LMFDB - Embedded newform 1300.2.bn.a.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(93,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 1]))

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

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

chi := DirichletCharacter("1300.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.bn (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:	$10.3805522628$
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:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1300.557
Dual form			1300.2.bn.a.1293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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	−0.323840	−	0.946112i	$-0.604974\pi$
$3$	−1.86603	−	0.500000i	−1.07735	−	0.288675i	−0.753510	+	0.657437i	$0.771641\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.23205	+	3.86603i	−0.843636	+	1.46122i	0.0431647	+	0.999068i	$0.486256\pi$
$7$	−2.23205	+	3.86603i	−0.843636	+	1.46122i	−0.886801	+	0.462152i	$0.847077\pi$
$8$		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			0
$16$		0			0
$17$	−0.866025	−	3.23205i	−0.210042	−	0.783887i	−0.987853	−	0.155390i	$-0.950337\pi$
$17$	−0.866025	−	3.23205i	−0.210042	−	0.783887i	0.777811	−	0.628498i	$-0.216330\pi$
$18$		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	$-0.645915\pi$
$23$	1.86603	−	6.96410i	0.389093	−	1.45212i	0.831612	−	0.555357i	$-0.187418\pi$
$24$		0			0
$25$		0			0
$26$		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
$35$		0			0
$36$		0			0
$37$	4.23205	+	7.33013i	0.695745	+	1.20507i	0.969929	+	0.243388i	$0.0782589\pi$
$37$	4.23205	+	7.33013i	0.695745	+	1.20507i	−0.274184	+	0.961677i	$0.588408\pi$
$38$		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	−0.522511	−	0.852633i	$-0.675004\pi$
$43$	−3.59808	+	0.964102i	−0.548701	+	0.147024i	−0.0261910	+	0.999657i	$0.508338\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.92820			−0.427122			−0.213561	−	0.976930i	$-0.568506\pi$
$47$	−2.92820			−0.427122			−0.213561	+	0.976930i	$0.568506\pi$
$48$		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	$-0.607246\pi$
$53$	4.46410	−	4.46410i	0.613192	−	0.613192i	0.943776	+	0.330585i	$0.107246\pi$
$54$		0			0
$55$		0			0
$56$		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
$65$		0			0
$66$		0			0
$67$	13.6244	−	7.86603i	1.66448	−	0.960988i	0.693945	−	0.720028i	$-0.255871\pi$
$67$	13.6244	−	7.86603i	1.66448	−	0.960988i	0.970535	−	0.240960i	$-0.0774622\pi$
$68$		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	$-0.980022\pi$
$73$		−	1.07180i		−	0.125444i	0.998031	−	0.0627222i	$-0.0199782\pi$
$74$		0			0
$75$		0			0
$76$		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	$-0.295261\pi$
$83$	10.9282			1.19953			0.599763	+	0.800178i	$0.295261\pi$
$84$		0			0
$85$		0			0
$86$		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
$95$		0			0
$96$		0			0
$97$	−3.69615	−	2.13397i	−0.375287	−	0.216672i	0.300478	−	0.953789i	$-0.402854\pi$
$97$	−3.69615	−	2.13397i	−0.375287	−	0.216672i	−0.675766	+	0.737116i	$0.736187\pi$
$98$		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	0.666394	−	0.745600i	$-0.267837\pi$
$103$	−0.803848	−	0.803848i	−0.0792055	−	0.0792055i	−0.745600	+	0.666394i	$0.767837\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.33013	−	4.96410i	0.128588	−	0.479898i	−0.871354	−	0.490655i	$-0.836758\pi$
$107$	1.33013	−	4.96410i	0.128588	−	0.479898i	0.999942	+	0.0107572i	$0.00342420\pi$
$108$		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	0.998530	−	0.0542046i	$-0.0172623\pi$
$113$	1.13397	+	4.23205i	0.106675	+	0.398118i	−0.891854	+	0.452322i	$0.850596\pi$
$114$		0			0
$115$		0			0
