LMFDB - Embedded newform 320.3.k.a.79.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(79,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, 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("320.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.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:	$8.71936845953$
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			79.18
Character	$\chi$	$=$	320.79
Dual form			320.3.k.a.239.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.39041 - 2.39041i) q^{3} +(-3.54593 + 3.52510i) q^{5} +5.08144i q^{7} -2.42812i q^{9} +O(q^{10})$	\(q+(2.39041 - 2.39041i) q^{3} +(-3.54593 + 3.52510i) q^{5} +5.08144i q^{7} -2.42812i q^{9} +(-9.77953 + 9.77953i) q^{11} +(16.0002 + 16.0002i) q^{13} +(-0.0497986 + 16.9027i) q^{15} -9.82261i q^{17} +(-2.54131 - 2.54131i) q^{19} +(12.1467 + 12.1467i) q^{21} +32.5737i q^{23} +(0.147309 - 24.9996i) q^{25} +(15.7095 + 15.7095i) q^{27} +(-8.31667 + 8.31667i) q^{29} -38.6552i q^{31} +46.7542i q^{33} +(-17.9126 - 18.0185i) q^{35} +(12.8743 - 12.8743i) q^{37} +76.4941 q^{39} -30.0736i q^{41} +(17.9578 + 17.9578i) q^{43} +(8.55937 + 8.60995i) q^{45} +5.99252 q^{47} +23.1790 q^{49} +(-23.4801 - 23.4801i) q^{51} +(-18.6201 + 18.6201i) q^{53} +(0.203734 - 69.1514i) q^{55} -12.1495 q^{57} +(-21.8610 + 21.8610i) q^{59} +(-80.6491 + 80.6491i) q^{61} +12.3383 q^{63} +(-113.138 - 0.333327i) q^{65} +(-51.4930 + 51.4930i) q^{67} +(77.8645 + 77.8645i) q^{69} +33.5962 q^{71} +80.6663 q^{73} +(-59.4071 - 60.1113i) q^{75} +(-49.6941 - 49.6941i) q^{77} +59.9317i q^{79} +96.9573 q^{81} +(34.7533 - 34.7533i) q^{83} +(34.6257 + 34.8303i) q^{85} +39.7605i q^{87} -64.5309i q^{89} +(-81.3041 + 81.3041i) q^{91} +(-92.4018 - 92.4018i) q^{93} +(17.9697 + 0.0529423i) q^{95} -137.264i q^{97} +(23.7459 + 23.7459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.39041	−	2.39041i	0.796803	−	0.796803i	−0.185787	−	0.982590i	$-0.559483\pi$
$3$	2.39041	−	2.39041i	0.796803	−	0.796803i	0.982590	+	0.185787i	$0.0594834\pi$
$4$		0			0
$5$	−3.54593	+	3.52510i	−0.709187	+	0.705020i
$5$	−3.54593	+	3.52510i	−0.709187	+	0.705020i
$6$		0			0
$7$			5.08144i			0.725920i	0.931805	+	0.362960i	$0.118234\pi$
$7$			5.08144i			0.725920i	−0.931805	+	0.362960i	$0.881766\pi$
$8$		0			0
$9$		−	2.42812i		−	0.269791i
$10$		0			0
$11$	−9.77953	+	9.77953i	−0.889048	+	0.889048i	−0.994432	−	0.105384i	$-0.966393\pi$
$11$	−9.77953	+	9.77953i	−0.889048	+	0.889048i	0.105384	+	0.994432i	$0.466393\pi$
$12$		0			0
$13$	16.0002	+	16.0002i	1.23079	+	1.23079i	0.963662	+	0.267123i	$0.0860732\pi$
$13$	16.0002	+	16.0002i	1.23079	+	1.23079i	0.267123	+	0.963662i	$0.413927\pi$
$14$		0			0
$15$	−0.0497986	+	16.9027i	−0.00331991	+	1.12685i
$16$		0			0
$17$		−	9.82261i		−	0.577800i	−0.957359	−	0.288900i	$-0.906710\pi$
$17$		−	9.82261i		−	0.577800i	0.957359	−	0.288900i	$-0.0932896\pi$
$18$		0			0
$19$	−2.54131	−	2.54131i	−0.133753	−	0.133753i	0.637061	−	0.770814i	$-0.280150\pi$
$19$	−2.54131	−	2.54131i	−0.133753	−	0.133753i	−0.770814	+	0.637061i	$0.780150\pi$
$20$		0			0
$21$	12.1467	+	12.1467i	0.578415	+	0.578415i
$22$		0			0
$23$			32.5737i			1.41625i	0.706088	+	0.708124i	$0.250458\pi$
$23$			32.5737i			1.41625i	−0.706088	+	0.708124i	$0.749542\pi$
$24$		0			0
$25$	0.147309	−	24.9996i	0.00589234	−	0.999983i
$26$		0			0
$27$	15.7095	+	15.7095i	0.581833	+	0.581833i
$28$		0			0
$29$	−8.31667	+	8.31667i	−0.286782	+	0.286782i	−0.835806	−	0.549025i	$-0.814999\pi$
$29$	−8.31667	+	8.31667i	−0.286782	+	0.286782i	0.549025	+	0.835806i	$0.314999\pi$
$30$		0			0
$31$		−	38.6552i		−	1.24694i	−0.781847	−	0.623471i	$-0.785722\pi$
$31$		−	38.6552i		−	1.24694i	0.781847	−	0.623471i	$-0.214278\pi$
$32$		0			0
$33$			46.7542i			1.41679i
$34$		0			0
$35$	−17.9126	−	18.0185i	−0.511788	−	0.514813i
$36$		0			0
$37$	12.8743	−	12.8743i	0.347954	−	0.347954i	−0.511393	−	0.859347i	$-0.670870\pi$
$37$	12.8743	−	12.8743i	0.347954	−	0.347954i	0.859347	+	0.511393i	$0.170870\pi$
$38$		0			0
$39$	76.4941			1.96139
$40$		0			0
$41$		−	30.0736i		−	0.733503i	−0.930319	−	0.366752i	$-0.880470\pi$
$41$		−	30.0736i		−	0.733503i	0.930319	−	0.366752i	$-0.119530\pi$
$42$		0			0
$43$	17.9578	+	17.9578i	0.417623	+	0.417623i	0.884384	−	0.466761i	$-0.154579\pi$
$43$	17.9578	+	17.9578i	0.417623	+	0.417623i	−0.466761	+	0.884384i	$0.654579\pi$
$44$		0			0
$45$	8.55937	+	8.60995i	0.190208	+	0.191332i
$46$		0			0
$47$	5.99252			0.127500			0.0637502	−	0.997966i	$-0.479694\pi$
$47$	5.99252			0.127500			0.0637502	+	0.997966i	$0.479694\pi$
$48$		0			0
$49$	23.1790			0.473040
$50$		0			0
$51$	−23.4801	−	23.4801i	−0.460393	−	0.460393i
$52$		0			0
$53$	−18.6201	+	18.6201i	−0.351323	+	0.351323i	−0.860602	−	0.509279i	$-0.829912\pi$
$53$	−18.6201	+	18.6201i	−0.351323	+	0.351323i	0.509279	+	0.860602i	$0.329912\pi$
$54$		0			0
$55$	0.203734	−	69.1514i	0.00370425	−	1.25730i
$56$		0			0
$57$	−12.1495			−0.213150
$58$		0			0
$59$	−21.8610	+	21.8610i	−0.370525	+	0.370525i	−0.867668	−	0.497143i	$-0.834382\pi$
$59$	−21.8610	+	21.8610i	−0.370525	+	0.370525i	0.497143	+	0.867668i	$0.334382\pi$
$60$		0			0
$61$	−80.6491	+	80.6491i	−1.32212	+	1.32212i	−0.410055	+	0.912061i	$0.634491\pi$
$61$	−80.6491	+	80.6491i	−1.32212	+	1.32212i	−0.912061	+	0.410055i	$0.865509\pi$
$62$		0			0
$63$	12.3383			0.195847
$64$		0			0
$65$	−113.138	−	0.333327i	−1.74059	−	0.00512811i
$66$		0			0
$67$	−51.4930	+	51.4930i	−0.768552	+	0.768552i	−0.977852	−	0.209300i	$-0.932882\pi$
$67$	−51.4930	+	51.4930i	−0.768552	+	0.768552i	0.209300	+	0.977852i	$0.432882\pi$
$68$		0			0
$69$	77.8645	+	77.8645i	1.12847	+	1.12847i
$70$		0			0
$71$	33.5962			0.473186			0.236593	−	0.971609i	$-0.423969\pi$
$71$	33.5962			0.473186			0.236593	+	0.971609i	$0.423969\pi$
$72$		0			0
$73$	80.6663			1.10502			0.552509	−	0.833507i	$-0.313670\pi$
$73$	80.6663			1.10502			0.552509	+	0.833507i	$0.313670\pi$
$74$		0			0
$75$	−59.4071	−	60.1113i	−0.792094	−	0.801485i
$76$		0			0
$77$	−49.6941	−	49.6941i	−0.645377	−	0.645377i
$78$		0			0
$79$			59.9317i			0.758629i	0.925268	+	0.379315i	$0.123840\pi$
$79$			59.9317i			0.758629i	−0.925268	+	0.379315i	$0.876160\pi$
$80$		0			0
$81$	96.9573			1.19700
$82$		0			0
$83$	34.7533	−	34.7533i	0.418715	−	0.418715i	−0.466046	−	0.884761i	$-0.654322\pi$
