	4.33226i	0.562764	+	0.154625i
$786$		0			0
$787$	−3.77567	−	14.0910i	−0.134588	−	0.502289i	−0.999999	−	0.00122700i	$-0.999609\pi$
$787$	−3.77567	−	14.0910i	−0.134588	−	0.502289i	0.865411	−	0.501062i	$-0.167057\pi$
$788$	−2.63734	−	9.84270i	−0.0939515	−	0.350632i
$789$		0			0
$790$	−17.3375	−	4.76363i	−0.616839	−	0.169482i
$791$	5.62403	+	3.57858i	0.199968	+	0.127240i
$792$		0			0
$793$	0.0849873	−	0.317177i	0.00301799	−	0.0112633i
$794$	3.77289	−	6.53484i	0.133895	−	0.231913i
$795$		0			0
$796$	−14.2305	−	24.6479i	−0.504386	−	0.873623i
$797$	9.55339	+	9.55339i	0.338398	+	0.338398i	0.855764	−	0.517366i	$-0.173087\pi$
$797$	9.55339	+	9.55339i	0.338398	+	0.338398i	−0.517366	+	0.855764i	$0.673087\pi$
$798$		0			0
$799$			80.1339i			2.83493i
$800$	18.1479	+	18.6143i	0.641624	+	0.658114i
$801$		0			0
$802$	1.01390	+	3.78393i	0.0358021	+	0.133615i
$803$	−5.42516	−	1.45367i	−0.191450	−	0.0512988i
$804$		0			0
$805$	−6.62279	−	4.27335i	−0.233423	−	0.150616i
$806$			2.17035i			0.0764472i
$807$		0			0
$808$	−22.4264	+	6.00914i	−0.788958	+	0.211401i
$809$	7.61415	−	13.1881i	0.267699	−	0.463669i	−0.700568	−	0.713586i	$-0.747070\pi$
$809$	7.61415	−	13.1881i	0.267699	−	0.463669i	0.968267	+	0.249917i	$0.0804033\pi$
$810$		0			0
$811$	52.1200			1.83018			0.915090	−	0.403250i	$-0.132120\pi$
$811$	52.1200			1.83018			0.915090	+	0.403250i	$0.132120\pi$
$812$	5.41545	−	17.2085i	0.190045	−	0.603898i
$813$		0			0
$814$	7.70607	−	4.44910i	0.270098	−	0.155941i
$815$	−19.6721	−	19.9233i	−0.689085	−	0.697883i
$816$		0			0
$817$	64.7827	+	17.3585i	2.26646	+	0.607296i
$818$	2.62740	−	2.62740i	0.0918647	−	0.0918647i
$819$		0			0
$820$	11.8336	+	20.7999i	0.413246	+	0.726365i
$821$	−6.44225	+	3.71943i	−0.224836	+	0.129809i	−0.608188	−	0.793793i	$-0.708103\pi$
$821$	−6.44225	+	3.71943i	−0.224836	+	0.129809i	0.383351	+	0.923603i	$0.374770\pi$
$822$		0			0
$823$	15.8800	−	4.25504i	0.553543	−	0.148321i	0.0288047	−	0.999585i	$-0.490830\pi$
$823$	15.8800	−	4.25504i	0.553543	−	0.148321i	0.524738	+	0.851264i	$0.324163\pi$
$824$	−9.97506	−	17.2773i	−0.347498	−	0.601884i
$825$		0			0
$826$	6.05817	−	9.52091i	0.210791	−	0.331275i
$827$	−38.3673	−	38.3673i	−1.33416	−	1.33416i	−0.901609	−	0.432552i	$-0.857613\pi$
$827$	−38.3673	−	38.3673i	−1.33416	−	1.33416i	−0.432552	−	0.901609i	$-0.642387\pi$
$828$		0			0
$829$	27.0695	+	15.6286i	0.940164	+	0.542804i	0.890012	−	0.455938i	$-0.150696\pi$
