LMFDB - Embedded newform 260.2.bk.b.193.1

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			193.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.193
Dual form			260.2.bk.b.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-0.232051 - 0.133975i) q^{7} +(2.36603 + 1.36603i) q^{9} +O(q^{10})$	\(q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-0.232051 - 0.133975i) q^{7} +(2.36603 + 1.36603i) q^{9} +(4.59808 + 1.23205i) q^{11} +(3.00000 + 2.00000i) q^{13} +(0.866025 + 0.767949i) q^{15} +(-2.86603 + 0.767949i) q^{17} +(-0.866025 - 3.23205i) q^{19} +(-0.0980762 + 0.0980762i) q^{21} +(-0.133975 - 0.0358984i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(2.09808 - 2.09808i) q^{27} +(-1.03590 + 0.598076i) q^{29} +(2.26795 + 2.26795i) q^{31} +(1.23205 - 2.13397i) q^{33} +(0.500000 - 0.330127i) q^{35} +(-3.23205 + 1.86603i) q^{37} +(1.40192 - 1.23205i) q^{39} +(-1.86603 + 6.96410i) q^{41} +(-2.66987 - 9.96410i) q^{43} +(-5.09808 + 3.36603i) q^{45} +7.46410i q^{47} +(-3.46410 - 6.00000i) q^{49} +1.53590i q^{51} +(-8.46410 - 8.46410i) q^{53} +(-7.06218 + 7.96410i) q^{55} -1.73205 q^{57} +(13.7942 - 3.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-0.366025 - 0.633975i) q^{63} +(-7.00000 + 4.00000i) q^{65} +(-6.23205 - 10.7942i) q^{67} +(-0.0358984 + 0.0621778i) q^{69} +(2.86603 - 0.767949i) q^{71} +0.928203 q^{73} +(-2.40192 + 0.964102i) q^{75} +(-0.901924 - 0.901924i) q^{77} -11.4641i q^{79} +(3.33013 + 5.76795i) q^{81} -3.46410i q^{83} +(1.33013 - 6.50000i) q^{85} +(0.160254 + 0.598076i) q^{87} +(-0.794229 + 2.96410i) q^{89} +(-0.428203 - 0.866025i) q^{91} +(1.43782 - 0.830127i) q^{93} +(7.33013 + 1.50000i) q^{95} +(1.23205 - 2.13397i) q^{97} +(9.19615 + 9.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.133975	−	0.500000i	0.0773503	−	0.288675i	−0.916406	−	0.400251i	$-0.868923\pi$
$3$	0.133975	−	0.500000i	0.0773503	−	0.288675i	0.993756	+	0.111576i	$0.0355897\pi$
$4$		0			0
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		0			0
$7$	−0.232051	−	0.133975i	−0.0877070	−	0.0506376i	0.455505	−	0.890233i	$-0.349459\pi$
$7$	−0.232051	−	0.133975i	−0.0877070	−	0.0506376i	−0.543212	+	0.839596i	$0.682792\pi$
$8$		0			0
$9$	2.36603	+	1.36603i	0.788675	+	0.455342i
$10$		0			0
$11$	4.59808	+	1.23205i	1.38637	+	0.371477i	0.873432	−	0.486947i	$-0.161889\pi$
$11$	4.59808	+	1.23205i	1.38637	+	0.371477i	0.512941	+	0.858424i	$0.328556\pi$
$12$		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	+	0.767949i	0.223607	+	0.198284i
$16$		0			0
$17$	−2.86603	+	0.767949i	−0.695113	+	0.186255i	−0.589041	−	0.808103i	$-0.700494\pi$
$17$	−2.86603	+	0.767949i	−0.695113	+	0.186255i	−0.106073	+	0.994358i	$0.533828\pi$
$18$		0			0
$19$	−0.866025	−	3.23205i	−0.198680	−	0.741483i	−0.991283	−	0.131746i	$-0.957942\pi$
$19$	−0.866025	−	3.23205i	−0.198680	−	0.741483i	0.792604	−	0.609737i	$-0.208725\pi$
$20$		0			0
$21$	−0.0980762	+	0.0980762i	−0.0214020	+	0.0214020i
$22$		0			0
$23$	−0.133975	−	0.0358984i	−0.0279356	−	0.00748533i	0.244824	−	0.969567i	$-0.421270\pi$
$23$	−0.133975	−	0.0358984i	−0.0279356	−	0.00748533i	−0.272760	+	0.962082i	$0.587936\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		0			0
$27$	2.09808	−	2.09808i	0.403775	−	0.403775i
$28$		0			0
$29$	−1.03590	+	0.598076i	−0.192362	+	0.111060i	−0.593088	−	0.805138i	$-0.702091\pi$
$29$	−1.03590	+	0.598076i	−0.192362	+	0.111060i	0.400726	+	0.916198i	$0.368758\pi$
$30$		0			0
$31$	2.26795	+	2.26795i	0.407336	+	0.407336i	0.880808	−	0.473473i	$-0.157000\pi$
$31$	2.26795	+	2.26795i	0.407336	+	0.407336i	−0.473473	+	0.880808i	$0.657000\pi$
$32$		0			0
$33$	1.23205	−	2.13397i	0.214473	−	0.371477i
$34$		0			0
$35$	0.500000	−	0.330127i	0.0845154	−	0.0558017i
$36$		0			0
$37$	−3.23205	+	1.86603i	−0.531346	+	0.306773i	−0.741564	−	0.670882i	$-0.765916\pi$
$37$	−3.23205	+	1.86603i	−0.531346	+	0.306773i	0.210218	+	0.977654i	$0.432582\pi$
$38$		0			0
$39$	1.40192	−	1.23205i	0.224487	−	0.197286i
$40$		0			0
$41$	−1.86603	+	6.96410i	−0.291424	+	1.08761i	0.652592	+	0.757710i	$0.273682\pi$
$41$	−1.86603	+	6.96410i	−0.291424	+	1.08761i	−0.944016	+	0.329900i	$0.892985\pi$
$42$		0			0
$43$	−2.66987	−	9.96410i	−0.407152	−	1.51951i	−0.800052	−	0.599930i	$-0.795195\pi$
$43$	−2.66987	−	9.96410i	−0.407152	−	1.51951i	0.392900	−	0.919581i	$-0.371472\pi$
$44$		0			0
$45$	−5.09808	+	3.36603i	−0.759976	+	0.501777i
$46$		0			0
$47$			7.46410i			1.08875i	0.838842	+	0.544376i	$0.183233\pi$
$47$			7.46410i			1.08875i	−0.838842	+	0.544376i	$0.816767\pi$
$48$		0			0
$49$	−3.46410	−	6.00000i	−0.494872	−	0.857143i
$50$		0			0
$51$			1.53590i			0.215069i
$52$		0			0
$53$	−8.46410	−	8.46410i	−1.16263	−	1.16263i	−0.983897	−	0.178737i	$-0.942799\pi$
$53$	−8.46410	−	8.46410i	−1.16263	−	1.16263i	−0.178737	−	0.983897i	$-0.557201\pi$
$54$		0			0
$55$	−7.06218	+	7.96410i	−0.952264	+	1.07388i
$56$		0			0
$57$	−1.73205			−0.229416
$58$		0			0
$59$	13.7942	−	3.69615i	1.79586	−	0.481198i	0.802537	−	0.596602i	$-0.203483\pi$
$59$	13.7942	−	3.69615i	1.79586	−	0.481198i	0.993319	+	0.115404i	$0.0368164\pi$
$60$		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
$63$	−0.366025	−	0.633975i	−0.0461149	−	0.0798733i
$64$		0			0
$65$	−7.00000	+	4.00000i	−0.868243	+	0.496139i
$66$		0			0
$67$	−6.23205	−	10.7942i	−0.761366	−	1.31872i	−0.942146	−	0.335201i	$-0.891196\pi$
$67$	−6.23205	−	10.7942i	−0.761366	−	1.31872i	0.180780	−	0.983524i	$-0.442138\pi$
$68$		0			0
$69$	−0.0358984	+	0.0621778i	−0.00432166	+	0.00748533i
$70$		0			0
$71$	2.86603	−	0.767949i	0.340135	−	0.0911388i	−0.0847085	−	0.996406i	$-0.526996\pi$
$71$	2.86603	−	0.767949i	0.340135	−	0.0911388i	0.424843	+	0.905267i	$0.360329\pi$
$72$		0			0
$73$	0.928203			0.108638			0.0543190	−	0.998524i	$-0.482701\pi$
$73$	0.928203			0.108638			0.0543190	+	0.998524i	$0.482701\pi$
$74$		0			0
$75$	−2.40192	+	0.964102i	−0.277350	+	0.111325i
$76$		0			0
$77$	−0.901924	−	0.901924i	−0.102784	−	0.102784i
$78$		0			0
$79$		−	11.4641i		−	1.28981i	−0.764262	−	0.644906i	$-0.776896\pi$
$79$		−	11.4641i		−	1.28981i	0.764262	−	0.644906i	$-0.223104\pi$
$80$		0			0
$81$	3.33013	+	5.76795i	0.370014	+	0.640883i
$82$		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
$85$	1.33013	−	6.50000i	0.144273	−	0.705024i
$86$		0			0
$87$	0.160254	+	0.598076i	0.0171810	+	0.0641205i
$88$		0			0
$89$	−0.794229	+	2.96410i	−0.0841881	+	0.314194i	−0.995159	−	0.0982760i	$-0.968667\pi$
$89$	−0.794229	+	2.96410i	−0.0841881	+	0.314194i	0.910971	+	0.412470i	$0.135334\pi$
$90$		0			0
$91$	−0.428203	−	0.866025i	−0.0448879	−	0.0907841i
$92$		0			0