$83$	34.7533	−	34.7533i	0.418715	−	0.418715i	0.884761	+	0.466046i	$0.154322\pi$
$84$		0			0
$85$	34.6257	+	34.8303i	0.407361	+	0.409769i
$86$		0			0
$87$			39.7605i			0.457017i
$88$		0			0
$89$		−	64.5309i		−	0.725067i	−0.931971	−	0.362533i	$-0.881912\pi$
$89$		−	64.5309i		−	0.725067i	0.931971	−	0.362533i	$-0.118088\pi$
$90$		0			0
$91$	−81.3041	+	81.3041i	−0.893452	+	0.893452i
$92$		0			0
$93$	−92.4018	−	92.4018i	−0.993567	−	0.993567i
$94$		0			0
$95$	17.9697	+	0.0529423i	0.189155	+	0.000557287i
$96$		0			0
$97$		−	137.264i		−	1.41509i	−0.706669	−	0.707544i	$-0.749803\pi$
$97$		−	137.264i		−	1.41509i	0.706669	−	0.707544i	$-0.250197\pi$
$98$		0			0
$99$	23.7459	+	23.7459i	0.239857	+	0.239857i
$100$		0			0
$101$	−115.953	−	115.953i	−1.14805	−	1.14805i	−0.986937	−	0.161109i	$-0.948493\pi$
$101$	−115.953	−	115.953i	−1.14805	−	1.14805i	−0.161109	−	0.986937i	$-0.551507\pi$
$102$		0			0
$103$		−	87.5329i		−	0.849834i	−0.905232	−	0.424917i	$-0.860303\pi$
$103$		−	87.5329i		−	0.849834i	0.905232	−	0.424917i	$-0.139697\pi$
$104$		0			0
$105$	−85.8899	−	0.253049i	−0.817999	−	0.00240999i
$106$		0			0
$107$	−25.2243	−	25.2243i	−0.235741	−	0.235741i	0.579343	−	0.815084i	$-0.303309\pi$
$107$	−25.2243	−	25.2243i	−0.235741	−	0.235741i	−0.815084	+	0.579343i	$0.803309\pi$
$108$		0			0
$109$	104.801	−	104.801i	0.961474	−	0.961474i	−0.0378105	−	0.999285i	$-0.512038\pi$
$109$	104.801	−	104.801i	0.961474	−	0.961474i	0.999285	+	0.0378105i	$0.0120383\pi$
$110$		0			0
$111$		−	61.5496i		−	0.554501i
$112$		0			0
$113$			27.4328i			0.242769i	0.992606	+	0.121384i	$0.0387333\pi$
$113$			27.4328i			0.242769i	−0.992606	+	0.121384i	$0.961267\pi$
$114$		0			0
$115$	−114.826	−	115.504i	−0.998483	−	1.00438i
$116$		0			0
$117$	38.8504	−	38.8504i	0.332055	−	0.332055i
$118$		0			0
$119$	49.9130			0.419437
$120$		0			0
$121$		−	70.2782i		−	0.580812i
$122$		0			0
$123$	−71.8883	−	71.8883i	−0.584458	−	0.584458i
$124$		0			0
$125$	87.6037	+	89.1661i	0.700829	+	0.713329i
$126$		0			0
$127$	33.5455			0.264138			0.132069	−	0.991241i	$-0.457838\pi$
$127$	33.5455			0.264138			0.132069	+	0.991241i	$0.457838\pi$
$128$		0			0
$129$	85.8529			0.665526
$130$		0			0
$131$	105.904	+	105.904i	0.808428	+	0.808428i	0.984396	−	0.175968i	$-0.0563055\pi$
$131$	105.904	+	105.904i	0.808428	+	0.808428i	−0.175968	+	0.984396i	$0.556305\pi$
$132$		0			0
$133$	12.9135	−	12.9135i	0.0970941	−	0.0970941i
$134$		0			0
$135$	−111.082	−	0.327271i	−0.822832	−	0.00242423i
$136$		0			0
$137$	−102.458			−0.747868			−0.373934	−	0.927455i	$-0.621991\pi$
$137$	−102.458			−0.747868			−0.373934	+	0.927455i	$0.621991\pi$
$138$		0			0
$139$	153.879	−	153.879i	1.10704	−	1.10704i	0.113502	−	0.993538i	$-0.463793\pi$
$139$	153.879	−	153.879i	1.10704	−	1.10704i	0.993538	−	0.113502i	$-0.0362069\pi$
$140$		0			0
$141$	14.3246	−	14.3246i	0.101593	−	0.101593i
$142$		0			0
$143$	−312.949			−2.18845
$144$		0			0
$145$	0.173258	−	58.8075i	0.00119489	−	0.405569i
$146$		0			0
$147$	55.4073	−	55.4073i	0.376920	−	0.376920i
$148$		0			0
$149$	121.007	+	121.007i	0.812126	+	0.812126i	0.984952	−	0.172826i	$-0.0552898\pi$
$149$	121.007	+	121.007i	0.812126	+	0.812126i	−0.172826	+	0.984952i	$0.555290\pi$
$150$		0			0
$151$	−120.496			−0.797990			−0.398995	−	0.916953i	$-0.630641\pi$
$151$	−120.496			−0.797990			−0.398995	+	0.916953i	$0.630641\pi$
$152$		0			0
$153$	−23.8505			−0.155885
$154$		0			0
$155$	136.264	+	137.069i	0.879119	+	0.884315i
$156$		0			0
$157$	146.326	+	146.326i	0.932012	+	0.932012i	0.997832	−	0.0658192i	$-0.0209660\pi$
$157$	146.326	+	146.326i	0.932012	+	0.932012i	−0.0658192	+	0.997832i	$0.520966\pi$
$158$		0			0
$159$			89.0194i			0.559870i
$160$		0			0
$161$	−165.521			−1.02808
$162$		0			0
$163$	208.182	−	208.182i	1.27719	−	1.27719i	0.334954	−	0.942235i	$-0.391279\pi$
$163$	208.182	−	208.182i	1.27719	−	1.27719i	0.942235	−	0.334954i	$-0.108721\pi$
$164$		0			0
$165$	−164.813	−	165.787i	−0.998868	−	1.00477i
$166$		0			0
$167$		−	114.093i		−	0.683193i	−0.939847	−	0.341597i	$-0.889032\pi$
$167$		−	114.093i		−	0.683193i	0.939847	−	0.341597i	$-0.110968\pi$
$168$		0			0
$169$			343.014i			2.02967i
$170$		0			0
$171$	−6.17061	+	6.17061i	−0.0360854	+	0.0360854i
$172$		0			0
$173$	−107.166	−	107.166i	−0.619456	−	0.619456i	0.325936	−	0.945392i	$-0.394321\pi$
$173$	−107.166	−	107.166i	−0.619456	−	0.619456i	−0.945392	+	0.325936i	$0.894321\pi$
$174$		0			0
$175$	127.034	+	0.748540i	0.725907	+	0.00427737i
$176$		0			0
$177$			104.513i			0.590471i
$178$		0			0
$179$	158.081	+	158.081i	0.883132	+	0.883132i	0.993852	−	0.110719i	$-0.0353154\pi$
$179$	158.081	+	158.081i	0.883132	+	0.883132i	−0.110719	+	0.993852i	$0.535315\pi$
$180$		0			0
$181$	−57.5726	−	57.5726i	−0.318081	−	0.318081i	0.529949	−	0.848030i	$-0.322211\pi$
$181$	−57.5726	−	57.5726i	−0.318081	−	0.318081i	−0.848030	+	0.529949i	$0.822211\pi$
$182$		0			0
$183$			385.569i			2.10693i
$184$		0			0
$185$	−0.268206	+	91.0345i	−0.00144976	+	0.492079i
$186$		0			0
$187$	96.0604	+	96.0604i	0.513692	+	0.513692i
$188$		0			0
$189$	−79.8268	+	79.8268i	−0.422364	+	0.422364i
$190$		0			0
$191$		−	116.104i		−	0.607875i	−0.952692	−	0.303937i	$-0.901699\pi$
$191$		−	116.104i		−	0.607875i	0.952692	−	0.303937i	$-0.0983013\pi$
$192$		0			0
$193$			28.9615i			0.150059i	0.997181	+	0.0750297i	$0.0239052\pi$
$193$			28.9615i			0.150059i	−0.997181	+	0.0750297i	$0.976095\pi$
$194$		0			0
$195$	−271.243	+	269.650i	−1.39099	+	1.38282i
$196$		0			0
$197$	−118.620	+	118.620i	−0.602131	+	0.602131i	−0.940878	−	0.338746i	$-0.889997\pi$
$197$	−118.620	+	118.620i	−0.602131	+	0.602131i	0.338746	+	0.940878i	$0.389997\pi$
$198$		0			0
$199$	11.1379			0.0559694			0.0279847	−	0.999608i	$-0.491091\pi$
$199$	11.1379			0.0559694			0.0279847	+	0.999608i	$0.491091\pi$
$200$		0			0
$201$			246.179i			1.22477i
$202$		0			0
$203$	−42.2606	−	42.2606i	−0.208180	−	0.208180i
$204$		0			0
$205$	106.013	+	106.639i	0.517135	+	0.520191i
$206$		0			0
$207$	79.0928			0.382091
$208$		0			0
$209$	49.7056			0.237826
$210$		0			0
$211$	0.884244	+	0.884244i	0.00419073	+	0.00419073i	0.709199	−	0.705008i	$-0.249057\pi$
$211$	0.884244	+	0.884244i	0.00419073	+	0.00419073i	−0.705008	+	0.709199i	$0.749057\pi$
$212$		0			0
$213$	80.3086	−	80.3086i	0.377036	−	0.377036i
