LMFDB - Embedded newform 260.2.bk.b.97.1

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			97.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.97
Dual form			260.2.bk.b.193.1

$q$-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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.133975	+	0.500000i	0.0773503	+	0.288675i	0.993756	−	0.111576i	$-0.0355897\pi$
$3$	0.133975	+	0.500000i	0.0773503	+	0.288675i	−0.916406	+	0.400251i	$0.868923\pi$
$4$		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	−0.543212	−	0.839596i	$-0.682792\pi$
$7$	−0.232051	+	0.133975i	−0.0877070	+	0.0506376i	0.455505	+	0.890233i	$0.349459\pi$
$8$		0			0
$9$	2.36603	−	1.36603i	0.788675	−	0.455342i
$10$		0			0
$11$	4.59808	−	1.23205i	1.38637	−	0.371477i	0.512941	−	0.858424i	$-0.328556\pi$
$11$	4.59808	−	1.23205i	1.38637	−	0.371477i	0.873432	+	0.486947i	$0.161889\pi$
$12$		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	−0.106073	−	0.994358i	$-0.533828\pi$
$17$	−2.86603	−	0.767949i	−0.695113	−	0.186255i	−0.589041	+	0.808103i	$0.700494\pi$
$18$		0			0
$19$	−0.866025	+	3.23205i	−0.198680	+	0.741483i	0.792604	+	0.609737i	$0.208725\pi$
$19$	−0.866025	+	3.23205i	−0.198680	+	0.741483i	−0.991283	+	0.131746i	$0.957942\pi$
$20$		0			0
$21$	−0.0980762	−	0.0980762i	−0.0214020	−	0.0214020i
$22$		0			0
$23$	−0.133975	+	0.0358984i	−0.0279356	+	0.00748533i	−0.272760	−	0.962082i	$-0.587936\pi$
$23$	−0.133975	+	0.0358984i	−0.0279356	+	0.00748533i	0.244824	+	0.969567i	$0.421270\pi$
$24$		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	0.400726	−	0.916198i	$-0.368758\pi$
$29$	−1.03590	−	0.598076i	−0.192362	−	0.111060i	−0.593088	+	0.805138i	$0.702091\pi$
$30$		0			0
$31$	2.26795	−	2.26795i	0.407336	−	0.407336i	−0.473473	−	0.880808i	$-0.657000\pi$
$31$	2.26795	−	2.26795i	0.407336	−	0.407336i	0.880808	+	0.473473i	$0.157000\pi$
$32$		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	0.210218	−	0.977654i	$-0.432582\pi$
$37$	−3.23205	−	1.86603i	−0.531346	−	0.306773i	−0.741564	+	0.670882i	$0.765916\pi$
$38$		0			0
$39$	1.40192	+	1.23205i	0.224487	+	0.197286i
$40$		0			0
$41$	−1.86603	−	6.96410i	−0.291424	−	1.08761i	−0.944016	−	0.329900i	$-0.892985\pi$
$41$	−1.86603	−	6.96410i	−0.291424	−	1.08761i	0.652592	−	0.757710i	$-0.273682\pi$
$42$		0			0
$43$	−2.66987	+	9.96410i	−0.407152	+	1.51951i	0.392900	+	0.919581i	$0.371472\pi$
$43$	−2.66987	+	9.96410i	−0.407152	+	1.51951i	−0.800052	+	0.599930i	$0.795195\pi$
$44$		0			0
$45$	−5.09808	−	3.36603i	−0.759976	−	0.501777i
$46$		0			0
$47$		−	7.46410i		−	1.08875i	−0.838842	−	0.544376i	$-0.816767\pi$
$47$		−	7.46410i		−	1.08875i	0.838842	−	0.544376i	$-0.183233\pi$
$48$		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	−0.178737	+	0.983897i	$0.557201\pi$
$53$	−8.46410	+	8.46410i	−1.16263	+	1.16263i	−0.983897	+	0.178737i	$0.942799\pi$
$54$		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	0.993319	−	0.115404i	$-0.0368164\pi$
$59$	13.7942	+	3.69615i	1.79586	+	0.481198i	0.802537	+	0.596602i	$0.203483\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		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	0.180780	+	0.983524i	$0.442138\pi$
$67$	−6.23205	+	10.7942i	−0.761366	+	1.31872i	−0.942146	+	0.335201i	$0.891196\pi$
$68$		0			0
$69$	−0.0358984	−	0.0621778i	−0.00432166	−	0.00748533i
$70$		0			0
$71$	2.86603	+	0.767949i	0.340135	+	0.0911388i	0.424843	−	0.905267i	$-0.360329\pi$
$71$	2.86603	+	0.767949i	0.340135	+	0.0911388i	−0.0847085	+	0.996406i	$0.526996\pi$
$72$		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	$0.223104\pi$
$79$			11.4641i			1.28981i	−0.764262	+	0.644906i	$0.776896\pi$
$80$		0			0
$81$	3.33013	−	5.76795i	0.370014	−	0.640883i
$82$		0			0
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$		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	0.910971	−	0.412470i	$-0.135334\pi$
