LMFDB - Embedded newform 666.2.be.c.467.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(125,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("666.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.be (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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			467.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	666.467
Dual form			666.2.be.c.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.67303 - 0.448288i) q^{5} +(2.36603 + 4.09808i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.67303 - 0.448288i) q^{5} +(2.36603 + 4.09808i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.73205 q^{10} +2.44949 q^{11} +(-1.36603 + 5.09808i) q^{13} +(3.34607 + 3.34607i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.120118 - 0.448288i) q^{17} +(0.0980762 - 0.366025i) q^{19} +(-1.67303 + 0.448288i) q^{20} +(2.36603 - 0.633975i) q^{22} +(2.44949 - 2.44949i) q^{23} +(-1.73205 - 1.00000i) q^{25} +5.27792i q^{26} +(4.09808 + 2.36603i) q^{28} +(6.12372 + 6.12372i) q^{29} +(2.26795 - 2.26795i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.232051 - 0.401924i) q^{34} +(-2.12132 - 7.91688i) q^{35} +(5.69615 - 2.13397i) q^{37} -0.378937i q^{38} +(-1.50000 + 0.866025i) q^{40} +(0.776457 + 1.34486i) q^{41} +(3.73205 + 3.73205i) q^{43} +(2.12132 - 1.22474i) q^{44} +(1.73205 - 3.00000i) q^{46} -4.24264i q^{47} +(-7.69615 + 13.3301i) q^{49} +(-1.93185 - 0.517638i) q^{50} +(1.36603 + 5.09808i) q^{52} +(-9.46979 - 5.46739i) q^{53} +(-4.09808 - 1.09808i) q^{55} +(4.57081 + 1.22474i) q^{56} +(7.50000 + 4.33013i) q^{58} +(-1.55291 - 5.79555i) q^{59} +(-1.13397 - 0.303848i) q^{61} +(1.60368 - 2.77766i) q^{62} -1.00000i q^{64} +(4.57081 - 7.91688i) q^{65} +(-5.36603 + 3.09808i) q^{67} +(-0.328169 - 0.328169i) q^{68} +(-4.09808 - 7.09808i) q^{70} +(-2.12132 + 1.22474i) q^{71} -14.3923i q^{73} +(4.94975 - 3.53553i) q^{74} +(-0.0980762 - 0.366025i) q^{76} +(5.79555 + 10.0382i) q^{77} +(-1.63397 + 6.09808i) q^{79} +(-1.22474 + 1.22474i) q^{80} +(1.09808 + 1.09808i) q^{82} +(-11.5911 - 6.69213i) q^{83} +0.803848i q^{85} +(4.57081 + 2.63896i) q^{86} +(1.73205 - 1.73205i) q^{88} +(-7.46859 + 2.00120i) q^{89} +(-24.1244 + 6.46410i) q^{91} +(0.896575 - 3.34607i) q^{92} +(-1.09808 - 4.09808i) q^{94} +(-0.328169 + 0.568406i) q^{95} +(-1.36603 - 1.36603i) q^{97} +(-3.98382 + 14.8678i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{7}+O(q^{10}) $ 8 * q + 12 * q^7	$ 8 q + 12 q^{7} - 4 q^{13} + 4 q^{16} - 20 q^{19} + 12 q^{22} + 12 q^{28} + 32 q^{31} + 12 q^{34} + 4 q^{37} - 12 q^{40} + 16 q^{43} - 20 q^{49} + 4 q^{52} - 12 q^{55} + 60 q^{58} - 16 q^{61} - 36 q^{67} - 12 q^{70} + 20 q^{76} - 20 q^{79} - 12 q^{82} - 96 q^{91} + 12 q^{94} - 4 q^{97}+O(q^{100}) $ 8 * q + 12 * q^7 - 4 * q^13 + 4 * q^16 - 20 * q^19 + 12 * q^22 + 12 * q^28 + 32 * q^31 + 12 * q^34 + 4 * q^37 - 12 * q^40 + 16 * q^43 - 20 * q^49 + 4 * q^52 - 12 * q^55 + 60 * q^58 - 16 * q^61 - 36 * q^67 - 12 * q^70 + 20 * q^76 - 20 * q^79 - 12 * q^82 - 96 * q^91 + 12 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.67303	−	0.448288i	−0.748203	−	0.200480i	−0.135482	−	0.990780i	$-0.543258\pi$
$5$	−1.67303	−	0.448288i	−0.748203	−	0.200480i	−0.612721	+	0.790299i	$0.709925\pi$
$6$		0			0
$7$	2.36603	+	4.09808i	0.894274	+	1.54893i	0.834701	+	0.550703i	$0.185640\pi$
$7$	2.36603	+	4.09808i	0.894274	+	1.54893i	0.0595724	+	0.998224i	$0.481026\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−1.73205			−0.547723
$11$	2.44949			0.738549			0.369274	−	0.929320i	$-0.379606\pi$
$11$	2.44949			0.738549			0.369274	+	0.929320i	$0.379606\pi$
$12$		0			0
$13$	−1.36603	+	5.09808i	−0.378867	+	1.41395i	0.468744	+	0.883334i	$0.344707\pi$
$13$	−1.36603	+	5.09808i	−0.378867	+	1.41395i	−0.847611	+	0.530618i	$0.821960\pi$
$14$	3.34607	+	3.34607i	0.894274	+	0.894274i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.120118	−	0.448288i	−0.0291330	−	0.108726i	0.949828	−	0.312772i	$-0.101257\pi$
$17$	−0.120118	−	0.448288i	−0.0291330	−	0.108726i	−0.978961	+	0.204046i	$0.934591\pi$
$18$		0			0
$19$	0.0980762	−	0.366025i	0.0225002	−	0.0839720i	−0.953763	−	0.300560i	$-0.902826\pi$
$19$	0.0980762	−	0.366025i	0.0225002	−	0.0839720i	0.976263	+	0.216588i	$0.0694930\pi$
$20$	−1.67303	+	0.448288i	−0.374101	+	0.100240i
$21$		0			0
$22$	2.36603	−	0.633975i	0.504438	−	0.135164i
$23$	2.44949	−	2.44949i	0.510754	−	0.510754i	−0.404004	−	0.914757i	$-0.632382\pi$
$23$	2.44949	−	2.44949i	0.510754	−	0.510754i	0.914757	+	0.404004i	$0.132382\pi$
$24$		0			0
$25$	−1.73205	−	1.00000i	−0.346410	−	0.200000i
$26$			5.27792i			1.03508i
$27$		0			0
$28$	4.09808	+	2.36603i	0.774464	+	0.447137i
$29$	6.12372	+	6.12372i	1.13715	+	1.13715i	0.988959	+	0.148188i	$0.0473440\pi$
$29$	6.12372	+	6.12372i	1.13715	+	1.13715i	0.148188	+	0.988959i	$0.452656\pi$
$30$		0			0
$31$	2.26795	−	2.26795i	0.407336	−	0.407336i	−0.473473	−	0.880808i	$-0.657000\pi$
$31$	2.26795	−	2.26795i	0.407336	−	0.407336i	0.880808	+	0.473473i	$0.157000\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$		0			0
$34$	−0.232051	−	0.401924i	−0.0397964	−	0.0689294i
$35$	−2.12132	−	7.91688i	−0.358569	−	1.33820i
$36$		0			0
$37$	5.69615	−	2.13397i	0.936442	−	0.350823i
$37$	5.69615	−	2.13397i	0.936442	−	0.350823i
$38$		−	0.378937i		−	0.0614718i
$39$		0			0
$40$	−1.50000	+	0.866025i	−0.237171	+	0.136931i
$41$	0.776457	+	1.34486i	0.121262	+	0.210032i	0.920266	−	0.391294i	$-0.127972\pi$
$41$	0.776457	+	1.34486i	0.121262	+	0.210032i	−0.799003	+	0.601326i	$0.794639\pi$
$42$		0			0
$43$	3.73205	+	3.73205i	0.569132	+	0.569132i	0.931885	−	0.362753i	$-0.118163\pi$
$43$	3.73205	+	3.73205i	0.569132	+	0.569132i	−0.362753	+	0.931885i	$0.618163\pi$
$44$	2.12132	−	1.22474i	0.319801	−	0.184637i
$45$		0			0
$46$	1.73205	−	3.00000i	0.255377	−	0.442326i
$47$		−	4.24264i		−	0.618853i	−0.950923	−	0.309426i	$-0.899863\pi$
$47$		−	4.24264i		−	0.618853i	0.950923	−	0.309426i	$-0.100137\pi$
$48$		0			0
$49$	−7.69615	+	13.3301i	−1.09945	+	1.90430i
$50$	−1.93185	−	0.517638i	−0.273205	−	0.0732051i
$51$		0			0
$52$	1.36603	+	5.09808i	0.189434	+	0.706976i
$53$	−9.46979	−	5.46739i	−1.30078	−	0.751003i	−0.320239	−	0.947337i	$-0.603763\pi$
$53$	−9.46979	−	5.46739i	−1.30078	−	0.751003i	−0.980537	+	0.196334i	$0.937096\pi$
$54$		0			0
$55$	−4.09808	−	1.09808i	−0.552584	−	0.148065i
$56$	4.57081	+	1.22474i	0.610800	+	0.163663i
$57$		0			0
$58$	7.50000	+	4.33013i	0.984798	+	0.568574i
$59$	−1.55291	−	5.79555i	−0.202172	−	0.754517i	−0.990293	−	0.138996i	$-0.955612\pi$
$59$	−1.55291	−	5.79555i	−0.202172	−	0.754517i	0.788121	−	0.615521i	$-0.211054\pi$
$60$		0			0
$61$	−1.13397	−	0.303848i	−0.145191	−	0.0389037i	0.185492	−	0.982646i	$-0.440612\pi$
$61$	−1.13397	−	0.303848i	−0.145191	−	0.0389037i	−0.330682	+	0.943742i	$0.607279\pi$
$62$	1.60368	−	2.77766i	0.203668	−	0.352763i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	4.57081	−	7.91688i	0.566939	−	0.981968i
$66$		0			0
$67$	−5.36603	+	3.09808i	−0.655564	+	0.378490i	−0.790585	−	0.612353i	$-0.790223\pi$
$67$	−5.36603	+	3.09808i	−0.655564	+	0.378490i	0.135020	+	0.990843i	$0.456890\pi$
$68$	−0.328169	−	0.328169i	−0.0397964	−	0.0397964i
$69$		0			0
$70$	−4.09808	−	7.09808i	−0.489814	−	0.848382i
$71$	−2.12132	+	1.22474i	−0.251754	+	0.145350i	−0.620567	−	0.784153i	$-0.713098\pi$
$71$	−2.12132	+	1.22474i	−0.251754	+	0.145350i	0.368813	+	0.929504i	$0.379764\pi$
$72$		0			0
