LMFDB - Embedded newform 819.2.fn.e.460.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(73,819)]

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, 2, 3]))

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

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

chi := DirichletCharacter("819.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fn (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 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			460.3
Character	$\chi$	$=$	819.460
Dual form			819.2.fn.e.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.423548 - 1.58070i) q^{2} +(-0.587174 + 0.339005i) q^{4} +(2.77274 - 0.742954i) q^{5} +(1.92960 + 1.81015i) q^{7} +(-1.52975 - 1.52975i) q^{8} +O(q^{10})$	\(q+(-0.423548 - 1.58070i) q^{2} +(-0.587174 + 0.339005i) q^{4} +(2.77274 - 0.742954i) q^{5} +(1.92960 + 1.81015i) q^{7} +(-1.52975 - 1.52975i) q^{8} +(-2.34878 - 4.06820i) q^{10} +(-0.894725 + 3.33916i) q^{11} +(2.29273 - 2.78269i) q^{13} +(2.04403 - 3.81681i) q^{14} +(-2.44816 + 4.24034i) q^{16} +(-3.22444 - 5.58489i) q^{17} +(2.93592 - 0.786677i) q^{19} +(-1.37622 + 1.37622i) q^{20} +5.65717 q^{22} +(2.97203 + 1.71590i) q^{23} +(2.80599 - 1.62004i) q^{25} +(-5.36969 - 2.44553i) q^{26} +(-1.74666 - 0.408727i) q^{28} +4.40371 q^{29} +(0.868206 - 3.24019i) q^{31} +(3.56028 + 0.953974i) q^{32} +(-7.46233 + 7.46233i) q^{34} +(6.69515 + 3.58547i) q^{35} +(3.75982 - 1.00744i) q^{37} +(-2.48700 - 4.30762i) q^{38} +(-5.37812 - 3.10506i) q^{40} +(3.03989 + 3.03989i) q^{41} -4.48958i q^{43} +(-0.606632 - 2.26398i) q^{44} +(1.45353 - 5.42467i) q^{46} +(1.47790 + 5.51561i) q^{47} +(0.446725 + 6.98573i) q^{49} +(-3.74927 - 3.74927i) q^{50} +(-0.402887 + 2.41117i) q^{52} +(-5.72526 - 9.91644i) q^{53} +9.92337i q^{55} +(-0.182733 - 5.72087i) q^{56} +(-1.86518 - 6.96095i) q^{58} +(-2.86050 - 0.766469i) q^{59} +(-3.03504 - 1.75228i) q^{61} -5.48950 q^{62} +3.76085i q^{64} +(4.28975 - 9.41908i) q^{65} +(-7.04645 - 1.88809i) q^{67} +(3.78661 + 2.18620i) q^{68} +(2.83184 - 12.1016i) q^{70} +(-8.31408 + 8.31408i) q^{71} +(4.51174 + 1.20892i) q^{73} +(-3.18492 - 5.51645i) q^{74} +(-1.45721 + 1.45721i) q^{76} +(-7.77084 + 4.82366i) q^{77} +(-0.543920 + 0.942097i) q^{79} +(-3.63774 + 13.5762i) q^{80} +(3.51762 - 6.09269i) q^{82} +(-2.01261 - 2.01261i) q^{83} +(-13.0898 - 13.0898i) q^{85} +(-7.09668 + 1.90155i) q^{86} +(6.47677 - 3.73937i) q^{88} +(-1.28423 - 4.79280i) q^{89} +(9.46115 - 1.21930i) q^{91} -2.32680 q^{92} +(8.09257 - 4.67225i) q^{94} +(7.55608 - 4.36250i) q^{95} +(-3.20816 - 3.20816i) q^{97} +(10.8531 - 3.66493i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.423548	−	1.58070i	−0.299493	−	1.11772i	−0.937583	−	0.347762i	$-0.886942\pi$
$2$	−0.423548	−	1.58070i	−0.299493	−	1.11772i	0.638089	−	0.769962i	$-0.279725\pi$
$3$		0			0
$3$		0			0
$4$	−0.587174	+	0.339005i	−0.293587	+	0.169502i
$5$	2.77274	−	0.742954i	1.24001	−	0.332259i	0.421539	−	0.906810i	$-0.361490\pi$
$5$	2.77274	−	0.742954i	1.24001	−	0.332259i	0.818469	+	0.574551i	$0.194823\pi$
$6$		0			0
$7$	1.92960	+	1.81015i	0.729321	+	0.684172i
$7$	1.92960	+	1.81015i	0.729321	+	0.684172i
$8$	−1.52975	−	1.52975i	−0.540847	−	0.540847i
$9$		0			0
$10$	−2.34878	−	4.06820i	−0.742749	−	1.28648i
$11$	−0.894725	+	3.33916i	−0.269770	+	1.00679i	0.689496	+	0.724290i	$0.257832\pi$
$11$	−0.894725	+	3.33916i	−0.269770	+	1.00679i	−0.959266	+	0.282505i	$0.908835\pi$
$12$		0			0
$13$	2.29273	−	2.78269i	0.635890	−	0.771780i
$13$	2.29273	−	2.78269i	0.635890	−	0.771780i
$14$	2.04403	−	3.81681i	0.546289	−	1.02008i
$15$		0			0
$16$	−2.44816	+	4.24034i	−0.612040	+	1.06008i
$17$	−3.22444	−	5.58489i	−0.782040	−	1.35453i	−0.930751	−	0.365653i	$-0.880846\pi$
$17$	−3.22444	−	5.58489i	−0.782040	−	1.35453i	0.148711	−	0.988881i	$-0.452488\pi$
$18$		0			0
$19$	2.93592	−	0.786677i	0.673546	−	0.180476i	0.0941943	−	0.995554i	$-0.469973\pi$
$19$	2.93592	−	0.786677i	0.673546	−	0.180476i	0.579352	+	0.815078i	$0.303306\pi$
$20$	−1.37622	+	1.37622i	−0.307731	+	0.307731i
$21$		0			0
$22$	5.65717			1.20611
$23$	2.97203	+	1.71590i	0.619712	+	0.357791i	0.776757	−	0.629801i	$-0.216863\pi$
$23$	2.97203	+	1.71590i	0.619712	+	0.357791i	−0.157045	+	0.987591i	$0.550197\pi$
$24$		0			0
$25$	2.80599	−	1.62004i	0.561198	−	0.324008i
$26$	−5.36969	−	2.44553i	−1.05308	−	0.479607i
$27$		0			0
$28$	−1.74666	−	0.408727i	−0.330088	−	0.0772422i
$29$	4.40371			0.817748			0.408874	−	0.912591i	$-0.365921\pi$
$29$	4.40371			0.817748			0.408874	+	0.912591i	$0.365921\pi$
$30$		0			0
$31$	0.868206	−	3.24019i	0.155934	−	0.581955i	−0.843089	−	0.537774i	$-0.819265\pi$
$31$	0.868206	−	3.24019i	0.155934	−	0.581955i	0.999024	−	0.0441812i	$-0.0140679\pi$
$32$	3.56028	+	0.953974i	0.629374	+	0.168640i
$33$		0			0
$34$	−7.46233	+	7.46233i	−1.27978	+	1.27978i
$35$	6.69515	+	3.58547i	1.13169	+	0.606055i
$36$		0			0
$37$	3.75982	−	1.00744i	0.618110	−	0.165622i	0.0638414	−	0.997960i	$-0.479665\pi$
$37$	3.75982	−	1.00744i	0.618110	−	0.165622i	0.554268	+	0.832338i	$0.312998\pi$
$38$	−2.48700	−	4.30762i	−0.403445	−	0.698787i
$39$		0			0
$40$	−5.37812	−	3.10506i	−0.850356	−	0.490953i
$41$	3.03989	+	3.03989i	0.474751	+	0.474751i	0.903448	−	0.428697i	$-0.141027\pi$
$41$	3.03989	+	3.03989i	0.474751	+	0.474751i	−0.428697	+	0.903448i	$0.641027\pi$
$42$		0			0
$43$		−	4.48958i		−	0.684654i	−0.939581	−	0.342327i	$-0.888785\pi$
$43$		−	4.48958i		−	0.684654i	0.939581	−	0.342327i	$-0.111215\pi$
$44$	−0.606632	−	2.26398i	−0.0914533	−	0.341308i
$45$		0			0
$46$	1.45353	−	5.42467i	0.214312	−	0.799823i
$47$	1.47790	+	5.51561i	0.215574	+	0.804535i	0.985964	+	0.166961i	$0.0533953\pi$
$47$	1.47790	+	5.51561i	0.215574	+	0.804535i	−0.770389	+	0.637574i	$0.779938\pi$
$48$		0			0
$49$	0.446725	+	6.98573i	0.0638179	+	0.997962i
$50$	−3.74927	−	3.74927i	−0.530227	−	0.530227i
$51$		0			0
$52$	−0.402887	+	2.41117i	−0.0558704	+	0.334369i
$53$	−5.72526	−	9.91644i	−0.786425	−	1.36213i	−0.928144	−	0.372221i	$-0.878596\pi$
$53$	−5.72526	−	9.91644i	−0.786425	−	1.36213i	0.141719	−	0.989907i	$-0.454737\pi$
$54$		0			0
$55$			9.92337i			1.33807i
$56$	−0.182733	−	5.72087i	−0.0244187	−	0.764483i
$57$		0			0
$58$	−1.86518	−	6.96095i	−0.244910	−	0.914018i
$59$	−2.86050	−	0.766469i	−0.372405	−	0.0997857i	0.0677619	−	0.997702i	$-0.478414\pi$
$59$	−2.86050	−	0.766469i	−0.372405	−	0.0997857i	−0.440167	+	0.897916i	$0.645081\pi$
$60$		0			0
$61$	−3.03504	−	1.75228i	−0.388598	−	0.224357i	0.292955	−	0.956126i	$-0.405361\pi$
$61$	−3.03504	−	1.75228i	−0.388598	−	0.224357i	−0.681552	+	0.731769i	$0.738695\pi$
$62$	−5.48950			−0.697167
$63$		0			0
$64$			3.76085i			0.470107i
$65$	4.28975	−	9.41908i	0.532078	−	1.16829i
$66$		0			0
$67$	−7.04645	−	1.88809i	−0.860861	−	0.230667i	−0.198729	−	0.980054i	$-0.563681\pi$
$67$	−7.04645	−	1.88809i	−0.860861	−	0.230667i	−0.662132	+	0.749387i	$0.730348\pi$
$68$	3.78661	+	2.18620i	0.459193	+	0.265115i
$69$		0			0
$70$	2.83184	−	12.1016i	0.338470	−	1.44642i
$71$	−8.31408	+	8.31408i	−0.986700	+	0.986700i	−0.999913	−	0.0132127i	$-0.995794\pi$
$71$	−8.31408	+	8.31408i	−0.986700	+	0.986700i	0.0132127	+	0.999913i	$0.495794\pi$
$72$		0			0
$73$	4.51174	+	1.20892i	0.528059	+	0.141493i	0.512992	−	0.858393i	$-0.328537\pi$
$73$	4.51174	+	1.20892i	0.528059	+	0.141493i	0.0150673	+	0.999886i	$0.495204\pi$
$74$	−3.18492	−	5.51645i	−0.370240	−	0.641274i
$75$		0			0
$76$	−1.45721	+	1.45721i	−0.167153	+	0.167153i
$77$	−7.77084	+	4.82366i	−0.885569	+	0.549708i
$78$		0			0