$116$		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
$125$		0			0
$126$		0			0
$127$	−3.33013	−	0.892305i	−0.295501	−	0.0791793i	0.108023	−	0.994148i	$-0.465548\pi$
$127$	−3.33013	−	0.892305i	−0.295501	−	0.0791793i	−0.403524	+	0.914969i	$0.632215\pi$
$128$		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
$135$		0			0
$136$		0			0
$137$	−10.1603	+	17.5981i	−0.868049	+	1.50351i	−0.00406165	+	0.999992i	$0.501293\pi$
$137$	−10.1603	+	17.5981i	−0.868049	+	1.50351i	−0.863987	+	0.503513i	$0.832040\pi$
$138$		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
$145$		0			0
$146$		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
$155$		0			0
$156$		0			0
$157$	0.464102	+	0.464102i	0.0370393	+	0.0370393i	0.725384	−	0.688345i	$-0.241662\pi$
$157$	0.464102	+	0.464102i	0.0370393	+	0.0370393i	−0.688345	+	0.725384i	$0.741662\pi$
$158$		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	0.723799	−	0.690011i	$-0.242394\pi$
$163$	6.23205	+	3.59808i	0.488132	+	0.281823i	−0.235667	+	0.971834i	$0.575728\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.76795	−	9.99038i	−0.446337	−	0.773079i	0.551807	−	0.833972i	$-0.313939\pi$
$167$	−5.76795	−	9.99038i	−0.446337	−	0.773079i	−0.998144	+	0.0608930i	$0.980605\pi$
$168$		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	0.779926	−	0.625871i	$-0.215256\pi$
$173$	23.2583	−	6.23205i	1.76830	−	0.473814i	0.988372	+	0.152057i	$0.0485898\pi$
$174$		0			0
$175$		0			0
$176$		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
$185$		0			0
$186$		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	−0.315596	−	0.948894i	$-0.602204\pi$
$193$	4.83975	−	2.79423i	0.348373	−	0.201133i	0.663968	+	0.747761i	$0.268871\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.69615	−	3.86603i	0.477081	−	0.275443i	−0.242118	−	0.970247i	$-0.577842\pi$
$197$	6.69615	−	3.86603i	0.477081	−	0.275443i	0.719199	+	0.694804i	$0.244509\pi$
$198$		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
$205$		0			0
$206$		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
$215$		0			0
$216$		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	0.972220	−	0.234070i	$-0.0752046\pi$
$223$	4.23205	+	7.33013i	0.283399	+	0.490862i	−0.688821	+	0.724932i	$0.741871\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.23205	+	3.59808i	0.413636	+	0.238813i	0.692351	−	0.721561i	$-0.256575\pi$
$227$	6.23205	+	3.59808i	0.413636	+	0.238813i	−0.278715	+	0.960374i	$0.589908\pi$
$228$		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	0.0263765	−	0.999652i	$-0.491603\pi$
$233$	−14.8564	−	14.8564i	−0.973276	−	0.973276i	−0.999652	+	0.0263765i	$0.991603\pi$
$234$		0			0
$235$		0			0
$236$		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
$245$		0			0
$246$		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
$255$		0			0
$256$		0			0
$257$	9.79423	+	2.62436i	0.610947	+	0.163703i	0.551009	−	0.834499i	$-0.314243\pi$
$257$	9.79423	+	2.62436i	0.610947	+	0.163703i	0.0599382	+	0.998202i	$0.480910\pi$
$258$		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	−0.645302	−	0.763928i	$-0.723268\pi$
$263$	−25.7224	−	6.89230i	−1.58611	−	0.424998i	−0.940812	+	0.338930i	$0.889935\pi$
$264$		0			0
$265$		0			0
$266$		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
$275$		0			0
$276$		0			0
$277$	1.66987	+	6.23205i	0.100333	+	0.374448i	0.997774	−	0.0666868i	$-0.0212428\pi$
$277$	1.66987	+	6.23205i	0.100333	+	0.374448i	−0.897441	+	0.441134i	$0.854576\pi$
$278$		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	−0.973685	−	0.227899i	$-0.926815\pi$
$283$	−0.277568	+	1.03590i	−0.0164997	+	0.0615778i	0.957185	+	0.289476i	$0.0934812\pi$
$284$		0			0
$285$		0			0