$214$		0			0
$215$	−126.980	−	0.374108i	−0.590605	−	0.00174004i
$216$		0			0
$217$	196.424			0.905180
$218$		0			0
$219$	192.826	−	192.826i	0.880482	−	0.880482i
$220$		0			0
$221$	157.164	−	157.164i	0.711149	−	0.711149i
$222$		0			0
$223$	241.623			1.08351			0.541755	−	0.840536i	$-0.317760\pi$
$223$	241.623			1.08351			0.541755	+	0.840536i	$0.317760\pi$
$224$		0			0
$225$	−60.7019	−	0.357683i	−0.269786	−	0.00158970i
$226$		0			0
$227$	−240.523	+	240.523i	−1.05957	+	1.05957i	−0.0614631	+	0.998109i	$0.519577\pi$
$227$	−240.523	+	240.523i	−1.05957	+	1.05957i	−0.998109	+	0.0614631i	$0.980423\pi$
$228$		0			0
$229$	−121.946	−	121.946i	−0.532514	−	0.532514i	0.388806	−	0.921320i	$-0.372888\pi$
$229$	−121.946	−	121.946i	−0.532514	−	0.532514i	−0.921320	+	0.388806i	$0.872888\pi$
$230$		0			0
$231$	−237.578			−1.02848
$232$		0			0
$233$	292.240			1.25425			0.627125	−	0.778918i	$-0.284231\pi$
$233$	292.240			1.25425			0.627125	+	0.778918i	$0.284231\pi$
$234$		0			0
$235$	−21.2491	+	21.1242i	−0.0904216	+	0.0898903i
$236$		0			0
$237$	143.261	+	143.261i	0.604478	+	0.604478i
$238$		0			0
$239$		−	60.9550i		−	0.255042i	−0.991836	−	0.127521i	$-0.959298\pi$
$239$		−	60.9550i		−	0.255042i	0.991836	−	0.127521i	$-0.0407020\pi$
$240$		0			0
$241$	83.2832			0.345573			0.172787	−	0.984959i	$-0.444723\pi$
$241$	83.2832			0.345573			0.172787	+	0.984959i	$0.444723\pi$
$242$		0			0
$243$	90.3823	−	90.3823i	0.371944	−	0.371944i
$244$		0			0
$245$	−82.1911	+	81.7083i	−0.335474	+	0.333503i
$246$		0			0
$247$		−	81.3230i		−	0.329243i
$248$		0			0
$249$		−	166.149i		−	0.667266i
$250$		0			0
$251$	195.109	−	195.109i	0.777326	−	0.777326i	−0.202049	−	0.979375i	$-0.564760\pi$
$251$	195.109	−	195.109i	0.777326	−	0.777326i	0.979375	+	0.202049i	$0.0647601\pi$
$252$		0			0
$253$	−318.555	−	318.555i	−1.25911	−	1.25911i
$254$		0			0
$255$	166.028	+	0.489152i	0.651092	+	0.00191824i
$256$		0			0
$257$			329.631i			1.28261i	0.767286	+	0.641305i	$0.221607\pi$
$257$			329.631i			1.28261i	−0.767286	+	0.641305i	$0.778393\pi$
$258$		0			0
$259$	65.4199	+	65.4199i	0.252586	+	0.252586i
$260$		0			0
$261$	20.1939	+	20.1939i	0.0773711	+	0.0773711i
$262$		0			0
$263$			56.1771i			0.213601i	0.994280	+	0.106801i	$0.0340607\pi$
$263$			56.1771i			0.213601i	−0.994280	+	0.106801i	$0.965939\pi$
$264$		0			0
$265$	0.387906	−	131.663i	0.00146380	−	0.496843i
$266$		0			0
$267$	−154.255	−	154.255i	−0.577736	−	0.577736i
$268$		0			0
$269$	287.851	−	287.851i	1.07008	−	1.07008i	0.0727268	−	0.997352i	$-0.476830\pi$
$269$	287.851	−	287.851i	1.07008	−	1.07008i	0.997352	−	0.0727268i	$-0.0231701\pi$
$270$		0			0
$271$			287.492i			1.06086i	0.847730	+	0.530428i	$0.177969\pi$
$271$			287.492i			1.06086i	−0.847730	+	0.530428i	$0.822031\pi$
$272$		0			0
$273$			388.700i			1.42381i
$274$		0			0
$275$	243.043	+	245.925i	0.883794	+	0.894271i
$276$		0			0
$277$	−50.1607	+	50.1607i	−0.181085	+	0.181085i	−0.791829	−	0.610743i	$-0.790871\pi$
$277$	−50.1607	+	50.1607i	−0.181085	+	0.181085i	0.610743	+	0.791829i	$0.290871\pi$
$278$		0			0
$279$	−93.8594			−0.336414
$280$		0			0
$281$			105.191i			0.374347i	0.982327	+	0.187173i	$0.0599326\pi$
$281$			105.191i			0.374347i	−0.982327	+	0.187173i	$0.940067\pi$
$282$		0			0
$283$	267.270	+	267.270i	0.944417	+	0.944417i	0.998535	−	0.0541177i	$-0.0172346\pi$
$283$	267.270	+	267.270i	0.944417	+	0.944417i	−0.0541177	+	0.998535i	$0.517235\pi$
$284$		0			0
$285$	43.0815	−	42.8284i	0.151163	−	0.150275i
$286$		0			0
$287$	152.817			0.532465
$288$		0			0
$289$	192.516			0.666147
$290$		0			0
$291$	−328.116	−	328.116i	−1.12755	−	1.12755i
$292$		0			0
$293$	−134.928	+	134.928i	−0.460507	+	0.460507i	−0.898822	−	0.438315i	$-0.855576\pi$
$293$	−134.928	+	134.928i	−0.460507	+	0.460507i	0.438315	+	0.898822i	$0.355576\pi$
$294$		0			0
$295$	0.455422	−	154.580i	0.00154380	−	0.523999i
$296$		0			0
$297$	−307.263			−1.03455
$298$		0			0
$299$	−521.186	+	521.186i	−1.74310	+	1.74310i
$300$		0			0
$301$	−91.2513	+	91.2513i	−0.303160	+	0.303160i
$302$		0			0
$303$	−554.348			−1.82953
$304$		0			0
$305$	1.68014	−	570.273i	0.00550864	−	1.86975i
$306$		0			0
$307$	198.450	−	198.450i	0.646415	−	0.646415i	−0.305709	−	0.952125i	$-0.598894\pi$
$307$	198.450	−	198.450i	0.646415	−	0.646415i	0.952125	+	0.305709i	$0.0988936\pi$
$308$		0			0
$309$	−209.240	−	209.240i	−0.677151	−	0.677151i
$310$		0			0
$311$	97.0520			0.312064			0.156032	−	0.987752i	$-0.450130\pi$
$311$	97.0520			0.312064			0.156032	+	0.987752i	$0.450130\pi$
$312$		0			0
$313$	175.107			0.559446			0.279723	−	0.960081i	$-0.409757\pi$
$313$	175.107			0.559446			0.279723	+	0.960081i	$0.409757\pi$
$314$		0			0
$315$	−43.7510	+	43.4939i	−0.138892	+	0.138076i
$316$		0			0
$317$	111.108	+	111.108i	0.350498	+	0.350498i	0.860295	−	0.509797i	$-0.170279\pi$
$317$	111.108	+	111.108i	0.350498	+	0.350498i	−0.509797	+	0.860295i	$0.670279\pi$
$318$		0			0
$319$		−	162.666i		−	0.509925i
$320$		0			0
$321$	−120.593			−0.375679
$322$		0			0
$323$	−24.9623	+	24.9623i	−0.0772826	+	0.0772826i
$324$		0			0
$325$	402.355	−	397.641i	1.23802	−	1.22351i
$326$		0			0
$327$		−	501.033i		−	1.53221i
$328$		0			0
$329$			30.4506i			0.0925550i
$330$		0			0
$331$	244.119	−	244.119i	0.737521	−	0.737521i	−0.234577	−	0.972098i	$-0.575370\pi$
$331$	244.119	−	244.119i	0.737521	−	0.737521i	0.972098	+	0.234577i	$0.0753705\pi$
$332$		0			0
$333$	−31.2603	−	31.2603i	−0.0938748	−	0.0938748i
$334$		0			0
$335$	1.07274	−	364.109i	0.00320220	−	1.08689i
$336$		0			0
$337$		−	333.980i		−	0.991037i	−0.868597	−	0.495519i	$-0.834978\pi$
$337$		−	333.980i		−	0.991037i	0.868597	−	0.495519i	$-0.165022\pi$
$338$		0			0
$339$	65.5758	+	65.5758i	0.193439	+	0.193439i
$340$		0			0
$341$	378.029	+	378.029i	1.10859	+	1.10859i
$342$		0			0
$343$			366.773i			1.06931i
$344$		0			0
$345$	−550.583	−	1.62212i	−1.59589	−	0.00470181i
$346$		0			0
$347$	−43.0694	−	43.0694i	−0.124119	−	0.124119i	0.642319	−	0.766438i	$-0.277973\pi$
$347$	−43.0694	−	43.0694i	−0.124119	−	0.124119i	−0.766438	+	0.642319i	$0.777973\pi$
$348$		0			0
$349$	−206.400	+	206.400i	−0.591404	+	0.591404i	−0.938011	−	0.346607i	$-0.887334\pi$
$349$	−206.400	+	206.400i	−0.591404	+	0.591404i	0.346607	+	0.938011i	$0.387334\pi$
$350$		0			0
