LMFDB - Embedded newform 936.2.dg.b.829.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(829,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("936.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dg (of order $6$, degree $2$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.b.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +3.73205 q^{5} +(-3.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(3.73205 + 3.73205i) q^{10} +(1.00000 + 1.73205i) q^{11} +(2.59808 + 2.50000i) q^{13} +(-1.26795 - 4.73205i) q^{14} -4.00000 q^{16} +(-0.232051 + 0.401924i) q^{17} +(-0.633975 + 1.09808i) q^{19} +7.46410i q^{20} +(-0.732051 + 2.73205i) q^{22} +(4.09808 + 7.09808i) q^{23} +8.92820 q^{25} +(0.0980762 + 5.09808i) q^{26} +(3.46410 - 6.00000i) q^{28} +(2.59808 - 1.50000i) q^{29} +4.73205i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.633975 + 0.169873i) q^{34} +(-11.1962 - 6.46410i) q^{35} +(-2.13397 - 3.69615i) q^{37} +(-1.73205 + 0.464102i) q^{38} +(-7.46410 + 7.46410i) q^{40} +(7.96410 - 4.59808i) q^{41} +(-2.19615 - 1.26795i) q^{43} +(-3.46410 + 2.00000i) q^{44} +(-3.00000 + 11.1962i) q^{46} -6.73205i q^{47} +(2.50000 + 4.33013i) q^{49} +(8.92820 + 8.92820i) q^{50} +(-5.00000 + 5.19615i) q^{52} -3.92820i q^{53} +(3.73205 + 6.46410i) q^{55} +(9.46410 - 2.53590i) q^{56} +(4.09808 + 1.09808i) q^{58} +(0.267949 - 0.464102i) q^{59} +(-0.866025 - 0.500000i) q^{61} +(-4.73205 + 4.73205i) q^{62} -8.00000i q^{64} +(9.69615 + 9.33013i) q^{65} +(-3.63397 - 6.29423i) q^{67} +(-0.803848 - 0.464102i) q^{68} +(-4.73205 - 17.6603i) q^{70} +(-8.02628 - 4.63397i) q^{71} -1.73205i q^{73} +(1.56218 - 5.83013i) q^{74} +(-2.19615 - 1.26795i) q^{76} -6.92820i q^{77} -10.3923 q^{79} -14.9282 q^{80} +(12.5622 + 3.36603i) q^{82} +1.46410 q^{83} +(-0.866025 + 1.50000i) q^{85} +(-0.928203 - 3.46410i) q^{86} +(-5.46410 - 1.46410i) q^{88} +(-6.46410 + 3.73205i) q^{89} +(-3.46410 - 12.0000i) q^{91} +(-14.1962 + 8.19615i) q^{92} +(6.73205 - 6.73205i) q^{94} +(-2.36603 + 4.09808i) q^{95} +(-5.19615 - 3.00000i) q^{97} +(-1.83013 + 6.83013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 8 q^{5} - 12 q^{7} - 8 q^{8} + 8 q^{10} + 4 q^{11} - 12 q^{14} - 16 q^{16} + 6 q^{17} - 6 q^{19} + 4 q^{22} + 6 q^{23} + 8 q^{25} - 10 q^{26} - 16 q^{32} - 6 q^{34} - 24 q^{35} - 12 q^{37}+ \cdots + 10 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 8 * q^5 - 12 * q^7 - 8 * q^8 + 8 * q^10 + 4 * q^11 - 12 * q^14 - 16 * q^16 + 6 * q^17 - 6 * q^19 + 4 * q^22 + 6 * q^23 + 8 * q^25 - 10 * q^26 - 16 * q^32 - 6 * q^34 - 24 * q^35 - 12 * q^37 - 16 * q^40 + 18 * q^41 + 12 * q^43 - 12 * q^46 + 10 * q^49 + 8 * q^50 - 20 * q^52 + 8 * q^55 + 24 * q^56 + 6 * q^58 + 8 * q^59 - 12 * q^62 + 18 * q^65 - 18 * q^67 - 24 * q^68 - 12 * q^70 + 6 * q^71 - 18 * q^74 + 12 * q^76 - 32 * q^80 + 26 * q^82 - 8 * q^83 + 24 * q^86 - 8 * q^88 - 12 * q^89 - 36 * q^92 + 20 * q^94 - 6 * q^95 + 10 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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 $

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$		0			0
$3$		0			0
$4$			2.00000i			1.00000i
$5$	3.73205			1.66902			0.834512	−	0.550990i	$-0.185750\pi$
$5$	3.73205			1.66902			0.834512	+	0.550990i	$0.185750\pi$
$6$		0			0
$7$	−3.00000	−	1.73205i	−1.13389	−	0.654654i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−3.00000	−	1.73205i	−1.13389	−	0.654654i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$	3.73205	+	3.73205i	1.18018	+	1.18018i
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		0			0
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$	−1.26795	−	4.73205i	−0.338874	−	1.26469i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	−0.232051	+	0.401924i	−0.0562806	+	0.0974808i	−0.892793	−	0.450467i	$-0.851257\pi$
$17$	−0.232051	+	0.401924i	−0.0562806	+	0.0974808i	0.836512	+	0.547948i	$0.184591\pi$
$18$		0			0
$19$	−0.633975	+	1.09808i	−0.145444	+	0.251916i	−0.929538	−	0.368725i	$-0.879794\pi$
$19$	−0.633975	+	1.09808i	−0.145444	+	0.251916i	0.784095	+	0.620641i	$0.213128\pi$
$20$			7.46410i			1.66902i
$21$		0			0
$22$	−0.732051	+	2.73205i	−0.156074	+	0.582475i
$23$	4.09808	+	7.09808i	0.854508	+	1.48005i	0.877101	+	0.480306i	$0.159475\pi$
$23$	4.09808	+	7.09808i	0.854508	+	1.48005i	−0.0225928	+	0.999745i	$0.507192\pi$
$24$		0			0
$25$	8.92820			1.78564
$26$	0.0980762	+	5.09808i	0.0192343	+	0.999815i
$27$		0			0
$28$	3.46410	−	6.00000i	0.654654	−	1.13389i
$29$	2.59808	−	1.50000i	0.482451	−	0.278543i	−0.238987	−	0.971023i	$-0.576815\pi$
$29$	2.59808	−	1.50000i	0.482451	−	0.278543i	0.721437	+	0.692480i	$0.243482\pi$
$30$		0			0
$31$			4.73205i			0.849901i	0.905216	+	0.424951i	$0.139709\pi$
$31$			4.73205i			0.849901i	−0.905216	+	0.424951i	$0.860291\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$		0			0
$34$	−0.633975	+	0.169873i	−0.108726	+	0.0291330i
$35$	−11.1962	−	6.46410i	−1.89250	−	1.09263i
$36$		0			0
$37$	−2.13397	−	3.69615i	−0.350823	−	0.607644i	0.635571	−	0.772043i	$-0.280765\pi$
$37$	−2.13397	−	3.69615i	−0.350823	−	0.607644i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	−1.73205	+	0.464102i	−0.280976	+	0.0752872i
$39$		0			0
$40$	−7.46410	+	7.46410i	−1.18018	+	1.18018i
$41$	7.96410	−	4.59808i	1.24378	−	0.718099i	0.273921	−	0.961752i	$-0.411679\pi$
$41$	7.96410	−	4.59808i	1.24378	−	0.718099i	0.969862	+	0.243653i	$0.0783459\pi$
$42$		0			0
$43$	−2.19615	−	1.26795i	−0.334910	−	0.193360i	0.323109	−	0.946362i	$-0.395272\pi$
$43$	−2.19615	−	1.26795i	−0.334910	−	0.193360i	−0.658019	+	0.753001i	$0.728605\pi$
$44$	−3.46410	+	2.00000i	−0.522233	+	0.301511i
$45$		0			0
$46$	−3.00000	+	11.1962i	−0.442326	+	1.65078i
$47$		−	6.73205i		−	0.981971i	−0.871168	−	0.490985i	$-0.836637\pi$
$47$		−	6.73205i		−	0.981971i	0.871168	−	0.490985i	$-0.163363\pi$
$48$		0			0
$49$	2.50000	+	4.33013i	0.357143	+	0.618590i
$50$	8.92820	+	8.92820i	1.26264	+	1.26264i
$51$		0			0
$52$	−5.00000	+	5.19615i	−0.693375	+	0.720577i
$53$		−	3.92820i		−	0.539580i	−0.962919	−	0.269790i	$-0.913046\pi$
$53$		−	3.92820i		−	0.539580i	0.962919	−	0.269790i	$-0.0869543\pi$
$54$		0			0
$55$	3.73205	+	6.46410i	0.503230	+	0.871619i
$56$	9.46410	−	2.53590i	1.26469	−	0.338874i
$57$		0			0
$58$	4.09808	+	1.09808i	0.538104	+	0.144184i
$59$	0.267949	−	0.464102i	0.0348840	−	0.0604209i	−0.848056	−	0.529906i	$-0.822227\pi$
$59$	0.267949	−	0.464102i	0.0348840	−	0.0604209i	0.882940	+	0.469485i	$0.155560\pi$
$60$		0			0
$61$	−0.866025	−	0.500000i	−0.110883	−	0.0640184i	0.443533	−	0.896258i	$-0.353725\pi$
$61$	−0.866025	−	0.500000i	−0.110883	−	0.0640184i	−0.554416	+	0.832240i	$0.687058\pi$
$62$	−4.73205	+	4.73205i	−0.600971	+	0.600971i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	9.69615	+	9.33013i	1.20266	+	1.15726i
$66$		0			0
$67$	−3.63397	−	6.29423i	−0.443961	−	0.768962i	0.554019	−	0.832504i	$-0.313094\pi$
$67$	−3.63397	−	6.29423i	−0.443961	−	0.768962i	−0.997979	+	0.0635419i	$0.979760\pi$
$68$	−0.803848	−	0.464102i	−0.0974808	−	0.0562806i
$69$		0			0
$70$	−4.73205	−	17.6603i	−0.565588	−	2.11080i
$71$	−8.02628	−	4.63397i	−0.952544	−	0.549952i	−0.0586738	−	0.998277i	$-0.518687\pi$
$71$	−8.02628	−	4.63397i	−0.952544	−	0.549952i	−0.893870	+	0.448326i	$0.852021\pi$
$72$		0			0
$73$		−	1.73205i		−	0.202721i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$		−	1.73205i		−	0.202721i	0.994850	−	0.101361i	$-0.0323196\pi$
