LMFDB - Embedded newform 260.2.bk.b.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 9, 11]))

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

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

chi := DirichletCharacter("260.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
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			197.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.197
Dual form			260.2.bk.b.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86603 + 0.500000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(3.23205 + 1.86603i) q^{7} +(0.633975 + 0.366025i) q^{9} +O(q^{10})$	\(q+(1.86603 + 0.500000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(3.23205 + 1.86603i) q^{7} +(0.633975 + 0.366025i) q^{9} +(-0.598076 + 2.23205i) q^{11} +(3.00000 - 2.00000i) q^{13} +(-0.866025 - 4.23205i) q^{15} +(-1.13397 - 4.23205i) q^{17} +(0.866025 - 0.232051i) q^{19} +(5.09808 + 5.09808i) q^{21} +(-1.86603 + 6.96410i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(-3.09808 - 3.09808i) q^{27} +(-7.96410 + 4.59808i) q^{29} +(5.73205 - 5.73205i) q^{31} +(-2.23205 + 3.86603i) q^{33} +(0.500000 - 8.33013i) q^{35} +(0.232051 - 0.133975i) q^{37} +(6.59808 - 2.23205i) q^{39} +(-0.133975 - 0.0358984i) q^{41} +(-11.3301 + 3.03590i) q^{43} +(0.0980762 - 1.63397i) q^{45} -0.535898i q^{47} +(3.46410 + 6.00000i) q^{49} -8.46410i q^{51} +(-1.53590 + 1.53590i) q^{53} +(5.06218 - 1.03590i) q^{55} +1.73205 q^{57} +(-1.79423 - 6.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(1.36603 + 2.36603i) q^{63} +(-7.00000 - 4.00000i) q^{65} +(-2.76795 - 4.79423i) q^{67} +(-6.96410 + 12.0622i) q^{69} +(1.13397 + 4.23205i) q^{71} -12.9282 q^{73} +(-7.59808 + 5.96410i) q^{75} +(-6.09808 + 6.09808i) q^{77} +4.53590i q^{79} +(-5.33013 - 9.23205i) q^{81} -3.46410i q^{83} +(-7.33013 + 6.50000i) q^{85} +(-17.1603 + 4.59808i) q^{87} +(14.7942 + 3.96410i) q^{89} +(13.4282 - 0.866025i) q^{91} +(13.5622 - 7.83013i) q^{93} +(-1.33013 - 1.50000i) q^{95} +(-2.23205 + 3.86603i) q^{97} +(-1.19615 + 1.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{5} + 6 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^5 + 6 * q^7 + 6 * q^9	$ 4 q + 4 q^{3} - 4 q^{5} + 6 q^{7} + 6 q^{9} + 8 q^{11} + 12 q^{13} - 8 q^{17} + 10 q^{21} - 4 q^{23} - 12 q^{25} - 2 q^{27} - 18 q^{29} + 16 q^{31} - 2 q^{33} + 2 q^{35} - 6 q^{37} + 16 q^{39} - 4 q^{41} - 28 q^{43} - 10 q^{45} - 20 q^{53} - 4 q^{55} + 24 q^{59} + 2 q^{61} + 2 q^{63} - 28 q^{65} - 18 q^{67} - 14 q^{69} + 8 q^{71} - 24 q^{73} - 20 q^{75} - 14 q^{77} - 4 q^{81} - 12 q^{85} - 34 q^{87} + 28 q^{89} + 26 q^{91} + 30 q^{93} + 12 q^{95} - 2 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^5 + 6 * q^7 + 6 * q^9 + 8 * q^11 + 12 * q^13 - 8 * q^17 + 10 * q^21 - 4 * q^23 - 12 * q^25 - 2 * q^27 - 18 * q^29 + 16 * q^31 - 2 * q^33 + 2 * q^35 - 6 * q^37 + 16 * q^39 - 4 * q^41 - 28 * q^43 - 10 * q^45 - 20 * q^53 - 4 * q^55 + 24 * q^59 + 2 * q^61 + 2 * q^63 - 28 * q^65 - 18 * q^67 - 14 * q^69 + 8 * q^71 - 24 * q^73 - 20 * q^75 - 14 * q^77 - 4 * q^81 - 12 * q^85 - 34 * q^87 + 28 * q^89 + 26 * q^91 + 30 * q^93 + 12 * q^95 - 2 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.86603	+	0.500000i	1.07735	+	0.288675i	0.753510	−	0.657437i	$-0.228359\pi$
$3$	1.86603	+	0.500000i	1.07735	+	0.288675i	0.323840	+	0.946112i	$0.395026\pi$
$4$		0			0
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$		0			0
$7$	3.23205	+	1.86603i	1.22160	+	0.705291i	0.965259	−	0.261295i	$-0.0841495\pi$
$7$	3.23205	+	1.86603i	1.22160	+	0.705291i	0.256341	+	0.966586i	$0.417483\pi$
$8$		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
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$14$		0			0
$15$	−0.866025	−	4.23205i	−0.223607	−	1.09271i
$16$		0			0
$17$	−1.13397	−	4.23205i	−0.275029	−	1.02642i	−0.955822	−	0.293947i	$-0.905031\pi$
$17$	−1.13397	−	4.23205i	−0.275029	−	1.02642i	0.680793	−	0.732476i	$-0.261636\pi$
$18$		0			0
$19$	0.866025	−	0.232051i	0.198680	−	0.0532361i	−0.158107	−	0.987422i	$-0.550539\pi$
$19$	0.866025	−	0.232051i	0.198680	−	0.0532361i	0.356787	+	0.934186i	$0.383872\pi$
$20$		0			0
$21$	5.09808	+	5.09808i	1.11249	+	1.11249i
$22$		0			0
$23$	−1.86603	+	6.96410i	−0.389093	+	1.45212i	0.442519	+	0.896759i	$0.354085\pi$
$23$	−1.86603	+	6.96410i	−0.389093	+	1.45212i	−0.831612	+	0.555357i	$0.812582\pi$
$24$		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	−0.999715	−	0.0238745i	$-0.992400\pi$
$29$	−7.96410	+	4.59808i	−1.47890	+	0.853841i	−0.479182	+	0.877716i	$0.659066\pi$
$30$		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
$33$	−2.23205	+	3.86603i	−0.388550	+	0.672989i
$34$		0			0
$35$	0.500000	−	8.33013i	0.0845154	−	1.40805i
$36$		0			0
$37$	0.232051	−	0.133975i	0.0381489	−	0.0220253i	−0.480804	−	0.876828i	$-0.659655\pi$
$37$	0.232051	−	0.133975i	0.0381489	−	0.0220253i	0.518953	+	0.854803i	$0.326322\pi$
$38$		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
$43$	−11.3301	+	3.03590i	−1.72783	+	0.462970i	−0.979681	−	0.200563i	$-0.935723\pi$
$43$	−11.3301	+	3.03590i	−1.72783	+	0.462970i	−0.748147	+	0.663533i	$0.769056\pi$
$44$		0			0
$45$	0.0980762	−	1.63397i	0.0146203	−	0.243579i
$46$		0			0
$47$		−	0.535898i		−	0.0781688i	−0.999236	−	0.0390844i	$-0.987556\pi$
$47$		−	0.535898i		−	0.0781688i	0.999236	−	0.0390844i	$-0.0124441\pi$
$48$		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	−0.804680	−	0.593708i	$-0.797663\pi$
$53$	−1.53590	+	1.53590i	−0.210972	+	0.210972i	0.593708	+	0.804680i	$0.297663\pi$
$54$		0			0
$55$	5.06218	−	1.03590i	0.682584	−	0.139681i
