LMFDB - Embedded newform 1920.2.bl.a.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(289,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("1920.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bl (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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			289.4
Character	$\chi$	$=$	1920.289
Dual form			1920.2.bl.a.1249.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(-0.404088 + 2.19925i) q^{5} +1.81567 q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.404088 + 2.19925i) q^{5} +1.81567 q^{7} -1.00000i q^{9} +(0.331965 - 0.331965i) q^{11} +(0.0310184 - 0.0310184i) q^{13} +(-1.26937 - 1.84084i) q^{15} -1.00474i q^{17} +(2.08203 + 2.08203i) q^{19} +(-1.28388 + 1.28388i) q^{21} +6.22794 q^{23} +(-4.67343 - 1.77739i) q^{25} +(0.707107 + 0.707107i) q^{27} +(6.28959 + 6.28959i) q^{29} +7.11301 q^{31} +0.469470i q^{33} +(-0.733693 + 3.99313i) q^{35} +(0.0723513 + 0.0723513i) q^{37} +0.0438667i q^{39} +3.06050i q^{41} +(-3.78495 - 3.78495i) q^{43} +(2.19925 + 0.404088i) q^{45} +10.0476i q^{47} -3.70333 q^{49} +(0.710461 + 0.710461i) q^{51} +(-7.04636 - 7.04636i) q^{53} +(0.595932 + 0.864219i) q^{55} -2.94443 q^{57} +(6.68042 - 6.68042i) q^{59} +(-2.89442 - 2.89442i) q^{61} -1.81567i q^{63} +(0.0556832 + 0.0807515i) q^{65} +(0.150837 - 0.150837i) q^{67} +(-4.40382 + 4.40382i) q^{69} +14.5503i q^{71} -15.0323 q^{73} +(4.56141 - 2.04781i) q^{75} +(0.602741 - 0.602741i) q^{77} +15.5985 q^{79} -1.00000 q^{81} +(-5.48985 + 5.48985i) q^{83} +(2.20969 + 0.406005i) q^{85} -8.89482 q^{87} +14.3520i q^{89} +(0.0563193 - 0.0563193i) q^{91} +(-5.02966 + 5.02966i) q^{93} +(-5.42023 + 3.73758i) q^{95} -13.5585i q^{97} +(-0.331965 - 0.331965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{19} - 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} + 16 q^{75} - 96 q^{79} - 48 q^{81} + 32 q^{91} - 48 q^{95}+O(q^{100}) $ 48 * q - 8 * q^19 - 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 + 16 * q^75 - 96 * q^79 - 48 * q^81 + 32 * q^91 - 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	−0.404088	+	2.19925i	−0.180714	+	0.983536i
$5$	−0.404088	+	2.19925i	−0.180714	+	0.983536i
$6$		0			0
$7$	1.81567			0.686260			0.343130	−	0.939288i	$-0.388513\pi$
$7$	1.81567			0.686260			0.343130	+	0.939288i	$0.388513\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	0.331965	−	0.331965i	0.100091	−	0.100091i	−0.655288	−	0.755379i	$-0.727453\pi$
$11$	0.331965	−	0.331965i	0.100091	−	0.100091i	0.755379	+	0.655288i	$0.227453\pi$
$12$		0			0
$13$	0.0310184	−	0.0310184i	0.00860296	−	0.00860296i	−0.702792	−	0.711395i	$-0.748064\pi$
$13$	0.0310184	−	0.0310184i	0.00860296	−	0.00860296i	0.711395	+	0.702792i	$0.248064\pi$
$14$		0			0
$15$	−1.26937	−	1.84084i	−0.327751	−	0.475303i
$16$		0			0
$17$		−	1.00474i		−	0.243686i	−0.992549	−	0.121843i	$-0.961120\pi$
$17$		−	1.00474i		−	0.243686i	0.992549	−	0.121843i	$-0.0388805\pi$
$18$		0			0
$19$	2.08203	+	2.08203i	0.477650	+	0.477650i	0.904379	−	0.426729i	$-0.140334\pi$
$19$	2.08203	+	2.08203i	0.477650	+	0.477650i	−0.426729	+	0.904379i	$0.640334\pi$
$20$		0			0
$21$	−1.28388	+	1.28388i	−0.280165	+	0.280165i
$22$		0			0
$23$	6.22794			1.29861			0.649307	−	0.760526i	$-0.275059\pi$
$23$	6.22794			1.29861			0.649307	+	0.760526i	$0.275059\pi$
$24$		0			0
$25$	−4.67343	−	1.77739i	−0.934685	−	0.355477i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	6.28959	+	6.28959i	1.16795	+	1.16795i	0.982690	+	0.185258i	$0.0593120\pi$
$29$	6.28959	+	6.28959i	1.16795	+	1.16795i	0.185258	+	0.982690i	$0.440688\pi$
$30$		0			0
$31$	7.11301			1.27753			0.638767	−	0.769400i	$-0.279445\pi$
$31$	7.11301			1.27753			0.638767	+	0.769400i	$0.279445\pi$
$32$		0			0
$33$			0.469470i			0.0817242i
$34$		0			0
$35$	−0.733693	+	3.99313i	−0.124017	+	0.674961i
$36$		0			0
$37$	0.0723513	+	0.0723513i	0.0118945	+	0.0118945i	0.713029	−	0.701135i	$-0.247323\pi$
$37$	0.0723513	+	0.0723513i	0.0118945	+	0.0118945i	−0.701135	+	0.713029i	$0.747323\pi$
$38$		0			0
$39$			0.0438667i			0.00702429i
$40$		0			0
$41$			3.06050i			0.477969i	0.971023	+	0.238985i	$0.0768145\pi$
$41$			3.06050i			0.477969i	−0.971023	+	0.238985i	$0.923185\pi$
$42$		0			0
$43$	−3.78495	−	3.78495i	−0.577199	−	0.577199i	0.356932	−	0.934131i	$-0.383823\pi$
$43$	−3.78495	−	3.78495i	−0.577199	−	0.577199i	−0.934131	+	0.356932i	$0.883823\pi$
$44$		0			0
$45$	2.19925	+	0.404088i	0.327845	+	0.0602379i
$46$		0			0
$47$			10.0476i			1.46559i	0.680450	+	0.732795i	$0.261785\pi$
$47$			10.0476i			1.46559i	−0.680450	+	0.732795i	$0.738215\pi$
$48$		0			0
$49$	−3.70333			−0.529047
$50$		0			0
$51$	0.710461	+	0.710461i	0.0994845	+	0.0994845i
$52$		0			0
$53$	−7.04636	−	7.04636i	−0.967892	−	0.967892i	0.0316087	−	0.999500i	$-0.489937\pi$
$53$	−7.04636	−	7.04636i	−0.967892	−	0.967892i	−0.999500	+	0.0316087i	$0.989937\pi$
$54$		0			0
$55$	0.595932	+	0.864219i	0.0803555	+	0.116531i
$56$		0			0
$57$	−2.94443			−0.390000
$58$		0			0
$59$	6.68042	−	6.68042i	0.869717	−	0.869717i	−0.122724	−	0.992441i	$-0.539163\pi$
$59$	6.68042	−	6.68042i	0.869717	−	0.869717i	0.992441	+	0.122724i	$0.0391629\pi$
$60$		0			0
$61$	−2.89442	−	2.89442i	−0.370592	−	0.370592i	0.497101	−	0.867693i	$-0.334398\pi$
$61$	−2.89442	−	2.89442i	−0.370592	−	0.370592i	−0.867693	+	0.497101i	$0.834398\pi$
$62$		0			0
$63$		−	1.81567i		−	0.228753i
$64$		0			0
$65$	0.0556832	+	0.0807515i	0.00690665	+	0.0100160i
$66$		0			0
$67$	0.150837	−	0.150837i	0.0184276	−	0.0184276i	−0.697833	−	0.716261i	$-0.745852\pi$
$67$	0.150837	−	0.150837i	0.0184276	−	0.0184276i	0.716261	+	0.697833i	$0.245852\pi$
$68$		0			0
$69$	−4.40382	+	4.40382i	−0.530157	+	0.530157i
$70$		0			0
$71$			14.5503i			1.72680i	0.504520	+	0.863400i	$0.331669\pi$
$71$			14.5503i			1.72680i	−0.504520	+	0.863400i	$0.668331\pi$
$72$		0			0
$73$	−15.0323			−1.75939			−0.879697	−	0.475534i	$-0.842255\pi$
$73$	−15.0323			−1.75939			−0.879697	+	0.475534i	$0.842255\pi$
$74$		0			0
$75$	4.56141	−	2.04781i	0.526706	−	0.236461i
$76$		0			0
$77$	0.602741	−	0.602741i	0.0686887	−	0.0686887i
$78$		0			0
$79$	15.5985			1.75497			0.877487	−	0.479601i	$-0.159219\pi$
$79$	15.5985			1.75497			0.877487	+	0.479601i	$0.159219\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−5.48985	+	5.48985i	−0.602590	+	0.602590i	−0.940999	−	0.338409i	$-0.890111\pi$