$74$	1.56218	−	5.83013i	0.181599	−	0.677738i
$75$		0			0
$76$	−2.19615	−	1.26795i	−0.251916	−	0.145444i
$77$		−	6.92820i		−	0.789542i
$78$		0			0
$79$	−10.3923			−1.16923			−0.584613	−	0.811312i	$-0.698754\pi$
$79$	−10.3923			−1.16923			−0.584613	+	0.811312i	$0.698754\pi$
$80$	−14.9282			−1.66902
$81$		0			0
$82$	12.5622	+	3.36603i	1.38726	+	0.371715i
$83$	1.46410			0.160706			0.0803530	−	0.996766i	$-0.474395\pi$
$83$	1.46410			0.160706			0.0803530	+	0.996766i	$0.474395\pi$
$84$		0			0
$85$	−0.866025	+	1.50000i	−0.0939336	+	0.162698i
$86$	−0.928203	−	3.46410i	−0.100091	−	0.373544i
$87$		0			0
$88$	−5.46410	−	1.46410i	−0.582475	−	0.156074i
$89$	−6.46410	+	3.73205i	−0.685193	+	0.395597i	−0.801809	−	0.597581i	$-0.796129\pi$
$89$	−6.46410	+	3.73205i	−0.685193	+	0.395597i	0.116615	+	0.993177i	$0.462795\pi$
$90$		0			0
$91$	−3.46410	−	12.0000i	−0.363137	−	1.25794i
$92$	−14.1962	+	8.19615i	−1.48005	+	0.854508i
$93$		0			0
$94$	6.73205	−	6.73205i	0.694358	−	0.694358i
$95$	−2.36603	+	4.09808i	−0.242749	+	0.420454i
$96$		0			0
$97$	−5.19615	−	3.00000i	−0.527589	−	0.304604i	0.212445	−	0.977173i	$-0.431857\pi$
$97$	−5.19615	−	3.00000i	−0.527589	−	0.304604i	−0.740034	+	0.672569i	$0.765191\pi$
$98$	−1.83013	+	6.83013i	−0.184871	+	0.689947i
$99$		0			0
$100$			17.8564i			1.78564i
$101$	−9.99038	+	5.76795i	−0.994080	+	0.573932i	−0.906491	−	0.422224i	$-0.861249\pi$
$101$	−9.99038	+	5.76795i	−0.994080	+	0.573932i	−0.0875887	+	0.996157i	$0.527916\pi$
$102$		0			0
$103$	6.19615			0.610525			0.305263	−	0.952268i	$-0.401256\pi$
$103$	6.19615			0.610525			0.305263	+	0.952268i	$0.401256\pi$
$104$	−10.1962	+	0.196152i	−0.999815	+	0.0192343i
$105$		0			0
$106$	3.92820	−	3.92820i	0.381541	−	0.381541i
$107$	15.2942	−	8.83013i	1.47855	−	0.853641i	0.478843	−	0.877900i	$-0.341056\pi$
$107$	15.2942	−	8.83013i	1.47855	−	0.853641i	0.999706	+	0.0242598i	$0.00772291\pi$
$108$		0			0
$109$	−6.00000			−0.574696			−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000			−0.574696			−0.287348	+	0.957826i	$0.592774\pi$
$110$	−2.73205	+	10.1962i	−0.260491	+	0.972165i
$111$		0			0
$112$	12.0000	+	6.92820i	1.13389	+	0.654654i
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	−0.927914	−	0.372794i	$-0.878400\pi$
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	0.786806	+	0.617200i	$0.211733\pi$
$114$		0			0
$115$	15.2942	+	26.4904i	1.42619	+	2.47024i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$		0			0
$118$	0.732051	−	0.196152i	0.0673907	−	0.0180573i
$119$	1.39230	−	0.803848i	0.127632	−	0.0736886i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−0.366025	−	1.36603i	−0.0331384	−	0.123674i
$123$		0			0
$124$	−9.46410			−0.849901
$125$	14.6603			1.31125
$126$		0			0
$127$	−0.169873	−	0.294229i	−0.0150738	−	0.0261086i	0.858390	−	0.512997i	$-0.171465\pi$
$127$	−0.169873	−	0.294229i	−0.0150738	−	0.0261086i	−0.873464	+	0.486889i	$0.838132\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$		0			0
$130$	0.366025	+	19.0263i	0.0321026	+	1.66872i
$131$		−	10.7321i		−	0.937664i	−0.883287	−	0.468832i	$-0.844675\pi$
$131$		−	10.7321i		−	0.937664i	0.883287	−	0.468832i	$-0.155325\pi$
$132$		0			0
$133$	3.80385	−	2.19615i	0.329835	−	0.190431i
$134$	2.66025	−	9.92820i	0.229811	−	0.857666i
$135$		0			0
$136$	−0.339746	−	1.26795i	−0.0291330	−	0.108726i
$137$	11.7679	+	6.79423i	1.00540	+	0.580470i	0.909843	−	0.414953i	$-0.136202\pi$
$137$	11.7679	+	6.79423i	1.00540	+	0.580470i	0.0955611	+	0.995424i	$0.469535\pi$
$138$		0			0
$139$	−8.19615	−	4.73205i	−0.695189	−	0.401367i	0.110364	−	0.993891i	$-0.464798\pi$
$139$	−8.19615	−	4.73205i	−0.695189	−	0.401367i	−0.805553	+	0.592524i	$0.798132\pi$
$140$	12.9282	−	22.3923i	1.09263	−	1.89250i
$141$		0			0
$142$	−3.39230	−	12.6603i	−0.284676	−	1.06242i
$143$	−1.73205	+	7.00000i	−0.144841	+	0.585369i
$144$		0			0
$145$	9.69615	−	5.59808i	0.805222	−	0.464895i
$146$	1.73205	−	1.73205i	0.143346	−	0.143346i
$147$		0			0
$148$	7.39230	−	4.26795i	0.607644	−	0.350823i
$149$	−5.86603	+	10.1603i	−0.480564	+	0.832360i	−0.999751	−	0.0222997i	$-0.992901\pi$
$149$	−5.86603	+	10.1603i	−0.480564	+	0.832360i	0.519188	+	0.854660i	$0.326235\pi$
$150$		0			0
$151$			2.19615i			0.178720i	0.995999	+	0.0893602i	$0.0284822\pi$
$151$			2.19615i			0.178720i	−0.995999	+	0.0893602i	$0.971518\pi$
$152$	−0.928203	−	3.46410i	−0.0752872	−	0.280976i
$153$		0			0
$154$	6.92820	−	6.92820i	0.558291	−	0.558291i
$155$			17.6603i			1.41851i
$156$		0			0
$157$		−	3.92820i		−	0.313505i	−0.987638	−	0.156752i	$-0.949898\pi$
$157$		−	3.92820i		−	0.313505i	0.987638	−	0.156752i	$-0.0501025\pi$
$158$	−10.3923	−	10.3923i	−0.826767	−	0.826767i
$159$		0			0
$160$	−14.9282	−	14.9282i	−1.18018	−	1.18018i
$161$		−	28.3923i		−	2.23763i
$162$		0			0
$163$	8.19615	−	14.1962i	0.641972	−	1.11193i	−0.343020	−	0.939328i	$-0.611450\pi$
$163$	8.19615	−	14.1962i	0.641972	−	1.11193i	0.984992	−	0.172600i	$-0.0552169\pi$
$164$	9.19615	+	15.9282i	0.718099	+	1.24378i
$165$		0			0
$166$	1.46410	+	1.46410i	0.113636	+	0.113636i
$167$	4.26795	−	2.46410i	0.330264	−	0.190678i	−0.325694	−	0.945475i	$-0.605598\pi$
$167$	4.26795	−	2.46410i	0.330264	−	0.190678i	0.655958	+	0.754797i	$0.272265\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	−2.36603	+	0.633975i	−0.181466	+	0.0486236i
$171$		0			0
$172$	2.53590	−	4.39230i	0.193360	−	0.334910i
$173$	−16.3923	−	9.46410i	−1.24628	−	0.719542i	−0.275918	−	0.961181i	$-0.588982\pi$
$173$	−16.3923	−	9.46410i	−1.24628	−	0.719542i	−0.970366	+	0.241639i	$0.922315\pi$
$174$		0			0
$175$	−26.7846	−	15.4641i	−2.02473	−	1.16898i
$176$	−4.00000	−	6.92820i	−0.301511	−	0.522233i
$177$		0			0
$178$	−10.1962	−	2.73205i	−0.764234	−	0.204776i
$179$	12.0000	−	6.92820i	0.896922	−	0.517838i	0.0207218	−	0.999785i	$-0.493404\pi$
$179$	12.0000	−	6.92820i	0.896922	−	0.517838i	0.876200	+	0.481947i	$0.160070\pi$
$180$		0			0
$181$			18.4641i			1.37243i	0.727401	+	0.686213i	$0.240728\pi$
$181$			18.4641i			1.37243i	−0.727401	+	0.686213i	$0.759272\pi$
$182$	8.53590	−	15.4641i	0.632723	−	1.14628i
$183$		0			0
$184$	−22.3923	−	6.00000i	−1.65078	−	0.442326i
$185$	−7.96410	−	13.7942i	−0.585532	−	1.01417i
$186$		0			0
$187$	−0.928203			−0.0678769
$188$	13.4641			0.981971
$189$		0			0
$190$	−6.46410	+	1.73205i	−0.468955	+	0.125656i
$191$	1.90192	−	3.29423i	0.137618	−	0.238362i	−0.788976	−	0.614424i	$-0.789389\pi$
$191$	1.90192	−	3.29423i	0.137618	−	0.238362i	0.926595	+	0.376062i	$0.122722\pi$
$192$		0			0
$193$	11.3038	−	6.52628i	0.813669	−	0.469772i	−0.0345595	−	0.999403i	$-0.511003\pi$
$193$	11.3038	−	6.52628i	0.813669	−	0.469772i	0.848228	+	0.529631i	$0.177670\pi$
$194$	−2.19615	−	8.19615i	−0.157675	−	0.588449i
$195$		0			0
$196$	−8.66025	+	5.00000i	−0.618590	+	0.357143i
$197$	−6.26795	−	10.8564i	−0.446573	−	0.773487i	0.551587	−	0.834117i	$-0.314022\pi$
$197$	−6.26795	−	10.8564i	−0.446573	−	0.773487i	−0.998160	+	0.0606302i	$0.980689\pi$
$198$		0			0
$199$	7.56218	−	13.0981i	0.536069	−	0.928498i	−0.463042	−	0.886336i	$-0.653242\pi$
$199$	7.56218	−	13.0981i	0.536069	−	0.928498i	0.999111	−	0.0421618i	$-0.0134245\pi$
$200$	−17.8564	+	17.8564i	−1.26264	+	1.26264i
$201$		0			0
$202$	−15.7583	−	4.22243i	−1.10875	−	0.297089i
$203$	−10.3923			−0.729397
$204$		0			0
$205$	29.7224	−	17.1603i	2.07590	−	1.19852i
