LMFDB - Embedded newform 260.2.i.a.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(61,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("260.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.i (of order $3$, degree $2$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	260.81
Dual form			260.2.i.a.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(1.00000 - 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-2.50000 + 4.33013i) q^{19} -1.00000 q^{21} +(-4.50000 - 7.79423i) q^{23} +1.00000 q^{25} -5.00000 q^{27} +(4.50000 + 7.79423i) q^{29} +8.00000 q^{31} +(-1.50000 + 2.59808i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-3.50000 + 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-1.00000 + 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{49} -3.00000 q^{51} +6.00000 q^{53} +(1.50000 + 2.59808i) q^{55} +5.00000 q^{57} +(-4.50000 + 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-1.00000 - 1.73205i) q^{63} +(-1.00000 + 3.46410i) q^{65} +(-2.50000 - 4.33013i) q^{67} +(-4.50000 + 7.79423i) q^{69} +(-4.50000 + 7.79423i) q^{71} +2.00000 q^{73} +(-0.500000 - 0.866025i) q^{75} -3.00000 q^{77} +8.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{85} +(4.50000 - 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{89} +(-2.50000 - 2.59808i) q^{91} +(-4.00000 - 6.92820i) q^{93} +(2.50000 - 4.33013i) q^{95} +(-8.50000 + 14.7224i) q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} - 2 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - q^3 - 2 * q^5 + q^7 + 2 * q^9	$ 2 q - q^{3} - 2 q^{5} + q^{7} + 2 q^{9} - 3 q^{11} + 2 q^{13} + q^{15} + 3 q^{17} - 5 q^{19} - 2 q^{21} - 9 q^{23} + 2 q^{25} - 10 q^{27} + 9 q^{29} + 16 q^{31} - 3 q^{33} - q^{35} + 7 q^{37} - 7 q^{39} - 3 q^{41} + q^{43} - 2 q^{45} + 6 q^{49} - 6 q^{51} + 12 q^{53} + 3 q^{55} + 10 q^{57} - 9 q^{59} + q^{61} - 2 q^{63} - 2 q^{65} - 5 q^{67} - 9 q^{69} - 9 q^{71} + 4 q^{73} - q^{75} - 6 q^{77} + 16 q^{79} - q^{81} - 3 q^{85} + 9 q^{87} - 3 q^{89} - 5 q^{91} - 8 q^{93} + 5 q^{95} - 17 q^{97} - 12 q^{99}+O(q^{100}) $ 2 * q - q^3 - 2 * q^5 + q^7 + 2 * q^9 - 3 * q^11 + 2 * q^13 + q^15 + 3 * q^17 - 5 * q^19 - 2 * q^21 - 9 * q^23 + 2 * q^25 - 10 * q^27 + 9 * q^29 + 16 * q^31 - 3 * q^33 - q^35 + 7 * q^37 - 7 * q^39 - 3 * q^41 + q^43 - 2 * q^45 + 6 * q^49 - 6 * q^51 + 12 * q^53 + 3 * q^55 + 10 * q^57 - 9 * q^59 + q^61 - 2 * q^63 - 2 * q^65 - 5 * q^67 - 9 * q^69 - 9 * q^71 + 4 * q^73 - q^75 - 6 * q^77 + 16 * q^79 - q^81 - 3 * q^85 + 9 * q^87 - 3 * q^89 - 5 * q^91 - 8 * q^93 + 5 * q^95 - 17 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$		0			0
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.768613	−	0.639713i	$-0.779053\pi$
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.169701	−	0.985496i	$-0.554280\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	0.893517	+	0.449029i	$0.148230\pi$
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	−0.0578882	+	0.998323i	$0.518437\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$		0			0
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$		0			0
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$		0			0
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$		0			0
$39$	−3.50000	+	0.866025i	−0.560449	+	0.138675i
$40$		0			0
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$		0			0
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$	−3.00000			−0.420084
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	1.50000	+	2.59808i	0.202260	+	0.350325i
$56$		0			0
$57$	5.00000			0.662266
$58$		0			0
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	0.408919	+	0.912571i	$0.365906\pi$
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	−0.994769	+	0.102151i	$0.967427\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$	−1.00000	−	1.73205i	−0.125988	−	0.218218i
$64$		0			0
$65$	−1.00000	+	3.46410i	−0.124035	+	0.429669i
$66$		0			0
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$		0			0
$69$	−4.50000	+	7.79423i	−0.541736	+	0.938315i
$70$		0			0
$71$	−4.50000	+	7.79423i	−0.534052	+	0.925005i	0.465157	+	0.885228i	$0.345998\pi$
$71$	−4.50000	+	7.79423i	−0.534052	+	0.925005i	−0.999209	+	0.0397765i	$0.987335\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$	−3.00000			−0.341882
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−1.50000	+	2.59808i	−0.162698	+	0.281801i
$86$		0			0
$87$	4.50000	−	7.79423i	0.482451	−	0.835629i
$88$		0			0
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	0.775509	−	0.631337i	$-0.217494\pi$
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	−0.934508	+	0.355942i	$0.884160\pi$
$90$		0			0
$91$	−2.50000	−	2.59808i	−0.262071	−	0.272352i
$92$		0			0
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$		0			0
$95$	2.50000	−	4.33013i	0.256495	−	0.444262i
$96$		0			0
$97$	−8.50000	+	14.7224i	−0.863044	+	1.49484i	0.00593185	+	0.999982i	$0.498112\pi$
$97$	−8.50000	+	14.7224i	−0.863044	+	1.49484i	−0.868976	+	0.494854i	$0.835222\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$		0			0
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		0			0
$105$	1.00000			0.0975900
$106$		0			0
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$	3.50000	−	6.06218i	0.332205	−	0.575396i
$112$		0			0
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	−0.260955	−	0.965351i	$-0.584038\pi$
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	0.966496	−	0.256681i	$-0.0826291\pi$
$114$		0			0