$56$		0			0
$57$	1.73205			0.229416
$58$		0			0
$59$	−1.79423	−	6.69615i	−0.233589	−	0.871765i	−0.978780	−	0.204914i	$-0.934309\pi$
$59$	−1.79423	−	6.69615i	−0.233589	−	0.871765i	0.745191	−	0.666851i	$-0.232358\pi$
$60$		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
$63$	1.36603	+	2.36603i	0.172103	+	0.298091i
$64$		0			0
$65$	−7.00000	−	4.00000i	−0.868243	−	0.496139i
$66$		0			0
$67$	−2.76795	−	4.79423i	−0.338159	−	0.585708i	0.645928	−	0.763399i	$-0.276471\pi$
$67$	−2.76795	−	4.79423i	−0.338159	−	0.585708i	−0.984086	+	0.177690i	$0.943137\pi$
$68$		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
$73$	−12.9282			−1.51313			−0.756566	−	0.653917i	$-0.773124\pi$
$73$	−12.9282			−1.51313			−0.756566	+	0.653917i	$0.773124\pi$
$74$		0			0
$75$	−7.59808	+	5.96410i	−0.877350	+	0.688675i
$76$		0			0
$77$	−6.09808	+	6.09808i	−0.694940	+	0.694940i
$78$		0			0
$79$			4.53590i			0.510328i	0.966898	+	0.255164i	$0.0821295\pi$
$79$			4.53590i			0.510328i	−0.966898	+	0.255164i	$0.917870\pi$
$80$		0			0
$81$	−5.33013	−	9.23205i	−0.592236	−	1.02578i
$82$		0			0
$83$		−	3.46410i		−	0.380235i	−0.981761	−	0.190117i	$-0.939113\pi$
$83$		−	3.46410i		−	0.380235i	0.981761	−	0.190117i	$-0.0608868\pi$
$84$		0			0
$85$	−7.33013	+	6.50000i	−0.795064	+	0.705024i
$86$		0			0
$87$	−17.1603	+	4.59808i	−1.83977	+	0.492966i
$88$		0			0
$89$	14.7942	+	3.96410i	1.56819	+	0.420194i	0.935243	−	0.354005i	$-0.115181\pi$
$89$	14.7942	+	3.96410i	1.56819	+	0.420194i	0.632942	+	0.774199i	$0.281847\pi$
$90$		0			0
$91$	13.4282	−	0.866025i	1.40766	−	0.0907841i
$92$		0			0
$93$	13.5622	−	7.83013i	1.40633	−	0.811946i
$94$		0			0
$95$	−1.33013	−	1.50000i	−0.136468	−	0.153897i
$96$		0			0
$97$	−2.23205	+	3.86603i	−0.226630	+	0.392535i	−0.956807	−	0.290723i	$-0.906104\pi$
$97$	−2.23205	+	3.86603i	−0.226630	+	0.392535i	0.730177	+	0.683258i	$0.239438\pi$
$98$		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	$-0.0963987\pi$
$103$	6.66025	+	6.66025i	0.656254	+	0.656254i	−0.298237	+	0.954492i	$0.596399\pi$
$104$		0			0
$105$	5.09808	−	15.2942i	0.497521	−	1.49256i
$106$		0			0
$107$	1.59808	−	5.96410i	0.154492	−	0.576571i	−0.844656	−	0.535309i	$-0.820195\pi$
$107$	1.59808	−	5.96410i	0.154492	−	0.576571i	0.999148	−	0.0412627i	$-0.0131381\pi$
$108$		0			0
$109$	9.39230	+	9.39230i	0.899620	+	0.899620i	0.995402	−	0.0957826i	$-0.0305354\pi$
$109$	9.39230	+	9.39230i	0.899620	+	0.899620i	−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	0.500000	−	0.133975i	0.0474579	−	0.0127163i
$112$		0			0
$113$	−3.52628	−	13.1603i	−0.331724	−	1.23801i	−0.907377	−	0.420318i	$-0.861919\pi$
$113$	−3.52628	−	13.1603i	−0.331724	−	1.23801i	0.575652	−	0.817695i	$-0.304748\pi$
$114$		0			0
$115$	15.7942	−	3.23205i	1.47282	−	0.301390i
$116$		0			0
$117$	2.63397	−	0.169873i	0.243511	−	0.0157048i
$118$		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
$123$	−0.232051	−	0.133975i	−0.0209233	−	0.0120801i
$124$		0			0
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$	16.7942	+	4.50000i	1.49025	+	0.399310i	0.909820	−	0.415002i	$-0.136219\pi$
$127$	16.7942	+	4.50000i	1.49025	+	0.399310i	0.580426	+	0.814313i	$0.302886\pi$
$128$		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
$133$	3.23205	+	0.866025i	0.280254	+	0.0750939i
$134$		0			0
$135$	−3.09808	+	9.29423i	−0.266640	+	0.799920i
$136$		0			0
$137$	−0.696152	−	0.401924i	−0.0594763	−	0.0343387i	0.469967	−	0.882684i	$-0.344266\pi$
$137$	−0.696152	−	0.401924i	−0.0594763	−	0.0343387i	−0.529443	+	0.848345i	$0.677599\pi$
$138$		0			0
$139$	−8.42820	−	4.86603i	−0.714871	−	0.412731i	0.0979911	−	0.995187i	$-0.468758\pi$
$139$	−8.42820	−	4.86603i	−0.714871	−	0.412731i	−0.812862	+	0.582456i	$0.802092\pi$
$140$		0			0
$141$	0.267949	−	1.00000i	0.0225654	−	0.0842152i
$142$		0			0
$143$	2.66987	+	7.89230i	0.223266	+	0.659988i
$144$		0			0
$145$	17.1603	+	11.3301i	1.42508	+	0.940916i
$146$		0			0
$147$	3.46410	+	12.9282i	0.285714	+	1.06630i
$148$		0			0
$149$	18.2583	−	4.89230i	1.49578	−	0.400793i	0.584096	−	0.811684i	$-0.301449\pi$
$149$	18.2583	−	4.89230i	1.49578	−	0.400793i	0.911684	+	0.410891i	$0.134782\pi$
$150$		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
$153$	0.830127	−	3.09808i	0.0671118	−	0.250465i
$154$		0			0
$155$	−17.1962	−	5.73205i	−1.38123	−	0.460409i
$156$		0			0
$157$	−7.39230	−	7.39230i	−0.589970	−	0.589970i	0.347653	−	0.937623i	$-0.386979\pi$
$157$	−7.39230	−	7.39230i	−0.589970	−	0.589970i	−0.937623	+	0.347653i	$0.886979\pi$
$158$		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
$163$	0.767949	−	1.33013i	0.0601504	−	0.104184i	−0.834382	−	0.551186i	$-0.814175\pi$
$163$	0.767949	−	1.33013i	0.0601504	−	0.104184i	0.894533	+	0.447003i	$0.147509\pi$
$164$		0			0
$165$	9.96410	+	0.598076i	0.775704	+	0.0465602i
$166$		0			0
$167$	−5.76795	+	3.33013i	−0.446337	+	0.257693i	−0.706282	−	0.707931i	$-0.749629\pi$
$167$	−5.76795	+	3.33013i	−0.446337	+	0.257693i	0.259945	+	0.965623i	$0.416296\pi$
$168$		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
$173$	8.59808	−	2.30385i	0.653700	−	0.175158i	0.0832986	−	0.996525i	$-0.473454\pi$
$173$	8.59808	−	2.30385i	0.653700	−	0.175158i	0.570401	+	0.821366i	$0.306788\pi$
$174$		0			0
$175$	−17.1603	+	7.33013i	−1.29719	+	0.554106i
$176$		0			0
$177$		−	13.3923i		−	1.00663i
$178$		0			0
$179$	5.96410	+	10.3301i	0.445778	+	0.772110i	0.998106	−	0.0615168i	$-0.0195938\pi$
$179$	5.96410	+	10.3301i	0.445778	+	0.772110i	−0.552328	+	0.833627i	$0.686260\pi$
$180$		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
$185$	−0.500000	−	0.330127i	−0.0367607	−	0.0242714i
