LMFDB - Embedded newform 260.2.bf.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(37,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 7]))

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

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

chi := DirichletCharacter("260.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bf (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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.37
Dual form			260.2.bf.b.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86603 + 0.500000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(2.23205 - 3.86603i) q^{7} +(0.633975 + 0.366025i) q^{9} +O(q^{10})$	\(q+(1.86603 + 0.500000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(2.23205 - 3.86603i) q^{7} +(0.633975 + 0.366025i) q^{9} +(-2.86603 - 0.767949i) q^{11} +(3.00000 + 2.00000i) q^{13} +(-0.866025 - 4.23205i) q^{15} +(0.866025 + 3.23205i) q^{17} +(1.13397 + 4.23205i) q^{19} +(6.09808 - 6.09808i) q^{21} +(-1.86603 + 6.96410i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(-3.09808 - 3.09808i) q^{27} +(1.50000 - 0.866025i) q^{29} +(5.19615 + 5.19615i) q^{31} +(-4.96410 - 2.86603i) q^{33} +(-9.96410 - 0.598076i) q^{35} +(-4.23205 - 7.33013i) q^{37} +(4.59808 + 5.23205i) q^{39} +(0.669873 - 2.50000i) q^{41} +(3.59808 - 0.964102i) q^{43} +(0.0980762 - 1.63397i) q^{45} +2.92820 q^{47} +(-6.46410 - 11.1962i) q^{49} +6.46410i q^{51} +(-4.46410 + 4.46410i) q^{53} +(1.33013 + 6.50000i) q^{55} +8.46410i q^{57} +(6.33013 - 1.69615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(2.83013 - 1.63397i) q^{63} +(1.00000 - 8.00000i) q^{65} +(-13.6244 + 7.86603i) q^{67} +(-6.96410 + 12.0622i) q^{69} +(-4.59808 + 1.23205i) q^{71} +1.07180i q^{73} +(-7.59808 + 5.96410i) q^{75} +(-9.36603 + 9.36603i) q^{77} +7.46410i q^{79} +(-5.33013 - 9.23205i) q^{81} -10.9282 q^{83} +(5.59808 - 4.96410i) q^{85} +(3.23205 - 0.866025i) q^{87} +(-0.794229 + 2.96410i) q^{89} +(14.4282 - 7.13397i) q^{91} +(7.09808 + 12.2942i) q^{93} +(7.33013 - 6.50000i) q^{95} +(3.69615 + 2.13397i) q^{97} +(-1.53590 - 1.53590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 + 6 * q^9	$ 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9} - 8 q^{11} + 12 q^{13} + 8 q^{19} + 14 q^{21} - 4 q^{23} - 12 q^{25} - 2 q^{27} + 6 q^{29} - 6 q^{33} - 26 q^{35} - 10 q^{37} + 8 q^{39} + 20 q^{41} + 4 q^{43} - 10 q^{45} - 16 q^{47} - 12 q^{49} - 4 q^{53} - 12 q^{55} + 8 q^{59} + 18 q^{61} - 6 q^{63} + 4 q^{65} - 6 q^{67} - 14 q^{69} - 8 q^{71} - 20 q^{75} - 34 q^{77} - 4 q^{81} - 16 q^{83} + 12 q^{85} + 6 q^{87} + 28 q^{89} + 30 q^{91} + 18 q^{93} + 12 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 + 6 * q^9 - 8 * q^11 + 12 * q^13 + 8 * q^19 + 14 * q^21 - 4 * q^23 - 12 * q^25 - 2 * q^27 + 6 * q^29 - 6 * q^33 - 26 * q^35 - 10 * q^37 + 8 * q^39 + 20 * q^41 + 4 * q^43 - 10 * q^45 - 16 * q^47 - 12 * q^49 - 4 * q^53 - 12 * q^55 + 8 * q^59 + 18 * q^61 - 6 * q^63 + 4 * q^65 - 6 * q^67 - 14 * q^69 - 8 * q^71 - 20 * q^75 - 34 * q^77 - 4 * q^81 - 16 * q^83 + 12 * q^85 + 6 * q^87 + 28 * q^89 + 30 * q^91 + 18 * q^93 + 12 * q^95 - 6 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	1.86603	+	0.500000i	1.07735	+	0.288675i	0.753510	−	0.657437i	$-0.228359\pi$
$3$	1.86603	+	0.500000i	1.07735	+	0.288675i	0.323840	+	0.946112i	$0.395026\pi$
$4$		0			0
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$		0			0
$7$	2.23205	−	3.86603i	0.843636	−	1.46122i	−0.0431647	−	0.999068i	$-0.513744\pi$
$7$	2.23205	−	3.86603i	0.843636	−	1.46122i	0.886801	−	0.462152i	$-0.152923\pi$
$8$		0			0
$9$	0.633975	+	0.366025i	0.211325	+	0.122008i
$10$		0			0
$11$	−2.86603	−	0.767949i	−0.864139	−	0.231545i	−0.200587	−	0.979676i	$-0.564285\pi$
$11$	−2.86603	−	0.767949i	−0.864139	−	0.231545i	−0.663552	+	0.748130i	$0.730952\pi$
$12$		0			0
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$14$		0			0
$15$	−0.866025	−	4.23205i	−0.223607	−	1.09271i
$16$		0			0
$17$	0.866025	+	3.23205i	0.210042	+	0.783887i	0.987853	+	0.155390i	$0.0496633\pi$
$17$	0.866025	+	3.23205i	0.210042	+	0.783887i	−0.777811	+	0.628498i	$0.783670\pi$
$18$		0			0
$19$	1.13397	+	4.23205i	0.260152	+	0.970899i	0.965152	+	0.261692i	$0.0842803\pi$
$19$	1.13397	+	4.23205i	0.260152	+	0.970899i	−0.705000	+	0.709207i	$0.749053\pi$
$20$		0			0
$21$	6.09808	−	6.09808i	1.33071	−	1.33071i
$22$		0			0
$23$	−1.86603	+	6.96410i	−0.389093	+	1.45212i	0.442519	+	0.896759i	$0.354085\pi$
$23$	−1.86603	+	6.96410i	−0.389093	+	1.45212i	−0.831612	+	0.555357i	$0.812582\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$		0			0
$27$	−3.09808	−	3.09808i	−0.596225	−	0.596225i
$28$		0			0
$29$	1.50000	−	0.866025i	0.278543	−	0.160817i	−0.354221	−	0.935162i	$-0.615254\pi$
$29$	1.50000	−	0.866025i	0.278543	−	0.160817i	0.632764	+	0.774345i	$0.281920\pi$
$30$		0			0
$31$	5.19615	+	5.19615i	0.933257	+	0.933257i	0.997908	−	0.0646514i	$-0.0205935\pi$
$31$	5.19615	+	5.19615i	0.933257	+	0.933257i	−0.0646514	+	0.997908i	$0.520594\pi$
$32$		0			0
$33$	−4.96410	−	2.86603i	−0.864139	−	0.498911i
$34$		0			0
$35$	−9.96410	−	0.598076i	−1.68424	−	0.101093i
$36$		0			0
$37$	−4.23205	−	7.33013i	−0.695745	−	1.20507i	−0.969929	−	0.243388i	$-0.921741\pi$
$37$	−4.23205	−	7.33013i	−0.695745	−	1.20507i	0.274184	−	0.961677i	$-0.411592\pi$
$38$		0			0
$39$	4.59808	+	5.23205i	0.736281	+	0.837799i
$40$		0			0
$41$	0.669873	−	2.50000i	0.104617	−	0.390434i	−0.893685	−	0.448695i	$-0.851889\pi$
$41$	0.669873	−	2.50000i	0.104617	−	0.390434i	0.998301	+	0.0582609i	$0.0185555\pi$
$42$		0			0
$43$	3.59808	−	0.964102i	0.548701	−	0.147024i	0.0261910	−	0.999657i	$-0.491662\pi$
$43$	3.59808	−	0.964102i	0.548701	−	0.147024i	0.522511	+	0.852633i	$0.324996\pi$
$44$		0			0
$45$	0.0980762	−	1.63397i	0.0146203	−	0.243579i
$46$		0			0
$47$	2.92820			0.427122			0.213561	−	0.976930i	$-0.431494\pi$
$47$	2.92820			0.427122			0.213561	+	0.976930i	$0.431494\pi$
$48$		0			0
$49$	−6.46410	−	11.1962i	−0.923443	−	1.59945i
$50$		0			0
$51$			6.46410i			0.905155i
$52$		0			0
$53$	−4.46410	+	4.46410i	−0.613192	+	0.613192i	−0.943776	−	0.330585i	$-0.892754\pi$
$53$	−4.46410	+	4.46410i	−0.613192	+	0.613192i	0.330585	+	0.943776i	$0.392754\pi$
$54$		0			0
$55$	1.33013	+	6.50000i	0.179354	+	0.876460i
$56$		0			0
$57$			8.46410i			1.12110i
$58$		0			0
$59$	6.33013	−	1.69615i	0.824112	−	0.220820i	0.177969	−	0.984036i	$-0.443047\pi$
$59$	6.33013	−	1.69615i	0.824112	−	0.220820i	0.646144	+	0.763216i	$0.276381\pi$
$60$		0			0
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	−0.419748	−	0.907641i	$-0.637882\pi$
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	0.995914	−	0.0903080i	$-0.0287851\pi$
$62$		0			0
$63$	2.83013	−	1.63397i	0.356562	−	0.205861i
$64$		0			0
$65$	1.00000	−	8.00000i	0.124035	−	0.992278i
$66$		0			0
$67$	−13.6244	+	7.86603i	−1.66448	+	0.960988i	−0.693945	+	0.720028i	$0.744129\pi$