$93$	1.43782	−	0.830127i	0.149095	−	0.0860802i
$94$		0			0
$95$	7.33013	+	1.50000i	0.752055	+	0.153897i
$96$		0			0
$97$	1.23205	−	2.13397i	0.125096	−	0.216672i	−0.796675	−	0.604408i	$-0.793410\pi$
$97$	1.23205	−	2.13397i	0.125096	−	0.216672i	0.921770	+	0.387736i	$0.126743\pi$
$98$		0			0
$99$	9.19615	+	9.19615i	0.924248	+	0.924248i
$100$		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
$103$	−10.6603	+	10.6603i	−1.05039	+	1.05039i	−0.0517247	+	0.998661i	$0.516472\pi$
$103$	−10.6603	+	10.6603i	−1.05039	+	1.05039i	−0.998661	+	0.0517247i	$0.983528\pi$
$104$		0			0
$105$	−0.0980762	−	0.294229i	−0.00957126	−	0.0287138i
$106$		0			0
$107$	−3.59808	−	0.964102i	−0.347839	−	0.0932032i	0.0806695	−	0.996741i	$-0.474294\pi$
$107$	−3.59808	−	0.964102i	−0.347839	−	0.0932032i	−0.428509	+	0.903538i	$0.640961\pi$
$108$		0			0
$109$	−11.3923	+	11.3923i	−1.09118	+	1.09118i	−0.0957826	+	0.995402i	$0.530535\pi$
$109$	−11.3923	+	11.3923i	−1.09118	+	1.09118i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$		0			0
$111$	0.500000	+	1.86603i	0.0474579	+	0.177115i
$112$		0			0
$113$	15.5263	−	4.16025i	1.46059	−	0.391364i	0.560896	−	0.827886i	$-0.310457\pi$
$113$	15.5263	−	4.16025i	1.46059	−	0.391364i	0.899693	+	0.436522i	$0.143790\pi$
$114$		0			0
$115$	0.205771	−	0.232051i	0.0191883	−	0.0216388i
$116$		0			0
$117$	4.36603	+	8.83013i	0.403639	+	0.816346i
$118$		0			0
$119$	0.767949	+	0.205771i	0.0703978	+	0.0188630i
$120$		0			0
$121$	10.0981	+	5.83013i	0.918007	+	0.530012i
$122$		0			0
$123$	3.23205	+	1.86603i	0.291424	+	0.168254i
$124$		0			0
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$	1.20577	−	4.50000i	0.106995	−	0.399310i	−0.891569	−	0.452885i	$-0.850395\pi$
$127$	1.20577	−	4.50000i	0.106995	−	0.399310i	0.998564	+	0.0535746i	$0.0170615\pi$
$128$		0			0
$129$	−5.33975			−0.470138
$130$		0			0
$131$	−13.8564			−1.21064			−0.605320	−	0.795982i	$-0.706955\pi$
$131$	−13.8564			−1.21064			−0.605320	+	0.795982i	$0.706955\pi$
$132$		0			0
$133$	−0.232051	+	0.866025i	−0.0201214	+	0.0750939i
$134$		0			0
$135$	2.09808	+	6.29423i	0.180574	+	0.541721i
$136$		0			0
$137$	9.69615	+	5.59808i	0.828398	+	0.478276i	0.853304	−	0.521414i	$-0.174595\pi$
$137$	9.69615	+	5.59808i	0.828398	+	0.478276i	−0.0249057	+	0.999690i	$0.507929\pi$
$138$		0			0
$139$	5.42820	+	3.13397i	0.460414	+	0.265820i	0.712218	−	0.701958i	$-0.247691\pi$
$139$	5.42820	+	3.13397i	0.460414	+	0.265820i	−0.251804	+	0.967778i	$0.581024\pi$
$140$		0			0
$141$	3.73205	+	1.00000i	0.314295	+	0.0842152i
$142$		0			0
$143$	11.3301	+	12.8923i	0.947473	+	1.07811i
$144$		0			0
$145$	−0.160254	−	2.66987i	−0.0133084	−	0.221721i
$146$		0			0
$147$	−3.46410	+	0.928203i	−0.285714	+	0.0765569i
$148$		0			0
$149$	−4.25833	−	15.8923i	−0.348856	−	1.30195i	−0.888042	−	0.459762i	$-0.847935\pi$
$149$	−4.25833	−	15.8923i	−0.348856	−	1.30195i	0.539186	−	0.842187i	$-0.318732\pi$
$150$		0			0
$151$	11.1962	−	11.1962i	0.911130	−	0.911130i	−0.0852312	−	0.996361i	$-0.527163\pi$
$151$	11.1962	−	11.1962i	0.911130	−	0.911130i	0.996361	+	0.0852312i	$0.0271629\pi$
$152$		0			0
$153$	−7.83013	−	2.09808i	−0.633028	−	0.169619i
$154$		0			0
$155$	−6.80385	+	2.26795i	−0.546498	+	0.182166i
$156$		0			0
$157$	13.3923	−	13.3923i	1.06882	−	1.06882i	0.0713726	−	0.997450i	$-0.477262\pi$
$157$	13.3923	−	13.3923i	1.06882	−	1.06882i	0.997450	−	0.0713726i	$-0.0227379\pi$
$158$		0			0
$159$	−5.36603	+	3.09808i	−0.425553	+	0.245693i
$160$		0			0
$161$	0.0262794	+	0.0262794i	0.00207111	+	0.00207111i
$162$		0			0
$163$	4.23205	−	7.33013i	0.331480	−	0.574140i	−0.651322	−	0.758801i	$-0.725785\pi$
$163$	4.23205	−	7.33013i	0.331480	−	0.574140i	0.982802	+	0.184661i	$0.0591188\pi$
$164$		0			0
$165$	3.03590	+	4.59808i	0.236344	+	0.357960i
$166$		0			0
$167$	−9.23205	+	5.33013i	−0.714398	+	0.412458i	−0.812687	−	0.582700i	$-0.801996\pi$
$167$	−9.23205	+	5.33013i	−0.714398	+	0.412458i	0.0982896	+	0.995158i	$0.468663\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$		0			0
$171$	2.36603	−	8.83013i	0.180934	−	0.675257i
$172$		0			0
$173$	3.40192	+	12.6962i	0.258643	+	0.965271i	0.966027	+	0.258441i	$0.0832087\pi$
$173$	3.40192	+	12.6962i	0.258643	+	0.965271i	−0.707384	+	0.706830i	$0.750125\pi$
$174$		0			0
$175$	0.160254	+	1.33013i	0.0121141	+	0.100548i
$176$		0			0
$177$		−	7.39230i		−	0.555640i
$178$		0			0
$179$	−0.964102	−	1.66987i	−0.0720603	−	0.124812i	0.827744	−	0.561106i	$-0.189624\pi$
$179$	−0.964102	−	1.66987i	−0.0720603	−	0.124812i	−0.899804	+	0.436294i	$0.856291\pi$
$180$		0			0
$181$			1.07180i			0.0796660i	0.999206	+	0.0398330i	$0.0126826\pi$
$181$			1.07180i			0.0796660i	−0.999206	+	0.0398330i	$0.987317\pi$
$182$		0			0
$183$	−0.366025	−	0.366025i	−0.0270574	−	0.0270574i
$184$		0			0
$185$	−0.500000	−	8.33013i	−0.0367607	−	0.612443i
$186$		0			0
$187$	−14.1244			−1.03288
$188$		0			0
$189$	−0.767949	+	0.205771i	−0.0558601	+	0.0149677i
$190$		0			0
$191$	−5.03590	+	8.72243i	−0.364385	+	0.631133i	−0.988677	−	0.150058i	$-0.952054\pi$
$191$	−5.03590	+	8.72243i	−0.364385	+	0.631133i	0.624292	+	0.781191i	$0.285387\pi$
$192$		0			0
$193$	−5.16025	−	8.93782i	−0.371443	−	0.643359i	0.618345	−	0.785907i	$-0.287804\pi$
$193$	−5.16025	−	8.93782i	−0.371443	−	0.643359i	−0.989788	+	0.142549i	$0.954470\pi$
$194$		0			0
$195$	1.06218	+	4.03590i	0.0760641	+	0.289017i
$196$		0			0
$197$	10.1603	+	17.5981i	0.723888	+	1.25381i	0.959430	+	0.281947i	$0.0909802\pi$
$197$	10.1603	+	17.5981i	0.723888	+	1.25381i	−0.235542	+	0.971864i	$0.575686\pi$
$198$		0			0
$199$	−1.96410	+	3.40192i	−0.139231	+	0.241156i	−0.927206	−	0.374552i	$-0.877797\pi$
$199$	−1.96410	+	3.40192i	−0.139231	+	0.241156i	0.787974	+	0.615708i	$0.211130\pi$
$200$		0			0
$201$	−6.23205	+	1.66987i	−0.439575	+	0.117784i
$202$		0			0
$203$	0.320508			0.0224953
$204$		0			0
$205$	−12.0622	−	10.6962i	−0.842459	−	0.747052i
$206$		0			0
$207$	−0.267949	−	0.267949i	−0.0186238	−	0.0186238i
$208$		0			0
$209$		−	15.9282i		−	1.10178i
$210$		0			0
$211$	−4.96410	−	8.59808i	−0.341743	−	0.591916i	0.643014	−	0.765855i	$-0.277684\pi$
$211$	−4.96410	−	8.59808i	−0.341743	−	0.591916i	−0.984756	+	0.173939i	$0.944351\pi$
$212$		0			0
$213$		−	1.53590i		−	0.105238i
$214$		0			0
$215$	22.5981	+	4.62436i	1.54118	+	0.315378i
$216$		0			0
$217$	−0.222432	−	0.830127i	−0.0150997	−	0.0563527i
$218$		0			0
$219$	0.124356	−	0.464102i	0.00840318	−	0.0313611i
$220$		0			0
$221$	−10.1340	−	3.42820i	−0.681685	−	0.230606i
$222$		0			0
$223$	−17.0885	+	9.86603i	−1.14433	+	0.660678i	−0.947499	−	0.319760i	$-0.896398\pi$
$223$	−17.0885	+	9.86603i	−1.14433	+	0.660678i	−0.196829	+	0.980438i	$0.563064\pi$