$186$		0			0
$187$	10.1244			0.740366
$188$		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
$193$	12.1603	+	21.0622i	0.875314	+	1.51609i	0.856428	+	0.516267i	$0.172679\pi$
$193$	12.1603	+	21.0622i	0.875314	+	1.51609i	0.0188866	+	0.999822i	$0.493988\pi$
$194$		0			0
$195$	−11.0622	−	10.9641i	−0.792179	−	0.785156i
$196$		0			0
$197$	−7.16025	−	12.4019i	−0.510147	−	0.883600i	−0.999931	−	0.0117566i	$-0.996258\pi$
$197$	−7.16025	−	12.4019i	−0.510147	−	0.883600i	0.489784	−	0.871844i	$-0.337076\pi$
$198$		0			0
$199$	4.96410	−	8.59808i	0.351896	−	0.609501i	−0.634686	−	0.772770i	$-0.718870\pi$
$199$	4.96410	−	8.59808i	0.351896	−	0.609501i	0.986582	+	0.163269i	$0.0522038\pi$
$200$		0			0
$201$	−2.76795	−	10.3301i	−0.195236	−	0.728631i
$202$		0			0
$203$	−34.3205			−2.40883
$204$		0			0
$205$	0.0621778	+	0.303848i	0.00434269	+	0.0212216i
$206$		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
$213$			8.46410i			0.579951i
$214$		0			0
$215$	17.4019	+	19.6244i	1.18680	+	1.33837i
$216$		0			0
$217$	29.2224	−	7.83013i	1.98375	−	0.531544i
$218$		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
$223$	14.0885	−	8.13397i	0.943433	−	0.544691i	0.0523981	−	0.998626i	$-0.483314\pi$
$223$	14.0885	−	8.13397i	0.943433	−	0.544691i	0.891035	+	0.453935i	$0.149980\pi$
$224$		0			0
$225$	−3.36603	+	1.43782i	−0.224402	+	0.0958548i
$226$		0			0
$227$	−3.23205	+	5.59808i	−0.214519	+	0.371557i	−0.953124	−	0.302581i	$-0.902152\pi$
$227$	−3.23205	+	5.59808i	−0.214519	+	0.371557i	0.738605	+	0.674139i	$0.235485\pi$
$228$		0			0
$229$	−16.8564	+	16.8564i	−1.11390	+	1.11390i	−0.121285	+	0.992618i	$0.538701\pi$
$229$	−16.8564	+	16.8564i	−1.11390	+	1.11390i	−0.992618	+	0.121285i	$0.961299\pi$
$230$		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	$-0.420194\pi$
$233$	−11.0000	−	11.0000i	−0.720634	−	0.720634i	−0.968734	+	0.248100i	$0.920194\pi$
$234$		0			0
$235$	−1.07180	+	0.535898i	−0.0699163	+	0.0349582i
$236$		0			0
$237$	−2.26795	+	8.46410i	−0.147319	+	0.549802i
$238$		0			0
$239$	1.19615	+	1.19615i	0.0773727	+	0.0773727i	0.744734	−	0.667361i	$-0.232576\pi$
$239$	1.19615	+	1.19615i	0.0773727	+	0.0773727i	−0.667361	+	0.744734i	$0.732576\pi$
$240$		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
$243$	−1.92820	−	7.19615i	−0.123694	−	0.461633i
$244$		0			0
$245$	8.53590	−	12.9282i	0.545339	−	0.825953i
$246$		0			0
$247$	2.13397	−	2.42820i	0.135782	−	0.154503i
$248$		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
$253$	−14.4282	−	8.33013i	−0.907093	−	0.523711i
$254$		0			0
$255$	−16.9282	+	8.46410i	−1.06009	+	0.530043i
$256$		0			0
$257$	15.5263	+	4.16025i	0.968503	+	0.259510i	0.708196	−	0.706016i	$-0.249510\pi$
$257$	15.5263	+	4.16025i	0.968503	+	0.259510i	0.260307	+	0.965526i	$0.416176\pi$
$258$		0			0
$259$	1.00000			0.0621370
$260$		0			0
$261$	−6.73205			−0.416703
$262$		0			0
$263$	10.7942	+	2.89230i	0.665601	+	0.178347i	0.575772	−	0.817610i	$-0.304701\pi$
$263$	10.7942	+	2.89230i	0.665601	+	0.178347i	0.0898284	+	0.995957i	$0.471368\pi$
$264$		0			0
$265$	4.60770	+	1.53590i	0.283048	+	0.0943495i
$266$		0			0
$267$	25.6244	+	14.7942i	1.56819	+	0.905392i
$268$		0			0
$269$	−9.57180	−	5.52628i	−0.583603	−	0.336943i	0.178961	−	0.983856i	$-0.442726\pi$
$269$	−9.57180	−	5.52628i	−0.583603	−	0.336943i	−0.762564	+	0.646913i	$0.776060\pi$
$270$		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
$273$	25.4904	+	5.09808i	1.54275	+	0.308550i
$274$		0			0
$275$	−7.13397	−	9.08846i	−0.430195	−	0.548055i
$276$		0			0
$277$	−2.99038	−	11.1603i	−0.179675	−	0.670555i	−0.995708	−	0.0925500i	$-0.970498\pi$
$277$	−2.99038	−	11.1603i	−0.179675	−	0.670555i	0.816033	−	0.578005i	$-0.196168\pi$
$278$		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
$283$	6.52628	−	24.3564i	0.387947	−	1.44784i	−0.445522	−	0.895271i	$-0.646982\pi$
$283$	6.52628	−	24.3564i	0.387947	−	1.44784i	0.833469	−	0.552567i	$-0.186352\pi$
$284$		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
$293$	7.76795	−	13.4545i	0.453808	−	0.786019i	−0.544810	−	0.838559i	$-0.683398\pi$
$293$	7.76795	−	13.4545i	0.453808	−	0.786019i	0.998619	+	0.0525400i	$0.0167317\pi$
$294$		0			0
$295$	−11.5981	+	10.2846i	−0.675266	+	0.598793i
$296$		0			0
$297$	8.76795	−	5.06218i	0.508768	−	0.293737i
$298$		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
$303$	3.23205	−	0.866025i	0.185676	−	0.0497519i
$304$		0			0
$305$	−2.23205	−	0.133975i	−0.127807	−	0.00767136i
$306$		0			0
$307$		−	9.60770i		−	0.548340i	−0.961681	−	0.274170i	$-0.911597\pi$
$307$		−	9.60770i		−	0.548340i	0.961681	−	0.274170i	$-0.0884031\pi$
$308$		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	−0.984549	−	0.175107i	$-0.943973\pi$
$313$	−14.3205	+	14.3205i	−0.809443	+	0.809443i	0.175107	+	0.984549i	$0.443973\pi$
$314$		0			0
$315$	3.36603	−	5.09808i	0.189654	−	0.287244i
$316$		0			0
$317$	−16.9282			−0.950783			−0.475391	−	0.879774i	$-0.657694\pi$
$317$	−16.9282			−0.950783			−0.475391	+	0.879774i	$0.657694\pi$
$318$		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
$323$	−1.96410	−	3.40192i	−0.109286	−	0.189288i
$324$		0			0
$325$	−1.00000	+	18.0000i	−0.0554700	+	0.998460i
$326$		0			0
$327$	12.8301	+	22.2224i	0.709508	+	1.22890i
$328$		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
$333$	0.196152			0.0107491
$334$		0			0
$335$	−6.82051	+	10.3301i	−0.372644	+	0.564395i
$336$		0			0
$337$	−13.9282	+	13.9282i	−0.758718	+	0.758718i	−0.976089	−	0.217371i	$-0.930252\pi$
$337$	−13.9282	+	13.9282i	−0.758718	+	0.758718i	0.217371	+	0.976089i	$0.430252\pi$
$338$		0			0
$339$		−	26.3205i		−	1.42953i