$79$	−0.543920	+	0.942097i	−0.0611957	+	0.105994i	−0.895000	−	0.446066i	$-0.852825\pi$
$79$	−0.543920	+	0.942097i	−0.0611957	+	0.105994i	0.833804	+	0.552060i	$0.186158\pi$
$80$	−3.63774	+	13.5762i	−0.406712	+	1.51787i
$81$		0			0
$82$	3.51762	−	6.09269i	0.388456	−	0.672825i
$83$	−2.01261	−	2.01261i	−0.220913	−	0.220913i	0.587970	−	0.808883i	$-0.299927\pi$
$83$	−2.01261	−	2.01261i	−0.220913	−	0.220913i	−0.808883	+	0.587970i	$0.799927\pi$
$84$		0			0
$85$	−13.0898	−	13.0898i	−1.41979	−	1.41979i
$86$	−7.09668	+	1.90155i	−0.765255	+	0.205049i
$87$		0			0
$88$	6.47677	−	3.73937i	0.690426	−	0.398618i
$89$	−1.28423	−	4.79280i	−0.136128	−	0.508036i	−0.999991	−	0.00430871i	$-0.998628\pi$
$89$	−1.28423	−	4.79280i	−0.136128	−	0.508036i	0.863863	−	0.503727i	$-0.168038\pi$
$90$		0			0
$91$	9.46115	−	1.21930i	0.991798	−	0.127817i
$92$	−2.32680			−0.242586
$93$		0			0
$94$	8.09257	−	4.67225i	0.834685	−	0.481906i
$95$	7.55608	−	4.36250i	0.775237	−	0.447584i
$96$		0			0
$97$	−3.20816	−	3.20816i	−0.325739	−	0.325739i	0.525225	−	0.850964i	$-0.323981\pi$
$97$	−3.20816	−	3.20816i	−0.325739	−	0.325739i	−0.850964	+	0.525225i	$0.823981\pi$
$98$	10.8531	−	3.66493i	1.09633	−	0.370214i
$99$		0			0
$100$	−1.09840	+	1.90249i	−0.109840	+	0.190249i
$101$	4.57037	+	7.91611i	0.454769	+	0.787682i	0.998675	−	0.0514637i	$-0.0163887\pi$
$101$	4.57037	+	7.91611i	0.454769	+	0.787682i	−0.543906	+	0.839146i	$0.683055\pi$
$102$		0			0
$103$	−2.56180	+	4.43716i	−0.252421	+	0.437207i	−0.964192	−	0.265205i	$-0.914560\pi$
$103$	−2.56180	+	4.43716i	−0.252421	+	0.437207i	0.711771	+	0.702412i	$0.247894\pi$
$104$	−7.76411	+	0.749511i	−0.761334	+	0.0734956i
$105$		0			0
$106$	−13.2500	+	13.2500i	−1.28696	+	1.28696i
$107$	−6.27683	+	10.8718i	−0.606804	+	1.05102i	0.384960	+	0.922933i	$0.374215\pi$
$107$	−6.27683	+	10.8718i	−0.606804	+	1.05102i	−0.991764	+	0.128082i	$0.959118\pi$
$108$		0			0
$109$	−18.8614	−	5.05389i	−1.80659	−	0.484075i	−0.811617	−	0.584190i	$-0.801412\pi$
$109$	−18.8614	−	5.05389i	−1.80659	−	0.484075i	−0.994976	+	0.100114i	$0.968079\pi$
$110$	15.6859	−	4.20302i	1.49559	−	0.400742i
$111$		0			0
$112$	−12.3996	+	3.75063i	−1.17165	+	0.354401i
$113$	−0.000230976	0		−2.17284e−5	0		−1.08642e−5	−	1.00000i	$-0.500003\pi$
$113$	−0.000230976	0		−2.17284e−5	0		−1.08642e−5		1.00000i	$0.500003\pi$
$114$		0			0
$115$	9.51552	+	2.54968i	0.887327	+	0.237759i
$116$	−2.58574	+	1.49288i	−0.240080	+	0.138610i
$117$		0			0
$118$			4.84623i			0.446132i
$119$	3.88760	−	16.6133i	0.356375	−	1.52294i
$120$		0			0
$121$	−0.823180	−	0.475263i	−0.0748345	−	0.0432057i
$122$	−1.48435	+	5.53967i	−0.134387	+	0.501539i
$123$		0			0
$124$	0.588652	+	2.19688i	0.0528625	+	0.197286i
$125$	−3.57226	+	3.57226i	−0.319513	+	0.319513i
$126$		0			0
$127$			12.4887i			1.10820i	0.832452	+	0.554098i	$0.186937\pi$
$127$			12.4887i			1.10820i	−0.832452	+	0.554098i	$0.813063\pi$
$128$	13.0653	−	3.50085i	1.15482	−	0.309434i
$129$		0			0
$130$	−16.7057	−	2.79138i	−1.46518	−	0.244820i
$131$	11.7665	+	6.79340i	1.02805	+	0.593542i	0.916424	−	0.400209i	$-0.131062\pi$
$131$	11.7665	+	6.79340i	1.02805	+	0.593542i	0.111621	+	0.993751i	$0.464396\pi$
$132$		0			0
$133$	7.08915	+	3.79647i	0.614708	+	0.329196i
$134$			11.9380i			1.03129i
$135$		0			0
$136$	−3.61089	+	13.4760i	−0.309631	+	1.15556i
$137$	−0.349865	+	1.30571i	−0.0298910	+	0.111555i	−0.979260	−	0.202610i	$-0.935058\pi$
$137$	−0.349865	+	1.30571i	−0.0298910	+	0.111555i	0.949369	+	0.314164i	$0.101724\pi$
$138$		0			0
$139$			18.8190i			1.59621i	0.602521	+	0.798103i	$0.294163\pi$
$139$			18.8190i			1.59621i	−0.602521	+	0.798103i	$0.705837\pi$
$140$	−5.14670	+	0.164393i	−0.434976	+	0.0138938i
$141$		0			0
$142$	16.6635	+	9.62067i	1.39837	+	0.807349i
$143$	7.24049	+	10.1456i	0.605480	+	0.848414i
$144$		0			0
$145$	12.2104	−	3.27175i	1.01401	−	0.271704i
$146$		−	7.64375i		−	0.632601i
$147$		0			0
$148$	−1.86614	+	1.86614i	−0.153396	+	0.153396i
$149$	5.52045	+	20.6026i	0.452253	+	1.68783i	0.696040	+	0.718003i	$0.254944\pi$
$149$	5.52045	+	20.6026i	0.452253	+	1.68783i	−0.243787	+	0.969829i	$0.578390\pi$
$150$		0			0
$151$	4.36658	−	16.2963i	0.355348	−	1.32618i	−0.524699	−	0.851288i	$-0.675822\pi$
$151$	4.36658	−	16.2963i	0.355348	−	1.32618i	0.880047	−	0.474887i	$-0.157511\pi$
$152$	−5.69463	−	3.28779i	−0.461895	−	0.266675i
$153$		0			0
$154$	10.9161	+	10.2403i	0.879644	+	0.825189i
$155$		−	9.62925i		−	0.773440i
$156$		0			0
$157$	−9.46297	+	5.46345i	−0.755227	+	0.436031i	−0.827580	−	0.561348i	$-0.810283\pi$
$157$	−9.46297	+	5.46345i	−0.755227	+	0.436031i	0.0723522	+	0.997379i	$0.476949\pi$
$158$	1.71955	+	0.460752i	0.136800	+	0.0366554i
$159$		0			0
$160$	10.5805			0.836462
$161$	2.62880	+	8.69084i	0.207178	+	0.684934i
$162$		0			0
$163$	8.37856	−	2.24503i	0.656259	−	0.175844i	0.0847019	−	0.996406i	$-0.473006\pi$
$163$	8.37856	−	2.24503i	0.656259	−	0.175844i	0.571557	+	0.820562i	$0.306340\pi$
$164$	−2.81548	−	0.754405i	−0.219852	−	0.0589091i
$165$		0			0
$166$	−2.32890	+	4.03377i	−0.180758	+	0.313082i
$167$	8.00174	−	8.00174i	0.619193	−	0.619193i	−0.326131	−	0.945324i	$-0.605745\pi$
$167$	8.00174	−	8.00174i	0.619193	−	0.619193i	0.945324	+	0.326131i	$0.105745\pi$
$168$		0			0
$169$	−2.48674	−	12.7599i	−0.191288	−	0.981534i
$170$	−15.1470	+	26.2353i	−1.16172	+	2.01216i
$171$		0			0
$172$	1.52199	+	2.63616i	0.116050	+	0.201005i
$173$	−1.63833	+	2.83768i	−0.124560	+	0.215745i	−0.921561	−	0.388234i	$-0.873085\pi$
$173$	−1.63833	+	2.83768i	−0.124560	+	0.215745i	0.797001	+	0.603978i	$0.206419\pi$
$174$		0			0
$175$	8.34696	+	1.95323i	0.630971	+	0.147650i
$176$	−11.9687	−	11.9687i	−0.902178	−	0.902178i
$177$		0			0
$178$	−7.03205	+	4.05996i	−0.527075	+	0.304307i
$179$	1.94863	−	1.12504i	0.145648	−	0.0840897i	−0.425405	−	0.905003i	$-0.639868\pi$
$179$	1.94863	−	1.12504i	0.145648	−	0.0840897i	0.571053	+	0.820913i	$0.306535\pi$
$180$		0			0
$181$	−15.5420			−1.15523			−0.577615	−	0.816310i	$-0.696016\pi$
$181$	−15.5420			−1.15523			−0.577615	+	0.816310i	$0.696016\pi$
$182$	−5.93459	−	14.4388i	−0.439901	−	1.07028i
$183$		0			0
$184$	−1.92156	−	7.17136i	−0.141659	−	0.528679i
$185$	9.67652	−	5.58674i	0.711432	−	0.410745i
$186$		0			0
$187$	21.5338	−	5.76997i	1.57471	−	0.421942i
$188$	−2.73761	−	2.73761i	−0.199660	−	0.199660i
$189$		0			0
$190$	−10.0962	−	10.0962i	−0.732454	−	0.732454i
$191$	−1.18897	+	2.05936i	−0.0860308	+	0.149010i	−0.905830	−	0.423641i	$-0.860752\pi$
$191$	−1.18897	+	2.05936i	−0.0860308	+	0.149010i	0.819799	+	0.572651i	$0.194085\pi$
$192$		0			0
$193$	−2.02038	+	7.54017i	−0.145430	+	0.542753i	0.854306	+	0.519771i	$0.173983\pi$
$193$	−2.02038	+	7.54017i	−0.145430	+	0.542753i	−0.999736	+	0.0229822i	$0.992684\pi$
$194$	−3.71233	+	6.42995i	−0.266530	+	0.461643i
$195$		0			0
$196$	−2.63050	−	3.95039i	−0.187893	−	0.282171i
$197$	10.9402	−	10.9402i	0.779454	−	0.779454i	−0.200284	−	0.979738i	$-0.564187\pi$
$197$	10.9402	−	10.9402i	0.779454	−	0.779454i	0.979738	+	0.200284i	$0.0641866\pi$
$198$		0			0
$199$	−10.0868	−	17.4708i	−0.715031	−	1.23847i	−0.962947	−	0.269689i	$-0.913079\pi$
$199$	−10.0868	−	17.4708i	−0.715031	−	1.23847i	0.247916	−	0.968781i	$-0.420254\pi$
$200$	−6.77070	−	1.81420i	−0.478761	−	0.128284i
$201$		0			0
$202$	10.5772	−	10.5772i	0.744212	−	0.744212i
$203$	8.49741	+	7.97137i	0.596401	+	0.559480i
$204$		0			0
$205$	10.6873	+	6.17033i	0.746435	+	0.430954i
$206$	8.09887	+	2.17009i	0.564275	+	0.151197i
$207$		0			0
$208$	6.18657	+	16.5344i	0.428962	+	1.14646i
$209$			10.5074i			0.726809i
$210$		0			0
