LMFDB - Embedded newform 819.2.fm.f.622.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			622.4
Character	$\chi$	$=$	819.622
Dual form			819.2.fm.f.370.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0473445 + 0.176692i) q^{2} +(1.70307 + 0.983269i) q^{4} +(2.80040 - 2.80040i) q^{5} +(1.70697 + 2.02145i) q^{7} +(-0.513062 + 0.513062i) q^{8} +O(q^{10})$	\(q+(-0.0473445 + 0.176692i) q^{2} +(1.70307 + 0.983269i) q^{4} +(2.80040 - 2.80040i) q^{5} +(1.70697 + 2.02145i) q^{7} +(-0.513062 + 0.513062i) q^{8} +(0.362225 + 0.627392i) q^{10} +(2.53602 + 0.679524i) q^{11} +(-1.37067 + 3.33485i) q^{13} +(-0.437989 + 0.205904i) q^{14} +(1.90018 + 3.29120i) q^{16} +(-1.43204 + 2.48037i) q^{17} +(-0.759707 - 2.83527i) q^{19} +(7.52284 - 2.01574i) q^{20} +(-0.240133 + 0.415922i) q^{22} +(-7.27090 + 4.19786i) q^{23} -10.6845i q^{25} +(-0.524348 - 0.400074i) q^{26} +(0.919475 + 5.12108i) q^{28} +(-1.66138 - 2.87760i) q^{29} +(6.75045 - 6.75045i) q^{31} +(-2.07320 + 0.555513i) q^{32} +(-0.370463 - 0.370463i) q^{34} +(10.4411 + 0.880647i) q^{35} +(-6.77592 - 1.81560i) q^{37} +0.536937 q^{38} +2.87356i q^{40} +(-2.79099 - 0.747843i) q^{41} +(-2.43132 - 1.40372i) q^{43} +(3.65087 + 3.65087i) q^{44} +(-0.397491 - 1.48346i) q^{46} +(-4.85765 - 4.85765i) q^{47} +(-1.17248 + 6.90111i) q^{49} +(1.88787 + 0.505853i) q^{50} +(-5.61342 + 4.33176i) q^{52} +5.43259 q^{53} +(9.00481 - 5.19893i) q^{55} +(-1.91291 - 0.161343i) q^{56} +(0.587105 - 0.157314i) q^{58} +(-0.00666592 + 0.00178613i) q^{59} +(-5.65469 - 3.26474i) q^{61} +(0.873154 + 1.51235i) q^{62} +7.20808i q^{64} +(5.50050 + 13.1774i) q^{65} +(2.10207 - 7.84504i) q^{67} +(-4.87775 + 2.81617i) q^{68} +(-0.649930 + 1.80316i) q^{70} +(14.5933 - 3.91026i) q^{71} +(-0.321617 - 0.321617i) q^{73} +(0.641604 - 1.11129i) q^{74} +(1.49399 - 5.57566i) q^{76} +(2.95530 + 6.28635i) q^{77} +0.280448 q^{79} +(14.5379 + 3.89543i) q^{80} +(0.264276 - 0.457739i) q^{82} +(-2.42973 + 2.42973i) q^{83} +(2.93575 + 10.9564i) q^{85} +(0.363136 - 0.363136i) q^{86} +(-1.64977 + 0.952496i) q^{88} +(0.0536096 - 0.200074i) q^{89} +(-9.08093 + 2.92177i) q^{91} -16.5105 q^{92} +(1.08829 - 0.628324i) q^{94} +(-10.0674 - 5.81240i) q^{95} +(-0.197356 - 0.736543i) q^{97} +(-1.16386 - 0.533897i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$

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 $

$2$	−0.0473445	+	0.176692i	−0.0334776	+	0.124940i	−0.980642	−	0.195807i	$-0.937267\pi$
$2$	−0.0473445	+	0.176692i	−0.0334776	+	0.124940i	0.947165	+	0.320747i	$0.103934\pi$
$3$		0			0
$3$		0			0
$4$	1.70307	+	0.983269i	0.851536	+	0.491635i
$5$	2.80040	−	2.80040i	1.25238	−	1.25238i	0.297728	−	0.954651i	$-0.403771\pi$
$5$	2.80040	−	2.80040i	1.25238	−	1.25238i	0.954651	−	0.297728i	$-0.0962288\pi$
$6$		0			0
$7$	1.70697	+	2.02145i	0.645175	+	0.764034i
$7$	1.70697	+	2.02145i	0.645175	+	0.764034i
$8$	−0.513062	+	0.513062i	−0.181395	+	0.181395i
$9$		0			0
$10$	0.362225	+	0.627392i	0.114546	+	0.198399i
$11$	2.53602	+	0.679524i	0.764638	+	0.204884i	0.620001	−	0.784601i	$-0.287132\pi$
$11$	2.53602	+	0.679524i	0.764638	+	0.204884i	0.144637	+	0.989485i	$0.453799\pi$
$12$		0			0
$13$	−1.37067	+	3.33485i	−0.380156	+	0.924922i
$13$	−1.37067	+	3.33485i	−0.380156	+	0.924922i
$14$	−0.437989	+	0.205904i	−0.117057	+	0.0550302i
$15$		0			0
$16$	1.90018	+	3.29120i	0.475044	+	0.822800i
$17$	−1.43204	+	2.48037i	−0.347322	+	0.601579i	−0.985773	−	0.168083i	$-0.946242\pi$
$17$	−1.43204	+	2.48037i	−0.347322	+	0.601579i	0.638451	+	0.769663i	$0.279576\pi$
$18$		0			0
$19$	−0.759707	−	2.83527i	−0.174289	−	0.650455i	−0.996672	−	0.0815202i	$-0.974022\pi$
$19$	−0.759707	−	2.83527i	−0.174289	−	0.650455i	0.822383	−	0.568934i	$-0.192644\pi$
$20$	7.52284	−	2.01574i	1.68216	−	0.450733i
$21$		0			0
$22$	−0.240133	+	0.415922i	−0.0511965	+	0.0886749i
$23$	−7.27090	+	4.19786i	−1.51609	+	0.875314i	−0.516266	+	0.856428i	$0.672679\pi$
$23$	−7.27090	+	4.19786i	−1.51609	+	0.875314i	−0.999822	+	0.0188857i	$0.993988\pi$
$24$		0			0
$25$		−	10.6845i		−	2.13690i
$26$	−0.524348	−	0.400074i	−0.102833	−	0.0784609i
$27$		0			0
$28$	0.919475	+	5.12108i	0.173764	+	0.967794i
$29$	−1.66138	−	2.87760i	−0.308511	−	0.534356i	0.669526	−	0.742789i	$-0.266497\pi$
$29$	−1.66138	−	2.87760i	−0.308511	−	0.534356i	−0.978037	+	0.208432i	$0.933164\pi$
$30$		0			0
$31$	6.75045	−	6.75045i	1.21242	−	1.21242i	0.242188	−	0.970229i	$-0.422135\pi$
$31$	6.75045	−	6.75045i	1.21242	−	1.21242i	0.970229	−	0.242188i	$-0.0778651\pi$
$32$	−2.07320	+	0.555513i	−0.366494	+	0.0982017i
$33$		0			0
$34$	−0.370463	−	0.370463i	−0.0635339	−	0.0635339i
$35$	10.4411	+	0.880647i	1.76486	+	0.148856i
$36$		0			0
$37$	−6.77592	−	1.81560i	−1.11395	−	0.298483i	−0.345519	−	0.938412i	$-0.612297\pi$
$37$	−6.77592	−	1.81560i	−1.11395	−	0.298483i	−0.768434	+	0.639929i	$0.778964\pi$
$38$	0.536937			0.0871026
$39$		0			0
$40$			2.87356i			0.454350i
$41$	−2.79099	−	0.747843i	−0.435879	−	0.116793i	0.0342056	−	0.999415i	$-0.489110\pi$
$41$	−2.79099	−	0.747843i	−0.435879	−	0.116793i	−0.470085	+	0.882621i	$0.655777\pi$
$42$		0			0
$43$	−2.43132	−	1.40372i	−0.370773	−	0.214066i	0.303023	−	0.952983i	$-0.402004\pi$
$43$	−2.43132	−	1.40372i	−0.370773	−	0.214066i	−0.673796	+	0.738917i	$0.735337\pi$
$44$	3.65087	+	3.65087i	0.550389	+	0.550389i
$45$		0			0
$46$	−0.397491	−	1.48346i	−0.0586068	−	0.218724i
$47$	−4.85765	−	4.85765i	−0.708561	−	0.708561i	0.257672	−	0.966232i	$-0.417045\pi$
$47$	−4.85765	−	4.85765i	−0.708561	−	0.708561i	−0.966232	+	0.257672i	$0.917045\pi$
$48$		0			0
$49$	−1.17248	+	6.90111i	−0.167497	+	0.985873i
$50$	1.88787	+	0.505853i	0.266985	+	0.0715384i
$51$		0			0
$52$	−5.61342	+	4.33176i	−0.778441	+	0.600707i
$53$	5.43259			0.746224			0.373112	−	0.927786i	$-0.378291\pi$
$53$	5.43259			0.746224			0.373112	+	0.927786i	$0.378291\pi$
$54$		0			0
$55$	9.00481	−	5.19893i	1.21421	−	0.701024i
$56$	−1.91291	−	0.161343i	−0.255623	−	0.0215604i
$57$		0			0
$58$	0.587105	−	0.157314i	0.0770907	−	0.0206564i
$59$	−0.00666592	+	0.00178613i	−0.000867829	+	0.000232534i	−0.259253	−	0.965809i	$-0.583476\pi$
$59$	−0.00666592	+	0.00178613i	−0.000867829	+	0.000232534i	0.258385	+	0.966042i	$0.416810\pi$
$60$		0			0
$61$	−5.65469	−	3.26474i	−0.724009	−	0.418007i	0.0922177	−	0.995739i	$-0.470604\pi$
$61$	−5.65469	−	3.26474i	−0.724009	−	0.418007i	−0.816226	+	0.577732i	$0.803938\pi$
$62$	0.873154	+	1.51235i	0.110891	+	0.192068i
$63$		0			0
$64$			7.20808i			0.901010i
$65$	5.50050	+	13.1774i	0.682253	+	1.63445i
$66$		0			0
$67$	2.10207	−	7.84504i	0.256809	−	0.958424i	−0.710266	−	0.703933i	$-0.751425\pi$
$67$	2.10207	−	7.84504i	0.256809	−	0.958424i	0.967075	−	0.254491i	$-0.0819079\pi$
$68$	−4.87775	+	2.81617i	−0.591514	+	0.341511i
$69$		0			0
$70$	−0.649930	+	1.80316i	−0.0776815	+	0.215519i
$71$	14.5933	−	3.91026i	1.73191	−	0.464063i	0.751286	−	0.659977i	$-0.229434\pi$
$71$	14.5933	−	3.91026i	1.73191	−	0.464063i	0.980621	+	0.195914i	$0.0627675\pi$
$72$		0			0
$73$	−0.321617	−	0.321617i	−0.0376425	−	0.0376425i	0.688035	−	0.725677i	$-0.258474\pi$
$73$	−0.321617	−	0.321617i	−0.0376425	−	0.0376425i	−0.725677	+	0.688035i	$0.758474\pi$
$74$	0.641604	−	1.11129i	0.0745850	−	0.129185i
$75$		0			0
$76$	1.49399	−	5.57566i	0.171373	−	0.639572i
$77$	2.95530	+	6.28635i	0.336787	+	0.716396i
$78$		0			0
$79$	0.280448			0.0315529			0.0157764	−	0.999876i	$-0.494978\pi$
$79$	0.280448			0.0315529			0.0157764	+	0.999876i	$0.494978\pi$
$80$	14.5379	+	3.89543i	1.62539	+	0.435522i