$224$		0			0
$225$	−1.63397	−	13.5622i	−0.108932	−	0.904145i
$226$		0			0
$227$	0.232051	−	0.401924i	0.0154018	−	0.0266766i	−0.858222	−	0.513279i	$-0.828431\pi$
$227$	0.232051	−	0.401924i	0.0154018	−	0.0266766i	0.873624	+	0.486602i	$0.161764\pi$
$228$		0			0
$229$	10.8564	+	10.8564i	0.717412	+	0.717412i	0.968074	−	0.250663i	$-0.0806486\pi$
$229$	10.8564	+	10.8564i	0.717412	+	0.717412i	−0.250663	+	0.968074i	$0.580649\pi$
$230$		0			0
$231$	−0.571797	+	0.330127i	−0.0376215	+	0.0217208i
$232$		0			0
$233$	−11.0000	+	11.0000i	−0.720634	+	0.720634i	−0.968734	−	0.248100i	$-0.920194\pi$
$233$	−11.0000	+	11.0000i	−0.720634	+	0.720634i	0.248100	+	0.968734i	$0.420194\pi$
$234$		0			0
$235$	−14.9282	−	7.46410i	−0.973809	−	0.486904i
$236$		0			0
$237$	−5.73205	−	1.53590i	−0.372337	−	0.0997673i
$238$		0			0
$239$	−9.19615	+	9.19615i	−0.594850	+	0.594850i	−0.938937	−	0.344088i	$-0.888188\pi$
$239$	−9.19615	+	9.19615i	−0.594850	+	0.594850i	0.344088	+	0.938937i	$0.388188\pi$
$240$		0			0
$241$	−4.93782	−	18.4282i	−0.318073	−	1.18706i	−0.921094	−	0.389340i	$-0.872703\pi$
$241$	−4.93782	−	18.4282i	−0.318073	−	1.18706i	0.603021	−	0.797725i	$-0.293963\pi$
$242$		0			0
$243$	11.9282	−	3.19615i	0.765195	−	0.205033i
$244$		0			0
$245$	15.4641	−	0.928203i	0.987965	−	0.0593007i
$246$		0			0
$247$	3.86603	−	11.4282i	0.245989	−	0.727159i
$248$		0			0
$249$	−1.73205	−	0.464102i	−0.109764	−	0.0294112i
$250$		0			0
$251$	−23.8923	−	13.7942i	−1.50807	−	0.870684i	−0.999956	−	0.00939359i	$-0.997010\pi$
$251$	−23.8923	−	13.7942i	−1.50807	−	0.870684i	−0.508113	−	0.861290i	$-0.669657\pi$
$252$		0			0
$253$	−0.571797	−	0.330127i	−0.0359486	−	0.0207549i
$254$		0			0
$255$	−3.07180	−	1.53590i	−0.192363	−	0.0961817i
$256$		0			0
$257$	−3.52628	+	13.1603i	−0.219963	+	0.820914i	0.764397	+	0.644746i	$0.223037\pi$
$257$	−3.52628	+	13.1603i	−0.219963	+	0.820914i	−0.984360	+	0.176168i	$0.943630\pi$
$258$		0			0
$259$	1.00000			0.0621370
$260$		0			0
$261$	−3.26795			−0.202281
$262$		0			0
$263$	−4.79423	+	17.8923i	−0.295625	+	1.10329i	0.645095	+	0.764102i	$0.276818\pi$
$263$	−4.79423	+	17.8923i	−0.295625	+	1.10329i	−0.940720	+	0.339184i	$0.889849\pi$
$264$		0			0
$265$	25.3923	−	8.46410i	1.55984	−	0.519946i
$266$		0			0
$267$	1.37564	+	0.794229i	0.0841881	+	0.0486060i
$268$		0			0
$269$	−23.4282	−	13.5263i	−1.42844	−	0.824712i	−0.431445	−	0.902139i	$-0.641996\pi$
$269$	−23.4282	−	13.5263i	−1.42844	−	0.824712i	−0.996998	+	0.0774275i	$0.975329\pi$
$270$		0			0
$271$	−19.7942	−	5.30385i	−1.20241	−	0.322186i	−0.398633	−	0.917111i	$-0.630515\pi$
$271$	−19.7942	−	5.30385i	−1.20241	−	0.322186i	−0.803781	+	0.594925i	$0.797182\pi$
$272$		0			0
$273$	−0.490381	+	0.0980762i	−0.0296792	+	0.00593584i
$274$		0			0
$275$	−8.86603	−	22.0885i	−0.534641	−	1.33198i
$276$		0			0
$277$	22.9904	−	6.16025i	1.38136	−	0.370134i	0.509744	−	0.860326i	$-0.329740\pi$
$277$	22.9904	−	6.16025i	1.38136	−	0.370134i	0.871614	+	0.490192i	$0.163073\pi$
$278$		0			0
$279$	2.26795	+	8.46410i	0.135779	+	0.506733i
$280$		0			0
$281$	−7.39230	+	7.39230i	−0.440988	+	0.440988i	−0.892344	−	0.451356i	$-0.850940\pi$
$281$	−7.39230	+	7.39230i	−0.440988	+	0.440988i	0.451356	+	0.892344i	$0.350940\pi$
$282$		0			0
$283$	−12.5263	−	3.35641i	−0.744610	−	0.199518i	−0.133484	−	0.991051i	$-0.542616\pi$
$283$	−12.5263	−	3.35641i	−0.744610	−	0.199518i	−0.611126	+	0.791533i	$0.709283\pi$
$284$		0			0
$285$	1.73205	−	3.46410i	0.102598	−	0.205196i
$286$		0			0
$287$	1.36603	−	1.36603i	0.0806339	−	0.0806339i
$288$		0			0
$289$	−7.09808	+	4.09808i	−0.417534	+	0.241063i
$290$		0			0
$291$	−0.901924	−	0.901924i	−0.0528717	−	0.0528717i
$292$		0			0
$293$	11.2321	−	19.4545i	0.656183	−	1.13654i	−0.325412	−	0.945572i	$-0.605503\pi$
$293$	11.2321	−	19.4545i	0.656183	−	1.13654i	0.981596	−	0.190971i	$-0.0611636\pi$
$294$		0			0
$295$	−6.40192	+	31.2846i	−0.372734	+	1.82146i
$296$		0			0
$297$	12.2321	−	7.06218i	0.709776	−	0.409789i
$298$		0			0
$299$	−0.330127	−	0.375644i	−0.0190917	−	0.0217241i
$300$		0			0
$301$	−0.715390	+	2.66987i	−0.0412344	+	0.153889i
$302$		0			0
$303$	−0.232051	−	0.866025i	−0.0133310	−	0.0497519i
$304$		0			0
$305$	1.23205	+	1.86603i	0.0705470	+	0.106848i
$306$		0			0
$307$			30.3923i			1.73458i	0.497803	+	0.867290i	$0.334140\pi$
$307$			30.3923i			1.73458i	−0.497803	+	0.867290i	$0.665860\pi$
$308$		0			0
$309$	3.90192	+	6.75833i	0.221973	+	0.384468i
$310$		0			0
$311$		−	16.2487i		−	0.921380i	−0.887561	−	0.460690i	$-0.847602\pi$
$311$		−	16.2487i		−	0.921380i	0.887561	−	0.460690i	$-0.152398\pi$
$312$		0			0
$313$	20.3205	+	20.3205i	1.14858	+	1.14858i	0.986832	+	0.161752i	$0.0517143\pi$
$313$	20.3205	+	20.3205i	1.14858	+	1.14858i	0.161752	+	0.986832i	$0.448286\pi$
$314$		0			0
$315$	1.63397	−	0.0980762i	0.0920640	−	0.00552597i
$316$		0			0
$317$	−3.07180			−0.172529			−0.0862646	−	0.996272i	$-0.527493\pi$
$317$	−3.07180			−0.172529			−0.0862646	+	0.996272i	$0.527493\pi$
$318$		0			0
$319$	−5.50000	+	1.47372i	−0.307941	+	0.0825125i
$320$		0			0
$321$	−0.964102	+	1.66987i	−0.0538109	+	0.0932032i
$322$		0			0
$323$	4.96410	+	8.59808i	0.276210	+	0.478410i
$324$		0			0
$325$	−1.00000	−	18.0000i	−0.0554700	−	0.998460i
$326$		0			0
$327$	4.16987	+	7.22243i	0.230595	+	0.399401i
$328$		0			0
$329$	1.00000	−	1.73205i	0.0551318	−	0.0954911i
$330$		0			0
$331$	10.3301	−	2.76795i	0.567795	−	0.152140i	0.0365099	−	0.999333i	$-0.488376\pi$
$331$	10.3301	−	2.76795i	0.567795	−	0.152140i	0.531285	+	0.847193i	$0.321709\pi$
$332$		0			0
$333$	−10.1962			−0.558746
$334$		0			0
$335$	27.8205	−	1.66987i	1.52000	−	0.0912349i
$336$		0			0
$337$	−0.0717968	−	0.0717968i	−0.00391102	−	0.00391102i	0.705149	−	0.709060i	$-0.250880\pi$
$337$	−0.0717968	−	0.0717968i	−0.00391102	−	0.00391102i	−0.709060	+	0.705149i	$0.750880\pi$
$338$		0			0
$339$		−	8.32051i		−	0.451908i
$340$		0			0
$341$	7.63397	+	13.2224i	0.413403	+	0.716035i
$342$		0			0
$343$			3.73205i			0.201512i
$344$		0			0
$345$	−0.0884573	−	0.133975i	−0.00476238	−	0.00721295i
$346$		0			0
$347$	−6.66987	−	24.8923i	−0.358058	−	1.33629i	−0.876593	−	0.481233i	$-0.840189\pi$
$347$	−6.66987	−	24.8923i	−0.358058	−	1.33629i	0.518535	−	0.855056i	$-0.326477\pi$
$348$		0			0
$349$	−5.47372	+	20.4282i	−0.293002	+	1.09350i	0.649790	+	0.760114i	$0.274857\pi$
$349$	−5.47372	+	20.4282i	−0.293002	+	1.09350i	−0.942792	+	0.333383i	$0.891810\pi$
$350$		0			0
$351$	10.4904	−	2.09808i	0.559935	−	0.111987i
$352$		0			0
$353$	−13.6244	+	7.86603i	−0.725151	+	0.418666i	−0.816646	−	0.577139i	$-0.804169\pi$
