LMFDB - Embedded newform 666.2.be.c.467.1

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			467.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	666.467
Dual form			666.2.be.c.251.1

$q$-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	0.612721	−	0.790299i	$-0.290075\pi$
$5$	1.67303	+	0.448288i	0.748203	+	0.200480i	0.135482	+	0.990780i	$0.456742\pi$
$6$		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	$-0.620394\pi$
$11$	−2.44949			−0.738549			−0.369274	+	0.929320i	$0.620394\pi$
$12$		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	0.978961	−	0.204046i	$-0.0654092\pi$
$17$	0.120118	+	0.448288i	0.0291330	+	0.108726i	−0.949828	+	0.312772i	$0.898743\pi$
$18$		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	−0.914757	−	0.404004i	$-0.867618\pi$
$23$	−2.44949	+	2.44949i	−0.510754	+	0.510754i	0.404004	+	0.914757i	$0.367618\pi$
$24$		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	$-0.952656\pi$
$29$	−6.12372	−	6.12372i	−1.13715	−	1.13715i	−0.148188	−	0.988959i	$-0.547344\pi$
$30$		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	0.799003	−	0.601326i	$-0.205361\pi$
$41$	−0.776457	−	1.34486i	−0.121262	−	0.210032i	−0.920266	+	0.391294i	$0.872028\pi$
$42$		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	$0.100137\pi$
$47$			4.24264i			0.618853i	−0.950923	+	0.309426i	$0.899863\pi$
$48$		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	0.980537	−	0.196334i	$-0.0629036\pi$
$53$	9.46979	+	5.46739i	1.30078	+	0.751003i	0.320239	+	0.947337i	$0.396237\pi$
$54$		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	$0.0443876\pi$
$59$	1.55291	+	5.79555i	0.202172	+	0.754517i	−0.788121	+	0.615521i	$0.788946\pi$
$60$		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	−0.368813	−	0.929504i	$-0.620236\pi$
$71$	2.12132	−	1.22474i	0.251754	−	0.145350i	0.620567	+	0.784153i	$0.286902\pi$
$72$		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	0.975418	−	0.220361i	$-0.0707235\pi$
$83$	11.5911	+	6.69213i	1.27229	+	0.734557i	0.296871	+	0.954918i	$0.404057\pi$
$84$		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	0.159746	−	0.987158i	$-0.448933\pi$
$89$	7.46859	−	2.00120i	0.791669	−	0.212127i	0.631923	+	0.775031i	$0.282266\pi$
$90$		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	$-0.233330\pi$
$101$	14.9372			1.48630			0.743152	+	0.669122i	$0.233330\pi$
$102$		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	−0.225583	−	0.974224i	$-0.572429\pi$
$107$	5.22715	−	3.01790i	0.505328	−	0.291751i	0.730911	+	0.682473i	$0.239095\pi$
$108$		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	−0.994634	−	0.103455i	$-0.967010\pi$
$113$	−19.1798	+	5.13922i	−1.80429	+	0.483457i	−0.809651	+	0.586911i	$0.800344\pi$
$114$		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	0.709097	−	0.705111i	$-0.249103\pi$
$131$	19.1798	−	5.13922i	1.67575	−	0.449015i	0.966651	+	0.256096i	$0.0824362\pi$
$132$		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	$0.197733\pi$
$137$			13.6245i			1.16402i	−0.813182	+	0.582010i	$0.802267\pi$
$138$		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	$-0.846072\pi$
$149$		−	11.3509i		−	0.929900i	0.885337	−	0.464950i	$-0.153928\pi$
$150$		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	0.647652	−	0.761936i	$-0.275751\pi$
$167$	10.6945	+	2.86559i	0.827568	+	0.221746i	0.179915	+	0.983682i	$0.442418\pi$
$168$		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	$0.339962\pi$
$173$	−6.81225	+	11.7992i	−0.517926	+	0.897074i	−0.999783	+	0.0208240i	$0.993371\pi$
$174$		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	0.663345	−	0.748314i	$-0.269136\pi$
$179$	−1.13681	−	1.13681i	−0.0849693	−	0.0849693i	−0.748314	+	0.663345i	$0.769136\pi$
$180$		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	−0.682962	−	0.730453i	$-0.739309\pi$
