LMFDB - Embedded newform 260.2.bf.a.93.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("260.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			93.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.93
Dual form			260.2.bf.a.137.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 1.86603i) q^{3} +(2.00000 + 1.00000i) q^{5} +(1.86603 - 3.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 1.86603i) q^{3} +(2.00000 + 1.00000i) q^{5} +(1.86603 - 3.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +(-0.598076 + 2.23205i) q^{11} +(2.00000 + 3.00000i) q^{13} +(-2.86603 + 3.23205i) q^{15} +(-4.23205 + 1.13397i) q^{17} +(-0.866025 + 0.232051i) q^{19} +(5.09808 + 5.09808i) q^{21} +(-6.96410 - 1.86603i) q^{23} +(3.00000 + 4.00000i) q^{25} +(-3.09808 + 3.09808i) q^{27} +(7.96410 - 4.59808i) q^{29} +(5.73205 - 5.73205i) q^{31} +(-3.86603 - 2.23205i) q^{33} +(6.96410 - 4.59808i) q^{35} +(-0.133975 - 0.232051i) q^{37} +(-6.59808 + 2.23205i) q^{39} +(-0.133975 - 0.0358984i) q^{41} +(-3.03590 - 11.3301i) q^{43} +(-0.901924 - 1.36603i) q^{45} -0.535898 q^{47} +(-3.46410 - 6.00000i) q^{49} -8.46410i q^{51} +(-1.53590 - 1.53590i) q^{53} +(-3.42820 + 3.86603i) q^{55} -1.73205i q^{57} +(1.79423 + 6.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-2.36603 + 1.36603i) q^{63} +(1.00000 + 8.00000i) q^{65} +(-4.79423 + 2.76795i) q^{67} +(6.96410 - 12.0622i) q^{69} +(1.13397 + 4.23205i) q^{71} -12.9282i q^{73} +(-8.96410 + 3.59808i) q^{75} +(6.09808 + 6.09808i) q^{77} -4.53590i q^{79} +(-5.33013 - 9.23205i) q^{81} +3.46410 q^{83} +(-9.59808 - 1.96410i) q^{85} +(4.59808 + 17.1603i) q^{87} +(-14.7942 - 3.96410i) q^{89} +(13.4282 - 0.866025i) q^{91} +(7.83013 + 13.5622i) q^{93} +(-1.96410 - 0.401924i) q^{95} +(3.86603 + 2.23205i) q^{97} +(1.19615 - 1.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 8 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 8 * q^5 + 4 * q^7 - 6 * q^9	$ 4 q - 2 q^{3} + 8 q^{5} + 4 q^{7} - 6 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 10 q^{17} + 10 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} + 18 q^{29} + 16 q^{31} - 12 q^{33} + 14 q^{35} - 4 q^{37} - 16 q^{39} - 4 q^{41} - 26 q^{43} - 14 q^{45} - 16 q^{47} - 20 q^{53} + 14 q^{55} - 24 q^{59} + 2 q^{61} - 6 q^{63} + 4 q^{65} + 12 q^{67} + 14 q^{69} + 8 q^{71} - 22 q^{75} + 14 q^{77} - 4 q^{81} - 28 q^{85} + 8 q^{87} - 28 q^{89} + 26 q^{91} + 14 q^{93} + 6 q^{95} + 12 q^{97} - 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 8 * q^5 + 4 * q^7 - 6 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 10 * q^17 + 10 * q^21 - 14 * q^23 + 12 * q^25 - 2 * q^27 + 18 * q^29 + 16 * q^31 - 12 * q^33 + 14 * q^35 - 4 * q^37 - 16 * q^39 - 4 * q^41 - 26 * q^43 - 14 * q^45 - 16 * q^47 - 20 * q^53 + 14 * q^55 - 24 * q^59 + 2 * q^61 - 6 * q^63 + 4 * q^65 + 12 * q^67 + 14 * q^69 + 8 * q^71 - 22 * q^75 + 14 * q^77 - 4 * q^81 - 28 * q^85 + 8 * q^87 - 28 * q^89 + 26 * q^91 + 14 * q^93 + 6 * q^95 + 12 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	1.86603i	−0.288675	+	1.07735i	0.657437	+	0.753510i	$0.271641\pi$
$3$	−0.500000	+	1.86603i	−0.288675	+	1.07735i	−0.946112	+	0.323840i	$0.895026\pi$
$4$		0			0
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$		0			0
$7$	1.86603	−	3.23205i	0.705291	−	1.22160i	−0.261295	−	0.965259i	$-0.584150\pi$
$7$	1.86603	−	3.23205i	0.705291	−	1.22160i	0.966586	−	0.256341i	$-0.0825171\pi$
$8$		0			0
$9$	−0.633975	−	0.366025i	−0.211325	−	0.122008i
$10$		0			0
$11$	−0.598076	+	2.23205i	−0.180327	+	0.672989i	0.815256	+	0.579101i	$0.196596\pi$
$11$	−0.598076	+	2.23205i	−0.180327	+	0.672989i	−0.995583	+	0.0938879i	$0.970070\pi$
$12$		0			0
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$14$		0			0
$15$	−2.86603	+	3.23205i	−0.740005	+	0.834512i
$16$		0			0
$17$	−4.23205	+	1.13397i	−1.02642	+	0.275029i	−0.732476	−	0.680793i	$-0.761636\pi$
$17$	−4.23205	+	1.13397i	−1.02642	+	0.275029i	−0.293947	+	0.955822i	$0.594969\pi$
$18$		0			0
$19$	−0.866025	+	0.232051i	−0.198680	+	0.0532361i	−0.356787	−	0.934186i	$-0.616128\pi$
$19$	−0.866025	+	0.232051i	−0.198680	+	0.0532361i	0.158107	+	0.987422i	$0.449461\pi$
$20$		0			0
$21$	5.09808	+	5.09808i	1.11249	+	1.11249i
$22$		0			0
$23$	−6.96410	−	1.86603i	−1.45212	−	0.389093i	−0.555357	−	0.831612i	$-0.687418\pi$
$23$	−6.96410	−	1.86603i	−1.45212	−	0.389093i	−0.896759	+	0.442519i	$0.854085\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		0			0
$27$	−3.09808	+	3.09808i	−0.596225	+	0.596225i
$28$		0			0
$29$	7.96410	−	4.59808i	1.47890	−	0.853841i	0.479182	−	0.877716i	$-0.340934\pi$
$29$	7.96410	−	4.59808i	1.47890	−	0.853841i	0.999715	+	0.0238745i	$0.00760020\pi$
$30$		0			0
$31$	5.73205	−	5.73205i	1.02951	−	1.02951i	0.0299555	−	0.999551i	$-0.490463\pi$
$31$	5.73205	−	5.73205i	1.02951	−	1.02951i	0.999551	−	0.0299555i	$-0.00953655\pi$
$32$		0			0
$33$	−3.86603	−	2.23205i	−0.672989	−	0.388550i
$34$		0			0
$35$	6.96410	−	4.59808i	1.17715	−	0.777217i
$36$		0			0
$37$	−0.133975	−	0.232051i	−0.0220253	−	0.0381489i	0.854803	−	0.518953i	$-0.173678\pi$
$37$	−0.133975	−	0.232051i	−0.0220253	−	0.0381489i	−0.876828	+	0.480804i	$0.840345\pi$
$38$		0			0
$39$	−6.59808	+	2.23205i	−1.05654	+	0.357414i
$40$		0			0
$41$	−0.133975	−	0.0358984i	−0.0209233	−	0.00560639i	0.248342	−	0.968672i	$-0.420114\pi$
$41$	−0.133975	−	0.0358984i	−0.0209233	−	0.00560639i	−0.269266	+	0.963066i	$0.586781\pi$
$42$		0			0
$43$	−3.03590	−	11.3301i	−0.462970	−	1.72783i	−0.663533	−	0.748147i	$-0.730944\pi$
$43$	−3.03590	−	11.3301i	−0.462970	−	1.72783i	0.200563	−	0.979681i	$-0.435723\pi$
$44$		0			0
$45$	−0.901924	−	1.36603i	−0.134451	−	0.203635i
$46$		0			0
$47$	−0.535898			−0.0781688			−0.0390844	−	0.999236i	$-0.512444\pi$
$47$	−0.535898			−0.0781688			−0.0390844	+	0.999236i	$0.512444\pi$
$48$		0			0
$49$	−3.46410	−	6.00000i	−0.494872	−	0.857143i
$50$		0			0
$51$		−	8.46410i		−	1.18521i
$52$		0			0
$53$	−1.53590	−	1.53590i	−0.210972	−	0.210972i	0.593708	−	0.804680i	$-0.297663\pi$
$53$	−1.53590	−	1.53590i	−0.210972	−	0.210972i	−0.804680	+	0.593708i	$0.797663\pi$
$54$		0			0
$55$	−3.42820	+	3.86603i	−0.462259	+	0.521295i
$56$		0			0
$57$		−	1.73205i		−	0.229416i
$58$		0			0
$59$	1.79423	+	6.69615i	0.233589	+	0.871765i	0.978780	+	0.204914i	$0.0656915\pi$
$59$	1.79423	+	6.69615i	0.233589	+	0.871765i	−0.745191	+	0.666851i	$0.767642\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$	−2.36603	+	1.36603i	−0.298091	+	0.172103i
$64$		0			0
$65$	1.00000	+	8.00000i	0.124035	+	0.992278i
$66$		0			0
$67$	−4.79423	+	2.76795i	−0.585708	+	0.338159i	−0.763399	−	0.645928i	$-0.776471\pi$
$67$	−4.79423	+	2.76795i	−0.585708	+	0.338159i	0.177690	+	0.984086i	$0.443137\pi$
$68$		0			0
$69$	6.96410	−	12.0622i	0.838379	−	1.45212i
$70$		0			0
$71$	1.13397	+	4.23205i	0.134578	+	0.502252i	0.999999	+	0.00120705i	$0.000384217\pi$