$89$	−0.794229	−	2.96410i	−0.0841881	−	0.314194i	−0.995159	+	0.0982760i	$0.968667\pi$
$90$		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	0.921770	−	0.387736i	$-0.126743\pi$
$97$	1.23205	+	2.13397i	0.125096	+	0.216672i	−0.796675	+	0.604408i	$0.793410\pi$
$98$		0			0
$99$	9.19615	−	9.19615i	0.924248	−	0.924248i
$100$		0			0
$101$	1.50000	+	0.866025i	0.149256	+	0.0861727i	0.572768	−	0.819718i	$-0.305870\pi$
$101$	1.50000	+	0.866025i	0.149256	+	0.0861727i	−0.423512	+	0.905890i	$0.639203\pi$
$102$		0			0
$103$	−10.6603	−	10.6603i	−1.05039	−	1.05039i	−0.998661	−	0.0517247i	$-0.983528\pi$
$103$	−10.6603	−	10.6603i	−1.05039	−	1.05039i	−0.0517247	−	0.998661i	$-0.516472\pi$
$104$		0			0
$105$	−0.0980762	+	0.294229i	−0.00957126	+	0.0287138i
$106$		0			0
$107$	−3.59808	+	0.964102i	−0.347839	+	0.0932032i	−0.428509	−	0.903538i	$-0.640961\pi$
$107$	−3.59808	+	0.964102i	−0.347839	+	0.0932032i	0.0806695	+	0.996741i	$0.474294\pi$
$108$		0			0
$109$	−11.3923	−	11.3923i	−1.09118	−	1.09118i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$	−11.3923	−	11.3923i	−1.09118	−	1.09118i	−0.0957826	−	0.995402i	$-0.530535\pi$
$110$		0			0
$111$	0.500000	−	1.86603i	0.0474579	−	0.177115i
$112$		0			0
$113$	15.5263	+	4.16025i	1.46059	+	0.391364i	0.899693	−	0.436522i	$-0.143790\pi$
$113$	15.5263	+	4.16025i	1.46059	+	0.391364i	0.560896	+	0.827886i	$0.310457\pi$
$114$		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	0.998564	−	0.0535746i	$-0.0170615\pi$
$127$	1.20577	+	4.50000i	0.106995	+	0.399310i	−0.891569	+	0.452885i	$0.850395\pi$
$128$		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	−0.0249057	−	0.999690i	$-0.507929\pi$
$137$	9.69615	−	5.59808i	0.828398	−	0.478276i	0.853304	+	0.521414i	$0.174595\pi$
$138$		0			0
$139$	5.42820	−	3.13397i	0.460414	−	0.265820i	−0.251804	−	0.967778i	$-0.581024\pi$
$139$	5.42820	−	3.13397i	0.460414	−	0.265820i	0.712218	+	0.701958i	$0.247691\pi$
$140$		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	0.539186	+	0.842187i	$0.318732\pi$
$149$	−4.25833	+	15.8923i	−0.348856	+	1.30195i	−0.888042	+	0.459762i	$0.847935\pi$
$150$		0			0
$151$	11.1962	+	11.1962i	0.911130	+	0.911130i	0.996361	−	0.0852312i	$-0.0271629\pi$
$151$	11.1962	+	11.1962i	0.911130	+	0.911130i	−0.0852312	+	0.996361i	$0.527163\pi$
$152$		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	0.997450	+	0.0713726i	$0.0227379\pi$
$157$	13.3923	+	13.3923i	1.06882	+	1.06882i	0.0713726	+	0.997450i	$0.477262\pi$
$158$		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	0.982802	−	0.184661i	$-0.0591188\pi$
$163$	4.23205	+	7.33013i	0.331480	+	0.574140i	−0.651322	+	0.758801i	$0.725785\pi$
$164$		0			0
$165$	3.03590	−	4.59808i	0.236344	−	0.357960i
$166$		0			0
$167$	−9.23205	−	5.33013i	−0.714398	−	0.412458i	0.0982896	−	0.995158i	$-0.468663\pi$
$167$	−9.23205	−	5.33013i	−0.714398	−	0.412458i	−0.812687	+	0.582700i	$0.801996\pi$
$168$		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	−0.707384	−	0.706830i	$-0.750125\pi$
$173$	3.40192	−	12.6962i	0.258643	−	0.965271i	0.966027	−	0.258441i	$-0.0832087\pi$
$174$		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	−0.899804	−	0.436294i	$-0.856291\pi$
$179$	−0.964102	+	1.66987i	−0.0720603	+	0.124812i	0.827744	+	0.561106i	$0.189624\pi$
$180$		0			0
$181$		−	1.07180i		−	0.0796660i	−0.999206	−	0.0398330i	$-0.987317\pi$
$181$		−	1.07180i		−	0.0796660i	0.999206	−	0.0398330i	$-0.0126826\pi$
$182$		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	0.624292	−	0.781191i	$-0.285387\pi$
$191$	−5.03590	−	8.72243i	−0.364385	−	0.631133i	−0.988677	+	0.150058i	$0.952054\pi$
$192$		0			0
$193$	−5.16025	+	8.93782i	−0.371443	+	0.643359i	−0.989788	−	0.142549i	$-0.954470\pi$