$206$	6.19615	+	6.19615i	0.431706	+	0.431706i
$207$		0			0
$208$	−10.3923	−	10.0000i	−0.720577	−	0.693375i
$209$	−2.53590			−0.175412
$210$		0			0
$211$	24.7583	−	14.2942i	1.70443	−	0.984055i	0.763285	−	0.646061i	$-0.223585\pi$
$211$	24.7583	−	14.2942i	1.70443	−	0.984055i	0.941148	−	0.337994i	$-0.109748\pi$
$212$	7.85641			0.539580
$213$		0			0
$214$	24.1244	+	6.46410i	1.64911	+	0.441877i
$215$	−8.19615	−	4.73205i	−0.558973	−	0.322723i
$216$		0			0
$217$	8.19615	−	14.1962i	0.556391	−	0.963698i
$218$	−6.00000	−	6.00000i	−0.406371	−	0.406371i
$219$		0			0
$220$	−12.9282	+	7.46410i	−0.871619	+	0.503230i
$221$	−1.60770	+	0.464102i	−0.108145	+	0.0312189i
$222$		0			0
$223$	−22.0981	+	12.7583i	−1.47980	+	0.854361i	−0.999738	−	0.0228756i	$-0.992718\pi$
$223$	−22.0981	+	12.7583i	−1.47980	+	0.854361i	−0.480058	+	0.877237i	$0.659385\pi$
$224$	5.07180	+	18.9282i	0.338874	+	1.26469i
$225$		0			0
$226$	−4.09808	+	1.09808i	−0.272600	+	0.0730429i
$227$	13.0263	−	22.5622i	0.864585	−	1.49750i	−0.00287459	−	0.999996i	$-0.500915\pi$
$227$	13.0263	−	22.5622i	0.864585	−	1.49750i	0.867459	−	0.497508i	$-0.165752\pi$
$228$		0			0
$229$	−12.9282			−0.854320			−0.427160	−	0.904176i	$-0.640486\pi$
$229$	−12.9282			−0.854320			−0.427160	+	0.904176i	$0.640486\pi$
$230$	−11.1962	+	41.7846i	−0.738252	+	2.75520i
$231$		0			0
$232$	−2.19615	+	8.19615i	−0.144184	+	0.538104i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$		−	25.1244i		−	1.63893i
$236$	0.928203	+	0.535898i	0.0604209	+	0.0348840i
$237$		0			0
$238$	2.19615	+	0.588457i	0.142355	+	0.0381440i
$239$			18.3923i			1.18970i	0.803837	+	0.594850i	$0.202788\pi$
$239$			18.3923i			1.18970i	−0.803837	+	0.594850i	$0.797212\pi$
$240$		0			0
$241$	9.69615	+	5.59808i	0.624584	+	0.360604i	0.778652	−	0.627457i	$-0.215904\pi$
$241$	9.69615	+	5.59808i	0.624584	+	0.360604i	−0.154068	+	0.988060i	$0.549237\pi$
$242$	9.56218	−	2.56218i	0.614680	−	0.164703i
$243$		0			0
$244$	1.00000	−	1.73205i	0.0640184	−	0.110883i
$245$	9.33013	+	16.1603i	0.596080	+	1.03244i
$246$		0			0
$247$	−4.39230	+	1.26795i	−0.279476	+	0.0806777i
$248$	−9.46410	−	9.46410i	−0.600971	−	0.600971i
$249$		0			0
$250$	14.6603	+	14.6603i	0.927196	+	0.927196i
$251$	−7.09808	−	4.09808i	−0.448027	−	0.258668i	0.258970	−	0.965885i	$-0.416617\pi$
$251$	−7.09808	−	4.09808i	−0.448027	−	0.258668i	−0.706996	+	0.707217i	$0.749950\pi$
$252$		0			0
$253$	−8.19615	+	14.1962i	−0.515288	+	0.892504i
$254$	0.124356	−	0.464102i	0.00780277	−	0.0291203i
$255$		0			0
$256$	16.0000			1.00000
$257$	11.4282	+	19.7942i	0.712872	+	1.23473i	0.963775	+	0.266718i	$0.0859392\pi$
$257$	11.4282	+	19.7942i	0.712872	+	1.23473i	−0.250903	+	0.968012i	$0.580727\pi$
$258$		0			0
$259$			14.7846i			0.918671i
$260$	−18.6603	+	19.3923i	−1.15726	+	1.20266i
$261$		0			0
$262$	10.7321	−	10.7321i	0.663028	−	0.663028i
$263$	8.19615	+	14.1962i	0.505396	+	0.875372i	0.999981	+	0.00624249i	$0.00198706\pi$
$263$	8.19615	+	14.1962i	0.505396	+	0.875372i	−0.494584	+	0.869130i	$0.664680\pi$
$264$		0			0
$265$		−	14.6603i		−	0.900572i
$266$	6.00000	+	1.60770i	0.367884	+	0.0985741i
$267$		0			0
$268$	12.5885	−	7.26795i	0.768962	−	0.443961i
$269$	8.19615	+	4.73205i	0.499728	+	0.288518i	0.728601	−	0.684938i	$-0.240171\pi$
$269$	8.19615	+	4.73205i	0.499728	+	0.288518i	−0.228873	+	0.973456i	$0.573504\pi$
$270$		0			0
$271$	−15.0000	+	8.66025i	−0.911185	+	0.526073i	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−15.0000	+	8.66025i	−0.911185	+	0.526073i	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	0.928203	−	1.60770i	0.0562806	−	0.0974808i
$273$		0			0
$274$	4.97372	+	18.5622i	0.300473	+	1.12138i
$275$	8.92820	+	15.4641i	0.538391	+	0.932520i
$276$		0			0
$277$	−12.4019	−	7.16025i	−0.745159	−	0.430218i	0.0787828	−	0.996892i	$-0.474897\pi$
$277$	−12.4019	−	7.16025i	−0.745159	−	0.430218i	−0.823942	+	0.566674i	$0.808230\pi$
$278$	−3.46410	−	12.9282i	−0.207763	−	0.775382i
$279$		0			0
$280$	35.3205	−	9.46410i	2.11080	−	0.565588i
$281$		−	10.6603i		−	0.635937i	−0.948101	−	0.317969i	$-0.896999\pi$
$281$		−	10.6603i		−	0.635937i	0.948101	−	0.317969i	$-0.103001\pi$
$282$		0			0
$283$	−26.6603	+	15.3923i	−1.58479	+	0.914978i	−0.590641	+	0.806934i	$0.701125\pi$
$283$	−26.6603	+	15.3923i	−1.58479	+	0.914978i	−0.994146	+	0.108043i	$0.965541\pi$
$284$	9.26795	−	16.0526i	0.549952	−	0.952544i
$285$		0			0
$286$	−8.73205	+	5.26795i	−0.516337	+	0.311500i
$287$	−31.8564			−1.88042
$288$		0			0
$289$	8.39230	+	14.5359i	0.493665	+	0.855053i
$290$	15.2942	+	4.09808i	0.898108	+	0.240647i
$291$		0			0
$292$	3.46410			0.202721
$293$	1.40192	−	2.42820i	0.0819013	−	0.141857i	−0.822165	−	0.569249i	$-0.807234\pi$
$293$	1.40192	−	2.42820i	0.0819013	−	0.141857i	0.904067	+	0.427392i	$0.140567\pi$
$294$		0			0
$295$	1.00000	−	1.73205i	0.0582223	−	0.100844i
$296$	11.6603	+	3.12436i	0.677738	+	0.181599i
$297$		0			0
$298$	−16.0263	+	4.29423i	−0.928377	+	0.248758i
$299$	−7.09808	+	28.6865i	−0.410492	+	1.65899i
$300$		0			0
$301$	4.39230	+	7.60770i	0.253168	+	0.438500i
$302$	−2.19615	+	2.19615i	−0.126374	+	0.126374i
$303$		0			0
$304$	2.53590	−	4.39230i	0.145444	−	0.251916i
$305$	−3.23205	−	1.86603i	−0.185067	−	0.106848i
$306$		0			0
$307$	−2.19615			−0.125341			−0.0626705	−	0.998034i	$-0.519962\pi$
$307$	−2.19615			−0.125341			−0.0626705	+	0.998034i	$0.519962\pi$
$308$	13.8564			0.789542
$309$		0			0
$310$	−17.6603	+	17.6603i	−1.00304	+	1.00304i
$311$	18.5885			1.05405			0.527027	−	0.849848i	$-0.323307\pi$
$311$	18.5885			1.05405			0.527027	+	0.849848i	$0.323307\pi$
$312$		0			0
$313$	−2.53590			−0.143337			−0.0716687	−	0.997428i	$-0.522832\pi$
$313$	−2.53590			−0.143337			−0.0716687	+	0.997428i	$0.522832\pi$
$314$	3.92820	−	3.92820i	0.221681	−	0.221681i
$315$		0			0
$316$		−	20.7846i		−	1.16923i
$317$	25.1962			1.41516			0.707578	−	0.706635i	$-0.249788\pi$
$317$	25.1962			1.41516			0.707578	+	0.706635i	$0.249788\pi$
$318$		0			0
$319$	5.19615	+	3.00000i	0.290929	+	0.167968i
$320$		−	29.8564i		−	1.66902i
$321$		0			0
$322$	28.3923	−	28.3923i	1.58224	−	1.58224i
$323$	−0.294229	−	0.509619i	−0.0163713	−	0.0283560i
$324$		0			0
$325$	23.1962	+	22.3205i	1.28669	+	1.23812i
$326$	22.3923	−	6.00000i	1.24020	−	0.332309i
$327$		0			0
$328$	−6.73205	+	25.1244i	−0.371715	+	1.38726i
$329$	−11.6603	+	20.1962i	−0.642851	+	1.11345i
$330$		0			0
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	−0.982470	−	0.186421i	$-0.940311\pi$
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	0.652680	+	0.757634i	$0.273645\pi$
$332$			2.92820i			0.160706i
$333$		0			0
$334$	6.73205	+	1.80385i	0.368361	+	0.0987021i
$335$	−13.5622	−	23.4904i	−0.740981	−	1.28342i
$336$		0			0
$337$	−33.2487			−1.81117			−0.905586	−	0.424162i	$-0.860569\pi$
$337$	−33.2487			−1.81117			−0.905586	+	0.424162i	$0.860569\pi$
$338$	−12.4904	+	13.4904i	−0.679387	+	0.733780i
$339$		0			0
$340$	−3.00000	−	1.73205i	−0.162698	−	0.0939336i
$341$	−8.19615	+	4.73205i	−0.443847	+	0.256255i
$342$		0			0
$343$			6.92820i			0.374088i
$344$	6.92820	−	1.85641i	0.373544	−	0.100091i
$345$		0			0
$346$	−6.92820	−	25.8564i	−0.372463	−	1.39005i
$347$	−1.09808	−	0.633975i	−0.0589478	−	0.0340335i	0.470236	−	0.882540i	$-0.344169\pi$
$347$	−1.09808	−	0.633975i	−0.0589478	−	0.0340335i	−0.529184	+	0.848507i	$0.677502\pi$
$348$		0			0