$83$	−5.48985	+	5.48985i	−0.602590	+	0.602590i	0.338409	+	0.940999i	$0.390111\pi$
$84$		0			0
$85$	2.20969	+	0.406005i	0.239674	+	0.0440375i
$86$		0			0
$87$	−8.89482			−0.953625
$88$		0			0
$89$			14.3520i			1.52131i	0.649157	+	0.760655i	$0.275122\pi$
$89$			14.3520i			1.52131i	−0.649157	+	0.760655i	$0.724878\pi$
$90$		0			0
$91$	0.0563193	−	0.0563193i	0.00590387	−	0.00590387i
$92$		0			0
$93$	−5.02966	+	5.02966i	−0.521551	+	0.521551i
$94$		0			0
$95$	−5.42023	+	3.73758i	−0.556104	+	0.383468i
$96$		0			0
$97$		−	13.5585i		−	1.37666i	−0.725399	−	0.688329i	$-0.758345\pi$
$97$		−	13.5585i		−	1.37666i	0.725399	−	0.688329i	$-0.241655\pi$
$98$		0			0
$99$	−0.331965	−	0.331965i	−0.0333638	−	0.0333638i
$100$		0			0
$101$	−10.5132	+	10.5132i	−1.04610	+	1.04610i	−0.0472186	+	0.998885i	$0.515036\pi$
$101$	−10.5132	+	10.5132i	−1.04610	+	1.04610i	−0.998885	+	0.0472186i	$0.984964\pi$
$102$		0			0
$103$	−6.14387			−0.605373			−0.302687	−	0.953090i	$-0.597884\pi$
$103$	−6.14387			−0.605373			−0.302687	+	0.953090i	$0.597884\pi$
$104$		0			0
$105$	−2.30477	−	3.34237i	−0.224922	−	0.326181i
$106$		0			0
$107$	6.91512	+	6.91512i	0.668510	+	0.668510i	0.957371	−	0.288861i	$-0.0932767\pi$
$107$	6.91512	+	6.91512i	0.668510	+	0.668510i	−0.288861	+	0.957371i	$0.593277\pi$
$108$		0			0
$109$	6.15941	+	6.15941i	0.589964	+	0.589964i	0.937622	−	0.347657i	$-0.113023\pi$
$109$	6.15941	+	6.15941i	0.589964	+	0.589964i	−0.347657	+	0.937622i	$0.613023\pi$
$110$		0			0
$111$	−0.102320			−0.00971180
$112$		0			0
$113$			2.13102i			0.200470i	0.994964	+	0.100235i	$0.0319594\pi$
$113$			2.13102i			0.200470i	−0.994964	+	0.100235i	$0.968041\pi$
$114$		0			0
$115$	−2.51664	+	13.6968i	−0.234678	+	1.27723i
$116$		0			0
$117$	−0.0310184	−	0.0310184i	−0.00286765	−	0.00286765i
$118$		0			0
$119$		−	1.82429i		−	0.167232i
$120$		0			0
$121$			10.7796i			0.979963i
$122$		0			0
$123$	−2.16410	−	2.16410i	−0.195130	−	0.195130i
$124$		0			0
$125$	5.79740	−	9.55982i	0.518535	−	0.855056i
$126$		0			0
$127$			10.5491i			0.936077i	0.883708	+	0.468039i	$0.155039\pi$
$127$			10.5491i			0.936077i	−0.883708	+	0.468039i	$0.844961\pi$
$128$		0			0
$129$	5.35272			0.471281
$130$		0			0
$131$	−5.82338	−	5.82338i	−0.508791	−	0.508791i	0.405364	−	0.914155i	$-0.367145\pi$
$131$	−5.82338	−	5.82338i	−0.508791	−	0.508791i	−0.914155	+	0.405364i	$0.867145\pi$
$132$		0			0
$133$	3.78028	+	3.78028i	0.327792	+	0.327792i
$134$		0			0
$135$	−1.84084	+	1.26937i	−0.158434	+	0.109250i
$136$		0			0
$137$	15.6554			1.33753			0.668764	−	0.743475i	$-0.266824\pi$
$137$	15.6554			1.33753			0.668764	+	0.743475i	$0.266824\pi$
$138$		0			0
$139$	1.14177	−	1.14177i	0.0968440	−	0.0968440i	−0.657025	−	0.753869i	$-0.728185\pi$
$139$	1.14177	−	1.14177i	0.0968440	−	0.0968440i	0.753869	+	0.657025i	$0.228185\pi$
$140$		0			0
$141$	−7.10471	−	7.10471i	−0.598325	−	0.598325i
$142$		0			0
$143$		−	0.0205941i		−	0.00172216i
$144$		0			0
$145$	−16.3740	+	11.2908i	−1.35978	+	0.937654i
$146$		0			0
$147$	2.61865	−	2.61865i	0.215983	−	0.215983i
$148$		0			0
$149$	1.81817	−	1.81817i	0.148951	−	0.148951i	−0.628698	−	0.777649i	$-0.716412\pi$
$149$	1.81817	−	1.81817i	0.148951	−	0.148951i	0.777649	+	0.628698i	$0.216412\pi$
$150$		0			0
$151$		−	11.2409i		−	0.914774i	−0.889268	−	0.457387i	$-0.848785\pi$
$151$		−	11.2409i		−	0.914774i	0.889268	−	0.457387i	$-0.151215\pi$
$152$		0			0
$153$	−1.00474			−0.0812287
$154$		0			0
$155$	−2.87429	+	15.6433i	−0.230868	+	1.25650i
$156$		0			0
$157$	−14.8194	+	14.8194i	−1.18272	+	1.18272i	−0.203681	+	0.979037i	$0.565291\pi$
$157$	−14.8194	+	14.8194i	−1.18272	+	1.18272i	−0.979037	+	0.203681i	$0.934709\pi$
$158$		0			0
$159$	9.96505			0.790280
$160$		0			0
$161$	11.3079			0.891187
$162$		0			0
$163$	6.87622	−	6.87622i	0.538587	−	0.538587i	−0.384527	−	0.923114i	$-0.625635\pi$
$163$	6.87622	−	6.87622i	0.538587	−	0.538587i	0.923114	+	0.384527i	$0.125635\pi$
$164$		0			0
$165$	−1.03248	−	0.189707i	−0.0803787	−	0.0147687i
$166$		0			0
$167$	−12.8174			−0.991838			−0.495919	−	0.868369i	$-0.665169\pi$
$167$	−12.8174			−0.991838			−0.495919	+	0.868369i	$0.665169\pi$
$168$		0			0
$169$			12.9981i			0.999852i
$170$		0			0
$171$	2.08203	−	2.08203i	0.159217	−	0.159217i
$172$		0			0
$173$	5.88931	−	5.88931i	0.447756	−	0.447756i	−0.446852	−	0.894608i	$-0.647455\pi$
$173$	5.88931	−	5.88931i	0.447756	−	0.447756i	0.894608	+	0.446852i	$0.147455\pi$
$174$		0			0
$175$	−8.48542	−	3.22715i	−0.641437	−	0.243950i
$176$		0			0
$177$			9.44755i			0.710121i
$178$		0			0
$179$	10.1383	+	10.1383i	0.757769	+	0.757769i	0.975916	−	0.218147i	$-0.0700011\pi$
$179$	10.1383	+	10.1383i	0.757769	+	0.757769i	−0.218147	+	0.975916i	$0.570001\pi$
$180$		0			0
$181$	10.8678	−	10.8678i	0.807798	−	0.807798i	−0.176503	−	0.984300i	$-0.556478\pi$
$181$	10.8678	−	10.8678i	0.807798	−	0.807798i	0.984300	+	0.176503i	$0.0564784\pi$
$182$		0			0
$183$	4.09332			0.302587
$184$		0			0
$185$	−0.188355	+	0.129882i	−0.0138481	+	0.00954915i
$186$		0			0
$187$	−0.333540	−	0.333540i	−0.0243909	−	0.0243909i
$188$		0			0
$189$	1.28388	+	1.28388i	0.0933882	+	0.0933882i
$190$		0			0
$191$	−1.57307			−0.113823			−0.0569116	−	0.998379i	$-0.518125\pi$
$191$	−1.57307			−0.113823			−0.0569116	+	0.998379i	$0.518125\pi$
$192$		0			0
$193$			3.91815i			0.282034i	0.990007	+	0.141017i	$0.0450373\pi$
$193$			3.91815i			0.282034i	−0.990007	+	0.141017i	$0.954963\pi$
$194$		0			0
$195$	−0.0964739	−	0.0177260i	−0.00690864	−	0.00126939i
$196$		0			0
$197$	2.72966	+	2.72966i	0.194480	+	0.194480i	0.797629	−	0.603149i	$-0.206087\pi$
$197$	2.72966	+	2.72966i	0.194480	+	0.194480i	−0.603149	+	0.797629i	$0.706087\pi$
$198$		0			0
$199$		−	19.6851i		−	1.39544i	−0.716371	−	0.697719i	$-0.754198\pi$
$199$		−	19.6851i		−	1.39544i	0.716371	−	0.697719i	$-0.245802\pi$
$200$		0			0
$201$			0.213315i			0.0150461i
$202$		0			0
$203$	11.4198	+	11.4198i	0.801516	+	0.801516i
$204$		0			0
$205$	−6.73080	−	1.23671i	−0.470100	−	0.0863756i
$206$		0			0
$207$		−	6.22794i		−	0.432872i
$208$		0			0
$209$	1.38232			0.0956172
$210$		0			0
$211$	−1.93798	−	1.93798i	−0.133416	−	0.133416i	0.637245	−	0.770661i	$-0.280074\pi$
$211$	−1.93798	−	1.93798i	−0.133416	−	0.133416i	−0.770661	+	0.637245i	$0.780074\pi$
$212$		0			0
$213$	−10.2886	−	10.2886i	−0.704963	−	0.704963i
$214$		0			0
$215$	9.85351	−	6.79460i	0.672004	−	0.463388i
