LMFDB - Embedded newform 666.2.be.a.125.1

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			125.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	666.125
Dual form			666.2.be.a.341.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.448288 + 1.67303i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.448288 + 1.67303i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.73205 q^{10} +3.86370 q^{11} +(-4.09808 - 1.09808i) q^{13} +(-1.41421 + 1.41421i) q^{14} +(0.500000 - 0.866025i) q^{16} +(5.53674 - 1.48356i) q^{17} +(1.00000 + 0.267949i) q^{19} +(-0.448288 - 1.67303i) q^{20} +(-1.00000 - 3.73205i) q^{22} +(3.86370 + 3.86370i) q^{23} +(1.73205 + 1.00000i) q^{25} +4.24264i q^{26} +(1.73205 + 1.00000i) q^{28} +(6.50266 - 6.50266i) q^{29} +(1.26795 + 1.26795i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-2.86603 - 4.96410i) q^{34} +(3.34607 - 0.896575i) q^{35} +(2.59808 - 5.50000i) q^{37} -1.03528i q^{38} +(-1.50000 + 0.866025i) q^{40} +(0.258819 + 0.448288i) q^{41} +(4.73205 - 4.73205i) q^{43} +(-3.34607 + 1.93185i) q^{44} +(2.73205 - 4.73205i) q^{46} +5.93426i q^{47} +(1.50000 - 2.59808i) q^{49} +(0.517638 - 1.93185i) q^{50} +(4.09808 - 1.09808i) q^{52} +(1.22474 + 0.707107i) q^{53} +(-1.73205 + 6.46410i) q^{55} +(0.517638 - 1.93185i) q^{56} +(-7.96410 - 4.59808i) q^{58} +(-9.14162 + 2.44949i) q^{59} +(-2.42820 + 9.06218i) q^{61} +(0.896575 - 1.55291i) q^{62} +1.00000i q^{64} +(3.67423 - 6.36396i) q^{65} +(9.00000 - 5.19615i) q^{67} +(-4.05317 + 4.05317i) q^{68} +(-1.73205 - 3.00000i) q^{70} +(-7.58871 + 4.38134i) q^{71} -4.00000i q^{73} +(-5.98502 - 1.08604i) q^{74} +(-1.00000 + 0.267949i) q^{76} +(-3.86370 - 6.69213i) q^{77} +(-13.9282 - 3.73205i) q^{79} +(1.22474 + 1.22474i) q^{80} +(0.366025 - 0.366025i) q^{82} +(-4.89898 - 2.82843i) q^{83} +9.92820i q^{85} +(-5.79555 - 3.34607i) q^{86} +(2.73205 + 2.73205i) q^{88} +(0.258819 + 0.965926i) q^{89} +(2.19615 + 8.19615i) q^{91} +(-5.27792 - 1.41421i) q^{92} +(5.73205 - 1.53590i) q^{94} +(-0.896575 + 1.55291i) q^{95} +(3.63397 - 3.63397i) q^{97} +(-2.89778 - 0.776457i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^7	$ 8 q - 8 q^{7} - 12 q^{13} + 4 q^{16} + 8 q^{19} - 8 q^{22} + 24 q^{31} - 16 q^{34} - 12 q^{40} + 24 q^{43} + 8 q^{46} + 12 q^{49} + 12 q^{52} - 36 q^{58} + 36 q^{61} + 72 q^{67} - 8 q^{76} - 56 q^{79} - 4 q^{82} + 8 q^{88} - 24 q^{91} + 32 q^{94} + 36 q^{97}+O(q^{100}) $ 8 * q - 8 * q^7 - 12 * q^13 + 4 * q^16 + 8 * q^19 - 8 * q^22 + 24 * q^31 - 16 * q^34 - 12 * q^40 + 24 * q^43 + 8 * q^46 + 12 * q^49 + 12 * q^52 - 36 * q^58 + 36 * q^61 + 72 * q^67 - 8 * q^76 - 56 * q^79 - 4 * q^82 + 8 * q^88 - 24 * q^91 + 32 * q^94 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.448288	+	1.67303i	−0.200480	+	0.748203i	0.790299	+	0.612721i	$0.209925\pi$
$5$	−0.448288	+	1.67303i	−0.200480	+	0.748203i	−0.990780	+	0.135482i	$0.956742\pi$
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.73205			0.547723
$11$	3.86370			1.16495			0.582475	−	0.812848i	$-0.302084\pi$
$11$	3.86370			1.16495			0.582475	+	0.812848i	$0.302084\pi$
$12$		0			0
$13$	−4.09808	−	1.09808i	−1.13660	−	0.304552i	−0.359018	−	0.933331i	$-0.616888\pi$
$13$	−4.09808	−	1.09808i	−1.13660	−	0.304552i	−0.777584	+	0.628779i	$0.783555\pi$
$14$	−1.41421	+	1.41421i	−0.377964	+	0.377964i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	5.53674	−	1.48356i	1.34286	−	0.359817i	0.485363	−	0.874313i	$-0.338688\pi$
$17$	5.53674	−	1.48356i	1.34286	−	0.359817i	0.857493	+	0.514496i	$0.172021\pi$
$18$		0			0
$19$	1.00000	+	0.267949i	0.229416	+	0.0614718i	0.371695	−	0.928355i	$-0.378777\pi$
$19$	1.00000	+	0.267949i	0.229416	+	0.0614718i	−0.142280	+	0.989826i	$0.545443\pi$
$20$	−0.448288	−	1.67303i	−0.100240	−	0.374101i
$21$		0			0
$22$	−1.00000	−	3.73205i	−0.213201	−	0.795676i
$23$	3.86370	+	3.86370i	0.805638	+	0.805638i	0.983970	−	0.178332i	$-0.0570703\pi$
$23$	3.86370	+	3.86370i	0.805638	+	0.805638i	−0.178332	+	0.983970i	$0.557070\pi$
$24$		0			0
$25$	1.73205	+	1.00000i	0.346410	+	0.200000i
$26$			4.24264i			0.832050i
$27$		0			0
$28$	1.73205	+	1.00000i	0.327327	+	0.188982i
$29$	6.50266	−	6.50266i	1.20751	−	1.20751i	0.235684	−	0.971830i	$-0.424267\pi$
$29$	6.50266	−	6.50266i	1.20751	−	1.20751i	0.971830	−	0.235684i	$-0.0757331\pi$
$30$		0			0
$31$	1.26795	+	1.26795i	0.227730	+	0.227730i	0.811744	−	0.584014i	$-0.198519\pi$
$31$	1.26795	+	1.26795i	0.227730	+	0.227730i	−0.584014	+	0.811744i	$0.698519\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$		0			0
$34$	−2.86603	−	4.96410i	−0.491519	−	0.851336i
$35$	3.34607	−	0.896575i	0.565588	−	0.151549i
$36$		0			0
$37$	2.59808	−	5.50000i	0.427121	−	0.904194i
$37$	2.59808	−	5.50000i	0.427121	−	0.904194i
$38$		−	1.03528i		−	0.167944i
$39$		0			0
$40$	−1.50000	+	0.866025i	−0.237171	+	0.136931i
$41$	0.258819	+	0.448288i	0.0404207	+	0.0700108i	0.885528	−	0.464586i	$-0.153797\pi$
$41$	0.258819	+	0.448288i	0.0404207	+	0.0700108i	−0.845107	+	0.534597i	$0.820464\pi$
$42$		0			0
$43$	4.73205	−	4.73205i	0.721631	−	0.721631i	−0.247306	−	0.968937i	$-0.579545\pi$
$43$	4.73205	−	4.73205i	0.721631	−	0.721631i	0.968937	+	0.247306i	$0.0795454\pi$
$44$	−3.34607	+	1.93185i	−0.504438	+	0.291238i
$45$		0			0
$46$	2.73205	−	4.73205i	0.402819	−	0.697703i
$47$			5.93426i			0.865600i	0.901490	+	0.432800i	$0.142474\pi$
$47$			5.93426i			0.865600i	−0.901490	+	0.432800i	$0.857526\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	0.517638	−	1.93185i	0.0732051	−	0.273205i
$51$		0			0
$52$	4.09808	−	1.09808i	0.568301	−	0.152276i
$53$	1.22474	+	0.707107i	0.168232	+	0.0971286i	0.581752	−	0.813366i	$-0.302368\pi$
$53$	1.22474	+	0.707107i	0.168232	+	0.0971286i	−0.413520	+	0.910495i	$0.635701\pi$
$54$		0			0
$55$	−1.73205	+	6.46410i	−0.233550	+	0.871619i
$56$	0.517638	−	1.93185i	0.0691723	−	0.258155i
$57$		0			0
$58$	−7.96410	−	4.59808i	−1.04574	−	0.603757i
$59$	−9.14162	+	2.44949i	−1.19014	+	0.318896i	−0.798940	−	0.601410i	$-0.794606\pi$
$59$	−9.14162	+	2.44949i	−1.19014	+	0.318896i	−0.391197	+	0.920307i	$0.627939\pi$
$60$		0			0
$61$	−2.42820	+	9.06218i	−0.310900	+	1.16029i	0.616847	+	0.787083i	$0.288410\pi$
$61$	−2.42820	+	9.06218i	−0.310900	+	1.16029i	−0.927747	+	0.373210i	$0.878257\pi$
$62$	0.896575	−	1.55291i	0.113865	−	0.197220i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	3.67423	−	6.36396i	0.455733	−	0.789352i
$66$		0			0
$67$	9.00000	−	5.19615i	1.09952	−	0.634811i	0.163429	−	0.986555i	$-0.447745\pi$
$67$	9.00000	−	5.19615i	1.09952	−	0.634811i	0.936096	+	0.351744i	$0.114411\pi$
$68$	−4.05317	+	4.05317i	−0.491519	+	0.491519i
$69$		0			0
$70$	−1.73205	−	3.00000i	−0.207020	−	0.358569i
$71$	−7.58871	+	4.38134i	−0.900614	+	0.519970i	−0.877399	−	0.479761i	$-0.840723\pi$
$71$	−7.58871	+	4.38134i	−0.900614	+	0.519970i	−0.0232145	+	0.999731i	$0.507390\pi$
$72$		0			0
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$	−5.98502	−	1.08604i	−0.695745	−	0.126250i
$75$		0			0
$76$	−1.00000	+	0.267949i	−0.114708	+	0.0307359i
$77$	−3.86370	−	6.69213i	−0.440310	−	0.762639i
$78$		0			0
$79$	−13.9282	−	3.73205i	−1.56705	−	0.419889i	−0.632160	−	0.774838i	$-0.717831\pi$
$79$	−13.9282	−	3.73205i	−1.56705	−	0.419889i	−0.934885	+	0.354950i	$0.884498\pi$
$80$	1.22474	+	1.22474i	0.136931	+	0.136931i
$81$		0			0
$82$	0.366025	−	0.366025i	0.0404207	−	0.0404207i
