LMFDB - Embedded newform 666.2.be.b.341.1

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			341.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	666.341
Dual form			666.2.be.b.125.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.896575 + 3.34607i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.896575 + 3.34607i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.46410 q^{10} +3.86370 q^{11} +(5.59808 - 1.50000i) q^{13} +(0.707107 + 0.707107i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.63896 + 0.707107i) q^{17} +(-6.09808 + 1.63397i) q^{19} +(0.896575 - 3.34607i) q^{20} +(-1.00000 + 3.73205i) q^{22} +(-1.93185 + 1.93185i) q^{23} +(-6.06218 + 3.50000i) q^{25} +5.79555i q^{26} +(-0.866025 + 0.500000i) q^{28} +(0.138701 + 0.138701i) q^{29} +(-3.63397 + 3.63397i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.36603 + 2.36603i) q^{34} +(3.34607 + 0.896575i) q^{35} +(6.00000 + 1.00000i) q^{37} -6.31319i q^{38} +(3.00000 + 1.73205i) q^{40} +(1.03528 - 1.79315i) q^{41} +(-7.56218 - 7.56218i) q^{43} +(-3.34607 - 1.93185i) q^{44} +(-1.36603 - 2.36603i) q^{46} +8.76268i q^{47} +(3.00000 + 5.19615i) q^{49} +(-1.81173 - 6.76148i) q^{50} +(-5.59808 - 1.50000i) q^{52} +(-2.44949 + 1.41421i) q^{53} +(3.46410 + 12.9282i) q^{55} +(-0.258819 - 0.965926i) q^{56} +(-0.169873 + 0.0980762i) q^{58} +(4.57081 + 1.22474i) q^{59} +(-0.633975 - 2.36603i) q^{61} +(-2.56961 - 4.45069i) q^{62} -1.00000i q^{64} +(10.0382 + 17.3867i) q^{65} +(-2.59808 - 1.50000i) q^{67} +(-1.93185 - 1.93185i) q^{68} +(-1.73205 + 3.00000i) q^{70} +(2.44949 + 1.41421i) q^{71} -15.3923i q^{73} +(-2.51884 + 5.53674i) q^{74} +(6.09808 + 1.63397i) q^{76} +(1.93185 - 3.34607i) q^{77} +(-0.133975 + 0.0358984i) q^{79} +(-2.44949 + 2.44949i) q^{80} +(1.46410 + 1.46410i) q^{82} +(-13.9527 + 8.05558i) q^{83} +9.46410i q^{85} +(9.26174 - 5.34727i) q^{86} +(2.73205 - 2.73205i) q^{88} +(2.17209 - 8.10634i) q^{89} +(1.50000 - 5.59808i) q^{91} +(2.63896 - 0.707107i) q^{92} +(-8.46410 - 2.26795i) q^{94} +(-10.9348 - 18.9396i) q^{95} +(11.0263 + 11.0263i) q^{97} +(-5.79555 + 1.55291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} + 24 q^{13} + 4 q^{16} - 28 q^{19} - 8 q^{22} - 36 q^{31} - 4 q^{34} + 48 q^{37} + 24 q^{40} - 12 q^{43} - 4 q^{46} + 24 q^{49} - 24 q^{52} - 36 q^{58} - 12 q^{61} + 28 q^{76} - 8 q^{79} - 16 q^{82} + 8 q^{88} + 12 q^{91} - 40 q^{94} + 12 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 + 24 * q^13 + 4 * q^16 - 28 * q^19 - 8 * q^22 - 36 * q^31 - 4 * q^34 + 48 * q^37 + 24 * q^40 - 12 * q^43 - 4 * q^46 + 24 * q^49 - 24 * q^52 - 36 * q^58 - 12 * q^61 + 28 * q^76 - 8 * q^79 - 16 * q^82 + 8 * q^88 + 12 * q^91 - 40 * q^94 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	0.896575	+	3.34607i	0.400961	+	1.49641i	0.811386	+	0.584511i	$0.198714\pi$
$5$	0.896575	+	3.34607i	0.400961	+	1.49641i	−0.410425	+	0.911894i	$0.634620\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−3.46410			−1.09545
$11$	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
$13$	5.59808	−	1.50000i	1.55263	−	0.416025i	0.622307	−	0.782773i	$-0.286196\pi$
$13$	5.59808	−	1.50000i	1.55263	−	0.416025i	0.930320	+	0.366748i	$0.119529\pi$
$14$	0.707107	+	0.707107i	0.188982	+	0.188982i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.63896	+	0.707107i	0.640041	+	0.171499i	0.564222	−	0.825623i	$-0.309176\pi$
$17$	2.63896	+	0.707107i	0.640041	+	0.171499i	0.0758192	+	0.997122i	$0.475843\pi$
$18$		0			0
$19$	−6.09808	+	1.63397i	−1.39899	+	0.374859i	−0.877984	−	0.478691i	$-0.841112\pi$
$19$	−6.09808	+	1.63397i	−1.39899	+	0.374859i	−0.521011	+	0.853550i	$0.674445\pi$
$20$	0.896575	−	3.34607i	0.200480	−	0.748203i
$21$		0			0
$22$	−1.00000	+	3.73205i	−0.213201	+	0.795676i
$23$	−1.93185	+	1.93185i	−0.402819	+	0.402819i	−0.879225	−	0.476406i	$-0.841939\pi$
$23$	−1.93185	+	1.93185i	−0.402819	+	0.402819i	0.476406	+	0.879225i	$0.341939\pi$
$24$		0			0
$25$	−6.06218	+	3.50000i	−1.21244	+	0.700000i
$26$			5.79555i			1.13660i
$27$		0			0
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	0.138701	+	0.138701i	0.0257561	+	0.0257561i	0.719868	−	0.694111i	$-0.244203\pi$
$29$	0.138701	+	0.138701i	0.0257561	+	0.0257561i	−0.694111	+	0.719868i	$0.744203\pi$
$30$		0			0
$31$	−3.63397	+	3.63397i	−0.652681	+	0.652681i	−0.953638	−	0.300957i	$-0.902694\pi$
$31$	−3.63397	+	3.63397i	−0.652681	+	0.652681i	0.300957	+	0.953638i	$0.402694\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$	−1.36603	+	2.36603i	−0.234271	+	0.405770i
$35$	3.34607	+	0.896575i	0.565588	+	0.151549i
$36$		0			0
$37$	6.00000	+	1.00000i	0.986394	+	0.164399i
$37$	6.00000	+	1.00000i	0.986394	+	0.164399i
$38$		−	6.31319i		−	1.02414i
$39$		0			0
$40$	3.00000	+	1.73205i	0.474342	+	0.273861i
$41$	1.03528	−	1.79315i	0.161683	−	0.280043i	−0.773789	−	0.633443i	$-0.781641\pi$
$41$	1.03528	−	1.79315i	0.161683	−	0.280043i	0.935472	+	0.353400i	$0.114974\pi$
$42$		0			0
$43$	−7.56218	−	7.56218i	−1.15322	−	1.15322i	−0.985903	−	0.167318i	$-0.946489\pi$
$43$	−7.56218	−	7.56218i	−1.15322	−	1.15322i	−0.167318	−	0.985903i	$-0.553511\pi$
$44$	−3.34607	−	1.93185i	−0.504438	−	0.291238i
$45$		0			0
$46$	−1.36603	−	2.36603i	−0.201409	−	0.348851i
$47$			8.76268i			1.27817i	0.769137	+	0.639084i	$0.220687\pi$
$47$			8.76268i			1.27817i	−0.769137	+	0.639084i	$0.779313\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	−1.81173	−	6.76148i	−0.256218	−	0.956218i
$51$		0			0
$52$	−5.59808	−	1.50000i	−0.776313	−	0.208013i
$53$	−2.44949	+	1.41421i	−0.336463	+	0.194257i	−0.658707	−	0.752400i	$-0.728896\pi$
$53$	−2.44949	+	1.41421i	−0.336463	+	0.194257i	0.322244	+	0.946657i	$0.395563\pi$
$54$		0			0
$55$	3.46410	+	12.9282i	0.467099	+	1.74324i
$56$	−0.258819	−	0.965926i	−0.0345861	−	0.129077i
$57$		0			0
$58$	−0.169873	+	0.0980762i	−0.0223054	+	0.0128780i
$59$	4.57081	+	1.22474i	0.595069	+	0.159448i	0.543769	−	0.839235i	$-0.316997\pi$
$59$	4.57081	+	1.22474i	0.595069	+	0.159448i	0.0513000	+	0.998683i	$0.483664\pi$
$60$		0			0
$61$	−0.633975	−	2.36603i	−0.0811721	−	0.302939i	0.913390	−	0.407086i	$-0.133455\pi$
$61$	−0.633975	−	2.36603i	−0.0811721	−	0.302939i	−0.994562	+	0.104148i	$0.966789\pi$
$62$	−2.56961	−	4.45069i	−0.326341	−	0.565238i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	10.0382	+	17.3867i	1.24508	+	2.15655i
$66$		0			0
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	0.332830	−	0.942987i	$-0.391996\pi$
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	−0.650236	+	0.759733i	$0.725330\pi$
$68$	−1.93185	−	1.93185i	−0.234271	−	0.234271i
$69$		0			0
$70$	−1.73205	+	3.00000i	−0.207020	+	0.358569i
$71$	2.44949	+	1.41421i	0.290701	+	0.167836i	0.638258	−	0.769823i	$-0.279655\pi$
$71$	2.44949	+	1.41421i	0.290701	+	0.167836i	−0.347557	+	0.937659i	$0.612989\pi$
$72$		0			0
$73$		−	15.3923i		−	1.80153i	−0.434304	−	0.900767i	$-0.643006\pi$
$73$		−	15.3923i		−	1.80153i	0.434304	−	0.900767i	$-0.356994\pi$
$74$	−2.51884	+	5.53674i	−0.292809	+	0.643632i
$75$		0			0
$76$	6.09808	+	1.63397i	0.699497	+	0.187430i
$77$	1.93185	−	3.34607i	0.220155	−	0.381320i
$78$		0			0
$79$	−0.133975	+	0.0358984i	−0.0150733	+	0.00403888i	−0.266348	−	0.963877i	$-0.585817\pi$
$79$	−0.133975	+	0.0358984i	−0.0150733	+	0.00403888i	0.251275	+	0.967916i	$0.419150\pi$
$80$	−2.44949	+	2.44949i	−0.273861	+	0.273861i
$81$		0			0
$82$	1.46410	+	1.46410i	0.161683	+	0.161683i