$67$	−13.6244	+	7.86603i	−1.66448	+	0.960988i	−0.970535	+	0.240960i	$0.922538\pi$
$68$		0			0
$69$	−6.96410	+	12.0622i	−0.838379	+	1.45212i
$70$		0			0
$71$	−4.59808	+	1.23205i	−0.545691	+	0.146218i	−0.521125	−	0.853481i	$-0.674487\pi$
$71$	−4.59808	+	1.23205i	−0.545691	+	0.146218i	−0.0245667	+	0.999698i	$0.507821\pi$
$72$		0			0
$73$			1.07180i			0.125444i	0.998031	+	0.0627222i	$0.0199782\pi$
$73$			1.07180i			0.125444i	−0.998031	+	0.0627222i	$0.980022\pi$
$74$		0			0
$75$	−7.59808	+	5.96410i	−0.877350	+	0.688675i
$76$		0			0
$77$	−9.36603	+	9.36603i	−1.06736	+	1.06736i
$78$		0			0
$79$			7.46410i			0.839777i	0.907576	+	0.419889i	$0.137931\pi$
$79$			7.46410i			0.839777i	−0.907576	+	0.419889i	$0.862069\pi$
$80$		0			0
$81$	−5.33013	−	9.23205i	−0.592236	−	1.02578i
$82$		0			0
$83$	−10.9282			−1.19953			−0.599763	−	0.800178i	$-0.704739\pi$
$83$	−10.9282			−1.19953			−0.599763	+	0.800178i	$0.704739\pi$
$84$		0			0
$85$	5.59808	−	4.96410i	0.607197	−	0.538432i
$86$		0			0
$87$	3.23205	−	0.866025i	0.346512	−	0.0928477i
$88$		0			0
$89$	−0.794229	+	2.96410i	−0.0841881	+	0.314194i	−0.995159	−	0.0982760i	$-0.968667\pi$
$89$	−0.794229	+	2.96410i	−0.0841881	+	0.314194i	0.910971	+	0.412470i	$0.135334\pi$
$90$		0			0
$91$	14.4282	−	7.13397i	1.51249	−	0.747844i
$92$		0			0
$93$	7.09808	+	12.2942i	0.736036	+	1.27485i
$94$		0			0
$95$	7.33013	−	6.50000i	0.752055	−	0.666886i
$96$		0			0
$97$	3.69615	+	2.13397i	0.375287	+	0.216672i	0.675766	−	0.737116i	$-0.263813\pi$
$97$	3.69615	+	2.13397i	0.375287	+	0.216672i	−0.300478	+	0.953789i	$0.597146\pi$
$98$		0			0
$99$	−1.53590	−	1.53590i	−0.154364	−	0.154364i
$100$		0			0
$101$	5.89230	−	3.40192i	0.586306	−	0.338504i	−0.177329	−	0.984152i	$-0.556746\pi$
$101$	5.89230	−	3.40192i	0.586306	−	0.338504i	0.763636	+	0.645647i	$0.223412\pi$
$102$		0			0
$103$	0.803848	+	0.803848i	0.0792055	+	0.0792055i	0.745600	−	0.666394i	$-0.232163\pi$
$103$	0.803848	+	0.803848i	0.0792055	+	0.0792055i	−0.666394	+	0.745600i	$0.732163\pi$
$104$		0			0
$105$	−18.2942	−	6.09808i	−1.78533	−	0.595111i
$106$		0			0
$107$	−1.33013	+	4.96410i	−0.128588	+	0.479898i	−0.999942	−	0.0107572i	$-0.996576\pi$
$107$	−1.33013	+	4.96410i	−0.128588	+	0.479898i	0.871354	+	0.490655i	$0.163242\pi$
$108$		0			0
$109$	10.4641	−	10.4641i	1.00228	−	1.00228i	0.00228176	−	0.999997i	$-0.499274\pi$
$109$	10.4641	−	10.4641i	1.00228	−	1.00228i	0.999997	−	0.00228176i	$-0.000726308\pi$
$110$		0			0
$111$	−4.23205	−	15.7942i	−0.401688	−	1.49912i
$112$		0			0
$113$	−1.13397	−	4.23205i	−0.106675	−	0.398118i	0.891854	−	0.452322i	$-0.149404\pi$
$113$	−1.13397	−	4.23205i	−0.106675	−	0.398118i	−0.998530	+	0.0542046i	$0.982738\pi$
$114$		0			0
$115$	15.7942	−	3.23205i	1.47282	−	0.301390i
$116$		0			0
$117$	1.16987	+	2.36603i	0.108155	+	0.218739i
$118$		0			0
$119$	14.4282	+	3.86603i	1.32263	+	0.354398i
$120$		0			0
$121$	−1.90192	−	1.09808i	−0.172902	−	0.0998251i
$122$		0			0
$123$	2.50000	−	4.33013i	0.225417	−	0.390434i
$124$		0			0
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$	3.33013	+	0.892305i	0.295501	+	0.0791793i	0.403524	−	0.914969i	$-0.367785\pi$
$127$	3.33013	+	0.892305i	0.295501	+	0.0791793i	−0.108023	+	0.994148i	$0.534452\pi$
$128$		0			0
$129$	7.19615			0.633586
$130$		0			0
$131$	−21.8564			−1.90960			−0.954802	−	0.297244i	$-0.903933\pi$
$131$	−21.8564			−1.90960			−0.954802	+	0.297244i	$0.903933\pi$
$132$		0			0
$133$	18.8923	+	5.06218i	1.63817	+	0.438946i
$134$		0			0
$135$	−3.09808	+	9.29423i	−0.266640	+	0.799920i
$136$		0			0
$137$	10.1603	−	17.5981i	0.868049	−	1.50351i	0.00406165	−	0.999992i	$-0.498707\pi$
$137$	10.1603	−	17.5981i	0.868049	−	1.50351i	0.863987	−	0.503513i	$-0.167960\pi$
$138$		0			0
$139$	4.50000	+	2.59808i	0.381685	+	0.220366i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	4.50000	+	2.59808i	0.381685	+	0.220366i	−0.296866	+	0.954919i	$0.595942\pi$
$140$		0			0
$141$	5.46410	+	1.46410i	0.460160	+	0.123300i
$142$		0			0
$143$	−7.06218	−	8.03590i	−0.590569	−	0.671996i
$144$		0			0
$145$	−3.23205	−	2.13397i	−0.268407	−	0.177217i
$146$		0			0
$147$	−6.46410	−	24.1244i	−0.533150	−	1.98974i
$148$		0			0
$149$	−5.33013	−	19.8923i	−0.436661	−	1.62964i	−0.737060	−	0.675827i	$-0.763786\pi$
$149$	−5.33013	−	19.8923i	−0.436661	−	1.62964i	0.300399	−	0.953814i	$-0.402880\pi$
$150$		0			0
$151$	−3.73205	+	3.73205i	−0.303710	+	0.303710i	−0.842463	−	0.538753i	$-0.818895\pi$
$151$	−3.73205	+	3.73205i	−0.303710	+	0.303710i	0.538753	+	0.842463i	$0.318895\pi$
$152$		0			0
$153$	−0.633975	+	2.36603i	−0.0512538	+	0.191282i
$154$		0			0
$155$	5.19615	−	15.5885i	0.417365	−	1.25210i
$156$		0			0
$157$	−0.464102	−	0.464102i	−0.0370393	−	0.0370393i	0.688345	−	0.725384i	$-0.258338\pi$
$157$	−0.464102	−	0.464102i	−0.0370393	−	0.0370393i	−0.725384	+	0.688345i	$0.758338\pi$
$158$		0			0
$159$	−10.5622	+	6.09808i	−0.837635	+	0.483609i
$160$		0			0
$161$	22.7583	+	22.7583i	1.79361	+	1.79361i
$162$		0			0
$163$	−6.23205	−	3.59808i	−0.488132	−	0.281823i	0.235667	−	0.971834i	$-0.424272\pi$
$163$	−6.23205	−	3.59808i	−0.488132	−	0.281823i	−0.723799	+	0.690011i	$0.757606\pi$
$164$		0			0
$165$	−0.767949	+	12.7942i	−0.0597848	+	0.996029i
$166$		0			0
$167$	5.76795	+	9.99038i	0.446337	+	0.773079i	0.998144	−	0.0608930i	$-0.0193948\pi$
$167$	5.76795	+	9.99038i	0.446337	+	0.773079i	−0.551807	+	0.833972i	$0.686061\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$		0			0
$171$	−0.830127	+	3.09808i	−0.0634814	+	0.236916i
$172$		0			0
$173$	−23.2583	+	6.23205i	−1.76830	+	0.473814i	−0.988372	−	0.152057i	$-0.951410\pi$
$173$	−23.2583	+	6.23205i	−1.76830	+	0.473814i	−0.779926	+	0.625871i	$0.784744\pi$
$174$		0			0
$175$	8.76795	+	20.5263i	0.662795	+	1.55164i
$176$		0			0
$177$	12.6603			0.951603
$178$		0			0
$179$	−0.0358984	−	0.0621778i	−0.00268317	−	0.00464739i	0.864681	−	0.502322i	$-0.167521\pi$
$179$	−0.0358984	−	0.0621778i	−0.00268317	−	0.00464739i	−0.867364	+	0.497675i	$0.834187\pi$
$180$		0			0
$181$			9.07180i			0.674301i	0.941451	+	0.337151i	$0.109463\pi$
$181$			9.07180i			0.674301i	−0.941451	+	0.337151i	$0.890537\pi$
$182$		0			0
$183$	12.2942	−	12.2942i	0.908816	−	0.908816i
$184$		0			0
$185$	−10.4282	+	15.7942i	−0.766697	+	1.16121i
$186$		0			0
$187$		−	9.92820i		−	0.726022i
$188$		0			0
$189$	−18.8923	+	5.06218i	−1.37421	+	0.368219i
$190$		0			0
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	−0.456068	−	0.889945i	$-0.650743\pi$
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	0.998749	−	0.0500060i	$-0.0159241\pi$
$192$		0			0
$193$	−4.83975	+	2.79423i	−0.348373	+	0.201133i	−0.663968	−	0.747761i	$-0.731129\pi$
$193$	−4.83975	+	2.79423i	−0.348373	+	0.201133i	0.315596	+	0.948894i	$0.397796\pi$
$194$		0			0
$195$	5.86603	−	14.4282i	0.420075	−	1.03323i
$196$		0			0
$197$	−6.69615	+	3.86603i	−0.477081	+	0.275443i	−0.719199	−	0.694804i	$-0.755491\pi$
