LMFDB - Embedded newform 666.2.be.b.125.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("666.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	666.125
Dual form			666.2.be.b.341.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.896575 + 3.34607i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.896575 + 3.34607i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.707107 - 0.707107i) q^{8} -3.46410 q^{10} -3.86370 q^{11} +(5.59808 + 1.50000i) q^{13} +(-0.707107 + 0.707107i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.63896 + 0.707107i) q^{17} +(-6.09808 - 1.63397i) q^{19} +(-0.896575 - 3.34607i) q^{20} +(-1.00000 - 3.73205i) q^{22} +(1.93185 + 1.93185i) q^{23} +(-6.06218 - 3.50000i) q^{25} +5.79555i q^{26} +(-0.866025 - 0.500000i) q^{28} +(-0.138701 + 0.138701i) q^{29} +(-3.63397 - 3.63397i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-1.36603 - 2.36603i) q^{34} +(-3.34607 + 0.896575i) q^{35} +(6.00000 - 1.00000i) q^{37} -6.31319i q^{38} +(3.00000 - 1.73205i) q^{40} +(-1.03528 - 1.79315i) q^{41} +(-7.56218 + 7.56218i) q^{43} +(3.34607 - 1.93185i) q^{44} +(-1.36603 + 2.36603i) q^{46} +8.76268i q^{47} +(3.00000 - 5.19615i) q^{49} +(1.81173 - 6.76148i) q^{50} +(-5.59808 + 1.50000i) q^{52} +(2.44949 + 1.41421i) q^{53} +(3.46410 - 12.9282i) q^{55} +(0.258819 - 0.965926i) q^{56} +(-0.169873 - 0.0980762i) q^{58} +(-4.57081 + 1.22474i) q^{59} +(-0.633975 + 2.36603i) q^{61} +(2.56961 - 4.45069i) q^{62} +1.00000i q^{64} +(-10.0382 + 17.3867i) q^{65} +(-2.59808 + 1.50000i) q^{67} +(1.93185 - 1.93185i) q^{68} +(-1.73205 - 3.00000i) q^{70} +(-2.44949 + 1.41421i) q^{71} +15.3923i q^{73} +(2.51884 + 5.53674i) q^{74} +(6.09808 - 1.63397i) q^{76} +(-1.93185 - 3.34607i) q^{77} +(-0.133975 - 0.0358984i) q^{79} +(2.44949 + 2.44949i) q^{80} +(1.46410 - 1.46410i) q^{82} +(13.9527 + 8.05558i) q^{83} -9.46410i q^{85} +(-9.26174 - 5.34727i) q^{86} +(2.73205 + 2.73205i) q^{88} +(-2.17209 - 8.10634i) q^{89} +(1.50000 + 5.59808i) q^{91} +(-2.63896 - 0.707107i) q^{92} +(-8.46410 + 2.26795i) q^{94} +(10.9348 - 18.9396i) q^{95} +(11.0263 - 11.0263i) q^{97} +(5.79555 + 1.55291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

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

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
$5$	−0.896575	+	3.34607i	−0.400961	+	1.49641i	0.410425	+	0.911894i	$0.365380\pi$
$5$	−0.896575	+	3.34607i	−0.400961	+	1.49641i	−0.811386	+	0.584511i	$0.801286\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−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	$-0.697916\pi$
$11$	−3.86370			−1.16495			−0.582475	+	0.812848i	$0.697916\pi$
$12$		0			0
$13$	5.59808	+	1.50000i	1.55263	+	0.416025i	0.930320	−	0.366748i	$-0.119529\pi$
$13$	5.59808	+	1.50000i	1.55263	+	0.416025i	0.622307	+	0.782773i	$0.286196\pi$
$14$	−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	$-0.690824\pi$
$17$	−2.63896	+	0.707107i	−0.640041	+	0.171499i	−0.0758192	+	0.997122i	$0.524157\pi$
$18$		0			0
$19$	−6.09808	−	1.63397i	−1.39899	−	0.374859i	−0.521011	−	0.853550i	$-0.674445\pi$
$19$	−6.09808	−	1.63397i	−1.39899	−	0.374859i	−0.877984	+	0.478691i	$0.841112\pi$
$20$	−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	$-0.158061\pi$
$23$	1.93185	+	1.93185i	0.402819	+	0.402819i	−0.476406	+	0.879225i	$0.658061\pi$
$24$		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	$-0.755797\pi$
$29$	−0.138701	+	0.138701i	−0.0257561	+	0.0257561i	0.694111	+	0.719868i	$0.255797\pi$
$30$		0			0
$31$	−3.63397	−	3.63397i	−0.652681	−	0.652681i	0.300957	−	0.953638i	$-0.402694\pi$