$829$	27.0695	+	15.6286i	0.940164	+	0.542804i	0.0501521	+	0.998742i	$0.484029\pi$
$830$	−13.9459	−	0.0884645i	−0.484068	−	0.00307065i
$831$		0			0
$832$	2.55887	−	2.55887i	0.0887129	−	0.0887129i
$833$	31.6517	−	26.6180i	1.09667	−	0.922261i
$834$		0			0
$835$	−7.11949	+	1.85934i	−0.246380	+	0.0643451i
$836$	43.0453	+	24.8522i	1.48875	+	0.859532i
$837$		0			0
$838$	4.51681	−	16.8570i	0.156030	−	0.582314i
$839$	10.1912			0.351841			0.175920	−	0.984404i	$-0.443710\pi$
$839$	10.1912			0.351841			0.175920	+	0.984404i	$0.443710\pi$
$840$		0			0
$841$	−13.3065			−0.458846
$842$	3.09253	−	11.5415i	0.106576	−	0.397745i
$843$		0			0
$844$	4.88515	+	2.82044i	0.168154	+	0.0970836i
$845$	19.1565	+	11.2226i	0.659004	+	0.386071i
$846$		0			0
$847$	−10.7737	+	9.88316i	−0.370190	+	0.339589i
$848$	−14.7168	+	14.7168i	−0.505378	+	0.505378i
$849$		0			0
$850$	−13.6051	+	7.62645i	−0.466652	+	0.261585i
$851$	−4.78321	−	2.76159i	−0.163966	−	0.0946661i
$852$		0			0
$853$	8.72828	+	8.72828i	0.298851	+	0.298851i	0.840564	−	0.541713i	$-0.182224\pi$
$853$	8.72828	+	8.72828i	0.298851	+	0.298851i	−0.541713	+	0.840564i	$0.682224\pi$
$854$	−0.120989	−	0.232108i	−0.00414017	−	0.00794258i
$855$		0			0
$856$	6.49590	+	11.2512i	0.222025	+	0.384559i
$857$	−19.7044	+	5.27977i	−0.673089	+	0.180354i	−0.579146	−	0.815224i	$-0.696614\pi$
$857$	−19.7044	+	5.27977i	−0.673089	+	0.180354i	−0.0939430	+	0.995578i	$0.529947\pi$
$858$		0			0
$859$	−2.51166	+	1.45011i	−0.0856967	+	0.0494770i	−0.542236	−	0.840226i	$-0.682422\pi$
$859$	−2.51166	+	1.45011i	−0.0856967	+	0.0494770i	0.456539	+	0.889703i	$0.349089\pi$
$860$	−35.0399	−	9.62754i	−1.19485	−	0.328297i
$861$		0			0
$862$	−12.1207	+	12.1207i	−0.412834	+	0.412834i
$863$	−26.2315	−	7.02870i	−0.892930	−	0.239260i	−0.216953	−	0.976182i	$-0.569612\pi$
$863$	−26.2315	−	7.02870i	−0.892930	−	0.239260i	−0.675978	+	0.736922i	$0.736278\pi$
$864$		0			0
$865$	1.34252	−	1.32559i	0.0456469	−	0.0450714i
$866$	2.48350	−	1.43385i	0.0843929	−	0.0487243i
$867$		0			0
$868$	−7.22094	−	7.87162i	−0.245095	−	0.267180i
$869$	61.9105			2.10017
$870$		0			0
$871$	−0.440570	+	0.763090i	−0.0149281	+	0.0258563i
$872$	20.9333	−	5.60905i	0.708889	−	0.189946i
$873$		0			0
$874$			4.99675i			0.169018i
$875$	5.86754	+	28.9926i	0.198359	+	0.980129i
$876$		0			0
$877$	−43.3778	−	11.6230i	−1.46476	−	0.392482i	−0.563631	−	0.826027i	$-0.690596\pi$
$877$	−43.3778	−	11.6230i	−1.46476	−	0.392482i	−0.901132	+	0.433544i	$0.857263\pi$
