LMFDB - Embedded newform 640.3.k.a.159.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,3,Mod(159,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("640.159");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	640.k (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:	$17.4387369191$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			159.16
Character	$\chi$	$=$	640.159
Dual form			640.3.k.a.479.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37405 - 1.37405i) q^{3} +(1.48609 - 4.77405i) q^{5} +5.00956i q^{7} +5.22398i q^{9} +O(q^{10})$	\(q+(1.37405 - 1.37405i) q^{3} +(1.48609 - 4.77405i) q^{5} +5.00956i q^{7} +5.22398i q^{9} +(-6.42909 + 6.42909i) q^{11} +(11.0519 + 11.0519i) q^{13} +(-4.51781 - 8.60173i) q^{15} +14.8302i q^{17} +(17.5407 + 17.5407i) q^{19} +(6.88338 + 6.88338i) q^{21} +4.37435i q^{23} +(-20.5831 - 14.1894i) q^{25} +(19.5444 + 19.5444i) q^{27} +(18.8676 - 18.8676i) q^{29} +32.9924i q^{31} +17.6678i q^{33} +(23.9159 + 7.44468i) q^{35} +(18.0984 - 18.0984i) q^{37} +30.3717 q^{39} -76.1027i q^{41} +(-19.1807 - 19.1807i) q^{43} +(24.9395 + 7.76333i) q^{45} -59.1180 q^{47} +23.9043 q^{49} +(20.3775 + 20.3775i) q^{51} +(-21.5406 + 21.5406i) q^{53} +(21.1385 + 40.2470i) q^{55} +48.2036 q^{57} +(53.6021 - 53.6021i) q^{59} +(25.4876 - 25.4876i) q^{61} -26.1699 q^{63} +(69.1865 - 36.3381i) q^{65} +(-5.92820 + 5.92820i) q^{67} +(6.01056 + 6.01056i) q^{69} +25.9177 q^{71} +31.2154 q^{73} +(-47.7790 + 8.78525i) q^{75} +(-32.2069 - 32.2069i) q^{77} +122.054i q^{79} +6.69413 q^{81} +(-115.988 + 115.988i) q^{83} +(70.8003 + 22.0391i) q^{85} -51.8499i q^{87} +85.3925i q^{89} +(-55.3652 + 55.3652i) q^{91} +(45.3332 + 45.3332i) q^{93} +(109.807 - 57.6731i) q^{95} +16.3915i q^{97} +(-33.5855 - 33.5855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{5}+O(q^{10}) $ 44 * q + 2 * q^5	$ 44 q + 2 q^{5} - 4 q^{11} - 36 q^{19} - 32 q^{21} + 4 q^{29} + 8 q^{39} - 30 q^{45} - 148 q^{49} + 128 q^{51} + 260 q^{55} - 68 q^{59} - 28 q^{61} - 20 q^{65} - 128 q^{69} + 264 q^{71} + 60 q^{75} - 116 q^{81} - 48 q^{85} + 384 q^{91} + 484 q^{99}+O(q^{100}) $ 44 * q + 2 * q^5 - 4 * q^11 - 36 * q^19 - 32 * q^21 + 4 * q^29 + 8 * q^39 - 30 * q^45 - 148 * q^49 + 128 * q^51 + 260 * q^55 - 68 * q^59 - 28 * q^61 - 20 * q^65 - 128 * q^69 + 264 * q^71 + 60 * q^75 - 116 * q^81 - 48 * q^85 + 384 * q^91 + 484 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$	1.37405	−	1.37405i	0.458016	−	0.458016i	−0.439988	−	0.898004i	$-0.645017\pi$
$3$	1.37405	−	1.37405i	0.458016	−	0.458016i	0.898004	+	0.439988i	$0.145017\pi$
$4$		0			0
$5$	1.48609	−	4.77405i	0.297219	−	0.954809i
$5$	1.48609	−	4.77405i	0.297219	−	0.954809i
$6$		0			0
$7$			5.00956i			0.715652i	0.933788	+	0.357826i	$0.116482\pi$
$7$			5.00956i			0.715652i	−0.933788	+	0.357826i	$0.883518\pi$
$8$		0			0
$9$			5.22398i			0.580443i
$10$		0			0
$11$	−6.42909	+	6.42909i	−0.584463	+	0.584463i	−0.936126	−	0.351664i	$-0.885616\pi$
$11$	−6.42909	+	6.42909i	−0.584463	+	0.584463i	0.351664	+	0.936126i	$0.385616\pi$
$12$		0			0
$13$	11.0519	+	11.0519i	0.850146	+	0.850146i	0.990151	−	0.140005i	$-0.0447117\pi$
$13$	11.0519	+	11.0519i	0.850146	+	0.850146i	−0.140005	+	0.990151i	$0.544712\pi$
$14$		0			0
$15$	−4.51781	−	8.60173i	−0.301187	−	0.573449i
$16$		0			0
$17$			14.8302i			0.872367i	0.899858	+	0.436184i	$0.143670\pi$
$17$			14.8302i			0.872367i	−0.899858	+	0.436184i	$0.856330\pi$
$18$		0			0
$19$	17.5407	+	17.5407i	0.923196	+	0.923196i	0.997254	−	0.0740578i	$-0.0235949\pi$
$19$	17.5407	+	17.5407i	0.923196	+	0.923196i	−0.0740578	+	0.997254i	$0.523595\pi$
$20$		0			0
$21$	6.88338	+	6.88338i	0.327780	+	0.327780i
$22$		0			0
$23$			4.37435i			0.190189i	0.995468	+	0.0950945i	$0.0303153\pi$
$23$			4.37435i			0.190189i	−0.995468	+	0.0950945i	$0.969685\pi$
$24$		0			0
$25$	−20.5831	−	14.1894i	−0.823322	−	0.567574i
$26$		0			0
$27$	19.5444	+	19.5444i	0.723868	+	0.723868i
$28$		0			0
$29$	18.8676	−	18.8676i	0.650605	−	0.650605i	−0.302533	−	0.953139i	$-0.597832\pi$
$29$	18.8676	−	18.8676i	0.650605	−	0.650605i	0.953139	+	0.302533i	$0.0978324\pi$
$30$		0			0
$31$			32.9924i			1.06427i	0.846659	+	0.532136i	$0.178611\pi$
$31$			32.9924i			1.06427i	−0.846659	+	0.532136i	$0.821389\pi$
$32$		0			0
$33$			17.6678i			0.535386i
$34$		0			0
$35$	23.9159	+	7.44468i	0.683311	+	0.212705i
$36$		0			0
$37$	18.0984	−	18.0984i	0.489146	−	0.489146i	−0.418891	−	0.908037i	$-0.637581\pi$
$37$	18.0984	−	18.0984i	0.489146	−	0.489146i	0.908037	+	0.418891i	$0.137581\pi$
$38$		0			0
$39$	30.3717			0.778761
$40$		0			0
$41$		−	76.1027i		−	1.85616i	−0.372376	−	0.928082i	$-0.621457\pi$
$41$		−	76.1027i		−	1.85616i	0.372376	−	0.928082i	$-0.378543\pi$
$42$		0			0
$43$	−19.1807	−	19.1807i	−0.446062	−	0.446062i	0.447981	−	0.894043i	$-0.352143\pi$
$43$	−19.1807	−	19.1807i	−0.446062	−	0.446062i	−0.894043	+	0.447981i	$0.852143\pi$
$44$		0			0
$45$	24.9395	+	7.76333i	0.554212	+	0.172518i
$46$		0			0
$47$	−59.1180			−1.25783			−0.628915	−	0.777474i	$-0.716501\pi$
$47$	−59.1180			−1.25783			−0.628915	+	0.777474i	$0.716501\pi$
$48$		0			0
$49$	23.9043			0.487842
$50$		0			0
$51$	20.3775	+	20.3775i	0.399558	+	0.399558i
$52$		0			0
$53$	−21.5406	+	21.5406i	−0.406427	+	0.406427i	−0.880491	−	0.474064i	$-0.842787\pi$
$53$	−21.5406	+	21.5406i	−0.406427	+	0.406427i	0.474064	+	0.880491i	$0.342787\pi$
$54$		0			0
$55$	21.1385	+	40.2470i	0.384337	+	0.731764i
$56$		0			0
$57$	48.2036			0.845677
$58$		0			0
$59$	53.6021	−	53.6021i	0.908511	−	0.908511i	−0.0876411	−	0.996152i	$-0.527933\pi$
$59$	53.6021	−	53.6021i	0.908511	−	0.908511i	0.996152	+	0.0876411i	$0.0279329\pi$
$60$		0			0
$61$	25.4876	−	25.4876i	0.417830	−	0.417830i	−0.466625	−	0.884455i	$-0.654530\pi$
$61$	25.4876	−	25.4876i	0.417830	−	0.417830i	0.884455	+	0.466625i	$0.154530\pi$
$62$		0			0
$63$	−26.1699			−0.415395
$64$		0			0
$65$	69.1865	−	36.3381i	1.06441	−	0.559048i
$66$		0			0
$67$	−5.92820	+	5.92820i	−0.0884806	+	0.0884806i	−0.749962	−	0.661481i	$-0.769928\pi$
$67$	−5.92820	+	5.92820i	−0.0884806	+	0.0884806i	0.661481	+	0.749962i	$0.269928\pi$
$68$		0			0
$69$	6.01056	+	6.01056i	0.0871096	+	0.0871096i
$70$		0			0
$71$	25.9177			0.365038			0.182519	−	0.983202i	$-0.441575\pi$
$71$	25.9177			0.365038			0.182519	+	0.983202i	$0.441575\pi$
$72$		0			0
$73$	31.2154			0.427608			0.213804	−	0.976877i	$-0.431415\pi$
$73$	31.2154			0.427608			0.213804	+	0.976877i	$0.431415\pi$