$193$	−5.16025	+	8.93782i	−0.371443	+	0.643359i	0.618345	+	0.785907i	$0.287804\pi$
$194$		0			0
$195$	1.06218	−	4.03590i	0.0760641	−	0.289017i
$196$		0			0
$197$	10.1603	−	17.5981i	0.723888	−	1.25381i	−0.235542	−	0.971864i	$-0.575686\pi$
$197$	10.1603	−	17.5981i	0.723888	−	1.25381i	0.959430	−	0.281947i	$-0.0909802\pi$
$198$		0			0
$199$	−1.96410	−	3.40192i	−0.139231	−	0.241156i	0.787974	−	0.615708i	$-0.211130\pi$
$199$	−1.96410	−	3.40192i	−0.139231	−	0.241156i	−0.927206	+	0.374552i	$0.877797\pi$
$200$		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	−0.984756	−	0.173939i	$-0.944351\pi$
$211$	−4.96410	+	8.59808i	−0.341743	+	0.591916i	0.643014	+	0.765855i	$0.277684\pi$
$212$		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	−0.196829	−	0.980438i	$-0.563064\pi$
$223$	−17.0885	−	9.86603i	−1.14433	−	0.660678i	−0.947499	+	0.319760i	$0.896398\pi$
$224$		0			0
$225$	−1.63397	+	13.5622i	−0.108932	+	0.904145i
$226$		0			0
$227$	0.232051	+	0.401924i	0.0154018	+	0.0266766i	0.873624	−	0.486602i	$-0.161764\pi$
$227$	0.232051	+	0.401924i	0.0154018	+	0.0266766i	−0.858222	+	0.513279i	$0.828431\pi$
$228$		0			0
$229$	10.8564	−	10.8564i	0.717412	−	0.717412i	−0.250663	−	0.968074i	$-0.580649\pi$
$229$	10.8564	−	10.8564i	0.717412	−	0.717412i	0.968074	+	0.250663i	$0.0806486\pi$
$230$		0			0
$231$	−0.571797	−	0.330127i	−0.0376215	−	0.0217208i
$232$		0			0
$233$	−11.0000	−	11.0000i	−0.720634	−	0.720634i	0.248100	−	0.968734i	$-0.420194\pi$
$233$	−11.0000	−	11.0000i	−0.720634	−	0.720634i	−0.968734	+	0.248100i	$0.920194\pi$
$234$		0			0
$235$	−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	0.344088	−	0.938937i	$-0.388188\pi$
$239$	−9.19615	−	9.19615i	−0.594850	−	0.594850i	−0.938937	+	0.344088i	$0.888188\pi$
$240$		0			0
$241$	−4.93782	+	18.4282i	−0.318073	+	1.18706i	0.603021	+	0.797725i	$0.293963\pi$
$241$	−4.93782	+	18.4282i	−0.318073	+	1.18706i	−0.921094	+	0.389340i	$0.872703\pi$
$242$		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	−0.508113	+	0.861290i	$0.669657\pi$
$251$	−23.8923	+	13.7942i	−1.50807	+	0.870684i	−0.999956	+	0.00939359i	$0.997010\pi$
$252$		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	−0.984360	−	0.176168i	$-0.943630\pi$
$257$	−3.52628	−	13.1603i	−0.219963	−	0.820914i	0.764397	−	0.644746i	$-0.223037\pi$
$258$		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	−0.940720	−	0.339184i	$-0.889849\pi$
$263$	−4.79423	−	17.8923i	−0.295625	−	1.10329i	0.645095	−	0.764102i	$-0.276818\pi$
$264$		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	−0.996998	−	0.0774275i	$-0.975329\pi$
$269$	−23.4282	+	13.5263i	−1.42844	+	0.824712i	−0.431445	+	0.902139i	$0.641996\pi$
$270$		0			0
$271$	−19.7942	+	5.30385i	−1.20241	+	0.322186i	−0.803781	−	0.594925i	$-0.797182\pi$
$271$	−19.7942	+	5.30385i	−1.20241	+	0.322186i	−0.398633	+	0.917111i	$0.630515\pi$
$272$		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	0.871614	−	0.490192i	$-0.163073\pi$
$277$	22.9904	+	6.16025i	1.38136	+	0.370134i	0.509744	+	0.860326i	$0.329740\pi$
$278$		0			0
$279$	2.26795	−	8.46410i	0.135779	−	0.506733i
$280$		0			0
$281$	−7.39230	−	7.39230i	−0.440988	−	0.440988i	0.451356	−	0.892344i	$-0.350940\pi$
$281$	−7.39230	−	7.39230i	−0.440988	−	0.440988i	−0.892344	+	0.451356i	$0.850940\pi$
$282$		0			0
$283$	−12.5263	+	3.35641i	−0.744610	+	0.199518i	−0.611126	−	0.791533i	$-0.709283\pi$
$283$	−12.5263	+	3.35641i	−0.744610	+	0.199518i	−0.133484	+	0.991051i	$0.542616\pi$
$284$		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	0.981596	+	0.190971i	$0.0611636\pi$
$293$	11.2321	+	19.4545i	0.656183	+	1.13654i	−0.325412	+	0.945572i	$0.605503\pi$
$294$		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	$-0.665860\pi$
$307$		−	30.3923i		−	1.73458i	0.497803	−	0.867290i	$-0.334140\pi$
$308$		0			0