$286$		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	0.969174	−	0.246379i	$-0.0792409\pi$
$293$	21.2321	+	12.2583i	1.24039	+	0.716139i	0.271216	+	0.962518i	$0.412574\pi$
$294$		0			0
$295$		0			0
$296$		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
$305$		0			0
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		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	$-0.584007\pi$
$313$	12.4641	−	12.4641i	0.704513	−	0.704513i	0.965376	+	0.260863i	$0.0840071\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			5.07180i			0.284860i	0.989805	+	0.142430i	$0.0454917\pi$
$317$			5.07180i			0.284860i	−0.989805	+	0.142430i	$0.954508\pi$
$318$		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
$325$		0			0
$326$		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
$335$		0			0
$336$		0			0
$337$	−2.07180	+	2.07180i	−0.112858	+	0.112858i	−0.761281	−	0.648423i	$-0.775429\pi$
$337$	−2.07180	+	2.07180i	−0.112858	+	0.112858i	0.648423	+	0.761281i	$0.275429\pi$
$338$		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
$345$		0			0
$346$		0			0
$347$	12.7942	−	3.42820i	0.686830	−	0.184036i	0.101506	−	0.994835i	$-0.467634\pi$
$347$	12.7942	−	3.42820i	0.686830	−	0.184036i	0.585324	+	0.810799i	$0.300967\pi$
$348$		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	0.815134	−	0.579273i	$-0.196664\pi$
$353$	−1.76795	−	3.06218i	−0.0940984	−	0.162983i	−0.909232	+	0.416290i	$0.863330\pi$
$354$		0			0
$355$		0			0
$356$		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
$365$		0			0
$366$		0			0
$367$	0.794229	−	2.96410i	0.0414584	−	0.154725i	−0.942094	−	0.335350i	$-0.891145\pi$
$367$	0.794229	−	2.96410i	0.0414584	−	0.154725i	0.983552	+	0.180625i	$0.0578121\pi$
$368$		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	$0.0548796\pi$
$373$	4.20577	+	15.6962i	0.217767	+	0.812716i	−0.767408	+	0.641159i	$0.778454\pi$
$374$		0			0
$375$		0			0
$376$		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	$0.477995\pi$
$383$	−16.2321	+	28.1147i	−0.829419	+	1.43660i	−0.898495	+	0.438985i	$0.855338\pi$
$384$		0			0
$385$		0			0
$386$		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
$395$		0			0
$396$		0			0
$397$	−4.69615	+	8.13397i	−0.235693	+	0.408232i	−0.959474	−	0.281798i	$-0.909069\pi$
$397$	−4.69615	+	8.13397i	−0.235693	+	0.408232i	0.723781	+	0.690030i	$0.242403\pi$
$398$		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
$405$		0			0
$406$		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
$415$		0			0
$416$		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
$425$		0			0
$426$		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	0.276148	−	0.961115i	$-0.410942\pi$
$433$	20.7224	−	5.55256i	0.995857	−	0.266839i	0.719709	+	0.694276i	$0.244275\pi$
$434$		0			0
$435$		0			0
$436$		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	−0.972699	−	0.232069i	$-0.925450\pi$
$443$	−15.5885	+	15.5885i	−0.740630	+	0.740630i	0.232069	+	0.972699i	$0.425450\pi$
$444$		0			0
$445$		0			0
$446$		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
$455$		0			0
$456$		0			0
$457$	15.2321	−	8.79423i	0.712525	−	0.411377i	−0.0994701	−	0.995041i	$-0.531715\pi$
$457$	15.2321	−	8.79423i	0.712525	−	0.411377i	0.811995	+	0.583664i	$0.198381\pi$
$458$		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	$-0.555075\pi$
$463$		−	42.3923i		−	1.97014i	0.172161	−	0.985069i	$-0.444925\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.660254	+	0.660254i	−0.0305529	+	0.0305529i	−0.722218	−	0.691665i	$-0.756877\pi$
$467$	−0.660254	+	0.660254i	−0.0305529	+	0.0305529i	0.691665	+	0.722218i	$0.256877\pi$
$468$		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
