LMFDB - Embedded newform 640.3.k.b.479.16

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			479.16
Character	$\chi$	$=$	640.479
Dual form			640.3.k.b.159.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37405 + 1.37405i) q^{3} +(-4.77405 - 1.48609i) q^{5} -5.00956i q^{7} -5.22398i q^{9} +O(q^{10})$	\(q+(1.37405 + 1.37405i) q^{3} +(-4.77405 - 1.48609i) q^{5} -5.00956i q^{7} -5.22398i q^{9} +(6.42909 + 6.42909i) q^{11} +(-11.0519 + 11.0519i) q^{13} +(-4.51781 - 8.60173i) q^{15} +14.8302i q^{17} +(-17.5407 + 17.5407i) q^{19} +(6.88338 - 6.88338i) q^{21} -4.37435i q^{23} +(20.5831 + 14.1894i) q^{25} +(19.5444 - 19.5444i) q^{27} +(18.8676 + 18.8676i) q^{29} +32.9924i q^{31} +17.6678i q^{33} +(-7.44468 + 23.9159i) q^{35} +(-18.0984 - 18.0984i) q^{37} -30.3717 q^{39} +76.1027i q^{41} +(-19.1807 + 19.1807i) q^{43} +(-7.76333 + 24.9395i) q^{45} -59.1180 q^{47} +23.9043 q^{49} +(-20.3775 + 20.3775i) q^{51} +(21.5406 + 21.5406i) q^{53} +(-21.1385 - 40.2470i) q^{55} -48.2036 q^{57} +(-53.6021 - 53.6021i) q^{59} +(25.4876 + 25.4876i) q^{61} -26.1699 q^{63} +(69.1865 - 36.3381i) q^{65} +(-5.92820 - 5.92820i) q^{67} +(6.01056 - 6.01056i) q^{69} -25.9177 q^{71} -31.2154 q^{73} +(8.78525 + 47.7790i) q^{75} +(32.2069 - 32.2069i) q^{77} +122.054i q^{79} +6.69413 q^{81} +(-115.988 - 115.988i) q^{83} +(22.0391 - 70.8003i) q^{85} +51.8499i q^{87} -85.3925i q^{89} +(55.3652 + 55.3652i) q^{91} +(-45.3332 + 45.3332i) q^{93} +(109.807 - 57.6731i) q^{95} +16.3915i q^{97} +(33.5855 - 33.5855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	1.37405	+	1.37405i	0.458016	+	0.458016i	0.898004	−	0.439988i	$-0.145017\pi$
$3$	1.37405	+	1.37405i	0.458016	+	0.458016i	−0.439988	+	0.898004i	$0.645017\pi$
$4$		0			0
$5$	−4.77405	−	1.48609i	−0.954809	−	0.297219i
$5$	−4.77405	−	1.48609i	−0.954809	−	0.297219i
$6$		0			0
$7$		−	5.00956i		−	0.715652i	−0.933788	−	0.357826i	$-0.883518\pi$
$7$		−	5.00956i		−	0.715652i	0.933788	−	0.357826i	$-0.116482\pi$
$8$		0			0
$9$		−	5.22398i		−	0.580443i
$10$		0			0
$11$	6.42909	+	6.42909i	0.584463	+	0.584463i	0.936126	−	0.351664i	$-0.114384\pi$
$11$	6.42909	+	6.42909i	0.584463	+	0.584463i	−0.351664	+	0.936126i	$0.614384\pi$
$12$		0			0
$13$	−11.0519	+	11.0519i	−0.850146	+	0.850146i	−0.990151	−	0.140005i	$-0.955288\pi$
$13$	−11.0519	+	11.0519i	−0.850146	+	0.850146i	0.140005	+	0.990151i	$0.455288\pi$
$14$		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	$-0.976405\pi$
$19$	−17.5407	+	17.5407i	−0.923196	+	0.923196i	0.0740578	+	0.997254i	$0.476405\pi$
$20$		0			0
$21$	6.88338	−	6.88338i	0.327780	−	0.327780i
$22$		0			0
$23$		−	4.37435i		−	0.190189i	−0.995468	−	0.0950945i	$-0.969685\pi$
$23$		−	4.37435i		−	0.190189i	0.995468	−	0.0950945i	$-0.0303153\pi$
$24$		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	0.953139	−	0.302533i	$-0.0978324\pi$
$29$	18.8676	+	18.8676i	0.650605	+	0.650605i	−0.302533	+	0.953139i	$0.597832\pi$
$30$		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
$35$	−7.44468	+	23.9159i	−0.212705	+	0.683311i
$36$		0			0
$37$	−18.0984	−	18.0984i	−0.489146	−	0.489146i	0.418891	−	0.908037i	$-0.362419\pi$
$37$	−18.0984	−	18.0984i	−0.489146	−	0.489146i	−0.908037	+	0.418891i	$0.862419\pi$
$38$		0			0
$39$	−30.3717			−0.778761
$40$		0			0
$41$			76.1027i			1.85616i	0.372376	+	0.928082i	$0.378543\pi$
$41$			76.1027i			1.85616i	−0.372376	+	0.928082i	$0.621457\pi$
$42$		0			0
$43$	−19.1807	+	19.1807i	−0.446062	+	0.446062i	−0.894043	−	0.447981i	$-0.852143\pi$
$43$	−19.1807	+	19.1807i	−0.446062	+	0.446062i	0.447981	+	0.894043i	$0.352143\pi$
$44$		0			0
$45$	−7.76333	+	24.9395i	−0.172518	+	0.554212i
$46$		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	$-0.157213\pi$
$53$	21.5406	+	21.5406i	0.406427	+	0.406427i	−0.474064	+	0.880491i	$0.657213\pi$
$54$		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	$-0.472067\pi$