$211$	2.36943			0.163118			0.0815591	−	0.996669i	$-0.474010\pi$
$211$	2.36943			0.163118			0.0815591	+	0.996669i	$0.474010\pi$
$212$	6.72344	+	3.88178i	0.461768	+	0.266602i
$213$		0			0
$214$	19.8436	+	5.31707i	1.35648	+	0.363468i
$215$	−3.33555	−	12.4484i	−0.227483	−	0.848976i
$216$		0			0
$217$	7.54051	−	4.68069i	0.511883	−	0.317746i
$218$			31.9548i			2.16425i
$219$		0			0
$220$	−3.36407	−	5.82674i	−0.226806	−	0.392839i
$221$	−22.9338	−	3.83205i	−1.54269	−	0.257771i
$222$		0			0
$223$	9.67825	+	9.67825i	0.648103	+	0.648103i	0.952534	−	0.304431i	$-0.0984663\pi$
$223$	9.67825	+	9.67825i	0.648103	+	0.648103i	−0.304431	+	0.952534i	$0.598466\pi$
$224$	5.14309	+	8.28542i	0.343637	+	0.553593i
$225$		0			0
$226$	9.78292e−5	0	0.000365104i	6.50750e−6	0	2.42863e-5i
$227$	3.37455	−	12.5940i	0.223977	−	0.835894i	−0.758835	−	0.651283i	$-0.774231\pi$
$227$	3.37455	−	12.5940i	0.223977	−	0.835894i	0.982812	−	0.184611i	$-0.0591024\pi$
$228$		0			0
$229$	3.93373	+	14.6809i	0.259948	+	0.970139i	0.965270	+	0.261253i	$0.0841356\pi$
$229$	3.93373	+	14.6809i	0.259948	+	0.970139i	−0.705322	+	0.708887i	$0.749198\pi$
$230$		−	16.1211i		−	1.06299i
$231$		0			0
$232$	−6.73656	−	6.73656i	−0.442277	−	0.442277i
$233$	6.69859	+	3.86743i	0.438839	+	0.253364i	0.703105	−	0.711086i	$-0.251796\pi$
$233$	6.69859	+	3.86743i	0.438839	+	0.253364i	−0.264266	+	0.964450i	$0.585130\pi$
$234$		0			0
$235$	8.19569	+	14.1954i	0.534628	+	0.926003i
$236$	1.93945	−	0.519673i	0.126247	−	0.0338278i
$237$		0			0
$238$	−27.9073	+	0.891400i	−1.80896	+	0.0577809i
$239$	−2.10971	+	2.10971i	−0.136466	+	0.136466i	−0.772040	−	0.635574i	$-0.780763\pi$
$239$	−2.10971	+	2.10971i	−0.136466	+	0.136466i	0.635574	+	0.772040i	$0.280763\pi$
$240$		0			0
$241$	25.5066	+	6.83448i	1.64303	+	0.440247i	0.957648	−	0.287941i	$-0.0929707\pi$
$241$	25.5066	+	6.83448i	1.64303	+	0.440247i	0.685377	+	0.728188i	$0.259637\pi$
$242$	−0.402593	+	1.50250i	−0.0258797	+	0.0965843i
$243$		0			0
$244$	2.37613			0.152116
$245$	6.42873	+	19.0377i	0.410717	+	1.21628i
$246$		0			0
$247$	4.54220	−	9.97340i	0.289013	−	0.634592i
$248$	−6.28480	+	3.62853i	−0.399085	+	0.230412i
$249$		0			0
$250$	7.15971	+	4.13366i	0.452820	+	0.261436i
$251$	−7.06132			−0.445707			−0.222853	−	0.974852i	$-0.571537\pi$
$251$	−7.06132			−0.445707			−0.222853	+	0.974852i	$0.571537\pi$
$252$		0			0
$253$	−8.38884	+	8.38884i	−0.527402	+	0.527402i
$254$	19.7409	−	5.28957i	1.23866	−	0.331897i
$255$		0			0
$256$	−7.30674	−	12.6556i	−0.456671	−	0.790978i
$257$	−6.52671	+	11.3046i	−0.407125	+	0.705161i	−0.994566	−	0.104106i	$-0.966802\pi$
$257$	−6.52671	+	11.3046i	−0.407125	+	0.705161i	0.587441	+	0.809267i	$0.300135\pi$
$258$		0			0
$259$	9.07856	+	4.86187i	0.564114	+	0.302102i
$260$	0.674288	+	6.98488i	0.0418175	+	0.433184i
$261$		0			0
$262$	5.75466	−	21.4767i	0.355524	−	1.32683i
$263$	11.1673	+	19.3423i	0.688606	+	1.19270i	0.972289	+	0.233782i	$0.0751101\pi$
$263$	11.1673	+	19.3423i	0.688606	+	1.19270i	−0.283684	+	0.958918i	$0.591557\pi$
$264$		0			0
$265$	−23.2421	−	23.2421i	−1.42775	−	1.42775i
$266$	2.99850	−	12.8138i	0.183850	−	0.785666i
$267$		0			0
$268$	4.77756	−	1.28014i	0.291836	−	0.0781972i
$269$	−2.71439	+	1.56715i	−0.165499	+	0.0955511i	−0.580462	−	0.814287i	$-0.697128\pi$
$269$	−2.71439	+	1.56715i	−0.165499	+	0.0955511i	0.414963	+	0.909838i	$0.363795\pi$
$270$		0			0
$271$	−4.09187	−	15.2711i	−0.248563	−	0.927651i	−0.971559	−	0.236798i	$-0.923902\pi$
$271$	−4.09187	−	15.2711i	−0.248563	−	0.927651i	0.722995	−	0.690853i	$-0.242765\pi$
$272$	31.5757			1.91456
$273$		0			0
$274$	2.21213			0.133639
$275$	2.89898	+	10.8191i	0.174815	+	0.652419i
$276$		0			0
$277$	−25.5340	+	14.7421i	−1.53419	+	0.885765i	−0.535028	+	0.844834i	$0.679699\pi$
$277$	−25.5340	+	14.7421i	−1.53419	+	0.885765i	−0.999162	+	0.0409305i	$0.986968\pi$
$278$	29.7472	−	7.97074i	1.78412	−	0.478053i
$279$		0			0
$280$	−4.75701	−	15.7267i	−0.284286	−	0.939852i
$281$	−16.8969	−	16.8969i	−1.00798	−	1.00798i	−0.999968	−	0.00801615i	$-0.997448\pi$
$281$	−16.8969	−	16.8969i	−1.00798	−	1.00798i	−0.00801615	−	0.999968i	$-0.502552\pi$
$282$		0			0
$283$	4.66719	+	8.08381i	0.277436	+	0.480533i	0.970747	−	0.240106i	$-0.0771822\pi$
$283$	4.66719	+	8.08381i	0.277436	+	0.480533i	−0.693311	+	0.720638i	$0.743849\pi$
$284$	2.06330	−	7.70032i	0.122434	−	0.456930i
$285$		0			0
$286$	12.9704	−	15.7422i	0.766956	−	0.930854i
$287$	0.363124	+	11.3684i	0.0214346	+	0.671057i
$288$		0			0
$289$	−12.2940	+	21.2938i	−0.723174	+	1.25257i
$290$	−10.3433	−	17.9152i	−0.607381	−	1.05202i
$291$		0			0
$292$	−3.05900	+	0.819657i	−0.179015	+	0.0479668i
$293$	−2.08232	+	2.08232i	−0.121650	+	0.121650i	−0.765311	−	0.643661i	$-0.777415\pi$
$293$	−2.08232	+	2.08232i	−0.121650	+	0.121650i	0.643661	+	0.765311i	$0.277415\pi$
$294$		0			0
$295$	−8.50088			−0.494940
$296$	−7.29269	−	4.21044i	−0.423879	−	0.244727i
$297$		0			0
$298$	30.2284	−	17.4524i	1.75108	−	1.01099i
$299$	11.5889	−	4.33614i	0.670204	−	0.250766i
$300$		0			0
$301$	8.12680	−	8.66309i	0.468421	−	0.499332i
$302$	−27.6091			−1.58872
$303$		0			0
$304$	−3.85182	+	14.3752i	−0.220917	+	0.824474i
$305$	−9.71726	−	2.60373i	−0.556409	−	0.149089i
$306$		0			0
$307$	−3.85597	+	3.85597i	−0.220072	+	0.220072i	−0.808529	−	0.588457i	$-0.799736\pi$
$307$	−3.85597	+	3.85597i	−0.220072	+	0.220072i	0.588457	+	0.808529i	$0.299736\pi$
$308$	2.92759	−	5.46668i	0.166815	−	0.311493i
$309$		0			0
$310$	−15.2210	+	4.07844i	−0.864493	+	0.231640i
$311$	7.03750	+	12.1893i	0.399060	+	0.691192i	0.993610	−	0.112866i	$-0.0360032\pi$
$311$	7.03750	+	12.1893i	0.399060	+	0.691192i	−0.594550	+	0.804058i	$0.702670\pi$
$312$		0			0
$313$	4.07599	+	2.35327i	0.230388	+	0.133015i	0.610751	−	0.791823i	$-0.290868\pi$
$313$	4.07599	+	2.35327i	0.230388	+	0.133015i	−0.380363	+	0.924837i	$0.624201\pi$
$314$	12.6441	+	12.6441i	0.713548	+	0.713548i
$315$		0			0
$316$		−	0.737566i		−	0.0414913i
$317$	−7.57921	−	28.2860i	−0.425691	−	1.58870i	−0.762410	−	0.647094i	$-0.775984\pi$
$317$	−7.57921	−	28.2860i	−0.425691	−	1.58870i	0.336720	−	0.941605i	$-0.390683\pi$
$318$		0			0
$319$	−3.94011	+	14.7047i	−0.220604	+	0.823305i
$320$	2.79414	+	10.4279i	0.156197	+	0.582936i
$321$		0			0
$322$	12.6242	−	7.83633i	0.703519	−	0.436702i
$323$	−13.8602	−	13.8602i	−0.771201	−	0.771201i
$324$		0			0
$325$	1.92532	−	11.5225i	0.106798	−	0.639155i
$326$	−7.09744	−	12.2931i	−0.393091	−	0.680853i
$327$		0			0
$328$		−	9.30051i		−	0.513535i
$329$	−7.13231	+	13.3182i	−0.393217	+	0.734254i
$330$		0			0
$331$	3.83537	+	14.3138i	0.210811	+	0.786757i	0.987599	+	0.156996i	$0.0501808\pi$
$331$	3.83537	+	14.3138i	0.210811	+	0.786757i	−0.776788	+	0.629762i	$0.783152\pi$
$332$	1.86404	+	0.499467i	0.102302	+	0.0274118i
$333$		0			0
$334$	−16.0375	−	9.25924i	−0.877532	−	0.506643i
$335$	−20.9408			−1.14412
$336$		0			0
$337$		−	9.51919i		−	0.518543i	−0.965804	−	0.259272i	$-0.916518\pi$
$337$		−	9.51919i		−	0.518543i	0.965804	−	0.259272i	$-0.0834825\pi$
$338$	−19.1164	+	9.33524i	−1.03980	+	0.507770i
$339$		0			0
$340$	12.1235	+	3.24849i	0.657491	+	0.176174i
$341$	10.0427	+	5.79816i	0.543843	+	0.313988i
$342$		0			0
$343$	−11.7832	+	14.2883i	−0.636233	+	0.771497i
$344$	−6.86791	+	6.86791i	−0.370293	+	0.370293i
$345$		0			0
$346$	5.17944	+	1.38783i	0.278448	+	0.0746100i
$347$	−17.5649	−	30.4233i	−0.942933	−	1.63321i	−0.759838	−	0.650112i	$-0.774722\pi$
$347$	−17.5649	−	30.4233i	−0.942933	−	1.63321i	−0.183095	−	0.983095i	$-0.558612\pi$
$348$		0			0
$349$	−6.64759	+	6.64759i	−0.355837	+	0.355837i	−0.862276	−	0.506439i	$-0.830962\pi$