$216$		0			0
$217$	12.9149			0.876721
$218$		0			0
$219$	10.6294	−	10.6294i	0.718270	−	0.718270i
$220$		0			0
$221$	−0.0311656	−	0.0311656i	−0.00209642	−	0.00209642i
$222$		0			0
$223$		−	9.22040i		−	0.617443i	−0.951152	−	0.308722i	$-0.900099\pi$
$223$		−	9.22040i		−	0.617443i	0.951152	−	0.308722i	$-0.0999012\pi$
$224$		0			0
$225$	−1.77739	+	4.67343i	−0.118492	+	0.311562i
$226$		0			0
$227$	11.0458	−	11.0458i	0.733132	−	0.733132i	−0.238107	−	0.971239i	$-0.576527\pi$
$227$	11.0458	−	11.0458i	0.733132	−	0.733132i	0.971239	+	0.238107i	$0.0765267\pi$
$228$		0			0
$229$	−5.23103	+	5.23103i	−0.345676	+	0.345676i	−0.858496	−	0.512820i	$-0.828601\pi$
$229$	−5.23103	+	5.23103i	−0.345676	+	0.345676i	0.512820	+	0.858496i	$0.328601\pi$
$230$		0			0
$231$			0.852404i			0.0560841i
$232$		0			0
$233$	14.5509			0.953262			0.476631	−	0.879103i	$-0.341858\pi$
$233$	14.5509			0.953262			0.476631	+	0.879103i	$0.341858\pi$
$234$		0			0
$235$	−22.0972	−	4.06011i	−1.44146	−	0.264852i
$236$		0			0
$237$	−11.0298	+	11.0298i	−0.716465	+	0.716465i
$238$		0			0
$239$	−8.23404			−0.532616			−0.266308	−	0.963888i	$-0.585804\pi$
$239$	−8.23404			−0.532616			−0.266308	+	0.963888i	$0.585804\pi$
$240$		0			0
$241$	−6.81789			−0.439179			−0.219589	−	0.975592i	$-0.570472\pi$
$241$	−6.81789			−0.439179			−0.219589	+	0.975592i	$0.570472\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	1.49647	−	8.14456i	0.0956061	−	0.520337i
$246$		0			0
$247$	0.129162			0.00821841
$248$		0			0
$249$		−	7.76382i		−	0.492012i
$250$		0			0
$251$	−12.1421	+	12.1421i	−0.766403	+	0.766403i	−0.977471	−	0.211068i	$-0.932306\pi$
$251$	−12.1421	+	12.1421i	−0.766403	+	0.766403i	0.211068	+	0.977471i	$0.432306\pi$
$252$		0			0
$253$	2.06746	−	2.06746i	0.129980	−	0.129980i
$254$		0			0
$255$	−1.84957	+	1.27539i	−0.115825	+	0.0798683i
$256$		0			0
$257$		−	13.9667i		−	0.871217i	−0.900136	−	0.435609i	$-0.856533\pi$
$257$		−	13.9667i		−	0.871217i	0.900136	−	0.435609i	$-0.143467\pi$
$258$		0			0
$259$	0.131366	+	0.131366i	0.00816271	+	0.00816271i
$260$		0			0
$261$	6.28959	−	6.28959i	0.389316	−	0.389316i
$262$		0			0
$263$	3.31340			0.204313			0.102157	−	0.994768i	$-0.467426\pi$
$263$	3.31340			0.204313			0.102157	+	0.994768i	$0.467426\pi$
$264$		0			0
$265$	18.3441	−	12.6494i	1.12687	−	0.777045i
$266$		0			0
$267$	−10.1484	−	10.1484i	−0.621072	−	0.621072i
$268$		0			0
$269$	14.5006	+	14.5006i	0.884120	+	0.884120i	0.993950	−	0.109831i	$-0.0350308\pi$
$269$	14.5006	+	14.5006i	0.884120	+	0.884120i	−0.109831	+	0.993950i	$0.535031\pi$
$270$		0			0
$271$	−7.51560			−0.456540			−0.228270	−	0.973598i	$-0.573307\pi$
$271$	−7.51560			−0.456540			−0.228270	+	0.973598i	$0.573307\pi$
$272$		0			0
$273$			0.0796476i			0.00482049i
$274$		0			0
$275$	−2.14144	+	0.961384i	−0.129134	+	0.0579737i
$276$		0			0
$277$	−11.7421	−	11.7421i	−0.705512	−	0.705512i	0.260076	−	0.965588i	$-0.416252\pi$
$277$	−11.7421	−	11.7421i	−0.705512	−	0.705512i	−0.965588	+	0.260076i	$0.916252\pi$
$278$		0			0
$279$		−	7.11301i		−	0.425845i
$280$		0			0
$281$		−	32.4999i		−	1.93878i	−0.245523	−	0.969391i	$-0.578960\pi$
$281$		−	32.4999i		−	1.93878i	0.245523	−	0.969391i	$-0.421040\pi$
$282$		0			0
$283$	3.88285	+	3.88285i	0.230811	+	0.230811i	0.813031	−	0.582220i	$-0.197816\pi$
$283$	3.88285	+	3.88285i	0.230811	+	0.230811i	−0.582220	+	0.813031i	$0.697816\pi$
$284$		0			0
$285$	1.18981	−	6.47555i	0.0704783	−	0.383579i
$286$		0			0
$287$			5.55686i			0.328011i
$288$		0			0
$289$	15.9905			0.940617
$290$		0			0
$291$	9.58731	+	9.58731i	0.562018	+	0.562018i
$292$		0			0
$293$	10.6693	+	10.6693i	0.623305	+	0.623305i	0.946375	−	0.323070i	$-0.104715\pi$
$293$	10.6693	+	10.6693i	0.623305	+	0.623305i	−0.323070	+	0.946375i	$0.604715\pi$
$294$		0			0
$295$	11.9925	+	17.3914i	0.698228	+	1.01257i
$296$		0			0
$297$	0.469470			0.0272414
$298$		0			0
$299$	0.193181	−	0.193181i	0.0111719	−	0.0111719i
$300$		0			0
$301$	−6.87223	−	6.87223i	−0.396109	−	0.396109i
$302$		0			0
$303$		−	14.8679i		−	0.854140i
$304$		0			0
$305$	7.53516	−	5.19596i	0.431462	−	0.297520i
$306$		0			0
$307$	16.3961	−	16.3961i	0.935778	−	0.935778i	−0.0622811	−	0.998059i	$-0.519838\pi$
$307$	16.3961	−	16.3961i	0.935778	−	0.935778i	0.998059	+	0.0622811i	$0.0198375\pi$
$308$		0			0
$309$	4.34437	−	4.34437i	0.247143	−	0.247143i
$310$		0			0
$311$			10.1406i			0.575023i	0.957777	+	0.287512i	$0.0928280\pi$
$311$			10.1406i			0.575023i	−0.957777	+	0.287512i	$0.907172\pi$
$312$		0			0
$313$	−23.3811			−1.32158			−0.660790	−	0.750571i	$-0.729779\pi$
$313$	−23.3811			−1.32158			−0.660790	+	0.750571i	$0.729779\pi$
$314$		0			0
$315$	3.99313	+	0.733693i	0.224987	+	0.0413389i
$316$		0			0
$317$	−10.8253	+	10.8253i	−0.608009	+	0.608009i	−0.942425	−	0.334416i	$-0.891461\pi$
$317$	−10.8253	+	10.8253i	−0.608009	+	0.608009i	0.334416	+	0.942425i	$0.391461\pi$
$318$		0			0
$319$	4.17585			0.233803
$320$		0			0
$321$	−9.77945			−0.545836
$322$		0			0
$323$	2.09191	−	2.09191i	0.116397	−	0.116397i
$324$		0			0
$325$	−0.200094	+	0.0898306i	−0.0110992	+	0.00498290i
$326$		0			0
$327$	−8.71072			−0.481704
$328$		0			0
$329$			18.2431i			1.00578i
$330$		0			0
$331$	−12.1611	+	12.1611i	−0.668432	+	0.668432i	−0.957353	−	0.288921i	$-0.906704\pi$
$331$	−12.1611	+	12.1611i	−0.668432	+	0.668432i	0.288921	+	0.957353i	$0.406704\pi$
$332$		0			0
$333$	0.0723513	−	0.0723513i	0.00396483	−	0.00396483i
$334$		0			0
$335$	0.270776	+	0.392679i	0.0147941	+	0.0214543i
$336$		0			0
$337$		−	1.91202i		−	0.104154i	−0.998643	−	0.0520772i	$-0.983416\pi$
$337$		−	1.91202i		−	0.104154i	0.998643	−	0.0520772i	$-0.0165842\pi$
$338$		0			0
$339$	−1.50686	−	1.50686i	−0.0818414	−	0.0818414i
$340$		0			0
$341$	2.36127	−	2.36127i	0.127870	−	0.127870i
$342$		0			0
$343$	−19.4338			−1.04932
$344$		0			0
$345$	−7.90557	−	11.4646i	−0.425622	−	0.617235i
$346$		0			0
$347$	−0.274551	−	0.274551i	−0.0147386	−	0.0147386i	0.699699	−	0.714438i	$-0.253317\pi$
$347$	−0.274551	−	0.274551i	−0.0147386	−	0.0147386i	−0.714438	+	0.699699i	$0.753317\pi$
$348$		0			0
$349$	1.33045	+	1.33045i	0.0712172	+	0.0712172i	0.741818	−	0.670601i	$-0.233964\pi$
$349$	1.33045	+	1.33045i	0.0712172	+	0.0712172i	−0.670601	+	0.741818i	$0.733964\pi$
$350$		0			0
$351$	0.0438667			0.00234143
$352$		0			0
$353$		−	27.5571i		−	1.46672i	−0.679841	−	0.733359i	$-0.737951\pi$
