LMFDB - Embedded newform 260.2.bk.c.97.3

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:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.3
Root			$-2.86589i$ of defining polynomial
Character	$\chi$	$=$	260.97
Dual form			260.2.bk.c.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.355132 + 1.32537i) q^{3} +(1.50965 + 1.64953i) q^{5} +(-3.40883 + 1.96809i) q^{7} +(0.967585 - 0.558635i) q^{9} +O(q^{10})$	\(q+(0.355132 + 1.32537i) q^{3} +(1.50965 + 1.64953i) q^{5} +(-3.40883 + 1.96809i) q^{7} +(0.967585 - 0.558635i) q^{9} +(-1.83141 + 0.490724i) q^{11} +(2.65910 + 2.43499i) q^{13} +(-1.65012 + 2.58665i) q^{15} +(-3.15223 - 0.844638i) q^{17} +(0.920754 - 3.43630i) q^{19} +(-3.81904 - 3.81904i) q^{21} +(1.88280 - 0.504494i) q^{23} +(-0.441931 + 4.98043i) q^{25} +(3.99474 + 3.99474i) q^{27} +(7.43876 + 4.29477i) q^{29} +(2.37363 - 2.37363i) q^{31} +(-1.30078 - 2.25302i) q^{33} +(-8.39256 - 2.65186i) q^{35} +(-1.28885 - 0.744119i) q^{37} +(-2.28293 + 4.38904i) q^{39} +(-1.45054 - 5.41349i) q^{41} +(1.51311 - 5.64699i) q^{43} +(2.38220 + 0.752723i) q^{45} +3.50747i q^{47} +(4.24675 - 7.35558i) q^{49} -4.47783i q^{51} +(8.97315 - 8.97315i) q^{53} +(-3.57424 - 2.28015i) q^{55} +4.88136 q^{57} +(-4.27489 - 1.14545i) q^{59} +(-6.33455 - 10.9718i) q^{61} +(-2.19889 + 3.80859i) q^{63} +(-0.00229698 + 8.06226i) q^{65} +(2.54852 - 4.41417i) q^{67} +(1.33729 + 2.31625i) q^{69} +(5.68768 + 1.52401i) q^{71} -7.07919 q^{73} +(-6.75787 + 1.18299i) q^{75} +(5.27716 - 5.27716i) q^{77} -14.3886i q^{79} +(-2.19995 + 3.81042i) q^{81} +17.5256i q^{83} +(-3.36550 - 6.47482i) q^{85} +(-3.05042 + 11.3843i) q^{87} +(2.12894 + 7.94530i) q^{89} +(-13.8567 - 3.06712i) q^{91} +(3.98890 + 2.30299i) q^{93} +(7.05831 - 3.66879i) q^{95} +(-1.64859 - 2.85545i) q^{97} +(-1.49790 + 1.49790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	0.355132	+	1.32537i	0.205036	+	0.765204i	0.989439	+	0.144952i	$0.0463028\pi$
$3$	0.355132	+	1.32537i	0.205036	+	0.765204i	−0.784403	+	0.620252i	$0.787031\pi$
$4$		0			0
$5$	1.50965	+	1.64953i	0.675135	+	0.737694i
$5$	1.50965	+	1.64953i	0.675135	+	0.737694i
$6$		0			0
$7$	−3.40883	+	1.96809i	−1.28842	+	0.743868i	−0.978372	−	0.206854i	$-0.933677\pi$
$7$	−3.40883	+	1.96809i	−1.28842	+	0.743868i	−0.310045	+	0.950722i	$0.600344\pi$
$8$		0			0
$9$	0.967585	−	0.558635i	0.322528	−	0.186212i
$10$		0			0
$11$	−1.83141	+	0.490724i	−0.552189	+	0.147959i	−0.524116	−	0.851647i	$-0.675604\pi$
$11$	−1.83141	+	0.490724i	−0.552189	+	0.147959i	−0.0280738	+	0.999606i	$0.508937\pi$
$12$		0			0
$13$	2.65910	+	2.43499i	0.737502	+	0.675345i
$13$	2.65910	+	2.43499i	0.737502	+	0.675345i
$14$		0			0
$15$	−1.65012	+	2.58665i	−0.426060	+	0.667869i
$16$		0			0
$17$	−3.15223	−	0.844638i	−0.764528	−	0.204855i	−0.144575	−	0.989494i	$-0.546182\pi$
$17$	−3.15223	−	0.844638i	−0.764528	−	0.204855i	−0.619953	+	0.784639i	$0.712848\pi$
$18$		0			0
$19$	0.920754	−	3.43630i	0.211235	−	0.788341i	−0.776223	−	0.630459i	$-0.782867\pi$
$19$	0.920754	−	3.43630i	0.211235	−	0.788341i	0.987458	−	0.157882i	$-0.0504667\pi$
$20$		0			0
$21$	−3.81904	−	3.81904i	−0.833382	−	0.833382i
$22$		0			0
$23$	1.88280	−	0.504494i	0.392591	−	0.105194i	−0.0571230	−	0.998367i	$-0.518193\pi$
$23$	1.88280	−	0.504494i	0.392591	−	0.105194i	0.449714	+	0.893173i	$0.351526\pi$
$24$		0			0
$25$	−0.441931	+	4.98043i	−0.0883862	+	0.996086i
$26$		0			0
$27$	3.99474	+	3.99474i	0.768788	+	0.768788i
$28$		0			0
$29$	7.43876	+	4.29477i	1.38134	+	0.797519i	0.992319	−	0.123709i	$-0.0394788\pi$
$29$	7.43876	+	4.29477i	1.38134	+	0.797519i	0.389025	+	0.921227i	$0.372812\pi$
$30$		0			0
$31$	2.37363	−	2.37363i	0.426317	−	0.426317i	−0.461055	−	0.887372i	$-0.652529\pi$
$31$	2.37363	−	2.37363i	0.426317	−	0.426317i	0.887372	+	0.461055i	$0.152529\pi$
$32$		0			0
$33$	−1.30078	−	2.25302i	−0.226437	−	0.392201i
$34$		0			0
$35$	−8.39256	−	2.65186i	−1.41860	−	0.448247i
$36$		0			0
$37$	−1.28885	−	0.744119i	−0.211886	−	0.122332i	0.390302	−	0.920687i	$-0.372371\pi$
$37$	−1.28885	−	0.744119i	−0.211886	−	0.122332i	−0.602188	+	0.798355i	$0.705704\pi$
$38$		0			0
$39$	−2.28293	+	4.38904i	−0.365562	+	0.702809i
$40$		0			0
$41$	−1.45054	−	5.41349i	−0.226536	−	0.845445i	−0.981783	−	0.190005i	$-0.939150\pi$
$41$	−1.45054	−	5.41349i	−0.226536	−	0.845445i	0.755247	−	0.655441i	$-0.227517\pi$
$42$		0			0
$43$	1.51311	−	5.64699i	0.230747	−	0.861158i	−0.749274	−	0.662261i	$-0.769597\pi$
$43$	1.51311	−	5.64699i	0.230747	−	0.861158i	0.980020	−	0.198898i	$-0.0637362\pi$
$44$		0			0
$45$	2.38220	+	0.752723i	0.355117	+	0.112209i
$46$		0			0
$47$			3.50747i			0.511617i	0.966727	+	0.255809i	$0.0823417\pi$
$47$			3.50747i			0.511617i	−0.966727	+	0.255809i	$0.917658\pi$
$48$		0			0
$49$	4.24675	−	7.35558i	0.606678	−	1.05080i
$50$		0			0
$51$		−	4.47783i		−	0.627022i
$52$		0			0
$53$	8.97315	−	8.97315i	1.23256	−	1.23256i	0.269578	−	0.962979i	$-0.413116\pi$
$53$	8.97315	−	8.97315i	1.23256	−	1.23256i	0.962979	−	0.269578i	$-0.0868843\pi$
$54$		0			0
$55$	−3.57424	−	2.28015i	−0.481951	−	0.307455i
$56$		0			0
$57$	4.88136			0.646553
$58$		0			0
$59$	−4.27489	−	1.14545i	−0.556543	−	0.149125i	−0.0304252	−	0.999537i	$-0.509686\pi$
$59$	−4.27489	−	1.14545i	−0.556543	−	0.149125i	−0.526118	+	0.850412i	$0.676353\pi$
$60$		0			0
$61$	−6.33455	−	10.9718i	−0.811056	−	1.40479i	−0.912126	−	0.409911i	$-0.865560\pi$
$61$	−6.33455	−	10.9718i	−0.811056	−	1.40479i	0.101070	−	0.994879i	$-0.467774\pi$
$62$		0			0
$63$	−2.19889	+	3.80859i	−0.277034	+	0.479837i
$64$		0			0
$65$	−0.00229698	+	8.06226i	−0.000284905	+	1.00000i
$66$		0			0
$67$	2.54852	−	4.41417i	0.311352	−	0.539277i	−0.667303	−	0.744786i	$-0.732552\pi$
$67$	2.54852	−	4.41417i	0.311352	−	0.539277i	0.978655	+	0.205509i	$0.0658849\pi$
$68$		0			0
$69$	1.33729	+	2.31625i	0.160990	+	0.278843i
$70$		0			0
$71$	5.68768	+	1.52401i	0.675003	+	0.180867i	0.580008	−	0.814611i	$-0.303050\pi$
$71$	5.68768	+	1.52401i	0.675003	+	0.180867i	0.0949958	+	0.995478i	$0.469716\pi$
$72$		0			0
$73$	−7.07919			−0.828556			−0.414278	−	0.910150i	$-0.635966\pi$
$73$	−7.07919			−0.828556			−0.414278	+	0.910150i	$0.635966\pi$
$74$		0			0
$75$	−6.75787	+	1.18299i	−0.780331	+	0.136600i
$76$		0			0
$77$	5.27716	−	5.27716i	0.601388	−	0.601388i
$78$		0			0
$79$		−	14.3886i		−	1.61884i	−0.587230	−	0.809420i	$-0.699781\pi$
$79$		−	14.3886i		−	1.61884i	0.587230	−	0.809420i	$-0.300219\pi$
$80$		0			0
$81$	−2.19995	+	3.81042i	−0.244439	+	0.423380i
$82$		0			0
$83$			17.5256i			1.92368i	0.273608	+	0.961841i	$0.411783\pi$
$83$			17.5256i			1.92368i	−0.273608	+	0.961841i	$0.588217\pi$
$84$		0			0