$74$		0			0
$75$	−47.7790	+	8.78525i	−0.637053	+	0.117137i
$76$		0			0
$77$	−32.2069	−	32.2069i	−0.418272	−	0.418272i
$78$		0			0
$79$			122.054i			1.54499i	0.635019	+	0.772497i	$0.280992\pi$
$79$			122.054i			1.54499i	−0.635019	+	0.772497i	$0.719008\pi$
$80$		0			0
$81$	6.69413			0.0826436
$82$		0			0
$83$	−115.988	+	115.988i	−1.39745	+	1.39745i	−0.590169	+	0.807280i	$0.700939\pi$
$83$	−115.988	+	115.988i	−1.39745	+	1.39745i	−0.807280	+	0.590169i	$0.799061\pi$
$84$		0			0
$85$	70.8003	+	22.0391i	0.832945	+	0.259284i
$86$		0			0
$87$		−	51.8499i		−	0.595975i
$88$		0			0
$89$			85.3925i			0.959466i	0.877415	+	0.479733i	$0.159266\pi$
$89$			85.3925i			0.959466i	−0.877415	+	0.479733i	$0.840734\pi$
$90$		0			0
$91$	−55.3652	+	55.3652i	−0.608409	+	0.608409i
$92$		0			0
$93$	45.3332	+	45.3332i	0.487454	+	0.487454i
$94$		0			0
$95$	109.807	−	57.6731i	1.15587	−	0.607085i
$96$		0			0
$97$			16.3915i			0.168984i	0.996424	+	0.0844921i	$0.0269268\pi$
$97$			16.3915i			0.168984i	−0.996424	+	0.0844921i	$0.973073\pi$
$98$		0			0
$99$	−33.5855	−	33.5855i	−0.339247	−	0.339247i
$100$		0			0
$101$	−105.008	−	105.008i	−1.03969	−	1.03969i	−0.999179	−	0.0405066i	$-0.987103\pi$
$101$	−105.008	−	105.008i	−1.03969	−	1.03969i	−0.0405066	−	0.999179i	$-0.512897\pi$
$102$		0			0
$103$			47.2447i			0.458687i	0.973346	+	0.229343i	$0.0736579\pi$
$103$			47.2447i			0.458687i	−0.973346	+	0.229343i	$0.926342\pi$
$104$		0			0
$105$	43.0909	−	22.6322i	0.410390	−	0.215545i
$106$		0			0
$107$	55.7447	+	55.7447i	0.520979	+	0.520979i	0.917867	−	0.396888i	$-0.129910\pi$
$107$	55.7447	+	55.7447i	0.520979	+	0.520979i	−0.396888	+	0.917867i	$0.629910\pi$
$108$		0			0
$109$	129.985	−	129.985i	1.19253	−	1.19253i	0.216169	−	0.976356i	$-0.430644\pi$
$109$	129.985	−	129.985i	1.19253	−	1.19253i	0.976356	−	0.216169i	$-0.0693563\pi$
$110$		0			0
$111$		−	49.7362i		−	0.448074i
$112$		0			0
$113$			47.6474i			0.421658i	0.977523	+	0.210829i	$0.0676164\pi$
$113$			47.6474i			0.421658i	−0.977523	+	0.210829i	$0.932384\pi$
$114$		0			0
$115$	20.8833	+	6.50068i	0.181594	+	0.0565277i
$116$		0			0
$117$	−57.7350	+	57.7350i	−0.493461	+	0.493461i
$118$		0			0
$119$	−74.2931			−0.624312
$120$		0			0
$121$			38.3336i			0.316807i
$122$		0			0
$123$	−104.569	−	104.569i	−0.850153	−	0.850153i
$124$		0			0
$125$	−98.3290	+	77.1778i	−0.786632	+	0.617422i
$126$		0			0
$127$	178.817			1.40801			0.704005	−	0.710195i	$-0.251393\pi$
$127$	178.817			1.40801			0.704005	+	0.710195i	$0.251393\pi$
$128$		0			0
$129$	−52.7103			−0.408607
$130$		0			0
$131$	50.1661	+	50.1661i	0.382948	+	0.382948i	0.872163	−	0.489215i	$-0.162717\pi$
$131$	50.1661	+	50.1661i	0.382948	+	0.382948i	−0.489215	+	0.872163i	$0.662717\pi$
$132$		0			0
$133$	−87.8714	+	87.8714i	−0.660687	+	0.660687i
$134$		0			0
$135$	122.351	−	64.2612i	0.906303	−	0.476009i
$136$		0			0
$137$	4.72138			0.0344626			0.0172313	−	0.999852i	$-0.494515\pi$
$137$	4.72138			0.0344626			0.0172313	+	0.999852i	$0.494515\pi$
$138$		0			0
$139$	72.2925	−	72.2925i	0.520090	−	0.520090i	−0.397509	−	0.917598i	$-0.630125\pi$
$139$	72.2925	−	72.2925i	0.520090	−	0.520090i	0.917598	+	0.397509i	$0.130125\pi$
$140$		0			0
$141$	−81.2310	+	81.2310i	−0.576106	+	0.576106i
$142$		0			0
$143$	−142.107			−0.993757
$144$		0			0
$145$	−62.0357	−	118.114i	−0.427832	−	0.814576i
$146$		0			0
$147$	32.8456	−	32.8456i	0.223439	−	0.223439i
$148$		0			0
$149$	−82.5656	−	82.5656i	−0.554131	−	0.554131i	0.373499	−	0.927631i	$-0.378158\pi$
$149$	−82.5656	−	82.5656i	−0.554131	−	0.554131i	−0.927631	+	0.373499i	$0.878158\pi$
$150$		0			0
$151$	−95.3210			−0.631265			−0.315632	−	0.948882i	$-0.602217\pi$
$151$	−95.3210			−0.631265			−0.315632	+	0.948882i	$0.602217\pi$
$152$		0			0
$153$	−77.4730			−0.506359
$154$		0			0
$155$	157.508	+	49.0298i	1.01618	+	0.316322i
$156$		0			0
$157$	−103.454	−	103.454i	−0.658941	−	0.658941i	0.296188	−	0.955130i	$-0.404284\pi$
$157$	−103.454	−	103.454i	−0.658941	−	0.658941i	−0.955130	+	0.296188i	$0.904284\pi$
$158$		0			0
$159$			59.1957i			0.372300i
$160$		0			0
$161$	−21.9136			−0.136109
$162$		0			0
$163$	129.670	−	129.670i	0.795524	−	0.795524i	−0.186862	−	0.982386i	$-0.559832\pi$
$163$	129.670	−	129.670i	0.795524	−	0.795524i	0.982386	+	0.186862i	$0.0598318\pi$
$164$		0			0
$165$	84.3467	+	26.2559i	0.511192	+	0.159127i
$166$		0			0
$167$		−	50.8326i		−	0.304387i	−0.988351	−	0.152193i	$-0.951366\pi$
$167$		−	50.8326i		−	0.304387i	0.988351	−	0.152193i	$-0.0486337\pi$
$168$		0			0
$169$			75.2890i			0.445497i
$170$		0			0
$171$	−91.6325	+	91.6325i	−0.535862	+	0.535862i
$172$		0			0
$173$	118.979	+	118.979i	0.687738	+	0.687738i	0.961732	−	0.273993i	$-0.0883446\pi$
$173$	118.979	+	118.979i	0.687738	+	0.687738i	−0.273993	+	0.961732i	$0.588345\pi$
$174$		0			0
$175$	71.0825	−	103.112i	0.406186	−	0.589212i
$176$		0			0
$177$		−	147.304i		−	0.832225i
$178$		0			0
$179$	−171.651	−	171.651i	−0.958946	−	0.958946i	0.0402443	−	0.999190i	$-0.487186\pi$
$179$	−171.651	−	171.651i	−0.958946	−	0.958946i	−0.999190	+	0.0402443i	$0.987186\pi$
$180$		0			0
$181$	144.176	+	144.176i	0.796550	+	0.796550i	0.982550	−	0.186000i	$-0.0595524\pi$
$181$	144.176	+	144.176i	0.796550	+	0.796550i	−0.186000	+	0.982550i	$0.559552\pi$
$182$		0			0
$183$		−	70.0424i		−	0.382746i
$184$		0			0
$185$	−59.5067	−	113.299i	−0.321658	−	0.612425i
$186$		0			0
$187$	−95.3450	−	95.3450i	−0.509866	−	0.509866i
$188$		0			0
$189$	−97.9091	+	97.9091i	−0.518038	+	0.518038i
$190$		0			0
$191$		−	49.0166i		−	0.256631i	−0.991733	−	0.128316i	$-0.959043\pi$
$191$		−	49.0166i		−	0.256631i	0.991733	−	0.128316i	$-0.0409571\pi$
$192$		0			0
$193$			371.977i			1.92734i	0.267094	+	0.963671i	$0.413937\pi$
$193$			371.977i			1.92734i	−0.267094	+	0.963671i	$0.586063\pi$
$194$		0			0
$195$	45.1352	−	144.996i	0.231462	−	0.743569i
$196$		0			0
$197$	164.712	−	164.712i	0.836102	−	0.836102i	−0.152241	−	0.988343i	$-0.548649\pi$
$197$	164.712	−	164.712i	0.836102	−	0.836102i	0.988343	+	0.152241i	$0.0486490\pi$
$198$		0			0
$199$	−141.117			−0.709130			−0.354565	−	0.935031i	$-0.615371\pi$
$199$	−141.117			−0.709130			−0.354565	+	0.935031i	$0.615371\pi$
$200$		0			0
$201$			16.2913i			0.0810511i
$202$		0			0
$203$	94.5182	+	94.5182i	0.465607	+	0.465607i
$204$		0			0
$205$	−363.318	−	113.096i	−1.77228	−	0.551686i
$206$		0			0
$207$	−22.8515			−0.110394
$208$		0			0