$115$	4.50000	+	7.79423i	0.419627	+	0.726816i
$116$		0			0
$117$	−5.00000	−	5.19615i	−0.462250	−	0.480384i
$118$		0			0
$119$	−1.50000	−	2.59808i	−0.137505	−	0.238165i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	−1.50000	+	2.59808i	−0.135250	+	0.234261i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−8.50000	−	14.7224i	−0.754253	−	1.30640i	−0.945745	−	0.324910i	$-0.894666\pi$
$127$	−8.50000	−	14.7224i	−0.754253	−	1.30640i	0.191492	−	0.981494i	$-0.438667\pi$
$128$		0			0
$129$	−1.00000			−0.0880451
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	2.50000	+	4.33013i	0.216777	+	0.375470i
$134$		0			0
$135$	5.00000			0.430331
$136$		0			0
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−10.5000	+	2.59808i	−0.878054	+	0.217262i
$144$		0			0
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$		0			0
$147$	3.00000	−	5.19615i	0.247436	−	0.428571i
$148$		0			0
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	−0.620701	−	0.784047i	$-0.713152\pi$
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	0.989355	+	0.145519i	$0.0464853\pi$
$150$		0			0
$151$	20.0000			1.62758			0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000			1.62758			0.813788	+	0.581161i	$0.197401\pi$
$152$		0			0
$153$	−3.00000	−	5.19615i	−0.242536	−	0.420084i
$154$		0			0
$155$	−8.00000			−0.642575
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$		0			0
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$		0			0
$161$	−9.00000			−0.709299
$162$		0			0
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	−0.845780	−	0.533533i	$-0.820864\pi$
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	0.884943	+	0.465700i	$0.154198\pi$
$164$		0			0
$165$	1.50000	−	2.59808i	0.116775	−	0.202260i
$166$		0			0
$167$	7.50000	+	12.9904i	0.580367	+	1.00523i	0.995436	+	0.0954356i	$0.0304244\pi$
$167$	7.50000	+	12.9904i	0.580367	+	1.00523i	−0.415068	+	0.909790i	$0.636242\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$	5.00000	+	8.66025i	0.382360	+	0.662266i
$172$		0			0
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	0.122422	+	0.992478i	$0.460934\pi$
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	−0.920722	+	0.390218i	$0.872399\pi$
$174$		0			0
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$		0			0
$177$	9.00000			0.676481
$178$		0			0
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	−0.997446	−	0.0714220i	$-0.977246\pi$
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	0.436870	−	0.899525i	$-0.356087\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$		0			0
$185$	−3.50000	−	6.06218i	−0.257325	−	0.445700i
$186$		0			0
$187$	−9.00000			−0.658145
$188$		0			0
$189$	−2.50000	+	4.33013i	−0.181848	+	0.314970i
$190$		0			0
$191$	1.50000	−	2.59808i	0.108536	−	0.187990i	−0.806641	−	0.591041i	$-0.798717\pi$
$191$	1.50000	−	2.59808i	0.108536	−	0.187990i	0.915177	+	0.403051i	$0.132050\pi$
$192$		0			0
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$		0			0
$195$	3.50000	−	0.866025i	0.250640	−	0.0620174i
$196$		0			0
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	0.914501	−	0.404584i	$-0.132584\pi$
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	−0.807630	+	0.589689i	$0.799250\pi$
$198$		0			0
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$		0			0
$201$	−2.50000	+	4.33013i	−0.176336	+	0.305424i
$202$		0			0
$203$	9.00000			0.631676
$204$		0			0
$205$	1.50000	+	2.59808i	0.104765	+	0.181458i
$206$		0			0
$207$	−18.0000			−1.25109
$208$		0			0
$209$	15.0000			1.03757
$210$		0			0
$211$	12.5000	+	21.6506i	0.860535	+	1.49049i	0.871413	+	0.490550i	$0.163204\pi$
$211$	12.5000	+	21.6506i	0.860535	+	1.49049i	−0.0108774	+	0.999941i	$0.503462\pi$
$212$		0			0
$213$	9.00000			0.616670
$214$		0			0
$215$	−0.500000	+	0.866025i	−0.0340997	+	0.0590624i
$216$		0			0
$217$	4.00000	−	6.92820i	0.271538	−	0.470317i
$218$		0			0
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$		0			0
$221$	−7.50000	−	7.79423i	−0.504505	−	0.524297i
$222$		0			0
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$		0			0
$225$	1.00000	−	1.73205i	0.0666667	−	0.115470i
$226$		0			0
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	−0.999997	−	0.00254715i	$-0.999189\pi$
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	0.502204	+	0.864749i	$0.332523\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	1.50000	+	2.59808i	0.0986928	+	0.170941i
$232$		0			0
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−11.5000	+	19.9186i	−0.740780	+	1.28307i	0.211360	+	0.977408i	$0.432211\pi$
$241$	−11.5000	+	19.9186i	−0.740780	+	1.28307i	−0.952141	+	0.305661i	$0.901123\pi$
$242$		0			0
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$		0			0
$245$	−3.00000	−	5.19615i	−0.191663	−	0.331970i
$246$		0			0
$247$	12.5000	+	12.9904i	0.795356	+	0.826558i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4.50000	+	7.79423i	−0.284037	+	0.491967i	−0.972375	−	0.233423i	$-0.925007\pi$
$251$	−4.50000	+	7.79423i	−0.284037	+	0.491967i	0.688338	+	0.725390i	$0.258341\pi$
$252$		0			0
$253$	−13.5000	+	23.3827i	−0.848738	+	1.47006i
$254$		0			0
$255$	3.00000			0.187867
$256$		0			0
$257$	13.5000	+	23.3827i	0.842107	+	1.45857i	0.888110	+	0.459631i	$0.152018\pi$
$257$	13.5000	+	23.3827i	0.842107	+	1.45857i	−0.0460033	+	0.998941i	$0.514648\pi$
$258$		0			0
$259$	7.00000			0.434959
$260$		0			0
$261$	18.0000			1.11417
$262$		0			0
$263$	1.50000	+	2.59808i	0.0924940	+	0.160204i	0.908560	−	0.417755i	$-0.137183\pi$