$85$	−3.36550	−	6.47482i	−0.365039	−	0.702293i
$86$		0			0
$87$	−3.05042	+	11.3843i	−0.327040	+	1.22053i
$88$		0			0
$89$	2.12894	+	7.94530i	0.225667	+	0.842200i	0.982136	+	0.188171i	$0.0602559\pi$
$89$	2.12894	+	7.94530i	0.225667	+	0.842200i	−0.756470	+	0.654029i	$0.773077\pi$
$90$		0			0
$91$	−13.8567	−	3.06712i	−1.45258	−	0.321522i
$92$		0			0
$93$	3.98890	+	2.30299i	0.413629	+	0.238809i
$94$		0			0
$95$	7.05831	−	3.66879i	0.724167	−	0.376409i
$96$		0			0
$97$	−1.64859	−	2.85545i	−0.167389	−	0.289927i	0.770112	−	0.637909i	$-0.220200\pi$
$97$	−1.64859	−	2.85545i	−0.167389	−	0.289927i	−0.937501	+	0.347982i	$0.886867\pi$
$98$		0			0
$99$	−1.49790	+	1.49790i	−0.150545	+	0.150545i
$100$		0			0
$101$	9.78232	+	5.64782i	0.973377	+	0.561979i	0.900264	−	0.435344i	$-0.143373\pi$
$101$	9.78232	+	5.64782i	0.973377	+	0.561979i	0.0731129	+	0.997324i	$0.476707\pi$
$102$		0			0
$103$	9.51034	+	9.51034i	0.937081	+	0.937081i	0.998135	−	0.0610531i	$-0.0194459\pi$
$103$	9.51034	+	9.51034i	0.937081	+	0.937081i	−0.0610531	+	0.998135i	$0.519446\pi$
$104$		0			0
$105$	0.534236	−	12.0650i	0.0521361	−	1.17743i
$106$		0			0
$107$	−11.2044	+	3.00221i	−1.08317	+	0.290235i	−0.755894	−	0.654694i	$-0.772797\pi$
$107$	−11.2044	+	3.00221i	−1.08317	+	0.290235i	−0.327276	+	0.944929i	$0.606131\pi$
$108$		0			0
$109$	−13.0996	−	13.0996i	−1.25471	−	1.25471i	−0.953585	−	0.301125i	$-0.902638\pi$
$109$	−13.0996	−	13.0996i	−1.25471	−	1.25471i	−0.301125	−	0.953585i	$-0.597362\pi$
$110$		0			0
$111$	0.528522	−	1.97247i	0.0501651	−	0.187219i
$112$		0			0
$113$	3.34358	+	0.895908i	0.314537	+	0.0842800i	0.412634	−	0.910897i	$-0.364609\pi$
$113$	3.34358	+	0.895908i	0.314537	+	0.0842800i	−0.0980969	+	0.995177i	$0.531276\pi$
$114$		0			0
$115$	3.67454	+	2.34413i	0.342653	+	0.218592i
$116$		0			0
$117$	3.93318	+	0.870592i	0.363622	+	0.0804863i
$118$		0			0
$119$	12.4077	−	3.32464i	1.13742	−	0.304770i
$120$		0			0
$121$	−6.41304	+	3.70257i	−0.583004	+	0.336598i
$122$		0			0
$123$	6.65976	−	3.84501i	0.600490	−	0.346693i
$124$		0			0
$125$	−8.88256	+	6.78971i	−0.794480	+	0.607290i
$126$		0			0
$127$	1.50527	+	5.61773i	0.133571	+	0.498493i	1.00000		0.000807685i	$-0.000257094\pi$
$127$	1.50527	+	5.61773i	0.133571	+	0.498493i	−0.866429	+	0.499300i	$0.833590\pi$
$128$		0			0
$129$	8.02172			0.706273
$130$		0			0
$131$	−1.68008			−0.146789			−0.0733946	−	0.997303i	$-0.523383\pi$
$131$	−1.68008			−0.146789			−0.0733946	+	0.997303i	$0.523383\pi$
$132$		0			0
$133$	3.62425	+	13.5259i	0.314262	+	1.17284i
$134$		0			0
$135$	−0.558815	+	12.6201i	−0.0480951	+	1.08617i
$136$		0			0
$137$	2.06410	−	1.19171i	0.176348	−	0.101815i	−0.409228	−	0.912432i	$-0.634202\pi$
$137$	2.06410	−	1.19171i	0.176348	−	0.101815i	0.585576	+	0.810618i	$0.300868\pi$
$138$		0			0
$139$	−7.97525	+	4.60451i	−0.676452	+	0.390550i	−0.798517	−	0.601972i	$-0.794382\pi$
$139$	−7.97525	+	4.60451i	−0.676452	+	0.390550i	0.122065	+	0.992522i	$0.461048\pi$
$140$		0			0
$141$	−4.64870	+	1.24562i	−0.391491	+	0.104900i
$142$		0			0
$143$	−6.06480	−	3.15457i	−0.507164	−	0.263798i
$144$		0			0
$145$	4.14553	+	18.7541i	0.344268	+	1.55744i
$146$		0			0
$147$	11.2570	+	3.01631i	0.928465	+	0.248781i
$148$		0			0
$149$	−5.50931	+	20.5610i	−0.451340	+	1.68442i	0.247290	+	0.968941i	$0.420460\pi$
$149$	−5.50931	+	20.5610i	−0.451340	+	1.68442i	−0.698630	+	0.715483i	$0.746207\pi$
$150$		0			0
$151$	14.1541	+	14.1541i	1.15184	+	1.15184i	0.986183	+	0.165660i	$0.0529756\pi$
$151$	14.1541	+	14.1541i	1.15184	+	1.15184i	0.165660	+	0.986183i	$0.447024\pi$
$152$		0			0
$153$	−3.52189	+	0.943689i	−0.284728	+	0.0762927i
$154$		0			0
$155$	7.49874	+	0.332042i	0.602313	+	0.0266703i
$156$		0			0
$157$	−9.43479	−	9.43479i	−0.752978	−	0.752978i	0.222056	−	0.975034i	$-0.428723\pi$
$157$	−9.43479	−	9.43479i	−0.752978	−	0.752978i	−0.975034	+	0.222056i	$0.928723\pi$
$158$		0			0
$159$	15.0794	+	8.70610i	1.19588	+	0.690439i
$160$		0			0
$161$	−5.42525	+	5.42525i	−0.427570	+	0.427570i
$162$		0			0
$163$	−11.2839	−	19.5443i	−0.883824	−	1.53083i	−0.847056	−	0.531504i	$-0.821627\pi$
$163$	−11.2839	−	19.5443i	−0.883824	−	1.53083i	−0.0367678	−	0.999324i	$-0.511706\pi$
$164$		0			0
$165$	1.75271	−	5.54695i	0.136449	−	0.431830i
$166$		0			0
$167$	−10.4774	−	6.04914i	−0.810767	−	0.468097i	0.0364550	−	0.999335i	$-0.488393\pi$
$167$	−10.4774	−	6.04914i	−0.810767	−	0.468097i	−0.847222	+	0.531239i	$0.821727\pi$
$168$		0			0
$169$	1.14164	+	12.9498i	0.0878186	+	0.996136i
$170$		0			0
$171$	−1.02873	−	3.83928i	−0.0786691	−	0.293597i
$172$		0			0
$173$	1.42843	−	5.33097i	0.108601	−	0.405306i	−0.890127	−	0.455712i	$-0.849385\pi$
$173$	1.42843	−	5.33097i	0.108601	−	0.405306i	0.998729	+	0.0504057i	$0.0160514\pi$
$174$		0			0
$175$	−8.29547	−	17.8472i	−0.627078	−	1.34912i
$176$		0			0
$177$		−	6.07260i		−	0.456445i
$178$		0			0
$179$	11.2279	−	19.4473i	0.839214	−	1.45356i	−0.0513388	−	0.998681i	$-0.516349\pi$
$179$	11.2279	−	19.4473i	0.839214	−	1.45356i	0.890553	−	0.454880i	$-0.150318\pi$
$180$		0			0
$181$			13.2607i			0.985659i	0.870126	+	0.492829i	$0.164037\pi$
$181$			13.2607i			0.985659i	−0.870126	+	0.492829i	$0.835963\pi$
$182$		0			0
$183$	12.2921	−	12.2921i	0.908655	−	0.908655i
$184$		0			0
$185$	−0.718262	−	3.24937i	−0.0528077	−	0.238898i
$186$		0			0
$187$	6.18749			0.452474
$188$		0			0
$189$	−21.4794	−	5.75538i	−1.56240	−	0.418643i
$190$		0			0
$191$	2.68516	+	4.65083i	0.194291	+	0.336522i	0.946668	−	0.322211i	$-0.104426\pi$
$191$	2.68516	+	4.65083i	0.194291	+	0.336522i	−0.752377	+	0.658733i	$0.771093\pi$
$192$		0			0
$193$	1.31236	−	2.27308i	0.0944659	−	0.163620i	−0.814920	−	0.579574i	$-0.803219\pi$
$193$	1.31236	−	2.27308i	0.0944659	−	0.163620i	0.909386	+	0.415954i	$0.136552\pi$
$194$		0			0
$195$	−10.6863	+	2.86012i	−0.765262	+	0.204818i
$196$		0			0
$197$	−3.25778	+	5.64263i	−0.232107	+	0.402021i	−0.958428	−	0.285335i	$-0.907895\pi$
$197$	−3.25778	+	5.64263i	−0.232107	+	0.402021i	0.726321	+	0.687356i	$0.241229\pi$
$198$		0			0
$199$	−2.74150	−	4.74843i	−0.194340	−	0.336607i	0.752344	−	0.658771i	$-0.228923\pi$
$199$	−2.74150	−	4.74843i	−0.194340	−	0.336607i	−0.946684	+	0.322164i	$0.895590\pi$
$200$		0			0
$201$	6.75549	+	1.81013i	0.476495	+	0.127677i
$202$		0			0
$203$	−33.8100			−2.37299
$204$		0			0
$205$	6.73994	−	10.5652i	0.470738	−	0.737904i
$206$		0			0
$207$	1.53994	−	1.53994i	0.107033	−	0.107033i
$208$		0			0
$209$			6.74509i			0.466568i
$210$		0			0
$211$	7.16194	−	12.4048i	0.493048	−	0.853984i	−0.506920	−	0.861993i	$-0.669216\pi$
$211$	7.16194	−	12.4048i	0.493048	−	0.853984i	0.999968	+	0.00800885i	$0.00254932\pi$
$212$		0			0
$213$			8.07952i			0.553599i