$209$	−225.542			−1.07915
$210$		0			0
$211$	−167.007	−	167.007i	−0.791502	−	0.791502i	0.190236	−	0.981738i	$-0.439075\pi$
$211$	−167.007	−	167.007i	−0.791502	−	0.791502i	−0.981738	+	0.190236i	$0.939075\pi$
$212$		0			0
$213$	35.6122	−	35.6122i	0.167193	−	0.167193i
$214$		0			0
$215$	−120.074	+	63.0652i	−0.558482	+	0.293326i
$216$		0			0
$217$	−165.278			−0.761649
$218$		0			0
$219$	42.8914	−	42.8914i	0.195851	−	0.195851i
$220$		0			0
$221$	−163.902	+	163.902i	−0.741640	+	0.741640i
$222$		0			0
$223$	−360.595			−1.61702			−0.808508	−	0.588485i	$-0.799725\pi$
$223$	−360.595			−1.61702			−0.808508	+	0.588485i	$0.799725\pi$
$224$		0			0
$225$	74.1250	−	107.526i	0.329444	−	0.477891i
$226$		0			0
$227$	162.621	−	162.621i	0.716392	−	0.716392i	−0.251472	−	0.967865i	$-0.580915\pi$
$227$	162.621	−	162.621i	0.716392	−	0.716392i	0.967865	+	0.251472i	$0.0809147\pi$
$228$		0			0
$229$	6.11249	+	6.11249i	0.0266921	+	0.0266921i	0.720327	−	0.693635i	$-0.243992\pi$
$229$	6.11249	+	6.11249i	0.0266921	+	0.0266921i	−0.693635	+	0.720327i	$0.743992\pi$
$230$		0			0
$231$	−88.5078			−0.383150
$232$		0			0
$233$	−121.619			−0.521968			−0.260984	−	0.965343i	$-0.584047\pi$
$233$	−121.619			−0.521968			−0.260984	+	0.965343i	$0.584047\pi$
$234$		0			0
$235$	−87.8549	+	282.232i	−0.373850	+	1.20099i
$236$		0			0
$237$	167.709	+	167.709i	0.707632	+	0.707632i
$238$		0			0
$239$		−	224.468i		−	0.939196i	−0.882880	−	0.469598i	$-0.844399\pi$
$239$		−	224.468i		−	0.939196i	0.882880	−	0.469598i	$-0.155601\pi$
$240$		0			0
$241$	−128.007			−0.531150			−0.265575	−	0.964090i	$-0.585562\pi$
$241$	−128.007			−0.531150			−0.265575	+	0.964090i	$0.585562\pi$
$242$		0			0
$243$	−166.702	+	166.702i	−0.686016	+	0.686016i
$244$		0			0
$245$	35.5240	−	114.120i	0.144996	−	0.465796i
$246$		0			0
$247$			387.717i			1.56970i
$248$		0			0
$249$			318.747i			1.28011i
$250$		0			0
$251$	145.552	−	145.552i	0.579888	−	0.579888i	−0.354984	−	0.934872i	$-0.615514\pi$
$251$	145.552	−	145.552i	0.579888	−	0.579888i	0.934872	+	0.354984i	$0.115514\pi$
$252$		0			0
$253$	−28.1231	−	28.1231i	−0.111158	−	0.111158i
$254$		0			0
$255$	127.566	−	67.0002i	0.500258	−	0.262746i
$256$		0			0
$257$		−	450.082i		−	1.75129i	−0.482953	−	0.875646i	$-0.660436\pi$
$257$		−	450.082i		−	1.75129i	0.482953	−	0.875646i	$-0.339564\pi$
$258$		0			0
$259$	90.6652	+	90.6652i	0.350059	+	0.350059i
$260$		0			0
$261$	98.5638	+	98.5638i	0.377639	+	0.377639i
$262$		0			0
$263$		−	199.203i		−	0.757427i	−0.925514	−	0.378713i	$-0.876367\pi$
$263$		−	199.203i		−	0.757427i	0.925514	−	0.378713i	$-0.123633\pi$
$264$		0			0
$265$	70.8246	+	134.847i	0.267263	+	0.508858i
$266$		0			0
$267$	117.333	+	117.333i	0.439451	+	0.439451i
$268$		0			0
$269$	48.1424	−	48.1424i	0.178968	−	0.178968i	−0.611938	−	0.790906i	$-0.709610\pi$
$269$	48.1424	−	48.1424i	0.178968	−	0.178968i	0.790906	+	0.611938i	$0.209610\pi$
$270$		0			0
$271$		−	317.904i		−	1.17308i	−0.809921	−	0.586538i	$-0.800490\pi$
$271$		−	317.904i		−	1.17308i	0.809921	−	0.586538i	$-0.199510\pi$
$272$		0			0
$273$			152.149i			0.557322i
$274$		0			0
$275$	223.555	−	41.1056i	0.812927	−	0.149475i
$276$		0			0
$277$	68.3059	−	68.3059i	0.246592	−	0.246592i	−0.572979	−	0.819570i	$-0.694212\pi$
$277$	68.3059	−	68.3059i	0.246592	−	0.246592i	0.819570	+	0.572979i	$0.194212\pi$
$278$		0			0
$279$	−172.352			−0.617749
$280$		0			0
$281$		−	131.237i		−	0.467035i	−0.972353	−	0.233517i	$-0.924976\pi$
$281$		−	131.237i		−	0.467035i	0.972353	−	0.233517i	$-0.0750236\pi$
$282$		0			0
$283$	−386.539	−	386.539i	−1.36586	−	1.36586i	−0.866246	−	0.499618i	$-0.833474\pi$
$283$	−386.539	−	386.539i	−1.36586	−	1.36586i	−0.499618	−	0.866246i	$-0.666526\pi$
$284$		0			0
$285$	71.6350	−	230.126i	0.251351	−	0.807461i
$286$		0			0
$287$	381.241			1.32837
$288$		0			0
$289$	69.0638			0.238975
$290$		0			0
$291$	22.5227	+	22.5227i	0.0773975	+	0.0773975i
$292$		0			0
$293$	−221.104	+	221.104i	−0.754620	+	0.754620i	−0.975338	−	0.220718i	$-0.929160\pi$
$293$	−221.104	+	221.104i	−0.754620	+	0.754620i	0.220718	+	0.975338i	$0.429160\pi$
$294$		0			0
$295$	−176.241	−	335.557i	−0.597428	−	1.13748i
$296$		0			0
$297$	−251.306			−0.846148
$298$		0			0
$299$	−48.3448	+	48.3448i	−0.161688	+	0.161688i
$300$		0			0
$301$	96.0868	−	96.0868i	0.319225	−	0.319225i
$302$		0			0
$303$	−288.573			−0.952386
$304$		0			0
$305$	−83.8021	−	159.556i	−0.274761	−	0.523135i
$306$		0			0
$307$	−80.4368	+	80.4368i	−0.262009	+	0.262009i	−0.825870	−	0.563861i	$-0.809315\pi$
$307$	−80.4368	+	80.4368i	−0.262009	+	0.262009i	0.563861	+	0.825870i	$0.309315\pi$
$308$		0			0
$309$	64.9165	+	64.9165i	0.210086	+	0.210086i
$310$		0			0
$311$	433.169			1.39283			0.696413	−	0.717641i	$-0.254778\pi$
$311$	433.169			1.39283			0.696413	+	0.717641i	$0.254778\pi$
$312$		0			0
$313$	269.601			0.861346			0.430673	−	0.902508i	$-0.358276\pi$
$313$	269.601			0.861346			0.430673	+	0.902508i	$0.358276\pi$
$314$		0			0
$315$	−38.8909	+	124.936i	−0.123463	+	0.396623i
$316$		0			0
$317$	−20.0627	−	20.0627i	−0.0632894	−	0.0632894i	0.674754	−	0.738043i	$-0.264250\pi$
$317$	−20.0627	−	20.0627i	−0.0632894	−	0.0632894i	−0.738043	+	0.674754i	$0.764250\pi$
$318$		0			0
$319$			242.602i			0.760509i
$320$		0			0
$321$	153.192			0.477233
$322$		0			0
$323$	−260.133	+	260.133i	−0.805366	+	0.805366i
$324$		0			0
$325$	−70.6625	−	384.301i	−0.217423	−	1.18247i
$326$		0			0
$327$		−	357.212i		−	1.09239i
$328$		0			0
$329$		−	296.155i		−	0.900169i
$330$		0			0
$331$	162.499	−	162.499i	0.490933	−	0.490933i	−0.417667	−	0.908600i	$-0.637152\pi$
$331$	162.499	−	162.499i	0.490933	−	0.490933i	0.908600	+	0.417667i	$0.137152\pi$
$332$		0			0
$333$	94.5458	+	94.5458i	0.283921	+	0.283921i
$334$		0			0
$335$	19.4917	+	37.1114i	0.0581840	+	0.110780i
$336$		0			0
$337$			331.372i			0.983301i	0.870793	+	0.491650i	$0.163606\pi$
$337$			331.372i			0.983301i	−0.870793	+	0.491650i	$0.836394\pi$
$338$		0			0
$339$	65.4698	+	65.4698i	0.193126	+	0.193126i
$340$		0			0
$341$	−212.111	−	212.111i	−0.622028	−	0.622028i
$342$		0			0
$343$			365.219i			1.06478i
$344$		0			0
$345$	37.6270	−	19.7624i	0.109064	−	0.0572825i
$346$		0			0
$347$	−140.935	−	140.935i	−0.406154	−	0.406154i	0.474241	−	0.880395i	$-0.342722\pi$
$347$	−140.935	−	140.935i	−0.406154	−	0.406154i	−0.880395	+	0.474241i	$0.842722\pi$
$348$		0			0
$349$	−94.5429	+	94.5429i	−0.270897	+	0.270897i	−0.829461	−	0.558564i	$-0.811352\pi$