$31$	−3.63397	−	3.63397i	−0.652681	−	0.652681i	−0.953638	+	0.300957i	$0.902694\pi$
$32$	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	$-0.218359\pi$
$41$	−1.03528	−	1.79315i	−0.161683	−	0.280043i	−0.935472	+	0.353400i	$0.885026\pi$
$42$		0			0
$43$	−7.56218	+	7.56218i	−1.15322	+	1.15322i	−0.167318	+	0.985903i	$0.553511\pi$
$43$	−7.56218	+	7.56218i	−1.15322	+	1.15322i	−0.985903	+	0.167318i	$0.946489\pi$
$44$	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	$-0.271104\pi$
$53$	2.44949	+	1.41421i	0.336463	+	0.194257i	−0.322244	+	0.946657i	$0.604437\pi$
$54$		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	$-0.683003\pi$
$59$	−4.57081	+	1.22474i	−0.595069	+	0.159448i	−0.0513000	+	0.998683i	$0.516336\pi$
$60$		0			0
$61$	−0.633975	+	2.36603i	−0.0811721	+	0.302939i	−0.994562	−	0.104148i	$-0.966789\pi$
$61$	−0.633975	+	2.36603i	−0.0811721	+	0.302939i	0.913390	+	0.407086i	$0.133455\pi$
$62$	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	−0.650236	−	0.759733i	$-0.725330\pi$
$67$	−2.59808	+	1.50000i	−0.317406	+	0.183254i	0.332830	+	0.942987i	$0.391996\pi$
$68$	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	$-0.720345\pi$
$71$	−2.44949	+	1.41421i	−0.290701	+	0.167836i	0.347557	+	0.937659i	$0.387011\pi$
$72$		0			0
$73$			15.3923i			1.80153i	0.434304	+	0.900767i	$0.356994\pi$
$73$			15.3923i			1.80153i	−0.434304	+	0.900767i	$0.643006\pi$
$74$	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	0.251275	−	0.967916i	$-0.419150\pi$
$79$	−0.133975	−	0.0358984i	−0.0150733	−	0.00403888i	−0.266348	+	0.963877i	$0.585817\pi$
$80$	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	0.999293	+	0.0376028i	$0.0119722\pi$
$83$	13.9527	+	8.05558i	1.53150	+	0.884214i	0.532211	+	0.846611i	$0.321361\pi$
$84$		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	−0.980237	−	0.197828i	$-0.936611\pi$
$89$	−2.17209	−	8.10634i	−0.230241	−	0.859271i	0.749996	−	0.661443i	$-0.230055\pi$
$90$		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	0.127742	−	0.991807i	$-0.459227\pi$
$97$	11.0263	−	11.0263i	1.11955	−	1.11955i	0.991807	−	0.127742i	$-0.0407728\pi$
$98$	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	$-0.182985\pi$
$101$	16.8690			1.67853			0.839265	+	0.543722i	$0.182985\pi$
$102$		0			0
$103$	13.3923	+	13.3923i	1.31958	+	1.31958i	0.914105	+	0.405478i	$0.132895\pi$
$103$	13.3923	+	13.3923i	1.31958	+	1.31958i	0.405478	+	0.914105i	$0.367105\pi$
$104$	−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	$-0.646456\pi$
$107$	1.13681	−	0.656339i	0.109900	−	0.0634507i	0.553942	+	0.832555i	$0.313123\pi$
$108$		0			0
$109$	3.33013	+	12.4282i	0.318968	+	1.19041i	0.920238	+	0.391360i	$0.127995\pi$
$109$	3.33013	+	12.4282i	0.318968	+	1.19041i	−0.601269	+	0.799046i	$0.705338\pi$
$110$	13.3843			1.27614
$111$		0			0
$112$	1.00000			0.0944911
$113$	−3.62347	−	13.5230i	−0.340867	−	1.27213i	−0.897367	−	0.441285i	$-0.854523\pi$
$113$	−3.62347	−	13.5230i	−0.340867	−	1.27213i	0.556500	−	0.830848i	$-0.312144\pi$
$114$		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	−0.860020	−	0.510260i	$-0.829549\pi$
$127$	0.133975	−	0.232051i	0.0118883	−	0.0205912i	0.871908	+	0.489669i	$0.162882\pi$
$128$	−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	$-0.142014\pi$
$131$	−1.08604	−	4.05317i	−0.0948881	−	0.354127i	−0.997002	+	0.0773698i	$0.975348\pi$
$132$		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	0.818158	−	0.574993i	$-0.194995\pi$
$139$	8.59808	+	4.96410i	0.729279	+	0.421050i	−0.0888792	+	0.996042i	$0.528328\pi$
$140$	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	−0.831130	−	0.556078i	$-0.812306\pi$