$83$	−4.89898	−	2.82843i	−0.537733	−	0.310460i	0.206427	−	0.978462i	$-0.433816\pi$
$83$	−4.89898	−	2.82843i	−0.537733	−	0.310460i	−0.744160	+	0.668002i	$0.767150\pi$
$84$		0			0
$85$			9.92820i			1.07686i
$86$	−5.79555	−	3.34607i	−0.624951	−	0.360815i
$87$		0			0
$88$	2.73205	+	2.73205i	0.291238	+	0.291238i
$89$	0.258819	+	0.965926i	0.0274348	+	0.102388i	0.978286	−	0.207261i	$-0.0664550\pi$
$89$	0.258819	+	0.965926i	0.0274348	+	0.102388i	−0.950851	+	0.309649i	$0.899788\pi$
$90$		0			0
$91$	2.19615	+	8.19615i	0.230219	+	0.859190i
$92$	−5.27792	−	1.41421i	−0.550261	−	0.147442i
$93$		0			0
$94$	5.73205	−	1.53590i	0.591216	−	0.158416i
$95$	−0.896575	+	1.55291i	−0.0919867	+	0.159326i
$96$		0			0
$97$	3.63397	−	3.63397i	0.368974	−	0.368974i	−0.498129	−	0.867103i	$-0.665979\pi$
$97$	3.63397	−	3.63397i	0.368974	−	0.368974i	0.867103	+	0.498129i	$0.165979\pi$
$98$	−2.89778	−	0.776457i	−0.292720	−	0.0784340i
$99$		0			0
$100$	−2.00000			−0.200000
$101$	19.4572			1.93607			0.968033	−	0.250824i	$-0.0807015\pi$
$101$	19.4572			1.93607			0.968033	+	0.250824i	$0.0807015\pi$
$102$		0			0
$103$	−8.19615	−	8.19615i	−0.807591	−	0.807591i	0.176678	−	0.984269i	$-0.443465\pi$
$103$	−8.19615	−	8.19615i	−0.807591	−	0.807591i	−0.984269	+	0.176678i	$0.943465\pi$
$104$	−2.12132	−	3.67423i	−0.208013	−	0.360288i
$105$		0			0
$106$	0.366025	−	1.36603i	0.0355515	−	0.132680i
$107$	6.93237	−	4.00240i	0.670177	−	0.386927i	−0.125967	−	0.992034i	$-0.540203\pi$
$107$	6.93237	−	4.00240i	0.670177	−	0.386927i	0.796144	+	0.605107i	$0.206870\pi$
$108$		0			0
$109$	4.42820	+	16.5263i	0.424145	+	1.58293i	0.765783	+	0.643099i	$0.222352\pi$
$109$	4.42820	+	16.5263i	0.424145	+	1.58293i	−0.341638	+	0.939832i	$0.610982\pi$
$110$	6.69213			0.638070
$111$		0			0
$112$	−2.00000			−0.188982
$113$	−2.58819	−	9.65926i	−0.243476	−	0.908667i	−0.974143	−	0.225932i	$-0.927457\pi$
$113$	−2.58819	−	9.65926i	−0.243476	−	0.908667i	0.730667	−	0.682734i	$-0.239209\pi$
$114$		0			0
$115$	−8.19615	+	4.73205i	−0.764295	+	0.441266i
$116$	−2.38014	+	8.88280i	−0.220990	+	0.824747i
$117$		0			0
$118$	4.73205	+	8.19615i	0.435621	+	0.754517i
$119$	−8.10634	−	8.10634i	−0.743107	−	0.743107i
$120$		0			0
$121$	3.92820			0.357109
$122$	9.38186			0.849393
$123$		0			0
$124$	−1.73205	−	0.464102i	−0.155543	−	0.0416776i
$125$	−8.57321	+	8.57321i	−0.766812	+	0.766812i
$126$		0			0
$127$	−3.26795	+	5.66025i	−0.289984	+	0.502266i	−0.973805	−	0.227383i	$-0.926983\pi$
$127$	−3.26795	+	5.66025i	−0.289984	+	0.502266i	0.683822	+	0.729649i	$0.260317\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$		0			0
$130$	−7.09808	−	1.90192i	−0.622542	−	0.166810i
$131$	3.20736	+	11.9700i	0.280229	+	1.04583i	0.952256	+	0.305301i	$0.0987572\pi$
$131$	3.20736	+	11.9700i	0.280229	+	1.04583i	−0.672027	+	0.740527i	$0.734576\pi$
$132$		0			0
$133$	−0.535898	−	2.00000i	−0.0464683	−	0.173422i
$134$	−7.34847	−	7.34847i	−0.634811	−	0.634811i
$135$		0			0
$136$	4.96410	+	2.86603i	0.425668	+	0.245760i
$137$			5.13922i			0.439073i	0.975604	+	0.219536i	$0.0704545\pi$
$137$			5.13922i			0.439073i	−0.975604	+	0.219536i	$0.929546\pi$
$138$		0			0
$139$	6.00000	+	3.46410i	0.508913	+	0.293821i	0.732387	−	0.680889i	$-0.238406\pi$
$139$	6.00000	+	3.46410i	0.508913	+	0.293821i	−0.223474	+	0.974710i	$0.571740\pi$
$140$	−2.44949	+	2.44949i	−0.207020	+	0.207020i
$141$		0			0
$142$	6.19615	+	6.19615i	0.519970	+	0.519970i
$143$	−15.8338	−	4.24264i	−1.32408	−	0.354787i
$144$		0			0
$145$	7.96410	+	13.7942i	0.661383	+	1.14555i
$146$	−3.86370	+	1.03528i	−0.319762	+	0.0856801i
$147$		0			0
$148$	0.500000	+	6.06218i	0.0410997	+	0.498308i
$149$			16.8319i			1.37892i	0.724324	+	0.689460i	$0.242152\pi$
$149$			16.8319i			1.37892i	−0.724324	+	0.689460i	$0.757848\pi$
$150$		0			0
$151$	−8.19615	+	4.73205i	−0.666993	+	0.385089i	−0.794936	−	0.606693i	$-0.792496\pi$
$151$	−8.19615	+	4.73205i	−0.666993	+	0.385089i	0.127943	+	0.991782i	$0.459163\pi$
$152$	0.517638	+	0.896575i	0.0419860	+	0.0727219i
$153$		0			0
$154$	−5.46410	+	5.46410i	−0.440310	+	0.440310i
$155$	−2.68973	+	1.55291i	−0.216044	+	0.124733i
$156$		0			0
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$			14.4195i			1.14716i
$159$		0			0
$160$	0.866025	−	1.50000i	0.0684653	−	0.118585i
$161$	2.82843	−	10.5558i	0.222911	−	0.831916i
$162$		0			0
$163$	−6.46410	+	1.73205i	−0.506308	+	0.135665i	−0.502926	−	0.864330i	$-0.667743\pi$
$163$	−6.46410	+	1.73205i	−0.506308	+	0.135665i	−0.00338172	+	0.999994i	$0.501076\pi$
$164$	−0.448288	−	0.258819i	−0.0350054	−	0.0202104i
$165$		0			0
$166$	−1.46410	+	5.46410i	−0.113636	+	0.424097i
$167$	−0.933740	+	3.48477i	−0.0722550	+	0.269659i	−0.992597	−	0.121456i	$-0.961244\pi$
$167$	−0.933740	+	3.48477i	−0.0722550	+	0.269659i	0.920342	+	0.391115i	$0.127910\pi$
$168$		0			0
$169$	4.33013	+	2.50000i	0.333087	+	0.192308i
$170$	9.58991	−	2.56961i	0.735512	−	0.197080i
$171$		0			0
$172$	−1.73205	+	6.46410i	−0.132068	+	0.492883i
$173$	5.72620	−	9.91808i	0.435355	−	0.754057i	−0.561969	−	0.827158i	$-0.689956\pi$
$173$	5.72620	−	9.91808i	0.435355	−	0.754057i	0.997325	+	0.0731006i	$0.0232894\pi$
$174$		0			0
$175$		−	4.00000i		−	0.302372i
$176$	1.93185	−	3.34607i	0.145619	−	0.252219i
$177$		0			0
$178$	0.866025	−	0.500000i	0.0649113	−	0.0374766i
$179$	9.52056	−	9.52056i	0.711600	−	0.711600i	−0.255270	−	0.966870i	$-0.582164\pi$
$179$	9.52056	−	9.52056i	0.711600	−	0.711600i	0.966870	+	0.255270i	$0.0821643\pi$
$180$		0			0
$181$	−6.96410	−	12.0622i	−0.517638	−	0.896575i	−0.999790	−	0.0204873i	$-0.993478\pi$
$181$	−6.96410	−	12.0622i	−0.517638	−	0.896575i	0.482153	−	0.876087i	$-0.339855\pi$
$182$	7.34847	−	4.24264i	0.544705	−	0.314485i
$183$		0			0
$184$			5.46410i			0.402819i
$185$	8.03699	+	6.81225i	0.590892	+	0.500846i
$186$		0			0
$187$	21.3923	−	5.73205i	1.56436	−	0.419169i
$188$	−2.96713	−	5.13922i	−0.216400	−	0.374816i
$189$		0			0
$190$	1.73205	+	0.464102i	0.125656	+	0.0336695i
$191$	−1.79315	−	1.79315i	−0.129748	−	0.129748i	0.639251	−	0.768998i	$-0.279245\pi$
$191$	−1.79315	−	1.79315i	−0.129748	−	0.129748i	−0.768998	+	0.639251i	$0.779245\pi$
$192$		0			0
$193$	−6.16987	+	6.16987i	−0.444117	+	0.444117i	−0.893393	−	0.449276i	$-0.851682\pi$
$193$	−6.16987	+	6.16987i	−0.444117	+	0.444117i	0.449276	+	0.893393i	$0.351682\pi$
$194$	−4.45069	−	2.56961i	−0.319541	−	0.184487i
$195$		0			0
$196$			3.00000i			0.214286i
$197$	−1.67303	−	0.965926i	−0.119199	−	0.0688194i	0.439215	−	0.898382i	$-0.355257\pi$
$197$	−1.67303	−	0.965926i	−0.119199	−	0.0688194i	−0.558414	+	0.829562i	$0.688590\pi$
$198$		0			0
$199$	−9.26795	−	9.26795i	−0.656987	−	0.656987i	0.297679	−	0.954666i	$-0.403788\pi$
$199$	−9.26795	−	9.26795i	−0.656987	−	0.656987i	−0.954666	+	0.297679i	$0.903788\pi$
$200$	0.517638	+	1.93185i	0.0366025	+	0.136603i
$201$		0			0
$202$	−5.03590	−	18.7942i	−0.354325	−	1.32236i
$203$	−17.7656	−	4.76028i	−1.24690	−	0.334106i
$204$		0			0
$205$	−0.866025	+	0.232051i	−0.0604858	+	0.0162071i
$206$	−5.79555	+	10.0382i	−0.403795	+	0.699394i
$207$		0			0
$208$	−3.00000	+	3.00000i	−0.208013	+	0.208013i
$209$	3.86370	+	1.03528i	0.267258	+	0.0716116i
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	−1.41421			−0.0971286
$213$		0			0
$214$	−5.66025	−	5.66025i	−0.386927	−	0.386927i
$215$	5.79555	+	10.0382i	0.395254	+	0.684599i
$216$		0			0
$217$	0.928203	−	3.46410i	0.0630105	−	0.235159i