$263$	1.50000	+	2.59808i	0.0924940	+	0.160204i	−0.816066	+	0.577959i	$0.803849\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	−1.50000	+	2.59808i	−0.0917985	+	0.159000i
$268$		0			0
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	0.985389	−	0.170321i	$-0.0544803\pi$
$270$		0			0
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	0.993082	−	0.117426i	$-0.0374643\pi$
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	−0.598235	+	0.801321i	$0.704131\pi$
$272$		0			0
$273$	−1.00000	+	3.46410i	−0.0605228	+	0.209657i
$274$		0			0
$275$	−1.50000	−	2.59808i	−0.0904534	−	0.156670i
$276$		0			0
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	−0.425684	−	0.904872i	$-0.639967\pi$
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	0.996484	−	0.0837823i	$-0.0267000\pi$
$278$		0			0
$279$	8.00000	−	13.8564i	0.478947	−	0.829561i
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$		0			0
$283$	−8.50000	−	14.7224i	−0.505273	−	0.875158i	−0.999981	−	0.00609896i	$-0.998059\pi$
$283$	−8.50000	−	14.7224i	−0.505273	−	0.875158i	0.494709	−	0.869059i	$-0.335275\pi$
$284$		0			0
$285$	−5.00000			−0.296174
$286$		0			0
$287$	−3.00000			−0.177084
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	17.0000			0.996558
$292$		0			0
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	−0.818878	−	0.573967i	$-0.805404\pi$
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	0.906509	+	0.422186i	$0.138737\pi$
$294$		0			0
$295$	4.50000	−	7.79423i	0.262000	−	0.453798i
$296$		0			0
$297$	7.50000	+	12.9904i	0.435194	+	0.753778i
$298$		0			0
$299$	−31.5000	+	7.79423i	−1.82169	+	0.450752i
$300$		0			0
$301$	−0.500000	−	0.866025i	−0.0288195	−	0.0499169i
$302$		0			0
$303$	−7.50000	+	12.9904i	−0.430864	+	0.746278i
$304$		0			0
$305$	−0.500000	+	0.866025i	−0.0286299	+	0.0495885i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$	−4.00000	−	6.92820i	−0.227552	−	0.394132i
$310$		0			0
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		0			0
$315$	1.00000	+	1.73205i	0.0563436	+	0.0975900i
$316$		0			0
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$		0			0
$319$	13.5000	−	23.3827i	0.755855	−	1.30918i
$320$		0			0
$321$	1.50000	−	2.59808i	0.0837218	−	0.145010i
$322$		0			0
$323$	7.50000	+	12.9904i	0.417311	+	0.722804i
$324$		0			0
$325$	1.00000	−	3.46410i	0.0554700	−	0.192154i
$326$		0			0
$327$	−7.00000	−	12.1244i	−0.387101	−	0.670478i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	9.50000	−	16.4545i	0.522167	−	0.904420i	−0.477500	−	0.878632i	$-0.658457\pi$
$331$	9.50000	−	16.4545i	0.522167	−	0.904420i	0.999667	−	0.0257885i	$-0.00820965\pi$
$332$		0			0
$333$	14.0000			0.767195
$334$		0			0
$335$	2.50000	+	4.33013i	0.136590	+	0.236580i
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$		0			0
$339$	−15.0000			−0.814688
$340$		0			0
$341$	−12.0000	−	20.7846i	−0.649836	−	1.12555i
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$	4.50000	−	7.79423i	0.242272	−	0.419627i
$346$		0			0
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	−0.719590	−	0.694399i	$-0.755670\pi$
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	0.961162	+	0.275983i	$0.0890035\pi$
$348$		0			0
$349$	−17.5000	−	30.3109i	−0.936754	−	1.62250i	−0.771477	−	0.636257i	$-0.780482\pi$
$349$	−17.5000	−	30.3109i	−0.936754	−	1.62250i	−0.165277	−	0.986247i	$-0.552852\pi$
$350$		0			0
$351$	−5.00000	+	17.3205i	−0.266880	+	0.924500i
$352$		0			0
$353$	13.5000	+	23.3827i	0.718532	+	1.24453i	0.961581	+	0.274521i	$0.0885192\pi$
$353$	13.5000	+	23.3827i	0.718532	+	1.24453i	−0.243049	+	0.970014i	$0.578147\pi$
$354$		0			0
$355$	4.50000	−	7.79423i	0.238835	−	0.413675i
$356$		0			0
$357$	−1.50000	+	2.59808i	−0.0793884	+	0.137505i
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$		0			0
$363$	−2.00000			−0.104973
$364$		0			0
$365$	−2.00000			−0.104685
$366$		0			0
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	−0.997960	+	0.0638362i	$0.979666\pi$
$368$		0			0
$369$	−6.00000			−0.312348
$370$		0			0
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		0			0
$373$	−2.50000	+	4.33013i	−0.129445	+	0.224205i	−0.923462	−	0.383691i	$-0.874653\pi$
$373$	−2.50000	+	4.33013i	−0.129445	+	0.224205i	0.794017	+	0.607896i	$0.207986\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	31.5000	−	7.79423i	1.62233	−	0.401423i
$378$		0			0
$379$	−5.50000	−	9.52628i	−0.282516	−	0.489332i	0.689488	−	0.724297i	$-0.257836\pi$
$379$	−5.50000	−	9.52628i	−0.282516	−	0.489332i	−0.972004	+	0.234965i	$0.924502\pi$
$380$		0			0
$381$	−8.50000	+	14.7224i	−0.435468	+	0.754253i
$382$		0			0
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	−0.462563	−	0.886586i	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$		0			0
$385$	3.00000			0.152894
$386$		0			0
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$		0			0
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	−27.0000			−1.36545
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.00000			−0.402524
$396$		0			0
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	−0.957839	+	0.287307i	$0.907240\pi$
$398$		0			0
$399$	2.50000	−	4.33013i	0.125157	−	0.216777i
$400$		0			0
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	0.615725	−	0.787961i	$-0.288863\pi$
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	−0.990257	+	0.139253i	$0.955530\pi$
$402$		0			0
$403$	8.00000	−	27.7128i	0.398508	−	1.38047i
$404$		0			0
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$		0			0