$349$	−94.5429	+	94.5429i	−0.270897	+	0.270897i	0.558564	+	0.829461i	$0.311352\pi$
$350$		0			0
$351$			432.006i			1.23079i
$352$		0			0
$353$			232.200i			0.657791i	0.944366	+	0.328896i	$0.106676\pi$
$353$			232.200i			0.657791i	−0.944366	+	0.328896i	$0.893324\pi$
$354$		0			0
$355$	38.5161	−	123.732i	0.108496	−	0.348542i
$356$		0			0
$357$	−102.082	+	102.082i	−0.285945	+	0.285945i
$358$		0			0
$359$	701.851			1.95502			0.977508	−	0.210899i	$-0.0676392\pi$
$359$	701.851			1.95502			0.977508	+	0.210899i	$0.0676392\pi$
$360$		0			0
$361$			254.354i			0.704582i
$362$		0			0
$363$	52.6722	+	52.6722i	0.145103	+	0.145103i
$364$		0			0
$365$	46.3889	−	149.024i	0.127093	−	0.408284i
$366$		0			0
$367$	126.106			0.343612			0.171806	−	0.985131i	$-0.445040\pi$
$367$	126.106			0.343612			0.171806	+	0.985131i	$0.445040\pi$
$368$		0			0
$369$	397.559			1.07740
$370$		0			0
$371$	−107.909	−	107.909i	−0.290860	−	0.290860i
$372$		0			0
$373$	−414.853	+	414.853i	−1.11221	+	1.11221i	−0.119356	+	0.992852i	$0.538083\pi$
$373$	−414.853	+	414.853i	−1.11221	+	1.11221i	−0.992852	+	0.119356i	$0.961917\pi$
$374$		0			0
$375$	−29.0628	+	241.155i	−0.0775008	+	0.643079i
$376$		0			0
$377$	417.045			1.10622
$378$		0			0
$379$	−117.567	+	117.567i	−0.310204	+	0.310204i	−0.844989	−	0.534784i	$-0.820393\pi$
$379$	−117.567	+	117.567i	−0.310204	+	0.310204i	0.534784	+	0.844989i	$0.320393\pi$
$380$		0			0
$381$	245.703	−	245.703i	0.644891	−	0.644891i
$382$		0			0
$383$	254.533			0.664577			0.332289	−	0.943178i	$-0.392179\pi$
$383$	254.533			0.664577			0.332289	+	0.943178i	$0.392179\pi$
$384$		0			0
$385$	−201.620	+	105.895i	−0.523688	+	0.275052i
$386$		0			0
$387$	100.200	−	100.200i	0.258914	−	0.258914i
$388$		0			0
$389$	−32.2185	−	32.2185i	−0.0828240	−	0.0828240i	0.664481	−	0.747305i	$-0.268653\pi$
$389$	−32.2185	−	32.2185i	−0.0828240	−	0.0828240i	−0.747305	+	0.664481i	$0.768653\pi$
$390$		0			0
$391$	−64.8726			−0.165915
$392$		0			0
$393$	137.861			0.350792
$394$		0			0
$395$	582.694	+	181.384i	1.47517	+	0.459201i
$396$		0			0
$397$	−105.079	−	105.079i	−0.264682	−	0.264682i	0.562271	−	0.826953i	$-0.309928\pi$
$397$	−105.079	−	105.079i	−0.264682	−	0.264682i	−0.826953	+	0.562271i	$0.809928\pi$
$398$		0			0
$399$			241.479i			0.605211i
$400$		0			0
$401$	248.416			0.619492			0.309746	−	0.950819i	$-0.399756\pi$
$401$	248.416			0.619492			0.309746	+	0.950819i	$0.399756\pi$
$402$		0			0
$403$	−364.629	+	364.629i	−0.904787	+	0.904787i
$404$		0			0
$405$	9.94810	−	31.9581i	0.0245632	−	0.0789089i
$406$		0			0
$407$			232.713i			0.571775i
$408$		0			0
$409$		−	455.293i		−	1.11318i	−0.830786	−	0.556592i	$-0.812109\pi$
$409$		−	455.293i		−	1.11318i	0.830786	−	0.556592i	$-0.187891\pi$
$410$		0			0
$411$	6.48740	−	6.48740i	0.0157844	−	0.0157844i
$412$		0			0
$413$	268.523	+	268.523i	0.650178	+	0.650178i
$414$		0			0
$415$	381.364	+	726.103i	0.918949	+	1.74964i
$416$		0			0
$417$		−	198.667i		−	0.476419i
$418$		0			0
$419$	296.148	+	296.148i	0.706797	+	0.706797i	0.965860	−	0.259063i	$-0.0834139\pi$
$419$	296.148	+	296.148i	0.706797	+	0.706797i	−0.259063	+	0.965860i	$0.583414\pi$
$420$		0			0
$421$	354.858	+	354.858i	0.842893	+	0.842893i	0.989234	−	0.146341i	$-0.0467496\pi$
$421$	354.858	+	354.858i	0.842893	+	0.842893i	−0.146341	+	0.989234i	$0.546750\pi$
$422$		0			0
$423$		−	308.832i		−	0.730098i
$424$		0			0
$425$	210.432	−	305.252i	0.495133	−	0.718239i
$426$		0			0
$427$	127.682	+	127.682i	0.299021	+	0.299021i
$428$		0			0
$429$	−195.262	+	195.262i	−0.455157	+	0.455157i
$430$		0			0
$431$			79.8832i			0.185344i	0.995697	+	0.0926719i	$0.0295408\pi$
$431$			79.8832i			0.185344i	−0.995697	+	0.0926719i	$0.970459\pi$
$432$		0			0
$433$			1.57519i			0.00363785i	0.999998	+	0.00181892i	$0.000578982\pi$
$433$			1.57519i			0.00363785i	−0.999998	+	0.00181892i	$0.999421\pi$
$434$		0			0
$435$	−247.534	−	77.0537i	−0.569043	−	0.177135i
$436$		0			0
$437$	−76.7292	+	76.7292i	−0.175582	+	0.175582i
$438$		0			0
$439$	−249.750			−0.568907			−0.284453	−	0.958690i	$-0.591812\pi$
$439$	−249.750			−0.568907			−0.284453	+	0.958690i	$0.591812\pi$
$440$		0			0
$441$			124.875i			0.283164i
$442$		0			0
$443$	−121.031	−	121.031i	−0.273208	−	0.273208i	0.557182	−	0.830390i	$-0.311882\pi$
$443$	−121.031	−	121.031i	−0.273208	−	0.273208i	−0.830390	+	0.557182i	$0.811882\pi$
$444$		0			0
$445$	407.668	+	126.901i	0.916107	+	0.285171i
$446$		0			0
$447$	−226.898			−0.507602
$448$		0			0
$449$	−297.105			−0.661703			−0.330852	−	0.943683i	$-0.607336\pi$
$449$	−297.105			−0.661703			−0.330852	+	0.943683i	$0.607336\pi$
$450$		0			0
$451$	489.271	+	489.271i	1.08486	+	1.08486i
$452$		0			0
$453$	−130.976	+	130.976i	−0.289129	+	0.289129i
$454$		0			0
$455$	182.038	+	346.594i	0.400084	+	0.761745i
$456$		0			0
$457$	361.107			0.790169			0.395085	−	0.918645i	$-0.370715\pi$
$457$	361.107			0.790169			0.395085	+	0.918645i	$0.370715\pi$
$458$		0			0
$459$	−289.849	+	289.849i	−0.631479	+	0.631479i
$460$		0			0
$461$	166.498	−	166.498i	0.361167	−	0.361167i	−0.503075	−	0.864243i	$-0.667798\pi$
$461$	166.498	−	166.498i	0.361167	−	0.361167i	0.864243	+	0.503075i	$0.167798\pi$
$462$		0			0
$463$	−712.425			−1.53871			−0.769357	−	0.638819i	$-0.779423\pi$
$463$	−712.425			−1.53871			−0.769357	+	0.638819i	$0.779423\pi$
$464$		0			0
$465$	283.792	−	149.054i	0.610306	−	0.320545i
$466$		0			0
$467$	−205.618	+	205.618i	−0.440295	+	0.440295i	−0.892111	−	0.451816i	$-0.850776\pi$
$467$	−205.618	+	205.618i	−0.440295	+	0.440295i	0.451816	+	0.892111i	$0.350776\pi$
$468$		0			0
$469$	−29.6977	−	29.6977i	−0.0633213	−	0.0633213i
$470$		0			0
$471$	−284.301			−0.603611
$472$		0			0
$473$	246.629			0.521413
$474$		0			0
$475$	−112.150	−	609.933i	−0.236105	−	1.28407i
$476$		0			0
$477$	−112.528	−	112.528i	−0.235908	−	0.235908i
$478$		0			0
$479$		−	775.000i		−	1.61795i	−0.587841	−	0.808977i	$-0.700022\pi$
$479$		−	775.000i		−	1.61795i	0.587841	−	0.808977i	$-0.299978\pi$
$480$		0			0
$481$	400.044			0.831692
$482$		0			0
$483$	−30.1103	+	30.1103i	−0.0623401	+	0.0623401i
$484$		0			0
$485$	78.2537	+	24.3593i	0.161348	+	0.0502253i
$486$		0			0
$487$		−	267.618i		−	0.549523i	−0.961512	−	0.274762i	$-0.911401\pi$
$487$		−	267.618i		−	0.549523i	0.961512	−	0.274762i	$-0.0885989\pi$
$488$		0			0
$489$		−	356.347i		−	0.728725i
$490$		0			0
$491$	−41.1597	+	41.1597i	−0.0838283	+	0.0838283i	−0.747778	−	0.663949i	$-0.768879\pi$