$71$	1.13397	+	4.23205i	0.134578	+	0.502252i	−0.865421	+	0.501045i	$0.832949\pi$
$72$		0			0
$73$		−	12.9282i		−	1.51313i	−0.653917	−	0.756566i	$-0.726876\pi$
$73$		−	12.9282i		−	1.51313i	0.653917	−	0.756566i	$-0.273124\pi$
$74$		0			0
$75$	−8.96410	+	3.59808i	−1.03509	+	0.415470i
$76$		0			0
$77$	6.09808	+	6.09808i	0.694940	+	0.694940i
$78$		0			0
$79$		−	4.53590i		−	0.510328i	−0.966898	−	0.255164i	$-0.917870\pi$
$79$		−	4.53590i		−	0.510328i	0.966898	−	0.255164i	$-0.0821295\pi$
$80$		0			0
$81$	−5.33013	−	9.23205i	−0.592236	−	1.02578i
$82$		0			0
$83$	3.46410			0.380235			0.190117	−	0.981761i	$-0.439113\pi$
$83$	3.46410			0.380235			0.190117	+	0.981761i	$0.439113\pi$
$84$		0			0
$85$	−9.59808	−	1.96410i	−1.04106	−	0.213037i
$86$		0			0
$87$	4.59808	+	17.1603i	0.492966	+	1.83977i
$88$		0			0
$89$	−14.7942	−	3.96410i	−1.56819	−	0.420194i	−0.632942	−	0.774199i	$-0.718153\pi$
$89$	−14.7942	−	3.96410i	−1.56819	−	0.420194i	−0.935243	+	0.354005i	$0.884819\pi$
$90$		0			0
$91$	13.4282	−	0.866025i	1.40766	−	0.0907841i
$92$		0			0
$93$	7.83013	+	13.5622i	0.811946	+	1.40633i
$94$		0			0
$95$	−1.96410	−	0.401924i	−0.201513	−	0.0412365i
$96$		0			0
$97$	3.86603	+	2.23205i	0.392535	+	0.226630i	0.683258	−	0.730177i	$-0.260562\pi$
$97$	3.86603	+	2.23205i	0.392535	+	0.226630i	−0.290723	+	0.956807i	$0.593896\pi$
$98$		0			0
$99$	1.19615	−	1.19615i	0.120218	−	0.120218i
$100$		0			0
$101$	1.50000	−	0.866025i	0.149256	−	0.0861727i	−0.423512	−	0.905890i	$-0.639203\pi$
$101$	1.50000	−	0.866025i	0.149256	−	0.0861727i	0.572768	+	0.819718i	$0.305870\pi$
$102$		0			0
$103$	−6.66025	+	6.66025i	−0.656254	+	0.656254i	−0.954492	−	0.298237i	$-0.903601\pi$
$103$	−6.66025	+	6.66025i	−0.656254	+	0.656254i	0.298237	+	0.954492i	$0.403601\pi$
$104$		0			0
$105$	5.09808	+	15.2942i	0.497521	+	1.49256i
$106$		0			0
$107$	−5.96410	−	1.59808i	−0.576571	−	0.154492i	−0.0412627	−	0.999148i	$-0.513138\pi$
$107$	−5.96410	−	1.59808i	−0.576571	−	0.154492i	−0.535309	+	0.844656i	$0.679805\pi$
$108$		0			0
$109$	−9.39230	−	9.39230i	−0.899620	−	0.899620i	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	−9.39230	−	9.39230i	−0.899620	−	0.899620i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$		0			0
$111$	0.500000	−	0.133975i	0.0474579	−	0.0127163i
$112$		0			0
$113$	13.1603	−	3.52628i	1.23801	−	0.331724i	0.420318	−	0.907377i	$-0.361919\pi$
$113$	13.1603	−	3.52628i	1.23801	−	0.331724i	0.817695	+	0.575652i	$0.195252\pi$
$114$		0			0
$115$	−12.0622	−	10.6962i	−1.12480	−	0.997421i
$116$		0			0
$117$	−0.169873	−	2.63397i	−0.0157048	−	0.243511i
$118$		0			0
$119$	−4.23205	+	15.7942i	−0.387951	+	1.44785i
$120$		0			0
$121$	4.90192	+	2.83013i	0.445629	+	0.257284i
$122$		0			0
$123$	0.133975	−	0.232051i	0.0120801	−	0.0209233i
$124$		0			0
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$	4.50000	−	16.7942i	0.399310	−	1.49025i	−0.415002	−	0.909820i	$-0.636219\pi$
$127$	4.50000	−	16.7942i	0.399310	−	1.49025i	0.814313	−	0.580426i	$-0.197114\pi$
$128$		0			0
$129$	22.6603			1.99512
$130$		0			0
$131$	13.8564			1.21064			0.605320	−	0.795982i	$-0.293045\pi$
$131$	13.8564			1.21064			0.605320	+	0.795982i	$0.293045\pi$
$132$		0			0
$133$	−0.866025	+	3.23205i	−0.0750939	+	0.280254i
$134$		0			0
$135$	−9.29423	+	3.09808i	−0.799920	+	0.266640i
$136$		0			0
$137$	−0.401924	+	0.696152i	−0.0343387	+	0.0594763i	−0.882684	−	0.469967i	$-0.844266\pi$
$137$	−0.401924	+	0.696152i	−0.0343387	+	0.0594763i	0.848345	+	0.529443i	$0.177599\pi$
$138$		0			0
$139$	8.42820	+	4.86603i	0.714871	+	0.412731i	0.812862	−	0.582456i	$-0.197908\pi$
$139$	8.42820	+	4.86603i	0.714871	+	0.412731i	−0.0979911	+	0.995187i	$0.531242\pi$
$140$		0			0
$141$	0.267949	−	1.00000i	0.0225654	−	0.0842152i
$142$		0			0
$143$	−7.89230	+	2.66987i	−0.659988	+	0.223266i
$144$		0			0
$145$	20.5263	−	1.23205i	1.70461	−	0.102316i
$146$		0			0
$147$	12.9282	−	3.46410i	1.06630	−	0.285714i
$148$		0			0
$149$	−18.2583	+	4.89230i	−1.49578	+	0.400793i	−0.911684	−	0.410891i	$-0.865218\pi$
$149$	−18.2583	+	4.89230i	−1.49578	+	0.400793i	−0.584096	+	0.811684i	$0.698551\pi$
$150$		0			0
$151$	0.803848	+	0.803848i	0.0654162	+	0.0654162i	0.739058	−	0.673642i	$-0.235271\pi$
$151$	0.803848	+	0.803848i	0.0654162	+	0.0654162i	−0.673642	+	0.739058i	$0.735271\pi$
$152$		0			0
$153$	3.09808	+	0.830127i	0.250465	+	0.0671118i
$154$		0			0
$155$	17.1962	−	5.73205i	1.38123	−	0.460409i
$156$		0			0
$157$	−7.39230	+	7.39230i	−0.589970	+	0.589970i	−0.937623	−	0.347653i	$-0.886979\pi$
$157$	−7.39230	+	7.39230i	−0.589970	+	0.589970i	0.347653	+	0.937623i	$0.386979\pi$
$158$		0			0
$159$	3.63397	−	2.09808i	0.288193	−	0.166388i
$160$		0			0
$161$	−19.0263	+	19.0263i	−1.49948	+	1.49948i
$162$		0			0
$163$	1.33013	+	0.767949i	0.104184	+	0.0601504i	0.551186	−	0.834382i	$-0.314175\pi$
$163$	1.33013	+	0.767949i	0.104184	+	0.0601504i	−0.447003	+	0.894533i	$0.647509\pi$
$164$		0			0
$165$	−5.50000	−	8.33013i	−0.428174	−	0.648500i
$166$		0			0
$167$	3.33013	+	5.76795i	0.257693	+	0.446337i	0.965623	−	0.259945i	$-0.0837044\pi$
$167$	3.33013	+	5.76795i	0.257693	+	0.446337i	−0.707931	+	0.706282i	$0.750371\pi$
$168$		0			0
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$		0			0
$171$	0.633975	+	0.169873i	0.0484812	+	0.0129905i
$172$		0			0
$173$	2.30385	+	8.59808i	0.175158	+	0.653700i	0.996525	+	0.0832986i	$0.0265455\pi$
$173$	2.30385	+	8.59808i	0.175158	+	0.653700i	−0.821366	+	0.570401i	$0.806788\pi$
$174$		0			0
$175$	18.5263	−	2.23205i	1.40046	−	0.168727i
$176$		0			0
$177$	−13.3923			−1.00663
$178$		0			0
$179$	−5.96410	−	10.3301i	−0.445778	−	0.772110i	0.552328	−	0.833627i	$-0.313740\pi$
$179$	−5.96410	−	10.3301i	−0.445778	−	0.772110i	−0.998106	+	0.0615168i	$0.980406\pi$
$180$		0			0
$181$		−	14.9282i		−	1.10960i	−0.831982	−	0.554802i	$-0.812794\pi$
$181$		−	14.9282i		−	1.10960i	0.831982	−	0.554802i	$-0.187206\pi$
$182$		0			0
$183$	1.36603	+	1.36603i	0.100980	+	0.100980i
$184$		0			0
$185$	−0.0358984	−	0.598076i	−0.00263930	−	0.0439714i
$186$		0			0
$187$		−	10.1244i		−	0.740366i
$188$		0			0
$189$	4.23205	+	15.7942i	0.307836	+	1.14886i
$190$		0			0
$191$	−11.9641	+	20.7224i	−0.865692	+	1.49942i	0.000666402		1.00000i	$0.499788\pi$
$191$	−11.9641	+	20.7224i	−0.865692	+	1.49942i	−0.866358	+	0.499423i	$0.833545\pi$
$192$		0			0
$193$	−21.0622	+	12.1603i	−1.51609	+	0.875314i	−0.516267	+	0.856428i	$0.672679\pi$
$193$	−21.0622	+	12.1603i	−1.51609	+	0.875314i	−0.999822	+	0.0188866i	$0.993988\pi$
$194$		0			0
$195$	−15.4282	−	2.13397i	−1.10484	−	0.152817i
$196$		0			0
$197$	−12.4019	+	7.16025i	−0.883600	+	0.510147i	−0.871844	−	0.489784i	$-0.837076\pi$
$197$	−12.4019	+	7.16025i	−0.883600	+	0.510147i	−0.0117566	+	0.999931i	$0.503742\pi$
$198$		0			0
$199$	−4.96410	+	8.59808i	−0.351896	+	0.609501i	−0.986582	−	0.163269i	$-0.947796\pi$
$199$	−4.96410	+	8.59808i	−0.351896	+	0.609501i	0.634686	+	0.772770i	$0.281130\pi$
$200$		0			0