$151$	−9.40192	+	5.42820i	−0.765118	+	0.441741i	0.0660125	+	0.997819i	$0.478972\pi$
$152$	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	−0.748852	−	0.662738i	$-0.769394\pi$
$157$	2.50000	−	4.33013i	0.199522	−	0.345582i	0.948373	+	0.317156i	$0.102728\pi$
$158$		−	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	−0.146273	−	0.989244i	$-0.546728\pi$
$163$	2.83013	−	0.758330i	0.221673	−	0.0593970i	0.367946	+	0.929847i	$0.380061\pi$
$164$	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	−0.590560	−	0.806994i	$-0.701093\pi$
$167$	4.19187	−	15.6443i	0.324377	−	1.21059i	0.914937	−	0.403597i	$-0.132240\pi$
$168$		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	−0.160411	+	0.987050i	$0.551282\pi$
$173$	−12.2982	+	21.3011i	−0.935016	+	1.61950i	−0.774605	+	0.632445i	$0.782051\pi$
$174$		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	$-0.641715\pi$
$179$	6.31319	−	6.31319i	0.471870	−	0.471870i	0.902519	+	0.430649i	$0.141715\pi$
$180$		0			0
$181$	9.42820	+	16.3301i	0.700793	+	1.21381i	0.968188	+	0.250222i	$0.0805036\pi$
$181$	9.42820	+	16.3301i	0.700793	+	1.21381i	−0.267396	+	0.963587i	$0.586163\pi$
$182$	−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	$-0.495522\pi$
$191$	−13.6245	−	13.6245i	−0.985834	−	0.985834i	−0.999901	+	0.0140670i	$0.995522\pi$
$192$		0			0
$193$	−4.56218	+	4.56218i	−0.328393	+	0.328393i	−0.851975	−	0.523582i	$-0.824595\pi$
$193$	−4.56218	+	4.56218i	−0.328393	+	0.328393i	0.523582	+	0.851975i	$0.324595\pi$
$194$	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	$-0.316137\pi$
$197$	1.31268	+	0.757875i	0.0935244	+	0.0539963i	−0.452508	+	0.891760i	$0.649471\pi$
$198$		0			0
$199$	12.8301	+	12.8301i	0.909504	+	0.909504i	0.996232	−	0.0867284i	$-0.0276412\pi$
$199$	12.8301	+	12.8301i	0.909504	+	0.909504i	−0.0867284	+	0.996232i	$0.527641\pi$
$200$	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	−0.824247	−	0.566231i	$-0.808401\pi$
$227$	2.60179	−	9.71003i	0.172687	−	0.644477i	0.996934	−	0.0782466i	$-0.0249321\pi$
$228$		0			0
$229$	−0.330127	−	0.571797i	−0.0218154	−	0.0377854i	0.854912	−	0.518774i	$-0.173611\pi$
$229$	−0.330127	−	0.571797i	−0.0218154	−	0.0377854i	−0.876727	+	0.480988i	$0.840278\pi$
$230$	−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	$-0.243167\pi$
$233$	22.0454			1.44424			0.722121	+	0.691766i	$0.243167\pi$
$234$		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	$-0.574317\pi$
$239$	0.845807	−	0.226633i	0.0547107	−	0.0146597i	0.286071	+	0.958209i	$0.407651\pi$
$240$		0			0
$241$	−22.5263	−	6.03590i	−1.45105	−	0.388806i	−0.554658	−	0.832078i	$-0.687151\pi$
$241$	−22.5263	−	6.03590i	−1.45105	−	0.388806i	−0.896387	+	0.443272i	$0.853818\pi$
$242$	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	−0.0859757	+	0.996297i	$0.527401\pi$
$251$	−17.1464	+	17.1464i	−1.08227	+	1.08227i	−0.996297	+	0.0859757i	$0.972599\pi$
$252$		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	$-0.592550\pi$
$257$	−0.896575	+	0.240237i	−0.0559268	+	0.0149856i	0.230747	+	0.973014i	$0.425883\pi$
$258$		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	$-0.224222\pi$
$263$	−2.91636	−	5.05128i	−0.179830	−	0.311475i	−0.941822	+	0.336111i	$0.890888\pi$
$264$		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	−0.172375	−	0.985031i	$-0.555144\pi$
$271$	12.6244	−	21.8660i	0.766875	−	1.32827i	0.939250	−	0.343235i	$-0.111523\pi$
$272$	−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	0.647063	+	0.762436i	$0.275997\pi$
$277$	−4.90192	+	18.2942i	−0.294528	+	1.09919i	−0.941591	+	0.336757i	$0.890670\pi$