$214$		0			0
$215$	11.5992	−	6.02904i	0.791057	−	0.411177i
$216$		0			0
$217$	−3.41979	+	12.7628i	−0.232150	+	0.866397i
$218$		0			0
$219$	−2.51405	−	9.38256i	−0.169884	−	0.634014i
$220$		0			0
$221$	−6.32542	−	9.92163i	−0.425493	−	0.667401i
$222$		0			0
$223$	−7.01942	−	4.05266i	−0.470055	−	0.271386i	0.246208	−	0.969217i	$-0.420815\pi$
$223$	−7.01942	−	4.05266i	−0.470055	−	0.271386i	−0.716263	+	0.697831i	$0.754149\pi$
$224$		0			0
$225$	2.35464	+	5.06587i	0.156976	+	0.337725i
$226$		0			0
$227$	−3.32655	−	5.76176i	−0.220791	−	0.382421i	0.734257	−	0.678871i	$-0.237531\pi$
$227$	−3.32655	−	5.76176i	−0.220791	−	0.382421i	−0.955048	+	0.296450i	$0.904197\pi$
$228$		0			0
$229$	−6.32634	+	6.32634i	−0.418056	+	0.418056i	−0.884533	−	0.466477i	$-0.845523\pi$
$229$	−6.32634	+	6.32634i	−0.418056	+	0.418056i	0.466477	+	0.884533i	$0.345523\pi$
$230$		0			0
$231$	8.86829	+	5.12011i	0.583491	+	0.336879i
$232$		0			0
$233$	−12.8923	−	12.8923i	−0.844601	−	0.844601i	0.144852	−	0.989453i	$-0.453729\pi$
$233$	−12.8923	−	12.8923i	−0.844601	−	0.844601i	−0.989453	+	0.144852i	$0.953729\pi$
$234$		0			0
$235$	−5.78569	+	5.29504i	−0.377417	+	0.345410i
$236$		0			0
$237$	19.0702	−	5.10985i	1.23874	−	0.331920i
$238$		0			0
$239$	6.58614	+	6.58614i	0.426022	+	0.426022i	0.887271	−	0.461249i	$-0.152598\pi$
$239$	6.58614	+	6.58614i	0.426022	+	0.426022i	−0.461249	+	0.887271i	$0.652598\pi$
$240$		0			0
$241$	4.00770	−	14.9569i	0.258158	−	0.963461i	−0.708148	−	0.706065i	$-0.750469\pi$
$241$	4.00770	−	14.9569i	0.258158	−	0.963461i	0.966306	−	0.257396i	$-0.0828645\pi$
$242$		0			0
$243$	10.5392	+	2.82398i	0.676093	+	0.181159i
$244$		0			0
$245$	18.5444	−	4.09918i	1.18476	−	0.261887i
$246$		0			0
$247$	10.8157	−	6.89544i	0.688189	−	0.438747i
$248$		0			0
$249$	−23.2279	+	6.22390i	−1.47201	+	0.394424i
$250$		0			0
$251$	−1.46212	+	0.844158i	−0.0922885	+	0.0532828i	−0.545434	−	0.838154i	$-0.683635\pi$
$251$	−1.46212	+	0.844158i	−0.0922885	+	0.0532828i	0.453145	+	0.891437i	$0.350302\pi$
$252$		0			0
$253$	−3.20060	+	1.84787i	−0.201220	+	0.116174i
$254$		0			0
$255$	7.38635	−	6.75995i	0.462551	−	0.423325i
$256$		0			0
$257$	−2.68207	−	10.0096i	−0.167303	−	0.624384i	−0.997735	−	0.0672638i	$-0.978573\pi$
$257$	−2.68207	−	10.0096i	−0.167303	−	0.624384i	0.830432	−	0.557120i	$-0.188094\pi$
$258$		0			0
$259$	5.85797			0.363997
$260$		0			0
$261$	9.59684			0.594030
$262$		0			0
$263$	0.527501	+	1.96866i	0.0325271	+	0.121393i	0.980280	−	0.197611i	$-0.0633183\pi$
$263$	0.527501	+	1.96866i	0.0325271	+	0.121393i	−0.947753	+	0.319004i	$0.896652\pi$
$264$		0			0
$265$	28.3478	+	1.25523i	1.74139	+	0.0771084i
$266$		0			0
$267$	−9.77442	+	5.64326i	−0.598185	+	0.345362i
$268$		0			0
$269$	−2.59298	+	1.49706i	−0.158097	+	0.0912773i	−0.576961	−	0.816772i	$-0.695762\pi$
$269$	−2.59298	+	1.49706i	−0.158097	+	0.0912773i	0.418864	+	0.908049i	$0.362428\pi$
$270$		0			0
$271$	27.2999	−	7.31498i	1.65835	−	0.444353i	0.696416	−	0.717639i	$-0.254777\pi$
$271$	27.2999	−	7.31498i	1.65835	−	0.444353i	0.961933	+	0.273285i	$0.0881103\pi$
$272$		0			0
$273$	−0.855887	−	19.4545i	−0.0518006	−	1.17744i
$274$		0			0
$275$	−1.63466	−	9.33805i	−0.0985737	−	0.563106i
$276$		0			0
$277$	−26.0241	−	6.97314i	−1.56364	−	0.418975i	−0.629824	−	0.776738i	$-0.716873\pi$
$277$	−26.0241	−	6.97314i	−1.56364	−	0.418975i	−0.933813	+	0.357762i	$0.883540\pi$
$278$		0			0
$279$	0.970696	−	3.62268i	0.0581140	−	0.216884i
$280$		0			0
$281$	−1.76202	−	1.76202i	−0.105113	−	0.105113i	0.652594	−	0.757707i	$-0.273681\pi$
$281$	−1.76202	−	1.76202i	−0.105113	−	0.105113i	−0.757707	+	0.652594i	$0.773681\pi$
$282$		0			0
$283$	−8.28547	+	2.22009i	−0.492520	+	0.131970i	−0.496527	−	0.868022i	$-0.665391\pi$
$283$	−8.28547	+	2.22009i	−0.492520	+	0.131970i	0.00400621	+	0.999992i	$0.498725\pi$
$284$		0			0
$285$	7.36914	+	8.05198i	0.436510	+	0.476958i
$286$		0			0
$287$	15.5989	+	15.5989i	0.920773	+	0.920773i
$288$		0			0
$289$	−5.49929	−	3.17502i	−0.323488	−	0.186766i
$290$		0			0
$291$	3.19906	−	3.19906i	0.187532	−	0.187532i
$292$		0			0
$293$	−4.80103	−	8.31563i	−0.280479	−	0.485804i	0.691024	−	0.722832i	$-0.257160\pi$
$293$	−4.80103	−	8.31563i	−0.280479	−	0.485804i	−0.971503	+	0.237028i	$0.923827\pi$
$294$		0			0
$295$	−4.56411	−	8.78080i	−0.265733	−	0.511238i
$296$		0			0
$297$	−9.27630	−	5.35567i	−0.538265	−	0.310768i
$298$		0			0
$299$	6.23499	+	3.24310i	0.360579	+	0.187553i
$300$		0			0
$301$	5.95586	+	22.2276i	0.343290	+	1.28118i
$302$		0			0
$303$	−4.01145	+	14.9709i	−0.230452	+	0.860058i
$304$		0			0
$305$	8.53537	−	27.0126i	0.488734	−	1.54673i
$306$		0			0
$307$		−	16.6845i		−	0.952235i	−0.879382	−	0.476118i	$-0.842044\pi$
$307$		−	16.6845i		−	0.952235i	0.879382	−	0.476118i	$-0.157956\pi$
$308$		0			0
$309$	−9.22731	+	15.9822i	−0.524923	+	0.909193i
$310$		0			0
$311$			32.6023i			1.84870i	0.381540	+	0.924352i	$0.375394\pi$
$311$			32.6023i			1.84870i	−0.381540	+	0.924352i	$0.624606\pi$
$312$		0			0
$313$	−4.98087	+	4.98087i	−0.281535	+	0.281535i	−0.833721	−	0.552186i	$-0.813794\pi$
$313$	−4.98087	+	4.98087i	−0.281535	+	0.281535i	0.552186	+	0.833721i	$0.313794\pi$
$314$		0			0
$315$	−9.60194	+	2.12248i	−0.541008	+	0.119588i
$316$		0			0
$317$	−22.4470			−1.26075			−0.630375	−	0.776291i	$-0.717099\pi$
$317$	−22.4470			−1.26075			−0.630375	+	0.776291i	$0.717099\pi$
$318$		0			0
$319$	−15.7309	−	4.21509i	−0.880763	−	0.236000i
$320$		0			0
$321$	−7.95809	−	13.7838i	−0.444177	−	0.769337i
$322$		0			0
$323$	−5.80486	+	10.0543i	−0.322991	+	0.559437i
$324$		0			0
$325$	−13.3024	+	12.1674i	−0.737887	+	0.674925i
$326$		0			0
$327$	12.7097	−	22.0138i	0.702848	−	1.21737i
$328$		0			0
$329$	−6.90301	−	11.9564i	−0.380575	−	0.659176i
$330$		0			0
$331$	−9.70050	−	2.59924i	−0.533188	−	0.142867i	−0.0178279	−	0.999841i	$-0.505675\pi$
$331$	−9.70050	−	2.59924i	−0.533188	−	0.142867i	−0.515360	+	0.856974i	$0.672342\pi$
$332$		0			0
$333$	−1.66277			−0.0911190
$334$		0			0
$335$	11.1287	−	2.45997i	0.608026	−	0.134402i
$336$		0			0
$337$	6.79849	−	6.79849i	0.370337	−	0.370337i	−0.497263	−	0.867600i	$-0.665662\pi$
$337$	6.79849	−	6.79849i	0.370337	−	0.370337i	0.867600	+	0.497263i	$0.165662\pi$
$338$		0			0
$339$			4.74965i			0.257965i
$340$		0			0
$341$	−3.18228	+	5.51188i	−0.172330	+	0.298485i
$342$		0			0
$343$			5.87867i			0.317418i
$344$		0			0
$345$	−1.80190	+	5.70261i	−0.0970110	+	0.307018i
$346$		0			0
$347$	−1.10140	+	4.11047i	−0.0591260	+	0.220661i	−0.989167	−	0.146794i	$-0.953104\pi$
$347$	−1.10140	+	4.11047i	−0.0591260	+	0.220661i	0.930041	+	0.367456i	$0.119771\pi$
$348$		0			0