$59$	−53.6021	−	53.6021i	−0.908511	−	0.908511i	−0.996152	+	0.0876411i	$0.972067\pi$
$60$		0			0
$61$	25.4876	+	25.4876i	0.417830	+	0.417830i	0.884455	−	0.466625i	$-0.154530\pi$
$61$	25.4876	+	25.4876i	0.417830	+	0.417830i	−0.466625	+	0.884455i	$0.654530\pi$
$62$		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	0.661481	−	0.749962i	$-0.269928\pi$
$67$	−5.92820	−	5.92820i	−0.0884806	−	0.0884806i	−0.749962	+	0.661481i	$0.769928\pi$
$68$		0			0
$69$	6.01056	−	6.01056i	0.0871096	−	0.0871096i
$70$		0			0
$71$	−25.9177			−0.365038			−0.182519	−	0.983202i	$-0.558425\pi$
$71$	−25.9177			−0.365038			−0.182519	+	0.983202i	$0.558425\pi$
$72$		0			0
$73$	−31.2154			−0.427608			−0.213804	−	0.976877i	$-0.568585\pi$
$73$	−31.2154			−0.427608			−0.213804	+	0.976877i	$0.568585\pi$
$74$		0			0
$75$	8.78525	+	47.7790i	0.117137	+	0.637053i
$76$		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	−0.807280	−	0.590169i	$-0.799061\pi$
$83$	−115.988	−	115.988i	−1.39745	−	1.39745i	−0.590169	−	0.807280i	$-0.700939\pi$
$84$		0			0
$85$	22.0391	−	70.8003i	0.259284	−	0.832945i
$86$		0			0
$87$			51.8499i			0.595975i
$88$		0			0
$89$		−	85.3925i		−	0.959466i	−0.877415	−	0.479733i	$-0.840734\pi$
$89$		−	85.3925i		−	0.959466i	0.877415	−	0.479733i	$-0.159266\pi$
$90$		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	−0.0405066	+	0.999179i	$0.512897\pi$
$101$	−105.008	+	105.008i	−1.03969	+	1.03969i	−0.999179	+	0.0405066i	$0.987103\pi$
$102$		0			0
$103$		−	47.2447i		−	0.458687i	−0.973346	−	0.229343i	$-0.926342\pi$
$103$		−	47.2447i		−	0.458687i	0.973346	−	0.229343i	$-0.0736579\pi$
$104$		0			0
$105$	−43.0909	+	22.6322i	−0.410390	+	0.215545i
$106$		0			0
$107$	55.7447	−	55.7447i	0.520979	−	0.520979i	−0.396888	−	0.917867i	$-0.629910\pi$
$107$	55.7447	−	55.7447i	0.520979	−	0.520979i	0.917867	+	0.396888i	$0.129910\pi$
$108$		0			0
$109$	129.985	+	129.985i	1.19253	+	1.19253i	0.976356	+	0.216169i	$0.0693563\pi$
$109$	129.985	+	129.985i	1.19253	+	1.19253i	0.216169	+	0.976356i	$0.430644\pi$
$110$		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
$115$	−6.50068	+	20.8833i	−0.0565277	+	0.181594i
$116$		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
$125$	−77.1778	−	98.3290i	−0.617422	−	0.786632i
$126$		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	$-0.837283\pi$
$131$	−50.1661	+	50.1661i	−0.382948	+	0.382948i	0.489215	+	0.872163i	$0.337283\pi$
$132$		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	$-0.505485\pi$
$137$	−4.72138			−0.0344626			−0.0172313	+	0.999852i	$0.505485\pi$
$138$		0			0
$139$	−72.2925	−	72.2925i	−0.520090	−	0.520090i	0.397509	−	0.917598i	$-0.369875\pi$
$139$	−72.2925	−	72.2925i	−0.520090	−	0.520090i	−0.917598	+	0.397509i	$0.869875\pi$
$140$		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	−0.927631	−	0.373499i	$-0.878158\pi$
$149$	−82.5656	+	82.5656i	−0.554131	+	0.554131i	0.373499	+	0.927631i	$0.378158\pi$
$150$		0			0
$151$	95.3210			0.631265			0.315632	−	0.948882i	$-0.397783\pi$
$151$	95.3210			0.631265			0.315632	+	0.948882i	$0.397783\pi$
$152$		0			0
$153$	77.4730			0.506359
$154$		0			0
$155$	49.0298	−	157.508i	0.316322	−	1.01618i
$156$		0			0
$157$	103.454	−	103.454i	0.658941	−	0.658941i	−0.296188	−	0.955130i	$-0.595716\pi$
$157$	103.454	−	103.454i	0.658941	−	0.658941i	0.955130	+	0.296188i	$0.0957156\pi$
$158$		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	0.982386	−	0.186862i	$-0.0598318\pi$
$163$	129.670	+	129.670i	0.795524	+	0.795524i	−0.186862	+	0.982386i	$0.559832\pi$
$164$		0			0
$165$	26.2559	−	84.3467i	0.159127	−	0.511192i
$166$		0			0
$167$			50.8326i			0.304387i	0.988351	+	0.152193i	$0.0486337\pi$
$167$			50.8326i			0.304387i	−0.988351	+	0.152193i	$0.951366\pi$
$168$		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	$-0.911655\pi$
$173$	−118.979	+	118.979i	−0.687738	+	0.687738i	0.273993	+	0.961732i	$0.411655\pi$