$83$	−13.9527	+	8.05558i	−1.53150	+	0.884214i	−0.532211	+	0.846611i	$0.678639\pi$
$83$	−13.9527	+	8.05558i	−1.53150	+	0.884214i	−0.999293	+	0.0376028i	$0.988028\pi$
$84$		0			0
$85$			9.46410i			1.02653i
$86$	9.26174	−	5.34727i	0.998719	−	0.576611i
$87$		0			0
$88$	2.73205	−	2.73205i	0.291238	−	0.291238i
$89$	2.17209	−	8.10634i	0.230241	−	0.859271i	−0.749996	−	0.661443i	$-0.769945\pi$
$89$	2.17209	−	8.10634i	0.230241	−	0.859271i	0.980237	−	0.197828i	$-0.0633888\pi$
$90$		0			0
$91$	1.50000	−	5.59808i	0.157243	−	0.586838i
$92$	2.63896	−	0.707107i	0.275130	−	0.0737210i
$93$		0			0
$94$	−8.46410	−	2.26795i	−0.873005	−	0.233921i
$95$	−10.9348	−	18.9396i	−1.12188	−	1.94316i
$96$		0			0
$97$	11.0263	+	11.0263i	1.11955	+	1.11955i	0.991807	+	0.127742i	$0.0407728\pi$
$97$	11.0263	+	11.0263i	1.11955	+	1.11955i	0.127742	+	0.991807i	$0.459227\pi$
$98$	−5.79555	+	1.55291i	−0.585439	+	0.156868i
$99$		0			0
$100$	7.00000			0.700000
$101$	−16.8690			−1.67853			−0.839265	−	0.543722i	$-0.817015\pi$
$101$	−16.8690			−1.67853			−0.839265	+	0.543722i	$0.817015\pi$
$102$		0			0
$103$	13.3923	−	13.3923i	1.31958	−	1.31958i	0.405478	−	0.914105i	$-0.367105\pi$
$103$	13.3923	−	13.3923i	1.31958	−	1.31958i	0.914105	−	0.405478i	$-0.132895\pi$
$104$	2.89778	−	5.01910i	0.284150	−	0.492163i
$105$		0			0
$106$	−0.732051	−	2.73205i	−0.0711031	−	0.265360i
$107$	−1.13681	−	0.656339i	−0.109900	−	0.0634507i	0.444043	−	0.896006i	$-0.353544\pi$
$107$	−1.13681	−	0.656339i	−0.109900	−	0.0634507i	−0.553942	+	0.832555i	$0.686877\pi$
$108$		0			0
$109$	3.33013	−	12.4282i	0.318968	−	1.19041i	−0.601269	−	0.799046i	$-0.705338\pi$
$109$	3.33013	−	12.4282i	0.318968	−	1.19041i	0.920238	−	0.391360i	$-0.127995\pi$
$110$	−13.3843			−1.27614
$111$		0			0
$112$	1.00000			0.0944911
$113$	3.62347	−	13.5230i	0.340867	−	1.27213i	−0.556500	−	0.830848i	$-0.687856\pi$
$113$	3.62347	−	13.5230i	0.340867	−	1.27213i	0.897367	−	0.441285i	$-0.145477\pi$
$114$		0			0
$115$	−8.19615	−	4.73205i	−0.764295	−	0.441266i
$116$	−0.0507680	−	0.189469i	−0.00471369	−	0.0175917i
$117$		0			0
$118$	−2.36603	+	4.09808i	−0.217810	+	0.377258i
$119$	1.93185	−	1.93185i	0.177093	−	0.177093i
$120$		0			0
$121$	3.92820			0.357109
$122$	2.44949			0.221766
$123$		0			0
$124$	4.96410	−	1.33013i	0.445789	−	0.119449i
$125$	−4.89898	−	4.89898i	−0.438178	−	0.438178i
$126$		0			0
$127$	0.133975	+	0.232051i	0.0118883	+	0.0205912i	0.871908	−	0.489669i	$-0.162882\pi$
$127$	0.133975	+	0.232051i	0.0118883	+	0.0205912i	−0.860020	+	0.510260i	$0.829549\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$	−19.3923	+	5.19615i	−1.70082	+	0.455733i
$131$	1.08604	−	4.05317i	0.0948881	−	0.354127i	−0.902114	−	0.431497i	$-0.857986\pi$
$131$	1.08604	−	4.05317i	0.0948881	−	0.354127i	0.997002	+	0.0773698i	$0.0246522\pi$
$132$		0			0
$133$	−1.63397	+	6.09808i	−0.141684	+	0.528770i
$134$	2.12132	−	2.12132i	0.183254	−	0.183254i
$135$		0			0
$136$	2.36603	−	1.36603i	0.202885	−	0.117136i
$137$			13.3843i			1.14349i	0.820430	+	0.571747i	$0.193734\pi$
$137$			13.3843i			1.14349i	−0.820430	+	0.571747i	$0.806266\pi$
$138$		0			0
$139$	8.59808	−	4.96410i	0.729279	−	0.421050i	−0.0888792	−	0.996042i	$-0.528328\pi$
$139$	8.59808	−	4.96410i	0.729279	−	0.421050i	0.818158	+	0.574993i	$0.194995\pi$
$140$	−2.44949	−	2.44949i	−0.207020	−	0.207020i
$141$		0			0
$142$	−2.00000	+	2.00000i	−0.167836	+	0.167836i
$143$	21.6293	−	5.79555i	1.80873	−	0.484649i
$144$		0			0
$145$	−0.339746	+	0.588457i	−0.0282144	+	0.0488687i
$146$	14.8678	+	3.98382i	1.23047	+	0.329703i
$147$		0			0
$148$	−4.69615	−	3.86603i	−0.386021	−	0.317785i
$149$			7.07107i			0.579284i	0.957135	+	0.289642i	$0.0935363\pi$
$149$			7.07107i			0.579284i	−0.957135	+	0.289642i	$0.906464\pi$
$150$		0			0
$151$	−9.40192	−	5.42820i	−0.765118	−	0.441741i	0.0660125	−	0.997819i	$-0.478972\pi$
$151$	−9.40192	−	5.42820i	−0.765118	−	0.441741i	−0.831130	+	0.556078i	$0.812306\pi$
$152$	−3.15660	+	5.46739i	−0.256034	+	0.443464i
$153$		0			0
$154$	2.73205	+	2.73205i	0.220155	+	0.220155i
$155$	−15.4176	−	8.90138i	−1.23838	−	0.714976i
$156$		0			0
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	0.948373	−	0.317156i	$-0.102728\pi$
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	−0.748852	+	0.662738i	$0.769394\pi$
$158$		−	0.138701i		−	0.0110344i
$159$		0			0
$160$	−1.73205	−	3.00000i	−0.136931	−	0.237171i
$161$	0.707107	+	2.63896i	0.0557278	+	0.207979i
$162$		0			0
$163$	2.83013	+	0.758330i	0.221673	+	0.0593970i	0.367946	−	0.929847i	$-0.380061\pi$
$163$	2.83013	+	0.758330i	0.221673	+	0.0593970i	−0.146273	+	0.989244i	$0.546728\pi$
$164$	−1.79315	+	1.03528i	−0.140022	+	0.0808415i
$165$		0			0
$166$	−4.16987	−	15.5622i	−0.323645	−	1.20786i
$167$	−4.19187	−	15.6443i	−0.324377	−	1.21059i	−0.914937	−	0.403597i	$-0.867760\pi$
$167$	−4.19187	−	15.6443i	−0.324377	−	1.21059i	0.590560	−	0.806994i	$-0.298907\pi$
$168$		0			0
$169$	17.8301	−	10.2942i	1.37155	−	0.791864i
$170$	−9.14162	−	2.44949i	−0.701130	−	0.187867i
$171$		0			0
$172$	2.76795	+	10.3301i	0.211054	+	0.787665i
$173$	12.2982	+	21.3011i	0.935016	+	1.61950i	0.774605	+	0.632445i	$0.217949\pi$
$173$	12.2982	+	21.3011i	0.935016	+	1.61950i	0.160411	+	0.987050i	$0.448718\pi$
$174$		0			0
$175$			7.00000i			0.529150i
$176$	1.93185	+	3.34607i	0.145619	+	0.252219i
$177$		0			0
$178$	7.26795	+	4.19615i	0.544756	+	0.314515i
$179$	−6.31319	−	6.31319i	−0.471870	−	0.471870i	0.430649	−	0.902519i	$-0.358285\pi$
$179$	−6.31319	−	6.31319i	−0.471870	−	0.471870i	−0.902519	+	0.430649i	$0.858285\pi$
$180$		0			0
$181$	9.42820	−	16.3301i	0.700793	−	1.21381i	−0.267396	−	0.963587i	$-0.586163\pi$
$181$	9.42820	−	16.3301i	0.700793	−	1.21381i	0.968188	−	0.250222i	$-0.0805036\pi$
$182$	5.01910	+	2.89778i	0.372040	+	0.214798i
$183$		0			0
$184$			2.73205i			0.201409i
$185$	2.03339	+	20.9730i	0.149498	+	1.54196i
$186$		0			0
$187$	10.1962	+	2.73205i	0.745617	+	0.199787i
$188$	4.38134	−	7.58871i	0.319542	−	0.553463i
$189$		0			0
$190$	21.1244	−	5.66025i	1.53252	−	0.410638i
$191$	13.6245	−	13.6245i	0.985834	−	0.985834i	−0.0140670	−	0.999901i	$-0.504478\pi$
$191$	13.6245	−	13.6245i	0.985834	−	0.985834i	0.999901	+	0.0140670i	$0.00447782\pi$
$192$		0			0
$193$	−4.56218	−	4.56218i	−0.328393	−	0.328393i	0.523582	−	0.851975i	$-0.324595\pi$
$193$	−4.56218	−	4.56218i	−0.328393	−	0.328393i	−0.851975	+	0.523582i	$0.824595\pi$
$194$	−13.5044	+	7.79676i	−0.969558	+	0.559775i
$195$		0			0
$196$		−	6.00000i		−	0.428571i
$197$	−1.31268	+	0.757875i	−0.0935244	+	0.0539963i	−0.546033	−	0.837764i	$-0.683863\pi$
$197$	−1.31268	+	0.757875i	−0.0935244	+	0.0539963i	0.452508	+	0.891760i	$0.350529\pi$
$198$		0			0
$199$	12.8301	−	12.8301i	0.909504	−	0.909504i	−0.0867284	−	0.996232i	$-0.527641\pi$
$199$	12.8301	−	12.8301i	0.909504	−	0.909504i	0.996232	+	0.0867284i	$0.0276412\pi$
$200$	−1.81173	+	6.76148i	−0.128109	+	0.478109i
$201$		0			0
$202$	4.36603	−	16.2942i	0.307192	−	1.14646i
$203$	0.189469	−	0.0507680i	0.0132981	−	0.00356321i
$204$		0			0
$205$	6.92820	+	1.85641i	0.483887	+	0.129657i
$206$	9.46979	+	16.4022i	0.659792	+	1.14279i
$207$		0			0
$208$	4.09808	+	4.09808i	0.284150	+	0.284150i
$209$	−23.5612	+	6.31319i	−1.62976	+	0.436693i
$210$		0			0
$211$	0.607695			0.0418355			0.0209177	−	0.999781i	$-0.493341\pi$
$211$	0.607695			0.0418355			0.0209177	+	0.999781i	$0.493341\pi$
