LMFDB - Embedded newform 260.2.bf.c.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("260.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$20$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.3
Root			$2.86589i$ of defining polynomial
Character	$\chi$	$=$	260.37
Dual form			260.2.bf.c.253.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32537 - 0.355132i) q^{3} +(-1.64953 + 1.50965i) q^{5} +(1.96809 - 3.40883i) q^{7} +(-0.967585 - 0.558635i) q^{9} +O(q^{10})$	\(q+(-1.32537 - 0.355132i) q^{3} +(-1.64953 + 1.50965i) q^{5} +(1.96809 - 3.40883i) q^{7} +(-0.967585 - 0.558635i) q^{9} +(-1.83141 - 0.490724i) q^{11} +(-2.43499 - 2.65910i) q^{13} +(2.72237 - 1.41504i) q^{15} +(-0.844638 - 3.15223i) q^{17} +(-0.920754 - 3.43630i) q^{19} +(-3.81904 + 3.81904i) q^{21} +(0.504494 - 1.88280i) q^{23} +(0.441931 - 4.98043i) q^{25} +(3.99474 + 3.99474i) q^{27} +(-7.43876 + 4.29477i) q^{29} +(2.37363 + 2.37363i) q^{31} +(2.25302 + 1.30078i) q^{33} +(1.89970 + 8.59410i) q^{35} +(-0.744119 - 1.28885i) q^{37} +(2.28293 + 4.38904i) q^{39} +(-1.45054 + 5.41349i) q^{41} +(5.64699 - 1.51311i) q^{43} +(2.43941 - 0.539223i) q^{45} +3.50747 q^{47} +(-4.24675 - 7.35558i) q^{49} +4.47783i q^{51} +(8.97315 - 8.97315i) q^{53} +(3.76179 - 1.95531i) q^{55} +4.88136i q^{57} +(4.27489 - 1.14545i) q^{59} +(-6.33455 + 10.9718i) q^{61} +(-3.80859 + 2.19889i) q^{63} +(8.03091 + 0.710304i) q^{65} +(-4.41417 + 2.54852i) q^{67} +(-1.33729 + 2.31625i) q^{69} +(5.68768 - 1.52401i) q^{71} +7.07919i q^{73} +(-2.35443 + 6.44398i) q^{75} +(-5.27716 + 5.27716i) q^{77} -14.3886i q^{79} +(-2.19995 - 3.81042i) q^{81} -17.5256 q^{83} +(6.15201 + 3.92461i) q^{85} +(11.3843 - 3.05042i) q^{87} +(-2.12894 + 7.94530i) q^{89} +(-13.8567 + 3.06712i) q^{91} +(-2.30299 - 3.98890i) q^{93} +(6.70642 + 4.27828i) q^{95} +(-2.85545 - 1.64859i) q^{97} +(1.49790 + 1.49790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.32537	−	0.355132i	−0.765204	−	0.205036i	−0.144952	−	0.989439i	$-0.546303\pi$
$3$	−1.32537	−	0.355132i	−0.765204	−	0.205036i	−0.620252	+	0.784403i	$0.712969\pi$
$4$		0			0
$5$	−1.64953	+	1.50965i	−0.737694	+	0.675135i
$5$	−1.64953	+	1.50965i	−0.737694	+	0.675135i
$6$		0			0
$7$	1.96809	−	3.40883i	0.743868	−	1.28842i	−0.206854	−	0.978372i	$-0.566323\pi$
$7$	1.96809	−	3.40883i	0.743868	−	1.28842i	0.950722	−	0.310045i	$-0.100344\pi$
$8$		0			0
$9$	−0.967585	−	0.558635i	−0.322528	−	0.186212i
$10$		0			0
$11$	−1.83141	−	0.490724i	−0.552189	−	0.147959i	−0.0280738	−	0.999606i	$-0.508937\pi$
$11$	−1.83141	−	0.490724i	−0.552189	−	0.147959i	−0.524116	+	0.851647i	$0.675604\pi$
$12$		0			0
$13$	−2.43499	−	2.65910i	−0.675345	−	0.737502i
$13$	−2.43499	−	2.65910i	−0.675345	−	0.737502i
$14$		0			0
$15$	2.72237	−	1.41504i	0.702913	−	0.365362i
$16$		0			0
$17$	−0.844638	−	3.15223i	−0.204855	−	0.764528i	−0.989494	−	0.144575i	$-0.953818\pi$
$17$	−0.844638	−	3.15223i	−0.204855	−	0.764528i	0.784639	−	0.619953i	$-0.212848\pi$
$18$		0			0
$19$	−0.920754	−	3.43630i	−0.211235	−	0.788341i	−0.987458	−	0.157882i	$-0.949533\pi$
$19$	−0.920754	−	3.43630i	−0.211235	−	0.788341i	0.776223	−	0.630459i	$-0.217133\pi$
$20$		0			0
$21$	−3.81904	+	3.81904i	−0.833382	+	0.833382i
$22$		0			0
$23$	0.504494	−	1.88280i	0.105194	−	0.392591i	−0.893173	−	0.449714i	$-0.851526\pi$
$23$	0.504494	−	1.88280i	0.105194	−	0.392591i	0.998367	+	0.0571230i	$0.0181927\pi$
$24$		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	$-0.960521\pi$
$29$	−7.43876	+	4.29477i	−1.38134	+	0.797519i	−0.389025	+	0.921227i	$0.627188\pi$
$30$		0			0
$31$	2.37363	+	2.37363i	0.426317	+	0.426317i	0.887372	−	0.461055i	$-0.152529\pi$
$31$	2.37363	+	2.37363i	0.426317	+	0.426317i	−0.461055	+	0.887372i	$0.652529\pi$
$32$		0			0
$33$	2.25302	+	1.30078i	0.392201	+	0.226437i
$34$		0			0
$35$	1.89970	+	8.59410i	0.321108	+	1.45267i
$36$		0			0
$37$	−0.744119	−	1.28885i	−0.122332	−	0.211886i	0.798355	−	0.602188i	$-0.205704\pi$
$37$	−0.744119	−	1.28885i	−0.122332	−	0.211886i	−0.920687	+	0.390302i	$0.872371\pi$
$38$		0			0
$39$	2.28293	+	4.38904i	0.365562	+	0.702809i
$40$		0			0
$41$	−1.45054	+	5.41349i	−0.226536	+	0.845445i	0.755247	+	0.655441i	$0.227517\pi$
$41$	−1.45054	+	5.41349i	−0.226536	+	0.845445i	−0.981783	+	0.190005i	$0.939150\pi$
$42$		0			0
$43$	5.64699	−	1.51311i	0.861158	−	0.230747i	0.198898	−	0.980020i	$-0.436264\pi$
$43$	5.64699	−	1.51311i	0.861158	−	0.230747i	0.662261	+	0.749274i	$0.269597\pi$
$44$		0			0
$45$	2.43941	−	0.539223i	0.363645	−	0.0803826i
$46$		0			0
$47$	3.50747			0.511617			0.255809	−	0.966727i	$-0.417658\pi$
$47$	3.50747			0.511617			0.255809	+	0.966727i	$0.417658\pi$
$48$		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
$55$	3.76179	−	1.95531i	0.507239	−	0.263654i
$56$		0			0
$57$			4.88136i			0.646553i
$58$		0			0
$59$	4.27489	−	1.14545i	0.556543	−	0.149125i	0.0304252	−	0.999537i	$-0.490314\pi$
$59$	4.27489	−	1.14545i	0.556543	−	0.149125i	0.526118	+	0.850412i	$0.323647\pi$
$60$		0			0
$61$	−6.33455	+	10.9718i	−0.811056	+	1.40479i	0.101070	+	0.994879i	$0.467774\pi$
$61$	−6.33455	+	10.9718i	−0.811056	+	1.40479i	−0.912126	+	0.409911i	$0.865560\pi$
$62$		0			0
$63$	−3.80859	+	2.19889i	−0.479837	+	0.277034i
$64$		0			0
$65$	8.03091	+	0.710304i	0.996111	+	0.0881024i
$66$		0			0
$67$	−4.41417	+	2.54852i	−0.539277	+	0.311352i	−0.744786	−	0.667303i	$-0.767448\pi$
$67$	−4.41417	+	2.54852i	−0.539277	+	0.311352i	0.205509	+	0.978655i	$0.434115\pi$
$68$		0			0
$69$	−1.33729	+	2.31625i	−0.160990	+	0.278843i
$70$		0			0
$71$	5.68768	−	1.52401i	0.675003	−	0.180867i	0.0949958	−	0.995478i	$-0.469716\pi$
$71$	5.68768	−	1.52401i	0.675003	−	0.180867i	0.580008	+	0.814611i	$0.303050\pi$
$72$		0			0
$73$			7.07919i			0.828556i	0.910150	+	0.414278i	$0.135966\pi$
$73$			7.07919i			0.828556i	−0.910150	+	0.414278i	$0.864034\pi$
$74$		0			0
$75$	−2.35443	+	6.44398i	−0.271867	+	0.744087i
$76$		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