$174$		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	$-0.512814\pi$
$179$	171.651	−	171.651i	0.958946	−	0.958946i	0.999190	+	0.0402443i	$0.0128136\pi$
$180$		0			0
$181$	144.176	−	144.176i	0.796550	−	0.796550i	−0.186000	−	0.982550i	$-0.559552\pi$
$181$	144.176	−	144.176i	0.796550	−	0.796550i	0.982550	+	0.186000i	$0.0595524\pi$
$182$		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
$195$	144.996	+	45.1352i	0.743569	+	0.231462i
$196$		0			0
$197$	−164.712	−	164.712i	−0.836102	−	0.836102i	0.152241	−	0.988343i	$-0.451351\pi$
$197$	−164.712	−	164.712i	−0.836102	−	0.836102i	−0.988343	+	0.152241i	$0.951351\pi$
$198$		0			0
$199$	141.117			0.709130			0.354565	−	0.935031i	$-0.384629\pi$
$199$	141.117			0.709130			0.354565	+	0.935031i	$0.384629\pi$
$200$		0			0
$201$		−	16.2913i		−	0.0810511i
$202$		0			0
$203$	94.5182	−	94.5182i	0.465607	−	0.465607i
$204$		0			0
$205$	113.096	−	363.318i	0.551686	−	1.77228i
$206$		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	$-0.560925\pi$
$211$	167.007	−	167.007i	0.791502	−	0.791502i	0.981738	+	0.190236i	$0.0609254\pi$
$212$		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	0.967865	−	0.251472i	$-0.0809147\pi$
$227$	162.621	+	162.621i	0.716392	+	0.716392i	−0.251472	+	0.967865i	$0.580915\pi$
$228$		0			0
$229$	6.11249	−	6.11249i	0.0266921	−	0.0266921i	−0.693635	−	0.720327i	$-0.743992\pi$
$229$	6.11249	−	6.11249i	0.0266921	−	0.0266921i	0.720327	+	0.693635i	$0.243992\pi$
$230$		0			0
$231$	88.5078			0.383150
$232$		0			0
$233$	121.619			0.521968			0.260984	−	0.965343i	$-0.415953\pi$
$233$	121.619			0.521968			0.260984	+	0.965343i	$0.415953\pi$
$234$		0			0
$235$	282.232	+	87.8549i	1.20099	+	0.373850i
$236$		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
$245$	−114.120	−	35.5240i	−0.465796	−	0.144996i
$246$		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	$-0.384486\pi$
$251$	−145.552	−	145.552i	−0.579888	−	0.579888i	−0.934872	+	0.354984i	$0.884486\pi$
$252$		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	$0.123633\pi$
$263$			199.203i			0.757427i	−0.925514	+	0.378713i	$0.876367\pi$
$264$		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	0.790906	−	0.611938i	$-0.209610\pi$
$269$	48.1424	+	48.1424i	0.178968	+	0.178968i	−0.611938	+	0.790906i	$0.709610\pi$
$270$		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
$275$	41.1056	+	223.555i	0.149475	+	0.812927i
$276$		0			0
$277$	−68.3059	−	68.3059i	−0.246592	−	0.246592i	0.572979	−	0.819570i	$-0.305788\pi$
$277$	−68.3059	−	68.3059i	−0.246592	−	0.246592i	−0.819570	+	0.572979i	$0.805788\pi$
$278$		0			0
$279$	172.352			0.617749
$280$		0			0
$281$			131.237i			0.467035i	0.972353	+	0.233517i	$0.0750236\pi$
$281$			131.237i			0.467035i	−0.972353	+	0.233517i	$0.924976\pi$
$282$		0			0
$283$	−386.539	+	386.539i	−1.36586	+	1.36586i	−0.499618	+	0.866246i	$0.666526\pi$
$283$	−386.539	+	386.539i	−1.36586	+	1.36586i	−0.866246	+	0.499618i	$0.833474\pi$
$284$		0			0
$285$	230.126	+	71.6350i	0.807461	+	0.251351i
$286$		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	$-0.0708400\pi$
$293$	221.104	+	221.104i	0.754620	+	0.754620i	−0.220718	+	0.975338i	$0.570840\pi$
$294$		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	0.563861	−	0.825870i	$-0.309315\pi$
$307$	−80.4368	−	80.4368i	−0.262009	−	0.262009i	−0.825870	+	0.563861i	$0.809315\pi$
$308$		0			0
$309$	64.9165	−	64.9165i	0.210086	−	0.210086i
$310$		0			0
$311$	−433.169			−1.39283			−0.696413	−	0.717641i	$-0.745222\pi$
$311$	−433.169			−1.39283			−0.696413	+	0.717641i	$0.745222\pi$
$312$		0			0
$313$	−269.601			−0.861346			−0.430673	−	0.902508i	$-0.641724\pi$
$313$	−269.601			−0.861346			−0.430673	+	0.902508i	$0.641724\pi$
$314$		0			0
$315$	124.936	+	38.8909i	0.396623	+	0.123463i
$316$		0			0
$317$	20.0627	−	20.0627i	0.0632894	−	0.0632894i	−0.674754	−	0.738043i	$-0.735750\pi$