$475$		0			0
$476$		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			0
$486$		0			0
$487$	−25.6244	−	14.7942i	−1.16115	−	0.670390i	−0.209571	−	0.977793i	$-0.567207\pi$
$487$	−25.6244	−	14.7942i	−1.16115	−	0.670390i	−0.951579	+	0.307403i	$0.900540\pi$
$488$		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
$495$		0			0
$496$		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	$0.106694\pi$
$503$	6.52628	+	24.3564i	0.290992	+	1.08600i	−0.653356	+	0.757051i	$0.726639\pi$
$504$		0			0
$505$		0			0
$506$		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			0
$516$		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	0.572625	−	0.819818i	$-0.305925\pi$
$523$	15.0622	+	4.03590i	0.658623	+	0.176478i	0.0859985	+	0.996295i	$0.472592\pi$
$524$		0			0
$525$		0			0
$526$		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
$535$		0			0
$536$		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
$545$		0			0
$546$		0			0
$547$	−24.1244	−	24.1244i	−1.03148	−	1.03148i	−0.999488	−	0.0319949i	$-0.989814\pi$
$547$	−24.1244	−	24.1244i	−1.03148	−	1.03148i	−0.0319949	−	0.999488i	$-0.510186\pi$
$548$		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
$555$		0			0
$556$		0			0
$557$	−2.69615	−	4.66987i	−0.114240	−	0.197869i	0.803236	−	0.595661i	$-0.203110\pi$
$557$	−2.69615	−	4.66987i	−0.114240	−	0.197869i	−0.917476	+	0.397792i	$0.869777\pi$
$558$		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	0.0791284	−	0.996864i	$-0.474786\pi$
$563$	15.3301	−	4.10770i	0.646088	−	0.173119i	0.566959	+	0.823746i	$0.308120\pi$
$564$		0			0
$565$		0			0
$566$		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
$575$		0			0
$576$		0			0
$577$			20.7846i			0.865275i	0.901568	+	0.432637i	$0.142417\pi$
$577$			20.7846i			0.865275i	−0.901568	+	0.432637i	$0.857583\pi$
$578$		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
$585$		0			0
$586$		0			0
$587$	9.91154	−	5.72243i	0.409093	−	0.236190i	−0.281307	−	0.959618i	$-0.590768\pi$
$587$	9.91154	−	5.72243i	0.409093	−	0.236190i	0.690400	+	0.723428i	$0.257435\pi$
$588$		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	$-0.886002\pi$
$593$		−	17.0718i		−	0.701055i	0.936553	−	0.350527i	$-0.113998\pi$
$594$		0			0
$595$		0			0
$596$		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			0
$606$		0			0
$607$	37.1865	−	9.96410i	1.50935	−	0.404430i	0.593134	−	0.805104i	$-0.297890\pi$
$607$	37.1865	−	9.96410i	1.50935	−	0.404430i	0.916221	+	0.400673i	$0.131224\pi$
$608$		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	0.986969	−	0.160908i	$-0.0514423\pi$
$613$	8.76795	+	15.1865i	0.354134	+	0.613378i	−0.632835	+	0.774286i	$0.718109\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.7679	+	6.79423i	0.473760	+	0.273525i	0.717812	−	0.696237i	$-0.245144\pi$
$617$	11.7679	+	6.79423i	0.473760	+	0.273525i	−0.244053	+	0.969762i	$0.578477\pi$
$618$		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
$625$		0			0
$626$		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
$635$		0			0
$636$		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	$-0.660695\pi$
$643$	13.0885	−	22.6699i	0.516158	−	0.894013i	0.999824	−	0.0187597i	$-0.00597174\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.33013	−	2.50000i	−0.366805	−	0.0982851i	0.0707082	−	0.997497i	$-0.477474\pi$
$647$	−9.33013	−	2.50000i	−0.366805	−	0.0982851i	−0.437513	+	0.899212i	$0.644141\pi$
$648$		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	−0.653882	−	0.756597i	$-0.726861\pi$
$653$	−40.8468	−	10.9449i	−1.59846	−	0.428306i	−0.944577	+	0.328291i	$0.893527\pi$
$654$		0			0
$655$		0			0
$656$		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
$665$		0			0