$349$	1.59334	+	5.94641i	0.0852893	+	0.318304i	0.995369	−	0.0961297i	$-0.0306464\pi$
$349$	1.59334	+	5.94641i	0.0852893	+	0.318304i	−0.910080	+	0.414434i	$0.863980\pi$
$350$		0			0
$351$	0.895264	+	20.3496i	0.0477857	+	1.08618i
$352$		0			0
$353$	−0.343121	−	0.198101i	−0.0182625	−	0.0105439i	0.490841	−	0.871249i	$-0.336690\pi$
$353$	−0.343121	−	0.198101i	−0.0182625	−	0.0105439i	−0.509103	+	0.860705i	$0.670023\pi$
$354$		0			0
$355$	6.07248	+	11.6827i	0.322294	+	0.620056i
$356$		0			0
$357$	8.81278	+	15.2642i	0.466422	+	0.807866i
$358$		0			0
$359$	1.01878	−	1.01878i	0.0537691	−	0.0537691i	−0.679711	−	0.733480i	$-0.737895\pi$
$359$	1.01878	−	1.01878i	0.0537691	−	0.0537691i	0.733480	+	0.679711i	$0.237895\pi$
$360$		0			0
$361$	5.49411	+	3.17203i	0.289164	+	0.166949i
$362$		0			0
$363$	−7.18476	−	7.18476i	−0.377102	−	0.377102i
$364$		0			0
$365$	−10.6871	−	11.6774i	−0.559387	−	0.611221i
$366$		0			0
$367$	−0.538690	+	0.144342i	−0.0281194	+	0.00753457i	−0.272851	−	0.962056i	$-0.587967\pi$
$367$	−0.538690	+	0.144342i	−0.0281194	+	0.00753457i	0.244732	+	0.969591i	$0.421300\pi$
$368$		0			0
$369$	−4.42769	−	4.42769i	−0.230496	−	0.230496i
$370$		0			0
$371$	−12.9280	+	48.2479i	−0.671187	+	2.50491i
$372$		0			0
$373$	27.3357	+	7.32458i	1.41539	+	0.379253i	0.883846	−	0.467778i	$-0.154945\pi$
$373$	27.3357	+	7.32458i	1.41539	+	0.379253i	0.531544	+	0.847031i	$0.321612\pi$
$374$		0			0
$375$	−12.1534	−	9.36144i	−0.627598	−	0.483423i
$376$		0			0
$377$	9.32269	+	29.5335i	0.480143	+	1.52105i
$378$		0			0
$379$	31.8036	−	8.52176i	1.63364	−	0.437733i	0.678674	−	0.734440i	$-0.262555\pi$
$379$	31.8036	−	8.52176i	1.63364	−	0.437733i	0.954969	+	0.296707i	$0.0958883\pi$
$380$		0			0
$381$	−6.91101	+	3.99007i	−0.354062	+	0.204418i
$382$		0			0
$383$	−14.5203	+	8.38333i	−0.741955	+	0.428368i	−0.822780	−	0.568360i	$-0.807578\pi$
$383$	−14.5203	+	8.38333i	−0.741955	+	0.428368i	0.0808246	+	0.996728i	$0.474245\pi$
$384$		0			0
$385$	16.6715	+	0.738210i	0.849659	+	0.0376227i
$386$		0			0
$387$	−1.69055	−	6.30922i	−0.0859355	−	0.320716i
$388$		0			0
$389$	8.29738			0.420694			0.210347	−	0.977627i	$-0.432541\pi$
$389$	8.29738			0.420694			0.210347	+	0.977627i	$0.432541\pi$
$390$		0			0
$391$	−6.36113			−0.321696
$392$		0			0
$393$	−0.596651	−	2.22673i	−0.0300970	−	0.112324i
$394$		0			0
$395$	23.7344	−	21.7217i	1.19421	−	1.09294i
$396$		0			0
$397$	28.4794	−	16.4426i	1.42934	−	0.825230i	0.432272	−	0.901743i	$-0.357712\pi$
$397$	28.4794	−	16.4426i	1.42934	−	0.825230i	0.997069	+	0.0765132i	$0.0243787\pi$
$398$		0			0
$399$	−16.6397	+	9.60696i	−0.833029	+	0.480950i
$400$		0			0
$401$	−4.40754	+	1.18100i	−0.220102	+	0.0589762i	−0.367185	−	0.930148i	$-0.619678\pi$
$401$	−4.40754	+	1.18100i	−0.220102	+	0.0589762i	0.147083	+	0.989124i	$0.453012\pi$
$402$		0			0
$403$	12.0915	−	0.531957i	0.602320	−	0.0264986i
$404$		0			0
$405$	−9.60656	+	2.12350i	−0.477354	+	0.105518i
$406$		0			0
$407$	2.72557	+	0.730314i	0.135101	+	0.0362003i
$408$		0			0
$409$	−2.97968	+	11.1203i	−0.147336	+	0.549865i	0.852304	+	0.523046i	$0.175204\pi$
$409$	−2.97968	+	11.1203i	−0.147336	+	0.549865i	−0.999640	+	0.0268189i	$0.991462\pi$
$410$		0			0
$411$	2.31249	+	2.31249i	0.114067	+	0.114067i
$412$		0			0
$413$	16.8267	−	4.50870i	0.827988	−	0.221859i
$414$		0			0
$415$	−28.9091	+	26.4574i	−1.41909	+	1.29875i
$416$		0			0
$417$	−8.93496	−	8.93496i	−0.437547	−	0.437547i
$418$		0			0
$419$	−0.961220	−	0.554961i	−0.0469587	−	0.0271116i	0.476337	−	0.879263i	$-0.341964\pi$
$419$	−0.961220	−	0.554961i	−0.0469587	−	0.0271116i	−0.523296	+	0.852151i	$0.675298\pi$
$420$		0			0
$421$	−8.20503	+	8.20503i	−0.399888	+	0.399888i	−0.878194	−	0.478305i	$-0.841251\pi$
$421$	−8.20503	+	8.20503i	−0.399888	+	0.399888i	0.478305	+	0.878194i	$0.341251\pi$
$422$		0			0
$423$	1.95940	+	3.39377i	0.0952691	+	0.165011i
$424$		0			0
$425$	5.59973	−	15.3262i	0.271627	−	0.743430i
$426$		0			0
$427$	43.1868	+	24.9339i	2.08996	+	1.20664i
$428$		0			0
$429$	2.02717	−	9.15840i	0.0978728	−	0.442172i
$430$		0			0
$431$	−1.85441	−	6.92074i	−0.0893236	−	0.333360i	0.906774	−	0.421617i	$-0.138537\pi$
$431$	−1.85441	−	6.92074i	−0.0893236	−	0.333360i	−0.996098	+	0.0882564i	$0.971871\pi$
$432$		0			0
$433$	−4.74484	+	17.7080i	−0.228022	+	0.850991i	0.753149	+	0.657850i	$0.228534\pi$
$433$	−4.74484	+	17.7080i	−0.228022	+	0.850991i	−0.981171	+	0.193140i	$0.938133\pi$
$434$		0			0
$435$	−23.3839	+	12.1545i	−1.12117	+	0.582766i
$436$		0			0
$437$		−	6.93438i		−	0.331716i
$438$		0			0
$439$	−17.8096	+	30.8472i	−0.850008	+	1.47226i	0.0311922	+	0.999513i	$0.490070\pi$
$439$	−17.8096	+	30.8472i	−0.850008	+	1.47226i	−0.881200	+	0.472743i	$0.843264\pi$
$440$		0			0
$441$		−	9.48953i		−	0.451883i
$442$		0			0
$443$	24.4503	−	24.4503i	1.16167	−	1.16167i	0.177558	−	0.984110i	$-0.443180\pi$
$443$	24.4503	−	24.4503i	1.16167	−	1.16167i	0.984110	−	0.177558i	$-0.0568197\pi$
$444$		0			0
$445$	−9.89210	+	15.5063i	−0.468931	+	0.735071i
$446$		0			0
$447$	−29.2075			−1.38147
$448$		0			0
$449$	29.2540	+	7.83860i	1.38058	+	0.369926i	0.871333	−	0.490692i	$-0.163256\pi$
$449$	29.2540	+	7.83860i	1.38058	+	0.369926i	0.509250	+	0.860618i	$0.329923\pi$
$450$		0			0
$451$	5.31306	+	9.20248i	0.250182	+	0.433328i
$452$		0			0
$453$	−13.7329	+	23.7860i	−0.645226	+	1.11756i
$454$		0			0
$455$	−15.8594	−	27.4874i	−0.743501	−	1.28863i
$456$		0			0
$457$	−1.85187	+	3.20754i	−0.0866270	+	0.150042i	−0.906083	−	0.423099i	$-0.860942\pi$
$457$	−1.85187	+	3.20754i	−0.0866270	+	0.150042i	0.819456	+	0.573142i	$0.194276\pi$
$458$		0			0
$459$	−9.21823	−	15.9664i	−0.430270	−	0.745250i
$460$		0			0
$461$	27.9827	+	7.49794i	1.30328	+	0.349214i	0.842691	−	0.538398i	$-0.180970\pi$
$461$	27.9827	+	7.49794i	1.30328	+	0.349214i	0.460593	+	0.887611i	$0.347637\pi$
$462$		0			0
$463$	−12.9117			−0.600056			−0.300028	−	0.953930i	$-0.596996\pi$
$463$	−12.9117			−0.600056			−0.300028	+	0.953930i	$0.596996\pi$
$464$		0			0
$465$	2.22296	+	10.0565i	0.103087	+	0.466360i
$466$		0			0
$467$	3.85556	−	3.85556i	0.178414	−	0.178414i	−0.612250	−	0.790664i	$-0.709735\pi$
$467$	3.85556	−	3.85556i	0.178414	−	0.178414i	0.790664	+	0.612250i	$0.209735\pi$
$468$		0			0
$469$			20.0629i			0.926418i
$470$		0			0
$471$	9.15400	−	15.8552i	0.421794	−	0.730569i
$472$		0			0
$473$			11.0844i			0.509664i
$474$		0			0
$475$	16.7073	+	6.10436i	0.766586	+	0.280087i
$476$		0			0
$477$	3.66956	−	13.6950i	0.168018	−	0.627051i
$478$		0			0
$479$	−7.71558	−	28.7949i	−0.352534	−	1.31567i	−0.883560	−	0.468319i	$-0.844860\pi$
$479$	−7.71558	−	28.7949i	−0.352534	−	1.31567i	0.531026	−	0.847356i	$-0.321807\pi$
$480$		0			0