$218$	14.8171	−	8.55463i	1.00354	−	0.579393i
$219$		0			0
$220$	−1.73205	−	6.46410i	−0.116775	−	0.435810i
$221$	−24.3190			−1.63588
$222$		0			0
$223$	−8.39230			−0.561990			−0.280995	−	0.959709i	$-0.590664\pi$
$223$	−8.39230			−0.561990			−0.280995	+	0.959709i	$0.590664\pi$
$224$	0.517638	+	1.93185i	0.0345861	+	0.129077i
$225$		0			0
$226$	−8.66025	+	5.00000i	−0.576072	+	0.332595i
$227$	0.240237	−	0.896575i	0.0159451	−	0.0595078i	−0.957495	−	0.288450i	$-0.906860\pi$
$227$	0.240237	−	0.896575i	0.0159451	−	0.0595078i	0.973440	+	0.228942i	$0.0735267\pi$
$228$		0			0
$229$	10.0622	+	17.4282i	0.664927	+	1.15169i	0.979305	+	0.202390i	$0.0648709\pi$
$229$	10.0622	+	17.4282i	0.664927	+	1.15169i	−0.314378	+	0.949298i	$0.601796\pi$
$230$	6.69213	+	6.69213i	0.441266	+	0.441266i
$231$		0			0
$232$	9.19615			0.603757
$233$	−1.55291			−0.101735			−0.0508674	−	0.998705i	$-0.516199\pi$
$233$	−1.55291			−0.101735			−0.0508674	+	0.998705i	$0.516199\pi$
$234$		0			0
$235$	−9.92820	−	2.66025i	−0.647645	−	0.173536i
$236$	6.69213	−	6.69213i	0.435621	−	0.435621i
$237$		0			0
$238$	−5.73205	+	9.92820i	−0.371554	+	0.643550i
$239$	0.138701	−	0.0371647i	0.00897180	−	0.00240399i	−0.254330	−	0.967117i	$-0.581855\pi$
$239$	0.138701	−	0.0371647i	0.00897180	−	0.00240399i	0.263302	+	0.964713i	$0.415188\pi$
$240$		0			0
$241$	−21.0263	−	5.63397i	−1.35442	−	0.362916i	−0.492657	−	0.870224i	$-0.663974\pi$
$241$	−21.0263	−	5.63397i	−1.35442	−	0.362916i	−0.861765	+	0.507308i	$0.830641\pi$
$242$	−1.01669	−	3.79435i	−0.0653556	−	0.243910i
$243$		0			0
$244$	−2.42820	−	9.06218i	−0.155450	−	0.580146i
$245$	3.67423	+	3.67423i	0.234738	+	0.234738i
$246$		0			0
$247$	−3.80385	−	2.19615i	−0.242033	−	0.139738i
$248$			1.79315i			0.113865i
$249$		0			0
$250$	10.5000	+	6.06218i	0.664078	+	0.383406i
$251$	−20.7327	+	20.7327i	−1.30864	+	1.30864i	−0.386240	+	0.922398i	$0.626226\pi$
$251$	−20.7327	+	20.7327i	−1.30864	+	1.30864i	−0.922398	+	0.386240i	$0.873774\pi$
$252$		0			0
$253$	14.9282	+	14.9282i	0.938528	+	0.938528i
$254$	6.31319	+	1.69161i	0.396125	+	0.106141i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.4865	+	2.80984i	−0.654129	+	0.175273i	−0.570595	−	0.821232i	$-0.693287\pi$
$257$	−10.4865	+	2.80984i	−0.654129	+	0.175273i	−0.0835339	+	0.996505i	$0.526621\pi$
$258$		0			0
$259$	−12.1244	+	1.00000i	−0.753371	+	0.0621370i
$260$			7.34847i			0.455733i
$261$		0			0
$262$	10.7321	−	6.19615i	0.663028	−	0.382800i
$263$	−8.10634	−	14.0406i	−0.499859	−	0.865780i	0.500141	−	0.865944i	$-0.333281\pi$
$263$	−8.10634	−	14.0406i	−0.499859	−	0.865780i	−1.00000		0.000163285i	$0.999948\pi$
$264$		0			0
$265$	−1.73205	+	1.73205i	−0.106399	+	0.106399i
$266$	−1.79315	+	1.03528i	−0.109945	+	0.0634769i
$267$		0			0
$268$	−5.19615	+	9.00000i	−0.317406	+	0.549762i
$269$		−	7.62587i		−	0.464958i	−0.972601	−	0.232479i	$-0.925316\pi$
$269$		−	7.62587i		−	0.464958i	0.972601	−	0.232479i	$-0.0746836\pi$
$270$		0			0
$271$	11.9282	−	20.6603i	0.724587	−	1.25502i	−0.234557	−	0.972102i	$-0.575364\pi$
$271$	11.9282	−	20.6603i	0.724587	−	1.25502i	0.959144	−	0.282919i	$-0.0913027\pi$
$272$	1.48356	−	5.53674i	0.0899543	−	0.335714i
$273$		0			0
$274$	4.96410	−	1.33013i	0.299892	−	0.0803559i
$275$	6.69213	+	3.86370i	0.403551	+	0.232990i
$276$		0			0
$277$	5.89230	−	21.9904i	0.354034	−	1.32127i	−0.527661	−	0.849455i	$-0.676931\pi$
$277$	5.89230	−	21.9904i	0.354034	−	1.32127i	0.881695	−	0.471819i	$-0.156402\pi$
$278$	1.79315	−	6.69213i	0.107546	−	0.401367i
$279$		0			0
$280$	3.00000	+	1.73205i	0.179284	+	0.103510i
$281$	7.79676	−	2.08913i	0.465116	−	0.124627i	−0.0186479	−	0.999826i	$-0.505936\pi$
$281$	7.79676	−	2.08913i	0.465116	−	0.124627i	0.483763	+	0.875199i	$0.339270\pi$
$282$		0			0
$283$	−3.58846	+	13.3923i	−0.213312	+	0.796090i	0.773442	+	0.633867i	$0.218533\pi$
$283$	−3.58846	+	13.3923i	−0.213312	+	0.796090i	−0.986754	+	0.162223i	$0.948134\pi$
$284$	4.38134	−	7.58871i	0.259985	−	0.450307i
$285$		0			0
$286$			16.3923i			0.969297i
$287$	0.517638	−	0.896575i	0.0305552	−	0.0529232i
$288$		0			0
$289$	13.7321	−	7.92820i	0.807768	−	0.466365i
$290$	11.2629	−	11.2629i	0.661383	−	0.661383i
$291$		0			0
$292$	2.00000	+	3.46410i	0.117041	+	0.202721i
$293$	10.2462	−	5.91567i	0.598592	−	0.345597i	−0.169895	−	0.985462i	$-0.554343\pi$
$293$	10.2462	−	5.91567i	0.598592	−	0.345597i	0.768488	+	0.639865i	$0.221010\pi$
$294$		0			0
$295$		−	16.3923i		−	0.954397i
$296$	5.72620	−	2.05197i	0.332829	−	0.119268i
$297$		0			0
$298$	16.2583	−	4.35641i	0.941820	−	0.252360i
$299$	−11.5911	−	20.0764i	−0.670331	−	1.16105i
$300$		0			0
$301$	−12.9282	−	3.46410i	−0.745169	−	0.199667i
$302$	6.69213	+	6.69213i	0.385089	+	0.385089i
$303$		0			0
$304$	0.732051	−	0.732051i	0.0419860	−	0.0419860i
$305$	−14.0728	−	8.12493i	−0.805805	−	0.465232i
$306$		0			0
$307$		−	27.8564i		−	1.58985i	−0.606708	−	0.794925i	$-0.707510\pi$
$307$		−	27.8564i		−	1.58985i	0.606708	−	0.794925i	$-0.292490\pi$
$308$	6.69213	+	3.86370i	0.381320	+	0.220155i
$309$		0			0
$310$	2.19615	+	2.19615i	0.124733	+	0.124733i
$311$	7.48717	+	27.9425i	0.424558	+	1.58447i	0.764885	+	0.644167i	$0.222796\pi$
$311$	7.48717	+	27.9425i	0.424558	+	1.58447i	−0.340327	+	0.940307i	$0.610538\pi$
$312$		0			0
$313$	5.72243	+	21.3564i	0.323451	+	1.20714i	0.915860	+	0.401498i	$0.131510\pi$
$313$	5.72243	+	21.3564i	0.323451	+	1.20714i	−0.592409	+	0.805637i	$0.701823\pi$
$314$	6.76148	+	1.81173i	0.381572	+	0.102242i
$315$		0			0
$316$	13.9282	−	3.73205i	0.783523	−	0.209944i
$317$	7.22835	−	12.5199i	0.405985	−	0.703186i	−0.588451	−	0.808533i	$-0.700262\pi$
$317$	7.22835	−	12.5199i	0.405985	−	0.703186i	0.994436	+	0.105347i	$0.0335953\pi$
$318$		0			0
$319$	25.1244	−	25.1244i	1.40669	−	1.40669i
$320$	−1.67303	−	0.448288i	−0.0935254	−	0.0250600i
$321$		0			0
$322$	−10.9282			−0.609005
$323$	5.93426			0.330191
$324$		0			0
$325$	−6.00000	−	6.00000i	−0.332820	−	0.332820i
$326$	3.34607	+	5.79555i	0.185321	+	0.320986i
$327$		0			0
$328$	−0.133975	+	0.500000i	−0.00739751	+	0.0276079i
$329$	10.2784	−	5.93426i	0.566668	−	0.327166i
$330$		0			0
$331$	−5.46410	−	20.3923i	−0.300334	−	1.12086i	−0.936888	−	0.349630i	$-0.886307\pi$
$331$	−5.46410	−	20.3923i	−0.300334	−	1.12086i	0.636554	−	0.771232i	$-0.280359\pi$
$332$	5.65685			0.310460
$333$		0			0
$334$	3.60770			0.197404
$335$	4.65874	+	17.3867i	0.254534	+	0.949935i
$336$		0			0
$337$	24.3564	−	14.0622i	1.32678	−	0.766016i	0.341978	−	0.939708i	$-0.388903\pi$
$337$	24.3564	−	14.0622i	1.32678	−	0.766016i	0.984800	+	0.173692i	$0.0555698\pi$
$338$	1.29410	−	4.82963i	0.0703895	−	0.262697i
$339$		0			0
$340$	−4.96410	−	8.59808i	−0.269216	−	0.466296i
$341$	4.89898	+	4.89898i	0.265295	+	0.265295i
$342$		0			0
$343$	−20.0000			−1.07990
$344$	6.69213			0.360815
$345$		0			0
$346$	−11.0622	−	2.96410i	−0.594706	−	0.159351i
$347$	−16.7675	+	16.7675i	−0.900126	+	0.900126i	−0.995447	−	0.0953206i	$-0.969612\pi$
$347$	−16.7675	+	16.7675i	−0.900126	+	0.900126i	0.0953206	+	0.995447i	$0.469612\pi$
$348$		0			0
$349$	−3.52628	+	6.10770i	−0.188757	+	0.326937i	−0.944836	−	0.327543i	$-0.893779\pi$
$349$	−3.52628	+	6.10770i	−0.188757	+	0.326937i	0.756079	+	0.654481i	$0.227113\pi$
$350$	−3.86370	+	1.03528i	−0.206524	+	0.0553378i
$351$		0			0
$352$	−3.73205	−	1.00000i	−0.198919	−	0.0533002i
$353$	−2.53244	−	9.45121i	−0.134788	−	0.503037i	−0.999999	−	0.00162788i	$-0.999482\pi$