$73$		−	14.3923i		−	1.68449i	−0.539093	−	0.842246i	$-0.681233\pi$
$73$		−	14.3923i		−	1.68449i	0.539093	−	0.842246i	$-0.318767\pi$
$74$	4.94975	−	3.53553i	0.575396	−	0.410997i
$75$		0			0
$76$	−0.0980762	−	0.366025i	−0.0112501	−	0.0419860i
$77$	5.79555	+	10.0382i	0.660465	+	1.14396i
$78$		0			0
$79$	−1.63397	+	6.09808i	−0.183837	+	0.686087i	0.811040	+	0.584991i	$0.198902\pi$
$79$	−1.63397	+	6.09808i	−0.183837	+	0.686087i	−0.994877	+	0.101097i	$0.967765\pi$
$80$	−1.22474	+	1.22474i	−0.136931	+	0.136931i
$81$		0			0
$82$	1.09808	+	1.09808i	0.121262	+	0.121262i
$83$	−11.5911	−	6.69213i	−1.27229	−	0.734557i	−0.296871	−	0.954918i	$-0.595943\pi$
$83$	−11.5911	−	6.69213i	−1.27229	−	0.734557i	−0.975418	+	0.220361i	$0.929277\pi$
$84$		0			0
$85$			0.803848i			0.0871895i
$86$	4.57081	+	2.63896i	0.492883	+	0.284566i
$87$		0			0
$88$	1.73205	−	1.73205i	0.184637	−	0.184637i
$89$	−7.46859	+	2.00120i	−0.791669	+	0.212127i	−0.631923	−	0.775031i	$-0.717734\pi$
$89$	−7.46859	+	2.00120i	−0.791669	+	0.212127i	−0.159746	+	0.987158i	$0.551067\pi$
$90$		0			0
$91$	−24.1244	+	6.46410i	−2.52892	+	0.677622i
$92$	0.896575	−	3.34607i	0.0934745	−	0.348851i
$93$		0			0
$94$	−1.09808	−	4.09808i	−0.113258	−	0.422684i
$95$	−0.328169	+	0.568406i	−0.0336695	+	0.0583172i
$96$		0			0
$97$	−1.36603	−	1.36603i	−0.138699	−	0.138699i	0.634348	−	0.773047i	$-0.281268\pi$
$97$	−1.36603	−	1.36603i	−0.138699	−	0.138699i	−0.773047	+	0.634348i	$0.781268\pi$
$98$	−3.98382	+	14.8678i	−0.402427	+	1.50188i
$99$		0			0
$100$	−2.00000			−0.200000
$101$	−14.9372			−1.48630			−0.743152	−	0.669122i	$-0.766670\pi$
$101$	−14.9372			−1.48630			−0.743152	+	0.669122i	$0.766670\pi$
$102$		0			0
$103$	−0.267949	+	0.267949i	−0.0264018	+	0.0264018i	−0.720184	−	0.693783i	$-0.755943\pi$
$103$	−0.267949	+	0.267949i	−0.0264018	+	0.0264018i	0.693783	+	0.720184i	$0.255943\pi$
$104$	2.63896	+	4.57081i	0.258771	+	0.448205i
$105$		0			0
$106$	−10.5622	−	2.83013i	−1.02589	−	0.274886i
$107$	−5.22715	+	3.01790i	−0.505328	+	0.291751i	−0.730911	−	0.682473i	$-0.760905\pi$
$107$	−5.22715	+	3.01790i	−0.505328	+	0.291751i	0.225583	+	0.974224i	$0.427571\pi$
$108$		0			0
$109$	14.7942	−	3.96410i	1.41703	−	0.379692i	0.532601	−	0.846367i	$-0.321215\pi$
$109$	14.7942	−	3.96410i	1.41703	−	0.379692i	0.884429	+	0.466674i	$0.154548\pi$
$110$	−4.24264			−0.404520
$111$		0			0
$112$	4.73205			0.447137
$113$	19.1798	−	5.13922i	1.80429	−	0.483457i	0.809651	−	0.586911i	$-0.199656\pi$
$113$	19.1798	−	5.13922i	1.80429	−	0.483457i	0.994634	+	0.103455i	$0.0329897\pi$
$114$		0			0
$115$	−5.19615	+	3.00000i	−0.484544	+	0.279751i
$116$	8.36516	+	2.24144i	0.776686	+	0.208112i
$117$		0			0
$118$	−3.00000	−	5.19615i	−0.276172	−	0.478345i
$119$	1.55291	−	1.55291i	0.142355	−	0.142355i
$120$		0			0
$121$	−5.00000			−0.454545
$122$	−1.17398			−0.106287
$123$		0			0
$124$	0.830127	−	3.09808i	0.0745476	−	0.278215i
$125$	8.57321	+	8.57321i	0.766812	+	0.766812i
$126$		0			0
$127$	9.19615	−	15.9282i	0.816027	−	1.41340i	−0.0925619	−	0.995707i	$-0.529506\pi$
$127$	9.19615	−	15.9282i	0.816027	−	1.41340i	0.908588	−	0.417693i	$-0.137161\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$		0			0
$130$	2.36603	−	8.83013i	0.207514	−	0.774453i
$131$	−19.1798	+	5.13922i	−1.67575	+	0.449015i	−0.966651	−	0.256096i	$-0.917564\pi$
$131$	−19.1798	+	5.13922i	−1.67575	+	0.449015i	−0.709097	+	0.705111i	$0.750897\pi$
$132$		0			0
$133$	1.73205	−	0.464102i	0.150188	−	0.0402427i
$134$	−4.38134	+	4.38134i	−0.378490	+	0.378490i
$135$		0			0
$136$	−0.401924	−	0.232051i	−0.0344647	−	0.0198982i
$137$		−	13.6245i		−	1.16402i	−0.813182	−	0.582010i	$-0.802267\pi$
$137$		−	13.6245i		−	1.16402i	0.813182	−	0.582010i	$-0.197733\pi$
$138$		0			0
$139$	17.6603	+	10.1962i	1.49792	+	0.864826i	0.999997	−	0.00239313i	$-0.000761756\pi$
$139$	17.6603	+	10.1962i	1.49792	+	0.864826i	0.497926	+	0.867219i	$0.334095\pi$
$140$	−5.79555	−	5.79555i	−0.489814	−	0.489814i
$141$		0			0
$142$	−1.73205	+	1.73205i	−0.145350	+	0.145350i
$143$	−3.34607	+	12.4877i	−0.279812	+	1.04427i
$144$		0			0
$145$	−7.50000	−	12.9904i	−0.622841	−	1.07879i
$146$	−3.72500	−	13.9019i	−0.308283	−	1.15053i
$147$		0			0
$148$	3.86603	−	4.69615i	0.317785	−	0.386021i
$149$			11.3509i			0.929900i	0.885337	+	0.464950i	$0.153928\pi$
$149$			11.3509i			0.929900i	−0.885337	+	0.464950i	$0.846072\pi$
$150$		0			0
$151$	15.0000	−	8.66025i	1.22068	−	0.704761i	0.255619	−	0.966778i	$-0.417721\pi$
$151$	15.0000	−	8.66025i	1.22068	−	0.704761i	0.965064	+	0.262016i	$0.0843873\pi$
$152$	−0.189469	−	0.328169i	−0.0153679	−	0.0266181i
$153$		0			0
$154$	8.19615	+	8.19615i	0.660465	+	0.660465i
$155$	−4.81105	+	2.77766i	−0.386433	+	0.223107i
$156$		0			0
$157$	9.06218	−	15.6962i	0.723241	−	1.25269i	−0.236454	−	0.971643i	$-0.575985\pi$
$157$	9.06218	−	15.6962i	0.723241	−	1.25269i	0.959694	−	0.281047i	$-0.0906815\pi$
$158$			6.31319i			0.502251i
$159$		0			0
$160$	−0.866025	+	1.50000i	−0.0684653	+	0.118585i
$161$	15.8338	+	4.24264i	1.24787	+	0.334367i
$162$		0			0
$163$	1.36603	+	5.09808i	0.106995	+	0.399312i	0.998564	−	0.0535737i	$-0.0170612\pi$
$163$	1.36603	+	5.09808i	0.106995	+	0.399312i	−0.891569	+	0.452886i	$0.850395\pi$
$164$	1.34486	+	0.776457i	0.105016	+	0.0606311i
$165$		0			0
$166$	−12.9282	−	3.46410i	−1.00342	−	0.268866i
$167$	−10.6945	−	2.86559i	−0.827568	−	0.221746i	−0.179915	−	0.983682i	$-0.557582\pi$
$167$	−10.6945	−	2.86559i	−0.827568	−	0.221746i	−0.647652	+	0.761936i	$0.724249\pi$
$168$		0			0
$169$	−12.8660	−	7.42820i	−0.989694	−	0.571400i
$170$	0.208051	+	0.776457i	0.0159568	+	0.0595515i
$171$		0			0
$172$	5.09808	+	1.36603i	0.388725	+	0.104158i
$173$	6.81225	−	11.7992i	0.517926	−	0.897074i	−0.481857	−	0.876250i	$-0.660038\pi$
$173$	6.81225	−	11.7992i	0.517926	−	0.897074i	0.999783	−	0.0208240i	$-0.00662896\pi$
$174$		0			0
$175$		−	9.46410i		−	0.715419i
$176$	1.22474	−	2.12132i	0.0923186	−	0.159901i
$177$		0			0
$178$	−6.69615	+	3.86603i	−0.501898	+	0.289771i
$179$	1.13681	+	1.13681i	0.0849693	+	0.0849693i	0.748314	−	0.663345i	$-0.230864\pi$
$179$	1.13681	+	1.13681i	0.0849693	+	0.0849693i	−0.663345	+	0.748314i	$0.730864\pi$
$180$		0			0
$181$	−3.40192	−	5.89230i	−0.252863	−	0.437972i	0.711450	−	0.702737i	$-0.248039\pi$
$181$	−3.40192	−	5.89230i	−0.252863	−	0.437972i	−0.964313	+	0.264765i	$0.914706\pi$
$182$	−21.6293	+	12.4877i	−1.60327	+	0.925649i
$183$		0			0
$184$		−	3.46410i		−	0.255377i
$185$	−10.4865	+	1.01669i	−0.770982	+	0.0747488i
$186$		0			0
$187$	−0.294229	−	1.09808i	−0.0215161	−	0.0802993i
$188$	−2.12132	−	3.67423i	−0.154713	−	0.267971i
$189$		0			0
$190$	−0.169873	+	0.633975i	−0.0123239	+	0.0459934i
$191$	−0.656339	+	0.656339i	−0.0474910	+	0.0474910i	−0.730453	−	0.682962i	$-0.760691\pi$
$191$	−0.656339	+	0.656339i	−0.0474910	+	0.0474910i	0.682962	+	0.730453i	$0.260691\pi$
$192$		0			0
$193$	−8.09808	−	8.09808i	−0.582912	−	0.582912i	0.352790	−	0.935702i	$-0.385233\pi$
$193$	−8.09808	−	8.09808i	−0.582912	−	0.582912i	−0.935702	+	0.352790i	$0.885233\pi$
$194$	−1.67303	−	0.965926i	−0.120117	−	0.0693494i
$195$		0			0
$196$			15.3923i			1.09945i
$197$	16.0418	+	9.26174i	1.14293	+	0.659872i	0.947155	−	0.320777i	$-0.103944\pi$
$197$	16.0418	+	9.26174i	1.14293	+	0.659872i	0.195776	+	0.980649i	$0.437277\pi$
$198$		0			0
$199$	−11.5885	+	11.5885i	−0.821484	+	0.821484i	−0.986321	−	0.164837i	$-0.947290\pi$
$199$	−11.5885	+	11.5885i	−0.821484	+	0.821484i	0.164837	+	0.986321i	$0.447290\pi$
$200$	−1.93185	+	0.517638i	−0.136603	+	0.0366025i