$481$	−1.61527	−	5.11703i	−0.0736498	−	0.233317i
$482$		0			0
$483$	−9.11716	−	5.26379i	−0.414845	−	0.239511i
$484$		0			0
$485$	2.22137	−	7.03013i	0.100867	−	0.319222i
$486$		0			0
$487$	−0.523570	−	0.906849i	−0.0237252	−	0.0410933i	0.853919	−	0.520406i	$-0.174219\pi$
$487$	−0.523570	−	0.906849i	−0.0237252	−	0.0410933i	−0.877644	+	0.479313i	$0.840886\pi$
$488$		0			0
$489$	21.8962	−	21.8962i	0.990180	−	0.990180i
$490$		0			0
$491$	−37.2673	−	21.5163i	−1.68185	−	0.971016i	−0.960431	−	0.278517i	$-0.910157\pi$
$491$	−37.2673	−	21.5163i	−1.68185	−	0.971016i	−0.721418	−	0.692500i	$-0.756509\pi$
$492$		0			0
$493$	−19.8212	−	19.8212i	−0.892700	−	0.892700i
$494$		0			0
$495$	−4.73215	−	0.209538i	−0.212694	−	0.00941805i
$496$		0			0
$497$	−22.3877	+	5.99877i	−1.00423	+	0.269082i
$498$		0			0
$499$	−23.9380	−	23.9380i	−1.07161	−	1.07161i	−0.997230	−	0.0743807i	$-0.976302\pi$
$499$	−23.9380	−	23.9380i	−1.07161	−	1.07161i	−0.0743807	−	0.997230i	$-0.523698\pi$
$500$		0			0
$501$	4.29649	−	16.0347i	0.191953	−	0.716379i
$502$		0			0
$503$	16.5893	+	4.44508i	0.739678	+	0.198196i	0.608935	−	0.793220i	$-0.291597\pi$
$503$	16.5893	+	4.44508i	0.739678	+	0.198196i	0.130743	+	0.991416i	$0.458264\pi$
$504$		0			0
$505$	5.45157	+	24.6625i	0.242591	+	1.09747i
$506$		0			0
$507$	−16.7578	+	6.11198i	−0.744241	+	0.271443i
$508$		0			0
$509$	31.9359	−	8.55721i	1.41554	−	0.379291i	0.531638	−	0.846972i	$-0.321577\pi$
$509$	31.9359	−	8.55721i	1.41554	−	0.379291i	0.883898	+	0.467681i	$0.154910\pi$
$510$		0			0
$511$	24.1318	−	13.9325i	1.06753	−	0.616336i
$512$		0			0
$513$	17.4053	−	10.0490i	0.768462	−	0.443672i
$514$		0			0
$515$	−1.33038	+	30.0449i	−0.0586235	+	1.32394i
$516$		0			0
$517$	−1.72120	−	6.42360i	−0.0756982	−	0.282510i
$518$		0			0
$519$	7.57280			0.332409
$520$		0			0
$521$	−30.4907			−1.33582			−0.667910	−	0.744242i	$-0.732811\pi$
$521$	−30.4907			−1.33582			−0.667910	+	0.744242i	$0.732811\pi$
$522$		0			0
$523$	−4.10869	−	15.3338i	−0.179660	−	0.670502i	−0.995711	−	0.0925209i	$-0.970508\pi$
$523$	−4.10869	−	15.3338i	−0.179660	−	0.670502i	0.816050	−	0.577981i	$-0.196159\pi$
$524$		0			0
$525$	20.7082	−	17.3327i	0.903780	−	0.756461i
$526$		0			0
$527$	−9.48709	+	5.47738i	−0.413264	+	0.238598i
$528$		0			0
$529$	−16.6282	+	9.60028i	−0.722964	+	0.417403i
$530$		0			0
$531$	−4.77621	+	1.27978i	−0.207270	+	0.0555377i
$532$		0			0
$533$	9.32467	−	17.9271i	0.403896	−	0.776508i
$534$		0			0
$535$	−21.8669	−	13.9498i	−0.945390	−	0.603101i
$536$		0			0
$537$	29.7623	+	7.97479i	1.28434	+	0.344138i
$538$		0			0
$539$	−4.16796	+	15.5550i	−0.179527	+	0.670003i
$540$		0			0
$541$	3.14795	+	3.14795i	0.135341	+	0.135341i	0.771532	−	0.636191i	$-0.219491\pi$
$541$	3.14795	+	3.14795i	0.135341	+	0.135341i	−0.636191	+	0.771532i	$0.719491\pi$
$542$		0			0
$543$	−17.5753	+	4.70930i	−0.754230	+	0.202095i
$544$		0			0
$545$	1.83247	−	41.3839i	0.0784942	−	1.77269i
$546$		0			0
$547$	16.4832	+	16.4832i	0.704771	+	0.704771i	0.965431	−	0.260660i	$-0.0839401\pi$
$547$	16.4832	+	16.4832i	0.704771	+	0.704771i	−0.260660	+	0.965431i	$0.583940\pi$
$548$		0			0
$549$	−12.2584	−	7.07741i	−0.523177	−	0.302056i
$550$		0			0
$551$	21.6074	−	21.6074i	0.920506	−	0.920506i
$552$		0			0
$553$	28.3180	+	49.0482i	1.20420	+	2.08574i
$554$		0			0
$555$	4.05154	−	2.10592i	0.171978	−	0.0893913i
$556$		0			0
$557$	−36.2108	−	20.9063i	−1.53430	−	0.885828i	−0.999156	−	0.0410659i	$-0.986925\pi$
$557$	−36.2108	−	20.9063i	−1.53430	−	0.885828i	−0.535142	−	0.844762i	$-0.679742\pi$
$558$		0			0
$559$	17.7739	−	11.3315i	0.751755	−	0.479272i
$560$		0			0
$561$	2.19738	+	8.20073i	0.0927734	+	0.346235i
$562$		0			0
$563$	2.61558	−	9.76146i	0.110233	−	0.411396i	−0.888653	−	0.458581i	$-0.848358\pi$
$563$	2.61558	−	9.76146i	0.110233	−	0.411396i	0.998886	+	0.0471841i	$0.0150247\pi$
$564$		0			0
$565$	3.56979	+	6.86785i	0.150182	+	0.288933i
$566$		0			0
$567$		−	17.3188i		−	0.727320i
$568$		0			0
$569$	−9.12942	+	15.8126i	−0.382725	+	0.662899i	−0.991451	−	0.130482i	$-0.958348\pi$
$569$	−9.12942	+	15.8126i	−0.382725	+	0.662899i	0.608726	+	0.793381i	$0.291681\pi$
$570$		0			0
$571$		−	29.0252i		−	1.21467i	−0.794447	−	0.607334i	$-0.792239\pi$
$571$		−	29.0252i		−	1.21467i	0.794447	−	0.607334i	$-0.207761\pi$
$572$		0			0
$573$	−5.21049	+	5.21049i	−0.217671	+	0.217671i
$574$		0			0
$575$	1.68053	+	9.60010i	0.0700831	+	0.400352i
$576$		0			0
$577$	−8.27590			−0.344530			−0.172265	−	0.985051i	$-0.555109\pi$
$577$	−8.27590			−0.344530			−0.172265	+	0.985051i	$0.555109\pi$
$578$		0			0
$579$	3.47873	+	0.932124i	0.144571	+	0.0387378i
$580$		0			0
$581$	−34.4919	−	59.7417i	−1.43097	−	2.47850i
$582$		0			0
$583$	−12.0301	+	20.8368i	−0.498237	+	0.862972i
$584$		0			0
$585$	4.50164	+	7.80220i	0.186120	+	0.322581i
$586$		0			0
$587$	−11.8497	+	20.5242i	−0.489088	+	0.847125i	−0.999921	−	0.0125547i	$-0.996004\pi$
$587$	−11.8497	+	20.5242i	−0.489088	+	0.847125i	0.510833	+	0.859680i	$0.329337\pi$
$588$		0			0
$589$	−5.97098	−	10.3420i	−0.246030	−	0.426136i
$590$		0			0
$591$	−8.63553	−	2.31388i	−0.355218	−	0.0951804i
$592$		0			0
$593$	27.0364			1.11025			0.555125	−	0.831767i	$-0.312670\pi$
$593$	27.0364			1.11025			0.555125	+	0.831767i	$0.312670\pi$
$594$		0			0
$595$	24.2154	+	15.4480i	0.992736	+	0.633305i
$596$		0			0
$597$	5.31983	−	5.31983i	0.217726	−	0.217726i
$598$		0			0
$599$			35.7007i			1.45869i	0.684146	+	0.729345i	$0.260175\pi$
$599$			35.7007i			1.45869i	−0.684146	+	0.729345i	$0.739825\pi$
$600$		0			0
$601$	14.8079	−	25.6480i	0.604027	−	1.04620i	−0.388178	−	0.921584i	$-0.626895\pi$
$601$	14.8079	−	25.6480i	0.604027	−	1.04620i	0.992205	−	0.124620i	$-0.0397713\pi$
$602$		0			0
$603$		−	5.69478i		−	0.231910i
$604$		0			0
$605$	−15.7890	−	4.98896i	−0.641912	−	0.202830i
$606$		0			0
$607$	−7.84122	+	29.2638i	−0.318265	+	1.18778i	0.602646	+	0.798009i	$0.294113\pi$
$607$	−7.84122	+	29.2638i	−0.318265	+	1.18778i	−0.920911	+	0.389773i	$0.872554\pi$
$608$		0			0
$609$	−12.0070	−	44.8108i	−0.486549	−	1.81582i
$610$		0			0
$611$	−8.54066	+	9.32672i	−0.345518	+	0.377319i
$612$		0			0
$613$	−20.6003	−	11.8936i	−0.832036	−	0.480376i	0.0225130	−	0.999747i	$-0.492833\pi$
$613$	−20.6003	−	11.8936i	−0.832036	−	0.480376i	−0.854549	+	0.519370i	$0.826167\pi$
$614$		0			0
$615$	16.3964	+	5.18089i	0.661165	+	0.208914i
$616$		0			0
$617$	4.90280	+	8.49190i	0.197379	+	0.341871i	0.947678	−	0.319228i	$-0.103424\pi$
$617$	4.90280	+	8.49190i	0.197379	+	0.341871i	−0.750299	+	0.661099i	$0.770090\pi$
$618$		0			0
$619$	−0.211255	+	0.211255i	−0.00849105	+	0.00849105i	−0.711340	−	0.702849i	$-0.751911\pi$