$81$		0			0
$82$	0.264276	−	0.457739i	0.0291844	−	0.0505488i
$83$	−2.42973	+	2.42973i	−0.266698	+	0.266698i	−0.827768	−	0.561070i	$-0.810390\pi$
$83$	−2.42973	+	2.42973i	−0.266698	+	0.266698i	0.561070	+	0.827768i	$0.310390\pi$
$84$		0			0
$85$	2.93575	+	10.9564i	0.318426	+	1.18838i
$86$	0.363136	−	0.363136i	0.0391580	−	0.0391580i
$87$		0			0
$88$	−1.64977	+	0.952496i	−0.175866	+	0.101536i
$89$	0.0536096	−	0.200074i	0.00568261	−	0.0212078i	−0.963026	−	0.269407i	$-0.913172\pi$
$89$	0.0536096	−	0.200074i	0.00568261	−	0.0212078i	0.968709	+	0.248200i	$0.0798389\pi$
$90$		0			0
$91$	−9.08093	+	2.92177i	−0.951940	+	0.306285i
$92$	−16.5105			−1.72134
$93$		0			0
$94$	1.08829	−	0.628324i	0.112249	−	0.0648067i
$95$	−10.0674	−	5.81240i	−1.03289	−	0.596340i
$96$		0			0
$97$	−0.197356	−	0.736543i	−0.0200385	−	0.0747847i	0.955183	−	0.296017i	$-0.0956586\pi$
$97$	−0.197356	−	0.736543i	−0.0200385	−	0.0747847i	−0.975221	+	0.221233i	$0.928992\pi$
$98$	−1.16386	−	0.533897i	−0.117568	−	0.0539318i
$99$		0			0
$100$	10.5058	−	18.1965i	1.05058	−	1.81965i
$101$	0.682084	+	1.18140i	0.0678699	+	0.117554i	0.897963	−	0.440070i	$-0.145046\pi$
$101$	0.682084	+	1.18140i	0.0678699	+	0.117554i	−0.830094	+	0.557624i	$0.811713\pi$
$102$		0			0
$103$	4.43543			0.437036			0.218518	−	0.975833i	$-0.429878\pi$
$103$	4.43543			0.437036			0.218518	+	0.975833i	$0.429878\pi$
$104$	−1.00775	−	2.41423i	−0.0988177	−	0.236734i
$105$		0			0
$106$	−0.257203	+	0.959895i	−0.0249818	+	0.0932333i
$107$	1.81150	+	3.13761i	0.175124	+	0.303324i	0.940204	−	0.340611i	$-0.110634\pi$
$107$	1.81150	+	3.13761i	0.175124	+	0.303324i	−0.765080	+	0.643935i	$0.777301\pi$
$108$		0			0
$109$	11.1249	+	11.1249i	1.06557	+	1.06557i	0.997694	+	0.0678792i	$0.0216232\pi$
$109$	11.1249	+	11.1249i	1.06557	+	1.06557i	0.0678792	+	0.997694i	$0.478377\pi$
$110$	0.492281	+	1.83722i	0.0469372	+	0.175172i
$111$		0			0
$112$	−3.40943	+	9.45909i	−0.322161	+	0.893800i
$113$	2.74763	−	4.75903i	0.258475	−	0.447692i	−0.707358	−	0.706855i	$-0.750113\pi$
$113$	2.74763	−	4.75903i	0.258475	−	0.447692i	0.965834	+	0.259163i	$0.0834466\pi$
$114$		0			0
$115$	−8.60577	+	32.1172i	−0.802492	+	2.99494i
$116$		−	6.53434i		−	0.606698i
$117$		0			0
$118$		−	0.00126238i		−	0.000116211i
$119$	−7.45840	+	1.33913i	−0.683711	+	0.122758i
$120$		0			0
$121$	−3.55665	−	2.05343i	−0.323331	−	0.186675i
$122$	0.844571	−	0.844571i	0.0764638	−	0.0764638i
$123$		0			0
$124$	18.1340	−	4.85900i	1.62848	−	0.436351i
$125$	−15.9190	−	15.9190i	−1.42383	−	1.42383i
$126$		0			0
$127$	8.80555	−	5.08389i	0.781367	−	0.451122i	−0.0555478	−	0.998456i	$-0.517691\pi$
$127$	8.80555	−	5.08389i	0.781367	−	0.451122i	0.836914	+	0.547334i	$0.184357\pi$
$128$	−5.42001	−	1.45229i	−0.479066	−	0.128365i
$129$		0			0
$130$	−2.58875	+	0.348018i	−0.227049	+	0.0305232i
$131$		−	19.5230i		−	1.70573i	−0.522129	−	0.852867i	$-0.674862\pi$
$131$		−	19.5230i		−	1.70573i	0.522129	−	0.852867i	$-0.325138\pi$
$132$		0			0
$133$	4.43453	−	6.37543i	0.384523	−	0.552820i
$134$	1.28663	+	0.742838i	0.111148	+	0.0641715i
$135$		0			0
$136$	−0.537858	−	2.00731i	−0.0461209	−	0.172126i
$137$	3.09421	+	11.5477i	0.264356	+	0.986590i	0.962643	+	0.270773i	$0.0872791\pi$
$137$	3.09421	+	11.5477i	0.264356	+	0.986590i	−0.698287	+	0.715818i	$0.746054\pi$
$138$		0			0
$139$	−14.4291	−	8.33062i	−1.22386	−	0.706594i	−0.258119	−	0.966113i	$-0.583103\pi$
$139$	−14.4291	−	8.33062i	−1.22386	−	0.706594i	−0.965738	+	0.259519i	$0.916436\pi$
$140$	16.9160	+	11.7662i	1.42966	+	0.994425i
$141$		0			0
$142$			2.76365i			0.231920i
$143$	−5.74217	+	7.52585i	−0.480184	+	0.629343i
$144$		0			0
$145$	−12.7110	−	3.40589i	−1.05559	−	0.282844i
$146$	0.0720540	−	0.0416004i	0.00596323	−	0.00344287i
$147$		0			0
$148$	−9.75465	−	9.75465i	−0.801827	−	0.801827i
$149$	−14.7603	+	3.95502i	−1.20921	+	0.324008i	−0.806454	−	0.591297i	$-0.798616\pi$
$149$	−14.7603	+	3.95502i	−1.20921	+	0.324008i	−0.402761	+	0.915305i	$0.631949\pi$
$150$		0			0
$151$	−7.50367	+	7.50367i	−0.610640	+	0.610640i	−0.943113	−	0.332473i	$-0.892117\pi$
$151$	−7.50367	+	7.50367i	−0.610640	+	0.610640i	0.332473	+	0.943113i	$0.392117\pi$
$152$	1.84444	+	1.06489i	0.149604	+	0.0863740i
$153$		0			0
$154$	−1.25066	+	0.224553i	−0.100781	+	0.0180950i
$155$		−	37.8080i		−	3.03681i
$156$		0			0
$157$		−	13.4871i		−	1.07639i	−0.842820	−	0.538195i	$-0.819106\pi$
$157$		−	13.4871i		−	1.07639i	0.842820	−	0.538195i	$-0.180894\pi$
$158$	−0.0132777	+	0.0495530i	−0.00105632	+	0.00394222i
$159$		0			0
$160$	−4.25014	+	7.36146i	−0.336003	+	0.581975i
$161$	−20.8970	−	7.53210i	−1.64691	−	0.593612i
$162$		0			0
$163$	−1.07320	−	4.00525i	−0.0840598	−	0.313716i	0.911075	−	0.412241i	$-0.135254\pi$
$163$	−1.07320	−	4.00525i	−0.0840598	−	0.313716i	−0.995134	+	0.0985258i	$0.968587\pi$
$164$	−4.01792	−	4.01792i	−0.313747	−	0.313747i
$165$		0			0
$166$	−0.314280	−	0.544349i	−0.0243928	−	0.0422496i
$167$	3.62497	−	13.5286i	0.280508	−	1.04687i	−0.671551	−	0.740958i	$-0.734372\pi$
$167$	3.62497	−	13.5286i	0.280508	−	1.04687i	0.952059	−	0.305913i	$-0.0989618\pi$
$168$		0			0
$169$	−9.24251	−	9.14199i	−0.710962	−	0.703230i
$170$	−2.07489			−0.159137
$171$		0			0
$172$	−2.76048	−	4.78129i	−0.210484	−	0.364570i
$173$	−7.63123	+	13.2177i	−0.580192	+	1.00492i	0.415265	+	0.909701i	$0.363689\pi$
$173$	−7.63123	+	13.2177i	−0.580192	+	1.00492i	−0.995456	+	0.0952206i	$0.969644\pi$
$174$		0			0
$175$	21.5982	−	18.2382i	1.63267	−	1.37868i
$176$	2.58243	+	9.63776i	0.194658	+	0.726473i
$177$		0			0
$178$	0.0328133	+	0.0189448i	0.00245946	+	0.00141997i
$179$	−6.94881	+	4.01190i	−0.519379	+	0.299863i	−0.736680	−	0.676241i	$-0.763608\pi$
$179$	−6.94881	+	4.01190i	−0.519379	+	0.299863i	0.217302	+	0.976104i	$0.430274\pi$
$180$		0			0
$181$	−9.08130			−0.675008			−0.337504	−	0.941324i	$-0.609583\pi$
$181$	−9.08130			−0.675008			−0.337504	+	0.941324i	$0.609583\pi$
$182$	−0.0863213	−	1.74286i	−0.00639856	−	0.129189i
$183$		0			0
$184$	1.57666	−	5.88418i	0.116233	−	0.433788i
$185$	−24.0597	+	13.8909i	−1.76891	+	1.02128i
$186$		0			0
$187$	−5.31717	+	5.31717i	−0.388830	+	0.388830i
$188$	−3.49655	−	13.0493i	−0.255012	−	0.951718i
$189$		0			0
$190$	1.50364	−	1.50364i	0.109085	−	0.109085i
$191$	10.2571	−	17.7658i	0.742179	−	1.28549i	−0.209323	−	0.977847i	$-0.567126\pi$
$191$	10.2571	−	17.7658i	0.742179	−	1.28549i	0.951501	−	0.307645i	$-0.0995408\pi$
$192$		0			0
$193$	14.0081	+	3.75346i	1.00832	+	0.270180i	0.724929	−	0.688823i	$-0.241872\pi$
$193$	14.0081	+	3.75346i	1.00832	+	0.270180i	0.283396	+	0.959003i	$0.408539\pi$
$194$	0.139485			0.0100144
$195$		0			0
$196$	−8.78247	+	10.6002i	−0.627319	+	0.757159i
$197$	−4.65346	+	17.3669i	−0.331545	+	1.23734i	0.576022	+	0.817434i	$0.304604\pi$
$197$	−4.65346	+	17.3669i	−0.331545	+	1.23734i	−0.907567	+	0.419908i	$0.862062\pi$
$198$		0			0
$199$	−1.63893	+	2.83871i	−0.116181	+	0.201231i	−0.918251	−	0.395999i	$-0.870399\pi$
$199$	−1.63893	+	2.83871i	−0.116181	+	0.201231i	0.802070	+	0.597230i	$0.203732\pi$
$200$	5.48182	+	5.48182i	0.387623	+	0.387623i
$201$		0			0
$202$	−0.241037	+	0.0645858i	−0.0169593	+	0.00454424i
$203$	2.98097	−	8.27037i	0.209223	−	0.580466i
$204$		0			0
$205$	−9.91015	+	5.72163i	−0.692155	+	0.399616i
$206$	−0.209993	+	0.783706i	−0.0146309	+	0.0546034i
$207$		0			0
$208$	−13.5802	+	1.82565i	−0.941617	+	0.126586i
$209$		−	7.70652i		−	0.533071i
$210$		0			0
$211$	12.5254	+	21.6946i	0.862283	+	1.49352i	0.869719	+	0.493546i	$0.164300\pi$