$407$	10.5000	−	18.1865i	0.520466	−	0.901473i
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$	−3.00000			−0.147979
$412$		0			0
$413$	4.50000	+	7.79423i	0.221431	+	0.383529i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.00000			0.244851
$418$		0			0
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	0.999887	+	0.0150285i	$0.00478389\pi$
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	−0.486928	+	0.873442i	$0.661883\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.50000	−	2.59808i	0.0727607	−	0.126025i
$426$		0			0
$427$	−0.500000	−	0.866025i	−0.0241967	−	0.0419099i
$428$		0			0
$429$	7.50000	+	7.79423i	0.362103	+	0.376309i
$430$		0			0
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	0.827636	−	0.561266i	$-0.189685\pi$
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	−0.899888	+	0.436121i	$0.856352\pi$
$432$		0			0
$433$	−2.50000	+	4.33013i	−0.120142	+	0.208093i	−0.919824	−	0.392332i	$-0.871668\pi$
$433$	−2.50000	+	4.33013i	−0.120142	+	0.208093i	0.799681	+	0.600425i	$0.205002\pi$
$434$		0			0
$435$	−4.50000	+	7.79423i	−0.215758	+	0.373705i
$436$		0			0
$437$	45.0000			2.15264
$438$		0			0
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	0.877711	−	0.479191i	$-0.159070\pi$
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	−0.853847	+	0.520524i	$0.825737\pi$
$440$		0			0
$441$	12.0000			0.571429
$442$		0			0
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		0			0
$445$	1.50000	+	2.59808i	0.0711068	+	0.123161i
$446$		0			0
$447$	−9.00000			−0.425685
$448$		0			0
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	−0.986937	−	0.161106i	$-0.948494\pi$
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	0.632990	+	0.774160i	$0.281827\pi$
$450$		0			0
$451$	−4.50000	+	7.79423i	−0.211897	+	0.367016i
$452$		0			0
$453$	−10.0000	−	17.3205i	−0.469841	−	0.813788i
$454$		0			0
$455$	2.50000	+	2.59808i	0.117202	+	0.121800i
$456$		0			0
$457$	−20.5000	−	35.5070i	−0.958950	−	1.66095i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	−20.5000	−	35.5070i	−0.958950	−	1.66095i	−0.233890	−	0.972263i	$-0.575146\pi$
$458$		0			0
$459$	−7.50000	+	12.9904i	−0.350070	+	0.606339i
$460$		0			0
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	−0.986127	−	0.165992i	$-0.946917\pi$
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	0.636817	+	0.771015i	$0.280251\pi$
$462$		0			0
$463$	−40.0000			−1.85896			−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000			−1.85896			−0.929479	+	0.368875i	$0.879743\pi$
$464$		0			0
$465$	4.00000	+	6.92820i	0.185496	+	0.321288i
$466$		0			0
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	−5.00000			−0.230879
$470$		0			0
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$		0			0
$473$	−3.00000			−0.137940
$474$		0			0
$475$	−2.50000	+	4.33013i	−0.114708	+	0.198680i
$476$		0			0
$477$	6.00000	−	10.3923i	0.274721	−	0.475831i
$478$		0			0
$479$	−7.50000	−	12.9904i	−0.342684	−	0.593546i	0.642246	−	0.766498i	$-0.278003\pi$
$479$	−7.50000	−	12.9904i	−0.342684	−	0.593546i	−0.984930	+	0.172953i	$0.944669\pi$
$480$		0			0
$481$	24.5000	−	6.06218i	1.11710	−	0.276412i
$482$		0			0
$483$	4.50000	+	7.79423i	0.204757	+	0.354650i
$484$		0			0
$485$	8.50000	−	14.7224i	0.385965	−	0.668511i
$486$		0			0
$487$	−17.5000	+	30.3109i	−0.793001	+	1.37352i	0.131100	+	0.991369i	$0.458149\pi$
$487$	−17.5000	+	30.3109i	−0.793001	+	1.37352i	−0.924101	+	0.382148i	$0.875184\pi$
$488$		0			0
$489$	−1.00000			−0.0452216
$490$		0			0
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	0.645675	−	0.763612i	$-0.276576\pi$
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	−0.984145	+	0.177365i	$0.943243\pi$
$492$		0			0
$493$	27.0000			1.21602
$494$		0			0
$495$	6.00000			0.269680
$496$		0			0
$497$	4.50000	+	7.79423i	0.201853	+	0.349619i
$498$		0			0
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$		0			0
$501$	7.50000	−	12.9904i	0.335075	−	0.580367i
$502$		0			0
$503$	−19.5000	+	33.7750i	−0.869462	+	1.50595i	−0.00691465	+	0.999976i	$0.502201\pi$
$503$	−19.5000	+	33.7750i	−0.869462	+	1.50595i	−0.862547	+	0.505976i	$0.831132\pi$
$504$		0			0
$505$	7.50000	+	12.9904i	0.333746	+	0.578064i
$506$		0			0
$507$	−0.500000	+	12.9904i	−0.0222058	+	0.576923i
$508$		0			0
$509$	16.5000	+	28.5788i	0.731350	+	1.26673i	0.956306	+	0.292366i	$0.0944425\pi$
$509$	16.5000	+	28.5788i	0.731350	+	1.26673i	−0.224957	+	0.974369i	$0.572224\pi$
$510$		0			0
$511$	1.00000	−	1.73205i	0.0442374	−	0.0766214i
$512$		0			0
$513$	12.5000	−	21.6506i	0.551888	−	0.955899i
$514$		0			0
$515$	−8.00000			−0.352522
$516$		0			0
$517$		0			0
$518$		0			0
$519$	21.0000			0.921798
$520$		0			0
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$		0			0
$523$	−2.50000	−	4.33013i	−0.109317	−	0.189343i	0.806177	−	0.591675i	$-0.201533\pi$
$523$	−2.50000	−	4.33013i	−0.109317	−	0.189343i	−0.915494	+	0.402332i	$0.868200\pi$
$524$		0			0
$525$	−1.00000			−0.0436436
$526$		0			0
$527$	12.0000	−	20.7846i	0.522728	−	0.905392i
$528$		0			0
$529$	−29.0000	+	50.2295i	−1.26087	+	2.18389i
$530$		0			0
$531$	9.00000	+	15.5885i	0.390567	+	0.676481i
$532$		0			0
$533$	−10.5000	+	2.59808i	−0.454805	+	0.112535i
$534$		0			0
$535$	−1.50000	−	2.59808i	−0.0648507	−	0.112325i
$536$		0			0
$537$	−7.50000	+	12.9904i	−0.323649	+	0.560576i
$538$		0			0
$539$	9.00000	−	15.5885i	0.387657	−	0.671442i
$540$		0			0
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$		0			0
$543$	5.00000	+	8.66025i	0.214571	+	0.371647i