$619$	−0.211255	+	0.211255i	−0.00849105	+	0.00849105i	0.702849	+	0.711340i	$0.251911\pi$
$620$		0			0
$621$	9.53661	+	5.50596i	0.382691	+	0.220947i
$622$		0			0
$623$	−22.8942	−	22.8942i	−0.917238	−	0.917238i
$624$		0			0
$625$	−24.6094	−	4.40201i	−0.984376	−	0.176080i
$626$		0			0
$627$	−8.93976	+	2.39540i	−0.357019	+	0.0956631i
$628$		0			0
$629$	3.43425	+	3.43425i	0.136932	+	0.136932i
$630$		0			0
$631$	3.19224	−	11.9136i	0.127081	−	0.474273i	−0.872824	−	0.488035i	$-0.837714\pi$
$631$	3.19224	−	11.9136i	0.127081	−	0.474273i	0.999905	+	0.0137616i	$0.00438059\pi$
$632$		0			0
$633$	18.9845	+	5.08687i	0.754564	+	0.202185i
$634$		0			0
$635$	−6.99422	+	10.9638i	−0.277557	+	0.435084i
$636$		0			0
$637$	29.2033	−	9.21845i	1.15708	−	0.365248i
$638$		0			0
$639$	6.35468	−	1.70273i	0.251387	−	0.0673590i
$640$		0			0
$641$	8.13416	−	4.69626i	0.321280	−	0.185491i	−0.330683	−	0.943742i	$-0.607279\pi$
$641$	8.13416	−	4.69626i	0.321280	−	0.185491i	0.651963	+	0.758251i	$0.273946\pi$
$642$		0			0
$643$	32.0818	−	18.5225i	1.26518	−	0.730454i	0.291111	−	0.956689i	$-0.405975\pi$
$643$	32.0818	−	18.5225i	1.26518	−	0.730454i	0.974073	+	0.226235i	$0.0726416\pi$
$644$		0			0
$645$	12.1100	+	13.2321i	0.476829	+	0.521014i
$646$		0			0
$647$	−5.71989	−	21.3469i	−0.224872	−	0.839234i	−0.982456	−	0.186496i	$-0.940287\pi$
$647$	−5.71989	−	21.3469i	−0.224872	−	0.839234i	0.757584	−	0.652738i	$-0.226380\pi$
$648$		0			0
$649$	8.39115			0.329381
$650$		0			0
$651$	−18.1300			−0.710569
$652$		0			0
$653$	−5.48243	−	20.4607i	−0.214544	−	0.800689i	−0.986327	−	0.164803i	$-0.947301\pi$
$653$	−5.48243	−	20.4607i	−0.214544	−	0.800689i	0.771783	−	0.635886i	$-0.219365\pi$
$654$		0			0
$655$	−2.53633	−	2.77135i	−0.0991025	−	0.108286i
$656$		0			0
$657$	−6.84972	+	3.95469i	−0.267233	+	0.154287i
$658$		0			0
$659$	2.59430	−	1.49782i	0.101060	−	0.0583468i	−0.448618	−	0.893723i	$-0.648084\pi$
$659$	2.59430	−	1.49782i	0.101060	−	0.0583468i	0.549678	+	0.835377i	$0.314750\pi$
$660$		0			0
$661$	12.0257	−	3.22227i	0.467744	−	0.125332i	−0.0172459	−	0.999851i	$-0.505490\pi$
$661$	12.0257	−	3.22227i	0.467744	−	0.125332i	0.484990	+	0.874520i	$0.338823\pi$
$662$		0			0
$663$	10.9035	−	11.9070i	0.423456	−	0.462430i
$664$		0			0
$665$	−16.8401	+	26.3976i	−0.653031	+	1.02366i
$666$		0			0
$667$	16.1724	+	4.33337i	0.626197	+	0.167789i
$668$		0			0
$669$	2.87846	−	10.7426i	0.111288	−	0.415332i
$670$		0			0
$671$	16.9852	+	16.9852i	0.655708	+	0.655708i
$672$		0			0
$673$	−11.5724	+	3.10082i	−0.446084	+	0.119528i	−0.474867	−	0.880058i	$-0.657504\pi$
$673$	−11.5724	+	3.10082i	−0.446084	+	0.119528i	0.0287825	+	0.999586i	$0.490837\pi$
$674$		0			0
$675$	−21.6609	+	18.1301i	−0.833729	+	0.697829i
$676$		0			0
$677$	20.8173	+	20.8173i	0.800072	+	0.800072i	0.983107	−	0.183034i	$-0.0585919\pi$
$677$	20.8173	+	20.8173i	0.800072	+	0.800072i	−0.183034	+	0.983107i	$0.558592\pi$
$678$		0			0
$679$	11.2395	+	6.48916i	0.431334	+	0.249031i
$680$		0			0
$681$	6.45510	−	6.45510i	0.247360	−	0.247360i
$682$		0			0
$683$	13.1132	+	22.7128i	0.501764	+	0.869080i	0.999998	+	0.00203769i	$0.000648618\pi$
$683$	13.1132	+	22.7128i	0.501764	+	0.869080i	−0.498234	+	0.867042i	$0.666018\pi$
$684$		0			0
$685$	5.08183	+	1.60575i	0.194167	+	0.0613524i
$686$		0			0
$687$	−10.6314	−	6.13807i	−0.405615	−	0.234182i
$688$		0			0
$689$	45.7100	−	2.01098i	1.74141	−	0.0766122i
$690$		0			0
$691$	−0.868516	−	3.24135i	−0.0330399	−	0.123307i	0.947436	−	0.319945i	$-0.103664\pi$
$691$	−0.868516	−	3.24135i	−0.0330399	−	0.123307i	−0.980476	+	0.196638i	$0.936998\pi$
$692$		0			0
$693$	2.15809	−	8.05411i	0.0819791	−	0.305950i
$694$		0			0
$695$	−19.6351	−	6.20426i	−0.744802	−	0.235341i
$696$		0			0
$697$			18.2898i			0.692774i
$698$		0			0
$699$	12.5086	−	21.6655i	0.473118	−	0.819465i
$700$		0			0
$701$			12.3175i			0.465226i	0.972569	+	0.232613i	$0.0747276\pi$
$701$			12.3175i			0.465226i	−0.972569	+	0.232613i	$0.925272\pi$
$702$		0			0
$703$	−3.74373	+	3.74373i	−0.141198	+	0.141198i
$704$		0			0
$705$	−9.07259	−	5.78776i	−0.341693	−	0.217979i
$706$		0			0
$707$	−44.4617			−1.67215
$708$		0			0
$709$	30.1347	+	8.07458i	1.13173	+	0.303247i	0.775623	−	0.631197i	$-0.217436\pi$
$709$	30.1347	+	8.07458i	1.13173	+	0.303247i	0.356111	+	0.934444i	$0.384103\pi$
$710$		0			0
$711$	−8.03796	−	13.9222i	−0.301447	−	0.522122i
$712$		0			0
$713$	3.27159	−	5.66655i	0.122522	−	0.212214i
$714$		0			0
$715$	−3.95213	−	14.7664i	−0.147801	−	0.552232i
$716$		0			0
$717$	−6.39013	+	11.0680i	−0.238644	+	0.413343i
$718$		0			0
$719$	20.3069	+	35.1725i	0.757318	+	1.31171i	0.944214	+	0.329334i	$0.106824\pi$
$719$	20.3069	+	35.1725i	0.757318	+	1.31171i	−0.186895	+	0.982380i	$0.559843\pi$
$720$		0			0
$721$	−51.1363	−	13.7019i	−1.90442	−	0.510287i
$722$		0			0
$723$	21.2468			0.790175
$724$		0			0
$725$	−24.6772	+	35.1502i	−0.916489	+	1.30545i
$726$		0			0
$727$	−17.4875	+	17.4875i	−0.648577	+	0.648577i	−0.952649	−	0.304072i	$-0.901654\pi$
$727$	−17.4875	+	17.4875i	−0.648577	+	0.648577i	0.304072	+	0.952649i	$0.401654\pi$
$728$		0			0
$729$			28.1710i			1.04337i
$730$		0			0
$731$	−9.53933	+	16.5226i	−0.352825	+	0.611110i
$732$		0			0
$733$			31.8347i			1.17584i	0.808918	+	0.587921i	$0.200053\pi$
$733$			31.8347i			1.17584i	−0.808918	+	0.587921i	$0.799947\pi$
$734$		0			0
$735$	12.0186	+	23.1225i	0.443314	+	0.852884i
$736$		0			0
$737$	−2.50124	+	9.33476i	−0.0921344	+	0.343850i
$738$		0			0
$739$	1.90923	+	7.12535i	0.0702322	+	0.262110i	0.992110	−	0.125371i	$-0.0400120\pi$
$739$	1.90923	+	7.12535i	0.0702322	+	0.262110i	−0.921878	+	0.387481i	$0.873345\pi$
$740$		0			0
$741$	12.9800	+	11.8861i	0.476834	+	0.436646i
$742$		0			0
$743$	−38.0656	−	21.9772i	−1.39649	−	0.806265i	−0.402469	−	0.915434i	$-0.631848\pi$
$743$	−38.0656	−	21.9772i	−1.39649	−	0.806265i	−0.994023	+	0.109169i	$0.965181\pi$
$744$		0			0
$745$	−42.2332	+	21.9521i	−1.54731	+	0.804262i
$746$		0			0
$747$	9.79041	+	16.9575i	0.358212	+	0.620442i
$748$		0			0
$749$	32.2853	−	32.2853i	1.17968	−	1.17968i
$750$		0			0
$751$	−39.4235	−	22.7612i	−1.43858	−	0.830567i	−0.440832	−	0.897590i	$-0.645317\pi$
$751$	−39.4235	−	22.7612i	−1.43858	−	0.830567i	−0.997751	+	0.0670229i	$0.978650\pi$
$752$		0			0
$753$	−1.63807	−	1.63807i	−0.0596946	−	0.0596946i
$754$		0			0
$755$	−1.97998	+	44.7153i	−0.0720590	+	1.62736i
$756$		0			0
$757$	28.5214	−	7.64229i	1.03663	−	0.277764i	0.299913	−	0.953967i	$-0.403042\pi$
$757$	28.5214	−	7.64229i	1.03663	−	0.277764i	0.736715	+	0.676203i	$0.236376\pi$
$758$		0			0
$759$	−3.58575	−	3.58575i	−0.130154	−	0.130154i
$760$		0			0
$761$	−2.80150	+	10.4553i	−0.101554	+	0.379006i	−0.997932	−	0.0642862i	$-0.979523\pi$