$278$	−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	$-0.553626\pi$
$281$	3.01790	−	0.808643i	0.180033	−	0.0482396i	0.347709	+	0.937603i	$0.386960\pi$
$282$		0			0
$283$	−1.79423	+	6.69615i	−0.106656	+	0.398045i	−0.998528	−	0.0542431i	$-0.982725\pi$
$283$	−1.79423	+	6.69615i	−0.106656	+	0.398045i	0.891872	+	0.452288i	$0.149392\pi$
$284$	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	$-0.438074\pi$
$293$	19.5080	−	11.2629i	1.13967	−	0.657988i	0.946349	+	0.323148i	$0.104741\pi$
$294$		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	$-0.756499\pi$
$307$		−	24.2679i		−	1.38505i	0.721396	−	0.692523i	$-0.243501\pi$
$308$	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	−0.682772	−	0.730631i	$-0.739226\pi$
$311$	−8.05558	−	30.0638i	−0.456790	−	1.70476i	0.225982	−	0.974131i	$-0.427441\pi$
$312$		0			0
$313$	−6.57180	−	24.5263i	−0.371460	−	1.38631i	−0.858449	−	0.512899i	$-0.828571\pi$
$313$	−6.57180	−	24.5263i	−0.371460	−	1.38631i	0.486989	−	0.873408i	$-0.338095\pi$
$314$	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	0.453214	+	0.891402i	$0.350277\pi$
$317$	−9.71003	+	16.8183i	−0.545369	+	0.944608i	−0.998584	+	0.0532059i	$0.983056\pi$
$318$		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	0.964874	+	0.262714i	$0.0846177\pi$
$331$	4.74167	+	17.6962i	0.260626	+	0.972669i	−0.704248	+	0.709954i	$0.748716\pi$
$332$	−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	−0.506307	−	0.862353i	$-0.668990\pi$
$337$	−0.232051	+	0.133975i	−0.0126406	+	0.00729806i	0.493666	+	0.869651i	$0.335656\pi$
$338$	−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	$-0.706079\pi$
$347$	3.62347	−	3.62347i	0.194518	−	0.194518i	0.797645	+	0.603127i	$0.206079\pi$
$348$		0			0
$349$	−6.92820	+	12.0000i	−0.370858	+	0.642345i	−0.989698	−	0.143172i	$-0.954270\pi$
$349$	−6.92820	+	12.0000i	−0.370858	+	0.642345i	0.618840	+	0.785517i	$0.287603\pi$
$350$	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	−0.990642	−	0.136486i	$-0.956419\pi$
$353$	−3.77577	−	14.0914i	−0.200964	−	0.750008i	0.789678	−	0.613522i	$-0.210248\pi$
$354$		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	0.593406	−	0.804904i	$-0.297783\pi$
$367$	−7.66987	−	13.2846i	−0.400364	−	0.693451i	−0.993770	+	0.111453i	$0.964450\pi$
$368$	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	−0.702068	−	0.712110i	$-0.747740\pi$
$373$	−8.42820	+	4.86603i	−0.436396	+	0.251953i	0.265672	+	0.964064i	$0.414406\pi$
$374$	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	−0.756574	−	0.653909i	$-0.773128\pi$
$379$	3.66025	−	6.33975i	0.188015	−	0.325651i	0.944588	+	0.328258i	$0.106461\pi$
$380$			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	0.457602	+	0.889157i	$0.348709\pi$
$383$	−7.50077	+	27.9933i	−0.383272	+	1.43039i	−0.840873	+	0.541232i	$0.817958\pi$
$384$		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	$-0.883168\pi$
$389$	1.07244	−	4.00240i	0.0543749	−	0.202930i	0.987769	+	0.155922i	$0.0498349\pi$
$390$		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	$-0.696197\pi$
$397$		−	32.5167i		−	1.63196i	0.578077	−	0.815982i	$-0.303803\pi$
$398$	−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	$-0.947841\pi$
$401$	−16.4901	+	16.4901i	−0.823476	+	0.823476i	0.163129	+	0.986605i	$0.447841\pi$
$402$		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	0.385917	−	0.922533i	$-0.373885\pi$
$409$	23.8923	−	6.40192i	1.18140	−	0.316555i	0.795481	+	0.605979i	$0.207218\pi$
$410$	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	$-0.211589\pi$
$419$	13.2320	+	7.63947i	0.646423	+	0.373213i	−0.140661	+	0.990058i	$0.544923\pi$