$201$	−2.76795	−	10.3301i	−0.195236	−	0.728631i
$202$		0			0
$203$		−	34.3205i		−	2.40883i
$204$		0			0
$205$	−0.232051	−	0.205771i	−0.0162071	−	0.0143717i
$206$		0			0
$207$	3.73205	+	3.73205i	0.259395	+	0.259395i
$208$		0			0
$209$		−	2.07180i		−	0.143309i
$210$		0			0
$211$	1.96410	+	3.40192i	0.135214	+	0.234198i	0.925679	−	0.378309i	$-0.123494\pi$
$211$	1.96410	+	3.40192i	0.135214	+	0.234198i	−0.790465	+	0.612507i	$0.790161\pi$
$212$		0			0
$213$	−8.46410			−0.579951
$214$		0			0
$215$	5.25833	−	25.6962i	0.358615	−	1.75246i
$216$		0			0
$217$	−7.83013	−	29.2224i	−0.531544	−	1.98375i
$218$		0			0
$219$	24.1244	+	6.46410i	1.63017	+	0.436804i
$220$		0			0
$221$	−11.8660	−	10.4282i	−0.798195	−	0.701477i
$222$		0			0
$223$	8.13397	+	14.0885i	0.544691	+	0.943433i	0.998626	+	0.0523981i	$0.0166865\pi$
$223$	8.13397	+	14.0885i	0.544691	+	0.943433i	−0.453935	+	0.891035i	$0.649980\pi$
$224$		0			0
$225$	−0.437822	−	3.63397i	−0.0291881	−	0.242265i
$226$		0			0
$227$	5.59808	+	3.23205i	0.371557	+	0.214519i	0.674139	−	0.738605i	$-0.264515\pi$
$227$	5.59808	+	3.23205i	0.371557	+	0.214519i	−0.302581	+	0.953124i	$0.597848\pi$
$228$		0			0
$229$	16.8564	−	16.8564i	1.11390	−	1.11390i	0.121285	−	0.992618i	$-0.461299\pi$
$229$	16.8564	−	16.8564i	1.11390	−	1.11390i	0.992618	−	0.121285i	$-0.0387015\pi$
$230$		0			0
$231$	−14.4282	+	8.33013i	−0.949306	+	0.548082i
$232$		0			0
$233$	11.0000	−	11.0000i	0.720634	−	0.720634i	−0.248100	−	0.968734i	$-0.579806\pi$
$233$	11.0000	−	11.0000i	0.720634	−	0.720634i	0.968734	+	0.248100i	$0.0798063\pi$
$234$		0			0
$235$	−1.07180	−	0.535898i	−0.0699163	−	0.0349582i
$236$		0			0
$237$	8.46410	+	2.26795i	0.549802	+	0.147319i
$238$		0			0
$239$	−1.19615	−	1.19615i	−0.0773727	−	0.0773727i	0.667361	−	0.744734i	$-0.267424\pi$
$239$	−1.19615	−	1.19615i	−0.0773727	−	0.0773727i	−0.744734	+	0.667361i	$0.767424\pi$
$240$		0			0
$241$	−17.0622	+	4.57180i	−1.09907	+	0.294495i	−0.762386	−	0.647122i	$-0.775972\pi$
$241$	−17.0622	+	4.57180i	−1.09907	+	0.294495i	−0.336685	+	0.941617i	$0.609306\pi$
$242$		0			0
$243$	7.19615	−	1.92820i	0.461633	−	0.123694i
$244$		0			0
$245$	−0.928203	−	15.4641i	−0.0593007	−	0.987965i
$246$		0			0
$247$	−2.42820	−	2.13397i	−0.154503	−	0.135782i
$248$		0			0
$249$	−1.73205	+	6.46410i	−0.109764	+	0.409646i
$250$		0			0
$251$	−3.10770	−	1.79423i	−0.196156	−	0.113251i	0.398705	−	0.917079i	$-0.369460\pi$
$251$	−3.10770	−	1.79423i	−0.196156	−	0.113251i	−0.594861	+	0.803828i	$0.702793\pi$
$252$		0			0
$253$	8.33013	−	14.4282i	0.523711	−	0.907093i
$254$		0			0
$255$	8.46410	−	16.9282i	0.530043	−	1.06009i
$256$		0			0
$257$	4.16025	−	15.5263i	0.259510	−	0.968503i	−0.706016	−	0.708196i	$-0.749510\pi$
$257$	4.16025	−	15.5263i	0.259510	−	0.968503i	0.965526	−	0.260307i	$-0.0838238\pi$
$258$		0			0
$259$	−1.00000			−0.0621370
$260$		0			0
$261$	−6.73205			−0.416703
$262$		0			0
$263$	−2.89230	+	10.7942i	−0.178347	+	0.665601i	0.817610	+	0.575772i	$0.195299\pi$
$263$	−2.89230	+	10.7942i	−0.178347	+	0.665601i	−0.995957	+	0.0898284i	$0.971368\pi$
$264$		0			0
$265$	−1.53590	−	4.60770i	−0.0943495	−	0.283048i
$266$		0			0
$267$	14.7942	−	25.6244i	0.905392	−	1.56819i
$268$		0			0
$269$	9.57180	+	5.52628i	0.583603	+	0.336943i	0.762564	−	0.646913i	$-0.223940\pi$
$269$	9.57180	+	5.52628i	0.583603	+	0.336943i	−0.178961	+	0.983856i	$0.557274\pi$
$270$		0			0
$271$	−4.20577	+	15.6962i	−0.255482	+	0.953473i	0.712339	+	0.701836i	$0.247636\pi$
$271$	−4.20577	+	15.6962i	−0.255482	+	0.953473i	−0.967821	+	0.251638i	$0.919031\pi$
$272$		0			0
$273$	−5.09808	+	25.4904i	−0.308550	+	1.54275i
$274$		0			0
$275$	−10.7224	+	4.30385i	−0.646587	+	0.259532i
$276$		0			0
$277$	−11.1603	+	2.99038i	−0.670555	+	0.179675i	−0.578005	−	0.816033i	$-0.696168\pi$
$277$	−11.1603	+	2.99038i	−0.670555	+	0.179675i	−0.0925500	+	0.995708i	$0.529502\pi$
$278$		0			0
$279$	−5.73205	+	1.53590i	−0.343169	+	0.0919518i
$280$		0			0
$281$	13.3923	+	13.3923i	0.798918	+	0.798918i	0.982925	−	0.184007i	$-0.0589069\pi$
$281$	13.3923	+	13.3923i	0.798918	+	0.798918i	−0.184007	+	0.982925i	$0.558907\pi$
$282$		0			0
$283$	24.3564	+	6.52628i	1.44784	+	0.387947i	0.895271	−	0.445522i	$-0.146982\pi$
$283$	24.3564	+	6.52628i	1.44784	+	0.387947i	0.552567	+	0.833469i	$0.313648\pi$
$284$		0			0
$285$	1.73205	−	3.46410i	0.102598	−	0.205196i
$286$		0			0
$287$	−0.366025	+	0.366025i	−0.0216058	+	0.0216058i
$288$		0			0
$289$	1.90192	−	1.09808i	0.111878	−	0.0645927i
$290$		0			0
$291$	−6.09808	+	6.09808i	−0.357476	+	0.357476i
$292$		0			0
$293$	13.4545	+	7.76795i	0.786019	+	0.453808i	0.838559	−	0.544810i	$-0.183398\pi$
$293$	13.4545	+	7.76795i	0.786019	+	0.453808i	−0.0525400	+	0.998619i	$0.516732\pi$
$294$		0			0
$295$	−3.10770	+	15.1865i	−0.180937	+	0.884194i
$296$		0			0
$297$	−5.06218	−	8.76795i	−0.293737	−	0.508768i
$298$		0			0
$299$	−8.33013	−	24.6244i	−0.481744	−	1.42406i
$300$		0			0
$301$	−42.2846	−	11.3301i	−2.43724	−	0.653058i
$302$		0			0
$303$	0.866025	+	3.23205i	0.0497519	+	0.185676i
$304$		0			0
$305$	1.86603	−	1.23205i	0.106848	−	0.0705470i
$306$		0			0
$307$	−9.60770			−0.548340			−0.274170	−	0.961681i	$-0.588403\pi$
$307$	−9.60770			−0.548340			−0.274170	+	0.961681i	$0.588403\pi$
$308$		0			0
$309$	−9.09808	−	15.7583i	−0.517571	−	0.896460i
$310$		0			0
$311$		−	32.2487i		−	1.82866i	−0.404974	−	0.914328i	$-0.632719\pi$
$311$		−	32.2487i		−	1.82866i	0.404974	−	0.914328i	$-0.367281\pi$
$312$		0			0
$313$	−14.3205	−	14.3205i	−0.809443	−	0.809443i	0.175107	−	0.984549i	$-0.443973\pi$
$313$	−14.3205	−	14.3205i	−0.809443	−	0.809443i	−0.984549	+	0.175107i	$0.943973\pi$
$314$		0			0
$315$	−6.09808	+	0.366025i	−0.343588	+	0.0206232i
$316$		0			0
$317$			16.9282i			0.950783i	0.879774	+	0.475391i	$0.157694\pi$
$317$			16.9282i			0.950783i	−0.879774	+	0.475391i	$0.842306\pi$
$318$		0			0
$319$	5.50000	+	20.5263i	0.307941	+	1.14925i
$320$		0			0
$321$	5.96410	−	10.3301i	0.332884	−	0.576571i
$322$		0			0
$323$	3.40192	−	1.96410i	0.189288	−	0.109286i
$324$		0			0
$325$	−6.00000	+	17.0000i	−0.332820	+	0.942990i
$326$		0			0
$327$	22.2224	−	12.8301i	1.22890	−	0.709508i
$328$		0			0
$329$	−1.00000	+	1.73205i	−0.0551318	+	0.0954911i
$330$		0			0
$331$	1.66987	+	6.23205i	0.0917845	+	0.342544i	0.996512	−	0.0834456i	$-0.0265925\pi$
$331$	1.66987	+	6.23205i	0.0917845	+	0.342544i	−0.904728	+	0.425990i	$0.859926\pi$
$332$		0			0
$333$			0.196152i			0.0107491i
$334$		0			0
$335$	−12.3564	+	0.741670i	−0.675103	+	0.0405217i
$336$		0			0
$337$	13.9282	+	13.9282i	0.758718	+	0.758718i	0.976089	−	0.217371i	$-0.0697483\pi$
$337$	13.9282	+	13.9282i	0.758718	+	0.758718i	−0.217371	+	0.976089i	$0.569748\pi$
$338$		0			0
$339$			26.3205i			1.42953i
$340$		0			0
$341$	9.36603	+	16.2224i	0.507199	+	0.878494i
$342$		0			0
$343$	0.267949			0.0144679
$344$		0			0
$345$	25.9904	−	17.1603i	1.39928	−	0.923877i
$346$		0			0