$544$		0			0
$545$	−14.0000			−0.599694
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$		0			0
$551$	−45.0000			−1.91706
$552$		0			0
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$		0			0
$555$	−3.50000	+	6.06218i	−0.148567	+	0.257325i
$556$		0			0
$557$	19.5000	+	33.7750i	0.826242	+	1.43109i	0.900967	+	0.433888i	$0.142859\pi$
$557$	19.5000	+	33.7750i	0.826242	+	1.43109i	−0.0747252	+	0.997204i	$0.523808\pi$
$558$		0			0
$559$	−2.50000	−	2.59808i	−0.105739	−	0.109887i
$560$		0			0
$561$	4.50000	+	7.79423i	0.189990	+	0.329073i
$562$		0			0
$563$	16.5000	−	28.5788i	0.695392	−	1.20445i	−0.274656	−	0.961542i	$-0.588564\pi$
$563$	16.5000	−	28.5788i	0.695392	−	1.20445i	0.970048	−	0.242912i	$-0.0781026\pi$
$564$		0			0
$565$	−7.50000	+	12.9904i	−0.315527	+	0.546509i
$566$		0			0
$567$	−1.00000			−0.0419961
$568$		0			0
$569$	16.5000	+	28.5788i	0.691716	+	1.19809i	0.971275	+	0.237959i	$0.0764783\pi$
$569$	16.5000	+	28.5788i	0.691716	+	1.19809i	−0.279559	+	0.960128i	$0.590188\pi$
$570$		0			0
$571$	44.0000			1.84134			0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000			1.84134			0.920671	+	0.390339i	$0.127642\pi$
$572$		0			0
$573$	−3.00000			−0.125327
$574$		0			0
$575$	−4.50000	−	7.79423i	−0.187663	−	0.325042i
$576$		0			0
$577$	−22.0000			−0.915872			−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000			−0.915872			−0.457936	+	0.888985i	$0.651411\pi$
$578$		0			0
$579$	−2.50000	+	4.33013i	−0.103896	+	0.179954i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$		0			0
$585$	5.00000	+	5.19615i	0.206725	+	0.214834i
$586$		0			0
$587$	13.5000	+	23.3827i	0.557205	+	0.965107i	0.997728	+	0.0673658i	$0.0214594\pi$
$587$	13.5000	+	23.3827i	0.557205	+	0.965107i	−0.440524	+	0.897741i	$0.645207\pi$
$588$		0			0
$589$	−20.0000	+	34.6410i	−0.824086	+	1.42736i
$590$		0			0
$591$	1.50000	−	2.59808i	0.0617018	−	0.106871i
$592$		0			0
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$		0			0
$595$	1.50000	+	2.59808i	0.0614940	+	0.106511i
$596$		0			0
$597$	−7.00000			−0.286491
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	0.500000	+	0.866025i	0.0203954	+	0.0353259i	0.876043	−	0.482233i	$-0.160174\pi$
$601$	0.500000	+	0.866025i	0.0203954	+	0.0353259i	−0.855648	+	0.517559i	$0.826841\pi$
$602$		0			0
$603$	−10.0000			−0.407231
$604$		0			0
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$		0			0
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	−0.999279	−	0.0379540i	$-0.987916\pi$
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	0.532509	+	0.846424i	$0.321249\pi$
$608$		0			0
$609$	−4.50000	−	7.79423i	−0.182349	−	0.315838i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	−0.994794	−	0.101905i	$-0.967506\pi$
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	0.409145	−	0.912470i	$-0.365827\pi$
$614$		0			0
$615$	1.50000	−	2.59808i	0.0604858	−	0.104765i
$616$		0			0
$617$	13.5000	−	23.3827i	0.543490	−	0.941351i	−0.455211	−	0.890384i	$-0.650436\pi$
$617$	13.5000	−	23.3827i	0.543490	−	0.941351i	0.998700	−	0.0509678i	$-0.0162306\pi$
$618$		0			0
$619$	−28.0000			−1.12542			−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000			−1.12542			−0.562708	+	0.826656i	$0.690240\pi$
$620$		0			0
$621$	22.5000	+	38.9711i	0.902894	+	1.56386i
$622$		0			0
$623$	−3.00000			−0.120192
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−7.50000	−	12.9904i	−0.299521	−	0.518786i
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	3.50000	−	6.06218i	0.139333	−	0.241331i	−0.787911	−	0.615789i	$-0.788838\pi$
$631$	3.50000	−	6.06218i	0.139333	−	0.241331i	0.927244	+	0.374457i	$0.122171\pi$
$632$		0			0
$633$	12.5000	−	21.6506i	0.496830	−	0.860535i
$634$		0			0
$635$	8.50000	+	14.7224i	0.337312	+	0.584242i
$636$		0			0
$637$	21.0000	−	5.19615i	0.832050	−	0.205879i
$638$		0			0
$639$	9.00000	+	15.5885i	0.356034	+	0.616670i
$640$		0			0
$641$	−1.50000	+	2.59808i	−0.0592464	+	0.102618i	−0.894127	−	0.447813i	$-0.852203\pi$
$641$	−1.50000	+	2.59808i	−0.0592464	+	0.102618i	0.834881	+	0.550431i	$0.185536\pi$
$642$		0			0
$643$	12.5000	−	21.6506i	0.492952	−	0.853818i	−0.507015	−	0.861937i	$-0.669251\pi$
$643$	12.5000	−	21.6506i	0.492952	−	0.853818i	0.999967	+	0.00811944i	$0.00258453\pi$
$644$		0			0
$645$	1.00000			0.0393750
$646$		0			0
$647$	13.5000	+	23.3827i	0.530740	+	0.919268i	0.999357	+	0.0358667i	$0.0114192\pi$
$647$	13.5000	+	23.3827i	0.530740	+	0.919268i	−0.468617	+	0.883402i	$0.655247\pi$
$648$		0			0
$649$	27.0000			1.05984
$650$		0			0
$651$	−8.00000			−0.313545
$652$		0			0
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.00000	−	3.46410i	0.0780274	−	0.135147i
$658$		0			0
$659$	−22.5000	+	38.9711i	−0.876476	+	1.51810i	−0.0212930	+	0.999773i	$0.506778\pi$
$659$	−22.5000	+	38.9711i	−0.876476	+	1.51810i	−0.855183	+	0.518327i	$0.826555\pi$
$660$		0			0
$661$	−17.5000	−	30.3109i	−0.680671	−	1.17896i	−0.974776	−	0.223184i	$-0.928355\pi$
$661$	−17.5000	−	30.3109i	−0.680671	−	1.17896i	0.294105	−	0.955773i	$-0.404978\pi$
$662$		0			0
$663$	−3.00000	+	10.3923i	−0.116510	+	0.403604i
$664$		0			0
$665$	−2.50000	−	4.33013i	−0.0969458	−	0.167915i
$666$		0			0
$667$	40.5000	−	70.1481i	1.56817	−	2.71614i
$668$		0			0
$669$	9.50000	−	16.4545i	0.367291	−	0.636167i
$670$		0			0
$671$	−3.00000			−0.115814
$672$		0			0
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	0.988968	−	0.148132i	$-0.0473259\pi$
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	−0.622770	+	0.782405i	$0.713993\pi$