$420$		0			0
$421$	8.12436	+	8.12436i	0.395957	+	0.395957i	0.876804	−	0.480847i	$-0.159671\pi$
$421$	8.12436	+	8.12436i	0.395957	+	0.395957i	−0.480847	+	0.876804i	$0.659671\pi$
$422$	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	$-0.287482\pi$
$431$	15.8338	+	4.24264i	0.762685	+	0.204361i	0.143547	+	0.989643i	$0.454149\pi$
$432$		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	0.763370	+	0.645961i	$0.223543\pi$
$439$	−4.62436	+	17.2583i	−0.220708	+	0.823695i	−0.984079	+	0.177734i	$0.943123\pi$
$440$	−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	$-0.216802\pi$
$443$	32.7028			1.55376			0.776878	+	0.629651i	$0.216802\pi$
$444$		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	0.728488	+	0.685059i	$0.240223\pi$
$449$	−5.18998	+	19.3693i	−0.244930	+	0.914093i	−0.973418	+	0.229034i	$0.926443\pi$
$450$		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	−0.398118	−	0.917334i	$-0.630337\pi$
$457$	−25.6865	−	6.88269i	−1.20157	−	0.321958i	−0.803447	+	0.595376i	$0.797003\pi$
$458$	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	$-0.757945\pi$
$461$	−21.6293	+	5.79555i	−1.00738	+	0.269926i	−0.282844	+	0.959166i	$0.591278\pi$
$462$		0			0
$463$	19.8923	+	5.33013i	0.924474	+	0.247712i	0.689497	−	0.724289i	$-0.257832\pi$
$463$	19.8923	+	5.33013i	0.924474	+	0.247712i	0.234977	+	0.972001i	$0.424498\pi$
$464$	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	$-0.271582\pi$
$467$	−2.07055	−	2.07055i	−0.0958137	−	0.0958137i	−0.753389	+	0.657575i	$0.771582\pi$
$468$		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	$-0.692598\pi$
$479$	−14.2301	+	3.81294i	−0.650188	+	0.174217i	−0.0813744	+	0.996684i	$0.525931\pi$
$480$		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	−0.125350	+	0.992113i	$0.540005\pi$
$487$	−24.6603	+	24.6603i	−1.11746	+	1.11746i	−0.992113	+	0.125350i	$0.959995\pi$
$488$	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	−0.953580	−	0.301138i	$-0.902633\pi$
$499$	0.509619	−	1.90192i	0.0228137	−	0.0851418i	0.976394	+	0.215997i	$0.0693000\pi$
$500$	−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	$-0.320389\pi$
$503$	31.8570	−	8.53605i	1.42043	−	0.380604i	0.885637	+	0.464378i	$0.153722\pi$
$504$		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	−0.222365	−	0.974963i	$-0.571378\pi$
$509$	16.5409	−	28.6496i	0.733161	−	1.26987i	0.955526	−	0.294908i	$-0.0952890\pi$
$510$		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	$-0.155577\pi$
$521$	0.795040	+	1.37705i	0.0348313	+	0.0603296i	−0.848084	+	0.529861i	$0.822244\pi$
$522$		0			0
$523$	9.52628	+	2.55256i	0.416555	+	0.111616i	0.461008	−	0.887396i	$-0.347488\pi$
$523$	9.52628	+	2.55256i	0.416555	+	0.111616i	−0.0444531	+	0.999011i	$0.514155\pi$
$524$	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	−0.829346	−	0.558736i	$-0.811287\pi$
$541$	−6.29423	+	6.29423i	−0.270610	+	0.270610i	0.558736	+	0.829346i	$0.311287\pi$
$542$	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	0.210019	−	0.977697i	$-0.432647\pi$
$547$	−17.9545	−	17.9545i	−0.767678	−	0.767678i	−0.977697	+	0.210019i	$0.932647\pi$
$548$	−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	$-0.116272\pi$
$557$	−1.26191	−	4.70951i	−0.0534688	−	0.199548i	−0.987493	+	0.157660i	$0.949605\pi$
$558$		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	$-0.198750\pi$
$563$	5.37945	+	5.37945i	0.226717	+	0.226717i	−0.584603	+	0.811320i	$0.698750\pi$
$564$		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	$-0.658563\pi$
$569$	9.55772	−	9.55772i	0.400681	−	0.400681i	0.878473	+	0.477792i	$0.158563\pi$