$201$		0			0
$202$	−14.4282	+	3.86603i	−1.01516	+	0.272013i
$203$	−10.6066	+	39.5844i	−0.744438	+	2.77828i
$204$		0			0
$205$	−0.696152	−	2.59808i	−0.0486214	−	0.181458i
$206$	−0.189469	+	0.328169i	−0.0132009	+	0.0228646i
$207$		0			0
$208$	3.73205	+	3.73205i	0.258771	+	0.258771i
$209$	0.240237	−	0.896575i	0.0166175	−	0.0620174i
$210$		0			0
$211$	−28.1962			−1.94110			−0.970552	−	0.240893i	$-0.922560\pi$
$211$	−28.1962			−1.94110			−0.970552	+	0.240893i	$0.922560\pi$
$212$	−10.9348			−0.751003
$213$		0			0
$214$	−4.26795	+	4.26795i	−0.291751	+	0.291751i
$215$	−4.57081	−	7.91688i	−0.311727	−	0.539926i
$216$		0			0
$217$	14.6603	+	3.92820i	0.995203	+	0.266664i
$218$	13.2641	−	7.65806i	0.898361	−	0.518669i
$219$		0			0
$220$	−4.09808	+	1.09808i	−0.276292	+	0.0740323i
$221$	2.44949			0.164771
$222$		0			0
$223$	−2.39230			−0.160201			−0.0801003	−	0.996787i	$-0.525524\pi$
$223$	−2.39230			−0.160201			−0.0801003	+	0.996787i	$0.525524\pi$
$224$	4.57081	−	1.22474i	0.305400	−	0.0818317i
$225$		0			0
$226$	17.1962	−	9.92820i	1.14387	−	0.660414i
$227$	9.46979	+	2.53742i	0.628532	+	0.168415i	0.559003	−	0.829165i	$-0.311184\pi$
$227$	9.46979	+	2.53742i	0.628532	+	0.168415i	0.0695285	+	0.997580i	$0.477851\pi$
$228$		0			0
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	0.849032	−	0.528341i	$-0.177186\pi$
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	−0.882073	+	0.471113i	$0.843853\pi$
$230$	−4.24264	+	4.24264i	−0.279751	+	0.279751i
$231$		0			0
$232$	8.66025			0.568574
$233$	11.8313			0.775097			0.387549	−	0.921849i	$-0.373322\pi$
$233$	11.8313			0.775097			0.387549	+	0.921849i	$0.373322\pi$
$234$		0			0
$235$	−1.90192	+	7.09808i	−0.124068	+	0.463027i
$236$	−4.24264	−	4.24264i	−0.276172	−	0.276172i
$237$		0			0
$238$	1.09808	−	1.90192i	0.0711777	−	0.123283i
$239$	−1.64085	−	6.12372i	−0.106138	−	0.396111i	0.892334	−	0.451375i	$-0.149066\pi$
$239$	−1.64085	−	6.12372i	−0.106138	−	0.396111i	−0.998472	+	0.0552646i	$0.982400\pi$
$240$		0			0
$241$	2.29423	−	8.56218i	0.147784	−	0.551538i	−0.851831	−	0.523816i	$-0.824508\pi$
$241$	2.29423	−	8.56218i	0.147784	−	0.551538i	0.999616	−	0.0277223i	$-0.00882541\pi$
$242$	−4.82963	+	1.29410i	−0.310460	+	0.0831876i
$243$		0			0
$244$	−1.13397	+	0.303848i	−0.0725953	+	0.0194518i
$245$	18.8516	−	18.8516i	1.20439	−	1.20439i
$246$		0			0
$247$	1.73205	+	1.00000i	0.110208	+	0.0636285i
$248$		−	3.20736i		−	0.203668i
$249$		0			0
$250$	10.5000	+	6.06218i	0.664078	+	0.383406i
$251$	7.58871	+	7.58871i	0.478995	+	0.478995i	0.904810	−	0.425815i	$-0.140013\pi$
$251$	7.58871	+	7.58871i	0.478995	+	0.478995i	−0.425815	+	0.904810i	$0.640013\pi$
$252$		0			0
$253$	6.00000	−	6.00000i	0.377217	−	0.377217i
$254$	4.76028	−	17.7656i	0.298686	−	1.11471i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.69093	+	17.5068i	0.292612	+	1.09204i	0.943095	+	0.332523i	$0.107900\pi$
$257$	4.69093	+	17.5068i	0.292612	+	1.09204i	−0.650483	+	0.759521i	$0.725434\pi$
$258$		0			0
$259$	22.2224	+	18.2942i	1.38083	+	1.13675i
$260$		−	9.14162i		−	0.566939i
$261$		0			0
$262$	−17.1962	+	9.92820i	−1.06238	+	0.613366i
$263$	−14.9372	−	25.8719i	−0.921066	−	1.59533i	−0.797769	−	0.602963i	$-0.793987\pi$
$263$	−14.9372	−	25.8719i	−0.921066	−	1.59533i	−0.123296	−	0.992370i	$-0.539347\pi$
$264$		0			0
$265$	13.3923	+	13.3923i	0.822683	+	0.822683i
$266$	1.55291	−	0.896575i	0.0952153	−	0.0549726i
$267$		0			0
$268$	−3.09808	+	5.36603i	−0.189245	+	0.327782i
$269$			4.24264i			0.258678i	0.991600	+	0.129339i	$0.0412856\pi$
$269$			4.24264i			0.258678i	−0.991600	+	0.129339i	$0.958714\pi$
$270$		0			0
$271$	1.43782	−	2.49038i	0.0873415	−	0.151280i	−0.819045	−	0.573729i	$-0.805496\pi$
$271$	1.43782	−	2.49038i	0.0873415	−	0.151280i	0.906387	+	0.422449i	$0.138830\pi$
$272$	−0.448288	−	0.120118i	−0.0271814	−	0.00728324i
$273$		0			0
$274$	−3.52628	−	13.1603i	−0.213030	−	0.795040i
$275$	−4.24264	−	2.44949i	−0.255841	−	0.147710i
$276$		0			0
$277$	5.06218	+	1.35641i	0.304157	+	0.0814986i	0.407669	−	0.913130i	$-0.366342\pi$
$277$	5.06218	+	1.35641i	0.304157	+	0.0814986i	−0.103513	+	0.994628i	$0.533008\pi$
$278$	19.6975	+	5.27792i	1.18137	+	0.316548i
$279$		0			0
$280$	−7.09808	−	4.09808i	−0.424191	−	0.244907i
$281$	−4.27483	−	15.9539i	−0.255015	−	0.951728i	−0.968082	−	0.250633i	$-0.919361\pi$
$281$	−4.27483	−	15.9539i	−0.255015	−	0.951728i	0.713068	−	0.701095i	$-0.247305\pi$
$282$		0			0
$283$	24.2224	+	6.49038i	1.43987	+	0.385813i	0.892490	−	0.451068i	$-0.148957\pi$
$283$	24.2224	+	6.49038i	1.43987	+	0.385813i	0.547385	+	0.836881i	$0.315624\pi$
$284$	−1.22474	+	2.12132i	−0.0726752	+	0.125877i
$285$		0			0
$286$			12.9282i			0.764461i
$287$	−3.67423	+	6.36396i	−0.216883	+	0.375653i
$288$		0			0
$289$	14.5359	−	8.39230i	0.855053	−	0.493665i
$290$	−10.6066	−	10.6066i	−0.622841	−	0.622841i
$291$		0			0
$292$	−7.19615	−	12.4641i	−0.421123	−	0.729406i
$293$	−8.12493	+	4.69093i	−0.474663	+	0.274047i	−0.718190	−	0.695847i	$-0.755029\pi$
$293$	−8.12493	+	4.69093i	−0.474663	+	0.274047i	0.243527	+	0.969894i	$0.421696\pi$
$294$		0			0
$295$			10.3923i			0.605063i
$296$	2.51884	−	5.53674i	0.146405	−	0.321816i
$297$		0			0
$298$	2.93782	+	10.9641i	0.170183	+	0.635133i
$299$	9.14162	+	15.8338i	0.528674	+	0.915689i
$300$		0			0
$301$	−6.46410	+	24.1244i	−0.372585	+	1.39050i
$302$	12.2474	−	12.2474i	0.704761	−	0.704761i
$303$		0			0
$304$	−0.267949	−	0.267949i	−0.0153679	−	0.0153679i
$305$	1.76097	+	1.01669i	0.100833	+	0.0582157i
$306$		0			0
$307$		−	8.87564i		−	0.506560i	−0.967393	−	0.253280i	$-0.918491\pi$
$307$		−	8.87564i		−	0.506560i	0.967393	−	0.253280i	$-0.0815094\pi$
$308$	10.0382	+	5.79555i	0.571979	+	0.330232i
$309$		0			0
$310$	−3.92820	+	3.92820i	−0.223107	+	0.223107i
$311$	26.2001	−	7.02030i	1.48567	−	0.398085i	0.577399	−	0.816462i	$-0.304068\pi$
$311$	26.2001	−	7.02030i	1.48567	−	0.398085i	0.908273	+	0.418377i	$0.137401\pi$
$312$		0			0
$313$	−14.5263	+	3.89230i	−0.821074	+	0.220006i	−0.644816	−	0.764338i	$-0.723066\pi$
$313$	−14.5263	+	3.89230i	−0.821074	+	0.220006i	−0.176258	+	0.984344i	$0.556399\pi$
$314$	4.69093	−	17.5068i	0.264724	−	0.987965i
$315$		0			0
$316$	1.63397	+	6.09808i	0.0919183	+	0.343044i
$317$	−11.3831	+	19.7160i	−0.639336	+	1.10736i	0.346242	+	0.938145i	$0.387457\pi$
$317$	−11.3831	+	19.7160i	−0.639336	+	1.10736i	−0.985579	+	0.169218i	$0.945876\pi$
$318$		0			0
$319$	15.0000	+	15.0000i	0.839839	+	0.839839i
$320$	−0.448288	+	1.67303i	−0.0250600	+	0.0935254i
$321$		0			0
$322$	16.3923			0.913507
$323$	−0.175865			−0.00978542
$324$		0			0
$325$	7.46410	−	7.46410i	0.414034	−	0.414034i
$326$	2.63896	+	4.57081i	0.146158	+	0.253154i
$327$		0			0
$328$	1.50000	+	0.401924i	0.0828236	+	0.0221925i
$329$	17.3867	−	10.0382i	0.958558	−	0.553424i
$330$		0			0
$331$	−21.8564	+	5.85641i	−1.20134	+	0.321897i	−0.803357	−	0.595497i	$-0.796955\pi$
$331$	−21.8564	+	5.85641i	−1.20134	+	0.321897i	−0.397979	+	0.917394i	$0.630288\pi$
$332$	−13.3843			−0.734557
$333$		0			0
$334$	−11.0718			−0.605822
$335$	10.3664	−	2.77766i	0.566375	−	0.151760i
$336$		0			0
$337$	10.2846	−	5.93782i	0.560238	−	0.323454i	−0.193003	−	0.981198i	$-0.561823\pi$
$337$	10.2846	−	5.93782i	0.560238	−	0.323454i	0.753241	+	0.657744i	$0.228489\pi$
$338$	−14.3502	−	3.84512i	−0.780547	−	0.209147i
$339$		0			0
$340$	0.401924	+	0.696152i	0.0217974	+	0.0377542i
$341$	5.55532	−	5.55532i	0.300837	−	0.300837i
$342$		0			0
$343$	−39.7128			−2.14429
$344$	5.27792			0.284566
$345$		0			0
