LMFDB - Embedded newform 260.2.bk.a.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(33,260)]

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, 9, 11]))

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

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

chi := DirichletCharacter("260.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bk (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:	$1$
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			193.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.193
Dual form			260.2.bk.a.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 1.86603i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 1.86603i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +(-2.86603 - 0.767949i) q^{11} +(-2.00000 + 3.00000i) q^{13} +(2.86603 - 3.23205i) q^{15} +(3.23205 - 0.866025i) q^{17} +(-1.13397 - 4.23205i) q^{19} +(6.09808 - 6.09808i) q^{21} +(-6.96410 - 1.86603i) q^{23} +(3.00000 + 4.00000i) q^{25} +(-3.09808 + 3.09808i) q^{27} +(-1.50000 + 0.866025i) q^{29} +(5.19615 + 5.19615i) q^{31} +(2.86603 - 4.96410i) q^{33} +(5.50000 + 8.33013i) q^{35} +(-7.33013 + 4.23205i) q^{37} +(-4.59808 - 5.23205i) q^{39} +(0.669873 - 2.50000i) q^{41} +(0.964102 + 3.59808i) q^{43} +(0.901924 + 1.36603i) q^{45} -2.92820i q^{47} +(6.46410 + 11.1962i) q^{49} +6.46410i q^{51} +(-4.46410 - 4.46410i) q^{53} +(4.96410 + 4.40192i) q^{55} +8.46410 q^{57} +(-6.33013 + 1.69615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(1.63397 + 2.83013i) q^{63} +(7.00000 - 4.00000i) q^{65} +(7.86603 + 13.6244i) q^{67} +(6.96410 - 12.0622i) q^{69} +(-4.59808 + 1.23205i) q^{71} -1.07180 q^{73} +(-8.96410 + 3.59808i) q^{75} +(9.36603 + 9.36603i) q^{77} -7.46410i q^{79} +(-5.33013 - 9.23205i) q^{81} -10.9282i q^{83} +(-7.33013 - 1.50000i) q^{85} +(-0.866025 - 3.23205i) q^{87} +(0.794229 - 2.96410i) q^{89} +(14.4282 - 7.13397i) q^{91} +(-12.2942 + 7.09808i) q^{93} +(-1.96410 + 9.59808i) q^{95} +(2.13397 - 3.69615i) q^{97} +(1.53590 + 1.53590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 8 * q^5 - 12 * q^7 - 6 * q^9	$ 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9} - 8 q^{11} - 8 q^{13} + 8 q^{15} + 6 q^{17} - 8 q^{19} + 14 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} - 6 q^{29} + 8 q^{33} + 22 q^{35} - 12 q^{37} - 8 q^{39} + 20 q^{41} - 10 q^{43} + 14 q^{45} + 12 q^{49} - 4 q^{53} + 6 q^{55} + 20 q^{57} - 8 q^{59} + 18 q^{61} + 10 q^{63} + 28 q^{65} + 28 q^{67} + 14 q^{69} - 8 q^{71} - 32 q^{73} - 22 q^{75} + 34 q^{77} - 4 q^{81} - 12 q^{85} - 28 q^{89} + 30 q^{91} - 18 q^{93} + 6 q^{95} + 12 q^{97} + 20 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 8 * q^5 - 12 * q^7 - 6 * q^9 - 8 * q^11 - 8 * q^13 + 8 * q^15 + 6 * q^17 - 8 * q^19 + 14 * q^21 - 14 * q^23 + 12 * q^25 - 2 * q^27 - 6 * q^29 + 8 * q^33 + 22 * q^35 - 12 * q^37 - 8 * q^39 + 20 * q^41 - 10 * q^43 + 14 * q^45 + 12 * q^49 - 4 * q^53 + 6 * q^55 + 20 * q^57 - 8 * q^59 + 18 * q^61 + 10 * q^63 + 28 * q^65 + 28 * q^67 + 14 * q^69 - 8 * q^71 - 32 * q^73 - 22 * q^75 + 34 * q^77 - 4 * q^81 - 12 * q^85 - 28 * q^89 + 30 * q^91 - 18 * q^93 + 6 * q^95 + 12 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.500000	+	1.86603i	−0.288675	+	1.07735i	0.657437	+	0.753510i	$0.271641\pi$
$3$	−0.500000	+	1.86603i	−0.288675	+	1.07735i	−0.946112	+	0.323840i	$0.895026\pi$
$4$		0			0
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$	−3.86603	−	2.23205i	−1.46122	−	0.843636i	−0.462152	−	0.886801i	$-0.652923\pi$
$7$	−3.86603	−	2.23205i	−1.46122	−	0.843636i	−0.999068	+	0.0431647i	$0.986256\pi$
$8$		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
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$14$		0			0
$15$	2.86603	−	3.23205i	0.740005	−	0.834512i
$16$		0			0
$17$	3.23205	−	0.866025i	0.783887	−	0.210042i	0.155390	−	0.987853i	$-0.450337\pi$
$17$	3.23205	−	0.866025i	0.783887	−	0.210042i	0.628498	+	0.777811i	$0.283670\pi$
$18$		0			0
$19$	−1.13397	−	4.23205i	−0.260152	−	0.970899i	−0.965152	−	0.261692i	$-0.915720\pi$
$19$	−1.13397	−	4.23205i	−0.260152	−	0.970899i	0.705000	−	0.709207i	$-0.250947\pi$
$20$		0			0
$21$	6.09808	−	6.09808i	1.33071	−	1.33071i
$22$		0			0
$23$	−6.96410	−	1.86603i	−1.45212	−	0.389093i	−0.555357	−	0.831612i	$-0.687418\pi$
$23$	−6.96410	−	1.86603i	−1.45212	−	0.389093i	−0.896759	+	0.442519i	$0.854085\pi$
$24$		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	−0.632764	−	0.774345i	$-0.718080\pi$
$29$	−1.50000	+	0.866025i	−0.278543	+	0.160817i	0.354221	+	0.935162i	$0.384746\pi$
$30$		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
$33$	2.86603	−	4.96410i	0.498911	−	0.864139i
$34$		0			0
$35$	5.50000	+	8.33013i	0.929670	+	1.40805i
$36$		0			0
$37$	−7.33013	+	4.23205i	−1.20507	+	0.695745i	−0.961677	−	0.274184i	$-0.911592\pi$
$37$	−7.33013	+	4.23205i	−1.20507	+	0.695745i	−0.243388	+	0.969929i	$0.578259\pi$
$38$		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
$43$	0.964102	+	3.59808i	0.147024	+	0.548701i	0.999657	+	0.0261910i	$0.00833780\pi$
$43$	0.964102	+	3.59808i	0.147024	+	0.548701i	−0.852633	+	0.522511i	$0.824996\pi$
$44$		0			0
$45$	0.901924	+	1.36603i	0.134451	+	0.203635i
$46$		0			0
$47$		−	2.92820i		−	0.427122i	−0.976930	−	0.213561i	$-0.931494\pi$
$47$		−	2.92820i		−	0.427122i	0.976930	−	0.213561i	$-0.0685063\pi$
$48$		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	0.330585	−	0.943776i	$-0.392754\pi$
$53$	−4.46410	−	4.46410i	−0.613192	−	0.613192i	−0.943776	+	0.330585i	$0.892754\pi$
$54$		0			0
$55$	4.96410	+	4.40192i	0.669359	+	0.593555i