$197$	−6.69615	+	3.86603i	−0.477081	+	0.275443i	0.242118	+	0.970247i	$0.422158\pi$
$198$		0			0
$199$	4.42820	−	7.66987i	0.313907	−	0.543703i	−0.665298	−	0.746578i	$-0.731695\pi$
$199$	4.42820	−	7.66987i	0.313907	−	0.543703i	0.979205	+	0.202875i	$0.0650286\pi$
$200$		0			0
$201$	−29.3564	+	7.86603i	−2.07064	+	0.554827i
$202$		0			0
$203$		−	7.73205i		−	0.542684i
$204$		0			0
$205$	−5.66987	+	1.16025i	−0.396001	+	0.0810357i
$206$		0			0
$207$	−3.73205	+	3.73205i	−0.259395	+	0.259395i
$208$		0			0
$209$		−	13.0000i		−	0.899229i
$210$		0			0
$211$	3.96410	+	6.86603i	0.272900	+	0.472677i	0.969603	−	0.244683i	$-0.0786838\pi$
$211$	3.96410	+	6.86603i	0.272900	+	0.472677i	−0.696703	+	0.717360i	$0.745351\pi$
$212$		0			0
$213$	−9.19615			−0.630110
$214$		0			0
$215$	−5.52628	−	6.23205i	−0.376889	−	0.425022i
$216$		0			0
$217$	31.6865	−	8.49038i	2.15102	−	0.576365i
$218$		0			0
$219$	−0.535898	+	2.00000i	−0.0362127	+	0.135147i
$220$		0			0
$221$	−3.86603	+	11.4282i	−0.260057	+	0.768744i
$222$		0			0
$223$	−4.23205	−	7.33013i	−0.283399	−	0.490862i	0.688821	−	0.724932i	$-0.258129\pi$
$223$	−4.23205	−	7.33013i	−0.283399	−	0.490862i	−0.972220	+	0.234070i	$0.924795\pi$
$224$		0			0
$225$	−3.36603	+	1.43782i	−0.224402	+	0.0958548i
$226$		0			0
$227$	−6.23205	−	3.59808i	−0.413636	−	0.238813i	0.278715	−	0.960374i	$-0.410092\pi$
$227$	−6.23205	−	3.59808i	−0.413636	−	0.238813i	−0.692351	+	0.721561i	$0.743425\pi$
$228$		0			0
$229$	−13.9282	−	13.9282i	−0.920402	−	0.920402i	0.0766560	−	0.997058i	$-0.475576\pi$
$229$	−13.9282	−	13.9282i	−0.920402	−	0.920402i	−0.997058	+	0.0766560i	$0.975576\pi$
$230$		0			0
$231$	−22.1603	+	12.7942i	−1.45804	+	0.841798i
$232$		0			0
$233$	14.8564	+	14.8564i	0.973276	+	0.973276i	0.999652	−	0.0263765i	$-0.00839688\pi$
$233$	14.8564	+	14.8564i	0.973276	+	0.973276i	−0.0263765	+	0.999652i	$0.508397\pi$
$234$		0			0
$235$	−2.92820	−	5.85641i	−0.191015	−	0.382030i
$236$		0			0
$237$	−3.73205	+	13.9282i	−0.242423	+	0.904734i
$238$		0			0
$239$	0.660254	−	0.660254i	0.0427083	−	0.0427083i	−0.685430	−	0.728138i	$-0.740386\pi$
$239$	0.660254	−	0.660254i	0.0427083	−	0.0427083i	0.728138	+	0.685430i	$0.240386\pi$
$240$		0			0
$241$	2.66987	+	9.96410i	0.171982	+	0.641844i	0.997046	+	0.0768056i	$0.0244721\pi$
$241$	2.66987	+	9.96410i	0.171982	+	0.641844i	−0.825064	+	0.565039i	$0.808861\pi$
$242$		0			0
$243$	−1.92820	−	7.19615i	−0.123694	−	0.461633i
$244$		0			0
$245$	−15.9282	+	24.1244i	−1.01762	+	1.54125i
$246$		0			0
$247$	−5.06218	+	14.9641i	−0.322099	+	0.952143i
$248$		0			0
$249$	−20.3923	−	5.46410i	−1.29231	−	0.346273i
$250$		0			0
$251$	12.3564	+	7.13397i	0.779929	+	0.450292i	0.836405	−	0.548111i	$-0.184653\pi$
$251$	12.3564	+	7.13397i	0.779929	+	0.450292i	−0.0564758	+	0.998404i	$0.517986\pi$
$252$		0			0
$253$	10.6962	−	18.5263i	0.672461	−	1.16474i
$254$		0			0
$255$	12.9282	−	6.46410i	0.809595	−	0.404798i
$256$		0			0
$257$	−9.79423	−	2.62436i	−0.610947	−	0.163703i	−0.0599382	−	0.998202i	$-0.519090\pi$
$257$	−9.79423	−	2.62436i	−0.610947	−	0.163703i	−0.551009	+	0.834499i	$0.685757\pi$
$258$		0			0
$259$	−37.7846			−2.34782
$260$		0			0
$261$	1.26795			0.0784841
$262$		0			0
$263$	25.7224	+	6.89230i	1.58611	+	0.424998i	0.940812	−	0.338930i	$-0.110065\pi$
$263$	25.7224	+	6.89230i	1.58611	+	0.424998i	0.645302	+	0.763928i	$0.276732\pi$
$264$		0			0
$265$	13.3923	+	4.46410i	0.822683	+	0.274228i
$266$		0			0
$267$	−2.96410	+	5.13397i	−0.181400	+	0.314194i
$268$		0			0
$269$	18.8205	+	10.8660i	1.14751	+	0.662513i	0.948278	−	0.317440i	$-0.102823\pi$
$269$	18.8205	+	10.8660i	1.14751	+	0.662513i	0.199228	+	0.979953i	$0.436156\pi$
$270$		0			0
$271$	−4.33013	−	1.16025i	−0.263036	−	0.0704804i	0.124890	−	0.992171i	$-0.460142\pi$
$271$	−4.33013	−	1.16025i	−0.263036	−	0.0704804i	−0.387927	+	0.921690i	$0.626809\pi$
$272$		0			0
$273$	30.4904	−	6.09808i	1.84536	−	0.369072i
$274$		0			0
$275$	11.6699	−	9.16025i	0.703720	−	0.552384i
$276$		0			0
$277$	−1.66987	−	6.23205i	−0.100333	−	0.374448i	0.897441	−	0.441134i	$-0.145424\pi$
$277$	−1.66987	−	6.23205i	−0.100333	−	0.374448i	−0.997774	+	0.0666868i	$0.978757\pi$
$278$		0			0
$279$	1.39230	+	5.19615i	0.0833551	+	0.311086i
$280$		0			0
$281$	−9.53590	+	9.53590i	−0.568864	+	0.568864i	−0.931810	−	0.362946i	$-0.881771\pi$
$281$	−9.53590	+	9.53590i	−0.568864	+	0.568864i	0.362946	+	0.931810i	$0.381771\pi$
$282$		0			0
$283$	0.277568	−	1.03590i	0.0164997	−	0.0615778i	−0.957185	−	0.289476i	$-0.906519\pi$
$283$	0.277568	−	1.03590i	0.0164997	−	0.0615778i	0.973685	+	0.227899i	$0.0731855\pi$
$284$		0			0
$285$	16.9282	−	8.46410i	1.00274	−	0.501370i
$286$		0			0
$287$	−8.16987	−	8.16987i	−0.482252	−	0.482252i
$288$		0			0
$289$	5.02628	−	2.90192i	0.295663	−	0.170701i
$290$		0			0
$291$	5.83013	+	5.83013i	0.341768	+	0.341768i
$292$		0			0
$293$	−21.2321	−	12.2583i	−1.24039	−	0.716139i	−0.271216	−	0.962518i	$-0.587426\pi$
$293$	−21.2321	−	12.2583i	−1.24039	−	0.716139i	−0.969174	+	0.246379i	$0.920759\pi$
$294$		0			0
$295$	−9.72243	−	10.9641i	−0.566062	−	0.638355i
$296$		0			0
$297$	6.50000	+	11.2583i	0.377168	+	0.653275i
$298$		0			0
$299$	−19.5263	+	17.1603i	−1.12923	+	0.992403i
$300$		0			0
$301$	4.30385	−	16.0622i	0.248070	−	0.925809i
$302$		0			0
$303$	12.6962	−	3.40192i	0.729375	−	0.195435i
$304$		0			0
$305$	−20.0885	−	1.20577i	−1.15026	−	0.0690423i
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$	1.09808	+	1.90192i	0.0624674	+	0.108197i
$310$		0			0
$311$			3.46410i			0.196431i	0.995165	+	0.0982156i	$0.0313135\pi$
$311$			3.46410i			0.196431i	−0.995165	+	0.0982156i	$0.968687\pi$
$312$		0			0
$313$	−12.4641	+	12.4641i	−0.704513	+	0.704513i	−0.965376	−	0.260863i	$-0.915993\pi$
$313$	−12.4641	+	12.4641i	−0.704513	+	0.704513i	0.260863	+	0.965376i	$0.415993\pi$
$314$		0			0
$315$	−6.09808	−	4.02628i	−0.343588	−	0.226855i
$316$		0			0
$317$		−	5.07180i		−	0.284860i	−0.989805	−	0.142430i	$-0.954508\pi$
$317$		−	5.07180i		−	0.284860i	0.989805	−	0.142430i	$-0.0454917\pi$
$318$		0			0
$319$	−4.96410	+	1.33013i	−0.277936	+	0.0744728i
$320$		0			0
$321$	−4.96410	+	8.59808i	−0.277069	+	0.479898i
$322$		0			0
$323$	−12.6962	+	7.33013i	−0.706433	+	0.407859i
$324$		0			0
$325$	−17.0000	+	6.00000i	−0.942990	+	0.332820i
$326$		0			0
$327$	24.7583	−	14.2942i	1.36914	−	0.790473i
$328$		0			0
$329$	6.53590	−	11.3205i	0.360336	−	0.624120i
$330$		0			0
$331$	−28.4545	+	7.62436i	−1.56400	+	0.419072i	−0.933927	−	0.357464i	$-0.883642\pi$
$331$	−28.4545	+	7.62436i	−1.56400	+	0.419072i	−0.630073	+	0.776536i	$0.716975\pi$
$332$		0			0
$333$		−	6.19615i		−	0.339547i
$334$		0			0
$335$	29.3564	+	19.3827i	1.60391	+	1.05899i
$336$		0			0
$337$	2.07180	−	2.07180i	0.112858	−	0.112858i	−0.648423	−	0.761281i	$-0.724571\pi$
$337$	2.07180	−	2.07180i	0.112858	−	0.112858i	0.761281	+	0.648423i	$0.224571\pi$
$338$		0			0
$339$		−	8.46410i		−	0.459707i
$340$		0			0
$341$	−10.9019	−	18.8827i	−0.590372	−	1.02255i