$212$	2.82843			0.194257
$213$		0			0
$214$	0.928203	−	0.928203i	0.0634507	−	0.0634507i
$215$	18.5235	−	32.0836i	1.26329	−	2.18808i
$216$		0			0
$217$	1.33013	+	4.96410i	0.0902949	+	0.336985i
$218$	11.1428	+	6.43331i	0.754687	+	0.435719i
$219$		0			0
$220$	3.46410	−	12.9282i	0.233550	−	0.871619i
$221$	15.8338			1.06509
$222$		0			0
$223$	−13.5885			−0.909950			−0.454975	−	0.890504i	$-0.650352\pi$
$223$	−13.5885			−0.909950			−0.454975	+	0.890504i	$0.650352\pi$
$224$	−0.258819	+	0.965926i	−0.0172931	+	0.0645386i
$225$		0			0
$226$	12.1244	+	7.00000i	0.806500	+	0.465633i
$227$	−2.60179	−	9.71003i	−0.172687	−	0.644477i	−0.996934	−	0.0782466i	$-0.975068\pi$
$227$	−2.60179	−	9.71003i	−0.172687	−	0.644477i	0.824247	−	0.566231i	$-0.191599\pi$
$228$		0			0
$229$	−0.330127	+	0.571797i	−0.0218154	+	0.0377854i	−0.876727	−	0.480988i	$-0.840278\pi$
$229$	−0.330127	+	0.571797i	−0.0218154	+	0.0377854i	0.854912	+	0.518774i	$0.173611\pi$
$230$	6.69213	−	6.69213i	0.441266	−	0.441266i
$231$		0			0
$232$	0.196152			0.0128780
$233$	−22.0454			−1.44424			−0.722121	−	0.691766i	$-0.756833\pi$
$233$	−22.0454			−1.44424			−0.722121	+	0.691766i	$0.756833\pi$
$234$		0			0
$235$	−29.3205	+	7.85641i	−1.91266	+	0.512495i
$236$	−3.34607	−	3.34607i	−0.217810	−	0.217810i
$237$		0			0
$238$	1.36603	+	2.36603i	0.0885463	+	0.153367i
$239$	−0.845807	−	0.226633i	−0.0547107	−	0.0146597i	0.231360	−	0.972868i	$-0.425683\pi$
$239$	−0.845807	−	0.226633i	−0.0547107	−	0.0146597i	−0.286071	+	0.958209i	$0.592349\pi$
$240$		0			0
$241$	−22.5263	+	6.03590i	−1.45105	+	0.388806i	−0.896387	−	0.443272i	$-0.853818\pi$
$241$	−22.5263	+	6.03590i	−1.45105	+	0.388806i	−0.554658	+	0.832078i	$0.687151\pi$
$242$	−1.01669	+	3.79435i	−0.0653556	+	0.243910i
$243$		0			0
$244$	−0.633975	+	2.36603i	−0.0405861	+	0.151469i
$245$	−14.6969	+	14.6969i	−0.938953	+	0.938953i
$246$		0			0
$247$	−31.6865	+	18.2942i	−2.01617	+	1.16403i
$248$			5.13922i			0.326341i
$249$		0			0
$250$	6.00000	−	3.46410i	0.379473	−	0.219089i
$251$	17.1464	+	17.1464i	1.08227	+	1.08227i	0.996297	+	0.0859757i	$0.0274007\pi$
$251$	17.1464	+	17.1464i	1.08227	+	1.08227i	0.0859757	+	0.996297i	$0.472599\pi$
$252$		0			0
$253$	−7.46410	+	7.46410i	−0.469264	+	0.469264i
$254$	−0.258819	+	0.0693504i	−0.0162398	+	0.00435143i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.896575	+	0.240237i	0.0559268	+	0.0149856i	0.286674	−	0.958028i	$-0.407450\pi$
$257$	0.896575	+	0.240237i	0.0559268	+	0.0149856i	−0.230747	+	0.973014i	$0.574117\pi$
$258$		0			0
$259$	3.86603	−	4.69615i	0.240223	−	0.291805i
$260$		−	20.0764i		−	1.24508i
$261$		0			0
$262$	3.63397	+	2.09808i	0.224508	+	0.129620i
$263$	2.91636	−	5.05128i	0.179830	−	0.311475i	−0.761992	−	0.647587i	$-0.775778\pi$
$263$	2.91636	−	5.05128i	0.179830	−	0.311475i	0.941822	+	0.336111i	$0.109112\pi$
$264$		0			0
$265$	−6.92820	−	6.92820i	−0.425596	−	0.425596i
$266$	−5.46739	−	3.15660i	−0.335227	−	0.193543i
$267$		0			0
$268$	1.50000	+	2.59808i	0.0916271	+	0.158703i
$269$		−	14.4195i		−	0.879175i	−0.898200	−	0.439587i	$-0.855125\pi$
$269$		−	14.4195i		−	0.879175i	0.898200	−	0.439587i	$-0.144875\pi$
$270$		0			0
$271$	12.6244	+	21.8660i	0.766875	+	1.32827i	0.939250	+	0.343235i	$0.111523\pi$
$271$	12.6244	+	21.8660i	0.766875	+	1.32827i	−0.172375	+	0.985031i	$0.555144\pi$
$272$	0.707107	+	2.63896i	0.0428746	+	0.160010i
$273$		0			0
$274$	−12.9282	−	3.46410i	−0.781021	−	0.209274i
$275$	−23.4225	+	13.5230i	−1.41243	+	0.815465i
$276$		0			0
$277$	−4.90192	−	18.2942i	−0.294528	−	1.09919i	−0.941591	−	0.336757i	$-0.890670\pi$
$277$	−4.90192	−	18.2942i	−0.294528	−	1.09919i	0.647063	−	0.762436i	$-0.275997\pi$
$278$	2.56961	+	9.58991i	0.154115	+	0.575164i
$279$		0			0
$280$	3.00000	−	1.73205i	0.179284	−	0.103510i
$281$	−3.01790	−	0.808643i	−0.180033	−	0.0482396i	0.167676	−	0.985842i	$-0.446374\pi$
$281$	−3.01790	−	0.808643i	−0.180033	−	0.0482396i	−0.347709	+	0.937603i	$0.613040\pi$
$282$		0			0
$283$	−1.79423	−	6.69615i	−0.106656	−	0.398045i	0.891872	−	0.452288i	$-0.149392\pi$
$283$	−1.79423	−	6.69615i	−0.106656	−	0.398045i	−0.998528	+	0.0542431i	$0.982725\pi$
$284$	−1.41421	−	2.44949i	−0.0839181	−	0.145350i
$285$		0			0
$286$			22.3923i			1.32408i
$287$	−1.03528	−	1.79315i	−0.0611104	−	0.105846i
$288$		0			0
$289$	−8.25833	−	4.76795i	−0.485784	−	0.280468i
$290$	−0.480473	−	0.480473i	−0.0282144	−	0.0282144i
$291$		0			0
$292$	−7.69615	+	13.3301i	−0.450383	+	0.780087i
$293$	−19.5080	−	11.2629i	−1.13967	−	0.657988i	−0.193320	−	0.981136i	$-0.561926\pi$
$293$	−19.5080	−	11.2629i	−1.13967	−	0.657988i	−0.946349	+	0.323148i	$0.895259\pi$
$294$		0			0
$295$			16.3923i			0.954397i
$296$	4.94975	−	3.53553i	0.287698	−	0.205499i
$297$		0			0
$298$	−6.83013	−	1.83013i	−0.395659	−	0.106016i
$299$	−7.91688	+	13.7124i	−0.457845	+	0.793010i
$300$		0			0
$301$	−10.3301	+	2.76795i	−0.595419	+	0.159542i
$302$	7.67664	−	7.67664i	0.441741	−	0.441741i
$303$		0			0
$304$	−4.46410	−	4.46410i	−0.256034	−	0.256034i
$305$	7.34847	−	4.24264i	0.420772	−	0.242933i
$306$		0			0
$307$			24.2679i			1.38505i	0.721396	+	0.692523i	$0.243501\pi$
$307$			24.2679i			1.38505i	−0.721396	+	0.692523i	$0.756499\pi$
$308$	−3.34607	+	1.93185i	−0.190660	+	0.110077i
$309$		0			0
$310$	12.5885	−	12.5885i	0.714976	−	0.714976i
$311$	8.05558	−	30.0638i	0.456790	−	1.70476i	−0.225982	−	0.974131i	$-0.572559\pi$
$311$	8.05558	−	30.0638i	0.456790	−	1.70476i	0.682772	−	0.730631i	$-0.260774\pi$
$312$		0			0
$313$	−6.57180	+	24.5263i	−0.371460	+	1.38631i	0.486989	+	0.873408i	$0.338095\pi$
$313$	−6.57180	+	24.5263i	−0.371460	+	1.38631i	−0.858449	+	0.512899i	$0.828571\pi$
$314$	−4.82963	+	1.29410i	−0.272552	+	0.0730300i
$315$		0			0
$316$	0.133975	+	0.0358984i	0.00753666	+	0.00201944i
$317$	9.71003	+	16.8183i	0.545369	+	0.944608i	0.998584	+	0.0532059i	$0.0169440\pi$
$317$	9.71003	+	16.8183i	0.545369	+	0.944608i	−0.453214	+	0.891402i	$0.649723\pi$
$318$		0			0
$319$	0.535898	+	0.535898i	0.0300045	+	0.0300045i
$320$	3.34607	−	0.896575i	0.187051	−	0.0501201i
$321$		0			0
$322$	−2.73205			−0.152251
$323$	−17.2480			−0.959702
$324$		0			0
$325$	−28.6865	+	28.6865i	−1.59124	+	1.59124i
$326$	−1.46498	+	2.53742i	−0.0811378	+	0.140535i
$327$		0			0
$328$	−0.535898	−	2.00000i	−0.0295900	−	0.110432i
$329$	7.58871	+	4.38134i	0.418379	+	0.241551i
$330$		0			0
$331$	4.74167	−	17.6962i	0.260626	−	0.972669i	−0.704248	−	0.709954i	$-0.748716\pi$
$331$	4.74167	−	17.6962i	0.260626	−	0.972669i	0.964874	−	0.262714i	$-0.0846177\pi$
$332$	16.1112			0.884214
$333$		0			0
$334$	16.1962			0.886214
$335$	2.68973	−	10.0382i	0.146955	−	0.548445i
$336$		0			0
$337$	−0.232051	−	0.133975i	−0.0126406	−	0.00729806i	0.493666	−	0.869651i	$-0.335656\pi$
$337$	−0.232051	−	0.133975i	−0.0126406	−	0.00729806i	−0.506307	+	0.862353i	$0.668990\pi$
$338$	5.32868	+	19.8869i	0.289842	+	1.08171i
$339$		0			0
$340$	4.73205	−	8.19615i	0.256631	−	0.444499i
$341$	−14.0406	+	14.0406i	−0.760341	+	0.760341i
$342$		0			0
$343$	13.0000			0.701934
$344$	−10.6945			−0.576611
$345$		0			0
$346$	−23.7583	+	6.36603i	−1.27726	+	0.342240i
$347$	−3.62347	−	3.62347i	−0.194518	−	0.194518i	0.603127	−	0.797645i	$-0.293921\pi$
$347$	−3.62347	−	3.62347i	−0.194518	−	0.194518i	−0.797645	+	0.603127i	$0.793921\pi$
$348$		0			0
$349$	−6.92820	−	12.0000i	−0.370858	−	0.642345i	0.618840	−	0.785517i	$-0.287603\pi$