$349$	−2.66025	−	4.60770i	−0.142400	−	0.246644i	0.786000	−	0.618227i	$-0.212149\pi$
$349$	−2.66025	−	4.60770i	−0.142400	−	0.246644i	−0.928400	+	0.371582i	$0.878815\pi$
$350$	−11.3205	−	42.2487i	−0.605107	−	2.25829i
$351$		0			0
$352$	2.92820	−	10.9282i	0.156074	−	0.582475i
$353$	15.8205	−	9.13397i	0.842041	−	0.486152i	−0.0159167	−	0.999873i	$-0.505067\pi$
$353$	15.8205	−	9.13397i	0.842041	−	0.486152i	0.857957	+	0.513721i	$0.171733\pi$
$354$		0			0
$355$	−29.9545	−	17.2942i	−1.58982	−	0.917882i
$356$	−7.46410	−	12.9282i	−0.395597	−	0.685193i
$357$		0			0
$358$	18.9282	+	5.07180i	1.00039	+	0.268053i
$359$			13.0718i			0.689903i	0.938621	+	0.344952i	$0.112105\pi$
$359$			13.0718i			0.689903i	−0.938621	+	0.344952i	$0.887895\pi$
$360$		0			0
$361$	8.69615	+	15.0622i	0.457692	+	0.792746i
$362$	−18.4641	+	18.4641i	−0.970452	+	0.970452i
$363$		0			0
$364$	24.0000	−	6.92820i	1.25794	−	0.363137i
$365$		−	6.46410i		−	0.338347i
$366$		0			0
$367$	14.0981	+	24.4186i	0.735914	+	1.27464i	0.954321	+	0.298782i	$0.0965804\pi$
$367$	14.0981	+	24.4186i	0.735914	+	1.27464i	−0.218408	+	0.975858i	$0.570086\pi$
$368$	−16.3923	−	28.3923i	−0.854508	−	1.48005i
$369$		0			0
$370$	5.83013	−	21.7583i	0.303094	−	1.13116i
$371$	−6.80385	+	11.7846i	−0.353238	+	0.611826i
$372$		0			0
$373$	−22.3301	−	12.8923i	−1.15621	−	0.667538i	−0.205817	−	0.978590i	$-0.565985\pi$
$373$	−22.3301	−	12.8923i	−1.15621	−	0.667538i	−0.950393	+	0.311052i	$0.899319\pi$
$374$	−0.928203	−	0.928203i	−0.0479962	−	0.0479962i
$375$		0			0
$376$	13.4641	+	13.4641i	0.694358	+	0.694358i
$377$	10.5000	+	2.59808i	0.540778	+	0.133808i
$378$		0			0
$379$	11.0263	+	19.0981i	0.566382	+	0.981002i	0.996920	+	0.0784297i	$0.0249906\pi$
$379$	11.0263	+	19.0981i	0.566382	+	0.981002i	−0.430538	+	0.902573i	$0.641676\pi$
$380$	−8.19615	−	4.73205i	−0.420454	−	0.242749i
$381$		0			0
$382$	5.19615	−	1.39230i	0.265858	−	0.0712365i
$383$	−17.3205	−	10.0000i	−0.885037	−	0.510976i	−0.0127209	−	0.999919i	$-0.504049\pi$
$383$	−17.3205	−	10.0000i	−0.885037	−	0.510976i	−0.872316	+	0.488943i	$0.837383\pi$
$384$		0			0
$385$		−	25.8564i		−	1.31776i
$386$	17.8301	+	4.77757i	0.907530	+	0.243172i
$387$		0			0
$388$	6.00000	−	10.3923i	0.304604	−	0.527589i
$389$			18.7128i			0.948777i	0.880316	+	0.474389i	$0.157331\pi$
$389$			18.7128i			0.948777i	−0.880316	+	0.474389i	$0.842669\pi$
$390$		0			0
$391$	−3.80385			−0.192369
$392$	−13.6603	−	3.66025i	−0.689947	−	0.184871i
$393$		0			0
$394$	4.58846	−	17.1244i	0.231163	−	0.862713i
$395$	−38.7846			−1.95147
$396$		0			0
$397$	12.1244	−	21.0000i	0.608504	−	1.05396i	−0.382983	−	0.923755i	$-0.625103\pi$
$397$	12.1244	−	21.0000i	0.608504	−	1.05396i	0.991487	−	0.130204i	$-0.0415634\pi$
$398$	20.6603	−	5.53590i	1.03560	−	0.277490i
$399$		0			0
$400$	−35.7128			−1.78564
$401$	−8.42820	+	4.86603i	−0.420884	+	0.242998i	−0.695456	−	0.718569i	$-0.744797\pi$
$401$	−8.42820	+	4.86603i	−0.420884	+	0.242998i	0.274571	+	0.961567i	$0.411464\pi$
$402$		0			0
$403$	−11.8301	+	12.2942i	−0.589301	+	0.612419i
$404$	−11.5359	−	19.9808i	−0.573932	−	0.994080i
$405$		0			0
$406$	−10.3923	−	10.3923i	−0.515761	−	0.515761i
$407$	4.26795	−	7.39230i	0.211554	−	0.366423i
$408$		0			0
$409$	0.696152	+	0.401924i	0.0344225	+	0.0198739i	0.517113	−	0.855917i	$-0.327007\pi$
$409$	0.696152	+	0.401924i	0.0344225	+	0.0198739i	−0.482690	+	0.875791i	$0.660340\pi$
$410$	46.8827	+	12.5622i	2.31537	+	0.620402i
$411$		0			0
$412$			12.3923i			0.610525i
$413$	−1.60770	+	0.928203i	−0.0791095	+	0.0456739i
$414$		0			0
$415$	5.46410			0.268222
$416$	−0.392305	−	20.3923i	−0.0192343	−	0.999815i
$417$		0			0
$418$	−2.53590	−	2.53590i	−0.124035	−	0.124035i
$419$	−16.9019	+	9.75833i	−0.825713	+	0.476726i	−0.852383	−	0.522919i	$-0.824843\pi$
$419$	−16.9019	+	9.75833i	−0.825713	+	0.476726i	0.0266696	+	0.999644i	$0.491510\pi$
$420$		0			0
$421$	30.1244			1.46817			0.734086	−	0.679057i	$-0.237611\pi$
$421$	30.1244			1.46817			0.734086	+	0.679057i	$0.237611\pi$
$422$	39.0526	+	10.4641i	1.90105	+	0.509384i
$423$		0			0
$424$	7.85641	+	7.85641i	0.381541	+	0.381541i
$425$	−2.07180	+	3.58846i	−0.100497	+	0.174066i
$426$		0			0
$427$	1.73205	+	3.00000i	0.0838198	+	0.145180i
$428$	17.6603	+	30.5885i	0.853641	+	1.47855i
$429$		0			0
$430$	−3.46410	−	12.9282i	−0.167054	−	0.623453i
$431$	−15.4641	+	8.92820i	−0.744880	+	0.430056i	−0.823841	−	0.566821i	$-0.808173\pi$
$431$	−15.4641	+	8.92820i	−0.744880	+	0.430056i	0.0789612	+	0.996878i	$0.474840\pi$
$432$		0			0
$433$	−10.5000	+	18.1865i	−0.504598	+	0.873989i	0.495388	+	0.868672i	$0.335026\pi$
$433$	−10.5000	+	18.1865i	−0.504598	+	0.873989i	−0.999986	+	0.00531724i	$0.998307\pi$
$434$	22.3923	−	6.00000i	1.07487	−	0.288009i
$435$		0			0
$436$		−	12.0000i		−	0.574696i
$437$	−10.3923			−0.497131
$438$		0			0
$439$	−7.80385	−	13.5167i	−0.372457	−	0.645115i	0.617486	−	0.786582i	$-0.288151\pi$
$439$	−7.80385	−	13.5167i	−0.372457	−	0.645115i	−0.989943	+	0.141467i	$0.954818\pi$
$440$	−20.3923	−	5.46410i	−0.972165	−	0.260491i
$441$		0			0
$442$	−2.07180	−	1.14359i	−0.0985453	−	0.0543952i
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$	−24.1244	+	13.9282i	−1.14360	+	0.660260i
$446$	−34.8564	−	9.33975i	−1.65050	−	0.442250i
$447$		0			0
$448$	−13.8564	+	24.0000i	−0.654654	+	1.13389i
$449$	−18.4641	−	10.6603i	−0.871375	−	0.503088i	−0.00356996	−	0.999994i	$-0.501136\pi$
$449$	−18.4641	−	10.6603i	−0.871375	−	0.503088i	−0.867805	+	0.496905i	$0.834470\pi$
$450$		0			0
$451$	15.9282	+	9.19615i	0.750030	+	0.433030i
$452$	−5.19615	−	3.00000i	−0.244406	−	0.141108i
$453$		0			0
$454$	35.5885	−	9.53590i	1.67025	−	0.447542i
$455$	−12.9282	−	44.7846i	−0.606084	−	2.09953i
$456$		0			0
$457$	6.69615	−	3.86603i	0.313233	−	0.180845i	−0.335139	−	0.942169i	$-0.608783\pi$
$457$	6.69615	−	3.86603i	0.313233	−	0.180845i	0.648372	+	0.761324i	$0.275450\pi$
$458$	−12.9282	−	12.9282i	−0.604095	−	0.604095i
$459$		0			0
$460$	−52.9808	+	30.5885i	−2.47024	+	1.42619i
$461$	−14.3301	+	24.8205i	−0.667421	+	1.15601i	0.311202	+	0.950344i	$0.399268\pi$
$461$	−14.3301	+	24.8205i	−0.667421	+	1.15601i	−0.978623	+	0.205663i	$0.934065\pi$
$462$		0			0
$463$		−	16.3923i		−	0.761815i	−0.924613	−	0.380908i	$-0.875612\pi$
$463$		−	16.3923i		−	0.761815i	0.924613	−	0.380908i	$-0.124388\pi$
$464$	−10.3923	+	6.00000i	−0.482451	+	0.278543i
$465$		0			0
$466$		0			0
$467$			20.5359i			0.950288i	0.879908	+	0.475144i	$0.157604\pi$
$467$			20.5359i			0.950288i	−0.879908	+	0.475144i	$0.842396\pi$
$468$		0			0
$469$			25.1769i			1.16256i
$470$	25.1244	−	25.1244i	1.15890	−	1.15890i
$471$		0			0
$472$	0.392305	+	1.46410i	0.0180573	+	0.0673907i
$473$		−	5.07180i		−	0.233201i
$474$		0			0
$475$	−5.66025	+	9.80385i	−0.259710	+	0.449831i
$476$	1.60770	+	2.78461i	0.0736886	+	0.127632i
$477$		0			0
$478$	−18.3923	+	18.3923i	−0.841244	+	0.841244i
$479$	25.3468	−	14.6340i	1.15812	−	0.668643i	0.207271	−	0.978284i	$-0.433542\pi$
$479$	25.3468	−	14.6340i	1.15812	−	0.668643i	0.950854	+	0.309640i	$0.100209\pi$
$480$		0			0
$481$	3.69615	−	14.9378i	0.168530	−	0.681106i
$482$	4.09808	+	15.2942i	0.186662	+	0.696633i
$483$		0			0
$484$	12.1244	+	7.00000i	0.551107	+	0.318182i
$485$	−19.3923	−	11.1962i	−0.880559	−	0.508391i
$486$		0			0
$487$	20.1962	+	11.6603i	0.915175	+	0.528377i	0.882093	−	0.471076i	$-0.156134\pi$
$487$	20.1962	+	11.6603i	0.915175	+	0.528377i	0.0330824	+	0.999453i	$0.489468\pi$
