LMFDB - Embedded newform 1248.2.bb.f.655.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1248,2,Mod(463,1248)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1248, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 1]))

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

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

chi := DirichletCharacter("1248.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.bb (of order $4$, 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:	$9.96533017226$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			655.1
Character	$\chi$	$=$	1248.655
Dual form			1248.2.bb.f.463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +(-3.08779 - 3.08779i) q^{5} +(2.85816 - 2.85816i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +(-3.08779 - 3.08779i) q^{5} +(2.85816 - 2.85816i) q^{7} +1.00000 q^{9} +(-2.57668 - 2.57668i) q^{11} +(3.51077 - 0.821294i) q^{13} +(-3.08779 - 3.08779i) q^{15} +1.07196i q^{17} +(-1.46161 + 1.46161i) q^{19} +(2.85816 - 2.85816i) q^{21} -5.52786 q^{23} +14.0688i q^{25} +1.00000 q^{27} -0.512377i q^{29} +(-2.85816 - 2.85816i) q^{31} +(-2.57668 - 2.57668i) q^{33} -17.6508 q^{35} +(-1.97885 + 1.97885i) q^{37} +(3.51077 - 0.821294i) q^{39} +(-0.0336607 + 0.0336607i) q^{41} -3.49466i q^{43} +(-3.08779 - 3.08779i) q^{45} +(6.45565 - 6.45565i) q^{47} -9.33817i q^{49} +1.07196i q^{51} +8.04121i q^{53} +15.9125i q^{55} +(-1.46161 + 1.46161i) q^{57} +(-1.23075 - 1.23075i) q^{59} -4.66832i q^{61} +(2.85816 - 2.85816i) q^{63} +(-13.3765 - 8.30451i) q^{65} +(-2.03305 + 2.03305i) q^{67} -5.52786 q^{69} +(-5.60969 - 5.60969i) q^{71} +(-5.73067 - 5.73067i) q^{73} +14.0688i q^{75} -14.7292 q^{77} -6.65963i q^{79} +1.00000 q^{81} +(-0.153984 + 0.153984i) q^{83} +(3.30998 - 3.30998i) q^{85} -0.512377i q^{87} +(11.3765 + 11.3765i) q^{89} +(7.68694 - 12.3817i) q^{91} +(-2.85816 - 2.85816i) q^{93} +9.02631 q^{95} +(8.80263 - 8.80263i) q^{97} +(-2.57668 - 2.57668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{9} - 8 q^{11} - 20 q^{19} + 24 q^{27} - 8 q^{33} - 16 q^{35} - 12 q^{41} - 20 q^{57} + 16 q^{59} - 76 q^{65} - 28 q^{67} - 8 q^{73} + 24 q^{81} + 72 q^{83} + 28 q^{89} + 4 q^{91} + 24 q^{97} - 8 q^{99}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^9 - 8 * q^11 - 20 * q^19 + 24 * q^27 - 8 * q^33 - 16 * q^35 - 12 * q^41 - 20 * q^57 + 16 * q^59 - 76 * q^65 - 28 * q^67 - 8 * q^73 + 24 * q^81 + 72 * q^83 + 28 * q^89 + 4 * q^91 + 24 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−3.08779	−	3.08779i	−1.38090	−	1.38090i	−0.843024	−	0.537875i	$-0.819227\pi$
$5$	−3.08779	−	3.08779i	−1.38090	−	1.38090i	−0.537875	−	0.843024i	$-0.680773\pi$
$6$		0			0
$7$	2.85816	−	2.85816i	1.08028	−	1.08028i	0.0838010	−	0.996483i	$-0.473294\pi$
$7$	2.85816	−	2.85816i	1.08028	−	1.08028i	0.996483	−	0.0838010i	$-0.0267060\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.57668	−	2.57668i	−0.776900	−	0.776900i	0.202403	−	0.979302i	$-0.435125\pi$
$11$	−2.57668	−	2.57668i	−0.776900	−	0.776900i	−0.979302	+	0.202403i	$0.935125\pi$
$12$		0			0
$13$	3.51077	−	0.821294i	0.973711	−	0.227786i
$13$	3.51077	−	0.821294i	0.973711	−	0.227786i
$14$		0			0
$15$	−3.08779	−	3.08779i	−0.797263	−	0.797263i
$16$		0			0
$17$			1.07196i			0.259989i	0.991515	+	0.129994i	$0.0414959\pi$
$17$			1.07196i			0.259989i	−0.991515	+	0.129994i	$0.958504\pi$
$18$		0			0
$19$	−1.46161	+	1.46161i	−0.335317	+	0.335317i	−0.854602	−	0.519284i	$-0.826199\pi$
$19$	−1.46161	+	1.46161i	−0.335317	+	0.335317i	0.519284	+	0.854602i	$0.326199\pi$
$20$		0			0
$21$	2.85816	−	2.85816i	0.623702	−	0.623702i
$22$		0			0
$23$	−5.52786			−1.15264			−0.576319	−	0.817225i	$-0.695511\pi$
$23$	−5.52786			−1.15264			−0.576319	+	0.817225i	$0.695511\pi$
$24$		0			0
$25$			14.0688i			2.81377i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$		−	0.512377i		−	0.0951460i	−0.998868	−	0.0475730i	$-0.984851\pi$
$29$		−	0.512377i		−	0.0951460i	0.998868	−	0.0475730i	$-0.0151487\pi$
$30$		0			0
$31$	−2.85816	−	2.85816i	−0.513341	−	0.513341i	0.402208	−	0.915549i	$-0.368243\pi$
$31$	−2.85816	−	2.85816i	−0.513341	−	0.513341i	−0.915549	+	0.402208i	$0.868243\pi$
$32$		0			0
$33$	−2.57668	−	2.57668i	−0.448543	−	0.448543i
$34$		0			0
$35$	−17.6508			−2.98353
$36$		0			0
$37$	−1.97885	+	1.97885i	−0.325321	+	0.325321i	−0.850804	−	0.525483i	$-0.823885\pi$
$37$	−1.97885	+	1.97885i	−0.325321	+	0.325321i	0.525483	+	0.850804i	$0.323885\pi$
$38$		0			0
$39$	3.51077	−	0.821294i	0.562172	−	0.131512i
$40$		0			0
$41$	−0.0336607	+	0.0336607i	−0.00525692	+	0.00525692i	−0.709730	−	0.704473i	$-0.751183\pi$
$41$	−0.0336607	+	0.0336607i	−0.00525692	+	0.00525692i	0.704473	+	0.709730i	$0.251183\pi$
$42$		0			0
$43$		−	3.49466i		−	0.532931i	−0.963844	−	0.266465i	$-0.914144\pi$
$43$		−	3.49466i		−	0.532931i	0.963844	−	0.266465i	$-0.0858558\pi$
$44$		0			0
$45$	−3.08779	−	3.08779i	−0.460300	−	0.460300i
$46$		0			0
$47$	6.45565	−	6.45565i	0.941653	−	0.941653i	−0.0567363	−	0.998389i	$-0.518069\pi$
$47$	6.45565	−	6.45565i	0.941653	−	0.941653i	0.998389	+	0.0567363i	$0.0180694\pi$
$48$		0			0
$49$		−	9.33817i		−	1.33402i
$50$		0			0
$51$			1.07196i			0.150104i
$52$		0			0
$53$			8.04121i			1.10455i	0.833663	+	0.552273i	$0.186239\pi$
$53$			8.04121i			1.10455i	−0.833663	+	0.552273i	$0.813761\pi$
$54$		0			0
$55$			15.9125i			2.14564i
$56$		0			0
$57$	−1.46161	+	1.46161i	−0.193596	+	0.193596i
$58$		0			0
$59$	−1.23075	−	1.23075i	−0.160231	−	0.160231i	0.622438	−	0.782669i	$-0.286142\pi$
$59$	−1.23075	−	1.23075i	−0.160231	−	0.160231i	−0.782669	+	0.622438i	$0.786142\pi$
$60$		0			0
$61$		−	4.66832i		−	0.597717i	−0.954297	−	0.298859i	$-0.903394\pi$
$61$		−	4.66832i		−	0.597717i	0.954297	−	0.298859i	$-0.0966059\pi$
$62$		0			0
$63$	2.85816	−	2.85816i	0.360094	−	0.360094i
$64$		0			0
$65$	−13.3765	−	8.30451i	−1.65915	−	1.03005i
$66$		0			0
$67$	−2.03305	+	2.03305i	−0.248376	+	0.248376i	−0.820304	−	0.571928i	$-0.806196\pi$
$67$	−2.03305	+	2.03305i	−0.248376	+	0.248376i	0.571928	+	0.820304i	$0.306196\pi$
$68$		0			0
$69$	−5.52786			−0.665476
$70$		0			0
$71$	−5.60969	−	5.60969i	−0.665747	−	0.665747i	0.290981	−	0.956729i	$-0.406018\pi$
$71$	−5.60969	−	5.60969i	−0.665747	−	0.665747i	−0.956729	+	0.290981i	$0.906018\pi$