$211$	12.5254	+	21.6946i	0.862283	+	1.49352i	−0.00743594	+	0.999972i	$0.502367\pi$
$212$	9.25209	+	5.34170i	0.635436	+	0.366869i
$213$		0			0
$214$	−0.640155	+	0.171529i	−0.0437601	+	0.0117255i
$215$	−10.7397	+	2.87769i	−0.732440	+	0.196257i
$216$		0			0
$217$	25.1685	+	2.12282i	1.70855	+	0.144107i
$218$	−2.49238	+	1.43898i	−0.168806	+	0.0974599i
$219$		0			0
$220$	20.4478			1.37859
$221$	−6.30882	−	8.17544i	−0.424377	−	0.549940i
$222$		0			0
$223$	−9.63125	−	2.58069i	−0.644956	−	0.172816i	−0.0785089	−	0.996913i	$-0.525016\pi$
$223$	−9.63125	−	2.58069i	−0.644956	−	0.172816i	−0.566447	+	0.824098i	$0.691683\pi$
$224$	−4.66184	−	3.24262i	−0.311482	−	0.216657i
$225$		0			0
$226$	0.710798	+	0.710798i	0.0472816	+	0.0472816i
$227$	4.05289	+	15.1256i	0.269000	+	1.00392i	0.959757	+	0.280833i	$0.0906108\pi$
$227$	4.05289	+	15.1256i	0.269000	+	1.00392i	−0.690757	+	0.723087i	$0.742722\pi$
$228$		0			0
$229$	1.59130	+	1.59130i	0.105156	+	0.105156i	0.757727	−	0.652571i	$-0.226310\pi$
$229$	1.59130	+	1.59130i	0.105156	+	0.105156i	−0.652571	+	0.757727i	$0.726310\pi$
$230$	−5.26741	−	3.04114i	−0.347323	−	0.200527i
$231$		0			0
$232$	2.32878	+	0.623994i	0.152892	+	0.0409672i
$233$		−	8.49682i		−	0.556645i	−0.960488	−	0.278323i	$-0.910222\pi$
$233$		−	8.49682i		−	0.556645i	0.960488	−	0.278323i	$-0.0897784\pi$
$234$		0			0
$235$	−27.2067			−1.77477
$236$	−0.0131088	−	0.00351249i	−0.000853310	−	0.000228644i
$237$		0			0
$238$	0.116500	−	1.38124i	0.00755157	−	0.0895325i
$239$	6.87958	+	6.87958i	0.445003	+	0.445003i	0.893689	−	0.448686i	$-0.148108\pi$
$239$	6.87958	+	6.87958i	0.445003	+	0.445003i	−0.448686	+	0.893689i	$0.648108\pi$
$240$		0			0
$241$	−19.8128	+	5.30883i	−1.27626	+	0.341972i	−0.832424	−	0.554139i	$-0.813048\pi$
$241$	−19.8128	+	5.30883i	−1.27626	+	0.341972i	−0.443831	+	0.896110i	$0.646381\pi$
$242$	0.531212	−	0.531212i	0.0341476	−	0.0341476i
$243$		0			0
$244$	−6.42023	−	11.1202i	−0.411013	−	0.711895i
$245$	16.0425	+	22.6093i	1.02492	+	1.44446i
$246$		0			0
$247$	10.4965	+	1.35271i	0.667877	+	0.0860709i
$248$			6.92680i			0.439852i
$249$		0			0
$250$	3.56642	−	2.05908i	0.225561	−	0.130227i
$251$	4.35546	−	7.54388i	0.274914	−	0.476165i	−0.695199	−	0.718817i	$-0.744684\pi$
$251$	4.35546	−	7.54388i	0.274914	−	0.476165i	0.970113	+	0.242652i	$0.0780172\pi$
$252$		0			0
$253$	−21.2917	+	5.70509i	−1.33860	+	0.358676i
$254$	0.481388	+	1.79656i	0.0302050	+	0.112726i
$255$		0			0
$256$	−6.69487	+	11.5958i	−0.418429	+	0.724741i
$257$	6.96099	+	12.0568i	0.434215	+	0.752082i	0.997231	−	0.0743637i	$-0.0236926\pi$
$257$	6.96099	+	12.0568i	0.434215	+	0.752082i	−0.563016	+	0.826446i	$0.690359\pi$
$258$		0			0
$259$	−7.89617	−	16.7963i	−0.490644	−	1.04367i
$260$	−3.58916	+	27.8505i	−0.222590	+	1.72721i
$261$		0			0
$262$	3.44956	+	0.924307i	0.213114	+	0.0571039i
$263$	5.34924	+	9.26516i	0.329848	+	0.571314i	0.982482	−	0.186360i	$-0.0596690\pi$
$263$	5.34924	+	9.26516i	0.329848	+	0.571314i	−0.652633	+	0.757674i	$0.726336\pi$
$264$		0			0
$265$	15.2134	−	15.2134i	0.934555	−	0.934555i
$266$	0.916537	+	1.08539i	0.0561965	+	0.0665494i
$267$		0			0
$268$	11.2938	−	11.2938i	0.689877	−	0.689877i
$269$	7.98188	+	4.60834i	0.486664	+	0.280976i	0.723189	−	0.690650i	$-0.242675\pi$
$269$	7.98188	+	4.60834i	0.486664	+	0.280976i	−0.236526	+	0.971625i	$0.576009\pi$
$270$		0			0
$271$	0.262832	−	0.980903i	0.0159659	−	0.0595856i	−0.957483	−	0.288489i	$-0.906847\pi$
$271$	0.262832	−	0.980903i	0.0159659	−	0.0595856i	0.973449	+	0.228903i	$0.0735139\pi$
$272$	−10.8845			−0.659972
$273$		0			0
$274$	−2.18689			−0.132115
$275$	7.26039	−	27.0961i	0.437818	−	1.63396i
$276$		0			0
$277$	0.795438	+	0.459247i	0.0477933	+	0.0275935i	0.523706	−	0.851899i	$-0.324549\pi$
$277$	0.795438	+	0.459247i	0.0477933	+	0.0275935i	−0.475913	+	0.879492i	$0.657882\pi$
$278$	2.15509	−	2.15509i	0.129254	−	0.129254i
$279$		0			0
$280$	−5.80874	+	4.90509i	−0.347139	+	0.293135i
$281$	−3.41893	+	3.41893i	−0.203956	+	0.203956i	−0.801693	−	0.597737i	$-0.796067\pi$
$281$	−3.41893	+	3.41893i	−0.203956	+	0.203956i	0.597737	+	0.801693i	$0.296067\pi$
$282$		0			0
$283$	−7.94500	−	13.7611i	−0.472281	−	0.818015i	0.527216	−	0.849731i	$-0.323236\pi$
$283$	−7.94500	−	13.7611i	−0.472281	−	0.818015i	−0.999497	+	0.0317167i	$0.989903\pi$
$284$	28.6983	+	7.68968i	1.70293	+	0.456299i
$285$		0			0
$286$	−1.05790	−	1.37090i	−0.0625547	−	0.0810631i
$287$	−3.25242	−	6.91838i	−0.191984	−	0.408379i
$288$		0			0
$289$	4.39849	+	7.61842i	0.258735	+	0.448142i
$290$	1.20359	−	2.08468i	0.0706771	−	0.122416i
$291$		0			0
$292$	−0.231501	−	0.863974i	−0.0135476	−	0.0505603i
$293$	−14.2807	+	3.82651i	−0.834288	+	0.223547i	−0.650584	−	0.759435i	$-0.725476\pi$
$293$	−14.2807	+	3.82651i	−0.834288	+	0.223547i	−0.183705	+	0.982981i	$0.558809\pi$
$294$		0			0
$295$	−0.0136654	+	0.0236692i	−0.000795630	+	0.00137807i
$296$	4.40798	−	2.54495i	0.256209	−	0.147922i
$297$		0			0
$298$		−	2.79528i		−	0.161926i
$299$	−4.03321	−	30.0013i	−0.233247	−	1.73502i
$300$		0			0
$301$	−1.31265	−	7.31090i	−0.0756599	−	0.421393i
$302$	−0.970581	−	1.68110i	−0.0558506	−	0.0967362i
$303$		0			0
$304$	7.88785	−	7.88785i	0.452399	−	0.452399i
$305$	−24.9780	+	6.69283i	−1.43024	+	0.383230i
$306$		0			0
$307$	11.9699	+	11.9699i	0.683157	+	0.683157i	0.960710	−	0.277553i	$-0.0895234\pi$
$307$	11.9699	+	11.9699i	0.683157	+	0.683157i	−0.277553	+	0.960710i	$0.589523\pi$
$308$	−1.14809	+	13.6120i	−0.0654187	+	0.775613i
$309$		0			0
$310$	6.68037	+	1.79000i	0.379419	+	0.101665i
$311$	22.3022			1.26464			0.632322	−	0.774706i	$-0.282102\pi$
$311$	22.3022			1.26464			0.632322	+	0.774706i	$0.282102\pi$
$312$		0			0
$313$			21.7630i			1.23012i	0.788481	+	0.615059i	$0.210868\pi$
$313$			21.7630i			1.23012i	−0.788481	+	0.615059i	$0.789132\pi$
$314$	2.38307	+	0.638541i	0.134484	+	0.0360349i
$315$		0			0
$316$	0.477624	+	0.275756i	0.0268684	+	0.0155125i
$317$	−3.88719	−	3.88719i	−0.218327	−	0.218327i	0.589466	−	0.807793i	$-0.299338\pi$
$317$	−3.88719	−	3.88719i	−0.218327	−	0.218327i	−0.807793	+	0.589466i	$0.799338\pi$
$318$		0			0
$319$	−2.25790	−	8.42659i	−0.126418	−	0.471798i
$320$	20.1855	+	20.1855i	1.12841	+	1.12841i
$321$		0			0
$322$	2.32022	−	3.33573i	0.129301	−	0.185893i
$323$	8.12046	+	2.17587i	0.451834	+	0.121069i
$324$		0			0
$325$	35.6313	+	14.6450i	1.97647	+	0.812358i
$326$	0.758506			0.0420098
$327$		0			0
$328$	1.81564	−	1.04826i	0.100252	−	0.0578804i
$329$	1.52759	−	18.1113i	0.0842188	−	0.998510i
$330$		0			0
$331$	−17.6440	+	4.72770i	−0.969802	+	0.259858i	−0.708744	−	0.705466i	$-0.750738\pi$
$331$	−17.6440	+	4.72770i	−0.969802	+	0.259858i	−0.261058	+	0.965323i	$0.584071\pi$
$332$	−6.52709	+	1.74893i	−0.358221	+	0.0959849i
$333$		0			0
$334$	2.21877	+	1.28101i	0.121406	+	0.0700935i
$335$	−16.0826	−	27.8559i	−0.878688	−	1.52193i
$336$		0			0
$337$		−	12.4905i		−	0.680402i	−0.940353	−	0.340201i	$-0.889505\pi$
$337$		−	12.4905i		−	0.680402i	0.940353	−	0.340201i	$-0.110495\pi$
$338$	2.05290	−	1.20025i	0.111663	−	0.0652852i
$339$		0			0
$340$	−5.77326	+	21.5461i	−0.313099	+	1.16850i
$341$	21.7064	−	12.5322i	1.17547	−	0.678655i
$342$		0			0
$343$	−15.9516	+	9.40990i	−0.861306	+	0.508087i
$344$	1.96762	−	0.527221i	0.106087	−	0.0284258i
$345$		0			0
$346$	−1.97416	−	1.97416i	−0.106132	−	0.106132i
$347$	2.70509	−	4.68534i	0.145217	−	0.251522i	−0.784237	−	0.620461i	$-0.786945\pi$
$347$	2.70509	−	4.68534i	0.145217	−	0.251522i	0.929454	+	0.368939i	$0.120279\pi$
$348$		0			0