$340$		0			0
$341$	9.36603	+	16.2224i	0.507199	+	0.878494i
$342$		0			0
$343$		−	0.267949i		−	0.0144679i
$344$		0			0
$345$	31.0885	+	1.86603i	1.67375	+	0.100463i
$346$		0			0
$347$	−15.3301	+	4.10770i	−0.822964	+	0.220513i	−0.645642	−	0.763640i	$-0.723410\pi$
$347$	−15.3301	+	4.10770i	−0.822964	+	0.220513i	−0.177322	+	0.984153i	$0.556744\pi$
$348$		0			0
$349$	−24.5263	−	6.57180i	−1.31286	−	0.351780i	−0.466563	−	0.884488i	$-0.654508\pi$
$349$	−24.5263	−	6.57180i	−1.31286	−	0.351780i	−0.846299	+	0.532708i	$0.821174\pi$
$350$		0			0
$351$	−15.4904	−	3.09808i	−0.826815	−	0.165363i
$352$		0			0
$353$	10.6244	−	6.13397i	0.565477	−	0.326479i	−0.189864	−	0.981810i	$-0.560805\pi$
$353$	10.6244	−	6.13397i	0.565477	−	0.326479i	0.755341	+	0.655332i	$0.227471\pi$
$354$		0			0
$355$	7.33013	−	6.50000i	0.389043	−	0.344984i
$356$		0			0
$357$	15.7942	−	27.3564i	0.835919	−	1.44785i
$358$		0			0
$359$	23.5885	−	23.5885i	1.24495	−	1.24495i	0.287029	−	0.957922i	$-0.407332\pi$
$359$	23.5885	−	23.5885i	1.24495	−	1.24495i	0.957922	−	0.287029i	$-0.0926677\pi$
$360$		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
$367$	−4.79423	+	17.8923i	−0.250257	+	0.933971i	0.720411	+	0.693547i	$0.243953\pi$
$367$	−4.79423	+	17.8923i	−0.250257	+	0.933971i	−0.970668	+	0.240424i	$0.922714\pi$
$368$		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
$373$	1.00962	+	3.76795i	0.0522761	+	0.195097i	0.987126	−	0.159947i	$-0.0511324\pi$
$373$	1.00962	+	3.76795i	0.0522761	+	0.195097i	−0.934849	+	0.355044i	$0.884466\pi$
$374$		0			0
$375$	19.5263	+	9.23205i	1.00833	+	0.476741i
$376$		0			0
$377$	−14.6962	+	29.7224i	−0.756890	+	1.53078i
$378$		0			0
$379$	4.47372	−	16.6962i	0.229800	−	0.857624i	−0.750625	−	0.660729i	$-0.770247\pi$
$379$	4.47372	−	16.6962i	0.229800	−	0.857624i	0.980425	−	0.196895i	$-0.0630859\pi$
$380$		0			0
$381$	29.0885	+	16.7942i	1.49025	+	0.860394i
$382$		0			0
$383$	−9.69615	−	5.59808i	−0.495450	−	0.286048i	0.231382	−	0.972863i	$-0.425675\pi$
$383$	−9.69615	−	5.59808i	−0.495450	−	0.286048i	−0.726833	+	0.686815i	$0.759008\pi$
$384$		0			0
$385$	18.2942	+	6.09808i	0.932360	+	0.310787i
$386$		0			0
$387$	−8.29423	−	2.22243i	−0.421619	−	0.112973i
$388$		0			0
$389$	23.8564			1.20957			0.604784	−	0.796390i	$-0.293259\pi$
$389$	23.8564			1.20957			0.604784	+	0.796390i	$0.293259\pi$
$390$		0			0
$391$	31.5885			1.59750
$392$		0			0
$393$	25.8564	+	6.92820i	1.30428	+	0.349482i
$394$		0			0
$395$	9.07180	−	4.53590i	0.456452	−	0.228226i
$396$		0			0
$397$	−31.6244	−	18.2583i	−1.58718	−	0.916359i	−0.993769	−	0.111460i	$-0.964447\pi$
$397$	−31.6244	−	18.2583i	−1.58718	−	0.916359i	−0.593412	−	0.804899i	$-0.702220\pi$
$398$		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
$403$	5.73205	−	28.6603i	0.285534	−	1.42767i
$404$		0			0
$405$	−13.1340	+	19.8923i	−0.652632	+	0.988457i
$406$		0			0
$407$	0.160254	+	0.598076i	0.00794350	+	0.0296455i
$408$		0			0
$409$	−9.06218	+	2.42820i	−0.448096	+	0.120067i	−0.475808	−	0.879549i	$-0.657844\pi$
$409$	−9.06218	+	2.42820i	−0.448096	+	0.120067i	0.0277124	+	0.999616i	$0.491178\pi$
$410$		0			0
$411$	−1.09808	−	1.09808i	−0.0541641	−	0.0541641i
$412$		0			0
$413$	6.69615	−	24.9904i	0.329496	−	1.22970i
$414$		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	−0.508681	−	0.860955i	$-0.669867\pi$
$419$	−0.356406	+	0.205771i	−0.0174116	+	0.0100526i	0.491269	+	0.871008i	$0.336533\pi$
$420$		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
$423$	0.196152	−	0.339746i	0.00953726	−	0.0165190i
$424$		0			0
$425$	20.3301	+	8.16025i	0.986156	+	0.395830i
$426$		0			0
$427$	3.23205	−	1.86603i	0.156410	−	0.0903033i
$428$		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
$433$	−26.7224	+	7.16025i	−1.28420	+	0.344100i	−0.835454	−	0.549560i	$-0.814795\pi$
$433$	−26.7224	+	7.16025i	−1.28420	+	0.344100i	−0.448744	+	0.893660i	$0.648129\pi$
$434$		0			0
$435$	26.3564	+	29.7224i	1.26369	+	1.42508i
$436$		0			0
$437$			6.46410i			0.309220i
$438$		0			0
$439$	−0.964102	−	1.66987i	−0.0460141	−	0.0796987i	0.842101	−	0.539320i	$-0.181319\pi$
$439$	−0.964102	−	1.66987i	−0.0460141	−	0.0796987i	−0.888115	+	0.459621i	$0.847985\pi$
$440$		0			0
$441$			5.07180i			0.241514i
$442$		0			0
$443$	−11.0526	+	11.0526i	−0.525123	+	0.525123i	−0.919114	−	0.393991i	$-0.871094\pi$
$443$	−11.0526	+	11.0526i	−0.525123	+	0.525123i	0.393991	+	0.919114i	$0.371094\pi$
$444$		0			0
$445$	−6.86603	−	33.5526i	−0.325481	−	1.59054i
$446$		0			0
$447$	36.5167			1.72718
$448$		0			0
$449$	1.99038	+	7.42820i	0.0939319	+	0.350559i	0.996855	−	0.0792428i	$-0.0252502\pi$
$449$	1.99038	+	7.42820i	0.0939319	+	0.350559i	−0.902923	+	0.429801i	$0.858584\pi$
$450$		0			0
$451$	0.160254	−	0.277568i	0.00754607	−	0.0130702i
$452$		0			0
$453$	1.09808	+	1.90192i	0.0515921	+	0.0893602i
$454$		0			0
$455$	−15.1603	−	25.9904i	−0.710724	−	1.21845i
$456$		0			0
$457$	4.30385	+	7.45448i	0.201325	+	0.348706i	0.948956	−	0.315409i	$-0.102142\pi$
$457$	4.30385	+	7.45448i	0.201325	+	0.348706i	−0.747630	+	0.664115i	$0.768808\pi$
$458$		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
$463$	−2.14359			−0.0996212			−0.0498106	−	0.998759i	$-0.515862\pi$
$463$	−2.14359			−0.0996212			−0.0498106	+	0.998759i	$0.515862\pi$
$464$		0			0
$465$	−29.2224	−	19.2942i	−1.35516	−	0.894748i
$466$		0			0
$467$	−4.12436	+	4.12436i	−0.190852	+	0.190852i	−0.796064	−	0.605212i	$-0.793088\pi$
$467$	−4.12436	+	4.12436i	−0.190852	+	0.190852i	0.605212	+	0.796064i	$0.293088\pi$
$468$		0			0
$469$		−	20.6603i		−	0.954002i
$470$		0			0
$471$	−10.0981	−	17.4904i	−0.465295	−	0.805914i