$56$		0			0
$57$	8.46410			1.12110
$58$		0			0
$59$	−6.33013	+	1.69615i	−0.824112	+	0.220820i	−0.646144	−	0.763216i	$-0.723619\pi$
$59$	−6.33013	+	1.69615i	−0.824112	+	0.220820i	−0.177969	+	0.984036i	$0.556953\pi$
$60$		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
$63$	1.63397	+	2.83013i	0.205861	+	0.356562i
$64$		0			0
$65$	7.00000	−	4.00000i	0.868243	−	0.496139i
$66$		0			0
$67$	7.86603	+	13.6244i	0.960988	+	1.66448i	0.720028	+	0.693945i	$0.244129\pi$
$67$	7.86603	+	13.6244i	0.960988	+	1.66448i	0.240960	+	0.970535i	$0.422538\pi$
$68$		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
$73$	−1.07180			−0.125444			−0.0627222	−	0.998031i	$-0.519978\pi$
$73$	−1.07180			−0.125444			−0.0627222	+	0.998031i	$0.519978\pi$
$74$		0			0
$75$	−8.96410	+	3.59808i	−1.03509	+	0.415470i
$76$		0			0
$77$	9.36603	+	9.36603i	1.06736	+	1.06736i
$78$		0			0
$79$		−	7.46410i		−	0.839777i	−0.907576	−	0.419889i	$-0.862069\pi$
$79$		−	7.46410i		−	0.839777i	0.907576	−	0.419889i	$-0.137931\pi$
$80$		0			0
$81$	−5.33013	−	9.23205i	−0.592236	−	1.02578i
$82$		0			0
$83$		−	10.9282i		−	1.19953i	−0.800178	−	0.599763i	$-0.795261\pi$
$83$		−	10.9282i		−	1.19953i	0.800178	−	0.599763i	$-0.204739\pi$
$84$		0			0
$85$	−7.33013	−	1.50000i	−0.795064	−	0.162698i
$86$		0			0
$87$	−0.866025	−	3.23205i	−0.0928477	−	0.346512i
$88$		0			0
$89$	0.794229	−	2.96410i	0.0841881	−	0.314194i	−0.910971	−	0.412470i	$-0.864666\pi$
$89$	0.794229	−	2.96410i	0.0841881	−	0.314194i	0.995159	+	0.0982760i	$0.0313328\pi$
$90$		0			0
$91$	14.4282	−	7.13397i	1.51249	−	0.747844i
$92$		0			0
$93$	−12.2942	+	7.09808i	−1.27485	+	0.736036i
$94$		0			0
$95$	−1.96410	+	9.59808i	−0.201513	+	0.984742i
$96$		0			0
$97$	2.13397	−	3.69615i	0.216672	−	0.375287i	−0.737116	−	0.675766i	$-0.763813\pi$
$97$	2.13397	−	3.69615i	0.216672	−	0.375287i	0.953789	+	0.300478i	$0.0971464\pi$
$98$		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	$-0.767837\pi$
$103$	−0.803848	+	0.803848i	−0.0792055	+	0.0792055i	0.666394	+	0.745600i	$0.267837\pi$
$104$		0			0
$105$	−18.2942	+	6.09808i	−1.78533	+	0.595111i
$106$		0			0
$107$	4.96410	+	1.33013i	0.479898	+	0.128588i	0.490655	−	0.871354i	$-0.336758\pi$
$107$	4.96410	+	1.33013i	0.479898	+	0.128588i	−0.0107572	+	0.999942i	$0.503424\pi$
$108$		0			0
$109$	−10.4641	+	10.4641i	−1.00228	+	1.00228i	−0.00228176	+	0.999997i	$0.500726\pi$
$109$	−10.4641	+	10.4641i	−1.00228	+	1.00228i	−0.999997	+	0.00228176i	$0.999274\pi$
$110$		0			0
$111$	−4.23205	−	15.7942i	−0.401688	−	1.49912i
$112$		0			0
$113$	4.23205	−	1.13397i	0.398118	−	0.106675i	−0.0542046	−	0.998530i	$-0.517262\pi$
$113$	4.23205	−	1.13397i	0.398118	−	0.106675i	0.452322	+	0.891854i	$0.350596\pi$
$114$		0			0
$115$	12.0622	+	10.6962i	1.12480	+	0.997421i
$116$		0			0
$117$	2.36603	−	1.16987i	0.218739	−	0.108155i
$118$		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
$123$	4.33013	+	2.50000i	0.390434	+	0.225417i
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	0.892305	−	3.33013i	0.0791793	−	0.295501i	−0.914969	−	0.403524i	$-0.867785\pi$
$127$	0.892305	−	3.33013i	0.0791793	−	0.295501i	0.994148	+	0.108023i	$0.0344519\pi$
$128$		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
$133$	−5.06218	+	18.8923i	−0.438946	+	1.63817i
$134$		0			0
$135$	9.29423	−	3.09808i	0.799920	−	0.266640i
$136$		0			0
$137$	−17.5981	−	10.1603i	−1.50351	−	0.868049i	−0.999992	−	0.00406165i	$-0.998707\pi$
$137$	−17.5981	−	10.1603i	−1.50351	−	0.868049i	−0.503513	−	0.863987i	$-0.667960\pi$
$138$		0			0
$139$	−4.50000	−	2.59808i	−0.381685	−	0.220366i	0.296866	−	0.954919i	$-0.404058\pi$
$139$	−4.50000	−	2.59808i	−0.381685	−	0.220366i	−0.678551	+	0.734553i	$0.737392\pi$
$140$		0			0
$141$	5.46410	+	1.46410i	0.460160	+	0.123300i
$142$		0			0
$143$	8.03590	−	7.06218i	0.671996	−	0.590569i
$144$		0			0
$145$	3.86603	−	0.232051i	0.321056	−	0.0192708i
$146$		0			0
$147$	−24.1244	+	6.46410i	−1.98974	+	0.533150i
$148$		0			0
$149$	5.33013	+	19.8923i	0.436661	+	1.62964i	0.737060	+	0.675827i	$0.236214\pi$
$149$	5.33013	+	19.8923i	0.436661	+	1.62964i	−0.300399	+	0.953814i	$0.597120\pi$
$150$		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
$153$	−2.36603	−	0.633975i	−0.191282	−	0.0512538i
$154$		0			0
$155$	−5.19615	−	15.5885i	−0.417365	−	1.25210i
$156$		0			0
$157$	−0.464102	+	0.464102i	−0.0370393	+	0.0370393i	−0.725384	−	0.688345i	$-0.758338\pi$
$157$	−0.464102	+	0.464102i	−0.0370393	+	0.0370393i	0.688345	+	0.725384i	$0.258338\pi$
$158$		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
$163$	3.59808	−	6.23205i	0.281823	−	0.488132i	−0.690011	−	0.723799i	$-0.742394\pi$
$163$	3.59808	−	6.23205i	0.281823	−	0.488132i	0.971834	+	0.235667i	$0.0757275\pi$
$164$		0			0
$165$	−10.6962	+	7.06218i	−0.832694	+	0.549790i
$166$		0			0
$167$	9.99038	−	5.76795i	0.773079	−	0.446337i	−0.0608930	−	0.998144i	$-0.519395\pi$
$167$	9.99038	−	5.76795i	0.773079	−	0.446337i	0.833972	+	0.551807i	$0.186061\pi$
$168$		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
$173$	−6.23205	−	23.2583i	−0.473814	−	1.76830i	−0.625871	−	0.779926i	$-0.715256\pi$
$173$	−6.23205	−	23.2583i	−0.473814	−	1.76830i	0.152057	−	0.988372i	$-0.451410\pi$
$174$		0			0
$175$	−2.66987	−	22.1603i	−0.201823	−	1.67516i
$176$		0			0
$177$		−	12.6603i		−	0.951603i
$178$		0			0
$179$	0.0358984	+	0.0621778i	0.00268317	+	0.00464739i	0.867364	−	0.497675i	$-0.165813\pi$
$179$	0.0358984	+	0.0621778i	0.00268317	+	0.00464739i	−0.864681	+	0.502322i	$0.832479\pi$
$180$		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