$72$		0			0
$73$	−5.73067	−	5.73067i	−0.670724	−	0.670724i	0.287159	−	0.957883i	$-0.407289\pi$
$73$	−5.73067	−	5.73067i	−0.670724	−	0.670724i	−0.957883	+	0.287159i	$0.907289\pi$
$74$		0			0
$75$			14.0688i			1.62453i
$76$		0			0
$77$	−14.7292			−1.67854
$78$		0			0
$79$		−	6.65963i		−	0.749267i	−0.927173	−	0.374633i	$-0.877769\pi$
$79$		−	6.65963i		−	0.749267i	0.927173	−	0.374633i	$-0.122231\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−0.153984	+	0.153984i	−0.0169020	+	0.0169020i	−0.715507	−	0.698605i	$-0.753804\pi$
$83$	−0.153984	+	0.153984i	−0.0169020	+	0.0169020i	0.698605	+	0.715507i	$0.253804\pi$
$84$		0			0
$85$	3.30998	−	3.30998i	0.359018	−	0.359018i
$86$		0			0
$87$		−	0.512377i		−	0.0549326i
$88$		0			0
$89$	11.3765	+	11.3765i	1.20590	+	1.20590i	0.972342	+	0.233562i	$0.0750381\pi$
$89$	11.3765	+	11.3765i	1.20590	+	1.20590i	0.233562	+	0.972342i	$0.424962\pi$
$90$		0			0
$91$	7.68694	−	12.3817i	0.805811	−	1.29796i
$92$		0			0
$93$	−2.85816	−	2.85816i	−0.296378	−	0.296378i
$94$		0			0
$95$	9.02631			0.926079
$96$		0			0
$97$	8.80263	−	8.80263i	0.893772	−	0.893772i	−0.101104	−	0.994876i	$-0.532238\pi$
$97$	8.80263	−	8.80263i	0.893772	−	0.893772i	0.994876	+	0.101104i	$0.0322376\pi$
$98$		0			0
$99$	−2.57668	−	2.57668i	−0.258967	−	0.258967i
$100$		0			0
$101$	2.89040			0.287605			0.143803	−	0.989606i	$-0.454067\pi$
$101$	2.89040			0.287605			0.143803	+	0.989606i	$0.454067\pi$
$102$		0			0
$103$	−7.15687			−0.705187			−0.352594	−	0.935777i	$-0.614700\pi$
$103$	−7.15687			−0.705187			−0.352594	+	0.935777i	$0.614700\pi$
$104$		0			0
$105$	−17.6508			−1.72254
$106$		0			0
$107$	10.6510			1.02967			0.514833	−	0.857290i	$-0.327854\pi$
$107$	10.6510			1.02967			0.514833	+	0.857290i	$0.327854\pi$
$108$		0			0
$109$	1.78060	+	1.78060i	0.170551	+	0.170551i	0.787221	−	0.616671i	$-0.211519\pi$
$109$	1.78060	+	1.78060i	0.170551	+	0.170551i	−0.616671	+	0.787221i	$0.711519\pi$
$110$		0			0
$111$	−1.97885	+	1.97885i	−0.187824	+	0.187824i
$112$		0			0
$113$	2.99536			0.281780			0.140890	−	0.990025i	$-0.455004\pi$
$113$	2.99536			0.281780			0.140890	+	0.990025i	$0.455004\pi$
$114$		0			0
$115$	17.0688	+	17.0688i	1.59168	+	1.59168i
$116$		0			0
$117$	3.51077	−	0.821294i	0.324570	−	0.0759287i
$118$		0			0
$119$	3.06383	+	3.06383i	0.280861	+	0.280861i
$120$		0			0
$121$			2.27861i			0.207146i
$122$		0			0
$123$	−0.0336607	+	0.0336607i	−0.00303508	+	0.00303508i
$124$		0			0
$125$	28.0026	−	28.0026i	2.50463	−	2.50463i
$126$		0			0
$127$	−16.1639			−1.43431			−0.717156	−	0.696913i	$-0.754557\pi$
$127$	−16.1639			−1.43431			−0.717156	+	0.696913i	$0.754557\pi$
$128$		0			0
$129$		−	3.49466i		−	0.307688i
$130$		0			0
$131$	0.118526			0.0103557			0.00517783	−	0.999987i	$-0.498352\pi$
$131$	0.118526			0.0103557			0.00517783	+	0.999987i	$0.498352\pi$
$132$		0			0
$133$			8.35506i			0.724476i
$134$		0			0
$135$	−3.08779	−	3.08779i	−0.265754	−	0.265754i
$136$		0			0
$137$	8.38715	+	8.38715i	0.716563	+	0.716563i	0.967900	−	0.251337i	$-0.0808702\pi$
$137$	8.38715	+	8.38715i	0.716563	+	0.716563i	−0.251337	+	0.967900i	$0.580870\pi$
$138$		0			0
$139$	9.73531			0.825738			0.412869	−	0.910790i	$-0.364527\pi$
$139$	9.73531			0.825738			0.412869	+	0.910790i	$0.364527\pi$
$140$		0			0
$141$	6.45565	−	6.45565i	0.543664	−	0.543664i
$142$		0			0
$143$	−11.1624	−	6.92992i	−0.933443	−	0.579509i
$144$		0			0
$145$	−1.58211	+	1.58211i	−0.131387	+	0.131387i
$146$		0			0
$147$		−	9.33817i		−	0.770200i
$148$		0			0
$149$	−6.39777	−	6.39777i	−0.524126	−	0.524126i	0.394689	−	0.918815i	$-0.370852\pi$
$149$	−6.39777	−	6.39777i	−0.524126	−	0.524126i	−0.918815	+	0.394689i	$0.870852\pi$
$150$		0			0
$151$	6.23105	−	6.23105i	0.507076	−	0.507076i	−0.406552	−	0.913628i	$-0.633269\pi$
$151$	6.23105	−	6.23105i	0.507076	−	0.507076i	0.913628	+	0.406552i	$0.133269\pi$
$152$		0			0
$153$			1.07196i			0.0866628i
$154$		0			0
$155$			17.6508i			1.41774i
$156$		0			0
$157$			23.8222i			1.90122i	0.310393	+	0.950608i	$0.399539\pi$
$157$			23.8222i			1.90122i	−0.310393	+	0.950608i	$0.600461\pi$
$158$		0			0
$159$			8.04121i			0.637710i
$160$		0			0
$161$	−15.7995	+	15.7995i	−1.24518	+	1.24518i
$162$		0			0
$163$	−4.03428	−	4.03428i	−0.315989	−	0.315989i	0.531235	−	0.847224i	$-0.321728\pi$
$163$	−4.03428	−	4.03428i	−0.315989	−	0.315989i	−0.847224	+	0.531235i	$0.821728\pi$
$164$		0			0
$165$			15.9125i			1.23879i
$166$		0			0
$167$	4.78853	−	4.78853i	0.370548	−	0.370548i	−0.497129	−	0.867677i	$-0.665612\pi$
$167$	4.78853	−	4.78853i	0.370548	−	0.370548i	0.867677	+	0.497129i	$0.165612\pi$
$168$		0			0
$169$	11.6510	−	5.76674i	0.896227	−	0.443596i
$170$		0			0
$171$	−1.46161	+	1.46161i	−0.111772	+	0.111772i
$172$		0			0
$173$	1.81603			0.138070			0.0690350	−	0.997614i	$-0.478008\pi$
$173$	1.81603			0.138070			0.0690350	+	0.997614i	$0.478008\pi$
$174$		0			0
$175$	40.2110	+	40.2110i	3.03967	+	3.03967i
$176$		0			0
$177$	−1.23075	−	1.23075i	−0.0925092	−	0.0925092i
$178$		0			0
$179$		−	10.4962i		−	0.784521i	−0.919854	−	0.392261i	$-0.871693\pi$
$179$		−	10.4962i		−	0.784521i	0.919854	−	0.392261i	$-0.128307\pi$
$180$		0			0
$181$	−14.0565			−1.04481			−0.522407	−	0.852696i	$-0.674966\pi$
$181$	−14.0565			−1.04481			−0.522407	+	0.852696i	$0.674966\pi$
$182$		0			0
$183$		−	4.66832i		−	0.345092i
$184$		0			0
$185$	12.2205			0.898470
$186$		0			0
$187$	2.76210	−	2.76210i	0.201985	−	0.201985i
$188$		0			0
$189$	2.85816	−	2.85816i	0.207901	−	0.207901i
$190$		0			0
$191$		−	15.1540i		−	1.09650i	−0.836313	−	0.548252i	$-0.815294\pi$
$191$		−	15.1540i		−	1.09650i	0.836313	−	0.548252i	$-0.184706\pi$
$192$		0			0
$193$	−16.5694	−	16.5694i	−1.19269	−	1.19269i	−0.976309	−	0.216380i	$-0.930575\pi$
$193$	−16.5694	−	16.5694i	−1.19269	−	1.19269i	−0.216380	−	0.976309i	$-0.569425\pi$
$194$		0			0
$195$	−13.3765	−	8.30451i	−0.957909	−	0.594698i
$196$		0			0
$197$	6.24885	+	6.24885i	0.445212	+	0.445212i	0.893759	−	0.448547i	$-0.148058\pi$
$197$	6.24885	+	6.24885i	0.445212	+	0.445212i	−0.448547	+	0.893759i	$0.648058\pi$
$198$		0			0
$199$	4.22848			0.299749			0.149875	−	0.988705i	$-0.452113\pi$
$199$	4.22848			0.299749			0.149875	+	0.988705i	$0.452113\pi$
$200$		0			0
$201$	−2.03305	+	2.03305i	−0.143400	+	0.143400i
$202$		0			0