$191$	0.656339	−	0.656339i	0.0474910	−	0.0474910i	0.730453	+	0.682962i	$0.239309\pi$
$192$		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	−0.195776	−	0.980649i	$-0.562723\pi$
$197$	−16.0418	−	9.26174i	−1.14293	−	0.659872i	−0.947155	+	0.320777i	$0.896056\pi$
$198$		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	−0.0695285	−	0.997580i	$-0.522149\pi$
$227$	−9.46979	−	2.53742i	−0.628532	−	0.168415i	−0.559003	+	0.829165i	$0.688816\pi$
$228$		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	$-0.626678\pi$
$233$	−11.8313			−0.775097			−0.387549	+	0.921849i	$0.626678\pi$
$234$		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	0.998472	−	0.0552646i	$-0.0176002\pi$
$239$	1.64085	+	6.12372i	0.106138	+	0.396111i	−0.892334	+	0.451375i	$0.850934\pi$
$240$		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	0.425815	−	0.904810i	$-0.359987\pi$
$251$	−7.58871	−	7.58871i	−0.478995	−	0.478995i	−0.904810	+	0.425815i	$0.859987\pi$
$252$		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	$-0.892100\pi$
$257$	−4.69093	−	17.5068i	−0.292612	−	1.09204i	0.650483	−	0.759521i	$-0.274566\pi$
$258$		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	$0.206013\pi$
$263$	14.9372	+	25.8719i	0.921066	+	1.59533i	0.123296	+	0.992370i	$0.460653\pi$
$264$		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	$-0.958714\pi$
$269$		−	4.24264i		−	0.258678i	0.991600	−	0.129339i	$-0.0412856\pi$
$270$		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	$0.0806386\pi$
$281$	4.27483	+	15.9539i	0.255015	+	0.951728i	−0.713068	+	0.701095i	$0.752695\pi$
$282$		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	−0.243527	−	0.969894i	$-0.578304\pi$
$293$	8.12493	−	4.69093i	0.474663	−	0.274047i	0.718190	+	0.695847i	$0.244971\pi$
$294$		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	−0.908273	−	0.418377i	$-0.862599\pi$
$311$	−26.2001	+	7.02030i	−1.48567	+	0.398085i	−0.577399	+	0.816462i	$0.695932\pi$
$312$		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	$-0.612543\pi$
$317$	11.3831	−	19.7160i	0.639336	−	1.10736i	0.985579	−	0.169218i	$-0.0541241\pi$
$318$		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	0.796785	−	0.604263i	$-0.206532\pi$
$347$	3.58630	+	3.58630i	0.192523	+	0.192523i	−0.604263	+	0.796785i	$0.706532\pi$
$348$		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	−0.578226	−	0.815877i	$-0.696255\pi$
$353$	−12.6078	+	3.37825i	−0.671046	+	0.179806i	−0.0928199	+	0.995683i	$0.529588\pi$
$354$		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	$0.0989499\pi$
$359$			11.5911i			0.611755i	−0.952071	+	0.305878i	$0.901050\pi$
$360$		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	−0.0655934	−	0.997846i	$-0.520894\pi$
$383$	−12.1595	−	3.25813i	−0.621322	−	0.166483i	−0.555729	+	0.831364i	$0.687561\pi$
$384$		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	−0.153257	−	0.988186i	$-0.548976\pi$
$389$	−15.3855	−	4.12252i	−0.780074	−	0.209020i	−0.626817	+	0.779166i	$0.715643\pi$
$390$		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	$-0.969136\pi$
$401$	−21.8695	−	21.8695i	−1.09211	−	1.09211i	−0.0968099	−	0.995303i	$-0.530864\pi$
$402$		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	0.964023	−	0.265817i	$-0.0856417\pi$
$419$	24.8874	+	14.3688i	1.21583	+	0.701960i	0.251807	+	0.967777i	$0.418975\pi$
$420$		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	−0.999726	−	0.0234290i	$-0.992542\pi$
$431$	−2.53742	+	9.46979i	−0.122223	+	0.456144i	0.877502	+	0.479573i	$0.159208\pi$
$432$		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	$-0.352939\pi$
$443$	18.7637			0.891491			0.445745	+	0.895160i	$0.352939\pi$
$444$		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	0.0589608	−	0.998260i	$-0.481221\pi$
