LMFDB - Embedded newform 676.2.h.b.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(361,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("676.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.h (of order $6$, degree $2$, not 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:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	676.361
Dual form			676.2.h.b.485.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 - 2.59808i) q^{3} -2.00000i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-3.00000 + 5.19615i) q^{9} +(-4.33013 + 2.50000i) q^{11} +(-5.19615 + 3.00000i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-2.59808 - 1.50000i) q^{19} +3.00000i q^{21} +(-0.500000 - 0.866025i) q^{23} +1.00000 q^{25} +9.00000 q^{27} +(0.500000 + 0.866025i) q^{29} +8.00000i q^{31} +(12.9904 + 7.50000i) q^{33} +(-1.00000 + 1.73205i) q^{35} +(2.59808 - 1.50000i) q^{37} +(-2.59808 + 1.50000i) q^{41} +(0.500000 - 0.866025i) q^{43} +(10.3923 + 6.00000i) q^{45} +4.00000i q^{47} +(-3.00000 - 5.19615i) q^{49} -9.00000 q^{51} -6.00000 q^{53} +(5.00000 + 8.66025i) q^{55} +9.00000i q^{57} +(-4.33013 - 2.50000i) q^{59} +(2.50000 - 4.33013i) q^{61} +(5.19615 - 3.00000i) q^{63} +(-6.06218 + 3.50000i) q^{67} +(-1.50000 + 2.59808i) q^{69} +(-9.52628 - 5.50000i) q^{71} +14.0000i q^{73} +(-1.50000 - 2.59808i) q^{75} +5.00000 q^{77} -4.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} -12.0000i q^{83} +(-5.19615 - 3.00000i) q^{85} +(1.50000 - 2.59808i) q^{87} +(-7.79423 + 4.50000i) q^{89} +(20.7846 - 12.0000i) q^{93} +(-3.00000 + 5.19615i) q^{95} +(-0.866025 - 0.500000i) q^{97} -30.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 12 q^{9} + 6 q^{17} - 2 q^{23} + 4 q^{25} + 36 q^{27} + 2 q^{29} - 4 q^{35} + 2 q^{43} - 12 q^{49} - 36 q^{51} - 24 q^{53} + 20 q^{55} + 10 q^{61} - 6 q^{69} - 6 q^{75} + 20 q^{77} - 16 q^{79}+ \cdots - 12 q^{95}+O(q^{100}) $ 4 * q - 6 * q^3 - 12 * q^9 + 6 * q^17 - 2 * q^23 + 4 * q^25 + 36 * q^27 + 2 * q^29 - 4 * q^35 + 2 * q^43 - 12 * q^49 - 36 * q^51 - 24 * q^53 + 20 * q^55 + 10 * q^61 - 6 * q^69 - 6 * q^75 + 20 * q^77 - 16 * q^79 - 18 * q^81 + 6 * q^87 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	2.59808i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−1.50000	−	2.59808i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$4$		0			0
$5$		−	2.00000i		−	0.894427i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$		−	2.00000i		−	0.894427i	0.894427	−	0.447214i	$-0.147584\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	0.327327	−	0.944911i	$-0.393852\pi$
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	−0.654654	+	0.755929i	$0.727186\pi$
$8$		0			0
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$		0			0
$11$	−4.33013	+	2.50000i	−1.30558	+	0.753778i	−0.981356	−	0.192201i	$-0.938437\pi$
$11$	−4.33013	+	2.50000i	−1.30558	+	0.753778i	−0.324227	+	0.945979i	$0.605104\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−5.19615	+	3.00000i	−1.34164	+	0.774597i
$16$		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
$19$	−2.59808	−	1.50000i	−0.596040	−	0.344124i	0.171442	−	0.985194i	$-0.445157\pi$
$19$	−2.59808	−	1.50000i	−0.596040	−	0.344124i	−0.767482	+	0.641071i	$0.778491\pi$
$20$		0			0
$21$			3.00000i			0.654654i
$22$		0			0
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	9.00000			1.73205
$28$		0			0
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$		0			0
$31$			8.00000i			1.43684i	0.695608	+	0.718421i	$0.255135\pi$
$31$			8.00000i			1.43684i	−0.695608	+	0.718421i	$0.744865\pi$
$32$		0			0
$33$	12.9904	+	7.50000i	2.26134	+	1.30558i
$34$		0			0
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$		0			0
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	−0.270998	−	0.962580i	$-0.587354\pi$
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	0.698119	+	0.715981i	$0.254020\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	−0.688963	−	0.724797i	$-0.741934\pi$
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	0.283211	+	0.959058i	$0.408600\pi$
$42$		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
$45$	10.3923	+	6.00000i	1.54919	+	0.894427i
$46$		0			0
$47$			4.00000i			0.583460i	0.956501	+	0.291730i	$0.0942309\pi$
$47$			4.00000i			0.583460i	−0.956501	+	0.291730i	$0.905769\pi$
$48$		0			0
$49$	−3.00000	−	5.19615i	−0.428571	−	0.742307i
$50$		0			0
$51$	−9.00000			−1.26025
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	5.00000	+	8.66025i	0.674200	+	1.16775i
$56$		0			0
$57$			9.00000i			1.19208i
$58$		0			0
$59$	−4.33013	−	2.50000i	−0.563735	−	0.325472i	0.190909	−	0.981608i	$-0.438857\pi$
$59$	−4.33013	−	2.50000i	−0.563735	−	0.325472i	−0.754643	+	0.656136i	$0.772190\pi$
$60$		0			0
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$		0			0
$63$	5.19615	−	3.00000i	0.654654	−	0.377964i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	−0.822292	−	0.569066i	$-0.807305\pi$
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	0.0816792	+	0.996659i	$0.473972\pi$
$68$		0			0
$69$	−1.50000	+	2.59808i	−0.180579	+	0.312772i
$70$		0			0
$71$	−9.52628	−	5.50000i	−1.13056	−	0.652730i	−0.186485	−	0.982458i	$-0.559710\pi$
$71$	−9.52628	−	5.50000i	−1.13056	−	0.652730i	−0.944076	+	0.329728i	$0.893043\pi$
$72$		0			0
$73$			14.0000i			1.63858i	0.573382	+	0.819288i	$0.305631\pi$
$73$			14.0000i			1.63858i	−0.573382	+	0.819288i	$0.694369\pi$
$74$		0			0
$75$	−1.50000	−	2.59808i	−0.173205	−	0.300000i
$76$		0			0
$77$	5.00000			0.569803
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$		0			0
$85$	−5.19615	−	3.00000i	−0.563602	−	0.325396i
$86$		0			0
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$		0			0
$89$	−7.79423	+	4.50000i	−0.826187	+	0.476999i	−0.852545	−	0.522654i	$-0.824942\pi$
$89$	−7.79423	+	4.50000i	−0.826187	+	0.476999i	0.0263586	+	0.999653i	$0.491609\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	20.7846	−	12.0000i	2.15526	−	1.24434i
$94$		0			0
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$		0			0
$97$	−0.866025	−	0.500000i	−0.0879316	−	0.0507673i	0.455389	−	0.890292i	$-0.349500\pi$