$349$	1.60376	−	5.98531i	0.0858472	−	0.320386i	−0.909626	−	0.415428i	$-0.863632\pi$
$349$	1.60376	−	5.98531i	0.0858472	−	0.320386i	0.995473	+	0.0950418i	$0.0302985\pi$
$350$	2.19999	+	4.67970i	0.117594	+	0.250141i
$351$		0			0
$352$	−5.63516			−0.300355
$353$	34.1022	+	9.13766i	1.81508	+	0.486348i	0.996159	−	0.0875628i	$-0.0279078\pi$
$353$	34.1022	+	9.13766i	1.81508	+	0.486348i	0.818918	+	0.573911i	$0.194575\pi$
$354$		0			0
$355$	29.9168	−	51.8175i	1.58782	−	2.75019i
$356$	0.288028	−	0.288028i	0.0152654	−	0.0152654i
$357$		0			0
$358$	−0.379882	−	1.41774i	−0.0200774	−	0.0749299i
$359$	−7.81387	+	7.81387i	−0.412400	+	0.412400i	−0.882574	−	0.470174i	$-0.844191\pi$
$359$	−7.81387	+	7.81387i	−0.412400	+	0.412400i	0.470174	+	0.882574i	$0.344191\pi$
$360$		0			0
$361$	8.99290	−	5.19206i	0.473311	−	0.273266i
$362$	0.429949	−	1.60459i	0.0225976	−	0.0843355i
$363$		0			0
$364$	−18.3384	−	3.95301i	−0.961191	−	0.207194i
$365$	−1.80132			−0.0942852
$366$		0			0
$367$	−19.4308	+	11.2184i	−1.01428	+	0.585593i	−0.912441	−	0.409208i	$-0.865805\pi$
$367$	−19.4308	+	11.2184i	−1.01428	+	0.585593i	−0.101836	+	0.994801i	$0.532472\pi$
$368$	−27.6320	−	15.9533i	−1.44042	−	0.831625i
$369$		0			0
$370$	−1.31531	−	4.90882i	−0.0683799	−	0.255197i
$371$	9.27329	+	10.9817i	0.481445	+	0.570141i
$372$		0			0
$373$	−3.45623	+	5.98637i	−0.178957	+	0.309962i	−0.941523	−	0.336947i	$-0.890606\pi$
$373$	−3.45623	+	5.98637i	−0.178957	+	0.309962i	0.762567	+	0.646910i	$0.223939\pi$
$374$	−0.687762	−	1.19124i	−0.0355633	−	0.0615975i
$375$		0			0
$376$	4.98455			0.257058
$377$	11.8736	−	1.59622i	0.611520	−	0.0822095i
$378$		0			0
$379$	2.16569	−	8.08246i	0.111244	−	0.415168i	−0.887735	−	0.460356i	$-0.847722\pi$
$379$	2.16569	−	8.08246i	0.111244	−	0.415168i	0.998979	+	0.0451875i	$0.0143885\pi$
$380$	−11.4303	−	19.7979i	−0.586363	−	1.01561i
$381$		0			0
$382$	2.65346	+	2.65346i	0.135763	+	0.135763i
$383$	−0.572661	−	2.13720i	−0.0292616	−	0.109206i	0.949750	−	0.313008i	$-0.101337\pi$
$383$	−0.572661	−	2.13720i	−0.0292616	−	0.109206i	−0.979012	+	0.203802i	$0.934670\pi$
$384$		0			0
$385$	25.8803	+	9.32830i	1.31898	+	0.475414i
$386$	−1.32641	+	2.29741i	−0.0675126	+	0.116935i
$387$		0			0
$388$	0.388109	−	1.44844i	0.0197032	−	0.0735334i
$389$			24.7852i			1.25666i	0.777946	+	0.628331i	$0.216262\pi$
$389$			24.7852i			1.25666i	−0.777946	+	0.628331i	$0.783738\pi$
$390$		0			0
$391$		−	24.0461i		−	1.21606i
$392$	−2.93914	−	4.14225i	−0.148449	−	0.209215i
$393$		0			0
$394$	−2.84828	−	1.64446i	−0.143494	−	0.0828465i
$395$	0.785368	−	0.785368i	0.0395162	−	0.0395162i
$396$		0			0
$397$	−11.9456	+	3.20082i	−0.599534	+	0.160645i	−0.545807	−	0.837911i	$-0.683777\pi$
$397$	−11.9456	+	3.20082i	−0.599534	+	0.160645i	−0.0537271	+	0.998556i	$0.517110\pi$
$398$	−0.423983	−	0.423983i	−0.0212524	−	0.0212524i
$399$		0			0
$400$	35.1649	−	20.3025i	1.75824	−	1.01512i
$401$	27.4395	+	7.35239i	1.37026	+	0.367161i	0.867575	−	0.497307i	$-0.165678\pi$
$401$	27.4395	+	7.35239i	1.37026	+	0.367161i	0.502688	+	0.864468i	$0.332344\pi$
$402$		0			0
$403$	13.2591	+	31.7644i	0.660484	+	1.58230i
$404$			2.68269i			0.133469i
$405$		0			0
$406$	1.32018	+	0.918270i	0.0655192	+	0.0455730i
$407$	−15.9501	−	9.20880i	−0.790617	−	0.456463i
$408$		0			0
$409$	8.06083	+	30.0834i	0.398583	+	1.48753i	0.815592	+	0.578628i	$0.196412\pi$
$409$	8.06083	+	30.0834i	0.398583	+	1.48753i	−0.417009	+	0.908902i	$0.636922\pi$
$410$	−0.541775	−	2.02193i	−0.0267564	−	0.0998561i
$411$		0			0
$412$	7.55386	+	4.36123i	0.372152	+	0.214862i
$413$	−0.0149891	−	0.0104259i	−0.000737566	−	0.000513026i
$414$		0			0
$415$			13.6085i			0.668013i
$416$	0.989128	−	7.67525i	0.0484960	−	0.376310i
$417$		0			0
$418$	1.36168	+	0.364861i	0.0666020	+	0.0178460i
$419$	−15.4180	+	8.90159i	−0.753219	+	0.434871i	−0.826856	−	0.562414i	$-0.809873\pi$
$419$	−15.4180	+	8.90159i	−0.753219	+	0.434871i	0.0736368	+	0.997285i	$0.476539\pi$
$420$		0			0
$421$	−7.27536	−	7.27536i	−0.354579	−	0.354579i	0.507231	−	0.861810i	$-0.330669\pi$
$421$	−7.27536	−	7.27536i	−0.354579	−	0.354579i	−0.861810	+	0.507231i	$0.830669\pi$
$422$	−4.42627	+	1.18602i	−0.215468	+	0.0577344i
$423$		0			0
$424$	−2.78725	+	2.78725i	−0.135361	+	0.135361i
$425$	26.5016	+	15.3007i	1.28552	+	0.742194i
$426$		0			0
$427$	−3.05292	−	17.0035i	−0.147741	−	0.822855i
$428$			7.12477i			0.344389i
$429$		0			0
$430$		−	2.03386i		−	0.0980813i
$431$	5.92484	−	22.1118i	0.285389	−	1.06509i	−0.663165	−	0.748473i	$-0.730787\pi$
$431$	5.92484	−	22.1118i	0.285389	−	1.06509i	0.948554	−	0.316615i	$-0.102546\pi$
$432$		0			0
$433$	−3.70820	+	6.42278i	−0.178205	+	0.308659i	−0.941266	−	0.337667i	$-0.890362\pi$
$433$	−3.70820	+	6.42278i	−0.178205	+	0.308659i	0.763061	+	0.646326i	$0.223696\pi$
$434$	−1.56668	+	4.34657i	−0.0752029	+	0.208642i
$435$		0			0
$436$	8.00774	+	29.8853i	0.383501	+	1.43125i
$437$	17.4258	+	17.4258i	0.833589	+	0.833589i
$438$		0			0
$439$	18.4110	+	31.8888i	0.878709	+	1.52197i	0.852758	+	0.522306i	$0.174928\pi$
$439$	18.4110	+	31.8888i	0.878709	+	1.52197i	0.0259510	+	0.999663i	$0.491739\pi$
$440$	−1.95265	+	7.28740i	−0.0930891	+	0.347413i
$441$		0			0
$442$	1.74322	−	0.727656i	0.0829167	−	0.0346111i
$443$	−25.6906			−1.22060			−0.610298	−	0.792172i	$-0.708950\pi$
$443$	−25.6906			−1.22060			−0.610298	+	0.792172i	$0.708950\pi$
$444$		0			0
$445$	−0.410159	−	0.710416i	−0.0194434	−	0.0336770i
$446$	0.911973	−	1.57958i	0.0431832	−	0.0747955i
$447$		0			0
$448$	−14.5707	+	12.3040i	−0.688403	+	0.581310i
$449$	1.26128	+	4.70715i	0.0595234	+	0.222144i	0.989280	−	0.146030i	$-0.0466496\pi$
$449$	1.26128	+	4.70715i	0.0595234	+	0.222144i	−0.929757	+	0.368174i	$0.879983\pi$
$450$		0			0
$451$	−6.56982	−	3.79308i	−0.309361	−	0.178609i
$452$	9.35882	−	5.40332i	0.440202	−	0.254151i
$453$		0			0
$454$	−2.86445			−0.134435
$455$	−17.2481	+	33.6124i	−0.808605	+	1.57577i
$456$		0			0
$457$	−1.32032	+	4.92751i	−0.0617621	+	0.230499i	−0.989907	−	0.141721i	$-0.954737\pi$
$457$	−1.32032	+	4.92751i	−0.0617621	+	0.230499i	0.928145	+	0.372220i	$0.121403\pi$
$458$	−0.356509	+	0.205830i	−0.0166586	+	0.00961783i
$459$		0			0
$460$	−46.2361	+	46.2361i	−2.15577	+	2.15577i
$461$	−2.21189	−	8.25490i	−0.103018	−	0.384469i	0.895095	−	0.445876i	$-0.147108\pi$
$461$	−2.21189	−	8.25490i	−0.103018	−	0.384469i	−0.998113	+	0.0614071i	$0.980441\pi$
$462$		0			0
$463$	0.176712	−	0.176712i	0.00821253	−	0.00821253i	−0.702989	−	0.711201i	$-0.748152\pi$
$463$	0.176712	−	0.176712i	0.00821253	−	0.00821253i	0.711201	+	0.702989i	$0.248152\pi$
$464$	6.31383	−	10.9359i	0.293112	−	0.507685i
$465$		0			0
$466$	1.50132	+	0.402277i	0.0695473	+	0.0186351i
$467$	−23.3883			−1.08228			−0.541140	−	0.840932i	$-0.682007\pi$
$467$	−23.3883			−1.08228			−0.541140	+	0.840932i	$0.682007\pi$
$468$		0			0
$469$	19.4465	−	9.14205i	0.897956	−	0.422141i
$470$	1.28809	−	4.80721i	0.0594151	−	0.221740i
$471$		0			0
$472$	0.00250364	−	0.00433642i	0.000115239	−	0.000199600i
$473$	−5.21201	−	5.21201i	−0.239648	−	0.239648i
$474$		0			0
$475$	−30.2935	+	8.11711i	−1.38996	+	0.372438i
$476$	−14.0189	−	5.05298i	−0.642557	−	0.231603i
$477$		0			0
$478$	−1.54128	+	0.889857i	−0.0704964	+	0.0407011i
$479$	−8.63573	+	32.2290i	−0.394577	+	1.47258i	0.427924	+	0.903815i	$0.359245\pi$
$479$	−8.63573	+	32.2290i	−0.394577	+	1.47258i	−0.822500	+	0.568765i	$0.807421\pi$
$480$		0			0
$481$	15.3423	−	20.1081i	0.699550	−	0.916851i
$482$		−	3.75211i		−	0.170904i
$483$		0			0