$185$	18.8923	−	1.13397i	1.38899	−	0.0833715i
$186$		0			0
$187$	−9.92820			−0.726022
$188$		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
$193$	−2.79423	−	4.83975i	−0.201133	−	0.348373i	0.747761	−	0.663968i	$-0.231129\pi$
$193$	−2.79423	−	4.83975i	−0.201133	−	0.348373i	−0.948894	+	0.315596i	$0.897796\pi$
$194$		0			0
$195$	3.96410	+	15.0622i	0.283875	+	1.07862i
$196$		0			0
$197$	3.86603	+	6.69615i	0.275443	+	0.477081i	0.970247	−	0.242118i	$-0.0778422\pi$
$197$	3.86603	+	6.69615i	0.275443	+	0.477081i	−0.694804	+	0.719199i	$0.744509\pi$
$198$		0			0
$199$	−4.42820	+	7.66987i	−0.313907	+	0.543703i	−0.979205	−	0.202875i	$-0.934971\pi$
$199$	−4.42820	+	7.66987i	−0.313907	+	0.543703i	0.665298	+	0.746578i	$0.268305\pi$
$200$		0			0
$201$	−29.3564	+	7.86603i	−2.07064	+	0.554827i
$202$		0			0
$203$	7.73205			0.542684
$204$		0			0
$205$	−3.83975	+	4.33013i	−0.268179	+	0.302429i
$206$		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
$213$		−	9.19615i		−	0.630110i
$214$		0			0
$215$	1.66987	−	8.16025i	0.113884	−	0.556525i
$216$		0			0
$217$	−8.49038	−	31.6865i	−0.576365	−	2.15102i
$218$		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
$223$	7.33013	−	4.23205i	0.490862	−	0.283399i	−0.234070	−	0.972220i	$-0.575205\pi$
$223$	7.33013	−	4.23205i	0.490862	−	0.283399i	0.724932	+	0.688821i	$0.241871\pi$
$224$		0			0
$225$	−0.437822	−	3.63397i	−0.0291881	−	0.242265i
$226$		0			0
$227$	−3.59808	+	6.23205i	−0.238813	+	0.413636i	−0.960374	−	0.278715i	$-0.910092\pi$
$227$	−3.59808	+	6.23205i	−0.238813	+	0.413636i	0.721561	+	0.692351i	$0.243425\pi$
$228$		0			0
$229$	13.9282	+	13.9282i	0.920402	+	0.920402i	0.997058	−	0.0766560i	$-0.0244243\pi$
$229$	13.9282	+	13.9282i	0.920402	+	0.920402i	−0.0766560	+	0.997058i	$0.524424\pi$
$230$		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	$-0.991603\pi$
$233$	−14.8564	+	14.8564i	−0.973276	+	0.973276i	0.0263765	+	0.999652i	$0.491603\pi$
$234$		0			0
$235$	−2.92820	+	5.85641i	−0.191015	+	0.382030i
$236$		0			0
$237$	13.9282	+	3.73205i	0.904734	+	0.242423i
$238$		0			0
$239$	−0.660254	+	0.660254i	−0.0427083	+	0.0427083i	−0.728138	−	0.685430i	$-0.759614\pi$
$239$	−0.660254	+	0.660254i	−0.0427083	+	0.0427083i	0.685430	+	0.728138i	$0.259614\pi$
$240$		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
$243$	7.19615	−	1.92820i	0.461633	−	0.123694i
$244$		0			0
$245$	−1.73205	−	28.8564i	−0.110657	−	1.84357i
$246$		0			0
$247$	14.9641	+	5.06218i	0.952143	+	0.322099i
$248$		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
$253$	18.5263	+	10.6962i	1.16474	+	0.672461i
$254$		0			0
$255$	6.46410	−	12.9282i	0.404798	−	0.809595i
$256$		0			0
$257$	−2.62436	+	9.79423i	−0.163703	+	0.610947i	0.834499	+	0.551009i	$0.185757\pi$
$257$	−2.62436	+	9.79423i	−0.163703	+	0.610947i	−0.998202	+	0.0599382i	$0.980910\pi$
$258$		0			0
$259$	37.7846			2.34782
$260$		0			0
$261$	1.26795			0.0784841
$262$		0			0
$263$	−6.89230	+	25.7224i	−0.424998	+	1.58611i	0.338930	+	0.940812i	$0.389935\pi$
$263$	−6.89230	+	25.7224i	−0.424998	+	1.58611i	−0.763928	+	0.645302i	$0.776732\pi$
$264$		0			0
$265$	4.46410	+	13.3923i	0.274228	+	0.822683i
$266$		0			0
$267$	5.13397	+	2.96410i	0.314194	+	0.181400i
$268$		0			0
$269$	−18.8205	−	10.8660i	−1.14751	−	0.662513i	−0.199228	−	0.979953i	$-0.563844\pi$
$269$	−18.8205	−	10.8660i	−1.14751	−	0.662513i	−0.948278	+	0.317440i	$0.897177\pi$
$270$		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
$273$	6.09808	+	30.4904i	0.369072	+	1.84536i
$274$		0			0
$275$	−5.52628	−	13.7679i	−0.333247	−	0.830239i
$276$		0			0
$277$	−6.23205	+	1.66987i	−0.374448	+	0.100333i	−0.441134	−	0.897441i	$-0.645424\pi$
$277$	−6.23205	+	1.66987i	−0.374448	+	0.100333i	0.0666868	+	0.997774i	$0.478757\pi$
$278$		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
$283$	1.03590	+	0.277568i	0.0615778	+	0.0164997i	0.289476	−	0.957185i	$-0.406519\pi$
$283$	1.03590	+	0.277568i	0.0615778	+	0.0164997i	−0.227899	+	0.973685i	$0.573185\pi$
$284$		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
$293$	12.2583	−	21.2321i	0.716139	−	1.24039i	−0.246379	−	0.969174i	$-0.579241\pi$
$293$	12.2583	−	21.2321i	0.716139	−	1.24039i	0.962518	−	0.271216i	$-0.0874258\pi$
$294$		0			0
$295$	14.3564	+	2.93782i	0.835862	+	0.171047i
$296$		0			0
$297$	11.2583	−	6.50000i	0.653275	−	0.377168i
$298$		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
$303$	3.40192	+	12.6962i	0.195435	+	0.729375i
$304$		0			0
$305$	−16.7942	+	11.0885i	−0.961635	+	0.634923i
$306$		0			0
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		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	0.260863	−	0.965376i	$-0.415993\pi$
$313$	−12.4641	−	12.4641i	−0.704513	−	0.704513i	−0.965376	+	0.260863i	$0.915993\pi$
$314$		0			0
$315$	−0.437822	−	7.29423i	−0.0246685	−	0.410983i
$316$		0			0
$317$	−5.07180			−0.284860			−0.142430	−	0.989805i	$-0.545492\pi$
$317$	−5.07180			−0.284860			−0.142430	+	0.989805i	$0.545492\pi$
$318$		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
$323$	−7.33013	−	12.6962i	−0.407859	−	0.706433i
$324$		0			0
$325$	−18.0000	+	1.00000i	−0.998460	+	0.0554700i
$326$		0			0
$327$	−14.2942	−	24.7583i	−0.790473	−	1.36914i
$328$		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
$333$	6.19615			0.339547
$334$		0			0
$335$	−2.10770	−	35.1147i	−0.115156	−	1.91852i
$336$		0			0
$337$	−2.07180	−	2.07180i	−0.112858	−	0.112858i	0.648423	−	0.761281i	$-0.275429\pi$
$337$	−2.07180	−	2.07180i	−0.112858	−	0.112858i	−0.761281	+	0.648423i	$0.775429\pi$
$338$		0			0
$339$			8.46410i			0.459707i
$340$		0			0