$349$	−6.64759	+	6.64759i	−0.355837	+	0.355837i	0.506439	+	0.862276i	$0.330962\pi$
$350$	−0.447862	−	14.0213i	−0.0239393	−	0.749472i
$351$		0			0
$352$	−6.37094	+	11.0348i	−0.339572	+	0.588157i
$353$	−3.20243	+	11.9516i	−0.170448	+	0.636121i	0.826834	+	0.562446i	$0.190139\pi$
$353$	−3.20243	+	11.9516i	−0.170448	+	0.636121i	−0.997282	+	0.0736752i	$0.976527\pi$
$354$		0			0
$355$	−16.8758	+	29.2298i	−0.895676	+	1.55136i
$356$	2.37885	+	2.37885i	0.126079	+	0.126079i
$357$		0			0
$358$	−2.60370	−	2.60370i	−0.137610	−	0.137610i
$359$	−4.14143	+	1.10969i	−0.218576	+	0.0585673i	−0.366445	−	0.930440i	$-0.619425\pi$
$359$	−4.14143	+	1.10969i	−0.218576	+	0.0585673i	0.147869	+	0.989007i	$0.452759\pi$
$360$		0			0
$361$	−8.45373	+	4.88076i	−0.444933	+	0.256882i
$362$	6.58279	+	24.5673i	0.345984	+	1.29123i
$363$		0			0
$364$	−5.14199	+	3.92331i	−0.269513	+	0.205638i
$365$	13.4081			0.701810
$366$		0			0
$367$	−21.4207	+	12.3672i	−1.11815	+	0.645565i	−0.940928	−	0.338606i	$-0.890045\pi$
$367$	−21.4207	+	12.3672i	−1.11815	+	0.645565i	−0.177223	+	0.984171i	$0.556711\pi$
$368$	−14.5520	+	8.40162i	−0.758577	+	0.437965i
$369$		0			0
$370$	−12.9294	−	12.9294i	−0.672169	−	0.672169i
$371$	6.90276	−	29.4984i	0.358373	−	1.53148i
$372$		0			0
$373$	3.95677	−	6.85332i	0.204874	−	0.354852i	−0.745219	−	0.666820i	$-0.767655\pi$
$373$	3.95677	−	6.85332i	0.204874	−	0.354852i	0.950092	+	0.311968i	$0.100988\pi$
$374$	−18.2412	−	31.5947i	−0.943230	−	1.63372i
$375$		0			0
$376$	6.17667	−	10.6983i	0.318537	−	0.551723i
$377$	10.0965	−	12.2542i	0.519998	−	0.631122i
$378$		0			0
$379$	3.32389	−	3.32389i	0.170737	−	0.170737i	−0.616566	−	0.787303i	$-0.711477\pi$
$379$	3.32389	−	3.32389i	0.170737	−	0.170737i	0.787303	+	0.616566i	$0.211477\pi$
$380$	−2.95782	+	5.12309i	−0.151733	+	0.262809i
$381$		0			0
$382$	3.75881	+	1.00717i	0.192318	+	0.0515313i
$383$	8.74833	−	2.34411i	0.447019	−	0.119778i	−0.0282852	−	0.999600i	$-0.509005\pi$
$383$	8.74833	−	2.34411i	0.447019	−	0.119778i	0.475304	+	0.879822i	$0.342338\pi$
$384$		0			0
$385$	−17.9628	+	19.1482i	−0.915468	+	0.975880i
$386$	12.7745			0.650204
$387$		0			0
$388$	2.97133	+	0.796165i	0.150846	+	0.0404191i
$389$	−18.5856	+	10.7304i	−0.942328	+	0.544053i	−0.890689	−	0.454612i	$-0.849778\pi$
$389$	−18.5856	+	10.7304i	−0.942328	+	0.544053i	−0.0516387	+	0.998666i	$0.516444\pi$
$390$		0			0
$391$		−	22.1313i		−	1.11923i
$392$	10.0030	−	11.3698i	0.505229	−	0.574260i
$393$		0			0
$394$	−21.9268	−	12.6594i	−1.10466	−	0.637773i
$395$	−0.808215	+	3.01630i	−0.0406657	+	0.151766i
$396$		0			0
$397$	−3.38387	−	12.6288i	−0.169831	−	0.633819i	−0.997374	−	0.0724172i	$-0.976929\pi$
$397$	−3.38387	−	12.6288i	−0.169831	−	0.633819i	0.827543	−	0.561402i	$-0.189738\pi$
$398$	−23.3439	+	23.3439i	−1.17012	+	1.17012i
$399$		0			0
$400$			15.8645i			0.793224i
$401$	−20.5002	+	5.49301i	−1.02373	+	0.274308i	−0.731356	−	0.681996i	$-0.761112\pi$
$401$	−20.5002	+	5.49301i	−1.02373	+	0.274308i	−0.292375	+	0.956304i	$0.594445\pi$
$402$		0			0
$403$	−7.02588	−	9.84484i	−0.349984	−	0.490406i
$404$	−5.36720	−	3.09875i	−0.267028	−	0.154169i
$405$		0			0
$406$	9.00130	−	16.8081i	0.446727	−	0.834173i
$407$			13.4560i			0.666990i
$408$		0			0
$409$	−2.20463	+	8.22781i	−0.109012	+	0.406839i	−0.998769	−	0.0495951i	$-0.984207\pi$
$409$	−2.20463	+	8.22781i	−0.109012	+	0.406839i	0.889757	+	0.456434i	$0.150874\pi$
$410$	5.22686	−	19.5069i	0.258136	−	0.963377i
$411$		0			0
$412$		−	3.47385i		−	0.171144i
$413$	−4.13220	−	6.65691i	−0.203332	−	0.327565i
$414$		0			0
$415$	−7.07573	−	4.08517i	−0.347334	−	0.200533i
$416$	10.8174	−	7.71995i	0.530366	−	0.378502i
$417$		0			0
$418$	16.6090	−	4.45037i	0.812373	−	0.217675i
$419$			8.39090i			0.409922i	0.978770	+	0.204961i	$0.0657068\pi$
$419$			8.39090i			0.409922i	−0.978770	+	0.204961i	$0.934293\pi$
$420$		0			0
$421$	20.5414	−	20.5414i	1.00113	−	1.00113i	0.00112764	−	0.999999i	$-0.499641\pi$
$421$	20.5414	−	20.5414i	1.00113	−	1.00113i	0.999999	−	0.00112764i	$-0.000358939\pi$
$422$	−1.00357	−	3.74536i	−0.0488528	−	0.182321i
$423$		0			0
$424$	−6.41144	+	23.9278i	−0.311367	+	1.16204i
$425$	−18.0955	−	10.4474i	−0.877760	−	0.506775i
$426$		0			0
$427$	−2.68453	−	8.87509i	−0.129914	−	0.429496i
$428$		−	8.51150i		−	0.411419i
$429$		0			0
$430$	−18.2645	+	10.5450i	−0.880792	+	0.508526i
$431$	9.66314	+	2.58923i	0.465457	+	0.124719i	0.483923	−	0.875111i	$-0.339212\pi$
$431$	9.66314	+	2.58923i	0.465457	+	0.124719i	−0.0184658	+	0.999829i	$0.505878\pi$
$432$		0			0
$433$	41.3846			1.98882			0.994409	−	0.105595i	$-0.0336746\pi$
$433$	41.3846			1.98882			0.994409	+	0.105595i	$0.0336746\pi$
$434$	−10.5925	−	9.93681i	−0.508458	−	0.476982i
$435$		0			0
$436$	12.7882	−	3.42659i	0.612444	−	0.164104i
$437$	10.0755	+	2.69973i	0.481977	+	0.129145i
$438$		0			0
$439$	−0.0712884	+	0.123475i	−0.00340241	+	0.00589314i	−0.867722	−	0.497051i	$-0.834416\pi$
$439$	−0.0712884	+	0.123475i	−0.00340241	+	0.00589314i	0.864319	+	0.502944i	$0.167750\pi$
$440$	15.1802	−	15.1802i	0.723689	−	0.723689i
$441$		0			0
$442$	3.65623	+	37.8745i	0.173909	+	1.80151i
$443$	12.9368	−	22.4072i	0.614647	−	1.06460i	−0.375800	−	0.926701i	$-0.622632\pi$
$443$	12.9368	−	22.4072i	0.614647	−	1.06460i	0.990446	−	0.137898i	$-0.0440347\pi$
$444$		0			0
$445$	−7.12166	−	12.3351i	−0.337599	−	0.584738i
$446$	11.1992	−	19.3976i	0.530298	−	0.918504i
$447$		0			0
$448$	−6.80770	+	7.25695i	−0.321634	+	0.342859i
$449$	−1.26645	−	1.26645i	−0.0597675	−	0.0597675i	0.676591	−	0.736359i	$-0.263456\pi$
$449$	−1.26645	−	1.26645i	−0.0597675	−	0.0597675i	−0.736359	+	0.676591i	$0.763456\pi$
$450$		0			0
$451$	−12.8705	+	7.43081i	−0.606050	+	0.349903i
$452$	0.000135623	0	7.83019e-5i	6.37916e−6	0	3.68301e-6i
$453$		0			0
$454$	−21.3367			−1.00138
$455$	25.3274	−	10.4100i	1.18737	−	0.488028i
$456$		0			0
$457$	−1.20672	−	4.50353i	−0.0564479	−	0.210666i	0.931941	−	0.362609i	$-0.118114\pi$
$457$	−1.20672	−	4.50353i	−0.0564479	−	0.210666i	−0.988389	+	0.151942i	$0.951447\pi$
$458$	21.5400	−	12.4361i	1.00650	−	0.581101i
$459$		0			0
$460$	−6.45162	+	1.72871i	−0.300808	+	0.0806013i
$461$	−3.60896	−	3.60896i	−0.168086	−	0.168086i	0.618052	−	0.786137i	$-0.287922\pi$
$461$	−3.60896	−	3.60896i	−0.168086	−	0.168086i	−0.786137	+	0.618052i	$0.787922\pi$
$462$		0			0
$463$	−4.00230	−	4.00230i	−0.186003	−	0.186003i	0.607963	−	0.793965i	$-0.291987\pi$
$463$	−4.00230	−	4.00230i	−0.186003	−	0.186003i	−0.793965	+	0.607963i	$0.791987\pi$
$464$	−10.7810	+	18.6732i	−0.500495	+	0.866883i
$465$		0			0
$466$	3.27608	−	12.2265i	0.151762	−	0.566382i
$467$	20.0309	−	34.6946i	0.926921	−	1.60547i	0.138479	−	0.990365i	$-0.455779\pi$
$467$	20.0309	−	34.6946i	0.926921	−	1.60547i	0.788442	−	0.615109i	$-0.210888\pi$
$468$		0			0
$469$	−10.1791	−	16.3984i	−0.470028	−	0.757207i
$470$	18.9674	−	18.9674i	0.874899	−	0.874899i
$471$		0			0
$472$	3.20334	+	5.54834i	0.147446	+	0.255383i
$473$	14.9914	+	4.01694i	0.689306	+	0.184699i
$474$		0			0
$475$	6.96371	−	6.96371i	0.319517	−	0.319517i
$476$	3.34930	+	11.0728i	0.153515	+	0.507521i
$477$		0			0
$478$	4.22838	+	2.44126i	0.193402	+	0.111661i
$479$	−11.3889	−	3.05163i	−0.520370	−	0.139433i	−0.0109323	−	0.999940i	$-0.503480\pi$
$479$	−11.3889	−	3.05163i	−0.520370	−	0.139433i	−0.509438	+	0.860508i	$0.670147\pi$
$480$		0			0
$481$	5.81686	−	12.7722i	0.265226	−	0.582362i
$482$		−	43.2131i		−	1.96830i
$483$		0			0
$484$	0.644466			0.0292939
$485$	−11.2789	−	6.51188i	−0.512149	−	0.295689i
$486$		0			0