$484$	−4.03815	−	6.99428i	−0.183552	−	0.317922i
$485$	−2.61530	−	1.50994i	−0.118754	−	0.0685629i
$486$		0			0
$487$	−14.6137	+	3.91573i	−0.662211	+	0.177439i	−0.574243	−	0.818685i	$-0.694704\pi$
$487$	−14.6137	+	3.91573i	−0.662211	+	0.177439i	−0.0879671	+	0.996123i	$0.528037\pi$
$488$	4.57622	−	1.22619i	0.207156	−	0.0555072i
$489$		0			0
$490$	−4.75440	+	1.76415i	−0.214782	+	0.0796961i
$491$	11.7579	−	6.78843i	0.530627	−	0.306357i	−0.210645	−	0.977563i	$-0.567556\pi$
$491$	11.7579	−	6.78843i	0.530627	−	0.306357i	0.741272	+	0.671205i	$0.234223\pi$
$492$		0			0
$493$	9.51669			0.428610
$494$	−0.735965	+	1.79061i	−0.0331126	+	0.0805632i
$495$		0			0
$496$	35.0441	+	9.39005i	1.57353	+	0.421626i
$497$	32.8148	+	22.8248i	1.47194	+	1.02383i
$498$		0			0
$499$	9.45211	+	9.45211i	0.423135	+	0.423135i	0.886282	−	0.463147i	$-0.153280\pi$
$499$	9.45211	+	9.45211i	0.423135	+	0.423135i	−0.463147	+	0.886282i	$0.653280\pi$
$500$	−11.4585	−	42.7637i	−0.512440	−	1.91245i
$501$		0			0
$502$	1.12674	+	1.12674i	0.0502887	+	0.0502887i
$503$	1.20476	+	0.695570i	0.0537177	+	0.0310140i	0.526618	−	0.850102i	$-0.323460\pi$
$503$	1.20476	+	0.695570i	0.0537177	+	0.0310140i	−0.472901	+	0.881116i	$0.656793\pi$
$504$		0			0
$505$	5.21852	+	1.39830i	0.232221	+	0.0622234i
$506$		−	4.03217i		−	0.179252i
$507$		0			0
$508$	19.9953			0.887149
$509$	−22.4834	−	6.02441i	−0.996559	−	0.267027i	−0.276556	−	0.960998i	$-0.589193\pi$
$509$	−22.4834	−	6.02441i	−0.996559	−	0.267027i	−0.720003	+	0.693971i	$0.755860\pi$
$510$		0			0
$511$	0.101139	−	1.19912i	0.00447415	−	0.0530461i
$512$	−9.66738	−	9.66738i	−0.427242	−	0.427242i
$513$		0			0
$514$	−2.45990	+	0.659129i	−0.108502	+	0.0290729i
$515$	12.4210	−	12.4210i	0.547335	−	0.547335i
$516$		0			0
$517$	−9.01819	−	15.6200i	−0.396620	−	0.686965i
$518$	3.34162	−	0.599977i	0.146822	−	0.0263615i
$519$		0			0
$520$	−9.58291	−	3.93871i	−0.420238	−	0.172724i
$521$		−	6.02463i		−	0.263944i	−0.991253	−	0.131972i	$-0.957869\pi$
$521$		−	6.02463i		−	0.263944i	0.991253	−	0.131972i	$-0.0421309\pi$
$522$		0			0
$523$	−2.29311	+	1.32393i	−0.100271	+	0.0578914i	−0.549297	−	0.835627i	$-0.685104\pi$
$523$	−2.29311	+	1.32393i	−0.100271	+	0.0578914i	0.449026	+	0.893519i	$0.351771\pi$
$524$	19.1964	−	33.2491i	0.838598	−	1.45249i
$525$		0			0
$526$	−1.89034	+	0.506514i	−0.0824226	+	0.0220851i
$527$	7.07670	+	26.4106i	0.308266	+	1.15046i
$528$		0			0
$529$	23.7440	−	41.1258i	1.03235	−	1.78808i
$530$	1.96782	+	3.40837i	0.0854767	+	0.148050i
$531$		0			0
$532$	13.8211	−	6.49748i	0.599221	−	0.281701i
$533$	6.31948	−	8.28249i	0.273727	−	0.358754i
$534$		0			0
$535$	13.8595	+	3.71364i	0.599199	+	0.160555i
$536$	2.94650	+	5.10348i	0.127269	+	0.220437i
$537$		0			0
$538$	−1.19215	+	1.19215i	−0.0513974	+	0.0513974i
$539$	−7.66290	+	16.7046i	−0.330064	+	0.719518i
$540$		0			0
$541$	−22.5427	+	22.5427i	−0.969185	+	0.969185i	−0.999539	−	0.0303542i	$-0.990336\pi$
$541$	−22.5427	+	22.5427i	−0.969185	+	0.969185i	0.0303542	+	0.999539i	$0.490336\pi$
$542$	0.160874	+	0.0928807i	0.00691013	+	0.00398957i
$543$		0			0
$544$	1.59104	−	5.93784i	0.0682152	−	0.254583i
$545$	62.3085			2.66900
$546$		0			0
$547$	24.3001			1.03900			0.519500	−	0.854471i	$-0.326118\pi$
$547$	24.3001			1.03900			0.519500	+	0.854471i	$0.326118\pi$
$548$	−6.08488	+	22.7091i	−0.259933	+	0.970084i
$549$		0			0
$550$	4.44393	+	2.56570i	0.189490	+	0.109402i
$551$	−6.89659	+	6.89659i	−0.293805	+	0.293805i
$552$		0			0
$553$	0.478718	+	0.566911i	0.0203572	+	0.0241075i
$554$	−0.118805	+	0.118805i	−0.00504753	+	0.00504753i
$555$		0			0
$556$	−16.3825	−	28.3753i	−0.694772	−	1.20338i
$557$	4.94226	+	1.32427i	0.209410	+	0.0561113i	0.361999	−	0.932178i	$-0.382094\pi$
$557$	4.94226	+	1.32427i	0.209410	+	0.0561113i	−0.152589	+	0.988290i	$0.548761\pi$
$558$		0			0
$559$	8.01376	−	6.18406i	0.338946	−	0.261558i
$560$	16.9415	+	36.0371i	0.715909	+	1.52284i
$561$		0			0
$562$	−0.442230	−	0.765964i	−0.0186543	−	0.0323102i
$563$	−10.0206	+	17.3563i	−0.422320	+	0.731480i	−0.996166	−	0.0874837i	$-0.972117\pi$
$563$	−10.0206	+	17.3563i	−0.422320	+	0.731480i	0.573846	+	0.818963i	$0.305451\pi$
$564$		0			0
$565$	−5.63274	−	21.0217i	−0.236971	−	0.884389i
$566$	2.80763	−	0.752303i	0.118014	−	0.0316217i
$567$		0			0
$568$	−5.48106	+	9.49347i	−0.229980	+	0.398337i
$569$	29.3938	−	16.9705i	1.23225	−	0.711441i	0.264754	−	0.964316i	$-0.414709\pi$
$569$	29.3938	−	16.9705i	1.23225	−	0.711441i	0.967499	+	0.252875i	$0.0813760\pi$
$570$		0			0
$571$			19.5735i			0.819124i	0.912282	+	0.409562i	$0.134319\pi$
$571$			19.5735i			0.819124i	−0.912282	+	0.409562i	$0.865681\pi$
$572$	−17.1793	+	7.17096i	−0.718301	+	0.299833i
$573$		0			0
$574$	1.37641	−	0.247129i	0.0574500	−	0.0103150i
$575$	44.8521	+	77.6861i	1.87046	+	3.23973i
$576$		0			0
$577$	32.3003	−	32.3003i	1.34468	−	1.34468i	0.453345	−	0.891335i	$-0.350231\pi$
$577$	32.3003	−	32.3003i	1.34468	−	1.34468i	0.891335	−	0.453345i	$-0.149769\pi$
$578$	−1.55436	+	0.416489i	−0.0646527	+	0.0173237i
$579$		0			0
$580$	−18.2988	−	18.2988i	−0.759816	−	0.759816i
$581$	−9.05906	−	0.764081i	−0.375833	−	0.0316994i
$582$		0			0
$583$	13.7771	+	3.69158i	0.570591	+	0.152889i
$584$	0.330019			0.0136563
$585$		0			0
$586$		−	2.70445i		−	0.111720i
$587$	−12.7987	−	3.42941i	−0.528260	−	0.141547i	−0.0151751	−	0.999885i	$-0.504831\pi$
$587$	−12.7987	−	3.42941i	−0.528260	−	0.141547i	−0.513084	+	0.858338i	$0.671497\pi$
$588$		0			0
$589$	−24.2677	−	14.0110i	−0.999933	−	0.577312i
$590$	−0.00353517	−	0.00353517i	−0.000145541	−	0.000145541i
$591$		0			0
$592$	−6.89992	−	25.7509i	−0.283585	−	1.05835i
$593$	28.9194	+	28.9194i	1.18758	+	1.18758i	0.977735	+	0.209843i	$0.0672954\pi$
$593$	28.9194	+	28.9194i	1.18758	+	1.18758i	0.209843	+	0.977735i	$0.432705\pi$
$594$		0			0
$595$	−17.1364	+	24.6367i	−0.702525	+	1.01000i
$596$	−29.0268	−	7.77770i	−1.18898	−	0.318587i
$597$		0			0
$598$	5.49194	+	0.707759i	0.224582	+	0.0289424i
$599$	−10.2540			−0.418967			−0.209484	−	0.977812i	$-0.567178\pi$
$599$	−10.2540			−0.418967			−0.209484	+	0.977812i	$0.567178\pi$
$600$		0			0
$601$	−27.4693	+	15.8594i	−1.12050	+	0.646919i	−0.941528	−	0.336936i	$-0.890610\pi$
$601$	−27.4693	+	15.8594i	−1.12050	+	0.646919i	−0.178969	+	0.983855i	$0.557276\pi$
$602$	1.35392	+	0.114196i	0.0551818	+	0.00465428i
$603$		0			0
$604$	−20.1574	+	5.40116i	−0.820194	+	0.219770i
$605$	−15.7105	+	4.20961i	−0.638722	+	0.171145i
$606$		0			0
$607$	23.1914	+	13.3895i	0.941309	+	0.543465i	0.890370	−	0.455237i	$-0.150445\pi$
$607$	23.1914	+	13.3895i	0.941309	+	0.543465i	0.0509383	+	0.998702i	$0.483779\pi$
$608$	3.15005	+	5.45605i	0.127752	+	0.221272i
$609$		0			0
$610$		−	4.73028i		−	0.191523i
$611$	22.8578	−	9.54130i	0.924727	−	0.386000i
$612$		0			0
$613$	8.17678	−	30.5162i	0.330257	−	1.23254i	−0.578663	−	0.815567i	$-0.696425\pi$
$613$	8.17678	−	30.5162i	0.330257	−	1.23254i	0.908920	−	0.416970i	$-0.136908\pi$
$614$	−2.68169	+	1.54827i	−0.108224	+	0.0624833i
$615$		0			0
$616$	−4.74154	−	1.70904i	−0.191042	−	0.0688591i
$617$	−35.9374	+	9.62939i	−1.44678	+	0.387665i	−0.894904	−	0.446259i	$-0.852756\pi$
$617$	−35.9374	+	9.62939i	−1.44678	+	0.387665i	−0.551880	+	0.833923i	$0.686089\pi$
$618$		0			0
$619$	−13.9520	−	13.9520i	−0.560777	−	0.560777i	0.368751	−	0.929528i	$-0.379785\pi$
$619$	−13.9520	−	13.9520i	−0.560777	−	0.560777i	−0.929528	+	0.368751i	$0.879785\pi$
$620$	37.1754	−	64.3897i	1.49300	−	2.58595i
$621$		0			0
$622$	−1.05589	+	3.94062i	−0.0423372	+	0.158005i