$83$	−17.5256			−1.92368			−0.961841	−	0.273608i	$-0.911783\pi$
$83$	−17.5256			−1.92368			−0.961841	+	0.273608i	$0.911783\pi$
$84$		0			0
$85$	6.15201	+	3.92461i	0.667280	+	0.425684i
$86$		0			0
$87$	11.3843	−	3.05042i	1.22053	−	0.327040i
$88$		0			0
$89$	−2.12894	+	7.94530i	−0.225667	+	0.842200i	0.756470	+	0.654029i	$0.226923\pi$
$89$	−2.12894	+	7.94530i	−0.225667	+	0.842200i	−0.982136	+	0.188171i	$0.939744\pi$
$90$		0			0
$91$	−13.8567	+	3.06712i	−1.45258	+	0.321522i
$92$		0			0
$93$	−2.30299	−	3.98890i	−0.238809	−	0.413629i
$94$		0			0
$95$	6.70642	+	4.27828i	0.688064	+	0.438943i
$96$		0			0
$97$	−2.85545	−	1.64859i	−0.289927	−	0.167389i	0.347982	−	0.937501i	$-0.386867\pi$
$97$	−2.85545	−	1.64859i	−0.289927	−	0.167389i	−0.637909	+	0.770112i	$0.720200\pi$
$98$		0			0
$99$	1.49790	+	1.49790i	0.150545	+	0.150545i
$100$		0			0
$101$	9.78232	−	5.64782i	0.973377	−	0.561979i	0.0731129	−	0.997324i	$-0.476707\pi$
$101$	9.78232	−	5.64782i	0.973377	−	0.561979i	0.900264	+	0.435344i	$0.143373\pi$
$102$		0			0
$103$	−9.51034	−	9.51034i	−0.937081	−	0.937081i	0.0610531	−	0.998135i	$-0.480554\pi$
$103$	−9.51034	−	9.51034i	−0.937081	−	0.937081i	−0.998135	+	0.0610531i	$0.980554\pi$
$104$		0			0
$105$	0.534236	−	12.0650i	0.0521361	−	1.17743i
$106$		0			0
$107$	3.00221	−	11.2044i	0.290235	−	1.08317i	−0.654694	−	0.755894i	$-0.727203\pi$
$107$	3.00221	−	11.2044i	0.290235	−	1.08317i	0.944929	−	0.327276i	$-0.106131\pi$
$108$		0			0
$109$	13.0996	−	13.0996i	1.25471	−	1.25471i	0.301125	−	0.953585i	$-0.402638\pi$
$109$	13.0996	−	13.0996i	1.25471	−	1.25471i	0.953585	−	0.301125i	$-0.0973621\pi$
$110$		0			0
$111$	0.528522	+	1.97247i	0.0501651	+	0.187219i
$112$		0			0
$113$	−0.895908	−	3.34358i	−0.0842800	−	0.314537i	0.910897	−	0.412634i	$-0.135391\pi$
$113$	−0.895908	−	3.34358i	−0.0842800	−	0.314537i	−0.995177	+	0.0980969i	$0.968724\pi$
$114$		0			0
$115$	2.01018	+	3.86735i	0.187450	+	0.360632i
$116$		0			0
$117$	0.870592	+	3.93318i	0.0804863	+	0.363622i
$118$		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
$123$	3.84501	−	6.65976i	0.346693	−	0.600490i
$124$		0			0
$125$	6.78971	+	8.88256i	0.607290	+	0.794480i
$126$		0			0
$127$	5.61773	+	1.50527i	0.498493	+	0.133571i	0.499300	−	0.866429i	$-0.333590\pi$
$127$	5.61773	+	1.50527i	0.498493	+	0.133571i	−0.000807685		1.00000i	$0.500257\pi$
$128$		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
$133$	−13.5259	−	3.62425i	−1.17284	−	0.314262i
$134$		0			0
$135$	−12.6201	−	0.558815i	−1.08617	−	0.0480951i
$136$		0			0
$137$	−1.19171	+	2.06410i	−0.101815	+	0.176348i	−0.912432	−	0.409228i	$-0.865798\pi$
$137$	−1.19171	+	2.06410i	−0.101815	+	0.176348i	0.810618	+	0.585576i	$0.199132\pi$
$138$		0			0
$139$	7.97525	+	4.60451i	0.676452	+	0.390550i	0.798517	−	0.601972i	$-0.205618\pi$
$139$	7.97525	+	4.60451i	0.676452	+	0.390550i	−0.122065	+	0.992522i	$0.538952\pi$
$140$		0			0
$141$	−4.64870	−	1.24562i	−0.391491	−	0.104900i
$142$		0			0
$143$	3.15457	+	6.06480i	0.263798	+	0.507164i
$144$		0			0
$145$	5.78691	−	18.3143i	0.480576	−	1.52092i
$146$		0			0
$147$	3.01631	+	11.2570i	0.248781	+	0.928465i
$148$		0			0
$149$	5.50931	+	20.5610i	0.451340	+	1.68442i	0.698630	+	0.715483i	$0.253793\pi$
$149$	5.50931	+	20.5610i	0.451340	+	1.68442i	−0.247290	+	0.968941i	$0.579540\pi$
$150$		0			0
$151$	14.1541	−	14.1541i	1.15184	−	1.15184i	0.165660	−	0.986183i	$-0.447024\pi$
$151$	14.1541	−	14.1541i	1.15184	−	1.15184i	0.986183	−	0.165660i	$-0.0529756\pi$
$152$		0			0
$153$	−0.943689	+	3.52189i	−0.0762927	+	0.284728i
$154$		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
$163$	19.5443	+	11.2839i	1.53083	+	0.883824i	0.999324	+	0.0367678i	$0.0117062\pi$
$163$	19.5443	+	11.2839i	1.53083	+	0.883824i	0.531504	+	0.847056i	$0.321627\pi$
$164$		0			0
$165$	−5.68016	+	1.25558i	−0.442200	+	0.0977468i
$166$		0			0
$167$	−6.04914	−	10.4774i	−0.468097	−	0.810767i	0.531239	−	0.847222i	$-0.321727\pi$
$167$	−6.04914	−	10.4774i	−0.468097	−	0.810767i	−0.999335	+	0.0364550i	$0.988393\pi$
$168$		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
$173$	5.33097	−	1.42843i	0.405306	−	0.108601i	−0.0504057	−	0.998729i	$-0.516051\pi$
$173$	5.33097	−	1.42843i	0.405306	−	0.108601i	0.455712	+	0.890127i	$0.349385\pi$
$174$		0			0
$175$	−16.1077	−	11.3084i	−1.21763	−	0.854835i
$176$		0			0
$177$	−6.07260			−0.456445
$178$		0			0
$179$	−11.2279	−	19.4473i	−0.839214	−	1.45356i	−0.890553	−	0.454880i	$-0.849682\pi$
$179$	−11.2279	−	19.4473i	−0.839214	−	1.45356i	0.0513388	−	0.998681i	$-0.483651\pi$
$180$		0			0
$181$		−	13.2607i		−	0.985659i	−0.870126	−	0.492829i	$-0.835963\pi$
$181$		−	13.2607i		−	0.985659i	0.870126	−	0.492829i	$-0.164037\pi$
$182$		0			0
$183$	12.2921	−	12.2921i	0.908655	−	0.908655i
$184$		0			0
$185$	3.17316	+	1.00265i	0.233296	+	0.0737163i
$186$		0			0
$187$			6.18749i			0.452474i
$188$		0			0
$189$	21.4794	−	5.75538i	1.56240	−	0.418643i
$190$		0			0
$191$	2.68516	−	4.65083i	0.194291	−	0.336522i	−0.752377	−	0.658733i	$-0.771093\pi$
$191$	2.68516	−	4.65083i	0.194291	−	0.336522i	0.946668	+	0.322211i	$0.104426\pi$
$192$		0			0
$193$	2.27308	−	1.31236i	0.163620	−	0.0944659i	−0.415954	−	0.909386i	$-0.636552\pi$
$193$	2.27308	−	1.31236i	0.163620	−	0.0944659i	0.579574	+	0.814920i	$0.303219\pi$
$194$		0			0
$195$	−10.3917	−	3.79345i	−0.744164	−	0.271655i
$196$		0			0
$197$	5.64263	−	3.25778i	0.402021	−	0.232107i	−0.285335	−	0.958428i	$-0.592105\pi$
$197$	5.64263	−	3.25778i	0.402021	−	0.232107i	0.687356	+	0.726321i	$0.258771\pi$
$198$		0			0
$199$	2.74150	−	4.74843i	0.194340	−	0.336607i	−0.752344	−	0.658771i	$-0.771077\pi$
$199$	2.74150	−	4.74843i	0.194340	−	0.336607i	0.946684	+	0.322164i	$0.104410\pi$
$200$		0			0
$201$	6.75549	−	1.81013i	0.476495	−	0.127677i
$202$		0			0
$203$			33.8100i			2.37299i
$204$		0			0
$205$	−5.77975	−	11.1195i	−0.403675	−	0.776623i