$347$	4.10770	+	15.3301i	0.220513	+	0.822964i	0.984153	+	0.177322i	$0.0567435\pi$
$347$	4.10770	+	15.3301i	0.220513	+	0.822964i	−0.763640	+	0.645642i	$0.776590\pi$
$348$		0			0
$349$	24.5263	+	6.57180i	1.31286	+	0.351780i	0.846299	−	0.532708i	$-0.178826\pi$
$349$	24.5263	+	6.57180i	1.31286	+	0.351780i	0.466563	+	0.884488i	$0.345492\pi$
$350$		0			0
$351$	−15.4904	−	3.09808i	−0.826815	−	0.165363i
$352$		0			0
$353$	6.13397	+	10.6244i	0.326479	+	0.565477i	0.981810	−	0.189864i	$-0.0608046\pi$
$353$	6.13397	+	10.6244i	0.326479	+	0.565477i	−0.655332	+	0.755341i	$0.727471\pi$
$354$		0			0
$355$	−1.96410	+	9.59808i	−0.104244	+	0.509413i
$356$		0			0
$357$	−27.3564	−	15.7942i	−1.44785	−	0.835919i
$358$		0			0
$359$	−23.5885	+	23.5885i	−1.24495	+	1.24495i	−0.287029	+	0.957922i	$0.592668\pi$
$359$	−23.5885	+	23.5885i	−1.24495	+	1.24495i	−0.957922	+	0.287029i	$0.907332\pi$
$360$		0			0
$361$	−15.7583	+	9.09808i	−0.829386	+	0.478846i
$362$		0			0
$363$	−7.73205	+	7.73205i	−0.405827	+	0.405827i
$364$		0			0
$365$	12.9282	−	25.8564i	0.676693	−	1.35339i
$366$		0			0
$367$	17.8923	+	4.79423i	0.933971	+	0.250257i	0.693547	−	0.720411i	$-0.256047\pi$
$367$	17.8923	+	4.79423i	0.933971	+	0.250257i	0.240424	+	0.970668i	$0.422714\pi$
$368$		0			0
$369$	0.0717968	+	0.0717968i	0.00373759	+	0.00373759i
$370$		0			0
$371$	−7.83013	+	2.09808i	−0.406520	+	0.108927i
$372$		0			0
$373$	−3.76795	+	1.00962i	−0.195097	+	0.0522761i	−0.355044	−	0.934849i	$-0.615534\pi$
$373$	−3.76795	+	1.00962i	−0.195097	+	0.0522761i	0.159947	+	0.987126i	$0.448868\pi$
$374$		0			0
$375$	−21.5263	−	1.76795i	−1.11161	−	0.0912965i
$376$		0			0
$377$	29.7224	+	14.6962i	1.53078	+	0.756890i
$378$		0			0
$379$	−4.47372	+	16.6962i	−0.229800	+	0.857624i	0.750625	+	0.660729i	$0.229753\pi$
$379$	−4.47372	+	16.6962i	−0.229800	+	0.857624i	−0.980425	+	0.196895i	$0.936914\pi$
$380$		0			0
$381$	29.0885	+	16.7942i	1.49025	+	0.860394i
$382$		0			0
$383$	5.59808	−	9.69615i	0.286048	−	0.495450i	−0.686815	−	0.726833i	$-0.740992\pi$
$383$	5.59808	−	9.69615i	0.286048	−	0.495450i	0.972863	+	0.231382i	$0.0743249\pi$
$384$		0			0
$385$	6.09808	+	18.2942i	0.310787	+	0.932360i
$386$		0			0
$387$	−2.22243	+	8.29423i	−0.112973	+	0.421619i
$388$		0			0
$389$	−23.8564			−1.20957			−0.604784	−	0.796390i	$-0.706741\pi$
$389$	−23.8564			−1.20957			−0.604784	+	0.796390i	$0.706741\pi$
$390$		0			0
$391$	31.5885			1.59750
$392$		0			0
$393$	−6.92820	+	25.8564i	−0.349482	+	1.30428i
$394$		0			0
$395$	4.53590	−	9.07180i	0.228226	−	0.456452i
$396$		0			0
$397$	−18.2583	+	31.6244i	−0.916359	+	1.58718i	−0.111460	+	0.993769i	$0.535553\pi$
$397$	−18.2583	+	31.6244i	−0.916359	+	1.58718i	−0.804899	+	0.593412i	$0.797780\pi$
$398$		0			0
$399$	−5.59808	−	3.23205i	−0.280254	−	0.161805i
$400$		0			0
$401$	4.13397	−	15.4282i	0.206441	−	0.770448i	−0.782565	−	0.622569i	$-0.786089\pi$
$401$	4.13397	−	15.4282i	0.206441	−	0.770448i	0.989006	−	0.147878i	$-0.0472444\pi$
$402$		0			0
$403$	28.6603	+	5.73205i	1.42767	+	0.285534i
$404$		0			0
$405$	−1.42820	−	23.7942i	−0.0709680	−	1.18234i
$406$		0			0
$407$	0.598076	−	0.160254i	0.0296455	−	0.00794350i
$408$		0			0
$409$	9.06218	−	2.42820i	0.448096	−	0.120067i	−0.0277124	−	0.999616i	$-0.508822\pi$
$409$	9.06218	−	2.42820i	0.448096	−	0.120067i	0.475808	+	0.879549i	$0.342156\pi$
$410$		0			0
$411$	−1.09808	−	1.09808i	−0.0541641	−	0.0541641i
$412$		0			0
$413$	24.9904	+	6.69615i	1.22970	+	0.329496i
$414$		0			0
$415$	6.92820	+	3.46410i	0.340092	+	0.170046i
$416$		0			0
$417$	−13.2942	+	13.2942i	−0.651021	+	0.651021i
$418$		0			0
$419$	0.356406	−	0.205771i	0.0174116	−	0.0100526i	−0.491269	−	0.871008i	$-0.663467\pi$
$419$	0.356406	−	0.205771i	0.0174116	−	0.0100526i	0.508681	+	0.860955i	$0.330133\pi$
$420$		0			0
$421$	27.9282	−	27.9282i	1.36114	−	1.36114i	0.488667	−	0.872470i	$-0.337483\pi$
$421$	27.9282	−	27.9282i	1.36114	−	1.36114i	0.872470	−	0.488667i	$-0.162517\pi$
$422$		0			0
$423$	0.339746	+	0.196152i	0.0165190	+	0.00953726i
$424$		0			0
$425$	−17.2321	−	13.5263i	−0.835877	−	0.656121i
$426$		0			0
$427$	−1.86603	−	3.23205i	−0.0903033	−	0.156410i
$428$		0			0
$429$	−1.03590	−	16.0622i	−0.0500136	−	0.775489i
$430$		0			0
$431$	27.5263	+	7.37564i	1.32589	+	0.355272i	0.851183	−	0.524869i	$-0.175886\pi$
$431$	27.5263	+	7.37564i	1.32589	+	0.355272i	0.474711	+	0.880142i	$0.342552\pi$
$432$		0			0
$433$	−7.16025	−	26.7224i	−0.344100	−	1.28420i	−0.893660	−	0.448744i	$-0.851871\pi$
$433$	−7.16025	−	26.7224i	−0.344100	−	1.28420i	0.549560	−	0.835454i	$-0.314795\pi$
$434$		0			0
$435$	−7.96410	+	38.9186i	−0.381849	+	1.86600i
$436$		0			0
$437$	6.46410			0.309220
$438$		0			0
$439$	0.964102	+	1.66987i	0.0460141	+	0.0796987i	0.888115	−	0.459621i	$-0.152015\pi$
$439$	0.964102	+	1.66987i	0.0460141	+	0.0796987i	−0.842101	+	0.539320i	$0.818681\pi$
$440$		0			0
$441$			5.07180i			0.241514i
$442$		0			0
$443$	−11.0526	−	11.0526i	−0.525123	−	0.525123i	0.393991	−	0.919114i	$-0.371094\pi$
$443$	−11.0526	−	11.0526i	−0.525123	−	0.525123i	−0.919114	+	0.393991i	$0.871094\pi$
$444$		0			0
$445$	−25.6244	−	22.7224i	−1.21471	−	1.07715i
$446$		0			0
$447$		−	36.5167i		−	1.72718i
$448$		0			0
$449$	−1.99038	−	7.42820i	−0.0939319	−	0.350559i	0.902923	−	0.429801i	$-0.141416\pi$
$449$	−1.99038	−	7.42820i	−0.0939319	−	0.350559i	−0.996855	+	0.0792428i	$0.974750\pi$
$450$		0			0
$451$	0.160254	−	0.277568i	0.00754607	−	0.0130702i
$452$		0			0
$453$	−1.90192	+	1.09808i	−0.0893602	+	0.0515921i
$454$		0			0
$455$	27.7224	+	11.6962i	1.29965	+	0.548324i
$456$		0			0
$457$	7.45448	−	4.30385i	0.348706	−	0.201325i	−0.315409	−	0.948956i	$-0.602142\pi$
$457$	7.45448	−	4.30385i	0.348706	−	0.201325i	0.664115	+	0.747630i	$0.268808\pi$
$458$		0			0
$459$	9.59808	−	16.6244i	0.448000	−	0.775958i
$460$		0			0
$461$	1.99038	+	7.42820i	0.0927013	+	0.345966i	0.996661	−	0.0816519i	$-0.0260196\pi$
$461$	1.99038	+	7.42820i	0.0927013	+	0.345966i	−0.903960	+	0.427618i	$0.859353\pi$
$462$		0			0
$463$		−	2.14359i		−	0.0996212i	−0.998759	−	0.0498106i	$-0.984138\pi$
$463$		−	2.14359i		−	0.0996212i	0.998759	−	0.0498106i	$-0.0158618\pi$
$464$		0			0
$465$	2.09808	+	34.9545i	0.0972960	+	1.62098i
$466$		0			0
$467$	4.12436	+	4.12436i	0.190852	+	0.190852i	0.796064	−	0.605212i	$-0.206912\pi$
$467$	4.12436	+	4.12436i	0.190852	+	0.190852i	−0.605212	+	0.796064i	$0.706912\pi$
$468$		0			0
$469$			20.6603i			0.954002i
$470$		0			0
$471$	−10.0981	−	17.4904i	−0.465295	−	0.805914i
$472$		0			0
$473$	27.1051			1.24629
$474$		0			0
$475$	−3.52628	−	2.76795i	−0.161797	−	0.127002i
$476$		0			0
$477$	0.411543	+	1.53590i	0.0188432	+	0.0703240i
$478$		0			0
$479$	−26.9904	−	7.23205i	−1.23322	−	0.330441i	−0.417389	−	0.908728i	$-0.637055\pi$
$479$	−26.9904	−	7.23205i	−1.23322	−	0.330441i	−0.815833	+	0.578287i	$0.803721\pi$
$480$		0			0
$481$	0.428203	−	0.866025i	0.0195244	−	0.0394874i
$482$		0			0
$483$	−25.9904	−	45.0167i	−1.18260	−	2.04833i