$97$	−0.866025	−	0.500000i	−0.0879316	−	0.0507673i	−0.543321	+	0.839525i	$0.682833\pi$
$98$		0			0
$99$		−	30.0000i		−	3.01511i
$100$		0			0
$101$	9.50000	+	16.4545i	0.945285	+	1.63728i	0.755179	+	0.655519i	$0.227550\pi$
$101$	9.50000	+	16.4545i	0.945285	+	1.63728i	0.190106	+	0.981763i	$0.439117\pi$
$102$		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
$105$	6.00000			0.585540
$106$		0			0
$107$	−5.50000	−	9.52628i	−0.531705	−	0.920940i	−0.999315	−	0.0370053i	$-0.988218\pi$
$107$	−5.50000	−	9.52628i	−0.531705	−	0.920940i	0.467610	−	0.883935i	$-0.345115\pi$
$108$		0			0
$109$		−	10.0000i		−	0.957826i	−0.877862	−	0.478913i	$-0.841031\pi$
$109$		−	10.0000i		−	0.957826i	0.877862	−	0.478913i	$-0.158969\pi$
$110$		0			0
$111$	−7.79423	−	4.50000i	−0.739795	−	0.427121i
$112$		0			0
$113$	−5.50000	+	9.52628i	−0.517396	+	0.896157i	0.482399	+	0.875951i	$0.339765\pi$
$113$	−5.50000	+	9.52628i	−0.517396	+	0.896157i	−0.999796	+	0.0202056i	$0.993568\pi$
$114$		0			0
$115$	−1.73205	+	1.00000i	−0.161515	+	0.0932505i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.59808	+	1.50000i	−0.238165	+	0.137505i
$120$		0			0
$121$	7.00000	−	12.1244i	0.636364	−	1.10221i
$122$		0			0
$123$	7.79423	+	4.50000i	0.702782	+	0.405751i
$124$		0			0
$125$		−	12.0000i		−	1.07331i
$126$		0			0
$127$	−2.50000	−	4.33013i	−0.221839	−	0.384237i	0.733527	−	0.679660i	$-0.237873\pi$
$127$	−2.50000	−	4.33013i	−0.221839	−	0.384237i	−0.955366	+	0.295423i	$0.904539\pi$
$128$		0			0
$129$	−3.00000			−0.264135
$130$		0			0
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$	1.50000	+	2.59808i	0.130066	+	0.225282i
$134$		0			0
$135$		−	18.0000i		−	1.54919i
$136$		0			0
$137$	−12.9904	−	7.50000i	−1.10984	−	0.640768i	−0.171054	−	0.985262i	$-0.554717\pi$
$137$	−12.9904	−	7.50000i	−1.10984	−	0.640768i	−0.938789	+	0.344493i	$0.888051\pi$
$138$		0			0
$139$	5.50000	−	9.52628i	0.466504	−	0.808008i	−0.532764	−	0.846264i	$-0.678847\pi$
$139$	5.50000	−	9.52628i	0.466504	−	0.808008i	0.999268	+	0.0382553i	$0.0121800\pi$
$140$		0			0
$141$	10.3923	−	6.00000i	0.875190	−	0.505291i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	1.73205	−	1.00000i	0.143839	−	0.0830455i
$146$		0			0
$147$	−9.00000	+	15.5885i	−0.742307	+	1.28571i
$148$		0			0
$149$	−18.1865	−	10.5000i	−1.48990	−	0.860194i	−0.489966	−	0.871742i	$-0.662991\pi$
$149$	−18.1865	−	10.5000i	−1.48990	−	0.860194i	−0.999933	+	0.0115483i	$0.996324\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$	9.00000	+	15.5885i	0.727607	+	1.26025i
$154$		0			0
$155$	16.0000			1.28515
$156$		0			0
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$		0			0
$159$	9.00000	+	15.5885i	0.713746	+	1.23625i
$160$		0			0
$161$			1.00000i			0.0788110i
$162$		0			0
$163$	6.06218	+	3.50000i	0.474826	+	0.274141i	0.718258	−	0.695777i	$-0.244940\pi$
$163$	6.06218	+	3.50000i	0.474826	+	0.274141i	−0.243432	+	0.969918i	$0.578273\pi$
$164$		0			0
$165$	15.0000	−	25.9808i	1.16775	−	2.02260i
$166$		0			0
$167$	−7.79423	+	4.50000i	−0.603136	+	0.348220i	−0.770274	−	0.637713i	$-0.779881\pi$
$167$	−7.79423	+	4.50000i	−0.603136	+	0.348220i	0.167139	+	0.985933i	$0.446547\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	15.5885	−	9.00000i	1.19208	−	0.688247i
$172$		0			0
$173$	5.50000	−	9.52628i	0.418157	−	0.724270i	−0.577597	−	0.816322i	$-0.696009\pi$
$173$	5.50000	−	9.52628i	0.418157	−	0.724270i	0.995754	+	0.0920525i	$0.0293428\pi$
$174$		0			0
$175$	−0.866025	−	0.500000i	−0.0654654	−	0.0377964i
$176$		0			0
$177$			15.0000i			1.12747i
$178$		0			0
$179$	−10.5000	−	18.1865i	−0.784807	−	1.35933i	−0.929114	−	0.369792i	$-0.879429\pi$
$179$	−10.5000	−	18.1865i	−0.784807	−	1.35933i	0.144308	−	0.989533i	$-0.453905\pi$
$180$		0			0
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$	−15.0000			−1.10883
$184$		0			0
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$		0			0
$187$			15.0000i			1.09691i
$188$		0			0
$189$	−7.79423	−	4.50000i	−0.566947	−	0.327327i
$190$		0			0
$191$	−0.500000	+	0.866025i	−0.0361787	+	0.0626634i	−0.883548	−	0.468341i	$-0.844852\pi$
$191$	−0.500000	+	0.866025i	−0.0361787	+	0.0626634i	0.847369	+	0.531004i	$0.178185\pi$
$192$		0			0
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	−0.116289	−	0.993215i	$-0.537100\pi$
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	0.802005	+	0.597317i	$0.203766\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.79423	−	4.50000i	0.555316	−	0.320612i	−0.195947	−	0.980614i	$-0.562778\pi$
$197$	7.79423	−	4.50000i	0.555316	−	0.320612i	0.751263	+	0.660003i	$0.229445\pi$
$198$		0			0
$199$	−9.50000	+	16.4545i	−0.673437	+	1.16643i	0.303486	+	0.952836i	$0.401849\pi$
$199$	−9.50000	+	16.4545i	−0.673437	+	1.16643i	−0.976923	+	0.213591i	$0.931484\pi$
$200$		0			0
$201$	18.1865	+	10.5000i	1.28278	+	0.740613i
$202$		0			0
$203$		−	1.00000i		−	0.0701862i
$204$		0			0
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$		0			0
$207$	6.00000			0.417029
$208$		0			0
$209$	15.0000			1.03757
$210$		0			0
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$			33.0000i			2.26112i
$214$		0			0
$215$	−1.73205	−	1.00000i	−0.118125	−	0.0681994i
$216$		0			0
$217$	4.00000	−	6.92820i	0.271538	−	0.470317i
$218$		0			0
$219$	36.3731	−	21.0000i	2.45786	−	1.41905i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	7.79423	−	4.50000i	0.521940	−	0.301342i	−0.215788	−	0.976440i	$-0.569232\pi$
$223$	7.79423	−	4.50000i	0.521940	−	0.301342i	0.737728	+	0.675098i	$0.235899\pi$
$224$		0			0
$225$	−3.00000	+	5.19615i	−0.200000	+	0.346410i
$226$		0			0
$227$	18.1865	+	10.5000i	1.20708	+	0.696909i	0.962121	−	0.272623i	$-0.0878913\pi$
$227$	18.1865	+	10.5000i	1.20708	+	0.696909i	0.244962	+	0.969533i	$0.421225\pi$
$228$		0			0
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$		0			0
$231$	−7.50000	−	12.9904i	−0.493464	−	0.854704i
$232$		0			0
$233$	−22.0000			−1.44127			−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000			−1.44127			−0.720634	+	0.693316i	$0.756149\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$		0			0
$237$	6.00000	+	10.3923i	0.389742	+	0.675053i
$238$		0			0
$239$		−	24.0000i		−	1.55243i	−0.630468	−	0.776215i	$-0.717137\pi$