$570$		0			0
$571$	23.0622	−	39.9449i	0.965122	−	1.67164i	0.255835	−	0.966720i	$-0.417649\pi$
$571$	23.0622	−	39.9449i	0.965122	−	1.67164i	0.709287	−	0.704920i	$-0.249017\pi$
$572$	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	−0.907984	−	0.419005i	$-0.862379\pi$
$577$	−7.95448	−	29.6865i	−0.331149	−	1.23587i	0.576834	−	0.816861i	$-0.304288\pi$
$578$	−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	$-0.203277\pi$
$587$	29.0793	+	7.79178i	1.20023	+	0.321601i	0.397309	+	0.917685i	$0.369944\pi$
$588$		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	0.517497	−	0.855685i	$-0.326864\pi$
$599$	37.1349	−	21.4398i	1.51729	−	0.876008i	0.999793	−	0.0203229i	$-0.00646942\pi$
$600$		0			0
$601$	−13.7942	+	23.8923i	−0.562678	+	0.974587i	0.434583	+	0.900632i	$0.356896\pi$
$601$	−13.7942	+	23.8923i	−0.562678	+	0.974587i	−0.997262	+	0.0739558i	$0.976438\pi$
$602$		−	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	0.660493	−	0.750832i	$-0.270347\pi$
$607$	39.6147	−	10.6147i	1.60791	−	0.430839i	0.947420	+	0.319993i	$0.103681\pi$
$608$	−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	0.973635	−	0.228113i	$-0.0732555\pi$
$613$	31.2679	+	18.0526i	1.26290	+	0.729136i	0.289266	+	0.957249i	$0.406589\pi$
$614$	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	0.437854	+	0.899046i	$0.355739\pi$
$617$	−13.9019	+	24.0788i	−0.559669	+	0.969376i	−0.997524	+	0.0703299i	$0.977595\pi$
$618$		0			0
$619$			39.0526i			1.56965i	0.619714	+	0.784827i	$0.287248\pi$
$619$			39.0526i			1.56965i	−0.619714	+	0.784827i	$0.712752\pi$
$620$	−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	0.0206747	−	0.999786i	$-0.493419\pi$
$631$	13.5263	−	3.62436i	0.538473	−	0.144283i	0.517798	+	0.855503i	$0.326752\pi$
$632$	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	$-0.442798\pi$
$641$	−14.7849	−	8.53605i	−0.583967	−	0.337154i	−0.762708	+	0.646742i	$0.776131\pi$
$642$		0			0
$643$	10.1506	+	10.1506i	0.400302	+	0.400302i	0.878339	−	0.478037i	$-0.158652\pi$
$643$	10.1506	+	10.1506i	0.400302	+	0.400302i	−0.478037	+	0.878339i	$0.658652\pi$
$644$	−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	$-0.445086\pi$
$647$	−4.38134	−	1.17398i	−0.172248	−	0.0461538i	−0.343912	+	0.939002i	$0.611752\pi$
$648$		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	$-0.373383\pi$
$653$	6.69213	+	1.79315i	0.261883	+	0.0701714i	−0.125488	+	0.992095i	$0.540050\pi$
$654$		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	0.992513	+	0.122142i	$0.0389762\pi$
$659$	15.4548	+	26.7685i	0.602034	+	1.04275i	−0.390479	+	0.920612i	$0.627690\pi$
$660$		0			0
$661$	−4.74167	+	17.6962i	−0.184430	+	0.688301i	0.810322	+	0.585984i	$0.199292\pi$
$661$	−4.74167	+	17.6962i	−0.184430	+	0.688301i	−0.994752	+	0.102316i	$0.967375\pi$
$662$	−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	0.975587	+	0.219615i	$0.0704800\pi$
$673$	17.5885	+	30.4641i	0.677985	+	1.17430i	−0.297601	+	0.954690i	$0.596187\pi$
$674$	−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	$-0.474643\pi$
$677$	4.14110			0.159156			0.0795778	+	0.996829i	$0.474643\pi$
$678$		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	$-0.822332\pi$
$683$	−34.4452	+	9.22955i	−1.31801	+	0.353159i	−0.469776	+	0.882785i	$0.655665\pi$
$684$		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	0.700631	−	0.713523i	$-0.252902\pi$
$691$	11.3827	+	6.57180i	0.433018	+	0.250003i	−0.267614	+	0.963526i	$0.586235\pi$
$692$		−	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	$-0.272689\pi$
$701$	42.3620	−	11.3509i	1.59999	−	0.428717i	0.945040	+	0.326954i	$0.106022\pi$