$349$	−6.92820	−	12.0000i	−0.370858	−	0.642345i	−0.989698	+	0.143172i	$0.954270\pi$
$350$	−6.76148	−	1.81173i	−0.361416	−	0.0968412i
$351$		0			0
$352$	−3.73205	+	1.00000i	−0.198919	+	0.0533002i
$353$	3.77577	−	14.0914i	0.200964	−	0.750008i	−0.789678	−	0.613522i	$-0.789752\pi$
$353$	3.77577	−	14.0914i	0.200964	−	0.750008i	0.990642	−	0.136486i	$-0.0435810\pi$
$354$		0			0
$355$	−2.53590	+	9.46410i	−0.134592	+	0.502302i
$356$	−5.93426	+	5.93426i	−0.314515	+	0.314515i
$357$		0			0
$358$	7.73205	−	4.46410i	0.408652	−	0.235935i
$359$		−	19.1427i		−	1.01031i	−0.863028	−	0.505155i	$-0.831435\pi$
$359$		−	19.1427i		−	1.01031i	0.863028	−	0.505155i	$-0.168565\pi$
$360$		0			0
$361$	18.0622	−	10.4282i	0.950641	−	0.548853i
$362$	13.3335	+	13.3335i	0.700793	+	0.700793i
$363$		0			0
$364$	−4.09808	+	4.09808i	−0.214798	+	0.214798i
$365$	51.5037	−	13.8004i	2.69582	−	0.722344i
$366$		0			0
$367$	−7.66987	+	13.2846i	−0.400364	+	0.693451i	−0.993770	−	0.111453i	$-0.964450\pi$
$367$	−7.66987	+	13.2846i	−0.400364	+	0.693451i	0.593406	+	0.804904i	$0.297783\pi$
$368$	−2.63896	−	0.707107i	−0.137565	−	0.0368605i
$369$		0			0
$370$	−20.7846	−	3.46410i	−1.08054	−	0.180090i
$371$			2.82843i			0.146845i
$372$		0			0
$373$	−8.42820	−	4.86603i	−0.436396	−	0.251953i	0.265672	−	0.964064i	$-0.414406\pi$
$373$	−8.42820	−	4.86603i	−0.436396	−	0.251953i	−0.702068	+	0.712110i	$0.747740\pi$
$374$	−5.27792	+	9.14162i	−0.272915	+	0.472702i
$375$		0			0
$376$	6.19615	+	6.19615i	0.319542	+	0.319542i
$377$	0.984508	+	0.568406i	0.0507048	+	0.0292744i
$378$		0			0
$379$	3.66025	+	6.33975i	0.188015	+	0.325651i	0.944588	−	0.328258i	$-0.106461\pi$
$379$	3.66025	+	6.33975i	0.188015	+	0.325651i	−0.756574	+	0.653909i	$0.773128\pi$
$380$			21.8695i			1.12188i
$381$		0			0
$382$	9.63397	+	16.6865i	0.492917	+	0.853757i
$383$	7.50077	+	27.9933i	0.383272	+	1.43039i	0.840873	+	0.541232i	$0.182042\pi$
$383$	7.50077	+	27.9933i	0.383272	+	1.43039i	−0.457602	+	0.889157i	$0.651291\pi$
$384$		0			0
$385$	12.9282	+	3.46410i	0.658882	+	0.176547i
$386$	5.58750	−	3.22595i	0.284396	−	0.164196i
$387$		0			0
$388$	−4.03590	−	15.0622i	−0.204892	−	0.764666i
$389$	−1.07244	−	4.00240i	−0.0543749	−	0.202930i	0.933394	−	0.358852i	$-0.116832\pi$
$389$	−1.07244	−	4.00240i	−0.0543749	−	0.202930i	−0.987769	+	0.155922i	$0.950165\pi$
$390$		0			0
$391$	−6.46410	+	3.73205i	−0.326904	+	0.188738i
$392$	5.79555	+	1.55291i	0.292720	+	0.0784340i
$393$		0			0
$394$	−0.392305	−	1.46410i	−0.0197640	−	0.0737604i
$395$	−0.240237	−	0.416102i	−0.0120876	−	0.0209364i
$396$		0			0
$397$			32.5167i			1.63196i	0.578077	+	0.815982i	$0.303803\pi$
$397$			32.5167i			1.63196i	−0.578077	+	0.815982i	$0.696197\pi$
$398$	9.07227	+	15.7136i	0.454752	+	0.787653i
$399$		0			0
$400$	−6.06218	−	3.50000i	−0.303109	−	0.175000i
$401$	16.4901	+	16.4901i	0.823476	+	0.823476i	0.986605	−	0.163129i	$-0.0521587\pi$
$401$	16.4901	+	16.4901i	0.823476	+	0.823476i	−0.163129	+	0.986605i	$0.552159\pi$
$402$		0			0
$403$	−14.8923	+	25.7942i	−0.741839	+	1.28490i
$404$	14.6090	+	8.43451i	0.726825	+	0.419633i
$405$		0			0
$406$			0.196152i			0.00973488i
$407$	23.1822	+	3.86370i	1.14910	+	0.191517i
$408$		0			0
$409$	23.8923	+	6.40192i	1.18140	+	0.316555i	0.795481	−	0.605979i	$-0.207218\pi$
$409$	23.8923	+	6.40192i	1.18140	+	0.316555i	0.385917	+	0.922533i	$0.373885\pi$
$410$	−3.58630	+	6.21166i	−0.177115	+	0.306772i
$411$		0			0
$412$	−18.2942	+	4.90192i	−0.901292	+	0.241500i
$413$	3.34607	−	3.34607i	0.164649	−	0.164649i
$414$		0			0
$415$	−39.4641	−	39.4641i	−1.93722	−	1.93722i
$416$	−5.01910	+	2.89778i	−0.246082	+	0.142075i
$417$		0			0
$418$		−	24.3923i		−	1.19307i
$419$	−13.2320	+	7.63947i	−0.646423	+	0.373213i	−0.787085	−	0.616845i	$-0.788411\pi$
$419$	−13.2320	+	7.63947i	−0.646423	+	0.373213i	0.140661	+	0.990058i	$0.455077\pi$
$420$		0			0
$421$	8.12436	−	8.12436i	0.395957	−	0.395957i	−0.480847	−	0.876804i	$-0.659671\pi$
$421$	8.12436	−	8.12436i	0.395957	−	0.395957i	0.876804	+	0.480847i	$0.159671\pi$
$422$	−0.157283	+	0.586988i	−0.00765642	+	0.0285742i
$423$		0			0
$424$	−0.732051	+	2.73205i	−0.0355515	+	0.132680i
$425$	−18.4727	+	4.94975i	−0.896058	+	0.240098i
$426$		0			0
$427$	−2.36603	−	0.633975i	−0.114500	−	0.0306802i
$428$	0.656339	+	1.13681i	0.0317253	+	0.0549499i
$429$		0			0
$430$	26.1962	+	26.1962i	1.26329	+	1.26329i
$431$	−15.8338	+	4.24264i	−0.762685	+	0.204361i	−0.619137	−	0.785283i	$-0.712518\pi$
$431$	−15.8338	+	4.24264i	−0.762685	+	0.204361i	−0.143547	+	0.989643i	$0.545851\pi$
$432$		0			0
$433$	15.8564			0.762010			0.381005	−	0.924573i	$-0.375578\pi$
$433$	15.8564			0.762010			0.381005	+	0.924573i	$0.375578\pi$
$434$	−5.13922			−0.246690
$435$		0			0
$436$	−9.09808	+	9.09808i	−0.435719	+	0.435719i
$437$	8.62398	−	14.9372i	0.412541	−	0.714542i
$438$		0			0
$439$	−4.62436	−	17.2583i	−0.220708	−	0.823695i	−0.984079	−	0.177734i	$-0.943123\pi$
$439$	−4.62436	−	17.2583i	−0.220708	−	0.823695i	0.763370	−	0.645961i	$-0.223543\pi$
$440$	11.5911	+	6.69213i	0.552584	+	0.319035i
$441$		0			0
$442$	−4.09808	+	15.2942i	−0.194926	+	0.727472i
$443$	−32.7028			−1.55376			−0.776878	−	0.629651i	$-0.783198\pi$
$443$	−32.7028			−1.55376			−0.776878	+	0.629651i	$0.783198\pi$
$444$		0			0
$445$	29.0718			1.37814
$446$	3.51695	−	13.1254i	0.166532	−	0.621508i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	5.18998	+	19.3693i	0.244930	+	0.914093i	0.973418	+	0.229034i	$0.0735568\pi$
$449$	5.18998	+	19.3693i	0.244930	+	0.914093i	−0.728488	+	0.685059i	$0.759777\pi$
$450$		0			0
$451$	4.00000	−	6.92820i	0.188353	−	0.326236i
$452$	−9.89949	+	9.89949i	−0.465633	+	0.465633i
$453$		0			0
$454$	10.0526			0.471790
$455$	20.0764			0.941196
$456$		0			0
$457$	−25.6865	+	6.88269i	−1.20157	+	0.321958i	−0.803447	−	0.595376i	$-0.797003\pi$
$457$	−25.6865	+	6.88269i	−1.20157	+	0.321958i	−0.398118	+	0.917334i	$0.630337\pi$
$458$	−0.466870	−	0.466870i	−0.0218154	−	0.0218154i
$459$		0			0
$460$	4.73205	+	8.19615i	0.220633	+	0.382148i
$461$	21.6293	+	5.79555i	1.00738	+	0.269926i	0.724533	−	0.689240i	$-0.242055\pi$
$461$	21.6293	+	5.79555i	1.00738	+	0.269926i	0.282844	+	0.959166i	$0.408722\pi$
$462$		0			0
$463$	19.8923	−	5.33013i	0.924474	−	0.247712i	0.234977	−	0.972001i	$-0.424498\pi$
$463$	19.8923	−	5.33013i	0.924474	−	0.247712i	0.689497	+	0.724289i	$0.257832\pi$
$464$	−0.0507680	+	0.189469i	−0.00235684	+	0.00879586i
$465$		0			0
$466$	5.70577	−	21.2942i	0.264315	−	0.986436i
$467$	2.07055	−	2.07055i	0.0958137	−	0.0958137i	−0.657575	−	0.753389i	$-0.728418\pi$
$467$	2.07055	−	2.07055i	0.0958137	−	0.0958137i	0.753389	+	0.657575i	$0.228418\pi$
$468$		0			0
$469$	−2.59808	+	1.50000i	−0.119968	+	0.0692636i
$470$		−	30.3548i		−	1.40016i
$471$		0			0
$472$	4.09808	−	2.36603i	0.188629	−	0.108905i
$473$	−29.2180	−	29.2180i	−1.34345	−	1.34345i
$474$		0			0
$475$	31.2487	−	31.2487i	1.43379	−	1.43379i
$476$	−2.63896	+	0.707107i	−0.120956	+	0.0324102i
$477$		0			0
$478$	0.437822	−	0.758330i	0.0200255	−	0.0346852i
$479$	14.2301	+	3.81294i	0.650188	+	0.174217i	0.568814	−	0.822466i	$-0.307402\pi$
$479$	14.2301	+	3.81294i	0.650188	+	0.174217i	0.0813744	+	0.996684i	$0.474069\pi$
$480$		0			0
$481$	35.0885	−	3.40192i	1.59990	−	0.155114i
$482$		−	23.3209i		−	1.06224i
$483$		0			0
$484$	−3.40192	−	1.96410i	−0.154633	−	0.0892773i
$485$	−27.0088	+	46.7805i	−1.22640	+	2.12419i
$486$		0			0