$488$	2.73205	−	0.732051i	0.123674	−	0.0331384i
$489$		0			0
$490$	−6.83013	+	25.4904i	−0.308554	+	1.15154i
$491$	−6.58846	+	3.80385i	−0.297333	+	0.171665i	−0.641244	−	0.767337i	$-0.721581\pi$
$491$	−6.58846	+	3.80385i	−0.297333	+	0.171665i	0.343911	+	0.939002i	$0.388248\pi$
$492$		0			0
$493$			1.39230i			0.0627063i
$494$	−5.66025	−	3.12436i	−0.254667	−	0.140571i
$495$		0			0
$496$		−	18.9282i		−	0.849901i
$497$	16.0526	+	27.8038i	0.720056	+	1.24717i
$498$		0			0
$499$	−8.87564			−0.397328			−0.198664	−	0.980068i	$-0.563660\pi$
$499$	−8.87564			−0.397328			−0.198664	+	0.980068i	$0.563660\pi$
$500$			29.3205i			1.31125i
$501$		0			0
$502$	−3.00000	−	11.1962i	−0.133897	−	0.499709i
$503$	4.39230	−	7.60770i	0.195843	−	0.339210i	−0.751333	−	0.659923i	$-0.770589\pi$
$503$	4.39230	−	7.60770i	0.195843	−	0.339210i	0.947177	+	0.320712i	$0.103922\pi$
$504$		0			0
$505$	−37.2846	+	21.5263i	−1.65914	+	0.957907i
$506$	−22.3923	+	6.00000i	−0.995459	+	0.266733i
$507$		0			0
$508$	0.588457	−	0.339746i	0.0261086	−	0.0150738i
$509$	3.93782	+	6.82051i	0.174541	+	0.302314i	0.940002	−	0.341168i	$-0.110823\pi$
$509$	3.93782	+	6.82051i	0.174541	+	0.302314i	−0.765461	+	0.643482i	$0.777489\pi$
$510$		0			0
$511$	−3.00000	+	5.19615i	−0.132712	+	0.229864i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$	−8.36603	+	31.2224i	−0.369010	+	1.37716i
$515$	23.1244			1.01898
$516$		0			0
$517$	11.6603	−	6.73205i	0.512817	−	0.296075i
$518$	−14.7846	+	14.7846i	−0.649598	+	0.649598i
$519$		0			0
$520$	−38.0526	+	0.732051i	−1.66872	+	0.0321026i
$521$	−9.24871			−0.405193			−0.202597	−	0.979262i	$-0.564938\pi$
$521$	−9.24871			−0.405193			−0.202597	+	0.979262i	$0.564938\pi$
$522$		0			0
$523$	0.803848	−	0.464102i	0.0351498	−	0.0202937i	−0.482322	−	0.875994i	$-0.660207\pi$
$523$	0.803848	−	0.464102i	0.0351498	−	0.0202937i	0.517472	+	0.855700i	$0.326873\pi$
$524$	21.4641			0.937664
$525$		0			0
$526$	−6.00000	+	22.3923i	−0.261612	+	0.976351i
$527$	−1.90192	−	1.09808i	−0.0828491	−	0.0478330i
$528$		0			0
$529$	−22.0885	+	38.2583i	−0.960368	+	1.66341i
$530$	14.6603	−	14.6603i	0.636801	−	0.636801i
$531$		0			0
$532$	4.39230	+	7.60770i	0.190431	+	0.329835i
$533$	32.1865	+	7.96410i	1.39415	+	0.344964i
$534$		0			0
$535$	57.0788	−	32.9545i	2.46773	−	1.42475i
$536$	19.8564	+	5.32051i	0.857666	+	0.229811i
$537$		0			0
$538$	3.46410	+	12.9282i	0.149348	+	0.557374i
$539$	−5.00000	+	8.66025i	−0.215365	+	0.373024i
$540$		0			0
$541$	−35.4449			−1.52389			−0.761947	−	0.647640i	$-0.775756\pi$
$541$	−35.4449			−1.52389			−0.761947	+	0.647640i	$0.775756\pi$
$542$	−23.6603	−	6.33975i	−1.01629	−	0.272315i
$543$		0			0
$544$	2.53590	−	0.679492i	0.108726	−	0.0291330i
$545$	−22.3923			−0.959181
$546$		0			0
$547$			18.5885i			0.794785i	0.917649	+	0.397393i	$0.130085\pi$
$547$			18.5885i			0.794785i	−0.917649	+	0.397393i	$0.869915\pi$
$548$	−13.5885	+	23.5359i	−0.580470	+	1.00540i
$549$		0			0
$550$	−6.53590	+	24.3923i	−0.278692	+	1.04009i
$551$			3.80385i			0.162049i
$552$		0			0
$553$	31.1769	+	18.0000i	1.32578	+	0.765438i
$554$	−5.24167	−	19.5622i	−0.222697	−	0.831117i
$555$		0			0
$556$	9.46410	−	16.3923i	0.401367	−	0.695189i
$557$	−2.40192	−	4.16025i	−0.101773	−	0.176276i	0.810642	−	0.585542i	$-0.199118\pi$
$557$	−2.40192	−	4.16025i	−0.101773	−	0.176276i	−0.912415	+	0.409266i	$0.865785\pi$
$558$		0			0
$559$	−2.53590	−	8.78461i	−0.107257	−	0.371549i
$560$	44.7846	+	25.8564i	1.89250	+	1.09263i
$561$		0			0
$562$	10.6603	−	10.6603i	0.449676	−	0.449676i
$563$	13.9808	+	8.07180i	0.589219	+	0.340186i	0.764789	−	0.644281i	$-0.222843\pi$
$563$	13.9808	+	8.07180i	0.589219	+	0.340186i	−0.175570	+	0.984467i	$0.556177\pi$
$564$		0			0
$565$	−5.59808	+	9.69615i	−0.235513	+	0.407920i
$566$	−42.0526	−	11.2679i	−1.76760	−	0.473627i
$567$		0			0
$568$	25.3205	−	6.78461i	1.06242	−	0.284676i
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	−0.999994	−	0.00354413i	$-0.998872\pi$
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	0.496928	−	0.867792i	$-0.334461\pi$
$570$		0			0
$571$		−	2.39230i		−	0.100115i	−0.998746	−	0.0500574i	$-0.984060\pi$
$571$		−	2.39230i		−	0.100115i	0.998746	−	0.0500574i	$-0.0159404\pi$
$572$	−14.0000	−	3.46410i	−0.585369	−	0.144841i
$573$		0			0
$574$	−31.8564	−	31.8564i	−1.32966	−	1.32966i
$575$	36.5885	+	63.3731i	1.52584	+	2.64284i
$576$		0			0
$577$		−	34.2679i		−	1.42659i	−0.700862	−	0.713297i	$-0.747201\pi$
$577$		−	34.2679i		−	1.42659i	0.700862	−	0.713297i	$-0.252799\pi$
$578$	−6.14359	+	22.9282i	−0.255540	+	0.953688i
$579$		0			0
$580$	11.1962	+	19.3923i	0.464895	+	0.805222i
$581$	−4.39230	−	2.53590i	−0.182224	−	0.105207i
$582$		0			0
$583$	6.80385	−	3.92820i	0.281787	−	0.162690i
$584$	3.46410	+	3.46410i	0.143346	+	0.143346i
$585$		0			0
$586$	3.83013	−	1.02628i	0.158221	−	0.0423952i
$587$	−22.5885	−	39.1244i	−0.932325	−	1.61483i	−0.779335	−	0.626607i	$-0.784443\pi$
$587$	−22.5885	−	39.1244i	−0.932325	−	1.61483i	−0.152990	−	0.988228i	$-0.548890\pi$
$588$		0			0
$589$	−5.19615	−	3.00000i	−0.214104	−	0.123613i
$590$	2.73205	−	0.732051i	0.112477	−	0.0301381i
$591$		0			0
$592$	8.53590	+	14.7846i	0.350823	+	0.607644i
$593$		−	1.58846i		−	0.0652301i	−0.999468	−	0.0326151i	$-0.989616\pi$
$593$		−	1.58846i		−	0.0652301i	0.999468	−	0.0326151i	$-0.0103835\pi$
$594$		0			0
$595$	5.19615	−	3.00000i	0.213021	−	0.122988i
$596$	−20.3205	−	11.7321i	−0.832360	−	0.480564i
$597$		0			0
$598$	−35.7846	+	21.5885i	−1.46334	+	0.882818i
$599$	13.2679			0.542114			0.271057	−	0.962563i	$-0.412627\pi$
$599$	13.2679			0.542114			0.271057	+	0.962563i	$0.412627\pi$
$600$		0			0
$601$	−13.0359	−	22.5788i	−0.531745	−	0.921010i	−0.999313	−	0.0370529i	$-0.988203\pi$
$601$	−13.0359	−	22.5788i	−0.531745	−	0.921010i	0.467568	−	0.883957i	$-0.345130\pi$
$602$	−3.21539	+	12.0000i	−0.131050	+	0.489083i
$603$		0			0
$604$	−4.39230			−0.178720
$605$	13.0622	−	22.6244i	0.531053	−	0.919811i
$606$		0			0
$607$	−1.29423	+	2.24167i	−0.0525311	+	0.0909866i	−0.891095	−	0.453816i	$-0.850062\pi$
$607$	−1.29423	+	2.24167i	−0.0525311	+	0.0909866i	0.838564	+	0.544803i	$0.183396\pi$
$608$	6.92820	−	1.85641i	0.280976	−	0.0752872i
$609$		0			0
$610$	−1.36603	−	5.09808i	−0.0553088	−	0.206415i
$611$	16.8301	−	17.4904i	0.680874	−	0.707585i
$612$		0			0
$613$	−20.2583	−	35.0885i	−0.818226	−	1.41721i	−0.906988	−	0.421157i	$-0.861624\pi$
$613$	−20.2583	−	35.0885i	−0.818226	−	1.41721i	0.0887617	−	0.996053i	$-0.471709\pi$
$614$	−2.19615	−	2.19615i	−0.0886295	−	0.0886295i
$615$		0			0
$616$	13.8564	+	13.8564i	0.558291	+	0.558291i
$617$	−15.3564	−	8.86603i	−0.618226	−	0.356933i	0.157952	−	0.987447i	$-0.449511\pi$
$617$	−15.3564	−	8.86603i	−0.618226	−	0.356933i	−0.776178	+	0.630514i	$0.782844\pi$
$618$		0			0
$619$	24.2487			0.974638			0.487319	−	0.873224i	$-0.337975\pi$
$619$	24.2487			0.974638			0.487319	+	0.873224i	$0.337975\pi$
$620$	−35.3205			−1.41851
$621$		0			0
$622$	18.5885	+	18.5885i	0.745329	+	0.745329i
$623$	25.8564			1.03592
$624$		0			0
$625$	10.0718			0.402872
$626$	−2.53590	−	2.53590i	−0.101355	−	0.101355i
$627$		0			0
$628$	7.85641			0.313505
$629$	1.98076			0.0789782
$630$		0			0
$631$	−14.7846	−	8.53590i	−0.588566	−	0.339809i	0.175964	−	0.984397i	$-0.443696\pi$
$631$	−14.7846	−	8.53590i	−0.588566	−	0.339809i	−0.764530	+	0.644588i	$0.777029\pi$