$203$	−1.46446	−	1.46446i	−0.102785	−	0.102785i
$204$		0			0
$205$	0.207874			0.0145186
$206$		0			0
$207$	−5.52786			−0.384213
$208$		0			0
$209$	7.53224			0.521016
$210$		0			0
$211$	24.8295			1.70934			0.854668	−	0.519175i	$-0.173761\pi$
$211$	24.8295			1.70934			0.854668	+	0.519175i	$0.173761\pi$
$212$		0			0
$213$	−5.60969	−	5.60969i	−0.384369	−	0.384369i
$214$		0			0
$215$	−10.7908	+	10.7908i	−0.735924	+	0.735924i
$216$		0			0
$217$	−16.3382			−1.10911
$218$		0			0
$219$	−5.73067	−	5.73067i	−0.387243	−	0.387243i
$220$		0			0
$221$	0.880394	+	3.76340i	0.0592217	+	0.253154i
$222$		0			0
$223$	−1.83341	−	1.83341i	−0.122774	−	0.122774i	0.643050	−	0.765824i	$-0.277669\pi$
$223$	−1.83341	−	1.83341i	−0.122774	−	0.122774i	−0.765824	+	0.643050i	$0.777669\pi$
$224$		0			0
$225$			14.0688i			0.937923i
$226$		0			0
$227$	−9.42020	+	9.42020i	−0.625240	+	0.625240i	−0.946867	−	0.321626i	$-0.895771\pi$
$227$	−9.42020	+	9.42020i	−0.625240	+	0.625240i	0.321626	+	0.946867i	$0.395771\pi$
$228$		0			0
$229$	−4.97977	+	4.97977i	−0.329073	+	0.329073i	−0.852234	−	0.523161i	$-0.824753\pi$
$229$	−4.97977	+	4.97977i	−0.329073	+	0.329073i	0.523161	+	0.852234i	$0.324753\pi$
$230$		0			0
$231$	−14.7292			−0.969108
$232$		0			0
$233$		−	5.38474i		−	0.352766i	−0.984322	−	0.176383i	$-0.943560\pi$
$233$		−	5.38474i		−	0.352766i	0.984322	−	0.176383i	$-0.0564397\pi$
$234$		0			0
$235$	−39.8673			−2.60066
$236$		0			0
$237$		−	6.65963i		−	0.432589i
$238$		0			0
$239$	−6.48045	−	6.48045i	−0.419186	−	0.419186i	0.465737	−	0.884923i	$-0.345789\pi$
$239$	−6.48045	−	6.48045i	−0.419186	−	0.419186i	−0.884923	+	0.465737i	$0.845789\pi$
$240$		0			0
$241$	16.2281	+	16.2281i	1.04534	+	1.04534i	0.998922	+	0.0464205i	$0.0147814\pi$
$241$	16.2281	+	16.2281i	1.04534	+	1.04534i	0.0464205	+	0.998922i	$0.485219\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−28.8343	+	28.8343i	−1.84215	+	1.84215i
$246$		0			0
$247$	−3.93097	+	6.33180i	−0.250122	+	0.402883i
$248$		0			0
$249$	−0.153984	+	0.153984i	−0.00975835	+	0.00975835i
$250$		0			0
$251$			0.990551i			0.0625230i	0.999511	+	0.0312615i	$0.00995247\pi$
$251$			0.990551i			0.0625230i	−0.999511	+	0.0312615i	$0.990048\pi$
$252$		0			0
$253$	14.2435	+	14.2435i	0.895484	+	0.895484i
$254$		0			0
$255$	3.30998	−	3.30998i	0.207279	−	0.207279i
$256$		0			0
$257$		−	16.9182i		−	1.05533i	−0.849453	−	0.527665i	$-0.823068\pi$
$257$		−	16.9182i		−	1.05533i	0.849453	−	0.527665i	$-0.176932\pi$
$258$		0			0
$259$			11.3117i			0.702877i
$260$		0			0
$261$		−	0.512377i		−	0.0317153i
$262$		0			0
$263$			28.7035i			1.76993i	0.465655	+	0.884966i	$0.345819\pi$
$263$			28.7035i			1.76993i	−0.465655	+	0.884966i	$0.654181\pi$
$264$		0			0
$265$	24.8295	−	24.8295i	1.52527	−	1.52527i
$266$		0			0
$267$	11.3765	+	11.3765i	0.696229	+	0.696229i
$268$		0			0
$269$		−	25.8818i		−	1.57804i	−0.614366	−	0.789021i	$-0.710588\pi$
$269$		−	25.8818i		−	1.57804i	0.614366	−	0.789021i	$-0.289412\pi$
$270$		0			0
$271$	−6.06113	+	6.06113i	−0.368187	+	0.368187i	−0.866816	−	0.498628i	$-0.833837\pi$
$271$	−6.06113	+	6.06113i	−0.368187	+	0.368187i	0.498628	+	0.866816i	$0.333837\pi$
$272$		0			0
$273$	7.68694	−	12.3817i	0.465235	−	0.749376i
$274$		0			0
$275$	36.2510	−	36.2510i	2.18602	−	2.18602i
$276$		0			0
$277$	2.49785			0.150081			0.0750407	−	0.997180i	$-0.476091\pi$
$277$	2.49785			0.150081			0.0750407	+	0.997180i	$0.476091\pi$
$278$		0			0
$279$	−2.85816	−	2.85816i	−0.171114	−	0.171114i
$280$		0			0
$281$	−6.26380	−	6.26380i	−0.373667	−	0.373667i	0.495144	−	0.868811i	$-0.335115\pi$
$281$	−6.26380	−	6.26380i	−0.373667	−	0.373667i	−0.868811	+	0.495144i	$0.835115\pi$
$282$		0			0
$283$		−	11.9847i		−	0.712416i	−0.934407	−	0.356208i	$-0.884069\pi$
$283$		−	11.9847i		−	0.712416i	0.934407	−	0.356208i	$-0.115931\pi$
$284$		0			0
$285$	9.02631			0.534672
$286$		0			0
$287$			0.192415i			0.0113579i
$288$		0			0
$289$	15.8509			0.932406
$290$		0			0
$291$	8.80263	−	8.80263i	0.516019	−	0.516019i
$292$		0			0
$293$	3.26151	−	3.26151i	0.190539	−	0.190539i	−0.605390	−	0.795929i	$-0.706983\pi$
$293$	3.26151	−	3.26151i	0.190539	−	0.190539i	0.795929	+	0.605390i	$0.206983\pi$
$294$		0			0
$295$			7.60061i			0.442525i
$296$		0			0
$297$	−2.57668	−	2.57668i	−0.149514	−	0.149514i
$298$		0			0
$299$	−19.4070	+	4.54000i	−1.12234	+	0.262555i
$300$		0			0
$301$	−9.98830	−	9.98830i	−0.575716	−	0.575716i
$302$		0			0
$303$	2.89040			0.166049
$304$		0			0
$305$	−14.4148	+	14.4148i	−0.825387	+	0.825387i
$306$		0			0
$307$	7.00180	+	7.00180i	0.399614	+	0.399614i	0.878097	−	0.478483i	$-0.158813\pi$
$307$	7.00180	+	7.00180i	0.399614	+	0.399614i	−0.478483	+	0.878097i	$0.658813\pi$
$308$		0			0
$309$	−7.15687			−0.407140
$310$		0			0
$311$	29.2550			1.65890			0.829450	−	0.558582i	$-0.188654\pi$
$311$	29.2550			1.65890			0.829450	+	0.558582i	$0.188654\pi$
$312$		0			0
$313$	2.65852			0.150269			0.0751343	−	0.997173i	$-0.476061\pi$
$313$	2.65852			0.150269			0.0751343	+	0.997173i	$0.476061\pi$
$314$		0			0
$315$	−17.6508			−0.994509
$316$		0			0
$317$	−5.19502	−	5.19502i	−0.291781	−	0.291781i	0.546002	−	0.837784i	$-0.316149\pi$
$317$	−5.19502	−	5.19502i	−0.291781	−	0.291781i	−0.837784	+	0.546002i	$0.816149\pi$
$318$		0			0
$319$	−1.32023	+	1.32023i	−0.0739189	+	0.0739189i
$320$		0			0
$321$	10.6510			0.594478
$322$		0			0
$323$	−1.56679	−	1.56679i	−0.0871787	−	0.0871787i
$324$		0			0
$325$	11.5547	+	49.3924i	0.640937	+	2.73980i
$326$		0			0
$327$	1.78060	+	1.78060i	0.0984675	+	0.0984675i
$328$		0			0
$329$		−	36.9026i		−	2.03450i
$330$		0			0
$331$	14.6385	−	14.6385i	0.804603	−	0.804603i	−0.179208	−	0.983811i	$-0.557353\pi$
$331$	14.6385	−	14.6385i	0.804603	−	0.804603i	0.983811	+	0.179208i	$0.0573535\pi$
$332$		0			0
$333$	−1.97885	+	1.97885i	−0.108440	+	0.108440i
$334$		0			0
$335$	12.5552			0.685965
$336$		0			0
$337$			19.9550i			1.08702i	0.839404	+	0.543508i	$0.182904\pi$
$337$			19.9550i			1.08702i	−0.839404	+	0.543508i	$0.817096\pi$
$338$		0			0
$339$	2.99536			0.162686
$340$		0			0
$341$			14.7292i			0.797629i
$342$		0			0
$343$	−6.68288	−	6.68288i	−0.360841	−	0.360841i
$344$		0			0
$345$	17.0688	+	17.0688i	0.918956	+	0.918956i
$346$		0			0
$347$	13.2961			0.713770			0.356885	−	0.934148i	$-0.383839\pi$