$353$	−2.53244	−	9.45121i	−0.134788	−	0.503037i	0.865210	−	0.501409i	$-0.167185\pi$
$354$		0			0
$355$	−3.92820	−	14.6603i	−0.208487	−	0.778085i
$356$	−0.707107	−	0.707107i	−0.0374766	−	0.0374766i
$357$		0			0
$358$	−11.6603	−	6.73205i	−0.616264	−	0.355800i
$359$			23.3853i			1.23423i	0.786874	+	0.617114i	$0.211698\pi$
$359$			23.3853i			1.23423i	−0.786874	+	0.617114i	$0.788302\pi$
$360$		0			0
$361$	−15.5263	−	8.96410i	−0.817173	−	0.471795i
$362$	−9.84873	+	9.84873i	−0.517638	+	0.517638i
$363$		0			0
$364$	−6.00000	−	6.00000i	−0.314485	−	0.314485i
$365$	6.69213	+	1.79315i	0.350282	+	0.0938578i
$366$		0			0
$367$	−15.4641	−	26.7846i	−0.807220	−	1.39815i	−0.914782	−	0.403947i	$-0.867638\pi$
$367$	−15.4641	−	26.7846i	−0.807220	−	1.39815i	0.107563	−	0.994198i	$-0.465695\pi$
$368$	5.27792	−	1.41421i	0.275130	−	0.0737210i
$369$		0			0
$370$	4.50000	−	9.52628i	0.233944	−	0.495248i
$371$		−	2.82843i		−	0.146845i
$372$		0			0
$373$	19.9641	−	11.5263i	1.03370	−	0.596808i	0.115659	−	0.993289i	$-0.463102\pi$
$373$	19.9641	−	11.5263i	1.03370	−	0.596808i	0.918043	+	0.396481i	$0.129769\pi$
$374$	−11.0735	−	19.1798i	−0.572596	−	0.991765i
$375$		0			0
$376$	−4.19615	+	4.19615i	−0.216400	+	0.216400i
$377$	−33.7888	+	19.5080i	−1.74021	+	1.00471i
$378$		0			0
$379$	−16.3205	+	28.2679i	−0.838328	+	1.45203i	0.0529634	+	0.998596i	$0.483133\pi$
$379$	−16.3205	+	28.2679i	−0.838328	+	1.45203i	−0.891292	+	0.453431i	$0.850200\pi$
$380$		−	1.79315i		−	0.0919867i
$381$		0			0
$382$	−1.26795	+	2.19615i	−0.0648739	+	0.112365i
$383$	−4.65874	+	17.3867i	−0.238051	+	0.888417i	0.738699	+	0.674035i	$0.235440\pi$
$383$	−4.65874	+	17.3867i	−0.238051	+	0.888417i	−0.976750	+	0.214382i	$0.931226\pi$
$384$		0			0
$385$	12.9282	−	3.46410i	0.658882	−	0.176547i
$386$	7.55652	+	4.36276i	0.384617	+	0.222059i
$387$		0			0
$388$	−1.33013	+	4.96410i	−0.0675270	+	0.252014i
$389$	7.46859	−	27.8731i	0.378672	−	1.41322i	−0.469232	−	0.883075i	$-0.655469\pi$
$389$	7.46859	−	27.8731i	0.378672	−	1.41322i	0.847904	−	0.530150i	$-0.177864\pi$
$390$		0			0
$391$	27.1244	+	15.6603i	1.37174	+	0.791973i
$392$	2.89778	−	0.776457i	0.146360	−	0.0392170i
$393$		0			0
$394$	−0.500000	+	1.86603i	−0.0251896	+	0.0940090i
$395$	12.4877	−	21.6293i	0.628324	−	1.08829i
$396$		0			0
$397$		−	37.9282i		−	1.90356i	−0.306778	−	0.951781i	$-0.599251\pi$
$397$		−	37.9282i		−	1.90356i	0.306778	−	0.951781i	$-0.400749\pi$
$398$	−6.55343	+	11.3509i	−0.328494	+	0.568968i
$399$		0			0
$400$	1.73205	−	1.00000i	0.0866025	−	0.0500000i
$401$	28.0812	−	28.0812i	1.40231	−	1.40231i	0.609596	−	0.792713i	$-0.291332\pi$
$401$	28.0812	−	28.0812i	1.40231	−	1.40231i	0.792713	−	0.609596i	$-0.208668\pi$
$402$		0			0
$403$	−3.80385	−	6.58846i	−0.189483	−	0.328194i
$404$	−16.8504	+	9.72861i	−0.838341	+	0.484016i
$405$		0			0
$406$			18.3923i			0.912795i
$407$	10.0382	−	21.2504i	0.497575	−	1.05334i
$408$		0			0
$409$	−0.401924	+	0.107695i	−0.0198739	+	0.00532518i	−0.268742	−	0.963212i	$-0.586608\pi$
$409$	−0.401924	+	0.107695i	−0.0198739	+	0.00532518i	0.248868	+	0.968537i	$0.419941\pi$
$410$	0.448288	+	0.776457i	0.0221394	+	0.0383465i
$411$		0			0
$412$	11.1962	+	3.00000i	0.551595	+	0.147799i
$413$	13.3843	+	13.3843i	0.658596	+	0.658596i
$414$		0			0
$415$	6.92820	−	6.92820i	0.340092	−	0.340092i
$416$	3.67423	+	2.12132i	0.180144	+	0.104006i
$417$		0			0
$418$		−	4.00000i		−	0.195646i
$419$	−2.20925	−	1.27551i	−0.107929	−	0.0623129i	0.445064	−	0.895499i	$-0.353181\pi$
$419$	−2.20925	−	1.27551i	−0.107929	−	0.0623129i	−0.552993	+	0.833186i	$0.686514\pi$
$420$		0			0
$421$	20.4186	+	20.4186i	0.995141	+	0.995141i	0.999988	−	0.00484734i	$-0.00154296\pi$
$421$	20.4186	+	20.4186i	0.995141	+	0.995141i	−0.00484734	+	0.999988i	$0.501543\pi$
$422$	−3.62347	−	13.5230i	−0.176388	−	0.658287i
$423$		0			0
$424$	0.366025	+	1.36603i	0.0177758	+	0.0663401i
$425$	11.0735	+	2.96713i	0.537142	+	0.143927i
$426$		0			0
$427$	18.1244	−	4.85641i	0.877099	−	0.235018i
$428$	−4.00240	+	6.93237i	−0.193464	+	0.335089i
$429$		0			0
$430$	8.19615	−	8.19615i	0.395254	−	0.395254i
$431$	−10.0382	−	2.68973i	−0.483523	−	0.129560i	0.00881965	−	0.999961i	$-0.497193\pi$
$431$	−10.0382	−	2.68973i	−0.483523	−	0.129560i	−0.492343	+	0.870402i	$0.663859\pi$
$432$		0			0
$433$	−14.5167			−0.697626			−0.348813	−	0.937192i	$-0.613415\pi$
$433$	−14.5167			−0.697626			−0.348813	+	0.937192i	$0.613415\pi$
$434$	−3.58630			−0.172148
$435$		0			0
$436$	−12.0981	−	12.0981i	−0.579393	−	0.579393i
$437$	2.82843	+	4.89898i	0.135302	+	0.234350i
$438$		0			0
$439$	−6.92820	+	25.8564i	−0.330665	+	1.23406i	0.577828	+	0.816159i	$0.303901\pi$
$439$	−6.92820	+	25.8564i	−0.330665	+	1.23406i	−0.908493	+	0.417900i	$0.862766\pi$
$440$	−5.79555	+	3.34607i	−0.276292	+	0.159517i
$441$		0			0
$442$	6.29423	+	23.4904i	0.299386	+	1.11732i
$443$	−6.41473			−0.304773			−0.152386	−	0.988321i	$-0.548696\pi$
$443$	−6.41473			−0.304773			−0.152386	+	0.988321i	$0.548696\pi$
$444$		0			0
$445$	−1.73205			−0.0821071
$446$	2.17209	+	8.10634i	0.102851	+	0.383847i
$447$		0			0
$448$	1.73205	−	1.00000i	0.0818317	−	0.0472456i
$449$	−2.31079	+	8.62398i	−0.109053	+	0.406991i	−0.998773	−	0.0495148i	$-0.984233\pi$
$449$	−2.31079	+	8.62398i	−0.109053	+	0.406991i	0.889721	+	0.456506i	$0.150899\pi$
$450$		0			0
$451$	1.00000	+	1.73205i	0.0470882	+	0.0815591i
$452$	7.07107	+	7.07107i	0.332595	+	0.332595i
$453$		0			0
$454$	−0.928203			−0.0435627
$455$	−14.6969			−0.689003
$456$		0			0
$457$	10.7942	+	2.89230i	0.504933	+	0.135296i	0.502288	−	0.864700i	$-0.332492\pi$
$457$	10.7942	+	2.89230i	0.504933	+	0.135296i	0.00264437	+	0.999997i	$0.499158\pi$
$458$	14.2301	−	14.2301i	0.664927	−	0.664927i
$459$		0			0
$460$	4.73205	−	8.19615i	0.220633	−	0.382148i
$461$	5.79555	−	1.55291i	0.269926	−	0.0723264i	−0.121317	−	0.992614i	$-0.538712\pi$
$461$	5.79555	−	1.55291i	0.269926	−	0.0723264i	0.391243	+	0.920287i	$0.372045\pi$
$462$		0			0
$463$	−31.5885	−	8.46410i	−1.46804	−	0.393360i	−0.565781	−	0.824555i	$-0.691425\pi$
$463$	−31.5885	−	8.46410i	−1.46804	−	0.393360i	−0.902259	+	0.431195i	$0.858092\pi$
$464$	−2.38014	−	8.88280i	−0.110495	−	0.412374i
$465$		0			0
$466$	0.401924	+	1.50000i	0.0186188	+	0.0694862i
$467$	15.9353	+	15.9353i	0.737397	+	0.737397i	0.972074	−	0.234676i	$-0.0754031\pi$
$467$	15.9353	+	15.9353i	0.737397	+	0.737397i	−0.234676	+	0.972074i	$0.575403\pi$
$468$		0			0
$469$	−18.0000	−	10.3923i	−0.831163	−	0.479872i
$470$			10.2784i			0.474109i
$471$		0			0
$472$	−8.19615	−	4.73205i	−0.377258	−	0.217810i
$473$	18.2832	−	18.2832i	0.840664	−	0.840664i
$474$		0			0
$475$	1.46410	+	1.46410i	0.0671776	+	0.0671776i
$476$	11.0735	+	2.96713i	0.507552	+	0.135998i
$477$		0			0
$478$	−0.0717968	−	0.124356i	−0.00328391	−	0.00568790i
$479$	−16.8690	+	4.52004i	−0.770766	+	0.206526i	−0.622710	−	0.782453i	$-0.713968\pi$
$479$	−16.8690	+	4.52004i	−0.770766	+	0.206526i	−0.148056	+	0.988979i	$0.547302\pi$
$480$		0			0
$481$	−16.6865	+	19.6865i	−0.760840	+	0.897629i
$482$			21.7680i			0.991506i
$483$		0			0
$484$	−3.40192	+	1.96410i	−0.154633	+	0.0892773i
$485$	4.45069	+	7.70882i	0.202096	+	0.350040i
$486$		0			0
$487$	−23.8564	+	23.8564i	−1.08104	+	1.08104i	−0.0846240	+	0.996413i	$0.526969\pi$
$487$	−23.8564	+	23.8564i	−1.08104	+	1.08104i	−0.996413	+	0.0846240i	$0.973031\pi$