$353$	−13.6244	+	7.86603i	−0.725151	+	0.418666i	0.0914944	+	0.995806i	$0.470836\pi$
$354$		0			0
$355$	−1.33013	+	6.50000i	−0.0705958	+	0.344984i
$356$		0			0
$357$	0.205771	−	0.356406i	0.0108906	−	0.0188630i
$358$		0			0
$359$	−7.58846	−	7.58846i	−0.400503	−	0.400503i	0.477907	−	0.878410i	$-0.341396\pi$
$359$	−7.58846	−	7.58846i	−0.400503	−	0.400503i	−0.878410	+	0.477907i	$0.841396\pi$
$360$		0			0
$361$	6.75833	−	3.90192i	0.355702	−	0.205364i
$362$		0			0
$363$	4.26795	−	4.26795i	0.224009	−	0.224009i
$364$		0			0
$365$	−0.928203	+	1.85641i	−0.0485844	+	0.0971688i
$366$		0			0
$367$	10.7942	+	2.89230i	0.563454	+	0.150977i	0.529293	−	0.848439i	$-0.322457\pi$
$367$	10.7942	+	2.89230i	0.563454	+	0.150977i	0.0341614	+	0.999416i	$0.489124\pi$
$368$		0			0
$369$	−13.9282	+	13.9282i	−0.725073	+	0.725073i
$370$		0			0
$371$	0.830127	+	3.09808i	0.0430980	+	0.160844i
$372$		0			0
$373$	26.9904	−	7.23205i	1.39751	−	0.374461i	0.520059	−	0.854130i	$-0.325910\pi$
$373$	26.9904	−	7.23205i	1.39751	−	0.374461i	0.877450	+	0.479669i	$0.159243\pi$
$374$		0			0
$375$	0.473721	−	5.76795i	0.0244628	−	0.297856i
$376$		0			0
$377$	−4.30385	−	0.277568i	−0.221659	−	0.0142955i
$378$		0			0
$379$	23.5263	+	6.30385i	1.20846	+	0.323807i	0.806159	−	0.591699i	$-0.201543\pi$
$379$	23.5263	+	6.30385i	1.20846	+	0.323807i	0.402305	+	0.915506i	$0.368209\pi$
$380$		0			0
$381$	−2.08846	−	1.20577i	−0.106995	−	0.0617735i
$382$		0			0
$383$	0.696152	+	0.401924i	0.0355717	+	0.0205373i	0.517680	−	0.855574i	$-0.326796\pi$
$383$	0.696152	+	0.401924i	0.0355717	+	0.0205373i	−0.482109	+	0.876111i	$0.660129\pi$
$384$		0			0
$385$	2.70577	−	0.901924i	0.137899	−	0.0459663i
$386$		0			0
$387$	7.29423	−	27.2224i	0.370786	−	1.38379i
$388$		0			0
$389$	−3.85641			−0.195528			−0.0977638	−	0.995210i	$-0.531169\pi$
$389$	−3.85641			−0.195528			−0.0977638	+	0.995210i	$0.531169\pi$
$390$		0			0
$391$	0.411543			0.0208126
$392$		0			0
$393$	−1.85641	+	6.92820i	−0.0936433	+	0.349482i
$394$		0			0
$395$	22.9282	+	11.4641i	1.15364	+	0.576822i
$396$		0			0
$397$	−7.37564	−	4.25833i	−0.370173	−	0.213719i	0.303361	−	0.952876i	$-0.401891\pi$
$397$	−7.37564	−	4.25833i	−0.370173	−	0.213719i	−0.673534	+	0.739156i	$0.735225\pi$
$398$		0			0
$399$	0.401924	+	0.232051i	0.0201214	+	0.0116171i
$400$		0			0
$401$	5.86603	+	1.57180i	0.292935	+	0.0784918i	0.402294	−	0.915511i	$-0.368213\pi$
$401$	5.86603	+	1.57180i	0.292935	+	0.0784918i	−0.109359	+	0.994002i	$0.534880\pi$
$402$		0			0
$403$	2.26795	+	11.3397i	0.112975	+	0.564873i
$404$		0			0
$405$	−14.8660	+	0.892305i	−0.738699	+	0.0443390i
$406$		0			0
$407$	−17.1603	+	4.59808i	−0.850602	+	0.227918i
$408$		0			0
$409$	3.06218	+	11.4282i	0.151415	+	0.565088i	0.999386	+	0.0350453i	$0.0111575\pi$
$409$	3.06218	+	11.4282i	0.151415	+	0.565088i	−0.847971	+	0.530043i	$0.822176\pi$
$410$		0			0
$411$	4.09808	−	4.09808i	0.202143	−	0.202143i
$412$		0			0
$413$	−3.69615	−	0.990381i	−0.181876	−	0.0487335i
$414$		0			0
$415$	6.92820	+	3.46410i	0.340092	+	0.170046i
$416$		0			0
$417$	2.29423	−	2.29423i	0.112349	−	0.112349i
$418$		0			0
$419$	27.3564	−	15.7942i	1.33645	−	0.771599i	0.350169	−	0.936687i	$-0.386124\pi$
$419$	27.3564	−	15.7942i	1.33645	−	0.771599i	0.986279	+	0.165088i	$0.0527908\pi$
$420$		0			0
$421$	14.0718	+	14.0718i	0.685817	+	0.685817i	0.961305	−	0.275487i	$-0.0888392\pi$
$421$	14.0718	+	14.0718i	0.685817	+	0.685817i	−0.275487	+	0.961305i	$0.588839\pi$
$422$		0			0
$423$	−10.1962	+	17.6603i	−0.495754	+	0.858671i
$424$		0			0
$425$	11.6699	+	9.16025i	0.566072	+	0.444338i
$426$		0			0
$427$	−0.232051	+	0.133975i	−0.0112297	+	0.00648349i
$428$		0			0
$429$	7.96410	−	3.93782i	0.384510	−	0.190120i
$430$		0			0
$431$	8.47372	−	31.6244i	0.408165	−	1.52329i	−0.389979	−	0.920824i	$-0.627518\pi$
$431$	8.47372	−	31.6244i	0.408165	−	1.52329i	0.798143	−	0.602468i	$-0.205816\pi$
$432$		0			0
$433$	2.72243	+	10.1603i	0.130832	+	0.488271i	0.999980	−	0.00628046i	$-0.00199914\pi$
$433$	2.72243	+	10.1603i	0.130832	+	0.488271i	−0.869149	+	0.494551i	$0.835332\pi$
$434$		0			0
$435$	−1.35641	−	0.277568i	−0.0650347	−	0.0133084i
$436$		0			0
$437$			0.464102i			0.0222010i
$438$		0			0
$439$	5.96410	+	10.3301i	0.284651	+	0.493030i	0.972524	−	0.232801i	$-0.0747889\pi$
$439$	5.96410	+	10.3301i	0.284651	+	0.493030i	−0.687873	+	0.725831i	$0.741456\pi$
$440$		0			0
$441$		−	18.9282i		−	0.901343i
$442$		0			0
$443$	27.0526	+	27.0526i	1.28531	+	1.28531i	0.937606	+	0.347700i	$0.113037\pi$
$443$	27.0526	+	27.0526i	1.28531	+	1.28531i	0.347700	+	0.937606i	$0.386963\pi$
$444$		0			0
$445$	−5.13397	−	4.55256i	−0.243374	−	0.215812i
$446$		0			0
$447$	−8.51666			−0.402824
$448$		0			0
$449$	−23.9904	+	6.42820i	−1.13218	+	0.303366i	−0.775801	−	0.630977i	$-0.782654\pi$
$449$	−23.9904	+	6.42820i	−1.13218	+	0.303366i	−0.356375	+	0.934343i	$0.615987\pi$
$450$		0			0
$451$	−17.1603	+	29.7224i	−0.808045	+	1.39957i
$452$		0			0
$453$	−4.09808	−	7.09808i	−0.192544	−	0.333497i
$454$		0			0
$455$	2.16025	+	0.00961894i	0.101274	+	0.000450943i
$456$		0			0
$457$	14.6962	+	25.4545i	0.687457	+	1.19071i	0.972658	+	0.232243i	$0.0746064\pi$
$457$	14.6962	+	25.4545i	0.687457	+	1.19071i	−0.285201	+	0.958468i	$0.592060\pi$
$458$		0			0
$459$	−4.40192	+	7.62436i	−0.205464	+	0.355874i
$460$		0			0
$461$	−23.9904	+	6.42820i	−1.11734	+	0.299391i	−0.769808	−	0.638276i	$-0.779648\pi$
$461$	−23.9904	+	6.42820i	−1.11734	+	0.299391i	−0.347535	+	0.937667i	$0.612981\pi$
$462$		0			0
$463$	−29.8564			−1.38754			−0.693772	−	0.720194i	$-0.744053\pi$
$463$	−29.8564			−1.38754			−0.693772	+	0.720194i	$0.744053\pi$
$464$		0			0
$465$	0.222432	+	3.70577i	0.0103150	+	0.171851i
$466$		0			0
$467$	20.1244	+	20.1244i	0.931244	+	0.931244i	0.997784	−	0.0665397i	$-0.0211959\pi$
$467$	20.1244	+	20.1244i	0.931244	+	0.931244i	−0.0665397	+	0.997784i	$0.521196\pi$
$468$		0			0
$469$			3.33975i			0.154215i
$470$		0			0
$471$	−4.90192	−	8.49038i	−0.225869	−	0.391216i
$472$		0			0
$473$		−	49.1051i		−	2.25786i
$474$		0			0
$475$	−10.3301	+	13.1603i	−0.473979	+	0.603834i
$476$		0			0
$477$	−8.46410	−	31.5885i	−0.387545	−	1.44634i
$478$		0			0
$479$	1.00962	−	3.76795i	0.0461307	−	0.172162i	−0.939017	−	0.343870i	$-0.888262\pi$
$479$	1.00962	−	3.76795i	0.0461307	−	0.172162i	0.985148	+	0.171708i	$0.0549286\pi$
$480$		0			0
$481$	−13.4282	−	0.866025i	−0.612273	−	0.0394874i
$482$		0			0
$483$	0.0166605	−	0.00961894i	0.000758079	−	0.000437677i
$484$		0			0
$485$	3.03590	+	4.59808i	0.137853	+	0.208788i
$486$		0			0
$487$	17.1603	−	29.7224i	0.777605	−	1.34685i	−0.155713	−	0.987802i	$-0.549768\pi$