$472$		0			0
$473$		−	27.1051i		−	1.24629i
$474$		0			0
$475$	−1.66987	+	4.16025i	−0.0766190	+	0.190886i
$476$		0			0
$477$	−1.53590	+	0.411543i	−0.0703240	+	0.0188432i
$478$		0			0
$479$	26.9904	+	7.23205i	1.23322	+	0.330441i	0.815833	−	0.578287i	$-0.196279\pi$
$479$	26.9904	+	7.23205i	1.23322	+	0.330441i	0.417389	+	0.908728i	$0.362945\pi$
$480$		0			0
$481$	0.428203	−	0.866025i	0.0195244	−	0.0394874i
$482$		0			0
$483$	−45.0167	+	25.9904i	−2.04833	+	1.18260i
$484$		0			0
$485$	9.96410	+	0.598076i	0.452447	+	0.0271572i
$486$		0			0
$487$	−0.160254	+	0.277568i	−0.00726180	+	0.0125778i	−0.869633	−	0.493698i	$-0.835645\pi$
$487$	−0.160254	+	0.277568i	−0.00726180	+	0.0125778i	0.862372	+	0.506276i	$0.168978\pi$
$488$		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
$497$	−4.23205	+	15.7942i	−0.189833	+	0.708468i
$498$		0			0
$499$	−7.19615	−	7.19615i	−0.322144	−	0.322144i	0.527445	−	0.849589i	$-0.323150\pi$
$499$	−7.19615	−	7.19615i	−0.322144	−	0.322144i	−0.849589	+	0.527445i	$0.823150\pi$
$500$		0			0
$501$	−12.4282	+	3.33013i	−0.555251	+	0.148779i
$502$		0			0
$503$	2.93782	+	10.9641i	0.130991	+	0.488865i	0.999982	−	0.00596240i	$-0.00189790\pi$
$503$	2.93782	+	10.9641i	0.130991	+	0.488865i	−0.868991	+	0.494828i	$0.835231\pi$
$504$		0			0
$505$	−3.23205	−	2.13397i	−0.143824	−	0.0949606i
$506$		0			0
$507$	15.3301	−	19.8923i	0.680835	−	0.883448i
$508$		0			0
$509$	−6.79423	+	25.3564i	−0.301149	+	1.12390i	0.635061	+	0.772462i	$0.280975\pi$
$509$	−6.79423	+	25.3564i	−0.301149	+	1.12390i	−0.936210	+	0.351441i	$0.885692\pi$
$510$		0			0
$511$	−41.7846	−	24.1244i	−1.84844	−	1.06720i
$512$		0			0
$513$	−3.40192	−	1.96410i	−0.150199	−	0.0867172i
$514$		0			0
$515$	6.66025	−	19.9808i	0.293486	−	0.880458i
$516$		0			0
$517$	1.19615	+	0.320508i	0.0526067	+	0.0140959i
$518$		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
$523$	−3.06218	−	0.820508i	−0.133900	−	0.0358783i	0.191247	−	0.981542i	$-0.438747\pi$
$523$	−3.06218	−	0.820508i	−0.133900	−	0.0358783i	−0.325146	+	0.945664i	$0.605414\pi$
$524$		0			0
$525$	−35.6865	+	5.09808i	−1.55749	+	0.222498i
$526$		0			0
$527$	−30.7583	−	17.7583i	−1.33985	−	0.773565i
$528$		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
$533$	−0.473721	+	0.160254i	−0.0205191	+	0.00694137i
$534$		0			0
$535$	−13.5263	+	2.76795i	−0.584792	+	0.119669i
$536$		0			0
$537$	5.96410	+	22.2583i	0.257370	+	0.960518i
$538$		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
$543$	7.46410	−	27.8564i	0.320315	−	1.19543i
$544$		0			0
$545$	9.39230	−	28.1769i	0.402322	−	1.20697i
$546$		0			0
$547$	1.19615	+	1.19615i	0.0511438	+	0.0511438i	0.732216	−	0.681072i	$-0.238486\pi$
$547$	1.19615	+	1.19615i	0.0511438	+	0.0511438i	−0.681072	+	0.732216i	$0.738486\pi$
$548$		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
$553$	−8.46410	+	14.6603i	−0.359930	+	0.623417i
$554$		0			0
$555$	−0.767949	−	0.866025i	−0.0325976	−	0.0367607i
$556$		0			0
$557$	−21.2321	+	12.2583i	−0.899631	+	0.519402i	−0.877080	−	0.480344i	$-0.840512\pi$
$557$	−21.2321	+	12.2583i	−0.899631	+	0.519402i	−0.0225505	+	0.999746i	$0.507179\pi$
$558$		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
$563$	10.5263	−	2.82051i	0.443630	−	0.118870i	−0.0300874	−	0.999547i	$-0.509579\pi$
$563$	10.5263	−	2.82051i	0.443630	−	0.118870i	0.473717	+	0.880677i	$0.342912\pi$
$564$		0			0
$565$	−22.7942	+	20.2128i	−0.958960	+	0.850359i
$566$		0			0
$567$		−	39.7846i		−	1.67080i
$568$		0			0
$569$	15.4282	+	26.7224i	0.646784	+	1.12026i	0.983886	+	0.178795i	$0.0572198\pi$
$569$	15.4282	+	26.7224i	0.646784	+	1.12026i	−0.337102	+	0.941468i	$0.609447\pi$
$570$		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
$575$	−22.2583	−	28.3564i	−0.928237	−	1.18254i
$576$		0			0
$577$	−15.0718			−0.627447			−0.313724	−	0.949514i	$-0.601577\pi$
$577$	−15.0718			−0.627447			−0.313724	+	0.949514i	$0.601577\pi$
$578$		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
$583$	−2.50962	−	4.34679i	−0.103938	−	0.180026i
$584$		0			0
$585$	−2.97372	−	5.09808i	−0.122948	−	0.210780i
$586$		0			0
$587$	4.16025	+	7.20577i	0.171712	+	0.297414i	0.939019	−	0.343867i	$-0.111737\pi$
$587$	4.16025	+	7.20577i	0.171712	+	0.297414i	−0.767306	+	0.641281i	$0.778403\pi$
$588$		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
$593$	−20.9282			−0.859418			−0.429709	−	0.902967i	$-0.641384\pi$
$593$	−20.9282			−0.859418			−0.429709	+	0.902967i	$0.641384\pi$
$594$		0			0
$595$	−35.8205	+	7.33013i	−1.46850	+	0.300506i
$596$		0			0
$597$	13.5622	−	13.5622i	0.555063	−	0.555063i
$598$		0			0
$599$			26.3923i			1.07836i	0.842190	+	0.539180i	$0.181266\pi$
$599$			26.3923i			1.07836i	−0.842190	+	0.539180i	$0.818734\pi$
$600$		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
$603$		−	4.05256i		−	0.165033i
$604$		0			0
$605$	0.758330	−	12.6340i	0.0308305	−	0.513644i
$606$		0			0
$607$	21.0622	−	5.64359i	0.854887	−	0.229066i	0.195346	−	0.980734i	$-0.437417\pi$
$607$	21.0622	−	5.64359i	0.854887	−	0.229066i	0.659542	+	0.751668i	$0.270750\pi$
$608$		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
$613$	−5.76795	+	3.33013i	−0.232965	+	0.134503i	−0.611939	−	0.790905i	$-0.709610\pi$
$613$	−5.76795	+	3.33013i	−0.232965	+	0.134503i	0.378974	+	0.925407i	$0.376277\pi$
$614$		0			0
$615$	−0.0358984	+	0.598076i	−0.00144756	+	0.0241168i
$616$		0			0
$617$	15.0885	−	26.1340i	0.607438	−	1.05211i	−0.384223	−	0.923240i	$-0.625530\pi$
$617$	15.0885	−	26.1340i	0.607438	−	1.05211i	0.991661	−	0.128874i	$-0.0411362\pi$
$618$		0			0
$619$	30.1244	−	30.1244i	1.21080	−	1.21080i	0.240036	−	0.970764i	$-0.422841\pi$