$488$	−8.12493	+	4.69093i	−0.367798	+	0.212348i
$489$		0			0
$490$	2.59808	−	4.50000i	0.117369	−	0.203289i
$491$		−	10.2784i		−	0.463859i	−0.972733	−	0.231930i	$-0.925496\pi$
$491$		−	10.2784i		−	0.463859i	0.972733	−	0.231930i	$-0.0745039\pi$
$492$		0			0
$493$	26.3564	−	45.6506i	1.18703	−	2.05600i
$494$	−1.13681	+	4.24264i	−0.0511476	+	0.190885i
$495$		0			0
$496$	1.73205	−	0.464102i	0.0777714	−	0.0208388i
$497$	15.1774	+	8.76268i	0.680800	+	0.393060i
$498$		0			0
$499$	−9.00000	+	33.5885i	−0.402895	+	1.50363i	0.405009	+	0.914313i	$0.367268\pi$
$499$	−9.00000	+	33.5885i	−0.402895	+	1.50363i	−0.807905	+	0.589313i	$0.799398\pi$
$500$	3.13801	−	11.7112i	0.140336	−	0.523742i
$501$		0			0
$502$	25.3923	+	14.6603i	1.13331	+	0.654319i
$503$	−33.9783	+	9.10446i	−1.51502	+	0.405948i	−0.918098	−	0.396354i	$-0.870275\pi$
$503$	−33.9783	+	9.10446i	−1.51502	+	0.405948i	−0.596919	+	0.802301i	$0.703609\pi$
$504$		0			0
$505$	−8.72243	+	32.5526i	−0.388143	+	1.44857i
$506$	10.5558	−	18.2832i	0.469264	−	0.812789i
$507$		0			0
$508$		−	6.53590i		−	0.289984i
$509$	1.77457	−	3.07364i	0.0786564	−	0.136237i	−0.824014	−	0.566569i	$-0.808270\pi$
$509$	1.77457	−	3.07364i	0.0786564	−	0.136237i	0.902670	+	0.430332i	$0.141604\pi$
$510$		0			0
$511$	−6.92820	+	4.00000i	−0.306486	+	0.176950i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	5.42820	+	9.40192i	0.239428	+	0.414701i
$515$	17.3867	−	10.0382i	0.766148	−	0.442336i
$516$		0			0
$517$			22.9282i			1.00838i
$518$	4.10394	+	11.4524i	0.180317	+	0.503190i
$519$		0			0
$520$	7.09808	−	1.90192i	0.311271	−	0.0834049i
$521$	10.2277	+	17.7148i	0.448082	+	0.776101i	0.998261	−	0.0589457i	$-0.0187739\pi$
$521$	10.2277	+	17.7148i	0.448082	+	0.776101i	−0.550179	+	0.835047i	$0.685441\pi$
$522$		0			0
$523$	15.1244	+	4.05256i	0.661342	+	0.177206i	0.573852	−	0.818959i	$-0.305449\pi$
$523$	15.1244	+	4.05256i	0.661342	+	0.177206i	0.0874903	+	0.996165i	$0.472115\pi$
$524$	−8.76268	−	8.76268i	−0.382800	−	0.382800i
$525$		0			0
$526$	−11.4641	+	11.4641i	−0.499859	+	0.499859i
$527$	8.90138	+	5.13922i	0.387750	+	0.223868i
$528$		0			0
$529$			6.85641i			0.298105i
$530$	2.12132	+	1.22474i	0.0921443	+	0.0531995i
$531$		0			0
$532$	1.46410	+	1.46410i	0.0634769	+	0.0634769i
$533$	−0.568406	−	2.12132i	−0.0246204	−	0.0918846i
$534$		0			0
$535$	3.58846	+	13.3923i	0.155143	+	0.579000i
$536$	10.0382	+	2.68973i	0.433584	+	0.116178i
$537$		0			0
$538$	−7.36603	+	1.97372i	−0.317572	+	0.0850931i
$539$	5.79555	−	10.0382i	0.249632	−	0.432376i
$540$		0			0
$541$	−17.4904	+	17.4904i	−0.751970	+	0.751970i	−0.974847	−	0.222876i	$-0.928455\pi$
$541$	−17.4904	+	17.4904i	−0.751970	+	0.751970i	0.222876	+	0.974847i	$0.428455\pi$
$542$	−23.0435	−	6.17449i	−0.989804	−	0.265217i
$543$		0			0
$544$	−5.73205			−0.245760
$545$	−29.6341			−1.26939
$546$		0			0
$547$	15.1244	+	15.1244i	0.646671	+	0.646671i	0.952187	−	0.305516i	$-0.0988290\pi$
$547$	15.1244	+	15.1244i	0.646671	+	0.646671i	−0.305516	+	0.952187i	$0.598829\pi$
$548$	−2.56961	−	4.45069i	−0.109768	−	0.190124i
$549$		0			0
$550$	2.00000	−	7.46410i	0.0852803	−	0.318270i
$551$	8.24504	−	4.76028i	0.351251	−	0.202795i
$552$		0			0
$553$	7.46410	+	27.8564i	0.317406	+	1.18457i
$554$	−22.7661			−0.967240
$555$		0			0
$556$	−6.92820			−0.293821
$557$	1.77457	+	6.62278i	0.0751909	+	0.280616i	0.993277	−	0.115766i	$-0.0369322\pi$
$557$	1.77457	+	6.62278i	0.0751909	+	0.280616i	−0.918086	+	0.396382i	$0.870266\pi$
$558$		0			0
$559$	−24.5885	+	14.1962i	−1.03998	+	0.600433i
$560$	0.896575	−	3.34607i	0.0378872	−	0.141397i
$561$		0			0
$562$	−4.03590	−	6.99038i	−0.170244	−	0.294871i
$563$	−20.0764	−	20.0764i	−0.846119	−	0.846119i	0.143527	−	0.989646i	$-0.454156\pi$
$563$	−20.0764	−	20.0764i	−0.846119	−	0.846119i	−0.989646	+	0.143527i	$0.954156\pi$
$564$		0			0
$565$	17.3205			0.728679
$566$	13.8647			0.582778
$567$		0			0
$568$	−8.46410	−	2.26795i	−0.355146	−	0.0951610i
$569$	−21.7172	+	21.7172i	−0.910434	+	0.910434i	−0.996306	−	0.0858722i	$-0.972632\pi$
$569$	−21.7172	+	21.7172i	−0.910434	+	0.910434i	0.0858722	+	0.996306i	$0.472632\pi$
$570$		0			0
$571$	−4.92820	+	8.53590i	−0.206239	+	0.357216i	−0.950527	−	0.310643i	$-0.899456\pi$
$571$	−4.92820	+	8.53590i	−0.206239	+	0.357216i	0.744288	+	0.667859i	$0.232789\pi$
$572$	15.8338	−	4.24264i	0.662042	−	0.177394i
$573$		0			0
$574$	−1.00000	−	0.267949i	−0.0417392	−	0.0111840i
$575$	2.82843	+	10.5558i	0.117954	+	0.440209i
$576$		0			0
$577$	−8.16987	−	30.4904i	−0.340116	−	1.26933i	−0.898215	−	0.439557i	$-0.855136\pi$
$577$	−8.16987	−	30.4904i	−0.340116	−	1.26933i	0.558099	−	0.829775i	$-0.311531\pi$
$578$	−11.2122	−	11.2122i	−0.466365	−	0.466365i
$579$		0			0
$580$	−13.7942	−	7.96410i	−0.572774	−	0.330691i
$581$			11.3137i			0.469372i
$582$		0			0
$583$	4.73205	+	2.73205i	0.195982	+	0.113150i
$584$	2.82843	−	2.82843i	0.117041	−	0.117041i
$585$		0			0
$586$	−8.36603	−	8.36603i	−0.345597	−	0.345597i
$587$	40.0512	+	10.7317i	1.65309	+	0.442945i	0.960476	−	0.278362i	$-0.0897916\pi$
$587$	40.0512	+	10.7317i	1.65309	+	0.442945i	0.692616	+	0.721307i	$0.256458\pi$
$588$		0			0
$589$	0.928203	+	1.60770i	0.0382459	+	0.0662439i
$590$	−15.8338	+	4.24264i	−0.651865	+	0.174667i
$591$		0			0
$592$	−3.46410	−	5.00000i	−0.142374	−	0.205499i
$593$			11.4524i			0.470294i	0.971960	+	0.235147i	$0.0755572\pi$
$593$			11.4524i			0.470294i	−0.971960	+	0.235147i	$0.924443\pi$
$594$		0			0
$595$	17.1962	−	9.92820i	0.704974	−	0.407017i
$596$	−8.41593	−	14.5768i	−0.344730	−	0.597090i
$597$		0			0
$598$	−16.3923	+	16.3923i	−0.670331	+	0.670331i
$599$	5.97142	−	3.44760i	0.243986	−	0.140865i	−0.373022	−	0.927823i	$-0.621678\pi$
$599$	5.97142	−	3.44760i	0.243986	−	0.140865i	0.617007	+	0.786957i	$0.288345\pi$
$600$		0			0
$601$	−4.50000	+	7.79423i	−0.183559	+	0.317933i	−0.943090	−	0.332538i	$-0.892095\pi$
$601$	−4.50000	+	7.79423i	−0.183559	+	0.317933i	0.759531	+	0.650471i	$0.225428\pi$
$602$			13.3843i			0.545502i
$603$		0			0
$604$	4.73205	−	8.19615i	0.192544	−	0.333497i
$605$	−1.76097	+	6.57201i	−0.0715934	+	0.267190i
$606$		0			0
$607$	11.7321	−	3.14359i	0.476189	−	0.127595i	−0.0127384	−	0.999919i	$-0.504055\pi$
$607$	11.7321	−	3.14359i	0.476189	−	0.127595i	0.488928	+	0.872324i	$0.337388\pi$
$608$	−0.896575	−	0.517638i	−0.0363609	−	0.0209930i
$609$		0			0
$610$	−4.20577	+	15.6962i	−0.170287	+	0.635519i
$611$	6.51626	−	24.3190i	0.263620	−	0.983843i
$612$		0			0
$613$	−3.52628	−	2.03590i	−0.142425	−	0.0822292i	0.427094	−	0.904207i	$-0.359537\pi$
$613$	−3.52628	−	2.03590i	−0.142425	−	0.0822292i	−0.569519	+	0.821978i	$0.692871\pi$
$614$	−26.9072	+	7.20977i	−1.08589	+	0.290963i
$615$		0			0
$616$	2.00000	−	7.46410i	0.0805823	−	0.300737i
$617$	4.84821	−	8.39735i	0.195182	−	0.338065i	−0.751778	−	0.659416i	$-0.770804\pi$
$617$	4.84821	−	8.39735i	0.195182	−	0.338065i	0.946960	+	0.321351i	$0.104137\pi$
$618$		0			0
$619$			32.2487i			1.29619i	0.761562	+	0.648093i	$0.224433\pi$
$619$			32.2487i			1.29619i	−0.761562	+	0.648093i	$0.775567\pi$
$620$	1.55291	−	2.68973i	0.0623665	−	0.108022i
$621$		0			0
$622$	25.0526	−	14.4641i	1.00452	−	0.579958i
$623$	1.41421	−	1.41421i	0.0566593	−	0.0566593i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	19.1476	−	11.0549i	0.765293	−	0.441842i
$627$		0			0
$628$		−	7.00000i		−	0.279330i
$629$	6.22526	−	34.3065i	0.248217	−	1.36789i
$630$		0			0