$674$		0			0
$675$	−5.00000			−0.192450
$676$		0			0
$677$	−18.0000			−0.691796			−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$678$		0			0
$679$	8.50000	+	14.7224i	0.326200	+	0.564995i
$680$		0			0
$681$	15.0000			0.574801
$682$		0			0
$683$	10.5000	−	18.1865i	0.401771	−	0.695888i	−0.592168	−	0.805814i	$-0.701728\pi$
$683$	10.5000	−	18.1865i	0.401771	−	0.695888i	0.993940	+	0.109926i	$0.0350613\pi$
$684$		0			0
$685$	−1.50000	+	2.59808i	−0.0573121	+	0.0992674i
$686$		0			0
$687$	11.0000	+	19.0526i	0.419676	+	0.726900i
$688$		0			0
$689$	6.00000	−	20.7846i	0.228582	−	0.791831i
$690$		0			0
$691$	−11.5000	−	19.9186i	−0.437481	−	0.757739i	0.560014	−	0.828483i	$-0.310796\pi$
$691$	−11.5000	−	19.9186i	−0.437481	−	0.757739i	−0.997494	+	0.0707446i	$0.977462\pi$
$692$		0			0
$693$	−3.00000	+	5.19615i	−0.113961	+	0.197386i
$694$		0			0
$695$	2.50000	−	4.33013i	0.0948304	−	0.164251i
$696$		0			0
$697$	−9.00000			−0.340899
$698$		0			0
$699$	3.00000	+	5.19615i	0.113470	+	0.196537i
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	−35.0000			−1.32005
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.0000			−0.564133
$708$		0			0
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	0.324104	+	0.946021i	$0.394937\pi$
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	−0.981331	+	0.192328i	$0.938396\pi$
$710$		0			0
$711$	8.00000	−	13.8564i	0.300023	−	0.519656i
$712$		0			0
$713$	−36.0000	−	62.3538i	−1.34821	−	2.33517i
$714$		0			0
$715$	10.5000	−	2.59808i	0.392678	−	0.0971625i
$716$		0			0
$717$	−12.0000	−	20.7846i	−0.448148	−	0.776215i
$718$		0			0
$719$	−22.5000	+	38.9711i	−0.839108	+	1.45338i	0.0515326	+	0.998671i	$0.483589\pi$
$719$	−22.5000	+	38.9711i	−0.839108	+	1.45338i	−0.890641	+	0.454707i	$0.849744\pi$
$720$		0			0
$721$	4.00000	−	6.92820i	0.148968	−	0.258020i
$722$		0			0
$723$	23.0000			0.855379
$724$		0			0
$725$	4.50000	+	7.79423i	0.167126	+	0.289470i
$726$		0			0
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$		0			0
$733$	−34.0000			−1.25582			−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000			−1.25582			−0.627909	+	0.778287i	$0.716089\pi$
$734$		0			0
$735$	−3.00000	+	5.19615i	−0.110657	+	0.191663i
$736$		0			0
$737$	−7.50000	+	12.9904i	−0.276266	+	0.478507i
$738$		0			0
$739$	−5.50000	−	9.52628i	−0.202321	−	0.350430i	0.746955	−	0.664875i	$-0.231515\pi$
$739$	−5.50000	−	9.52628i	−0.202321	−	0.350430i	−0.949276	+	0.314445i	$0.898182\pi$
$740$		0			0
$741$	5.00000	−	17.3205i	0.183680	−	0.636285i
$742$		0			0
$743$	−16.5000	−	28.5788i	−0.605326	−	1.04846i	−0.992000	−	0.126239i	$-0.959709\pi$
$743$	−16.5000	−	28.5788i	−0.605326	−	1.04846i	0.386674	−	0.922217i	$-0.373624\pi$
$744$		0			0
$745$	−4.50000	+	7.79423i	−0.164867	+	0.285558i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.00000			0.109618
$750$		0			0
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	0.959906	−	0.280321i	$-0.0904408\pi$
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	−0.722718	+	0.691143i	$0.757107\pi$
$752$		0			0
$753$	9.00000			0.327978
$754$		0			0
$755$	−20.0000			−0.727875
$756$		0			0
$757$	−2.50000	−	4.33013i	−0.0908640	−	0.157381i	0.817011	−	0.576622i	$-0.195630\pi$
$757$	−2.50000	−	4.33013i	−0.0908640	−	0.157381i	−0.907875	+	0.419241i	$0.862296\pi$
$758$		0			0
$759$	27.0000			0.980038
$760$		0			0
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	−0.772863	−	0.634573i	$-0.781176\pi$
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	0.935988	+	0.352032i	$0.114509\pi$
$762$		0			0
$763$	7.00000	−	12.1244i	0.253417	−	0.438931i
$764$		0			0
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$		0			0
$767$	22.5000	+	23.3827i	0.812428	+	0.844300i
$768$		0			0
$769$	−5.50000	−	9.52628i	−0.198335	−	0.343526i	0.749654	−	0.661830i	$-0.230220\pi$
$769$	−5.50000	−	9.52628i	−0.198335	−	0.343526i	−0.947989	+	0.318304i	$0.896887\pi$
$770$		0			0
$771$	13.5000	−	23.3827i	0.486191	−	0.842107i
$772$		0			0
$773$	7.50000	−	12.9904i	0.269756	−	0.467232i	−0.699043	−	0.715080i	$-0.746390\pi$
$773$	7.50000	−	12.9904i	0.269756	−	0.467232i	0.968799	+	0.247849i	$0.0797235\pi$
$774$		0			0
$775$	8.00000			0.287368
$776$		0			0
$777$	−3.50000	−	6.06218i	−0.125562	−	0.217479i
$778$		0			0
$779$	15.0000			0.537431
$780$		0			0
$781$	27.0000			0.966136
$782$		0			0
$783$	−22.5000	−	38.9711i	−0.804084	−	1.39272i
$784$		0			0
$785$	−14.0000			−0.499681
$786$		0			0
$787$	24.5000	−	42.4352i	0.873331	−	1.51265i	0.0148003	−	0.999890i	$-0.495289\pi$
$787$	24.5000	−	42.4352i	0.873331	−	1.51265i	0.858530	−	0.512763i	$-0.171378\pi$
$788$		0			0
$789$	1.50000	−	2.59808i	0.0534014	−	0.0924940i
$790$		0			0
$791$	−7.50000	−	12.9904i	−0.266669	−	0.461885i
$792$		0			0
$793$	−2.50000	−	2.59808i	−0.0887776	−	0.0922604i
$794$		0			0
$795$	3.00000	+	5.19615i	0.106399	+	0.184289i
$796$		0			0
$797$	13.5000	−	23.3827i	0.478195	−	0.828257i	−0.521493	−	0.853256i	$-0.674625\pi$
$797$	13.5000	−	23.3827i	0.478195	−	0.828257i	0.999687	+	0.0249984i	$0.00795805\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−6.00000			−0.212000
$802$		0			0
$803$	−3.00000	−	5.19615i	−0.105868	−	0.183368i
$804$		0			0
$805$	9.00000			0.317208
$806$		0			0
$807$	−21.0000			−0.739235
$808$		0			0
$809$	−19.5000	−	33.7750i	−0.685583	−	1.18747i	−0.973253	−	0.229736i	$-0.926214\pi$
$809$	−19.5000	−	33.7750i	−0.685583	−	1.18747i	0.287670	−	0.957730i	$-0.407120\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$		0			0