$342$		0			0
$343$	−26.4641			−1.42893
$344$		0			0
$345$	31.0885	+	1.86603i	1.67375	+	0.100463i
$346$		0			0
$347$	−12.7942	+	3.42820i	−0.686830	+	0.184036i	−0.585324	−	0.810799i	$-0.699033\pi$
$347$	−12.7942	+	3.42820i	−0.686830	+	0.184036i	−0.101506	+	0.994835i	$0.532366\pi$
$348$		0			0
$349$	6.13397	−	22.8923i	0.328344	−	1.22540i	−0.582563	−	0.812786i	$-0.697950\pi$
$349$	6.13397	−	22.8923i	0.328344	−	1.22540i	0.910907	−	0.412611i	$-0.135383\pi$
$350$		0			0
$351$	−3.09808	−	15.4904i	−0.165363	−	0.826815i
$352$		0			0
$353$	1.76795	+	3.06218i	0.0940984	+	0.162983i	0.909232	−	0.416290i	$-0.136670\pi$
$353$	1.76795	+	3.06218i	0.0940984	+	0.162983i	−0.815134	+	0.579273i	$0.803336\pi$
$354$		0			0
$355$	7.06218	+	7.96410i	0.374821	+	0.422691i
$356$		0			0
$357$	24.9904	+	14.4282i	1.32263	+	0.763621i
$358$		0			0
$359$	−2.80385	−	2.80385i	−0.147981	−	0.147981i	0.629234	−	0.777216i	$-0.283369\pi$
$359$	−2.80385	−	2.80385i	−0.147981	−	0.147981i	−0.777216	+	0.629234i	$0.783369\pi$
$360$		0			0
$361$	−0.169873	+	0.0980762i	−0.00894068	+	0.00516191i
$362$		0			0
$363$	−3.00000	−	3.00000i	−0.157459	−	0.157459i
$364$		0			0
$365$	2.14359	−	1.07180i	0.112201	−	0.0561004i
$366$		0			0
$367$	−0.794229	+	2.96410i	−0.0414584	+	0.154725i	−0.983552	−	0.180625i	$-0.942188\pi$
$367$	−0.794229	+	2.96410i	−0.0414584	+	0.154725i	0.942094	+	0.335350i	$0.108855\pi$
$368$		0			0
$369$	1.33975	−	1.33975i	0.0697444	−	0.0697444i
$370$		0			0
$371$	7.29423	+	27.2224i	0.378697	+	1.41332i
$372$		0			0
$373$	−4.20577	−	15.6962i	−0.217767	−	0.812716i	−0.985174	−	0.171557i	$-0.945120\pi$
$373$	−4.20577	−	15.6962i	−0.217767	−	0.812716i	0.767408	−	0.641159i	$-0.221546\pi$
$374$		0			0
$375$	19.5263	+	9.23205i	1.00833	+	0.476741i
$376$		0			0
$377$	6.23205	+	0.401924i	0.320967	+	0.0207001i
$378$		0			0
$379$	2.59808	+	0.696152i	0.133454	+	0.0357589i	0.324928	−	0.945739i	$-0.394660\pi$
$379$	2.59808	+	0.696152i	0.133454	+	0.0357589i	−0.191474	+	0.981498i	$0.561327\pi$
$380$		0			0
$381$	5.76795	+	3.33013i	0.295501	+	0.170608i
$382$		0			0
$383$	16.2321	−	28.1147i	0.829419	−	1.43660i	−0.0690756	−	0.997611i	$-0.522005\pi$
$383$	16.2321	−	28.1147i	0.829419	−	1.43660i	0.898495	−	0.438985i	$-0.144662\pi$
$384$		0			0
$385$	28.0981	+	9.36603i	1.43201	+	0.477337i
$386$		0			0
$387$	2.63397	+	0.705771i	0.133892	+	0.0358764i
$388$		0			0
$389$	28.9282			1.46672			0.733359	−	0.679842i	$-0.237951\pi$
$389$	28.9282			1.46672			0.733359	+	0.679842i	$0.237951\pi$
$390$		0			0
$391$	−24.1244			−1.22002
$392$		0			0
$393$	−40.7846	−	10.9282i	−2.05731	−	0.551255i
$394$		0			0
$395$	14.9282	−	7.46410i	0.751119	−	0.375560i
$396$		0			0
$397$	4.69615	−	8.13397i	0.235693	−	0.408232i	−0.723781	−	0.690030i	$-0.757597\pi$
$397$	4.69615	−	8.13397i	0.235693	−	0.408232i	0.959474	+	0.281798i	$0.0909306\pi$
$398$		0			0
$399$	32.7224	+	18.8923i	1.63817	+	0.945798i
$400$		0			0
$401$	11.3301	+	3.03590i	0.565800	+	0.151606i	0.530369	−	0.847767i	$-0.322053\pi$
$401$	11.3301	+	3.03590i	0.565800	+	0.151606i	0.0354301	+	0.999372i	$0.488720\pi$
$402$		0			0
$403$	5.19615	+	25.9808i	0.258839	+	1.29419i
$404$		0			0
$405$	−13.1340	+	19.8923i	−0.652632	+	0.988457i
$406$		0			0
$407$	6.50000	+	24.2583i	0.322193	+	1.20244i
$408$		0			0
$409$	0.526279	+	1.96410i	0.0260228	+	0.0971186i	0.977716	−	0.209932i	$-0.0673244\pi$
$409$	0.526279	+	1.96410i	0.0260228	+	0.0971186i	−0.951693	+	0.307051i	$0.900658\pi$
$410$		0			0
$411$	27.7583	−	27.7583i	1.36922	−	1.36922i
$412$		0			0
$413$	7.57180	−	28.2583i	0.372584	−	1.39050i
$414$		0			0
$415$	10.9282	+	21.8564i	0.536444	+	1.07289i
$416$		0			0
$417$	7.09808	+	7.09808i	0.347594	+	0.347594i
$418$		0			0
$419$	31.5000	−	18.1865i	1.53888	−	0.888470i	0.539971	−	0.841684i	$-0.318435\pi$
$419$	31.5000	−	18.1865i	1.53888	−	0.888470i	0.998905	−	0.0467865i	$-0.0148981\pi$
$420$		0			0
$421$	−20.8564	−	20.8564i	−1.01648	−	1.01648i	−0.999862	−	0.0166171i	$-0.994710\pi$
$421$	−20.8564	−	20.8564i	−1.01648	−	1.01648i	−0.0166171	−	0.999862i	$-0.505290\pi$
$422$		0			0
$423$	1.85641	+	1.07180i	0.0902616	+	0.0521125i
$424$		0			0
$425$	−15.5263	−	6.23205i	−0.753135	−	0.302299i
$426$		0			0
$427$	−20.0885	−	34.7942i	−0.972149	−	1.68381i
$428$		0			0
$429$	−9.16025	−	18.5263i	−0.442261	−	0.894457i
$430$		0			0
$431$	−0.741670	+	2.76795i	−0.0357250	+	0.133327i	−0.981485	−	0.191538i	$-0.938652\pi$
$431$	−0.741670	+	2.76795i	−0.0357250	+	0.133327i	0.945760	+	0.324866i	$0.105319\pi$
$432$		0			0
$433$	−20.7224	+	5.55256i	−0.995857	+	0.266839i	−0.719709	−	0.694276i	$-0.755725\pi$
$433$	−20.7224	+	5.55256i	−0.995857	+	0.266839i	−0.276148	+	0.961115i	$0.589058\pi$
$434$		0			0
$435$	−4.96410	−	5.59808i	−0.238010	−	0.268407i
$436$		0			0
$437$	−31.5885			−1.51108
$438$		0			0
$439$	−6.96410	−	12.0622i	−0.332378	−	0.575696i	0.650599	−	0.759421i	$-0.274518\pi$
$439$	−6.96410	−	12.0622i	−0.332378	−	0.575696i	−0.982978	+	0.183725i	$0.941184\pi$
$440$		0			0
$441$		−	9.46410i		−	0.450672i
$442$		0			0
$443$	15.5885	−	15.5885i	0.740630	−	0.740630i	−0.232069	−	0.972699i	$-0.574550\pi$
$443$	15.5885	−	15.5885i	0.740630	−	0.740630i	0.972699	+	0.232069i	$0.0745496\pi$
$444$		0			0
$445$	6.72243	−	1.37564i	0.318674	−	0.0652118i
$446$		0			0
$447$		−	39.7846i		−	1.88175i
$448$		0			0
$449$	20.7942	−	5.57180i	0.981340	−	0.262949i	0.267731	−	0.963494i	$-0.413726\pi$
$449$	20.7942	−	5.57180i	0.981340	−	0.262949i	0.713609	+	0.700544i	$0.247059\pi$
$450$		0			0
$451$	−3.83975	+	6.65064i	−0.180807	+	0.313166i
$452$		0			0
$453$	−8.83013	+	5.09808i	−0.414876	+	0.239529i
$454$		0			0
$455$	−28.6962	−	21.7224i	−1.34530	−	1.01836i
$456$		0			0
$457$	−15.2321	+	8.79423i	−0.712525	+	0.411377i	−0.811995	−	0.583664i	$-0.801619\pi$
$457$	−15.2321	+	8.79423i	−0.712525	+	0.411377i	0.0994701	+	0.995041i	$0.468285\pi$
$458$		0			0
$459$	7.33013	−	12.6962i	0.342141	−	0.592606i
$460$		0			0
$461$	37.1865	−	9.96410i	1.73195	−	0.464074i	0.751319	−	0.659940i	$-0.229418\pi$
$461$	37.1865	−	9.96410i	1.73195	−	0.464074i	0.980631	+	0.195865i	$0.0627515\pi$
$462$		0			0
$463$			42.3923i			1.97014i	0.172161	+	0.985069i	$0.444925\pi$
$463$			42.3923i			1.97014i	−0.172161	+	0.985069i	$0.555075\pi$
$464$		0			0
$465$	17.4904	−	26.4904i	0.811097	−	1.22846i
$466$		0			0
$467$	0.660254	−	0.660254i	0.0305529	−	0.0305529i	−0.691665	−	0.722218i	$-0.743123\pi$
$467$	0.660254	−	0.660254i	0.0305529	−	0.0305529i	0.722218	+	0.691665i	$0.243123\pi$
$468$		0			0
$469$			70.2295i			3.24290i
$470$		0			0
$471$	−0.633975	−	1.09808i	−0.0292120	−	0.0505967i
$472$		0			0
$473$	−11.0526			−0.508197
$474$		0			0
$475$	−20.3301	−	8.16025i	−0.932810	−	0.374418i
$476$		0			0
$477$	−4.46410	+	1.19615i	−0.204397	+	0.0547681i
$478$		0			0
$479$	4.86603	−	18.1603i	0.222334	−	0.829763i	−0.761121	−	0.648610i	$-0.775350\pi$
$479$	4.86603	−	18.1603i	0.222334	−	0.829763i	0.983455	−	0.181153i	$-0.0579829\pi$