$623$	0.495949	−	0.233152i	0.0198698	−	0.00934104i
$624$		0			0
$625$	−35.7364			−1.42945
$626$	−3.84535	−	1.03036i	−0.153691	−	0.0411814i
$627$		0			0
$628$	13.2615	−	22.9695i	0.529190	−	0.916585i
$629$	14.2068	−	14.2068i	0.566462	−	0.566462i
$630$		0			0
$631$	−2.16532	−	8.08109i	−0.0862001	−	0.321703i	0.909339	−	0.416057i	$-0.136588\pi$
$631$	−2.16532	−	8.08109i	−0.0862001	−	0.321703i	−0.995539	+	0.0943536i	$0.969922\pi$
$632$	−0.143887	+	0.143887i	−0.00572353	+	0.00572353i
$633$		0			0
$634$	0.870873	−	0.502799i	0.0345868	−	0.0199687i
$635$	10.4222	−	38.8960i	0.413591	−	1.54354i
$636$		0			0
$637$	−21.4071	−	13.3692i	−0.848180	−	0.529708i
$638$	1.59581			0.0631787
$639$		0			0
$640$	−19.2452	+	11.1112i	−0.760734	+	0.439210i
$641$	19.7158	+	11.3829i	0.778726	+	0.449598i	0.835979	−	0.548762i	$-0.184901\pi$
$641$	19.7158	+	11.3829i	0.778726	+	0.449598i	−0.0572524	+	0.998360i	$0.518234\pi$
$642$		0			0
$643$	3.68359	+	13.7474i	0.145267	+	0.542143i	0.999743	+	0.0226531i	$0.00721132\pi$
$643$	3.68359	+	13.7474i	0.145267	+	0.542143i	−0.854477	+	0.519490i	$0.826122\pi$
$644$	−28.1830	−	33.3751i	−1.11057	−	1.31516i
$645$		0			0
$646$	−0.768917	+	1.33180i	−0.0302527	+	0.0523991i
$647$	−22.6826	−	39.2874i	−0.891744	−	1.54455i	−0.837783	−	0.546003i	$-0.816149\pi$
$647$	−22.6826	−	39.2874i	−0.891744	−	1.54455i	−0.0539612	−	0.998543i	$-0.517185\pi$
$648$		0			0
$649$	−0.0181186			−0.000711218
$650$	−4.27460	+	5.60241i	−0.167663	+	0.219745i
$651$		0			0
$652$	2.11050	−	7.87648i	0.0826534	−	0.308467i
$653$	−5.43437	−	9.41260i	−0.212663	−	0.368344i	0.739884	−	0.672735i	$-0.234880\pi$
$653$	−5.43437	−	9.41260i	−0.212663	−	0.368344i	−0.952547	+	0.304391i	$0.901547\pi$
$654$		0			0
$655$	−54.6723	−	54.6723i	−2.13622	−	2.13622i
$656$	−2.84206	−	10.6067i	−0.110964	−	0.414123i
$657$		0			0
$658$	3.12781	+	1.12738i	0.121935	+	0.0439500i
$659$	4.13172	−	7.15635i	0.160949	−	0.278772i	−0.774260	−	0.632867i	$-0.781878\pi$
$659$	4.13172	−	7.15635i	0.160949	−	0.278772i	0.935209	+	0.354096i	$0.115211\pi$
$660$		0			0
$661$	−0.844712	+	3.15251i	−0.0328555	+	0.122618i	−0.980406	−	0.196988i	$-0.936884\pi$
$661$	−0.844712	+	3.15251i	−0.0328555	+	0.122618i	0.947550	+	0.319606i	$0.103551\pi$
$662$		−	3.34138i		−	0.129867i
$663$		0			0
$664$		−	2.49321i		−	0.0967552i
$665$	−5.43529	−	30.2723i	−0.210772	−	1.17391i
$666$		0			0
$667$	24.1595	+	13.9485i	0.935459	+	0.540088i
$668$	19.4758	−	19.4758i	0.753542	−	0.753542i
$669$		0			0
$670$	5.68334	−	1.52285i	0.219567	−	0.0588327i
$671$	−12.1219	−	12.1219i	−0.467962	−	0.467962i
$672$		0			0
$673$	−29.2655	+	16.8964i	−1.12810	+	0.651310i	−0.943457	−	0.331495i	$-0.892447\pi$
$673$	−29.2655	+	16.8964i	−1.12810	+	0.651310i	−0.184645	+	0.982805i	$0.559114\pi$
$674$	2.20697	+	0.591357i	0.0850095	+	0.0227782i
$675$		0			0
$676$	−6.75162	−	24.6573i	−0.259678	−	0.948360i
$677$		−	26.7526i		−	1.02819i	−0.857734	−	0.514093i	$-0.828129\pi$
$677$		−	26.7526i		−	1.02819i	0.857734	−	0.514093i	$-0.171871\pi$
$678$		0			0
$679$	1.15200	−	1.65621i	0.0442097	−	0.0635593i
$680$	−7.12751	−	4.11507i	−0.273327	−	0.157806i
$681$		0			0
$682$	1.18666	+	4.42867i	0.0454395	+	0.169583i
$683$	4.61892	+	17.2380i	0.176738	+	0.659595i	0.996249	+	0.0865317i	$0.0275784\pi$
$683$	4.61892	+	17.2380i	0.176738	+	0.659595i	−0.819511	+	0.573063i	$0.805755\pi$
$684$		0			0
$685$	41.0034	+	23.6733i	1.56666	+	0.904511i
$686$	−0.907434	−	3.26403i	−0.0346460	−	0.124621i
$687$		0			0
$688$		−	10.6693i		−	0.406763i
$689$	−7.44631	+	18.1169i	−0.283682	+	0.690199i
$690$		0			0
$691$	−28.7650	−	7.70756i	−1.09427	−	0.293209i	−0.333842	−	0.942629i	$-0.608345\pi$
$691$	−28.7650	−	7.70756i	−1.09427	−	0.293209i	−0.760430	+	0.649420i	$0.775012\pi$
$692$	−25.9931	+	15.0071i	−0.988108	+	0.570484i
$693$		0			0
$694$	0.699792	+	0.699792i	0.0265637	+	0.0265637i
$695$	−63.7363	+	17.0781i	−2.41766	+	0.647809i
$696$		0			0
$697$	5.85175	−	5.85175i	0.221651	−	0.221651i
$698$	0.981627	+	0.566743i	0.0371551	+	0.0214515i
$699$		0			0
$700$	54.7163	−	9.82415i	2.06808	−	0.371318i
$701$		−	23.3038i		−	0.880172i	−0.897956	−	0.440086i	$-0.854948\pi$
$701$		−	23.3038i		−	0.880172i	0.897956	−	0.440086i	$-0.145052\pi$
$702$		0			0
$703$			20.5909i			0.776599i
$704$	−4.89806	+	18.2798i	−0.184603	+	0.688947i
$705$		0			0
$706$	−3.22910	+	5.59297i	−0.121529	+	0.210494i
$707$	−1.22384	+	3.39542i	−0.0460274	+	0.127698i
$708$		0			0
$709$	2.40630	+	8.98045i	0.0903706	+	0.337268i	0.996277	−	0.0862104i	$-0.0274757\pi$
$709$	2.40630	+	8.98045i	0.0903706	+	0.337268i	−0.905906	+	0.423478i	$0.860809\pi$
$710$	7.73933	+	7.73933i	0.290452	+	0.290452i
$711$		0			0
$712$	0.0751452	+	0.130155i	0.00281619	+	0.00487778i
$713$	−20.7444	+	77.4193i	−0.776886	+	2.89938i
$714$		0			0
$715$	4.99502	+	37.1558i	0.186803	+	1.38955i
$716$	−15.7791			−0.589693
$717$		0			0
$718$	−1.01070	−	1.75059i	−0.0377191	−	0.0653315i
$719$	7.87045	−	13.6320i	0.293518	−	0.508388i	−0.681121	−	0.732171i	$-0.738507\pi$
$719$	7.87045	−	13.6320i	0.293518	−	0.508388i	0.974639	+	0.223783i	$0.0718405\pi$
$720$		0			0
$721$	7.57117	+	8.96599i	0.281965	+	0.333911i
$722$	0.491630	+	1.83479i	0.0182966	+	0.0682838i
$723$		0			0
$724$	−15.4661	−	8.92936i	−0.574793	−	0.331857i
$725$	−30.7457	+	17.7511i	−1.14187	+	0.659258i
$726$		0			0
$727$	−5.72068			−0.212168			−0.106084	−	0.994357i	$-0.533831\pi$
$727$	−5.72068			−0.212168			−0.106084	+	0.994357i	$0.533831\pi$
$728$	3.16003	−	6.15813i	0.117118	−	0.228235i
$729$		0			0
$730$	0.0852824	−	0.318278i	0.00315644	−	0.0117800i
$731$	6.96352	−	4.02039i	0.257555	−	0.148700i
$732$		0			0
$733$	−12.5077	+	12.5077i	−0.461982	+	0.461982i	−0.899305	−	0.437322i	$-0.855927\pi$
$733$	−12.5077	+	12.5077i	−0.461982	+	0.461982i	0.437322	+	0.899305i	$0.355927\pi$
$734$	−1.06225	−	3.96439i	−0.0392085	−	0.146328i
$735$		0			0
$736$	12.7421	−	12.7421i	0.469680	−	0.469680i
$737$	10.6618	−	18.4668i	0.392732	−	0.680232i
$738$		0			0
$739$	34.5884	+	9.26794i	1.27236	+	0.340927i	0.830933	−	0.556372i	$-0.187807\pi$
$739$	34.5884	+	9.26794i	1.27236	+	0.340927i	0.441423	+	0.897299i	$0.354474\pi$
$740$	−54.6339			−2.00838
$741$		0			0
$742$	−2.37941	+	1.11859i	−0.0873510	+	0.0410649i
$743$	1.35076	−	5.04112i	0.0495547	−	0.184941i	−0.936712	−	0.350101i	$-0.886147\pi$
$743$	1.35076	−	5.04112i	0.0495547	−	0.184941i	0.986267	+	0.165160i	$0.0528140\pi$
$744$		0			0
$745$	−30.2593	+	52.4106i	−1.10861	+	1.92017i
$746$	−0.894109	−	0.894109i	−0.0327357	−	0.0327357i
$747$		0			0
$748$	−14.2837	+	3.82731i	−0.522265	+	0.139940i
$749$	−3.25032	+	9.01766i	−0.118764	+	0.329498i
$750$		0			0
$751$	24.9221	−	14.3888i	0.909421	−	0.525055i	0.0291764	−	0.999574i	$-0.490712\pi$
$751$	24.9221	−	14.3888i	0.909421	−	0.525055i	0.880245	+	0.474520i	$0.157378\pi$
$752$	6.75711	−	25.2179i	0.246406	−	0.919601i
$753$		0			0
$754$	−0.280109	+	2.17354i	−0.0102010	+	0.0791556i
$755$			42.0266i			1.52950i
$756$		0			0
$757$	8.90997	+	15.4325i	0.323838	+	0.560905i	0.981277	−	0.192604i	$-0.0616933\pi$
$757$	8.90997	+	15.4325i	0.323838	+	0.560905i	−0.657438	+	0.753508i	$0.728360\pi$
$758$	1.32557	+	0.765320i	0.0481470	+	0.0277977i
$759$		0			0
$760$	8.14731	−	2.18306i	0.295534	−	0.0791881i
$761$	−52.7426	+	14.1323i	−1.91192	+	0.512296i	−0.918872	+	0.394556i	$0.870899\pi$
$761$	−52.7426	+	14.1323i	−1.91192	+	0.512296i	−0.993044	+	0.117741i	$0.962435\pi$
$762$		0			0
$763$	−3.49846	+	41.4783i	−0.126653	+	1.50162i
$764$	34.9372	−	20.1710i	1.26398	−	0.729761i
$765$		0			0