$317$	20.0627	−	20.0627i	0.0632894	−	0.0632894i	0.738043	+	0.674754i	$0.235750\pi$
$318$		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
$325$	−384.301	+	70.6625i	−1.18247	+	0.217423i
$326$		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	$-0.362848\pi$
$331$	−162.499	−	162.499i	−0.490933	−	0.490933i	−0.908600	+	0.417667i	$0.862848\pi$
$332$		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	−0.880395	−	0.474241i	$-0.842722\pi$
$347$	−140.935	+	140.935i	−0.406154	+	0.406154i	0.474241	+	0.880395i	$0.342722\pi$
$348$		0			0
$349$	−94.5429	−	94.5429i	−0.270897	−	0.270897i	0.558564	−	0.829461i	$-0.311352\pi$
$349$	−94.5429	−	94.5429i	−0.270897	−	0.270897i	−0.829461	+	0.558564i	$0.811352\pi$
$350$		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
$355$	123.732	+	38.5161i	0.348542	+	0.108496i
$356$		0			0
$357$	102.082	+	102.082i	0.285945	+	0.285945i
$358$		0			0
$359$	−701.851			−1.95502			−0.977508	−	0.210899i	$-0.932361\pi$
$359$	−701.851			−1.95502			−0.977508	+	0.210899i	$0.932361\pi$
$360$		0			0
$361$		−	254.354i		−	0.704582i
$362$		0			0
$363$	52.6722	−	52.6722i	0.145103	−	0.145103i
$364$		0			0
$365$	149.024	+	46.3889i	0.408284	+	0.127093i
$366$		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	0.992852	+	0.119356i	$0.0380829\pi$
$373$	414.853	+	414.853i	1.11221	+	1.11221i	0.119356	+	0.992852i	$0.461917\pi$
$374$		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	$-0.179607\pi$
$379$	117.567	+	117.567i	0.310204	+	0.310204i	−0.534784	+	0.844989i	$0.679607\pi$
$380$		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	−0.747305	−	0.664481i	$-0.768653\pi$
$389$	−32.2185	+	32.2185i	−0.0828240	+	0.0828240i	0.664481	+	0.747305i	$0.268653\pi$
$390$		0			0
$391$	64.8726			0.165915
$392$		0			0
$393$	−137.861			−0.350792
$394$		0			0
$395$	181.384	−	582.694i	0.459201	−	1.47517i
$396$		0			0
$397$	105.079	−	105.079i	0.264682	−	0.264682i	−0.562271	−	0.826953i	$-0.690072\pi$
$397$	105.079	−	105.079i	0.264682	−	0.264682i	0.826953	+	0.562271i	$0.190072\pi$
$398$		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
$405$	−31.9581	−	9.94810i	−0.0789089	−	0.0245632i
$406$		0			0
$407$		−	232.713i		−	0.571775i
$408$		0			0
$409$			455.293i			1.11318i	0.830786	+	0.556592i	$0.187891\pi$
$409$			455.293i			1.11318i	−0.830786	+	0.556592i	$0.812109\pi$
$410$		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	$-0.916586\pi$
$419$	−296.148	+	296.148i	−0.706797	+	0.706797i	0.259063	+	0.965860i	$0.416586\pi$
$420$		0			0
$421$	354.858	−	354.858i	0.842893	−	0.842893i	−0.146341	−	0.989234i	$-0.546750\pi$
$421$	354.858	−	354.858i	0.842893	−	0.842893i	0.989234	+	0.146341i	$0.0467496\pi$
$422$		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
$435$	77.0537	−	247.534i	0.177135	−	0.569043i
$436$		0			0
$437$	76.7292	+	76.7292i	0.175582	+	0.175582i
$438$		0			0
$439$	249.750			0.568907			0.284453	−	0.958690i	$-0.408188\pi$
$439$	249.750			0.568907			0.284453	+	0.958690i	$0.408188\pi$
$440$		0			0
$441$		−	124.875i		−	0.283164i
$442$		0			0
$443$	−121.031	+	121.031i	−0.273208	+	0.273208i	−0.830390	−	0.557182i	$-0.811882\pi$
$443$	−121.031	+	121.031i	−0.273208	+	0.273208i	0.557182	+	0.830390i	$0.311882\pi$
$444$		0			0
$445$	−126.901	+	407.668i	−0.285171	+	0.916107i
$446$		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	$-0.629285\pi$
$457$	−361.107			−0.790169			−0.395085	+	0.918645i	$0.629285\pi$
$458$		0			0
$459$	289.849	+	289.849i	0.631479	+	0.631479i
$460$		0			0
$461$	166.498	+	166.498i	0.361167	+	0.361167i	0.864243	−	0.503075i	$-0.167798\pi$
$461$	166.498	+	166.498i	0.361167	+	0.361167i	−0.503075	+	0.864243i	$0.667798\pi$
$462$		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	0.451816	−	0.892111i	$-0.350776\pi$
$467$	−205.618	−	205.618i	−0.440295	−	0.440295i	−0.892111	+	0.451816i	$0.850776\pi$