$309$	3.90192	−	6.75833i	0.221973	−	0.384468i
$310$		0			0
$311$			16.2487i			0.921380i	0.887561	+	0.460690i	$0.152398\pi$
$311$			16.2487i			0.921380i	−0.887561	+	0.460690i	$0.847602\pi$
$312$		0			0
$313$	20.3205	−	20.3205i	1.14858	−	1.14858i	0.161752	−	0.986832i	$-0.448286\pi$
$313$	20.3205	−	20.3205i	1.14858	−	1.14858i	0.986832	−	0.161752i	$-0.0517143\pi$
$314$		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	0.531285	−	0.847193i	$-0.321709\pi$
$331$	10.3301	+	2.76795i	0.567795	+	0.152140i	0.0365099	+	0.999333i	$0.488376\pi$
$332$		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	−0.709060	−	0.705149i	$-0.750880\pi$
$337$	−0.0717968	+	0.0717968i	−0.00391102	+	0.00391102i	0.705149	+	0.709060i	$0.250880\pi$
$338$		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	0.518535	+	0.855056i	$0.326477\pi$
$347$	−6.66987	+	24.8923i	−0.358058	+	1.33629i	−0.876593	+	0.481233i	$0.840189\pi$
$348$		0			0
$349$	−5.47372	−	20.4282i	−0.293002	−	1.09350i	−0.942792	−	0.333383i	$-0.891810\pi$
$349$	−5.47372	−	20.4282i	−0.293002	−	1.09350i	0.649790	−	0.760114i	$-0.274857\pi$
$350$		0			0
$351$	10.4904	+	2.09808i	0.559935	+	0.111987i
$352$		0			0
$353$	−13.6244	−	7.86603i	−0.725151	−	0.418666i	0.0914944	−	0.995806i	$-0.470836\pi$
$353$	−13.6244	−	7.86603i	−0.725151	−	0.418666i	−0.816646	+	0.577139i	$0.804169\pi$
$354$		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	−0.878410	−	0.477907i	$-0.841396\pi$
$359$	−7.58846	+	7.58846i	−0.400503	+	0.400503i	0.477907	+	0.878410i	$0.341396\pi$
$360$		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	0.0341614	−	0.999416i	$-0.489124\pi$
$367$	10.7942	−	2.89230i	0.563454	−	0.150977i	0.529293	+	0.848439i	$0.322457\pi$
$368$		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	0.877450	−	0.479669i	$-0.159243\pi$
$373$	26.9904	+	7.23205i	1.39751	+	0.374461i	0.520059	+	0.854130i	$0.325910\pi$
$374$		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	0.402305	−	0.915506i	$-0.368209\pi$
$379$	23.5263	−	6.30385i	1.20846	−	0.323807i	0.806159	+	0.591699i	$0.201543\pi$
$380$		0			0
$381$	−2.08846	+	1.20577i	−0.106995	+	0.0617735i
$382$		0			0
$383$	0.696152	−	0.401924i	0.0355717	−	0.0205373i	−0.482109	−	0.876111i	$-0.660129\pi$
$383$	0.696152	−	0.401924i	0.0355717	−	0.0205373i	0.517680	+	0.855574i	$0.326796\pi$
$384$		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	−0.673534	−	0.739156i	$-0.735225\pi$
$397$	−7.37564	+	4.25833i	−0.370173	+	0.213719i	0.303361	+	0.952876i	$0.401891\pi$
$398$		0			0
$399$	0.401924	−	0.232051i	0.0201214	−	0.0116171i
$400$		0			0
$401$	5.86603	−	1.57180i	0.292935	−	0.0784918i	−0.109359	−	0.994002i	$-0.534880\pi$
$401$	5.86603	−	1.57180i	0.292935	−	0.0784918i	0.402294	+	0.915511i	$0.368213\pi$
$402$		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	−0.847971	−	0.530043i	$-0.822176\pi$
$409$	3.06218	−	11.4282i	0.151415	−	0.565088i	0.999386	−	0.0350453i	$-0.0111575\pi$
$410$		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	0.986279	−	0.165088i	$-0.0527908\pi$
$419$	27.3564	+	15.7942i	1.33645	+	0.771599i	0.350169	+	0.936687i	$0.386124\pi$
$420$		0			0
$421$	14.0718	−	14.0718i	0.685817	−	0.685817i	−0.275487	−	0.961305i	$-0.588839\pi$
$421$	14.0718	−	14.0718i	0.685817	−	0.685817i	0.961305	+	0.275487i	$0.0888392\pi$
$422$		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	0.798143	+	0.602468i	$0.205816\pi$
$431$	8.47372	+	31.6244i	0.408165	+	1.52329i	−0.389979	+	0.920824i	$0.627518\pi$
$432$		0			0
$433$	2.72243	−	10.1603i	0.130832	−	0.488271i	−0.869149	−	0.494551i	$-0.835332\pi$
$433$	2.72243	−	10.1603i	0.130832	−	0.488271i	0.999980	+	0.00628046i	$0.00199914\pi$
$434$		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	−0.687873	−	0.725831i	$-0.741456\pi$