$878$	−1.77668	−	6.63065i	−0.0599600	−	0.223774i
$879$		0			0
$880$	−18.8638	−	11.0511i	−0.635898	−	0.372534i
$881$			15.9582i			0.537645i	0.963190	+	0.268822i	$0.0866344\pi$
$881$			15.9582i			0.537645i	−0.963190	+	0.268822i	$0.913366\pi$
$882$		0			0
$883$	22.9239	+	22.9239i	0.771449	+	0.771449i	0.978360	−	0.206911i	$-0.0663409\pi$
$883$	22.9239	+	22.9239i	0.771449	+	0.771449i	−0.206911	+	0.978360i	$0.566341\pi$
$884$	8.91041	+	15.4333i	0.299690	+	0.519077i
$885$		0			0
$886$	−5.61239	+	9.72094i	−0.188552	+	0.326581i
$887$	13.4291	−	50.1181i	0.450905	−	1.68280i	−0.248949	−	0.968517i	$-0.580085\pi$
$887$	13.4291	−	50.1181i	0.450905	−	1.68280i	0.699855	−	0.714285i	$-0.253248\pi$
$888$		0			0
$889$	−27.3170	−	17.3818i	−0.916181	−	0.582967i
$890$	−0.705606	+	2.56809i	−0.0236520	+	0.0860824i
$891$		0			0
$892$	5.61859	+	20.9689i	0.188124	+	0.702089i
$893$	−24.9368	−	93.0655i	−0.834479	−	3.11432i
$894$		0			0
$895$	15.7161	+	27.6243i	0.525332	+	0.923379i
$896$	1.30928	−	30.3689i	0.0437401	−	1.01455i
$897$		0			0
$898$	3.41279	−	12.7367i	0.113886	−	0.425030i
$899$	4.64614	−	8.04735i	0.154957	−	0.268394i
$900$		0			0
$901$	−25.5630	−	44.2764i	−0.851627	−	1.47506i
$902$	9.43666	+	9.43666i	0.314206	+	0.314206i
$903$		0			0
$904$			4.95025i			0.164643i
$905$	−22.1123	+	37.7447i	−0.735039	+	1.25468i
$906$		0			0
$907$	−11.7074	−	43.6928i	−0.388739	−	1.45079i	−0.832188	−	0.554494i	$-0.812912\pi$
$907$	−11.7074	−	43.6928i	−0.388739	−	1.45079i	0.443449	−	0.896300i	$-0.353755\pi$
$908$	13.0229	+	3.48948i	0.432180	+	0.115802i
$909$		0			0
$910$	−5.35097	+	1.15378i	−0.177383	+	0.0382475i
$911$			3.87183i			0.128279i	0.997941	+	0.0641397i	$0.0204303\pi$
$911$			3.87183i			0.128279i	−0.997941	+	0.0641397i	$0.979570\pi$
$912$		0			0
$913$	46.3846	−	12.4287i	1.53511	−	0.411330i
$914$	2.71104	−	4.69565i	0.0896731	−	0.155318i
$915$		0			0
$916$	15.7246			0.519557
$917$	−1.46855	−	1.60088i	−0.0484957	−	0.0528657i
$918$		0			0
$919$	21.5873	−	12.4634i	0.712100	−	0.411131i	−0.0997384	−	0.995014i	$-0.531801\pi$
$919$	21.5873	−	12.4634i	0.712100	−	0.411131i	0.811838	+	0.583883i	$0.198467\pi$
$920$	0.0371279	−	5.85298i	0.00122407	−	0.192967i
$921$		0			0
$922$	3.22515	+	0.864176i	0.106215	+	0.0284601i
$923$	15.9380	−	15.9380i	0.524605	−	0.524605i
$924$		0			0
$925$	5.11048	+	20.0886i	0.168032	+	0.660509i
$926$	−10.1522	+	5.86140i	−0.333623	+	0.192617i
$927$		0			0
$928$	19.8955	−	5.33098i	0.653101	−	0.174998i