$491$	−41.1597	+	41.1597i	−0.0838283	+	0.0838283i	0.663949	+	0.747778i	$0.268879\pi$
$492$		0			0
$493$	279.810	+	279.810i	0.567567	+	0.567567i
$494$		0			0
$495$	−210.250	+	110.427i	−0.424747	+	0.223086i
$496$		0			0
$497$			129.836i			0.261240i
$498$		0			0
$499$	−165.335	−	165.335i	−0.331332	−	0.331332i	0.521760	−	0.853092i	$-0.325276\pi$
$499$	−165.335	−	165.335i	−0.331332	−	0.331332i	−0.853092	+	0.521760i	$0.825276\pi$
$500$		0			0
$501$	−69.8464	−	69.8464i	−0.139414	−	0.139414i
$502$		0			0
$503$			427.936i			0.850767i	0.905013	+	0.425384i	$0.139861\pi$
$503$			427.936i			0.850767i	−0.905013	+	0.425384i	$0.860139\pi$
$504$		0			0
$505$	−657.367	+	345.262i	−1.30172	+	0.683688i
$506$		0			0
$507$	103.451	+	103.451i	0.204045	+	0.204045i
$508$		0			0
$509$	465.764	−	465.764i	0.915056	−	0.915056i	−0.0816082	−	0.996664i	$-0.526006\pi$
$509$	465.764	−	465.764i	0.915056	−	0.915056i	0.996664	+	0.0816082i	$0.0260056\pi$
$510$		0			0
$511$			156.375i			0.306018i
$512$		0			0
$513$			685.647i			1.33654i
$514$		0			0
$515$	225.549	+	70.2101i	0.437958	+	0.136330i
$516$		0			0
$517$	380.075	−	380.075i	0.735155	−	0.735155i
$518$		0			0
$519$	326.965			0.629990
$520$		0			0
$521$			262.979i			0.504758i	0.967628	+	0.252379i	$0.0812129\pi$
$521$			262.979i			0.504758i	−0.967628	+	0.252379i	$0.918787\pi$
$522$		0			0
$523$	−142.934	−	142.934i	−0.273296	−	0.273296i	0.557129	−	0.830426i	$-0.311903\pi$
$523$	−142.934	−	142.934i	−0.273296	−	0.273296i	−0.830426	+	0.557129i	$0.811903\pi$
$524$		0			0
$525$	−44.0103	−	239.352i	−0.0838291	−	0.455908i
$526$		0			0
$527$	−489.286			−0.928437
$528$		0			0
$529$	509.865			0.963828
$530$		0			0
$531$	280.017	+	280.017i	0.527339	+	0.527339i
$532$		0			0
$533$	841.080	−	841.080i	1.57801	−	1.57801i
$534$		0			0
$535$	348.970	−	183.286i	0.652280	−	0.342591i
$536$		0			0
$537$	−471.714			−0.878425
$538$		0			0
$539$	−153.683	+	153.683i	−0.285125	+	0.285125i
$540$		0			0
$541$	214.719	−	214.719i	0.396892	−	0.396892i	−0.480243	−	0.877135i	$-0.659452\pi$
$541$	214.719	−	214.719i	0.396892	−	0.396892i	0.877135	+	0.480243i	$0.159452\pi$
$542$		0			0
$543$	396.208			0.729665
$544$		0			0
$545$	−427.386	−	813.726i	−0.784194	−	1.49307i
$546$		0			0
$547$	247.657	−	247.657i	0.452754	−	0.452754i	−0.443513	−	0.896268i	$-0.646268\pi$
$547$	247.657	−	247.657i	0.452754	−	0.452754i	0.896268	+	0.443513i	$0.146268\pi$
$548$		0			0
$549$	133.147	+	133.147i	0.242526	+	0.242526i
$550$		0			0
$551$	661.901			1.20127
$552$		0			0
$553$	−611.440			−1.10568
$554$		0			0
$555$	−237.443	−	73.9126i	−0.427825	−	0.133176i
$556$		0			0
$557$	−252.575	−	252.575i	−0.453456	−	0.453456i	0.443044	−	0.896500i	$-0.353899\pi$
$557$	−252.575	−	252.575i	−0.453456	−	0.453456i	−0.896500	+	0.443044i	$0.853899\pi$
$558$		0			0
$559$		−	423.966i		−	0.758436i
$560$		0			0
$561$	−262.017			−0.467054
$562$		0			0
$563$	274.938	−	274.938i	0.488345	−	0.488345i	−0.419439	−	0.907784i	$-0.637773\pi$
$563$	274.938	−	274.938i	0.488345	−	0.488345i	0.907784	+	0.419439i	$0.137773\pi$
$564$		0			0
$565$	227.471	+	70.8084i	0.402603	+	0.125325i
$566$		0			0
$567$			33.5347i			0.0591441i
$568$		0			0
$569$		−	985.556i		−	1.73208i	−0.499971	−	0.866042i	$-0.666656\pi$
$569$		−	985.556i		−	1.73208i	0.499971	−	0.866042i	$-0.333344\pi$
$570$		0			0
$571$	246.409	−	246.409i	0.431539	−	0.431539i	−0.457613	−	0.889152i	$-0.651295\pi$
$571$	246.409	−	246.409i	0.431539	−	0.431539i	0.889152	+	0.457613i	$0.151295\pi$
$572$		0			0
$573$	−67.3511	−	67.3511i	−0.117541	−	0.117541i
$574$		0			0
$575$	62.0692	−	90.0374i	0.107946	−	0.156587i
$576$		0			0
$577$			374.750i			0.649481i	0.945803	+	0.324740i	$0.105277\pi$
$577$			374.750i			0.649481i	−0.945803	+	0.324740i	$0.894723\pi$
$578$		0			0
$579$	511.114	+	511.114i	0.882753	+	0.882753i
$580$		0			0
$581$	−581.051	−	581.051i	−1.00009	−	1.00009i
$582$		0			0
$583$		−	276.973i		−	0.475083i
$584$		0			0
$585$	189.830	+	361.429i	0.324496	+	0.617827i
$586$		0			0
$587$	558.540	+	558.540i	0.951517	+	0.951517i	0.998878	−	0.0473610i	$-0.0150811\pi$
$587$	558.540	+	558.540i	0.951517	+	0.951517i	−0.0473610	+	0.998878i	$0.515081\pi$
$588$		0			0
$589$	−578.712	+	578.712i	−0.982532	+	0.982532i
$590$		0			0
$591$		−	452.645i		−	0.765897i
$592$		0			0
$593$		−	217.889i		−	0.367435i	−0.982979	−	0.183717i	$-0.941187\pi$
$593$		−	217.889i		−	0.367435i	0.982979	−	0.183717i	$-0.0588131\pi$
$594$		0			0
$595$	−110.406	+	354.679i	−0.185557	+	0.596099i
$596$		0			0
$597$	−193.901	+	193.901i	−0.324793	+	0.324793i
$598$		0			0
$599$	−238.766			−0.398607			−0.199304	−	0.979938i	$-0.563868\pi$
$599$	−238.766			−0.398607			−0.199304	+	0.979938i	$0.563868\pi$
$600$		0			0
$601$		−	307.946i		−	0.512390i	−0.966625	−	0.256195i	$-0.917531\pi$
$601$		−	307.946i		−	0.512390i	0.966625	−	0.256195i	$-0.0824688\pi$
$602$		0			0
$603$	−30.9688	−	30.9688i	−0.0513579	−	0.0513579i
$604$		0			0
$605$	183.007	+	56.9673i	0.302490	+	0.0941609i
$606$		0			0
$607$	−257.142			−0.423627			−0.211814	−	0.977310i	$-0.567937\pi$
$607$	−257.142			−0.423627			−0.211814	+	0.977310i	$0.567937\pi$
$608$		0			0
$609$	259.745			0.426511
$610$		0			0
$611$	−653.366	−	653.366i	−1.06934	−	1.06934i
$612$		0			0
$613$	−352.976	+	352.976i	−0.575817	+	0.575817i	−0.933748	−	0.357931i	$-0.883482\pi$
$613$	−352.976	+	352.976i	−0.575817	+	0.575817i	0.357931	+	0.933748i	$0.383482\pi$
$614$		0			0
$615$	−654.615	+	343.817i	−1.06442	+	0.559053i
$616$		0			0
$617$	−188.628			−0.305719			−0.152859	−	0.988248i	$-0.548848\pi$
$617$	−188.628			−0.305719			−0.152859	+	0.988248i	$0.548848\pi$
$618$		0			0
$619$	−387.137	+	387.137i	−0.625424	+	0.625424i	−0.946913	−	0.321490i	$-0.895817\pi$
$619$	−387.137	+	387.137i	−0.625424	+	0.625424i	0.321490	+	0.946913i	$0.395817\pi$
$620$		0			0
$621$	−85.4941	+	85.4941i	−0.137672	+	0.137672i
$622$		0			0
$623$	−427.779			−0.686644
$624$		0			0
$625$	222.324	+	584.121i	0.355719	+	0.934593i
$626$		0			0
$627$	−309.905	+	309.905i	−0.494267	+	0.494267i
$628$		0			0
$629$	268.404	+	268.404i	0.426715	+	0.426715i
$630$		0			0
$631$	−561.749			−0.890252			−0.445126	−	0.895468i	$-0.646841\pi$
$631$	−561.749			−0.890252			−0.445126	+	0.895468i	$0.646841\pi$
$632$		0			0
$633$	−458.951			−0.725041
$634$		0			0
$635$	265.739	−	853.682i	0.418487	−	1.34438i
$636$		0			0
$637$	264.188	+	264.188i	0.414737	+	0.414737i