$468$		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
$475$	−609.933	+	112.150i	−1.28407	+	0.236105i
$476$		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
$485$	24.3593	−	78.2537i	0.0502253	−	0.161348i
$486$		0			0
$487$			267.618i			0.549523i	0.961512	+	0.274762i	$0.0885989\pi$
$487$			267.618i			0.549523i	−0.961512	+	0.274762i	$0.911401\pi$
$488$		0			0
$489$			356.347i			0.728725i
$490$		0			0
$491$	41.1597	+	41.1597i	0.0838283	+	0.0838283i	0.747778	−	0.663949i	$-0.231121\pi$
$491$	41.1597	+	41.1597i	0.0838283	+	0.0838283i	−0.663949	+	0.747778i	$0.731121\pi$
$492$		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	$-0.674724\pi$
$499$	165.335	−	165.335i	0.331332	−	0.331332i	0.853092	+	0.521760i	$0.174724\pi$
$500$		0			0
$501$	−69.8464	+	69.8464i	−0.139414	+	0.139414i
$502$		0			0
$503$		−	427.936i		−	0.850767i	−0.905013	−	0.425384i	$-0.860139\pi$
$503$		−	427.936i		−	0.850767i	0.905013	−	0.425384i	$-0.139861\pi$
$504$		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	0.996664	−	0.0816082i	$-0.0260056\pi$
$509$	465.764	+	465.764i	0.915056	+	0.915056i	−0.0816082	+	0.996664i	$0.526006\pi$
$510$		0			0
$511$			156.375i			0.306018i
$512$		0			0
$513$			685.647i			1.33654i
$514$		0			0
$515$	−70.2101	+	225.549i	−0.136330	+	0.437958i
$516$		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	$-0.918787\pi$
$521$		−	262.979i		−	0.504758i	0.967628	−	0.252379i	$-0.0812129\pi$
$522$		0			0
$523$	−142.934	+	142.934i	−0.273296	+	0.273296i	−0.830426	−	0.557129i	$-0.811903\pi$
$523$	−142.934	+	142.934i	−0.273296	+	0.273296i	0.557129	+	0.830426i	$0.311903\pi$
$524$		0			0
$525$	239.352	−	44.0103i	0.455908	−	0.0838291i
$526$		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	0.877135	−	0.480243i	$-0.159452\pi$
$541$	214.719	+	214.719i	0.396892	+	0.396892i	−0.480243	+	0.877135i	$0.659452\pi$
$542$		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	0.896268	−	0.443513i	$-0.146268\pi$
$547$	247.657	+	247.657i	0.452754	+	0.452754i	−0.443513	+	0.896268i	$0.646268\pi$
$548$		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
$555$	−73.9126	+	237.443i	−0.133176	+	0.427825i
$556$		0			0
$557$	252.575	−	252.575i	0.453456	−	0.453456i	−0.443044	−	0.896500i	$-0.646101\pi$
$557$	252.575	−	252.575i	0.453456	−	0.453456i	0.896500	+	0.443044i	$0.146101\pi$
$558$		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	0.907784	−	0.419439i	$-0.137773\pi$
$563$	274.938	+	274.938i	0.488345	+	0.488345i	−0.419439	+	0.907784i	$0.637773\pi$
$564$		0			0
$565$	70.8084	−	227.471i	0.125325	−	0.402603i
$566$		0			0
$567$		−	33.5347i		−	0.0591441i
$568$		0			0
$569$			985.556i			1.73208i	0.499971	+	0.866042i	$0.333344\pi$
$569$			985.556i			1.73208i	−0.499971	+	0.866042i	$0.666656\pi$
$570$		0			0
$571$	−246.409	−	246.409i	−0.431539	−	0.431539i	0.457613	−	0.889152i	$-0.348705\pi$
$571$	−246.409	−	246.409i	−0.431539	−	0.431539i	−0.889152	+	0.457613i	$0.848705\pi$
$572$		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	−0.0473610	−	0.998878i	$-0.515081\pi$
$587$	558.540	−	558.540i	0.951517	−	0.951517i	0.998878	+	0.0473610i	$0.0150811\pi$
$588$		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
$595$	−354.679	−	110.406i	−0.596099	−	0.185557i
$596$		0			0
$597$	193.901	+	193.901i	0.324793	+	0.324793i
$598$		0			0
$599$	238.766			0.398607			0.199304	−	0.979938i	$-0.436132\pi$
$599$	238.766			0.398607			0.199304	+	0.979938i	$0.436132\pi$
$600$		0			0
$601$			307.946i			0.512390i	0.966625	+	0.256195i	$0.0824688\pi$
$601$			307.946i			0.512390i	−0.966625	+	0.256195i	$0.917531\pi$
$602$		0			0
$603$	−30.9688	+	30.9688i	−0.0513579	+	0.0513579i
$604$		0			0
$605$	−56.9673	+	183.007i	−0.0941609	+	0.302490i
$606$		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	$-0.116518\pi$
$613$	352.976	+	352.976i	0.575817	+	0.575817i	−0.357931	+	0.933748i	$0.616518\pi$
$614$		0			0