$480$		0			0
$481$	1.96410	−	30.4545i	0.0895553	−	1.38860i
$482$		0			0
$483$	31.0885	+	53.8468i	1.41457	+	2.45011i
$484$		0			0
$485$	0.571797	−	9.52628i	0.0259640	−	0.432566i
$486$		0			0
$487$	25.6244	+	14.7942i	1.16115	+	0.670390i	0.951579	−	0.307403i	$-0.0994599\pi$
$487$	25.6244	+	14.7942i	1.16115	+	0.670390i	0.209571	+	0.977793i	$0.432793\pi$
$488$		0			0
$489$	−9.83013	−	9.83013i	−0.444534	−	0.444534i
$490$		0			0
$491$	−14.8923	+	8.59808i	−0.672080	+	0.388026i	−0.796864	−	0.604158i	$-0.793510\pi$
$491$	−14.8923	+	8.59808i	−0.672080	+	0.388026i	0.124784	+	0.992184i	$0.460176\pi$
$492$		0			0
$493$	4.09808	+	4.09808i	0.184568	+	0.184568i
$494$		0			0
$495$	−1.53590	+	4.60770i	−0.0690335	+	0.207100i
$496$		0			0
$497$	−5.50000	+	20.5263i	−0.246709	+	0.920729i
$498$		0			0
$499$	−23.7321	+	23.7321i	−1.06239	+	1.06239i	−0.0644731	+	0.997919i	$0.520537\pi$
$499$	−23.7321	+	23.7321i	−1.06239	+	1.06239i	−0.997919	+	0.0644731i	$0.979463\pi$
$500$		0			0
$501$	5.76795	+	21.5263i	0.257693	+	0.961723i
$502$		0			0
$503$	−6.52628	−	24.3564i	−0.290992	−	1.08600i	−0.944348	−	0.328947i	$-0.893306\pi$
$503$	−6.52628	−	24.3564i	−0.290992	−	1.08600i	0.653356	−	0.757051i	$-0.273361\pi$
$504$		0			0
$505$	−12.6962	−	8.38269i	−0.564971	−	0.373025i
$506$		0			0
$507$	3.33013	+	24.8923i	0.147896	+	1.10551i
$508$		0			0
$509$	−25.4545	−	6.82051i	−1.12825	−	0.302314i	−0.354032	−	0.935233i	$-0.615190\pi$
$509$	−25.4545	−	6.82051i	−1.12825	−	0.302314i	−0.774218	+	0.632919i	$0.781856\pi$
$510$		0			0
$511$	4.14359	+	2.39230i	0.183302	+	0.105829i
$512$		0			0
$513$	9.59808	−	16.6244i	0.423765	−	0.733983i
$514$		0			0
$515$	0.803848	−	2.41154i	0.0354218	−	0.106265i
$516$		0			0
$517$	−8.39230	−	2.24871i	−0.369093	−	0.0988982i
$518$		0			0
$519$	−46.5167			−2.04185
$520$		0			0
$521$	19.8564			0.869925			0.434962	−	0.900449i	$-0.356762\pi$
$521$	19.8564			0.869925			0.434962	+	0.900449i	$0.356762\pi$
$522$		0			0
$523$	−15.0622	−	4.03590i	−0.658623	−	0.176478i	−0.0859985	−	0.996295i	$-0.527408\pi$
$523$	−15.0622	−	4.03590i	−0.658623	−	0.176478i	−0.572625	+	0.819818i	$0.694075\pi$
$524$		0			0
$525$	6.09808	+	42.6865i	0.266142	+	1.86299i
$526$		0			0
$527$	−12.2942	+	21.2942i	−0.535545	+	0.927591i
$528$		0			0
$529$	−25.0981	−	14.4904i	−1.09122	−	0.630017i
$530$		0			0
$531$	4.63397	+	1.24167i	0.201097	+	0.0538839i
$532$		0			0
$533$	7.00962	−	6.16025i	0.303620	−	0.266830i
$534$		0			0
$535$	11.2583	−	2.30385i	0.486740	−	0.0996040i
$536$		0			0
$537$	−0.0358984	−	0.133975i	−0.00154913	−	0.00578143i
$538$		0			0
$539$	9.92820	+	37.0526i	0.427638	+	1.59597i
$540$		0			0
$541$	−19.7846	+	19.7846i	−0.850607	+	0.850607i	−0.990208	−	0.139601i	$-0.955418\pi$
$541$	−19.7846	+	19.7846i	−0.850607	+	0.850607i	0.139601	+	0.990208i	$0.455418\pi$
$542$		0			0
$543$	−4.53590	+	16.9282i	−0.194654	+	0.726459i
$544$		0			0
$545$	−31.3923	−	10.4641i	−1.34470	−	0.448233i
$546$		0			0
$547$	24.1244	+	24.1244i	1.03148	+	1.03148i	0.999488	+	0.0319949i	$0.0101860\pi$
$547$	24.1244	+	24.1244i	1.03148	+	1.03148i	0.0319949	+	0.999488i	$0.489814\pi$
$548$		0			0
$549$	5.70577	−	3.29423i	0.243516	−	0.140594i
$550$		0			0
$551$	5.36603	+	5.36603i	0.228600	+	0.228600i
$552$		0			0
$553$	28.8564	+	16.6603i	1.22710	+	0.708466i
$554$		0			0
$555$	−27.3564	+	24.2583i	−1.16121	+	1.02971i
$556$		0			0
$557$	2.69615	+	4.66987i	0.114240	+	0.197869i	0.917476	−	0.397792i	$-0.130223\pi$
$557$	2.69615	+	4.66987i	0.114240	+	0.197869i	−0.803236	+	0.595661i	$0.796890\pi$
$558$		0			0
$559$	12.7224	+	4.30385i	0.538102	+	0.182033i
$560$		0			0
$561$	4.96410	−	18.5263i	0.209585	−	0.782180i
$562$		0			0
$563$	−15.3301	+	4.10770i	−0.646088	+	0.173119i	−0.566959	−	0.823746i	$-0.691880\pi$
$563$	−15.3301	+	4.10770i	−0.646088	+	0.173119i	−0.0791284	+	0.996864i	$0.525214\pi$
$564$		0			0
$565$	−7.33013	+	6.50000i	−0.308381	+	0.273457i
$566$		0			0
$567$	−47.5885			−1.99853
$568$		0			0
$569$	15.8205	+	27.4019i	0.663230	+	1.14875i	0.979762	+	0.200166i	$0.0641483\pi$
$569$	15.8205	+	27.4019i	0.663230	+	1.14875i	−0.316532	+	0.948582i	$0.602518\pi$
$570$		0			0
$571$		−	42.3923i		−	1.77406i	−0.461709	−	0.887031i	$-0.652764\pi$
$571$		−	42.3923i		−	1.77406i	0.461709	−	0.887031i	$-0.347236\pi$
$572$		0			0
$573$	20.4904	−	20.4904i	0.855998	−	0.855998i
$574$		0			0
$575$	−22.2583	−	28.3564i	−0.928237	−	1.18254i
$576$		0			0
$577$		−	20.7846i		−	0.865275i	−0.901568	−	0.432637i	$-0.857583\pi$
$577$		−	20.7846i		−	0.865275i	0.901568	−	0.432637i	$-0.142417\pi$
$578$		0			0
$579$	−10.4282	+	2.79423i	−0.433381	+	0.116124i
$580$		0			0
$581$	−24.3923	+	42.2487i	−1.01196	+	1.75277i
$582$		0			0
$583$	16.2224	−	9.36603i	0.671864	−	0.387901i
$584$		0			0
$585$	3.56218	−	4.70577i	0.147278	−	0.194560i
$586$		0			0
$587$	−9.91154	+	5.72243i	−0.409093	+	0.236190i	−0.690400	−	0.723428i	$-0.742565\pi$
$587$	−9.91154	+	5.72243i	−0.409093	+	0.236190i	0.281307	+	0.959618i	$0.409232\pi$
$588$		0			0
$589$	−16.0981	+	27.8827i	−0.663310	+	1.14889i
$590$		0			0
$591$	−14.4282	+	3.86603i	−0.593497	+	0.159027i
$592$		0			0
$593$			17.0718i			0.701055i	0.936553	+	0.350527i	$0.113998\pi$
$593$			17.0718i			0.701055i	−0.936553	+	0.350527i	$0.886002\pi$
$594$		0			0
$595$	−6.69615	−	32.7224i	−0.274515	−	1.34149i
$596$		0			0
$597$	12.0981	−	12.0981i	0.495141	−	0.495141i
$598$		0			0
$599$		−	12.2487i		−	0.500469i	−0.968185	−	0.250234i	$-0.919492\pi$
$599$		−	12.2487i		−	0.500469i	0.968185	−	0.250234i	$-0.0805077\pi$
$600$		0			0
$601$	−6.42820	−	11.1340i	−0.262212	−	0.454164i	0.704618	−	0.709587i	$-0.251119\pi$
$601$	−6.42820	−	11.1340i	−0.262212	−	0.454164i	−0.966829	+	0.255423i	$0.917785\pi$
$602$		0			0
$603$	−11.5167			−0.468995
$604$		0			0
$605$	−0.294229	+	4.90192i	−0.0119621	+	0.199292i
$606$		0			0
$607$	−37.1865	+	9.96410i	−1.50935	+	0.404430i	−0.916221	−	0.400673i	$-0.868776\pi$
$607$	−37.1865	+	9.96410i	−1.50935	+	0.404430i	−0.593134	+	0.805104i	$0.702110\pi$
$608$		0			0
$609$	3.86603	−	14.4282i	0.156659	−	0.584660i
$610$		0			0
$611$	8.78461	+	5.85641i	0.355387	+	0.236925i
$612$		0			0
$613$	−8.76795	−	15.1865i	−0.354134	−	0.613378i	0.632835	−	0.774286i	$-0.281891\pi$
$613$	−8.76795	−	15.1865i	−0.354134	−	0.613378i	−0.986969	+	0.160908i	$0.948558\pi$
$614$		0			0
$615$	−11.1603	−	0.669873i	−0.450025	−	0.0270119i
$616$		0			0
$617$	−11.7679	−	6.79423i	−0.473760	−	0.273525i	0.244053	−	0.969762i	$-0.421523\pi$
$617$	−11.7679	−	6.79423i	−0.473760	−	0.273525i	−0.717812	+	0.696237i	$0.754856\pi$
$618$		0			0
$619$	2.66025	+	2.66025i	0.106925	+	0.106925i	0.758545	−	0.651620i	$-0.225911\pi$
$619$	2.66025	+	2.66025i	0.106925	+	0.106925i	−0.651620	+	0.758545i	$0.725911\pi$
$620$		0			0
$621$	27.3564	−	15.7942i	1.09777	−	0.633801i
$622$		0			0
$623$	9.68653	+	9.68653i	0.388083	+	0.388083i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$	6.50000	−	24.2583i	0.259585	−	0.968784i