$239$		−	24.0000i		−	1.55243i	0.630468	−	0.776215i	$-0.282863\pi$
$240$		0			0
$241$	18.1865	+	10.5000i	1.17150	+	0.676364i	0.954032	−	0.299704i	$-0.0968878\pi$
$241$	18.1865	+	10.5000i	1.17150	+	0.676364i	0.217465	+	0.976068i	$0.430221\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−10.3923	+	6.00000i	−0.663940	+	0.383326i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−31.1769	+	18.0000i	−1.97576	+	1.14070i
$250$		0			0
$251$	4.50000	−	7.79423i	0.284037	−	0.491967i	−0.688338	−	0.725390i	$-0.741659\pi$
$251$	4.50000	−	7.79423i	0.284037	−	0.491967i	0.972375	+	0.233423i	$0.0749927\pi$
$252$		0			0
$253$	4.33013	+	2.50000i	0.272233	+	0.157174i
$254$		0			0
$255$			18.0000i			1.12720i
$256$		0			0
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$		0			0
$259$	−3.00000			−0.186411
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	−7.50000	−	12.9904i	−0.462470	−	0.801021i	0.536614	−	0.843828i	$-0.319703\pi$
$263$	−7.50000	−	12.9904i	−0.462470	−	0.801021i	−0.999083	+	0.0428069i	$0.986370\pi$
$264$		0			0
$265$			12.0000i			0.737154i
$266$		0			0
$267$	23.3827	+	13.5000i	1.43100	+	0.826187i
$268$		0			0
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	−0.998816	−	0.0486418i	$-0.984511\pi$
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	0.541533	+	0.840679i	$0.317844\pi$
$270$		0			0
$271$	−14.7224	+	8.50000i	−0.894324	+	0.516338i	−0.875354	−	0.483482i	$-0.839372\pi$
$271$	−14.7224	+	8.50000i	−0.894324	+	0.516338i	−0.0189696	+	0.999820i	$0.506039\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.33013	+	2.50000i	−0.261116	+	0.150756i
$276$		0			0
$277$	−4.50000	+	7.79423i	−0.270379	+	0.468310i	−0.968959	−	0.247222i	$-0.920482\pi$
$277$	−4.50000	+	7.79423i	−0.270379	+	0.468310i	0.698580	+	0.715532i	$0.253816\pi$
$278$		0			0
$279$	−41.5692	−	24.0000i	−2.48868	−	1.43684i
$280$		0			0
$281$		−	2.00000i		−	0.119310i	−0.998219	−	0.0596550i	$-0.981000\pi$
$281$		−	2.00000i		−	0.119310i	0.998219	−	0.0596550i	$-0.0190001\pi$
$282$		0			0
$283$	9.50000	+	16.4545i	0.564716	+	0.978117i	0.997076	+	0.0764162i	$0.0243478\pi$
$283$	9.50000	+	16.4545i	0.564716	+	0.978117i	−0.432360	+	0.901701i	$0.642319\pi$
$284$		0			0
$285$	18.0000			1.06623
$286$		0			0
$287$	3.00000			0.177084
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$			3.00000i			0.175863i
$292$		0			0
$293$	−16.4545	−	9.50000i	−0.961281	−	0.554996i	−0.0647140	−	0.997904i	$-0.520614\pi$
$293$	−16.4545	−	9.50000i	−0.961281	−	0.554996i	−0.896567	+	0.442908i	$0.853947\pi$
$294$		0			0
$295$	−5.00000	+	8.66025i	−0.291111	+	0.504219i
$296$		0			0
$297$	−38.9711	+	22.5000i	−2.26134	+	1.30558i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−0.866025	+	0.500000i	−0.0499169	+	0.0288195i
$302$		0			0
$303$	28.5000	−	49.3634i	1.63728	−	2.83586i
$304$		0			0
$305$	−8.66025	−	5.00000i	−0.495885	−	0.286299i
$306$		0			0
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		0			0
$309$	−12.0000	−	20.7846i	−0.682656	−	1.18240i
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$		0			0
$315$	−6.00000	−	10.3923i	−0.338062	−	0.585540i
$316$		0			0
$317$		−	30.0000i		−	1.68497i	−0.538721	−	0.842484i	$-0.681092\pi$
$317$		−	30.0000i		−	1.68497i	0.538721	−	0.842484i	$-0.318908\pi$
$318$		0			0
$319$	−4.33013	−	2.50000i	−0.242441	−	0.139973i
$320$		0			0
$321$	−16.5000	+	28.5788i	−0.920940	+	1.59512i
$322$		0			0
$323$	−7.79423	+	4.50000i	−0.433682	+	0.250387i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−25.9808	+	15.0000i	−1.43674	+	0.829502i
$328$		0			0
$329$	2.00000	−	3.46410i	0.110264	−	0.190982i
$330$		0			0
$331$	14.7224	+	8.50000i	0.809218	+	0.467202i	0.846684	−	0.532096i	$-0.178595\pi$
$331$	14.7224	+	8.50000i	0.809218	+	0.467202i	−0.0374662	+	0.999298i	$0.511929\pi$
$332$		0			0
$333$			18.0000i			0.986394i
$334$		0			0
$335$	7.00000	+	12.1244i	0.382451	+	0.662424i
$336$		0			0
$337$	10.0000			0.544735			0.272367	−	0.962193i	$-0.412193\pi$
$337$	10.0000			0.544735			0.272367	+	0.962193i	$0.412193\pi$
$338$		0			0
$339$	33.0000			1.79231
$340$		0			0
$341$	−20.0000	−	34.6410i	−1.08306	−	1.87592i
$342$		0			0
$343$			13.0000i			0.701934i
$344$		0			0
$345$	5.19615	+	3.00000i	0.279751	+	0.161515i
$346$		0			0
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.0409337	+	0.999162i	$0.513033\pi$
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.844833	+	0.535031i	$0.820300\pi$
$348$		0			0
$349$	16.4545	−	9.50000i	0.880788	−	0.508523i	0.00987003	−	0.999951i	$-0.496858\pi$
$349$	16.4545	−	9.50000i	0.880788	−	0.508523i	0.870918	+	0.491428i	$0.163525\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.06218	+	3.50000i	−0.322657	+	0.186286i	−0.652576	−	0.757723i	$-0.726312\pi$
$353$	−6.06218	+	3.50000i	−0.322657	+	0.186286i	0.329919	+	0.944009i	$0.392979\pi$
$354$		0			0
$355$	−11.0000	+	19.0526i	−0.583819	+	1.01120i
$356$		0			0
$357$	7.79423	+	4.50000i	0.412514	+	0.238165i
$358$		0			0
$359$		−	24.0000i		−	1.26667i	−0.773877	−	0.633336i	$-0.781685\pi$
$359$		−	24.0000i		−	1.26667i	0.773877	−	0.633336i	$-0.218315\pi$
$360$		0			0
$361$	−5.00000	−	8.66025i	−0.263158	−	0.455803i
$362$		0			0
$363$	−42.0000			−2.20443
$364$		0			0
$365$	28.0000			1.46559
$366$		0			0
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	−0.992776	−	0.119982i	$-0.961716\pi$
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	0.392481	−	0.919760i	$-0.371617\pi$
$368$		0			0
$369$		−	18.0000i		−	0.937043i
$370$		0			0
$371$	5.19615	+	3.00000i	0.269771	+	0.155752i
$372$		0			0
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	0.398036	+	0.917370i	$0.369692\pi$
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	−0.993484	+	0.113975i	$0.963641\pi$
$374$		0			0
$375$	−31.1769	+	18.0000i	−1.60997	+	0.929516i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	4.33013	−	2.50000i	0.222424	−	0.128416i	−0.384648	−	0.923063i	$-0.625677\pi$
$379$	4.33013	−	2.50000i	0.222424	−	0.128416i	0.607072	+	0.794647i	$0.292344\pi$
$380$		0			0
$381$	−7.50000	+	12.9904i	−0.384237	+	0.665517i
$382$		0			0
$383$	7.79423	+	4.50000i	0.398266	+	0.229939i	0.685736	−	0.727851i	$-0.259481\pi$