$487$	−0.531550	−	0.142428i	−0.0240868	−	0.00645405i	0.246756	−	0.969078i	$-0.420636\pi$
$487$	−0.531550	−	0.142428i	−0.0240868	−	0.00645405i	−0.270842	+	0.962624i	$0.587302\pi$
$488$	1.96230	+	7.32340i	0.0888291	+	0.331515i
$489$		0			0
$490$	27.3701	−	18.2253i	1.23646	−	0.823335i
$491$		−	3.02403i		−	0.136472i	−0.997669	−	0.0682362i	$-0.978263\pi$
$491$		−	3.02403i		−	0.136472i	0.997669	−	0.0682362i	$-0.0217372\pi$
$492$		0			0
$493$	−14.1995	−	24.5942i	−0.639512	−	1.10767i
$494$	−17.6888	−	2.95565i	−0.795857	−	0.132981i
$495$		0			0
$496$	11.6140	+	11.6140i	0.521484	+	0.521484i
$497$	−31.0926	+	0.993144i	−1.39469	+	0.0445486i
$498$		0			0
$499$	−9.92557	−	37.0427i	−0.444330	−	1.65826i	−0.717701	−	0.696352i	$-0.754805\pi$
$499$	−9.92557	−	37.0427i	−0.444330	−	1.65826i	0.273371	−	0.961909i	$-0.411861\pi$
$500$	0.886524	−	3.30855i	0.0396466	−	0.147963i
$501$		0			0
$502$	2.99081	+	11.1618i	0.133486	+	0.498178i
$503$			27.2615i			1.21553i	0.794117	+	0.607765i	$0.207934\pi$
$503$			27.2615i			1.21553i	−0.794117	+	0.607765i	$0.792066\pi$
$504$		0			0
$505$	18.5538	+	18.5538i	0.825631	+	0.825631i
$506$	16.8133	+	9.70717i	0.747443	+	0.431536i
$507$		0			0
$508$	−4.23374	−	7.33305i	−0.187842	−	0.325351i
$509$	17.4575	−	4.67772i	0.773790	−	0.207336i	0.149745	−	0.988725i	$-0.452155\pi$
$509$	17.4575	−	4.67772i	0.773790	−	0.207336i	0.624045	+	0.781388i	$0.285488\pi$
$510$		0			0
$511$	6.51754	+	10.4996i	0.288319	+	0.464477i
$512$	2.21895	−	2.21895i	0.0980646	−	0.0980646i
$513$		0			0
$514$	20.6336	+	5.52874i	0.910107	+	0.243862i
$515$	−3.80660	+	14.2064i	−0.167739	+	0.626009i
$516$		0			0
$517$	−19.7398			−0.868157
$518$	3.83996	−	16.4097i	0.168718	−	0.721002i
$519$		0			0
$520$	−20.9710	+	7.84658i	−0.919640	+	0.344095i
$521$	−10.0266	+	5.78888i	−0.439275	+	0.253616i	−0.703290	−	0.710903i	$-0.748286\pi$
$521$	−10.0266	+	5.78888i	−0.439275	+	0.253616i	0.264015	+	0.964519i	$0.414953\pi$
$522$		0			0
$523$	−8.36503	−	4.82955i	−0.365777	−	0.211182i	0.305835	−	0.952085i	$-0.401065\pi$
$523$	−8.36503	−	4.82955i	−0.365777	−	0.211182i	−0.671612	+	0.740903i	$0.734398\pi$
$524$	−9.21198			−0.402427
$525$		0			0
$526$	25.8446	−	25.8446i	1.12688	−	1.12688i
$527$	−20.8956	+	5.59895i	−0.910225	+	0.243894i
$528$		0			0
$529$	−5.61134	−	9.71913i	−0.243971	−	0.422571i
$530$	−26.8947	+	46.5830i	−1.16823	+	2.02344i
$531$		0			0
$532$	−5.44959	+	0.174068i	−0.236270	+	0.00754680i
$533$	15.4287	−	1.48942i	0.668292	−	0.0645138i
$534$		0			0
$535$	−9.32679	+	34.8081i	−0.403232	+	1.50488i
$536$	7.89098	+	13.6676i	0.340839	+	0.590350i
$537$		0			0
$538$	3.62688	+	3.62688i	0.156366	+	0.156366i
$539$	−23.7262	−	4.75862i	−1.02196	−	0.204968i
$540$		0			0
$541$	−29.4151	+	7.88175i	−1.26465	+	0.338863i	−0.827980	−	0.560757i	$-0.810510\pi$
$541$	−29.4151	+	7.88175i	−1.26465	+	0.338863i	−0.436673	+	0.899620i	$0.643843\pi$
$542$	−22.4059	+	12.9360i	−0.962415	+	0.555651i
$543$		0			0
$544$	−6.15205	−	22.9598i	−0.263767	−	0.984392i
$545$	−56.0526			−2.40103
$546$		0			0
$547$	41.0288			1.75427			0.877133	−	0.480247i	$-0.159453\pi$
$547$	41.0288			1.75427			0.877133	+	0.480247i	$0.159453\pi$
$548$	−0.237212	−	0.885286i	−0.0101332	−	0.0378176i
$549$		0			0
$550$	15.8740	−	9.16485i	0.676869	−	0.390790i
$551$	12.9289	−	3.46430i	0.550791	−	0.147584i
$552$		0			0
$553$	−2.75488	+	0.833296i	−0.117150	+	0.0354353i
$554$	34.1177	+	34.1177i	1.44952	+	1.44952i
$555$		0			0
$556$	−6.37973	−	11.0500i	−0.270561	−	0.468625i
$557$	−1.02281	+	3.81720i	−0.0433381	+	0.161740i	−0.984204	−	0.177040i	$-0.943348\pi$
$557$	−1.02281	+	3.81720i	−0.0433381	+	0.161740i	0.940866	+	0.338780i	$0.110014\pi$
$558$		0			0
$559$	−12.4931	−	10.2934i	−0.528402	−	0.435365i
$560$	−31.5944	+	19.6119i	−1.33511	+	0.828753i
$561$		0			0
$562$	−19.5523	+	33.8656i	−0.824764	+	1.42853i
$563$	14.8777	+	25.7689i	0.627018	+	1.08603i	0.988147	+	0.153512i	$0.0490583\pi$
$563$	14.8777	+	25.7689i	0.627018	+	1.08603i	−0.361128	+	0.932516i	$0.617608\pi$
$564$		0			0
$565$	−0.000640436	0	0.000171604i	−2.69433e−5	0	7.21945e-6i
$566$	10.8013	−	10.8013i	0.454013	−	0.454013i
$567$		0			0
$568$	25.4369			1.06731
$569$	10.3301	+	5.96411i	0.433062	+	0.250028i	0.700650	−	0.713505i	$-0.252893\pi$
$569$	10.3301	+	5.96411i	0.433062	+	0.250028i	−0.267588	+	0.963533i	$0.586227\pi$
$570$		0			0
$571$	−9.93851	+	5.73800i	−0.415914	+	0.240128i	−0.693328	−	0.720623i	$-0.743856\pi$
$571$	−9.93851	+	5.73800i	−0.415914	+	0.240128i	0.277414	+	0.960751i	$0.410523\pi$
$572$	−7.69081	−	3.50264i	−0.321569	−	0.146453i
$573$		0			0
$574$	17.8163	−	5.38906i	0.743637	−	0.224935i
$575$	11.1193			0.463708
$576$		0			0
$577$	0.995790	−	3.71634i	0.0414553	−	0.154713i	−0.942096	−	0.335344i	$-0.891147\pi$
$577$	0.995790	−	3.71634i	0.0414553	−	0.154713i	0.983551	+	0.180631i	$0.0578140\pi$
$578$	38.8662	+	10.4142i	1.61662	+	0.433172i
$579$		0			0
$580$	−6.06046	+	6.06046i	−0.251647	+	0.251647i
$581$	−0.240413	−	7.52666i	−0.00997401	−	0.312259i
$582$		0			0
$583$	38.2351	−	10.2451i	1.58354	−	0.424308i
$584$	−5.05248	−	8.75115i	−0.209073	−	0.362125i
$585$		0			0
$586$	4.17348	+	2.40956i	0.172405	+	0.0995380i
$587$	26.9080	+	26.9080i	1.11061	+	1.11061i	0.993068	+	0.117543i	$0.0375018\pi$
$587$	26.9080	+	26.9080i	1.11061	+	1.11061i	0.117543	+	0.993068i	$0.462498\pi$
$588$		0			0
$589$		−	10.1959i		−	0.420116i
$590$	3.60053	+	13.4374i	0.148231	+	0.553207i
$591$		0			0
$592$	−4.93275	+	18.4093i	−0.202735	+	0.756616i
$593$	−2.64245	−	9.86174i	−0.108512	−	0.404973i	0.890208	−	0.455555i	$-0.150559\pi$
$593$	−2.64245	−	9.86174i	−0.108512	−	0.404973i	−0.998720	+	0.0505817i	$0.983892\pi$
$594$		0			0
$595$	−1.56362	−	48.9527i	−0.0641023	−	2.00687i
$596$	−10.2258	−	10.2258i	−0.418867	−	0.418867i
$597$		0			0
$598$	−11.7626	−	16.4821i	−0.481009	−	0.674001i
$599$	−11.3254	−	19.6162i	−0.462745	−	0.801498i	0.536352	−	0.843995i	$-0.319802\pi$
$599$	−11.3254	−	19.6162i	−0.462745	−	0.801498i	−0.999097	+	0.0424970i	$0.986469\pi$
$600$		0			0
$601$			8.02946i			0.327529i	0.986499	+	0.163764i	$0.0523637\pi$
$601$			8.02946i			0.327529i	−0.986499	+	0.163764i	$0.947636\pi$
$602$	−17.1359	−	9.17681i	−0.698405	−	0.374019i
$603$		0			0
$604$	2.96059	+	11.0491i	0.120465	+	0.449580i
$605$	−2.63556	−	0.706197i	−0.107151	−	0.0287110i
$606$		0			0
$607$	2.91774	+	1.68456i	0.118427	+	0.0683741i	0.558044	−	0.829812i	$-0.311552\pi$
$607$	2.91774	+	1.68456i	0.118427	+	0.0683741i	−0.439616	+	0.898186i	$0.644886\pi$
$608$	11.2032			0.454348
$609$		0			0
$610$			16.4629i			0.666563i
$611$	18.7367	+	8.53328i	0.758005	+	0.345220i
$612$		0			0
$613$	31.4399	+	8.42429i	1.26984	+	0.340254i	0.829971	−	0.557806i	$-0.188357\pi$
$613$	31.4399	+	8.42429i	1.26984	+	0.340254i	0.439873	+	0.898060i	$0.355023\pi$
$614$	7.72832	+	4.46195i	0.311889	+	0.180069i
$615$		0			0
$616$	19.2664	+	4.50843i	0.776265	+	0.181650i
$617$	24.9178	−	24.9178i	1.00315	−	1.00315i	0.00315687	−	0.999995i	$-0.498995\pi$
$617$	24.9178	−	24.9178i	1.00315	−	1.00315i	0.999995	−	0.00315687i	$-0.00100487\pi$
$618$		0			0
$619$	15.3745	+	4.11957i	0.617951	+	0.165580i	0.554196	−	0.832386i	$-0.313026\pi$
$619$	15.3745	+	4.11957i	0.617951	+	0.165580i	0.0637551	+	0.997966i	$0.479692\pi$
$620$	3.26436	+	5.65404i	0.131100	+	0.227072i
$621$		0			0
$622$	16.2869	−	16.2869i	0.653047	−	0.653047i
$623$	6.19763	−	11.5728i	0.248303	−	0.463656i
$624$		0			0
$625$	−15.3511	+	26.5890i	−0.614046	+	1.06356i
$626$	1.99345	−	7.43964i	0.0796741	−	0.297348i
$627$		0			0
$628$	3.70427	−	6.41599i	0.147817	−	0.256026i