$638$		0			0
$639$			135.394i			0.211884i
$640$		0			0
$641$	−1009.43			−1.57477			−0.787387	−	0.616459i	$-0.788567\pi$
$641$	−1009.43			−1.57477			−0.787387	+	0.616459i	$0.788567\pi$
$642$		0			0
$643$	775.300	−	775.300i	1.20575	−	1.20575i	0.233364	−	0.972389i	$-0.425027\pi$
$643$	775.300	−	775.300i	1.20575	−	1.20575i	0.972389	−	0.233364i	$-0.0749735\pi$
$644$		0			0
$645$	−78.3325	+	251.642i	−0.121446	+	0.390142i
$646$		0			0
$647$			5.25109i			0.00811606i	0.999992	+	0.00405803i	$0.00129171\pi$
$647$			5.25109i			0.00811606i	−0.999992	+	0.00405803i	$0.998708\pi$
$648$		0			0
$649$			689.226i			1.06198i
$650$		0			0
$651$	−227.100	+	227.100i	−0.348847	+	0.348847i
$652$		0			0
$653$	15.2963	+	15.2963i	0.0234247	+	0.0234247i	0.718722	−	0.695297i	$-0.244727\pi$
$653$	15.2963	+	15.2963i	0.0234247	+	0.0234247i	−0.695297	+	0.718722i	$0.744727\pi$
$654$		0			0
$655$	314.047	−	164.944i	0.479461	−	0.251823i
$656$		0			0
$657$			163.069i			0.248202i
$658$		0			0
$659$	−378.187	−	378.187i	−0.573880	−	0.573880i	0.359330	−	0.933211i	$-0.383005\pi$
$659$	−378.187	−	378.187i	−0.573880	−	0.573880i	−0.933211	+	0.359330i	$0.883005\pi$
$660$		0			0
$661$	42.5546	+	42.5546i	0.0643791	+	0.0643791i	0.738563	−	0.674184i	$-0.235505\pi$
$661$	42.5546	+	42.5546i	0.0643791	+	0.0643791i	−0.674184	+	0.738563i	$0.735505\pi$
$662$		0			0
$663$			450.420i			0.679366i
$664$		0			0
$665$	288.917	+	550.087i	0.434462	+	0.827199i
$666$		0			0
$667$	82.5332	+	82.5332i	0.123738	+	0.123738i
$668$		0			0
$669$	−495.475	+	495.475i	−0.740620	+	0.740620i
$670$		0			0
$671$			327.724i			0.488412i
$672$		0			0
$673$		−	1181.74i		−	1.75593i	−0.478727	−	0.877964i	$-0.658902\pi$
$673$		−	1181.74i		−	1.75593i	0.478727	−	0.877964i	$-0.341098\pi$
$674$		0			0
$675$	−124.961	−	679.607i	−0.185128	−	1.00683i
$676$		0			0
$677$	71.0492	−	71.0492i	0.104947	−	0.104947i	−0.652684	−	0.757631i	$-0.726357\pi$
$677$	71.0492	−	71.0492i	0.104947	−	0.104947i	0.757631	+	0.652684i	$0.226357\pi$
$678$		0			0
$679$	−82.1141			−0.120934
$680$		0			0
$681$		−	446.898i		−	0.656238i
$682$		0			0
$683$	246.349	+	246.349i	0.360687	+	0.360687i	0.864066	−	0.503379i	$-0.167910\pi$
$683$	246.349	+	246.349i	0.360687	+	0.360687i	−0.503379	+	0.864066i	$0.667910\pi$
$684$		0			0
$685$	7.01641	−	22.5401i	0.0102429	−	0.0329052i
$686$		0			0
$687$	16.7977			0.0244508
$688$		0			0
$689$	−476.130			−0.691045
$690$		0			0
$691$	−176.426	−	176.426i	−0.255320	−	0.255320i	0.567827	−	0.823148i	$-0.307784\pi$
$691$	−176.426	−	176.426i	−0.255320	−	0.255320i	−0.823148	+	0.567827i	$0.807784\pi$
$692$		0			0
$693$	168.249	−	168.249i	0.242783	−	0.242783i
$694$		0			0
$695$	−237.694	−	452.561i	−0.342006	−	0.651167i
$696$		0			0
$697$	1128.62			1.61926
$698$		0			0
$699$	−167.110	+	167.110i	−0.239070	+	0.239070i
$700$		0			0
$701$	−715.573	+	715.573i	−1.02079	+	1.02079i	−0.0210094	+	0.999779i	$0.506688\pi$
$701$	−715.573	+	715.573i	−1.02079	+	1.02079i	−0.999779	+	0.0210094i	$0.993312\pi$
$702$		0			0
$703$	634.919			0.903156
$704$		0			0
$705$	267.084	+	508.517i	0.378842	+	0.721301i
$706$		0			0
$707$	526.046	−	526.046i	0.744053	−	0.744053i
$708$		0			0
$709$	306.482	+	306.482i	0.432273	+	0.432273i	0.889401	−	0.457128i	$-0.151122\pi$
$709$	306.482	+	306.482i	0.432273	+	0.432273i	−0.457128	+	0.889401i	$0.651122\pi$
$710$		0			0
$711$	−637.611			−0.896780
$712$		0			0
$713$	−144.320			−0.202413
$714$		0			0
$715$	−211.185	+	678.427i	−0.295363	+	0.948849i
$716$		0			0
$717$	−308.430	−	308.430i	−0.430167	−	0.430167i
$718$		0			0
$719$		−	87.8746i		−	0.122218i	−0.998131	−	0.0611089i	$-0.980536\pi$
$719$		−	87.8746i		−	0.122218i	0.998131	−	0.0611089i	$-0.0194637\pi$
$720$		0			0
$721$	−236.676			−0.328260
$722$		0			0
$723$	−175.888	+	175.888i	−0.243275	+	0.243275i
$724$		0			0
$725$	−656.070	+	120.633i	−0.904925	+	0.166391i
$726$		0			0
$727$		−	370.209i		−	0.509228i	−0.967043	−	0.254614i	$-0.918052\pi$
$727$		−	370.209i		−	0.509228i	0.967043	−	0.254614i	$-0.0819484\pi$
$728$		0			0
$729$			518.360i			0.711056i
$730$		0			0
$731$	284.454	−	284.454i	0.389130	−	0.389130i
$732$		0			0
$733$	−626.686	−	626.686i	−0.854960	−	0.854960i	0.135779	−	0.990739i	$-0.456646\pi$
$733$	−626.686	−	626.686i	−0.854960	−	0.854960i	−0.990739	+	0.135779i	$0.956646\pi$
$734$		0			0
$735$	−107.995	−	205.618i	−0.146932	−	0.279753i
$736$		0			0
$737$		−	76.2259i		−	0.103427i
$738$		0			0
$739$	−388.772	−	388.772i	−0.526078	−	0.526078i	0.393322	−	0.919401i	$-0.371326\pi$
$739$	−388.772	−	388.772i	−0.526078	−	0.526078i	−0.919401	+	0.393322i	$0.871326\pi$
$740$		0			0
$741$	532.741	+	532.741i	0.718949	+	0.718949i
$742$		0			0
$743$		−	121.878i		−	0.164035i	−0.996631	−	0.0820173i	$-0.973864\pi$
$743$		−	121.878i		−	0.164035i	0.996631	−	0.0820173i	$-0.0261363\pi$
$744$		0			0
$745$	−516.872	+	271.472i	−0.693788	+	0.364392i
$746$		0			0
$747$	−605.921	−	605.921i	−0.811139	−	0.811139i
$748$		0			0
$749$	−279.257	+	279.257i	−0.372840	+	0.372840i
$750$		0			0
$751$			914.610i			1.21786i	0.793225	+	0.608928i	$0.208400\pi$
$751$			914.610i			1.21786i	−0.793225	+	0.608928i	$0.791600\pi$
$752$		0			0
$753$		−	399.991i		−	0.531196i
$754$		0			0
$755$	−141.656	+	455.067i	−0.187624	+	0.602737i
$756$		0			0
$757$	−129.143	+	129.143i	−0.170599	+	0.170599i	−0.787242	−	0.616644i	$-0.788492\pi$
$757$	−129.143	+	129.143i	−0.170599	+	0.170599i	0.616644	+	0.787242i	$0.288492\pi$
$758$		0			0
$759$	−77.2849			−0.101825
$760$		0			0
$761$			352.217i			0.462835i	0.972855	+	0.231417i	$0.0743363\pi$
$761$			352.217i			0.462835i	−0.972855	+	0.231417i	$0.925664\pi$
$762$		0			0
$763$	651.169	+	651.169i	0.853433	+	0.853433i
$764$		0			0
$765$	−115.132	+	369.860i	−0.150499	+	0.483477i
$766$		0			0
$767$	1184.81			1.54473
$768$		0			0
$769$	105.447			0.137122			0.0685611	−	0.997647i	$-0.478159\pi$
$769$	105.447			0.137122			0.0685611	+	0.997647i	$0.478159\pi$
$770$		0			0
$771$	−618.434	−	618.434i	−0.802120	−	0.802120i
$772$		0			0
$773$	124.080	−	124.080i	0.160518	−	0.160518i	−0.622278	−	0.782796i	$-0.713793\pi$
$773$	124.080	−	124.080i	0.160518	−	0.160518i	0.782796	+	0.622278i	$0.213793\pi$
$774$		0			0
$775$	468.142	−	679.085i	0.604054	−	0.876239i
$776$		0			0
$777$	249.157			0.320665
$778$		0			0
$779$	1334.90	−	1334.90i	1.71360	−	1.71360i
$780$		0			0
$781$	−166.627	+	166.627i	−0.213351	+	0.213351i
$782$		0			0