$353$		−	27.5571i		−	1.46672i	0.679841	−	0.733359i	$-0.262049\pi$
$354$		0			0
$355$	−31.9997	−	5.87960i	−1.69837	−	0.312057i
$356$		0			0
$357$	1.28997	+	1.28997i	0.0682722	+	0.0682722i
$358$		0			0
$359$		−	9.65759i		−	0.509708i	−0.966980	−	0.254854i	$-0.917973\pi$
$359$		−	9.65759i		−	0.509708i	0.966980	−	0.254854i	$-0.0820274\pi$
$360$		0			0
$361$		−	10.3303i		−	0.543701i
$362$		0			0
$363$	−7.62233	−	7.62233i	−0.400068	−	0.400068i
$364$		0			0
$365$	6.07437	−	33.0598i	0.317947	−	1.73043i
$366$		0			0
$367$		−	5.40212i		−	0.281988i	−0.990010	−	0.140994i	$-0.954970\pi$
$367$		−	5.40212i		−	0.281988i	0.990010	−	0.140994i	$-0.0450299\pi$
$368$		0			0
$369$	3.06050			0.159323
$370$		0			0
$371$	−12.7939	−	12.7939i	−0.664225	−	0.664225i
$372$		0			0
$373$	6.54862	+	6.54862i	0.339075	+	0.339075i	0.856019	−	0.516944i	$-0.172931\pi$
$373$	6.54862	+	6.54862i	0.339075	+	0.339075i	−0.516944	+	0.856019i	$0.672931\pi$
$374$		0			0
$375$	2.66044	+	10.8592i	0.137384	+	0.560766i
$376$		0			0
$377$	0.390186			0.0200956
$378$		0			0
$379$	24.8255	−	24.8255i	1.27520	−	1.27520i	0.331877	−	0.943323i	$-0.392318\pi$
$379$	24.8255	−	24.8255i	1.27520	−	1.27520i	0.943323	−	0.331877i	$-0.107682\pi$
$380$		0			0
$381$	−7.45931	−	7.45931i	−0.382152	−	0.382152i
$382$		0			0
$383$		−	0.293274i		−	0.0149856i	−0.999972	−	0.00749279i	$-0.997615\pi$
$383$		−	0.293274i		−	0.0149856i	0.999972	−	0.00749279i	$-0.00238505\pi$
$384$		0			0
$385$	1.08202	+	1.56914i	0.0551448	+	0.0799707i
$386$		0			0
$387$	−3.78495	+	3.78495i	−0.192400	+	0.192400i
$388$		0			0
$389$	0.442101	−	0.442101i	0.0224154	−	0.0224154i	−0.695810	−	0.718226i	$-0.744955\pi$
$389$	0.442101	−	0.442101i	0.0224154	−	0.0224154i	0.718226	+	0.695810i	$0.244955\pi$
$390$		0			0
$391$		−	6.25748i		−	0.316454i
$392$		0			0
$393$	8.23550			0.415426
$394$		0			0
$395$	−6.30319	+	34.3051i	−0.317148	+	1.72608i
$396$		0			0
$397$	24.4503	−	24.4503i	1.22712	−	1.22712i	0.262078	−	0.965047i	$-0.415592\pi$
$397$	24.4503	−	24.4503i	1.22712	−	1.22712i	0.965047	−	0.262078i	$-0.0844076\pi$
$398$		0			0
$399$	−5.34613			−0.267641
$400$		0			0
$401$	−17.3106			−0.864451			−0.432226	−	0.901765i	$-0.642272\pi$
$401$	−17.3106			−0.864451			−0.432226	+	0.901765i	$0.642272\pi$
$402$		0			0
$403$	0.220634	−	0.220634i	0.0109906	−	0.0109906i
$404$		0			0
$405$	0.404088	−	2.19925i	0.0200793	−	0.109282i
$406$		0			0
$407$	0.0480362			0.00238107
$408$		0			0
$409$		−	7.62314i		−	0.376940i	−0.982079	−	0.188470i	$-0.939647\pi$
$409$		−	7.62314i		−	0.376940i	0.982079	−	0.188470i	$-0.0603528\pi$
$410$		0			0
$411$	−11.0700	+	11.0700i	−0.546044	+	0.546044i
$412$		0			0
$413$	12.1295	−	12.1295i	0.596852	−	0.596852i
$414$		0			0
$415$	−9.85519	−	14.2920i	−0.483772	−	0.701565i
$416$		0			0
$417$			1.61471i			0.0790728i
$418$		0			0
$419$	−3.21455	−	3.21455i	−0.157041	−	0.157041i	0.624213	−	0.781254i	$-0.285420\pi$
$419$	−3.21455	−	3.21455i	−0.157041	−	0.157041i	−0.781254	+	0.624213i	$0.785420\pi$
$420$		0			0
$421$	8.12907	−	8.12907i	0.396187	−	0.396187i	−0.480699	−	0.876886i	$-0.659617\pi$
$421$	8.12907	−	8.12907i	0.396187	−	0.396187i	0.876886	+	0.480699i	$0.159617\pi$
$422$		0			0
$423$	10.0476			0.488530
$424$		0			0
$425$	−1.78582	+	4.69560i	−0.0866249	+	0.227770i
$426$		0			0
$427$	−5.25532	−	5.25532i	−0.254323	−	0.254323i
$428$		0			0
$429$	0.0145622	+	0.0145622i	0.000703070	+	0.000703070i
$430$		0			0
$431$	−34.3410			−1.65415			−0.827074	−	0.562093i	$-0.809996\pi$
$431$	−34.3410			−1.65415			−0.827074	+	0.562093i	$0.809996\pi$
$432$		0			0
$433$			31.2038i			1.49956i	0.661687	+	0.749780i	$0.269841\pi$
$433$			31.2038i			1.49956i	−0.661687	+	0.749780i	$0.730159\pi$
$434$		0			0
$435$	3.59430	−	19.5620i	0.172333	−	0.937925i
$436$		0			0
$437$	12.9667	+	12.9667i	0.620283	+	0.620283i
$438$		0			0
$439$			25.1727i			1.20143i	0.799464	+	0.600714i	$0.205117\pi$
$439$			25.1727i			1.20143i	−0.799464	+	0.600714i	$0.794883\pi$
$440$		0			0
$441$			3.70333i			0.176349i
$442$		0			0
$443$	−4.89367	−	4.89367i	−0.232505	−	0.232505i	0.581232	−	0.813738i	$-0.302571\pi$
$443$	−4.89367	−	4.89367i	−0.232505	−	0.232505i	−0.813738	+	0.581232i	$0.802571\pi$
$444$		0			0
$445$	−31.5637	−	5.79948i	−1.49626	−	0.274922i
$446$		0			0
$447$			2.57129i			0.121618i
$448$		0			0
$449$	36.7865			1.73606			0.868031	−	0.496511i	$-0.165386\pi$
$449$	36.7865			1.73606			0.868031	+	0.496511i	$0.165386\pi$
$450$		0			0
$451$	1.01598	+	1.01598i	0.0478405	+	0.0478405i
$452$		0			0
$453$	7.94854	+	7.94854i	0.373455	+	0.373455i
$454$		0			0
$455$	0.101102	+	0.146618i	0.00473976	+	0.00687358i
$456$		0			0
$457$	3.78613			0.177108			0.0885539	−	0.996071i	$-0.471775\pi$
$457$	3.78613			0.177108			0.0885539	+	0.996071i	$0.471775\pi$
$458$		0			0
$459$	0.710461	−	0.710461i	0.0331615	−	0.0331615i
$460$		0			0
$461$	24.6710	+	24.6710i	1.14904	+	1.14904i	0.986741	+	0.162303i	$0.0518921\pi$
$461$	24.6710	+	24.6710i	1.14904	+	1.14904i	0.162303	+	0.986741i	$0.448108\pi$
$462$		0			0
$463$		−	3.86935i		−	0.179824i	−0.995950	−	0.0899120i	$-0.971341\pi$
$463$		−	3.86935i		−	0.179824i	0.995950	−	0.0899120i	$-0.0286586\pi$
$464$		0			0
$465$	−9.02906	−	13.0939i	−0.418713	−	0.607216i
$466$		0			0
$467$	−12.5440	+	12.5440i	−0.580469	+	0.580469i	−0.935032	−	0.354563i	$-0.884630\pi$
$467$	−12.5440	+	12.5440i	−0.580469	+	0.580469i	0.354563	+	0.935032i	$0.384630\pi$
$468$		0			0
$469$	0.273870	−	0.273870i	0.0126461	−	0.0126461i
$470$		0			0
$471$		−	20.9578i		−	0.965686i
$472$		0			0
$473$	−2.51294			−0.115545
$474$		0			0
$475$	−6.02964	−	13.4308i	−0.276659	−	0.616246i
$476$		0			0
$477$	−7.04636	+	7.04636i	−0.322631	+	0.322631i
$478$		0			0
$479$	26.9702			1.23230			0.616150	−	0.787629i	$-0.288692\pi$
$479$	26.9702			1.23230			0.616150	+	0.787629i	$0.288692\pi$
$480$		0			0
$481$	0.00448844			0.000204655
$482$		0			0
$483$	−7.99589	+	7.99589i	−0.363826	+	0.363826i
$484$		0			0
$485$	29.8186	+	5.47883i	1.35399	+	0.248781i
$486$		0			0
$487$	25.1835			1.14117			0.570586	−	0.821238i	$-0.306716\pi$
$487$	25.1835			1.14117			0.570586	+	0.821238i	$0.306716\pi$
$488$		0			0
$489$			9.72445i			0.439755i
$490$		0			0
$491$	17.0641	−	17.0641i	0.770094	−	0.770094i	−0.208029	−	0.978123i	$-0.566705\pi$
$491$	17.0641	−	17.0641i	0.770094	−	0.770094i	0.978123	+	0.208029i	$0.0667048\pi$
$492$		0			0