$629$	−17.7497	−	17.7497i	−0.707727	−	0.707727i
$630$		0			0
$631$	−31.7103	−	31.7103i	−1.26237	−	1.26237i	−0.949942	−	0.312427i	$-0.898858\pi$
$631$	−31.7103	−	31.7103i	−1.26237	−	1.26237i	−0.312427	−	0.949942i	$-0.601142\pi$
$632$	2.27323	−	0.609110i	0.0904241	−	0.0242291i
$633$		0			0
$634$	−41.5015	+	23.9609i	−1.64824	+	0.951610i
$635$	9.27855	+	34.6280i	0.368208	+	1.37417i
$636$		0			0
$637$	20.4634	+	14.7733i	0.810788	+	0.585340i
$638$	24.9126			0.986298
$639$		0			0
$640$	33.6259	−	19.4139i	1.32918	−	0.767402i
$641$	3.56700	−	2.05941i	0.140888	−	0.0813418i	−0.427899	−	0.903827i	$-0.640746\pi$
$641$	3.56700	−	2.05941i	0.140888	−	0.0813418i	0.568787	+	0.822485i	$0.307413\pi$
$642$		0			0
$643$	6.89221	+	6.89221i	0.271802	+	0.271802i	0.829825	−	0.558023i	$-0.188440\pi$
$643$	6.89221	+	6.89221i	0.271802	+	0.271802i	−0.558023	+	0.829825i	$0.688440\pi$
$644$	−4.48980	−	4.21185i	−0.176923	−	0.165970i
$645$		0			0
$646$	−16.0384	+	27.7793i	−0.631021	+	1.09296i
$647$	6.39418	+	11.0750i	0.251381	+	0.435405i	0.963906	−	0.266242i	$-0.0857820\pi$
$647$	6.39418	+	11.0750i	0.251381	+	0.435405i	−0.712525	+	0.701646i	$0.752449\pi$
$648$		0			0
$649$	5.11872	−	8.86589i	0.200927	−	0.348017i
$650$	−19.0291	+	1.83698i	−0.746384	+	0.0720524i
$651$		0			0
$652$	−4.15859	+	4.15859i	−0.162863	+	0.162863i
$653$	7.12903	−	12.3479i	0.278981	−	0.483209i	−0.692151	−	0.721753i	$-0.743337\pi$
$653$	7.12903	−	12.3479i	0.278981	−	0.483209i	0.971132	+	0.238544i	$0.0766701\pi$
$654$		0			0
$655$	37.6727	+	10.0944i	1.47199	+	0.394420i
$656$	−20.3323	+	5.44802i	−0.793842	+	0.212709i
$657$		0			0
$658$	24.0729	+	5.63318i	0.938460	+	0.219604i
$659$	−18.4714			−0.719542			−0.359771	−	0.933041i	$-0.617145\pi$
$659$	−18.4714			−0.719542			−0.359771	+	0.933041i	$0.617145\pi$
$660$		0			0
$661$	−31.6076	−	8.46923i	−1.22939	−	0.329415i	−0.415050	−	0.909799i	$-0.636236\pi$
$661$	−31.6076	−	8.46923i	−1.22939	−	0.329415i	−0.814343	+	0.580384i	$0.802903\pi$
$662$	21.0014	−	12.1251i	0.816242	−	0.471257i
$663$		0			0
$664$			6.15757i			0.238960i
$665$	22.4770	+	5.25973i	0.871621	+	0.203964i
$666$		0			0
$667$	13.0880	+	7.55635i	0.506768	+	0.292583i
$668$	−1.98578	+	7.41104i	−0.0768322	+	0.286742i
$669$		0			0
$670$	8.86941	+	33.1011i	0.342655	+	1.27881i
$671$	8.56669	−	8.56669i	0.330713	−	0.330713i
$672$		0			0
$673$			35.6367i			1.37370i	0.726801	+	0.686848i	$0.241006\pi$
$673$			35.6367i			1.37370i	−0.726801	+	0.686848i	$0.758994\pi$
$674$	−15.0470	+	4.03183i	−0.579588	+	0.155300i
$675$		0			0
$676$	5.78583	+	6.64928i	0.222532	+	0.255742i
$677$	−23.9548	−	13.8303i	−0.920657	−	0.531542i	−0.0368124	−	0.999322i	$-0.511720\pi$
$677$	−23.9548	−	13.8303i	−0.920657	−	0.531542i	−0.883845	+	0.467781i	$0.845054\pi$
$678$		0			0
$679$	−0.383225	−	11.9977i	−0.0147068	−	0.460430i
$680$			40.0483i			1.53578i
$681$		0			0
$682$	4.91159	−	18.3303i	0.188075	−	0.701904i
$683$	0.418104	−	1.56039i	0.0159983	−	0.0597065i	−0.957465	−	0.288549i	$-0.906827\pi$
$683$	0.418104	−	1.56039i	0.0159983	−	0.0597065i	0.973464	+	0.228842i	$0.0734940\pi$
$684$		0			0
$685$			3.88034i			0.148260i
$686$	27.5763	+	12.5740i	1.05287	+	0.480076i
$687$		0			0
$688$	19.0373	+	10.9912i	0.725791	+	0.419036i
$689$	−40.7209	−	6.80413i	−1.55134	−	0.259217i
$690$		0			0
$691$	−25.7402	+	6.89707i	−0.979204	+	0.262377i	−0.712709	−	0.701460i	$-0.752532\pi$
$691$	−25.7402	+	6.89707i	−0.979204	+	0.262377i	−0.266494	+	0.963836i	$0.585865\pi$
$692$		−	2.22161i		−	0.0844531i
$693$		0			0
$694$	−40.6506	+	40.6506i	−1.54307	+	1.54307i
$695$	13.9816	+	52.1802i	0.530354	+	1.97931i
$696$		0			0
$697$	7.17550	−	26.7793i	0.271792	−	1.01434i
$698$	13.3234	+	7.69228i	0.504299	+	0.291157i
$699$		0			0
$700$	−5.56327	+	1.68277i	−0.210272	+	0.0636029i
$701$		−	5.72322i		−	0.216163i	−0.994142	−	0.108081i	$-0.965529\pi$
$701$		−	5.72322i		−	0.216163i	0.994142	−	0.108081i	$-0.0344707\pi$
$702$		0			0
$703$	10.2460	−	5.91552i	0.386434	−	0.223108i
$704$	−12.5581	−	3.36493i	−0.473301	−	0.126821i
$705$		0			0
$706$	20.2483			0.762056
$707$	−5.51034	+	23.5480i	−0.207238	+	0.885613i
$708$		0			0
$709$	11.5808	−	3.10307i	0.434927	−	0.116538i	−0.0347112	−	0.999397i	$-0.511051\pi$
$709$	11.5808	−	3.10307i	0.434927	−	0.116538i	0.469638	+	0.882859i	$0.344384\pi$
$710$	53.3513	+	14.2954i	2.00224	+	0.536498i
$711$		0			0
$712$	−5.36722	+	9.29630i	−0.201145	+	0.348394i
$713$	8.14019	−	8.14019i	0.304853	−	0.304853i
$714$		0			0
$715$	27.6137	+	22.7516i	1.03269	+	0.850863i
$716$	−0.762791	+	1.32119i	−0.0285068	+	0.0493753i
$717$		0			0
$718$	3.50818	+	6.07635i	0.130924	+	0.226767i
$719$	7.61939	−	13.1972i	0.284155	−	0.492172i	−0.688249	−	0.725475i	$-0.741620\pi$
$719$	7.61939	−	13.1972i	0.284155	−	0.492172i	0.972404	+	0.233303i	$0.0749535\pi$
$720$		0			0
$721$	−12.9752	+	3.92472i	−0.483221	+	0.146164i
$722$	11.2956	+	11.2956i	0.420378	+	0.420378i
$723$		0			0
$724$	9.12586	−	5.26882i	0.339160	−	0.195814i
$725$	12.3568	−	7.13419i	0.458919	−	0.264957i
$726$		0			0
$727$	−19.4937			−0.722981			−0.361491	−	0.932376i	$-0.617732\pi$
$727$	−19.4937			−0.722981			−0.361491	+	0.932376i	$0.617732\pi$
$728$	−16.3384	−	12.6079i	−0.605540	−	0.467281i
$729$		0			0
$730$	−5.67895	−	21.1941i	−0.210187	−	0.784430i
$731$	−25.0738	+	14.4763i	−0.927387	+	0.535427i
$732$		0			0
$733$	28.6716	−	7.68254i	1.05901	−	0.283761i	0.313040	−	0.949740i	$-0.398652\pi$
$733$	28.6716	−	7.68254i	1.05901	−	0.283761i	0.745971	+	0.665979i	$0.231986\pi$
$734$	28.6216	+	28.6216i	1.05644	+	1.05644i
$735$		0			0
$736$	8.94434	+	8.94434i	0.329693	+	0.329693i
$737$	12.6093	−	21.8399i	0.464469	−	0.804484i
$738$		0			0
$739$	−0.217474	+	0.811625i	−0.00799992	+	0.0298561i	−0.969810	−	0.243860i	$-0.921586\pi$
$739$	−0.217474	+	0.811625i	−0.00799992	+	0.0298561i	0.961811	+	0.273716i	$0.0882529\pi$
$740$	−3.78786	+	6.56077i	−0.139245	+	0.241179i
$741$		0			0
$742$	−49.5517	+	1.58276i	−1.81910	+	0.0581048i
$743$	−22.5891	+	22.5891i	−0.828715	+	0.828715i	−0.987339	−	0.158624i	$-0.949294\pi$
$743$	−22.5891	+	22.5891i	−0.828715	+	0.828715i	0.158624	+	0.987339i	$0.449294\pi$
$744$		0			0
$745$	30.6136	+	53.0243i	1.12160	+	1.94266i
$746$	−12.5089	−	3.35176i	−0.457985	−	0.122717i
$747$		0			0
$748$	−10.6880	+	10.6880i	−0.390793	+	0.390793i
$749$	−31.7913	+	9.61623i	−1.16163	+	0.351369i
$750$		0			0
$751$	−12.9789	−	7.49334i	−0.473605	−	0.273436i	0.244143	−	0.969739i	$-0.421494\pi$
$751$	−12.9789	−	7.49334i	−0.473605	−	0.273436i	−0.717748	+	0.696303i	$0.754827\pi$
$752$	−27.0062	−	7.23629i	−0.984815	−	0.263880i
$753$		0			0
$754$	−23.6465	−	10.7694i	−0.861156	−	0.392198i
$755$		−	48.4296i		−	1.76254i
$756$		0			0
$757$	−4.27355			−0.155325			−0.0776624	−	0.996980i	$-0.524746\pi$
$757$	−4.27355			−0.155325			−0.0776624	+	0.996980i	$0.524746\pi$
$758$	−6.66191	−	3.84626i	−0.241971	−	0.139702i
$759$		0			0
$760$	−18.2324	−	4.88536i	−0.661359	−	0.177211i
$761$	2.03075	+	7.57885i	0.0736145	+	0.274733i	0.992916	−	0.118822i	$-0.0379118\pi$
$761$	2.03075	+	7.57885i	0.0736145	+	0.274733i	−0.919301	+	0.393555i	$0.871245\pi$
$762$		0			0
$763$	−27.2467	−	43.8939i	−0.986396	−	1.58907i
$764$		−	1.61227i		−	0.0583297i
$765$		0			0
$766$	−7.41067	−	12.8357i	−0.267758	−	0.463771i
$767$	−8.69121	+	6.20258i	−0.313821	+	0.223962i
$768$		0			0
$769$	−5.34450	−	5.34450i	−0.192727	−	0.192727i	0.604146	−	0.796874i	$-0.293514\pi$
$769$	−5.34450	−	5.34450i	−0.192727	−	0.192727i	−0.796874	+	0.604146i	$0.793514\pi$
$770$	37.8756	+	20.2836i	1.36494	+	0.730971i