$487$	−24.6603	−	24.6603i	−1.11746	−	1.11746i	−0.992113	−	0.125350i	$-0.959995\pi$
$487$	−24.6603	−	24.6603i	−1.11746	−	1.11746i	−0.125350	−	0.992113i	$-0.540005\pi$
$488$	−2.12132	−	1.22474i	−0.0960277	−	0.0554416i
$489$		0			0
$490$	−10.3923	−	18.0000i	−0.469476	−	0.813157i
$491$		−	31.0112i		−	1.39951i	−0.714381	−	0.699757i	$-0.753292\pi$
$491$		−	31.0112i		−	1.39951i	0.714381	−	0.699757i	$-0.246708\pi$
$492$		0			0
$493$	0.267949	+	0.464102i	0.0120678	+	0.0209021i
$494$	−9.46979	−	35.3417i	−0.426066	−	1.59010i
$495$		0			0
$496$	−4.96410	−	1.33013i	−0.222895	−	0.0597245i
$497$	2.44949	−	1.41421i	0.109875	−	0.0634361i
$498$		0			0
$499$	0.509619	+	1.90192i	0.0228137	+	0.0851418i	0.976394	−	0.215997i	$-0.0693000\pi$
$499$	0.509619	+	1.90192i	0.0228137	+	0.0851418i	−0.953580	+	0.301138i	$0.902633\pi$
$500$	1.79315	+	6.69213i	0.0801921	+	0.299281i
$501$		0			0
$502$	−21.0000	+	12.1244i	−0.937276	+	0.541136i
$503$	−31.8570	−	8.53605i	−1.42043	−	0.380604i	−0.534795	−	0.844982i	$-0.679611\pi$
$503$	−31.8570	−	8.53605i	−1.42043	−	0.380604i	−0.885637	+	0.464378i	$0.846278\pi$
$504$		0			0
$505$	−15.1244	−	56.4449i	−0.673025	−	2.51176i
$506$	−5.27792	−	9.14162i	−0.234632	−	0.406395i
$507$		0			0
$508$		−	0.267949i		−	0.0118883i
$509$	−16.5409	−	28.6496i	−0.733161	−	1.26987i	−0.955526	−	0.294908i	$-0.904711\pi$
$509$	−16.5409	−	28.6496i	−0.733161	−	1.26987i	0.222365	−	0.974963i	$-0.428622\pi$
$510$		0			0
$511$	−13.3301	−	7.69615i	−0.589690	−	0.340458i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−0.464102	+	0.803848i	−0.0204706	+	0.0354562i
$515$	56.8187	+	32.8043i	2.50373	+	1.44553i
$516$		0			0
$517$			33.8564i			1.48900i
$518$	3.53553	+	4.94975i	0.155342	+	0.217479i
$519$		0			0
$520$	19.3923	+	5.19615i	0.850409	+	0.227866i
$521$	−0.795040	+	1.37705i	−0.0348313	+	0.0603296i	−0.882916	−	0.469532i	$-0.844423\pi$
$521$	−0.795040	+	1.37705i	−0.0348313	+	0.0603296i	0.848084	+	0.529861i	$0.177756\pi$
$522$		0			0
$523$	9.52628	−	2.55256i	0.416555	−	0.111616i	−0.0444531	−	0.999011i	$-0.514155\pi$
$523$	9.52628	−	2.55256i	0.416555	−	0.111616i	0.461008	+	0.887396i	$0.347488\pi$
$524$	−2.96713	+	2.96713i	−0.129620	+	0.129620i
$525$		0			0
$526$	4.12436	+	4.12436i	0.179830	+	0.179830i
$527$	−12.1595	+	7.02030i	−0.529677	+	0.305809i
$528$		0			0
$529$			15.5359i			0.675474i
$530$	8.48528	−	4.89898i	0.368577	−	0.212798i
$531$		0			0
$532$	4.46410	−	4.46410i	0.193543	−	0.193543i
$533$	3.10583	−	11.5911i	0.134528	−	0.502067i
$534$		0			0
$535$	1.17691	−	4.39230i	0.0508825	−	0.189896i
$536$	−2.89778	+	0.776457i	−0.125165	+	0.0335378i
$537$		0			0
$538$	13.9282	+	3.73205i	0.600487	+	0.160900i
$539$	11.5911	+	20.0764i	0.499264	+	0.864751i
$540$		0			0
$541$	−6.29423	−	6.29423i	−0.270610	−	0.270610i	0.558736	−	0.829346i	$-0.311287\pi$
$541$	−6.29423	−	6.29423i	−0.270610	−	0.270610i	−0.829346	+	0.558736i	$0.811287\pi$
$542$	−24.3884	+	6.53485i	−1.04757	+	0.280696i
$543$		0			0
$544$	−2.73205			−0.117136
$545$	44.5713			1.90922
$546$		0			0
$547$	−17.9545	+	17.9545i	−0.767678	+	0.767678i	−0.977697	−	0.210019i	$-0.932647\pi$
$547$	−17.9545	+	17.9545i	−0.767678	+	0.767678i	0.210019	+	0.977697i	$0.432647\pi$
$548$	6.69213	−	11.5911i	0.285874	−	0.495148i
$549$		0			0
$550$	−7.00000	−	26.1244i	−0.298481	−	1.11395i
$551$	−1.07244	−	0.619174i	−0.0456875	−	0.0263777i
$552$		0			0
$553$	−0.0358984	+	0.133975i	−0.00152655	+	0.00569718i
$554$	18.9396			0.804666
$555$		0			0
$556$	−9.92820			−0.421050
$557$	1.26191	−	4.70951i	0.0534688	−	0.199548i	−0.934025	−	0.357209i	$-0.883728\pi$
$557$	1.26191	−	4.70951i	0.0534688	−	0.199548i	0.987493	+	0.157660i	$0.0503951\pi$
$558$		0			0
$559$	−53.6769	−	30.9904i	−2.27029	−	1.31075i
$560$	0.896575	+	3.34607i	0.0378872	+	0.141397i
$561$		0			0
$562$	1.56218	−	2.70577i	0.0658965	−	0.114136i
$563$	−5.37945	+	5.37945i	−0.226717	+	0.226717i	−0.811320	−	0.584603i	$-0.801250\pi$
$563$	−5.37945	+	5.37945i	−0.226717	+	0.226717i	0.584603	+	0.811320i	$0.301250\pi$
$564$		0			0
$565$	48.4974			2.04030
$566$	6.93237			0.291389
$567$		0			0
$568$	2.73205	−	0.732051i	0.114634	−	0.0307162i
$569$	−9.55772	−	9.55772i	−0.400681	−	0.400681i	0.477792	−	0.878473i	$-0.341437\pi$
$569$	−9.55772	−	9.55772i	−0.400681	−	0.400681i	−0.878473	+	0.477792i	$0.841437\pi$
$570$		0			0
$571$	23.0622	+	39.9449i	0.965122	+	1.67164i	0.709287	+	0.704920i	$0.249017\pi$
$571$	23.0622	+	39.9449i	0.965122	+	1.67164i	0.255835	+	0.966720i	$0.417649\pi$
$572$	−21.6293	−	5.79555i	−0.904367	−	0.242324i
$573$		0			0
$574$	2.00000	−	0.535898i	0.0834784	−	0.0223680i
$575$	4.94975	−	18.4727i	0.206419	−	0.770365i
$576$		0			0
$577$	−7.95448	+	29.6865i	−0.331149	+	1.23587i	0.576834	+	0.816861i	$0.304288\pi$
$577$	−7.95448	+	29.6865i	−0.331149	+	1.23587i	−0.907984	+	0.419005i	$0.862379\pi$
$578$	6.74290	−	6.74290i	0.280468	−	0.280468i
$579$		0			0
$580$	0.588457	−	0.339746i	0.0244344	−	0.0141072i
$581$			16.1112i			0.668403i
$582$		0			0
$583$	−9.46410	+	5.46410i	−0.391963	+	0.226300i
$584$	−10.8840	−	10.8840i	−0.450383	−	0.450383i
$585$		0			0
$586$	15.9282	−	15.9282i	0.657988	−	0.657988i
$587$	−29.0793	+	7.79178i	−1.20023	+	0.321601i	−0.802922	−	0.596084i	$-0.796723\pi$
$587$	−29.0793	+	7.79178i	−1.20023	+	0.321601i	−0.397309	+	0.917685i	$0.630056\pi$
$588$		0			0
$589$	16.2224	−	28.0981i	0.668434	−	1.15776i
$590$	−15.8338	−	4.24264i	−0.651865	−	0.174667i
$591$		0			0
$592$	2.13397	+	5.69615i	0.0877058	+	0.234110i
$593$		−	42.7038i		−	1.75364i	−0.480823	−	0.876818i	$-0.659662\pi$
$593$		−	42.7038i		−	1.75364i	0.480823	−	0.876818i	$-0.340338\pi$
$594$		0			0
$595$	8.19615	+	4.73205i	0.336009	+	0.193995i
$596$	3.53553	−	6.12372i	0.144821	−	0.250838i
$597$		0			0
$598$	−11.1962	−	11.1962i	−0.457845	−	0.457845i
$599$	−37.1349	−	21.4398i	−1.51729	−	0.876008i	−0.999793	−	0.0203229i	$-0.993531\pi$
$599$	−37.1349	−	21.4398i	−1.51729	−	0.876008i	−0.517497	−	0.855685i	$-0.673136\pi$
$600$		0			0
$601$	−13.7942	−	23.8923i	−0.562678	−	0.974587i	−0.997262	−	0.0739558i	$-0.976438\pi$
$601$	−13.7942	−	23.8923i	−0.562678	−	0.974587i	0.434583	−	0.900632i	$-0.356896\pi$
$602$		−	10.6945i		−	0.435877i
$603$		0			0
$604$	5.42820	+	9.40192i	0.220870	+	0.382559i
$605$	3.52193	+	13.1440i	0.143187	+	0.534381i
$606$		0			0
$607$	39.6147	+	10.6147i	1.60791	+	0.430839i	0.947420	−	0.319993i	$-0.103681\pi$
$607$	39.6147	+	10.6147i	1.60791	+	0.430839i	0.660493	+	0.750832i	$0.270347\pi$
$608$	5.46739	−	3.15660i	0.221732	−	0.128017i
$609$		0			0
$610$	2.19615	+	8.19615i	0.0889196	+	0.331853i
$611$	13.1440	+	49.0542i	0.531750	+	1.98452i
$612$		0			0
$613$	31.2679	−	18.0526i	1.26290	−	0.729136i	0.289266	−	0.957249i	$-0.406589\pi$
$613$	31.2679	−	18.0526i	1.26290	−	0.729136i	0.973635	+	0.228113i	$0.0732555\pi$
$614$	−23.4410	−	6.28101i	−0.946003	−	0.253481i
$615$		0			0
$616$	−1.00000	−	3.73205i	−0.0402911	−	0.150369i
$617$	13.9019	+	24.0788i	0.559669	+	0.969376i	0.997524	+	0.0703299i	$0.0224052\pi$
$617$	13.9019	+	24.0788i	0.559669	+	0.969376i	−0.437854	+	0.899046i	$0.644261\pi$
$618$		0			0
$619$		−	39.0526i		−	1.56965i	−0.619714	−	0.784827i	$-0.712752\pi$
$619$		−	39.0526i		−	1.56965i	0.619714	−	0.784827i	$-0.287248\pi$
$620$	8.90138	+	15.4176i	0.357488	+	0.619188i
$621$		0			0
$622$	26.9545	+	15.5622i	1.08078	+	0.623986i
$623$	−5.93426	−	5.93426i	−0.237751	−	0.237751i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−21.9897	−	12.6957i	−0.878884	−	0.507424i