$206$		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	0.999968	−	0.00800885i	$-0.00254932\pi$
$211$	7.16194	+	12.4048i	0.493048	+	0.853984i	−0.506920	+	0.861993i	$0.669216\pi$
$212$		0			0
$213$	−8.07952			−0.553599
$214$		0			0
$215$	−7.03065	+	11.0209i	−0.479487	+	0.751619i
$216$		0			0
$217$	12.7628	−	3.41979i	0.866397	−	0.232150i
$218$		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
$223$	4.05266	+	7.01942i	0.271386	+	0.470055i	0.969217	−	0.246208i	$-0.0791845\pi$
$223$	4.05266	+	7.01942i	0.271386	+	0.470055i	−0.697831	+	0.716263i	$0.745851\pi$
$224$		0			0
$225$	−3.20985	+	4.57211i	−0.213990	+	0.304807i
$226$		0			0
$227$	−5.76176	−	3.32655i	−0.382421	−	0.220791i	0.296450	−	0.955048i	$-0.404197\pi$
$227$	−5.76176	−	3.32655i	−0.382421	−	0.220791i	−0.678871	+	0.734257i	$0.737531\pi$
$228$		0			0
$229$	6.32634	+	6.32634i	0.418056	+	0.418056i	0.884533	−	0.466477i	$-0.154477\pi$
$229$	6.32634	+	6.32634i	0.418056	+	0.418056i	−0.466477	+	0.884533i	$0.654477\pi$
$230$		0			0
$231$	8.86829	−	5.12011i	0.583491	−	0.336879i
$232$		0			0
$233$	12.8923	+	12.8923i	0.844601	+	0.844601i	0.989453	−	0.144852i	$-0.0462707\pi$
$233$	12.8923	+	12.8923i	0.844601	+	0.844601i	−0.144852	+	0.989453i	$0.546271\pi$
$234$		0			0
$235$	−5.78569	+	5.29504i	−0.377417	+	0.345410i
$236$		0			0
$237$	−5.10985	+	19.0702i	−0.331920	+	1.23874i
$238$		0			0
$239$	−6.58614	+	6.58614i	−0.426022	+	0.426022i	−0.887271	−	0.461249i	$-0.847402\pi$
$239$	−6.58614	+	6.58614i	−0.426022	+	0.426022i	0.461249	+	0.887271i	$0.347402\pi$
$240$		0			0
$241$	4.00770	+	14.9569i	0.258158	+	0.963461i	0.966306	+	0.257396i	$0.0828645\pi$
$241$	4.00770	+	14.9569i	0.258158	+	0.963461i	−0.708148	+	0.706065i	$0.750469\pi$
$242$		0			0
$243$	−2.82398	−	10.5392i	−0.181159	−	0.676093i
$244$		0			0
$245$	18.1095	+	5.72220i	1.15697	+	0.365578i
$246$		0			0
$247$	−6.89544	+	10.8157i	−0.438747	+	0.688189i
$248$		0			0
$249$	23.2279	+	6.22390i	1.47201	+	0.394424i
$250$		0			0
$251$	−1.46212	−	0.844158i	−0.0922885	−	0.0532828i	0.453145	−	0.891437i	$-0.350302\pi$
$251$	−1.46212	−	0.844158i	−0.0922885	−	0.0532828i	−0.545434	+	0.838154i	$0.683635\pi$
$252$		0			0
$253$	−1.84787	+	3.20060i	−0.116174	+	0.201220i
$254$		0			0
$255$	−6.75995	−	7.38635i	−0.423325	−	0.462551i
$256$		0			0
$257$	−10.0096	−	2.68207i	−0.624384	−	0.167303i	−0.0672638	−	0.997735i	$-0.521427\pi$
$257$	−10.0096	−	2.68207i	−0.624384	−	0.167303i	−0.557120	+	0.830432i	$0.688094\pi$
$258$		0			0
$259$	−5.85797			−0.363997
$260$		0			0
$261$	9.59684			0.594030
$262$		0			0
$263$	−1.96866	−	0.527501i	−0.121393	−	0.0325271i	0.197611	−	0.980280i	$-0.436682\pi$
$263$	−1.96866	−	0.527501i	−0.121393	−	0.0325271i	−0.319004	+	0.947753i	$0.603348\pi$
$264$		0			0
$265$	−1.25523	+	28.3478i	−0.0771084	+	1.74139i
$266$		0			0
$267$	5.64326	−	9.77442i	0.345362	−	0.598185i
$268$		0			0
$269$	2.59298	+	1.49706i	0.158097	+	0.0912773i	0.576961	−	0.816772i	$-0.304238\pi$
$269$	2.59298	+	1.49706i	0.158097	+	0.0912773i	−0.418864	+	0.908049i	$0.637572\pi$
$270$		0			0
$271$	27.2999	+	7.31498i	1.65835	+	0.444353i	0.961933	−	0.273285i	$-0.0881103\pi$
$271$	27.2999	+	7.31498i	1.65835	+	0.444353i	0.696416	+	0.717639i	$0.254777\pi$
$272$		0			0
$273$	19.4545	+	0.855887i	1.17744	+	0.0518006i
$274$		0			0
$275$	−3.25337	+	8.90432i	−0.196186	+	0.536951i
$276$		0			0
$277$	−6.97314	−	26.0241i	−0.418975	−	1.56364i	−0.776738	−	0.629824i	$-0.783127\pi$
$277$	−6.97314	−	26.0241i	−0.418975	−	1.56364i	0.357762	−	0.933813i	$-0.383540\pi$
$278$		0			0
$279$	−0.970696	−	3.62268i	−0.0581140	−	0.216884i
$280$		0			0
$281$	−1.76202	+	1.76202i	−0.105113	+	0.105113i	−0.757707	−	0.652594i	$-0.773681\pi$
$281$	−1.76202	+	1.76202i	−0.105113	+	0.105113i	0.652594	+	0.757707i	$0.273681\pi$
$282$		0			0
$283$	−2.22009	+	8.28547i	−0.131970	+	0.492520i	−0.999992	−	0.00400621i	$-0.998725\pi$
$283$	−2.22009	+	8.28547i	−0.131970	+	0.492520i	0.868022	+	0.496527i	$0.165391\pi$
$284$		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
$293$	8.31563	+	4.80103i	0.485804	+	0.280479i	0.722832	−	0.691024i	$-0.242840\pi$
$293$	8.31563	+	4.80103i	0.485804	+	0.280479i	−0.237028	+	0.971503i	$0.576173\pi$
$294$		0			0
$295$	−5.32235	+	8.34303i	−0.309879	+	0.485750i
$296$		0			0
$297$	−5.35567	−	9.27630i	−0.310768	−	0.538265i
$298$		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
$303$	−14.9709	+	4.01145i	−0.860058	+	0.230452i
$304$		0			0
$305$	−6.11443	−	27.6612i	−0.350111	−	1.58388i
$306$		0			0
$307$	−16.6845			−0.952235			−0.476118	−	0.879382i	$-0.657956\pi$
$307$	−16.6845			−0.952235			−0.476118	+	0.879382i	$0.657956\pi$
$308$		0			0
$309$	9.22731	+	15.9822i	0.524923	+	0.909193i
$310$		0			0
$311$		−	32.6023i		−	1.84870i	−0.381540	−	0.924352i	$-0.624606\pi$
$311$		−	32.6023i		−	1.84870i	0.381540	−	0.924352i	$-0.375394\pi$
$312$		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
$315$	2.96285	−	9.37676i	0.166938	−	0.528321i
$316$		0			0
$317$		−	22.4470i		−	1.26075i	−0.776291	−	0.630375i	$-0.782901\pi$
$317$		−	22.4470i		−	1.26075i	0.776291	−	0.630375i	$-0.217099\pi$
$318$		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
$323$	−10.0543	+	5.80486i	−0.559437	+	0.322991i
$324$		0			0
$325$	−14.3196	+	10.9522i	−0.794307	+	0.607517i
$326$		0			0
$327$	−22.0138	+	12.7097i	−1.21737	+	0.702848i
$328$		0			0
$329$	6.90301	−	11.9564i	0.380575	−	0.659176i
$330$		0			0
$331$	−9.70050	+	2.59924i	−0.533188	+	0.142867i	−0.515360	−	0.856974i	$-0.672342\pi$
$331$	−9.70050	+	2.59924i	−0.533188	+	0.142867i	−0.0178279	+	0.999841i	$0.505675\pi$
$332$		0			0
$333$			1.66277i			0.0911190i
$334$		0			0
$335$	3.43396	−	10.8677i	0.187617	−	0.593767i
$336$		0			0
$337$	−6.79849	+	6.79849i	−0.370337	+	0.370337i	−0.867600	−	0.497263i	$-0.834338\pi$
$337$	−6.79849	+	6.79849i	−0.370337	+	0.370337i	0.497263	+	0.867600i	$0.334338\pi$
$338$		0			0
$339$			4.74965i			0.257965i
$340$		0			0
$341$	−3.18228	−	5.51188i	−0.172330	−	0.298485i