$493$	6.31943	−	6.31943i	0.284613	−	0.284613i
$494$		0			0
$495$	0.864219	−	0.595932i	0.0388437	−	0.0267852i
$496$		0			0
$497$			26.4186i			1.18503i
$498$		0			0
$499$	−11.2471	−	11.2471i	−0.503488	−	0.503488i	0.409032	−	0.912520i	$-0.365867\pi$
$499$	−11.2471	−	11.2471i	−0.503488	−	0.503488i	−0.912520	+	0.409032i	$0.865867\pi$
$500$		0			0
$501$	9.06325	−	9.06325i	0.404916	−	0.404916i
$502$		0			0
$503$	37.0584			1.65235			0.826176	−	0.563412i	$-0.190512\pi$
$503$	37.0584			1.65235			0.826176	+	0.563412i	$0.190512\pi$
$504$		0			0
$505$	−18.8729	−	27.3695i	−0.839834	−	1.21793i
$506$		0			0
$507$	−9.19103	−	9.19103i	−0.408188	−	0.408188i
$508$		0			0
$509$	−6.60068	−	6.60068i	−0.292570	−	0.292570i	0.545525	−	0.838095i	$-0.316330\pi$
$509$	−6.60068	−	6.60068i	−0.292570	−	0.292570i	−0.838095	+	0.545525i	$0.816330\pi$
$510$		0			0
$511$	−27.2937			−1.20740
$512$		0			0
$513$			2.94443i			0.130000i
$514$		0			0
$515$	2.48267	−	13.5119i	0.109399	−	0.595406i
$516$		0			0
$517$	3.33545	+	3.33545i	0.146693	+	0.146693i
$518$		0			0
$519$			8.32874i			0.365591i
$520$		0			0
$521$		−	11.8337i		−	0.518442i	−0.965818	−	0.259221i	$-0.916534\pi$
$521$		−	11.8337i		−	0.518442i	0.965818	−	0.259221i	$-0.0834657\pi$
$522$		0			0
$523$	−8.02817	−	8.02817i	−0.351047	−	0.351047i	0.509452	−	0.860499i	$-0.329848\pi$
$523$	−8.02817	−	8.02817i	−0.351047	−	0.351047i	−0.860499	+	0.509452i	$0.829848\pi$
$524$		0			0
$525$	8.28204	−	3.71815i	0.361458	−	0.162274i
$526$		0			0
$527$		−	7.14676i		−	0.311318i
$528$		0			0
$529$	15.7872			0.686400
$530$		0			0
$531$	−6.68042	−	6.68042i	−0.289906	−	0.289906i
$532$		0			0
$533$	0.0949317	+	0.0949317i	0.00411195	+	0.00411195i
$534$		0			0
$535$	−18.0024	+	12.4138i	−0.778312	+	0.536694i
$536$		0			0
$537$	−14.3377			−0.618716
$538$		0			0
$539$	−1.22938	+	1.22938i	−0.0529530	+	0.0529530i
$540$		0			0
$541$	−10.9990	−	10.9990i	−0.472882	−	0.472882i	0.429964	−	0.902846i	$-0.358526\pi$
$541$	−10.9990	−	10.9990i	−0.472882	−	0.472882i	−0.902846	+	0.429964i	$0.858526\pi$
$542$		0			0
$543$			15.3694i			0.659564i
$544$		0			0
$545$	−16.0350	+	11.0571i	−0.686866	+	0.473636i
$546$		0			0
$547$	21.3064	−	21.3064i	0.910997	−	0.910997i	−0.0853539	−	0.996351i	$-0.527202\pi$
$547$	21.3064	−	21.3064i	0.910997	−	0.910997i	0.996351	+	0.0853539i	$0.0272021\pi$
$548$		0			0
$549$	−2.89442	+	2.89442i	−0.123531	+	0.123531i
$550$		0			0
$551$			26.1902i			1.11574i
$552$		0			0
$553$	28.3219			1.20437
$554$		0			0
$555$	0.0413464	−	0.225028i	0.00175506	−	0.00955190i
$556$		0			0
$557$	18.9715	−	18.9715i	0.803846	−	0.803846i	−0.179848	−	0.983694i	$-0.557561\pi$
$557$	18.9715	−	18.9715i	0.803846	−	0.803846i	0.983694	+	0.179848i	$0.0575606\pi$
$558$		0			0
$559$	−0.234806			−0.00993124
$560$		0			0
$561$	0.471697			0.0199151
$562$		0			0
$563$	0.478449	−	0.478449i	0.0201642	−	0.0201642i	−0.696953	−	0.717117i	$-0.745461\pi$
$563$	0.478449	−	0.478449i	0.0201642	−	0.0201642i	0.717117	+	0.696953i	$0.245461\pi$
$564$		0			0
$565$	−4.68666	−	0.861121i	−0.197169	−	0.0362276i
$566$		0			0
$567$	−1.81567			−0.0762511
$568$		0			0
$569$			11.7904i			0.494278i	0.968980	+	0.247139i	$0.0794904\pi$
$569$			11.7904i			0.494278i	−0.968980	+	0.247139i	$0.920510\pi$
$570$		0			0
$571$	6.72738	−	6.72738i	0.281532	−	0.281532i	−0.552188	−	0.833720i	$-0.686207\pi$
$571$	6.72738	−	6.72738i	0.281532	−	0.281532i	0.833720	+	0.552188i	$0.186207\pi$
$572$		0			0
$573$	1.11233	−	1.11233i	0.0464681	−	0.0464681i
$574$		0			0
$575$	−29.1058	−	11.0694i	−1.21380	−	0.461628i
$576$		0			0
$577$		−	27.7420i		−	1.15491i	−0.816421	−	0.577457i	$-0.804045\pi$
$577$		−	27.7420i		−	1.15491i	0.816421	−	0.577457i	$-0.195955\pi$
$578$		0			0
$579$	−2.77055	−	2.77055i	−0.115140	−	0.115140i
$580$		0			0
$581$	−9.96778	+	9.96778i	−0.413533	+	0.413533i
$582$		0			0
$583$	−4.67829			−0.193755
$584$		0			0
$585$	0.0807515	−	0.0556832i	0.00333866	−	0.00230222i
$586$		0			0
$587$	−9.78016	−	9.78016i	−0.403670	−	0.403670i	0.475854	−	0.879524i	$-0.342139\pi$
$587$	−9.78016	−	9.78016i	−0.403670	−	0.403670i	−0.879524	+	0.475854i	$0.842139\pi$
$588$		0			0
$589$	14.8095	+	14.8095i	0.610214	+	0.610214i
$590$		0			0
$591$	−3.86032			−0.158792
$592$		0			0
$593$			12.8018i			0.525707i	0.964836	+	0.262854i	$0.0846637\pi$
$593$			12.8018i			0.525707i	−0.964836	+	0.262854i	$0.915336\pi$
$594$		0			0
$595$	4.01207	+	0.737174i	0.164479	+	0.0302212i
$596$		0			0
$597$	13.9195	+	13.9195i	0.569685	+	0.569685i
$598$		0			0
$599$		−	35.6315i		−	1.45586i	−0.685650	−	0.727932i	$-0.740482\pi$
$599$		−	35.6315i		−	1.45586i	0.685650	−	0.727932i	$-0.259518\pi$
$600$		0			0
$601$		−	43.3118i		−	1.76672i	−0.468692	−	0.883362i	$-0.655275\pi$
$601$		−	43.3118i		−	1.76672i	0.468692	−	0.883362i	$-0.344725\pi$
$602$		0			0
$603$	−0.150837	−	0.150837i	−0.00614254	−	0.00614254i
$604$		0			0
$605$	−23.7071	−	4.35591i	−0.963829	−	0.177093i
$606$		0			0
$607$		−	18.4382i		−	0.748385i	−0.927351	−	0.374192i	$-0.877920\pi$
$607$		−	18.4382i		−	0.748385i	0.927351	−	0.374192i	$-0.122080\pi$
$608$		0			0
$609$	−16.1501			−0.654435
$610$		0			0
$611$	0.311660	+	0.311660i	0.0126084	+	0.0126084i
$612$		0			0
$613$	9.81446	+	9.81446i	0.396402	+	0.396402i	0.876962	−	0.480560i	$-0.159566\pi$
$613$	9.81446	+	9.81446i	0.396402	+	0.396402i	−0.480560	+	0.876962i	$0.659566\pi$
$614$		0			0
$615$	5.63388	−	3.88491i	0.227180	−	0.156655i
$616$		0			0
$617$	−9.02339			−0.363268			−0.181634	−	0.983366i	$-0.558139\pi$
$617$	−9.02339			−0.363268			−0.181634	+	0.983366i	$0.558139\pi$
$618$		0			0
$619$	15.6705	−	15.6705i	0.629850	−	0.629850i	−0.318181	−	0.948030i	$-0.603072\pi$
$619$	15.6705	−	15.6705i	0.629850	−	0.629850i	0.948030	+	0.318181i	$0.103072\pi$
$620$		0			0
$621$	4.40382	+	4.40382i	0.176719	+	0.176719i
$622$		0			0
$623$			26.0586i			1.04401i
$624$		0			0
$625$	18.6818	+	16.6130i	0.747272	+	0.664518i
$626$		0			0
$627$	−0.977449	+	0.977449i	−0.0390356	+	0.0390356i
$628$		0			0
$629$	0.0726945	−	0.0726945i	0.00289852	−	0.00289852i
$630$		0			0
$631$			7.32472i			0.291593i	0.989315	+	0.145796i	$0.0465744\pi$
$631$			7.32472i			0.291593i	−0.989315	+	0.145796i	$0.953426\pi$
$632$		0			0
$633$	2.74071			0.108933
$634$		0			0
$635$	−23.2000	−	4.26275i	−0.920666	−	0.169162i
$636$		0			0
$637$	−0.114871	+	0.114871i	−0.00455137	+	0.00455137i
$638$		0			0
$639$	14.5503			0.575600