$627$		0			0
$628$		−	5.00000i		−	0.199522i
$629$	15.1266	+	6.88160i	0.603139	+	0.274387i
$630$		0			0
$631$	13.5263	+	3.62436i	0.538473	+	0.144283i	0.517798	−	0.855503i	$-0.326752\pi$
$631$	13.5263	+	3.62436i	0.538473	+	0.144283i	0.0206747	+	0.999786i	$0.493419\pi$
$632$	−0.0693504	+	0.120118i	−0.00275861	+	0.00477805i
$633$		0			0
$634$	−18.7583	+	5.02628i	−0.744988	+	0.199619i
$635$	−0.656339	+	0.656339i	−0.0260460	+	0.0260460i
$636$		0			0
$637$	24.5885	+	24.5885i	0.974230	+	0.974230i
$638$	−0.656339	+	0.378937i	−0.0259847	+	0.0150023i
$639$		0			0
$640$			3.46410i			0.136931i
$641$	14.7849	−	8.53605i	0.583967	−	0.337154i	−0.178741	−	0.983896i	$-0.557202\pi$
$641$	14.7849	−	8.53605i	0.583967	−	0.337154i	0.762708	+	0.646742i	$0.223869\pi$
$642$		0			0
$643$	10.1506	−	10.1506i	0.400302	−	0.400302i	−0.478037	−	0.878339i	$-0.658652\pi$
$643$	10.1506	−	10.1506i	0.400302	−	0.400302i	0.878339	+	0.478037i	$0.158652\pi$
$644$	0.707107	−	2.63896i	0.0278639	−	0.103990i
$645$		0			0
$646$	4.46410	−	16.6603i	0.175638	−	0.655489i
$647$	4.38134	−	1.17398i	0.172248	−	0.0461538i	−0.171664	−	0.985156i	$-0.554914\pi$
$647$	4.38134	−	1.17398i	0.172248	−	0.0461538i	0.343912	+	0.939002i	$0.388248\pi$
$648$		0			0
$649$	17.6603	+	4.73205i	0.693226	+	0.185749i
$650$	−20.2844	−	35.1337i	−0.795621	−	1.37806i
$651$		0			0
$652$	−2.07180	−	2.07180i	−0.0811378	−	0.0811378i
$653$	−6.69213	+	1.79315i	−0.261883	+	0.0701714i	−0.387372	−	0.921924i	$-0.626617\pi$
$653$	−6.69213	+	1.79315i	−0.261883	+	0.0701714i	0.125488	+	0.992095i	$0.459950\pi$
$654$		0			0
$655$	14.5359			0.567965
$656$	2.07055			0.0808415
$657$		0			0
$658$	−6.19615	+	6.19615i	−0.241551	+	0.241551i
$659$	−15.4548	+	26.7685i	−0.602034	+	1.04275i	0.390479	+	0.920612i	$0.372310\pi$
$659$	−15.4548	+	26.7685i	−0.602034	+	1.04275i	−0.992513	+	0.122142i	$0.961024\pi$
$660$		0			0
$661$	−4.74167	−	17.6962i	−0.184430	−	0.688301i	−0.994752	−	0.102316i	$-0.967375\pi$
$661$	−4.74167	−	17.6962i	−0.184430	−	0.688301i	0.810322	−	0.585984i	$-0.199292\pi$
$662$	15.8659	+	9.16020i	0.616647	+	0.356021i
$663$		0			0
$664$	−4.16987	+	15.5622i	−0.161822	+	0.603930i
$665$	−21.8695			−0.848064
$666$		0			0
$667$	−0.535898			−0.0207501
$668$	−4.19187	+	15.6443i	−0.162188	+	0.605295i
$669$		0			0
$670$	9.00000	+	5.19615i	0.347700	+	0.200745i
$671$	−2.44949	−	9.14162i	−0.0945615	−	0.352908i
$672$		0			0
$673$	17.5885	−	30.4641i	0.677985	−	1.17430i	−0.297601	−	0.954690i	$-0.596187\pi$
$673$	17.5885	−	30.4641i	0.677985	−	1.17430i	0.975587	−	0.219615i	$-0.0704800\pi$
$674$	0.189469	−	0.189469i	0.00729806	−	0.00729806i
$675$		0			0
$676$	−20.5885			−0.791864
$677$	−4.14110			−0.159156			−0.0795778	−	0.996829i	$-0.525357\pi$
$677$	−4.14110			−0.159156			−0.0795778	+	0.996829i	$0.525357\pi$
$678$		0			0
$679$	15.0622	−	4.03590i	0.578033	−	0.154884i
$680$	6.69213	+	6.69213i	0.256631	+	0.256631i
$681$		0			0
$682$	−9.92820	−	17.1962i	−0.380171	−	0.658475i
$683$	34.4452	+	9.22955i	1.31801	+	0.353159i	0.848231	−	0.529626i	$-0.177668\pi$
$683$	34.4452	+	9.22955i	1.31801	+	0.353159i	0.469776	+	0.882785i	$0.344335\pi$
$684$		0			0
$685$	−44.7846	+	12.0000i	−1.71113	+	0.458496i
$686$	−3.36465	+	12.5570i	−0.128463	+	0.479430i
$687$		0			0
$688$	2.76795	−	10.3301i	0.105527	−	0.393832i
$689$	−11.5911	+	11.5911i	−0.441586	+	0.441586i
$690$		0			0
$691$	11.3827	−	6.57180i	0.433018	−	0.250003i	−0.267614	−	0.963526i	$-0.586235\pi$
$691$	11.3827	−	6.57180i	0.433018	−	0.250003i	0.700631	+	0.713523i	$0.252902\pi$
$692$		−	24.5964i		−	0.935016i
$693$		0			0
$694$	4.43782	−	2.56218i	0.168457	−	0.0972589i
$695$	24.3190	+	24.3190i	0.922473	+	0.922473i
$696$		0			0
$697$	4.00000	−	4.00000i	0.151511	−	0.151511i
$698$	13.3843	−	3.58630i	0.506602	−	0.135744i
$699$		0			0
$700$	3.50000	−	6.06218i	0.132288	−	0.229129i
$701$	−42.3620	−	11.3509i	−1.59999	−	0.428717i	−0.654952	−	0.755671i	$-0.727311\pi$
$701$	−42.3620	−	11.3509i	−1.59999	−	0.428717i	−0.945040	+	0.326954i	$0.893978\pi$
$702$		0			0
$703$	−38.2224	+	3.70577i	−1.44159	+	0.139766i
$704$		−	3.86370i		−	0.145619i
$705$		0			0
$706$	12.6340	+	7.29423i	0.475486	+	0.274522i
$707$	−8.43451	+	14.6090i	−0.317213	+	0.549428i
$708$		0			0
$709$	−15.2224	−	15.2224i	−0.571690	−	0.571690i	0.360910	−	0.932601i	$-0.382466\pi$
$709$	−15.2224	−	15.2224i	−0.571690	−	0.571690i	−0.932601	+	0.360910i	$0.882466\pi$
$710$	−8.48528	−	4.89898i	−0.318447	−	0.183855i
$711$		0			0
$712$	−4.19615	−	7.26795i	−0.157257	−	0.272378i
$713$		−	14.0406i		−	0.525825i
$714$		0			0
$715$	38.7846	+	67.1769i	1.45046	+	2.51227i
$716$	2.31079	+	8.62398i	0.0863582	+	0.322293i
$717$		0			0
$718$	18.4904	+	4.95448i	0.690055	+	0.184900i
$719$	32.9802	−	19.0411i	1.22995	−	0.710114i	0.262933	−	0.964814i	$-0.415310\pi$
$719$	32.9802	−	19.0411i	1.22995	−	0.710114i	0.967020	+	0.254700i	$0.0819768\pi$
$720$		0			0
$721$	−4.90192	−	18.2942i	−0.182557	−	0.681313i
$722$	5.39804	+	20.1457i	0.200894	+	0.749747i
$723$		0			0
$724$	−16.3301	+	9.42820i	−0.606904	+	0.350396i
$725$	−1.32628	−	0.355376i	−0.0492568	−	0.0131983i
$726$		0			0
$727$	−7.01666	−	26.1865i	−0.260234	−	0.971205i	−0.965104	−	0.261868i	$-0.915661\pi$
$727$	−7.01666	−	26.1865i	−0.260234	−	0.971205i	0.704870	−	0.709336i	$-0.251005\pi$
$728$	−2.89778	−	5.01910i	−0.107399	−	0.186020i
$729$		0			0
$730$			53.3205i			1.97348i
$731$	−14.6090	−	25.3035i	−0.540334	−	0.935885i
$732$		0			0
$733$	8.25833	+	4.76795i	0.305028	+	0.176108i	0.644700	−	0.764436i	$-0.276982\pi$
$733$	8.25833	+	4.76795i	0.305028	+	0.176108i	−0.339671	+	0.940544i	$0.610316\pi$
$734$	−10.8468	−	10.8468i	−0.400364	−	0.400364i
$735$		0			0
$736$	1.36603	−	2.36603i	0.0503524	−	0.0872129i
$737$	−10.0382	−	5.79555i	−0.369762	−	0.213482i
$738$		0			0
$739$		−	9.32051i		−	0.342860i	−0.985196	−	0.171430i	$-0.945161\pi$
$739$		−	9.32051i		−	0.342860i	0.985196	−	0.171430i	$-0.0548388\pi$
$740$	8.72552	−	19.1798i	0.320756	−	0.705064i
$741$		0			0
$742$	−2.73205	−	0.732051i	−0.100297	−	0.0268744i
$743$	−15.4040	+	26.6806i	−0.565120	+	0.978816i	0.431919	+	0.901912i	$0.357837\pi$
$743$	−15.4040	+	26.6806i	−0.565120	+	0.978816i	−0.997039	+	0.0769034i	$0.975497\pi$
$744$		0			0
$745$	−23.6603	+	6.33975i	−0.866845	+	0.232270i
$746$	6.88160	−	6.88160i	0.251953	−	0.251953i
$747$		0			0
$748$	−7.46410	−	7.46410i	−0.272915	−	0.272915i
$749$	−1.13681	+	0.656339i	−0.0415382	+	0.0239821i
$750$		0			0
$751$		−	7.19615i		−	0.262591i	−0.991343	−	0.131296i	$-0.958086\pi$
$751$		−	7.19615i		−	0.262591i	0.991343	−	0.131296i	$-0.0419137\pi$
$752$	−7.58871	+	4.38134i	−0.276732	+	0.159771i
$753$		0			0
$754$	−0.803848	+	0.803848i	−0.0292744	+	0.0292744i
$755$	9.73359	−	36.3262i	0.354242	−	1.32205i
$756$		0			0
$757$	4.55256	−	16.9904i	0.165466	−	0.617526i	−0.832515	−	0.554003i	$-0.813100\pi$
$757$	4.55256	−	16.9904i	0.165466	−	0.617526i	0.997980	−	0.0635231i	$-0.0202337\pi$
$758$	−7.07107	+	1.89469i	−0.256833	+	0.0688181i
$759$		0			0
$760$	−21.1244	−	5.66025i	−0.766261	−	0.205319i
$761$	−22.6274	−	39.1918i	−0.820243	−	1.42070i	−0.905501	−	0.424344i	$-0.860505\pi$
$761$	−22.6274	−	39.1918i	−0.820243	−	1.42070i	0.0852578	−	0.996359i	$-0.472829\pi$
$762$		0			0
$763$	−9.09808	−	9.09808i	−0.329372	−	0.329372i
$764$	−18.6114	+	4.98691i	−0.673337	+	0.180420i
$765$		0			0
$766$	−28.9808			−1.04712
$767$	27.4249			0.990254