$342$		0			0
$343$	−5.87867			−0.317418
$344$		0			0
$345$	−1.29082	−	5.83956i	−0.0694952	−	0.314391i
$346$		0			0
$347$	4.11047	−	1.10140i	0.220661	−	0.0591260i	−0.146794	−	0.989167i	$-0.546896\pi$
$347$	4.11047	−	1.10140i	0.220661	−	0.0591260i	0.367456	+	0.930041i	$0.380229\pi$
$348$		0			0
$349$	−1.59334	+	5.94641i	−0.0852893	+	0.318304i	−0.995369	−	0.0961297i	$-0.969354\pi$
$349$	−1.59334	+	5.94641i	−0.0852893	+	0.318304i	0.910080	+	0.414434i	$0.136020\pi$
$350$		0			0
$351$	0.895264	−	20.3496i	0.0477857	−	1.08618i
$352$		0			0
$353$	0.198101	+	0.343121i	0.0105439	+	0.0182625i	0.871249	−	0.490841i	$-0.163310\pi$
$353$	0.198101	+	0.343121i	0.0105439	+	0.0182625i	−0.860705	+	0.509103i	$0.829977\pi$
$354$		0			0
$355$	−7.08131	+	11.1003i	−0.375837	+	0.589143i
$356$		0			0
$357$	15.2642	+	8.81278i	0.807866	+	0.466422i
$358$		0			0
$359$	−1.01878	−	1.01878i	−0.0537691	−	0.0537691i	0.679711	−	0.733480i	$-0.262105\pi$
$359$	−1.01878	−	1.01878i	−0.0537691	−	0.0537691i	−0.733480	+	0.679711i	$0.762105\pi$
$360$		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
$367$	0.144342	−	0.538690i	0.00753457	−	0.0281194i	−0.962056	−	0.272851i	$-0.912033\pi$
$367$	0.144342	−	0.538690i	0.00753457	−	0.0281194i	0.969591	+	0.244732i	$0.0787000\pi$
$368$		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
$373$	−7.32458	−	27.3357i	−0.379253	−	1.41539i	−0.847031	−	0.531544i	$-0.821612\pi$
$373$	−7.32458	−	27.3357i	−0.379253	−	1.41539i	0.467778	−	0.883846i	$-0.345055\pi$
$374$		0			0
$375$	−5.84441	−	14.1839i	−0.301804	−	0.732455i
$376$		0			0
$377$	29.5335	+	9.32269i	1.52105	+	0.480143i
$378$		0			0
$379$	−31.8036	−	8.52176i	−1.63364	−	0.437733i	−0.678674	−	0.734440i	$-0.737445\pi$
$379$	−31.8036	−	8.52176i	−1.63364	−	0.437733i	−0.954969	+	0.296707i	$0.904112\pi$
$380$		0			0
$381$	−6.91101	−	3.99007i	−0.354062	−	0.204418i
$382$		0			0
$383$	−8.38333	+	14.5203i	−0.428368	+	0.741955i	−0.996728	−	0.0808246i	$-0.974245\pi$
$383$	−8.38333	+	14.5203i	−0.428368	+	0.741955i	0.568360	+	0.822780i	$0.307578\pi$
$384$		0			0
$385$	0.738210	−	16.6715i	0.0376227	−	0.849659i
$386$		0			0
$387$	−6.30922	−	1.69055i	−0.320716	−	0.0859355i
$388$		0			0
$389$	−8.29738			−0.420694			−0.210347	−	0.977627i	$-0.567459\pi$
$389$	−8.29738			−0.420694			−0.210347	+	0.977627i	$0.567459\pi$
$390$		0			0
$391$	−6.36113			−0.321696
$392$		0			0
$393$	2.22673	+	0.596651i	0.112324	+	0.0300970i
$394$		0			0
$395$	21.7217	+	23.7344i	1.09294	+	1.19421i
$396$		0			0
$397$	−16.4426	+	28.4794i	−0.825230	+	1.42934i	0.0765132	+	0.997069i	$0.475621\pi$
$397$	−16.4426	+	28.4794i	−0.825230	+	1.42934i	−0.901743	+	0.432272i	$0.857712\pi$
$398$		0			0
$399$	16.6397	+	9.60696i	0.833029	+	0.480950i
$400$		0			0
$401$	−4.40754	−	1.18100i	−0.220102	−	0.0589762i	0.147083	−	0.989124i	$-0.453012\pi$
$401$	−4.40754	−	1.18100i	−0.220102	−	0.0589762i	−0.367185	+	0.930148i	$0.619678\pi$
$402$		0			0
$403$	0.531957	−	12.0915i	0.0264986	−	0.602320i
$404$		0			0
$405$	9.38128	+	2.96428i	0.466159	+	0.147296i
$406$		0			0
$407$	0.730314	+	2.72557i	0.0362003	+	0.135101i
$408$		0			0
$409$	2.97968	+	11.1203i	0.147336	+	0.549865i	0.999640	+	0.0268189i	$0.00853774\pi$
$409$	2.97968	+	11.1203i	0.147336	+	0.549865i	−0.852304	+	0.523046i	$0.824796\pi$
$410$		0			0
$411$	2.31249	−	2.31249i	0.114067	−	0.114067i
$412$		0			0
$413$	4.50870	−	16.8267i	0.221859	−	0.827988i
$414$		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	$-0.658036\pi$
$419$	0.961220	−	0.554961i	0.0469587	−	0.0271116i	0.523296	+	0.852151i	$0.324702\pi$
$420$		0			0
$421$	−8.20503	−	8.20503i	−0.399888	−	0.399888i	0.478305	−	0.878194i	$-0.341251\pi$
$421$	−8.20503	−	8.20503i	−0.399888	−	0.399888i	−0.878194	+	0.478305i	$0.841251\pi$
$422$		0			0
$423$	−3.39377	−	1.95940i	−0.165011	−	0.0952691i
$424$		0			0
$425$	−16.0727	+	2.81359i	−0.779642	+	0.136479i
$426$		0			0
$427$	24.9339	+	43.1868i	1.20664	+	2.08996i
$428$		0			0
$429$	−2.02717	−	9.15840i	−0.0978728	−	0.442172i
$430$		0			0
$431$	−1.85441	+	6.92074i	−0.0893236	+	0.333360i	−0.996098	−	0.0882564i	$-0.971871\pi$
$431$	−1.85441	+	6.92074i	−0.0893236	+	0.333360i	0.906774	+	0.421617i	$0.138537\pi$
$432$		0			0
$433$	−17.7080	+	4.74484i	−0.850991	+	0.228022i	−0.657850	−	0.753149i	$-0.728534\pi$
$433$	−17.7080	+	4.74484i	−0.850991	+	0.228022i	−0.193140	+	0.981171i	$0.561867\pi$
$434$		0			0
$435$	−14.1738	+	22.2181i	−0.679581	+	1.06528i
$436$		0			0
$437$	−6.93438			−0.331716
$438$		0			0
$439$	17.8096	+	30.8472i	0.850008	+	1.47226i	0.881200	+	0.472743i	$0.156736\pi$
$439$	17.8096	+	30.8472i	0.850008	+	1.47226i	−0.0311922	+	0.999513i	$0.509930\pi$
$440$		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
$445$	−8.48284	−	16.3200i	−0.402125	−	0.773642i
$446$		0			0
$447$		−	29.2075i		−	1.38147i
$448$		0			0
$449$	−29.2540	+	7.83860i	−1.38058	+	0.369926i	−0.871333	−	0.490692i	$-0.836744\pi$
$449$	−29.2540	+	7.83860i	−1.38058	+	0.369926i	−0.509250	+	0.860618i	$0.670077\pi$
$450$		0			0
$451$	5.31306	−	9.20248i	0.250182	−	0.433328i
$452$		0			0
$453$	−23.7860	+	13.7329i	−1.11756	+	0.645226i
$454$		0			0
$455$	18.2268	−	25.9781i	0.854488	−	1.21787i
$456$		0			0
$457$	3.20754	−	1.85187i	0.150042	−	0.0866270i	−0.423099	−	0.906083i	$-0.639058\pi$
$457$	3.20754	−	1.85187i	0.150042	−	0.0866270i	0.573142	+	0.819456i	$0.305724\pi$
$458$		0			0
$459$	9.21823	−	15.9664i	0.430270	−	0.745250i
$460$		0			0
$461$	27.9827	−	7.49794i	1.30328	−	0.349214i	0.460593	−	0.887611i	$-0.347637\pi$
$461$	27.9827	−	7.49794i	1.30328	−	0.349214i	0.842691	+	0.538398i	$0.180970\pi$
$462$		0			0
$463$			12.9117i			0.600056i	0.953930	+	0.300028i	$0.0969960\pi$
$463$			12.9117i			0.600056i	−0.953930	+	0.300028i	$0.903004\pi$
$464$		0			0
$465$	9.82069	+	3.10312i	0.455424	+	0.143904i
$466$		0			0
$467$	−3.85556	+	3.85556i	−0.178414	+	0.178414i	−0.790664	−	0.612250i	$-0.790265\pi$