$346$	3.52628	−	13.1603i	0.189574	−	0.707500i
$347$	−3.58630	−	3.58630i	−0.192523	−	0.192523i	0.604263	−	0.796785i	$-0.293468\pi$
$347$	−3.58630	−	3.58630i	−0.192523	−	0.192523i	−0.796785	+	0.604263i	$0.793468\pi$
$348$		0			0
$349$	−6.23205	+	10.7942i	−0.333594	+	0.577802i	−0.983214	−	0.182458i	$-0.941595\pi$
$349$	−6.23205	+	10.7942i	−0.333594	+	0.577802i	0.649620	+	0.760259i	$0.274928\pi$
$350$	−2.44949	−	9.14162i	−0.130931	−	0.488640i
$351$		0			0
$352$	0.633975	−	2.36603i	0.0337910	−	0.126110i
$353$	12.6078	−	3.37825i	0.671046	−	0.179806i	0.0928199	−	0.995683i	$-0.470412\pi$
$353$	12.6078	−	3.37825i	0.671046	−	0.179806i	0.578226	+	0.815877i	$0.303745\pi$
$354$		0			0
$355$	4.09808	−	1.09808i	0.217503	−	0.0582798i
$356$	−5.46739	+	5.46739i	−0.289771	+	0.289771i
$357$		0			0
$358$	1.39230	+	0.803848i	0.0735856	+	0.0424847i
$359$		−	11.5911i		−	0.611755i	−0.952071	−	0.305878i	$-0.901050\pi$
$359$		−	11.5911i		−	0.611755i	0.952071	−	0.305878i	$-0.0989499\pi$
$360$		0			0
$361$	16.3301	+	9.42820i	0.859480	+	0.496221i
$362$	−4.81105	−	4.81105i	−0.252863	−	0.252863i
$363$		0			0
$364$	−17.6603	+	17.6603i	−0.925649	+	0.925649i
$365$	−6.45189	+	24.0788i	−0.337708	+	1.26034i
$366$		0			0
$367$	−16.5885	−	28.7321i	−0.865910	−	1.49980i	−0.866140	−	0.499801i	$-0.833407\pi$
$367$	−16.5885	−	28.7321i	−0.865910	−	1.49980i	0.000229920	−	1.00000i	$-0.499927\pi$
$368$	−0.896575	−	3.34607i	−0.0467372	−	0.174426i
$369$		0			0
$370$	−9.86603	+	3.69615i	−0.512910	+	0.192154i
$371$		−	51.7439i		−	2.68641i
$372$		0			0
$373$	6.06218	−	3.50000i	0.313888	−	0.181223i	−0.334777	−	0.942297i	$-0.608661\pi$
$373$	6.06218	−	3.50000i	0.313888	−	0.181223i	0.648665	+	0.761074i	$0.275328\pi$
$374$	−0.568406	−	0.984508i	−0.0293916	−	0.0509077i
$375$		0			0
$376$	−3.00000	−	3.00000i	−0.154713	−	0.154713i
$377$	−39.5844	+	22.8541i	−2.03870	+	1.17704i
$378$		0			0
$379$	7.56218	−	13.0981i	0.388443	−	0.672803i	−0.603797	−	0.797138i	$-0.706346\pi$
$379$	7.56218	−	13.0981i	0.388443	−	0.672803i	0.992240	+	0.124335i	$0.0396797\pi$
$380$			0.656339i			0.0336695i
$381$		0			0
$382$	−0.464102	+	0.803848i	−0.0237455	+	0.0411284i
$383$	12.1595	+	3.25813i	0.621322	+	0.166483i	0.555729	−	0.831364i	$-0.312439\pi$
$383$	12.1595	+	3.25813i	0.621322	+	0.166483i	0.0655934	+	0.997846i	$0.479106\pi$
$384$		0			0
$385$	−5.19615	−	19.3923i	−0.264820	−	0.988323i
$386$	−9.91808	−	5.72620i	−0.504817	−	0.291456i
$387$		0			0
$388$	−1.86603	−	0.500000i	−0.0947331	−	0.0253837i
$389$	15.3855	+	4.12252i	0.780074	+	0.209020i	0.626817	−	0.779166i	$-0.284357\pi$
$389$	15.3855	+	4.12252i	0.780074	+	0.209020i	0.153257	+	0.988186i	$0.451024\pi$
$390$		0			0
$391$	−1.39230	−	0.803848i	−0.0704119	−	0.0406523i
$392$	3.98382	+	14.8678i	0.201213	+	0.750939i
$393$		0			0
$394$	17.8923	+	4.79423i	0.901401	+	0.241530i
$395$	5.46739	−	9.46979i	0.275094	−	0.476477i
$396$		0			0
$397$			23.5885i			1.18387i	0.805985	+	0.591935i	$0.201636\pi$
$397$			23.5885i			1.18387i	−0.805985	+	0.591935i	$0.798364\pi$
$398$	−8.19428	+	14.1929i	−0.410742	+	0.711426i
$399$		0			0
$400$	−1.73205	+	1.00000i	−0.0866025	+	0.0500000i
$401$	21.8695	+	21.8695i	1.09211	+	1.09211i	0.995303	+	0.0968099i	$0.0308639\pi$
$401$	21.8695	+	21.8695i	1.09211	+	1.09211i	0.0968099	+	0.995303i	$0.469136\pi$
$402$		0			0
$403$	8.46410	+	14.6603i	0.421627	+	0.730279i
$404$	−12.9360	+	7.46859i	−0.643589	+	0.371576i
$405$		0			0
$406$			40.9808i			2.03384i
$407$	13.9527	−	5.22715i	0.691608	−	0.259100i
$408$		0			0
$409$	4.74167	+	17.6962i	0.234460	+	0.875018i	0.978391	+	0.206762i	$0.0662925\pi$
$409$	4.74167	+	17.6962i	0.234460	+	0.875018i	−0.743931	+	0.668257i	$0.767041\pi$
$410$	−1.34486	−	2.32937i	−0.0664181	−	0.115039i
$411$		0			0
$412$	−0.0980762	+	0.366025i	−0.00483187	+	0.0180328i
$413$	20.0764	−	20.0764i	0.987895	−	0.987895i
$414$		0			0
$415$	16.3923	+	16.3923i	0.804667	+	0.804667i
$416$	4.57081	+	2.63896i	0.224102	+	0.129386i
$417$		0			0
$418$		−	0.928203i		−	0.0453999i
$419$	−24.8874	−	14.3688i	−1.21583	−	0.701960i	−0.251807	−	0.967777i	$-0.581025\pi$
$419$	−24.8874	−	14.3688i	−1.21583	−	0.701960i	−0.964023	+	0.265817i	$0.914358\pi$
$420$		0			0
$421$	−2.16987	+	2.16987i	−0.105753	+	0.105753i	−0.758004	−	0.652250i	$-0.773825\pi$
$421$	−2.16987	+	2.16987i	−0.105753	+	0.105753i	0.652250	+	0.758004i	$0.273825\pi$
$422$	−27.2354	+	7.29770i	−1.32580	+	0.355247i
$423$		0			0
$424$	−10.5622	+	2.83013i	−0.512945	+	0.137443i
$425$	−0.240237	+	0.896575i	−0.0116532	+	0.0434903i
$426$		0			0
$427$	−1.43782	−	5.36603i	−0.0695811	−	0.259680i
$428$	−3.01790	+	5.22715i	−0.145876	+	0.252664i
$429$		0			0
$430$	−6.46410	−	6.46410i	−0.311727	−	0.311727i
$431$	2.53742	−	9.46979i	0.122223	−	0.456144i	−0.877502	−	0.479573i	$-0.840792\pi$
$431$	2.53742	−	9.46979i	0.122223	−	0.456144i	0.999726	+	0.0234290i	$0.00745835\pi$
$432$		0			0
$433$	29.1962			1.40308			0.701539	−	0.712631i	$-0.252497\pi$
$433$	29.1962			1.40308			0.701539	+	0.712631i	$0.252497\pi$
$434$	15.1774			0.728539
$435$		0			0
$436$	10.8301	−	10.8301i	0.518669	−	0.518669i
$437$	−0.656339	−	1.13681i	−0.0313969	−	0.0543811i
$438$		0			0
$439$	−9.66025	−	2.58846i	−0.461059	−	0.123540i	0.0208105	−	0.999783i	$-0.493375\pi$
$439$	−9.66025	−	2.58846i	−0.461059	−	0.123540i	−0.481869	+	0.876243i	$0.660042\pi$
$440$	−3.67423	+	2.12132i	−0.175162	+	0.101130i
$441$		0			0
$442$	2.36603	−	0.633975i	0.112540	−	0.0301551i
$443$	−18.7637			−0.891491			−0.445745	−	0.895160i	$-0.647061\pi$
$443$	−18.7637			−0.891491			−0.445745	+	0.895160i	$0.647061\pi$
$444$		0			0
$445$	13.3923			0.634856
$446$	−2.31079	+	0.619174i	−0.109419	+	0.0293187i
$447$		0			0
$448$	4.09808	−	2.36603i	0.193616	−	0.111784i
$449$	8.24504	+	2.20925i	0.389108	+	0.104261i	0.448069	−	0.893999i	$-0.352112\pi$
$449$	8.24504	+	2.20925i	0.389108	+	0.104261i	−0.0589608	+	0.998260i	$0.518779\pi$
$450$		0			0
$451$	1.90192	+	3.29423i	0.0895581	+	0.155119i
$452$	14.0406	−	14.0406i	0.660414	−	0.660414i
$453$		0			0
$454$	9.80385			0.460117
$455$	43.2586			2.02799
$456$		0			0
$457$	9.33013	−	34.8205i	0.436445	−	1.62883i	−0.301140	−	0.953580i	$-0.597367\pi$
$457$	9.33013	−	34.8205i	0.436445	−	1.62883i	0.737585	−	0.675255i	$-0.235966\pi$
$458$	−0.707107	−	0.707107i	−0.0330409	−	0.0330409i
$459$		0			0
$460$	−3.00000	+	5.19615i	−0.139876	+	0.242272i
$461$	0.656339	+	2.44949i	0.0305687	+	0.114084i	0.979524	−	0.201325i	$-0.0645248\pi$
$461$	0.656339	+	2.44949i	0.0305687	+	0.114084i	−0.948956	+	0.315409i	$0.897858\pi$
$462$		0			0
$463$	−8.04552	+	30.0263i	−0.373907	+	1.39544i	0.481028	+	0.876705i	$0.340263\pi$
$463$	−8.04552	+	30.0263i	−0.373907	+	1.39544i	−0.854935	+	0.518735i	$0.826403\pi$
$464$	8.36516	−	2.24144i	0.388343	−	0.104056i
$465$		0			0
$466$	11.4282	−	3.06218i	0.529401	−	0.141853i
$467$	−20.7327	+	20.7327i	−0.959396	+	0.959396i	−0.999207	−	0.0398109i	$-0.987324\pi$
$467$	−20.7327	+	20.7327i	−0.959396	+	0.959396i	0.0398109	+	0.999207i	$0.487324\pi$
$468$		0			0
$469$	−25.3923	−	14.6603i	−1.17251	−	0.676948i
$470$			7.34847i			0.338960i
$471$		0			0
$472$	−5.19615	−	3.00000i	−0.239172	−	0.138086i
$473$	9.14162	+	9.14162i	0.420332	+	0.420332i
$474$		0			0
$475$	−0.535898	+	0.535898i	−0.0245887	+	0.0245887i
$476$	0.568406	−	2.12132i	0.0260528	−	0.0972306i
$477$		0			0
$478$	−3.16987	−	5.49038i	−0.144987	−	0.251124i
$479$	10.0382	+	37.4631i	0.458657	+	1.71173i	0.677109	+	0.735883i	$0.263233\pi$
$479$	10.0382	+	37.4631i	0.458657	+	1.71173i	−0.218452	+	0.975848i	$0.570101\pi$