$383$	7.79423	+	4.50000i	0.398266	+	0.229939i	−0.287469	+	0.957790i	$0.592814\pi$
$384$		0			0
$385$		−	10.0000i		−	0.509647i
$386$		0			0
$387$	3.00000	+	5.19615i	0.152499	+	0.264135i
$388$		0			0
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	−3.00000			−0.151717
$392$		0			0
$393$	6.00000	+	10.3923i	0.302660	+	0.524222i
$394$		0			0
$395$			8.00000i			0.402524i
$396$		0			0
$397$	21.6506	+	12.5000i	1.08661	+	0.627357i	0.932673	−	0.360723i	$-0.117470\pi$
$397$	21.6506	+	12.5000i	1.08661	+	0.627357i	0.153941	+	0.988080i	$0.450803\pi$
$398$		0			0
$399$	4.50000	−	7.79423i	0.225282	−	0.390199i
$400$		0			0
$401$	23.3827	−	13.5000i	1.16768	−	0.674158i	0.214544	−	0.976714i	$-0.431173\pi$
$401$	23.3827	−	13.5000i	1.16768	−	0.674158i	0.953131	+	0.302556i	$0.0978401\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−15.5885	+	9.00000i	−0.774597	+	0.447214i
$406$		0			0
$407$	−7.50000	+	12.9904i	−0.371761	+	0.643909i
$408$		0			0
$409$	−4.33013	−	2.50000i	−0.214111	−	0.123617i	0.389109	−	0.921192i	$-0.372783\pi$
$409$	−4.33013	−	2.50000i	−0.214111	−	0.123617i	−0.603220	+	0.797574i	$0.706116\pi$
$410$		0			0
$411$			45.0000i			2.21969i
$412$		0			0
$413$	2.50000	+	4.33013i	0.123017	+	0.213072i
$414$		0			0
$415$	−24.0000			−1.17811
$416$		0			0
$417$	−33.0000			−1.61602
$418$		0			0
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	0.622601	−	0.782540i	$-0.286076\pi$
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	−0.989000	+	0.147918i	$0.952743\pi$
$420$		0			0
$421$		−	10.0000i		−	0.487370i	−0.969854	−	0.243685i	$-0.921644\pi$
$421$		−	10.0000i		−	0.487370i	0.969854	−	0.243685i	$-0.0783563\pi$
$422$		0			0
$423$	−20.7846	−	12.0000i	−1.01058	−	0.583460i
$424$		0			0
$425$	1.50000	−	2.59808i	0.0727607	−	0.126025i
$426$		0			0
$427$	−4.33013	+	2.50000i	−0.209550	+	0.120983i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.59808	+	1.50000i	−0.125145	+	0.0722525i	−0.561266	−	0.827636i	$-0.689685\pi$
$431$	−2.59808	+	1.50000i	−0.125145	+	0.0722525i	0.436121	+	0.899888i	$0.356352\pi$
$432$		0			0
$433$	9.50000	−	16.4545i	0.456541	−	0.790752i	−0.542234	−	0.840227i	$-0.682422\pi$
$433$	9.50000	−	16.4545i	0.456541	−	0.790752i	0.998775	+	0.0494752i	$0.0157549\pi$
$434$		0			0
$435$	−5.19615	−	3.00000i	−0.249136	−	0.143839i
$436$		0			0
$437$			3.00000i			0.143509i
$438$		0			0
$439$	−6.50000	−	11.2583i	−0.310228	−	0.537331i	0.668184	−	0.743996i	$-0.267072\pi$
$439$	−6.50000	−	11.2583i	−0.310228	−	0.537331i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		0			0
$441$	36.0000			1.71429
$442$		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
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$		0			0
$447$			63.0000i			2.97980i
$448$		0			0
$449$	4.33013	+	2.50000i	0.204351	+	0.117982i	0.598684	−	0.800986i	$-0.295691\pi$
$449$	4.33013	+	2.50000i	0.204351	+	0.117982i	−0.394332	+	0.918968i	$0.629024\pi$
$450$		0			0
$451$	7.50000	−	12.9904i	0.353161	−	0.611693i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	14.7224	−	8.50000i	0.688686	−	0.397613i	−0.114433	−	0.993431i	$-0.536505\pi$
$457$	14.7224	−	8.50000i	0.688686	−	0.397613i	0.803120	+	0.595818i	$0.203172\pi$
$458$		0			0
$459$	13.5000	−	23.3827i	0.630126	−	1.09141i
$460$		0			0
$461$	−7.79423	−	4.50000i	−0.363013	−	0.209586i	0.307388	−	0.951584i	$-0.400545\pi$
$461$	−7.79423	−	4.50000i	−0.363013	−	0.209586i	−0.670402	+	0.741998i	$0.733878\pi$
$462$		0			0
$463$			40.0000i			1.85896i	0.368875	+	0.929479i	$0.379743\pi$
$463$			40.0000i			1.85896i	−0.368875	+	0.929479i	$0.620257\pi$
$464$		0			0
$465$	−24.0000	−	41.5692i	−1.11297	−	1.92773i
$466$		0			0
$467$	16.0000			0.740392			0.370196	−	0.928954i	$-0.379291\pi$
$467$	16.0000			0.740392			0.370196	+	0.928954i	$0.379291\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$		0			0
$471$	33.0000	+	57.1577i	1.52056	+	2.63369i
$472$		0			0
$473$			5.00000i			0.229900i
$474$		0			0
$475$	−2.59808	−	1.50000i	−0.119208	−	0.0688247i
$476$		0			0
$477$	18.0000	−	31.1769i	0.824163	−	1.42749i
$478$		0			0
$479$	2.59808	−	1.50000i	0.118709	−	0.0685367i	−0.439470	−	0.898257i	$-0.644834\pi$
$479$	2.59808	−	1.50000i	0.118709	−	0.0685367i	0.558179	+	0.829721i	$0.311500\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	2.59808	−	1.50000i	0.118217	−	0.0682524i
$484$		0			0
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$		0			0
$487$	25.1147	+	14.5000i	1.13806	+	0.657058i	0.945949	−	0.324316i	$-0.105134\pi$
$487$	25.1147	+	14.5000i	1.13806	+	0.657058i	0.192109	+	0.981374i	$0.438467\pi$
$488$		0			0
$489$		−	21.0000i		−	0.949653i
$490$		0			0
$491$	15.5000	+	26.8468i	0.699505	+	1.21158i	0.968638	+	0.248476i	$0.0799296\pi$
$491$	15.5000	+	26.8468i	0.699505	+	1.21158i	−0.269133	+	0.963103i	$0.586737\pi$
$492$		0			0
$493$	3.00000			0.135113
$494$		0			0
$495$	−60.0000			−2.69680
$496$		0			0
$497$	5.50000	+	9.52628i	0.246709	+	0.427312i
$498$		0			0
$499$		−	4.00000i		−	0.179065i	−0.995984	−	0.0895323i	$-0.971463\pi$
$499$		−	4.00000i		−	0.179065i	0.995984	−	0.0895323i	$-0.0285372\pi$
$500$		0			0
$501$	23.3827	+	13.5000i	1.04466	+	0.603136i
$502$		0			0
$503$	11.5000	−	19.9186i	0.512760	−	0.888126i	−0.487131	−	0.873329i	$-0.661957\pi$
$503$	11.5000	−	19.9186i	0.512760	−	0.888126i	0.999891	−	0.0147968i	$-0.00471014\pi$
$504$		0			0
$505$	32.9090	−	19.0000i	1.46443	−	0.845489i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.33013	−	2.50000i	0.191930	−	0.110811i	−0.400956	−	0.916097i	$-0.631322\pi$
$509$	4.33013	−	2.50000i	0.191930	−	0.110811i	0.592886	+	0.805287i	$0.297989\pi$
$510$		0			0
$511$	7.00000	−	12.1244i	0.309662	−	0.536350i
$512$		0			0
$513$	−23.3827	−	13.5000i	−1.03237	−	0.596040i
$514$		0			0
$515$		−	16.0000i		−	0.705044i
$516$		0			0
$517$	−10.0000	−	17.3205i	−0.439799	−	0.761755i
$518$		0			0
$519$	−33.0000			−1.44854
$520$		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
$523$	−7.50000	−	12.9904i	−0.327952	−	0.568030i	0.654153	−	0.756362i	$-0.273025\pi$
$523$	−7.50000	−	12.9904i	−0.327952	−	0.568030i	−0.982105	+	0.188332i	$0.939692\pi$
$524$		0			0
$525$			3.00000i			0.130931i
$526$		0			0