$467$	−3.85556	+	3.85556i	−0.178414	+	0.178414i	0.612250	+	0.790664i	$0.290265\pi$
$468$		0			0
$469$			20.0629i			0.926418i
$470$		0			0
$471$	9.15400	+	15.8552i	0.421794	+	0.730569i
$472$		0			0
$473$	−11.0844			−0.509664
$474$		0			0
$475$	−17.5212	+	3.06714i	−0.803926	+	0.140730i
$476$		0			0
$477$	−13.6950	+	3.66956i	−0.627051	+	0.168018i
$478$		0			0
$479$	7.71558	−	28.7949i	0.352534	−	1.31567i	−0.531026	−	0.847356i	$-0.678193\pi$
$479$	7.71558	−	28.7949i	0.352534	−	1.31567i	0.883560	−	0.468319i	$-0.155140\pi$
$480$		0			0
$481$	−1.61527	+	5.11703i	−0.0736498	+	0.233317i
$482$		0			0
$483$	5.26379	+	9.11716i	0.239511	+	0.414845i
$484$		0			0
$485$	7.19895	−	1.59131i	0.326888	−	0.0722575i
$486$		0			0
$487$	−0.906849	−	0.523570i	−0.0410933	−	0.0237252i	0.479313	−	0.877644i	$-0.340886\pi$
$487$	−0.906849	−	0.523570i	−0.0410933	−	0.0237252i	−0.520406	+	0.853919i	$0.674219\pi$
$488$		0			0
$489$	−21.8962	−	21.8962i	−0.990180	−	0.990180i
$490$		0			0
$491$	−37.2673	+	21.5163i	−1.68185	+	0.971016i	−0.721418	+	0.692500i	$0.756509\pi$
$491$	−37.2673	+	21.5163i	−1.68185	+	0.971016i	−0.960431	+	0.278517i	$0.910157\pi$
$492$		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
$497$	5.99877	−	22.3877i	0.269082	−	1.00423i
$498$		0			0
$499$	23.9380	−	23.9380i	1.07161	−	1.07161i	0.0743807	−	0.997230i	$-0.476302\pi$
$499$	23.9380	−	23.9380i	1.07161	−	1.07161i	0.997230	−	0.0743807i	$-0.0236980\pi$
$500$		0			0
$501$	4.29649	+	16.0347i	0.191953	+	0.716379i
$502$		0			0
$503$	−4.44508	−	16.5893i	−0.198196	−	0.739678i	−0.991416	−	0.130743i	$-0.958264\pi$
$503$	−4.44508	−	16.5893i	−0.198196	−	0.739678i	0.793220	−	0.608935i	$-0.208403\pi$
$504$		0			0
$505$	−7.61005	+	24.0841i	−0.338643	+	1.07173i
$506$		0			0
$507$	6.11198	−	16.7578i	0.271443	−	0.744241i
$508$		0			0
$509$	−31.9359	−	8.55721i	−1.41554	−	0.379291i	−0.531638	−	0.846972i	$-0.678423\pi$
$509$	−31.9359	−	8.55721i	−1.41554	−	0.379291i	−0.883898	+	0.467681i	$0.845090\pi$
$510$		0			0
$511$	24.1318	+	13.9325i	1.06753	+	0.616336i
$512$		0			0
$513$	10.0490	−	17.4053i	0.443672	−	0.768462i
$514$		0			0
$515$	30.0449	+	1.33038i	1.32394	+	0.0586235i
$516$		0			0
$517$	−6.42360	−	1.72120i	−0.282510	−	0.0756982i
$518$		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
$523$	15.3338	+	4.10869i	0.670502	+	0.179660i	0.577981	−	0.816050i	$-0.303841\pi$
$523$	15.3338	+	4.10869i	0.670502	+	0.179660i	0.0925209	+	0.995711i	$0.470508\pi$
$524$		0			0
$525$	17.3327	+	20.7082i	0.756461	+	0.903780i
$526$		0			0
$527$	5.47738	−	9.48709i	0.238598	−	0.413264i
$528$		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
$533$	17.9271	−	9.32467i	0.776508	−	0.403896i
$534$		0			0
$535$	11.9624	+	23.0143i	0.517181	+	0.994996i
$536$		0			0
$537$	7.97479	+	29.7623i	0.344138	+	1.28434i
$538$		0			0
$539$	4.16796	+	15.5550i	0.179527	+	0.670003i
$540$		0			0
$541$	3.14795	−	3.14795i	0.135341	−	0.135341i	−0.636191	−	0.771532i	$-0.719491\pi$
$541$	3.14795	−	3.14795i	0.135341	−	0.135341i	0.771532	+	0.636191i	$0.219491\pi$
$542$		0			0
$543$	−4.70930	+	17.5753i	−0.202095	+	0.754230i
$544$		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
$553$	−49.0482	−	28.3180i	−2.08574	−	1.20420i
$554$		0			0
$555$	−3.84955	−	2.45578i	−0.163404	−	0.104242i
$556$		0			0
$557$	−20.9063	−	36.2108i	−0.885828	−	1.53430i	−0.844762	−	0.535142i	$-0.820258\pi$
$557$	−20.9063	−	36.2108i	−0.885828	−	1.53430i	−0.0410659	−	0.999156i	$-0.513075\pi$
$558$		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
$563$	9.76146	−	2.61558i	0.411396	−	0.110233i	−0.0471841	−	0.998886i	$-0.515025\pi$
$563$	9.76146	−	2.61558i	0.411396	−	0.110233i	0.458581	+	0.888653i	$0.348358\pi$
$564$		0			0
$565$	6.52545	+	4.16284i	0.274528	+	0.175132i
$566$		0			0
$567$	−17.3188			−0.727320
$568$		0			0
$569$	9.12942	+	15.8126i	0.382725	+	0.662899i	0.991451	−	0.130482i	$-0.0416523\pi$
$569$	9.12942	+	15.8126i	0.382725	+	0.662899i	−0.608726	+	0.793381i	$0.708319\pi$
$570$		0			0
$571$			29.0252i			1.21467i	0.794447	+	0.607334i	$0.207761\pi$
$571$			29.0252i			1.21467i	−0.794447	+	0.607334i	$0.792239\pi$
$572$		0			0
$573$	−5.21049	+	5.21049i	−0.217671	+	0.217671i
$574$		0			0
$575$	−9.15420	−	3.34467i	−0.381756	−	0.139482i
$576$		0			0
$577$		−	8.27590i		−	0.344530i	−0.985051	−	0.172265i	$-0.944891\pi$
$577$		−	8.27590i		−	0.344530i	0.985051	−	0.172265i	$-0.0551086\pi$
$578$		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
$583$	−20.8368	+	12.0301i	−0.862972	+	0.498237i
$584$		0			0
$585$	−7.37378	−	5.17363i	−0.304868	−	0.213903i
$586$		0			0
$587$	20.5242	−	11.8497i	0.847125	−	0.489088i	−0.0125547	−	0.999921i	$-0.503996\pi$
$587$	20.5242	−	11.8497i	0.847125	−	0.489088i	0.859680	+	0.510833i	$0.170663\pi$
$588$		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
$593$		−	27.0364i		−	1.11025i	−0.831767	−	0.555125i	$-0.812670\pi$
$593$		−	27.0364i		−	1.11025i	0.831767	−	0.555125i	$-0.187330\pi$
$594$		0			0
$595$	25.4860	−	13.2472i	1.04483	−	0.543082i
$596$		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	0.992205	+	0.124620i	$0.0397713\pi$
$601$	14.8079	+	25.6480i	0.604027	+	1.04620i	−0.388178	+	0.921584i	$0.626895\pi$
$602$		0			0
$603$	5.69478			0.231910
$604$		0			0
$605$	16.1681	−	3.57391i	0.657328	−	0.145300i
$606$		0			0
$607$	29.2638	−	7.84122i	1.18778	−	0.318265i	0.389773	−	0.920911i	$-0.372554\pi$
$607$	29.2638	−	7.84122i	1.18778	−	0.318265i	0.798009	+	0.602646i	$0.205887\pi$
$608$		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
$613$	11.8936	+	20.6003i	0.480376	+	0.832036i	0.999747	−	0.0225130i	$-0.00716670\pi$
$613$	11.8936	+	20.6003i	0.480376	+	0.832036i	−0.519370	+	0.854549i	$0.673833\pi$
$614$		0			0
$615$	3.71140	+	16.7901i	0.149658	+	0.677043i
$616$		0			0
$617$	8.49190	+	4.90280i	0.341871	+	0.197379i	0.661099	−	0.750299i	$-0.270090\pi$
$617$	8.49190	+	4.90280i	0.341871	+	0.197379i	−0.319228	+	0.947678i	$0.603424\pi$
$618$		0			0