$487$	17.1603	−	29.7224i	0.777605	−	1.34685i	0.933318	−	0.359050i	$-0.116899\pi$
$488$		0			0
$489$	−3.09808	−	3.09808i	−0.140100	−	0.140100i
$490$		0			0
$491$	−13.9641	+	8.06218i	−0.630191	+	0.363841i	−0.780826	−	0.624748i	$-0.785202\pi$
$491$	−13.9641	+	8.06218i	−0.630191	+	0.363841i	0.150635	+	0.988589i	$0.451868\pi$
$492$		0			0
$493$	2.50962	−	2.50962i	0.113028	−	0.113028i
$494$		0			0
$495$	−27.5885	+	9.19615i	−1.24001	+	0.413336i
$496$		0			0
$497$	−0.767949	−	0.205771i	−0.0344472	−	0.00923011i
$498$		0			0
$499$	3.19615	−	3.19615i	0.143079	−	0.143079i	−0.631939	−	0.775018i	$-0.717741\pi$
$499$	3.19615	−	3.19615i	0.143079	−	0.143079i	0.775018	+	0.631939i	$0.217741\pi$
$500$		0			0
$501$	1.42820	+	5.33013i	0.0638074	+	0.238133i
$502$		0			0
$503$	15.0622	−	4.03590i	0.671589	−	0.179952i	0.0931187	−	0.995655i	$-0.470316\pi$
$503$	15.0622	−	4.03590i	0.671589	−	0.179952i	0.578471	+	0.815703i	$0.303650\pi$
$504$		0			0
$505$	0.232051	+	3.86603i	0.0103261	+	0.172036i
$506$		0			0
$507$	6.66987	−	0.892305i	0.296219	−	0.0396286i
$508$		0			0
$509$	8.79423	+	2.35641i	0.389797	+	0.104446i	0.448394	−	0.893836i	$-0.351996\pi$
$509$	8.79423	+	2.35641i	0.389797	+	0.104446i	−0.0585970	+	0.998282i	$0.518663\pi$
$510$		0			0
$511$	−0.215390	−	0.124356i	−0.00952831	−	0.00550117i
$512$		0			0
$513$	−8.59808	−	4.96410i	−0.379614	−	0.219170i
$514$		0			0
$515$	−10.6603	−	31.9808i	−0.469747	−	1.40924i
$516$		0			0
$517$	−9.19615	+	34.3205i	−0.404446	+	1.50941i
$518$		0			0
$519$	6.80385			0.298656
$520$		0			0
$521$	3.85641			0.168952			0.0844761	−	0.996426i	$-0.473078\pi$
$521$	3.85641			0.168952			0.0844761	+	0.996426i	$0.473078\pi$
$522$		0			0
$523$	9.06218	−	33.8205i	0.396261	−	1.47887i	−0.423360	−	0.905962i	$-0.639149\pi$
$523$	9.06218	−	33.8205i	0.396261	−	1.47887i	0.819621	−	0.572906i	$-0.194184\pi$
$524$		0			0
$525$	0.686533	+	0.0980762i	0.0299628	+	0.00428040i
$526$		0			0
$527$	−8.24167	−	4.75833i	−0.359013	−	0.207276i
$528$		0			0
$529$	−19.9019	−	11.4904i	−0.865301	−	0.499582i
$530$		0			0
$531$	37.6865	+	10.0981i	1.63546	+	0.438219i
$532$		0			0
$533$	−19.5263	+	17.1603i	−0.845777	+	0.743293i
$534$		0			0
$535$	5.52628	−	6.23205i	0.238922	−	0.269435i
$536$		0			0
$537$	−0.964102	+	0.258330i	−0.0416041	+	0.0111478i
$538$		0			0
$539$	−8.53590	−	31.8564i	−0.367667	−	1.37215i
$540$		0			0
$541$	14.0718	−	14.0718i	0.604994	−	0.604994i	−0.336640	−	0.941634i	$-0.609290\pi$
$541$	14.0718	−	14.0718i	0.604994	−	0.604994i	0.941634	+	0.336640i	$0.109290\pi$
$542$		0			0
$543$	0.535898	+	0.143594i	0.0229976	+	0.00616219i
$544$		0			0
$545$	−11.3923	−	34.1769i	−0.487993	−	1.46398i
$546$		0			0
$547$	−9.19615	+	9.19615i	−0.393199	+	0.393199i	−0.875826	−	0.482627i	$-0.839683\pi$
$547$	−9.19615	+	9.19615i	−0.393199	+	0.393199i	0.482627	+	0.875826i	$0.339683\pi$
$548$		0			0
$549$	2.36603	−	1.36603i	0.100980	−	0.0583005i
$550$		0			0
$551$	2.83013	+	2.83013i	0.120567	+	0.120567i
$552$		0			0
$553$	−1.53590	+	2.66025i	−0.0653130	+	0.113126i
$554$		0			0
$555$	−4.23205	−	0.866025i	−0.179641	−	0.0367607i
$556$		0			0
$557$	−17.7679	+	10.2583i	−0.752852	+	0.434659i	−0.826724	−	0.562608i	$-0.809798\pi$
$557$	−17.7679	+	10.2583i	−0.752852	+	0.434659i	0.0738714	+	0.997268i	$0.476465\pi$
$558$		0			0
$559$	11.9186	−	35.2321i	0.504102	−	1.49016i
$560$		0			0
$561$	−1.89230	+	7.06218i	−0.0798932	+	0.298165i
$562$		0			0
$563$	−8.52628	−	31.8205i	−0.359340	−	1.34107i	−0.874934	−	0.484242i	$-0.839096\pi$
$563$	−8.52628	−	31.8205i	−0.359340	−	1.34107i	0.515594	−	0.856833i	$-0.327571\pi$
$564$		0			0
$565$	−7.20577	+	35.2128i	−0.303149	+	1.48141i
$566$		0			0
$567$		−	1.78461i		−	0.0749466i
$568$		0			0
$569$	1.57180	+	2.72243i	0.0658931	+	0.114130i	0.897090	−	0.441848i	$-0.145677\pi$
$569$	1.57180	+	2.72243i	0.0658931	+	0.114130i	−0.831197	+	0.555978i	$0.812344\pi$
$570$		0			0
$571$			42.1051i			1.76204i	0.473075	+	0.881022i	$0.343144\pi$
$571$			42.1051i			1.76204i	−0.473075	+	0.881022i	$0.656856\pi$
$572$		0			0
$573$	3.68653	+	3.68653i	0.154007	+	0.154007i
$574$		0			0
$575$	0.258330	+	0.643594i	0.0107731	+	0.0268397i
$576$		0			0
$577$	−28.9282			−1.20430			−0.602148	−	0.798384i	$-0.705688\pi$
$577$	−28.9282			−1.20430			−0.602148	+	0.798384i	$0.705688\pi$
$578$		0			0
$579$	−5.16025	+	1.38269i	−0.214453	+	0.0574625i
$580$		0			0
$581$	−0.464102	+	0.803848i	−0.0192542	+	0.0333492i
$582$		0			0
$583$	−28.4904	−	49.3468i	−1.17995	−	2.04374i
$584$		0			0
$585$	−22.0263	−	0.0980762i	−0.910675	−	0.00405495i
$586$		0			0
$587$	−13.1603	−	22.7942i	−0.543182	−	0.940819i	−0.998719	−	0.0506017i	$-0.983886\pi$
$587$	−13.1603	−	22.7942i	−0.543182	−	0.940819i	0.455537	−	0.890217i	$-0.349447\pi$
$588$		0			0
$589$	5.36603	−	9.29423i	0.221103	−	0.382962i
$590$		0			0
$591$	10.1603	−	2.72243i	0.417937	−	0.111986i
$592$		0			0
$593$	−7.07180			−0.290404			−0.145202	−	0.989402i	$-0.546383\pi$
$593$	−7.07180			−0.290404			−0.145202	+	0.989402i	$0.546383\pi$
$594$		0			0
$595$	−1.17949	+	1.33013i	−0.0483545	+	0.0545299i
$596$		0			0
$597$	1.43782	+	1.43782i	0.0588461	+	0.0588461i
$598$		0			0
$599$		−	5.60770i		−	0.229124i	−0.993416	−	0.114562i	$-0.963454\pi$
$599$		−	5.60770i		−	0.229124i	0.993416	−	0.114562i	$-0.0365465\pi$
$600$		0			0
$601$	−4.57180	−	7.91858i	−0.186487	−	0.323006i	0.757589	−	0.652732i	$-0.226377\pi$
$601$	−4.57180	−	7.91858i	−0.186487	−	0.323006i	−0.944077	+	0.329726i	$0.893044\pi$
$602$		0			0
$603$		−	34.0526i		−	1.38673i
$604$		0			0
$605$	−21.7583	+	14.3660i	−0.884602	+	0.584062i
$606$		0			0
$607$	8.93782	+	33.3564i	0.362775	+	1.35389i	0.870412	+	0.492324i	$0.163852\pi$
$607$	8.93782	+	33.3564i	0.362775	+	1.35389i	−0.507637	+	0.861571i	$0.669481\pi$
$608$		0			0
$609$	0.0429399	−	0.160254i	0.00174001	−	0.00649382i
$610$		0			0
$611$	−14.9282	+	22.3923i	−0.603930	+	0.905896i
$612$		0			0
$613$	−9.23205	+	5.33013i	−0.372879	+	0.215282i	−0.674715	−	0.738078i	$-0.735734\pi$
$613$	−9.23205	+	5.33013i	−0.372879	+	0.215282i	0.301836	+	0.953360i	$0.402400\pi$
$614$		0			0
$615$	−6.96410	+	4.59808i	−0.280820	+	0.185412i
$616$		0			0
$617$	−16.0885	+	27.8660i	−0.647697	+	1.12184i	0.335975	+	0.941871i	$0.390934\pi$
$617$	−16.0885	+	27.8660i	−0.647697	+	1.12184i	−0.983672	+	0.179973i	$0.942399\pi$
$618$		0			0
$619$	5.87564	+	5.87564i	0.236162	+	0.236162i	0.815259	−	0.579097i	$-0.196595\pi$
$619$	5.87564	+	5.87564i	0.236162	+	0.236162i	−0.579097	+	0.815259i	$0.696595\pi$
$620$		0			0
$621$	−0.356406	+	0.205771i	−0.0143021	+	0.00825732i
$622$		0			0