$813$	6.50000	−	11.2583i	0.227965	−	0.394847i
$814$		0			0
$815$	−0.500000	+	0.866025i	−0.0175142	+	0.0303355i
$816$		0			0
$817$	2.50000	+	4.33013i	0.0874639	+	0.151492i
$818$		0			0
$819$	−7.00000	+	1.73205i	−0.244600	+	0.0605228i
$820$		0			0
$821$	10.5000	+	18.1865i	0.366453	+	0.634714i	0.989008	−	0.147861i	$-0.0472389\pi$
$821$	10.5000	+	18.1865i	0.366453	+	0.634714i	−0.622556	+	0.782576i	$0.713906\pi$
$822$		0			0
$823$	−23.5000	+	40.7032i	−0.819159	+	1.41882i	0.0871445	+	0.996196i	$0.472226\pi$
$823$	−23.5000	+	40.7032i	−0.819159	+	1.41882i	−0.906303	+	0.422628i	$0.861108\pi$
$824$		0			0
$825$	−1.50000	+	2.59808i	−0.0522233	+	0.0904534i
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	0.754567	−	0.656223i	$-0.227847\pi$
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	−0.945589	+	0.325362i	$0.894514\pi$
$830$		0			0
$831$	−19.0000			−0.659103
$832$		0			0
$833$	18.0000			0.623663
$834$		0			0
$835$	−7.50000	−	12.9904i	−0.259548	−	0.449551i
$836$		0			0
$837$	−40.0000			−1.38260
$838$		0			0
$839$	7.50000	−	12.9904i	0.258929	−	0.448478i	−0.707026	−	0.707187i	$-0.749964\pi$
$839$	7.50000	−	12.9904i	0.258929	−	0.448478i	0.965955	+	0.258709i	$0.0832972\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$		0			0
$843$	9.00000	+	15.5885i	0.309976	+	0.536895i
$844$		0			0
$845$	11.0000	+	6.92820i	0.378412	+	0.238337i
$846$		0			0
$847$	−1.00000	−	1.73205i	−0.0343604	−	0.0595140i
$848$		0			0
$849$	−8.50000	+	14.7224i	−0.291719	+	0.505273i
$850$		0			0
$851$	31.5000	−	54.5596i	1.07981	−	1.87028i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$		0			0
$855$	−5.00000	−	8.66025i	−0.170996	−	0.296174i
$856$		0			0
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$		0			0
$859$	8.00000			0.272956			0.136478	−	0.990643i	$-0.456422\pi$
$859$	8.00000			0.272956			0.136478	+	0.990643i	$0.456422\pi$
$860$		0			0
$861$	1.50000	+	2.59808i	0.0511199	+	0.0885422i
$862$		0			0
$863$	48.0000			1.63394			0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000			1.63394			0.816970	+	0.576681i	$0.195652\pi$
$864$		0			0
$865$	10.5000	−	18.1865i	0.357011	−	0.618361i
$866$		0			0
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$		0			0
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	−17.5000	+	4.33013i	−0.592965	+	0.146721i
$872$		0			0
$873$	17.0000	+	29.4449i	0.575363	+	0.996558i
$874$		0			0
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$		0			0
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	−0.973098	−	0.230391i	$-0.925999\pi$
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	0.686074	+	0.727532i	$0.259333\pi$
$878$		0			0
$879$	−3.00000			−0.101187
$880$		0			0
$881$	−1.50000	−	2.59808i	−0.0505363	−	0.0875314i	0.839651	−	0.543127i	$-0.182760\pi$
$881$	−1.50000	−	2.59808i	−0.0505363	−	0.0875314i	−0.890187	+	0.455595i	$0.849426\pi$
$882$		0			0
$883$	56.0000			1.88455			0.942275	−	0.334840i	$-0.108682\pi$
$883$	56.0000			1.88455			0.942275	+	0.334840i	$0.108682\pi$
$884$		0			0
$885$	−9.00000			−0.302532
$886$		0			0
$887$	−16.5000	−	28.5788i	−0.554016	−	0.959583i	−0.997979	−	0.0635387i	$-0.979761\pi$
$887$	−16.5000	−	28.5788i	−0.554016	−	0.959583i	0.443964	−	0.896045i	$-0.353572\pi$
$888$		0			0
$889$	−17.0000			−0.570162
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	7.50000	+	12.9904i	0.250697	+	0.434221i
$896$		0			0
$897$	22.5000	+	23.3827i	0.751253	+	0.780725i
$898$		0			0
$899$	36.0000	+	62.3538i	1.20067	+	2.07962i
$900$		0			0
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$		0			0
$903$	−0.500000	+	0.866025i	−0.0166390	+	0.0288195i
$904$		0			0
$905$	10.0000			0.332411
$906$		0			0
$907$	27.5000	+	47.6314i	0.913123	+	1.58157i	0.809627	+	0.586945i	$0.199669\pi$
$907$	27.5000	+	47.6314i	0.913123	+	1.58157i	0.103495	+	0.994630i	$0.466997\pi$
$908$		0			0
$909$	−30.0000			−0.995037
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	1.00000			0.0330590
$916$		0			0
$917$		0			0
$918$		0			0
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	−0.802507	−	0.596643i	$-0.796501\pi$
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	0.917961	+	0.396670i	$0.129834\pi$
$920$		0			0
$921$	2.00000	+	3.46410i	0.0659022	+	0.114146i
$922$		0			0
$923$	22.5000	+	23.3827i	0.740597	+	0.769650i
$924$		0			0
$925$	3.50000	+	6.06218i	0.115079	+	0.199323i
$926$		0			0
$927$	8.00000	−	13.8564i	0.262754	−	0.455104i
$928$		0			0
$929$	−1.50000	+	2.59808i	−0.0492134	+	0.0852401i	−0.889583	−	0.456774i	$-0.849005\pi$
$929$	−1.50000	+	2.59808i	−0.0492134	+	0.0852401i	0.840369	+	0.542014i	$0.182338\pi$
$930$		0			0
$931$	−30.0000			−0.983210
$932$		0			0
$933$	−6.00000	−	10.3923i	−0.196431	−	0.340229i
$934$		0			0
$935$	9.00000			0.294331
$936$		0			0
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$		0			0
$939$	5.00000	+	8.66025i	0.163169	+	0.282617i
$940$		0			0
$941$	18.0000			0.586783			0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000			0.586783			0.293392	+	0.955992i	$0.405216\pi$
$942$		0			0
$943$	−13.5000	+	23.3827i	−0.439620	+	0.761445i
$944$		0			0
$945$	2.50000	−	4.33013i	0.0813250	−	0.140859i
$946$		0			0
$947$	25.5000	+	44.1673i	0.828639	+	1.43524i	0.899106	+	0.437730i	$0.144217\pi$
$947$	25.5000	+	44.1673i	0.828639	+	1.43524i	−0.0704677	+	0.997514i	$0.522449\pi$
$948$		0			0
$949$	2.00000	−	6.92820i	0.0649227	−	0.224899i
$950$		0			0
$951$	9.00000	+	15.5885i	0.291845	+	0.505490i
$952$		0			0