$619$	0.211255	+	0.211255i	0.00849105	+	0.00849105i	0.711340	−	0.702849i	$-0.248089\pi$
$619$	0.211255	+	0.211255i	0.00849105	+	0.00849105i	−0.702849	+	0.711340i	$0.748089\pi$
$620$		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
$627$	2.39540	−	8.93976i	0.0956631	−	0.357019i
$628$		0			0
$629$	−3.43425	+	3.43425i	−0.136932	+	0.136932i
$630$		0			0
$631$	3.19224	+	11.9136i	0.127081	+	0.474273i	0.999905	−	0.0137616i	$-0.00438059\pi$
$631$	3.19224	+	11.9136i	0.127081	+	0.474273i	−0.872824	+	0.488035i	$0.837714\pi$
$632$		0			0
$633$	−5.08687	−	18.9845i	−0.202185	−	0.754564i
$634$		0			0
$635$	−11.5391	+	5.99780i	−0.457913	+	0.238015i
$636$		0			0
$637$	−9.21845	+	29.2033i	−0.365248	+	1.15708i
$638$		0			0
$639$	−6.35468	−	1.70273i	−0.251387	−	0.0673590i
$640$		0			0
$641$	8.13416	+	4.69626i	0.321280	+	0.185491i	0.651963	−	0.758251i	$-0.273946\pi$
$641$	8.13416	+	4.69626i	0.321280	+	0.185491i	−0.330683	+	0.943742i	$0.607279\pi$
$642$		0			0
$643$	18.5225	−	32.0818i	0.730454	−	1.26518i	−0.226235	−	0.974073i	$-0.572642\pi$
$643$	18.5225	−	32.0818i	0.730454	−	1.26518i	0.956689	−	0.291111i	$-0.0940250\pi$
$644$		0			0
$645$	13.2321	−	12.1100i	0.521014	−	0.476829i
$646$		0			0
$647$	−21.3469	−	5.71989i	−0.839234	−	0.224872i	−0.186496	−	0.982456i	$-0.559713\pi$
$647$	−21.3469	−	5.71989i	−0.839234	−	0.224872i	−0.652738	+	0.757584i	$0.726380\pi$
$648$		0			0
$649$	−8.39115			−0.329381
$650$		0			0
$651$	−18.1300			−0.710569
$652$		0			0
$653$	20.4607	+	5.48243i	0.800689	+	0.214544i	0.635886	−	0.771783i	$-0.280635\pi$
$653$	20.4607	+	5.48243i	0.800689	+	0.214544i	0.164803	+	0.986327i	$0.447301\pi$
$654$		0			0
$655$	2.77135	−	2.53633i	0.108286	−	0.0991025i
$656$		0			0
$657$	3.95469	−	6.84972i	0.154287	−	0.267233i
$658$		0			0
$659$	−2.59430	−	1.49782i	−0.101060	−	0.0583468i	0.448618	−	0.893723i	$-0.351916\pi$
$659$	−2.59430	−	1.49782i	−0.101060	−	0.0583468i	−0.549678	+	0.835377i	$0.685250\pi$
$660$		0			0
$661$	12.0257	+	3.22227i	0.467744	+	0.125332i	0.484990	−	0.874520i	$-0.338823\pi$
$661$	12.0257	+	3.22227i	0.467744	+	0.125332i	−0.0172459	+	0.999851i	$0.505490\pi$
$662$		0			0
$663$	11.9070	−	10.9035i	0.462430	−	0.423456i
$664$		0			0
$665$	27.7828	−	14.4410i	1.07737	−	0.559998i
$666$		0			0
$667$	4.33337	+	16.1724i	0.167789	+	0.626197i
$668$		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
$673$	−3.10082	+	11.5724i	−0.119528	+	0.446084i	−0.999586	−	0.0287825i	$-0.990837\pi$
$673$	−3.10082	+	11.5724i	−0.119528	+	0.446084i	0.880058	+	0.474867i	$0.157504\pi$
$674$		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
$683$	−22.7128	−	13.1132i	−0.869080	−	0.501764i	−0.00203769	−	0.999998i	$-0.500649\pi$
$683$	−22.7128	−	13.1132i	−0.869080	−	0.501764i	−0.867042	+	0.498234i	$0.833982\pi$
$684$		0			0
$685$	−1.15030	−	5.20387i	−0.0439507	−	0.198830i
$686$		0			0
$687$	−6.13807	−	10.6314i	−0.234182	−	0.405615i
$688$		0			0
$689$	−45.7100	−	2.01098i	−1.74141	−	0.0766122i
$690$		0			0
$691$	−0.868516	+	3.24135i	−0.0330399	+	0.123307i	−0.980476	−	0.196638i	$-0.936998\pi$
$691$	−0.868516	+	3.24135i	−0.0330399	+	0.123307i	0.947436	+	0.319945i	$0.103664\pi$
$692$		0			0
$693$	8.05411	−	2.15809i	0.305950	−	0.0819791i
$694$		0			0
$695$	−20.1066	+	4.44451i	−0.762688	+	0.168590i
$696$		0			0
$697$	18.2898			0.692774
$698$		0			0
$699$	−12.5086	−	21.6655i	−0.473118	−	0.819465i
$700$		0			0
$701$		−	12.3175i		−	0.465226i	−0.972569	−	0.232613i	$-0.925272\pi$
$701$		−	12.3175i		−	0.465226i	0.972569	−	0.232613i	$-0.0747276\pi$
$702$		0			0
$703$	−3.74373	+	3.74373i	−0.141198	+	0.141198i
$704$		0			0
$705$	9.54864	−	4.96321i	0.359622	−	0.186925i
$706$		0			0
$707$		−	44.4617i		−	1.67215i
$708$		0			0
$709$	−30.1347	+	8.07458i	−1.13173	+	0.303247i	−0.775623	−	0.631197i	$-0.782564\pi$
$709$	−30.1347	+	8.07458i	−1.13173	+	0.303247i	−0.356111	+	0.934444i	$0.615897\pi$
$710$		0			0
$711$	−8.03796	+	13.9222i	−0.301447	+	0.522122i
$712$		0			0
$713$	5.66655	−	3.27159i	0.212214	−	0.122522i
$714$		0			0
$715$	−14.3593	−	5.24181i	−0.537007	−	0.196033i
$716$		0			0
$717$	11.0680	−	6.39013i	0.413343	−	0.238644i
$718$		0			0
$719$	−20.3069	+	35.1725i	−0.757318	+	1.31171i	0.186895	+	0.982380i	$0.440157\pi$
$719$	−20.3069	+	35.1725i	−0.757318	+	1.31171i	−0.944214	+	0.329334i	$0.893176\pi$
$720$		0			0
$721$	−51.1363	+	13.7019i	−1.90442	+	0.510287i
$722$		0			0
$723$		−	21.2468i		−	0.790175i
$724$		0			0
$725$	18.1024	+	38.9462i	0.672306	+	1.44643i
$726$		0			0
$727$	17.4875	−	17.4875i	0.648577	−	0.648577i	−0.304072	−	0.952649i	$-0.598346\pi$
$727$	17.4875	−	17.4875i	0.648577	−	0.648577i	0.952649	+	0.304072i	$0.0983464\pi$
$728$		0			0
$729$			28.1710i			1.04337i
$730$		0			0
$731$	−9.53933	−	16.5226i	−0.352825	−	0.611110i
$732$		0			0
$733$	−31.8347			−1.17584			−0.587921	−	0.808918i	$-0.700053\pi$
$733$	−31.8347			−1.17584			−0.587921	+	0.808918i	$0.700053\pi$
$734$		0			0
$735$	−21.9697	−	14.0153i	−0.810364	−	0.516962i
$736$		0			0
$737$	9.33476	−	2.50124i	0.343850	−	0.0921344i
$738$		0			0
$739$	−1.90923	+	7.12535i	−0.0702322	+	0.262110i	−0.992110	−	0.125371i	$-0.959988\pi$
$739$	−1.90923	+	7.12535i	−0.0702322	+	0.262110i	0.921878	+	0.387481i	$0.126655\pi$
$740$		0			0
$741$	12.9800	−	11.8861i	0.476834	−	0.436646i
$742$		0			0
$743$	21.9772	+	38.0656i	0.806265	+	1.39649i	0.915434	+	0.402469i	$0.131848\pi$
$743$	21.9772	+	38.0656i	0.806265	+	1.39649i	−0.109169	+	0.994023i	$0.534819\pi$
$744$		0			0
$745$	−40.1277	−	25.5990i	−1.47016	−	0.937875i
$746$		0			0
$747$	16.9575	+	9.79041i	0.620442	+	0.358212i
$748$		0			0
$749$	−32.2853	−	32.2853i	−1.17968	−	1.17968i
$750$		0			0
$751$	−39.4235	+	22.7612i	−1.43858	+	0.830567i	−0.997751	−	0.0670229i	$-0.978650\pi$
$751$	−39.4235	+	22.7612i	−1.43858	+	0.830567i	−0.440832	+	0.897590i	$0.645317\pi$
$752$		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
$757$	−7.64229	+	28.5214i	−0.277764	+	1.03663i	0.676203	+	0.736715i	$0.263624\pi$