$623$	0.581416	−	0.581416i	0.0232939	−	0.0232939i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	−7.96410	−	2.13397i	−0.318056	−	0.0852227i
$628$		0			0
$629$	7.83013	−	7.83013i	0.312208	−	0.312208i
$630$		0			0
$631$	6.20577	+	23.1603i	0.247048	+	0.921995i	0.972343	+	0.233557i	$0.0750366\pi$
$631$	6.20577	+	23.1603i	0.247048	+	0.921995i	−0.725295	+	0.688438i	$0.758297\pi$
$632$		0			0
$633$	−4.96410	+	1.33013i	−0.197305	+	0.0528678i
$634$		0			0
$635$	7.79423	+	6.91154i	0.309305	+	0.274276i
$636$		0			0
$637$	1.60770	−	24.9282i	0.0636992	−	0.987691i
$638$		0			0
$639$	7.83013	+	2.09808i	0.309755	+	0.0829986i
$640$		0			0
$641$	40.2846	+	23.2583i	1.59115	+	0.918649i	0.993111	+	0.117179i	$0.0373852\pi$
$641$	40.2846	+	23.2583i	1.59115	+	0.918649i	0.598036	+	0.801470i	$0.295948\pi$
$642$		0			0
$643$	35.7679	+	20.6506i	1.41055	+	0.814382i	0.995440	−	0.0953896i	$-0.0304097\pi$
$643$	35.7679	+	20.6506i	1.41055	+	0.814382i	0.415110	+	0.909771i	$0.363743\pi$
$644$		0			0
$645$	5.33975	−	10.6795i	0.210252	−	0.420505i
$646$		0			0
$647$	−0.794229	+	2.96410i	−0.0312243	+	0.116531i	−0.979779	−	0.200082i	$-0.935879\pi$
$647$	−0.794229	+	2.96410i	−0.0312243	+	0.116531i	0.948555	+	0.316613i	$0.102546\pi$
$648$		0			0
$649$	67.9808			2.66848
$650$		0			0
$651$	−0.444864			−0.0174356
$652$		0			0
$653$	0.186533	−	0.696152i	0.00729962	−	0.0272425i	−0.962180	−	0.272415i	$-0.912178\pi$
$653$	0.186533	−	0.696152i	0.00729962	−	0.0272425i	0.969480	+	0.245172i	$0.0788444\pi$
$654$		0			0
$655$	13.8564	−	27.7128i	0.541415	−	1.08283i
$656$		0			0
$657$	2.19615	+	1.26795i	0.0856801	+	0.0494674i
$658$		0			0
$659$	−29.2128	−	16.8660i	−1.13797	−	0.657007i	−0.192043	−	0.981387i	$-0.561511\pi$
$659$	−29.2128	−	16.8660i	−1.13797	−	0.657007i	−0.945927	+	0.324380i	$0.894845\pi$
$660$		0			0
$661$	−1.59808	−	0.428203i	−0.0621580	−	0.0166552i	0.227606	−	0.973753i	$-0.426910\pi$
$661$	−1.59808	−	0.428203i	−0.0621580	−	0.0166552i	−0.289764	+	0.957098i	$0.593577\pi$
$662$		0			0
$663$	−3.07180	+	4.60770i	−0.119299	+	0.178948i
$664$		0			0
$665$	−1.50000	−	1.33013i	−0.0581675	−	0.0515801i
$666$		0			0
$667$	0.160254	−	0.0429399i	0.00620506	−	0.00166264i
$668$		0			0
$669$	2.64359	+	9.86603i	0.102207	+	0.381443i
$670$		0			0
$671$	3.36603	−	3.36603i	0.129944	−	0.129944i
$672$		0			0
$673$	26.9904	+	7.23205i	1.04040	+	0.278775i	0.738280	−	0.674494i	$-0.235638\pi$
$673$	26.9904	+	7.23205i	1.04040	+	0.278775i	0.302122	+	0.953269i	$0.402305\pi$
$674$		0			0
$675$	−14.6865	−	2.09808i	−0.565285	−	0.0807550i
$676$		0			0
$677$	−10.3205	+	10.3205i	−0.396649	+	0.396649i	−0.877049	−	0.480400i	$-0.840491\pi$
$677$	−10.3205	+	10.3205i	−0.396649	+	0.396649i	0.480400	+	0.877049i	$0.340491\pi$
$678$		0			0
$679$	−0.571797	+	0.330127i	−0.0219435	+	0.0126691i
$680$		0			0
$681$	−0.169873	−	0.169873i	−0.00650955	−	0.00650955i
$682$		0			0
$683$	−15.2321	+	26.3827i	−0.582838	+	1.00951i	0.412303	+	0.911047i	$0.364725\pi$
$683$	−15.2321	+	26.3827i	−0.582838	+	1.00951i	−0.995141	+	0.0984586i	$0.968609\pi$
$684$		0			0
$685$	−20.8923	+	13.7942i	−0.798254	+	0.527050i
$686$		0			0
$687$	6.88269	−	3.97372i	0.262591	−	0.151607i
$688$		0			0
$689$	−8.46410	−	42.3205i	−0.322457	−	1.61228i
$690$		0			0
$691$	−0.0621778	+	0.232051i	−0.00236536	+	0.00882763i	−0.967098	−	0.254403i	$-0.918121\pi$
$691$	−0.0621778	+	0.232051i	−0.00236536	+	0.00882763i	0.964733	+	0.263230i	$0.0847879\pi$
$692$		0			0
$693$	−0.901924	−	3.36603i	−0.0342613	−	0.127865i
$694$		0			0
$695$	−11.6962	+	7.72243i	−0.443660	+	0.292929i
$696$		0			0
$697$		−	21.3923i		−	0.810291i
$698$		0			0
$699$	4.02628	+	6.97372i	0.152288	+	0.263770i
$700$		0			0
$701$		−	29.0718i		−	1.09803i	−0.835814	−	0.549013i	$-0.815004\pi$
$701$		−	29.0718i		−	1.09803i	0.835814	−	0.549013i	$-0.184996\pi$
$702$		0			0
$703$	8.83013	+	8.83013i	0.333035	+	0.333035i
$704$		0			0
$705$	−5.73205	+	6.46410i	−0.215882	+	0.243452i
$706$		0			0
$707$	−0.464102			−0.0174543
$708$		0			0
$709$	−5.59808	+	1.50000i	−0.210240	+	0.0563337i	−0.362402	−	0.932022i	$-0.618043\pi$
$709$	−5.59808	+	1.50000i	−0.210240	+	0.0563337i	0.152162	+	0.988356i	$0.451377\pi$
$710$		0			0
$711$	15.6603	−	27.1244i	0.587305	−	1.01724i
$712$		0			0
$713$	−0.222432	−	0.385263i	−0.00833014	−	0.0144282i
$714$		0			0
$715$	−37.1147	+	9.76795i	−1.38801	+	0.365301i
$716$		0			0
$717$	3.36603	+	5.83013i	0.125707	+	0.217730i
$718$		0			0
$719$	−14.8923	+	25.7942i	−0.555389	+	0.961962i	0.442484	+	0.896776i	$0.354097\pi$
$719$	−14.8923	+	25.7942i	−0.555389	+	0.961962i	−0.997873	+	0.0651859i	$0.979236\pi$
$720$		0			0
$721$	3.90192	−	1.04552i	0.145315	−	0.0389371i
$722$		0			0
$723$	−9.87564			−0.367279
$724$		0			0
$725$	5.50000	+	2.34936i	0.204265	+	0.0872532i
$726$		0			0
$727$	13.5885	+	13.5885i	0.503968	+	0.503968i	0.912669	−	0.408701i	$-0.134018\pi$
$727$	13.5885	+	13.5885i	0.503968	+	0.503968i	−0.408701	+	0.912669i	$0.634018\pi$
$728$		0			0
$729$			13.5885i			0.503276i
$730$		0			0
$731$	15.3038	+	26.5070i	0.566033	+	0.980398i
$732$		0			0
$733$		−	38.6410i		−	1.42724i	−0.700534	−	0.713619i	$-0.747055\pi$
$733$		−	38.6410i		−	1.42724i	0.700534	−	0.713619i	$-0.252945\pi$
$734$		0			0
$735$	1.60770	−	7.85641i	0.0593007	−	0.289788i
$736$		0			0
$737$	−15.3564	−	57.3109i	−0.565661	−	2.11107i
$738$		0			0
$739$	−10.7417	+	40.0885i	−0.395139	+	1.47468i	0.426405	+	0.904532i	$0.359780\pi$
$739$	−10.7417	+	40.0885i	−0.395139	+	1.47468i	−0.821544	+	0.570145i	$0.806887\pi$
$740$		0			0
$741$	−5.19615	−	3.46410i	−0.190885	−	0.127257i
$742$		0			0
$743$	30.4808	−	17.5981i	1.11823	−	0.645611i	0.177282	−	0.984160i	$-0.443270\pi$
$743$	30.4808	−	17.5981i	1.11823	−	0.645611i	0.940949	+	0.338549i	$0.109936\pi$
$744$		0			0
$745$	36.0429	+	7.37564i	1.32051	+	0.270223i
$746$		0			0
$747$	4.73205	−	8.19615i	0.173137	−	0.299882i
$748$		0			0
$749$	0.705771	+	0.705771i	0.0257883	+	0.0257883i
$750$		0			0
$751$	31.7487	−	18.3301i	1.15853	−	0.668876i	0.207576	−	0.978219i	$-0.433442\pi$
$751$	31.7487	−	18.3301i	1.15853	−	0.668876i	0.950951	+	0.309343i	$0.100109\pi$
$752$		0			0
$753$	−10.0981	+	10.0981i	−0.367994	+	0.367994i
$754$		0			0
$755$	11.1962	+	33.5885i	0.407470	+	1.22241i
$756$		0			0
$757$	16.0622	+	4.30385i	0.583790	+	0.156426i	0.538613	−	0.842553i	$-0.318948\pi$
$757$	16.0622	+	4.30385i	0.583790	+	0.156426i	0.0451764	+	0.998979i	$0.485615\pi$
$758$		0			0
$759$	−0.241670	+	0.241670i	−0.00877206	+	0.00877206i
$760$		0			0
$761$	2.66987	+	9.96410i	0.0967828	+	0.361198i	0.997284	−	0.0736557i	$-0.0234666\pi$
$761$	2.66987	+	9.96410i	0.0967828	+	0.361198i	−0.900501	+	0.434854i	$0.856800\pi$