$351$			502.710i			1.43222i
$352$		0			0
$353$		−	86.0684i		−	0.243820i	−0.992541	−	0.121910i	$-0.961098\pi$
$353$		−	86.0684i		−	0.243820i	0.992541	−	0.121910i	$-0.0389019\pi$
$354$		0			0
$355$	−119.130	+	118.430i	−0.335577	+	0.333605i
$356$		0			0
$357$	119.312	−	119.312i	0.334209	−	0.334209i
$358$		0			0
$359$	26.9476			0.0750629			0.0375314	−	0.999295i	$-0.488051\pi$
$359$	26.9476			0.0750629			0.0375314	+	0.999295i	$0.488051\pi$
$360$		0			0
$361$		−	348.083i		−	0.964220i
$362$		0			0
$363$	−167.994	−	167.994i	−0.462793	−	0.462793i
$364$		0			0
$365$	−286.038	+	284.357i	−0.783664	+	0.779060i
$366$		0			0
$367$	−388.947			−1.05980			−0.529900	−	0.848060i	$-0.677771\pi$
$367$	−388.947			−1.05980			−0.529900	+	0.848060i	$0.677771\pi$
$368$		0			0
$369$	−73.0224			−0.197893
$370$		0			0
$371$	−94.6169	−	94.6169i	−0.255032	−	0.255032i
$372$		0			0
$373$	93.7772	−	93.7772i	0.251413	−	0.251413i	−0.570137	−	0.821550i	$-0.693110\pi$
$373$	93.7772	−	93.7772i	0.251413	−	0.251413i	0.821550	+	0.570137i	$0.193110\pi$
$374$		0			0
$375$	422.552	+	3.73485i	1.12681	+	0.00995961i
$376$		0			0
$377$	−266.137			−0.705933
$378$		0			0
$379$	−37.2892	+	37.2892i	−0.0983885	+	0.0983885i	−0.754588	−	0.656199i	$-0.772163\pi$
$379$	−37.2892	+	37.2892i	−0.0983885	+	0.0983885i	0.656199	+	0.754588i	$0.272163\pi$
$380$		0			0
$381$	80.1875	−	80.1875i	0.210466	−	0.210466i
$382$		0			0
$383$	−97.1930			−0.253768			−0.126884	−	0.991918i	$-0.540498\pi$
$383$	−97.1930			−0.253768			−0.126884	+	0.991918i	$0.540498\pi$
$384$		0			0
$385$	351.389	+	1.03526i	0.912698	+	0.00268899i
$386$		0			0
$387$	43.6036	−	43.6036i	0.112671	−	0.112671i
$388$		0			0
$389$	148.407	+	148.407i	0.381509	+	0.381509i	0.871646	−	0.490137i	$-0.163053\pi$
$389$	148.407	+	148.407i	0.381509	+	0.381509i	−0.490137	+	0.871646i	$0.663053\pi$
$390$		0			0
$391$	319.959			0.818308
$392$		0			0
$393$	506.308			1.28832
$394$		0			0
$395$	−211.265	−	212.514i	−0.534849	−	0.538010i
$396$		0			0
$397$	−188.053	−	188.053i	−0.473685	−	0.473685i	0.429420	−	0.903105i	$-0.358718\pi$
$397$	−188.053	−	188.053i	−0.473685	−	0.473685i	−0.903105	+	0.429420i	$0.858718\pi$
$398$		0			0
$399$		−	61.7372i		−	0.154730i
$400$		0			0
$401$	−692.545			−1.72705			−0.863523	−	0.504310i	$-0.831747\pi$
$401$	−692.545			−1.72705			−0.863523	+	0.504310i	$0.831747\pi$
$402$		0			0
$403$	618.491	−	618.491i	1.53472	−	1.53472i
$404$		0			0
$405$	−343.804	+	341.784i	−0.848900	+	0.843912i
$406$		0			0
$407$			251.809i			0.618695i
$408$		0			0
$409$		−	107.152i		−	0.261985i	−0.991383	−	0.130993i	$-0.958184\pi$
$409$		−	107.152i		−	0.261985i	0.991383	−	0.130993i	$-0.0418164\pi$
$410$		0			0
$411$	−244.916	+	244.916i	−0.595904	+	0.595904i
$412$		0			0
$413$	−111.085	−	111.085i	−0.268971	−	0.268971i
$414$		0			0
$415$	−0.724004	+	245.742i	−0.00174459	+	0.592149i
$416$		0			0
$417$		−	735.666i		−	1.76419i
$418$		0			0
$419$	−475.736	−	475.736i	−1.13541	−	1.13541i	−0.989263	−	0.146146i	$-0.953313\pi$
$419$	−475.736	−	475.736i	−1.13541	−	1.13541i	−0.146146	−	0.989263i	$-0.546687\pi$
$420$		0			0
$421$	264.190	+	264.190i	0.627530	+	0.627530i	0.947446	−	0.319916i	$-0.103655\pi$
$421$	264.190	+	264.190i	0.627530	+	0.627530i	−0.319916	+	0.947446i	$0.603655\pi$
$422$		0			0
$423$		−	14.5505i		−	0.0343984i
$424$		0			0
$425$	−245.561	−	1.44695i	−0.577790	−	0.00340460i
$426$		0			0
$427$	−409.813	−	409.813i	−0.959750	−	0.959750i
$428$		0			0
$429$	−748.076	+	748.076i	−1.74377	+	1.74377i
$430$		0			0
$431$		−	507.341i		−	1.17713i	−0.808451	−	0.588563i	$-0.799694\pi$
$431$		−	507.341i		−	1.17713i	0.808451	−	0.588563i	$-0.200306\pi$
$432$		0			0
$433$			495.619i			1.14462i	0.820039	+	0.572308i	$0.193952\pi$
$433$			495.619i			1.14462i	−0.820039	+	0.572308i	$0.806048\pi$
$434$		0			0
$435$	−140.160	−	140.988i	−0.322206	−	0.324111i
$436$		0			0
$437$	82.7799	−	82.7799i	0.189428	−	0.189428i
$438$		0			0
$439$	228.193			0.519801			0.259901	−	0.965635i	$-0.416310\pi$
$439$	228.193			0.519801			0.259901	+	0.965635i	$0.416310\pi$
$440$		0			0
$441$		−	56.2813i		−	0.127622i
$442$		0			0
$443$	113.426	+	113.426i	0.256041	+	0.256041i	0.823442	−	0.567401i	$-0.192051\pi$
$443$	113.426	+	113.426i	0.256041	+	0.256041i	−0.567401	+	0.823442i	$0.692051\pi$
$444$		0			0
$445$	227.478	+	228.823i	0.511187	+	0.514208i
$446$		0			0
$447$	578.512			1.29421
$448$		0			0
$449$	−385.638			−0.858881			−0.429441	−	0.903095i	$-0.641289\pi$
$449$	−385.638			−0.858881			−0.429441	+	0.903095i	$0.641289\pi$
$450$		0			0
$451$	294.106	+	294.106i	0.652120	+	0.652120i
$452$		0			0
$453$	−288.036	+	288.036i	−0.635841	+	0.635841i
$454$		0			0
$455$	1.69378	−	574.904i	0.00372260	−	1.26353i
$456$		0			0
$457$	29.4858			0.0645203			0.0322601	−	0.999480i	$-0.489729\pi$
$457$	29.4858			0.0645203			0.0322601	+	0.999480i	$0.489729\pi$
$458$		0			0
$459$	154.308	−	154.308i	0.336183	−	0.336183i
$460$		0			0
$461$	334.283	−	334.283i	0.725126	−	0.725126i	−0.244519	−	0.969645i	$-0.578630\pi$
$461$	334.283	−	334.283i	0.725126	−	0.725126i	0.969645	+	0.244519i	$0.0786300\pi$
$462$		0			0
$463$	218.319			0.471531			0.235765	−	0.971810i	$-0.424240\pi$
$463$	218.319			0.471531			0.235765	+	0.971810i	$0.424240\pi$
$464$		0			0
$465$	653.376	+	1.92498i	1.40511	+	0.00413973i
$466$		0			0
$467$	−205.296	+	205.296i	−0.439607	+	0.439607i	−0.891880	−	0.452273i	$-0.850613\pi$
$467$	−205.296	+	205.296i	−0.439607	+	0.439607i	0.452273	+	0.891880i	$0.350613\pi$
$468$		0			0
$469$	−261.658	−	261.658i	−0.557907	−	0.557907i
$470$		0			0
$471$	699.558			1.48526
$472$		0			0
$473$	−351.237			−0.742573
$474$		0			0
$475$	−63.9060	+	63.1573i	−0.134539	+	0.132963i
$476$		0			0
$477$	45.2118	+	45.2118i	0.0947837	+	0.0947837i
$478$		0			0
$479$		−	498.778i		−	1.04129i	−0.853773	−	0.520645i	$-0.825692\pi$
$479$		−	498.778i		−	1.04129i	0.853773	−	0.520645i	$-0.174308\pi$
$480$		0			0
$481$	411.983			0.856513
$482$		0			0
$483$	−395.664	+	395.664i	−0.819179	+	0.819179i
$484$		0			0
$485$	483.868	+	486.728i	0.997666	+	1.00356i
$486$		0			0
$487$			79.5802i			0.163409i	0.996657	+	0.0817045i	$0.0260364\pi$
$487$			79.5802i			0.163409i	−0.996657	+	0.0817045i	$0.973964\pi$
$488$		0			0
$489$		−	995.279i		−	2.03534i
$490$		0			0