$484$		0			0
$485$	5.50000	+	8.33013i	0.249742	+	0.378252i
$486$		0			0
$487$	0.277568	+	0.160254i	0.0125778	+	0.00726180i	0.506276	−	0.862372i	$-0.331022\pi$
$487$	0.277568	+	0.160254i	0.0125778	+	0.00726180i	−0.493698	+	0.869633i	$0.664355\pi$
$488$		0			0
$489$	−2.09808	+	2.09808i	−0.0948783	+	0.0948783i
$490$		0			0
$491$	−7.03590	+	4.06218i	−0.317526	+	0.183324i	−0.650289	−	0.759687i	$-0.725352\pi$
$491$	−7.03590	+	4.06218i	−0.317526	+	0.183324i	0.332763	+	0.943010i	$0.392019\pi$
$492$		0			0
$493$	−28.4904	+	28.4904i	−1.28314	+	1.28314i
$494$		0			0
$495$	3.58846	−	1.19615i	0.161289	−	0.0537631i
$496$		0			0
$497$	15.7942	+	4.23205i	0.708468	+	0.189833i
$498$		0			0
$499$	7.19615	+	7.19615i	0.322144	+	0.322144i	0.849589	−	0.527445i	$-0.176850\pi$
$499$	7.19615	+	7.19615i	0.322144	+	0.322144i	−0.527445	+	0.849589i	$0.676850\pi$
$500$		0			0
$501$	−12.4282	+	3.33013i	−0.555251	+	0.148779i
$502$		0			0
$503$	−10.9641	+	2.93782i	−0.488865	+	0.130991i	−0.494828	−	0.868991i	$-0.664769\pi$
$503$	−10.9641	+	2.93782i	−0.488865	+	0.130991i	0.00596240	+	0.999982i	$0.498102\pi$
$504$		0			0
$505$	3.86603	−	0.232051i	0.172036	−	0.0103261i
$506$		0			0
$507$	−19.8923	−	15.3301i	−0.883448	−	0.680835i
$508$		0			0
$509$	6.79423	−	25.3564i	0.301149	−	1.12390i	−0.635061	−	0.772462i	$-0.719025\pi$
$509$	6.79423	−	25.3564i	0.301149	−	1.12390i	0.936210	−	0.351441i	$-0.114308\pi$
$510$		0			0
$511$	−41.7846	−	24.1244i	−1.84844	−	1.06720i
$512$		0			0
$513$	1.96410	−	3.40192i	0.0867172	−	0.150199i
$514$		0			0
$515$	−19.9808	+	6.66025i	−0.880458	+	0.293486i
$516$		0			0
$517$	0.320508	−	1.19615i	0.0140959	−	0.0526067i
$518$		0			0
$519$	−17.1962			−0.754827
$520$		0			0
$521$	−23.8564			−1.04517			−0.522584	−	0.852588i	$-0.675032\pi$
$521$	−23.8564			−1.04517			−0.522584	+	0.852588i	$0.675032\pi$
$522$		0			0
$523$	0.820508	−	3.06218i	0.0358783	−	0.133900i	−0.945664	−	0.325146i	$-0.894586\pi$
$523$	0.820508	−	3.06218i	0.0358783	−	0.133900i	0.981542	+	0.191247i	$0.0612531\pi$
$524$		0			0
$525$	−5.09808	+	35.6865i	−0.222498	+	1.55749i
$526$		0			0
$527$	−17.7583	+	30.7583i	−0.773565	+	1.33985i
$528$		0			0
$529$	25.0981	+	14.4904i	1.09122	+	0.630017i
$530$		0			0
$531$	1.31347	−	4.90192i	0.0569996	−	0.212725i
$532$		0			0
$533$	−0.160254	−	0.473721i	−0.00694137	−	0.0205191i
$534$		0			0
$535$	−10.3301	−	9.16025i	−0.446610	−	0.396032i
$536$		0			0
$537$	22.2583	−	5.96410i	0.960518	−	0.257370i
$538$		0			0
$539$	15.4641	−	4.14359i	0.666086	−	0.178477i
$540$		0			0
$541$	27.9282	+	27.9282i	1.20073	+	1.20073i	0.973946	+	0.226782i	$0.0728204\pi$
$541$	27.9282	+	27.9282i	1.20073	+	1.20073i	0.226782	+	0.973946i	$0.427180\pi$
$542$		0			0
$543$	27.8564	+	7.46410i	1.19543	+	0.320315i
$544$		0			0
$545$	−9.39230	−	28.1769i	−0.402322	−	1.20697i
$546$		0			0
$547$	1.19615	−	1.19615i	0.0511438	−	0.0511438i	−0.681072	−	0.732216i	$-0.738486\pi$
$547$	1.19615	−	1.19615i	0.0511438	−	0.0511438i	0.732216	+	0.681072i	$0.238486\pi$
$548$		0			0
$549$	−0.633975	+	0.366025i	−0.0270574	+	0.0156216i
$550$		0			0
$551$	−5.83013	+	5.83013i	−0.248372	+	0.248372i
$552$		0			0
$553$	−14.6603	−	8.46410i	−0.623417	−	0.359930i
$554$		0			0
$555$	1.13397	+	0.232051i	0.0481345	+	0.00985001i
$556$		0			0
$557$	12.2583	+	21.2321i	0.519402	+	0.899631i	0.999746	+	0.0225505i	$0.00717864\pi$
$557$	12.2583	+	21.2321i	0.519402	+	0.899631i	−0.480344	+	0.877080i	$0.659488\pi$
$558$		0			0
$559$	27.9186	−	31.7679i	1.18083	−	1.34364i
$560$		0			0
$561$	18.8923	+	5.06218i	0.797634	+	0.213725i
$562$		0			0
$563$	2.82051	+	10.5263i	0.118870	+	0.443630i	0.999547	−	0.0300874i	$-0.00957856\pi$
$563$	2.82051	+	10.5263i	0.118870	+	0.443630i	−0.880677	+	0.473717i	$0.842912\pi$
$564$		0			0
$565$	29.8468	+	6.10770i	1.25566	+	0.256953i
$566$		0			0
$567$	−39.7846			−1.67080
$568$		0			0
$569$	−15.4282	−	26.7224i	−0.646784	−	1.12026i	−0.983886	−	0.178795i	$-0.942780\pi$
$569$	−15.4282	−	26.7224i	−0.646784	−	1.12026i	0.337102	−	0.941468i	$-0.390553\pi$
$570$		0			0
$571$			34.1051i			1.42725i	0.700525	+	0.713627i	$0.252949\pi$
$571$			34.1051i			1.42725i	−0.700525	+	0.713627i	$0.747051\pi$
$572$		0			0
$573$	−32.6865	−	32.6865i	−1.36550	−	1.36550i
$574$		0			0
$575$	−13.4282	−	33.4545i	−0.559995	−	1.39515i
$576$		0			0
$577$			15.0718i			0.627447i	0.949514	+	0.313724i	$0.101577\pi$
$577$			15.0718i			0.627447i	−0.949514	+	0.313724i	$0.898423\pi$
$578$		0			0
$579$	−12.1603	−	45.3827i	−0.505363	−	1.88604i
$580$		0			0
$581$	6.46410	−	11.1962i	0.268176	−	0.464495i
$582$		0			0
$583$	4.34679	−	2.50962i	0.180026	−	0.103938i
$584$		0			0
$585$	2.29423	−	5.43782i	0.0948547	−	0.224826i
$586$		0			0
$587$	7.20577	−	4.16025i	0.297414	−	0.171712i	−0.343867	−	0.939019i	$-0.611737\pi$
$587$	7.20577	−	4.16025i	0.297414	−	0.171712i	0.641281	+	0.767306i	$0.278403\pi$
$588$		0			0
$589$	−3.63397	+	6.29423i	−0.149735	+	0.259349i
$590$		0			0
$591$	−7.16025	−	26.7224i	−0.294533	−	1.09921i
$592$		0			0
$593$		−	20.9282i		−	0.859418i	−0.902967	−	0.429709i	$-0.858616\pi$
$593$		−	20.9282i		−	0.859418i	0.902967	−	0.429709i	$-0.141384\pi$
$594$		0			0
$595$	−24.2583	+	27.3564i	−0.994495	+	1.12150i
$596$		0			0
$597$	−13.5622	−	13.5622i	−0.555063	−	0.555063i
$598$		0			0
$599$		−	26.3923i		−	1.07836i	−0.842190	−	0.539180i	$-0.818734\pi$
$599$		−	26.3923i		−	1.07836i	0.842190	−	0.539180i	$-0.181266\pi$
$600$		0			0
$601$	−18.4282	−	31.9186i	−0.751702	−	1.30199i	−0.946997	−	0.321242i	$-0.895900\pi$
$601$	−18.4282	−	31.9186i	−0.751702	−	1.30199i	0.195295	−	0.980745i	$-0.437434\pi$
$602$		0			0
$603$	4.05256			0.165033
$604$		0			0
$605$	6.97372	+	10.5622i	0.283522	+	0.429414i
$606$		0			0
$607$	−5.64359	−	21.0622i	−0.229066	−	0.854887i	−0.980734	−	0.195346i	$-0.937417\pi$
$607$	−5.64359	−	21.0622i	−0.229066	−	0.854887i	0.751668	−	0.659542i	$-0.229250\pi$
$608$		0			0
$609$	64.0429	+	17.1603i	2.59515	+	0.695369i
$610$		0			0
$611$	−1.07180	−	1.60770i	−0.0433603	−	0.0650404i
$612$		0			0
$613$	−3.33013	−	5.76795i	−0.134503	−	0.232965i	0.790905	−	0.611939i	$-0.209610\pi$
$613$	−3.33013	−	5.76795i	−0.134503	−	0.232965i	−0.925407	+	0.378974i	$0.876277\pi$
$614$		0			0
$615$	0.500000	−	0.330127i	0.0201619	−	0.0133120i
$616$		0			0
$617$	−26.1340	−	15.0885i	−1.05211	−	0.607438i	−0.128874	−	0.991661i	$-0.541136\pi$
$617$	−26.1340	−	15.0885i	−1.05211	−	0.607438i	−0.923240	+	0.384223i	$0.874470\pi$
$618$		0			0
$619$	−30.1244	+	30.1244i	−1.21080	+	1.21080i	−0.240036	+	0.970764i	$0.577159\pi$
$619$	−30.1244	+	30.1244i	−1.21080	+	1.21080i	−0.970764	+	0.240036i	$0.922841\pi$
$620$		0			0
$621$	27.3564	−	15.7942i	1.09777	−	0.633801i
$622$		0			0
$623$	−40.4186	+	40.4186i	−1.61934	+	1.61934i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	3.86603	+	1.03590i	0.154394	+	0.0413698i
$628$		0			0
$629$	0.830127	+	0.830127i	0.0330993	+	0.0330993i
$630$		0			0