$632$	20.7846	−	20.7846i	0.826767	−	0.826767i
$633$		0			0
$634$	25.1962	+	25.1962i	1.00067	+	1.00067i
$635$	−0.633975	−	1.09808i	−0.0251585	−	0.0435758i
$636$		0			0
$637$	−4.33013	+	17.5000i	−0.171566	+	0.693375i
$638$	2.19615	+	8.19615i	0.0869465	+	0.324489i
$639$		0			0
$640$	29.8564	−	29.8564i	1.18018	−	1.18018i
$641$	−7.03590	+	12.1865i	−0.277901	+	0.481339i	−0.970863	−	0.239635i	$-0.922972\pi$
$641$	−7.03590	+	12.1865i	−0.277901	+	0.481339i	0.692962	+	0.720974i	$0.256305\pi$
$642$		0			0
$643$	19.3923	−	33.5885i	0.764758	−	1.32460i	−0.175617	−	0.984459i	$-0.556192\pi$
$643$	19.3923	−	33.5885i	0.764758	−	1.32460i	0.940375	−	0.340141i	$-0.110475\pi$
$644$	56.7846			2.23763
$645$		0			0
$646$	0.215390	−	0.803848i	0.00847442	−	0.0316270i
$647$	14.8301	+	25.6865i	0.583032	+	1.00984i	0.995118	+	0.0986965i	$0.0314673\pi$
$647$	14.8301	+	25.6865i	0.583032	+	1.00984i	−0.412085	+	0.911145i	$0.635199\pi$
$648$		0			0
$649$	1.07180			0.0420717
$650$	0.875644	+	45.5167i	0.0343456	+	1.78531i
$651$		0			0
$652$	28.3923	+	16.3923i	1.11193	+	0.641972i
$653$	−31.1769	+	18.0000i	−1.22005	+	0.704394i	−0.964928	−	0.262515i	$-0.915448\pi$
$653$	−31.1769	+	18.0000i	−1.22005	+	0.704394i	−0.255119	+	0.966910i	$0.582115\pi$
$654$		0			0
$655$		−	40.0526i		−	1.56498i
$656$	−31.8564	+	18.3923i	−1.24378	+	0.718099i
$657$		0			0
$658$	−31.8564	+	8.53590i	−1.24189	+	0.332764i
$659$	26.7846	+	15.4641i	1.04338	+	0.602396i	0.920789	−	0.390061i	$-0.127546\pi$
$659$	26.7846	+	15.4641i	1.04338	+	0.602396i	0.122591	+	0.992457i	$0.460880\pi$
$660$		0			0
$661$	−6.06218	−	10.5000i	−0.235791	−	0.408403i	0.723711	−	0.690103i	$-0.242435\pi$
$661$	−6.06218	−	10.5000i	−0.235791	−	0.408403i	−0.959502	+	0.281701i	$0.909102\pi$
$662$	−16.3923	+	4.39230i	−0.637105	+	0.170712i
$663$		0			0
$664$	−2.92820	+	2.92820i	−0.113636	+	0.113636i
$665$	14.1962	−	8.19615i	0.550503	−	0.317833i
$666$		0			0
$667$	21.2942	+	12.2942i	0.824516	+	0.476034i
$668$	4.92820	+	8.53590i	0.190678	+	0.330264i
$669$		0			0
$670$	9.92820	−	37.0526i	0.383560	−	1.43147i
$671$		−	2.00000i		−	0.0772091i
$672$		0			0
$673$	5.50000	+	9.52628i	0.212009	+	0.367211i	0.952343	−	0.305028i	$-0.0986659\pi$
$673$	5.50000	+	9.52628i	0.212009	+	0.367211i	−0.740334	+	0.672239i	$0.765333\pi$
$674$	−33.2487	−	33.2487i	−1.28069	−	1.28069i
$675$		0			0
$676$	−25.9808	+	1.00000i	−0.999260	+	0.0384615i
$677$			7.85641i			0.301946i	0.988538	+	0.150973i	$0.0482407\pi$
$677$			7.85641i			0.301946i	−0.988538	+	0.150973i	$0.951759\pi$
$678$		0			0
$679$	10.3923	+	18.0000i	0.398820	+	0.690777i
$680$	−1.26795	−	4.73205i	−0.0486236	−	0.181466i
$681$		0			0
$682$	−12.9282	−	3.46410i	−0.495046	−	0.132647i
$683$	5.63397	−	9.75833i	0.215578	−	0.373392i	−0.737873	−	0.674939i	$-0.764170\pi$
$683$	5.63397	−	9.75833i	0.215578	−	0.373392i	0.953451	+	0.301547i	$0.0975031\pi$
$684$		0			0
$685$	43.9186	+	25.3564i	1.67804	+	0.968818i
$686$	−6.92820	+	6.92820i	−0.264520	+	0.264520i
$687$		0			0
$688$	8.78461	+	5.07180i	0.334910	+	0.193360i
$689$	9.82051	−	10.2058i	0.374132	−	0.388809i
$690$		0			0
$691$	−9.00000	−	15.5885i	−0.342376	−	0.593013i	0.642497	−	0.766288i	$-0.277898\pi$
$691$	−9.00000	−	15.5885i	−0.342376	−	0.593013i	−0.984873	+	0.173275i	$0.944565\pi$
$692$	18.9282	−	32.7846i	0.719542	−	1.24628i
$693$		0			0
$694$	−0.464102	−	1.73205i	−0.0176171	−	0.0657477i
$695$	−30.5885	−	17.6603i	−1.16029	−	0.669892i
$696$		0			0
$697$			4.26795i			0.161660i
$698$	1.94744	−	7.26795i	0.0737117	−	0.275096i
$699$		0			0
$700$	30.9282	−	53.5692i	1.16898	−	2.02473i
$701$		−	8.78461i		−	0.331790i	−0.986143	−	0.165895i	$-0.946949\pi$
$701$		−	8.78461i		−	0.331790i	0.986143	−	0.165895i	$-0.0530513\pi$
$702$		0			0
$703$	5.41154			0.204100
$704$	13.8564	−	8.00000i	0.522233	−	0.301511i
$705$		0			0
$706$	24.9545	+	6.68653i	0.939174	+	0.251651i
$707$	39.9615			1.50291
$708$		0			0
$709$	−20.5981	+	35.6769i	−0.773577	+	1.33987i	0.162014	+	0.986788i	$0.448201\pi$
$709$	−20.5981	+	35.6769i	−0.773577	+	1.33987i	−0.935591	+	0.353086i	$0.885132\pi$
$710$	−12.6603	−	47.2487i	−0.475131	−	1.77321i
$711$		0			0
$712$	5.46410	−	20.3923i	0.204776	−	0.764234i
$713$	−33.5885	+	19.3923i	−1.25790	+	0.726248i
$714$		0			0
$715$	−6.46410	+	26.1244i	−0.241744	+	0.976996i
$716$	13.8564	+	24.0000i	0.517838	+	0.896922i
$717$		0			0
$718$	−13.0718	+	13.0718i	−0.487835	+	0.487835i
$719$	−16.8564	+	29.1962i	−0.628638	+	1.08883i	0.359187	+	0.933265i	$0.383054\pi$
$719$	−16.8564	+	29.1962i	−0.628638	+	1.08883i	−0.987825	+	0.155567i	$0.950279\pi$
$720$		0			0
$721$	−18.5885	−	10.7321i	−0.692270	−	0.399682i
$722$	−6.36603	+	23.7583i	−0.236919	+	0.884193i
$723$		0			0
$724$	−36.9282			−1.37243
$725$	23.1962	−	13.3923i	0.861483	−	0.497378i
$726$		0			0
$727$	−13.6077			−0.504681			−0.252341	−	0.967638i	$-0.581200\pi$
$727$	−13.6077			−0.504681			−0.252341	+	0.967638i	$0.581200\pi$
$728$	30.9282	+	17.0718i	1.14628	+	0.632723i
$729$		0			0
$730$	6.46410	−	6.46410i	0.239247	−	0.239247i
$731$	1.01924	−	0.588457i	0.0376979	−	0.0217649i
$732$		0			0
$733$	−4.94744			−0.182738			−0.0913690	−	0.995817i	$-0.529124\pi$
$733$	−4.94744			−0.182738			−0.0913690	+	0.995817i	$0.529124\pi$
$734$	−10.3205	+	38.5167i	−0.380937	+	1.42168i
$735$		0			0
$736$	12.0000	−	44.7846i	0.442326	−	1.65078i
$737$	7.26795	−	12.5885i	0.267718	−	0.463702i
$738$		0			0
$739$	−9.46410	−	16.3923i	−0.348143	−	0.603001i	0.637777	−	0.770221i	$-0.279854\pi$
$739$	−9.46410	−	16.3923i	−0.348143	−	0.603001i	−0.985920	+	0.167220i	$0.946521\pi$
$740$	27.5885	−	15.9282i	1.01417	−	0.585532i
$741$		0			0
$742$	−18.5885	+	4.98076i	−0.682404	+	0.182850i
$743$	−4.73205	+	2.73205i	−0.173602	+	0.100229i	−0.584283	−	0.811550i	$-0.698624\pi$
$743$	−4.73205	+	2.73205i	−0.173602	+	0.100229i	0.410681	+	0.911779i	$0.365291\pi$
$744$		0			0
$745$	−21.8923	+	37.9186i	−0.802072	+	1.38923i
$746$	−9.43782	−	35.2224i	−0.345543	−	1.28958i
$747$		0			0
$748$		−	1.85641i		−	0.0678769i
$749$	−61.1769			−2.23536
$750$		0			0
$751$	18.1962	+	31.5167i	0.663987	+	1.15006i	0.979559	+	0.201158i	$0.0644703\pi$
$751$	18.1962	+	31.5167i	0.663987	+	1.15006i	−0.315572	+	0.948902i	$0.602196\pi$
$752$			26.9282i			0.981971i
$753$		0			0
$754$	7.90192	+	13.0981i	0.287771	+	0.477004i
$755$			8.19615i			0.298289i
$756$		0			0
$757$	18.3397	−	10.5885i	0.666569	−	0.384844i	−0.128206	−	0.991748i	$-0.540922\pi$
$757$	18.3397	−	10.5885i	0.666569	−	0.384844i	0.794776	+	0.606904i	$0.207589\pi$
$758$	−8.07180	+	30.1244i	−0.293181	+	1.09417i
$759$		0			0
$760$	−3.46410	−	12.9282i	−0.125656	−	0.468955i
$761$	10.8564	+	6.26795i	0.393544	+	0.227213i	0.683695	−	0.729768i	$-0.260372\pi$
$761$	10.8564	+	6.26795i	0.393544	+	0.227213i	−0.290150	+	0.956981i	$0.593705\pi$
$762$		0			0
$763$	18.0000	+	10.3923i	0.651644	+	0.376227i
$764$	6.58846	+	3.80385i	0.238362	+	0.137618i
$765$		0			0
$766$	−7.32051	−	27.3205i	−0.264501	−	0.987130i
$767$	1.85641	−	0.535898i	0.0670310	−	0.0193502i
$768$		0			0
$769$	19.3923	−	11.1962i	0.699304	−	0.403744i	−0.107784	−	0.994174i	$-0.534375\pi$
$769$	19.3923	−	11.1962i	0.699304	−	0.403744i	0.807088	+	0.590431i	$0.201042\pi$
$770$	25.8564	−	25.8564i	0.931800	−	0.931800i
$771$		0			0
$772$	13.0526	+	22.6077i	0.469772	+	0.813669i
$773$	26.2487	−	45.4641i	0.944101	−	1.63523i	0.186558	−	0.982444i	$-0.440267\pi$