$491$	−310.801	+	310.801i	−0.632996	+	0.632996i	−0.948818	−	0.315823i	$-0.897720\pi$
$491$	−310.801	+	310.801i	−0.632996	+	0.632996i	0.315823	+	0.948818i	$0.397720\pi$
$492$		0			0
$493$	81.6913	+	81.6913i	0.165703	+	0.165703i
$494$		0			0
$495$	−167.908	−	0.494690i	−0.339208	−	0.000999373i
$496$		0			0
$497$			170.717i			0.343495i
$498$		0			0
$499$	−607.980	−	607.980i	−1.21840	−	1.21840i	−0.968193	−	0.250204i	$-0.919502\pi$
$499$	−607.980	−	607.980i	−1.21840	−	1.21840i	−0.250204	−	0.968193i	$-0.580498\pi$
$500$		0			0
$501$	−272.730	−	272.730i	−0.544370	−	0.544370i
$502$		0			0
$503$			325.228i			0.646576i	0.946301	+	0.323288i	$0.104788\pi$
$503$			325.228i			0.646576i	−0.946301	+	0.323288i	$0.895212\pi$
$504$		0			0
$505$	819.905	+	2.41560i	1.62357	+	0.00478337i
$506$		0			0
$507$	819.944	+	819.944i	1.61725	+	1.61725i
$508$		0			0
$509$	269.365	−	269.365i	0.529205	−	0.529205i	−0.391130	−	0.920335i	$-0.627916\pi$
$509$	269.365	−	269.365i	0.529205	−	0.529205i	0.920335	+	0.391130i	$0.127916\pi$
$510$		0			0
$511$			409.901i			0.802155i
$512$		0			0
$513$		−	79.8454i		−	0.155644i
$514$		0			0
$515$	308.562	+	310.386i	0.599150	+	0.602691i
$516$		0			0
$517$	−58.6040	+	58.6040i	−0.113354	+	0.113354i
$518$		0			0
$519$	−512.341			−0.987169
$520$		0			0
$521$		−	667.589i		−	1.28136i	−0.767807	−	0.640681i	$-0.778652\pi$
$521$		−	667.589i		−	1.28136i	0.767807	−	0.640681i	$-0.221348\pi$
$522$		0			0
$523$	−188.149	−	188.149i	−0.359749	−	0.359749i	0.503972	−	0.863720i	$-0.331872\pi$
$523$	−188.149	−	188.149i	−0.359749	−	0.359749i	−0.863720	+	0.503972i	$0.831872\pi$
$524$		0			0
$525$	305.452	−	301.873i	0.581814	−	0.574997i
$526$		0			0
$527$	−379.695			−0.720483
$528$		0			0
$529$	−532.045			−1.00576
$530$		0			0
$531$	53.0811	+	53.0811i	0.0999643	+	0.0999643i
$532$		0			0
$533$	481.185	−	481.185i	0.902786	−	0.902786i
$534$		0			0
$535$	178.362	+	0.525490i	0.333387	+	0.000982224i
$536$		0			0
$537$	755.755			1.40737
$538$		0			0
$539$	−226.679	+	226.679i	−0.420555	+	0.420555i
$540$		0			0
$541$	−249.000	+	249.000i	−0.460259	+	0.460259i	−0.898740	−	0.438481i	$-0.855517\pi$
$541$	−249.000	+	249.000i	−0.460259	+	0.460259i	0.438481	+	0.898740i	$0.355517\pi$
$542$		0			0
$543$	−275.244			−0.506896
$544$		0			0
$545$	−2.18328	+	741.050i	−0.00400602	+	1.35972i
$546$		0			0
$547$	−621.267	+	621.267i	−1.13577	+	1.13577i	−0.146571	+	0.989200i	$0.546824\pi$
$547$	−621.267	+	621.267i	−1.13577	+	1.13577i	−0.989200	+	0.146571i	$0.953176\pi$
$548$		0			0
$549$	195.826	+	195.826i	0.356695	+	0.356695i
$550$		0			0
$551$	42.2705			0.0767159
$552$		0			0
$553$	−304.539			−0.550704
$554$		0			0
$555$	216.969	+	218.251i	0.390935	+	0.393245i
$556$		0			0
$557$	−269.024	−	269.024i	−0.482987	−	0.482987i	0.423097	−	0.906084i	$-0.360943\pi$
$557$	−269.024	−	269.024i	−0.482987	−	0.482987i	−0.906084	+	0.423097i	$0.860943\pi$
$558$		0			0
$559$			574.656i			1.02801i
$560$		0			0
$561$	459.248			0.818623
$562$		0			0
$563$	366.055	−	366.055i	0.650186	−	0.650186i	−0.302852	−	0.953038i	$-0.597939\pi$
$563$	366.055	−	366.055i	0.650186	−	0.650186i	0.953038	+	0.302852i	$0.0979387\pi$
$564$		0			0
$565$	−96.7036	−	97.2751i	−0.171157	−	0.172168i
$566$		0			0
$567$			492.683i			0.868929i
$568$		0			0
$569$			761.087i			1.33759i	0.743448	+	0.668794i	$0.233189\pi$
$569$			761.087i			1.33759i	−0.743448	+	0.668794i	$0.766811\pi$
$570$		0			0
$571$	18.9101	−	18.9101i	0.0331175	−	0.0331175i	−0.690354	−	0.723472i	$-0.742545\pi$
$571$	18.9101	−	18.9101i	0.0331175	−	0.0331175i	0.723472	+	0.690354i	$0.242545\pi$
$572$		0			0
$573$	−277.536	−	277.536i	−0.484357	−	0.484357i
$574$		0			0
$575$	814.328	+	4.79838i	1.41622	+	0.00834502i
$576$		0			0
$577$			770.887i			1.33603i	0.744150	+	0.668013i	$0.232855\pi$
$577$			770.887i			1.33603i	−0.744150	+	0.668013i	$0.767145\pi$
$578$		0			0
$579$	69.2298	+	69.2298i	0.119568	+	0.119568i
$580$		0			0
$581$	176.597	+	176.597i	0.303953	+	0.303953i
$582$		0			0
$583$		−	364.192i		−	0.624685i
$584$		0			0
$585$	−0.809358	+	274.713i	−0.00138352	+	0.469595i
$586$		0			0
$587$	396.570	+	396.570i	0.675587	+	0.675587i	0.958998	−	0.283411i	$-0.0914662\pi$
$587$	396.570	+	396.570i	0.675587	+	0.675587i	−0.283411	+	0.958998i	$0.591466\pi$
$588$		0			0
$589$	−98.2349	+	98.2349i	−0.166782	+	0.166782i
$590$		0			0
$591$			567.100i			0.959560i
$592$		0			0
$593$			344.909i			0.581634i	0.956779	+	0.290817i	$0.0939272\pi$
$593$			344.909i			0.581634i	−0.956779	+	0.290817i	$0.906073\pi$
$594$		0			0
$595$	−176.988	+	175.948i	−0.297459	+	0.295712i
$596$		0			0
$597$	26.6242	−	26.6242i	0.0445966	−	0.0445966i
$598$		0			0
$599$	−970.796			−1.62069			−0.810347	−	0.585950i	$-0.800721\pi$
$599$	−970.796			−1.62069			−0.810347	+	0.585950i	$0.800721\pi$
$600$		0			0
$601$			588.278i			0.978832i	0.872051	+	0.489416i	$0.162790\pi$
$601$			588.278i			0.978832i	−0.872051	+	0.489416i	$0.837210\pi$
$602$		0			0
$603$	125.031	+	125.031i	0.207348	+	0.207348i
$604$		0			0
$605$	247.738	+	249.202i	0.409484	+	0.411904i
$606$		0			0
$607$	742.181			1.22270			0.611351	−	0.791359i	$-0.290626\pi$
$607$	742.181			1.22270			0.611351	+	0.791359i	$0.290626\pi$
$608$		0			0
$609$	−202.040			−0.331758
$610$		0			0
$611$	95.8815	+	95.8815i	0.156926	+	0.156926i
$612$		0			0
$613$	−282.998	+	282.998i	−0.461660	+	0.461660i	−0.899199	−	0.437539i	$-0.855850\pi$
$613$	−282.998	+	282.998i	−0.461660	+	0.461660i	0.437539	+	0.899199i	$0.355850\pi$
$614$		0			0
$615$	508.325	+	1.49763i	0.826545	+	0.00243516i
$616$		0			0
$617$	−521.001			−0.844411			−0.422205	−	0.906500i	$-0.638744\pi$
$617$	−521.001			−0.844411			−0.422205	+	0.906500i	$0.638744\pi$
$618$		0			0
$619$	−249.150	+	249.150i	−0.402505	+	0.402505i	−0.879115	−	0.476610i	$-0.841865\pi$
$619$	−249.150	+	249.150i	−0.402505	+	0.402505i	0.476610	+	0.879115i	$0.341865\pi$
$620$		0			0
$621$	−511.716	+	511.716i	−0.824019	+	0.824019i
$622$		0			0
$623$	327.910			0.526340
$624$		0			0
$625$	−624.957	−	7.36530i	−0.999931	−	0.0117845i
$626$		0			0
$627$	118.817	−	118.817i	0.189501	−	0.189501i
$628$		0			0
$629$	−126.459	−	126.459i	−0.201048	−	0.201048i
$630$		0			0
$631$	−815.349			−1.29215			−0.646077	−	0.763272i	$-0.723592\pi$
$631$	−815.349			−1.29215			−0.646077	+	0.763272i	$0.723592\pi$
$632$		0			0