$480$		0			0
$481$	3.09808	+	31.9545i	0.141260	+	1.45700i
$482$		−	8.86422i		−	0.403754i
$483$		0			0
$484$	−4.33013	+	2.50000i	−0.196824	+	0.113636i
$485$	1.67303	+	2.89778i	0.0759685	+	0.131581i
$486$		0			0
$487$	−12.7321	−	12.7321i	−0.576944	−	0.576944i	0.357116	−	0.934060i	$-0.383760\pi$
$487$	−12.7321	−	12.7321i	−0.576944	−	0.576944i	−0.934060	+	0.357116i	$0.883760\pi$
$488$	−1.01669	+	0.586988i	−0.0460236	+	0.0265717i
$489$		0			0
$490$	13.3301	−	23.0885i	0.602194	−	1.04303i
$491$		−	2.92996i		−	0.132227i	−0.997812	−	0.0661137i	$-0.978940\pi$
$491$		−	2.92996i		−	0.132227i	0.997812	−	0.0661137i	$-0.0210600\pi$
$492$		0			0
$493$	2.00962	−	3.48076i	0.0905087	−	0.156766i
$494$	1.93185	+	0.517638i	0.0869181	+	0.0232896i
$495$		0			0
$496$	−0.830127	−	3.09808i	−0.0372738	−	0.139108i
$497$	−10.0382	−	5.79555i	−0.450275	−	0.259966i
$498$		0			0
$499$	−1.36603	−	0.366025i	−0.0611517	−	0.0163855i	0.228113	−	0.973635i	$-0.426744\pi$
$499$	−1.36603	−	0.366025i	−0.0611517	−	0.0163855i	−0.289265	+	0.957249i	$0.593411\pi$
$500$	11.7112	+	3.13801i	0.523742	+	0.140336i
$501$		0			0
$502$	9.29423	+	5.36603i	0.414822	+	0.239497i
$503$	−3.67423	−	13.7124i	−0.163826	−	0.611407i	−0.998187	−	0.0601886i	$-0.980830\pi$
$503$	−3.67423	−	13.7124i	−0.163826	−	0.611407i	0.834361	−	0.551218i	$-0.185837\pi$
$504$		0			0
$505$	24.9904	+	6.69615i	1.11206	+	0.297975i
$506$	4.24264	−	7.34847i	0.188608	−	0.326679i
$507$		0			0
$508$		−	18.3923i		−	0.816027i
$509$	−7.14042	+	12.3676i	−0.316493	+	0.548183i	−0.979754	−	0.200206i	$-0.935839\pi$
$509$	−7.14042	+	12.3676i	−0.316493	+	0.548183i	0.663260	+	0.748389i	$0.269172\pi$
$510$		0			0
$511$	58.9808	−	34.0526i	2.60916	−	1.50640i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	9.06218	+	15.6962i	0.399716	+	0.692328i
$515$	0.568406	−	0.328169i	0.0250470	−	0.0144609i
$516$		0			0
$517$		−	10.3923i		−	0.457053i
$518$	26.2001	+	11.9193i	1.15117	+	0.523703i
$519$		0			0
$520$	−2.36603	−	8.83013i	−0.103757	−	0.387227i
$521$	−11.5032	−	19.9241i	−0.503963	−	0.872890i	−0.999990	−	0.00458254i	$-0.998541\pi$
$521$	−11.5032	−	19.9241i	−0.503963	−	0.872890i	0.496026	−	0.868308i	$-0.334792\pi$
$522$		0			0
$523$	−0.411543	+	1.53590i	−0.0179955	+	0.0671601i	−0.974340	−	0.225083i	$-0.927735\pi$
$523$	−0.411543	+	1.53590i	−0.0179955	+	0.0671601i	0.956344	+	0.292243i	$0.0944015\pi$
$524$	−14.0406	+	14.0406i	−0.613366	+	0.613366i
$525$		0			0
$526$	−21.1244	−	21.1244i	−0.921066	−	0.921066i
$527$	−1.28912	−	0.744272i	−0.0561548	−	0.0324210i
$528$		0			0
$529$			11.0000i			0.478261i
$530$	16.4022	+	9.46979i	0.712464	+	0.411341i
$531$		0			0
$532$	1.26795	−	1.26795i	0.0549726	−	0.0549726i
$533$	−7.91688	+	2.12132i	−0.342918	+	0.0918846i
$534$		0			0
$535$	10.0981	−	2.70577i	0.436578	−	0.116981i
$536$	−1.60368	+	5.98502i	−0.0692685	+	0.258514i
$537$		0			0
$538$	1.09808	+	4.09808i	0.0473414	+	0.176681i
$539$	−18.8516	+	32.6520i	−0.811998	+	1.40642i
$540$		0			0
$541$	−20.4186	−	20.4186i	−0.877864	−	0.877864i	0.115450	−	0.993313i	$-0.463169\pi$
$541$	−20.4186	−	20.4186i	−0.877864	−	0.877864i	−0.993313	+	0.115450i	$0.963169\pi$
$542$	0.744272	−	2.77766i	0.0319692	−	0.119311i
$543$		0			0
$544$	−0.464102			−0.0198982
$545$	−26.5283			−1.13635
$546$		0			0
$547$	6.32051	−	6.32051i	0.270245	−	0.270245i	−0.558954	−	0.829199i	$-0.688797\pi$
$547$	6.32051	−	6.32051i	0.270245	−	0.270245i	0.829199	+	0.558954i	$0.188797\pi$
$548$	−6.81225	−	11.7992i	−0.291005	−	0.504035i
$549$		0			0
$550$	−4.73205	−	1.26795i	−0.201775	−	0.0540655i
$551$	2.84203	−	1.64085i	0.121075	−	0.0699024i
$552$		0			0
$553$	−28.8564	+	7.73205i	−1.22710	+	0.328800i
$554$	5.24075			0.222658
$555$		0			0
$556$	20.3923			0.864826
$557$	−23.6305	+	6.33178i	−1.00126	+	0.268286i	−0.721972	−	0.691922i	$-0.756764\pi$
$557$	−23.6305	+	6.33178i	−1.00126	+	0.268286i	−0.279285	+	0.960208i	$0.590097\pi$
$558$		0			0
$559$	−24.1244	+	13.9282i	−1.02035	+	0.589100i
$560$	−7.91688	−	2.12132i	−0.334549	−	0.0896421i
$561$		0			0
$562$	−8.25833	−	14.3038i	−0.348357	−	0.603371i
$563$	−20.2523	+	20.2523i	−0.853531	+	0.853531i	−0.990566	−	0.137035i	$-0.956243\pi$
$563$	−20.2523	+	20.2523i	−0.853531	+	0.853531i	0.137035	+	0.990566i	$0.456243\pi$
$564$		0			0
$565$	−34.3923			−1.44690
$566$	25.0769			1.05406
$567$		0			0
$568$	−0.633975	+	2.36603i	−0.0266010	+	0.0992762i
$569$	9.22955	+	9.22955i	0.386923	+	0.386923i	0.873588	−	0.486665i	$-0.161787\pi$
$569$	9.22955	+	9.22955i	0.386923	+	0.386923i	−0.486665	+	0.873588i	$0.661787\pi$
$570$		0			0
$571$	−0.928203	+	1.60770i	−0.0388441	+	0.0672799i	−0.884794	−	0.465983i	$-0.845701\pi$
$571$	−0.928203	+	1.60770i	−0.0388441	+	0.0672799i	0.845950	+	0.533263i	$0.179034\pi$
$572$	3.34607	+	12.4877i	0.139906	+	0.522136i
$573$		0			0
$574$	−1.90192	+	7.09808i	−0.0793848	+	0.296268i
$575$	−6.69213	+	1.79315i	−0.279081	+	0.0747796i
$576$		0			0
$577$	−19.2942	+	5.16987i	−0.803229	+	0.215225i	−0.637001	−	0.770863i	$-0.719825\pi$
$577$	−19.2942	+	5.16987i	−0.803229	+	0.215225i	−0.166228	+	0.986087i	$0.553159\pi$
$578$	11.8685	−	11.8685i	0.493665	−	0.493665i
$579$		0			0
$580$	−12.9904	−	7.50000i	−0.539396	−	0.311421i
$581$		−	63.3350i		−	2.62758i
$582$		0			0
$583$	−23.1962	−	13.3923i	−0.960686	−	0.554653i
$584$	−10.1769	−	10.1769i	−0.421123	−	0.421123i
$585$		0			0
$586$	−6.63397	+	6.63397i	−0.274047	+	0.274047i
$587$	0.240237	−	0.896575i	0.00991563	−	0.0370056i	−0.960791	−	0.277274i	$-0.910569\pi$
$587$	0.240237	−	0.896575i	0.00991563	−	0.0370056i	0.970706	+	0.240269i	$0.0772356\pi$
$588$		0			0
$589$	−0.607695	−	1.05256i	−0.0250396	−	0.0433699i
$590$	2.68973	+	10.0382i	0.110734	+	0.413266i
$591$		0			0
$592$	1.00000	−	6.00000i	0.0410997	−	0.246598i
$593$			25.3915i			1.04270i	0.853342	+	0.521351i	$0.174572\pi$
$593$			25.3915i			1.04270i	−0.853342	+	0.521351i	$0.825428\pi$
$594$		0			0
$595$	−3.29423	+	1.90192i	−0.135050	+	0.0779713i
$596$	5.67544	+	9.83014i	0.232475	+	0.402658i
$597$		0			0
$598$	12.9282	+	12.9282i	0.528674	+	0.528674i
$599$	−36.4785	+	21.0609i	−1.49047	+	0.860525i	−0.999941	−	0.0108979i	$-0.996531\pi$
$599$	−36.4785	+	21.0609i	−1.49047	+	0.860525i	−0.490532	+	0.871423i	$0.663198\pi$
$600$		0			0
$601$	−8.76795	+	15.1865i	−0.357652	+	0.619472i	−0.987568	−	0.157192i	$-0.949756\pi$
$601$	−8.76795	+	15.1865i	−0.357652	+	0.619472i	0.629916	+	0.776663i	$0.283089\pi$
$602$			24.9754i			1.01792i
$603$		0			0
$604$	8.66025	−	15.0000i	0.352381	−	0.610341i
$605$	8.36516	+	2.24144i	0.340092	+	0.0911274i
$606$		0			0
$607$	−11.5096	−	42.9545i	−0.467161	−	1.74347i	−0.649624	−	0.760256i	$-0.725074\pi$
$607$	−11.5096	−	42.9545i	−0.467161	−	1.74347i	0.182463	−	0.983213i	$-0.441593\pi$
$608$	−0.328169	−	0.189469i	−0.0133090	−	0.00768397i
$609$		0			0
$610$	1.96410	+	0.526279i	0.0795241	+	0.0213084i
$611$	21.6293	+	5.79555i	0.875028	+	0.234463i
$612$		0			0
$613$	−5.08846	−	2.93782i	−0.205521	−	0.118658i	0.393707	−	0.919236i	$-0.371192\pi$
$613$	−5.08846	−	2.93782i	−0.205521	−	0.118658i	−0.599228	+	0.800578i	$0.704526\pi$
$614$	−2.29719	−	8.57321i	−0.0927069	−	0.345987i
$615$		0			0
$616$	11.1962	+	3.00000i	0.451106	+	0.120873i
$617$	−21.7172	+	37.6154i	−0.874303	+	1.51434i	−0.0167998	+	0.999859i	$0.505348\pi$
$617$	−21.7172	+	37.6154i	−0.874303	+	1.51434i	−0.857503	+	0.514479i	$0.827986\pi$
$618$		0			0
$619$			33.8038i			1.35869i	0.733818	+	0.679346i	$0.237736\pi$
$619$			33.8038i			1.35869i	−0.733818	+	0.679346i	$0.762264\pi$