$631$	37.1244	−	9.94744i	1.47790	−	0.396001i	0.572266	−	0.820068i	$-0.306064\pi$
$631$	37.1244	−	9.94744i	1.47790	−	0.396001i	0.905631	+	0.424067i	$0.139398\pi$
$632$	−7.20977	−	12.4877i	−0.286789	−	0.496733i
$633$		0			0
$634$	−13.9641	−	3.74167i	−0.554585	−	0.148601i
$635$	−8.00481	−	8.00481i	−0.317661	−	0.317661i
$636$		0			0
$637$	−9.00000	+	9.00000i	−0.356593	+	0.356593i
$638$	−30.7709	−	17.7656i	−1.21823	−	0.703347i
$639$		0			0
$640$			1.73205i			0.0684653i
$641$	−27.9611	−	16.1433i	−1.10440	−	0.637624i	−0.167024	−	0.985953i	$-0.553416\pi$
$641$	−27.9611	−	16.1433i	−1.10440	−	0.637624i	−0.937372	+	0.348329i	$0.886749\pi$
$642$		0			0
$643$	19.6603	+	19.6603i	0.775325	+	0.775325i	0.979032	−	0.203707i	$-0.0652990\pi$
$643$	19.6603	+	19.6603i	0.775325	+	0.775325i	−0.203707	+	0.979032i	$0.565299\pi$
$644$	2.82843	+	10.5558i	0.111456	+	0.415958i
$645$		0			0
$646$	−1.53590	−	5.73205i	−0.0604291	−	0.225525i
$647$	−15.6950	−	4.20548i	−0.617036	−	0.165334i	−0.0632561	−	0.997997i	$-0.520148\pi$
$647$	−15.6950	−	4.20548i	−0.617036	−	0.165334i	−0.553780	+	0.832663i	$0.686815\pi$
$648$		0			0
$649$	−35.3205	+	9.46410i	−1.38645	+	0.371498i
$650$	−4.24264	+	7.34847i	−0.166410	+	0.288231i
$651$		0			0
$652$	4.73205	−	4.73205i	0.185321	−	0.185321i
$653$	−35.4619	−	9.50198i	−1.38773	−	0.371841i	−0.513807	−	0.857906i	$-0.671765\pi$
$653$	−35.4619	−	9.50198i	−1.38773	−	0.371841i	−0.873923	+	0.486065i	$0.838432\pi$
$654$		0			0
$655$	−21.4641			−0.838672
$656$	0.517638			0.0202104
$657$		0			0
$658$	−8.39230	−	8.39230i	−0.327166	−	0.327166i
$659$	23.5612	+	40.8091i	0.917812	+	1.58970i	0.802731	+	0.596342i	$0.203380\pi$
$659$	23.5612	+	40.8091i	0.917812	+	1.58970i	0.115082	+	0.993356i	$0.463287\pi$
$660$		0			0
$661$	7.47372	−	27.8923i	0.290694	−	1.08488i	−0.653883	−	0.756596i	$-0.726861\pi$
$661$	7.47372	−	27.8923i	0.290694	−	1.08488i	0.944577	−	0.328289i	$-0.106472\pi$
$662$	−18.2832	+	10.5558i	−0.710598	+	0.410264i
$663$		0			0
$664$	−1.46410	−	5.46410i	−0.0568182	−	0.212048i
$665$	3.58630			0.139071
$666$		0			0
$667$	50.2487			1.94564
$668$	−0.933740	−	3.48477i	−0.0361275	−	0.134830i
$669$		0			0
$670$	15.5885	−	9.00000i	0.602235	−	0.347700i
$671$	−9.38186	+	35.0136i	−0.362183	+	1.35168i
$672$		0			0
$673$	17.0000	+	29.4449i	0.655302	+	1.13502i	0.981818	+	0.189824i	$0.0607919\pi$
$673$	17.0000	+	29.4449i	0.655302	+	1.13502i	−0.326516	+	0.945192i	$0.605875\pi$
$674$	−19.8869	−	19.8869i	−0.766016	−	0.766016i
$675$		0			0
$676$	−5.00000			−0.192308
$677$	−35.0879			−1.34854			−0.674269	−	0.738486i	$-0.735541\pi$
$677$	−35.0879			−1.34854			−0.674269	+	0.738486i	$0.735541\pi$
$678$		0			0
$679$	−9.92820	−	2.66025i	−0.381009	−	0.102091i
$680$	−7.02030	+	7.02030i	−0.269216	+	0.269216i
$681$		0			0
$682$	3.46410	−	6.00000i	0.132647	−	0.229752i
$683$	11.8313	−	3.17020i	0.452714	−	0.121304i	−0.0252551	−	0.999681i	$-0.508040\pi$
$683$	11.8313	−	3.17020i	0.452714	−	0.121304i	0.477969	+	0.878377i	$0.341373\pi$
$684$		0			0
$685$	−8.59808	−	2.30385i	−0.328516	−	0.0880255i
$686$	5.17638	+	19.3185i	0.197635	+	0.737584i
$687$		0			0
$688$	−1.73205	−	6.46410i	−0.0660338	−	0.246442i
$689$	−4.24264	−	4.24264i	−0.161632	−	0.161632i
$690$		0			0
$691$	0.803848	+	0.464102i	0.0305798	+	0.0176553i	0.515212	−	0.857063i	$-0.327713\pi$
$691$	0.803848	+	0.464102i	0.0305798	+	0.0176553i	−0.484632	+	0.874718i	$0.661047\pi$
$692$			11.4524i			0.435355i
$693$		0			0
$694$	20.5359	+	11.8564i	0.779532	+	0.450063i
$695$	−8.48528	+	8.48528i	−0.321865	+	0.321865i
$696$		0			0
$697$	2.09808	+	2.09808i	0.0794703	+	0.0794703i
$698$	6.81225	+	1.82534i	0.257847	+	0.0690900i
$699$		0			0
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	20.9730	−	5.61969i	0.792138	−	0.212253i	0.160009	−	0.987116i	$-0.448848\pi$
$701$	20.9730	−	5.61969i	0.792138	−	0.212253i	0.632129	+	0.774863i	$0.282181\pi$
$702$		0			0
$703$	4.07180	−	4.80385i	0.153571	−	0.181181i
$704$			3.86370i			0.145619i
$705$		0			0
$706$	−8.47372	+	4.89230i	−0.318913	+	0.184124i
$707$	−19.4572	−	33.7009i	−0.731764	−	1.26745i
$708$		0			0
$709$	−28.3205	+	28.3205i	−1.06360	+	1.06360i	−0.0657638	+	0.997835i	$0.520948\pi$
$709$	−28.3205	+	28.3205i	−1.06360	+	1.06360i	−0.997835	+	0.0657638i	$0.979052\pi$
$710$	−13.1440	+	7.58871i	−0.493286	+	0.284799i
$711$		0			0
$712$	−0.500000	+	0.866025i	−0.0187383	+	0.0324557i
$713$			9.79796i			0.366936i
$714$		0			0
$715$	14.1962	−	24.5885i	0.530906	−	0.919556i
$716$	−3.48477	+	13.0053i	−0.130232	+	0.486032i
$717$		0			0
$718$	22.5885	−	6.05256i	0.842994	−	0.225879i
$719$	−34.5975	−	19.9749i	−1.29027	−	0.744936i	−0.311566	−	0.950224i	$-0.600854\pi$
$719$	−34.5975	−	19.9749i	−1.29027	−	0.744936i	−0.978702	+	0.205288i	$0.934187\pi$
$720$		0			0
$721$	−6.00000	+	22.3923i	−0.223452	+	0.833933i
$722$	−4.64016	+	17.3173i	−0.172689	+	0.644484i
$723$		0			0
$724$	12.0622	+	6.96410i	0.448287	+	0.258819i
$725$	17.7656	−	4.76028i	0.659798	−	0.176792i
$726$		0			0
$727$	−4.92820	+	18.3923i	−0.182777	+	0.682133i	0.812319	+	0.583214i	$0.198205\pi$
$727$	−4.92820	+	18.3923i	−0.182777	+	0.682133i	−0.995096	+	0.0989188i	$0.968462\pi$
$728$	−4.24264	+	7.34847i	−0.157243	+	0.272352i
$729$		0			0
$730$		−	6.92820i		−	0.256424i
$731$	19.1798	−	33.2204i	0.709391	−	1.22870i
$732$		0			0
$733$	−32.1051	+	18.5359i	−1.18583	+	0.684639i	−0.957356	−	0.288911i	$-0.906707\pi$
$733$	−32.1051	+	18.5359i	−1.18583	+	0.684639i	−0.228474	+	0.973550i	$0.573373\pi$
$734$	−21.8695	+	21.8695i	−0.807220	+	0.807220i
$735$		0			0
$736$	−2.73205	−	4.73205i	−0.100705	−	0.174426i
$737$	34.7733	−	20.0764i	1.28089	−	0.739523i
$738$		0			0
$739$		−	21.8564i		−	0.804001i	−0.915639	−	0.402000i	$-0.868315\pi$
$739$		−	21.8564i		−	0.804001i	0.915639	−	0.402000i	$-0.131685\pi$
$740$	−10.3664	−	1.88108i	−0.381075	−	0.0691500i
$741$		0			0
$742$	−2.73205	+	0.732051i	−0.100297	+	0.0268744i
$743$	17.6641	+	30.5951i	0.648032	+	1.12242i	0.983592	+	0.180405i	$0.0577409\pi$
$743$	17.6641	+	30.5951i	0.648032	+	1.12242i	−0.335561	+	0.942019i	$0.608926\pi$
$744$		0			0
$745$	−28.1603	−	7.54552i	−1.03171	−	0.276446i
$746$	−16.3006	−	16.3006i	−0.596808	−	0.596808i
$747$		0			0
$748$	−15.6603	+	15.6603i	−0.572596	+	0.572596i
$749$	−13.8647	−	8.00481i	−0.506606	−	0.292489i
$750$		0			0
$751$			15.1769i			0.553813i	0.960897	+	0.276907i	$0.0893093\pi$
$751$			15.1769i			0.553813i	−0.960897	+	0.276907i	$0.910691\pi$
$752$	5.13922	+	2.96713i	0.187408	+	0.108200i
$753$		0			0
$754$	27.5885	+	27.5885i	1.00471	+	1.00471i
$755$	−4.24264	−	15.8338i	−0.154406	−	0.576249i
$756$		0			0
$757$	−0.643594	−	2.40192i	−0.0233918	−	0.0872994i	0.953243	−	0.302204i	$-0.0977225\pi$
$757$	−0.643594	−	2.40192i	−0.0233918	−	0.0872994i	−0.976635	+	0.214905i	$0.931056\pi$
$758$	31.5288	+	8.44812i	1.14518	+	0.306849i
$759$		0			0
$760$	−1.73205	+	0.464102i	−0.0628281	+	0.0168347i
$761$	−13.9341	+	24.1345i	−0.505110	+	0.874876i	0.494872	+	0.868966i	$0.335215\pi$
$761$	−13.9341	+	24.1345i	−0.505110	+	0.874876i	−0.999983	+	0.00591080i	$0.998119\pi$
$762$		0			0
$763$	24.1962	−	24.1962i	0.875960	−	0.875960i
$764$	2.44949	+	0.656339i	0.0886194	+	0.0237455i
$765$		0			0
$766$	18.0000			0.650366
$767$	40.1528			1.44983
$768$		0			0
$769$	−4.32051	−	4.32051i	−0.155802	−	0.155802i	0.624902	−	0.780703i	$-0.285139\pi$
$769$	−4.32051	−	4.32051i	−0.155802	−	0.155802i	−0.780703	+	0.624902i	$0.785139\pi$