$439$	5.96410	−	10.3301i	0.284651	−	0.493030i	0.972524	+	0.232801i	$0.0747889\pi$
$440$		0			0
$441$			18.9282i			0.901343i
$442$		0			0
$443$	27.0526	−	27.0526i	1.28531	−	1.28531i	0.347700	−	0.937606i	$-0.386963\pi$
$443$	27.0526	−	27.0526i	1.28531	−	1.28531i	0.937606	−	0.347700i	$-0.113037\pi$
$444$		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	−0.356375	−	0.934343i	$-0.615987\pi$
$449$	−23.9904	−	6.42820i	−1.13218	−	0.303366i	−0.775801	+	0.630977i	$0.782654\pi$
$450$		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	−0.285201	−	0.958468i	$-0.592060\pi$
$457$	14.6962	−	25.4545i	0.687457	−	1.19071i	0.972658	−	0.232243i	$-0.0746064\pi$
$458$		0			0
$459$	−4.40192	−	7.62436i	−0.205464	−	0.355874i
$460$		0			0
$461$	−23.9904	−	6.42820i	−1.11734	−	0.299391i	−0.347535	−	0.937667i	$-0.612981\pi$
$461$	−23.9904	−	6.42820i	−1.11734	−	0.299391i	−0.769808	+	0.638276i	$0.779648\pi$
$462$		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	−0.0665397	−	0.997784i	$-0.521196\pi$
$467$	20.1244	−	20.1244i	0.931244	−	0.931244i	0.997784	+	0.0665397i	$0.0211959\pi$
$468$		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	0.985148	−	0.171708i	$-0.0549286\pi$
$479$	1.00962	+	3.76795i	0.0461307	+	0.172162i	−0.939017	+	0.343870i	$0.888262\pi$
$480$		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	0.933318	+	0.359050i	$0.116899\pi$
$487$	17.1603	+	29.7224i	0.777605	+	1.34685i	−0.155713	+	0.987802i	$0.549768\pi$
$488$		0			0
$489$	−3.09808	+	3.09808i	−0.140100	+	0.140100i
$490$		0			0
$491$	−13.9641	−	8.06218i	−0.630191	−	0.363841i	0.150635	−	0.988589i	$-0.451868\pi$
$491$	−13.9641	−	8.06218i	−0.630191	−	0.363841i	−0.780826	+	0.624748i	$0.785202\pi$
$492$		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	0.775018	−	0.631939i	$-0.217741\pi$
$499$	3.19615	+	3.19615i	0.143079	+	0.143079i	−0.631939	+	0.775018i	$0.717741\pi$
$500$		0			0
$501$	1.42820	−	5.33013i	0.0638074	−	0.238133i
$502$		0			0
$503$	15.0622	+	4.03590i	0.671589	+	0.179952i	0.578471	−	0.815703i	$-0.303650\pi$
$503$	15.0622	+	4.03590i	0.671589	+	0.179952i	0.0931187	+	0.995655i	$0.470316\pi$
$504$		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	−0.0585970	−	0.998282i	$-0.518663\pi$
$509$	8.79423	−	2.35641i	0.389797	−	0.104446i	0.448394	+	0.893836i	$0.351996\pi$
$510$		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	0.819621	+	0.572906i	$0.194184\pi$
$523$	9.06218	+	33.8205i	0.396261	+	1.47887i	−0.423360	+	0.905962i	$0.639149\pi$
$524$		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	0.941634	−	0.336640i	$-0.109290\pi$
$541$	14.0718	+	14.0718i	0.604994	+	0.604994i	−0.336640	+	0.941634i	$0.609290\pi$
$542$		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	0.482627	−	0.875826i	$-0.339683\pi$
$547$	−9.19615	−	9.19615i	−0.393199	−	0.393199i	−0.875826	+	0.482627i	$0.839683\pi$
$548$		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	0.0738714	−	0.997268i	$-0.476465\pi$
$557$	−17.7679	−	10.2583i	−0.752852	−	0.434659i	−0.826724	+	0.562608i	$0.809798\pi$
$558$		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	0.515594	+	0.856833i	$0.327571\pi$
$563$	−8.52628	+	31.8205i	−0.359340	+	1.34107i	−0.874934	+	0.484242i	$0.839096\pi$
$564$		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	−0.831197	−	0.555978i	$-0.812344\pi$
$569$	1.57180	−	2.72243i	0.0658931	−	0.114130i	0.897090	+	0.441848i	$0.145677\pi$
$570$		0			0
$571$		−	42.1051i		−	1.76204i	−0.473075	−	0.881022i	$-0.656856\pi$
$571$		−	42.1051i		−	1.76204i	0.473075	−	0.881022i	$-0.343144\pi$
$572$		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	0.455537	+	0.890217i	$0.349447\pi$
$587$	−13.1603	+	22.7942i	−0.543182	+	0.940819i	−0.998719	+	0.0506017i	$0.983886\pi$
$588$		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	$0.0365465\pi$