$666$		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	$-0.822410\pi$
$673$	3.91858	−	14.6244i	0.151050	−	0.563727i	0.999411	−	0.0343092i	$-0.0109231\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−34.1769	−	34.1769i	−1.31353	−	1.31353i	−0.918798	−	0.394727i	$-0.870839\pi$
$677$	−34.1769	−	34.1769i	−1.31353	−	1.31353i	−0.394727	−	0.918798i	$-0.629161\pi$
$678$		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	0.455275	−	0.890351i	$-0.349541\pi$
$683$	−2.30385	−	1.33013i	−0.0881543	−	0.0508959i	−0.543429	+	0.839455i	$0.682874\pi$
$684$		0			0
$685$		0			0
$686$		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			0
$696$		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
$705$		0			0
$706$		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
$715$		0			0
$716$		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
$725$		0			0
$726$		0			0
$727$	−2.41154	+	2.41154i	−0.0894392	+	0.0894392i	−0.750411	−	0.660972i	$-0.770144\pi$
$727$	−2.41154	+	2.41154i	−0.0894392	+	0.0894392i	0.660972	+	0.750411i	$0.270144\pi$
$728$		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	$-0.411971\pi$
$733$	14.7846			0.546082			0.273041	+	0.962002i	$0.411971\pi$
$734$		0			0
$735$		0			0
$736$		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	0.730621	−	0.682784i	$-0.239231\pi$
$743$	−6.16025	−	10.6699i	−0.225998	−	0.391440i	−0.956618	+	0.291344i	$0.905898\pi$
$744$		0			0
$745$		0			0
$746$		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
$755$		0			0
$756$		0			0
$757$	−5.93782	+	22.1603i	−0.215814	+	0.805428i	0.770065	+	0.637966i	$0.220224\pi$
$757$	−5.93782	+	22.1603i	−0.215814	+	0.805428i	−0.985878	+	0.167462i	$0.946443\pi$
$758$		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
$765$		0			0
$766$		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	$-0.401904\pi$
$773$	27.1603	−	47.0429i	0.976886	−	1.69202i	0.673564	−	0.739129i	$-0.264763\pi$
$774$		0			0
$775$		0			0
$776$		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			0
$786$		0			0
$787$	−2.62436	+	4.54552i	−0.0935482	+	0.162030i	−0.909002	−	0.416792i	$-0.863154\pi$
$787$	−2.62436	+	4.54552i	−0.0935482	+	0.162030i	0.815454	+	0.578822i	$0.196488\pi$
$788$		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
$795$		0			0
$796$		0			0
$797$	4.99038	+	18.6244i	0.176768	+	0.659709i	0.996244	+	0.0865940i	$0.0275983\pi$
$797$	4.99038	+	18.6244i	0.176768	+	0.659709i	−0.819475	+	0.573114i	$0.805735\pi$
$798$		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
$805$		0			0
$806$		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			0
$816$		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	−0.455230	−	0.890374i	$-0.650443\pi$
$823$	−11.5981	+	3.10770i	−0.404284	+	0.108327i	0.0509463	+	0.998701i	$0.483776\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.85641			−0.0645536			−0.0322768	−	0.999479i	$-0.510276\pi$
$827$	−1.85641			−0.0645536			−0.0322768	+	0.999479i	$0.510276\pi$
$828$		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
$835$		0			0
$836$		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
$845$		0			0
$846$		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	$-0.852290\pi$
$853$		−	26.1436i		−	0.895140i	0.894249	−	0.447570i	$-0.147710\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	29.2487	−	29.2487i	0.999117	−	0.999117i	−0.000882665	−	1.00000i	$-0.500281\pi$
$857$	29.2487	−	29.2487i	0.999117	−	0.999117i	1.00000		0.000882665i	$0.000280961\pi$
$858$		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	$-0.330325\pi$
$863$	29.8564			1.01632			0.508162	+	0.861262i	$0.330325\pi$
$864$		0			0
$865$		0			0