$768$		0			0
$769$	7.97372	−	7.97372i	0.287540	−	0.287540i	−0.548567	−	0.836107i	$-0.684826\pi$
$769$	7.97372	−	7.97372i	0.287540	−	0.287540i	0.836107	+	0.548567i	$0.184826\pi$
$770$	−6.69213	+	11.5911i	−0.241168	+	0.417715i
$771$		0			0
$772$	1.66987	+	6.23205i	0.0601000	+	0.224296i
$773$	6.03579	+	3.48477i	0.217092	+	0.125338i	0.604603	−	0.796527i	$-0.293332\pi$
$773$	6.03579	+	3.48477i	0.217092	+	0.125338i	−0.387511	+	0.921865i	$0.626665\pi$
$774$		0			0
$775$	9.31089	−	34.7487i	0.334457	−	1.24821i
$776$	15.5935			0.559775
$777$		0			0
$778$	4.14359			0.148555
$779$	−3.38323	+	12.6264i	−0.121217	+	0.452387i
$780$		0			0
$781$	9.46410	+	5.46410i	0.338652	+	0.195521i
$782$	−1.93185	−	7.20977i	−0.0690829	−	0.257821i
$783$		0			0
$784$	−3.00000	+	5.19615i	−0.107143	+	0.185577i
$785$	−12.2474	+	12.2474i	−0.437130	+	0.437130i
$786$		0			0
$787$	11.2487			0.400973			0.200487	−	0.979696i	$-0.435748\pi$
$787$	11.2487			0.400973			0.200487	+	0.979696i	$0.435748\pi$
$788$	1.51575			0.0539963
$789$		0			0
$790$	0.464102	−	0.124356i	0.0165120	−	0.00442438i
$791$	−9.89949	−	9.89949i	−0.351986	−	0.351986i
$792$		0			0
$793$	−7.09808	−	12.2942i	−0.252060	−	0.436581i
$794$	−31.4087	−	8.41593i	−1.11465	−	0.298670i
$795$		0			0
$796$	−17.5263	+	4.69615i	−0.621203	+	0.166451i
$797$	6.05935	−	22.6138i	0.214633	−	0.801022i	−0.771662	−	0.636033i	$-0.780574\pi$
$797$	6.05935	−	22.6138i	0.214633	−	0.801022i	0.986295	−	0.164990i	$-0.0527590\pi$
$798$		0			0
$799$	−6.19615	+	23.1244i	−0.219204	+	0.818081i
$800$	4.94975	−	4.94975i	0.175000	−	0.175000i
$801$		0			0
$802$	−20.1962	+	11.6603i	−0.713151	+	0.411738i
$803$		−	59.4713i		−	2.09870i
$804$		0			0
$805$	−8.19615	+	4.73205i	−0.288876	+	0.166783i
$806$	−21.0609	−	21.0609i	−0.741839	−	0.741839i
$807$		0			0
$808$	−11.9282	+	11.9282i	−0.419633	+	0.419633i
$809$	−10.7453	+	2.87920i	−0.377785	+	0.101227i	−0.442714	−	0.896663i	$-0.645984\pi$
$809$	−10.7453	+	2.87920i	−0.377785	+	0.101227i	0.0649296	+	0.997890i	$0.479318\pi$
$810$		0			0
$811$	−18.1962	+	31.5167i	−0.638953	+	1.10670i	0.346709	+	0.937973i	$0.387299\pi$
$811$	−18.1962	+	31.5167i	−0.638953	+	1.10670i	−0.985663	+	0.168727i	$0.946034\pi$
$812$	−0.189469	−	0.0507680i	−0.00664905	−	0.00178161i
$813$		0			0
$814$	−9.73205	+	21.3923i	−0.341108	+	0.749800i
$815$			10.1497i			0.355528i
$816$		0			0
$817$	58.4711	+	33.7583i	2.04565	+	1.18105i
$818$	−12.3676	+	21.4213i	−0.432422	+	0.748977i
$819$		0			0
$820$	−5.07180	−	5.07180i	−0.177115	−	0.177115i
$821$	−23.5748	−	13.6109i	−0.822765	−	0.475023i	0.0286042	−	0.999591i	$-0.490894\pi$
$821$	−23.5748	−	13.6109i	−0.822765	−	0.475023i	−0.851369	+	0.524567i	$0.824227\pi$
$822$		0			0
$823$	1.20577	+	2.08846i	0.0420305	+	0.0727990i	0.886275	−	0.463159i	$-0.153284\pi$
$823$	1.20577	+	2.08846i	0.0420305	+	0.0727990i	−0.844245	+	0.535958i	$0.819951\pi$
$824$		−	18.9396i		−	0.659792i
$825$		0			0
$826$	2.36603	+	4.09808i	0.0823246	+	0.142590i
$827$	1.84392	+	6.88160i	0.0641193	+	0.239297i	0.990546	−	0.137177i	$-0.0438031\pi$
$827$	1.84392	+	6.88160i	0.0641193	+	0.239297i	−0.926427	+	0.376474i	$0.877136\pi$
$828$		0			0
$829$	−10.1603	−	2.72243i	−0.352880	−	0.0945540i	0.0780244	−	0.996951i	$-0.475139\pi$
$829$	−10.1603	−	2.72243i	−0.352880	−	0.0945540i	−0.430905	+	0.902397i	$0.641805\pi$
$830$	48.3335	−	27.9053i	1.67768	−	0.968608i
$831$		0			0
$832$	−1.50000	−	5.59808i	−0.0520031	−	0.194078i
$833$	4.24264	+	15.8338i	0.146999	+	0.548607i
$834$		0			0
$835$	48.5885	−	28.0526i	1.68147	−	0.970799i
$836$	23.5612	+	6.31319i	0.814880	+	0.218346i
$837$		0			0
$838$	−3.95448	−	14.7583i	−0.136605	−	0.509818i
$839$	14.2808	+	24.7351i	0.493029	+	0.853952i	0.999968	−	0.00803054i	$-0.00255623\pi$
$839$	14.2808	+	24.7351i	0.493029	+	0.853952i	−0.506939	+	0.861982i	$0.669223\pi$
$840$		0			0
$841$		−	28.9615i		−	0.998673i
$842$	5.74479	+	9.95026i	0.197978	+	0.342909i
$843$		0			0
$844$	−0.526279	−	0.303848i	−0.0181153	−	0.0104589i
$845$	50.4312	+	50.4312i	1.73489	+	1.73489i
$846$		0			0
$847$	1.96410	−	3.40192i	0.0674873	−	0.116891i
$848$	−2.44949	−	1.41421i	−0.0841158	−	0.0485643i
$849$		0			0
$850$		−	19.1244i		−	0.655960i
$851$	−13.5230	+	9.65926i	−0.463561	+	0.331115i
$852$		0			0
$853$	11.2942	+	3.02628i	0.386707	+	0.103618i	0.446934	−	0.894567i	$-0.352516\pi$
$853$	11.2942	+	3.02628i	0.386707	+	0.103618i	−0.0602271	+	0.998185i	$0.519182\pi$
$854$	1.22474	−	2.12132i	0.0419099	−	0.0725901i
$855$		0			0
$856$	−1.26795	+	0.339746i	−0.0433376	+	0.0116123i
$857$	−12.3490	+	12.3490i	−0.421833	+	0.421833i	−0.885835	−	0.464001i	$-0.846413\pi$
$857$	−12.3490	+	12.3490i	−0.421833	+	0.421833i	0.464001	+	0.885835i	$0.346413\pi$
$858$		0			0
$859$	35.7583	+	35.7583i	1.22006	+	1.22006i	0.967610	+	0.252448i	$0.0812357\pi$
$859$	35.7583	+	35.7583i	1.22006	+	1.22006i	0.252448	+	0.967610i	$0.418764\pi$
$860$	−32.0836	+	18.5235i	−1.09404	+	0.631645i
$861$		0			0
$862$		−	16.3923i		−	0.558324i
$863$	−45.9483	+	26.5283i	−1.56410	+	0.903033i	−0.567265	+	0.823536i	$0.691998\pi$
$863$	−45.9483	+	26.5283i	−1.56410	+	0.903033i	−0.996835	+	0.0794977i	$0.974668\pi$
$864$		0			0
$865$	−60.2487	+	60.2487i	−2.04852	+	2.04852i
$866$	−4.10394	+	15.3161i	−0.139458	+	0.520463i
$867$		0			0
$868$	1.33013	−	4.96410i	0.0451475	−	0.168493i
$869$	−0.517638	+	0.138701i	−0.0175597	+	0.00470510i
$870$		0			0
$871$	−16.7942	−	4.50000i	−0.569051	−	0.152477i
$872$	−6.43331	−	11.1428i	−0.217859	−	0.377344i
$873$		0			0
$874$	12.1962	+	12.1962i	0.412541	+	0.412541i
$875$	−6.69213	+	1.79315i	−0.226235	+	0.0606196i
$876$		0			0
$877$	−7.39230			−0.249620			−0.124810	−	0.992181i	$-0.539832\pi$
$877$	−7.39230			−0.249620			−0.124810	+	0.992181i	$0.539832\pi$
$878$	17.8671			0.602987
$879$		0			0
$880$	−9.46410	+	9.46410i	−0.319035	+	0.319035i
$881$	−1.46498	+	2.53742i	−0.0493565	+	0.0854879i	−0.889648	−	0.456647i	$-0.849050\pi$
$881$	−1.46498	+	2.53742i	−0.0493565	+	0.0854879i	0.840292	+	0.542135i	$0.182384\pi$
$882$		0			0
$883$	12.9737	+	48.4186i	0.436600	+	1.62942i	0.737207	+	0.675667i	$0.236144\pi$
$883$	12.9737	+	48.4186i	0.436600	+	1.62942i	−0.300607	+	0.953748i	$0.597189\pi$
$884$	−13.7124	−	7.91688i	−0.461199	−	0.266273i
$885$		0			0
$886$	8.46410	−	31.5885i	0.284357	−	1.06123i
$887$	−6.41473			−0.215386			−0.107693	−	0.994184i	$-0.534346\pi$
$887$	−6.41473			−0.215386			−0.107693	+	0.994184i	$0.534346\pi$
$888$		0			0
$889$	0.267949			0.00898673
$890$	−7.52433	+	28.0812i	−0.252216	+	0.941284i
$891$		0			0
$892$	11.7679	+	6.79423i	0.394020	+	0.227488i
$893$	−14.3180	−	53.4355i	−0.479134	−	1.78815i
$894$		0			0
$895$	15.4641	−	26.7846i	0.516908	−	0.895311i
$896$	0.707107	−	0.707107i	0.0236228	−	0.0236228i
$897$		0			0
$898$	−20.0526			−0.669163
$899$	−1.00807			−0.0336210
$900$		0			0
$901$	−7.46410	+	2.00000i	−0.248665	+	0.0666297i
$902$	5.65685	+	5.65685i	0.188353	+	0.188353i
$903$		0			0
$904$	−7.00000	−	12.1244i	−0.232817	−	0.403250i
$905$	63.0948	+	16.9062i	2.09734	+	0.561981i
$906$		0			0
$907$	−38.5526	+	10.3301i	−1.28012	+	0.343006i	−0.833898	−	0.551918i	$-0.813896\pi$
$907$	−38.5526	+	10.3301i	−1.28012	+	0.343006i	−0.446218	+	0.894924i	$0.647229\pi$
$908$	−2.60179	+	9.71003i	−0.0863436	+	0.322239i
$909$		0			0
$910$	−5.19615	+	19.3923i	−0.172251	+	0.642849i
$911$	21.2132	−	21.2132i	0.702825	−	0.702825i	−0.262191	−	0.965016i	$-0.584445\pi$