$766$	0.404738			0.0146238
$767$	0.00318032	−	0.0246781i	0.000114835	−	0.000891074i
$768$		0			0
$769$	23.1319	+	6.19819i	0.834159	+	0.223512i	0.650527	−	0.759483i	$-0.274548\pi$
$769$	23.1319	+	6.19819i	0.834159	+	0.223512i	0.183632	+	0.982995i	$0.441215\pi$
$770$	−2.87353	+	4.13120i	−0.103555	+	0.148878i
$771$		0			0
$772$	20.1661	+	20.1661i	0.725795	+	0.725795i
$773$	10.0708	+	37.5846i	0.362221	+	1.35183i	0.871150	+	0.491017i	$0.163375\pi$
$773$	10.0708	+	37.5846i	0.362221	+	1.35183i	−0.508929	+	0.860808i	$0.669958\pi$
$774$		0			0
$775$	−72.1254	−	72.1254i	−2.59082	−	2.59082i
$776$	0.479148	+	0.276636i	0.0172004	+	0.00993067i
$777$		0			0
$778$	−4.37935	−	1.17344i	−0.157007	−	0.0420700i
$779$			8.48133i			0.303875i
$780$		0			0
$781$	39.6660			1.41936
$782$	4.24875	+	1.13845i	0.151935	+	0.0407109i
$783$		0			0
$784$	−24.9408	+	9.25444i	−0.890744	+	0.330516i
$785$	−37.7694	−	37.7694i	−1.34805	−	1.34805i
$786$		0			0
$787$	17.8194	−	4.77470i	0.635194	−	0.170200i	0.0731686	−	0.997320i	$-0.476689\pi$
$787$	17.8194	−	4.77470i	0.635194	−	0.170200i	0.562026	+	0.827120i	$0.310022\pi$
$788$	−25.0015	+	25.0015i	−0.890643	+	0.890643i
$789$		0			0
$790$	0.101585	+	0.175951i	0.00361425	+	0.00626006i
$791$	14.3103	−	2.56936i	0.508814	−	0.0913561i
$792$		0			0
$793$	18.6381	−	14.3827i	0.661860	−	0.510744i
$794$		−	2.26224i		−	0.0802838i
$795$		0			0
$796$	−5.58244	+	3.22302i	−0.197864	+	0.114237i
$797$	−0.444897	+	0.770584i	−0.0157591	+	0.0272955i	−0.873797	−	0.486290i	$-0.838350\pi$
$797$	−0.444897	+	0.770584i	−0.0157591	+	0.0272955i	0.858038	+	0.513586i	$0.171683\pi$
$798$		0			0
$799$	19.0051	−	5.09241i	0.672354	−	0.180157i
$800$	5.93539	+	22.1512i	0.209848	+	0.783162i
$801$		0			0
$802$	−2.59822	+	4.50024i	−0.0917462	+	0.158909i
$803$	−0.597081	−	1.03417i	−0.0210705	−	0.0364952i
$804$		0			0
$805$	−79.6129	+	37.4271i	−2.80599	+	1.31913i
$806$	−6.24027	+	0.838908i	−0.219804	+	0.0295493i
$807$		0			0
$808$	−0.956084	−	0.256182i	−0.0336349	−	0.00901245i
$809$	−22.3601	−	38.7288i	−0.786138	−	1.36163i	−0.928317	−	0.371790i	$-0.878744\pi$
$809$	−22.3601	−	38.7288i	−0.786138	−	1.36163i	0.142179	−	0.989841i	$-0.454589\pi$
$810$		0			0
$811$	28.1862	−	28.1862i	0.989753	−	0.989753i	−0.0101954	−	0.999948i	$-0.503245\pi$
$811$	28.1862	−	28.1862i	0.989753	−	0.989753i	0.999948	+	0.0101954i	$0.00324535\pi$
$812$	13.2088	−	11.1539i	0.463538	−	0.391427i
$813$		0			0
$814$	2.38227	−	2.38227i	0.0834985	−	0.0834985i
$815$	−14.2217	−	8.21092i	−0.498165	−	0.287616i
$816$		0			0
$817$	−2.13284	+	7.95986i	−0.0746186	+	0.278480i
$818$	−5.69714			−0.199196
$819$		0			0
$820$	−22.5036			−0.785860
$821$	−0.320911	+	1.19766i	−0.0111999	+	0.0417986i	−0.971300	−	0.237859i	$-0.923554\pi$
$821$	−0.320911	+	1.19766i	−0.0111999	+	0.0417986i	0.960100	+	0.279658i	$0.0902210\pi$
$822$		0			0
$823$	−25.3229	−	14.6202i	−0.882701	−	0.509628i	−0.0111531	−	0.999938i	$-0.503550\pi$
$823$	−25.3229	−	14.6202i	−0.882701	−	0.509628i	−0.871548	+	0.490310i	$0.836884\pi$
$824$	−2.27565	+	2.27565i	−0.0792761	+	0.0792761i
$825$		0			0
$826$	0.00255183	−	0.00215485i	8.87895e−5	−	7.49767e-5i
$827$	27.0221	−	27.0221i	0.939649	−	0.939649i	−0.0586310	−	0.998280i	$-0.518674\pi$
$827$	27.0221	−	27.0221i	0.939649	−	0.939649i	0.998280	+	0.0586310i	$0.0186735\pi$
$828$		0			0
$829$	−9.30153	−	16.1107i	−0.323055	−	0.559548i	0.658061	−	0.752964i	$-0.271377\pi$
$829$	−9.30153	−	16.1107i	−0.323055	−	0.559548i	−0.981117	+	0.193416i	$0.938043\pi$
$830$	−2.40451	−	0.644285i	−0.0834616	−	0.0223635i
$831$		0			0
$832$	−24.0379	−	9.87993i	−0.833364	−	0.342525i
$833$	−15.4383	−	12.7909i	−0.534905	−	0.443178i
$834$		0			0
$835$	−27.7341	−	48.0368i	−0.959777	−	1.66238i
$836$	7.57759	−	13.1248i	0.262076	−	0.453930i
$837$		0			0
$838$	−0.842882	−	3.14568i	−0.0291169	−	0.108666i
$839$	17.3070	−	4.63740i	0.597504	−	0.160101i	0.0526236	−	0.998614i	$-0.483242\pi$
$839$	17.3070	−	4.63740i	0.597504	−	0.160101i	0.544881	+	0.838514i	$0.316575\pi$
$840$		0			0
$841$	8.97962	−	15.5532i	0.309642	−	0.536316i
$842$	1.62995	−	0.941050i	0.0561716	−	0.0324307i
$843$		0			0
$844$			49.2633i			1.69571i
$845$	−51.4840	+	0.281491i	−1.77110	+	0.00968359i
$846$		0			0
$847$	−1.92020	−	10.6947i	−0.0659790	−	0.367475i
$848$	10.3229	+	17.8797i	0.354489	+	0.613993i
$849$		0			0
$850$	−3.95822	+	3.95822i	−0.135766	+	0.135766i
$851$	56.8887	−	15.2433i	1.95012	−	0.522533i
$852$		0			0
$853$	36.5250	+	36.5250i	1.25059	+	1.25059i	0.955455	+	0.295137i	$0.0953652\pi$
$853$	36.5250	+	36.5250i	1.25059	+	1.25059i	0.295137	+	0.955455i	$0.404635\pi$
$854$	3.14891	+	0.265593i	0.107754	+	0.00908842i
$855$		0			0
$856$	−2.53920	−	0.680376i	−0.0867880	−	0.0232548i
$857$	−36.8519			−1.25884			−0.629418	−	0.777067i	$-0.716707\pi$
$857$	−36.8519			−1.25884			−0.629418	+	0.777067i	$0.716707\pi$
$858$		0			0
$859$			29.0833i			0.992310i	0.868234	+	0.496155i	$0.165255\pi$
$859$			29.0833i			0.992310i	−0.868234	+	0.496155i	$0.834745\pi$
$860$	−21.1200	−	5.65908i	−0.720185	−	0.192973i
$861$		0			0
$862$	3.62647	+	2.09374i	0.123518	+	0.0713132i
$863$	0.584660	+	0.584660i	0.0199021	+	0.0199021i	0.716988	−	0.697086i	$-0.245520\pi$
$863$	0.584660	+	0.584660i	0.0199021	+	0.0199021i	−0.697086	+	0.716988i	$0.745520\pi$
$864$		0			0
$865$	15.6443	+	58.3853i	0.531922	+	1.98516i
$866$	−0.959292	−	0.959292i	−0.0325981	−	0.0325981i
$867$		0			0
$868$	40.7765	+	28.3628i	1.38404	+	0.962695i
$869$	0.711222	+	0.190571i	0.0241266	+	0.00646469i
$870$		0			0
$871$	23.2808	+	17.7631i	0.788840	+	0.601879i
$872$	−11.4155			−0.386579
$873$		0			0
$874$	−3.90401	+	2.25398i	−0.132055	+	0.0762421i
$875$	5.00605	−	59.3525i	0.169236	−	2.00648i
$876$		0			0
$877$	24.9512	−	6.68566i	0.842543	−	0.225759i	0.188365	−	0.982099i	$-0.439681\pi$
$877$	24.9512	−	6.68566i	0.842543	−	0.225759i	0.654178	+	0.756340i	$0.273015\pi$
$878$	−6.50615	+	1.74332i	−0.219572	+	0.0588341i
$879$		0			0
$880$	34.2215	+	19.7578i	1.15360	+	0.666034i
$881$	16.3924	+	28.3925i	0.552275	+	0.956568i	0.998110	+	0.0614526i	$0.0195733\pi$
$881$	16.3924	+	28.3925i	0.552275	+	0.956568i	−0.445835	+	0.895115i	$0.647093\pi$
$882$		0			0
$883$		−	51.9581i		−	1.74853i	−0.485450	−	0.874265i	$-0.661344\pi$
$883$		−	51.9581i		−	1.74853i	0.485450	−	0.874265i	$-0.338656\pi$
$884$	−2.70572	−	20.1266i	−0.0910031	−	0.676932i
$885$		0			0
$886$	1.21631	−	4.53932i	0.0408627	−	0.152501i
$887$	28.3210	−	16.3512i	0.950928	−	0.549018i	0.0575587	−	0.998342i	$-0.481668\pi$
$887$	28.3210	−	16.3512i	0.950928	−	0.549018i	0.893369	+	0.449324i	$0.148335\pi$
$888$		0			0
$889$	25.3077	+	9.12188i	0.848791	+	0.305938i
$890$	0.144944	−	0.0388375i	0.00485852	−	0.00130184i
$891$		0			0
$892$	−13.8652	−	13.8652i	−0.464242	−	0.464242i
$893$	−10.0823	+	17.4631i	−0.337392	+	0.584381i
$894$		0			0
$895$	−8.22454	+	30.6944i	−0.274916	+	1.02600i
$896$	−6.31610	−	13.4353i	−0.211006	−	0.448841i
$897$		0			0
$898$	−0.891430			−0.0297474
$899$	−30.6402	−	8.21001i	−1.02191	−	0.273819i
$900$		0			0
$901$	−7.77971	+	13.4749i	−0.259180	+	0.448913i
$902$	0.981252	−	0.981252i	0.0326721	−	0.0326721i
$903$		0			0
$904$	1.03197	+	3.85138i	0.0343230	+	0.128095i
$905$	−25.4313	+	25.4313i	−0.845365	+	0.845365i
$906$		0			0
$907$	−17.5633	+	10.1402i	−0.583178	+	0.336698i	−0.762395	−	0.647111i	$-0.775977\pi$
$907$	−17.5633	+	10.1402i	−0.583178	+	0.336698i	0.179217	+	0.983810i	$0.442644\pi$
$908$	−7.97016	+	29.7451i	−0.264499	+	0.987124i
$909$		0			0