$631$	21.7942	−	5.83975i	0.867615	−	0.232477i	0.202559	−	0.979270i	$-0.435074\pi$
$631$	21.7942	−	5.83975i	0.867615	−	0.232477i	0.665056	+	0.746794i	$0.268408\pi$
$632$		0			0
$633$	−7.33013	+	1.96410i	−0.291346	+	0.0780660i
$634$		0			0
$635$	25.7942	−	29.0885i	1.02361	−	1.15434i
$636$		0			0
$637$	11.0718	−	22.3923i	0.438681	−	0.887215i
$638$		0			0
$639$	0.830127	−	3.09808i	0.0328393	−	0.122558i
$640$		0			0
$641$	−1.28461	−	0.741670i	−0.0507390	−	0.0292942i	0.474416	−	0.880301i	$-0.342659\pi$
$641$	−1.28461	−	0.741670i	−0.0507390	−	0.0292942i	−0.525155	+	0.851007i	$0.675993\pi$
$642$		0			0
$643$	−22.6506	+	39.2321i	−0.893254	+	1.54716i	−0.0573029	+	0.998357i	$0.518250\pi$
$643$	−22.6506	+	39.2321i	−0.893254	+	1.54716i	−0.835951	+	0.548804i	$0.815083\pi$
$644$		0			0
$645$	45.3205	+	22.6603i	1.78449	+	0.892247i
$646$		0			0
$647$	3.96410	−	14.7942i	0.155845	−	0.581621i	−0.843187	−	0.537621i	$-0.819323\pi$
$647$	3.96410	−	14.7942i	0.155845	−	0.581621i	0.999032	−	0.0440001i	$-0.0140102\pi$
$648$		0			0
$649$	−16.0192			−0.628810
$650$		0			0
$651$	58.4449			2.29063
$652$		0			0
$653$	9.69615	−	36.1865i	0.379440	−	1.41609i	−0.467308	−	0.884094i	$-0.654776\pi$
$653$	9.69615	−	36.1865i	0.379440	−	1.41609i	0.846748	−	0.531994i	$-0.178557\pi$
$654$		0			0
$655$	27.7128	+	13.8564i	1.08283	+	0.541415i
$656$		0			0
$657$	−4.73205	+	8.19615i	−0.184615	+	0.319762i
$658$		0			0
$659$	−26.2128	−	15.1340i	−1.02111	−	0.589536i	−0.106682	−	0.994293i	$-0.534023\pi$
$659$	−26.2128	−	15.1340i	−1.02111	−	0.589536i	−0.914424	+	0.404757i	$0.867356\pi$
$660$		0			0
$661$	3.59808	−	13.4282i	0.139949	−	0.522297i	−0.859979	−	0.510329i	$-0.829524\pi$
$661$	3.59808	−	13.4282i	0.139949	−	0.522297i	0.999928	−	0.0119679i	$-0.00380959\pi$
$662$		0			0
$663$	25.3923	−	16.9282i	0.986155	−	0.657437i
$664$		0			0
$665$	−4.96410	+	5.59808i	−0.192500	+	0.217084i
$666$		0			0
$667$	−64.0429	+	17.1603i	−2.47975	+	0.664448i
$668$		0			0
$669$	−30.3564	+	8.13397i	−1.17365	+	0.314478i
$670$		0			0
$671$	1.63397	+	1.63397i	0.0630789	+	0.0630789i
$672$		0			0
$673$	3.76795	+	1.00962i	0.145244	+	0.0389180i	0.330708	−	0.943733i	$-0.392712\pi$
$673$	3.76795	+	1.00962i	0.145244	+	0.0389180i	−0.185465	+	0.982651i	$0.559379\pi$
$674$		0			0
$675$	−21.6865	−	3.09808i	−0.834715	−	0.119245i
$676$		0			0
$677$	24.3205	−	24.3205i	0.934713	−	0.934713i	−0.0632826	−	0.997996i	$-0.520157\pi$
$677$	24.3205	−	24.3205i	0.934713	−	0.934713i	0.997996	+	0.0632826i	$0.0201569\pi$
$678$		0			0
$679$	14.4282	−	8.33013i	0.553704	−	0.319681i
$680$		0			0
$681$	−8.83013	+	8.83013i	−0.338371	+	0.338371i
$682$		0			0
$683$	−20.3827	−	11.7679i	−0.779922	−	0.450288i	0.0564808	−	0.998404i	$-0.482012\pi$
$683$	−20.3827	−	11.7679i	−0.779922	−	0.450288i	−0.836403	+	0.548116i	$0.815345\pi$
$684$		0			0
$685$	−1.50000	+	0.990381i	−0.0573121	+	0.0378405i
$686$		0			0
$687$	23.0263	+	39.8827i	0.878507	+	1.52162i
$688$		0			0
$689$	1.53590	−	7.67949i	0.0585131	−	0.292565i
$690$		0			0
$691$	12.0622	+	3.23205i	0.458867	+	0.122953i	0.480845	−	0.876805i	$-0.340330\pi$
$691$	12.0622	+	3.23205i	0.458867	+	0.122953i	−0.0219785	+	0.999758i	$0.506997\pi$
$692$		0			0
$693$	−1.63397	−	6.09808i	−0.0620696	−	0.231647i
$694$		0			0
$695$	11.9904	+	18.1603i	0.454821	+	0.688858i
$696$		0			0
$697$	0.607695			0.0230181
$698$		0			0
$699$	15.0263	+	26.0263i	0.568346	+	0.984404i
$700$		0			0
$701$			42.9282i			1.62138i	0.585479	+	0.810688i	$0.300907\pi$
$701$			42.9282i			1.62138i	−0.585479	+	0.810688i	$0.699093\pi$
$702$		0			0
$703$	0.169873	+	0.169873i	0.00640688	+	0.00640688i
$704$		0			0
$705$	1.53590	−	1.73205i	0.0578453	−	0.0652328i
$706$		0			0
$707$		−	6.46410i		−	0.243108i
$708$		0			0
$709$	0.401924	+	1.50000i	0.0150946	+	0.0563337i	0.973062	−	0.230542i	$-0.0740500\pi$
$709$	0.401924	+	1.50000i	0.0150946	+	0.0563337i	−0.957968	+	0.286876i	$0.907383\pi$
$710$		0			0
$711$	−1.66025	+	2.87564i	−0.0622644	+	0.107845i
$712$		0			0
$713$	−50.6147	+	29.2224i	−1.89554	+	1.09439i
$714$		0			0
$715$	−18.4545	−	2.55256i	−0.690159	−	0.0954603i
$716$		0			0
$717$	2.83013	−	1.63397i	0.105693	−	0.0610219i
$718$		0			0
$719$	−5.89230	+	10.2058i	−0.219746	+	0.380611i	−0.954730	−	0.297473i	$-0.903856\pi$
$719$	−5.89230	+	10.2058i	−0.219746	+	0.380611i	0.734984	+	0.678084i	$0.237189\pi$
$720$		0			0
$721$	9.09808	+	33.9545i	0.338830	+	1.26453i
$722$		0			0
$723$		−	34.1244i		−	1.26910i
$724$		0			0
$725$	42.2846	+	18.0622i	1.57041	+	0.670812i
$726$		0			0
$727$	17.5885	+	17.5885i	0.652320	+	0.652320i	0.953551	−	0.301231i	$-0.0973976\pi$
$727$	17.5885	+	17.5885i	0.652320	+	0.652320i	−0.301231	+	0.953551i	$0.597398\pi$
$728$		0			0
$729$		−	17.5885i		−	0.651424i
$730$		0			0
$731$	25.6962	+	44.5070i	0.950407	+	1.64615i
$732$		0			0
$733$	30.6410			1.13175			0.565876	−	0.824490i	$-0.308538\pi$
$733$	30.6410			1.13175			0.565876	+	0.824490i	$0.308538\pi$
$734$		0			0
$735$	29.3205	+	6.00000i	1.08150	+	0.221313i
$736$		0			0
$737$	−3.31089	−	12.3564i	−0.121958	−	0.455154i
$738$		0			0
$739$	33.2583	+	8.91154i	1.22343	+	0.327816i	0.812017	−	0.583634i	$-0.198370\pi$
$739$	33.2583	+	8.91154i	1.22343	+	0.327816i	0.411410	+	0.911450i	$0.365036\pi$
$740$		0			0
$741$	5.19615	−	3.46410i	0.190885	−	0.127257i
$742$		0			0
$743$	−12.4019	−	21.4808i	−0.454982	−	0.788053i	0.543705	−	0.839277i	$-0.317021\pi$
$743$	−12.4019	−	21.4808i	−0.454982	−	0.788053i	−0.998687	+	0.0512238i	$0.983688\pi$
$744$		0			0
$745$	−41.4090	−	8.47372i	−1.51711	−	0.310453i
$746$		0			0
$747$	−2.19615	−	1.26795i	−0.0803530	−	0.0463918i
$748$		0			0
$749$	−16.2942	+	16.2942i	−0.595378	+	0.595378i
$750$		0			0
$751$	−16.7487	+	9.66987i	−0.611169	+	0.352859i	−0.773423	−	0.633890i	$-0.781457\pi$
$751$	−16.7487	+	9.66987i	−0.611169	+	0.352859i	0.162254	+	0.986749i	$0.448124\pi$
$752$		0			0
$753$	4.90192	−	4.90192i	0.178636	−	0.178636i
$754$		0			0
$755$	0.803848	+	2.41154i	0.0292550	+	0.0877650i
$756$		0			0
$757$	−14.6962	−	3.93782i	−0.534141	−	0.143123i	−0.0183410	−	0.999832i	$-0.505838\pi$
$757$	−14.6962	−	3.93782i	−0.534141	−	0.143123i	−0.515800	+	0.856709i	$0.672505\pi$
$758$		0			0
$759$	22.7583	+	22.7583i	0.826075	+	0.826075i
$760$		0			0
$761$	11.3301	−	3.03590i	0.410717	−	0.110051i	−0.0475437	−	0.998869i	$-0.515139\pi$
$761$	11.3301	−	3.03590i	0.410717	−	0.110051i	0.458261	+	0.888818i	$0.348473\pi$
$762$		0			0
$763$	−47.8827	+	12.8301i	−1.73347	+	0.464482i
$764$		0			0
$765$	5.36603	+	4.75833i	0.194009	+	0.172038i
$766$		0			0
$767$	−16.5000	+	18.7750i	−0.595780	+	0.677926i
$768$		0			0
$769$	3.33013	−	12.4282i	0.120087	−	0.448172i	−0.879530	−	0.475844i	$-0.842143\pi$
$769$	3.33013	−	12.4282i	0.120087	−	0.448172i	0.999617	+	0.0276717i	$0.00880929\pi$
$770$		0			0
$771$	26.8923	+	15.5263i	0.968503	+	0.559165i
$772$		0			0
$773$	8.93782	−	15.4808i	0.321471	−	0.556804i	−0.659321	−	0.751862i	$-0.729156\pi$