$640$		0			0
$641$	−22.8353			−0.901939			−0.450970	−	0.892539i	$-0.648922\pi$
$641$	−22.8353			−0.901939			−0.450970	+	0.892539i	$0.648922\pi$
$642$		0			0
$643$	−15.9787	+	15.9787i	−0.630138	+	0.630138i	−0.948102	−	0.317965i	$-0.897001\pi$
$643$	−15.9787	+	15.9787i	−0.630138	+	0.630138i	0.317965	+	0.948102i	$0.397001\pi$
$644$		0			0
$645$	−2.16297	+	11.7720i	−0.0851670	+	0.463522i
$646$		0			0
$647$	−7.57070			−0.297635			−0.148817	−	0.988865i	$-0.547547\pi$
$647$	−7.57070			−0.297635			−0.148817	+	0.988865i	$0.547547\pi$
$648$		0			0
$649$		−	4.43534i		−	0.174102i
$650$		0			0
$651$	−9.13222	+	9.13222i	−0.357920	+	0.357920i
$652$		0			0
$653$	−8.64398	+	8.64398i	−0.338265	+	0.338265i	−0.855714	−	0.517449i	$-0.826882\pi$
$653$	−8.64398	+	8.64398i	−0.338265	+	0.338265i	0.517449	+	0.855714i	$0.326882\pi$
$654$		0			0
$655$	15.1602	−	10.4539i	0.592359	−	0.408468i
$656$		0			0
$657$			15.0323i			0.586465i
$658$		0			0
$659$	−22.8915	−	22.8915i	−0.891728	−	0.891728i	0.102958	−	0.994686i	$-0.467169\pi$
$659$	−22.8915	−	22.8915i	−0.891728	−	0.891728i	−0.994686	+	0.102958i	$0.967169\pi$
$660$		0			0
$661$	−16.8355	+	16.8355i	−0.654824	+	0.654824i	−0.954151	−	0.299326i	$-0.903238\pi$
$661$	−16.8355	+	16.8355i	−0.654824	+	0.654824i	0.299326	+	0.954151i	$0.403238\pi$
$662$		0			0
$663$	0.0440748			0.00171172
$664$		0			0
$665$	−9.84137	+	6.78623i	−0.381632	+	0.263159i
$666$		0			0
$667$	39.1712	+	39.1712i	1.51671	+	1.51671i
$668$		0			0
$669$	6.51980	+	6.51980i	0.252070	+	0.252070i
$670$		0			0
$671$	−1.92169			−0.0741861
$672$		0			0
$673$		−	5.34019i		−	0.205849i	−0.994689	−	0.102925i	$-0.967180\pi$
$673$		−	5.34019i		−	0.205849i	0.994689	−	0.102925i	$-0.0328200\pi$
$674$		0			0
$675$	−2.04781	−	4.56141i	−0.0788202	−	0.175569i
$676$		0			0
$677$	0.117760	+	0.117760i	0.00452590	+	0.00452590i	0.709366	−	0.704840i	$-0.248981\pi$
$677$	0.117760	+	0.117760i	0.00452590	+	0.00452590i	−0.704840	+	0.709366i	$0.748981\pi$
$678$		0			0
$679$		−	24.6178i		−	0.944745i
$680$		0			0
$681$			15.6211i			0.598600i
$682$		0			0
$683$	−11.0216	−	11.0216i	−0.421729	−	0.421729i	0.464070	−	0.885799i	$-0.346389\pi$
$683$	−11.0216	−	11.0216i	−0.421729	−	0.421729i	−0.885799	+	0.464070i	$0.846389\pi$
$684$		0			0
$685$	−6.32615	+	34.4301i	−0.241710	+	1.31551i
$686$		0			0
$687$		−	7.39779i		−	0.282243i
$688$		0			0
$689$	−0.437134			−0.0166535
$690$		0			0
$691$	33.0825	+	33.0825i	1.25852	+	1.25852i	0.951801	+	0.306716i	$0.0992301\pi$
$691$	33.0825	+	33.0825i	1.25852	+	1.25852i	0.306716	+	0.951801i	$0.400770\pi$
$692$		0			0
$693$	−0.602741	−	0.602741i	−0.0228962	−	0.0228962i
$694$		0			0
$695$	2.04967	+	2.97243i	0.0777485	+	0.112751i
$696$		0			0
$697$	3.07501			0.116474
$698$		0			0
$699$	−10.2890	+	10.2890i	−0.389168	+	0.389168i
$700$		0			0
$701$	−3.90473	−	3.90473i	−0.147480	−	0.147480i	0.629511	−	0.776991i	$-0.283255\pi$
$701$	−3.90473	−	3.90473i	−0.147480	−	0.147480i	−0.776991	+	0.629511i	$0.783255\pi$
$702$		0			0
$703$			0.301275i			0.0113628i
$704$		0			0
$705$	18.4960	−	12.7541i	0.696599	−	0.480348i
$706$		0			0
$707$	−19.0886	+	19.0886i	−0.717899	+	0.717899i
$708$		0			0
$709$	−7.84907	+	7.84907i	−0.294778	+	0.294778i	−0.838964	−	0.544186i	$-0.816838\pi$
$709$	−7.84907	+	7.84907i	−0.294778	+	0.294778i	0.544186	+	0.838964i	$0.316838\pi$
$710$		0			0
$711$		−	15.5985i		−	0.584991i
$712$		0			0
$713$	44.2994			1.65903
$714$		0			0
$715$	0.0452916	+	0.00832183i	0.00169381	+	0.000311219i
$716$		0			0
$717$	5.82235	−	5.82235i	0.217440	−	0.217440i
$718$		0			0
$719$	24.3830			0.909331			0.454665	−	0.890662i	$-0.349759\pi$
$719$	24.3830			0.909331			0.454665	+	0.890662i	$0.349759\pi$
$720$		0			0
$721$	−11.1553			−0.415444
$722$		0			0
$723$	4.82097	−	4.82097i	0.179294	−	0.179294i
$724$		0			0
$725$	−18.2149	−	40.5730i	−0.676485	−	1.50684i
$726$		0			0
$727$	25.7991			0.956834			0.478417	−	0.878133i	$-0.341211\pi$
$727$	25.7991			0.956834			0.478417	+	0.878133i	$0.341211\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−3.80290	+	3.80290i	−0.140655	+	0.140655i
$732$		0			0
$733$	−15.0948	+	15.0948i	−0.557537	+	0.557537i	−0.928606	−	0.371068i	$-0.878992\pi$
$733$	−15.0948	+	15.0948i	−0.557537	+	0.557537i	0.371068	+	0.928606i	$0.378992\pi$
$734$		0			0
$735$	4.70090	+	6.81724i	0.173395	+	0.251458i
$736$		0			0
$737$		−	0.100145i		−	0.00368889i
$738$		0			0
$739$	17.9291	+	17.9291i	0.659531	+	0.659531i	0.955269	−	0.295738i	$-0.0955656\pi$
$739$	17.9291	+	17.9291i	0.659531	+	0.659531i	−0.295738	+	0.955269i	$0.595566\pi$
$740$		0			0
$741$	−0.0913316	+	0.0913316i	−0.00335515	+	0.00335515i
$742$		0			0
$743$	−8.25344			−0.302789			−0.151395	−	0.988473i	$-0.548376\pi$
$743$	−8.25344			−0.302789			−0.151395	+	0.988473i	$0.548376\pi$
$744$		0			0
$745$	3.26392	+	4.73333i	0.119581	+	0.173416i
$746$		0			0
$747$	5.48985	+	5.48985i	0.200863	+	0.200863i
$748$		0			0
$749$	12.5556	+	12.5556i	0.458772	+	0.458772i
$750$		0			0
$751$	6.07037			0.221511			0.110755	−	0.993848i	$-0.464673\pi$
$751$	6.07037			0.221511			0.110755	+	0.993848i	$0.464673\pi$
$752$		0			0
$753$		−	17.1715i		−	0.625766i
$754$		0			0
$755$	24.7216	+	4.54233i	0.899713	+	0.165312i
$756$		0			0
$757$	−21.4003	−	21.4003i	−0.777806	−	0.777806i	0.201651	−	0.979457i	$-0.435369\pi$
$757$	−21.4003	−	21.4003i	−0.777806	−	0.777806i	−0.979457	+	0.201651i	$0.935369\pi$
$758$		0			0
$759$			2.92383i			0.106128i
$760$		0			0
$761$		−	20.8862i		−	0.757125i	−0.925576	−	0.378563i	$-0.876418\pi$
$761$		−	20.8862i		−	0.757125i	0.925576	−	0.378563i	$-0.123582\pi$
$762$		0			0
$763$	11.1835	+	11.1835i	0.404869	+	0.404869i
$764$		0			0
$765$	0.406005	−	2.20969i	0.0146792	−	0.0798914i
$766$		0			0
$767$		−	0.414432i		−	0.0149643i
$768$		0			0
$769$	−8.06017			−0.290657			−0.145329	−	0.989383i	$-0.546424\pi$
$769$	−8.06017			−0.290657			−0.145329	+	0.989383i	$0.546424\pi$
$770$		0			0
$771$	9.87593	+	9.87593i	0.355673	+	0.355673i
$772$		0			0
$773$	−11.9200	−	11.9200i	−0.428731	−	0.428731i	0.459465	−	0.888196i	$-0.348041\pi$
$773$	−11.9200	−	11.9200i	−0.428731	−	0.428731i	−0.888196	+	0.459465i	$0.848041\pi$
$774$		0			0
$775$	−33.2421	−	12.6426i	−1.19409	−	0.454134i
$776$		0			0
$777$	−0.185780			−0.00666482
$778$		0			0
$779$	−6.37204	+	6.37204i	−0.228302	+	0.228302i
$780$		0			0
$781$	4.83018	+	4.83018i	0.172838	+	0.172838i