$599$			5.60770i			0.229124i	−0.993416	+	0.114562i	$0.963454\pi$
$600$		0			0
$601$	−4.57180	+	7.91858i	−0.186487	+	0.323006i	−0.944077	−	0.329726i	$-0.893044\pi$
$601$	−4.57180	+	7.91858i	−0.186487	+	0.323006i	0.757589	+	0.652732i	$0.226377\pi$
$602$		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	−0.507637	−	0.861571i	$-0.669481\pi$
$607$	8.93782	−	33.3564i	0.362775	−	1.35389i	0.870412	−	0.492324i	$-0.163852\pi$
$608$		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	0.301836	−	0.953360i	$-0.402400\pi$
$613$	−9.23205	−	5.33013i	−0.372879	−	0.215282i	−0.674715	+	0.738078i	$0.735734\pi$
$614$		0			0
$615$	−6.96410	−	4.59808i	−0.280820	−	0.185412i
$616$		0			0
$617$	−16.0885	−	27.8660i	−0.647697	−	1.12184i	−0.983672	−	0.179973i	$-0.942399\pi$
$617$	−16.0885	−	27.8660i	−0.647697	−	1.12184i	0.335975	−	0.941871i	$-0.390934\pi$
$618$		0			0
$619$	5.87564	−	5.87564i	0.236162	−	0.236162i	−0.579097	−	0.815259i	$-0.696595\pi$
$619$	5.87564	−	5.87564i	0.236162	−	0.236162i	0.815259	+	0.579097i	$0.196595\pi$
$620$		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	−0.725295	−	0.688438i	$-0.758297\pi$
$631$	6.20577	−	23.1603i	0.247048	−	0.921995i	0.972343	−	0.233557i	$-0.0750366\pi$
$632$		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	0.598036	−	0.801470i	$-0.295948\pi$
$641$	40.2846	−	23.2583i	1.59115	−	0.918649i	0.993111	−	0.117179i	$-0.0373852\pi$
$642$		0			0
$643$	35.7679	−	20.6506i	1.41055	−	0.814382i	0.415110	−	0.909771i	$-0.363743\pi$
$643$	35.7679	−	20.6506i	1.41055	−	0.814382i	0.995440	+	0.0953896i	$0.0304097\pi$
$644$		0			0
$645$	5.33975	+	10.6795i	0.210252	+	0.420505i
$646$		0			0
$647$	−0.794229	−	2.96410i	−0.0312243	−	0.116531i	0.948555	−	0.316613i	$-0.102546\pi$
$647$	−0.794229	−	2.96410i	−0.0312243	−	0.116531i	−0.979779	+	0.200082i	$0.935879\pi$
$648$		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	0.969480	−	0.245172i	$-0.0788444\pi$
$653$	0.186533	+	0.696152i	0.00729962	+	0.0272425i	−0.962180	+	0.272415i	$0.912178\pi$
$654$		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	−0.945927	−	0.324380i	$-0.894845\pi$
$659$	−29.2128	+	16.8660i	−1.13797	+	0.657007i	−0.192043	+	0.981387i	$0.561511\pi$
$660$		0			0
$661$	−1.59808	+	0.428203i	−0.0621580	+	0.0166552i	−0.289764	−	0.957098i	$-0.593577\pi$
$661$	−1.59808	+	0.428203i	−0.0621580	+	0.0166552i	0.227606	+	0.973753i	$0.426910\pi$
$662$		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	0.302122	−	0.953269i	$-0.402305\pi$
$673$	26.9904	−	7.23205i	1.04040	−	0.278775i	0.738280	+	0.674494i	$0.235638\pi$
$674$		0			0
$675$	−14.6865	+	2.09808i	−0.565285	+	0.0807550i
$676$		0			0
$677$	−10.3205	−	10.3205i	−0.396649	−	0.396649i	0.480400	−	0.877049i	$-0.340491\pi$
$677$	−10.3205	−	10.3205i	−0.396649	−	0.396649i	−0.877049	+	0.480400i	$0.840491\pi$
$678$		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	−0.995141	−	0.0984586i	$-0.968609\pi$
$683$	−15.2321	−	26.3827i	−0.582838	−	1.00951i	0.412303	−	0.911047i	$-0.364725\pi$
$684$		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	0.964733	−	0.263230i	$-0.0847879\pi$
$691$	−0.0621778	−	0.232051i	−0.00236536	−	0.00882763i	−0.967098	+	0.254403i	$0.918121\pi$
$692$		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	$0.184996\pi$
$701$			29.0718i			1.09803i	−0.835814	+	0.549013i	$0.815004\pi$
$702$		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	0.152162	−	0.988356i	$-0.451377\pi$
$709$	−5.59808	−	1.50000i	−0.210240	−	0.0563337i	−0.362402	+	0.932022i	$0.618043\pi$
$710$		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	−0.997873	−	0.0651859i	$-0.979236\pi$
$719$	−14.8923	−	25.7942i	−0.555389	−	0.961962i	0.442484	−	0.896776i	$-0.354097\pi$
$720$		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	−0.408701	−	0.912669i	$-0.634018\pi$