$761$	−2.80150	+	10.4553i	−0.101554	+	0.379006i	0.896377	+	0.443292i	$0.146190\pi$
$762$		0			0
$763$	70.4352	+	18.8731i	2.54993	+	0.683251i
$764$		0			0
$765$	−6.87347	−	4.38485i	−0.248511	−	0.158535i
$766$		0			0
$767$	−8.57819	−	13.4552i	−0.309741	−	0.485838i
$768$		0			0
$769$	−21.4310	+	5.74241i	−0.772820	+	0.207077i	−0.623617	−	0.781730i	$-0.714337\pi$
$769$	−21.4310	+	5.74241i	−0.772820	+	0.207077i	−0.149203	+	0.988807i	$0.547671\pi$
$770$		0			0
$771$	12.3140	−	7.10949i	0.443478	−	0.256042i
$772$		0			0
$773$	15.0395	−	8.68305i	0.540933	−	0.312308i	−0.204524	−	0.978862i	$-0.565565\pi$
$773$	15.0395	−	8.68305i	0.540933	−	0.312308i	0.745457	+	0.666554i	$0.232231\pi$
$774$		0			0
$775$	10.7727	+	12.8707i	0.386968	+	0.462329i
$776$		0			0
$777$	2.08036	+	7.76399i	0.0746323	+	0.278532i
$778$		0			0
$779$	−19.9380			−0.714352
$780$		0			0
$781$	−11.1643			−0.399491
$782$		0			0
$783$	12.5594	+	46.8724i	0.448837	+	1.67508i
$784$		0			0
$785$	1.31981	−	29.8062i	0.0471061	−	1.06383i
$786$		0			0
$787$	−12.3020	+	7.10259i	−0.438521	+	0.253180i	−0.702970	−	0.711220i	$-0.748143\pi$
$787$	−12.3020	+	7.10259i	−0.438521	+	0.253180i	0.264449	+	0.964400i	$0.414810\pi$
$788$		0			0
$789$	−2.42187	+	1.39827i	−0.0862210	+	0.0497797i
$790$		0			0
$791$	−13.1609	+	3.52645i	−0.467948	+	0.125386i
$792$		0			0
$793$	9.87193	−	44.5996i	0.350562	−	1.58378i
$794$		0			0
$795$	8.40357	+	38.0172i	0.298044	+	1.34833i
$796$		0			0
$797$	−34.5731	−	9.26384i	−1.22464	−	0.328142i	−0.412151	−	0.911115i	$-0.635222\pi$
$797$	−34.5731	−	9.26384i	−1.22464	−	0.328142i	−0.812491	+	0.582974i	$0.801889\pi$
$798$		0			0
$799$	2.96254	−	11.0564i	0.104807	−	0.391146i
$800$		0			0
$801$	6.49845	+	6.49845i	0.229611	+	0.229611i
$802$		0			0
$803$	12.9649	−	3.47392i	0.457520	−	0.122592i
$804$		0			0
$805$	−17.1394	−	0.758926i	−0.604083	−	0.0267486i
$806$		0			0
$807$	−2.90501	−	2.90501i	−0.102261	−	0.102261i
$808$		0			0
$809$	−41.6902	−	24.0699i	−1.46575	−	0.846251i	−0.466483	−	0.884530i	$-0.654479\pi$
$809$	−41.6902	−	24.0699i	−1.46575	−	0.846251i	−0.999267	+	0.0382785i	$0.987813\pi$
$810$		0			0
$811$	−5.10824	+	5.10824i	−0.179375	+	0.179375i	−0.791083	−	0.611709i	$-0.790483\pi$
$811$	−5.10824	+	5.10824i	−0.179375	+	0.179375i	0.611709	+	0.791083i	$0.290483\pi$
$812$		0			0
$813$	19.3901	+	33.5847i	0.680041	+	1.17787i
$814$		0			0
$815$	15.2043	−	48.1182i	0.532583	−	1.68551i
$816$		0			0
$817$	−18.0116	−	10.3990i	−0.630145	−	0.363814i
$818$		0			0
$819$	−15.1209	+	4.77314i	−0.528368	+	0.166787i
$820$		0			0
$821$	6.56803	+	24.5122i	0.229226	+	0.855483i	0.980667	+	0.195683i	$0.0626923\pi$
$821$	6.56803	+	24.5122i	0.229226	+	0.855483i	−0.751441	+	0.659800i	$0.770641\pi$
$822$		0			0
$823$	−2.47310	+	9.22975i	−0.0862070	+	0.321729i	−0.995540	−	0.0943402i	$-0.969926\pi$
$823$	−2.47310	+	9.22975i	−0.0862070	+	0.321729i	0.909333	+	0.416069i	$0.136593\pi$
$824$		0			0
$825$	11.7959	−	5.48278i	0.410680	−	0.190886i
$826$		0			0
$827$		−	11.7291i		−	0.407860i	−0.978985	−	0.203930i	$-0.934629\pi$
$827$		−	11.7291i		−	0.407860i	0.978985	−	0.203930i	$-0.0653715\pi$
$828$		0			0
$829$	12.8966	−	22.3376i	0.447918	−	0.775817i	−0.550332	−	0.834946i	$-0.685499\pi$
$829$	12.8966	−	22.3376i	0.447918	−	0.775817i	0.998250	+	0.0591286i	$0.0188322\pi$
$830$		0			0
$831$		−	36.9680i		−	1.28241i
$832$		0			0
$833$	−19.5995	+	19.5995i	−0.679083	+	0.679083i
$834$		0			0
$835$	−5.83894	−	26.4149i	−0.202065	−	0.914127i
$836$		0			0
$837$	18.9641			0.655494
$838$		0			0
$839$	6.07419	+	1.62757i	0.209704	+	0.0561901i	0.362142	−	0.932123i	$-0.382046\pi$
$839$	6.07419	+	1.62757i	0.209704	+	0.0561901i	−0.152437	+	0.988313i	$0.548712\pi$
$840$		0			0
$841$	22.3901	+	38.7808i	0.772073	+	1.33727i
$842$		0			0
$843$	1.70958	−	2.96108i	0.0588810	−	0.101985i
$844$		0			0
$845$	−19.6376	+	21.4328i	−0.675555	+	0.737310i
$846$		0			0
$847$	14.5740	−	25.2429i	0.500768	−	0.867356i
$848$		0			0
$849$	−5.88488	−	10.1929i	−0.201969	−	0.349820i
$850$		0			0
$851$	−2.80205	−	0.750808i	−0.0960532	−	0.0257374i
$852$		0			0
$853$	−48.9142			−1.67479			−0.837394	−	0.546599i	$-0.815922\pi$
$853$	−48.9142			−1.67479			−0.837394	+	0.546599i	$0.815922\pi$
$854$		0			0
$855$	4.78000	−	7.49288i	0.163473	−	0.256251i
$856$		0			0
$857$	−5.72229	+	5.72229i	−0.195470	+	0.195470i	−0.798055	−	0.602585i	$-0.794137\pi$
$857$	−5.72229	+	5.72229i	−0.195470	+	0.195470i	0.602585	+	0.798055i	$0.294137\pi$
$858$		0			0
$859$			19.4601i			0.663971i	0.943284	+	0.331986i	$0.107719\pi$
$859$			19.4601i			0.663971i	−0.943284	+	0.331986i	$0.892281\pi$
$860$		0			0
$861$	−15.1346	+	26.2140i	−0.515787	+	0.893370i
$862$		0			0
$863$			9.62230i			0.327547i	0.986498	+	0.163773i	$0.0523666\pi$
$863$			9.62230i			0.327547i	−0.986498	+	0.163773i	$0.947633\pi$
$864$		0			0
$865$	10.9500	−	5.69164i	0.372313	−	0.193522i
$866$		0			0
$867$	2.25510	−	8.41615i	0.0765873	−	0.285828i
$868$		0			0
$869$	7.06081	+	26.3513i	0.239522	+	0.893907i
$870$		0			0
$871$	17.5253	−	5.53210i	0.593821	−	0.187448i
$872$		0			0
$873$	−3.19031	−	1.84192i	−0.107976	−	0.0623397i
$874$		0			0
$875$	16.9164	−	40.6266i	0.571877	−	1.37343i
$876$		0			0
$877$	16.8244	+	29.1407i	0.568120	+	0.984013i	0.996752	+	0.0805336i	$0.0256624\pi$
$877$	16.8244	+	29.1407i	0.568120	+	0.984013i	−0.428632	+	0.903479i	$0.641004\pi$
$878$		0			0
$879$	9.31630	−	9.31630i	0.314231	−	0.314231i
$880$		0			0
$881$	14.0355	+	8.10341i	0.472869	+	0.273011i	0.717440	−	0.696620i	$-0.245314\pi$
$881$	14.0355	+	8.10341i	0.472869	+	0.273011i	−0.244571	+	0.969631i	$0.578647\pi$
$882$		0			0
$883$	11.4033	+	11.4033i	0.383751	+	0.383751i	0.872451	−	0.488701i	$-0.162529\pi$
$883$	11.4033	+	11.4033i	0.383751	+	0.383751i	−0.488701	+	0.872451i	$0.662529\pi$
$884$		0			0
$885$	10.0170	−	9.16748i	0.336717	−	0.308162i
$886$		0			0
$887$	36.4811	−	9.77507i	1.22491	−	0.328215i	0.412317	−	0.911041i	$-0.364720\pi$
$887$	36.4811	−	9.77507i	1.22491	−	0.328215i	0.812597	+	0.582826i	$0.198053\pi$
$888$		0			0
$889$	−16.1874	−	16.1874i	−0.542907	−	0.542907i
$890$		0			0
$891$	2.15913	−	8.05799i	0.0723336	−	0.269953i
$892$		0			0
$893$	12.0527	+	3.22952i	0.403329	+	0.108072i
$894$		0			0
$895$	49.0292	−	10.8378i	1.63887	−	0.362266i
$896$		0			0
$897$	−2.08406	+	9.41541i	−0.0695847	+	0.314371i
$898$		0			0
$899$	27.8511	−	7.46267i	0.928886	−	0.248894i
$900$		0			0
$901$	−35.8645	+	20.7064i	−1.19482	+	0.689829i
$902$		0			0
$903$	−27.3447	+	15.7875i	−0.909974	+	0.525374i
$904$		0			0
$905$	−21.8740	+	20.0190i	−0.727115	+	0.665453i
$906$		0			0