$620$	−2.77766	+	4.81105i	−0.111553	+	0.193216i
$621$		0			0
$622$	23.4904	−	13.5622i	0.941878	−	0.543794i
$623$	−25.8719	−	25.8719i	−1.03654	−	1.03654i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−13.0239	+	7.51936i	−0.520540	+	0.300534i
$627$		0			0
$628$		−	18.1244i		−	0.723241i
$629$	−1.64085	−	2.29719i	−0.0654249	−	0.0915948i
$630$		0			0
$631$	−6.66025	−	24.8564i	−0.265141	−	0.989518i	−0.962164	−	0.272470i	$-0.912159\pi$
$631$	−6.66025	−	24.8564i	−0.265141	−	0.989518i	0.697024	−	0.717048i	$-0.254507\pi$
$632$	3.15660	+	5.46739i	0.125563	+	0.217481i
$633$		0			0
$634$	−5.89230	+	21.9904i	−0.234013	+	0.873350i
$635$	−22.5259	+	22.5259i	−0.893912	+	0.893912i
$636$		0			0
$637$	−57.4449	−	57.4449i	−2.27605	−	2.27605i
$638$	18.3712	+	10.6066i	0.727322	+	0.419919i
$639$		0			0
$640$			1.73205i			0.0684653i
$641$	−27.4806	−	15.8659i	−1.08542	−	0.626667i	−0.153066	−	0.988216i	$-0.548915\pi$
$641$	−27.4806	−	15.8659i	−1.08542	−	0.626667i	−0.932353	+	0.361549i	$0.882248\pi$
$642$		0			0
$643$	−30.6603	+	30.6603i	−1.20912	+	1.20912i	−0.237811	+	0.971311i	$0.576430\pi$
$643$	−30.6603	+	30.6603i	−1.20912	+	1.20912i	−0.971311	+	0.237811i	$0.923570\pi$
$644$	15.8338	−	4.24264i	0.623937	−	0.167183i
$645$		0			0
$646$	−0.169873	+	0.0455173i	−0.00668356	+	0.00179086i
$647$	9.88589	−	36.8947i	0.388655	−	1.45048i	−0.443670	−	0.896190i	$-0.646324\pi$
$647$	9.88589	−	36.8947i	0.388655	−	1.45048i	0.832325	−	0.554288i	$-0.187009\pi$
$648$		0			0
$649$	−3.80385	−	14.1962i	−0.149314	−	0.557248i
$650$	5.27792	−	9.14162i	0.207017	−	0.358564i
$651$		0			0
$652$	3.73205	+	3.73205i	0.146158	+	0.146158i
$653$	7.22835	−	26.9766i	0.282867	−	1.05567i	−0.667517	−	0.744595i	$-0.732643\pi$
$653$	7.22835	−	26.9766i	0.282867	−	1.05567i	0.950384	−	0.311080i	$-0.100691\pi$
$654$		0			0
$655$	34.3923			1.34382
$656$	1.55291			0.0606311
$657$		0			0
$658$	14.1962	−	14.1962i	0.553424	−	0.553424i
$659$	20.3166	+	35.1894i	0.791423	+	1.37079i	0.925086	+	0.379759i	$0.123993\pi$
$659$	20.3166	+	35.1894i	0.791423	+	1.37079i	−0.133662	+	0.991027i	$0.542674\pi$
$660$		0			0
$661$	30.5526	+	8.18653i	1.18836	+	0.318419i	0.798236	−	0.602345i	$-0.205767\pi$
$661$	30.5526	+	8.18653i	1.18836	+	0.318419i	0.390121	+	0.920764i	$0.372433\pi$
$662$	−19.5959	+	11.3137i	−0.761617	+	0.439720i
$663$		0			0
$664$	−12.9282	+	3.46410i	−0.501712	+	0.134433i
$665$	−3.10583			−0.120439
$666$		0			0
$667$	30.0000			1.16160
$668$	−10.6945	+	2.86559i	−0.413784	+	0.110873i
$669$		0			0
$670$	9.29423	−	5.36603i	0.359067	−	0.207308i
$671$	−2.77766	−	0.744272i	−0.107230	−	0.0287323i
$672$		0			0
$673$	−5.66025	−	9.80385i	−0.218187	−	0.377911i	0.736067	−	0.676909i	$-0.236681\pi$
$673$	−5.66025	−	9.80385i	−0.218187	−	0.377911i	−0.954254	+	0.298998i	$0.903348\pi$
$674$	8.39735	−	8.39735i	0.323454	−	0.323454i
$675$		0			0
$676$	−14.8564			−0.571400
$677$	−17.8671			−0.686690			−0.343345	−	0.939209i	$-0.611560\pi$
$677$	−17.8671			−0.686690			−0.343345	+	0.939209i	$0.611560\pi$
$678$		0			0
$679$	2.36603	−	8.83013i	0.0907997	−	0.338869i
$680$	0.568406	+	0.568406i	0.0217974	+	0.0217974i
$681$		0			0
$682$	3.92820	−	6.80385i	0.150419	−	0.260533i
$683$	−10.1261	−	37.7912i	−0.387466	−	1.44604i	−0.834244	−	0.551396i	$-0.814095\pi$
$683$	−10.1261	−	37.7912i	−0.387466	−	1.44604i	0.446778	−	0.894645i	$-0.352571\pi$
$684$		0			0
$685$	−6.10770	+	22.7942i	−0.233363	+	0.870923i
$686$	−38.3596	+	10.2784i	−1.46458	+	0.392432i
$687$		0			0
$688$	5.09808	−	1.36603i	0.194362	−	0.0520792i
$689$	40.8091	−	40.8091i	1.55470	−	1.55470i
$690$		0			0
$691$	−7.43782	−	4.29423i	−0.282948	−	0.163360i	0.351809	−	0.936072i	$-0.385567\pi$
$691$	−7.43782	−	4.29423i	−0.282948	−	0.163360i	−0.634757	+	0.772712i	$0.718900\pi$
$692$		−	13.6245i		−	0.517926i
$693$		0			0
$694$	−4.39230	−	2.53590i	−0.166730	−	0.0962614i
$695$	−24.9754	−	24.9754i	−0.947370	−	0.947370i
$696$		0			0
$697$	0.509619	−	0.509619i	0.0193032	−	0.0193032i
$698$	−3.22595	+	12.0394i	−0.122104	+	0.455698i
$699$		0			0
$700$	−4.73205	−	8.19615i	−0.178855	−	0.309785i
$701$	−1.13681	−	4.24264i	−0.0429368	−	0.160242i	0.941129	−	0.338048i	$-0.109767\pi$
$701$	−1.13681	−	4.24264i	−0.0429368	−	0.160242i	−0.984066	+	0.177806i	$0.943100\pi$
$702$		0			0
$703$	−0.222432	−	2.29423i	−0.00838918	−	0.0865285i
$704$		−	2.44949i		−	0.0923186i
$705$		0			0
$706$	11.3038	−	6.52628i	0.425426	−	0.245620i
$707$	−35.3417	−	61.2137i	−1.32916	−	2.30218i
$708$		0			0
$709$	−12.0718	−	12.0718i	−0.453366	−	0.453366i	0.443104	−	0.896470i	$-0.353877\pi$
$709$	−12.0718	−	12.0718i	−0.453366	−	0.453366i	−0.896470	+	0.443104i	$0.853877\pi$
$710$	3.67423	−	2.12132i	0.137892	−	0.0796117i
$711$		0			0
$712$	−3.86603	+	6.69615i	−0.144885	+	0.250949i
$713$		−	11.1106i		−	0.416097i
$714$		0			0
$715$	11.1962	−	19.3923i	0.418712	−	0.725231i
$716$	1.55291	+	0.416102i	0.0580351	+	0.0155505i
$717$		0			0
$718$	−3.00000	−	11.1962i	−0.111959	−	0.417837i
$719$	40.5689	+	23.4225i	1.51296	+	0.873510i	0.999885	+	0.0151689i	$0.00482861\pi$
$719$	40.5689	+	23.4225i	1.51296	+	0.873510i	0.513079	+	0.858341i	$0.328505\pi$
$720$		0			0
$721$	−1.73205	−	0.464102i	−0.0645049	−	0.0172840i
$722$	18.2139	+	4.88040i	0.677851	+	0.181630i
$723$		0			0
$724$	−5.89230	−	3.40192i	−0.218986	−	0.126432i
$725$	−4.48288	−	16.7303i	−0.166490	−	0.621349i
$726$		0			0
$727$	−4.53590	−	1.21539i	−0.168227	−	0.0450763i	0.173722	−	0.984795i	$-0.444420\pi$
$727$	−4.53590	−	1.21539i	−0.168227	−	0.0450763i	−0.341949	+	0.939718i	$0.611087\pi$
$728$	−12.4877	+	21.6293i	−0.462824	+	0.801635i
$729$		0			0
$730$			24.9282i			0.922634i
$731$	1.22474	−	2.12132i	0.0452988	−	0.0784599i
$732$		0			0
$733$	6.00000	−	3.46410i	0.221615	−	0.127950i	−0.385083	−	0.922882i	$-0.625827\pi$
$733$	6.00000	−	3.46410i	0.221615	−	0.127950i	0.606698	+	0.794933i	$0.292494\pi$
$734$	−23.4596	−	23.4596i	−0.865910	−	0.865910i
$735$		0			0
$736$	−1.73205	−	3.00000i	−0.0638442	−	0.110581i
$737$	−13.1440	+	7.58871i	−0.484166	+	0.279534i
$738$		0			0
$739$			7.60770i			0.279854i	0.990162	+	0.139927i	$0.0446867\pi$
$739$			7.60770i			0.279854i	−0.990162	+	0.139927i	$0.955313\pi$
$740$	−8.57321	+	6.12372i	−0.315158	+	0.225113i
$741$		0			0
$742$	−13.3923	−	49.9808i	−0.491647	−	1.83485i
$743$	−2.12132	−	3.67423i	−0.0778237	−	0.134795i	0.824487	−	0.565881i	$-0.191464\pi$
$743$	−2.12132	−	3.67423i	−0.0778237	−	0.134795i	−0.902311	+	0.431086i	$0.858130\pi$
$744$		0			0
$745$	5.08846	−	18.9904i	0.186427	−	0.695754i
$746$	4.94975	−	4.94975i	0.181223	−	0.181223i
$747$		0			0
$748$	−0.803848	−	0.803848i	−0.0293916	−	0.0293916i
$749$	−24.7351	−	14.2808i	−0.903802	−	0.521810i
$750$		0			0
$751$			19.4115i			0.708337i	0.935182	+	0.354169i	$0.115236\pi$
$751$			19.4115i			0.708337i	−0.935182	+	0.354169i	$0.884764\pi$
$752$	−3.67423	−	2.12132i	−0.133986	−	0.0773566i
$753$		0			0
$754$	−32.3205	+	32.3205i	−1.17704	+	1.17704i
$755$	−28.9778	+	7.76457i	−1.05461	+	0.282582i
$756$		0			0
$757$	−29.9186	+	8.01666i	−1.08741	+	0.291370i	−0.757628	−	0.652687i	$-0.773642\pi$
$757$	−29.9186	+	8.01666i	−1.08741	+	0.291370i	−0.329782	+	0.944057i	$0.606975\pi$
$758$	3.91447	−	14.6090i	0.142180	−	0.530623i
$759$		0			0
$760$	0.169873	+	0.633975i	0.00616194	+	0.0229967i
$761$	−2.89778	+	5.01910i	−0.105044	+	0.181942i	−0.913756	−	0.406263i	$-0.866832\pi$
$761$	−2.89778	+	5.01910i	−0.105044	+	0.181942i	0.808712	+	0.588205i	$0.200165\pi$
$762$		0			0
$763$	51.2487	+	51.2487i	1.85533	+	1.85533i