$619$	30.1244	−	30.1244i	1.21080	−	1.21080i	0.970764	−	0.240036i	$-0.0771593\pi$
$620$		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
$627$	−1.03590	+	3.86603i	−0.0413698	+	0.154394i
$628$		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
$633$	1.96410	+	7.33013i	0.0780660	+	0.291346i
$634$		0			0
$635$	−7.79423	−	38.0885i	−0.309305	−	1.51149i
$636$		0			0
$637$	22.3923	+	11.0718i	0.887215	+	0.438681i
$638$		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
$643$	39.2321	+	22.6506i	1.54716	+	0.893254i	0.998357	+	0.0573029i	$0.0182501\pi$
$643$	39.2321	+	22.6506i	1.54716	+	0.893254i	0.548804	+	0.835951i	$0.315083\pi$
$644$		0			0
$645$	22.6603	+	45.3205i	0.892247	+	1.78449i
$646$		0			0
$647$	14.7942	+	3.96410i	0.581621	+	0.155845i	0.537621	−	0.843187i	$-0.319323\pi$
$647$	14.7942	+	3.96410i	0.581621	+	0.155845i	0.0440001	+	0.999032i	$0.485990\pi$
$648$		0			0
$649$	16.0192			0.628810
$650$		0			0
$651$	58.4449			2.29063
$652$		0			0
$653$	−36.1865	−	9.69615i	−1.41609	−	0.379440i	−0.531994	−	0.846748i	$-0.678557\pi$
$653$	−36.1865	−	9.69615i	−1.41609	−	0.379440i	−0.884094	+	0.467308i	$0.845224\pi$
$654$		0			0
$655$	−13.8564	−	27.7128i	−0.541415	−	1.08283i
$656$		0			0
$657$	−8.19615	−	4.73205i	−0.319762	−	0.184615i
$658$		0			0
$659$	26.2128	+	15.1340i	1.02111	+	0.589536i	0.914424	−	0.404757i	$-0.132644\pi$
$659$	26.2128	+	15.1340i	1.02111	+	0.589536i	0.106682	+	0.994293i	$0.465977\pi$
$660$		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
$663$	−16.9282	−	25.3923i	−0.657437	−	0.986155i
$664$		0			0
$665$	−1.50000	−	7.33013i	−0.0581675	−	0.284250i
$666$		0			0
$667$	−17.1603	−	64.0429i	−0.664448	−	2.47975i
$668$		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
$673$	1.00962	−	3.76795i	0.0389180	−	0.145244i	−0.943733	−	0.330708i	$-0.892712\pi$
$673$	1.00962	−	3.76795i	0.0389180	−	0.145244i	0.982651	+	0.185465i	$0.0593790\pi$
$674$		0			0
$675$	21.6865	−	3.09808i	0.834715	−	0.119245i
$676$		0			0
$677$	24.3205	+	24.3205i	0.934713	+	0.934713i	0.997996	−	0.0632826i	$-0.0201569\pi$
$677$	24.3205	+	24.3205i	0.934713	+	0.934713i	−0.0632826	+	0.997996i	$0.520157\pi$
$678$		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
$683$	−11.7679	+	20.3827i	−0.450288	+	0.779922i	−0.998404	−	0.0564808i	$-0.982012\pi$
$683$	−11.7679	+	20.3827i	−0.450288	+	0.779922i	0.548116	+	0.836403i	$0.315345\pi$
$684$		0			0
$685$	−0.107695	+	1.79423i	−0.00411482	+	0.0685540i
$686$		0			0
$687$	−39.8827	+	23.0263i	−1.52162	+	0.878507i
$688$		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
$693$	−6.09808	+	1.63397i	−0.231647	+	0.0620696i
$694$		0			0
$695$	−1.30385	+	21.7224i	−0.0494578	+	0.823979i
$696$		0			0
$697$			0.607695i			0.0230181i
$698$		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
$705$	−2.26795	+	0.464102i	−0.0854159	+	0.0174791i
$706$		0			0
$707$	6.46410			0.243108
$708$		0			0
$709$	−0.401924	−	1.50000i	−0.0150946	−	0.0563337i	0.957968	−	0.286876i	$-0.0926167\pi$
$709$	−0.401924	−	1.50000i	−0.0150946	−	0.0563337i	−0.973062	+	0.230542i	$0.925950\pi$
$710$		0			0
$711$	−1.66025	+	2.87564i	−0.0622644	+	0.107845i
$712$		0			0
$713$	29.2224	+	50.6147i	1.09439	+	1.89554i
$714$		0			0
$715$	13.1147	−	13.2321i	0.490463	−	0.494851i
$716$		0			0
$717$	1.63397	+	2.83013i	0.0610219	+	0.105693i
$718$		0			0
$719$	5.89230	−	10.2058i	0.219746	−	0.380611i	−0.734984	−	0.678084i	$-0.762811\pi$
$719$	5.89230	−	10.2058i	0.219746	−	0.380611i	0.954730	+	0.297473i	$0.0961438\pi$
$720$		0			0
$721$	9.09808	+	33.9545i	0.338830	+	1.26453i
$722$		0			0
$723$	−34.1244			−1.26910
$724$		0			0
$725$	5.50000	−	45.6506i	0.204265	−	1.69542i
$726$		0			0
$727$	−17.5885	+	17.5885i	−0.652320	+	0.652320i	−0.953551	−	0.301231i	$-0.902602\pi$
$727$	−17.5885	+	17.5885i	−0.652320	+	0.652320i	0.301231	+	0.953551i	$0.402602\pi$
$728$		0			0
$729$			17.5885i			0.651424i
$730$		0			0
$731$	25.6962	+	44.5070i	0.950407	+	1.64615i
$732$		0			0
$733$		−	30.6410i		−	1.13175i	−0.824490	−	0.565876i	$-0.808538\pi$
$733$		−	30.6410i		−	1.13175i	0.824490	−	0.565876i	$-0.191462\pi$
$734$		0			0
$735$	22.3923	−	19.8564i	0.825953	−	0.732415i
$736$		0			0
$737$	12.3564	−	3.31089i	0.455154	−	0.121958i
$738$		0			0
$739$	−33.2583	−	8.91154i	−1.22343	−	0.327816i	−0.411410	−	0.911450i	$-0.634964\pi$
$739$	−33.2583	−	8.91154i	−1.22343	−	0.327816i	−0.812017	+	0.583634i	$0.801630\pi$
$740$		0			0
$741$	5.19615	−	3.46410i	0.190885	−	0.127257i
$742$		0			0
$743$	−21.4808	+	12.4019i	−0.788053	+	0.454982i	−0.839277	−	0.543705i	$-0.817021\pi$
$743$	−21.4808	+	12.4019i	−0.788053	+	0.454982i	0.0512238	+	0.998687i	$0.483688\pi$
$744$		0			0
$745$	−28.0429	−	31.6244i	−1.02741	−	1.15863i
$746$		0			0
$747$	1.26795	−	2.19615i	0.0463918	−	0.0803530i
$748$		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
$757$	3.93782	−	14.6962i	0.143123	−	0.534141i	−0.856709	−	0.515800i	$-0.827495\pi$
$757$	3.93782	−	14.6962i	0.143123	−	0.534141i	0.999832	−	0.0183410i	$-0.00583846\pi$
$758$		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
$763$	12.8301	+	47.8827i	0.464482	+	1.73347i
$764$		0			0
$765$	−7.02628	+	1.43782i	−0.254036	+	0.0519846i
$766$		0			0
$767$	−18.7750	−	16.5000i	−0.677926	−	0.595780i
$768$		0			0
$769$	−3.33013	+	12.4282i	−0.120087	+	0.448172i	−0.999617	−	0.0276717i	$-0.991191\pi$
$769$	−3.33013	+	12.4282i	−0.120087	+	0.448172i	0.879530	+	0.475844i	$0.157857\pi$
$770$		0			0
$771$	26.8923	+	15.5263i	0.968503	+	0.559165i
$772$		0			0
$773$	−15.4808	−	8.93782i	−0.556804	−	0.321471i	0.195058	−	0.980792i	$-0.437511\pi$