$773$	26.2487	−	45.4641i	0.944101	−	1.63523i	0.757542	−	0.652786i	$-0.226400\pi$
$774$		0			0
$775$			42.2487i			1.51762i
$776$	16.3923	−	4.39230i	0.588449	−	0.157675i
$777$		0			0
$778$	−18.7128	+	18.7128i	−0.670887	+	0.670887i
$779$			11.6603i			0.417772i
$780$		0			0
$781$		−	18.5359i		−	0.663267i
$782$	−3.80385	−	3.80385i	−0.136025	−	0.136025i
$783$		0			0
$784$	−10.0000	−	17.3205i	−0.357143	−	0.618590i
$785$		−	14.6603i		−	0.523247i
$786$		0			0
$787$	20.3660	−	35.2750i	0.725970	−	1.25742i	−0.232603	−	0.972572i	$-0.574724\pi$
$787$	20.3660	−	35.2750i	0.725970	−	1.25742i	0.958573	−	0.284846i	$-0.0919424\pi$
$788$	21.7128	−	12.5359i	0.773487	−	0.446573i
$789$		0			0
$790$	−38.7846	−	38.7846i	−1.37989	−	1.37989i
$791$	9.00000	−	5.19615i	0.320003	−	0.184754i
$792$		0			0
$793$	−1.00000	−	3.46410i	−0.0355110	−	0.123014i
$794$	33.1244	−	8.87564i	1.17554	−	0.314985i
$795$		0			0
$796$	26.1962	+	15.1244i	0.928498	+	0.536069i
$797$	15.8038	+	9.12436i	0.559801	+	0.323201i	0.753066	−	0.657945i	$-0.228574\pi$
$797$	15.8038	+	9.12436i	0.559801	+	0.323201i	−0.193265	+	0.981147i	$0.561908\pi$
$798$		0			0
$799$	2.70577	+	1.56218i	0.0957233	+	0.0552659i
$800$	−35.7128	−	35.7128i	−1.26264	−	1.26264i
$801$		0			0
$802$	−13.2942	−	3.56218i	−0.469436	−	0.125785i
$803$	3.00000	−	1.73205i	0.105868	−	0.0611227i
$804$		0			0
$805$		−	105.962i		−	3.73465i
$806$	−24.1244	+	0.464102i	−0.849744	+	0.0163473i
$807$		0			0
$808$	8.44486	−	31.5167i	0.297089	−	1.10875i
$809$	3.35641	+	5.81347i	0.118005	+	0.204391i	0.918977	−	0.394311i	$-0.129017\pi$
$809$	3.35641	+	5.81347i	0.118005	+	0.204391i	−0.800972	+	0.598702i	$0.795683\pi$
$810$		0			0
$811$	−32.4449			−1.13929			−0.569647	−	0.821890i	$-0.692920\pi$
$811$	−32.4449			−1.13929			−0.569647	+	0.821890i	$0.692920\pi$
$812$		−	20.7846i		−	0.729397i
$813$		0			0
$814$	11.6603	−	3.12436i	0.408692	−	0.109509i
$815$	30.5885	−	52.9808i	1.07147	−	1.85584i
$816$		0			0
$817$	2.78461	−	1.60770i	0.0974212	−	0.0562461i
$818$	0.294229	+	1.09808i	0.0102875	+	0.0383933i
$819$		0			0
$820$	34.3205	+	59.4449i	1.19852	+	2.07590i
$821$	−17.0000	−	29.4449i	−0.593304	−	1.02763i	−0.993784	−	0.111327i	$-0.964490\pi$
$821$	−17.0000	−	29.4449i	−0.593304	−	1.02763i	0.400480	−	0.916306i	$-0.368843\pi$
$822$		0			0
$823$	−15.7846	+	27.3397i	−0.550217	+	0.953004i	0.448042	+	0.894013i	$0.352122\pi$
$823$	−15.7846	+	27.3397i	−0.550217	+	0.953004i	−0.998259	+	0.0589909i	$0.981212\pi$
$824$	−12.3923	+	12.3923i	−0.431706	+	0.431706i
$825$		0			0
$826$	−2.53590	−	0.679492i	−0.0882352	−	0.0236425i
$827$	−27.5692			−0.958676			−0.479338	−	0.877630i	$-0.659123\pi$
$827$	−27.5692			−0.958676			−0.479338	+	0.877630i	$0.659123\pi$
$828$		0			0
$829$	−16.4545	+	9.50000i	−0.571488	+	0.329949i	−0.757743	−	0.652553i	$-0.773698\pi$
$829$	−16.4545	+	9.50000i	−0.571488	+	0.329949i	0.186256	+	0.982501i	$0.440365\pi$
$830$	5.46410	+	5.46410i	0.189662	+	0.189662i
$831$		0			0
$832$	20.0000	−	20.7846i	0.693375	−	0.720577i
$833$	−2.32051			−0.0804008
$834$		0			0
$835$	15.9282	−	9.19615i	0.551218	−	0.318246i
$836$		−	5.07180i		−	0.175412i
$837$		0			0
$838$	−26.6603	−	7.14359i	−0.920963	−	0.246771i
$839$	29.8301	+	17.2224i	1.02985	+	0.594584i	0.916942	−	0.399021i	$-0.130650\pi$
$839$	29.8301	+	17.2224i	1.02985	+	0.594584i	0.112909	+	0.993605i	$0.463983\pi$
$840$		0			0
$841$	−10.0000	+	17.3205i	−0.344828	+	0.597259i
$842$	30.1244	+	30.1244i	1.03815	+	1.03815i
$843$		0			0
$844$	28.5885	+	49.5167i	0.984055	+	1.70443i
$845$	1.86603	+	48.4808i	0.0641932	+	1.66779i
$846$		0			0
$847$	−21.0000	+	12.1244i	−0.721569	+	0.416598i
$848$			15.7128i			0.539580i
$849$		0			0
$850$	−5.66025	+	1.51666i	−0.194145	+	0.0520210i
$851$	17.4904	−	30.2942i	0.599563	−	1.03847i
$852$		0			0
$853$	23.1962			0.794221			0.397111	−	0.917771i	$-0.370013\pi$
$853$	23.1962			0.794221			0.397111	+	0.917771i	$0.370013\pi$
$854$	−1.26795	+	4.73205i	−0.0433883	+	0.161927i
$855$		0			0
$856$	−12.9282	+	48.2487i	−0.441877	+	1.64911i
$857$	9.67949			0.330645			0.165323	−	0.986240i	$-0.447133\pi$
$857$	9.67949			0.330645			0.165323	+	0.986240i	$0.447133\pi$
$858$		0			0
$859$			19.8038i			0.675699i	0.941200	+	0.337849i	$0.109699\pi$
$859$			19.8038i			0.675699i	−0.941200	+	0.337849i	$0.890301\pi$
$860$	9.46410	−	16.3923i	0.322723	−	0.558973i
$861$		0			0
$862$	−24.3923	−	6.53590i	−0.830805	−	0.222614i
$863$			9.32051i			0.317274i	0.987337	+	0.158637i	$0.0507099\pi$
$863$			9.32051i			0.317274i	−0.987337	+	0.158637i	$0.949290\pi$
$864$		0			0
$865$	−61.1769	−	35.3205i	−2.08008	−	1.20093i
$866$	−28.6865	+	7.68653i	−0.974808	+	0.261199i
$867$		0			0
$868$	28.3923	+	16.3923i	0.963698	+	0.556391i
$869$	−10.3923	−	18.0000i	−0.352535	−	0.610608i
$870$		0			0
$871$	6.29423	−	25.4378i	0.213272	−	0.861928i
$872$	12.0000	−	12.0000i	0.406371	−	0.406371i
$873$		0			0
$874$	−10.3923	−	10.3923i	−0.351525	−	0.351525i
$875$	−43.9808	−	25.3923i	−1.48682	−	0.858417i
$876$		0			0
$877$	−2.59808	+	4.50000i	−0.0877308	+	0.151954i	−0.906552	−	0.422095i	$-0.861295\pi$
$877$	−2.59808	+	4.50000i	−0.0877308	+	0.151954i	0.818821	+	0.574049i	$0.194628\pi$
$878$	5.71281	−	21.3205i	0.192798	−	0.719532i
$879$		0			0
$880$	−14.9282	−	25.8564i	−0.503230	−	0.871619i
$881$	14.3038	+	24.7750i	0.481909	+	0.834691i	0.999784	−	0.0207653i	$-0.00661029\pi$
$881$	14.3038	+	24.7750i	0.481909	+	0.834691i	−0.517876	+	0.855456i	$0.673277\pi$
$882$		0			0
$883$			42.1962i			1.42001i	0.704195	+	0.710007i	$0.251308\pi$
$883$			42.1962i			1.42001i	−0.704195	+	0.710007i	$0.748692\pi$
$884$	−0.928203	−	3.21539i	−0.0312189	−	0.108145i
$885$		0			0
$886$		0			0
$887$	−17.1962	−	29.7846i	−0.577390	−	1.00007i	−0.995777	−	0.0918005i	$-0.970738\pi$
$887$	−17.1962	−	29.7846i	−0.577390	−	1.00007i	0.418387	−	0.908269i	$-0.362596\pi$
$888$		0			0
$889$			1.17691i			0.0394724i
$890$	−38.0526	−	10.1962i	−1.27552	−	0.341776i
$891$		0			0
$892$	−25.5167	−	44.1962i	−0.854361	−	1.47980i
$893$	7.39230	+	4.26795i	0.247374	+	0.142821i
$894$		0			0
$895$	44.7846	−	25.8564i	1.49698	−	0.864284i
$896$	−37.8564	+	10.1436i	−1.26469	+	0.338874i
$897$		0			0
$898$	−7.80385	−	29.1244i	−0.260418	−	0.971892i
$899$	7.09808	+	12.2942i	0.236734	+	0.410035i
$900$		0			0
$901$	1.57884	+	0.911543i	0.0525987	+	0.0303679i
$902$	6.73205	+	25.1244i	0.224153	+	0.836550i
$903$		0			0
$904$	−2.19615	−	8.19615i	−0.0730429	−	0.272600i
$905$			68.9090i			2.29061i
$906$		0			0
$907$	4.48334	−	2.58846i	0.148867	−	0.0859483i	−0.423716	−	0.905795i	$-0.639275\pi$
$907$	4.48334	−	2.58846i	0.148867	−	0.0859483i	0.572583	+	0.819847i	$0.305941\pi$
$908$	45.1244	+	26.0526i	1.49750	+	0.864585i
$909$		0			0
$910$	31.8564	−	57.7128i	1.05603	−	1.91316i
$911$	−42.4974			−1.40800			−0.704001	−	0.710199i	$-0.748605\pi$
$911$	−42.4974			−1.40800			−0.704001	+	0.710199i	$0.748605\pi$
$912$		0			0
$913$	1.46410	+	2.53590i	0.0484547	+	0.0839260i
$914$	10.5622	+	2.83013i	0.349366	+	0.0936123i
$915$		0			0
$916$		−	25.8564i		−	0.854320i
$917$	−18.5885	+	32.1962i	−0.613845	+	1.06321i
$918$		0			0
$919$	12.7583	−	22.0981i	0.420858	−	0.728948i	−0.575165	−	0.818037i	$-0.695062\pi$
$919$	12.7583	−	22.0981i	0.420858	−	0.728948i	0.996024	+	0.0890890i	$0.0283956\pi$
$920$	−83.5692	−	22.3923i	−2.75520	−	0.738252i
$921$		0			0
$922$	−39.1506	+	10.4904i	−1.28936	+	0.345482i
$923$	−9.26795	−	32.1051i	−0.305058	−	1.05675i