$757$	−7.64229	+	28.5214i	−0.277764	+	1.03663i	−0.953967	+	0.299913i	$0.903042\pi$
$758$		0			0
$759$	3.58575	−	3.58575i	0.130154	−	0.130154i
$760$		0			0
$761$	−2.80150	−	10.4553i	−0.101554	−	0.379006i	0.896377	−	0.443292i	$-0.146190\pi$
$761$	−2.80150	−	10.4553i	−0.101554	−	0.379006i	−0.997932	+	0.0642862i	$0.979523\pi$
$762$		0			0
$763$	−18.8731	−	70.4352i	−0.683251	−	2.54993i
$764$		0			0
$765$	−3.76017	−	7.23413i	−0.135949	−	0.261550i
$766$		0			0
$767$	−13.4552	−	8.57819i	−0.485838	−	0.309741i
$768$		0			0
$769$	21.4310	+	5.74241i	0.772820	+	0.207077i	0.623617	−	0.781730i	$-0.285663\pi$
$769$	21.4310	+	5.74241i	0.772820	+	0.207077i	0.149203	+	0.988807i	$0.452329\pi$
$770$		0			0
$771$	12.3140	+	7.10949i	0.443478	+	0.256042i
$772$		0			0
$773$	8.68305	−	15.0395i	0.312308	−	0.540933i	−0.666554	−	0.745457i	$-0.732231\pi$
$773$	8.68305	−	15.0395i	0.312308	−	0.540933i	0.978862	+	0.204524i	$0.0655647\pi$
$774$		0			0
$775$	12.8707	−	10.7727i	0.462329	−	0.386968i
$776$		0			0
$777$	7.76399	+	2.08036i	0.278532	+	0.0746323i
$778$		0			0
$779$	19.9380			0.714352
$780$		0			0
$781$	−11.1643			−0.399491
$782$		0			0
$783$	−46.8724	−	12.5594i	−1.67508	−	0.448837i
$784$		0			0
$785$	29.8062	+	1.31981i	1.06383	+	0.0471061i
$786$		0			0
$787$	7.10259	−	12.3020i	0.253180	−	0.438521i	−0.711220	−	0.702970i	$-0.751857\pi$
$787$	7.10259	−	12.3020i	0.253180	−	0.438521i	0.964400	+	0.264449i	$0.0851902\pi$
$788$		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
$793$	44.5996	−	9.87193i	1.58378	−	0.350562i
$794$		0			0
$795$	11.7309	−	37.1256i	0.416051	−	1.31671i
$796$		0			0
$797$	−9.26384	−	34.5731i	−0.328142	−	1.22464i	−0.911115	−	0.412151i	$-0.864778\pi$
$797$	−9.26384	−	34.5731i	−0.328142	−	1.22464i	0.582974	−	0.812491i	$-0.301889\pi$
$798$		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
$803$	3.47392	−	12.9649i	0.122592	−	0.457520i
$804$		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	$-0.345521\pi$
$809$	41.6902	−	24.0699i	1.46575	−	0.846251i	0.999267	+	0.0382785i	$0.0121874\pi$
$810$		0			0
$811$	−5.10824	−	5.10824i	−0.179375	−	0.179375i	0.611709	−	0.791083i	$-0.290483\pi$
$811$	−5.10824	−	5.10824i	−0.179375	−	0.179375i	−0.791083	+	0.611709i	$0.790483\pi$
$812$		0			0
$813$	−33.5847	−	19.3901i	−1.17787	−	0.680041i
$814$		0			0
$815$	−49.2737	+	10.8918i	−1.72598	+	0.381523i
$816$		0			0
$817$	−10.3990	−	18.0116i	−0.363814	−	0.630145i
$818$		0			0
$819$	15.1209	+	4.77314i	0.528368	+	0.166787i
$820$		0			0
$821$	6.56803	−	24.5122i	0.229226	−	0.855483i	−0.751441	−	0.659800i	$-0.770641\pi$
$821$	6.56803	−	24.5122i	0.229226	−	0.855483i	0.980667	−	0.195683i	$-0.0626923\pi$
$822$		0			0
$823$	−9.22975	+	2.47310i	−0.321729	+	0.0862070i	−0.416069	−	0.909333i	$-0.636593\pi$
$823$	−9.22975	+	2.47310i	−0.321729	+	0.0862070i	0.0943402	+	0.995540i	$0.469926\pi$
$824$		0			0
$825$	7.47414	−	10.6462i	0.260216	−	0.370652i
$826$		0			0
$827$	−11.7291			−0.407860			−0.203930	−	0.978985i	$-0.565371\pi$
$827$	−11.7291			−0.407860			−0.203930	+	0.978985i	$0.565371\pi$
$828$		0			0
$829$	−12.8966	−	22.3376i	−0.447918	−	0.775817i	0.550332	−	0.834946i	$-0.314501\pi$
$829$	−12.8966	−	22.3376i	−0.447918	−	0.775817i	−0.998250	+	0.0591286i	$0.981168\pi$
$830$		0			0
$831$			36.9680i			1.28241i
$832$		0			0
$833$	−19.5995	+	19.5995i	−0.679083	+	0.679083i
$834$		0			0
$835$	25.7955	+	8.15080i	0.892689	+	0.282070i
$836$		0			0
$837$			18.9641i			0.655494i
$838$		0			0
$839$	−6.07419	+	1.62757i	−0.209704	+	0.0561901i	−0.362142	−	0.932123i	$-0.617954\pi$
$839$	−6.07419	+	1.62757i	−0.209704	+	0.0561901i	0.152437	+	0.988313i	$0.451288\pi$
$840$		0			0
$841$	22.3901	−	38.7808i	0.772073	−	1.33727i
$842$		0			0
$843$	2.96108	−	1.70958i	0.101985	−	0.0588810i
$844$		0			0
$845$	−17.6664	−	23.0846i	−0.607743	−	0.794134i
$846$		0			0
$847$	−25.2429	+	14.5740i	−0.867356	+	0.500768i
$848$		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
$853$			48.9142i			1.67479i	0.546599	+	0.837394i	$0.315922\pi$
$853$			48.9142i			1.67479i	−0.546599	+	0.837394i	$0.684078\pi$
$854$		0			0
$855$	−4.09903	−	7.88604i	−0.140184	−	0.269697i
$856$		0			0
$857$	5.72229	−	5.72229i	0.195470	−	0.195470i	−0.602585	−	0.798055i	$-0.705863\pi$
$857$	5.72229	−	5.72229i	0.195470	−	0.195470i	0.798055	+	0.602585i	$0.205863\pi$
$858$		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
$863$	−9.62230			−0.327547			−0.163773	−	0.986498i	$-0.552367\pi$
$863$	−9.62230			−0.327547			−0.163773	+	0.986498i	$0.552367\pi$
$864$		0			0
$865$	−6.63720	+	10.4041i	−0.225671	+	0.353751i
$866$		0			0
$867$	−8.41615	+	2.25510i	−0.285828	+	0.0765873i
$868$		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
$873$	1.84192	+	3.19031i	0.0623397	+	0.107976i
$874$		0			0
$875$	43.6419	−	5.66332i	1.47536	−	0.191455i
$876$		0			0
$877$	29.1407	+	16.8244i	0.984013	+	0.568120i	0.903479	−	0.428632i	$-0.141004\pi$
$877$	29.1407	+	16.8244i	0.984013	+	0.568120i	0.0805336	+	0.996752i	$0.474338\pi$
$878$		0			0
$879$	−9.31630	−	9.31630i	−0.314231	−	0.314231i
$880$		0			0
$881$	14.0355	−	8.10341i	0.472869	−	0.273011i	−0.244571	−	0.969631i	$-0.578647\pi$
$881$	14.0355	−	8.10341i	0.472869	−	0.273011i	0.717440	+	0.696620i	$0.245314\pi$
$882$		0			0
$883$	−11.4033	−	11.4033i	−0.383751	−	0.383751i	0.488701	−	0.872451i	$-0.337471\pi$
$883$	−11.4033	−	11.4033i	−0.383751	−	0.383751i	−0.872451	+	0.488701i	$0.837471\pi$
$884$		0			0
$885$	10.0170	−	9.16748i	0.336717	−	0.308162i
$886$		0			0
$887$	−9.77507	+	36.4811i	−0.328215	+	1.22491i	0.582826	+	0.812597i	$0.301947\pi$
$887$	−9.77507	+	36.4811i	−0.328215	+	1.22491i	−0.911041	+	0.412317i	$0.864720\pi$
$888$		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
$893$	−3.22952	−	12.0527i	−0.108072	−	0.403329i
$894$		0			0
$895$	47.8794	+	15.1288i	1.60043	+	0.505702i
$896$		0			0
$897$	9.41541	−	2.08406i	0.314371	−	0.0695847i