$702$		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	−0.932601	−	0.360910i	$-0.882466\pi$
$709$	−15.2224	+	15.2224i	−0.571690	+	0.571690i	0.360910	+	0.932601i	$0.382466\pi$
$710$	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	$-0.584690\pi$
$719$	−32.9802	−	19.0411i	−1.22995	−	0.710114i	−0.967020	+	0.254700i	$0.918023\pi$
$720$		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	0.704870	+	0.709336i	$0.251005\pi$
$727$	−7.01666	+	26.1865i	−0.260234	+	0.971205i	−0.965104	+	0.261868i	$0.915661\pi$
$728$	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	−0.339671	−	0.940544i	$-0.610316\pi$
$733$	8.25833	−	4.76795i	0.305028	−	0.176108i	0.644700	+	0.764436i	$0.276982\pi$
$734$	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	$0.0548388\pi$
$739$			9.32051i			0.342860i	−0.985196	+	0.171430i	$0.945161\pi$
$740$	−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	0.997039	+	0.0769034i	$0.0245033\pi$
$743$	15.4040	+	26.6806i	0.565120	+	0.978816i	−0.431919	+	0.901912i	$0.642163\pi$
$744$		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	$0.0419137\pi$
$751$			7.19615i			0.262591i	−0.991343	+	0.131296i	$0.958086\pi$
$752$	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	0.997980	+	0.0635231i	$0.0202337\pi$
$757$	4.55256	+	16.9904i	0.165466	+	0.617526i	−0.832515	+	0.554003i	$0.813100\pi$
$758$	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	−0.0852578	−	0.996359i	$-0.527171\pi$
$761$	22.6274	−	39.1918i	0.820243	−	1.42070i	0.905501	−	0.424344i	$-0.139495\pi$
$762$		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	0.836107	−	0.548567i	$-0.184826\pi$
$769$	7.97372	+	7.97372i	0.287540	+	0.287540i	−0.548567	+	0.836107i	$0.684826\pi$
$770$	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	$-0.706668\pi$
$773$	−6.03579	+	3.48477i	−0.217092	+	0.125338i	0.387511	+	0.921865i	$0.373335\pi$
$774$		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	−0.986295	−	0.164990i	$-0.947241\pi$
$797$	−6.05935	−	22.6138i	−0.214633	−	0.801022i	0.771662	−	0.636033i	$-0.219426\pi$
$798$		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	$-0.354016\pi$
$809$	10.7453	+	2.87920i	0.377785	+	0.101227i	−0.0649296	+	0.997890i	$0.520682\pi$
$810$		0			0
$811$	−18.1962	−	31.5167i	−0.638953	−	1.10670i	−0.985663	−	0.168727i	$-0.946034\pi$
$811$	−18.1962	−	31.5167i	−0.638953	−	1.10670i	0.346709	−	0.937973i	$-0.387299\pi$
$812$	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	$-0.509106\pi$
$821$	23.5748	−	13.6109i	0.822765	−	0.475023i	0.851369	+	0.524567i	$0.175773\pi$
$822$		0			0
$823$	1.20577	−	2.08846i	0.0420305	−	0.0727990i	−0.844245	−	0.535958i	$-0.819951\pi$
$823$	1.20577	−	2.08846i	0.0420305	−	0.0727990i	0.886275	+	0.463159i	$0.153284\pi$
$824$		−	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	$-0.956197\pi$
$827$	−1.84392	+	6.88160i	−0.0641193	+	0.239297i	0.926427	+	0.376474i	$0.122864\pi$
$828$		0			0
$829$	−10.1603	+	2.72243i	−0.352880	+	0.0945540i	−0.430905	−	0.902397i	$-0.641805\pi$
$829$	−10.1603	+	2.72243i	−0.352880	+	0.0945540i	0.0780244	+	0.996951i	$0.475139\pi$
$830$	−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	$-0.997444\pi$
$839$	−14.2808	+	24.7351i	−0.493029	+	0.853952i	0.506939	+	0.861982i	$0.330777\pi$
$840$		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	−0.0602271	−	0.998185i	$-0.519182\pi$
$853$	11.2942	−	3.02628i	0.386707	−	0.103618i	0.446934	+	0.894567i	$0.352516\pi$
$854$	−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	$-0.153587\pi$
$857$	12.3490	+	12.3490i	0.421833	+	0.421833i	−0.464001	+	0.885835i	$0.653587\pi$