$628$		0			0
$629$	20.0263	−	20.0263i	0.798500	−	0.798500i
$630$		0			0
$631$	−1.65064	−	6.16025i	−0.0657107	−	0.245236i	0.925256	−	0.379343i	$-0.123850\pi$
$631$	−1.65064	−	6.16025i	−0.0657107	−	0.245236i	−0.990967	+	0.134107i	$0.957183\pi$
$632$		0			0
$633$	3.96410	+	14.7942i	0.157559	+	0.588018i
$634$		0			0
$635$	−1.54552	−	7.55256i	−0.0613320	−	0.299714i
$636$		0			0
$637$	3.00000	−	46.5167i	0.118864	−	1.84306i
$638$		0			0
$639$	−3.36603	−	0.901924i	−0.133158	−	0.0356796i
$640$		0			0
$641$	33.3564	+	19.2583i	1.31750	+	0.760658i	0.983326	−	0.181853i	$-0.0582096\pi$
$641$	33.3564	+	19.2583i	1.31750	+	0.760658i	0.334173	+	0.942512i	$0.391543\pi$
$642$		0			0
$643$	−13.0885	+	22.6699i	−0.516158	+	0.894013i	0.483666	+	0.875253i	$0.339305\pi$
$643$	−13.0885	+	22.6699i	−0.516158	+	0.894013i	−0.999824	+	0.0187597i	$0.994028\pi$
$644$		0			0
$645$	−7.19615	−	14.3923i	−0.283348	−	0.566696i
$646$		0			0
$647$	9.33013	+	2.50000i	0.366805	+	0.0982851i	0.437513	−	0.899212i	$-0.355859\pi$
$647$	9.33013	+	2.50000i	0.366805	+	0.0982851i	−0.0707082	+	0.997497i	$0.522526\pi$
$648$		0			0
$649$	−19.4449			−0.763278
$650$		0			0
$651$	63.3731			2.48379
$652$		0			0
$653$	40.8468	+	10.9449i	1.59846	+	0.428306i	0.944577	−	0.328291i	$-0.106473\pi$
$653$	40.8468	+	10.9449i	1.59846	+	0.428306i	0.653882	+	0.756597i	$0.273139\pi$
$654$		0			0
$655$	21.8564	+	43.7128i	0.854000	+	1.70800i
$656$		0			0
$657$	−0.392305	+	0.679492i	−0.0153053	+	0.0265095i
$658$		0			0
$659$	21.5718	+	12.4545i	0.840318	+	0.485158i	0.857372	−	0.514697i	$-0.172096\pi$
$659$	21.5718	+	12.4545i	0.840318	+	0.485158i	−0.0170544	+	0.999855i	$0.505429\pi$
$660$		0			0
$661$	14.7942	+	3.96410i	0.575429	+	0.154186i	0.534785	−	0.844988i	$-0.320393\pi$
$661$	14.7942	+	3.96410i	0.575429	+	0.154186i	0.0406436	+	0.999174i	$0.487059\pi$
$662$		0			0
$663$	−12.9282	+	19.3923i	−0.502090	+	0.753135i
$664$		0			0
$665$	−8.76795	−	42.8468i	−0.340006	−	1.66153i
$666$		0			0
$667$	3.23205	+	12.0622i	0.125146	+	0.467049i
$668$		0			0
$669$	−4.23205	−	15.7942i	−0.163621	−	0.610640i
$670$		0			0
$671$	−18.8827	+	18.8827i	−0.728958	+	0.728958i
$672$		0			0
$673$	−3.91858	+	14.6244i	−0.151050	+	0.563727i	0.848361	+	0.529418i	$0.177590\pi$
$673$	−3.91858	+	14.6244i	−0.151050	+	0.563727i	−0.999411	+	0.0343092i	$0.989077\pi$
$674$		0			0
$675$	21.6865	−	3.09808i	0.834715	−	0.119245i
$676$		0			0
$677$	34.1769	+	34.1769i	1.31353	+	1.31353i	0.918798	+	0.394727i	$0.129161\pi$
$677$	34.1769	+	34.1769i	1.31353	+	1.31353i	0.394727	+	0.918798i	$0.370839\pi$
$678$		0			0
$679$	16.5000	−	9.52628i	0.633212	−	0.365585i
$680$		0			0
$681$	−9.83013	−	9.83013i	−0.376691	−	0.376691i
$682$		0			0
$683$	2.30385	+	1.33013i	0.0881543	+	0.0508959i	0.543429	−	0.839455i	$-0.317126\pi$
$683$	2.30385	+	1.33013i	0.0881543	+	0.0508959i	−0.455275	+	0.890351i	$0.650459\pi$
$684$		0			0
$685$	−45.3564	−	2.72243i	−1.73298	−	0.104019i
$686$		0			0
$687$	−19.0263	−	32.9545i	−0.725898	−	1.25729i
$688$		0			0
$689$	−22.3205	+	4.46410i	−0.850344	+	0.170069i
$690$		0			0
$691$	5.65064	−	21.0885i	0.214960	−	0.802243i	−0.771220	−	0.636568i	$-0.780353\pi$
$691$	5.65064	−	21.0885i	0.214960	−	0.802243i	0.986181	−	0.165674i	$-0.0529800\pi$
$692$		0			0
$693$	−9.36603	+	2.50962i	−0.355786	+	0.0953325i
$694$		0			0
$695$	0.696152	−	11.5981i	0.0264066	−	0.439940i
$696$		0			0
$697$	8.66025			0.328031
$698$		0			0
$699$	20.2942	+	35.1506i	0.767598	+	1.32952i
$700$		0			0
$701$		−	34.9282i		−	1.31922i	−0.751608	−	0.659610i	$-0.770721\pi$
$701$		−	34.9282i		−	1.31922i	0.751608	−	0.659610i	$-0.229279\pi$
$702$		0			0
$703$	26.2224	−	26.2224i	0.988998	−	0.988998i
$704$		0			0
$705$	−2.53590	−	12.3923i	−0.0955075	−	0.466721i
$706$		0			0
$707$		−	30.3731i		−	1.14230i
$708$		0			0
$709$	33.7224	−	9.03590i	1.26647	−	0.339350i	0.437794	−	0.899075i	$-0.355760\pi$
$709$	33.7224	−	9.03590i	1.26647	−	0.339350i	0.828678	+	0.559725i	$0.189093\pi$
$710$		0			0
$711$	−2.73205	+	4.73205i	−0.102460	+	0.177466i
$712$		0			0
$713$	−45.8827	+	26.4904i	−1.71832	+	0.992073i
$714$		0			0
$715$	−9.00962	+	22.1603i	−0.336941	+	0.828747i
$716$		0			0
$717$	1.56218	−	0.901924i	0.0583406	−	0.0336830i
$718$		0			0
$719$	14.0359	−	24.3109i	0.523451	−	0.906643i	−0.476177	−	0.879350i	$-0.657978\pi$
$719$	14.0359	−	24.3109i	0.523451	−	0.906643i	0.999627	−	0.0272936i	$-0.00868890\pi$
$720$		0			0
$721$	4.90192	−	1.31347i	0.182557	−	0.0489160i
$722$		0			0
$723$			19.9282i			0.741138i
$724$		0			0
$725$	−1.03590	+	8.59808i	−0.0384723	+	0.319325i
$726$		0			0
$727$	2.41154	−	2.41154i	0.0894392	−	0.0894392i	−0.660972	−	0.750411i	$-0.729856\pi$
$727$	2.41154	−	2.41154i	0.0894392	−	0.0894392i	0.750411	+	0.660972i	$0.229856\pi$
$728$		0			0
$729$			17.5885i			0.651424i
$730$		0			0
$731$	6.23205	+	10.7942i	0.230501	+	0.399239i
$732$		0			0
$733$	−14.7846			−0.546082			−0.273041	−	0.962002i	$-0.588029\pi$
$733$	−14.7846			−0.546082			−0.273041	+	0.962002i	$0.588029\pi$
$734$		0			0
$735$	−41.7846	+	37.0526i	−1.54125	+	1.36670i
$736$		0			0
$737$	45.0885	−	12.0814i	1.66085	−	0.445025i
$738$		0			0
$739$	−1.91858	+	7.16025i	−0.0705763	+	0.263394i	−0.992194	−	0.124705i	$-0.960202\pi$
$739$	−1.91858	+	7.16025i	−0.0705763	+	0.263394i	0.921618	+	0.388099i	$0.126868\pi$
$740$		0			0
$741$	−16.9282	+	25.3923i	−0.621873	+	0.932810i
$742$		0			0
$743$	6.16025	+	10.6699i	0.225998	+	0.391440i	0.956618	−	0.291344i	$-0.0941024\pi$
$743$	6.16025	+	10.6699i	0.225998	+	0.391440i	−0.730621	+	0.682784i	$0.760769\pi$
$744$		0			0
$745$	−34.4545	+	30.5526i	−1.26231	+	1.11936i
$746$		0			0
$747$	−6.92820	−	4.00000i	−0.253490	−	0.146352i
$748$		0			0
$749$	16.2224	+	16.2224i	0.592755	+	0.592755i
$750$		0			0
$751$	45.3564	−	26.1865i	1.65508	−	0.955560i	0.680141	−	0.733081i	$-0.261918\pi$
$751$	45.3564	−	26.1865i	1.65508	−	0.955560i	0.974937	−	0.222479i	$-0.0714149\pi$
$752$		0			0
$753$	19.4904	+	19.4904i	0.710269	+	0.710269i
$754$		0			0
$755$	11.1962	+	3.73205i	0.407470	+	0.135823i
$756$		0			0
$757$	5.93782	−	22.1603i	0.215814	−	0.805428i	−0.770065	−	0.637966i	$-0.779776\pi$
$757$	5.93782	−	22.1603i	0.215814	−	0.805428i	0.985878	−	0.167462i	$-0.0535572\pi$
$758$		0			0
$759$	29.2224	−	29.2224i	1.06071	−	1.06071i
$760$		0			0
$761$	−9.33013	−	34.8205i	−0.338217	−	1.26224i	−0.900339	−	0.435188i	$-0.856682\pi$
$761$	−9.33013	−	34.8205i	−0.338217	−	1.26224i	0.562123	−	0.827054i	$-0.309985\pi$
$762$		0			0
$763$	−17.0981	−	63.8109i	−0.618992	−	2.31011i
$764$		0			0
$765$	5.36603	−	1.09808i	0.194009	−	0.0397010i
$766$		0			0
$767$	22.3827	+	7.57180i	0.808192	+	0.273402i
$768$		0			0
$769$	−24.5263	−	6.57180i	−0.884440	−	0.236985i	−0.212118	−	0.977244i	$-0.568036\pi$
$769$	−24.5263	−	6.57180i	−0.884440	−	0.236985i	−0.672322	+	0.740259i	$0.734703\pi$
$770$		0			0
$771$	−16.9641	−	9.79423i	−0.610947	−	0.352731i
$772$		0			0