$929$	14.4873	+	25.0928i	0.475313	+	0.823266i	0.999600	−	0.0282751i	$-0.00900144\pi$
$929$	14.4873	+	25.0928i	0.475313	+	0.823266i	−0.524287	+	0.851542i	$0.675668\pi$
$930$		0			0
$931$	−28.4763	+	40.7632i	−0.933272	+	1.33596i
$932$	16.6283	+	16.6283i	0.544679	+	0.544679i
$933$		0			0
$934$	−6.51431	−	3.76104i	−0.213155	−	0.123065i
$935$	38.2151	−	37.7333i	1.24977	−	1.23401i
$936$		0			0
$937$	21.9095	−	21.9095i	0.715752	−	0.715752i	−0.251980	−	0.967732i	$-0.581082\pi$
$937$	21.9095	−	21.9095i	0.715752	−	0.715752i	0.967732	+	0.251980i	$0.0810819\pi$
$938$	0.152398	+	0.685648i	0.00497598	+	0.0223872i
$939$		0			0
$940$	13.1910	+	50.5090i	0.430243	+	1.64742i
$941$	−33.5878	−	19.3919i	−1.09493	−	0.632158i	−0.160045	−	0.987110i	$-0.551164\pi$
$941$	−33.5878	−	19.3919i	−1.09493	−	0.632158i	−0.934885	+	0.354951i	$0.884497\pi$
$942$		0			0
$943$	2.14396	−	8.00136i	0.0698169	−	0.260560i
$944$	−19.4294			−0.632373
$945$		0			0
$946$	−20.2650			−0.658873
$947$	9.63349	−	35.9527i	0.313046	−	1.16830i	−0.612748	−	0.790278i	$-0.709936\pi$
$947$	9.63349	−	35.9527i	0.313046	−	1.16830i	0.925795	−	0.378027i	$-0.123397\pi$
$948$		0			0
$949$	2.09682	+	1.21060i	0.0680656	+	0.0392977i
$950$	13.4274	−	13.0909i	0.435642	−	0.424726i
$951$		0			0
$952$	29.2952	+	9.21913i	0.949464	+	0.298794i
$953$	18.1385	−	18.1385i	0.587565	−	0.587565i	−0.349406	−	0.936971i	$-0.613617\pi$
$953$	18.1385	−	18.1385i	0.587565	−	0.587565i	0.936971	+	0.349406i	$0.113617\pi$
$954$		0			0
$955$	−0.369679	+	58.2776i	−0.0119625	+	1.88582i
$956$	15.6624	+	9.04270i	0.506559	+	0.292462i
$957$		0			0
$958$	−15.6059	−	15.6059i	−0.504204	−	0.504204i
$959$	18.7339	+	35.9395i	0.604949	+	1.16055i
$960$		0			0
$961$	12.7490	+	22.0819i	0.411257	+	0.712318i
$962$	−3.70516	+	0.992795i	−0.119459	+	0.0320090i
$963$		0			0
$964$	−30.7377	+	17.7464i	−0.989996	+	0.571575i
$965$	−8.02262	+	29.1987i	−0.258257	+	0.939939i
$966$		0			0
$967$	18.4391	−	18.4391i	0.592962	−	0.592962i	−0.345469	−	0.938430i	$-0.612280\pi$
$967$	18.4391	−	18.4391i	0.592962	−	0.592962i	0.938430	+	0.345469i	$0.112280\pi$
$968$	−10.4871	−	2.81002i	−0.337069	−	0.0903175i
$969$		0			0
$970$	13.3547	+	0.0847147i	0.428795	+	0.00272003i
$971$	12.5201	−	7.22846i	0.401788	−	0.231972i	−0.285467	−	0.958388i	$-0.592149\pi$
$971$	12.5201	−	7.22846i	0.401788	−	0.231972i	0.687255	+	0.726416i	$0.258815\pi$
$972$		0			0
$973$	−7.54226	+	1.67641i	−0.241794	+	0.0537433i