$782$		0			0
$783$			8.89482i			0.317875i
$784$		0			0
$785$	−26.6033	−	38.5800i	−0.949512	−	1.37698i
$786$		0			0
$787$	−38.1416	+	38.1416i	−1.35960	+	1.35960i	−0.485194	+	0.874407i	$0.661251\pi$
$787$	−38.1416	+	38.1416i	−1.35960	+	1.35960i	−0.874407	+	0.485194i	$0.838749\pi$
$788$		0			0
$789$	−2.34293	+	2.34293i	−0.0834105	+	0.0834105i
$790$		0			0
$791$			3.86924i			0.137574i
$792$		0			0
$793$	−0.179561			−0.00637638
$794$		0			0
$795$	−4.02676	+	21.9157i	−0.142815	+	0.777269i
$796$		0			0
$797$	−22.2285	+	22.2285i	−0.787373	+	0.787373i	−0.981063	−	0.193690i	$-0.937954\pi$
$797$	−22.2285	+	22.2285i	−0.787373	+	0.787373i	0.193690	+	0.981063i	$0.437954\pi$
$798$		0			0
$799$	10.0952			0.357144
$800$		0			0
$801$	14.3520			0.507103
$802$		0			0
$803$	−4.99019	+	4.99019i	−0.176100	+	0.176100i
$804$		0			0
$805$	−4.56939	+	24.8689i	−0.161050	+	0.876515i
$806$		0			0
$807$	−20.5070			−0.721881
$808$		0			0
$809$			41.1080i			1.44528i	0.691225	+	0.722639i	$0.257071\pi$
$809$			41.1080i			1.44528i	−0.691225	+	0.722639i	$0.742929\pi$
$810$		0			0
$811$	−10.2679	+	10.2679i	−0.360555	+	0.360555i	−0.864017	−	0.503462i	$-0.832059\pi$
$811$	−10.2679	+	10.2679i	−0.360555	+	0.360555i	0.503462	+	0.864017i	$0.332059\pi$
$812$		0			0
$813$	5.31433	−	5.31433i	0.186382	−	0.186382i
$814$		0			0
$815$	12.3439	+	17.9011i	0.432390	+	0.627050i
$816$		0			0
$817$		−	15.7607i		−	0.551398i
$818$		0			0
$819$	−0.0563193	−	0.0563193i	−0.00196796	−	0.00196796i
$820$		0			0
$821$	6.82793	−	6.82793i	0.238296	−	0.238296i	−0.577848	−	0.816144i	$-0.696107\pi$
$821$	6.82793	−	6.82793i	0.238296	−	0.238296i	0.816144	+	0.577848i	$0.196107\pi$
$822$		0			0
$823$	−40.4181			−1.40889			−0.704444	−	0.709760i	$-0.748803\pi$
$823$	−40.4181			−1.40889			−0.704444	+	0.709760i	$0.748803\pi$
$824$		0			0
$825$	0.834428	−	2.19403i	0.0290511	−	0.0763864i
$826$		0			0
$827$	−23.8197	−	23.8197i	−0.828291	−	0.828291i	0.158989	−	0.987280i	$-0.449176\pi$
$827$	−23.8197	−	23.8197i	−0.828291	−	0.828291i	−0.987280	+	0.158989i	$0.949176\pi$
$828$		0			0
$829$	13.6687	+	13.6687i	0.474734	+	0.474734i	0.903443	−	0.428709i	$-0.141031\pi$
$829$	13.6687	+	13.6687i	0.474734	+	0.474734i	−0.428709	+	0.903443i	$0.641031\pi$
$830$		0			0
$831$	16.6058			0.576048
$832$		0			0
$833$			3.72090i			0.128921i
$834$		0			0
$835$	5.17935	−	28.1886i	0.179239	−	0.975508i
$836$		0			0
$837$	5.02966	+	5.02966i	0.173850	+	0.173850i
$838$		0			0
$839$			0.00707031i			0.000244094i	1.00000		0.000122047i	$3.88488e-5\pi$
$839$			0.00707031i			0.000244094i	−1.00000		0.000122047i	$0.999961\pi$
$840$		0			0
$841$			50.1179i			1.72820i
$842$		0			0
$843$	22.9809	+	22.9809i	0.791504	+	0.791504i
$844$		0			0
$845$	−28.5861	−	5.25237i	−0.983390	−	0.180687i
$846$		0			0
$847$			19.5722i			0.672510i
$848$		0			0
$849$	−5.49118			−0.188457
$850$		0			0
$851$	0.450599	+	0.450599i	0.0154463	+	0.0154463i
$852$		0			0
$853$	−24.8778	−	24.8778i	−0.851800	−	0.851800i	0.138555	−	0.990355i	$-0.455754\pi$
$853$	−24.8778	−	24.8778i	−0.851800	−	0.851800i	−0.990355	+	0.138555i	$0.955754\pi$
$854$		0			0
$855$	3.73758	+	5.42023i	0.127823	+	0.185368i
$856$		0			0
$857$	−17.0079			−0.580979			−0.290490	−	0.956878i	$-0.593818\pi$
$857$	−17.0079			−0.580979			−0.290490	+	0.956878i	$0.593818\pi$
$858$		0			0
$859$	10.6241	−	10.6241i	0.362490	−	0.362490i	−0.502239	−	0.864729i	$-0.667490\pi$
$859$	10.6241	−	10.6241i	0.362490	−	0.362490i	0.864729	+	0.502239i	$0.167490\pi$
$860$		0			0
$861$	−3.92929	−	3.92929i	−0.133910	−	0.133910i
$862$		0			0
$863$			8.48545i			0.288848i	0.989516	+	0.144424i	$0.0461329\pi$
$863$			8.48545i			0.288848i	−0.989516	+	0.144424i	$0.953867\pi$
$864$		0			0
$865$	10.5723	+	15.3319i	0.359468	+	0.521300i
$866$		0			0
$867$	−11.3070	+	11.3070i	−0.384005	+	0.384005i
$868$		0			0
$869$	5.17817	−	5.17817i	0.175658	−	0.175658i
$870$		0			0
$871$		−	0.00935742i		−	0.000317064i
$872$		0			0
$873$	−13.5585			−0.458886
$874$		0			0
$875$	10.5262	−	17.3575i	0.355850	−	0.586791i
$876$		0			0
$877$	37.8615	−	37.8615i	1.27849	−	1.27849i	0.336982	−	0.941511i	$-0.390594\pi$
$877$	37.8615	−	37.8615i	1.27849	−	1.27849i	0.941511	−	0.336982i	$-0.109406\pi$
$878$		0			0
$879$	−15.0886			−0.508926
$880$		0			0
$881$	13.4706			0.453836			0.226918	−	0.973914i	$-0.427135\pi$
$881$	13.4706			0.453836			0.226918	+	0.973914i	$0.427135\pi$
$882$		0			0
$883$	9.55258	−	9.55258i	0.321470	−	0.321470i	−0.527861	−	0.849331i	$-0.677006\pi$
$883$	9.55258	−	9.55258i	0.321470	−	0.321470i	0.849331	+	0.527861i	$0.177006\pi$
$884$		0			0
$885$	−20.7775	−	3.81764i	−0.698429	−	0.128329i
$886$		0			0
$887$	0.288617			0.00969081			0.00484540	−	0.999988i	$-0.498458\pi$
$887$	0.288617			0.00969081			0.00484540	+	0.999988i	$0.498458\pi$
$888$		0			0
$889$			19.1536i			0.642393i
$890$		0			0
$891$	−0.331965	+	0.331965i	−0.0111213	+	0.0111213i
$892$		0			0
$893$	−20.9193	+	20.9193i	−0.700039	+	0.700039i
$894$		0			0
$895$	−26.3934	+	18.1998i	−0.882233	+	0.608354i
$896$		0			0
$897$			0.273199i			0.00912184i
$898$		0			0
$899$	44.7379	+	44.7379i	1.49209	+	1.49209i
$900$		0			0
$901$	−7.07979	+	7.07979i	−0.235862	+	0.235862i
$902$		0			0
$903$	9.71880			0.323421
$904$		0			0
$905$	19.5095	+	28.2926i	0.648518	+	0.940478i
$906$		0			0
$907$	38.0634	+	38.0634i	1.26387	+	1.26387i	0.949200	+	0.314672i	$0.101895\pi$
$907$	38.0634	+	38.0634i	1.26387	+	1.26387i	0.314672	+	0.949200i	$0.398105\pi$
$908$		0			0
$909$	10.5132	+	10.5132i	0.348701	+	0.348701i
$910$		0			0
$911$	27.9067			0.924591			0.462295	−	0.886726i	$-0.347026\pi$
$911$	27.9067			0.924591			0.462295	+	0.886726i	$0.347026\pi$
$912$		0			0
$913$			3.64488i			0.120628i
$914$		0			0
$915$	−1.65407	+	9.00226i	−0.0546817	+	0.297605i
$916$		0			0
$917$	−10.5734	−	10.5734i	−0.349163	−	0.349163i
$918$		0			0
$919$			27.9263i			0.921202i	0.887607	+	0.460601i	$0.152366\pi$
$919$			27.9263i			0.921202i	−0.887607	+	0.460601i	$0.847634\pi$
$920$		0			0
$921$			23.1877i			0.764059i
$922$		0			0
$923$	0.451327	+	0.451327i	0.0148556	+	0.0148556i
$924$		0			0
$925$	−0.209532	−	0.466724i	−0.00688938	−	0.0153458i
$926$		0			0
$927$			6.14387i			0.201791i
$928$		0			0
$929$	−24.8391			−0.814943			−0.407472	−	0.913218i	$-0.633589\pi$
$929$	−24.8391			−0.814943			−0.407472	+	0.913218i	$0.633589\pi$
$930$		0			0