$773$	−15.4808	−	8.93782i	−0.556804	−	0.321471i	−0.751862	+	0.659321i	$0.770844\pi$
$774$		0			0
$775$	5.73205	+	40.1244i	0.205901	+	1.44131i
$776$		0			0
$777$	1.86603	+	0.500000i	0.0669433	+	0.0179374i
$778$		0			0
$779$	−0.124356			−0.00445550
$780$		0			0
$781$	−10.1244			−0.362278
$782$		0			0
$783$	38.9186	+	10.4282i	1.39084	+	0.372674i
$784$		0			0
$785$	−7.39230	+	22.1769i	−0.263843	+	0.791528i
$786$		0			0
$787$	−6.91154	−	3.99038i	−0.246370	−	0.142242i	0.371731	−	0.928340i	$-0.378764\pi$
$787$	−6.91154	−	3.99038i	−0.246370	−	0.142242i	−0.618101	+	0.786099i	$0.712098\pi$
$788$		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
$793$	−0.232051	−	3.59808i	−0.00824037	−	0.127771i
$794$		0			0
$795$	7.83013	+	5.16987i	0.277706	+	0.183356i
$796$		0			0
$797$	4.72243	+	17.6244i	0.167277	+	0.624287i	0.997739	+	0.0672109i	$0.0214100\pi$
$797$	4.72243	+	17.6244i	0.167277	+	0.624287i	−0.830462	+	0.557076i	$0.811923\pi$
$798$		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
$803$	7.73205	−	28.8564i	0.272858	−	1.01832i
$804$		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	−0.331276	−	0.943534i	$-0.607479\pi$
$809$	9.10770	−	5.25833i	0.320210	−	0.184873i	0.651486	+	0.758661i	$0.274146\pi$
$810$		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
$813$	−15.6962	+	27.1865i	−0.550488	+	0.953473i
$814$		0			0
$815$	−3.42820	−	0.205771i	−0.120085	−	0.00720786i
$816$		0			0
$817$	−9.10770	+	5.25833i	−0.318638	+	0.183966i
$818$		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
$823$	34.9186	−	9.35641i	1.21719	−	0.326144i	0.407608	−	0.913157i	$-0.366363\pi$
$823$	34.9186	−	9.35641i	1.21719	−	0.326144i	0.809577	+	0.587013i	$0.199696\pi$
$824$		0			0
$825$	−8.76795	−	20.5263i	−0.305261	−	0.714633i
$826$		0			0
$827$		−	31.4641i		−	1.09411i	−0.837095	−	0.547057i	$-0.815748\pi$
$827$		−	31.4641i		−	1.09411i	0.837095	−	0.547057i	$-0.184252\pi$
$828$		0			0
$829$	7.96410	+	13.7942i	0.276605	+	0.479093i	0.970539	−	0.240945i	$-0.0774574\pi$
$829$	7.96410	+	13.7942i	0.276605	+	0.479093i	−0.693934	+	0.720039i	$0.744124\pi$
$830$		0			0
$831$		−	22.3205i		−	0.774290i
$832$		0			0
$833$	21.4641	−	21.4641i	0.743687	−	0.743687i
$834$		0			0
$835$	12.4282	+	8.20577i	0.430096	+	0.283972i
$836$		0			0
$837$	−35.5167			−1.22764
$838$		0			0
$839$	−6.47372	−	24.1603i	−0.223498	−	0.834105i	−0.983001	−	0.183601i	$-0.941225\pi$
$839$	−6.47372	−	24.1603i	−0.223498	−	0.834105i	0.759503	−	0.650504i	$-0.225442\pi$
$840$		0			0
$841$	27.7846	−	48.1244i	0.958090	−	1.65946i
$842$		0			0
$843$	18.2942	+	31.6865i	0.630087	+	1.09134i
$844$		0			0
$845$	−29.0000	+	2.00000i	−0.997630	+	0.0688021i
$846$		0			0
$847$	10.5622	+	18.2942i	0.362921	+	0.628597i
$848$		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
$853$	27.5692			0.943952			0.471976	−	0.881611i	$-0.343541\pi$
$853$	27.5692			0.943952			0.471976	+	0.881611i	$0.343541\pi$
$854$		0			0
$855$	−0.294229	−	1.43782i	−0.0100624	−	0.0491725i
$856$		0			0
$857$	29.3923	−	29.3923i	1.00402	−	1.00402i	0.00403013	−	0.999992i	$-0.498717\pi$
$857$	29.3923	−	29.3923i	1.00402	−	1.00402i	0.999992	−	0.00403013i	$-0.00128283\pi$
$858$		0			0
$859$			30.1051i			1.02717i	0.858038	+	0.513587i	$0.171684\pi$
$859$			30.1051i			1.02717i	−0.858038	+	0.513587i	$0.828316\pi$
$860$		0			0
$861$	−0.500000	−	0.866025i	−0.0170400	−	0.0295141i
$862$		0			0
$863$		−	28.2487i		−	0.961597i	−0.876831	−	0.480799i	$-0.840347\pi$
$863$		−	28.2487i		−	0.961597i	0.876831	−	0.480799i	$-0.159653\pi$
$864$		0			0
$865$	−13.2058	−	14.8923i	−0.449010	−	0.506354i
$866$		0			0
$867$	−4.09808	+	1.09808i	−0.139178	+	0.0372926i
$868$		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
$873$	−2.83013	+	1.63397i	−0.0957853	+	0.0553017i
$874$		0			0
$875$	31.8205	+	26.9904i	1.07573	+	0.912441i
$876$		0			0
$877$	−17.5526	+	30.4019i	−0.592708	+	1.02660i	0.401158	+	0.916009i	$0.368608\pi$
$877$	−17.5526	+	30.4019i	−0.592708	+	1.02660i	−0.993866	+	0.110591i	$0.964726\pi$
$878$		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	$-0.474044\pi$
$883$	−27.1962	−	27.1962i	−0.915223	−	0.915223i	−0.996677	+	0.0814537i	$0.974044\pi$
$884$		0			0
$885$	−26.7846	+	13.3923i	−0.900355	+	0.450177i
$886$		0			0
$887$	−12.7942	+	47.7487i	−0.429588	+	1.60324i	0.324107	+	0.946020i	$0.394936\pi$
$887$	−12.7942	+	47.7487i	−0.429588	+	1.60324i	−0.753695	+	0.657224i	$0.771730\pi$
$888$		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
$893$	−0.124356	−	0.464102i	−0.00416140	−	0.0155306i
$894$		0			0
$895$	14.6962	−	22.2583i	0.491238	−	0.744014i
$896$		0			0
$897$	3.23205	+	50.1147i	0.107915	+	1.67328i
$898$		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
$903$	−73.2391	−	42.2846i	−2.43724	−	1.40714i
$904$		0			0
$905$	−29.8564	+	14.9282i	−0.992461	+	0.496230i
$906$		0			0
$907$	−22.5263	−	6.03590i	−0.747973	−	0.200419i	−0.135354	−	0.990797i	$-0.543217\pi$
$907$	−22.5263	−	6.03590i	−0.747973	−	0.200419i	−0.612619	+	0.790379i	$0.709884\pi$
$908$		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
$913$	7.73205	+	2.07180i	0.255894	+	0.0685665i
$914$		0			0
$915$	−4.09808	−	1.36603i	−0.135478	−	0.0451594i
$916$		0			0
$917$	44.7846	+	25.8564i	1.47892	+	0.853854i
$918$		0			0
$919$	10.7487	+	6.20577i	0.354567	+	0.204710i	0.666695	−	0.745331i	$-0.267708\pi$
$919$	10.7487	+	6.20577i	0.354567	+	0.204710i	−0.312128	+	0.950040i	$0.601042\pi$
$920$		0			0
$921$	4.80385	−	17.9282i	0.158292	−	0.590754i
$922$		0			0
$923$	11.8660	+	10.4282i	0.390575	+	0.343248i
$924$		0			0
$925$	−0.160254	+	1.33013i	−0.00526912	+	0.0437343i
$926$		0			0