$910$	−5.12244	−	4.63897i	−0.169807	−	0.153780i
$911$	10.1023			0.334704			0.167352	−	0.985897i	$-0.446478\pi$
$911$	10.1023			0.334704			0.167352	+	0.985897i	$0.446478\pi$
$912$		0			0
$913$	−7.81291	+	4.51078i	−0.258569	+	0.149285i
$914$	−0.808142	−	0.466581i	−0.0267309	−	0.0154331i
$915$		0			0
$916$	1.14542	+	4.27477i	0.0378458	+	0.141242i
$917$	39.4647	−	33.3253i	1.30324	−	1.10050i
$918$		0			0
$919$	17.0100	−	29.4622i	0.561108	−	0.971867i	−0.436293	−	0.899805i	$-0.643709\pi$
$919$	17.0100	−	29.4622i	0.561108	−	0.971867i	0.997400	−	0.0720619i	$-0.0229579\pi$
$920$	−12.0628	−	20.8934i	−0.397699	−	0.688834i
$921$		0			0
$922$	1.56330			0.0514844
$923$	−6.96249	+	54.0262i	−0.229173	+	1.77830i
$924$		0			0
$925$	−19.3988	+	72.3974i	−0.637830	+	2.38041i
$926$	0.0228573	+	0.0395900i	0.000751138	+	0.00130101i
$927$		0			0
$928$	5.04292	+	5.04292i	0.165542	+	0.165542i
$929$	1.74577	+	6.51529i	0.0572768	+	0.213760i	0.988633	−	0.150350i	$-0.0480400\pi$
$929$	1.74577	+	6.51529i	0.0572768	+	0.213760i	−0.931356	+	0.364110i	$0.881373\pi$
$930$		0			0
$931$	20.4572	−	1.91853i	0.670458	−	0.0628772i
$932$	8.35466	−	14.4707i	0.273666	−	0.474003i
$933$		0			0
$934$	1.10731	−	4.13252i	0.0362321	−	0.135220i
$935$			29.7804i			0.973924i
$936$		0			0
$937$		−	37.1803i		−	1.21463i	−0.794461	−	0.607315i	$-0.792247\pi$
$937$		−	37.1803i		−	1.21463i	0.794461	−	0.607315i	$-0.207753\pi$
$938$	0.694643	+	3.86887i	0.0226809	+	0.126323i
$939$		0			0
$940$	−46.3350	−	26.7515i	−1.51128	−	0.872539i
$941$	38.8786	−	38.8786i	1.26741	−	1.26741i	0.319981	−	0.947424i	$-0.396323\pi$
$941$	38.8786	−	38.8786i	1.26741	−	1.26741i	0.947424	−	0.319981i	$-0.103677\pi$
$942$		0			0
$943$	23.4323	−	6.27867i	0.763062	−	0.204462i
$944$	−0.0185449	−	0.0185449i	−0.000603586	−	0.000603586i
$945$		0			0
$946$	1.16768	−	0.674160i	0.0379646	−	0.0219188i
$947$	20.0773	+	5.37969i	0.652424	+	0.174816i	0.569824	−	0.821766i	$-0.307011\pi$
$947$	20.0773	+	5.37969i	0.652424	+	0.174816i	0.0825993	+	0.996583i	$0.473678\pi$
$948$		0			0
$949$	1.51338	−	0.631715i	0.0491264	−	0.0205063i
$950$		−	5.73691i		−	0.186130i
$951$		0			0
$952$	3.13956	−	4.51368i	0.101754	−	0.146289i
$953$	−23.9622	−	13.8346i	−0.776212	−	0.448146i	0.0588741	−	0.998265i	$-0.481249\pi$
$953$	−23.9622	−	13.8346i	−0.776212	−	0.448146i	−0.835086	+	0.550119i	$0.814582\pi$
$954$		0			0
$955$	−21.0275	−	78.4756i	−0.680433	−	2.53941i
$956$	4.95194	+	18.4809i	0.160157	+	0.597715i
$957$		0			0
$958$	−5.28575	−	3.05173i	−0.170775	−	0.0985968i
$959$	−18.0614	+	25.9665i	−0.583233	+	0.838501i
$960$		0			0
$961$		−	60.1373i		−	1.93991i
$962$	2.82657	+	3.66287i	0.0911321	+	0.118096i
$963$		0			0
$964$	−38.9627	−	10.4400i	−1.25490	−	0.336250i
$965$	49.7395	−	28.7171i	1.60117	−	0.924437i
$966$		0			0
$967$	9.79059	+	9.79059i	0.314844	+	0.314844i	0.846783	−	0.531939i	$-0.178536\pi$
$967$	9.79059	+	9.79059i	0.314844	+	0.314844i	−0.531939	+	0.846783i	$0.678536\pi$
$968$	2.87832	−	0.771242i	0.0925126	−	0.0247887i
$969$		0			0
$970$	0.390614	−	0.390614i	0.0125419	−	0.0125419i
$971$	−18.5031	−	10.6828i	−0.593792	−	0.342826i	0.172803	−	0.984956i	$-0.444717\pi$
$971$	−18.5031	−	10.6828i	−0.593792	−	0.342826i	−0.766596	+	0.642130i	$0.778051\pi$
$972$		0			0
$973$	−7.79013	−	43.3877i	−0.249740	−	1.39095i
$974$		−	2.76751i		−	0.0886769i
$975$		0			0
$976$		−	24.8143i		−	0.794286i
$977$	9.16391	−	34.2002i	0.293179	−	1.09416i	−0.649473	−	0.760384i	$-0.725011\pi$
$977$	9.16391	−	34.2002i	0.293179	−	1.09416i	0.942653	−	0.333776i	$-0.108323\pi$
$978$		0			0
$979$	0.271910	−	0.470962i	0.00869028	−	0.0150520i
$980$	5.09045	+	54.2793i	0.162608	+	1.73389i
$981$		0			0
$982$	0.642789	+	2.39892i	0.0205122	+	0.0765526i
$983$	−21.6097	−	21.6097i	−0.689243	−	0.689243i	0.272822	−	0.962065i	$-0.412043\pi$
$983$	−21.6097	−	21.6097i	−0.689243	−	0.689243i	−0.962065	+	0.272822i	$0.912043\pi$
$984$		0			0
$985$	35.6029	+	61.6660i	1.13440	+	1.96484i
$986$	−0.450563	+	1.68152i	−0.0143488	+	0.0535506i
$987$		0			0
$988$	16.5462	+	12.6247i	0.526406	+	0.401644i
$989$	23.5705			0.749499
$990$		0			0
$991$	0.414264	+	0.717526i	0.0131595	+	0.0227930i	0.872530	−	0.488560i	$-0.162478\pi$
$991$	0.414264	+	0.717526i	0.0131595	+	0.0227930i	−0.859371	+	0.511353i	$0.829144\pi$
$992$	−10.2451	+	17.7450i	−0.325282	+	0.563405i
$993$		0			0
$994$	−5.58656	+	4.71748i	−0.177195	+	0.149629i
$995$	3.35987	+	12.5392i	0.106515	+	0.397520i
$996$		0			0
$997$	−35.7880	−	20.6622i	−1.13342	−	0.654379i	−0.188625	−	0.982049i	$-0.560403\pi$
$997$	−35.7880	−	20.6622i	−1.13342	−	0.654379i	−0.944792	+	0.327671i	$0.893736\pi$
$998$	−2.11762	+	1.22261i	−0.0670320	+	0.0387009i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.f.622.4		32
3.2	odd	2		273.2.by.c.76.5	✓	32
7.6	odd	2		819.2.fm.e.622.4		32
13.6	odd	12		819.2.fm.e.370.4		32
21.20	even	2		273.2.by.d.76.5	yes	32
39.32	even	12		273.2.by.d.97.5	yes	32
91.6	even	12	inner	819.2.fm.f.370.4		32
273.188	odd	12		273.2.by.c.97.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.5	✓	32	3.2	odd	2
273.2.by.c.97.5	yes	32	273.188	odd	12
273.2.by.d.76.5	yes	32	21.20	even	2
273.2.by.d.97.5	yes	32	39.32	even	12
819.2.fm.e.370.4		32	13.6	odd	12
819.2.fm.e.622.4		32	7.6	odd	2
819.2.fm.f.370.4		32	91.6	even	12	inner
819.2.fm.f.622.4		32	1.1	even	1	trivial

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

\(f(q)\)	\(=\)	\(q+(-0.0473445 + 0.176692i) q^{2} +(1.70307 + 0.983269i) q^{4} +(2.80040 - 2.80040i) q^{5} +(1.70697 + 2.02145i) q^{7} +(-0.513062 + 0.513062i) q^{8} +O(q^{10})\)	\(q+(-0.0473445 + 0.176692i) q^{2} +(1.70307 + 0.983269i) q^{4} +(2.80040 - 2.80040i) q^{5} +(1.70697 + 2.02145i) q^{7} +(-0.513062 + 0.513062i) q^{8} +(0.362225 + 0.627392i) q^{10} +(2.53602 + 0.679524i) q^{11} +(-1.37067 + 3.33485i) q^{13} +(-0.437989 + 0.205904i) q^{14} +(1.90018 + 3.29120i) q^{16} +(-1.43204 + 2.48037i) q^{17} +(-0.759707 - 2.83527i) q^{19} +(7.52284 - 2.01574i) q^{20} +(-0.240133 + 0.415922i) q^{22} +(-7.27090 + 4.19786i) q^{23} -10.6845i q^{25} +(-0.524348 - 0.400074i) q^{26} +(0.919475 + 5.12108i) q^{28} +(-1.66138 - 2.87760i) q^{29} +(6.75045 - 6.75045i) q^{31} +(-2.07320 + 0.555513i) q^{32} +(-0.370463 - 0.370463i) q^{34} +(10.4411 + 0.880647i) q^{35} +(-6.77592 - 1.81560i) q^{37} +0.536937 q^{38} +2.87356i q^{40} +(-2.79099 - 0.747843i) q^{41} +(-2.43132 - 1.40372i) q^{43} +(3.65087 + 3.65087i) q^{44} +(-0.397491 - 1.48346i) q^{46} +(-4.85765 - 4.85765i) q^{47} +(-1.17248 + 6.90111i) q^{49} +(1.88787 + 0.505853i) q^{50} +(-5.61342 + 4.33176i) q^{52} +5.43259 q^{53} +(9.00481 - 5.19893i) q^{55} +(-1.91291 - 0.161343i) q^{56} +(0.587105 - 0.157314i) q^{58} +(-0.00666592 + 0.00178613i) q^{59} +(-5.65469 - 3.26474i) q^{61} +(0.873154 + 1.51235i) q^{62} +7.20808i q^{64} +(5.50050 + 13.1774i) q^{65} +(2.10207 - 7.84504i) q^{67} +(-4.87775 + 2.81617i) q^{68} +(-0.649930 + 1.80316i) q^{70} +(14.5933 - 3.91026i) q^{71} +(-0.321617 - 0.321617i) q^{73} +(0.641604 - 1.11129i) q^{74} +(1.49399 - 5.57566i) q^{76} +(2.95530 + 6.28635i) q^{77} +0.280448 q^{79} +(14.5379 + 3.89543i) q^{80} +(0.264276 - 0.457739i) q^{82} +(-2.42973 + 2.42973i) q^{83} +(2.93575 + 10.9564i) q^{85} +(0.363136 - 0.363136i) q^{86} +(-1.64977 + 0.952496i) q^{88} +(0.0536096 - 0.200074i) q^{89} +(-9.08093 + 2.92177i) q^{91} -16.5105 q^{92} +(1.08829 - 0.628324i) q^{94} +(-10.0674 - 5.81240i) q^{95} +(-0.197356 - 0.736543i) q^{97} +(-1.16386 - 0.533897i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more