$347$	13.2961			0.713770			0.356885	+	0.934148i	$0.383839\pi$
$348$		0			0
$349$	20.5685	−	20.5685i	1.10101	−	1.10101i	0.106716	−	0.994290i	$-0.465967\pi$
$349$	20.5685	−	20.5685i	1.10101	−	1.10101i	0.994290	−	0.106716i	$-0.0340334\pi$
$350$		0			0
$351$	3.51077	−	0.821294i	0.187391	−	0.0438374i
$352$		0			0
$353$	3.37647	−	3.37647i	0.179712	−	0.179712i	−0.611519	−	0.791230i	$-0.709441\pi$
$353$	3.37647	−	3.37647i	0.179712	−	0.179712i	0.791230	+	0.611519i	$0.209441\pi$
$354$		0			0
$355$			34.6430i			1.83866i
$356$		0			0
$357$	3.06383	+	3.06383i	0.162155	+	0.162155i
$358$		0			0
$359$	−10.1733	+	10.1733i	−0.536927	+	0.536927i	−0.922625	−	0.385698i	$-0.873961\pi$
$359$	−10.1733	+	10.1733i	−0.536927	+	0.536927i	0.385698	+	0.922625i	$0.373961\pi$
$360$		0			0
$361$			14.7274i			0.775124i
$362$		0			0
$363$			2.27861i			0.119596i
$364$		0			0
$365$			35.3902i			1.85241i
$366$		0			0
$367$		−	12.7553i		−	0.665820i	−0.942959	−	0.332910i	$-0.891970\pi$
$367$		−	12.7553i		−	0.665820i	0.942959	−	0.332910i	$-0.108030\pi$
$368$		0			0
$369$	−0.0336607	+	0.0336607i	−0.00175231	+	0.00175231i
$370$		0			0
$371$	22.9831	+	22.9831i	1.19322	+	1.19322i
$372$		0			0
$373$			13.6959i			0.709147i	0.935028	+	0.354573i	$0.115374\pi$
$373$			13.6959i			0.709147i	−0.935028	+	0.354573i	$0.884626\pi$
$374$		0			0
$375$	28.0026	−	28.0026i	1.44605	−	1.44605i
$376$		0			0
$377$	−0.420812	−	1.79884i	−0.0216729	−	0.0926447i
$378$		0			0
$379$	16.8734	−	16.8734i	0.866730	−	0.866730i	−0.125379	−	0.992109i	$-0.540015\pi$
$379$	16.8734	−	16.8734i	0.866730	−	0.866730i	0.992109	+	0.125379i	$0.0400145\pi$
$380$		0			0
$381$	−16.1639			−0.828100
$382$		0			0
$383$	2.81081	+	2.81081i	0.143625	+	0.143625i	0.775263	−	0.631638i	$-0.217617\pi$
$383$	2.81081	+	2.81081i	0.143625	+	0.143625i	−0.631638	+	0.775263i	$0.717617\pi$
$384$		0			0
$385$	45.4805	+	45.4805i	2.31790	+	2.31790i
$386$		0			0
$387$		−	3.49466i		−	0.177644i
$388$		0			0
$389$	34.2597			1.73703			0.868517	−	0.495660i	$-0.165074\pi$
$389$	34.2597			1.73703			0.868517	+	0.495660i	$0.165074\pi$
$390$		0			0
$391$		−	5.92564i		−	0.299673i
$392$		0			0
$393$	0.118526			0.00597884
$394$		0			0
$395$	−20.5635	+	20.5635i	−1.03466	+	1.03466i
$396$		0			0
$397$	16.1956	−	16.1956i	0.812836	−	0.812836i	−0.172223	−	0.985058i	$-0.555095\pi$
$397$	16.1956	−	16.1956i	0.812836	−	0.812836i	0.985058	+	0.172223i	$0.0550948\pi$
$398$		0			0
$399$			8.35506i			0.418276i
$400$		0			0
$401$	18.5045	+	18.5045i	0.924069	+	0.924069i	0.997314	−	0.0732452i	$-0.0233356\pi$
$401$	18.5045	+	18.5045i	0.924069	+	0.924069i	−0.0732452	+	0.997314i	$0.523336\pi$
$402$		0			0
$403$	−12.3817	−	7.68694i	−0.616778	−	0.382914i
$404$		0			0
$405$	−3.08779	−	3.08779i	−0.153433	−	0.153433i
$406$		0			0
$407$	10.1977			0.505483
$408$		0			0
$409$	−19.3758	+	19.3758i	−0.958070	+	0.958070i	−0.999156	−	0.0410856i	$-0.986918\pi$
$409$	−19.3758	+	19.3758i	−0.958070	+	0.958070i	0.0410856	+	0.999156i	$0.486918\pi$
$410$		0			0
$411$	8.38715	+	8.38715i	0.413708	+	0.413708i
$412$		0			0
$413$	−7.03539			−0.346189
$414$		0			0
$415$	0.950941			0.0466798
$416$		0			0
$417$	9.73531			0.476740
$418$		0			0
$419$	−36.1631			−1.76668			−0.883341	−	0.468731i	$-0.844711\pi$
$419$	−36.1631			−1.76668			−0.883341	+	0.468731i	$0.844711\pi$
$420$		0			0
$421$	−0.701961	−	0.701961i	−0.0342115	−	0.0342115i	0.689794	−	0.724006i	$-0.257701\pi$
$421$	−0.701961	−	0.701961i	−0.0342115	−	0.0342115i	−0.724006	+	0.689794i	$0.757701\pi$
$422$		0			0
$423$	6.45565	−	6.45565i	0.313884	−	0.313884i
$424$		0			0
$425$	−15.0812			−0.731547
$426$		0			0
$427$	−13.3428	−	13.3428i	−0.645704	−	0.645704i
$428$		0			0
$429$	−11.1624	−	6.92992i	−0.538923	−	0.334580i
$430$		0			0
$431$	2.65259	+	2.65259i	0.127771	+	0.127771i	0.768100	−	0.640330i	$-0.221202\pi$
$431$	2.65259	+	2.65259i	0.127771	+	0.127771i	−0.640330	+	0.768100i	$0.721202\pi$
$432$		0			0
$433$		−	27.2434i		−	1.30923i	−0.755961	−	0.654617i	$-0.772830\pi$
$433$		−	27.2434i		−	1.30923i	0.755961	−	0.654617i	$-0.227170\pi$
$434$		0			0
$435$	−1.58211	+	1.58211i	−0.0758564	+	0.0758564i
$436$		0			0
$437$	8.07960	−	8.07960i	0.386500	−	0.386500i
$438$		0			0
$439$	28.4482			1.35776			0.678878	−	0.734251i	$-0.262466\pi$
$439$	28.4482			1.35776			0.678878	+	0.734251i	$0.262466\pi$
$440$		0			0
$441$		−	9.33817i		−	0.444675i
$442$		0			0
$443$	26.2562			1.24747			0.623735	−	0.781636i	$-0.285614\pi$
$443$	26.2562			1.24747			0.623735	+	0.781636i	$0.285614\pi$
$444$		0			0
$445$		−	70.2562i		−	3.33046i
$446$		0			0
$447$	−6.39777	−	6.39777i	−0.302604	−	0.302604i
$448$		0			0
$449$	−10.3557	−	10.3557i	−0.488717	−	0.488717i	0.419185	−	0.907901i	$-0.362316\pi$
$449$	−10.3557	−	10.3557i	−0.488717	−	0.488717i	−0.907901	+	0.419185i	$0.862316\pi$
$450$		0			0
$451$	0.173466			0.00816820
$452$		0			0
$453$	6.23105	−	6.23105i	0.292760	−	0.292760i
$454$		0			0
$455$	−61.9678	+	14.4965i	−2.90509	+	0.679605i
$456$		0			0
$457$	20.3069	−	20.3069i	0.949918	−	0.949918i	−0.0488865	−	0.998804i	$-0.515567\pi$
$457$	20.3069	−	20.3069i	0.949918	−	0.949918i	0.998804	+	0.0488865i	$0.0155673\pi$
$458$		0			0
$459$			1.07196i			0.0500348i
$460$		0			0
$461$	−13.3085	−	13.3085i	−0.619838	−	0.619838i	0.325652	−	0.945490i	$-0.394416\pi$
$461$	−13.3085	−	13.3085i	−0.619838	−	0.619838i	−0.945490	+	0.325652i	$0.894416\pi$
$462$		0			0
$463$	−3.24915	+	3.24915i	−0.151001	+	0.151001i	−0.778565	−	0.627564i	$-0.784052\pi$
$463$	−3.24915	+	3.24915i	−0.151001	+	0.151001i	0.627564	+	0.778565i	$0.284052\pi$
$464$		0			0
$465$			17.6508i			0.818535i
$466$		0			0
$467$		−	40.2993i		−	1.86483i	−0.361392	−	0.932414i	$-0.617698\pi$
$467$		−	40.2993i		−	1.86483i	0.361392	−	0.932414i	$-0.382302\pi$
$468$		0			0
$469$			11.6215i			0.536633i
$470$		0			0
$471$			23.8222i			1.09767i
$472$		0			0
$473$	−9.00464	+	9.00464i	−0.414034	+	0.414034i
$474$		0			0
$475$	−20.5632	−	20.5632i	−0.943506	−	0.943506i
$476$		0			0
$477$			8.04121i			0.368182i
$478$		0			0
$479$	−19.0201	+	19.0201i	−0.869049	+	0.869049i	−0.992367	−	0.123318i	$-0.960646\pi$
$479$	−19.0201	+	19.0201i	−0.869049	+	0.869049i	0.123318	+	0.992367i	$0.460646\pi$
$480$		0			0
$481$	−5.32206	+	8.57249i	−0.242665	+	0.390872i
$482$		0			0