$927$	1.78461	+	6.66025i	0.0586143	+	0.218751i
$928$		0			0
$929$	14.7942	−	3.96410i	0.485383	−	0.130058i	−0.00782508	−	0.999969i	$-0.502491\pi$
$929$	14.7942	−	3.96410i	0.485383	−	0.130058i	0.493208	+	0.869911i	$0.335824\pi$
$930$		0			0
$931$	4.39230	+	4.39230i	0.143952	+	0.143952i
$932$		0			0
$933$	16.1244	−	60.1769i	0.527888	−	1.97010i
$934$		0			0
$935$	−10.1244	−	20.2487i	−0.331102	−	0.662204i
$936$		0			0
$937$	0.215390	+	0.215390i	0.00703649	+	0.00703649i	0.710616	−	0.703580i	$-0.248416\pi$
$937$	0.215390	+	0.215390i	0.00703649	+	0.00703649i	−0.703580	+	0.710616i	$0.748416\pi$
$938$		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
$943$	0.500000	−	0.866025i	0.0162822	−	0.0282017i
$944$		0			0
$945$	−27.3564	+	24.2583i	−0.889904	+	0.789124i
$946$		0			0
$947$	−42.0167	+	24.2583i	−1.36536	+	0.788290i	−0.990331	−	0.138724i	$-0.955700\pi$
$947$	−42.0167	+	24.2583i	−1.36536	+	0.788290i	−0.375027	+	0.927014i	$0.622367\pi$
$948$		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
$953$	20.9904	−	5.62436i	0.679945	−	0.182191i	0.0977146	−	0.995214i	$-0.468847\pi$
$953$	20.9904	−	5.62436i	0.679945	−	0.182191i	0.582231	+	0.813024i	$0.302180\pi$
$954$		0			0
$955$	53.4090	+	3.20577i	1.72827	+	0.103736i
$956$		0			0
$957$		−	41.0526i		−	1.32704i
$958$		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
$965$	29.9641	−	45.3827i	0.964579	−	1.46092i
$966$		0			0
$967$	58.6410			1.88577			0.942884	−	0.333121i	$-0.108102\pi$
$967$	58.6410			1.88577			0.942884	+	0.333121i	$0.108102\pi$
$968$		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
$973$	−18.1603	−	31.4545i	−0.582191	−	1.00838i
$974$		0			0
$975$	−10.8660	+	33.0885i	−0.347991	+	1.05968i
$976$		0			0
$977$	−24.6244	−	42.6506i	−0.787803	−	1.36451i	−0.927310	−	0.374294i	$-0.877885\pi$
$977$	−24.6244	−	42.6506i	−0.787803	−	1.36451i	0.139507	−	0.990221i	$-0.455448\pi$
$978$		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
$983$	−29.0718			−0.927246			−0.463623	−	0.886032i	$-0.653451\pi$
$983$	−29.0718			−0.927246			−0.463623	+	0.886032i	$0.653451\pi$
$984$		0			0
$985$	−17.6436	+	26.7224i	−0.562172	+	0.851447i
$986$		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
$993$			12.4641i			0.395536i
$994$		0			0
$995$	−22.1603	−	1.33013i	−0.702527	−	0.0421679i
$996$		0			0
$997$	−6.33013	+	1.69615i	−0.200477	+	0.0537177i	−0.357660	−	0.933852i	$-0.616425\pi$
$997$	−6.33013	+	1.69615i	−0.200477	+	0.0537177i	0.157183	+	0.987569i	$0.449759\pi$
$998$		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.bk.b.197.1	yes	4
5.2	odd	4		1300.2.bn.b.93.1		4
5.3	odd	4		260.2.bf.a.93.1	✓	4
5.4	even	2		1300.2.bs.a.457.1		4
13.7	odd	12		260.2.bf.a.137.1	yes	4
65.7	even	12		1300.2.bs.a.293.1		4
65.33	even	12	inner	260.2.bk.b.33.1	yes	4
65.59	odd	12		1300.2.bn.b.657.1		4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.86603 + 0.500000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(3.23205 + 1.86603i) q^{7} +(0.633975 + 0.366025i) q^{9} +O(q^{10})\)	\(q+(1.86603 + 0.500000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(3.23205 + 1.86603i) q^{7} +(0.633975 + 0.366025i) q^{9} +(-0.598076 + 2.23205i) q^{11} +(3.00000 - 2.00000i) q^{13} +(-0.866025 - 4.23205i) q^{15} +(-1.13397 - 4.23205i) q^{17} +(0.866025 - 0.232051i) q^{19} +(5.09808 + 5.09808i) q^{21} +(-1.86603 + 6.96410i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(-3.09808 - 3.09808i) q^{27} +(-7.96410 + 4.59808i) q^{29} +(5.73205 - 5.73205i) q^{31} +(-2.23205 + 3.86603i) q^{33} +(0.500000 - 8.33013i) q^{35} +(0.232051 - 0.133975i) q^{37} +(6.59808 - 2.23205i) q^{39} +(-0.133975 - 0.0358984i) q^{41} +(-11.3301 + 3.03590i) q^{43} +(0.0980762 - 1.63397i) q^{45} -0.535898i q^{47} +(3.46410 + 6.00000i) q^{49} -8.46410i q^{51} +(-1.53590 + 1.53590i) q^{53} +(5.06218 - 1.03590i) q^{55} +1.73205 q^{57} +(-1.79423 - 6.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(1.36603 + 2.36603i) q^{63} +(-7.00000 - 4.00000i) q^{65} +(-2.76795 - 4.79423i) q^{67} +(-6.96410 + 12.0622i) q^{69} +(1.13397 + 4.23205i) q^{71} -12.9282 q^{73} +(-7.59808 + 5.96410i) q^{75} +(-6.09808 + 6.09808i) q^{77} +4.53590i q^{79} +(-5.33013 - 9.23205i) q^{81} -3.46410i q^{83} +(-7.33013 + 6.50000i) q^{85} +(-17.1603 + 4.59808i) q^{87} +(14.7942 + 3.96410i) q^{89} +(13.4282 - 0.866025i) q^{91} +(13.5622 - 7.83013i) q^{93} +(-1.33013 - 1.50000i) q^{95} +(-2.23205 + 3.86603i) q^{97} +(-1.19615 + 1.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{5} + 6 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^5 + 6 * q^7 + 6 * q^9	\( 4 q + 4 q^{3} - 4 q^{5} + 6 q^{7} + 6 q^{9} + 8 q^{11} + 12 q^{13} - 8 q^{17} + 10 q^{21} - 4 q^{23} - 12 q^{25} - 2 q^{27} - 18 q^{29} + 16 q^{31} - 2 q^{33} + 2 q^{35} - 6 q^{37} + 16 q^{39} - 4 q^{41} - 28 q^{43} - 10 q^{45} - 20 q^{53} - 4 q^{55} + 24 q^{59} + 2 q^{61} + 2 q^{63} - 28 q^{65} - 18 q^{67} - 14 q^{69} + 8 q^{71} - 24 q^{73} - 20 q^{75} - 14 q^{77} - 4 q^{81} - 12 q^{85} - 34 q^{87} + 28 q^{89} + 26 q^{91} + 30 q^{93} + 12 q^{95} - 2 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^5 + 6 * q^7 + 6 * q^9 + 8 * q^11 + 12 * q^13 - 8 * q^17 + 10 * q^21 - 4 * q^23 - 12 * q^25 - 2 * q^27 - 18 * q^29 + 16 * q^31 - 2 * q^33 + 2 * q^35 - 6 * q^37 + 16 * q^39 - 4 * q^41 - 28 * q^43 - 10 * q^45 - 20 * q^53 - 4 * q^55 + 24 * q^59 + 2 * q^61 + 2 * q^63 - 28 * q^65 - 18 * q^67 - 14 * q^69 + 8 * q^71 - 24 * q^73 - 20 * q^75 - 14 * q^77 - 4 * q^81 - 12 * q^85 - 34 * q^87 + 28 * q^89 + 26 * q^91 + 30 * q^93 + 12 * q^95 - 2 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more