$771$		0			0
$772$	−1.36984	−	5.11231i	−0.0493016	−	0.183996i
$773$	7.88945	−	29.4438i	0.283764	−	1.05902i	−0.665974	−	0.745975i	$-0.731984\pi$
$773$	7.88945	−	29.4438i	0.283764	−	1.05902i	0.949738	−	0.313046i	$-0.101349\pi$
$774$		0			0
$775$	−2.81306	−	10.4985i	−0.101048	−	0.377116i
$776$			9.81534i			0.352350i
$777$		0			0
$778$	24.8335	+	24.8335i	0.890323	+	0.890323i
$779$	11.3163	+	6.53345i	0.405447	+	0.234085i
$780$		0			0
$781$	−20.3232	−	35.2009i	−0.727222	−	1.25959i
$782$	−34.9830	+	9.37366i	−1.25099	+	0.335201i
$783$		0			0
$784$	−30.7155	−	15.2079i	−1.09698	−	0.543140i
$785$	−22.1793	+	22.1793i	−0.791613	+	0.791613i
$786$		0			0
$787$	−52.3495	−	14.0270i	−1.86606	−	0.500008i	−1.00000		6.28799e-5i	$-0.999980\pi$
$787$	−52.3495	−	14.0270i	−1.86606	−	0.500008i	−0.866057	−	0.499946i	$-0.833353\pi$
$788$	−2.71500	+	10.1325i	−0.0967180	+	0.360957i
$789$		0			0
$790$	5.11018			0.181812
$791$	−0.000445691	0	0.000418100i	−1.58470e−5	0	1.48659e-5i
$792$		0			0
$793$	−11.8346	+	4.42807i	−0.420259	+	0.157245i
$794$	−18.5291	+	10.6978i	−0.657572	+	0.379650i
$795$		0			0
$796$	11.8454	+	6.83892i	0.419847	+	0.242399i
$797$	28.0843			0.994797			0.497399	−	0.867522i	$-0.334289\pi$
$797$	28.0843			0.994797			0.497399	+	0.867522i	$0.334289\pi$
$798$		0			0
$799$	26.0387	−	26.0387i	0.921181	−	0.921181i
$800$	11.5356	−	3.09095i	0.407845	−	0.109282i
$801$		0			0
$802$	17.3656	+	30.0781i	0.613201	+	1.06210i
$803$	−8.07354	+	13.9838i	−0.284909	+	0.493477i
$804$		0			0
$805$	13.7459	+	22.1444i	0.484478	+	0.780487i
$806$	−12.5860	+	15.2756i	−0.443321	+	0.538059i
$807$		0			0
$808$	5.11813	−	19.1011i	0.180055	−	0.671976i
$809$	−6.38747	−	11.0634i	−0.224572	−	0.388969i	0.731619	−	0.681714i	$-0.238765\pi$
$809$	−6.38747	−	11.0634i	−0.224572	−	0.388969i	−0.956191	+	0.292744i	$0.905432\pi$
$810$		0			0
$811$	20.6613	+	20.6613i	0.725515	+	0.725515i	0.969723	−	0.244208i	$-0.0785279\pi$
$811$	20.6613	+	20.6613i	0.725515	+	0.725515i	−0.244208	+	0.969723i	$0.578528\pi$
$812$	−7.69178	−	1.79992i	−0.269929	−	0.0631646i
$813$		0			0
$814$	21.2699	−	5.69926i	0.745511	−	0.199759i
$815$	21.5636	−	12.4498i	0.755341	−	0.436096i
$816$		0			0
$817$	−3.53185	−	13.1810i	−0.123564	−	0.461146i
$818$	13.9395			0.487382
$819$		0			0
$820$	−8.36708			−0.292191
$821$	−0.330074	−	1.23185i	−0.0115197	−	0.0429920i	0.959927	−	0.280251i	$-0.0904177\pi$
$821$	−0.330074	−	1.23185i	−0.0115197	−	0.0429920i	−0.971446	+	0.237259i	$0.923751\pi$
$822$		0			0
$823$	19.1222	−	11.0402i	0.666559	−	0.384838i	−0.128213	−	0.991747i	$-0.540924\pi$
$823$	19.1222	−	11.0402i	0.666559	−	0.384838i	0.794771	+	0.606909i	$0.207591\pi$
$824$	10.7066	−	2.86883i	0.372983	−	0.0999406i
$825$		0			0
$826$	−8.77240	+	9.35130i	−0.305231	+	0.325373i
$827$	−9.30639	−	9.30639i	−0.323615	−	0.323615i	0.526537	−	0.850152i	$-0.323490\pi$
$827$	−9.30639	−	9.30639i	−0.323615	−	0.323615i	−0.850152	+	0.526537i	$0.823490\pi$
$828$		0			0
$829$	15.4841	+	26.8192i	0.537784	+	0.931469i	0.999023	+	0.0441933i	$0.0140718\pi$
$829$	15.4841	+	26.8192i	0.537784	+	0.931469i	−0.461239	+	0.887276i	$0.652595\pi$
$830$	−3.46053	+	12.9149i	−0.120117	+	0.448282i
$831$		0			0
$832$	10.4653	+	8.62263i	0.362819	+	0.298936i
$833$	37.5741	−	25.0199i	1.30186	−	0.866890i
$834$		0			0
$835$	16.2418	−	28.1317i	0.562072	−	0.973537i
$836$	−3.56205	−	6.16965i	−0.123196	−	0.213382i
$837$		0			0
$838$	13.2635	−	3.55395i	0.458180	−	0.122769i
$839$	22.1620	−	22.1620i	0.765116	−	0.765116i	−0.212126	−	0.977242i	$-0.568039\pi$
$839$	22.1620	−	22.1620i	0.765116	−	0.765116i	0.977242	+	0.212126i	$0.0680389\pi$
$840$		0			0
$841$	−9.60734			−0.331288
$842$	−41.1701	−	23.7696i	−1.41882	−	0.819153i
$843$		0			0
$844$	−1.39127	+	0.803248i	−0.0478893	+	0.0276489i
$845$	−16.3751	−	33.5325i	−0.563322	−	1.15355i
$846$		0			0
$847$	−0.728113	−	2.40715i	−0.0250182	−	0.0827105i
$848$	56.0654			1.92530
$849$		0			0
$850$	−8.84997	+	33.0285i	−0.303551	+	1.13287i
$851$	12.9030	+	3.45734i	0.442308	+	0.118516i
$852$		0			0
$853$	15.0740	−	15.0740i	0.516125	−	0.516125i	−0.400271	−	0.916397i	$-0.631084\pi$
$853$	15.0740	−	15.0740i	0.516125	−	0.516125i	0.916397	+	0.400271i	$0.131084\pi$
$854$	−12.8918	+	8.00247i	−0.441150	+	0.273839i
$855$		0			0
$856$	26.2330	−	7.02912i	0.896627	−	0.240250i
$857$	18.8426	+	32.6363i	0.643650	+	1.11483i	0.984612	+	0.174757i	$0.0559141\pi$
$857$	18.8426	+	32.6363i	0.643650	+	1.11483i	−0.340961	+	0.940077i	$0.610753\pi$
$858$		0			0
$859$	8.05583	+	4.65104i	0.274861	+	0.158691i	0.631095	−	0.775706i	$-0.282606\pi$
$859$	8.05583	+	4.65104i	0.274861	+	0.158691i	−0.356233	+	0.934397i	$0.615939\pi$
$860$	6.17863	+	6.17863i	0.210689	+	0.210689i
$861$		0			0
$862$		−	16.3712i		−	0.557605i
$863$	−5.95141	−	22.2110i	−0.202588	−	0.756070i	−0.990171	−	0.139861i	$-0.955334\pi$
$863$	−5.95141	−	22.2110i	−0.202588	−	0.756070i	0.787583	−	0.616209i	$-0.211332\pi$
$864$		0			0
$865$	−2.43441	+	9.08536i	−0.0827726	+	0.308911i
$866$	−17.5284	−	65.4167i	−0.595638	−	2.22295i
$867$		0			0
$868$	−2.84081	+	5.30465i	−0.0964235	+	0.180052i
$869$	−2.65915	−	2.65915i	−0.0902056	−	0.0902056i
$870$		0			0
$871$	−21.4096	+	15.2792i	−0.725437	+	0.517716i
$872$	21.1220	+	36.5843i	0.715280	+	1.23890i
$873$		0			0
$874$		−	17.0698i		−	0.577396i
$875$	−13.3594	+	0.426719i	−0.451629	+	0.0144257i
$876$		0			0
$877$	−2.73667	−	10.2134i	−0.0924108	−	0.344882i	0.904203	−	0.427102i	$-0.140466\pi$
$877$	−2.73667	−	10.2134i	−0.0924108	−	0.344882i	−0.996614	+	0.0822203i	$0.973799\pi$
$878$	0.225371	+	0.0603880i	0.00760591	+	0.00203800i
$879$		0			0
$880$	−42.0785	−	24.2940i	−1.41846	−	0.818951i
$881$	−19.0687			−0.642440			−0.321220	−	0.947005i	$-0.604093\pi$
$881$	−19.0687			−0.642440			−0.321220	+	0.947005i	$0.604093\pi$
$882$		0			0
$883$			4.27586i			0.143894i	0.997408	+	0.0719471i	$0.0229213\pi$
$883$			4.27586i			0.143894i	−0.997408	+	0.0719471i	$0.977079\pi$
$884$	14.7652	−	5.52459i	0.496607	−	0.185812i
$885$		0			0
$886$	−40.8985	−	10.9587i	−1.37401	−	0.368165i
$887$	−5.75705	−	3.32383i	−0.193303	−	0.111603i	0.400225	−	0.916417i	$-0.368932\pi$
$887$	−5.75705	−	3.32383i	−0.193303	−	0.111603i	−0.593528	+	0.804813i	$0.702265\pi$
$888$		0			0
$889$	−22.6064	+	24.0983i	−0.758196	+	0.808230i
$890$	−16.4817	+	16.4817i	−0.552468	+	0.552468i
$891$		0			0
$892$	−8.96378	−	2.40184i	−0.300130	−	0.0804195i
$893$	8.67801	+	15.0308i	0.290399	+	0.502985i
$894$		0			0
$895$	4.56720	−	4.56720i	0.152665	−	0.152665i
$896$	31.5480	+	16.8950i	1.05394	+	0.564421i
$897$		0			0
$898$	−1.46548	+	2.53828i	−0.0489036	+	0.0847036i
$899$	3.82333	−	14.2689i	0.127515	−	0.475893i
$900$		0			0
$901$	−36.9215	+	63.9499i	−1.23003	+	2.13048i
$902$	17.1972	+	17.1972i	0.572603	+	0.572603i
$903$		0			0
$904$	0.000353334	0	0.000353334i	1.17517e−5	0	1.17517e-5i
$905$	−43.0940	+	11.5470i	−1.43249	+	0.383835i
$906$		0			0
$907$	−12.7208	+	7.34433i	−0.422386	+	0.243865i	−0.696098	−	0.717947i	$-0.745082\pi$
$907$	−12.7208	+	7.34433i	−0.422386	+	0.243865i	0.273712	+	0.961812i	$0.411749\pi$
$908$	2.28798	+	8.53886i	0.0759293	+	0.283372i
$909$		0			0
$910$	−27.1825	−	35.6260i	−0.901090	−	1.18099i
$911$	−17.7868			−0.589301			−0.294651	−	0.955605i	$-0.595203\pi$
$911$	−17.7868			−0.589301			−0.294651	+	0.955605i	$0.595203\pi$
$912$		0			0
$913$	8.52117	−	4.91970i	0.282009	−	0.162818i
$914$	−6.60764	+	3.81492i	−0.218561	+	0.126186i
$915$		0			0
$916$	−7.28667	−	7.28667i	−0.240758	−	0.240758i
$917$	10.4076	+	34.4077i	0.343690	+	1.13624i
$918$		0			0