$527$	20.7846	+	12.0000i	0.905392	+	0.522728i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$		0			0
$531$	25.9808	−	15.0000i	1.12747	−	0.650945i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−19.0526	+	11.0000i	−0.823714	+	0.475571i
$536$		0			0
$537$	−31.5000	+	54.5596i	−1.35933	+	2.35442i
$538$		0			0
$539$	25.9808	+	15.0000i	1.11907	+	0.646096i
$540$		0			0
$541$		−	34.0000i		−	1.46177i	−0.682498	−	0.730887i	$-0.739107\pi$
$541$		−	34.0000i		−	1.46177i	0.682498	−	0.730887i	$-0.260893\pi$
$542$		0			0
$543$	27.0000	+	46.7654i	1.15868	+	2.00689i
$544$		0			0
$545$	−20.0000			−0.856706
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		0			0
$549$	15.0000	+	25.9808i	0.640184	+	1.10883i
$550$		0			0
$551$		−	3.00000i		−	0.127804i
$552$		0			0
$553$	3.46410	+	2.00000i	0.147309	+	0.0850487i
$554$		0			0
$555$	−9.00000	+	15.5885i	−0.382029	+	0.661693i
$556$		0			0
$557$	−28.5788	+	16.5000i	−1.21092	+	0.699127i	−0.962961	−	0.269642i	$-0.913095\pi$
$557$	−28.5788	+	16.5000i	−1.21092	+	0.699127i	−0.247964	+	0.968769i	$0.579761\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	38.9711	−	22.5000i	1.64536	−	0.949951i
$562$		0			0
$563$	−9.50000	+	16.4545i	−0.400377	+	0.693474i	−0.993771	−	0.111438i	$-0.964454\pi$
$563$	−9.50000	+	16.4545i	−0.400377	+	0.693474i	0.593394	+	0.804912i	$0.297788\pi$
$564$		0			0
$565$	19.0526	+	11.0000i	0.801547	+	0.462773i
$566$		0			0
$567$			9.00000i			0.377964i
$568$		0			0
$569$	3.50000	+	6.06218i	0.146728	+	0.254140i	0.930016	−	0.367519i	$-0.119793\pi$
$569$	3.50000	+	6.06218i	0.146728	+	0.254140i	−0.783289	+	0.621658i	$0.786459\pi$
$570$		0			0
$571$	−12.0000			−0.502184			−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000			−0.502184			−0.251092	+	0.967963i	$0.580790\pi$
$572$		0			0
$573$	3.00000			0.125327
$574$		0			0
$575$	−0.500000	−	0.866025i	−0.0208514	−	0.0361158i
$576$		0			0
$577$		−	6.00000i		−	0.249783i	−0.992170	−	0.124892i	$-0.960142\pi$
$577$		−	6.00000i		−	0.249783i	0.992170	−	0.124892i	$-0.0398583\pi$
$578$		0			0
$579$	−28.5788	−	16.5000i	−1.18770	−	0.685717i
$580$		0			0
$581$	−6.00000	+	10.3923i	−0.248922	+	0.431145i
$582$		0			0
$583$	25.9808	−	15.0000i	1.07601	−	0.621237i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.6506	−	12.5000i	0.893617	−	0.515930i	0.0184934	−	0.999829i	$-0.494113\pi$
$587$	21.6506	−	12.5000i	0.893617	−	0.515930i	0.875124	+	0.483899i	$0.160780\pi$
$588$		0			0
$589$	12.0000	−	20.7846i	0.494451	−	0.856415i
$590$		0			0
$591$	−23.3827	−	13.5000i	−0.961835	−	0.555316i
$592$		0			0
$593$		−	34.0000i		−	1.39621i	−0.715994	−	0.698106i	$-0.754026\pi$
$593$		−	34.0000i		−	1.39621i	0.715994	−	0.698106i	$-0.245974\pi$
$594$		0			0
$595$	3.00000	+	5.19615i	0.122988	+	0.213021i
$596$		0			0
$597$	57.0000			2.33285
$598$		0			0
$599$	−20.0000			−0.817178			−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000			−0.817178			−0.408589	+	0.912719i	$0.633979\pi$
$600$		0			0
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	0.604601	−	0.796528i	$-0.293332\pi$
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	−0.992114	+	0.125336i	$0.959999\pi$
$602$		0			0
$603$		−	42.0000i		−	1.71037i
$604$		0			0
$605$	−24.2487	−	14.0000i	−0.985850	−	0.569181i
$606$		0			0
$607$	13.5000	−	23.3827i	0.547948	−	0.949074i	−0.450467	−	0.892793i	$-0.648742\pi$
$607$	13.5000	−	23.3827i	0.547948	−	0.949074i	0.998415	−	0.0562808i	$-0.0179242\pi$
$608$		0			0
$609$	−2.59808	+	1.50000i	−0.105279	+	0.0607831i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−9.52628	+	5.50000i	−0.384763	+	0.222143i	−0.679888	−	0.733316i	$-0.737972\pi$
$613$	−9.52628	+	5.50000i	−0.384763	+	0.222143i	0.295126	+	0.955458i	$0.404638\pi$
$614$		0			0
$615$	9.00000	−	15.5885i	0.362915	−	0.628587i
$616$		0			0
$617$	6.06218	+	3.50000i	0.244054	+	0.140905i	0.617039	−	0.786933i	$-0.288332\pi$
$617$	6.06218	+	3.50000i	0.244054	+	0.140905i	−0.372985	+	0.927838i	$0.621666\pi$
$618$		0			0
$619$		−	20.0000i		−	0.803868i	−0.915669	−	0.401934i	$-0.868338\pi$
$619$		−	20.0000i		−	0.803868i	0.915669	−	0.401934i	$-0.131662\pi$
$620$		0			0
$621$	−4.50000	−	7.79423i	−0.180579	−	0.312772i
$622$		0			0
$623$	9.00000			0.360577
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$	−22.5000	−	38.9711i	−0.898563	−	1.55636i
$628$		0			0
$629$		−	9.00000i		−	0.358854i
$630$		0			0
$631$	−32.0429	−	18.5000i	−1.27561	−	0.736473i	−0.299571	−	0.954074i	$-0.596844\pi$
$631$	−32.0429	−	18.5000i	−1.27561	−	0.736473i	−0.976038	+	0.217601i	$0.930177\pi$
$632$		0			0
$633$	19.5000	−	33.7750i	0.775055	−	1.34244i
$634$		0			0
$635$	−8.66025	+	5.00000i	−0.343672	+	0.198419i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	57.1577	−	33.0000i	2.26112	−	1.30546i
$640$		0			0
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	−0.911165	−	0.412042i	$-0.864816\pi$
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	0.812421	+	0.583071i	$0.198149\pi$
$642$		0			0
$643$	−26.8468	−	15.5000i	−1.05873	−	0.611260i	−0.133652	−	0.991028i	$-0.542670\pi$
$643$	−26.8468	−	15.5000i	−1.05873	−	0.611260i	−0.925082	+	0.379768i	$0.876004\pi$
$644$		0			0
$645$			6.00000i			0.236250i
$646$		0			0
$647$	−14.5000	−	25.1147i	−0.570054	−	0.987362i	−0.996560	−	0.0828774i	$-0.973589\pi$
$647$	−14.5000	−	25.1147i	−0.570054	−	0.987362i	0.426506	−	0.904485i	$-0.359744\pi$
$648$		0			0
$649$	25.0000			0.981336
$650$		0			0
$651$	−24.0000			−0.940634
$652$		0			0
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	0.835182	−	0.549973i	$-0.185362\pi$
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	−0.893882	+	0.448303i	$0.852029\pi$
$654$		0			0
$655$			8.00000i			0.312586i
$656$		0			0
$657$	−72.7461	−	42.0000i	−2.83810	−	1.63858i
$658$		0			0
$659$	−16.5000	+	28.5788i	−0.642749	+	1.11327i	0.342068	+	0.939675i	$0.388873\pi$
$659$	−16.5000	+	28.5788i	−0.642749	+	1.11327i	−0.984817	+	0.173598i	$0.944461\pi$
$660$		0			0
$661$	−32.0429	+	18.5000i	−1.24633	+	0.719567i	−0.970375	−	0.241605i	$-0.922326\pi$
$661$	−32.0429	+	18.5000i	−1.24633	+	0.719567i	−0.275951	+	0.961172i	$0.588993\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.19615	−	3.00000i	0.201498	−	0.116335i