$931$	−7.71043	−	7.71043i	−0.252699	−	0.252699i
$932$		0			0
$933$	−7.17052	−	7.17052i	−0.234752	−	0.234752i
$934$		0			0
$935$	0.868319	−	0.598759i	0.0283971	−	0.0195815i
$936$		0			0
$937$	−14.2052			−0.464062			−0.232031	−	0.972708i	$-0.574537\pi$
$937$	−14.2052			−0.464062			−0.232031	+	0.972708i	$0.574537\pi$
$938$		0			0
$939$	16.5330	−	16.5330i	0.539533	−	0.539533i
$940$		0			0
$941$	−0.916857	−	0.916857i	−0.0298887	−	0.0298887i	0.692005	−	0.721893i	$-0.256728\pi$
$941$	−0.916857	−	0.916857i	−0.0298887	−	0.0298887i	−0.721893	+	0.692005i	$0.756728\pi$
$942$		0			0
$943$			19.0606i			0.620698i
$944$		0			0
$945$	−3.34237	+	2.30477i	−0.108727	+	0.0749741i
$946$		0			0
$947$	20.1404	−	20.1404i	0.654474	−	0.654474i	−0.299593	−	0.954067i	$-0.596851\pi$
$947$	20.1404	−	20.1404i	0.654474	−	0.654474i	0.954067	+	0.299593i	$0.0968509\pi$
$948$		0			0
$949$	−0.466277	+	0.466277i	−0.0151360	+	0.0151360i
$950$		0			0
$951$		−	15.3093i		−	0.496437i
$952$		0			0
$953$	−49.1705			−1.59279			−0.796394	−	0.604777i	$-0.793262\pi$
$953$	−49.1705			−1.59279			−0.796394	+	0.604777i	$0.793262\pi$
$954$		0			0
$955$	0.635658	−	3.45957i	0.0205694	−	0.111949i
$956$		0			0
$957$	−2.95277	+	2.95277i	−0.0954496	+	0.0954496i
$958$		0			0
$959$	28.4250			0.917892
$960$		0			0
$961$	19.5949			0.632095
$962$		0			0
$963$	6.91512	−	6.91512i	0.222837	−	0.222837i
$964$		0			0
$965$	−8.61700	−	1.58328i	−0.277391	−	0.0509675i
$966$		0			0
$967$	52.7223			1.69543			0.847717	−	0.530449i	$-0.177977\pi$
$967$	52.7223			1.69543			0.847717	+	0.530449i	$0.177977\pi$
$968$		0			0
$969$			2.95840i			0.0950375i
$970$		0			0
$971$	36.7211	−	36.7211i	1.17843	−	1.17843i	0.198292	−	0.980143i	$-0.436461\pi$
$971$	36.7211	−	36.7211i	1.17843	−	1.17843i	0.980143	−	0.198292i	$-0.0635394\pi$
$972$		0			0
$973$	2.07309	−	2.07309i	0.0664602	−	0.0664602i
$974$		0			0
$975$	0.0779680	−	0.205008i	0.00249697	−	0.00656550i
$976$		0			0
$977$			44.2340i			1.41517i	0.706628	+	0.707585i	$0.250215\pi$
$977$			44.2340i			1.41517i	−0.706628	+	0.707585i	$0.749785\pi$
$978$		0			0
$979$	4.76436	+	4.76436i	0.152270	+	0.152270i
$980$		0			0
$981$	6.15941	−	6.15941i	0.196655	−	0.196655i
$982$		0			0
$983$	−55.1017			−1.75747			−0.878736	−	0.477308i	$-0.841612\pi$
$983$	−55.1017			−1.75747			−0.878736	+	0.477308i	$0.841612\pi$
$984$		0			0
$985$	−7.10624	+	4.90019i	−0.226424	+	0.156133i
$986$		0			0
$987$	−12.8998	−	12.8998i	−0.410606	−	0.410606i
$988$		0			0
$989$	−23.5724	−	23.5724i	−0.749559	−	0.749559i
$990$		0			0
$991$	−0.865019			−0.0274782			−0.0137391	−	0.999906i	$-0.504373\pi$
$991$	−0.865019			−0.0274782			−0.0137391	+	0.999906i	$0.504373\pi$
$992$		0			0
$993$		−	17.1983i		−	0.545773i
$994$		0			0
$995$	43.2925	+	7.95451i	1.37246	+	0.252175i
$996$		0			0
$997$	−41.8219	−	41.8219i	−1.32451	−	1.32451i	−0.910080	−	0.414433i	$-0.863980\pi$
$997$	−41.8219	−	41.8219i	−1.32451	−	1.32451i	−0.414433	−	0.910080i	$-0.636020\pi$
$998$		0			0
$999$			0.102320i			0.00323727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bl.a.289.4		48
4.3	odd	2		1920.2.bl.b.289.21		48
5.4	even	2	inner	1920.2.bl.a.289.21		48
8.3	odd	2		960.2.bl.a.529.7		48
8.5	even	2		240.2.bl.a.109.2	✓	48
16.3	odd	4		960.2.bl.a.49.24		48
16.5	even	4	inner	1920.2.bl.a.1249.21		48
16.11	odd	4		1920.2.bl.b.1249.4		48
16.13	even	4		240.2.bl.a.229.23	yes	48
20.19	odd	2		1920.2.bl.b.289.4		48
24.5	odd	2		720.2.bm.h.109.23		48
40.19	odd	2		960.2.bl.a.529.24		48
40.29	even	2		240.2.bl.a.109.23	yes	48
48.29	odd	4		720.2.bm.h.469.2		48
80.19	odd	4		960.2.bl.a.49.7		48
80.29	even	4		240.2.bl.a.229.2	yes	48
80.59	odd	4		1920.2.bl.b.1249.21		48
80.69	even	4	inner	1920.2.bl.a.1249.4		48
120.29	odd	2		720.2.bm.h.109.2		48
240.29	odd	4		720.2.bm.h.469.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.2	✓	48	8.5	even	2
240.2.bl.a.109.23	yes	48	40.29	even	2
240.2.bl.a.229.2	yes	48	80.29	even	4
240.2.bl.a.229.23	yes	48	16.13	even	4
720.2.bm.h.109.2		48	120.29	odd	2
720.2.bm.h.109.23		48	24.5	odd	2
720.2.bm.h.469.2		48	48.29	odd	4
720.2.bm.h.469.23		48	240.29	odd	4
960.2.bl.a.49.7		48	80.19	odd	4
960.2.bl.a.49.24		48	16.3	odd	4
960.2.bl.a.529.7		48	8.3	odd	2
960.2.bl.a.529.24		48	40.19	odd	2
1920.2.bl.a.289.4		48	1.1	even	1	trivial
1920.2.bl.a.289.21		48	5.4	even	2	inner
1920.2.bl.a.1249.4		48	80.69	even	4	inner
1920.2.bl.a.1249.21		48	16.5	even	4	inner
1920.2.bl.b.289.4		48	20.19	odd	2
1920.2.bl.b.289.21		48	4.3	odd	2
1920.2.bl.b.1249.4		48	16.11	odd	4
1920.2.bl.b.1249.21		48	80.59	odd	4

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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bl (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.404088 + 2.19925i) q^{5} +1.81567 q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.404088 + 2.19925i) q^{5} +1.81567 q^{7} -1.00000i q^{9} +(0.331965 - 0.331965i) q^{11} +(0.0310184 - 0.0310184i) q^{13} +(-1.26937 - 1.84084i) q^{15} -1.00474i q^{17} +(2.08203 + 2.08203i) q^{19} +(-1.28388 + 1.28388i) q^{21} +6.22794 q^{23} +(-4.67343 - 1.77739i) q^{25} +(0.707107 + 0.707107i) q^{27} +(6.28959 + 6.28959i) q^{29} +7.11301 q^{31} +0.469470i q^{33} +(-0.733693 + 3.99313i) q^{35} +(0.0723513 + 0.0723513i) q^{37} +0.0438667i q^{39} +3.06050i q^{41} +(-3.78495 - 3.78495i) q^{43} +(2.19925 + 0.404088i) q^{45} +10.0476i q^{47} -3.70333 q^{49} +(0.710461 + 0.710461i) q^{51} +(-7.04636 - 7.04636i) q^{53} +(0.595932 + 0.864219i) q^{55} -2.94443 q^{57} +(6.68042 - 6.68042i) q^{59} +(-2.89442 - 2.89442i) q^{61} -1.81567i q^{63} +(0.0556832 + 0.0807515i) q^{65} +(0.150837 - 0.150837i) q^{67} +(-4.40382 + 4.40382i) q^{69} +14.5503i q^{71} -15.0323 q^{73} +(4.56141 - 2.04781i) q^{75} +(0.602741 - 0.602741i) q^{77} +15.5985 q^{79} -1.00000 q^{81} +(-5.48985 + 5.48985i) q^{83} +(2.20969 + 0.406005i) q^{85} -8.89482 q^{87} +14.3520i q^{89} +(0.0563193 - 0.0563193i) q^{91} +(-5.02966 + 5.02966i) q^{93} +(-5.42023 + 3.73758i) q^{95} -13.5585i q^{97} +(-0.331965 - 0.331965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{19} - 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} + 16 q^{75} - 96 q^{79} - 48 q^{81} + 32 q^{91} - 48 q^{95}+O(q^{100}) \) 48 * q - 8 * q^19 - 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 + 16 * q^75 - 96 * q^79 - 48 * q^81 + 32 * q^91 - 48 * q^95

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