$866$		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
$875$		0			0
$876$		0			0
$877$	−5.55256	−	3.20577i	−0.187497	−	0.108251i	0.403313	−	0.915062i	$-0.367858\pi$
$877$	−5.55256	−	3.20577i	−0.187497	−	0.108251i	−0.590810	+	0.806811i	$0.701192\pi$
$878$		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	0.869939	−	0.493159i	$-0.164158\pi$
$883$	11.1962	+	11.1962i	0.376781	+	0.376781i	−0.493159	+	0.869939i	$0.664158\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.86603	−	6.96410i	0.0626550	−	0.233832i	−0.927496	−	0.373832i	$-0.878044\pi$
$887$	1.86603	−	6.96410i	0.0626550	−	0.233832i	0.990151	+	0.140000i	$0.0447103\pi$
$888$		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			0
$896$		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
$905$		0			0
$906$		0			0
$907$	−54.6506	−	14.6436i	−1.81464	−	0.486233i	−0.818543	−	0.574445i	$-0.805218\pi$
$907$	−54.6506	−	14.6436i	−1.81464	−	0.486233i	−0.996102	+	0.0882129i	$0.971884\pi$
$908$		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
$915$		0			0
$916$		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
$925$		0			0
$926$		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
$935$		0			0
$936$		0			0
$937$	24.8564	+	24.8564i	0.812023	+	0.812023i	0.984937	−	0.172914i	$-0.0553181\pi$
$937$	24.8564	+	24.8564i	0.812023	+	0.812023i	−0.172914	+	0.984937i	$0.555318\pi$
$938$		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
$945$		0			0
$946$		0			0
$947$	−21.6244	−	37.4545i	−0.702697	−	1.21711i	−0.967516	−	0.252809i	$-0.918646\pi$
$947$	−21.6244	−	37.4545i	−0.702697	−	1.21711i	0.264819	−	0.964298i	$-0.414688\pi$
$948$		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	−0.880246	−	0.474517i	$-0.842623\pi$
$953$	−43.3827	+	11.6244i	−1.40530	+	0.376550i	−0.525057	+	0.851067i	$0.675956\pi$
$954$		0			0
$955$		0			0
$956$		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
$965$		0			0
$966$		0			0
$967$		−	37.6077i		−	1.20938i	−0.796460	−	0.604691i	$-0.793297\pi$
$967$		−	37.6077i		−	1.20938i	0.796460	−	0.604691i	$-0.206703\pi$
$968$		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
$975$		0			0
$976$		0			0
$977$	11.7679	−	6.79423i	0.376490	−	0.217367i	−0.299800	−	0.954002i	$-0.596920\pi$
$977$	11.7679	−	6.79423i	0.376490	−	0.217367i	0.676290	+	0.736635i	$0.263587\pi$
$978$		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	$0.116235\pi$
$983$			22.3923i			0.714204i	−0.934065	+	0.357102i	$0.883765\pi$
$984$		0			0
$985$		0			0
$986$		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
$995$		0			0
$996$		0			0
$997$	17.7942	−	4.76795i	0.563549	−	0.151002i	0.0342126	−	0.999415i	$-0.489108\pi$
$997$	17.7942	−	4.76795i	0.563549	−	0.151002i	0.529336	+	0.848412i	$0.322441\pi$
$998$		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	1300.2.bn.a.557.1		4
5.2	odd	4		260.2.bk.a.193.1	yes	4
5.3	odd	4		1300.2.bs.b.193.1		4
5.4	even	2		260.2.bf.b.37.1	✓	4
13.6	odd	12		1300.2.bs.b.357.1		4
65.19	odd	12		260.2.bk.a.97.1	yes	4
65.32	even	12		260.2.bf.b.253.1	yes	4
65.58	even	12	inner	1300.2.bn.a.1293.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.b.37.1	✓	4	5.4	even	2
260.2.bf.b.253.1	yes	4	65.32	even	12
260.2.bk.a.97.1	yes	4	65.19	odd	12
260.2.bk.a.193.1	yes	4	5.2	odd	4
1300.2.bn.a.557.1		4	1.1	even	1	trivial
1300.2.bn.a.1293.1		4	65.58	even	12	inner
1300.2.bs.b.193.1		4	5.3	odd	4
1300.2.bs.b.357.1		4	13.6	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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.bn (of order \(12\), degree \(4\), minimal)

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

Introduction

L-functions

Modular forms

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