$762$		0			0
$763$	4.16987	−	1.11731i	0.150960	−	0.0404495i
$764$		0			0
$765$	12.0263	−	13.5622i	0.434811	−	0.490342i
$766$		0			0
$767$	48.7750	+	16.5000i	1.76116	+	0.595780i
$768$		0			0
$769$	5.33013	+	1.42820i	0.192209	+	0.0515023i	0.353639	−	0.935382i	$-0.384944\pi$
$769$	5.33013	+	1.42820i	0.192209	+	0.0515023i	−0.161430	+	0.986884i	$0.551611\pi$
$770$		0			0
$771$	6.10770	+	3.52628i	0.219963	+	0.126996i
$772$		0			0
$773$	36.4808	+	21.0622i	1.31212	+	0.757554i	0.982447	−	0.186541i	$-0.0597276\pi$
$773$	36.4808	+	21.0622i	1.31212	+	0.757554i	0.329675	+	0.944095i	$0.393061\pi$
$774$		0			0
$775$	2.26795	−	15.8756i	0.0814671	−	0.570270i
$776$		0			0
$777$	0.133975	−	0.500000i	0.00480631	−	0.0179374i
$778$		0			0
$779$	24.1244			0.864345
$780$		0			0
$781$	14.1244			0.505409
$782$		0			0
$783$	−0.918584	+	3.42820i	−0.0328275	+	0.122514i
$784$		0			0
$785$	13.3923	+	40.1769i	0.477992	+	1.43398i
$786$		0			0
$787$	−38.0885	−	21.9904i	−1.35771	−	0.783872i	−0.368392	−	0.929670i	$-0.620092\pi$
$787$	−38.0885	−	21.9904i	−1.35771	−	0.783872i	−0.989314	+	0.145798i	$0.953425\pi$
$788$		0			0
$789$	8.30385	+	4.79423i	0.295625	+	0.170679i
$790$		0			0
$791$	−4.16025	−	1.11474i	−0.147922	−	0.0396355i
$792$		0			0
$793$	3.23205	−	1.59808i	0.114773	−	0.0567494i
$794$		0			0
$795$	−0.830127	−	13.8301i	−0.0294416	−	0.490504i
$796$		0			0
$797$	−24.7224	+	6.62436i	−0.875713	+	0.234647i	−0.668557	−	0.743661i	$-0.733088\pi$
$797$	−24.7224	+	6.62436i	−0.875713	+	0.234647i	−0.207157	+	0.978308i	$0.566421\pi$
$798$		0			0
$799$	−5.73205	−	21.3923i	−0.202785	−	0.756805i
$800$		0			0
$801$	−5.92820	+	5.92820i	−0.209463	+	0.209463i
$802$		0			0
$803$	4.26795	+	1.14359i	0.150613	+	0.0403565i
$804$		0			0
$805$	−0.0788383	+	0.0262794i	−0.00277869	+	0.000926229i
$806$		0			0
$807$	−9.90192	+	9.90192i	−0.348564	+	0.348564i
$808$		0			0
$809$	29.8923	−	17.2583i	1.05096	−	0.606771i	0.128040	−	0.991769i	$-0.459131\pi$
$809$	29.8923	−	17.2583i	1.05096	−	0.606771i	0.922917	+	0.384998i	$0.125798\pi$
$810$		0			0
$811$	32.1244	+	32.1244i	1.12804	+	1.12804i	0.990496	+	0.137543i	$0.0439205\pi$
$811$	32.1244	+	32.1244i	1.12804	+	1.12804i	0.137543	+	0.990496i	$0.456080\pi$
$812$		0			0
$813$	−5.30385	+	9.18653i	−0.186014	+	0.322186i
$814$		0			0
$815$	10.4282	+	15.7942i	0.365284	+	0.553248i
$816$		0			0
$817$	−29.8923	+	17.2583i	−1.04580	+	0.603793i
$818$		0			0
$819$	0.169873	−	2.63397i	0.00593584	−	0.0920385i
$820$		0			0
$821$	−4.40192	+	16.4282i	−0.153628	+	0.573348i	0.845591	+	0.533832i	$0.179248\pi$
$821$	−4.40192	+	16.4282i	−0.153628	+	0.573348i	−0.999219	+	0.0395165i	$0.987418\pi$
$822$		0			0
$823$	−4.91858	−	18.3564i	−0.171451	−	0.639864i	−0.997129	−	0.0757222i	$-0.975874\pi$
$823$	−4.91858	−	18.3564i	−0.171451	−	0.639864i	0.825678	−	0.564142i	$-0.190793\pi$
$824$		0			0
$825$	−12.2321	+	1.47372i	−0.425865	+	0.0513084i
$826$		0			0
$827$			24.5359i			0.853197i	0.904441	+	0.426598i	$0.140288\pi$
$827$			24.5359i			0.853197i	−0.904441	+	0.426598i	$0.859712\pi$
$828$		0			0
$829$	1.03590	+	1.79423i	0.0359782	+	0.0623161i	0.883454	−	0.468518i	$-0.155212\pi$
$829$	1.03590	+	1.79423i	0.0359782	+	0.0623161i	−0.847476	+	0.530834i	$0.821879\pi$
$830$		0			0
$831$		−	12.3205i		−	0.427394i
$832$		0			0
$833$	14.5359	+	14.5359i	0.503639	+	0.503639i
$834$		0			0
$835$	−1.42820	−	23.7942i	−0.0494250	−	0.823433i
$836$		0			0
$837$	9.51666			0.328944
$838$		0			0
$839$	−25.5263	+	6.83975i	−0.881265	+	0.236134i	−0.670953	−	0.741500i	$-0.734115\pi$
$839$	−25.5263	+	6.83975i	−0.881265	+	0.236134i	−0.210312	+	0.977634i	$0.567448\pi$
$840$		0			0
$841$	−13.7846	+	23.8756i	−0.475331	+	0.823298i
$842$		0			0
$843$	2.70577	+	4.68653i	0.0931917	+	0.161413i
$844$		0			0
$845$	−29.0000	−	2.00000i	−0.997630	−	0.0688021i
$846$		0			0
$847$	−1.56218	−	2.70577i	−0.0536771	−	0.0929714i
$848$		0			0
$849$	−3.35641	+	5.81347i	−0.115192	+	0.199518i
$850$		0			0
$851$	0.500000	−	0.133975i	0.0171398	−	0.00459259i
$852$		0			0
$853$	−55.5692			−1.90265			−0.951327	−	0.308184i	$-0.900279\pi$
$853$	−55.5692			−1.90265			−0.951327	+	0.308184i	$0.900279\pi$
$854$		0			0
$855$	15.2942	+	13.5622i	0.523052	+	0.463817i
$856$		0			0
$857$	8.60770	+	8.60770i	0.294033	+	0.294033i	0.838671	−	0.544638i	$-0.183333\pi$
$857$	8.60770	+	8.60770i	0.294033	+	0.294033i	−0.544638	+	0.838671i	$0.683333\pi$
$858$		0			0
$859$			46.1051i			1.57309i	0.617535	+	0.786543i	$0.288131\pi$
$859$			46.1051i			1.57309i	−0.617535	+	0.786543i	$0.711869\pi$
$860$		0			0
$861$	−0.500000	−	0.866025i	−0.0170400	−	0.0295141i
$862$		0			0
$863$		−	20.2487i		−	0.689274i	−0.938736	−	0.344637i	$-0.888002\pi$
$863$		−	20.2487i		−	0.689274i	0.938736	−	0.344637i	$-0.111998\pi$
$864$		0			0
$865$	−28.7942	−	5.89230i	−0.979033	−	0.200344i
$866$		0			0
$867$	1.09808	+	4.09808i	0.0372926	+	0.139178i
$868$		0			0
$869$	14.1244	−	52.7128i	0.479136	−	1.78816i
$870$		0			0
$871$	2.89230	−	44.8468i	0.0980020	−	1.51958i
$872$		0			0
$873$	5.83013	−	3.36603i	0.197320	−	0.113923i
$874$		0			0
$875$	−2.82051	−	1.00962i	−0.0953506	−	0.0341313i
$876$		0			0
$877$	20.5526	−	35.5981i	0.694011	−	1.20206i	−0.276502	−	0.961013i	$-0.589175\pi$
$877$	20.5526	−	35.5981i	0.694011	−	1.20206i	0.970513	−	0.241048i	$-0.0774913\pi$
$878$		0			0
$879$	−8.22243	−	8.22243i	−0.277336	−	0.277336i
$880$		0			0
$881$	−1.96410	+	1.13397i	−0.0661723	+	0.0382046i	−0.532721	−	0.846291i	$-0.678831\pi$
$881$	−1.96410	+	1.13397i	−0.0661723	+	0.0382046i	0.466549	+	0.884495i	$0.345497\pi$
$882$		0			0
$883$	−16.8038	+	16.8038i	−0.565494	+	0.565494i	−0.930863	−	0.365368i	$-0.880943\pi$
$883$	−16.8038	+	16.8038i	−0.565494	+	0.565494i	0.365368	+	0.930863i	$0.380943\pi$
$884$		0			0
$885$	14.7846	+	7.39230i	0.496979	+	0.248490i
$886$		0			0
$887$	2.79423	+	0.748711i	0.0938210	+	0.0251393i	0.305424	−	0.952216i	$-0.401202\pi$
$887$	2.79423	+	0.748711i	0.0938210	+	0.0251393i	−0.211603	+	0.977356i	$0.567868\pi$
$888$		0			0
$889$	−0.882686	+	0.882686i	−0.0296043	+	0.0296043i
$890$		0			0
$891$	8.20577	+	30.6244i	0.274904	+	1.02595i
$892$		0			0
$893$	24.1244	−	6.46410i	0.807291	−	0.216313i
$894$		0			0
$895$	4.30385	−	0.258330i	0.143862	−	0.00863503i
$896$		0			0
$897$	−0.232051	+	0.114737i	−0.00774795	+	0.00383095i
$898$		0			0
$899$	−3.70577	−	0.992958i	−0.123594	−	0.0331170i
$900$		0			0
$901$	30.7583	+	17.7583i	1.02471	+	0.591616i
$902$		0			0
$903$	1.23909	+	0.715390i	0.0412344	+	0.0238067i
$904$		0			0
$905$	−2.14359	−	1.07180i	−0.0712555	−	0.0356277i
$906$		0			0
$907$	−3.47372	+	12.9641i	−0.115343	+	0.430466i	−0.999312	−	0.0370789i	$-0.988195\pi$