$615$	654.615	−	343.817i	1.06442	−	0.559053i
$616$		0			0
$617$	188.628			0.305719			0.152859	−	0.988248i	$-0.451152\pi$
$617$	188.628			0.305719			0.152859	+	0.988248i	$0.451152\pi$
$618$		0			0
$619$	387.137	+	387.137i	0.625424	+	0.625424i	0.946913	−	0.321490i	$-0.104183\pi$
$619$	387.137	+	387.137i	0.625424	+	0.625424i	−0.321490	+	0.946913i	$0.604183\pi$
$620$		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	$-0.353159\pi$
$631$	561.749			0.890252			0.445126	+	0.895468i	$0.353159\pi$
$632$		0			0
$633$	458.951			0.725041
$634$		0			0
$635$	−853.682	−	265.739i	−1.34438	−	0.418487i
$636$		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	0.972389	+	0.233364i	$0.0749735\pi$
$643$	775.300	+	775.300i	1.20575	+	1.20575i	0.233364	+	0.972389i	$0.425027\pi$
$644$		0			0
$645$	251.642	+	78.3325i	0.390142	+	0.121446i
$646$		0			0
$647$		−	5.25109i		−	0.00811606i	−0.999992	−	0.00405803i	$-0.998708\pi$
$647$		−	5.25109i		−	0.00811606i	0.999992	−	0.00405803i	$-0.00129171\pi$
$648$		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	$-0.755273\pi$
$653$	−15.2963	+	15.2963i	−0.0234247	+	0.0234247i	0.695297	+	0.718722i	$0.255273\pi$
$654$		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	$-0.616995\pi$
$659$	378.187	−	378.187i	0.573880	−	0.573880i	0.933211	+	0.359330i	$0.116995\pi$
$660$		0			0
$661$	42.5546	−	42.5546i	0.0643791	−	0.0643791i	−0.674184	−	0.738563i	$-0.735505\pi$
$661$	42.5546	−	42.5546i	0.0643791	−	0.0643791i	0.738563	+	0.674184i	$0.235505\pi$
$662$		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
$675$	679.607	−	124.961i	1.00683	−	0.185128i
$676$		0			0
$677$	−71.0492	−	71.0492i	−0.104947	−	0.104947i	0.652684	−	0.757631i	$-0.273643\pi$
$677$	−71.0492	−	71.0492i	−0.104947	−	0.104947i	−0.757631	+	0.652684i	$0.773643\pi$
$678$		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	−0.503379	−	0.864066i	$-0.667910\pi$
$683$	246.349	−	246.349i	0.360687	−	0.360687i	0.864066	+	0.503379i	$0.167910\pi$
$684$		0			0
$685$	22.5401	+	7.01641i	0.0329052	+	0.0102429i
$686$		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	$-0.692216\pi$
$691$	176.426	−	176.426i	0.255320	−	0.255320i	0.823148	+	0.567827i	$0.192216\pi$
$692$		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	−0.999779	−	0.0210094i	$-0.993312\pi$
$701$	−715.573	−	715.573i	−1.02079	−	1.02079i	−0.0210094	−	0.999779i	$-0.506688\pi$
$702$		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	−0.457128	−	0.889401i	$-0.651122\pi$
$709$	306.482	−	306.482i	0.432273	−	0.432273i	0.889401	+	0.457128i	$0.151122\pi$
$710$		0			0
$711$	637.611			0.896780
$712$		0			0
$713$	144.320			0.202413
$714$		0			0
$715$	678.427	+	211.185i	0.948849	+	0.295363i
$716$		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
$725$	120.633	+	656.070i	0.166391	+	0.904925i
$726$		0			0
$727$			370.209i			0.509228i	0.967043	+	0.254614i	$0.0819484\pi$
$727$			370.209i			0.509228i	−0.967043	+	0.254614i	$0.918052\pi$
$728$		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	$-0.543354\pi$
$733$	626.686	−	626.686i	0.854960	−	0.854960i	0.990739	+	0.135779i	$0.0433536\pi$
$734$		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	$-0.628674\pi$
$739$	388.772	−	388.772i	0.526078	−	0.526078i	0.919401	+	0.393322i	$0.128674\pi$
$740$		0			0
$741$	532.741	−	532.741i	0.718949	−	0.718949i
$742$		0			0
$743$			121.878i			0.164035i	0.996631	+	0.0820173i	$0.0261363\pi$
$743$			121.878i			0.164035i	−0.996631	+	0.0820173i	$0.973864\pi$
$744$		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
$755$	−455.067	−	141.656i	−0.602737	−	0.187624i
$756$		0			0
$757$	129.143	+	129.143i	0.170599	+	0.170599i	0.787242	−	0.616644i	$-0.211508\pi$
$757$	129.143	+	129.143i	0.170599	+	0.170599i	−0.616644	+	0.787242i	$0.711508\pi$
$758$		0			0
$759$	77.2849			0.101825
$760$		0			0
$761$		−	352.217i		−	0.462835i	−0.972855	−	0.231417i	$-0.925664\pi$