$483$	−15.7995	+	15.7995i	−0.718903	+	0.718903i
$484$		0			0
$485$	−54.3613			−2.46842
$486$		0			0
$487$	8.43408	+	8.43408i	0.382184	+	0.382184i	0.871889	−	0.489704i	$-0.162895\pi$
$487$	8.43408	+	8.43408i	0.382184	+	0.382184i	−0.489704	+	0.871889i	$0.662895\pi$
$488$		0			0
$489$	−4.03428	−	4.03428i	−0.182436	−	0.182436i
$490$		0			0
$491$		−	23.3787i		−	1.05507i	−0.849534	−	0.527533i	$-0.823117\pi$
$491$		−	23.3787i		−	1.05507i	0.849534	−	0.527533i	$-0.176883\pi$
$492$		0			0
$493$	0.549248			0.0247369
$494$		0			0
$495$			15.9125i			0.715214i
$496$		0			0
$497$	−32.0668			−1.43839
$498$		0			0
$499$	18.6272	−	18.6272i	0.833867	−	0.833867i	−0.154176	−	0.988043i	$-0.549272\pi$
$499$	18.6272	−	18.6272i	0.833867	−	0.833867i	0.988043	+	0.154176i	$0.0492723\pi$
$500$		0			0
$501$	4.78853	−	4.78853i	0.213936	−	0.213936i
$502$		0			0
$503$		−	12.2441i		−	0.545939i	−0.962023	−	0.272969i	$-0.911994\pi$
$503$		−	12.2441i		−	0.545939i	0.962023	−	0.272969i	$-0.0880058\pi$
$504$		0			0
$505$	−8.92492	−	8.92492i	−0.397154	−	0.397154i
$506$		0			0
$507$	11.6510	−	5.76674i	0.517437	−	0.256110i
$508$		0			0
$509$	25.7075	+	25.7075i	1.13947	+	1.13947i	0.988546	+	0.150920i	$0.0482237\pi$
$509$	25.7075	+	25.7075i	1.13947	+	1.13947i	0.150920	+	0.988546i	$0.451776\pi$
$510$		0			0
$511$	−32.7584			−1.44914
$512$		0			0
$513$	−1.46161	+	1.46161i	−0.0645319	+	0.0645319i
$514$		0			0
$515$	22.0989	+	22.0989i	0.973793	+	0.973793i
$516$		0			0
$517$	−33.2683			−1.46314
$518$		0			0
$519$	1.81603			0.0797148
$520$		0			0
$521$	−41.6747			−1.82580			−0.912902	−	0.408179i	$-0.866164\pi$
$521$	−41.6747			−1.82580			−0.912902	+	0.408179i	$0.866164\pi$
$522$		0			0
$523$	−16.6394			−0.727591			−0.363796	−	0.931479i	$-0.618519\pi$
$523$	−16.6394			−0.727591			−0.363796	+	0.931479i	$0.618519\pi$
$524$		0			0
$525$	40.2110	+	40.2110i	1.75495	+	1.75495i
$526$		0			0
$527$	3.06383	−	3.06383i	0.133463	−	0.133463i
$528$		0			0
$529$	7.55722			0.328575
$530$		0			0
$531$	−1.23075	−	1.23075i	−0.0534102	−	0.0534102i
$532$		0			0
$533$	−0.0905295	+	0.145820i	−0.00392127	+	0.00631617i
$534$		0			0
$535$	−32.8879	−	32.8879i	−1.42187	−	1.42187i
$536$		0			0
$537$		−	10.4962i		−	0.452944i
$538$		0			0
$539$	−24.0615	+	24.0615i	−1.03640	+	1.03640i
$540$		0			0
$541$	−23.7679	+	23.7679i	−1.02186	+	1.02186i	−0.0221074	+	0.999756i	$0.507038\pi$
$541$	−23.7679	+	23.7679i	−1.02186	+	1.02186i	−0.999756	+	0.0221074i	$0.992962\pi$
$542$		0			0
$543$	−14.0565			−0.603223
$544$		0			0
$545$		−	10.9962i		−	0.471027i
$546$		0			0
$547$	−20.4838			−0.875824			−0.437912	−	0.899018i	$-0.644282\pi$
$547$	−20.4838			−0.875824			−0.437912	+	0.899018i	$0.644282\pi$
$548$		0			0
$549$		−	4.66832i		−	0.199239i
$550$		0			0
$551$	0.748898	+	0.748898i	0.0319041	+	0.0319041i
$552$		0			0
$553$	−19.0343	−	19.0343i	−0.809420	−	0.809420i
$554$		0			0
$555$	12.2205			0.518732
$556$		0			0
$557$	30.8045	−	30.8045i	1.30523	−	1.30523i	0.380408	−	0.924819i	$-0.375783\pi$
$557$	30.8045	−	30.8045i	1.30523	−	1.30523i	0.924819	−	0.380408i	$-0.124217\pi$
$558$		0			0
$559$	−2.87014	−	12.2689i	−0.121394	−	0.518921i
$560$		0			0
$561$	2.76210	−	2.76210i	0.116616	−	0.116616i
$562$		0			0
$563$			33.7226i			1.42124i	0.703578	+	0.710618i	$0.251585\pi$
$563$			33.7226i			1.42124i	−0.703578	+	0.710618i	$0.748415\pi$
$564$		0			0
$565$	−9.24903	−	9.24903i	−0.389110	−	0.389110i
$566$		0			0
$567$	2.85816	−	2.85816i	0.120031	−	0.120031i
$568$		0			0
$569$		−	37.5317i		−	1.57341i	−0.617329	−	0.786705i	$-0.711785\pi$
$569$		−	37.5317i		−	1.57341i	0.617329	−	0.786705i	$-0.288215\pi$
$570$		0			0
$571$			10.4261i			0.436318i	0.975913	+	0.218159i	$0.0700051\pi$
$571$			10.4261i			0.436318i	−0.975913	+	0.218159i	$0.929995\pi$
$572$		0			0
$573$		−	15.1540i		−	0.633066i
$574$		0			0
$575$		−	77.7706i		−	3.24326i
$576$		0			0
$577$	−5.95723	+	5.95723i	−0.248003	+	0.248003i	−0.820150	−	0.572148i	$-0.806110\pi$
$577$	−5.95723	+	5.95723i	−0.248003	+	0.248003i	0.572148	+	0.820150i	$0.306110\pi$
$578$		0			0
$579$	−16.5694	−	16.5694i	−0.688600	−	0.688600i
$580$		0			0
$581$			0.880223i			0.0365178i
$582$		0			0
$583$	20.7197	−	20.7197i	0.858121	−	0.858121i
$584$		0			0
$585$	−13.3765	−	8.30451i	−0.553049	−	0.343349i
$586$		0			0
$587$	−1.72078	+	1.72078i	−0.0710241	+	0.0710241i	−0.741727	−	0.670702i	$-0.765993\pi$
$587$	−1.72078	+	1.72078i	−0.0710241	+	0.0710241i	0.670702	+	0.741727i	$0.265993\pi$
$588$		0			0
$589$	8.35506			0.344264
$590$		0			0
$591$	6.24885	+	6.24885i	0.257044	+	0.257044i
$592$		0			0
$593$	13.4905	+	13.4905i	0.553990	+	0.553990i	0.927590	−	0.373600i	$-0.121877\pi$
$593$	13.4905	+	13.4905i	0.553990	+	0.553990i	−0.373600	+	0.927590i	$0.621877\pi$
$594$		0			0
$595$		−	18.9209i		−	0.775683i
$596$		0			0
$597$	4.22848			0.173060
$598$		0			0
$599$			37.0916i			1.51552i	0.652533	+	0.757760i	$0.273706\pi$
$599$			37.0916i			1.51552i	−0.652533	+	0.757760i	$0.726294\pi$
$600$		0			0
$601$	−17.3441			−0.707483			−0.353741	−	0.935343i	$-0.615091\pi$
$601$	−17.3441			−0.707483			−0.353741	+	0.935343i	$0.615091\pi$
$602$		0			0
$603$	−2.03305	+	2.03305i	−0.0827920	+	0.0827920i
$604$		0			0
$605$	7.03585	−	7.03585i	0.286048	−	0.286048i
$606$		0			0
$607$		−	0.0268909i		−	0.00109147i	−1.00000		0.000545735i	$-0.999826\pi$
$607$		−	0.0268909i		−	0.00109147i	1.00000		0.000545735i	$-0.000173713\pi$
$608$		0			0
$609$	−1.46446	−	1.46446i	−0.0593427	−	0.0593427i
$610$		0			0
$611$	17.3623	−	27.9662i	0.702403	−	1.13139i
$612$		0			0
$613$	−21.4415	−	21.4415i	−0.866013	−	0.866013i	0.126015	−	0.992028i	$-0.459781\pi$
$613$	−21.4415	−	21.4415i	−0.866013	−	0.866013i	−0.992028	+	0.126015i	$0.959781\pi$
$614$		0			0
$615$	0.207874			0.00838229
$616$		0			0
$617$	−10.1510	+	10.1510i	−0.408663	+	0.408663i	−0.881272	−	0.472609i	$-0.843312\pi$
$617$	−10.1510	+	10.1510i	−0.408663	+	0.408663i	0.472609	+	0.881272i	$0.343312\pi$
$618$		0			0
$619$	10.4442	+	10.4442i	0.419789	+	0.419789i	0.885131	−	0.465342i	$-0.154069\pi$
$619$	10.4442	+	10.4442i	0.419789	+	0.419789i	−0.465342	+	0.885131i	$0.654069\pi$
$620$		0			0
$621$	−5.52786			−0.221825
$622$		0			0
$623$	65.0316			2.60544
$624$		0			0
$625$	−102.588			−4.10352
$626$		0			0
$627$	7.53224			0.300809
$628$		0			0