$898$		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
$903$	−15.7875	+	27.3447i	−0.525374	+	0.909974i
$904$		0			0
$905$	20.0190	+	21.8740i	0.665453	+	0.727115i
$906$		0			0
$907$	10.8382	+	2.90409i	0.359877	+	0.0964288i	0.434227	−	0.900803i	$-0.357021\pi$
$907$	10.8382	+	2.90409i	0.359877	+	0.0964288i	−0.0743499	+	0.997232i	$0.523688\pi$
$908$		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
$913$	32.0964	+	8.60022i	1.06224	+	0.284626i
$914$		0			0
$915$	−1.71951	+	38.8329i	−0.0568452	+	1.28377i
$916$		0			0
$917$	−3.30655	+	5.72711i	−0.109192	+	0.189126i
$918$		0			0
$919$	30.8704	+	17.8231i	1.01832	+	0.587929i	0.913617	−	0.406575i	$-0.133277\pi$
$919$	30.8704	+	17.8231i	1.01832	+	0.587929i	0.104705	+	0.994503i	$0.466610\pi$
$920$		0			0
$921$	22.1132	+	5.92521i	0.728654	+	0.195242i
$922$		0			0
$923$	−17.9019	−	11.4132i	−0.589250	−	0.375669i
$924$		0			0
$925$	−6.74789	+	3.13645i	−0.221869	+	0.103126i
$926$		0			0
$927$	3.88925	+	14.5149i	0.127740	+	0.476731i
$928$		0			0
$929$	11.3000	+	42.1722i	0.370741	+	1.38363i	0.859469	+	0.511189i	$0.170795\pi$
$929$	11.3000	+	42.1722i	0.370741	+	1.38363i	−0.488727	+	0.872437i	$0.662539\pi$
$930$		0			0
$931$	−21.3658	+	21.3658i	−0.700235	+	0.700235i
$932$		0			0
$933$	−11.5781	+	43.2101i	−0.379050	+	1.41464i
$934$		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	0.979016	+	0.203784i	$0.0653242\pi$
$941$	36.2833	+	36.2833i	1.18280	+	1.18280i	0.203784	+	0.979016i	$0.434676\pi$
$942$		0			0
$943$	9.46073	+	5.46215i	0.308084	+	0.177872i
$944$		0			0
$945$	−26.7424	+	41.9200i	−0.869930	+	1.36366i
$946$		0			0
$947$	9.73003	+	16.8529i	0.316184	+	0.547646i	0.979688	−	0.200526i	$-0.0642651\pi$
$947$	9.73003	+	16.8529i	0.316184	+	0.547646i	−0.663505	+	0.748172i	$0.730932\pi$
$948$		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
$953$	−33.5346	+	8.98557i	−1.08629	+	0.291071i	−0.757171	−	0.653217i	$-0.773419\pi$
$953$	−33.5346	+	8.98557i	−1.08629	+	0.291071i	−0.329121	+	0.944288i	$0.606752\pi$
$954$		0			0
$955$	2.59185	+	11.7253i	0.0838702	+	0.379423i
$956$		0			0
$957$	−22.3462			−0.722351
$958$		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
$965$	−1.76832	+	5.59633i	−0.0569241	+	0.180152i
$966$		0			0
$967$		−	29.5727i		−	0.950993i	−0.879718	−	0.475497i	$-0.842268\pi$
$967$		−	29.5727i		−	0.950993i	0.879718	−	0.475497i	$-0.157732\pi$
$968$		0			0
$969$	15.3872	−	4.12298i	0.494308	−	0.132449i
$970$		0			0
$971$	15.2631	−	26.4365i	0.489817	−	0.848389i	−0.510114	−	0.860107i	$-0.670397\pi$
$971$	15.2631	−	26.4365i	0.489817	−	0.848389i	0.999931	+	0.0117182i	$0.00373011\pi$
$972$		0			0
$973$	31.3920	−	18.1242i	1.00638	−	0.581035i
$974$		0			0
$975$	22.8682	−	9.43035i	0.732369	−	0.302013i
$976$		0			0
$977$	−43.3063	+	25.0029i	−1.38549	+	0.799915i	−0.992803	−	0.119757i	$-0.961789\pi$
$977$	−43.3063	+	25.0029i	−1.38549	+	0.799915i	−0.392689	+	0.919671i	$0.628455\pi$
$978$		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
$983$		−	57.3856i		−	1.83032i	−0.403096	−	0.915158i	$-0.632066\pi$
$983$		−	57.3856i		−	1.83032i	0.403096	−	0.915158i	$-0.367934\pi$
$984$		0			0
$985$	−4.38963	+	13.8922i	−0.139865	+	0.442642i
$986$		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	0.755665	−	0.654959i	$-0.227314\pi$
$991$	−5.96166	−	10.3259i	−0.189378	−	0.328013i	−0.945043	+	0.326946i	$0.893981\pi$
$992$		0			0
$993$	13.7798			0.437290
$994$		0			0
$995$	2.64624	+	11.9714i	0.0838914	+	0.379519i
$996$		0			0
$997$	44.2347	−	11.8526i	1.40093	−	0.375377i	0.522249	−	0.852793i	$-0.325093\pi$
$997$	44.2347	−	11.8526i	1.40093	−	0.375377i	0.878677	+	0.477416i	$0.158427\pi$
$998$		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.bf.c.37.3	✓	20
5.2	odd	4		1300.2.bs.d.193.3		20
5.3	odd	4		260.2.bk.c.193.3	yes	20
5.4	even	2		1300.2.bn.d.557.3		20
13.6	odd	12		260.2.bk.c.97.3	yes	20
65.19	odd	12		1300.2.bs.d.357.3		20
65.32	even	12		1300.2.bn.d.1293.3		20
65.58	even	12	inner	260.2.bf.c.253.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.37.3	✓	20	1.1	even	1	trivial
260.2.bf.c.253.3	yes	20	65.58	even	12	inner
260.2.bk.c.97.3	yes	20	13.6	odd	12
260.2.bk.c.193.3	yes	20	5.3	odd	4
1300.2.bn.d.557.3		20	5.4	even	2
1300.2.bn.d.1293.3		20	65.32	even	12
1300.2.bs.d.193.3		20	5.2	odd	4
1300.2.bs.d.357.3		20	65.19	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.32537 - 0.355132i) q^{3} +(-1.64953 + 1.50965i) q^{5} +(1.96809 - 3.40883i) q^{7} +(-0.967585 - 0.558635i) q^{9} +O(q^{10})\)	\(q+(-1.32537 - 0.355132i) q^{3} +(-1.64953 + 1.50965i) q^{5} +(1.96809 - 3.40883i) q^{7} +(-0.967585 - 0.558635i) q^{9} +(-1.83141 - 0.490724i) q^{11} +(-2.43499 - 2.65910i) q^{13} +(2.72237 - 1.41504i) q^{15} +(-0.844638 - 3.15223i) q^{17} +(-0.920754 - 3.43630i) q^{19} +(-3.81904 + 3.81904i) q^{21} +(0.504494 - 1.88280i) q^{23} +(0.441931 - 4.98043i) q^{25} +(3.99474 + 3.99474i) q^{27} +(-7.43876 + 4.29477i) q^{29} +(2.37363 + 2.37363i) q^{31} +(2.25302 + 1.30078i) q^{33} +(1.89970 + 8.59410i) q^{35} +(-0.744119 - 1.28885i) q^{37} +(2.28293 + 4.38904i) q^{39} +(-1.45054 + 5.41349i) q^{41} +(5.64699 - 1.51311i) q^{43} +(2.43941 - 0.539223i) q^{45} +3.50747 q^{47} +(-4.24675 - 7.35558i) q^{49} +4.47783i q^{51} +(8.97315 - 8.97315i) q^{53} +(3.76179 - 1.95531i) q^{55} +4.88136i q^{57} +(4.27489 - 1.14545i) q^{59} +(-6.33455 + 10.9718i) q^{61} +(-3.80859 + 2.19889i) q^{63} +(8.03091 + 0.710304i) q^{65} +(-4.41417 + 2.54852i) q^{67} +(-1.33729 + 2.31625i) q^{69} +(5.68768 - 1.52401i) q^{71} +7.07919i q^{73} +(-2.35443 + 6.44398i) q^{75} +(-5.27716 + 5.27716i) q^{77} -14.3886i q^{79} +(-2.19995 - 3.81042i) q^{81} -17.5256 q^{83} +(6.15201 + 3.92461i) q^{85} +(11.3843 - 3.05042i) q^{87} +(-2.12894 + 7.94530i) q^{89} +(-13.8567 + 3.06712i) q^{91} +(-2.30299 - 3.98890i) q^{93} +(6.70642 + 4.27828i) q^{95} +(-2.85545 - 1.64859i) q^{97} +(1.49790 + 1.49790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more