$773$	−27.1603	+	47.0429i	−0.976886	+	1.69202i	−0.303323	+	0.952888i	$0.598096\pi$
$773$	−27.1603	+	47.0429i	−0.976886	+	1.69202i	−0.673564	+	0.739129i	$0.735237\pi$
$774$		0			0
$775$	−36.3731	+	5.19615i	−1.30656	+	0.186651i
$776$		0			0
$777$	−70.5070	−	18.8923i	−2.52943	−	0.677758i
$778$		0			0
$779$	11.3397			0.406289
$780$		0			0
$781$	14.1244			0.505409
$782$		0			0
$783$	−7.33013	−	1.96410i	−0.261957	−	0.0701913i
$784$		0			0
$785$	−0.464102	+	1.39230i	−0.0165645	+	0.0496935i
$786$		0			0
$787$	2.62436	−	4.54552i	0.0935482	−	0.162030i	−0.815454	−	0.578822i	$-0.803512\pi$
$787$	2.62436	−	4.54552i	0.0935482	−	0.162030i	0.909002	+	0.416792i	$0.136846\pi$
$788$		0			0
$789$	44.5526	+	25.7224i	1.58611	+	0.915743i
$790$		0			0
$791$	−18.8923	−	5.06218i	−0.671733	−	0.179990i
$792$		0			0
$793$	29.0885	−	14.3827i	1.03296	−	0.510744i
$794$		0			0
$795$	22.7583	+	15.0263i	0.807155	+	0.532927i
$796$		0			0
$797$	−4.99038	−	18.6244i	−0.176768	−	0.659709i	−0.996244	−	0.0865940i	$-0.972402\pi$
$797$	−4.99038	−	18.6244i	−0.176768	−	0.659709i	0.819475	−	0.573114i	$-0.194265\pi$
$798$		0			0
$799$	2.53590	+	9.46410i	0.0897136	+	0.334816i
$800$		0			0
$801$	−1.58846	+	1.58846i	−0.0561254	+	0.0561254i
$802$		0			0
$803$	0.823085	−	3.07180i	0.0290461	−	0.108401i
$804$		0			0
$805$	22.7583	−	68.2750i	0.802126	−	2.40638i
$806$		0			0
$807$	29.6865	+	29.6865i	1.04502	+	1.04502i
$808$		0			0
$809$	−31.2846	+	18.0622i	−1.09991	+	0.635032i	−0.936197	−	0.351476i	$-0.885680\pi$
$809$	−31.2846	+	18.0622i	−1.09991	+	0.635032i	−0.163711	+	0.986508i	$0.552347\pi$
$810$		0			0
$811$	15.0526	+	15.0526i	0.528567	+	0.528567i	0.920145	−	0.391578i	$-0.128071\pi$
$811$	15.0526	+	15.0526i	0.528567	+	0.528567i	−0.391578	+	0.920145i	$0.628071\pi$
$812$		0			0
$813$	−7.50000	−	4.33013i	−0.263036	−	0.151864i
$814$		0			0
$815$	−0.964102	+	16.0622i	−0.0337710	+	0.562634i
$816$		0			0
$817$	8.16025	+	14.1340i	0.285491	+	0.494485i
$818$		0			0
$819$	11.7583	+	0.758330i	0.410869	+	0.0264982i
$820$		0			0
$821$	5.45448	−	20.3564i	0.190363	−	0.710443i	−0.803056	−	0.595904i	$-0.796794\pi$
$821$	5.45448	−	20.3564i	0.190363	−	0.710443i	0.993419	−	0.114540i	$-0.0365393\pi$
$822$		0			0
$823$	11.5981	−	3.10770i	0.404284	−	0.108327i	−0.0509463	−	0.998701i	$-0.516224\pi$
$823$	11.5981	−	3.10770i	0.404284	−	0.108327i	0.455230	+	0.890374i	$0.349557\pi$
$824$		0			0
$825$	26.3564	−	11.2583i	0.917612	−	0.391965i
$826$		0			0
$827$	1.85641			0.0645536			0.0322768	−	0.999479i	$-0.489724\pi$
$827$	1.85641			0.0645536			0.0322768	+	0.999479i	$0.489724\pi$
$828$		0			0
$829$	9.42820	+	16.3301i	0.327455	+	0.567169i	0.982006	−	0.188849i	$-0.0604757\pi$
$829$	9.42820	+	16.3301i	0.327455	+	0.567169i	−0.654551	+	0.756018i	$0.727142\pi$
$830$		0			0
$831$		−	12.4641i		−	0.432375i
$832$		0			0
$833$	30.5885	−	30.5885i	1.05983	−	1.05983i
$834$		0			0
$835$	14.2128	−	21.5263i	0.491855	−	0.744948i
$836$		0			0
$837$		−	32.1962i		−	1.11286i
$838$		0			0
$839$	7.79423	−	2.08846i	0.269087	−	0.0721016i	−0.121753	−	0.992560i	$-0.538851\pi$
$839$	7.79423	−	2.08846i	0.269087	−	0.0721016i	0.390839	+	0.920459i	$0.372185\pi$
$840$		0			0
$841$	−13.0000	+	22.5167i	−0.448276	+	0.776437i
$842$		0			0
$843$	−22.5622	+	13.0263i	−0.777083	+	0.448649i
$844$		0			0
$845$	19.0000	−	22.0000i	0.653620	−	0.756823i
$846$		0			0
$847$	−8.49038	+	4.90192i	−0.291733	+	0.168432i
$848$		0			0
$849$	1.03590	−	1.79423i	0.0355519	−	0.0615778i
$850$		0			0
$851$	58.9449	−	15.7942i	2.02060	−	0.541419i
$852$		0			0
$853$			26.1436i			0.895140i	0.894249	+	0.447570i	$0.147710\pi$
$853$			26.1436i			0.895140i	−0.894249	+	0.447570i	$0.852290\pi$
$854$		0			0
$855$	7.02628	−	1.43782i	0.240294	−	0.0491725i
$856$		0			0
$857$	−29.2487	+	29.2487i	−0.999117	+	0.999117i	−1.00000		0.000882665i	$-0.999719\pi$
$857$	−29.2487	+	29.2487i	−0.999117	+	0.999117i	0.000882665		1.00000i	$0.499719\pi$
$858$		0			0
$859$			18.3923i			0.627537i	0.949499	+	0.313769i	$0.101592\pi$
$859$			18.3923i			0.627537i	−0.949499	+	0.313769i	$0.898408\pi$
$860$		0			0
$861$	−11.1603	−	19.3301i	−0.380340	−	0.658769i
$862$		0			0
$863$	−29.8564			−1.01632			−0.508162	−	0.861262i	$-0.669675\pi$
$863$	−29.8564			−1.01632			−0.508162	+	0.861262i	$0.669675\pi$
$864$		0			0
$865$	35.7224	+	40.2846i	1.21460	+	1.36972i
$866$		0			0
$867$	10.8301	−	2.90192i	0.367810	−	0.0985545i
$868$		0			0
$869$	5.73205	−	21.3923i	0.194447	−	0.725684i
$870$		0			0
$871$	−56.6051	−	3.65064i	−1.91799	−	0.123697i
$872$		0			0
$873$	1.56218	+	2.70577i	0.0528717	+	0.0915765i
$874$		0			0
$875$	32.2846	−	38.0622i	1.09142	−	1.28674i
$876$		0			0
$877$	5.55256	+	3.20577i	0.187497	+	0.108251i	0.590810	−	0.806811i	$-0.298808\pi$
$877$	5.55256	+	3.20577i	0.187497	+	0.108251i	−0.403313	+	0.915062i	$0.632142\pi$
$878$		0			0
$879$	−33.4904	−	33.4904i	−1.12960	−	1.12960i
$880$		0			0
$881$	−1.96410	+	1.13397i	−0.0661723	+	0.0382046i	−0.532721	−	0.846291i	$-0.678831\pi$
$881$	−1.96410	+	1.13397i	−0.0661723	+	0.0382046i	0.466549	+	0.884495i	$0.345497\pi$
$882$		0			0
$883$	−11.1962	−	11.1962i	−0.376781	−	0.376781i	0.493159	−	0.869939i	$-0.335842\pi$
$883$	−11.1962	−	11.1962i	−0.376781	−	0.376781i	−0.869939	+	0.493159i	$0.835842\pi$
$884$		0			0
$885$	−12.6603	−	25.3205i	−0.425570	−	0.851140i
$886$		0			0
$887$	−1.86603	+	6.96410i	−0.0626550	+	0.233832i	−0.990151	−	0.140000i	$-0.955290\pi$
$887$	−1.86603	+	6.96410i	−0.0626550	+	0.233832i	0.927496	+	0.373832i	$0.121956\pi$
$888$		0			0
$889$	10.8827	−	10.8827i	0.364994	−	0.364994i
$890$		0			0
$891$	8.18653	+	30.5526i	0.274259	+	1.02355i
$892$		0			0
$893$	3.32051	+	12.3923i	0.111117	+	0.414693i
$894$		0			0
$895$	−0.0884573	+	0.133975i	−0.00295680	+	0.00447828i
$896$		0			0
$897$	−45.0167	+	22.2583i	−1.50306	+	0.743184i
$898$		0			0
$899$	12.2942	+	3.29423i	0.410035	+	0.109869i
$900$		0			0
$901$	−18.2942	−	10.5622i	−0.609469	−	0.351877i
$902$		0			0
$903$	16.0622	−	27.8205i	0.534516	−	0.925809i
$904$		0			0
$905$	18.1436	−	9.07180i	0.603113	−	0.301557i
$906$		0			0
$907$	54.6506	+	14.6436i	1.81464	+	0.486233i	0.996102	−	0.0882129i	$-0.0281156\pi$
$907$	54.6506	+	14.6436i	1.81464	+	0.486233i	0.818543	+	0.574445i	$0.194782\pi$
$908$		0			0
$909$	4.98076			0.165201
$910$		0			0
$911$	−57.5692			−1.90735			−0.953677	−	0.300834i	$-0.902735\pi$
$911$	−57.5692			−1.90735			−0.953677	+	0.300834i	$0.902735\pi$
$912$		0			0
$913$	31.3205	+	8.39230i	1.03656	+	0.277745i
$914$		0			0
$915$	−36.8827	−	12.2942i	−1.21930	−	0.406435i
$916$		0			0
$917$	−48.7846	+	84.4974i	−1.61101	+	2.79035i
$918$		0			0
$919$	−36.1410	−	20.8660i	−1.19218	−	0.688307i	−0.233381	−	0.972385i	$-0.574979\pi$
$919$	−36.1410	−	20.8660i	−1.19218	−	0.688307i	−0.958801	+	0.284079i	$0.908312\pi$
$920$		0			0
$921$	7.46410	+	2.00000i	0.245951	+	0.0659022i
$922$		0			0
$923$	−16.2583	−	5.50000i	−0.535149	−	0.181035i
$924$		0			0