$773$	8.93782	−	15.4808i	0.321471	−	0.556804i	0.980792	+	0.195058i	$0.0624894\pi$
$774$		0			0
$775$	40.1244	+	5.73205i	1.44131	+	0.205901i
$776$		0			0
$777$	0.500000	−	1.86603i	0.0179374	−	0.0669433i
$778$		0			0
$779$	0.124356			0.00445550
$780$		0			0
$781$	−10.1244			−0.362278
$782$		0			0
$783$	−10.4282	+	38.9186i	−0.372674	+	1.39084i
$784$		0			0
$785$	−22.1769	+	7.39230i	−0.791528	+	0.263843i
$786$		0			0
$787$	−3.99038	+	6.91154i	−0.142242	+	0.246370i	−0.928340	−	0.371731i	$-0.878764\pi$
$787$	−3.99038	+	6.91154i	−0.142242	+	0.246370i	0.786099	+	0.618101i	$0.212098\pi$
$788$		0			0
$789$	−18.6962	−	10.7942i	−0.665601	−	0.384285i
$790$		0			0
$791$	13.1603	−	49.1147i	0.467925	−	1.74632i
$792$		0			0
$793$	3.59808	−	0.232051i	0.127771	−	0.00824037i
$794$		0			0
$795$	9.36603	−	0.562178i	0.332179	−	0.0199384i
$796$		0			0
$797$	17.6244	−	4.72243i	0.624287	−	0.167277i	0.0672109	−	0.997739i	$-0.478590\pi$
$797$	17.6244	−	4.72243i	0.624287	−	0.167277i	0.557076	+	0.830462i	$0.311923\pi$
$798$		0			0
$799$	2.26795	−	0.607695i	0.0802343	−	0.0214987i
$800$		0			0
$801$	7.92820	+	7.92820i	0.280129	+	0.280129i
$802$		0			0
$803$	28.8564	+	7.73205i	1.01832	+	0.272858i
$804$		0			0
$805$	−57.0788	+	19.0263i	−2.01176	+	0.670588i
$806$		0			0
$807$	−15.0981	+	15.0981i	−0.531477	+	0.531477i
$808$		0			0
$809$	−9.10770	+	5.25833i	−0.320210	+	0.184873i	−0.651486	−	0.758661i	$-0.725854\pi$
$809$	−9.10770	+	5.25833i	−0.320210	+	0.184873i	0.331276	+	0.943534i	$0.392521\pi$
$810$		0			0
$811$	7.87564	−	7.87564i	0.276551	−	0.276551i	−0.555179	−	0.831731i	$-0.687350\pi$
$811$	7.87564	−	7.87564i	0.276551	−	0.276551i	0.831731	+	0.555179i	$0.187350\pi$
$812$		0			0
$813$	−27.1865	−	15.6962i	−0.953473	−	0.550488i
$814$		0			0
$815$	1.89230	+	2.86603i	0.0662845	+	0.100392i
$816$		0			0
$817$	5.25833	+	9.10770i	0.183966	+	0.318638i
$818$		0			0
$819$	−8.83013	−	4.36603i	−0.308550	−	0.152561i
$820$		0			0
$821$	−9.59808	−	2.57180i	−0.334975	−	0.0897563i	0.0874109	−	0.996172i	$-0.472141\pi$
$821$	−9.59808	−	2.57180i	−0.334975	−	0.0897563i	−0.422386	+	0.906416i	$0.638807\pi$
$822$		0			0
$823$	9.35641	+	34.9186i	0.326144	+	1.21719i	0.913157	+	0.407608i	$0.133637\pi$
$823$	9.35641	+	34.9186i	0.326144	+	1.21719i	−0.587013	+	0.809577i	$0.699696\pi$
$824$		0			0
$825$	−2.66987	−	22.1603i	−0.0929530	−	0.771521i
$826$		0			0
$827$	−31.4641			−1.09411			−0.547057	−	0.837095i	$-0.684252\pi$
$827$	−31.4641			−1.09411			−0.547057	+	0.837095i	$0.684252\pi$
$828$		0			0
$829$	−7.96410	−	13.7942i	−0.276605	−	0.479093i	0.693934	−	0.720039i	$-0.255876\pi$
$829$	−7.96410	−	13.7942i	−0.276605	−	0.479093i	−0.970539	+	0.240945i	$0.922543\pi$
$830$		0			0
$831$		−	22.3205i		−	0.774290i
$832$		0			0
$833$	21.4641	+	21.4641i	0.743687	+	0.743687i
$834$		0			0
$835$	0.892305	+	14.8660i	0.0308795	+	0.514460i
$836$		0			0
$837$			35.5167i			1.22764i
$838$		0			0
$839$	6.47372	+	24.1603i	0.223498	+	0.834105i	0.983001	+	0.183601i	$0.0587754\pi$
$839$	6.47372	+	24.1603i	0.223498	+	0.834105i	−0.759503	+	0.650504i	$0.774558\pi$
$840$		0			0
$841$	27.7846	−	48.1244i	0.958090	−	1.65946i
$842$		0			0
$843$	−31.6865	+	18.2942i	−1.09134	+	0.630087i
$844$		0			0
$845$	−22.0000	+	19.0000i	−0.756823	+	0.653620i
$846$		0			0
$847$	18.2942	−	10.5622i	0.628597	−	0.362921i
$848$		0			0
$849$	−24.3564	+	42.1865i	−0.835910	+	1.44784i
$850$		0			0
$851$	0.500000	+	1.86603i	0.0171398	+	0.0639665i
$852$		0			0
$853$			27.5692i			0.943952i	0.881611	+	0.471976i	$0.156459\pi$
$853$			27.5692i			0.943952i	−0.881611	+	0.471976i	$0.843541\pi$
$854$		0			0
$855$	1.09808	+	0.973721i	0.0375534	+	0.0333005i
$856$		0			0
$857$	−29.3923	−	29.3923i	−1.00402	−	1.00402i	−0.999992	−	0.00403013i	$-0.998717\pi$
$857$	−29.3923	−	29.3923i	−1.00402	−	1.00402i	−0.00403013	−	0.999992i	$-0.501283\pi$
$858$		0			0
$859$		−	30.1051i		−	1.02717i	−0.858038	−	0.513587i	$-0.828316\pi$
$859$		−	30.1051i		−	1.02717i	0.858038	−	0.513587i	$-0.171684\pi$
$860$		0			0
$861$	−0.500000	−	0.866025i	−0.0170400	−	0.0295141i
$862$		0			0
$863$	28.2487			0.961597			0.480799	−	0.876831i	$-0.340347\pi$
$863$	28.2487			0.961597			0.480799	+	0.876831i	$0.340347\pi$
$864$		0			0
$865$	−3.99038	+	19.5000i	−0.135677	+	0.663020i
$866$		0			0
$867$	1.09808	+	4.09808i	0.0372926	+	0.139178i
$868$		0			0
$869$	10.1244	+	2.71281i	0.343445	+	0.0920259i
$870$		0			0
$871$	−17.8923	−	8.84679i	−0.606258	−	0.299762i
$872$		0			0
$873$	−1.63397	−	2.83013i	−0.0553017	−	0.0957853i
$874$		0			0
$875$	39.2846	+	14.0622i	1.32806	+	0.475388i
$876$		0			0
$877$	30.4019	+	17.5526i	1.02660	+	0.592708i	0.916009	−	0.401158i	$-0.131392\pi$
$877$	30.4019	+	17.5526i	1.02660	+	0.592708i	0.110591	+	0.993866i	$0.464726\pi$
$878$		0			0
$879$	−21.2224	+	21.2224i	−0.715815	+	0.715815i
$880$		0			0
$881$	4.96410	−	2.86603i	0.167245	−	0.0965588i	−0.414041	−	0.910258i	$-0.635883\pi$
$881$	4.96410	−	2.86603i	0.167245	−	0.0965588i	0.581286	+	0.813699i	$0.302550\pi$
$882$		0			0
$883$	27.1962	−	27.1962i	0.915223	−	0.915223i	−0.0814537	−	0.996677i	$-0.525956\pi$
$883$	27.1962	−	27.1962i	0.915223	−	0.915223i	0.996677	+	0.0814537i	$0.0259563\pi$
$884$		0			0
$885$	−26.7846	−	13.3923i	−0.900355	−	0.450177i
$886$		0			0
$887$	47.7487	+	12.7942i	1.60324	+	0.429588i	0.946020	−	0.324107i	$-0.105064\pi$
$887$	47.7487	+	12.7942i	1.60324	+	0.429588i	0.657224	+	0.753695i	$0.271730\pi$
$888$		0			0
$889$	−45.8827	−	45.8827i	−1.53886	−	1.53886i
$890$		0			0
$891$	23.7942	−	6.37564i	0.797137	−	0.213592i
$892$		0			0
$893$	0.464102	−	0.124356i	0.0155306	−	0.00416140i
$894$		0			0
$895$	−1.59808	−	26.6244i	−0.0534178	−	0.889954i
$896$		0			0
$897$	50.1147	−	3.23205i	1.67328	−	0.107915i
$898$		0			0
$899$	19.2942	−	72.0070i	0.643499	−	2.40157i
$900$		0			0
$901$	8.24167	+	4.75833i	0.274570	+	0.158523i
$902$		0			0
$903$	42.2846	−	73.2391i	1.40714	−	2.43724i
$904$		0			0
$905$	14.9282	−	29.8564i	0.496230	−	0.992461i
$906$		0			0
$907$	−6.03590	+	22.5263i	−0.200419	+	0.747973i	0.790379	+	0.612619i	$0.209884\pi$
$907$	−6.03590	+	22.5263i	−0.200419	+	0.747973i	−0.990797	+	0.135354i	$0.956783\pi$
$908$		0			0
$909$	−1.26795			−0.0420552
$910$		0			0
$911$	−42.9282			−1.42227			−0.711137	−	0.703053i	$-0.751820\pi$
$911$	−42.9282			−1.42227			−0.711137	+	0.703053i	$0.751820\pi$
$912$		0			0
$913$	−2.07180	+	7.73205i	−0.0685665	+	0.255894i
$914$		0			0
$915$	1.36603	+	4.09808i	0.0451594	+	0.135478i
$916$		0			0
$917$	25.8564	−	44.7846i	0.853854	−	1.47892i
$918$		0			0
$919$	−10.7487	−	6.20577i	−0.354567	−	0.204710i	0.312128	−	0.950040i	$-0.398958\pi$
$919$	−10.7487	−	6.20577i	−0.354567	−	0.204710i	−0.666695	+	0.745331i	$0.732292\pi$
$920$		0			0
$921$	4.80385	−	17.9282i	0.158292	−	0.590754i
$922$		0			0
$923$	−10.4282	+	11.8660i	−0.343248	+	0.390575i
$924$		0			0
$925$	0.526279	−	1.23205i	0.0173040	−	0.0405096i
$926$		0			0
$927$	6.66025	−	1.78461i	0.218751	−	0.0586143i