$629$	−2.12125	−	2.12125i	−0.0845796	−	0.0845796i
$630$		0			0
$631$	−21.3320	+	21.3320i	−0.849215	+	0.849215i	−0.990035	−	0.140820i	$-0.955026\pi$
$631$	−21.3320	+	21.3320i	−0.849215	+	0.849215i	0.140820	+	0.990035i	$0.455026\pi$
$632$		0			0
$633$	24.8295			0.986886
$634$		0			0
$635$	49.9106	+	49.9106i	1.98064	+	1.98064i
$636$		0			0
$637$	−7.66939	−	32.7841i	−0.303872	−	1.29895i
$638$		0			0
$639$	−5.60969	−	5.60969i	−0.221916	−	0.221916i
$640$		0			0
$641$			28.5426i			1.12736i	0.825992	+	0.563682i	$0.190616\pi$
$641$			28.5426i			1.12736i	−0.825992	+	0.563682i	$0.809384\pi$
$642$		0			0
$643$	−18.1283	+	18.1283i	−0.714912	+	0.714912i	−0.967559	−	0.252647i	$-0.918699\pi$
$643$	−18.1283	+	18.1283i	−0.714912	+	0.714912i	0.252647	+	0.967559i	$0.418699\pi$
$644$		0			0
$645$	−10.7908	+	10.7908i	−0.424886	+	0.424886i
$646$		0			0
$647$	23.0407			0.905824			0.452912	−	0.891555i	$-0.350385\pi$
$647$	23.0407			0.905824			0.452912	+	0.891555i	$0.350385\pi$
$648$		0			0
$649$			6.34253i			0.248966i
$650$		0			0
$651$	−16.3382			−0.640343
$652$		0			0
$653$		−	14.8261i		−	0.580191i	−0.956998	−	0.290095i	$-0.906313\pi$
$653$		−	14.8261i		−	0.580191i	0.956998	−	0.290095i	$-0.0936870\pi$
$654$		0			0
$655$	−0.365983	−	0.365983i	−0.0143001	−	0.0143001i
$656$		0			0
$657$	−5.73067	−	5.73067i	−0.223575	−	0.223575i
$658$		0			0
$659$	−14.8920			−0.580112			−0.290056	−	0.957010i	$-0.593674\pi$
$659$	−14.8920			−0.580112			−0.290056	+	0.957010i	$0.593674\pi$
$660$		0			0
$661$	−21.6359	+	21.6359i	−0.841538	+	0.841538i	−0.989059	−	0.147521i	$-0.952871\pi$
$661$	−21.6359	+	21.6359i	−0.841538	+	0.841538i	0.147521	+	0.989059i	$0.452871\pi$
$662$		0			0
$663$	0.880394	+	3.76340i	0.0341917	+	0.146158i
$664$		0			0
$665$	25.7986	−	25.7986i	1.00043	−	1.00043i
$666$		0			0
$667$			2.83235i			0.109669i
$668$		0			0
$669$	−1.83341	−	1.83341i	−0.0708836	−	0.0708836i
$670$		0			0
$671$	−12.0288	+	12.0288i	−0.464366	+	0.464366i
$672$		0			0
$673$		−	35.0331i		−	1.35043i	−0.737623	−	0.675213i	$-0.764052\pi$
$673$		−	35.0331i		−	1.35043i	0.737623	−	0.675213i	$-0.235948\pi$
$674$		0			0
$675$			14.0688i			0.541510i
$676$		0			0
$677$		−	7.24823i		−	0.278572i	−0.990252	−	0.139286i	$-0.955519\pi$
$677$		−	7.24823i		−	0.278572i	0.990252	−	0.139286i	$-0.0444807\pi$
$678$		0			0
$679$		−	50.3187i		−	1.93105i
$680$		0			0
$681$	−9.42020	+	9.42020i	−0.360983	+	0.360983i
$682$		0			0
$683$	7.11346	+	7.11346i	0.272189	+	0.272189i	0.829981	−	0.557792i	$-0.188351\pi$
$683$	7.11346	+	7.11346i	0.272189	+	0.272189i	−0.557792	+	0.829981i	$0.688351\pi$
$684$		0			0
$685$		−	51.7955i		−	1.97900i
$686$		0			0
$687$	−4.97977	+	4.97977i	−0.189990	+	0.189990i
$688$		0			0
$689$	6.60420	+	28.2308i	0.251600	+	1.07551i
$690$		0			0
$691$	−32.6940	+	32.6940i	−1.24374	+	1.24374i	−0.285298	+	0.958439i	$0.592092\pi$
$691$	−32.6940	+	32.6940i	−1.24374	+	1.24374i	−0.958439	+	0.285298i	$0.907908\pi$
$692$		0			0
$693$	−14.7292			−0.559515
$694$		0			0
$695$	−30.0605	−	30.0605i	−1.14026	−	1.14026i
$696$		0			0
$697$	−0.0360829	−	0.0360829i	−0.00136674	−	0.00136674i
$698$		0			0
$699$		−	5.38474i		−	0.203670i
$700$		0			0
$701$	−29.6221			−1.11881			−0.559406	−	0.828894i	$-0.688971\pi$
$701$	−29.6221			−1.11881			−0.559406	+	0.828894i	$0.688971\pi$
$702$		0			0
$703$		−	5.78463i		−	0.218171i
$704$		0			0
$705$	−39.8673			−1.50149
$706$		0			0
$707$	8.26122	−	8.26122i	0.310695	−	0.310695i
$708$		0			0
$709$	25.8554	−	25.8554i	0.971021	−	0.971021i	−0.0285709	−	0.999592i	$-0.509096\pi$
$709$	25.8554	−	25.8554i	0.971021	−	0.971021i	0.999592	+	0.0285709i	$0.00909562\pi$
$710$		0			0
$711$		−	6.65963i		−	0.249756i
$712$		0			0
$713$	15.7995	+	15.7995i	0.591696	+	0.591696i
$714$		0			0
$715$	13.0688	+	55.8651i	0.488747	+	2.08923i
$716$		0			0
$717$	−6.48045	−	6.48045i	−0.242017	−	0.242017i
$718$		0			0
$719$	31.2277			1.16460			0.582299	−	0.812975i	$-0.302153\pi$
$719$	31.2277			1.16460			0.582299	+	0.812975i	$0.302153\pi$
$720$		0			0
$721$	−20.4555	+	20.4555i	−0.761802	+	0.761802i
$722$		0			0
$723$	16.2281	+	16.2281i	0.603529	+	0.603529i
$724$		0			0
$725$	7.20855			0.267719
$726$		0			0
$727$	21.2172			0.786902			0.393451	−	0.919346i	$-0.371281\pi$
$727$	21.2172			0.786902			0.393451	+	0.919346i	$0.371281\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	3.74614			0.138556
$732$		0			0
$733$	23.8649	+	23.8649i	0.881469	+	0.881469i	0.993684	−	0.112215i	$-0.0357944\pi$
$733$	23.8649	+	23.8649i	0.881469	+	0.881469i	−0.112215	+	0.993684i	$0.535794\pi$
$734$		0			0
$735$	−28.8343	+	28.8343i	−1.06357	+	1.06357i
$736$		0			0
$737$	10.4770			0.385927
$738$		0			0
$739$	−28.5318	−	28.5318i	−1.04956	−	1.04956i	−0.998706	−	0.0508533i	$-0.983806\pi$
$739$	−28.5318	−	28.5318i	−1.04956	−	1.04956i	−0.0508533	−	0.998706i	$-0.516194\pi$
$740$		0			0
$741$	−3.93097	+	6.33180i	−0.144408	+	0.232605i
$742$		0			0
$743$	−14.7470	−	14.7470i	−0.541013	−	0.541013i	0.382813	−	0.923826i	$-0.374956\pi$
$743$	−14.7470	−	14.7470i	−0.541013	−	0.541013i	−0.923826	+	0.382813i	$0.874956\pi$
$744$		0			0
$745$			39.5099i			1.44753i
$746$		0			0
$747$	−0.153984	+	0.153984i	−0.00563399	+	0.00563399i
$748$		0			0
$749$	30.4421	−	30.4421i	1.11233	−	1.11233i
$750$		0			0
$751$	−44.2644			−1.61523			−0.807615	−	0.589710i	$-0.799242\pi$
$751$	−44.2644			−1.61523			−0.807615	+	0.589710i	$0.799242\pi$
$752$		0			0
$753$			0.990551i			0.0360977i
$754$		0			0
$755$	−38.4803			−1.40044
$756$		0			0
$757$		−	15.4803i		−	0.562641i	−0.959614	−	0.281320i	$-0.909228\pi$
$757$		−	15.4803i		−	0.562641i	0.959614	−	0.281320i	$-0.0907724\pi$
$758$		0			0
$759$	14.2435	+	14.2435i	0.517008	+	0.517008i
$760$		0			0
$761$	15.3450	+	15.3450i	0.556257	+	0.556257i	0.928240	−	0.371983i	$-0.121322\pi$
$761$	15.3450	+	15.3450i	0.556257	+	0.556257i	−0.371983	+	0.928240i	$0.621322\pi$
$762$		0			0
$763$	10.1785			0.368486
$764$		0			0
$765$	3.30998	−	3.30998i	0.119673	−	0.119673i
$766$		0			0
$767$	−5.33170	−	3.31008i	−0.192517	−	0.119520i
$768$		0			0
$769$	0.693724	−	0.693724i	0.0250163	−	0.0250163i	−0.694488	−	0.719504i	$-0.744369\pi$
$769$	0.693724	−	0.693724i	0.0250163	−	0.0250163i	0.719504	+	0.694488i	$0.244369\pi$
$770$		0			0
$771$		−	16.9182i		−	0.609295i
$772$		0			0