$974$	−2.76494			−0.0885943
$975$		0			0
$976$	−0.225329	+	0.390281i	−0.00721260	+	0.0124926i
$977$	12.2507	−	3.28257i	0.391935	−	0.105019i	−0.0574688	−	0.998347i	$-0.518303\pi$
$977$	12.2507	−	3.28257i	0.391935	−	0.105019i	0.449404	+	0.893329i	$0.351636\pi$
$978$		0			0
$979$		−	9.17041i		−	0.293087i
$980$	15.5686	−	21.9878i	0.497322	−	0.702374i
$981$		0			0
$982$	17.5035	+	4.69006i	0.558560	+	0.149666i
$983$	7.23542	+	27.0030i	0.230774	+	0.861260i	0.980008	+	0.198956i	$0.0637550\pi$
$983$	7.23542	+	27.0030i	0.230774	+	0.861260i	−0.749234	+	0.662305i	$0.769578\pi$
$984$		0			0
$985$	12.8082	−	3.34502i	0.408104	−	0.106581i
$986$			12.3574i			0.393539i
$987$		0			0
$988$	−15.1510	−	15.1510i	−0.482017	−	0.482017i
$989$	6.28933	+	10.8934i	0.199989	+	0.346391i
$990$		0			0
$991$	−16.7267	+	28.9716i	−0.531343	+	0.920312i	0.467988	+	0.883735i	$0.344979\pi$
$991$	−16.7267	+	28.9716i	−0.531343	+	0.920312i	−0.999331	+	0.0365778i	$0.988354\pi$
$992$	3.15653	−	11.7803i	0.100220	−	0.374026i
$993$		0			0
$994$	0.773887	−	17.9504i	0.0245462	−	0.569351i
$995$	32.1370	−	18.2835i	1.01881	−	0.579625i
$996$		0			0
$997$	−13.0358	−	48.6501i	−0.412847	−	1.54076i	−0.789110	−	0.614252i	$-0.789458\pi$
$997$	−13.0358	−	48.6501i	−0.412847	−	1.54076i	0.376264	−	0.926513i	$-0.377209\pi$
$998$	3.03537	+	11.3281i	0.0960828	+	0.358586i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.ch.a.53.14	✓	128
3.2	odd	2	inner	945.2.ch.a.53.19	yes	128
5.2	odd	4	inner	945.2.ch.a.242.14	yes	128
7.2	even	3	inner	945.2.ch.a.863.19	yes	128
15.2	even	4	inner	945.2.ch.a.242.19	yes	128
21.2	odd	6	inner	945.2.ch.a.863.14	yes	128
35.2	odd	12	inner	945.2.ch.a.107.19	yes	128
105.2	even	12	inner	945.2.ch.a.107.14	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.ch.a.53.14	✓	128	1.1	even	1	trivial
945.2.ch.a.53.19	yes	128	3.2	odd	2	inner
945.2.ch.a.107.14	yes	128	105.2	even	12	inner
945.2.ch.a.107.19	yes	128	35.2	odd	12	inner
945.2.ch.a.242.14	yes	128	5.2	odd	4	inner
945.2.ch.a.242.19	yes	128	15.2	even	4	inner
945.2.ch.a.863.14	yes	128	21.2	odd	6	inner
945.2.ch.a.863.19	yes	128	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.136653 + 0.509995i) q^{2} +(1.49063 + 0.860615i) q^{4} +(-1.13030 + 1.92936i) q^{5} +(0.574059 + 2.58272i) q^{7} +(-1.38929 + 1.38929i) q^{8} +O(q^{10})\)	\(q+(-0.136653 + 0.509995i) q^{2} +(1.49063 + 0.860615i) q^{4} +(-1.13030 + 1.92936i) q^{5} +(0.574059 + 2.58272i) q^{7} +(-1.38929 + 1.38929i) q^{8} +(-0.829507 - 0.840098i) q^{10} +(3.52057 + 2.03260i) q^{11} +(-1.23916 - 1.23916i) q^{13} +(-1.39562 - 0.0601690i) q^{14} +(1.20255 + 2.08287i) q^{16} +(-5.70675 + 1.52912i) q^{17} +(6.15182 - 3.55176i) q^{19} +(-3.34529 + 1.90321i) q^{20} +(-1.51771 + 1.51771i) q^{22} +(1.28687 + 0.344817i) q^{23} +(-2.44487 - 4.36149i) q^{25} +(0.801303 - 0.462633i) q^{26} +(-1.36702 + 4.34393i) q^{28} -3.96150 q^{29} +(-1.17282 + 2.03139i) q^{31} +(-5.02221 + 1.34570i) q^{32} -3.11937i q^{34} +(-5.63186 - 1.81167i) q^{35} +(-4.00443 - 1.07298i) q^{37} +(0.970715 + 3.62276i) q^{38} +(-1.11014 - 4.25076i) q^{40} -6.21768i q^{41} +(6.67617 + 6.67617i) q^{43} +(3.49858 + 6.05972i) q^{44} +(-0.351710 + 0.609179i) q^{46} +(3.51049 - 13.1013i) q^{47} +(-6.34091 + 2.96527i) q^{49} +(2.55844 - 0.650859i) q^{50} +(-0.780691 - 2.91358i) q^{52} +(2.23972 + 8.35874i) q^{53} +(-7.90091 + 4.49501i) q^{55} +(-4.38570 - 2.79062i) q^{56} +(0.541350 - 2.02035i) q^{58} +(-4.03921 + 6.99612i) q^{59} +(0.0936881 + 0.162272i) q^{61} +(-0.875730 - 0.875730i) q^{62} +2.06500i q^{64} +(3.79142 - 0.990173i) q^{65} +(-0.130136 - 0.485674i) q^{67} +(-9.82263 - 2.63196i) q^{68} +(1.69355 - 2.62465i) q^{70} +12.8619i q^{71} +(-1.33454 + 0.357588i) q^{73} +(1.09443 - 1.89562i) q^{74} +12.2268 q^{76} +(-3.22864 + 10.2595i) q^{77} +(13.1890 - 7.61468i) q^{79} +(-5.37785 - 0.0341139i) q^{80} +(3.17099 + 0.849663i) q^{82} +(8.35280 - 8.35280i) q^{83} +(3.50009 - 12.7387i) q^{85} +(-4.31713 + 2.49250i) q^{86} +(-7.71499 + 2.06723i) q^{88} +(-1.12791 - 1.95360i) q^{89} +(2.48906 - 3.91177i) q^{91} +(1.62150 + 1.62150i) q^{92} +(6.20190 + 3.58067i) q^{94} +(-0.100756 + 15.8836i) q^{95} +(-7.99875 + 7.99875i) q^{97} +(-0.645770 - 3.63905i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 8 q^{7}+O(q^{10}) \) 128 * q - 8 * q^7	\( 128 q - 8 q^{7} - 8 q^{10} + 64 q^{16} - 8 q^{25} + 8 q^{28} + 16 q^{31} - 8 q^{37} + 40 q^{40} - 32 q^{43} + 80 q^{52} + 32 q^{55} + 16 q^{58} - 24 q^{61} - 16 q^{67} - 80 q^{70} + 64 q^{73} - 160 q^{76} - 40 q^{82} - 64 q^{85} - 48 q^{88} - 136 q^{91} - 208 q^{97}+O(q^{100}) \) 128 * q - 8 * q^7 - 8 * q^10 + 64 * q^16 - 8 * q^25 + 8 * q^28 + 16 * q^31 - 8 * q^37 + 40 * q^40 - 32 * q^43 + 80 * q^52 + 32 * q^55 + 16 * q^58 - 24 * q^61 - 16 * q^67 - 80 * q^70 + 64 * q^73 - 160 * q^76 - 40 * q^82 - 64 * q^85 - 48 * q^88 - 136 * q^91 - 208 * q^97

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