$341$	−10.9019	−	18.8827i	−0.590372	−	1.02255i
$342$		0			0
$343$		−	26.4641i		−	1.42893i
$344$		0			0
$345$	−25.9904	+	17.1603i	−1.39928	+	0.923877i
$346$		0			0
$347$	3.42820	+	12.7942i	0.184036	+	0.686830i	0.994835	+	0.101506i	$0.0323661\pi$
$347$	3.42820	+	12.7942i	0.184036	+	0.686830i	−0.810799	+	0.585324i	$0.800967\pi$
$348$		0			0
$349$	−6.13397	+	22.8923i	−0.328344	+	1.22540i	0.582563	+	0.812786i	$0.302050\pi$
$349$	−6.13397	+	22.8923i	−0.328344	+	1.22540i	−0.910907	+	0.412611i	$0.864617\pi$
$350$		0			0
$351$	−3.09808	−	15.4904i	−0.165363	−	0.826815i
$352$		0			0
$353$	−3.06218	+	1.76795i	−0.162983	+	0.0940984i	−0.579273	−	0.815134i	$-0.696664\pi$
$353$	−3.06218	+	1.76795i	−0.162983	+	0.0940984i	0.416290	+	0.909232i	$0.363330\pi$
$354$		0			0
$355$	10.4282	+	2.13397i	0.553472	+	0.113260i
$356$		0			0
$357$	14.4282	−	24.9904i	0.763621	−	1.32263i
$358$		0			0
$359$	2.80385	+	2.80385i	0.147981	+	0.147981i	0.777216	−	0.629234i	$-0.216631\pi$
$359$	2.80385	+	2.80385i	0.147981	+	0.147981i	−0.629234	+	0.777216i	$0.716631\pi$
$360$		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
$367$	2.96410	+	0.794229i	0.154725	+	0.0414584i	0.335350	−	0.942094i	$-0.391145\pi$
$367$	2.96410	+	0.794229i	0.154725	+	0.0414584i	−0.180625	+	0.983552i	$0.557812\pi$
$368$		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
$373$	15.6962	−	4.20577i	0.812716	−	0.217767i	0.171557	−	0.985174i	$-0.445120\pi$
$373$	15.6962	−	4.20577i	0.812716	−	0.217767i	0.641159	+	0.767408i	$0.278454\pi$
$374$		0			0
$375$	21.5263	+	1.76795i	1.11161	+	0.0912965i
$376$		0			0
$377$	0.401924	−	6.23205i	0.0207001	−	0.320967i
$378$		0			0
$379$	−2.59808	−	0.696152i	−0.133454	−	0.0357589i	0.191474	−	0.981498i	$-0.438673\pi$
$379$	−2.59808	−	0.696152i	−0.133454	−	0.0357589i	−0.324928	+	0.945739i	$0.605340\pi$
$380$		0			0
$381$	5.76795	+	3.33013i	0.295501	+	0.170608i
$382$		0			0
$383$	28.1147	+	16.2321i	1.43660	+	0.829419i	0.997611	−	0.0690756i	$-0.0220050\pi$
$383$	28.1147	+	16.2321i	1.43660	+	0.829419i	0.438985	+	0.898495i	$0.355338\pi$
$384$		0			0
$385$	−9.36603	−	28.0981i	−0.477337	−	1.43201i
$386$		0			0
$387$	0.705771	−	2.63397i	0.0358764	−	0.133892i
$388$		0			0
$389$	−28.9282			−1.46672			−0.733359	−	0.679842i	$-0.762049\pi$
$389$	−28.9282			−1.46672			−0.733359	+	0.679842i	$0.762049\pi$
$390$		0			0
$391$	−24.1244			−1.22002
$392$		0			0
$393$	10.9282	−	40.7846i	0.551255	−	2.05731i
$394$		0			0
$395$	−7.46410	+	14.9282i	−0.375560	+	0.751119i
$396$		0			0
$397$	−8.13397	−	4.69615i	−0.408232	−	0.235693i	0.281798	−	0.959474i	$-0.409069\pi$
$397$	−8.13397	−	4.69615i	−0.408232	−	0.235693i	−0.690030	+	0.723781i	$0.742403\pi$
$398$		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
$403$	−25.9808	+	5.19615i	−1.29419	+	0.258839i
$404$		0			0
$405$	1.42820	+	23.7942i	0.0709680	+	1.18234i
$406$		0			0
$407$	24.2583	−	6.50000i	1.20244	−	0.322193i
$408$		0			0
$409$	−0.526279	−	1.96410i	−0.0260228	−	0.0971186i	0.951693	−	0.307051i	$-0.0993422\pi$
$409$	−0.526279	−	1.96410i	−0.0260228	−	0.0971186i	−0.977716	+	0.209932i	$0.932676\pi$
$410$		0			0
$411$	27.7583	−	27.7583i	1.36922	−	1.36922i
$412$		0			0
$413$	28.2583	+	7.57180i	1.39050	+	0.372584i
$414$		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	$0.681565\pi$
$419$	−31.5000	+	18.1865i	−1.53888	+	0.888470i	−0.998905	+	0.0467865i	$0.985102\pi$
$420$		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
$423$	−1.07180	+	1.85641i	−0.0521125	+	0.0902616i
$424$		0			0
$425$	13.1603	+	10.3301i	0.638366	+	0.501085i
$426$		0			0
$427$	−34.7942	+	20.0885i	−1.68381	+	0.972149i
$428$		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
$433$	−5.55256	−	20.7224i	−0.266839	−	0.995857i	−0.961115	−	0.276148i	$-0.910942\pi$
$433$	−5.55256	−	20.7224i	−0.266839	−	0.995857i	0.694276	−	0.719709i	$-0.255725\pi$
$434$		0			0
$435$	−1.50000	+	7.33013i	−0.0719195	+	0.351453i
$436$		0			0
$437$			31.5885i			1.51108i
$438$		0			0
$439$	6.96410	+	12.0622i	0.332378	+	0.575696i	0.982978	−	0.183725i	$-0.0588156\pi$
$439$	6.96410	+	12.0622i	0.332378	+	0.575696i	−0.650599	+	0.759421i	$0.725482\pi$
$440$		0			0
$441$		−	9.46410i		−	0.450672i
$442$		0			0
$443$	15.5885	+	15.5885i	0.740630	+	0.740630i	0.972699	−	0.232069i	$-0.0745496\pi$
$443$	15.5885	+	15.5885i	0.740630	+	0.740630i	−0.232069	+	0.972699i	$0.574550\pi$
$444$		0			0
$445$	−4.55256	+	5.13397i	−0.215812	+	0.243374i
$446$		0			0
$447$	−39.7846			−1.88175
$448$		0			0
$449$	−20.7942	+	5.57180i	−0.981340	+	0.262949i	−0.713609	−	0.700544i	$-0.752941\pi$
$449$	−20.7942	+	5.57180i	−0.981340	+	0.262949i	−0.267731	+	0.963494i	$0.586274\pi$
$450$		0			0
$451$	−3.83975	+	6.65064i	−0.180807	+	0.313166i
$452$		0			0
$453$	−5.09808	−	8.83013i	−0.239529	−	0.414876i
$454$		0			0
$455$	−35.9904	−	0.160254i	−1.68726	−	0.00751283i
$456$		0			0
$457$	8.79423	+	15.2321i	0.411377	+	0.712525i	0.995041	−	0.0994701i	$-0.0317148\pi$
$457$	8.79423	+	15.2321i	0.411377	+	0.712525i	−0.583664	+	0.811995i	$0.698381\pi$
$458$		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
$463$	−42.3923			−1.97014			−0.985069	−	0.172161i	$-0.944925\pi$
$463$	−42.3923			−1.97014			−0.985069	+	0.172161i	$0.944925\pi$
$464$		0			0
$465$	31.6865	−	1.90192i	1.46943	−	0.0881996i
$466$		0			0
$467$	−0.660254	−	0.660254i	−0.0305529	−	0.0305529i	0.691665	−	0.722218i	$-0.256877\pi$
$467$	−0.660254	−	0.660254i	−0.0305529	−	0.0305529i	−0.722218	+	0.691665i	$0.756877\pi$
$468$		0			0
$469$		−	70.2295i		−	3.24290i
$470$		0			0
$471$	−0.633975	−	1.09808i	−0.0292120	−	0.0505967i