$783$	737.512			0.941905
$784$		0			0
$785$	−647.635	+	340.151i	−0.825013	+	0.433314i
$786$		0			0
$787$	−615.831	+	615.831i	−0.782505	+	0.782505i	−0.980253	−	0.197748i	$-0.936637\pi$
$787$	−615.831	+	615.831i	−0.782505	+	0.782505i	0.197748	+	0.980253i	$0.436637\pi$
$788$		0			0
$789$	−273.715	−	273.715i	−0.346914	−	0.346914i
$790$		0			0
$791$	−238.693			−0.301761
$792$		0			0
$793$	563.373			0.710433
$794$		0			0
$795$	282.603	+	87.9704i	0.355476	+	0.110655i
$796$		0			0
$797$	56.7101	+	56.7101i	0.0711545	+	0.0711545i	0.741788	−	0.670634i	$-0.233978\pi$
$797$	56.7101	+	56.7101i	0.0711545	+	0.0711545i	−0.670634	+	0.741788i	$0.733978\pi$
$798$		0			0
$799$		−	876.735i		−	1.09729i
$800$		0			0
$801$	−446.089			−0.556915
$802$		0			0
$803$	−200.686	+	200.686i	−0.249921	+	0.249921i
$804$		0			0
$805$	−32.5656	+	104.616i	−0.0404542	+	0.129958i
$806$		0			0
$807$		−	132.300i		−	0.163940i
$808$		0			0
$809$			556.339i			0.687688i	0.939027	+	0.343844i	$0.111729\pi$
$809$			556.339i			0.687688i	−0.939027	+	0.343844i	$0.888271\pi$
$810$		0			0
$811$	−993.474	+	993.474i	−1.22500	+	1.22500i	−0.259166	+	0.965833i	$0.583448\pi$
$811$	−993.474	+	993.474i	−1.22500	+	1.22500i	−0.965833	+	0.259166i	$0.916552\pi$
$812$		0			0
$813$	−436.815	−	436.815i	−0.537288	−	0.537288i
$814$		0			0
$815$	−426.350	−	811.755i	−0.523129	−	0.996018i
$816$		0			0
$817$		−	672.886i		−	0.823606i
$818$		0			0
$819$	−289.227	−	289.227i	−0.353147	−	0.353147i
$820$		0			0
$821$	−620.009	−	620.009i	−0.755188	−	0.755188i	0.220255	−	0.975442i	$-0.429311\pi$
$821$	−620.009	−	620.009i	−0.755188	−	0.755188i	−0.975442	+	0.220255i	$0.929311\pi$
$822$		0			0
$823$		−	646.223i		−	0.785204i	−0.919708	−	0.392602i	$-0.871575\pi$
$823$		−	646.223i		−	0.785204i	0.919708	−	0.392602i	$-0.128425\pi$
$824$		0			0
$825$	250.694	−	363.656i	0.303872	−	0.440796i
$826$		0			0
$827$	−836.004	−	836.004i	−1.01089	−	1.01089i	−0.999940	−	0.0109471i	$-0.996515\pi$
$827$	−836.004	−	836.004i	−1.01089	−	1.01089i	−0.0109471	−	0.999940i	$-0.503485\pi$
$828$		0			0
$829$	234.984	−	234.984i	0.283454	−	0.283454i	−0.551031	−	0.834485i	$-0.685765\pi$
$829$	234.984	−	234.984i	0.283454	−	0.283454i	0.834485	+	0.551031i	$0.185765\pi$
$830$		0			0
$831$		−	187.711i		−	0.225886i
$832$		0			0
$833$			354.506i			0.425578i
$834$		0			0
$835$	−242.677	−	75.5420i	−0.290631	−	0.0904694i
$836$		0			0
$837$	−644.819	+	644.819i	−0.770393	+	0.770393i
$838$		0			0
$839$	219.575			0.261711			0.130855	−	0.991401i	$-0.458228\pi$
$839$	219.575			0.261711			0.130855	+	0.991401i	$0.458228\pi$
$840$		0			0
$841$			129.031i			0.153425i
$842$		0			0
$843$	−180.326	−	180.326i	−0.213909	−	0.213909i
$844$		0			0
$845$	359.433	+	111.887i	0.425365	+	0.132410i
$846$		0			0
$847$	−192.035			−0.226723
$848$		0			0
$849$	−1062.25			−1.25117
$850$		0			0
$851$	79.1687	+	79.1687i	0.0930302	+	0.0930302i
$852$		0			0
$853$	−47.0723	+	47.0723i	−0.0551844	+	0.0551844i	−0.734160	−	0.678976i	$-0.762424\pi$
$853$	−47.0723	+	47.0723i	−0.0551844	+	0.0551844i	0.678976	+	0.734160i	$0.262424\pi$
$854$		0			0
$855$	301.283	+	573.632i	0.352378	+	0.670915i
$856$		0			0
$857$	−1620.86			−1.89132			−0.945661	−	0.325154i	$-0.894584\pi$
$857$	−1620.86			−1.89132			−0.945661	+	0.325154i	$0.894584\pi$
$858$		0			0
$859$	−317.610	+	317.610i	−0.369744	+	0.369744i	−0.867384	−	0.497640i	$-0.834200\pi$
$859$	−317.610	+	317.610i	−0.369744	+	0.369744i	0.497640	+	0.867384i	$0.334200\pi$
$860$		0			0
$861$	523.844	−	523.844i	0.608414	−	0.608414i
$862$		0			0
$863$	1407.45			1.63088			0.815439	−	0.578842i	$-0.196495\pi$
$863$	1407.45			1.63088			0.815439	+	0.578842i	$0.196495\pi$
$864$		0			0
$865$	744.823	−	391.197i	0.861068	−	0.452250i
$866$		0			0
$867$	94.8970	−	94.8970i	0.109454	−	0.109454i
$868$		0			0
$869$	−784.699	−	784.699i	−0.902991	−	0.902991i
$870$		0			0
$871$	−131.036			−0.150443
$872$		0			0
$873$	−85.6288			−0.0980857
$874$		0			0
$875$	−386.627	−	492.585i	−0.441859	−	0.562955i
$876$		0			0
$877$	507.991	+	507.991i	0.579237	+	0.579237i	0.934693	−	0.355456i	$-0.115674\pi$
$877$	507.991	+	507.991i	0.579237	+	0.579237i	−0.355456	+	0.934693i	$0.615674\pi$
$878$		0			0
$879$			607.614i			0.691256i
$880$		0			0
$881$	1167.86			1.32561			0.662803	−	0.748793i	$-0.269367\pi$
$881$	1167.86			1.32561			0.662803	+	0.748793i	$0.269367\pi$
$882$		0			0
$883$	641.739	−	641.739i	0.726771	−	0.726771i	−0.243204	−	0.969975i	$-0.578198\pi$
$883$	641.739	−	641.739i	0.726771	−	0.726771i	0.969975	+	0.243204i	$0.0781984\pi$
$884$		0			0
$885$	−703.236	−	218.907i	−0.794616	−	0.247353i
$886$		0			0
$887$			172.729i			0.194734i	0.995249	+	0.0973670i	$0.0310420\pi$
$887$			172.729i			0.194734i	−0.995249	+	0.0973670i	$0.968958\pi$
$888$		0			0
$889$			895.796i			1.00764i
$890$		0			0
$891$	−43.0372	+	43.0372i	−0.0483021	+	0.0483021i
$892$		0			0
$893$	−1036.97	−	1036.97i	−1.16122	−	1.16122i
$894$		0			0
$895$	−1074.56	+	564.381i	−1.20063	+	0.630594i
$896$		0			0
$897$			132.856i			0.148112i
$898$		0			0
$899$	622.487	+	622.487i	0.692421	+	0.692421i
$900$		0			0
$901$	−319.453	−	319.453i	−0.354554	−	0.354554i
$902$		0			0
$903$		−	264.056i		−	0.292421i
$904$		0			0
$905$	902.559	−	474.043i	0.997303	−	0.523804i
$906$		0			0
$907$	83.4405	+	83.4405i	0.0919962	+	0.0919962i	0.751607	−	0.659611i	$-0.229279\pi$
$907$	83.4405	+	83.4405i	0.0919962	+	0.0919962i	−0.659611	+	0.751607i	$0.729279\pi$
$908$		0			0
$909$	548.562	−	548.562i	0.603478	−	0.603478i
$910$		0			0
$911$		−	692.752i		−	0.760430i	−0.924898	−	0.380215i	$-0.875850\pi$
$911$		−	692.752i		−	0.760430i	0.924898	−	0.380215i	$-0.124150\pi$
$912$		0			0
$913$		−	1491.40i		−	1.63351i
$914$		0			0
$915$	−334.386	−	104.090i	−0.365449	−	0.113759i
$916$		0			0
$917$	−251.310	+	251.310i	−0.274057	+	0.274057i
$918$		0			0
$919$	23.1013			0.0251374			0.0125687	−	0.999921i	$-0.495999\pi$
$919$	23.1013			0.0251374			0.0125687	+	0.999921i	$0.495999\pi$
$920$		0			0
$921$			221.048i			0.240009i
$922$		0			0
$923$	286.440	+	286.440i	0.310336	+	0.310336i
$924$		0			0
$925$	−629.325	+	115.716i	−0.680352	+	0.125098i
$926$		0			0
$927$	−246.806			−0.266241
$928$		0			0
$929$	862.326			0.928231			0.464115	−	0.885775i	$-0.346372\pi$
$929$	862.326			0.928231			0.464115	+	0.885775i	$0.346372\pi$
$930$		0			0
$931$	419.298	+	419.298i	0.450374	+	0.450374i
$932$		0			0
$933$	595.195	−	595.195i	0.637937	−	0.637937i
$934$		0			0