$907$	2.90409	+	10.8382i	0.0964288	+	0.359877i	0.997232	−	0.0743499i	$-0.0236882\pi$
$907$	2.90409	+	10.8382i	0.0964288	+	0.359877i	−0.900803	+	0.434227i	$0.857021\pi$
$908$		0			0
$909$	12.6203			0.418589
$910$		0			0
$911$	3.03630			0.100597			0.0502985	−	0.998734i	$-0.483983\pi$
$911$	3.03630			0.100597			0.0502985	+	0.998734i	$0.483983\pi$
$912$		0			0
$913$	−8.60022	−	32.0964i	−0.284626	−	1.06224i
$914$		0			0
$915$	38.8329	+	1.71951i	1.28377	+	0.0568452i
$916$		0			0
$917$	5.72711	−	3.30655i	0.189126	−	0.109192i
$918$		0			0
$919$	−30.8704	+	17.8231i	−1.01832	+	0.587929i	−0.913617	−	0.406575i	$-0.866723\pi$
$919$	−30.8704	+	17.8231i	−1.01832	+	0.587929i	−0.104705	+	0.994503i	$0.533390\pi$
$920$		0			0
$921$	22.1132	−	5.92521i	0.728654	−	0.195242i
$922$		0			0
$923$	11.4132	+	17.9019i	0.375669	+	0.589250i
$924$		0			0
$925$	4.27562	−	6.09019i	0.140581	−	0.200244i
$926$		0			0
$927$	14.5149	+	3.88925i	0.476731	+	0.127740i
$928$		0			0
$929$	−11.3000	+	42.1722i	−0.370741	+	1.38363i	0.488727	+	0.872437i	$0.337461\pi$
$929$	−11.3000	+	42.1722i	−0.370741	+	1.38363i	−0.859469	+	0.511189i	$0.829205\pi$
$930$		0			0
$931$	−21.3658	−	21.3658i	−0.700235	−	0.700235i
$932$		0			0
$933$	−43.2101	+	11.5781i	−1.41464	+	0.379050i
$934$		0			0
$935$	9.34093	+	10.2065i	0.305481	+	0.333788i
$936$		0			0
$937$	10.0726	+	10.0726i	0.329059	+	0.329059i	0.852228	−	0.523170i	$-0.175251\pi$
$937$	10.0726	+	10.0726i	0.329059	+	0.329059i	−0.523170	+	0.852228i	$0.675251\pi$
$938$		0			0
$939$	−8.37037	−	4.83263i	−0.273157	−	0.157707i
$940$		0			0
$941$	36.2833	−	36.2833i	1.18280	−	1.18280i	0.203784	−	0.979016i	$-0.434676\pi$
$941$	36.2833	−	36.2833i	1.18280	−	1.18280i	0.979016	−	0.203784i	$-0.0653242\pi$
$942$		0			0
$943$	−5.46215	−	9.46073i	−0.177872	−	0.308084i
$944$		0			0
$945$	−22.9326	−	44.1196i	−0.745997	−	1.43521i
$946$		0			0
$947$	16.8529	+	9.73003i	0.547646	+	0.316184i	0.748172	−	0.663505i	$-0.230932\pi$
$947$	16.8529	+	9.73003i	0.547646	+	0.316184i	−0.200526	+	0.979688i	$0.564265\pi$
$948$		0			0
$949$	−18.8243	−	17.2378i	−0.611062	−	0.559561i
$950$		0			0
$951$	−7.97165	−	29.7506i	−0.258499	−	0.964730i
$952$		0			0
$953$	−8.98557	+	33.5346i	−0.291071	+	1.08629i	0.653217	+	0.757171i	$0.273419\pi$
$953$	−8.98557	+	33.5346i	−0.291071	+	1.08629i	−0.944288	+	0.329121i	$0.893248\pi$
$954$		0			0
$955$	−3.61806	+	11.4504i	−0.117078	+	0.370525i
$956$		0			0
$957$		−	22.3462i		−	0.722351i
$958$		0			0
$959$	−4.69078	+	8.12467i	−0.151473	+	0.262359i
$960$		0			0
$961$			19.7317i			0.636508i
$962$		0			0
$963$	−9.16407	+	9.16407i	−0.295308	+	0.295308i
$964$		0			0
$965$	5.73072	−	1.26676i	0.184479	−	0.0407784i
$966$		0			0
$967$	−29.5727			−0.950993			−0.475497	−	0.879718i	$-0.657732\pi$
$967$	−29.5727			−0.950993			−0.475497	+	0.879718i	$0.657732\pi$
$968$		0			0
$969$	−15.3872	−	4.12298i	−0.494308	−	0.132449i
$970$		0			0
$971$	15.2631	+	26.4365i	0.489817	+	0.848389i	0.999931	−	0.0117182i	$-0.00373011\pi$
$971$	15.2631	+	26.4365i	0.489817	+	0.848389i	−0.510114	+	0.860107i	$0.670397\pi$
$972$		0			0
$973$	18.1242	−	31.3920i	0.581035	−	1.00638i
$974$		0			0
$975$	−20.8504	−	13.3097i	−0.667748	−	0.426250i
$976$		0			0
$977$	25.0029	−	43.3063i	0.799915	−	1.38549i	−0.119757	−	0.992803i	$-0.538211\pi$
$977$	25.0029	−	43.3063i	0.799915	−	1.38549i	0.919671	−	0.392689i	$-0.128455\pi$
$978$		0			0
$979$	−7.79789	−	13.5063i	−0.249222	−	0.431664i
$980$		0			0
$981$	−19.9928	−	5.35705i	−0.638321	−	0.171038i
$982$		0			0
$983$	57.3856			1.83032			0.915158	−	0.403096i	$-0.132066\pi$
$983$	57.3856			1.83032			0.915158	+	0.403096i	$0.132066\pi$
$984$		0			0
$985$	−14.2258	+	3.14457i	−0.453272	+	0.100194i
$986$		0			0
$987$	13.3952	−	13.3952i	0.426372	−	0.426372i
$988$		0			0
$989$		−	11.3955i		−	0.362356i
$990$		0			0
$991$	−5.96166	+	10.3259i	−0.189378	+	0.328013i	−0.945043	−	0.326946i	$-0.893981\pi$
$991$	−5.96166	+	10.3259i	−0.189378	+	0.328013i	0.755665	+	0.654959i	$0.227314\pi$
$992$		0			0
$993$		−	13.7798i		−	0.437290i
$994$		0			0
$995$	3.69399	−	11.6907i	0.117107	−	0.370619i
$996$		0			0
$997$	−11.8526	+	44.2347i	−0.375377	+	1.40093i	0.477416	+	0.878677i	$0.341573\pi$
$997$	−11.8526	+	44.2347i	−0.375377	+	1.40093i	−0.852793	+	0.522249i	$0.825093\pi$
$998$		0			0
$999$	−2.17607	−	8.12119i	−0.0688477	−	0.256943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bk.c.97.3	yes	20
5.2	odd	4		1300.2.bn.d.1293.3		20
5.3	odd	4		260.2.bf.c.253.3	yes	20
5.4	even	2		1300.2.bs.d.357.3		20
13.11	odd	12		260.2.bf.c.37.3	✓	20
65.24	odd	12		1300.2.bn.d.557.3		20
65.37	even	12		1300.2.bs.d.193.3		20
65.63	even	12	inner	260.2.bk.c.193.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.37.3	✓	20	13.11	odd	12
260.2.bf.c.253.3	yes	20	5.3	odd	4
260.2.bk.c.97.3	yes	20	1.1	even	1	trivial
260.2.bk.c.193.3	yes	20	65.63	even	12	inner
1300.2.bn.d.557.3		20	65.24	odd	12
1300.2.bn.d.1293.3		20	5.2	odd	4
1300.2.bs.d.193.3		20	65.37	even	12
1300.2.bs.d.357.3		20	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.355132 + 1.32537i) q^{3} +(1.50965 + 1.64953i) q^{5} +(-3.40883 + 1.96809i) q^{7} +(0.967585 - 0.558635i) q^{9} +O(q^{10})\)	\(q+(0.355132 + 1.32537i) q^{3} +(1.50965 + 1.64953i) q^{5} +(-3.40883 + 1.96809i) q^{7} +(0.967585 - 0.558635i) q^{9} +(-1.83141 + 0.490724i) q^{11} +(2.65910 + 2.43499i) q^{13} +(-1.65012 + 2.58665i) q^{15} +(-3.15223 - 0.844638i) q^{17} +(0.920754 - 3.43630i) q^{19} +(-3.81904 - 3.81904i) q^{21} +(1.88280 - 0.504494i) q^{23} +(-0.441931 + 4.98043i) q^{25} +(3.99474 + 3.99474i) q^{27} +(7.43876 + 4.29477i) q^{29} +(2.37363 - 2.37363i) q^{31} +(-1.30078 - 2.25302i) q^{33} +(-8.39256 - 2.65186i) q^{35} +(-1.28885 - 0.744119i) q^{37} +(-2.28293 + 4.38904i) q^{39} +(-1.45054 - 5.41349i) q^{41} +(1.51311 - 5.64699i) q^{43} +(2.38220 + 0.752723i) q^{45} +3.50747i q^{47} +(4.24675 - 7.35558i) q^{49} -4.47783i q^{51} +(8.97315 - 8.97315i) q^{53} +(-3.57424 - 2.28015i) q^{55} +4.88136 q^{57} +(-4.27489 - 1.14545i) q^{59} +(-6.33455 - 10.9718i) q^{61} +(-2.19889 + 3.80859i) q^{63} +(-0.00229698 + 8.06226i) q^{65} +(2.54852 - 4.41417i) q^{67} +(1.33729 + 2.31625i) q^{69} +(5.68768 + 1.52401i) q^{71} -7.07919 q^{73} +(-6.75787 + 1.18299i) q^{75} +(5.27716 - 5.27716i) q^{77} -14.3886i q^{79} +(-2.19995 + 3.81042i) q^{81} +17.5256i q^{83} +(-3.36550 - 6.47482i) q^{85} +(-3.05042 + 11.3843i) q^{87} +(2.12894 + 7.94530i) q^{89} +(-13.8567 - 3.06712i) q^{91} +(3.98890 + 2.30299i) q^{93} +(7.05831 - 3.66879i) q^{95} +(-1.64859 - 2.85545i) q^{97} +(-1.49790 + 1.49790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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