$858$		0			0
$859$	35.7583	−	35.7583i	1.22006	−	1.22006i	0.252448	−	0.967610i	$-0.418764\pi$
$859$	35.7583	−	35.7583i	1.22006	−	1.22006i	0.967610	−	0.252448i	$-0.0812357\pi$
$860$	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	0.996835	+	0.0794977i	$0.0253316\pi$
$863$	45.9483	+	26.5283i	1.56410	+	0.903033i	0.567265	+	0.823536i	$0.308002\pi$
$864$		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	$-0.150950\pi$
$881$	1.46498	+	2.53742i	0.0493565	+	0.0854879i	−0.840292	+	0.542135i	$0.817616\pi$
$882$		0			0
$883$	12.9737	−	48.4186i	0.436600	−	1.62942i	−0.300607	−	0.953748i	$-0.597189\pi$
$883$	12.9737	−	48.4186i	0.436600	−	1.62942i	0.737207	−	0.675667i	$-0.236144\pi$
$884$	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	$-0.465654\pi$
$887$	6.41473			0.215386			0.107693	+	0.994184i	$0.465654\pi$
$888$		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	−0.446218	−	0.894924i	$-0.647229\pi$
$907$	−38.5526	−	10.3301i	−1.28012	−	0.343006i	−0.833898	+	0.551918i	$0.813896\pi$
$908$	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	$-0.415555\pi$
$911$	−21.2132	−	21.2132i	−0.702825	−	0.702825i	−0.965016	+	0.262191i	$0.915555\pi$
$912$		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	0.936016	−	0.351957i	$-0.114484\pi$
$919$	17.7058	+	17.7058i	0.584060	+	0.584060i	−0.351957	+	0.936016i	$0.614484\pi$
$920$	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	−0.856377	−	0.516351i	$-0.827290\pi$
$929$	−26.6806	−	46.2121i	−0.875362	−	1.51617i	−0.0189848	−	0.999820i	$-0.506043\pi$
$930$		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	−0.946848	−	0.321682i	$-0.895752\pi$
$937$	−5.96410	+	10.3301i	−0.194839	+	0.337471i	0.752009	+	0.659153i	$0.229085\pi$
$938$	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	$-0.334246\pi$
$941$	−0.152304	−	0.0879327i	−0.00496497	−	0.00286652i	−0.502480	+	0.864589i	$0.667579\pi$
$942$		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	$-0.816260\pi$
$947$	−39.7231	+	10.6438i	−1.29083	+	0.345876i	−0.452852	+	0.891586i	$0.649593\pi$
$948$		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	0.420505	+	0.907290i	$0.361853\pi$
$953$	−17.7656	+	30.7709i	−0.575484	+	0.996768i	−0.995989	+	0.0894776i	$0.971480\pi$
$954$		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	−0.134050	−	0.990975i	$-0.542798\pi$
$967$	−23.1865	−	6.21281i	−0.745629	−	0.199791i	−0.611578	+	0.791184i	$0.709465\pi$
$968$	−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	$-0.145997\pi$
$971$	29.9623	+	17.2987i	0.961535	+	0.555143i	0.0648902	+	0.997892i	$0.479330\pi$
$972$		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	0.698862	+	0.715256i	$0.253690\pi$
$977$	14.1050	+	52.6405i	0.451258	+	1.68412i	−0.247604	+	0.968861i	$0.579643\pi$
$978$		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	$-0.968503\pi$
$983$	−12.9174	+	22.3736i	−0.412001	+	0.713606i	0.583108	+	0.812395i	$0.301837\pi$
$984$		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	0.625753	−	0.780022i	$-0.284792\pi$
$991$	−4.85641	−	4.85641i	−0.154269	−	0.154269i	−0.780022	+	0.625753i	$0.784792\pi$
$992$	−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	−0.868079	−	0.496425i	$-0.834646\pi$
$997$	−11.5096	−	42.9545i	−0.364513	−	1.36038i	0.503566	−	0.863957i	$-0.332021\pi$
$998$	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.125.2	yes	8
3.2	odd	2	inner	666.2.be.b.125.1	✓	8
37.8	odd	12	inner	666.2.be.b.341.1	yes	8
111.8	even	12	inner	666.2.be.b.341.2	yes	8

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

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