$449$	−8.24504	−	2.20925i	−0.389108	−	0.104261i	−0.448069	+	0.893999i	$0.647888\pi$
$450$		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	0.948956	−	0.315409i	$-0.102142\pi$
$461$	−0.656339	−	2.44949i	−0.0305687	−	0.114084i	−0.979524	+	0.201325i	$0.935475\pi$
$462$		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	−0.0398109	−	0.999207i	$-0.512676\pi$
$467$	20.7327	−	20.7327i	0.959396	−	0.959396i	0.999207	+	0.0398109i	$0.0126756\pi$
$468$		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	$-0.736767\pi$
$479$	−10.0382	−	37.4631i	−0.458657	−	1.71173i	0.218452	−	0.975848i	$-0.429899\pi$
$480$		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	$0.0210600\pi$
$491$			2.92996i			0.132227i	−0.997812	+	0.0661137i	$0.978940\pi$
$492$		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	$0.0191702\pi$
$503$	3.67423	+	13.7124i	0.163826	+	0.611407i	−0.834361	+	0.551218i	$0.814163\pi$
$504$		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	−0.663260	−	0.748389i	$-0.730828\pi$
$509$	7.14042	−	12.3676i	0.316493	−	0.548183i	0.979754	+	0.200206i	$0.0641611\pi$
$510$		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	$0.00145867\pi$
$521$	11.5032	+	19.9241i	0.503963	+	0.872890i	−0.496026	+	0.868308i	$0.665208\pi$
$522$		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	0.279285	−	0.960208i	$-0.409903\pi$
$557$	23.6305	−	6.33178i	1.00126	−	0.268286i	0.721972	+	0.691922i	$0.243236\pi$
$558$		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	−0.137035	−	0.990566i	$-0.543757\pi$
$563$	20.2523	−	20.2523i	0.853531	−	0.853531i	0.990566	+	0.137035i	$0.0437574\pi$
$564$		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	0.486665	−	0.873588i	$-0.338213\pi$
$569$	−9.22955	−	9.22955i	−0.386923	−	0.386923i	−0.873588	+	0.486665i	$0.838213\pi$
$570$		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	−0.970706	−	0.240269i	$-0.922764\pi$
$587$	−0.240237	+	0.896575i	−0.00991563	+	0.0370056i	0.960791	+	0.277274i	$0.0894311\pi$
$588$		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	$-0.825428\pi$
$593$		−	25.3915i		−	1.04270i	0.853342	−	0.521351i	$-0.174572\pi$
$594$		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	0.490532	−	0.871423i	$-0.336802\pi$
$599$	36.4785	−	21.0609i	1.49047	−	0.860525i	0.999941	+	0.0108979i	$0.00346898\pi$
$600$		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	$-0.494652\pi$
$617$	21.7172	−	37.6154i	0.874303	−	1.51434i	0.857503	−	0.514479i	$-0.172014\pi$
$618$		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	0.932353	−	0.361549i	$-0.117752\pi$
$641$	27.4806	+	15.8659i	1.08542	+	0.626667i	0.153066	+	0.988216i	$0.451085\pi$
$642$		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	$0.353676\pi$
$647$	−9.88589	+	36.8947i	−0.388655	+	1.45048i	−0.832325	+	0.554288i	$0.812991\pi$
$648$		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	$0.267357\pi$
$653$	−7.22835	+	26.9766i	−0.282867	+	1.05567i	−0.950384	+	0.311080i	$0.899309\pi$
$654$		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	$-0.876007\pi$
$659$	−20.3166	−	35.1894i	−0.791423	−	1.37079i	0.133662	−	0.991027i	$-0.457326\pi$
$660$		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	$-0.388440\pi$
$677$	17.8671			0.686690			0.343345	+	0.939209i	$0.388440\pi$
$678$		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	$0.185905\pi$
$683$	10.1261	+	37.7912i	0.387466	+	1.44604i	−0.446778	+	0.894645i	$0.647429\pi$
$684$		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	0.984066	−	0.177806i	$-0.0568999\pi$
$701$	1.13681	+	4.24264i	0.0429368	+	0.160242i	−0.941129	+	0.338048i	$0.890233\pi$
$702$		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	$-0.995171\pi$
$719$	−40.5689	−	23.4225i	−1.51296	−	0.873510i	−0.513079	−	0.858341i	$-0.671495\pi$