$472$		0			0
$473$		−	11.0526i		−	0.508197i
$474$		0			0
$475$	13.5263	−	17.2321i	0.620628	−	0.790661i
$476$		0			0
$477$	1.19615	+	4.46410i	0.0547681	+	0.204397i
$478$		0			0
$479$	−4.86603	+	18.1603i	−0.222334	+	0.829763i	0.761121	+	0.648610i	$0.224650\pi$
$479$	−4.86603	+	18.1603i	−0.222334	+	0.829763i	−0.983455	+	0.181153i	$0.942017\pi$
$480$		0			0
$481$	1.96410	−	30.4545i	0.0895553	−	1.38860i
$482$		0			0
$483$	−53.8468	+	31.0885i	−2.45011	+	1.41457i
$484$		0			0
$485$	−7.96410	+	5.25833i	−0.361631	+	0.238768i
$486$		0			0
$487$	14.7942	−	25.6244i	0.670390	−	1.16115i	−0.307403	−	0.951579i	$-0.599460\pi$
$487$	14.7942	−	25.6244i	0.670390	−	1.16115i	0.977793	−	0.209571i	$-0.0672067\pi$
$488$		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
$497$	20.5263	+	5.50000i	0.920729	+	0.246709i
$498$		0			0
$499$	23.7321	−	23.7321i	1.06239	−	1.06239i	0.0644731	−	0.997919i	$-0.479463\pi$
$499$	23.7321	−	23.7321i	1.06239	−	1.06239i	0.997919	−	0.0644731i	$-0.0205367\pi$
$500$		0			0
$501$	5.76795	+	21.5263i	0.257693	+	0.961723i
$502$		0			0
$503$	24.3564	−	6.52628i	1.08600	−	0.290992i	0.328947	−	0.944348i	$-0.393306\pi$
$503$	24.3564	−	6.52628i	1.08600	−	0.290992i	0.757051	+	0.653356i	$0.226639\pi$
$504$		0			0
$505$	−15.1865	+	0.911543i	−0.675792	+	0.0405631i
$506$		0			0
$507$	24.8923	−	3.33013i	1.10551	−	0.147896i
$508$		0			0
$509$	25.4545	+	6.82051i	1.12825	+	0.302314i	0.774218	−	0.632919i	$-0.218144\pi$
$509$	25.4545	+	6.82051i	1.12825	+	0.302314i	0.354032	+	0.935233i	$0.384810\pi$
$510$		0			0
$511$	4.14359	+	2.39230i	0.183302	+	0.105829i
$512$		0			0
$513$	16.6244	+	9.59808i	0.733983	+	0.423765i
$514$		0			0
$515$	2.41154	−	0.803848i	0.106265	−	0.0354218i
$516$		0			0
$517$	−2.24871	+	8.39230i	−0.0988982	+	0.369093i
$518$		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
$523$	4.03590	−	15.0622i	0.176478	−	0.658623i	−0.819818	−	0.572625i	$-0.805925\pi$
$523$	4.03590	−	15.0622i	0.176478	−	0.658623i	0.996295	−	0.0859985i	$-0.0274080\pi$
$524$		0			0
$525$	42.6865	+	6.09808i	1.86299	+	0.266142i
$526$		0			0
$527$	21.2942	+	12.2942i	0.927591	+	0.535545i
$528$		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
$533$	6.16025	+	7.00962i	0.266830	+	0.303620i
$534$		0			0
$535$	−8.59808	−	7.62436i	−0.371727	−	0.329630i
$536$		0			0
$537$	−0.133975	+	0.0358984i	−0.00578143	+	0.00154913i
$538$		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
$543$	−16.9282	−	4.53590i	−0.726459	−	0.194654i
$544$		0			0
$545$	31.3923	−	10.4641i	1.34470	−	0.448233i
$546$		0			0
$547$	24.1244	−	24.1244i	1.03148	−	1.03148i	0.0319949	−	0.999488i	$-0.489814\pi$
$547$	24.1244	−	24.1244i	1.03148	−	1.03148i	0.999488	−	0.0319949i	$-0.0101860\pi$
$548$		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
$553$	−16.6603	+	28.8564i	−0.708466	+	1.22710i
$554$		0			0
$555$	−7.33013	+	35.8205i	−0.311147	+	1.52050i
$556$		0			0
$557$	4.66987	−	2.69615i	0.197869	−	0.114240i	−0.397792	−	0.917476i	$-0.630223\pi$
$557$	4.66987	−	2.69615i	0.197869	−	0.114240i	0.595661	+	0.803236i	$0.296890\pi$
$558$		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
$563$	−4.10770	−	15.3301i	−0.173119	−	0.646088i	−0.996864	−	0.0791284i	$-0.974786\pi$
$563$	−4.10770	−	15.3301i	−0.173119	−	0.646088i	0.823746	−	0.566959i	$-0.191880\pi$
$564$		0			0
$565$	−9.59808	−	1.96410i	−0.403794	−	0.0826304i
$566$		0			0
$567$			47.5885i			1.99853i
$568$		0			0
$569$	−15.8205	−	27.4019i	−0.663230	−	1.14875i	−0.979762	−	0.200166i	$-0.935852\pi$
$569$	−15.8205	−	27.4019i	−0.663230	−	1.14875i	0.316532	−	0.948582i	$-0.397482\pi$
$570$		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
$575$	−13.4282	−	33.4545i	−0.559995	−	1.39515i
$576$		0			0
$577$	−20.7846			−0.865275			−0.432637	−	0.901568i	$-0.642417\pi$
$577$	−20.7846			−0.865275			−0.432637	+	0.901568i	$0.642417\pi$
$578$		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
$583$	9.36603	+	16.2224i	0.387901	+	0.671864i
$584$		0			0
$585$	−5.90192	−	0.0262794i	−0.244015	−	0.00108652i
$586$		0			0
$587$	5.72243	+	9.91154i	0.236190	+	0.409093i	0.959618	−	0.281307i	$-0.0907679\pi$
$587$	5.72243	+	9.91154i	0.236190	+	0.409093i	−0.723428	+	0.690400i	$0.757435\pi$
$588$		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
$593$	−17.0718			−0.701055			−0.350527	−	0.936553i	$-0.613998\pi$
$593$	−17.0718			−0.701055			−0.350527	+	0.936553i	$0.613998\pi$
$594$		0			0
$595$	24.9904	+	22.1603i	1.02451	+	0.908482i
$596$		0			0
$597$	−12.0981	−	12.0981i	−0.495141	−	0.495141i
$598$		0			0
$599$			12.2487i			0.500469i	0.968185	+	0.250234i	$0.0805077\pi$
$599$			12.2487i			0.500469i	−0.968185	+	0.250234i	$0.919492\pi$
$600$		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
$603$		−	11.5167i		−	0.468995i
$604$		0			0
$605$	2.70577	+	4.09808i	0.110005	+	0.166610i
$606$		0			0
$607$	9.96410	+	37.1865i	0.404430	+	1.50935i	0.805104	+	0.593134i	$0.202110\pi$
$607$	9.96410	+	37.1865i	0.404430	+	1.50935i	−0.400673	+	0.916221i	$0.631224\pi$
$608$		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
$613$	15.1865	−	8.76795i	0.613378	−	0.354134i	−0.160908	−	0.986969i	$-0.551442\pi$
$613$	15.1865	−	8.76795i	0.613378	−	0.354134i	0.774286	+	0.632835i	$0.218109\pi$
$614$		0			0
$615$	−6.16025	−	9.33013i	−0.248405	−	0.376227i
$616$		0			0
$617$	−6.79423	+	11.7679i	−0.273525	+	0.473760i	−0.969762	−	0.244053i	$-0.921523\pi$
$617$	−6.79423	+	11.7679i	−0.273525	+	0.473760i	0.696237	+	0.717812i	$0.254856\pi$
$618$		0			0
$619$	−2.66025	−	2.66025i	−0.106925	−	0.106925i	0.651620	−	0.758545i	$-0.274089\pi$