$935$	−596.873	+	313.490i	−0.638367	+	0.335283i
$936$		0			0
$937$	−968.975			−1.03412			−0.517062	−	0.855948i	$-0.672974\pi$
$937$	−968.975			−1.03412			−0.517062	+	0.855948i	$0.672974\pi$
$938$		0			0
$939$	370.445	−	370.445i	0.394510	−	0.394510i
$940$		0			0
$941$	−165.112	+	165.112i	−0.175465	+	0.175465i	−0.789375	−	0.613911i	$-0.789595\pi$
$941$	−165.112	+	165.112i	−0.175465	+	0.175465i	0.613911	+	0.789375i	$0.289595\pi$
$942$		0			0
$943$	332.900			0.353022
$944$		0			0
$945$	321.921	+	612.925i	0.340657	+	0.648598i
$946$		0			0
$947$	347.438	−	347.438i	0.366883	−	0.366883i	−0.499456	−	0.866339i	$-0.666467\pi$
$947$	347.438	−	347.438i	0.366883	−	0.366883i	0.866339	+	0.499456i	$0.166467\pi$
$948$		0			0
$949$	344.989	+	344.989i	0.363529	+	0.363529i
$950$		0			0
$951$	−55.1343			−0.0579751
$952$		0			0
$953$	1222.59			1.28288			0.641442	−	0.767171i	$-0.278336\pi$
$953$	1222.59			1.28288			0.641442	+	0.767171i	$0.278336\pi$
$954$		0			0
$955$	−234.008	−	72.8432i	−0.245034	−	0.0762756i
$956$		0			0
$957$	333.347	+	333.347i	0.348325	+	0.348325i
$958$		0			0
$959$			23.6520i			0.0246632i
$960$		0			0
$961$	−127.502			−0.132676
$962$		0			0
$963$	−291.210	+	291.210i	−0.302398	+	0.302398i
$964$		0			0
$965$	1775.84	+	552.792i	1.84024	+	0.572842i
$966$		0			0
$967$			967.881i			1.00091i	0.865762	+	0.500455i	$0.166834\pi$
$967$			967.881i			1.00091i	−0.865762	+	0.500455i	$0.833166\pi$
$968$		0			0
$969$			714.871i			0.737741i
$970$		0			0
$971$	−84.0735	+	84.0735i	−0.0865844	+	0.0865844i	−0.749072	−	0.662488i	$-0.769501\pi$
$971$	−84.0735	+	84.0735i	−0.0865844	+	0.0865844i	0.662488	+	0.749072i	$0.269501\pi$
$972$		0			0
$973$	362.154	+	362.154i	0.372203	+	0.372203i
$974$		0			0
$975$	−625.142	−	430.955i	−0.641171	−	0.442005i
$976$		0			0
$977$			759.084i			0.776954i	0.921458	+	0.388477i	$0.126999\pi$
$977$			759.084i			0.776954i	−0.921458	+	0.388477i	$0.873001\pi$
$978$		0			0
$979$	−548.996	−	548.996i	−0.560772	−	0.560772i
$980$		0			0
$981$	679.041	+	679.041i	0.692192	+	0.692192i
$982$		0			0
$983$		−	278.089i		−	0.282899i	−0.989945	−	0.141449i	$-0.954824\pi$
$983$		−	278.089i		−	0.282899i	0.989945	−	0.141449i	$-0.0451762\pi$
$984$		0			0
$985$	−541.566	−	1031.12i	−0.549813	−	1.04682i
$986$		0			0
$987$	−406.932	−	406.932i	−0.412292	−	0.412292i
$988$		0			0
$989$	83.9029	−	83.9029i	0.0848361	−	0.0848361i
$990$		0			0
$991$		−	722.074i		−	0.728632i	−0.931275	−	0.364316i	$-0.881303\pi$
$991$		−	722.074i		−	0.728632i	0.931275	−	0.364316i	$-0.118697\pi$
$992$		0			0
$993$		−	446.562i		−	0.449710i
$994$		0			0
$995$	−209.713	+	673.698i	−0.210767	+	0.677084i
$996$		0			0
$997$	388.829	−	388.829i	0.389999	−	0.389999i	−0.484688	−	0.874687i	$-0.661067\pi$
$997$	388.829	−	388.829i	0.389999	−	0.389999i	0.874687	+	0.484688i	$0.161067\pi$
$998$		0			0
$999$	707.447			0.708155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.3.k.a.159.16		44
4.3	odd	2		640.3.k.b.159.7		44
5.4	even	2	inner	640.3.k.a.159.7		44
8.3	odd	2		80.3.k.a.59.20	yes	44
8.5	even	2		320.3.k.a.79.7		44
16.3	odd	4	inner	640.3.k.a.479.7		44
16.5	even	4		80.3.k.a.19.3	✓	44
16.11	odd	4		320.3.k.a.239.16		44
16.13	even	4		640.3.k.b.479.16		44
20.19	odd	2		640.3.k.b.159.16		44
40.3	even	4		400.3.r.g.251.9		44
40.19	odd	2		80.3.k.a.59.3	yes	44
40.27	even	4		400.3.r.g.251.14		44
40.29	even	2		320.3.k.a.79.16		44
80.19	odd	4	inner	640.3.k.a.479.16		44
80.29	even	4		640.3.k.b.479.7		44
80.37	odd	4		400.3.r.g.51.14		44
80.53	odd	4		400.3.r.g.51.9		44
80.59	odd	4		320.3.k.a.239.7		44
80.69	even	4		80.3.k.a.19.20	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.k.a.19.3	✓	44	16.5	even	4
80.3.k.a.19.20	yes	44	80.69	even	4
80.3.k.a.59.3	yes	44	40.19	odd	2
80.3.k.a.59.20	yes	44	8.3	odd	2
320.3.k.a.79.7		44	8.5	even	2
320.3.k.a.79.16		44	40.29	even	2
320.3.k.a.239.7		44	80.59	odd	4
320.3.k.a.239.16		44	16.11	odd	4
400.3.r.g.51.9		44	80.53	odd	4
400.3.r.g.51.14		44	80.37	odd	4
400.3.r.g.251.9		44	40.3	even	4
400.3.r.g.251.14		44	40.27	even	4
640.3.k.a.159.7		44	5.4	even	2	inner
640.3.k.a.159.16		44	1.1	even	1	trivial
640.3.k.a.479.7		44	16.3	odd	4	inner
640.3.k.a.479.16		44	80.19	odd	4	inner
640.3.k.b.159.7		44	4.3	odd	2
640.3.k.b.159.16		44	20.19	odd	2
640.3.k.b.479.7		44	80.29	even	4
640.3.k.b.479.16		44	16.13	even	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	640.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.37405 - 1.37405i) q^{3} +(1.48609 - 4.77405i) q^{5} +5.00956i q^{7} +5.22398i q^{9} +O(q^{10})\)	\(q+(1.37405 - 1.37405i) q^{3} +(1.48609 - 4.77405i) q^{5} +5.00956i q^{7} +5.22398i q^{9} +(-6.42909 + 6.42909i) q^{11} +(11.0519 + 11.0519i) q^{13} +(-4.51781 - 8.60173i) q^{15} +14.8302i q^{17} +(17.5407 + 17.5407i) q^{19} +(6.88338 + 6.88338i) q^{21} +4.37435i q^{23} +(-20.5831 - 14.1894i) q^{25} +(19.5444 + 19.5444i) q^{27} +(18.8676 - 18.8676i) q^{29} +32.9924i q^{31} +17.6678i q^{33} +(23.9159 + 7.44468i) q^{35} +(18.0984 - 18.0984i) q^{37} +30.3717 q^{39} -76.1027i q^{41} +(-19.1807 - 19.1807i) q^{43} +(24.9395 + 7.76333i) q^{45} -59.1180 q^{47} +23.9043 q^{49} +(20.3775 + 20.3775i) q^{51} +(-21.5406 + 21.5406i) q^{53} +(21.1385 + 40.2470i) q^{55} +48.2036 q^{57} +(53.6021 - 53.6021i) q^{59} +(25.4876 - 25.4876i) q^{61} -26.1699 q^{63} +(69.1865 - 36.3381i) q^{65} +(-5.92820 + 5.92820i) q^{67} +(6.01056 + 6.01056i) q^{69} +25.9177 q^{71} +31.2154 q^{73} +(-47.7790 + 8.78525i) q^{75} +(-32.2069 - 32.2069i) q^{77} +122.054i q^{79} +6.69413 q^{81} +(-115.988 + 115.988i) q^{83} +(70.8003 + 22.0391i) q^{85} -51.8499i q^{87} +85.3925i q^{89} +(-55.3652 + 55.3652i) q^{91} +(45.3332 + 45.3332i) q^{93} +(109.807 - 57.6731i) q^{95} +16.3915i q^{97} +(-33.5855 - 33.5855i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{5}+O(q^{10}) \) 44 * q + 2 * q^5	\( 44 q + 2 q^{5} - 4 q^{11} - 36 q^{19} - 32 q^{21} + 4 q^{29} + 8 q^{39} - 30 q^{45} - 148 q^{49} + 128 q^{51} + 260 q^{55} - 68 q^{59} - 28 q^{61} - 20 q^{65} - 128 q^{69} + 264 q^{71} + 60 q^{75} - 116 q^{81} - 48 q^{85} + 384 q^{91} + 484 q^{99}+O(q^{100}) \) 44 * q + 2 * q^5 - 4 * q^11 - 36 * q^19 - 32 * q^21 + 4 * q^29 + 8 * q^39 - 30 * q^45 - 148 * q^49 + 128 * q^51 + 260 * q^55 - 68 * q^59 - 28 * q^61 - 20 * q^65 - 128 * q^69 + 264 * q^71 + 60 * q^75 - 116 * q^81 - 48 * q^85 + 384 * q^91 + 484 * q^99

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