$773$	2.77394	+	2.77394i	0.0997716	+	0.0997716i	0.755231	−	0.655459i	$-0.227525\pi$
$773$	2.77394	+	2.77394i	0.0997716	+	0.0997716i	−0.655459	+	0.755231i	$0.727525\pi$
$774$		0			0
$775$	40.2110	−	40.2110i	1.44442	−	1.44442i
$776$		0			0
$777$			11.3117i			0.405806i
$778$		0			0
$779$		−	0.0983980i		−	0.00352547i
$780$		0			0
$781$			28.9088i			1.03444i
$782$		0			0
$783$		−	0.512377i		−	0.0183109i
$784$		0			0
$785$	73.5578	−	73.5578i	2.62539	−	2.62539i
$786$		0			0
$787$	−9.16585	−	9.16585i	−0.326727	−	0.326727i	0.524613	−	0.851341i	$-0.324210\pi$
$787$	−9.16585	−	9.16585i	−0.326727	−	0.326727i	−0.851341	+	0.524613i	$0.824210\pi$
$788$		0			0
$789$			28.7035i			1.02187i
$790$		0			0
$791$	8.56123	−	8.56123i	0.304402	−	0.304402i
$792$		0			0
$793$	−3.83406	−	16.3894i	−0.136152	−	0.582004i
$794$		0			0
$795$	24.8295	−	24.8295i	0.880613	−	0.880613i
$796$		0			0
$797$	21.6299			0.766172			0.383086	−	0.923713i	$-0.374861\pi$
$797$	21.6299			0.766172			0.383086	+	0.923713i	$0.374861\pi$
$798$		0			0
$799$	6.92020	+	6.92020i	0.244819	+	0.244819i
$800$		0			0
$801$	11.3765	+	11.3765i	0.401968	+	0.401968i
$802$		0			0
$803$			29.5323i			1.04217i
$804$		0			0
$805$	97.5710			3.43893
$806$		0			0
$807$		−	25.8818i		−	0.911084i
$808$		0			0
$809$	−12.8260			−0.450937			−0.225468	−	0.974250i	$-0.572391\pi$
$809$	−12.8260			−0.450937			−0.225468	+	0.974250i	$0.572391\pi$
$810$		0			0
$811$	−5.35046	+	5.35046i	−0.187880	+	0.187880i	−0.794779	−	0.606899i	$-0.792413\pi$
$811$	−5.35046	+	5.35046i	−0.187880	+	0.187880i	0.606899	+	0.794779i	$0.292413\pi$
$812$		0			0
$813$	−6.06113	+	6.06113i	−0.212573	+	0.212573i
$814$		0			0
$815$			24.9140i			0.872698i
$816$		0			0
$817$	5.10785	+	5.10785i	0.178701	+	0.178701i
$818$		0			0
$819$	7.68694	−	12.3817i	0.268604	−	0.432653i
$820$		0			0
$821$	−11.7654	−	11.7654i	−0.410614	−	0.410614i	0.471338	−	0.881953i	$-0.343771\pi$
$821$	−11.7654	−	11.7654i	−0.410614	−	0.410614i	−0.881953	+	0.471338i	$0.843771\pi$
$822$		0			0
$823$	−9.95031			−0.346846			−0.173423	−	0.984847i	$-0.555483\pi$
$823$	−9.95031			−0.346846			−0.173423	+	0.984847i	$0.555483\pi$
$824$		0			0
$825$	36.2510	−	36.2510i	1.26210	−	1.26210i
$826$		0			0
$827$	0.583398	+	0.583398i	0.0202867	+	0.0202867i	0.717177	−	0.696891i	$-0.245434\pi$
$827$	0.583398	+	0.583398i	0.0202867	+	0.0202867i	−0.696891	+	0.717177i	$0.745434\pi$
$828$		0			0
$829$	−43.6976			−1.51768			−0.758840	−	0.651277i	$-0.774234\pi$
$829$	−43.6976			−1.51768			−0.758840	+	0.651277i	$0.774234\pi$
$830$		0			0
$831$	2.49785			0.0866496
$832$		0			0
$833$	10.0101			0.346831
$834$		0			0
$835$	−29.5719			−1.02338
$836$		0			0
$837$	−2.85816	−	2.85816i	−0.0987925	−	0.0987925i
$838$		0			0
$839$	25.4022	−	25.4022i	0.876982	−	0.876982i	−0.116239	−	0.993221i	$-0.537084\pi$
$839$	25.4022	−	25.4022i	0.876982	−	0.876982i	0.993221	+	0.116239i	$0.0370838\pi$
$840$		0			0
$841$	28.7375			0.990947
$842$		0			0
$843$	−6.26380	−	6.26380i	−0.215737	−	0.215737i
$844$		0			0
$845$	−53.7821	−	18.1692i	−1.85016	−	0.625039i
$846$		0			0
$847$	6.51263	+	6.51263i	0.223777	+	0.223777i
$848$		0			0
$849$		−	11.9847i		−	0.411314i
$850$		0			0
$851$	10.9388	−	10.9388i	0.374977	−	0.374977i
$852$		0			0
$853$	−15.3474	+	15.3474i	−0.525486	+	0.525486i	−0.919223	−	0.393737i	$-0.871182\pi$
$853$	−15.3474	+	15.3474i	−0.525486	+	0.525486i	0.393737	+	0.919223i	$0.371182\pi$
$854$		0			0
$855$	9.02631			0.308693
$856$		0			0
$857$			45.0479i			1.53881i	0.638762	+	0.769404i	$0.279447\pi$
$857$			45.0479i			1.53881i	−0.638762	+	0.769404i	$0.720553\pi$
$858$		0			0
$859$	24.0655			0.821106			0.410553	−	0.911837i	$-0.365336\pi$
$859$	24.0655			0.821106			0.410553	+	0.911837i	$0.365336\pi$
$860$		0			0
$861$			0.192415i			0.00655750i
$862$		0			0
$863$	−7.38306	−	7.38306i	−0.251322	−	0.251322i	0.570190	−	0.821513i	$-0.306869\pi$
$863$	−7.38306	−	7.38306i	−0.251322	−	0.251322i	−0.821513	+	0.570190i	$0.806869\pi$
$864$		0			0
$865$	−5.60750	−	5.60750i	−0.190661	−	0.190661i
$866$		0			0
$867$	15.8509			0.538325
$868$		0			0
$869$	−17.1598	+	17.1598i	−0.582105	+	0.582105i
$870$		0			0
$871$	−5.46782	+	8.80728i	−0.185270	+	0.298423i
$872$		0			0
$873$	8.80263	−	8.80263i	0.297924	−	0.297924i
$874$		0			0
$875$		−	160.072i		−	5.41143i
$876$		0			0
$877$	0.141964	+	0.141964i	0.00479380	+	0.00479380i	0.709500	−	0.704706i	$-0.248921\pi$
$877$	0.141964	+	0.141964i	0.00479380	+	0.00479380i	−0.704706	+	0.709500i	$0.748921\pi$
$878$		0			0
$879$	3.26151	−	3.26151i	0.110008	−	0.110008i
$880$		0			0
$881$			15.3692i			0.517802i	0.965904	+	0.258901i	$0.0833604\pi$
$881$			15.3692i			0.517802i	−0.965904	+	0.258901i	$0.916640\pi$
$882$		0			0
$883$			47.6748i			1.60438i	0.597066	+	0.802192i	$0.296333\pi$
$883$			47.6748i			1.60438i	−0.597066	+	0.802192i	$0.703667\pi$
$884$		0			0
$885$			7.60061i			0.255492i
$886$		0			0
$887$			50.4271i			1.69317i	0.532250	+	0.846587i	$0.321347\pi$
$887$			50.4271i			1.69317i	−0.532250	+	0.846587i	$0.678653\pi$
$888$		0			0
$889$	−46.1990	+	46.1990i	−1.54946	+	1.54946i
$890$		0			0
$891$	−2.57668	−	2.57668i	−0.0863222	−	0.0863222i
$892$		0			0
$893$			18.8713i			0.631505i
$894$		0			0
$895$	−32.4100	+	32.4100i	−1.08335	+	1.08335i
$896$		0			0
$897$	−19.4070	+	4.54000i	−0.647981	+	0.151586i
$898$		0			0
$899$	−1.46446	+	1.46446i	−0.0488423	+	0.0488423i
$900$		0			0
$901$	−8.61986			−0.287169
$902$		0			0
$903$	−9.98830	−	9.98830i	−0.332390	−	0.332390i
$904$		0			0
$905$	43.4036	+	43.4036i	1.44278	+	1.44278i
$906$		0			0
$907$		−	31.3735i		−	1.04174i	−0.853636	−	0.520870i	$-0.825608\pi$
$907$		−	31.3735i		−	1.04174i	0.853636	−	0.520870i	$-0.174392\pi$
$908$		0			0
$909$	2.89040			0.0958684
$910$		0			0
$911$			37.5437i			1.24388i	0.783066	+	0.621939i	$0.213655\pi$
$911$			37.5437i			1.24388i	−0.783066	+	0.621939i	$0.786345\pi$
$912$		0			0
$913$	0.793538			0.0262623
$914$		0			0
$915$	−14.4148	+	14.4148i	−0.476538	+	0.476538i
$916$		0			0
$917$	0.338766	−	0.338766i	0.0111870	−	0.0111870i
$918$		0			0
$919$		−	30.2192i		−	0.996841i	−0.866935	−	0.498420i	$-0.833914\pi$
$919$		−	30.2192i		−	0.996841i	0.866935	−	0.498420i	$-0.166086\pi$
$920$		0			0
$921$	7.00180	+	7.00180i	0.230717	+	0.230717i
$922$		0			0