$924$		0			0
$925$	−19.0526	−	33.0000i	−0.626444	−	1.08503i
$926$	16.3923	−	16.3923i	0.538685	−	0.538685i
$927$		0			0
$928$	−16.3923	−	4.39230i	−0.538104	−	0.144184i
$929$	−23.2128	−	13.4019i	−0.761588	−	0.439703i	0.0682778	−	0.997666i	$-0.478250\pi$
$929$	−23.2128	−	13.4019i	−0.761588	−	0.439703i	−0.829865	+	0.557963i	$0.811583\pi$
$930$		0			0
$931$	−6.33975			−0.207777
$932$		0			0
$933$		0			0
$934$	−20.5359	+	20.5359i	−0.671955	+	0.671955i
$935$	−3.46410			−0.113288
$936$		0			0
$937$	−43.6410			−1.42569			−0.712845	−	0.701322i	$-0.752594\pi$
$937$	−43.6410			−1.42569			−0.712845	+	0.701322i	$0.752594\pi$
$938$	−25.1769	+	25.1769i	−0.822055	+	0.822055i
$939$		0			0
$940$	50.2487			1.63893
$941$	7.21539			0.235215			0.117608	−	0.993060i	$-0.462478\pi$
$941$	7.21539			0.235215			0.117608	+	0.993060i	$0.462478\pi$
$942$		0			0
$943$	65.2750	+	37.6865i	2.12565	+	1.22724i
$944$	−1.07180	+	1.85641i	−0.0348840	+	0.0604209i
$945$		0			0
$946$	5.07180	−	5.07180i	0.164898	−	0.164898i
$947$	24.3468	+	42.1699i	0.791164	+	1.37034i	0.925246	+	0.379367i	$0.123858\pi$
$947$	24.3468	+	42.1699i	0.791164	+	1.37034i	−0.134082	+	0.990970i	$0.542809\pi$
$948$		0			0
$949$	4.33013	−	4.50000i	0.140562	−	0.146076i
$950$	−15.4641	+	4.14359i	−0.501722	+	0.134436i
$951$		0			0
$952$	−1.17691	+	4.39230i	−0.0381440	+	0.142355i
$953$	12.4641	−	21.5885i	0.403752	−	0.699319i	−0.590423	−	0.807094i	$-0.701039\pi$
$953$	12.4641	−	21.5885i	0.403752	−	0.699319i	0.994175	+	0.107775i	$0.0343726\pi$
$954$		0			0
$955$	7.09808	−	12.2942i	0.229688	−	0.397832i
$956$	−36.7846			−1.18970
$957$		0			0
$958$	39.9808	+	10.7128i	1.29172	+	0.346115i
$959$	−23.5359	−	40.7654i	−0.760014	−	1.31638i
$960$		0			0
$961$	8.60770			0.277668
$962$	18.6340	−	11.2417i	0.600783	−	0.362446i
$963$		0			0
$964$	−11.1962	+	19.3923i	−0.360604	+	0.624584i
$965$	42.1865	−	24.3564i	1.35803	−	0.784060i
$966$		0			0
$967$		−	8.87564i		−	0.285421i	−0.989764	−	0.142711i	$-0.954418\pi$
$967$		−	8.87564i		−	0.285421i	0.989764	−	0.142711i	$-0.0455819\pi$
$968$	5.12436	+	19.1244i	0.164703	+	0.614680i
$969$		0			0
$970$	−8.19615	−	30.5885i	−0.263163	−	0.982136i
$971$	5.70577	+	3.29423i	0.183107	+	0.105717i	0.588752	−	0.808314i	$-0.299620\pi$
$971$	5.70577	+	3.29423i	0.183107	+	0.105717i	−0.405645	+	0.914031i	$0.632953\pi$
$972$		0			0
$973$	16.3923	+	28.3923i	0.525513	+	0.910216i
$974$	8.53590	+	31.8564i	0.273508	+	1.02075i
$975$		0			0
$976$	3.46410	+	2.00000i	0.110883	+	0.0640184i
$977$	−28.1603	+	16.2583i	−0.900926	+	0.520150i	−0.877501	−	0.479576i	$-0.840791\pi$
$977$	−28.1603	+	16.2583i	−0.900926	+	0.520150i	−0.0234257	+	0.999726i	$0.507457\pi$
$978$		0			0
$979$	−12.9282	−	7.46410i	−0.413187	−	0.238554i
$980$	−32.3205	+	18.6603i	−1.03244	+	0.596080i
$981$		0			0
$982$	−10.3923	−	2.78461i	−0.331632	−	0.0888605i
$983$			59.7654i			1.90622i	0.302625	+	0.953110i	$0.402137\pi$
$983$			59.7654i			1.90622i	−0.302625	+	0.953110i	$0.597863\pi$
$984$		0			0
$985$	−23.3923	−	40.5167i	−0.745341	−	1.29097i
$986$	−1.39230	+	1.39230i	−0.0443400	+	0.0443400i
$987$		0			0
$988$	−2.53590	−	8.78461i	−0.0806777	−	0.279476i
$989$		−	20.7846i		−	0.660912i
$990$		0			0
$991$	−11.2942	−	19.5622i	−0.358773	−	0.621413i	0.628983	−	0.777419i	$-0.283471\pi$
$991$	−11.2942	−	19.5622i	−0.358773	−	0.621413i	−0.987756	+	0.156006i	$0.950138\pi$
$992$	18.9282	−	18.9282i	0.600971	−	0.600971i
$993$		0			0
$994$	−11.7513	+	43.8564i	−0.372728	+	1.39104i
$995$	28.2224	−	48.8827i	0.894711	−	1.54969i
$996$		0			0
$997$	45.9904	+	26.5526i	1.45653	+	0.840928i	0.998839	−	0.0481831i	$-0.0153431\pi$
$997$	45.9904	+	26.5526i	1.45653	+	0.840928i	0.457691	+	0.889111i	$0.348676\pi$
$998$	−8.87564	−	8.87564i	−0.280954	−	0.280954i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.b.829.2		4
3.2	odd	2		104.2.s.a.101.1	yes	4
8.5	even	2		936.2.dg.a.829.1		4
12.11	even	2		416.2.ba.b.49.1		4
13.4	even	6		936.2.dg.a.901.1		4
24.5	odd	2		104.2.s.b.101.2	yes	4
24.11	even	2		416.2.ba.a.49.2		4
39.17	odd	6		104.2.s.b.69.2	yes	4
104.69	even	6	inner	936.2.dg.b.901.1		4
156.95	even	6		416.2.ba.a.17.2		4
312.173	odd	6		104.2.s.a.69.2	✓	4
312.251	even	6		416.2.ba.b.17.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.s.a.69.2	✓	4	312.173	odd	6
104.2.s.a.101.1	yes	4	3.2	odd	2
104.2.s.b.69.2	yes	4	39.17	odd	6
104.2.s.b.101.2	yes	4	24.5	odd	2
416.2.ba.a.17.2		4	156.95	even	6
416.2.ba.a.49.2		4	24.11	even	2
416.2.ba.b.17.1		4	312.251	even	6
416.2.ba.b.49.1		4	12.11	even	2
936.2.dg.a.829.1		4	8.5	even	2
936.2.dg.a.901.1		4	13.4	even	6
936.2.dg.b.829.2		4	1.1	even	1	trivial
936.2.dg.b.901.1		4	104.69	even	6	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +3.73205 q^{5} +(-3.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(3.73205 + 3.73205i) q^{10} +(1.00000 + 1.73205i) q^{11} +(2.59808 + 2.50000i) q^{13} +(-1.26795 - 4.73205i) q^{14} -4.00000 q^{16} +(-0.232051 + 0.401924i) q^{17} +(-0.633975 + 1.09808i) q^{19} +7.46410i q^{20} +(-0.732051 + 2.73205i) q^{22} +(4.09808 + 7.09808i) q^{23} +8.92820 q^{25} +(0.0980762 + 5.09808i) q^{26} +(3.46410 - 6.00000i) q^{28} +(2.59808 - 1.50000i) q^{29} +4.73205i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.633975 + 0.169873i) q^{34} +(-11.1962 - 6.46410i) q^{35} +(-2.13397 - 3.69615i) q^{37} +(-1.73205 + 0.464102i) q^{38} +(-7.46410 + 7.46410i) q^{40} +(7.96410 - 4.59808i) q^{41} +(-2.19615 - 1.26795i) q^{43} +(-3.46410 + 2.00000i) q^{44} +(-3.00000 + 11.1962i) q^{46} -6.73205i q^{47} +(2.50000 + 4.33013i) q^{49} +(8.92820 + 8.92820i) q^{50} +(-5.00000 + 5.19615i) q^{52} -3.92820i q^{53} +(3.73205 + 6.46410i) q^{55} +(9.46410 - 2.53590i) q^{56} +(4.09808 + 1.09808i) q^{58} +(0.267949 - 0.464102i) q^{59} +(-0.866025 - 0.500000i) q^{61} +(-4.73205 + 4.73205i) q^{62} -8.00000i q^{64} +(9.69615 + 9.33013i) q^{65} +(-3.63397 - 6.29423i) q^{67} +(-0.803848 - 0.464102i) q^{68} +(-4.73205 - 17.6603i) q^{70} +(-8.02628 - 4.63397i) q^{71} -1.73205i q^{73} +(1.56218 - 5.83013i) q^{74} +(-2.19615 - 1.26795i) q^{76} -6.92820i q^{77} -10.3923 q^{79} -14.9282 q^{80} +(12.5622 + 3.36603i) q^{82} +1.46410 q^{83} +(-0.866025 + 1.50000i) q^{85} +(-0.928203 - 3.46410i) q^{86} +(-5.46410 - 1.46410i) q^{88} +(-6.46410 + 3.73205i) q^{89} +(-3.46410 - 12.0000i) q^{91} +(-14.1962 + 8.19615i) q^{92} +(6.73205 - 6.73205i) q^{94} +(-2.36603 + 4.09808i) q^{95} +(-5.19615 - 3.00000i) q^{97} +(-1.83013 + 6.83013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 8 q^{5} - 12 q^{7} - 8 q^{8} + 8 q^{10} + 4 q^{11} - 12 q^{14} - 16 q^{16} + 6 q^{17} - 6 q^{19} + 4 q^{22} + 6 q^{23} + 8 q^{25} - 10 q^{26} - 16 q^{32} - 6 q^{34} - 24 q^{35} - 12 q^{37}+ \cdots + 10 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 8 * q^5 - 12 * q^7 - 8 * q^8 + 8 * q^10 + 4 * q^11 - 12 * q^14 - 16 * q^16 + 6 * q^17 - 6 * q^19 + 4 * q^22 + 6 * q^23 + 8 * q^25 - 10 * q^26 - 16 * q^32 - 6 * q^34 - 24 * q^35 - 12 * q^37 - 16 * q^40 + 18 * q^41 + 12 * q^43 - 12 * q^46 + 10 * q^49 + 8 * q^50 - 20 * q^52 + 8 * q^55 + 24 * q^56 + 6 * q^58 + 8 * q^59 - 12 * q^62 + 18 * q^65 - 18 * q^67 - 24 * q^68 - 12 * q^70 + 6 * q^71 - 18 * q^74 + 12 * q^76 - 32 * q^80 + 26 * q^82 - 8 * q^83 + 24 * q^86 - 8 * q^88 - 12 * q^89 - 36 * q^92 + 20 * q^94 - 6 * q^95 + 10 * q^98

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