$761$		−	352.217i		−	0.462835i	0.972855	−	0.231417i	$-0.0743363\pi$
$762$		0			0
$763$	651.169	−	651.169i	0.853433	−	0.853433i
$764$		0			0
$765$	−369.860	−	115.132i	−0.483477	−	0.150499i
$766$		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	$-0.286207\pi$
$773$	−124.080	−	124.080i	−0.160518	−	0.160518i	−0.782796	+	0.622278i	$0.786207\pi$
$774$		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	0.197748	−	0.980253i	$-0.436637\pi$
$787$	−615.831	−	615.831i	−0.782505	−	0.782505i	−0.980253	+	0.197748i	$0.936637\pi$
$788$		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
$795$	87.9704	−	282.603i	0.110655	−	0.355476i
$796$		0			0
$797$	−56.7101	+	56.7101i	−0.0711545	+	0.0711545i	−0.741788	−	0.670634i	$-0.766022\pi$
$797$	−56.7101	+	56.7101i	−0.0711545	+	0.0711545i	0.670634	+	0.741788i	$0.266022\pi$
$798$		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
$805$	104.616	+	32.5656i	0.129958	+	0.0404542i
$806$		0			0
$807$			132.300i			0.163940i
$808$		0			0
$809$		−	556.339i		−	0.687688i	−0.939027	−	0.343844i	$-0.888271\pi$
$809$		−	556.339i		−	0.687688i	0.939027	−	0.343844i	$-0.111729\pi$
$810$		0			0
$811$	993.474	+	993.474i	1.22500	+	1.22500i	0.965833	+	0.259166i	$0.0834477\pi$
$811$	993.474	+	993.474i	1.22500	+	1.22500i	0.259166	+	0.965833i	$0.416552\pi$
$812$		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	−0.975442	−	0.220255i	$-0.929311\pi$
$821$	−620.009	+	620.009i	−0.755188	+	0.755188i	0.220255	+	0.975442i	$0.429311\pi$
$822$		0			0
$823$			646.223i			0.785204i	0.919708	+	0.392602i	$0.128425\pi$
$823$			646.223i			0.785204i	−0.919708	+	0.392602i	$0.871575\pi$
$824$		0			0
$825$	−250.694	+	363.656i	−0.303872	+	0.440796i
$826$		0			0
$827$	−836.004	+	836.004i	−1.01089	+	1.01089i	−0.0109471	+	0.999940i	$0.503485\pi$
$827$	−836.004	+	836.004i	−1.01089	+	1.01089i	−0.999940	+	0.0109471i	$0.996515\pi$
$828$		0			0
$829$	234.984	+	234.984i	0.283454	+	0.283454i	0.834485	−	0.551031i	$-0.185765\pi$
$829$	234.984	+	234.984i	0.283454	+	0.283454i	−0.551031	+	0.834485i	$0.685765\pi$
$830$		0			0
$831$		−	187.711i		−	0.225886i
$832$		0			0
$833$			354.506i			0.425578i
$834$		0			0
$835$	75.5420	−	242.677i	0.0904694	−	0.290631i
$836$		0			0
$837$	644.819	+	644.819i	0.770393	+	0.770393i
$838$		0			0
$839$	−219.575			−0.261711			−0.130855	−	0.991401i	$-0.541772\pi$
$839$	−219.575			−0.261711			−0.130855	+	0.991401i	$0.541772\pi$
$840$		0			0
$841$		−	129.031i		−	0.153425i
$842$		0			0
$843$	−180.326	+	180.326i	−0.213909	+	0.213909i
$844$		0			0
$845$	−111.887	+	359.433i	−0.132410	+	0.425365i
$846$		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	$-0.237576\pi$
$853$	47.0723	+	47.0723i	0.0551844	+	0.0551844i	−0.678976	+	0.734160i	$0.737576\pi$
$854$		0			0
$855$	−301.283	−	573.632i	−0.352378	−	0.670915i
$856$		0			0
$857$	1620.86			1.89132			0.945661	−	0.325154i	$-0.105416\pi$
$857$	1620.86			1.89132			0.945661	+	0.325154i	$0.105416\pi$
$858$		0			0
$859$	317.610	+	317.610i	0.369744	+	0.369744i	0.867384	−	0.497640i	$-0.165800\pi$
$859$	317.610	+	317.610i	0.369744	+	0.369744i	−0.497640	+	0.867384i	$0.665800\pi$
$860$		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
$875$	−492.585	+	386.627i	−0.562955	+	0.441859i
$876$		0			0
$877$	−507.991	+	507.991i	−0.579237	+	0.579237i	−0.934693	−	0.355456i	$-0.884326\pi$
$877$	−507.991	+	507.991i	−0.579237	+	0.579237i	0.355456	+	0.934693i	$0.384326\pi$
$878$		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	0.969975	−	0.243204i	$-0.0781984\pi$
$883$	641.739	+	641.739i	0.726771	+	0.726771i	−0.243204	+	0.969975i	$0.578198\pi$
$884$		0			0
$885$	−218.907	+	703.236i	−0.247353	+	0.794616i
$886$		0			0
$887$		−	172.729i		−	0.194734i	−0.995249	−	0.0973670i	$-0.968958\pi$
$887$		−	172.729i		−	0.194734i	0.995249	−	0.0973670i	$-0.0310420\pi$
$888$		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	−0.659611	−	0.751607i	$-0.729279\pi$