$764$	−0.240237	+	0.896575i	−0.00869146	+	0.0324370i
$765$		0			0
$766$	12.5885			0.454839
$767$	31.6675			1.14345
$768$		0			0
$769$	−16.8038	+	16.8038i	−0.605962	+	0.605962i	−0.941888	−	0.335926i	$-0.890951\pi$
$769$	−16.8038	+	16.8038i	−0.605962	+	0.605962i	0.335926	+	0.941888i	$0.390951\pi$
$770$	−10.0382	−	17.3867i	−0.361751	−	0.626572i
$771$		0			0
$772$	−11.0622	−	2.96410i	−0.398136	−	0.106680i
$773$	17.7470	−	10.2462i	0.638316	−	0.368532i	−0.145650	−	0.989336i	$-0.546527\pi$
$773$	17.7470	−	10.2462i	0.638316	−	0.368532i	0.783966	+	0.620804i	$0.213194\pi$
$774$		0			0
$775$	−6.19615	+	1.66025i	−0.222572	+	0.0596381i
$776$	−1.93185			−0.0693494
$777$		0			0
$778$	15.9282			0.571054
$779$	0.568406	−	0.152304i	0.0203653	−	0.00545686i
$780$		0			0
$781$	−5.19615	+	3.00000i	−0.185933	+	0.107348i
$782$	−1.55291	−	0.416102i	−0.0555321	−	0.0148798i
$783$		0			0
$784$	7.69615	+	13.3301i	0.274863	+	0.476076i
$785$	−22.1977	+	22.1977i	−0.792270	+	0.792270i
$786$		0			0
$787$	8.00000			0.285169			0.142585	−	0.989783i	$-0.454459\pi$
$787$	8.00000			0.285169			0.142585	+	0.989783i	$0.454459\pi$
$788$	18.5235			0.659872
$789$		0			0
$790$	2.83013	−	10.5622i	0.100691	−	0.375785i
$791$	66.4408	+	66.4408i	2.36236	+	2.36236i
$792$		0			0
$793$	3.09808	−	5.36603i	0.110016	−	0.190553i
$794$	6.10514	+	22.7847i	0.216663	+	0.808599i
$795$		0			0
$796$	−4.24167	+	15.8301i	−0.150342	+	0.561084i
$797$	33.2204	−	8.90138i	1.17673	−	0.315303i	0.383100	−	0.923707i	$-0.374857\pi$
$797$	33.2204	−	8.90138i	1.17673	−	0.315303i	0.793628	+	0.608404i	$0.208190\pi$
$798$		0			0
$799$	−1.90192	+	0.509619i	−0.0672852	+	0.0180290i
$800$	−1.41421	+	1.41421i	−0.0500000	+	0.0500000i
$801$		0			0
$802$	26.7846	+	15.4641i	0.945797	+	0.546056i
$803$		−	35.2538i		−	1.24408i
$804$		0			0
$805$	−24.5885	−	14.1962i	−0.866629	−	0.500349i
$806$	11.9700	+	11.9700i	0.421627	+	0.421627i
$807$		0			0
$808$	−10.5622	+	10.5622i	−0.371576	+	0.371576i
$809$	−1.79315	+	6.69213i	−0.0630438	+	0.235283i	−0.990257	−	0.139251i	$-0.955531\pi$
$809$	−1.79315	+	6.69213i	−0.0630438	+	0.235283i	0.927213	+	0.374534i	$0.122197\pi$
$810$		0			0
$811$	−15.0000	−	25.9808i	−0.526721	−	0.912308i	−0.999515	−	0.0311349i	$-0.990088\pi$
$811$	−15.0000	−	25.9808i	−0.526721	−	0.912308i	0.472794	−	0.881173i	$-0.343245\pi$
$812$	10.6066	+	39.5844i	0.372219	+	1.38914i
$813$		0			0
$814$	12.1244	−	8.66025i	0.424958	−	0.303542i
$815$		−	9.14162i		−	0.320217i
$816$		0			0
$817$	1.73205	−	1.00000i	0.0605968	−	0.0349856i
$818$	9.16020	+	15.8659i	0.320279	+	0.554739i
$819$		0			0
$820$	−1.90192	−	1.90192i	−0.0664181	−	0.0664181i
$821$	36.1739	−	20.8850i	1.26248	−	0.728893i	0.288926	−	0.957352i	$-0.406702\pi$
$821$	36.1739	−	20.8850i	1.26248	−	0.728893i	0.973554	+	0.228459i	$0.0733686\pi$
$822$		0			0
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$			0.378937i			0.0132009i
$825$		0			0
$826$	14.1962	−	24.5885i	0.493947	−	0.855542i
$827$	−40.1528	−	10.7589i	−1.39625	−	0.374124i	−0.519253	−	0.854621i	$-0.673790\pi$
$827$	−40.1528	−	10.7589i	−1.39625	−	0.374124i	−0.876996	+	0.480497i	$0.840456\pi$
$828$		0			0
$829$	6.58142	+	24.5622i	0.228582	+	0.853080i	0.980938	+	0.194323i	$0.0622508\pi$
$829$	6.58142	+	24.5622i	0.228582	+	0.853080i	−0.752356	+	0.658757i	$0.771082\pi$
$830$	20.0764	+	11.5911i	0.696862	+	0.402333i
$831$		0			0
$832$	5.09808	+	1.36603i	0.176744	+	0.0473584i
$833$	6.90018	+	1.84890i	0.239077	+	0.0640605i
$834$		0			0
$835$	16.6077	+	9.58846i	0.574733	+	0.331822i
$836$	−0.240237	−	0.896575i	−0.00830876	−	0.0310087i
$837$		0			0
$838$	−27.7583	−	7.43782i	−0.958896	−	0.256935i
$839$	−21.3891	+	37.0470i	−0.738433	+	1.27900i	0.214768	+	0.976665i	$0.431100\pi$
$839$	−21.3891	+	37.0470i	−0.738433	+	1.27900i	−0.953201	+	0.302338i	$0.902233\pi$
$840$		0			0
$841$			46.0000i			1.58621i
$842$	−1.53433	+	2.65754i	−0.0528766	+	0.0915849i
$843$		0			0
$844$	−24.4186	+	14.0981i	−0.840522	+	0.485276i
$845$	18.1953	+	18.1953i	0.625938	+	0.625938i
$846$		0			0
$847$	−11.8301	−	20.4904i	−0.406488	−	0.704058i
$848$	−9.46979	+	5.46739i	−0.325194	+	0.187751i
$849$		0			0
$850$			0.928203i			0.0318371i
$851$	8.72552	−	19.1798i	0.299107	−	0.657476i
$852$		0			0
$853$	6.96410	+	25.9904i	0.238446	+	0.889894i	0.976565	+	0.215223i	$0.0690478\pi$
$853$	6.96410	+	25.9904i	0.238446	+	0.889894i	−0.738119	+	0.674671i	$0.764286\pi$
$854$	−2.77766	−	4.81105i	−0.0950495	−	0.164631i
$855$		0			0
$856$	−1.56218	+	5.83013i	−0.0533941	+	0.199270i
$857$	−13.2963	+	13.2963i	−0.454194	+	0.454194i	−0.896744	−	0.442550i	$-0.854074\pi$
$857$	−13.2963	+	13.2963i	−0.454194	+	0.454194i	0.442550	+	0.896744i	$0.354074\pi$
$858$		0			0
$859$	−29.0000	−	29.0000i	−0.989467	−	0.989467i	0.0104779	−	0.999945i	$-0.496665\pi$
$859$	−29.0000	−	29.0000i	−0.989467	−	0.989467i	−0.999945	+	0.0104779i	$0.996665\pi$
$860$	−7.91688	−	4.57081i	−0.269963	−	0.155863i
$861$		0			0
$862$		−	9.80385i		−	0.333920i
$863$	50.6071	+	29.2180i	1.72269	+	0.994593i	0.913269	+	0.407357i	$0.133550\pi$
$863$	50.6071	+	29.2180i	1.72269	+	0.994593i	0.809416	+	0.587236i	$0.199784\pi$
$864$		0			0
$865$	−16.6865	+	16.6865i	−0.567359	+	0.567359i
$866$	28.2013	−	7.55652i	0.958320	−	0.256781i
$867$		0			0
$868$	14.6603	−	3.92820i	0.497601	−	0.133332i
$869$	−4.00240	+	14.9372i	−0.135772	+	0.506709i
$870$		0			0
$871$	−8.46410	−	31.5885i	−0.286795	−	1.07033i
$872$	7.65806	−	13.2641i	0.259335	−	0.449181i
$873$		0			0
$874$	−0.928203	−	0.928203i	−0.0313969	−	0.0313969i
$875$	−14.8492	+	55.4181i	−0.501996	+	1.87347i
$876$		0			0
$877$	52.2679			1.76496			0.882482	−	0.470347i	$-0.155871\pi$
$877$	52.2679			1.76496			0.882482	+	0.470347i	$0.155871\pi$
$878$	−10.0010			−0.337518
$879$		0			0
$880$	−3.00000	+	3.00000i	−0.101130	+	0.101130i
$881$	−20.6126	−	35.7021i	−0.694457	−	1.20283i	−0.970364	−	0.241650i	$-0.922312\pi$
$881$	−20.6126	−	35.7021i	−0.694457	−	1.20283i	0.275907	−	0.961184i	$-0.411022\pi$
$882$		0			0
$883$	−13.4641	−	3.60770i	−0.453103	−	0.121409i	0.0250479	−	0.999686i	$-0.492026\pi$
$883$	−13.4641	−	3.60770i	−0.453103	−	0.121409i	−0.478151	+	0.878278i	$0.658693\pi$
$884$	2.12132	−	1.22474i	0.0713477	−	0.0411926i
$885$		0			0
$886$	−18.1244	+	4.85641i	−0.608900	+	0.163154i
$887$	22.7017			0.762250			0.381125	−	0.924524i	$-0.375537\pi$
$887$	22.7017			0.762250			0.381125	+	0.924524i	$0.375537\pi$
$888$		0			0
$889$	87.0333			2.91900
$890$	12.9360	−	3.46618i	0.433615	−	0.116187i
$891$		0			0
$892$	−2.07180	+	1.19615i	−0.0693689	+	0.0400501i
$893$	−1.55291	−	0.416102i	−0.0519663	−	0.0139243i
$894$		0			0
$895$	−1.39230	−	2.41154i	−0.0465396	−	0.0806090i
$896$	3.34607	−	3.34607i	0.111784	−	0.111784i
$897$		0			0
$898$	8.53590			0.284847
$899$	27.7766			0.926401
$900$		0			0
$901$	−1.31347	+	4.90192i	−0.0437579	+	0.163307i
$902$	2.68973	+	2.68973i	0.0895581	+	0.0895581i
$903$		0			0
$904$	9.92820	−	17.1962i	0.330207	−	0.571936i
$905$	3.05008	+	11.3831i	0.101388	+	0.378386i
$906$		0			0
$907$	−8.56218	+	31.9545i	−0.284302	+	1.06103i	0.665045	+	0.746803i	$0.268412\pi$
$907$	−8.56218	+	31.9545i	−0.284302	+	1.06103i	−0.949348	+	0.314228i	$0.898254\pi$
$908$	9.46979	−	2.53742i	0.314266	−	0.0842073i
$909$		0			0
$910$	41.7846	−	11.1962i	1.38515	−	0.371149i
$911$	−12.7279	+	12.7279i	−0.421695	+	0.421695i	−0.885787	−	0.464092i	$-0.846381\pi$
$911$	−12.7279	+	12.7279i	−0.421695	+	0.421695i	0.464092	+	0.885787i	$0.346381\pi$
$912$		0			0
$913$	−28.3923	−	16.3923i	−0.939648	−	0.542506i