$619$	−2.66025	−	2.66025i	−0.106925	−	0.106925i	−0.758545	+	0.651620i	$0.774089\pi$
$620$		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
$627$	−24.2583	−	6.50000i	−0.968784	−	0.259585i
$628$		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
$633$	−14.7942	+	3.96410i	−0.588018	+	0.157559i
$634$		0			0
$635$	−5.11474	+	5.76795i	−0.202972	+	0.228894i
$636$		0			0
$637$	−46.5167	−	3.00000i	−1.84306	−	0.118864i
$638$		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
$643$	−22.6699	−	13.0885i	−0.894013	−	0.516158i	−0.0187597	−	0.999824i	$-0.505972\pi$
$643$	−22.6699	−	13.0885i	−0.894013	−	0.516158i	−0.875253	+	0.483666i	$0.839305\pi$
$644$		0			0
$645$	14.3923	+	7.19615i	0.566696	+	0.283348i
$646$		0			0
$647$	2.50000	−	9.33013i	0.0982851	−	0.366805i	−0.899212	−	0.437513i	$-0.855859\pi$
$647$	2.50000	−	9.33013i	0.0982851	−	0.366805i	0.997497	+	0.0707082i	$0.0225259\pi$
$648$		0			0
$649$	19.4449			0.763278
$650$		0			0
$651$	63.3731			2.48379
$652$		0			0
$653$	−10.9449	+	40.8468i	−0.428306	+	1.59846i	0.328291	+	0.944577i	$0.393527\pi$
$653$	−10.9449	+	40.8468i	−0.428306	+	1.59846i	−0.756597	+	0.653882i	$0.773139\pi$
$654$		0			0
$655$	43.7128	+	21.8564i	1.70800	+	0.854000i
$656$		0			0
$657$	0.679492	+	0.392305i	0.0265095	+	0.0153053i
$658$		0			0
$659$	−21.5718	−	12.4545i	−0.840318	−	0.485158i	0.0170544	−	0.999855i	$-0.494571\pi$
$659$	−21.5718	−	12.4545i	−0.840318	−	0.485158i	−0.857372	+	0.514697i	$0.827904\pi$
$660$		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
$663$	−19.3923	−	12.9282i	−0.753135	−	0.502090i
$664$		0			0
$665$	29.0167	−	32.7224i	1.12522	−	1.26892i
$666$		0			0
$667$	12.0622	−	3.23205i	0.467049	−	0.125146i
$668$		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
$673$	−14.6244	−	3.91858i	−0.563727	−	0.151050i	−0.0343092	−	0.999411i	$-0.510923\pi$
$673$	−14.6244	−	3.91858i	−0.563727	−	0.151050i	−0.529418	+	0.848361i	$0.677590\pi$
$674$		0			0
$675$	−21.6865	−	3.09808i	−0.834715	−	0.119245i
$676$		0			0
$677$	34.1769	−	34.1769i	1.31353	−	1.31353i	0.394727	−	0.918798i	$-0.370839\pi$
$677$	34.1769	−	34.1769i	1.31353	−	1.31353i	0.918798	−	0.394727i	$-0.129161\pi$
$678$		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
$683$	−1.33013	+	2.30385i	−0.0508959	+	0.0881543i	−0.890351	−	0.455275i	$-0.849541\pi$
$683$	−1.33013	+	2.30385i	−0.0508959	+	0.0881543i	0.839455	+	0.543429i	$0.182874\pi$
$684$		0			0
$685$	25.0359	+	37.9186i	0.956573	+	1.44879i
$686$		0			0
$687$	−32.9545	+	19.0263i	−1.25729	+	0.725898i
$688$		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
$693$	−2.50962	−	9.36603i	−0.0953325	−	0.355786i
$694$		0			0
$695$	6.40192	+	9.69615i	0.242839	+	0.367796i
$696$		0			0
$697$		−	8.66025i		−	0.328031i
$698$		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
$705$	−9.46410	−	8.39230i	−0.356439	−	0.316072i
$706$		0			0
$707$	−30.3731			−1.14230
$708$		0			0
$709$	−33.7224	+	9.03590i	−1.26647	+	0.339350i	−0.828678	−	0.559725i	$-0.810907\pi$
$709$	−33.7224	+	9.03590i	−1.26647	+	0.339350i	−0.437794	+	0.899075i	$0.644240\pi$
$710$		0			0
$711$	−2.73205	+	4.73205i	−0.102460	+	0.177466i
$712$		0			0
$713$	−26.4904	−	45.8827i	−0.992073	−	1.71832i
$714$		0			0
$715$	−23.1340	+	6.08846i	−0.865162	+	0.227695i
$716$		0			0
$717$	−0.901924	−	1.56218i	−0.0336830	−	0.0583406i
$718$		0			0
$719$	−14.0359	+	24.3109i	−0.523451	+	0.906643i	0.476177	+	0.879350i	$0.342022\pi$
$719$	−14.0359	+	24.3109i	−0.523451	+	0.906643i	−0.999627	+	0.0272936i	$0.991311\pi$
$720$		0			0
$721$	4.90192	−	1.31347i	0.182557	−	0.0489160i
$722$		0			0
$723$	−19.9282			−0.741138
$724$		0			0
$725$	−7.96410	−	3.40192i	−0.295779	−	0.126344i
$726$		0			0
$727$	−2.41154	−	2.41154i	−0.0894392	−	0.0894392i	0.660972	−	0.750411i	$-0.270144\pi$
$727$	−2.41154	−	2.41154i	−0.0894392	−	0.0894392i	−0.750411	+	0.660972i	$0.770144\pi$
$728$		0			0
$729$		−	17.5885i		−	0.651424i
$730$		0			0
$731$	6.23205	+	10.7942i	0.230501	+	0.399239i
$732$		0			0
$733$		−	14.7846i		−	0.546082i	−0.962002	−	0.273041i	$-0.911971\pi$
$733$		−	14.7846i		−	0.546082i	0.962002	−	0.273041i	$-0.0880295\pi$
$734$		0			0
$735$	54.7128	+	11.1962i	2.01811	+	0.412976i
$736$		0			0
$737$	−12.0814	−	45.0885i	−0.445025	−	1.66085i
$738$		0			0
$739$	1.91858	−	7.16025i	0.0705763	−	0.263394i	−0.921618	−	0.388099i	$-0.873132\pi$
$739$	1.91858	−	7.16025i	0.0705763	−	0.263394i	0.992194	+	0.124705i	$0.0397985\pi$
$740$		0			0
$741$	−16.9282	+	25.3923i	−0.621873	+	0.932810i
$742$		0			0
$743$	−10.6699	+	6.16025i	−0.391440	+	0.225998i	−0.682784	−	0.730621i	$-0.739231\pi$
$743$	−10.6699	+	6.16025i	−0.391440	+	0.225998i	0.291344	+	0.956618i	$0.405898\pi$
$744$		0			0
$745$	9.23205	−	45.1147i	0.338236	−	1.65288i
$746$		0			0
$747$	−4.00000	+	6.92820i	−0.146352	+	0.253490i
$748$		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
$757$	−22.1603	−	5.93782i	−0.805428	−	0.215814i	−0.167462	−	0.985878i	$-0.553557\pi$
$757$	−22.1603	−	5.93782i	−0.805428	−	0.215814i	−0.637966	+	0.770065i	$0.720224\pi$
$758$		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
$763$	63.8109	−	17.0981i	2.31011	−	0.618992i
$764$		0			0
$765$	4.09808	+	3.63397i	0.148166	+	0.131387i
$766$		0			0
$767$	7.57180	−	22.3827i	0.273402	−	0.808192i
$768$		0			0
$769$	24.5263	+	6.57180i	0.884440	+	0.236985i	0.672322	−	0.740259i	$-0.265297\pi$
$769$	24.5263	+	6.57180i	0.884440	+	0.236985i	0.212118	+	0.977244i	$0.431964\pi$
$770$		0			0
$771$	−16.9641	−	9.79423i	−0.610947	−	0.352731i
$772$		0			0
$773$	−47.0429	−	27.1603i	−1.69202	−	0.976886i	−0.952888	−	0.303323i	$-0.901904\pi$