$907$	83.4405	−	83.4405i	0.0919962	−	0.0919962i	0.751607	+	0.659611i	$0.229279\pi$
$908$		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
$915$	104.090	−	334.386i	0.113759	−	0.365449i
$916$		0			0
$917$	251.310	+	251.310i	0.274057	+	0.274057i
$918$		0			0
$919$	−23.1013			−0.0251374			−0.0125687	−	0.999921i	$-0.504001\pi$
$919$	−23.1013			−0.0251374			−0.0125687	+	0.999921i	$0.504001\pi$
$920$		0			0
$921$		−	221.048i		−	0.240009i
$922$		0			0
$923$	286.440	−	286.440i	0.310336	−	0.310336i
$924$		0			0
$925$	−115.716	−	629.325i	−0.125098	−	0.680352i
$926$		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	$-0.327026\pi$
$937$	968.975			1.03412			0.517062	+	0.855948i	$0.327026\pi$
$938$		0			0
$939$	−370.445	−	370.445i	−0.394510	−	0.394510i
$940$		0			0
$941$	−165.112	−	165.112i	−0.175465	−	0.175465i	0.613911	−	0.789375i	$-0.289595\pi$
$941$	−165.112	−	165.112i	−0.175465	−	0.175465i	−0.789375	+	0.613911i	$0.789595\pi$
$942$		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	0.866339	−	0.499456i	$-0.166467\pi$
$947$	347.438	+	347.438i	0.366883	+	0.366883i	−0.499456	+	0.866339i	$0.666467\pi$
$948$		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	$-0.721664\pi$
$953$	−1222.59			−1.28288			−0.641442	+	0.767171i	$0.721664\pi$
$954$		0			0
$955$	−72.8432	+	234.008i	−0.0762756	+	0.245034i
$956$		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
$965$	552.792	−	1775.84i	0.572842	−	1.84024i
$966$		0			0
$967$		−	967.881i		−	1.00091i	−0.865762	−	0.500455i	$-0.833166\pi$
$967$		−	967.881i		−	1.00091i	0.865762	−	0.500455i	$-0.166834\pi$
$968$		0			0
$969$		−	714.871i		−	0.737741i
$970$		0			0
$971$	84.0735	+	84.0735i	0.0865844	+	0.0865844i	0.749072	−	0.662488i	$-0.230499\pi$
$971$	84.0735	+	84.0735i	0.0865844	+	0.0865844i	−0.662488	+	0.749072i	$0.730499\pi$
$972$		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	$0.0451762\pi$
$983$			278.089i			0.282899i	−0.989945	+	0.141449i	$0.954824\pi$
$984$		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
$995$	−673.698	−	209.713i	−0.677084	−	0.210767i
$996$		0			0
$997$	−388.829	−	388.829i	−0.389999	−	0.389999i	0.484688	−	0.874687i	$-0.338933\pi$
$997$	−388.829	−	388.829i	−0.389999	−	0.389999i	−0.874687	+	0.484688i	$0.838933\pi$
$998$		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.b.479.16		44
4.3	odd	2		640.3.k.a.479.7		44
5.4	even	2	inner	640.3.k.b.479.7		44
8.3	odd	2		320.3.k.a.239.16		44
8.5	even	2		80.3.k.a.19.3	✓	44
16.3	odd	4		80.3.k.a.59.20	yes	44
16.5	even	4		640.3.k.a.159.16		44
16.11	odd	4	inner	640.3.k.b.159.7		44
16.13	even	4		320.3.k.a.79.7		44
20.19	odd	2		640.3.k.a.479.16		44
40.13	odd	4		400.3.r.g.51.9		44
40.19	odd	2		320.3.k.a.239.7		44
40.29	even	2		80.3.k.a.19.20	yes	44
40.37	odd	4		400.3.r.g.51.14		44
80.3	even	4		400.3.r.g.251.9		44
80.19	odd	4		80.3.k.a.59.3	yes	44
80.29	even	4		320.3.k.a.79.16		44
80.59	odd	4	inner	640.3.k.b.159.16		44
80.67	even	4		400.3.r.g.251.14		44
80.69	even	4		640.3.k.a.159.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.k.a.19.3	✓	44	8.5	even	2
80.3.k.a.19.20	yes	44	40.29	even	2
80.3.k.a.59.3	yes	44	80.19	odd	4
80.3.k.a.59.20	yes	44	16.3	odd	4
320.3.k.a.79.7		44	16.13	even	4
320.3.k.a.79.16		44	80.29	even	4
320.3.k.a.239.7		44	40.19	odd	2
320.3.k.a.239.16		44	8.3	odd	2
400.3.r.g.51.9		44	40.13	odd	4
400.3.r.g.51.14		44	40.37	odd	4
400.3.r.g.251.9		44	80.3	even	4
400.3.r.g.251.14		44	80.67	even	4
640.3.k.a.159.7		44	80.69	even	4
640.3.k.a.159.16		44	16.5	even	4
640.3.k.a.479.7		44	4.3	odd	2
640.3.k.a.479.16		44	20.19	odd	2
640.3.k.b.159.7		44	16.11	odd	4	inner
640.3.k.b.159.16		44	80.59	odd	4	inner
640.3.k.b.479.7		44	5.4	even	2	inner
640.3.k.b.479.16		44	1.1	even	1	trivial

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)

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