$633$	4.22741			0.00667838
$634$		0			0
$635$	−118.950	+	118.251i	−0.187323	+	0.186223i
$636$		0			0
$637$	370.869	+	370.869i	0.582211	+	0.582211i
$638$		0			0
$639$		−	81.5755i		−	0.127661i
$640$		0			0
$641$	778.586			1.21464			0.607321	−	0.794456i	$-0.292244\pi$
$641$	778.586			1.21464			0.607321	+	0.794456i	$0.292244\pi$
$642$		0			0
$643$	−338.184	+	338.184i	−0.525947	+	0.525947i	−0.919361	−	0.393415i	$-0.871294\pi$
$643$	−338.184	+	338.184i	−0.525947	+	0.525947i	0.393415	+	0.919361i	$0.371294\pi$
$644$		0			0
$645$	−304.429	+	302.640i	−0.471982	+	0.469209i
$646$		0			0
$647$			251.550i			0.388794i	0.980923	+	0.194397i	$0.0622750\pi$
$647$			251.550i			0.388794i	−0.980923	+	0.194397i	$0.937725\pi$
$648$		0			0
$649$		−	427.580i		−	0.658829i
$650$		0			0
$651$	469.534	−	469.534i	0.721250	−	0.721250i
$652$		0			0
$653$	658.816	+	658.816i	1.00891	+	1.00891i	0.999960	+	0.00894710i	$0.00284799\pi$
$653$	658.816	+	658.816i	1.00891	+	1.00891i	0.00894710	+	0.999960i	$0.497152\pi$
$654$		0			0
$655$	−748.852	−	2.20626i	−1.14329	−	0.00336834i
$656$		0			0
$657$		−	195.867i		−	0.298124i
$658$		0			0
$659$	693.169	+	693.169i	1.05185	+	1.05185i	0.998580	+	0.0532691i	$0.0169641\pi$
$659$	693.169	+	693.169i	1.05185	+	1.05185i	0.0532691	+	0.998580i	$0.483036\pi$
$660$		0			0
$661$	−517.616	−	517.616i	−0.783080	−	0.783080i	0.197269	−	0.980349i	$-0.436793\pi$
$661$	−517.616	−	517.616i	−0.783080	−	0.783080i	−0.980349	+	0.197269i	$0.936793\pi$
$662$		0			0
$663$		−	751.372i		−	1.13329i
$664$		0			0
$665$	−0.269023	+	91.3119i	−0.000404546	+	0.137311i
$666$		0			0
$667$	−270.904	−	270.904i	−0.406154	−	0.406154i
$668$		0			0
$669$	577.578	−	577.578i	0.863345	−	0.863345i
$670$		0			0
$671$		−	1577.42i		−	2.35085i
$672$		0			0
$673$		−	821.981i		−	1.22137i	−0.791874	−	0.610684i	$-0.790895\pi$
$673$		−	821.981i		−	1.22137i	0.791874	−	0.610684i	$-0.209105\pi$
$674$		0			0
$675$	395.045	−	390.416i	0.585251	−	0.578394i
$676$		0			0
$677$	256.582	−	256.582i	0.378998	−	0.378998i	−0.491743	−	0.870741i	$-0.663640\pi$
$677$	256.582	−	256.582i	0.378998	−	0.378998i	0.870741	+	0.491743i	$0.163640\pi$
$678$		0			0
$679$	697.497			1.02724
$680$		0			0
$681$			1149.90i			1.68854i
$682$		0			0
$683$	−841.969	−	841.969i	−1.23275	−	1.23275i	−0.962903	−	0.269849i	$-0.913026\pi$
$683$	−841.969	−	841.969i	−1.23275	−	1.23275i	−0.269849	−	0.962903i	$-0.586974\pi$
$684$		0			0
$685$	363.309	−	361.175i	0.530378	−	0.527262i
$686$		0			0
$687$	−583.000			−0.848617
$688$		0			0
$689$	−595.851			−0.864806
$690$		0			0
$691$	−79.9699	−	79.9699i	−0.115731	−	0.115731i	0.646870	−	0.762600i	$-0.276078\pi$
$691$	−79.9699	−	79.9699i	−0.115731	−	0.115731i	−0.762600	+	0.646870i	$0.776078\pi$
$692$		0			0
$693$	−120.663	+	120.663i	−0.174117	+	0.174117i
$694$		0			0
$695$	−3.20570	+	1088.08i	−0.00461252	+	1.56558i
$696$		0			0
$697$	−295.402			−0.423819
$698$		0			0
$699$	698.574	−	698.574i	0.999391	−	0.999391i
$700$		0			0
$701$	282.604	−	282.604i	0.403144	−	0.403144i	−0.476196	−	0.879339i	$-0.657985\pi$
$701$	282.604	−	282.604i	0.403144	−	0.403144i	0.879339	+	0.476196i	$0.157985\pi$
$702$		0			0
$703$	−65.4351			−0.0930798
$704$		0			0
$705$	−0.298419	+	101.290i	−0.000423289	+	0.143673i
$706$		0			0
$707$	589.206	−	589.206i	0.833389	−	0.833389i
$708$		0			0
$709$	−656.306	−	656.306i	−0.925678	−	0.925678i	0.0717452	−	0.997423i	$-0.477143\pi$
$709$	−656.306	−	656.306i	−0.925678	−	0.925678i	−0.997423	+	0.0717452i	$0.977143\pi$
$710$		0			0
$711$	145.521			0.204671
$712$		0			0
$713$	1259.14			1.76598
$714$		0			0
$715$	1109.70	−	1103.18i	1.55202	−	1.54291i
$716$		0			0
$717$	−145.707	−	145.707i	−0.203218	−	0.203218i
$718$		0			0
$719$			214.819i			0.298775i	0.988779	+	0.149387i	$0.0477301\pi$
$719$			214.819i			0.298775i	−0.988779	+	0.149387i	$0.952270\pi$
$720$		0			0
$721$	444.793			0.616912
$722$		0			0
$723$	199.081	−	199.081i	0.275354	−	0.275354i
$724$		0			0
$725$	206.688	+	209.138i	0.285087	+	0.288466i
$726$		0			0
$727$			939.330i			1.29206i	0.763311	+	0.646031i	$0.223572\pi$
$727$			939.330i			1.29206i	−0.763311	+	0.646031i	$0.776428\pi$
$728$		0			0
$729$			440.514i			0.604272i
$730$		0			0
$731$	176.392	−	176.392i	0.241302	−	0.241302i
$732$		0			0
$733$	−479.564	−	479.564i	−0.654248	−	0.654248i	0.299765	−	0.954013i	$-0.403092\pi$
$733$	−479.564	−	479.564i	−0.654248	−	0.654248i	−0.954013	+	0.299765i	$0.903092\pi$
$734$		0			0
$735$	−1.15428	+	391.787i	−0.00157045	+	0.533043i
$736$		0			0
$737$		−	1007.15i		−	1.36656i
$738$		0			0
$739$	−618.066	−	618.066i	−0.836355	−	0.836355i	0.152022	−	0.988377i	$-0.451421\pi$
$739$	−618.066	−	618.066i	−0.836355	−	0.836355i	−0.988377	+	0.152022i	$0.951421\pi$
$740$		0			0
$741$	−194.395	−	194.395i	−0.262342	−	0.262342i
$742$		0			0
$743$		−	305.455i		−	0.411110i	−0.978646	−	0.205555i	$-0.934100\pi$
$743$		−	305.455i		−	0.411110i	0.978646	−	0.205555i	$-0.0659000\pi$
$744$		0			0
$745$	−855.644	−	2.52090i	−1.14852	−	0.00338375i
$746$		0			0
$747$	−84.3852	−	84.3852i	−0.112965	−	0.112965i
$748$		0			0
$749$	128.176	−	128.176i	0.171129	−	0.171129i
$750$		0			0
$751$		−	853.156i		−	1.13603i	−0.823019	−	0.568013i	$-0.807712\pi$
$751$		−	853.156i		−	1.13603i	0.823019	−	0.568013i	$-0.192288\pi$
$752$		0			0
$753$		−	932.780i		−	1.23875i
$754$		0			0
$755$	427.273	−	424.762i	0.565924	−	0.562599i
$756$		0			0
$757$	−360.656	+	360.656i	−0.476428	+	0.476428i	−0.903987	−	0.427559i	$-0.859373\pi$
$757$	−360.656	+	360.656i	−0.476428	+	0.476428i	0.427559	+	0.903987i	$0.359373\pi$
$758$		0			0
$759$	−1522.96			−2.00653
$760$		0			0
$761$		−	241.725i		−	0.317641i	−0.987307	−	0.158821i	$-0.949231\pi$
$761$		−	241.725i		−	0.317641i	0.987307	−	0.158821i	$-0.0507691\pi$
$762$		0			0
$763$	532.538	+	532.538i	0.697953	+	0.697953i
$764$		0			0
$765$	84.5722	−	84.0753i	0.110552	−	0.109902i
$766$		0			0
$767$	−699.561			−0.912074
$768$		0			0
$769$	295.013			0.383632			0.191816	−	0.981431i	$-0.438562\pi$
$769$	295.013			0.383632			0.191816	+	0.981431i	$0.438562\pi$
$770$		0			0
$771$	787.953	+	787.953i	1.02199	+	1.02199i
$772$		0			0
$773$	55.1851	−	55.1851i	0.0713908	−	0.0713908i	−0.670510	−	0.741901i	$-0.733925\pi$
$773$	55.1851	−	55.1851i	0.0713908	−	0.0713908i	0.741901	+	0.670510i	$0.233925\pi$