$925$	42.0167	+	5.06218i	1.38150	+	0.166443i
$926$		0			0
$927$	0.215390	+	0.803848i	0.00707435	+	0.0264018i
$928$		0			0
$929$	3.99038	+	14.8923i	0.130920	+	0.488601i	0.999981	−	0.00610389i	$-0.00194294\pi$
$929$	3.99038	+	14.8923i	0.130920	+	0.488601i	−0.869061	+	0.494705i	$0.835276\pi$
$930$		0			0
$931$	40.0526	−	40.0526i	1.31267	−	1.31267i
$932$		0			0
$933$	−1.73205	+	6.46410i	−0.0567048	+	0.211625i
$934$		0			0
$935$	−19.8564	+	9.92820i	−0.649374	+	0.324687i
$936$		0			0
$937$	−24.8564	−	24.8564i	−0.812023	−	0.812023i	0.172914	−	0.984937i	$-0.444682\pi$
$937$	−24.8564	−	24.8564i	−0.812023	−	0.812023i	−0.984937	+	0.172914i	$0.944682\pi$
$938$		0			0
$939$	−29.4904	+	17.0263i	−0.962382	+	0.555632i
$940$		0			0
$941$	−20.8564	−	20.8564i	−0.679899	−	0.679899i	0.280078	−	0.959977i	$-0.409640\pi$
$941$	−20.8564	−	20.8564i	−0.679899	−	0.679899i	−0.959977	+	0.280078i	$0.909640\pi$
$942$		0			0
$943$	16.1603	+	9.33013i	0.526250	+	0.303831i
$944$		0			0
$945$	29.0167	+	32.7224i	0.943912	+	1.06446i
$946$		0			0
$947$	21.6244	+	37.4545i	0.702697	+	1.21711i	0.967516	+	0.252809i	$0.0813544\pi$
$947$	21.6244	+	37.4545i	0.702697	+	1.21711i	−0.264819	+	0.964298i	$0.585312\pi$
$948$		0			0
$949$	−2.14359	+	3.21539i	−0.0695840	+	0.104376i
$950$		0			0
$951$	2.53590	−	9.46410i	0.0822321	−	0.306895i
$952$		0			0
$953$	43.3827	−	11.6244i	1.40530	−	0.376550i	0.525057	−	0.851067i	$-0.324044\pi$
$953$	43.3827	−	11.6244i	1.40530	−	0.376550i	0.880246	+	0.474517i	$0.157377\pi$
$954$		0			0
$955$	−33.4808	−	2.00962i	−1.08341	−	0.0650297i
$956$		0			0
$957$	−9.92820			−0.320933
$958$		0			0
$959$	−45.3564	−	78.5596i	−1.46463	−	2.53682i
$960$		0			0
$961$			23.0000i			0.741935i
$962$		0			0
$963$	−2.66025	+	2.66025i	−0.0857255	+	0.0857255i
$964$		0			0
$965$	10.4282	+	6.88526i	0.335696	+	0.221644i
$966$		0			0
$967$			37.6077i			1.20938i	0.796460	+	0.604691i	$0.206703\pi$
$967$			37.6077i			1.20938i	−0.796460	+	0.604691i	$0.793297\pi$
$968$		0			0
$969$	−27.3564	+	7.33013i	−0.878814	+	0.235478i
$970$		0			0
$971$	−2.89230	+	5.00962i	−0.0928185	+	0.160766i	−0.908696	−	0.417458i	$-0.862921\pi$
$971$	−2.89230	+	5.00962i	−0.0928185	+	0.160766i	0.815878	+	0.578225i	$0.196254\pi$
$972$		0			0
$973$	20.0885	−	11.5981i	0.644006	−	0.371817i
$974$		0			0
$975$	−34.7224	+	2.69615i	−1.11201	+	0.0863460i
$976$		0			0
$977$	−11.7679	+	6.79423i	−0.376490	+	0.217367i	−0.676290	−	0.736635i	$-0.736413\pi$
$977$	−11.7679	+	6.79423i	−0.376490	+	0.217367i	0.299800	+	0.954002i	$0.403080\pi$
$978$		0			0
$979$	4.55256	−	7.88526i	0.145500	−	0.252014i
$980$		0			0
$981$	10.4641	−	2.80385i	0.334093	−	0.0895200i
$982$		0			0
$983$		−	22.3923i		−	0.714204i	−0.934065	−	0.357102i	$-0.883765\pi$
$983$		−	22.3923i		−	0.714204i	0.934065	−	0.357102i	$-0.116235\pi$
$984$		0			0
$985$	14.4282	+	9.52628i	0.459721	+	0.303533i
$986$		0			0
$987$	17.8564	−	17.8564i	0.568376	−	0.568376i
$988$		0			0
$989$			26.8564i			0.853984i
$990$		0			0
$991$	13.8205	+	23.9378i	0.439023	+	0.760410i	0.997614	−	0.0690329i	$-0.0219914\pi$
$991$	13.8205	+	23.9378i	0.439023	+	0.760410i	−0.558591	+	0.829443i	$0.688658\pi$
$992$		0			0
$993$	−56.9090			−1.80595
$994$		0			0
$995$	−19.7679	−	1.18653i	−0.626686	−	0.0376156i
$996$		0			0
$997$	−17.7942	+	4.76795i	−0.563549	+	0.151002i	−0.529336	−	0.848412i	$-0.677559\pi$
$997$	−17.7942	+	4.76795i	−0.563549	+	0.151002i	−0.0342126	+	0.999415i	$0.510892\pi$
$998$		0			0
$999$	−9.59808	+	35.8205i	−0.303670	+	1.13331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bf.b.37.1	✓	4
5.2	odd	4		1300.2.bs.b.193.1		4
5.3	odd	4		260.2.bk.a.193.1	yes	4
5.4	even	2		1300.2.bn.a.557.1		4
13.6	odd	12		260.2.bk.a.97.1	yes	4
65.19	odd	12		1300.2.bs.b.357.1		4
65.32	even	12		1300.2.bn.a.1293.1		4
65.58	even	12	inner	260.2.bf.b.253.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.b.37.1	✓	4	1.1	even	1	trivial
260.2.bf.b.253.1	yes	4	65.58	even	12	inner
260.2.bk.a.97.1	yes	4	13.6	odd	12
260.2.bk.a.193.1	yes	4	5.3	odd	4
1300.2.bn.a.557.1		4	5.4	even	2
1300.2.bn.a.1293.1		4	65.32	even	12
1300.2.bs.b.193.1		4	5.2	odd	4
1300.2.bs.b.357.1		4	65.19	odd	12

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86603 + 0.500000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(2.23205 - 3.86603i) q^{7} +(0.633975 + 0.366025i) q^{9} +O(q^{10})\)	\(q+(1.86603 + 0.500000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(2.23205 - 3.86603i) q^{7} +(0.633975 + 0.366025i) q^{9} +(-2.86603 - 0.767949i) q^{11} +(3.00000 + 2.00000i) q^{13} +(-0.866025 - 4.23205i) q^{15} +(0.866025 + 3.23205i) q^{17} +(1.13397 + 4.23205i) q^{19} +(6.09808 - 6.09808i) q^{21} +(-1.86603 + 6.96410i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(-3.09808 - 3.09808i) q^{27} +(1.50000 - 0.866025i) q^{29} +(5.19615 + 5.19615i) q^{31} +(-4.96410 - 2.86603i) q^{33} +(-9.96410 - 0.598076i) q^{35} +(-4.23205 - 7.33013i) q^{37} +(4.59808 + 5.23205i) q^{39} +(0.669873 - 2.50000i) q^{41} +(3.59808 - 0.964102i) q^{43} +(0.0980762 - 1.63397i) q^{45} +2.92820 q^{47} +(-6.46410 - 11.1962i) q^{49} +6.46410i q^{51} +(-4.46410 + 4.46410i) q^{53} +(1.33013 + 6.50000i) q^{55} +8.46410i q^{57} +(6.33013 - 1.69615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(2.83013 - 1.63397i) q^{63} +(1.00000 - 8.00000i) q^{65} +(-13.6244 + 7.86603i) q^{67} +(-6.96410 + 12.0622i) q^{69} +(-4.59808 + 1.23205i) q^{71} +1.07180i q^{73} +(-7.59808 + 5.96410i) q^{75} +(-9.36603 + 9.36603i) q^{77} +7.46410i q^{79} +(-5.33013 - 9.23205i) q^{81} -10.9282 q^{83} +(5.59808 - 4.96410i) q^{85} +(3.23205 - 0.866025i) q^{87} +(-0.794229 + 2.96410i) q^{89} +(14.4282 - 7.13397i) q^{91} +(7.09808 + 12.2942i) q^{93} +(7.33013 - 6.50000i) q^{95} +(3.69615 + 2.13397i) q^{97} +(-1.53590 - 1.53590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 + 6 * q^9	\( 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9} - 8 q^{11} + 12 q^{13} + 8 q^{19} + 14 q^{21} - 4 q^{23} - 12 q^{25} - 2 q^{27} + 6 q^{29} - 6 q^{33} - 26 q^{35} - 10 q^{37} + 8 q^{39} + 20 q^{41} + 4 q^{43} - 10 q^{45} - 16 q^{47} - 12 q^{49} - 4 q^{53} - 12 q^{55} + 8 q^{59} + 18 q^{61} - 6 q^{63} + 4 q^{65} - 6 q^{67} - 14 q^{69} - 8 q^{71} - 20 q^{75} - 34 q^{77} - 4 q^{81} - 16 q^{83} + 12 q^{85} + 6 q^{87} + 28 q^{89} + 30 q^{91} + 18 q^{93} + 12 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 + 6 * q^9 - 8 * q^11 + 12 * q^13 + 8 * q^19 + 14 * q^21 - 4 * q^23 - 12 * q^25 - 2 * q^27 + 6 * q^29 - 6 * q^33 - 26 * q^35 - 10 * q^37 + 8 * q^39 + 20 * q^41 + 4 * q^43 - 10 * q^45 - 16 * q^47 - 12 * q^49 - 4 * q^53 - 12 * q^55 + 8 * q^59 + 18 * q^61 - 6 * q^63 + 4 * q^65 - 6 * q^67 - 14 * q^69 - 8 * q^71 - 20 * q^75 - 34 * q^77 - 4 * q^81 - 16 * q^83 + 12 * q^85 + 6 * q^87 + 28 * q^89 + 30 * q^91 + 18 * q^93 + 12 * q^95 - 6 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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