$923$	−24.3015	−	15.0871i	−0.799894	−	0.496598i
$924$		0			0
$925$	−27.8401	−	27.8401i	−0.915377	−	0.915377i
$926$		0			0
$927$	−7.15687			−0.235062
$928$		0			0
$929$	21.2995	−	21.2995i	0.698815	−	0.698815i	−0.265340	−	0.964155i	$-0.585484\pi$
$929$	21.2995	−	21.2995i	0.698815	−	0.698815i	0.964155	+	0.265340i	$0.0854842\pi$
$930$		0			0
$931$	13.6488	+	13.6488i	0.447322	+	0.447322i
$932$		0			0
$933$	29.2550			0.957766
$934$		0			0
$935$	−17.0576			−0.557842
$936$		0			0
$937$	35.9894			1.17572			0.587861	−	0.808962i	$-0.299970\pi$
$937$	35.9894			1.17572			0.587861	+	0.808962i	$0.299970\pi$
$938$		0			0
$939$	2.65852			0.0867576
$940$		0			0
$941$	11.4948	+	11.4948i	0.374720	+	0.374720i	0.869193	−	0.494473i	$-0.164639\pi$
$941$	11.4948	+	11.4948i	0.374720	+	0.374720i	−0.494473	+	0.869193i	$0.664639\pi$
$942$		0			0
$943$	0.186072	−	0.186072i	0.00605932	−	0.00605932i
$944$		0			0
$945$	−17.6508			−0.574180
$946$		0			0
$947$	−5.55235	−	5.55235i	−0.180427	−	0.180427i	0.611115	−	0.791542i	$-0.290721\pi$
$947$	−5.55235	−	5.55235i	−0.180427	−	0.180427i	−0.791542	+	0.611115i	$0.790721\pi$
$948$		0			0
$949$	−24.8256	−	15.4125i	−0.805873	−	0.500310i
$950$		0			0
$951$	−5.19502	−	5.19502i	−0.168460	−	0.168460i
$952$		0			0
$953$			10.6622i			0.345384i	0.984976	+	0.172692i	$0.0552465\pi$
$953$			10.6622i			0.345384i	−0.984976	+	0.172692i	$0.944753\pi$
$954$		0			0
$955$	−46.7922	+	46.7922i	−1.51416	+	1.51416i
$956$		0			0
$957$	−1.32023	+	1.32023i	−0.0426771	+	0.0426771i
$958$		0			0
$959$	47.9437			1.54818
$960$		0			0
$961$		−	14.6618i		−	0.472962i
$962$		0			0
$963$	10.6510			0.343222
$964$		0			0
$965$			102.325i			3.29397i
$966$		0			0
$967$	0.807895	+	0.807895i	0.0259801	+	0.0259801i	0.719978	−	0.693997i	$-0.244152\pi$
$967$	0.807895	+	0.807895i	0.0259801	+	0.0259801i	−0.693997	+	0.719978i	$0.744152\pi$
$968$		0			0
$969$	−1.56679	−	1.56679i	−0.0503326	−	0.0503326i
$970$		0			0
$971$	−12.7850			−0.410290			−0.205145	−	0.978732i	$-0.565767\pi$
$971$	−12.7850			−0.410290			−0.205145	+	0.978732i	$0.565767\pi$
$972$		0			0
$973$	27.8251	−	27.8251i	0.892031	−	0.892031i
$974$		0			0
$975$	11.5547	+	49.3924i	0.370045	+	1.58182i
$976$		0			0
$977$	10.2997	−	10.2997i	0.329517	−	0.329517i	−0.522886	−	0.852403i	$-0.675145\pi$
$977$	10.2997	−	10.2997i	0.329517	−	0.329517i	0.852403	+	0.522886i	$0.175145\pi$
$978$		0			0
$979$		−	58.6272i		−	1.87373i
$980$		0			0
$981$	1.78060	+	1.78060i	0.0568502	+	0.0568502i
$982$		0			0
$983$	−36.2990	+	36.2990i	−1.15776	+	1.15776i	−0.172800	+	0.984957i	$0.555282\pi$
$983$	−36.2990	+	36.2990i	−1.15776	+	1.15776i	−0.984957	+	0.172800i	$0.944718\pi$
$984$		0			0
$985$		−	38.5902i		−	1.22959i
$986$		0			0
$987$		−	36.9026i		−	1.17462i
$988$		0			0
$989$			19.3180i			0.614276i
$990$		0			0
$991$			22.9756i			0.729843i	0.931038	+	0.364922i	$0.118904\pi$
$991$			22.9756i			0.729843i	−0.931038	+	0.364922i	$0.881096\pi$
$992$		0			0
$993$	14.6385	−	14.6385i	0.464538	−	0.464538i
$994$		0			0
$995$	−13.0566	−	13.0566i	−0.413923	−	0.413923i
$996$		0			0
$997$			38.3954i			1.21599i	0.793940	+	0.607997i	$0.208027\pi$
$997$			38.3954i			1.21599i	−0.793940	+	0.607997i	$0.791973\pi$
$998$		0			0
$999$	−1.97885	+	1.97885i	−0.0626080	+	0.0626080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.bb.f.655.1		24
4.3	odd	2		312.2.t.e.187.1	✓	24
8.3	odd	2	inner	1248.2.bb.f.655.12		24
8.5	even	2		312.2.t.e.187.6	yes	24
12.11	even	2		936.2.w.j.811.12		24
13.8	odd	4	inner	1248.2.bb.f.463.12		24
24.5	odd	2		936.2.w.j.811.7		24
52.47	even	4		312.2.t.e.307.6	yes	24
104.21	odd	4		312.2.t.e.307.1	yes	24
104.99	even	4	inner	1248.2.bb.f.463.1		24
156.47	odd	4		936.2.w.j.307.7		24
312.125	even	4		936.2.w.j.307.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.1	✓	24	4.3	odd	2
312.2.t.e.187.6	yes	24	8.5	even	2
312.2.t.e.307.1	yes	24	104.21	odd	4
312.2.t.e.307.6	yes	24	52.47	even	4
936.2.w.j.307.7		24	156.47	odd	4
936.2.w.j.307.12		24	312.125	even	4
936.2.w.j.811.7		24	24.5	odd	2
936.2.w.j.811.12		24	12.11	even	2
1248.2.bb.f.463.1		24	104.99	even	4	inner
1248.2.bb.f.463.12		24	13.8	odd	4	inner
1248.2.bb.f.655.1		24	1.1	even	1	trivial
1248.2.bb.f.655.12		24	8.3	odd	2	inner

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:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.bb (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-3.08779 - 3.08779i) q^{5} +(2.85816 - 2.85816i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +(-3.08779 - 3.08779i) q^{5} +(2.85816 - 2.85816i) q^{7} +1.00000 q^{9} +(-2.57668 - 2.57668i) q^{11} +(3.51077 - 0.821294i) q^{13} +(-3.08779 - 3.08779i) q^{15} +1.07196i q^{17} +(-1.46161 + 1.46161i) q^{19} +(2.85816 - 2.85816i) q^{21} -5.52786 q^{23} +14.0688i q^{25} +1.00000 q^{27} -0.512377i q^{29} +(-2.85816 - 2.85816i) q^{31} +(-2.57668 - 2.57668i) q^{33} -17.6508 q^{35} +(-1.97885 + 1.97885i) q^{37} +(3.51077 - 0.821294i) q^{39} +(-0.0336607 + 0.0336607i) q^{41} -3.49466i q^{43} +(-3.08779 - 3.08779i) q^{45} +(6.45565 - 6.45565i) q^{47} -9.33817i q^{49} +1.07196i q^{51} +8.04121i q^{53} +15.9125i q^{55} +(-1.46161 + 1.46161i) q^{57} +(-1.23075 - 1.23075i) q^{59} -4.66832i q^{61} +(2.85816 - 2.85816i) q^{63} +(-13.3765 - 8.30451i) q^{65} +(-2.03305 + 2.03305i) q^{67} -5.52786 q^{69} +(-5.60969 - 5.60969i) q^{71} +(-5.73067 - 5.73067i) q^{73} +14.0688i q^{75} -14.7292 q^{77} -6.65963i q^{79} +1.00000 q^{81} +(-0.153984 + 0.153984i) q^{83} +(3.30998 - 3.30998i) q^{85} -0.512377i q^{87} +(11.3765 + 11.3765i) q^{89} +(7.68694 - 12.3817i) q^{91} +(-2.85816 - 2.85816i) q^{93} +9.02631 q^{95} +(8.80263 - 8.80263i) q^{97} +(-2.57668 - 2.57668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{9} - 8 q^{11} - 20 q^{19} + 24 q^{27} - 8 q^{33} - 16 q^{35} - 12 q^{41} - 20 q^{57} + 16 q^{59} - 76 q^{65} - 28 q^{67} - 8 q^{73} + 24 q^{81} + 72 q^{83} + 28 q^{89} + 4 q^{91} + 24 q^{97} - 8 q^{99}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^9 - 8 * q^11 - 20 * q^19 + 24 * q^27 - 8 * q^33 - 16 * q^35 - 12 * q^41 - 20 * q^57 + 16 * q^59 - 76 * q^65 - 28 * q^67 - 8 * q^73 + 24 * q^81 + 72 * q^83 + 28 * q^89 + 4 * q^91 + 24 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

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