$774$		0			0
$775$	−966.363	−	5.69424i	−1.24692	−	0.00734741i
$776$		0			0
$777$	312.761			0.402523
$778$		0			0
$779$	−76.4265	+	76.4265i	−0.0981084	+	0.0981084i
$780$		0			0
$781$	−328.555	+	328.555i	−0.420685	+	0.420685i
$782$		0			0
$783$	−261.301			−0.333718
$784$		0			0
$785$	−1034.68	−	3.04836i	−1.31806	−	0.00388326i
$786$		0			0
$787$	236.729	−	236.729i	0.300800	−	0.300800i	−0.540527	−	0.841327i	$-0.681775\pi$
$787$	236.729	−	236.729i	0.300800	−	0.300800i	0.841327	+	0.540527i	$0.181775\pi$
$788$		0			0
$789$	134.286	+	134.286i	0.170198	+	0.170198i
$790$		0			0
$791$	−139.398			−0.176231
$792$		0			0
$793$	−2580.81			−3.25448
$794$		0			0
$795$	−313.802	−	315.657i	−0.394720	−	0.397053i
$796$		0			0
$797$	−190.629	−	190.629i	−0.239183	−	0.239183i	0.577329	−	0.816512i	$-0.304095\pi$
$797$	−190.629	−	190.629i	−0.239183	−	0.239183i	−0.816512	+	0.577329i	$0.804095\pi$
$798$		0			0
$799$		−	58.8621i		−	0.0736697i
$800$		0			0
$801$	−156.689			−0.195617
$802$		0			0
$803$	−788.878	+	788.878i	−0.982414	+	0.982414i
$804$		0			0
$805$	586.927	−	583.479i	0.729102	−	0.724819i
$806$		0			0
$807$		−	1376.16i		−	1.70528i
$808$		0			0
$809$			844.246i			1.04357i	0.853078	+	0.521784i	$0.174733\pi$
$809$			844.246i			1.04357i	−0.853078	+	0.521784i	$0.825267\pi$
$810$		0			0
$811$	−443.406	+	443.406i	−0.546740	+	0.546740i	−0.925496	−	0.378756i	$-0.876352\pi$
$811$	−443.406	+	443.406i	−0.546740	+	0.546740i	0.378756	+	0.925496i	$0.376352\pi$
$812$		0			0
$813$	687.224	+	687.224i	0.845294	+	0.845294i
$814$		0			0
$815$	−4.33698	+	1472.06i	−0.00532145	+	1.80621i
$816$		0			0
$817$		−	91.2725i		−	0.111717i
$818$		0			0
$819$	197.416	+	197.416i	0.241045	+	0.241045i
$820$		0			0
$821$	−64.3891	−	64.3891i	−0.0784277	−	0.0784277i	0.666805	−	0.745232i	$-0.267661\pi$
$821$	−64.3891	−	64.3891i	−0.0784277	−	0.0784277i	−0.745232	+	0.666805i	$0.767661\pi$
$822$		0			0
$823$		−	659.199i		−	0.800971i	−0.916303	−	0.400486i	$-0.868841\pi$
$823$		−	659.199i		−	0.800971i	0.916303	−	0.400486i	$-0.131159\pi$
$824$		0			0
$825$	1168.83	+	6.88729i	1.41677	+	0.00834823i
$826$		0			0
$827$	−565.628	−	565.628i	−0.683951	−	0.683951i	0.276937	−	0.960888i	$-0.410681\pi$
$827$	−565.628	−	565.628i	−0.683951	−	0.683951i	−0.960888	+	0.276937i	$0.910681\pi$
$828$		0			0
$829$	271.351	−	271.351i	0.327323	−	0.327323i	−0.524245	−	0.851568i	$-0.675652\pi$
$829$	271.351	−	271.351i	0.327323	−	0.327323i	0.851568	+	0.524245i	$0.175652\pi$
$830$		0			0
$831$			239.809i			0.288579i
$832$		0			0
$833$		−	227.678i		−	0.273323i
$834$		0			0
$835$	402.190	+	404.567i	0.481665	+	0.484512i
$836$		0			0
$837$	607.253	−	607.253i	0.725512	−	0.725512i
$838$		0			0
$839$	1187.06			1.41485			0.707425	−	0.706789i	$-0.249857\pi$
$839$	1187.06			1.41485			0.707425	+	0.706789i	$0.249857\pi$
$840$		0			0
$841$			702.666i			0.835513i
$842$		0			0
$843$	251.451	+	251.451i	0.298281	+	0.298281i
$844$		0			0
$845$	−1209.16	−	1216.30i	−1.43096	−	1.43941i
$846$		0			0
$847$	357.115			0.421623
$848$		0			0
$849$	1277.77			1.50503
$850$		0			0
$851$	419.363	+	419.363i	0.492788	+	0.492788i
$852$		0			0
$853$	84.9264	−	84.9264i	0.0995620	−	0.0995620i	−0.655571	−	0.755133i	$-0.727572\pi$
$853$	84.9264	−	84.9264i	0.0995620	−	0.0995620i	0.755133	+	0.655571i	$0.227572\pi$
$854$		0			0
$855$	0.128550	−	43.6326i	0.000150351	−	0.0510323i
$856$		0			0
$857$	222.414			0.259526			0.129763	−	0.991545i	$-0.458578\pi$
$857$	222.414			0.259526			0.129763	+	0.991545i	$0.458578\pi$
$858$		0			0
$859$	−2.04685	+	2.04685i	−0.00238283	+	0.00238283i	−0.708297	−	0.705914i	$-0.750536\pi$
$859$	−2.04685	+	2.04685i	−0.00238283	+	0.00238283i	0.705914	+	0.708297i	$0.250536\pi$
$860$		0			0
$861$	365.296	−	365.296i	0.424270	−	0.424270i
$862$		0			0
$863$	905.739			1.04952			0.524762	−	0.851249i	$-0.324154\pi$
$863$	905.739			1.04952			0.524762	+	0.851249i	$0.324154\pi$
$864$		0			0
$865$	757.774	+	2.23255i	0.876039	+	0.00258098i
$866$		0			0
$867$	460.193	−	460.193i	0.530788	−	0.530788i
$868$		0			0
$869$	−586.104	−	586.104i	−0.674458	−	0.674458i
$870$		0			0
$871$	−1647.80			−1.89185
$872$		0			0
$873$	−333.292			−0.381778
$874$		0			0
$875$	−453.092	+	445.153i	−0.517820	+	0.508746i
$876$		0			0
$877$	−349.241	−	349.241i	−0.398222	−	0.398222i	0.479383	−	0.877606i	$-0.340860\pi$
$877$	−349.241	−	349.241i	−0.398222	−	0.398222i	−0.877606	+	0.479383i	$0.840860\pi$
$878$		0			0
$879$			645.069i			0.733867i
$880$		0			0
$881$	−319.778			−0.362972			−0.181486	−	0.983394i	$-0.558091\pi$
$881$	−319.778			−0.362972			−0.181486	+	0.983394i	$0.558091\pi$
$882$		0			0
$883$	−1037.87	+	1037.87i	−1.17539	+	1.17539i	−0.194481	+	0.980906i	$0.562302\pi$
$883$	−1037.87	+	1037.87i	−1.17539	+	1.17539i	−0.980906	+	0.194481i	$0.937698\pi$
$884$		0			0
$885$	−368.420	−	370.598i	−0.416294	−	0.418754i
$886$		0			0
$887$		−	1514.15i		−	1.70704i	−0.521057	−	0.853522i	$-0.674462\pi$
$887$		−	1514.15i		−	1.70704i	0.521057	−	0.853522i	$-0.325538\pi$
$888$		0			0
$889$			170.460i			0.191743i
$890$		0			0
$891$	−948.197	+	948.197i	−1.06419	+	1.06419i
$892$		0			0
$893$	−15.2288	−	15.2288i	−0.0170536	−	0.0170536i
$894$		0			0
$895$	−1117.79	−	3.29324i	−1.24893	−	0.00367960i
$896$		0			0
$897$			2491.70i			2.77781i
$898$		0			0
$899$	321.482	+	321.482i	0.357600	+	0.357600i
$900$		0			0
$901$	182.898	+	182.898i	0.202994	+	0.202994i
$902$		0			0
$903$			436.256i			0.483119i
$904$		0			0
$905$	407.098	+	1.19939i	0.449832	+	0.00132529i
$906$		0			0
$907$	−822.168	−	822.168i	−0.906469	−	0.906469i	0.0895162	−	0.995985i	$-0.471468\pi$
$907$	−822.168	−	822.168i	−0.906469	−	0.906469i	−0.995985	+	0.0895162i	$0.971468\pi$
$908$		0			0
$909$	−281.547	+	281.547i	−0.309732	+	0.309732i
$910$		0			0
$911$		−	331.730i		−	0.364139i	−0.983286	−	0.182069i	$-0.941720\pi$
$911$		−	331.730i		−	0.364139i	0.983286	−	0.182069i	$-0.0582795\pi$
$912$		0			0
$913$			679.742i			0.744515i
$914$		0			0
$915$	−1359.17	−	1367.20i	−1.48543	−	1.49421i
$916$		0			0
$917$	−538.145	+	538.145i	−0.586854	+	0.586854i
$918$		0			0
$919$	820.793			0.893137			0.446568	−	0.894749i	$-0.352646\pi$
$919$	820.793			0.893137			0.446568	+	0.894749i	$0.352646\pi$
$920$		0			0
$921$		−	948.751i		−	1.03013i
$922$		0			0
$923$	537.546	+	537.546i	0.582390	+	0.582390i