$727$	13.5885	−	13.5885i	0.503968	−	0.503968i	0.912669	+	0.408701i	$0.134018\pi$
$728$		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	$0.252945\pi$
$733$			38.6410i			1.42724i	−0.700534	+	0.713619i	$0.747055\pi$
$734$		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	−0.821544	−	0.570145i	$-0.806887\pi$
$739$	−10.7417	−	40.0885i	−0.395139	−	1.47468i	0.426405	−	0.904532i	$-0.359780\pi$
$740$		0			0
$741$	−5.19615	+	3.46410i	−0.190885	+	0.127257i
$742$		0			0
$743$	30.4808	+	17.5981i	1.11823	+	0.645611i	0.940949	−	0.338549i	$-0.109936\pi$
$743$	30.4808	+	17.5981i	1.11823	+	0.645611i	0.177282	+	0.984160i	$0.443270\pi$
$744$		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	0.950951	−	0.309343i	$-0.100109\pi$
$751$	31.7487	+	18.3301i	1.15853	+	0.668876i	0.207576	+	0.978219i	$0.433442\pi$
$752$		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	0.0451764	−	0.998979i	$-0.485615\pi$
$757$	16.0622	−	4.30385i	0.583790	−	0.156426i	0.538613	+	0.842553i	$0.318948\pi$
$758$		0			0
$759$	−0.241670	−	0.241670i	−0.00877206	−	0.00877206i
$760$		0			0
$761$	2.66987	−	9.96410i	0.0967828	−	0.361198i	−0.900501	−	0.434854i	$-0.856800\pi$
$761$	2.66987	−	9.96410i	0.0967828	−	0.361198i	0.997284	+	0.0736557i	$0.0234666\pi$
$762$		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	−0.161430	−	0.986884i	$-0.551611\pi$
$769$	5.33013	−	1.42820i	0.192209	−	0.0515023i	0.353639	+	0.935382i	$0.384944\pi$
$770$		0			0
$771$	6.10770	−	3.52628i	0.219963	−	0.126996i
$772$		0			0
$773$	36.4808	−	21.0622i	1.31212	−	0.757554i	0.329675	−	0.944095i	$-0.393061\pi$
$773$	36.4808	−	21.0622i	1.31212	−	0.757554i	0.982447	+	0.186541i	$0.0597276\pi$
$774$		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	−0.989314	−	0.145798i	$-0.953425\pi$
$787$	−38.0885	+	21.9904i	−1.35771	+	0.783872i	−0.368392	+	0.929670i	$0.620092\pi$
$788$		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	−0.207157	−	0.978308i	$-0.566421\pi$
$797$	−24.7224	−	6.62436i	−0.875713	−	0.234647i	−0.668557	+	0.743661i	$0.733088\pi$
$798$		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	0.922917	−	0.384998i	$-0.125798\pi$
$809$	29.8923	+	17.2583i	1.05096	+	0.606771i	0.128040	+	0.991769i	$0.459131\pi$
$810$		0			0
$811$	32.1244	−	32.1244i	1.12804	−	1.12804i	0.137543	−	0.990496i	$-0.456080\pi$
$811$	32.1244	−	32.1244i	1.12804	−	1.12804i	0.990496	−	0.137543i	$-0.0439205\pi$
$812$		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	−0.999219	−	0.0395165i	$-0.987418\pi$
$821$	−4.40192	−	16.4282i	−0.153628	−	0.573348i	0.845591	−	0.533832i	$-0.179248\pi$
$822$		0			0
$823$	−4.91858	+	18.3564i	−0.171451	+	0.639864i	0.825678	+	0.564142i	$0.190793\pi$
$823$	−4.91858	+	18.3564i	−0.171451	+	0.639864i	−0.997129	+	0.0757222i	$0.975874\pi$
$824$		0			0
$825$	−12.2321	−	1.47372i	−0.425865	−	0.0513084i
$826$		0			0
$827$		−	24.5359i		−	0.853197i	−0.904441	−	0.426598i	$-0.859712\pi$
$827$		−	24.5359i		−	0.853197i	0.904441	−	0.426598i	$-0.140288\pi$
$828$		0			0
$829$	1.03590	−	1.79423i	0.0359782	−	0.0623161i	−0.847476	−	0.530834i	$-0.821879\pi$
$829$	1.03590	−	1.79423i	0.0359782	−	0.0623161i	0.883454	+	0.468518i	$0.155212\pi$
$830$		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	−0.210312	−	0.977634i	$-0.567448\pi$
$839$	−25.5263	−	6.83975i	−0.881265	−	0.236134i	−0.670953	+	0.741500i	$0.734115\pi$
$840$		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	−0.544638	−	0.838671i	$-0.683333\pi$
$857$	8.60770	−	8.60770i	0.294033	−	0.294033i	0.838671	+	0.544638i	$0.183333\pi$
$858$		0			0
$859$		−	46.1051i		−	1.57309i	−0.617535	−	0.786543i	$-0.711869\pi$
$859$		−	46.1051i		−	1.57309i	0.617535	−	0.786543i	$-0.288131\pi$
$860$		0			0
$861$	−0.500000	+	0.866025i	−0.0170400	+	0.0295141i
$862$		0			0