$907$	−3.47372	+	12.9641i	−0.115343	+	0.430466i	0.883969	+	0.467545i	$0.154861\pi$
$908$		0			0
$909$	4.73205			0.156952
$910$		0			0
$911$	−29.0718			−0.963192			−0.481596	−	0.876393i	$-0.659943\pi$
$911$	−29.0718			−0.963192			−0.481596	+	0.876393i	$0.659943\pi$
$912$		0			0
$913$	4.26795	−	15.9282i	0.141249	−	0.527147i
$914$		0			0
$915$	1.09808	−	0.366025i	0.0363013	−	0.0121004i
$916$		0			0
$917$	3.21539	+	1.85641i	0.106182	+	0.0613039i
$918$		0			0
$919$	−37.7487	−	21.7942i	−1.24522	−	0.718925i	−0.275064	−	0.961426i	$-0.588699\pi$
$919$	−37.7487	−	21.7942i	−1.24522	−	0.718925i	−0.970151	+	0.242501i	$0.922032\pi$
$920$		0			0
$921$	15.1962	+	4.07180i	0.500730	+	0.134170i
$922$		0			0
$923$	10.1340	+	3.42820i	0.333564	+	0.112841i
$924$		0			0
$925$	17.1603	+	7.33013i	0.564226	+	0.241013i
$926$		0			0
$927$	−39.7846	+	10.6603i	−1.30670	+	0.350129i
$928$		0			0
$929$	−0.794229	−	2.96410i	−0.0260578	−	0.0972490i	0.951672	−	0.307115i	$-0.0993638\pi$
$929$	−0.794229	−	2.96410i	−0.0260578	−	0.0972490i	−0.977730	+	0.209866i	$0.932697\pi$
$930$		0			0
$931$	−16.3923	+	16.3923i	−0.537236	+	0.537236i
$932$		0			0
$933$	−8.12436	−	2.17691i	−0.265979	−	0.0712690i
$934$		0			0
$935$	14.1244	−	28.2487i	0.461916	−	0.923832i
$936$		0			0
$937$	41.7846	−	41.7846i	1.36504	−	1.36504i	0.497687	−	0.867357i	$-0.334183\pi$
$937$	41.7846	−	41.7846i	1.36504	−	1.36504i	0.867357	−	0.497687i	$-0.165817\pi$
$938$		0			0
$939$	12.8827	−	7.43782i	0.420411	−	0.242724i
$940$		0			0
$941$	−19.0000	−	19.0000i	−0.619382	−	0.619382i	0.325991	−	0.945373i	$-0.394302\pi$
$941$	−19.0000	−	19.0000i	−0.619382	−	0.619382i	−0.945373	+	0.325991i	$0.894302\pi$
$942$		0			0
$943$	0.500000	−	0.866025i	0.0162822	−	0.0282017i
$944$		0			0
$945$	0.356406	−	1.74167i	0.0115939	−	0.0566565i
$946$		0			0
$947$	3.01666	−	1.74167i	0.0980283	−	0.0565967i	−0.450184	−	0.892936i	$-0.648642\pi$
$947$	3.01666	−	1.74167i	0.0980283	−	0.0565967i	0.548213	+	0.836339i	$0.315308\pi$
$948$		0			0
$949$	2.78461	+	1.85641i	0.0903923	+	0.0602615i
$950$		0			0
$951$	−0.411543	+	1.53590i	−0.0133452	+	0.0498049i
$952$		0			0
$953$	−4.99038	−	18.6244i	−0.161654	−	0.603302i	−0.998443	−	0.0557765i	$-0.982237\pi$
$953$	−4.99038	−	18.6244i	−0.161654	−	0.603302i	0.836789	−	0.547526i	$-0.184430\pi$
$954$		0			0
$955$	−12.4090	−	18.7942i	−0.401545	−	0.608167i
$956$		0			0
$957$			2.94744i			0.0952772i
$958$		0			0
$959$	−1.50000	−	2.59808i	−0.0484375	−	0.0838963i
$960$		0			0
$961$		−	20.7128i		−	0.668155i
$962$		0			0
$963$	−7.19615	−	7.19615i	−0.231893	−	0.231893i
$964$		0			0
$965$	23.0359	−	1.38269i	0.741552	−	0.0445102i
$966$		0			0
$967$	−10.6410			−0.342192			−0.171096	−	0.985254i	$-0.554731\pi$
$967$	−10.6410			−0.342192			−0.171096	+	0.985254i	$0.554731\pi$
$968$		0			0
$969$	4.96410	−	1.33013i	0.159470	−	0.0427298i
$970$		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
$973$	−0.839746	−	1.45448i	−0.0269210	−	0.0466286i
$974$		0			0
$975$	−9.13397	−	1.91154i	−0.292521	−	0.0612184i
$976$		0			0
$977$	−0.375644	−	0.650635i	−0.0120179	−	0.0208157i	0.859954	−	0.510372i	$-0.170492\pi$
$977$	−0.375644	−	0.650635i	−0.0120179	−	0.0208157i	−0.871972	+	0.489556i	$0.837159\pi$
$978$		0			0
$979$	−7.30385	+	12.6506i	−0.233432	+	0.404316i
$980$		0			0
$981$	−42.5167	+	11.3923i	−1.35745	+	0.363728i
$982$		0			0
$983$	−42.9282			−1.36920			−0.684599	−	0.728920i	$-0.740022\pi$
$983$	−42.9282			−1.36920			−0.684599	+	0.728920i	$0.740022\pi$
$984$		0			0
$985$	−45.3564	+	2.72243i	−1.44518	+	0.0867439i
$986$		0			0
$987$	−0.732051	−	0.732051i	−0.0233014	−	0.0233014i
$988$		0			0
$989$			1.43078i			0.0454962i
$990$		0			0
$991$	−18.0359	−	31.2391i	−0.572929	−	0.992342i	−0.996263	−	0.0863688i	$-0.972474\pi$
$991$	−18.0359	−	31.2391i	−0.572929	−	0.992342i	0.423334	−	0.905974i	$-0.360860\pi$
$992$		0			0
$993$		−	5.53590i		−	0.175676i
$994$		0			0
$995$	−4.83975	−	7.33013i	−0.153430	−	0.232381i
$996$		0			0
$997$	2.33013	+	8.69615i	0.0737959	+	0.275410i	0.992958	−	0.118470i	$-0.0377991\pi$
$997$	2.33013	+	8.69615i	0.0737959	+	0.275410i	−0.919162	+	0.393880i	$0.871132\pi$
$998$		0			0
$999$	−2.86603	+	10.6962i	−0.0906770	+	0.338411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bk.b.193.1	yes	4
5.2	odd	4		260.2.bf.a.37.1	✓	4
5.3	odd	4		1300.2.bn.b.557.1		4
5.4	even	2		1300.2.bs.a.193.1		4
13.6	odd	12		260.2.bf.a.253.1	yes	4
65.19	odd	12		1300.2.bn.b.1293.1		4
65.32	even	12	inner	260.2.bk.b.97.1	yes	4
65.58	even	12		1300.2.bs.a.357.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.a.37.1	✓	4	5.2	odd	4
260.2.bf.a.253.1	yes	4	13.6	odd	12
260.2.bk.b.97.1	yes	4	65.32	even	12	inner
260.2.bk.b.193.1	yes	4	1.1	even	1	trivial
1300.2.bn.b.557.1		4	5.3	odd	4
1300.2.bn.b.1293.1		4	65.19	odd	12
1300.2.bs.a.193.1		4	5.4	even	2
1300.2.bs.a.357.1		4	65.58	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-0.232051 - 0.133975i) q^{7} +(2.36603 + 1.36603i) q^{9} +O(q^{10})\)	\(q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-0.232051 - 0.133975i) q^{7} +(2.36603 + 1.36603i) q^{9} +(4.59808 + 1.23205i) q^{11} +(3.00000 + 2.00000i) q^{13} +(0.866025 + 0.767949i) q^{15} +(-2.86603 + 0.767949i) q^{17} +(-0.866025 - 3.23205i) q^{19} +(-0.0980762 + 0.0980762i) q^{21} +(-0.133975 - 0.0358984i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(2.09808 - 2.09808i) q^{27} +(-1.03590 + 0.598076i) q^{29} +(2.26795 + 2.26795i) q^{31} +(1.23205 - 2.13397i) q^{33} +(0.500000 - 0.330127i) q^{35} +(-3.23205 + 1.86603i) q^{37} +(1.40192 - 1.23205i) q^{39} +(-1.86603 + 6.96410i) q^{41} +(-2.66987 - 9.96410i) q^{43} +(-5.09808 + 3.36603i) q^{45} +7.46410i q^{47} +(-3.46410 - 6.00000i) q^{49} +1.53590i q^{51} +(-8.46410 - 8.46410i) q^{53} +(-7.06218 + 7.96410i) q^{55} -1.73205 q^{57} +(13.7942 - 3.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-0.366025 - 0.633975i) q^{63} +(-7.00000 + 4.00000i) q^{65} +(-6.23205 - 10.7942i) q^{67} +(-0.0358984 + 0.0621778i) q^{69} +(2.86603 - 0.767949i) q^{71} +0.928203 q^{73} +(-2.40192 + 0.964102i) q^{75} +(-0.901924 - 0.901924i) q^{77} -11.4641i q^{79} +(3.33013 + 5.76795i) q^{81} -3.46410i q^{83} +(1.33013 - 6.50000i) q^{85} +(0.160254 + 0.598076i) q^{87} +(-0.794229 + 2.96410i) q^{89} +(-0.428203 - 0.866025i) q^{91} +(1.43782 - 0.830127i) q^{93} +(7.33013 + 1.50000i) q^{95} +(1.23205 - 2.13397i) q^{97} +(9.19615 + 9.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{5} + 6 q^{7} + 6 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

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