$914$		−	36.0488i		−	1.19239i
$915$		0			0
$916$	−0.866025	−	0.500000i	−0.0286143	−	0.0165205i
$917$	−66.4408	−	66.4408i	−2.19407	−	2.19407i
$918$		0			0
$919$	13.1244	−	13.1244i	0.432933	−	0.432933i	−0.456692	−	0.889625i	$-0.650966\pi$
$919$	13.1244	−	13.1244i	0.432933	−	0.432933i	0.889625	+	0.456692i	$0.150966\pi$
$920$	−1.55291	+	5.79555i	−0.0511981	+	0.191074i
$921$		0			0
$922$	1.26795	+	2.19615i	0.0417577	+	0.0723264i
$923$	−3.34607	−	12.4877i	−0.110137	−	0.411037i
$924$		0			0
$925$	−12.0000	−	2.00000i	−0.394558	−	0.0657596i
$926$			31.0855i			1.02153i
$927$		0			0
$928$	7.50000	−	4.33013i	0.246200	−	0.142143i
$929$	18.1631	+	31.4595i	0.595913	+	1.03215i	0.993417	+	0.114551i	$0.0365429\pi$
$929$	18.1631	+	31.4595i	0.595913	+	1.03215i	−0.397505	+	0.917600i	$0.630124\pi$
$930$		0			0
$931$	4.12436	+	4.12436i	0.135170	+	0.135170i
$932$	10.2462	−	5.91567i	0.335627	−	0.193774i
$933$		0			0
$934$	−14.6603	+	25.3923i	−0.479698	+	0.830862i
$935$			1.96902i			0.0643937i
$936$		0			0
$937$	2.40192	−	4.16025i	0.0784674	−	0.135910i	−0.824121	−	0.566413i	$-0.808331\pi$
$937$	2.40192	−	4.16025i	0.0784674	−	0.135910i	0.902589	+	0.430504i	$0.141664\pi$
$938$	−28.3214	−	7.58871i	−0.924728	−	0.247780i
$939$		0			0
$940$	1.90192	+	7.09808i	0.0620339	+	0.231514i
$941$	−49.2622	−	28.4416i	−1.60590	−	0.927168i	−0.990274	−	0.139132i	$-0.955569\pi$
$941$	−49.2622	−	28.4416i	−1.60590	−	0.927168i	−0.615628	−	0.788037i	$-0.711098\pi$
$942$		0			0
$943$	5.19615	+	1.39230i	0.169210	+	0.0453397i
$944$	−5.79555	−	1.55291i	−0.188629	−	0.0505431i
$945$		0			0
$946$	11.1962	+	6.46410i	0.364018	+	0.210166i
$947$	−10.5187	−	39.2562i	−0.341811	−	1.27566i	−0.896294	−	0.443460i	$-0.853751\pi$
$947$	−10.5187	−	39.2562i	−0.341811	−	1.27566i	0.554483	−	0.832195i	$-0.312916\pi$
$948$		0			0
$949$	73.3731	+	19.6603i	2.38179	+	0.638199i
$950$	−0.378937	+	0.656339i	−0.0122944	+	0.0212944i
$951$		0			0
$952$		−	2.19615i		−	0.0711777i
$953$	9.71003	−	16.8183i	0.314539	−	0.544797i	−0.664801	−	0.747021i	$-0.731484\pi$
$953$	9.71003	−	16.8183i	0.314539	−	0.544797i	0.979339	+	0.202224i	$0.0648169\pi$
$954$		0			0
$955$	1.39230	−	0.803848i	0.0450539	−	0.0260119i
$956$	−4.48288	−	4.48288i	−0.144987	−	0.144987i
$957$		0			0
$958$	19.3923	+	33.5885i	0.626537	+	1.08519i
$959$	55.8342	−	32.2359i	1.80298	−	1.04095i
$960$		0			0
$961$			20.7128i			0.668155i
$962$	11.2629	+	30.0638i	0.363132	+	0.969296i
$963$		0			0
$964$	−2.29423	−	8.56218i	−0.0738921	−	0.275769i
$965$	9.91808	+	17.1786i	0.319274	+	0.552999i
$966$		0			0
$967$	−15.7321	+	58.7128i	−0.505909	+	1.88808i	−0.0484935	+	0.998823i	$0.515442\pi$
$967$	−15.7321	+	58.7128i	−0.505909	+	1.88808i	−0.457415	+	0.889253i	$0.651225\pi$
$968$	−3.53553	+	3.53553i	−0.113636	+	0.113636i
$969$		0			0
$970$	2.36603	+	2.36603i	0.0759685	+	0.0759685i
$971$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$971$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$972$		0			0
$973$			96.4974i			3.09357i
$974$	−15.5935	−	9.00292i	−0.499648	−	0.288472i
$975$		0			0
$976$	−0.830127	+	0.830127i	−0.0265717	+	0.0265717i
$977$	−30.5307	+	8.18067i	−0.976763	+	0.261723i	−0.711681	−	0.702503i	$-0.752066\pi$
$977$	−30.5307	+	8.18067i	−0.976763	+	0.261723i	−0.265082	+	0.964226i	$0.585399\pi$
$978$		0			0
$979$	−18.2942	+	4.90192i	−0.584686	+	0.156666i
$980$	6.90018	−	25.7518i	0.220418	−	0.822612i
$981$		0			0
$982$	−0.758330	−	2.83013i	−0.0241993	−	0.0903130i
$983$	4.81105	−	8.33298i	0.153449	−	0.265781i	−0.779044	−	0.626969i	$-0.784295\pi$
$983$	4.81105	−	8.33298i	0.153449	−	0.265781i	0.932493	+	0.361188i	$0.117629\pi$
$984$		0			0
$985$	−22.6865	−	22.6865i	−0.722853	−	0.722853i
$986$	1.04026	−	3.88229i	0.0331285	−	0.123637i
$987$		0			0
$988$	2.00000			0.0636285
$989$	18.2832			0.581373
$990$		0			0
$991$	17.3397	−	17.3397i	0.550815	−	0.550815i	−0.375861	−	0.926676i	$-0.622653\pi$
$991$	17.3397	−	17.3397i	0.550815	−	0.550815i	0.926676	+	0.375861i	$0.122653\pi$
$992$	−1.60368	−	2.77766i	−0.0509170	−	0.0881908i
$993$		0			0
$994$	−11.1962	−	3.00000i	−0.355120	−	0.0951542i
$995$	24.5828	−	14.1929i	0.779328	−	0.449945i
$996$		0			0
$997$	40.9545	−	10.9737i	1.29704	−	0.347541i	0.456711	−	0.889615i	$-0.349027\pi$
$997$	40.9545	−	10.9737i	1.29704	−	0.347541i	0.840331	+	0.542074i	$0.182361\pi$
$998$	−1.41421			−0.0447661
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.be.c.467.2	yes	8
3.2	odd	2	inner	666.2.be.c.467.1	yes	8
37.29	odd	12	inner	666.2.be.c.251.1	✓	8
111.29	even	12	inner	666.2.be.c.251.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.be.c.251.1	✓	8	37.29	odd	12	inner
666.2.be.c.251.2	yes	8	111.29	even	12	inner
666.2.be.c.467.1	yes	8	3.2	odd	2	inner
666.2.be.c.467.2	yes	8	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.67303 - 0.448288i) q^{5} +(2.36603 + 4.09808i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.67303 - 0.448288i) q^{5} +(2.36603 + 4.09808i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.73205 q^{10} +2.44949 q^{11} +(-1.36603 + 5.09808i) q^{13} +(3.34607 + 3.34607i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.120118 - 0.448288i) q^{17} +(0.0980762 - 0.366025i) q^{19} +(-1.67303 + 0.448288i) q^{20} +(2.36603 - 0.633975i) q^{22} +(2.44949 - 2.44949i) q^{23} +(-1.73205 - 1.00000i) q^{25} +5.27792i q^{26} +(4.09808 + 2.36603i) q^{28} +(6.12372 + 6.12372i) q^{29} +(2.26795 - 2.26795i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.232051 - 0.401924i) q^{34} +(-2.12132 - 7.91688i) q^{35} +(5.69615 - 2.13397i) q^{37} -0.378937i q^{38} +(-1.50000 + 0.866025i) q^{40} +(0.776457 + 1.34486i) q^{41} +(3.73205 + 3.73205i) q^{43} +(2.12132 - 1.22474i) q^{44} +(1.73205 - 3.00000i) q^{46} -4.24264i q^{47} +(-7.69615 + 13.3301i) q^{49} +(-1.93185 - 0.517638i) q^{50} +(1.36603 + 5.09808i) q^{52} +(-9.46979 - 5.46739i) q^{53} +(-4.09808 - 1.09808i) q^{55} +(4.57081 + 1.22474i) q^{56} +(7.50000 + 4.33013i) q^{58} +(-1.55291 - 5.79555i) q^{59} +(-1.13397 - 0.303848i) q^{61} +(1.60368 - 2.77766i) q^{62} -1.00000i q^{64} +(4.57081 - 7.91688i) q^{65} +(-5.36603 + 3.09808i) q^{67} +(-0.328169 - 0.328169i) q^{68} +(-4.09808 - 7.09808i) q^{70} +(-2.12132 + 1.22474i) q^{71} -14.3923i q^{73} +(4.94975 - 3.53553i) q^{74} +(-0.0980762 - 0.366025i) q^{76} +(5.79555 + 10.0382i) q^{77} +(-1.63397 + 6.09808i) q^{79} +(-1.22474 + 1.22474i) q^{80} +(1.09808 + 1.09808i) q^{82} +(-11.5911 - 6.69213i) q^{83} +0.803848i q^{85} +(4.57081 + 2.63896i) q^{86} +(1.73205 - 1.73205i) q^{88} +(-7.46859 + 2.00120i) q^{89} +(-24.1244 + 6.46410i) q^{91} +(0.896575 - 3.34607i) q^{92} +(-1.09808 - 4.09808i) q^{94} +(-0.328169 + 0.568406i) q^{95} +(-1.36603 - 1.36603i) q^{97} +(-3.98382 + 14.8678i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{7}+O(q^{10}) \) 8 * q + 12 * q^7	\( 8 q + 12 q^{7} - 4 q^{13} + 4 q^{16} - 20 q^{19} + 12 q^{22} + 12 q^{28} + 32 q^{31} + 12 q^{34} + 4 q^{37} - 12 q^{40} + 16 q^{43} - 20 q^{49} + 4 q^{52} - 12 q^{55} + 60 q^{58} - 16 q^{61} - 36 q^{67} - 12 q^{70} + 20 q^{76} - 20 q^{79} - 12 q^{82} - 96 q^{91} + 12 q^{94} - 4 q^{97}+O(q^{100}) \) 8 * q + 12 * q^7 - 4 * q^13 + 4 * q^16 - 20 * q^19 + 12 * q^22 + 12 * q^28 + 32 * q^31 + 12 * q^34 + 4 * q^37 - 12 * q^40 + 16 * q^43 - 20 * q^49 + 4 * q^52 - 12 * q^55 + 60 * q^58 - 16 * q^61 - 36 * q^67 - 12 * q^70 + 20 * q^76 - 20 * q^79 - 12 * q^82 - 96 * q^91 + 12 * q^94 - 4 * q^97

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