$666$		0			0
$667$	0.500000	−	0.866025i	0.0193601	−	0.0335326i
$668$		0			0
$669$	−23.3827	−	13.5000i	−0.904027	−	0.521940i
$670$		0			0
$671$			25.0000i			0.965114i
$672$		0			0
$673$	3.50000	+	6.06218i	0.134915	+	0.233680i	0.925565	−	0.378589i	$-0.123591\pi$
$673$	3.50000	+	6.06218i	0.134915	+	0.233680i	−0.790650	+	0.612268i	$0.790257\pi$
$674$		0			0
$675$	9.00000			0.346410
$676$		0			0
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$		0			0
$679$	0.500000	+	0.866025i	0.0191882	+	0.0332350i
$680$		0			0
$681$		−	63.0000i		−	2.41417i
$682$		0			0
$683$	9.52628	+	5.50000i	0.364513	+	0.210452i	0.671059	−	0.741404i	$-0.265840\pi$
$683$	9.52628	+	5.50000i	0.364513	+	0.210452i	−0.306546	+	0.951856i	$0.599173\pi$
$684$		0			0
$685$	−15.0000	+	25.9808i	−0.573121	+	0.992674i
$686$		0			0
$687$	−15.5885	+	9.00000i	−0.594737	+	0.343371i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	4.33013	−	2.50000i	0.164726	−	0.0951045i	−0.415371	−	0.909652i	$-0.636348\pi$
$691$	4.33013	−	2.50000i	0.164726	−	0.0951045i	0.580097	+	0.814548i	$0.303015\pi$
$692$		0			0
$693$	−15.0000	+	25.9808i	−0.569803	+	0.986928i
$694$		0			0
$695$	−19.0526	−	11.0000i	−0.722705	−	0.417254i
$696$		0			0
$697$			9.00000i			0.340899i
$698$		0			0
$699$	33.0000	+	57.1577i	1.24817	+	2.16190i
$700$		0			0
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	−9.00000			−0.339441
$704$		0			0
$705$	−12.0000	−	20.7846i	−0.451946	−	0.782794i
$706$		0			0
$707$		−	19.0000i		−	0.714569i
$708$		0			0
$709$	0.866025	+	0.500000i	0.0325243	+	0.0187779i	0.516174	−	0.856484i	$-0.327356\pi$
$709$	0.866025	+	0.500000i	0.0325243	+	0.0187779i	−0.483650	+	0.875262i	$0.660689\pi$
$710$		0			0
$711$	12.0000	−	20.7846i	0.450035	−	0.779484i
$712$		0			0
$713$	6.92820	−	4.00000i	0.259463	−	0.149801i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−62.3538	+	36.0000i	−2.32865	+	1.34444i
$718$		0			0
$719$	8.50000	−	14.7224i	0.316997	−	0.549054i	−0.662863	−	0.748740i	$-0.730659\pi$
$719$	8.50000	−	14.7224i	0.316997	−	0.549054i	0.979860	+	0.199686i	$0.0639923\pi$
$720$		0			0
$721$	−6.92820	−	4.00000i	−0.258020	−	0.148968i
$722$		0			0
$723$		−	63.0000i		−	2.34300i
$724$		0			0
$725$	0.500000	+	0.866025i	0.0185695	+	0.0321634i
$726$		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
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$		0			0
$733$		−	14.0000i		−	0.517102i	−0.965998	−	0.258551i	$-0.916755\pi$
$733$		−	14.0000i		−	0.517102i	0.965998	−	0.258551i	$-0.0832450\pi$
$734$		0			0
$735$	31.1769	+	18.0000i	1.14998	+	0.663940i
$736$		0			0
$737$	17.5000	−	30.3109i	0.644621	−	1.11652i
$738$		0			0
$739$	12.9904	−	7.50000i	0.477859	−	0.275892i	−0.241665	−	0.970360i	$-0.577693\pi$
$739$	12.9904	−	7.50000i	0.477859	−	0.275892i	0.719524	+	0.694468i	$0.244360\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	25.1147	−	14.5000i	0.921370	−	0.531953i	0.0372984	−	0.999304i	$-0.488125\pi$
$743$	25.1147	−	14.5000i	0.921370	−	0.531953i	0.884072	+	0.467351i	$0.154791\pi$
$744$		0			0
$745$	−21.0000	+	36.3731i	−0.769380	+	1.33261i
$746$		0			0
$747$	62.3538	+	36.0000i	2.28141	+	1.31717i
$748$		0			0
$749$			11.0000i			0.401931i
$750$		0			0
$751$	−4.50000	−	7.79423i	−0.164207	−	0.284415i	0.772166	−	0.635421i	$-0.219173\pi$
$751$	−4.50000	−	7.79423i	−0.164207	−	0.284415i	−0.936374	+	0.351005i	$0.885840\pi$
$752$		0			0
$753$	−27.0000			−0.983935
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	0.837478	−	0.546471i	$-0.184029\pi$
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	−0.891997	+	0.452042i	$0.850696\pi$
$758$		0			0
$759$		−	15.0000i		−	0.544466i
$760$		0			0
$761$	−23.3827	−	13.5000i	−0.847622	−	0.489375i	0.0122260	−	0.999925i	$-0.496108\pi$
$761$	−23.3827	−	13.5000i	−0.847622	−	0.489375i	−0.859848	+	0.510551i	$0.829442\pi$
$762$		0			0
$763$	−5.00000	+	8.66025i	−0.181012	+	0.313522i
$764$		0			0
$765$	31.1769	−	18.0000i	1.12720	−	0.650791i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	18.1865	−	10.5000i	0.655823	−	0.378640i	−0.134860	−	0.990865i	$-0.543059\pi$
$769$	18.1865	−	10.5000i	0.655823	−	0.378640i	0.790684	+	0.612225i	$0.209725\pi$
$770$		0			0
$771$	4.50000	−	7.79423i	0.162064	−	0.280702i
$772$		0			0
$773$	−0.866025	−	0.500000i	−0.0311488	−	0.0179838i	0.484345	−	0.874877i	$-0.339058\pi$
$773$	−0.866025	−	0.500000i	−0.0311488	−	0.0179838i	−0.515494	+	0.856893i	$0.672391\pi$
$774$		0			0
$775$			8.00000i			0.287368i
$776$		0			0
$777$	4.50000	+	7.79423i	0.161437	+	0.279616i
$778$		0			0
$779$	9.00000			0.322458
$780$		0			0
$781$	55.0000			1.96805
$782$		0			0
$783$	4.50000	+	7.79423i	0.160817	+	0.278543i
$784$		0			0
$785$			44.0000i			1.57043i
$786$		0			0
$787$	6.06218	+	3.50000i	0.216093	+	0.124762i	0.604140	−	0.796878i	$-0.293517\pi$
$787$	6.06218	+	3.50000i	0.216093	+	0.124762i	−0.388047	+	0.921640i	$0.626850\pi$
$788$		0			0
$789$	−22.5000	+	38.9711i	−0.801021	+	1.38741i
$790$		0			0
$791$	9.52628	−	5.50000i	0.338716	−	0.195557i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	31.1769	−	18.0000i	1.10573	−	0.638394i
$796$		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
$799$	10.3923	+	6.00000i	0.367653	+	0.212265i
$800$		0			0
$801$		−	54.0000i		−	1.90800i
$802$		0			0
$803$	−35.0000	−	60.6218i	−1.23512	−	2.13930i
$804$		0			0
$805$	2.00000			0.0704907
$806$		0			0
$807$	45.0000			1.58408
$808$		0			0
$809$	22.5000	+	38.9711i	0.791058	+	1.37015i	0.925312	+	0.379206i	$0.123803\pi$
$809$	22.5000	+	38.9711i	0.791058	+	1.37015i	−0.134255	+	0.990947i	$0.542864\pi$
$810$		0			0
$811$			40.0000i			1.40459i	0.711886	+	0.702295i	$0.247841\pi$
$811$			40.0000i			1.40459i	−0.711886	+	0.702295i	$0.752159\pi$
$812$		0			0
$813$	44.1673	+	25.5000i	1.54901	+	0.894324i
$814$		0			0
$815$	7.00000	−	12.1244i	0.245199	−	0.424698i
$816$		0			0
$817$	−2.59808	+	1.50000i	−0.0908952	+	0.0524784i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−40.7032	+	23.5000i	−1.42055	+	0.820156i	−0.996346	−	0.0854103i	$-0.972780\pi$
$821$	−40.7032	+	23.5000i	−1.42055	+	0.820156i	−0.424205	+	0.905566i	$0.639447\pi$
$822$		0			0