$919$	−11.1432	+	19.3006i	−0.367581	+	0.636670i	−0.989187	−	0.146661i	$-0.953147\pi$
$919$	−11.1432	+	19.3006i	−0.367581	+	0.636670i	0.621605	+	0.783331i	$0.286481\pi$
$920$	−10.6560	−	18.4567i	−0.351317	−	0.608499i
$921$		0			0
$922$	−4.17612	+	7.23325i	−0.137533	+	0.238214i
$923$	4.07355	+	42.1975i	0.134082	+	1.38895i
$924$		0			0
$925$	8.91792	−	8.91792i	0.293219	−	0.293219i
$926$	−4.63127	+	8.02160i	−0.152193	+	0.263606i
$927$		0			0
$928$	15.6784	+	4.20102i	0.514670	+	0.137905i
$929$	−41.4886	+	11.1168i	−1.36120	+	0.364731i	−0.864255	−	0.503054i	$-0.832210\pi$
$929$	−41.4886	+	11.1168i	−1.36120	+	0.364731i	−0.496940	+	0.867785i	$0.665543\pi$
$930$		0			0
$931$	6.80706	+	20.1581i	0.223092	+	0.660655i
$932$	−5.24431			−0.171783
$933$		0			0
$934$	−63.3258	−	16.9681i	−2.07208	−	0.555213i
$935$	55.4209	−	31.9973i	1.81246	−	1.04642i
$936$		0			0
$937$		−	52.3733i		−	1.71096i	−0.517835	−	0.855481i	$-0.673262\pi$
$937$		−	52.3733i		−	1.71096i	0.517835	−	0.855481i	$-0.326738\pi$
$938$	−21.6096	+	23.0357i	−0.705579	+	0.752141i
$939$		0			0
$940$	−9.62459	−	5.55676i	−0.313919	−	0.181241i
$941$	−4.03247	+	15.0494i	−0.131455	+	0.490596i	−0.999987	−	0.00503603i	$-0.998397\pi$
$941$	−4.03247	+	15.0494i	−0.131455	+	0.490596i	0.868532	+	0.495632i	$0.165064\pi$
$942$		0			0
$943$	3.81849	+	14.2508i	0.124347	+	0.464070i
$944$	10.2531	−	10.2531i	0.333708	−	0.333708i
$945$		0			0
$946$		−	25.3983i		−	0.825771i
$947$	41.1510	−	11.0264i	1.33723	−	0.358309i	0.481822	−	0.876269i	$-0.339975\pi$
$947$	41.1510	−	11.0264i	1.33723	−	0.358309i	0.855405	+	0.517960i	$0.173308\pi$
$948$		0			0
$949$	13.7083	−	9.78306i	0.444989	−	0.317571i
$950$	−13.9570	−	8.05809i	−0.452825	−	0.261439i
$951$		0			0
$952$	−31.3612	+	19.4671i	−1.01642	+	0.630933i
$953$		−	35.9437i		−	1.16433i	−0.813070	−	0.582165i	$-0.802206\pi$
$953$		−	35.9437i		−	1.16433i	0.813070	−	0.582165i	$-0.197794\pi$
$954$		0			0
$955$	−1.76670	+	6.59341i	−0.0571690	+	0.213358i
$956$	0.523564	−	1.95397i	0.0169333	−	0.0631958i
$957$		0			0
$958$			19.2949i			0.623390i
$959$	−3.03863	+	1.88620i	−0.0981226	+	0.0609086i
$960$		0			0
$961$	17.1017	+	9.87370i	0.551669	+	0.318506i
$962$	−22.6527	−	3.78509i	−0.730354	−	0.122036i
$963$		0			0
$964$	−17.2937	+	4.63384i	−0.556993	+	0.149246i
$965$			22.4080i			0.721339i
$966$		0			0
$967$	−31.7209	+	31.7209i	−1.02008	+	1.02008i	−0.0202813	+	0.999794i	$0.506456\pi$
$967$	−31.7209	+	31.7209i	−1.02008	+	1.02008i	−0.999794	+	0.0202813i	$0.993544\pi$
$968$	0.532224	+	1.98629i	0.0171063	+	0.0638417i
$969$		0			0
$970$	−5.51618	+	20.5867i	−0.177114	+	0.660998i
$971$	−20.7204	−	11.9629i	−0.664950	−	0.383909i	0.129210	−	0.991617i	$-0.458756\pi$
$971$	−20.7204	−	11.9629i	−0.664950	−	0.383909i	−0.794161	+	0.607708i	$0.792089\pi$
$972$		0			0
$973$	−34.0652	+	36.3132i	−1.09208	+	1.16415i
$974$			0.900548i			0.0288554i
$975$		0			0
$976$	14.8606	−	8.57975i	0.475675	−	0.274631i
$977$	−42.6772	−	11.4353i	−1.36537	−	0.365849i	−0.499582	−	0.866267i	$-0.666513\pi$
$977$	−42.6772	−	11.4353i	−1.36537	−	0.365849i	−0.865784	+	0.500418i	$0.833180\pi$
$978$		0			0
$979$	17.1530			0.548211
$980$	−10.2287	−	8.99908i	−0.326743	−	0.287465i
$981$		0			0
$982$	−4.78009	+	1.28082i	−0.152539	+	0.0408726i
$983$	3.90158	+	1.04542i	0.124441	+	0.0333439i	0.320502	−	0.947248i	$-0.396148\pi$
$983$	3.90158	+	1.04542i	0.124441	+	0.0333439i	−0.196061	+	0.980592i	$0.562815\pi$
$984$		0			0
$985$	22.2062	−	38.4623i	0.707548	−	1.22551i
$986$	−32.8620	+	32.8620i	−1.04654	+	1.04654i
$987$		0			0
$988$	0.713969	+	7.39594i	0.0227144	+	0.235296i
$989$	7.70369	−	13.3432i	0.244963	−	0.424288i
$990$		0			0
$991$	15.4084	+	26.6881i	0.489463	+	0.847774i	0.999926	−	0.0121250i	$-0.00385960\pi$
$991$	15.4084	+	26.6881i	0.489463	+	0.847774i	−0.510464	+	0.859899i	$0.670526\pi$
$992$	6.18211	−	10.7077i	0.196282	−	0.339971i
$993$		0			0
$994$	14.7391	+	48.7275i	0.467495	+	1.54554i
$995$	−40.9480	−	40.9480i	−1.29814	−	1.29814i
$996$		0			0
$997$	34.9509	−	20.1789i	1.10691	−	0.639072i	0.168879	−	0.985637i	$-0.445985\pi$
$997$	34.9509	−	20.1789i	1.10691	−	0.639072i	0.938026	+	0.346565i	$0.112652\pi$
$998$	−54.3496	+	31.3787i	−1.72040	+	0.993276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fn.e.460.3		32
3.2	odd	2		91.2.bb.a.5.6	✓	32
7.3	odd	6	inner	819.2.fn.e.577.6		32
13.8	odd	4	inner	819.2.fn.e.775.6		32
21.2	odd	6		637.2.i.a.538.11		32
21.5	even	6		637.2.i.a.538.12		32
21.11	odd	6		637.2.bc.b.31.3		32
21.17	even	6		91.2.bb.a.31.3	yes	32
21.20	even	2		637.2.bc.b.460.6		32
39.8	even	4		91.2.bb.a.47.3	yes	32
91.73	even	12	inner	819.2.fn.e.73.3		32
273.47	odd	12		637.2.i.a.489.12		32
273.86	even	12		637.2.i.a.489.11		32
273.125	odd	4		637.2.bc.b.411.3		32
273.164	odd	12		91.2.bb.a.73.6	yes	32
273.242	even	12		637.2.bc.b.619.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.6	✓	32	3.2	odd	2
91.2.bb.a.31.3	yes	32	21.17	even	6
91.2.bb.a.47.3	yes	32	39.8	even	4
91.2.bb.a.73.6	yes	32	273.164	odd	12
637.2.i.a.489.11		32	273.86	even	12
637.2.i.a.489.12		32	273.47	odd	12
637.2.i.a.538.11		32	21.2	odd	6
637.2.i.a.538.12		32	21.5	even	6
637.2.bc.b.31.3		32	21.11	odd	6
637.2.bc.b.411.3		32	273.125	odd	4
637.2.bc.b.460.6		32	21.20	even	2
637.2.bc.b.619.6		32	273.242	even	12
819.2.fn.e.73.3		32	91.73	even	12	inner
819.2.fn.e.460.3		32	1.1	even	1	trivial
819.2.fn.e.577.6		32	7.3	odd	6	inner
819.2.fn.e.775.6		32	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.423548 - 1.58070i) q^{2} +(-0.587174 + 0.339005i) q^{4} +(2.77274 - 0.742954i) q^{5} +(1.92960 + 1.81015i) q^{7} +(-1.52975 - 1.52975i) q^{8} +O(q^{10})\)	\(q+(-0.423548 - 1.58070i) q^{2} +(-0.587174 + 0.339005i) q^{4} +(2.77274 - 0.742954i) q^{5} +(1.92960 + 1.81015i) q^{7} +(-1.52975 - 1.52975i) q^{8} +(-2.34878 - 4.06820i) q^{10} +(-0.894725 + 3.33916i) q^{11} +(2.29273 - 2.78269i) q^{13} +(2.04403 - 3.81681i) q^{14} +(-2.44816 + 4.24034i) q^{16} +(-3.22444 - 5.58489i) q^{17} +(2.93592 - 0.786677i) q^{19} +(-1.37622 + 1.37622i) q^{20} +5.65717 q^{22} +(2.97203 + 1.71590i) q^{23} +(2.80599 - 1.62004i) q^{25} +(-5.36969 - 2.44553i) q^{26} +(-1.74666 - 0.408727i) q^{28} +4.40371 q^{29} +(0.868206 - 3.24019i) q^{31} +(3.56028 + 0.953974i) q^{32} +(-7.46233 + 7.46233i) q^{34} +(6.69515 + 3.58547i) q^{35} +(3.75982 - 1.00744i) q^{37} +(-2.48700 - 4.30762i) q^{38} +(-5.37812 - 3.10506i) q^{40} +(3.03989 + 3.03989i) q^{41} -4.48958i q^{43} +(-0.606632 - 2.26398i) q^{44} +(1.45353 - 5.42467i) q^{46} +(1.47790 + 5.51561i) q^{47} +(0.446725 + 6.98573i) q^{49} +(-3.74927 - 3.74927i) q^{50} +(-0.402887 + 2.41117i) q^{52} +(-5.72526 - 9.91644i) q^{53} +9.92337i q^{55} +(-0.182733 - 5.72087i) q^{56} +(-1.86518 - 6.96095i) q^{58} +(-2.86050 - 0.766469i) q^{59} +(-3.03504 - 1.75228i) q^{61} -5.48950 q^{62} +3.76085i q^{64} +(4.28975 - 9.41908i) q^{65} +(-7.04645 - 1.88809i) q^{67} +(3.78661 + 2.18620i) q^{68} +(2.83184 - 12.1016i) q^{70} +(-8.31408 + 8.31408i) q^{71} +(4.51174 + 1.20892i) q^{73} +(-3.18492 - 5.51645i) q^{74} +(-1.45721 + 1.45721i) q^{76} +(-7.77084 + 4.82366i) q^{77} +(-0.543920 + 0.942097i) q^{79} +(-3.63774 + 13.5762i) q^{80} +(3.51762 - 6.09269i) q^{82} +(-2.01261 - 2.01261i) q^{83} +(-13.0898 - 13.0898i) q^{85} +(-7.09668 + 1.90155i) q^{86} +(6.47677 - 3.73937i) q^{88} +(-1.28423 - 4.79280i) q^{89} +(9.46115 - 1.21930i) q^{91} -2.32680 q^{92} +(8.09257 - 4.67225i) q^{94} +(7.55608 - 4.36250i) q^{95} +(-3.20816 - 3.20816i) q^{97} +(10.8531 - 3.66493i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more