$773$	−47.0429	−	27.1603i	−1.69202	−	0.976886i	−0.739129	−	0.673564i	$-0.764763\pi$
$774$		0			0
$775$	−5.19615	+	36.3731i	−0.186651	+	1.30656i
$776$		0			0
$777$	−18.8923	+	70.5070i	−0.677758	+	2.52943i
$778$		0			0
$779$	−11.3397			−0.406289
$780$		0			0
$781$	14.1244			0.505409
$782$		0			0
$783$	1.96410	−	7.33013i	0.0701913	−	0.261957i
$784$		0			0
$785$	1.39230	−	0.464102i	0.0496935	−	0.0165645i
$786$		0			0
$787$	−4.54552	−	2.62436i	−0.162030	−	0.0935482i	0.416792	−	0.909002i	$-0.363154\pi$
$787$	−4.54552	−	2.62436i	−0.162030	−	0.0935482i	−0.578822	+	0.815454i	$0.696488\pi$
$788$		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
$793$	14.3827	+	29.0885i	0.510744	+	1.03296i
$794$		0			0
$795$	−27.2224	+	1.63397i	−0.965480	+	0.0579511i
$796$		0			0
$797$	−18.6244	+	4.99038i	−0.659709	+	0.176768i	−0.573114	−	0.819475i	$-0.694265\pi$
$797$	−18.6244	+	4.99038i	−0.659709	+	0.176768i	−0.0865940	+	0.996244i	$0.527598\pi$
$798$		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
$803$	3.07180	+	0.823085i	0.108401	+	0.0290461i
$804$		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	0.163711	−	0.986508i	$-0.447653\pi$
$809$	31.2846	−	18.0622i	1.09991	−	0.635032i	0.936197	+	0.351476i	$0.114320\pi$
$810$		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
$813$	4.33013	−	7.50000i	0.151864	−	0.263036i
$814$		0			0
$815$	−13.4282	+	8.86603i	−0.470369	+	0.310563i
$816$		0			0
$817$	14.1340	−	8.16025i	0.494485	−	0.285491i
$818$		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
$823$	3.10770	+	11.5981i	0.108327	+	0.404284i	0.998701	−	0.0509463i	$-0.0162237\pi$
$823$	3.10770	+	11.5981i	0.108327	+	0.404284i	−0.890374	+	0.455230i	$0.849557\pi$
$824$		0			0
$825$	28.4545	−	3.42820i	0.990658	−	0.119355i
$826$		0			0
$827$		−	1.85641i		−	0.0645536i	−0.999479	−	0.0322768i	$-0.989724\pi$
$827$		−	1.85641i		−	0.0645536i	0.999479	−	0.0322768i	$-0.0102758\pi$
$828$		0			0
$829$	−9.42820	−	16.3301i	−0.327455	−	0.567169i	0.654551	−	0.756018i	$-0.272858\pi$
$829$	−9.42820	−	16.3301i	−0.327455	−	0.567169i	−0.982006	+	0.188849i	$0.939524\pi$
$830$		0			0
$831$		−	12.4641i		−	0.432375i
$832$		0			0
$833$	30.5885	+	30.5885i	1.05983	+	1.05983i
$834$		0			0
$835$	−25.7487	+	1.54552i	−0.891071	+	0.0534848i
$836$		0			0
$837$	−32.1962			−1.11286
$838$		0			0
$839$	−7.79423	+	2.08846i	−0.269087	+	0.0721016i	−0.390839	−	0.920459i	$-0.627815\pi$
$839$	−7.79423	+	2.08846i	−0.269087	+	0.0721016i	0.121753	+	0.992560i	$0.461149\pi$
$840$		0			0
$841$	−13.0000	+	22.5167i	−0.448276	+	0.776437i
$842$		0			0
$843$	−13.0263	−	22.5622i	−0.448649	−	0.777083i
$844$		0			0
$845$	−2.00000	+	29.0000i	−0.0688021	+	0.997630i
$846$		0			0
$847$	4.90192	+	8.49038i	0.168432	+	0.291733i
$848$		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
$853$	−26.1436			−0.895140			−0.447570	−	0.894249i	$-0.647710\pi$
$853$	−26.1436			−0.895140			−0.447570	+	0.894249i	$0.647710\pi$
$854$		0			0
$855$	4.75833	−	5.36603i	0.162731	−	0.183514i
$856$		0			0
$857$	29.2487	+	29.2487i	0.999117	+	0.999117i	1.00000		0.000882665i	$-0.000280961\pi$
$857$	29.2487	+	29.2487i	0.999117	+	0.999117i	−0.000882665		1.00000i	$0.500281\pi$
$858$		0			0
$859$		−	18.3923i		−	0.627537i	−0.949499	−	0.313769i	$-0.898408\pi$
$859$		−	18.3923i		−	0.627537i	0.949499	−	0.313769i	$-0.101592\pi$
$860$		0			0
$861$	−11.1603	−	19.3301i	−0.380340	−	0.658769i
$862$		0			0
$863$		−	29.8564i		−	1.01632i	−0.861262	−	0.508162i	$-0.830325\pi$
$863$		−	29.8564i		−	1.01632i	0.861262	−	0.508162i	$-0.169675\pi$
$864$		0			0
$865$	−10.7942	+	52.7487i	−0.367015	+	1.79351i
$866$		0			0
$867$	−2.90192	−	10.8301i	−0.0985545	−	0.367810i
$868$		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
$873$	−2.70577	+	1.56218i	−0.0915765	+	0.0528717i
$874$		0			0
$875$	−16.8205	+	46.9904i	−0.568637	+	1.58856i
$876$		0			0
$877$	3.20577	−	5.55256i	0.108251	−	0.187497i	−0.806811	−	0.590810i	$-0.798808\pi$
$877$	3.20577	−	5.55256i	0.108251	−	0.187497i	0.915062	+	0.403313i	$0.132142\pi$
$878$		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	$-0.664158\pi$
$883$	11.1962	−	11.1962i	0.376781	−	0.376781i	0.869939	+	0.493159i	$0.164158\pi$
$884$		0			0
$885$	−12.6603	+	25.3205i	−0.425570	+	0.851140i
$886$		0			0
$887$	6.96410	+	1.86603i	0.233832	+	0.0626550i	0.373832	−	0.927496i	$-0.378044\pi$
$887$	6.96410	+	1.86603i	0.233832	+	0.0626550i	−0.140000	+	0.990151i	$0.544710\pi$
$888$		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
$893$	−12.3923	+	3.32051i	−0.414693	+	0.111117i
$894$		0			0
$895$	−0.00961894	−	0.160254i	−0.000321526	−	0.00535670i
$896$		0			0
$897$	22.2583	+	45.0167i	0.743184	+	1.50306i
$898$		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
$903$	27.8205	+	16.0622i	0.925809	+	0.534516i
$904$		0			0
$905$	9.07180	−	18.1436i	0.301557	−	0.603113i
$906$		0			0
$907$	14.6436	−	54.6506i	0.486233	−	1.81464i	−0.0882129	−	0.996102i	$-0.528116\pi$
$907$	14.6436	−	54.6506i	0.486233	−	1.81464i	0.574445	−	0.818543i	$-0.305218\pi$
$908$		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
$913$	−8.39230	+	31.3205i	−0.277745	+	1.03656i
$914$		0			0
$915$	−12.2942	−	36.8827i	−0.406435	−	1.21930i
$916$		0			0
$917$	84.4974	+	48.7846i	2.79035	+	1.61101i
$918$		0			0
$919$	36.1410	+	20.8660i	1.19218	+	0.688307i	0.958801	−	0.284079i	$-0.0916877\pi$
$919$	36.1410	+	20.8660i	1.19218	+	0.688307i	0.233381	+	0.972385i	$0.425021\pi$
$920$		0			0
$921$	7.46410	+	2.00000i	0.245951	+	0.0659022i
$922$		0			0
$923$	5.50000	−	16.2583i	0.181035	−	0.535149i