$720$		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	0.902311	−	0.431086i	$-0.141870\pi$
$743$	2.12132	+	3.67423i	0.0778237	+	0.134795i	−0.824487	+	0.565881i	$0.808536\pi$
$744$		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	−0.808712	−	0.588205i	$-0.799835\pi$
$761$	2.89778	−	5.01910i	0.105044	−	0.181942i	0.913756	+	0.406263i	$0.133168\pi$
$762$		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	−0.783966	−	0.620804i	$-0.786806\pi$
$773$	−17.7470	+	10.2462i	−0.638316	+	0.368532i	0.145650	+	0.989336i	$0.453473\pi$
$774$		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	−0.793628	−	0.608404i	$-0.791810\pi$
$797$	−33.2204	+	8.90138i	−1.17673	+	0.315303i	−0.383100	+	0.923707i	$0.625143\pi$
$798$		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	−0.927213	−	0.374534i	$-0.877803\pi$
$809$	1.79315	−	6.69213i	0.0630438	−	0.235283i	0.990257	+	0.139251i	$0.0444695\pi$
$810$		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	−0.973554	−	0.228459i	$-0.926631\pi$
$821$	−36.1739	+	20.8850i	−1.26248	+	0.728893i	−0.288926	+	0.957352i	$0.593298\pi$
$822$		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	0.876996	−	0.480497i	$-0.159544\pi$
$827$	40.1528	+	10.7589i	1.39625	+	0.374124i	0.519253	+	0.854621i	$0.326210\pi$
$828$		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	$-0.568900\pi$
$839$	21.3891	−	37.0470i	0.738433	−	1.27900i	0.953201	−	0.302338i	$-0.0977671\pi$
$840$		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	−0.442550	−	0.896744i	$-0.645926\pi$
$857$	13.2963	−	13.2963i	0.454194	−	0.454194i	0.896744	+	0.442550i	$0.145926\pi$
$858$		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	$-0.866450\pi$
$863$	−50.6071	−	29.2180i	−1.72269	−	0.994593i	−0.809416	−	0.587236i	$-0.800216\pi$
$864$		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	$0.0776885\pi$
$881$	20.6126	+	35.7021i	0.694457	+	1.20283i	−0.275907	+	0.961184i	$0.588978\pi$
$882$		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	$-0.624463\pi$
$887$	−22.7017			−0.762250			−0.381125	+	0.924524i	$0.624463\pi$
$888$		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	−0.464092	−	0.885787i	$-0.653619\pi$
$911$	12.7279	−	12.7279i	0.421695	−	0.421695i	0.885787	+	0.464092i	$0.153619\pi$
$912$		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	$-0.963457\pi$
$929$	−18.1631	−	31.4595i	−0.595913	−	1.03215i	0.397505	−	0.917600i	$-0.369876\pi$
$930$		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	$0.0444311\pi$
$941$	49.2622	+	28.4416i	1.60590	+	0.927168i	0.615628	+	0.788037i	$0.288902\pi$
$942$		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	$0.146249\pi$
$947$	10.5187	+	39.2562i	0.341811	+	1.27566i	−0.554483	+	0.832195i	$0.687084\pi$
$948$		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	−0.979339	−	0.202224i	$-0.935183\pi$
$953$	−9.71003	+	16.8183i	−0.314539	+	0.544797i	0.664801	+	0.747021i	$0.268516\pi$
$954$		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	0.265082	−	0.964226i	$-0.414601\pi$
$977$	30.5307	−	8.18067i	0.976763	−	0.261723i	0.711681	+	0.702503i	$0.247934\pi$
$978$		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	−0.932493	−	0.361188i	$-0.882371\pi$
$983$	−4.81105	+	8.33298i	−0.153449	+	0.265781i	0.779044	+	0.626969i	$0.215705\pi$
$984$		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.467.1	yes	8
3.2	odd	2	inner	666.2.be.c.467.2	yes	8
37.29	odd	12	inner	666.2.be.c.251.2	yes	8
111.29	even	12	inner	666.2.be.c.251.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.be.c.251.1	✓	8	111.29	even	12	inner
666.2.be.c.251.2	yes	8	37.29	odd	12	inner
666.2.be.c.467.1	yes	8	1.1	even	1	trivial
666.2.be.c.467.2	yes	8	3.2	odd	2	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more