$911$	21.2132	−	21.2132i	0.702825	−	0.702825i	0.965016	+	0.262191i	$0.0844451\pi$
$912$		0			0
$913$	−53.9090	+	31.1244i	−1.78413	+	1.03007i
$914$		−	26.5927i		−	0.879607i
$915$		0			0
$916$	0.571797	−	0.330127i	0.0188927	−	0.0109077i
$917$	−2.96713	−	2.96713i	−0.0979832	−	0.0979832i
$918$		0			0
$919$	17.7058	−	17.7058i	0.584060	−	0.584060i	−0.351957	−	0.936016i	$-0.614484\pi$
$919$	17.7058	−	17.7058i	0.584060	−	0.584060i	0.936016	+	0.351957i	$0.114484\pi$
$920$	−9.14162	+	2.44949i	−0.301390	+	0.0807573i
$921$		0			0
$922$	−11.1962	+	19.3923i	−0.368726	+	0.638652i
$923$	15.8338	+	4.24264i	0.521174	+	0.139648i
$924$		0			0
$925$	−39.8731	+	14.9378i	−1.31102	+	0.491153i
$926$			20.5940i			0.676762i
$927$		0			0
$928$	−0.169873	−	0.0980762i	−0.00557635	−	0.00321951i
$929$	26.6806	−	46.2121i	0.875362	−	1.51617i	0.0189848	−	0.999820i	$-0.493957\pi$
$929$	26.6806	−	46.2121i	0.875362	−	1.51617i	0.856377	−	0.516351i	$-0.172710\pi$
$930$		0			0
$931$	−26.7846	−	26.7846i	−0.877830	−	0.877830i
$932$	19.0919	+	11.0227i	0.625375	+	0.361061i
$933$		0			0
$934$	1.46410	+	2.53590i	0.0479069	+	0.0829771i
$935$			36.5665i			1.19585i
$936$		0			0
$937$	−5.96410	−	10.3301i	−0.194839	−	0.337471i	0.752009	−	0.659153i	$-0.229085\pi$
$937$	−5.96410	−	10.3301i	−0.194839	−	0.337471i	−0.946848	+	0.321682i	$0.895752\pi$
$938$	−0.776457	−	2.89778i	−0.0253522	−	0.0946158i
$939$		0			0
$940$	29.3205	+	7.85641i	0.956330	+	0.256248i
$941$	0.152304	−	0.0879327i	0.00496497	−	0.00286652i	−0.497515	−	0.867455i	$-0.665754\pi$
$941$	0.152304	−	0.0879327i	0.00496497	−	0.00286652i	0.502480	+	0.864589i	$0.332421\pi$
$942$		0			0
$943$	1.46410	+	5.46410i	0.0476777	+	0.177936i
$944$	1.22474	+	4.57081i	0.0398621	+	0.148767i
$945$		0			0
$946$	35.7846	−	20.6603i	1.16346	−	0.671723i
$947$	39.7231	+	10.6438i	1.29083	+	0.345876i	0.837974	−	0.545710i	$-0.183740\pi$
$947$	39.7231	+	10.6438i	1.29083	+	0.345876i	0.452852	+	0.891586i	$0.350407\pi$
$948$		0			0
$949$	−23.0885	−	86.1673i	−0.749483	−	2.79711i
$950$	22.0962	+	38.2717i	0.716895	+	1.24170i
$951$		0			0
$952$		−	2.73205i		−	0.0885463i
$953$	17.7656	+	30.7709i	0.575484	+	0.996768i	0.995989	+	0.0894776i	$0.0285198\pi$
$953$	17.7656	+	30.7709i	0.575484	+	0.996768i	−0.420505	+	0.907290i	$0.638147\pi$
$954$		0			0
$955$	57.8038	+	33.3731i	1.87049	+	1.07993i
$956$	0.619174	+	0.619174i	0.0200255	+	0.0200255i
$957$		0			0
$958$	−7.36603	+	12.7583i	−0.237985	+	0.412203i
$959$	11.5911	+	6.69213i	0.374296	+	0.216100i
$960$		0			0
$961$			4.58846i			0.148015i
$962$	−5.79555	+	34.7733i	−0.186856	+	1.12114i
$963$		0			0
$964$	22.5263	+	6.03590i	0.725523	+	0.194403i
$965$	11.1750	−	19.3557i	0.359736	−	0.623081i
$966$		0			0
$967$	−23.1865	+	6.21281i	−0.745629	+	0.199791i	−0.611578	−	0.791184i	$-0.709465\pi$
$967$	−23.1865	+	6.21281i	−0.745629	+	0.199791i	−0.134050	+	0.990975i	$0.542798\pi$
$968$	2.77766	−	2.77766i	0.0892773	−	0.0892773i
$969$		0			0
$970$	−38.1962	−	38.1962i	−1.22640	−	1.22640i
$971$	−29.9623	+	17.2987i	−0.961535	+	0.555143i	−0.896645	−	0.442750i	$-0.854003\pi$
$971$	−29.9623	+	17.2987i	−0.961535	+	0.555143i	−0.0648902	+	0.997892i	$0.520670\pi$
$972$		0			0
$973$		−	9.92820i		−	0.318284i
$974$	30.2025	−	17.4374i	0.967751	−	0.558731i
$975$		0			0
$976$	1.73205	−	1.73205i	0.0554416	−	0.0554416i
$977$	−14.1050	+	52.6405i	−0.451258	+	1.68412i	0.247604	+	0.968861i	$0.420357\pi$
$977$	−14.1050	+	52.6405i	−0.451258	+	1.68412i	−0.698862	+	0.715256i	$0.746310\pi$
$978$		0			0
$979$	8.39230	−	31.3205i	0.268219	−	1.00101i
$980$	20.0764	−	5.37945i	0.641317	−	0.171840i
$981$		0			0
$982$	29.9545	+	8.02628i	0.955886	+	0.256129i
$983$	12.9174	+	22.3736i	0.412001	+	0.713606i	0.995108	−	0.0987886i	$-0.0314968\pi$
$983$	12.9174	+	22.3736i	0.412001	+	0.713606i	−0.583108	+	0.812395i	$0.698163\pi$
$984$		0			0
$985$	−3.71281	−	3.71281i	−0.118300	−	0.118300i
$986$	−0.517638	+	0.138701i	−0.0164850	+	0.00441713i
$987$		0			0
$988$	36.5885			1.16403
$989$	29.2180			0.929079
$990$		0			0
$991$	−4.85641	+	4.85641i	−0.154269	+	0.154269i	−0.780022	−	0.625753i	$-0.784792\pi$
$991$	−4.85641	+	4.85641i	−0.154269	+	0.154269i	0.625753	+	0.780022i	$0.284792\pi$
$992$	2.56961	−	4.45069i	0.0815851	−	0.141310i
$993$		0			0
$994$	0.732051	+	2.73205i	0.0232192	+	0.0866554i
$995$	54.4336	+	31.4273i	1.72566	+	0.996311i
$996$		0			0
$997$	−11.5096	+	42.9545i	−0.364513	+	1.36038i	0.503566	+	0.863957i	$0.332021\pi$
$997$	−11.5096	+	42.9545i	−0.364513	+	1.36038i	−0.868079	+	0.496425i	$0.834646\pi$
$998$	−1.96902			−0.0623281
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.be.b.125.1	✓	8	111.14	even	12	inner
666.2.be.b.125.2	yes	8	37.14	odd	12	inner
666.2.be.b.341.1	yes	8	1.1	even	1	trivial
666.2.be.b.341.2	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)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.896575 + 3.34607i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.896575 + 3.34607i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.46410 q^{10} +3.86370 q^{11} +(5.59808 - 1.50000i) q^{13} +(0.707107 + 0.707107i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.63896 + 0.707107i) q^{17} +(-6.09808 + 1.63397i) q^{19} +(0.896575 - 3.34607i) q^{20} +(-1.00000 + 3.73205i) q^{22} +(-1.93185 + 1.93185i) q^{23} +(-6.06218 + 3.50000i) q^{25} +5.79555i q^{26} +(-0.866025 + 0.500000i) q^{28} +(0.138701 + 0.138701i) q^{29} +(-3.63397 + 3.63397i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.36603 + 2.36603i) q^{34} +(3.34607 + 0.896575i) q^{35} +(6.00000 + 1.00000i) q^{37} -6.31319i q^{38} +(3.00000 + 1.73205i) q^{40} +(1.03528 - 1.79315i) q^{41} +(-7.56218 - 7.56218i) q^{43} +(-3.34607 - 1.93185i) q^{44} +(-1.36603 - 2.36603i) q^{46} +8.76268i q^{47} +(3.00000 + 5.19615i) q^{49} +(-1.81173 - 6.76148i) q^{50} +(-5.59808 - 1.50000i) q^{52} +(-2.44949 + 1.41421i) q^{53} +(3.46410 + 12.9282i) q^{55} +(-0.258819 - 0.965926i) q^{56} +(-0.169873 + 0.0980762i) q^{58} +(4.57081 + 1.22474i) q^{59} +(-0.633975 - 2.36603i) q^{61} +(-2.56961 - 4.45069i) q^{62} -1.00000i q^{64} +(10.0382 + 17.3867i) q^{65} +(-2.59808 - 1.50000i) q^{67} +(-1.93185 - 1.93185i) q^{68} +(-1.73205 + 3.00000i) q^{70} +(2.44949 + 1.41421i) q^{71} -15.3923i q^{73} +(-2.51884 + 5.53674i) q^{74} +(6.09808 + 1.63397i) q^{76} +(1.93185 - 3.34607i) q^{77} +(-0.133975 + 0.0358984i) q^{79} +(-2.44949 + 2.44949i) q^{80} +(1.46410 + 1.46410i) q^{82} +(-13.9527 + 8.05558i) q^{83} +9.46410i q^{85} +(9.26174 - 5.34727i) q^{86} +(2.73205 - 2.73205i) q^{88} +(2.17209 - 8.10634i) q^{89} +(1.50000 - 5.59808i) q^{91} +(2.63896 - 0.707107i) q^{92} +(-8.46410 - 2.26795i) q^{94} +(-10.9348 - 18.9396i) q^{95} +(11.0263 + 11.0263i) q^{97} +(-5.79555 + 1.55291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} + 24 q^{13} + 4 q^{16} - 28 q^{19} - 8 q^{22} - 36 q^{31} - 4 q^{34} + 48 q^{37} + 24 q^{40} - 12 q^{43} - 4 q^{46} + 24 q^{49} - 24 q^{52} - 36 q^{58} - 12 q^{61} + 28 q^{76} - 8 q^{79} - 16 q^{82} + 8 q^{88} + 12 q^{91} - 40 q^{94} + 12 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 + 24 * q^13 + 4 * q^16 - 28 * q^19 - 8 * q^22 - 36 * q^31 - 4 * q^34 + 48 * q^37 + 24 * q^40 - 12 * q^43 - 4 * q^46 + 24 * q^49 - 24 * q^52 - 36 * q^58 - 12 * q^61 + 28 * q^76 - 8 * q^79 - 16 * q^82 + 8 * q^88 + 12 * q^91 - 40 * q^94 + 12 * q^97

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