$823$	−1.50000	+	2.59808i	−0.0522867	+	0.0905632i	−0.890984	−	0.454034i	$-0.849984\pi$
$823$	−1.50000	+	2.59808i	−0.0522867	+	0.0905632i	0.838697	+	0.544598i	$0.183318\pi$
$824$		0			0
$825$	12.9904	+	7.50000i	0.452267	+	0.261116i
$826$		0			0
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$		0			0
$829$	15.5000	+	26.8468i	0.538337	+	0.932427i	0.998994	+	0.0448490i	$0.0142807\pi$
$829$	15.5000	+	26.8468i	0.538337	+	0.932427i	−0.460657	+	0.887578i	$0.652386\pi$
$830$		0			0
$831$	27.0000			0.936620
$832$		0			0
$833$	−18.0000			−0.623663
$834$		0			0
$835$	9.00000	+	15.5885i	0.311458	+	0.539461i
$836$		0			0
$837$			72.0000i			2.48868i
$838$		0			0
$839$	37.2391	+	21.5000i	1.28564	+	0.742262i	0.977873	−	0.209200i	$-0.0670861\pi$
$839$	37.2391	+	21.5000i	1.28564	+	0.742262i	0.307763	+	0.951463i	$0.400419\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$		0			0
$843$	−5.19615	+	3.00000i	−0.178965	+	0.103325i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.1244	+	7.00000i	−0.416598	+	0.240523i
$848$		0			0
$849$	28.5000	−	49.3634i	0.978117	−	1.69415i
$850$		0			0
$851$	−2.59808	−	1.50000i	−0.0890609	−	0.0514193i
$852$		0			0
$853$			10.0000i			0.342393i	0.985237	+	0.171197i	$0.0547634\pi$
$853$			10.0000i			0.342393i	−0.985237	+	0.171197i	$0.945237\pi$
$854$		0			0
$855$	−18.0000	−	31.1769i	−0.615587	−	1.06623i
$856$		0			0
$857$	2.00000			0.0683187			0.0341593	−	0.999416i	$-0.489125\pi$
$857$	2.00000			0.0683187			0.0341593	+	0.999416i	$0.489125\pi$
$858$		0			0
$859$	−28.0000			−0.955348			−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000			−0.955348			−0.477674	+	0.878537i	$0.658520\pi$
$860$		0			0
$861$	−4.50000	−	7.79423i	−0.153360	−	0.265627i
$862$		0			0
$863$		−	16.0000i		−	0.544646i	−0.962206	−	0.272323i	$-0.912208\pi$
$863$		−	16.0000i		−	0.544646i	0.962206	−	0.272323i	$-0.0877920\pi$
$864$		0			0
$865$	−19.0526	−	11.0000i	−0.647806	−	0.374011i
$866$		0			0
$867$	12.0000	−	20.7846i	0.407541	−	0.705882i
$868$		0			0
$869$	17.3205	−	10.0000i	0.587558	−	0.339227i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	5.19615	−	3.00000i	0.175863	−	0.101535i
$874$		0			0
$875$	−6.00000	+	10.3923i	−0.202837	+	0.351324i
$876$		0			0
$877$	−38.9711	−	22.5000i	−1.31596	−	0.759771i	−0.332886	−	0.942967i	$-0.608022\pi$
$877$	−38.9711	−	22.5000i	−1.31596	−	0.759771i	−0.983076	+	0.183196i	$0.941356\pi$
$878$		0			0
$879$			57.0000i			1.92256i
$880$		0			0
$881$	25.5000	+	44.1673i	0.859117	+	1.48803i	0.872772	+	0.488127i	$0.162320\pi$
$881$	25.5000	+	44.1673i	0.859117	+	1.48803i	−0.0136556	+	0.999907i	$0.504347\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$		0			0
$885$	30.0000			1.00844
$886$		0			0
$887$	26.5000	+	45.8993i	0.889783	+	1.54115i	0.840132	+	0.542383i	$0.182478\pi$
$887$	26.5000	+	45.8993i	0.889783	+	1.54115i	0.0496513	+	0.998767i	$0.484189\pi$
$888$		0			0
$889$			5.00000i			0.167695i
$890$		0			0
$891$	38.9711	+	22.5000i	1.30558	+	0.753778i
$892$		0			0
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$		0			0
$895$	−36.3731	+	21.0000i	−1.21582	+	0.701953i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.92820	+	4.00000i	−0.231069	+	0.133407i
$900$		0			0
$901$	−9.00000	+	15.5885i	−0.299833	+	0.519327i
$902$		0			0
$903$	2.59808	+	1.50000i	0.0864586	+	0.0499169i
$904$		0			0
$905$			36.0000i			1.19668i
$906$		0			0
$907$	1.50000	+	2.59808i	0.0498067	+	0.0862677i	0.889854	−	0.456246i	$-0.150806\pi$
$907$	1.50000	+	2.59808i	0.0498067	+	0.0862677i	−0.840047	+	0.542513i	$0.817473\pi$
$908$		0			0
$909$	−114.000			−3.78114
$910$		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
$913$	30.0000	+	51.9615i	0.992855	+	1.71968i
$914$		0			0
$915$			30.0000i			0.991769i
$916$		0			0
$917$	3.46410	+	2.00000i	0.114395	+	0.0660458i
$918$		0			0
$919$	−16.5000	+	28.5788i	−0.544285	+	0.942729i	0.454367	+	0.890815i	$0.349866\pi$
$919$	−16.5000	+	28.5788i	−0.544285	+	0.942729i	−0.998652	+	0.0519142i	$0.983468\pi$
$920$		0			0
$921$	−10.3923	+	6.00000i	−0.342438	+	0.197707i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	2.59808	−	1.50000i	0.0854242	−	0.0493197i
$926$		0			0
$927$	−24.0000	+	41.5692i	−0.788263	+	1.36531i
$928$		0			0
$929$	−18.1865	−	10.5000i	−0.596681	−	0.344494i	0.171054	−	0.985262i	$-0.445283\pi$
$929$	−18.1865	−	10.5000i	−0.596681	−	0.344494i	−0.767735	+	0.640768i	$0.778616\pi$
$930$		0			0
$931$			18.0000i			0.589926i
$932$		0			0
$933$	−36.0000	−	62.3538i	−1.17859	−	2.04137i
$934$		0			0
$935$	30.0000			0.981105
$936$		0			0
$937$	−18.0000			−0.588034			−0.294017	−	0.955800i	$-0.594992\pi$
$937$	−18.0000			−0.588034			−0.294017	+	0.955800i	$0.594992\pi$
$938$		0			0
$939$	−21.0000	−	36.3731i	−0.685309	−	1.18699i
$940$		0			0
$941$			50.0000i			1.62995i	0.579494	+	0.814977i	$0.303250\pi$
$941$			50.0000i			1.62995i	−0.579494	+	0.814977i	$0.696750\pi$
$942$		0			0
$943$	2.59808	+	1.50000i	0.0846050	+	0.0488467i
$944$		0			0
$945$	−9.00000	+	15.5885i	−0.292770	+	0.507093i
$946$		0			0
$947$	23.3827	−	13.5000i	0.759835	−	0.438691i	−0.0694014	−	0.997589i	$-0.522109\pi$
$947$	23.3827	−	13.5000i	0.759835	−	0.438691i	0.829237	+	0.558898i	$0.188776\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−77.9423	+	45.0000i	−2.52745	+	1.45922i
$952$		0			0
$953$	−0.500000	+	0.866025i	−0.0161966	+	0.0280533i	−0.874010	−	0.485908i	$-0.838489\pi$
$953$	−0.500000	+	0.866025i	−0.0161966	+	0.0280533i	0.857814	+	0.513961i	$0.171822\pi$
$954$		0			0
$955$	1.73205	+	1.00000i	0.0560478	+	0.0323592i
$956$		0			0
$957$			15.0000i			0.484881i
$958$		0			0
$959$	7.50000	+	12.9904i	0.242188	+	0.419481i
$960$		0			0
$961$	−33.0000			−1.06452
$962$		0			0
$963$	66.0000			2.12682
$964$		0			0
$965$	−11.0000	−	19.0526i	−0.354103	−	0.613324i
$966$		0			0
$967$		−	32.0000i		−	1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$967$		−	32.0000i		−	1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$		0			0
$969$	23.3827	+	13.5000i	0.751160	+	0.433682i
$970$		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
$973$	−9.52628	+	5.50000i	−0.305398	+	0.176322i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−33.7750	+	19.5000i	−1.08056	+	0.623860i	−0.931047	−	0.364900i	$-0.881103\pi$