$924$		0			0
$925$	−319.955	−	323.748i	−0.345897	−	0.349998i
$926$		0			0
$927$	−212.540			−0.229278
$928$		0			0
$929$	−724.971			−0.780378			−0.390189	−	0.920735i	$-0.627590\pi$
$929$	−724.971			−0.780378			−0.390189	+	0.920735i	$0.627590\pi$
$930$		0			0
$931$	−58.9050	−	58.9050i	−0.0632706	−	0.0632706i
$932$		0			0
$933$	231.994	−	231.994i	0.248654	−	0.248654i
$934$		0			0
$935$	−679.247	−	2.00120i	−0.726467	−	0.00214032i
$936$		0			0
$937$	605.697			0.646422			0.323211	−	0.946327i	$-0.395238\pi$
$937$	605.697			0.646422			0.323211	+	0.946327i	$0.395238\pi$
$938$		0			0
$939$	418.576	−	418.576i	0.445768	−	0.445768i
$940$		0			0
$941$	934.190	−	934.190i	0.992763	−	0.992763i	−0.00721133	−	0.999974i	$-0.502295\pi$
$941$	934.190	−	934.190i	0.992763	−	0.992763i	0.999974	+	0.00721133i	$0.00229546\pi$
$942$		0			0
$943$	979.609			1.03882
$944$		0			0
$945$	1.66301	−	564.458i	0.00175979	−	0.597310i
$946$		0			0
$947$	328.488	−	328.488i	0.346872	−	0.346872i	−0.512071	−	0.858943i	$-0.671121\pi$
$947$	328.488	−	328.488i	0.346872	−	0.346872i	0.858943	+	0.512071i	$0.171121\pi$
$948$		0			0
$949$	1290.68	+	1290.68i	1.36004	+	1.36004i
$950$		0			0
$951$	531.187			0.558556
$952$		0			0
$953$	605.174			0.635020			0.317510	−	0.948255i	$-0.397153\pi$
$953$	605.174			0.635020			0.317510	+	0.948255i	$0.397153\pi$
$954$		0			0
$955$	409.279	+	411.697i	0.428564	+	0.431097i
$956$		0			0
$957$	−388.839	−	388.839i	−0.406310	−	0.406310i
$958$		0			0
$959$		−	520.634i		−	0.542892i
$960$		0			0
$961$	−533.224			−0.554864
$962$		0			0
$963$	−61.2476	+	61.2476i	−0.0636009	+	0.0636009i
$964$		0			0
$965$	−102.092	−	102.695i	−0.105795	−	0.106420i
$966$		0			0
$967$			587.364i			0.607408i	0.952766	+	0.303704i	$0.0982234\pi$
$967$			587.364i			0.607408i	−0.952766	+	0.303704i	$0.901777\pi$
$968$		0			0
$969$			119.340i			0.123158i
$970$		0			0
$971$	780.030	−	780.030i	0.803326	−	0.803326i	−0.180288	−	0.983614i	$-0.557703\pi$
$971$	780.030	−	780.030i	0.803326	−	0.803326i	0.983614	+	0.180288i	$0.0577029\pi$
$972$		0			0
$973$	781.924	+	781.924i	0.803622	+	0.803622i
$974$		0			0
$975$	11.2682	−	1912.32i	0.0115572	−	1.96135i
$976$		0			0
$977$			182.727i			0.187028i	0.995618	+	0.0935142i	$0.0298101\pi$
$977$			182.727i			0.187028i	−0.995618	+	0.0935142i	$0.970190\pi$
$978$		0			0
$979$	631.082	+	631.082i	0.644619	+	0.644619i
$980$		0			0
$981$	−254.469	−	254.469i	−0.259397	−	0.259397i
$982$		0			0
$983$			213.302i			0.216991i	0.994097	+	0.108495i	$0.0346033\pi$
$983$			213.302i			0.216991i	−0.994097	+	0.108495i	$0.965397\pi$
$984$		0			0
$985$	2.47117	−	838.765i	0.00250880	−	0.851538i
$986$		0			0
$987$	72.7894	+	72.7894i	0.0737482	+	0.0737482i
$988$		0			0
$989$	−584.951	+	584.951i	−0.591457	+	0.591457i
$990$		0			0
$991$			1722.88i			1.73853i	0.494345	+	0.869266i	$0.335408\pi$
$991$			1722.88i			1.73853i	−0.494345	+	0.869266i	$0.664592\pi$
$992$		0			0
$993$		−	1167.09i		−	1.17532i
$994$		0			0
$995$	−39.4943	+	39.2623i	−0.0396928	+	0.0394596i
$996$		0			0
$997$	−1133.95	+	1133.95i	−1.13737	+	1.13737i	−0.148445	+	0.988921i	$0.547427\pi$
$997$	−1133.95	+	1133.95i	−1.13737	+	1.13737i	−0.988921	+	0.148445i	$0.952573\pi$
$998$		0			0
$999$	404.497			0.404902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.k.a.79.18		44
4.3	odd	2		80.3.k.a.59.19	yes	44
5.4	even	2	inner	320.3.k.a.79.5		44
8.3	odd	2		640.3.k.b.159.18		44
8.5	even	2		640.3.k.a.159.5		44
16.3	odd	4	inner	320.3.k.a.239.5		44
16.5	even	4		640.3.k.b.479.5		44
16.11	odd	4		640.3.k.a.479.18		44
16.13	even	4		80.3.k.a.19.4	✓	44
20.3	even	4		400.3.r.g.251.15		44
20.7	even	4		400.3.r.g.251.8		44
20.19	odd	2		80.3.k.a.59.4	yes	44
40.19	odd	2		640.3.k.b.159.5		44
40.29	even	2		640.3.k.a.159.18		44
80.13	odd	4		400.3.r.g.51.15		44
80.19	odd	4	inner	320.3.k.a.239.18		44
80.29	even	4		80.3.k.a.19.19	yes	44
80.59	odd	4		640.3.k.a.479.5		44
80.69	even	4		640.3.k.b.479.18		44
80.77	odd	4		400.3.r.g.51.8		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.k.a.19.4	✓	44	16.13	even	4
80.3.k.a.19.19	yes	44	80.29	even	4
80.3.k.a.59.4	yes	44	20.19	odd	2
80.3.k.a.59.19	yes	44	4.3	odd	2
320.3.k.a.79.5		44	5.4	even	2	inner
320.3.k.a.79.18		44	1.1	even	1	trivial
320.3.k.a.239.5		44	16.3	odd	4	inner
320.3.k.a.239.18		44	80.19	odd	4	inner
400.3.r.g.51.8		44	80.77	odd	4
400.3.r.g.51.15		44	80.13	odd	4
400.3.r.g.251.8		44	20.7	even	4
400.3.r.g.251.15		44	20.3	even	4
640.3.k.a.159.5		44	8.5	even	2
640.3.k.a.159.18		44	40.29	even	2
640.3.k.a.479.5		44	80.59	odd	4
640.3.k.a.479.18		44	16.11	odd	4
640.3.k.b.159.5		44	40.19	odd	2
640.3.k.b.159.18		44	8.3	odd	2
640.3.k.b.479.5		44	16.5	even	4
640.3.k.b.479.18		44	80.69	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.39041 - 2.39041i) q^{3} +(-3.54593 + 3.52510i) q^{5} +5.08144i q^{7} -2.42812i q^{9} +O(q^{10})\)	\(q+(2.39041 - 2.39041i) q^{3} +(-3.54593 + 3.52510i) q^{5} +5.08144i q^{7} -2.42812i q^{9} +(-9.77953 + 9.77953i) q^{11} +(16.0002 + 16.0002i) q^{13} +(-0.0497986 + 16.9027i) q^{15} -9.82261i q^{17} +(-2.54131 - 2.54131i) q^{19} +(12.1467 + 12.1467i) q^{21} +32.5737i q^{23} +(0.147309 - 24.9996i) q^{25} +(15.7095 + 15.7095i) q^{27} +(-8.31667 + 8.31667i) q^{29} -38.6552i q^{31} +46.7542i q^{33} +(-17.9126 - 18.0185i) q^{35} +(12.8743 - 12.8743i) q^{37} +76.4941 q^{39} -30.0736i q^{41} +(17.9578 + 17.9578i) q^{43} +(8.55937 + 8.60995i) q^{45} +5.99252 q^{47} +23.1790 q^{49} +(-23.4801 - 23.4801i) q^{51} +(-18.6201 + 18.6201i) q^{53} +(0.203734 - 69.1514i) q^{55} -12.1495 q^{57} +(-21.8610 + 21.8610i) q^{59} +(-80.6491 + 80.6491i) q^{61} +12.3383 q^{63} +(-113.138 - 0.333327i) q^{65} +(-51.4930 + 51.4930i) q^{67} +(77.8645 + 77.8645i) q^{69} +33.5962 q^{71} +80.6663 q^{73} +(-59.4071 - 60.1113i) q^{75} +(-49.6941 - 49.6941i) q^{77} +59.9317i q^{79} +96.9573 q^{81} +(34.7533 - 34.7533i) q^{83} +(34.6257 + 34.8303i) q^{85} +39.7605i q^{87} -64.5309i q^{89} +(-81.3041 + 81.3041i) q^{91} +(-92.4018 - 92.4018i) q^{93} +(17.9697 + 0.0529423i) q^{95} -137.264i q^{97} +(23.7459 + 23.7459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{5}+O(q^{10}) \) 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

Introduction

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