$953$	−10.5000	+	18.1865i	−0.340128	+	0.589120i	−0.984456	−	0.175630i	$-0.943804\pi$
$953$	−10.5000	+	18.1865i	−0.340128	+	0.589120i	0.644328	+	0.764749i	$0.277137\pi$
$954$		0			0
$955$	−1.50000	+	2.59808i	−0.0485389	+	0.0840718i
$956$		0			0
$957$	−27.0000			−0.872786
$958$		0			0
$959$	−1.50000	−	2.59808i	−0.0484375	−	0.0838963i
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$	6.00000			0.193347
$964$		0			0
$965$	2.50000	+	4.33013i	0.0804778	+	0.139392i
$966$		0			0
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$		0			0
$969$	7.50000	−	12.9904i	0.240935	−	0.417311i
$970$		0			0
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	−0.720224	−	0.693742i	$-0.755961\pi$
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	0.960910	+	0.276861i	$0.0892941\pi$
$972$		0			0
$973$	2.50000	+	4.33013i	0.0801463	+	0.138817i
$974$		0			0
$975$	−3.50000	+	0.866025i	−0.112090	+	0.0277350i
$976$		0			0
$977$	1.50000	+	2.59808i	0.0479893	+	0.0831198i	0.889022	−	0.457864i	$-0.151385\pi$
$977$	1.50000	+	2.59808i	0.0479893	+	0.0831198i	−0.841033	+	0.540984i	$0.818052\pi$
$978$		0			0
$979$	−4.50000	+	7.79423i	−0.143821	+	0.249105i
$980$		0			0
$981$	14.0000	−	24.2487i	0.446986	−	0.774202i
$982$		0			0
$983$	−48.0000			−1.53096			−0.765481	−	0.643458i	$-0.777499\pi$
$983$	−48.0000			−1.53096			−0.765481	+	0.643458i	$0.777499\pi$
$984$		0			0
$985$	−1.50000	−	2.59808i	−0.0477940	−	0.0827816i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.00000			−0.286183
$990$		0			0
$991$	24.5000	+	42.4352i	0.778268	+	1.34800i	0.932939	+	0.360034i	$0.117235\pi$
$991$	24.5000	+	42.4352i	0.778268	+	1.34800i	−0.154671	+	0.987966i	$0.549432\pi$
$992$		0			0
$993$	−19.0000			−0.602947
$994$		0			0
$995$	−3.50000	+	6.06218i	−0.110957	+	0.192184i
$996$		0			0
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	−0.902895	−	0.429862i	$-0.858562\pi$
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	0.823719	+	0.566999i	$0.191896\pi$
$998$		0			0
$999$	−17.5000	−	30.3109i	−0.553675	−	0.958994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.i.a.81.1	yes	2
3.2	odd	2		2340.2.q.f.2161.1		2
4.3	odd	2		1040.2.q.i.81.1		2
5.2	odd	4		1300.2.bb.b.549.1		4
5.3	odd	4		1300.2.bb.b.549.2		4
5.4	even	2		1300.2.i.d.601.1		2
13.2	odd	12		3380.2.f.d.3041.2		2
13.3	even	3		3380.2.a.f.1.1		1
13.9	even	3	inner	260.2.i.a.61.1	✓	2
13.10	even	6		3380.2.a.i.1.1		1
13.11	odd	12		3380.2.f.d.3041.1		2
39.35	odd	6		2340.2.q.f.1621.1		2
52.35	odd	6		1040.2.q.i.321.1		2
65.9	even	6		1300.2.i.d.1101.1		2
65.22	odd	12		1300.2.bb.b.1049.2		4
65.48	odd	12		1300.2.bb.b.1049.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.i.a.61.1	✓	2	13.9	even	3	inner
260.2.i.a.81.1	yes	2	1.1	even	1	trivial
1040.2.q.i.81.1		2	4.3	odd	2
1040.2.q.i.321.1		2	52.35	odd	6
1300.2.i.d.601.1		2	5.4	even	2
1300.2.i.d.1101.1		2	65.9	even	6
1300.2.bb.b.549.1		4	5.2	odd	4
1300.2.bb.b.549.2		4	5.3	odd	4
1300.2.bb.b.1049.1		4	65.48	odd	12
1300.2.bb.b.1049.2		4	65.22	odd	12
2340.2.q.f.1621.1		2	39.35	odd	6
2340.2.q.f.2161.1		2	3.2	odd	2
3380.2.a.f.1.1		1	13.3	even	3
3380.2.a.i.1.1		1	13.10	even	6
3380.2.f.d.3041.1		2	13.11	odd	12
3380.2.f.d.3041.2		2	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(1.00000 - 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-2.50000 + 4.33013i) q^{19} -1.00000 q^{21} +(-4.50000 - 7.79423i) q^{23} +1.00000 q^{25} -5.00000 q^{27} +(4.50000 + 7.79423i) q^{29} +8.00000 q^{31} +(-1.50000 + 2.59808i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-3.50000 + 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-1.00000 + 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{49} -3.00000 q^{51} +6.00000 q^{53} +(1.50000 + 2.59808i) q^{55} +5.00000 q^{57} +(-4.50000 + 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-1.00000 - 1.73205i) q^{63} +(-1.00000 + 3.46410i) q^{65} +(-2.50000 - 4.33013i) q^{67} +(-4.50000 + 7.79423i) q^{69} +(-4.50000 + 7.79423i) q^{71} +2.00000 q^{73} +(-0.500000 - 0.866025i) q^{75} -3.00000 q^{77} +8.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{85} +(4.50000 - 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{89} +(-2.50000 - 2.59808i) q^{91} +(-4.00000 - 6.92820i) q^{93} +(2.50000 - 4.33013i) q^{95} +(-8.50000 + 14.7224i) q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} - 2 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - q^3 - 2 * q^5 + q^7 + 2 * q^9	\( 2 q - q^{3} - 2 q^{5} + q^{7} + 2 q^{9} - 3 q^{11} + 2 q^{13} + q^{15} + 3 q^{17} - 5 q^{19} - 2 q^{21} - 9 q^{23} + 2 q^{25} - 10 q^{27} + 9 q^{29} + 16 q^{31} - 3 q^{33} - q^{35} + 7 q^{37} - 7 q^{39} - 3 q^{41} + q^{43} - 2 q^{45} + 6 q^{49} - 6 q^{51} + 12 q^{53} + 3 q^{55} + 10 q^{57} - 9 q^{59} + q^{61} - 2 q^{63} - 2 q^{65} - 5 q^{67} - 9 q^{69} - 9 q^{71} + 4 q^{73} - q^{75} - 6 q^{77} + 16 q^{79} - q^{81} - 3 q^{85} + 9 q^{87} - 3 q^{89} - 5 q^{91} - 8 q^{93} + 5 q^{95} - 17 q^{97} - 12 q^{99}+O(q^{100}) \) 2 * q - q^3 - 2 * q^5 + q^7 + 2 * q^9 - 3 * q^11 + 2 * q^13 + q^15 + 3 * q^17 - 5 * q^19 - 2 * q^21 - 9 * q^23 + 2 * q^25 - 10 * q^27 + 9 * q^29 + 16 * q^31 - 3 * q^33 - q^35 + 7 * q^37 - 7 * q^39 - 3 * q^41 + q^43 - 2 * q^45 + 6 * q^49 - 6 * q^51 + 12 * q^53 + 3 * q^55 + 10 * q^57 - 9 * q^59 + q^61 - 2 * q^63 - 2 * q^65 - 5 * q^67 - 9 * q^69 - 9 * q^71 + 4 * q^73 - q^75 - 6 * q^77 + 16 * q^79 - q^81 - 3 * q^85 + 9 * q^87 - 3 * q^89 - 5 * q^91 - 8 * q^93 + 5 * q^95 - 17 * q^97 - 12 * q^99

Introduction

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