$928$		0			0
$929$	−14.7942	+	3.96410i	−0.485383	+	0.130058i	−0.493208	−	0.869911i	$-0.664176\pi$
$929$	−14.7942	+	3.96410i	−0.485383	+	0.130058i	0.00782508	+	0.999969i	$0.497509\pi$
$930$		0			0
$931$	4.39230	+	4.39230i	0.143952	+	0.143952i
$932$		0			0
$933$	60.1769	+	16.1244i	1.97010	+	0.527888i
$934$		0			0
$935$	10.1244	−	20.2487i	0.331102	−	0.662204i
$936$		0			0
$937$	0.215390	−	0.215390i	0.00703649	−	0.00703649i	−0.703580	−	0.710616i	$-0.748416\pi$
$937$	0.215390	−	0.215390i	0.00703649	−	0.00703649i	0.710616	+	0.703580i	$0.248416\pi$
$938$		0			0
$939$	33.8827	−	19.5622i	1.10572	−	0.638388i
$940$		0			0
$941$	−19.0000	+	19.0000i	−0.619382	+	0.619382i	−0.945373	−	0.325991i	$-0.894302\pi$
$941$	−19.0000	+	19.0000i	−0.619382	+	0.619382i	0.325991	+	0.945373i	$0.394302\pi$
$942$		0			0
$943$	0.866025	+	0.500000i	0.0282017	+	0.0162822i
$944$		0			0
$945$	−7.33013	+	35.8205i	−0.238449	+	1.16524i
$946$		0			0
$947$	24.2583	+	42.0167i	0.788290	+	1.36536i	0.927014	+	0.375027i	$0.122367\pi$
$947$	24.2583	+	42.0167i	0.788290	+	1.36536i	−0.138724	+	0.990331i	$0.544300\pi$
$948$		0			0
$949$	38.7846	−	25.8564i	1.25900	−	0.839334i
$950$		0			0
$951$	−31.5885	−	8.46410i	−1.02433	−	0.274467i
$952$		0			0
$953$	5.62436	+	20.9904i	0.182191	+	0.679945i	0.995214	+	0.0977146i	$0.0311532\pi$
$953$	5.62436	+	20.9904i	0.182191	+	0.679945i	−0.813024	+	0.582231i	$0.802180\pi$
$954$		0			0
$955$	−44.6506	+	29.4808i	−1.44486	+	0.953975i
$956$		0			0
$957$	−41.0526			−1.32704
$958$		0			0
$959$	1.50000	+	2.59808i	0.0484375	+	0.0838963i
$960$		0			0
$961$		−	34.7128i		−	1.11977i
$962$		0			0
$963$	3.19615	+	3.19615i	0.102995	+	0.102995i
$964$		0			0
$965$	−54.2846	+	3.25833i	−1.74748	+	0.104889i
$966$		0			0
$967$		−	58.6410i		−	1.88577i	−0.333121	−	0.942884i	$-0.608102\pi$
$967$		−	58.6410i		−	1.88577i	0.333121	−	0.942884i	$-0.391898\pi$
$968$		0			0
$969$	1.96410	+	7.33013i	0.0630960	+	0.235478i
$970$		0			0
$971$	−16.5000	+	28.5788i	−0.529510	+	0.917139i	0.469897	+	0.882721i	$0.344291\pi$
$971$	−16.5000	+	28.5788i	−0.529510	+	0.917139i	−0.999408	+	0.0344175i	$0.989042\pi$
$972$		0			0
$973$	31.4545	−	18.1603i	1.00838	−	0.582191i
$974$		0			0
$975$	−28.7224	−	19.6962i	−0.919854	−	0.630782i
$976$		0			0
$977$	−42.6506	+	24.6244i	−1.36451	+	0.787803i	−0.990221	−	0.139507i	$-0.955448\pi$
$977$	−42.6506	+	24.6244i	−1.36451	+	0.787803i	−0.374294	+	0.927310i	$0.622115\pi$
$978$		0			0
$979$	17.6962	−	30.6506i	0.565571	−	0.979599i
$980$		0			0
$981$	2.51666	+	9.39230i	0.0803508	+	0.299873i
$982$		0			0
$983$		−	29.0718i		−	0.927246i	−0.886032	−	0.463623i	$-0.846549\pi$
$983$		−	29.0718i		−	0.927246i	0.886032	−	0.463623i	$-0.153451\pi$
$984$		0			0
$985$	−31.9641	+	1.91858i	−1.01846	+	0.0611312i
$986$		0			0
$987$	−2.73205	−	2.73205i	−0.0869621	−	0.0869621i
$988$		0			0
$989$			84.5692i			2.68914i
$990$		0			0
$991$	−24.9641	−	43.2391i	−0.793011	−	1.37354i	−0.924095	−	0.382164i	$-0.875179\pi$
$991$	−24.9641	−	43.2391i	−0.793011	−	1.37354i	0.131084	−	0.991371i	$-0.458154\pi$
$992$		0			0
$993$	−12.4641			−0.395536
$994$		0			0
$995$	−18.5263	+	12.2321i	−0.587323	+	0.387782i
$996$		0			0
$997$	1.69615	+	6.33013i	0.0537177	+	0.200477i	0.987569	−	0.157183i	$-0.0502413\pi$
$997$	1.69615	+	6.33013i	0.0537177	+	0.200477i	−0.933852	+	0.357660i	$0.883575\pi$
$998$		0			0
$999$	1.13397	+	0.303848i	0.0358774	+	0.00961331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bf.a.93.1	✓	4
5.2	odd	4		260.2.bk.b.197.1	yes	4
5.3	odd	4		1300.2.bs.a.457.1		4
5.4	even	2		1300.2.bn.b.93.1		4
13.7	odd	12		260.2.bk.b.33.1	yes	4
65.7	even	12	inner	260.2.bf.a.137.1	yes	4
65.33	even	12		1300.2.bn.b.657.1		4
65.59	odd	12		1300.2.bs.a.293.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.a.93.1	✓	4	1.1	even	1	trivial
260.2.bf.a.137.1	yes	4	65.7	even	12	inner
260.2.bk.b.33.1	yes	4	13.7	odd	12
260.2.bk.b.197.1	yes	4	5.2	odd	4
1300.2.bn.b.93.1		4	5.4	even	2
1300.2.bn.b.657.1		4	65.33	even	12
1300.2.bs.a.293.1		4	65.59	odd	12
1300.2.bs.a.457.1		4	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 1.86603i) q^{3} +(2.00000 + 1.00000i) q^{5} +(1.86603 - 3.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 1.86603i) q^{3} +(2.00000 + 1.00000i) q^{5} +(1.86603 - 3.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +(-0.598076 + 2.23205i) q^{11} +(2.00000 + 3.00000i) q^{13} +(-2.86603 + 3.23205i) q^{15} +(-4.23205 + 1.13397i) q^{17} +(-0.866025 + 0.232051i) q^{19} +(5.09808 + 5.09808i) q^{21} +(-6.96410 - 1.86603i) q^{23} +(3.00000 + 4.00000i) q^{25} +(-3.09808 + 3.09808i) q^{27} +(7.96410 - 4.59808i) q^{29} +(5.73205 - 5.73205i) q^{31} +(-3.86603 - 2.23205i) q^{33} +(6.96410 - 4.59808i) q^{35} +(-0.133975 - 0.232051i) q^{37} +(-6.59808 + 2.23205i) q^{39} +(-0.133975 - 0.0358984i) q^{41} +(-3.03590 - 11.3301i) q^{43} +(-0.901924 - 1.36603i) q^{45} -0.535898 q^{47} +(-3.46410 - 6.00000i) q^{49} -8.46410i q^{51} +(-1.53590 - 1.53590i) q^{53} +(-3.42820 + 3.86603i) q^{55} -1.73205i q^{57} +(1.79423 + 6.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-2.36603 + 1.36603i) q^{63} +(1.00000 + 8.00000i) q^{65} +(-4.79423 + 2.76795i) q^{67} +(6.96410 - 12.0622i) q^{69} +(1.13397 + 4.23205i) q^{71} -12.9282i q^{73} +(-8.96410 + 3.59808i) q^{75} +(6.09808 + 6.09808i) q^{77} -4.53590i q^{79} +(-5.33013 - 9.23205i) q^{81} +3.46410 q^{83} +(-9.59808 - 1.96410i) q^{85} +(4.59808 + 17.1603i) q^{87} +(-14.7942 - 3.96410i) q^{89} +(13.4282 - 0.866025i) q^{91} +(7.83013 + 13.5622i) q^{93} +(-1.96410 - 0.401924i) q^{95} +(3.86603 + 2.23205i) q^{97} +(1.19615 - 1.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 8 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 8 * q^5 + 4 * q^7 - 6 * q^9	\( 4 q - 2 q^{3} + 8 q^{5} + 4 q^{7} - 6 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 10 q^{17} + 10 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} + 18 q^{29} + 16 q^{31} - 12 q^{33} + 14 q^{35} - 4 q^{37} - 16 q^{39} - 4 q^{41} - 26 q^{43} - 14 q^{45} - 16 q^{47} - 20 q^{53} + 14 q^{55} - 24 q^{59} + 2 q^{61} - 6 q^{63} + 4 q^{65} + 12 q^{67} + 14 q^{69} + 8 q^{71} - 22 q^{75} + 14 q^{77} - 4 q^{81} - 28 q^{85} + 8 q^{87} - 28 q^{89} + 26 q^{91} + 14 q^{93} + 6 q^{95} + 12 q^{97} - 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 8 * q^5 + 4 * q^7 - 6 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 10 * q^17 + 10 * q^21 - 14 * q^23 + 12 * q^25 - 2 * q^27 + 18 * q^29 + 16 * q^31 - 12 * q^33 + 14 * q^35 - 4 * q^37 - 16 * q^39 - 4 * q^41 - 26 * q^43 - 14 * q^45 - 16 * q^47 - 20 * q^53 + 14 * q^55 - 24 * q^59 + 2 * q^61 - 6 * q^63 + 4 * q^65 + 12 * q^67 + 14 * q^69 + 8 * q^71 - 22 * q^75 + 14 * q^77 - 4 * q^81 - 28 * q^85 + 8 * q^87 - 28 * q^89 + 26 * q^91 + 14 * q^93 + 6 * q^95 + 12 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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