$770$	−6.69213	−	11.5911i	−0.241168	−	0.417715i
$771$		0			0
$772$	2.25833	−	8.42820i	0.0812791	−	0.303338i
$773$	−10.7267	+	6.19307i	−0.385813	+	0.222749i	−0.680345	−	0.732892i	$-0.738170\pi$
$773$	−10.7267	+	6.19307i	−0.385813	+	0.222749i	0.294531	+	0.955642i	$0.404837\pi$
$774$		0			0
$775$	0.928203	+	3.46410i	0.0333420	+	0.124434i
$776$	5.13922			0.184487
$777$		0			0
$778$	−28.8564			−1.03455
$779$	0.138701	+	0.517638i	0.00496947	+	0.0185463i
$780$		0			0
$781$	−29.3205	+	16.9282i	−1.04917	+	0.605739i
$782$	8.10634	−	30.2533i	0.289882	−	1.08186i
$783$		0			0
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$	−8.57321	−	8.57321i	−0.305991	−	0.305991i
$786$		0			0
$787$	30.6410			1.09223			0.546117	−	0.837709i	$-0.316105\pi$
$787$	30.6410			1.09223			0.546117	+	0.837709i	$0.316105\pi$
$788$	1.93185			0.0688194
$789$		0			0
$790$	−24.1244	−	6.46410i	−0.858306	−	0.229982i
$791$	−14.1421	+	14.1421i	−0.502836	+	0.502836i
$792$		0			0
$793$	19.9019	−	34.4711i	0.706738	−	1.22411i
$794$	−36.6358	+	9.81654i	−1.30016	+	0.348376i
$795$		0			0
$796$	12.6603	+	3.39230i	0.448731	+	0.120237i
$797$	8.48528	+	31.6675i	0.300564	+	1.12172i	0.936697	+	0.350141i	$0.113866\pi$
$797$	8.48528	+	31.6675i	0.300564	+	1.12172i	−0.636133	+	0.771579i	$0.719467\pi$
$798$		0			0
$799$	8.80385	+	32.8564i	0.311458	+	1.16238i
$800$	−1.41421	−	1.41421i	−0.0500000	−	0.0500000i
$801$		0			0
$802$	−34.3923	−	19.8564i	−1.21443	−	0.701154i
$803$		−	15.4548i		−	0.545389i
$804$		0			0
$805$	16.3923	+	9.46410i	0.577753	+	0.333566i
$806$	−5.37945	+	5.37945i	−0.189483	+	0.189483i
$807$		0			0
$808$	13.7583	+	13.7583i	0.484016	+	0.484016i
$809$	40.4302	+	10.8332i	1.42145	+	0.380876i	0.885998	−	0.463690i	$-0.153475\pi$
$809$	40.4302	+	10.8332i	1.42145	+	0.380876i	0.535452	+	0.844566i	$0.320141\pi$
$810$		0			0
$811$	−13.8038	−	23.9090i	−0.484719	−	0.839557i	0.515127	−	0.857114i	$-0.327745\pi$
$811$	−13.8038	−	23.9090i	−0.484719	−	0.839557i	−0.999846	+	0.0175564i	$0.994411\pi$
$812$	17.7656	−	4.76028i	0.623450	−	0.167053i
$813$		0			0
$814$	−23.1244	−	4.19615i	−0.810508	−	0.147075i
$815$		−	11.5911i		−	0.406019i
$816$		0			0
$817$	6.00000	−	3.46410i	0.209913	−	0.121194i
$818$	0.208051	+	0.360355i	0.00727433	+	0.0125995i
$819$		0			0
$820$	0.633975	−	0.633975i	0.0221394	−	0.0221394i
$821$	−23.5748	+	13.6109i	−0.822765	+	0.475023i	−0.851369	−	0.524567i	$-0.824227\pi$
$821$	−23.5748	+	13.6109i	−0.822765	+	0.475023i	0.0286042	+	0.999591i	$0.490894\pi$
$822$		0			0
$823$	6.00000	−	10.3923i	0.209147	−	0.362253i	−0.742299	−	0.670069i	$-0.766265\pi$
$823$	6.00000	−	10.3923i	0.209147	−	0.362253i	0.951446	+	0.307816i	$0.0995980\pi$
$824$		−	11.5911i		−	0.403795i
$825$		0			0
$826$	9.46410	−	16.3923i	0.329298	−	0.570361i
$827$	13.5873	−	50.7086i	0.472478	−	1.76331i	−0.158344	−	0.987384i	$-0.550616\pi$
$827$	13.5873	−	50.7086i	0.472478	−	1.76331i	0.630822	−	0.775927i	$-0.282718\pi$
$828$		0			0
$829$	−25.5622	+	6.84936i	−0.887811	+	0.237888i	−0.673774	−	0.738937i	$-0.735328\pi$
$829$	−25.5622	+	6.84936i	−0.887811	+	0.237888i	−0.214037	+	0.976826i	$0.568661\pi$
$830$	−8.48528	−	4.89898i	−0.294528	−	0.170046i
$831$		0			0
$832$	1.09808	−	4.09808i	0.0380689	−	0.142075i
$833$	4.45069	−	16.6102i	0.154207	−	0.575510i
$834$		0			0
$835$	−5.41154	−	3.12436i	−0.187274	−	0.108123i
$836$	−3.86370	+	1.03528i	−0.133629	+	0.0358058i
$837$		0			0
$838$	−0.660254	+	2.46410i	−0.0228081	+	0.0851210i
$839$	−3.10583	+	5.37945i	−0.107225	+	0.185719i	−0.914645	−	0.404258i	$-0.867530\pi$
$839$	−3.10583	+	5.37945i	−0.107225	+	0.185719i	0.807420	+	0.589977i	$0.200863\pi$
$840$		0			0
$841$		−	55.5692i		−	1.91618i
$842$	14.4381	−	25.0076i	0.497570	−	0.861817i
$843$		0			0
$844$	−12.1244	+	7.00000i	−0.417338	+	0.240950i
$845$	−6.12372	+	6.12372i	−0.210663	+	0.210663i
$846$		0			0
$847$	−3.92820	−	6.80385i	−0.134975	−	0.233783i
$848$	1.22474	−	0.707107i	0.0420579	−	0.0242821i
$849$		0			0
$850$		−	11.4641i		−	0.393215i
$851$	31.2886	−	11.2122i	1.07256	−	0.384348i
$852$		0			0
$853$	47.1865	−	12.6436i	1.61564	−	0.432908i	0.665921	−	0.746023i	$-0.268039\pi$
$853$	47.1865	−	12.6436i	1.61564	−	0.432908i	0.949715	+	0.313114i	$0.101372\pi$
$854$	−9.38186	−	16.2499i	−0.321041	−	0.556059i
$855$		0			0
$856$	7.73205	+	2.07180i	0.264276	+	0.0708126i
$857$	9.84873	+	9.84873i	0.336426	+	0.336426i	0.855020	−	0.518594i	$-0.173544\pi$
$857$	9.84873	+	9.84873i	0.336426	+	0.336426i	−0.518594	+	0.855020i	$0.673544\pi$
$858$		0			0
$859$	−14.7321	+	14.7321i	−0.502651	+	0.502651i	−0.912261	−	0.409610i	$-0.865665\pi$
$859$	−14.7321	+	14.7321i	−0.502651	+	0.502651i	0.409610	+	0.912261i	$0.365665\pi$
$860$	−10.0382	−	5.79555i	−0.342300	−	0.197627i
$861$		0			0
$862$			10.3923i			0.353963i
$863$	20.9086	+	12.0716i	0.711737	+	0.410921i	0.811704	−	0.584069i	$-0.198540\pi$
$863$	20.9086	+	12.0716i	0.711737	+	0.410921i	−0.0999669	+	0.994991i	$0.531874\pi$
$864$		0			0
$865$	14.0263	+	14.0263i	0.476908	+	0.476908i
$866$	3.75719	+	14.0220i	0.127674	+	0.476488i
$867$		0			0
$868$	0.928203	+	3.46410i	0.0315053	+	0.117579i
$869$	−53.8144	−	14.4195i	−1.82553	−	0.489149i
$870$		0			0
$871$	−42.5885	+	11.4115i	−1.44305	+	0.386665i
$872$	−8.55463	+	14.8171i	−0.289696	+	0.501769i
$873$		0			0
$874$	4.00000	−	4.00000i	0.135302	−	0.135302i
$875$	23.4225	+	6.27603i	0.791824	+	0.212168i
$876$		0			0
$877$	41.7846			1.41097			0.705483	−	0.708727i	$-0.250730\pi$
$877$	41.7846			1.41097			0.705483	+	0.708727i	$0.250730\pi$
$878$	26.7685			0.903394
$879$		0			0
$880$	4.73205	+	4.73205i	0.159517	+	0.159517i
$881$	−0.536220	−	0.928761i	−0.0180657	−	0.0312908i	0.856851	−	0.515564i	$-0.172417\pi$
$881$	−0.536220	−	0.928761i	−0.0180657	−	0.0312908i	−0.874917	+	0.484273i	$0.839084\pi$
$882$		0			0
$883$	−11.3205	+	42.2487i	−0.380965	+	1.42178i	0.463464	+	0.886116i	$0.346606\pi$
$883$	−11.3205	+	42.2487i	−0.380965	+	1.42178i	−0.844430	+	0.535667i	$0.820060\pi$
$884$	21.0609	−	12.1595i	0.708355	−	0.408969i
$885$		0			0
$886$	1.66025	+	6.19615i	0.0557773	+	0.208164i
$887$	39.9497			1.34138			0.670690	−	0.741738i	$-0.265998\pi$
$887$	39.9497			1.34138			0.670690	+	0.741738i	$0.265998\pi$
$888$		0			0
$889$	13.0718			0.438414
$890$	0.448288	+	1.67303i	0.0150266	+	0.0560802i
$891$		0			0
$892$	7.26795	−	4.19615i	0.243349	−	0.140498i
$893$	−1.59008	+	5.93426i	−0.0532100	+	0.198582i
$894$		0			0
$895$	11.6603	+	20.1962i	0.389759	+	0.675083i
$896$	−1.41421	−	1.41421i	−0.0472456	−	0.0472456i
$897$		0			0
$898$	8.92820			0.297938
$899$	16.4901			0.549975
$900$		0			0
$901$	7.83013	+	2.09808i	0.260859	+	0.0698971i
$902$	1.41421	−	1.41421i	0.0470882	−	0.0470882i
$903$		0			0
$904$	5.00000	−	8.66025i	0.166298	−	0.288036i
$905$	23.3023	−	6.24384i	0.774596	−	0.207552i
$906$		0			0
$907$	−37.0526	−	9.92820i	−1.23031	−	0.329661i	−0.415610	−	0.909543i	$-0.636432\pi$
$907$	−37.0526	−	9.92820i	−1.23031	−	0.329661i	−0.814700	+	0.579882i	$0.803098\pi$
$908$	0.240237	+	0.896575i	0.00797253	+	0.0297539i
$909$		0			0
$910$	3.80385	+	14.1962i	0.126096	+	0.470598i
$911$	−17.8028	−	17.8028i	−0.589832	−	0.589832i	0.347754	−	0.937586i	$-0.386944\pi$
$911$	−17.8028	−	17.8028i	−0.589832	−	0.589832i	−0.937586	+	0.347754i	$0.886944\pi$
$912$		0			0
$913$	−18.9282	−	10.9282i	−0.626432	−	0.361671i
$914$		−	11.1750i		−	0.369636i
$915$		0			0