$863$			20.2487i			0.689274i	0.938736	+	0.344637i	$0.111998\pi$
$863$			20.2487i			0.689274i	−0.938736	+	0.344637i	$0.888002\pi$
$864$		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	0.970513	+	0.241048i	$0.0774913\pi$
$877$	20.5526	+	35.5981i	0.694011	+	1.20206i	−0.276502	+	0.961013i	$0.589175\pi$
$878$		0			0
$879$	−8.22243	+	8.22243i	−0.277336	+	0.277336i
$880$		0			0
$881$	−1.96410	−	1.13397i	−0.0661723	−	0.0382046i	0.466549	−	0.884495i	$-0.345497\pi$
$881$	−1.96410	−	1.13397i	−0.0661723	−	0.0382046i	−0.532721	+	0.846291i	$0.678831\pi$
$882$		0			0
$883$	−16.8038	−	16.8038i	−0.565494	−	0.565494i	0.365368	−	0.930863i	$-0.380943\pi$
$883$	−16.8038	−	16.8038i	−0.565494	−	0.565494i	−0.930863	+	0.365368i	$0.880943\pi$
$884$		0			0
$885$	14.7846	−	7.39230i	0.496979	−	0.248490i
$886$		0			0
$887$	2.79423	−	0.748711i	0.0938210	−	0.0251393i	−0.211603	−	0.977356i	$-0.567868\pi$
$887$	2.79423	−	0.748711i	0.0938210	−	0.0251393i	0.305424	+	0.952216i	$0.401202\pi$
$888$		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	0.883969	−	0.467545i	$-0.154861\pi$
$907$	−3.47372	−	12.9641i	−0.115343	−	0.430466i	−0.999312	+	0.0370789i	$0.988195\pi$
$908$		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	−0.970151	−	0.242501i	$-0.922032\pi$
$919$	−37.7487	+	21.7942i	−1.24522	+	0.718925i	−0.275064	+	0.961426i	$0.588699\pi$
$920$		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	−0.977730	−	0.209866i	$-0.932697\pi$
$929$	−0.794229	+	2.96410i	−0.0260578	+	0.0972490i	0.951672	+	0.307115i	$0.0993638\pi$
$930$		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	0.867357	+	0.497687i	$0.165817\pi$
$937$	41.7846	+	41.7846i	1.36504	+	1.36504i	0.497687	+	0.867357i	$0.334183\pi$
$938$		0			0
$939$	12.8827	+	7.43782i	0.420411	+	0.242724i
$940$		0			0
$941$	−19.0000	+	19.0000i	−0.619382	+	0.619382i	−0.945373	−	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
$945$	0.356406	+	1.74167i	0.0115939	+	0.0566565i
$946$		0			0
$947$	3.01666	+	1.74167i	0.0980283	+	0.0565967i	0.548213	−	0.836339i	$-0.315308\pi$
$947$	3.01666	+	1.74167i	0.0980283	+	0.0565967i	−0.450184	+	0.892936i	$0.648642\pi$
$948$		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	0.836789	+	0.547526i	$0.184430\pi$
$953$	−4.99038	+	18.6244i	−0.161654	+	0.603302i	−0.998443	+	0.0557765i	$0.982237\pi$
$954$		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	−0.999408	−	0.0344175i	$-0.989042\pi$
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	0.469897	−	0.882721i	$-0.344291\pi$
$972$		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	−0.871972	−	0.489556i	$-0.837159\pi$
$977$	−0.375644	+	0.650635i	−0.0120179	+	0.0208157i	0.859954	+	0.510372i	$0.170492\pi$
$978$		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	0.423334	+	0.905974i	$0.360860\pi$
$991$	−18.0359	+	31.2391i	−0.572929	+	0.992342i	−0.996263	+	0.0863688i	$0.972474\pi$
$992$		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	−0.919162	−	0.393880i	$-0.871132\pi$
$997$	2.33013	−	8.69615i	0.0737959	−	0.275410i	0.992958	+	0.118470i	$0.0377991\pi$
$998$		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.97.1	yes	4
5.2	odd	4		1300.2.bn.b.1293.1		4
5.3	odd	4		260.2.bf.a.253.1	yes	4
5.4	even	2		1300.2.bs.a.357.1		4
13.11	odd	12		260.2.bf.a.37.1	✓	4
65.24	odd	12		1300.2.bn.b.557.1		4
65.37	even	12		1300.2.bs.a.193.1		4
65.63	even	12	inner	260.2.bk.b.193.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.a.37.1	✓	4	13.11	odd	12
260.2.bf.a.253.1	yes	4	5.3	odd	4
260.2.bk.b.97.1	yes	4	1.1	even	1	trivial
260.2.bk.b.193.1	yes	4	65.63	even	12	inner
1300.2.bn.b.557.1		4	65.24	odd	12
1300.2.bn.b.1293.1		4	5.2	odd	4
1300.2.bs.a.193.1		4	65.37	even	12
1300.2.bs.a.357.1		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)

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