$977$	−33.7750	+	19.5000i	−1.08056	+	0.623860i	−0.149511	+	0.988760i	$0.547770\pi$
$978$		0			0
$979$	22.5000	−	38.9711i	0.719103	−	1.24552i
$980$		0			0
$981$	51.9615	+	30.0000i	1.65900	+	0.957826i
$982$		0			0
$983$		−	16.0000i		−	0.510321i	−0.966899	−	0.255160i	$-0.917872\pi$
$983$		−	16.0000i		−	0.510321i	0.966899	−	0.255160i	$-0.0821283\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		0			0
$987$	−12.0000			−0.381964
$988$		0			0
$989$	−1.00000			−0.0317982
$990$		0			0
$991$	−13.5000	−	23.3827i	−0.428842	−	0.742775i	0.567929	−	0.823078i	$-0.307745\pi$
$991$	−13.5000	−	23.3827i	−0.428842	−	0.742775i	−0.996771	+	0.0803021i	$0.974411\pi$
$992$		0			0
$993$		−	51.0000i		−	1.61844i
$994$		0			0
$995$	32.9090	+	19.0000i	1.04328	+	0.602340i
$996$		0			0
$997$	−17.5000	+	30.3109i	−0.554231	+	0.959955i	0.443732	+	0.896159i	$0.353654\pi$
$997$	−17.5000	+	30.3109i	−0.554231	+	0.959955i	−0.997963	+	0.0637961i	$0.979679\pi$
$998$		0			0
$999$	23.3827	−	13.5000i	0.739795	−	0.427121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.h.b.361.1		4
13.2	odd	12		676.2.a.d.1.1		1
13.3	even	3		676.2.d.d.337.1		2
13.4	even	6	inner	676.2.h.b.485.2		4
13.5	odd	4		676.2.e.a.653.1		2
13.6	odd	12		676.2.e.a.529.1		2
13.7	odd	12		52.2.e.a.9.1	✓	2
13.8	odd	4		52.2.e.a.29.1	yes	2
13.9	even	3	inner	676.2.h.b.485.1		4
13.10	even	6		676.2.d.d.337.2		2
13.11	odd	12		676.2.a.e.1.1		1
13.12	even	2	inner	676.2.h.b.361.2		4
39.2	even	12		6084.2.a.k.1.1		1
39.8	even	4		468.2.l.a.289.1		2
39.11	even	12		6084.2.a.f.1.1		1
39.20	even	12		468.2.l.a.217.1		2
39.23	odd	6		6084.2.b.l.4393.1		2
39.29	odd	6		6084.2.b.l.4393.2		2
52.3	odd	6		2704.2.f.a.337.1		2
52.7	even	12		208.2.i.d.113.1		2
52.11	even	12		2704.2.a.b.1.1		1
52.15	even	12		2704.2.a.a.1.1		1
52.23	odd	6		2704.2.f.a.337.2		2
52.47	even	4		208.2.i.d.81.1		2
65.7	even	12		1300.2.bb.f.1049.2		4
65.8	even	4		1300.2.bb.f.549.2		4
65.33	even	12		1300.2.bb.f.1049.1		4
65.34	odd	4		1300.2.i.f.601.1		2
65.47	even	4		1300.2.bb.f.549.1		4
65.59	odd	12		1300.2.i.f.1101.1		2
91.20	even	12		2548.2.k.d.1569.1		2
91.33	even	12		2548.2.i.h.165.1		2
91.34	even	4		2548.2.k.d.393.1		2
91.46	odd	12		2548.2.l.h.373.1		2
91.47	even	12		2548.2.l.a.1537.1		2
91.59	even	12		2548.2.l.a.373.1		2
91.60	odd	12		2548.2.i.a.1745.1		2
91.72	odd	12		2548.2.i.a.165.1		2
91.73	even	12		2548.2.i.h.1745.1		2
91.86	odd	12		2548.2.l.h.1537.1		2
104.21	odd	4		832.2.i.j.705.1		2
104.59	even	12		832.2.i.a.321.1		2
104.85	odd	12		832.2.i.j.321.1		2
104.99	even	4		832.2.i.a.705.1		2
156.47	odd	4		1872.2.t.f.289.1		2
156.59	odd	12		1872.2.t.f.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.e.a.9.1	✓	2	13.7	odd	12
52.2.e.a.29.1	yes	2	13.8	odd	4
208.2.i.d.81.1		2	52.47	even	4
208.2.i.d.113.1		2	52.7	even	12
468.2.l.a.217.1		2	39.20	even	12
468.2.l.a.289.1		2	39.8	even	4
676.2.a.d.1.1		1	13.2	odd	12
676.2.a.e.1.1		1	13.11	odd	12
676.2.d.d.337.1		2	13.3	even	3
676.2.d.d.337.2		2	13.10	even	6
676.2.e.a.529.1		2	13.6	odd	12
676.2.e.a.653.1		2	13.5	odd	4
676.2.h.b.361.1		4	1.1	even	1	trivial
676.2.h.b.361.2		4	13.12	even	2	inner
676.2.h.b.485.1		4	13.9	even	3	inner
676.2.h.b.485.2		4	13.4	even	6	inner
832.2.i.a.321.1		2	104.59	even	12
832.2.i.a.705.1		2	104.99	even	4
832.2.i.j.321.1		2	104.85	odd	12
832.2.i.j.705.1		2	104.21	odd	4
1300.2.i.f.601.1		2	65.34	odd	4
1300.2.i.f.1101.1		2	65.59	odd	12
1300.2.bb.f.549.1		4	65.47	even	4
1300.2.bb.f.549.2		4	65.8	even	4
1300.2.bb.f.1049.1		4	65.33	even	12
1300.2.bb.f.1049.2		4	65.7	even	12
1872.2.t.f.289.1		2	156.47	odd	4
1872.2.t.f.1153.1		2	156.59	odd	12
2548.2.i.a.165.1		2	91.72	odd	12
2548.2.i.a.1745.1		2	91.60	odd	12
2548.2.i.h.165.1		2	91.33	even	12
2548.2.i.h.1745.1		2	91.73	even	12
2548.2.k.d.393.1		2	91.34	even	4
2548.2.k.d.1569.1		2	91.20	even	12
2548.2.l.a.373.1		2	91.59	even	12
2548.2.l.a.1537.1		2	91.47	even	12
2548.2.l.h.373.1		2	91.46	odd	12
2548.2.l.h.1537.1		2	91.86	odd	12
2704.2.a.a.1.1		1	52.15	even	12
2704.2.a.b.1.1		1	52.11	even	12
2704.2.f.a.337.1		2	52.3	odd	6
2704.2.f.a.337.2		2	52.23	odd	6
6084.2.a.f.1.1		1	39.11	even	12
6084.2.a.k.1.1		1	39.2	even	12
6084.2.b.l.4393.1		2	39.23	odd	6
6084.2.b.l.4393.2		2	39.29	odd	6

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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{3} -2.00000i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-3.00000 + 5.19615i) q^{9} +(-4.33013 + 2.50000i) q^{11} +(-5.19615 + 3.00000i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-2.59808 - 1.50000i) q^{19} +3.00000i q^{21} +(-0.500000 - 0.866025i) q^{23} +1.00000 q^{25} +9.00000 q^{27} +(0.500000 + 0.866025i) q^{29} +8.00000i q^{31} +(12.9904 + 7.50000i) q^{33} +(-1.00000 + 1.73205i) q^{35} +(2.59808 - 1.50000i) q^{37} +(-2.59808 + 1.50000i) q^{41} +(0.500000 - 0.866025i) q^{43} +(10.3923 + 6.00000i) q^{45} +4.00000i q^{47} +(-3.00000 - 5.19615i) q^{49} -9.00000 q^{51} -6.00000 q^{53} +(5.00000 + 8.66025i) q^{55} +9.00000i q^{57} +(-4.33013 - 2.50000i) q^{59} +(2.50000 - 4.33013i) q^{61} +(5.19615 - 3.00000i) q^{63} +(-6.06218 + 3.50000i) q^{67} +(-1.50000 + 2.59808i) q^{69} +(-9.52628 - 5.50000i) q^{71} +14.0000i q^{73} +(-1.50000 - 2.59808i) q^{75} +5.00000 q^{77} -4.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} -12.0000i q^{83} +(-5.19615 - 3.00000i) q^{85} +(1.50000 - 2.59808i) q^{87} +(-7.79423 + 4.50000i) q^{89} +(20.7846 - 12.0000i) q^{93} +(-3.00000 + 5.19615i) q^{95} +(-0.866025 - 0.500000i) q^{97} -30.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 12 q^{9} + 6 q^{17} - 2 q^{23} + 4 q^{25} + 36 q^{27} + 2 q^{29} - 4 q^{35} + 2 q^{43} - 12 q^{49} - 36 q^{51} - 24 q^{53} + 20 q^{55} + 10 q^{61} - 6 q^{69} - 6 q^{75} + 20 q^{77} - 16 q^{79}+ \cdots - 12 q^{95}+O(q^{100}) \) 4 * q - 6 * q^3 - 12 * q^9 + 6 * q^17 - 2 * q^23 + 4 * q^25 + 36 * q^27 + 2 * q^29 - 4 * q^35 + 2 * q^43 - 12 * q^49 - 36 * q^51 - 24 * q^53 + 20 * q^55 + 10 * q^61 - 6 * q^69 - 6 * q^75 + 20 * q^77 - 16 * q^79 - 18 * q^81 + 6 * q^87 - 12 * q^95

Introduction

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