$916$	−17.4282	−	10.0622i	−0.575844	−	0.332464i
$917$	17.5254	−	17.5254i	0.578739	−	0.578739i
$918$		0			0
$919$	−38.7846	−	38.7846i	−1.27939	−	1.27939i	−0.941011	−	0.338375i	$-0.890123\pi$
$919$	−38.7846	−	38.7846i	−1.27939	−	1.27939i	−0.338375	−	0.941011i	$-0.609877\pi$
$920$	−9.14162	−	2.44949i	−0.301390	−	0.0807573i
$921$		0			0
$922$	−3.00000	−	5.19615i	−0.0987997	−	0.171126i
$923$	35.9101	−	9.62209i	1.18200	−	0.316715i
$924$		0			0
$925$	10.0000	−	6.92820i	0.328798	−	0.227798i
$926$			32.7028i			1.07468i
$927$		0			0
$928$	−7.96410	+	4.59808i	−0.261434	+	0.150939i
$929$	21.9253	+	37.9757i	0.719345	+	1.24594i	0.961259	+	0.275645i	$0.0888915\pi$
$929$	21.9253	+	37.9757i	0.719345	+	1.24594i	−0.241914	+	0.970298i	$0.577775\pi$
$930$		0			0
$931$	2.19615	−	2.19615i	0.0719760	−	0.0719760i
$932$	1.34486	−	0.776457i	0.0440525	−	0.0254337i
$933$		0			0
$934$	11.2679	−	19.5167i	0.368699	−	0.638605i
$935$			38.3596i			1.25449i
$936$		0			0
$937$	28.7224	−	49.7487i	0.938321	−	1.62522i	0.169719	−	0.985493i	$-0.445714\pi$
$937$	28.7224	−	49.7487i	0.938321	−	1.62522i	0.768602	−	0.639727i	$-0.220953\pi$
$938$	−5.37945	+	20.0764i	−0.175645	+	0.655517i
$939$		0			0
$940$	9.92820	−	2.66025i	0.323822	−	0.0867679i
$941$	8.12493	+	4.69093i	0.264865	+	0.152920i	0.626552	−	0.779380i	$-0.284466\pi$
$941$	8.12493	+	4.69093i	0.264865	+	0.152920i	−0.361687	+	0.932300i	$0.617799\pi$
$942$		0			0
$943$	−0.732051	+	2.73205i	−0.0238389	+	0.0889678i
$944$	−2.44949	+	9.14162i	−0.0797241	+	0.297534i
$945$		0			0
$946$	−22.3923	−	12.9282i	−0.728037	−	0.420332i
$947$	−29.9759	+	8.03201i	−0.974085	+	0.261005i	−0.710552	−	0.703645i	$-0.751555\pi$
$947$	−29.9759	+	8.03201i	−0.974085	+	0.261005i	−0.263534	+	0.964650i	$0.584888\pi$
$948$		0			0
$949$	−4.39230	+	16.3923i	−0.142580	+	0.532117i
$950$	1.03528	−	1.79315i	0.0335888	−	0.0581775i
$951$		0			0
$952$		−	11.4641i		−	0.371554i
$953$	−24.9246	+	43.1707i	−0.807387	+	1.39844i	0.107281	+	0.994229i	$0.465786\pi$
$953$	−24.9246	+	43.1707i	−0.807387	+	1.39844i	−0.914668	+	0.404207i	$0.867548\pi$
$954$		0			0
$955$	3.80385	−	2.19615i	0.123090	−	0.0710658i
$956$	−0.101536	+	0.101536i	−0.00328391	+	0.00328391i
$957$		0			0
$958$	8.73205	+	15.1244i	0.282120	+	0.488646i
$959$	8.90138	−	5.13922i	0.287441	−	0.165954i
$960$		0			0
$961$		−	27.7846i		−	0.896278i
$962$	23.3345	+	11.0227i	0.752335	+	0.355386i
$963$		0			0
$964$	21.0263	−	5.63397i	0.677211	−	0.181458i
$965$	−7.55652	−	13.0883i	−0.243253	−	0.421327i
$966$		0			0
$967$	16.5885	+	4.44486i	0.533449	+	0.142937i	0.515480	−	0.856901i	$-0.327613\pi$
$967$	16.5885	+	4.44486i	0.533449	+	0.142937i	0.0179684	+	0.999839i	$0.494280\pi$
$968$	2.77766	+	2.77766i	0.0892773	+	0.0892773i
$969$		0			0
$970$	6.29423	−	6.29423i	0.202096	−	0.202096i
$971$	−51.7439	−	29.8744i	−1.66054	−	0.958714i	−0.972457	−	0.233082i	$-0.925119\pi$
$971$	−51.7439	−	29.8744i	−1.66054	−	0.958714i	−0.688083	−	0.725632i	$-0.741548\pi$
$972$		0			0
$973$		−	13.8564i		−	0.444216i
$974$	29.2180	+	16.8690i	0.936205	+	0.540518i
$975$		0			0
$976$	6.63397	+	6.63397i	0.212348	+	0.212348i
$977$	10.6302	+	39.6723i	0.340089	+	1.26923i	0.898246	+	0.439494i	$0.144842\pi$
$977$	10.6302	+	39.6723i	0.340089	+	1.26923i	−0.558157	+	0.829736i	$0.688491\pi$
$978$		0			0
$979$	1.00000	+	3.73205i	0.0319601	+	0.119277i
$980$	−5.01910	−	1.34486i	−0.160329	−	0.0429601i
$981$		0			0
$982$	−9.92820	+	2.66025i	−0.316822	+	0.0848921i
$983$	−20.8714	+	36.1504i	−0.665695	+	1.15302i	0.313401	+	0.949621i	$0.398532\pi$
$983$	−20.8714	+	36.1504i	−0.665695	+	1.15302i	−0.979096	+	0.203397i	$0.934802\pi$
$984$		0			0
$985$	2.36603	−	2.36603i	0.0753878	−	0.0753878i
$986$	−50.9167	−	13.6431i	−1.62152	−	0.434484i
$987$		0			0
$988$	4.39230			0.139738
$989$	36.5665			1.16275
$990$		0			0
$991$	−34.0526	−	34.0526i	−1.08172	−	1.08172i	−0.996350	−	0.0853655i	$-0.972794\pi$
$991$	−34.0526	−	34.0526i	−1.08172	−	1.08172i	−0.0853655	−	0.996350i	$-0.527206\pi$
$992$	−0.896575	−	1.55291i	−0.0284663	−	0.0493051i
$993$		0			0
$994$	4.53590	−	16.9282i	0.143870	−	0.536930i
$995$	19.6603	−	11.3509i	0.623273	−	0.359847i
$996$		0			0
$997$	−4.70577	−	17.5622i	−0.149033	−	0.556200i	−0.999543	−	0.0302399i	$-0.990373\pi$
$997$	−4.70577	−	17.5622i	−0.149033	−	0.556200i	0.850509	−	0.525960i	$-0.176294\pi$
$998$	34.7733			1.10073
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.be.a.125.1	✓	8
3.2	odd	2	inner	666.2.be.a.125.2	yes	8
37.8	odd	12	inner	666.2.be.a.341.2	yes	8
111.8	even	12	inner	666.2.be.a.341.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.be.a.125.1	✓	8	1.1	even	1	trivial
666.2.be.a.125.2	yes	8	3.2	odd	2	inner
666.2.be.a.341.1	yes	8	111.8	even	12	inner
666.2.be.a.341.2	yes	8	37.8	odd	12	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)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.448288 + 1.67303i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.448288 + 1.67303i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.73205 q^{10} +3.86370 q^{11} +(-4.09808 - 1.09808i) q^{13} +(-1.41421 + 1.41421i) q^{14} +(0.500000 - 0.866025i) q^{16} +(5.53674 - 1.48356i) q^{17} +(1.00000 + 0.267949i) q^{19} +(-0.448288 - 1.67303i) q^{20} +(-1.00000 - 3.73205i) q^{22} +(3.86370 + 3.86370i) q^{23} +(1.73205 + 1.00000i) q^{25} +4.24264i q^{26} +(1.73205 + 1.00000i) q^{28} +(6.50266 - 6.50266i) q^{29} +(1.26795 + 1.26795i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-2.86603 - 4.96410i) q^{34} +(3.34607 - 0.896575i) q^{35} +(2.59808 - 5.50000i) q^{37} -1.03528i q^{38} +(-1.50000 + 0.866025i) q^{40} +(0.258819 + 0.448288i) q^{41} +(4.73205 - 4.73205i) q^{43} +(-3.34607 + 1.93185i) q^{44} +(2.73205 - 4.73205i) q^{46} +5.93426i q^{47} +(1.50000 - 2.59808i) q^{49} +(0.517638 - 1.93185i) q^{50} +(4.09808 - 1.09808i) q^{52} +(1.22474 + 0.707107i) q^{53} +(-1.73205 + 6.46410i) q^{55} +(0.517638 - 1.93185i) q^{56} +(-7.96410 - 4.59808i) q^{58} +(-9.14162 + 2.44949i) q^{59} +(-2.42820 + 9.06218i) q^{61} +(0.896575 - 1.55291i) q^{62} +1.00000i q^{64} +(3.67423 - 6.36396i) q^{65} +(9.00000 - 5.19615i) q^{67} +(-4.05317 + 4.05317i) q^{68} +(-1.73205 - 3.00000i) q^{70} +(-7.58871 + 4.38134i) q^{71} -4.00000i q^{73} +(-5.98502 - 1.08604i) q^{74} +(-1.00000 + 0.267949i) q^{76} +(-3.86370 - 6.69213i) q^{77} +(-13.9282 - 3.73205i) q^{79} +(1.22474 + 1.22474i) q^{80} +(0.366025 - 0.366025i) q^{82} +(-4.89898 - 2.82843i) q^{83} +9.92820i q^{85} +(-5.79555 - 3.34607i) q^{86} +(2.73205 + 2.73205i) q^{88} +(0.258819 + 0.965926i) q^{89} +(2.19615 + 8.19615i) q^{91} +(-5.27792 - 1.41421i) q^{92} +(5.73205 - 1.53590i) q^{94} +(-0.896575 + 1.55291i) q^{95} +(3.63397 - 3.63397i) q^{97} +(-2.89778 - 0.776457i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^7	\( 8 q - 8 q^{7} - 12 q^{13} + 4 q^{16} + 8 q^{19} - 8 q^{22} + 24 q^{31} - 16 q^{34} - 12 q^{40} + 24 q^{43} + 8 q^{46} + 12 q^{49} + 12 q^{52} - 36 q^{58} + 36 q^{61} + 72 q^{67} - 8 q^{76} - 56 q^{79} - 4 q^{82} + 8 q^{88} - 24 q^{91} + 32 q^{94} + 36 q^{97}+O(q^{100}) \) 8 * q - 8 * q^7 - 12 * q^13 + 4 * q^16 + 8 * q^19 - 8 * q^22 + 24 * q^31 - 16 * q^34 - 12 * q^40 + 24 * q^43 + 8 * q^46 + 12 * q^49 + 12 * q^52 - 36 * q^58 + 36 * q^61 + 72 * q^67 - 8 * q^76 - 56 * q^79 - 4 * q^82 + 8 * q^88 - 24 * q^91 + 32 * q^94 + 36 * q^97

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