$924$		0			0
$925$	−38.9186	−	16.6244i	−1.27964	−	0.546605i
$926$		0			0
$927$	0.803848	−	0.215390i	0.0264018	−	0.00707435i
$928$		0			0
$929$	−3.99038	−	14.8923i	−0.130920	−	0.488601i	0.869061	−	0.494705i	$-0.164724\pi$
$929$	−3.99038	−	14.8923i	−0.130920	−	0.488601i	−0.999981	+	0.00610389i	$0.998057\pi$
$930$		0			0
$931$	40.0526	−	40.0526i	1.31267	−	1.31267i
$932$		0			0
$933$	−6.46410	−	1.73205i	−0.211625	−	0.0567048i
$934$		0			0
$935$	19.8564	+	9.92820i	0.649374	+	0.324687i
$936$		0			0
$937$	−24.8564	+	24.8564i	−0.812023	+	0.812023i	−0.984937	−	0.172914i	$-0.944682\pi$
$937$	−24.8564	+	24.8564i	−0.812023	+	0.812023i	0.172914	+	0.984937i	$0.444682\pi$
$938$		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
$943$	−9.33013	+	16.1603i	−0.303831	+	0.526250i
$944$		0			0
$945$	−42.8468	−	8.76795i	−1.39381	−	0.285221i
$946$		0			0
$947$	37.4545	−	21.6244i	1.21711	−	0.702697i	0.252809	−	0.967516i	$-0.418646\pi$
$947$	37.4545	−	21.6244i	1.21711	−	0.702697i	0.964298	+	0.264819i	$0.0853122\pi$
$948$		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
$953$	11.6244	+	43.3827i	0.376550	+	1.40530i	0.851067	+	0.525057i	$0.175956\pi$
$953$	11.6244	+	43.3827i	0.376550	+	1.40530i	−0.474517	+	0.880246i	$0.657377\pi$
$954$		0			0
$955$	−27.9904	+	18.4808i	−0.905747	+	0.598023i
$956$		0			0
$957$			9.92820i			0.320933i
$958$		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
$965$	0.748711	+	12.4737i	0.0241019	+	0.401543i
$966$		0			0
$967$	37.6077			1.20938			0.604691	−	0.796460i	$-0.293297\pi$
$967$	37.6077			1.20938			0.604691	+	0.796460i	$0.293297\pi$
$968$		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
$973$	11.5981	+	20.0885i	0.371817	+	0.644006i
$974$		0			0
$975$	7.13397	−	34.0885i	0.228470	−	1.09170i
$976$		0			0
$977$	6.79423	+	11.7679i	0.217367	+	0.376490i	0.954002	−	0.299800i	$-0.0969199\pi$
$977$	6.79423	+	11.7679i	0.217367	+	0.376490i	−0.736635	+	0.676290i	$0.763587\pi$
$978$		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
$983$	22.3923			0.714204			0.357102	−	0.934065i	$-0.383765\pi$
$983$	22.3923			0.714204			0.357102	+	0.934065i	$0.383765\pi$
$984$		0			0
$985$	−1.03590	−	17.2583i	−0.0330065	−	0.549896i
$986$		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
$993$		−	56.9090i		−	1.80595i
$994$		0			0
$995$	16.5263	−	10.9115i	0.523918	−	0.345919i
$996$		0			0
$997$	4.76795	+	17.7942i	0.151002	+	0.563549i	0.999415	+	0.0342126i	$0.0108923\pi$
$997$	4.76795	+	17.7942i	0.151002	+	0.563549i	−0.848412	+	0.529336i	$0.822441\pi$
$998$		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.bk.a.193.1	yes	4
5.2	odd	4		260.2.bf.b.37.1	✓	4
5.3	odd	4		1300.2.bn.a.557.1		4
5.4	even	2		1300.2.bs.b.193.1		4
13.6	odd	12		260.2.bf.b.253.1	yes	4
65.19	odd	12		1300.2.bn.a.1293.1		4
65.32	even	12	inner	260.2.bk.a.97.1	yes	4
65.58	even	12		1300.2.bs.b.357.1		4

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 1.86603i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 1.86603i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +(-2.86603 - 0.767949i) q^{11} +(-2.00000 + 3.00000i) q^{13} +(2.86603 - 3.23205i) q^{15} +(3.23205 - 0.866025i) q^{17} +(-1.13397 - 4.23205i) q^{19} +(6.09808 - 6.09808i) q^{21} +(-6.96410 - 1.86603i) q^{23} +(3.00000 + 4.00000i) q^{25} +(-3.09808 + 3.09808i) q^{27} +(-1.50000 + 0.866025i) q^{29} +(5.19615 + 5.19615i) q^{31} +(2.86603 - 4.96410i) q^{33} +(5.50000 + 8.33013i) q^{35} +(-7.33013 + 4.23205i) q^{37} +(-4.59808 - 5.23205i) q^{39} +(0.669873 - 2.50000i) q^{41} +(0.964102 + 3.59808i) q^{43} +(0.901924 + 1.36603i) q^{45} -2.92820i q^{47} +(6.46410 + 11.1962i) q^{49} +6.46410i q^{51} +(-4.46410 - 4.46410i) q^{53} +(4.96410 + 4.40192i) q^{55} +8.46410 q^{57} +(-6.33013 + 1.69615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(1.63397 + 2.83013i) q^{63} +(7.00000 - 4.00000i) q^{65} +(7.86603 + 13.6244i) q^{67} +(6.96410 - 12.0622i) q^{69} +(-4.59808 + 1.23205i) q^{71} -1.07180 q^{73} +(-8.96410 + 3.59808i) q^{75} +(9.36603 + 9.36603i) q^{77} -7.46410i q^{79} +(-5.33013 - 9.23205i) q^{81} -10.9282i q^{83} +(-7.33013 - 1.50000i) q^{85} +(-0.866025 - 3.23205i) q^{87} +(0.794229 - 2.96410i) q^{89} +(14.4282 - 7.13397i) q^{91} +(-12.2942 + 7.09808i) q^{93} +(-1.96410 + 9.59808i) q^{95} +(2.13397 - 3.69615i) q^{97} +(1.53590 + 1.53590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 8 * q^5 - 12 * q^7 - 6 * q^9	\( 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9} - 8 q^{11} - 8 q^{13} + 8 q^{15} + 6 q^{17} - 8 q^{19} + 14 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} - 6 q^{29} + 8 q^{33} + 22 q^{35} - 12 q^{37} - 8 q^{39} + 20 q^{41} - 10 q^{43} + 14 q^{45} + 12 q^{49} - 4 q^{53} + 6 q^{55} + 20 q^{57} - 8 q^{59} + 18 q^{61} + 10 q^{63} + 28 q^{65} + 28 q^{67} + 14 q^{69} - 8 q^{71} - 32 q^{73} - 22 q^{75} + 34 q^{77} - 4 q^{81} - 12 q^{85} - 28 q^{89} + 30 q^{91} - 18 q^{93} + 6 q^{95} + 12 q^{97} + 20 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 8 * q^5 - 12 * q^7 - 6 * q^9 - 8 * q^11 - 8 * q^13 + 8 * q^15 + 6 * q^17 - 8 * q^19 + 14 * q^21 - 14 * q^23 + 12 * q^25 - 2 * q^27 - 6 * q^29 + 8 * q^33 + 22 * q^35 - 12 * q^37 - 8 * q^39 + 20 * q^41 - 10 * q^43 + 14 * q^45 + 12 * q^49 - 4 * q^53 + 6 * q^55 + 20 * q^57 - 8 * q^59 + 18 * q^61 + 10 * q^63 + 28 * q^65 + 28 * q^67 + 14 * q^69 - 8 * q^71 - 32 * q^73 - 22 * q^75 + 34 * q^77 - 4 * q^81 - 12 * q^85 - 28 * q^89 + 30 * q^91 - 18 * q^93 + 6 * q^95 + 12 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

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