LMFDB - Embedded newform 980.2.k.m.883.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(687,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.687"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,-4,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			883.11
Character	$\chi$	$=$	980.883
Dual form			980.2.k.m.687.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.405491 + 1.35483i) q^{2} +(-1.41506 + 1.41506i) q^{3} +(-1.67115 - 1.09875i) q^{4} +(-1.52518 - 1.63518i) q^{5} +(-1.34338 - 2.49096i) q^{6} +(2.16626 - 1.81861i) q^{8} -1.00477i q^{9} +(2.83385 - 1.40332i) q^{10} -5.68305i q^{11} +(3.91957 - 0.809992i) q^{12} +(4.82411 + 4.82411i) q^{13} +(4.47209 + 0.155660i) q^{15} +(1.58552 + 3.67235i) q^{16} +(-2.67652 + 2.67652i) q^{17} +(1.36130 + 0.407425i) q^{18} -1.12884 q^{19} +(0.752163 + 4.40843i) q^{20} +(7.69959 + 2.30442i) q^{22} +(3.44481 - 3.44481i) q^{23} +(-0.491941 + 5.63881i) q^{24} +(-0.347648 + 4.98790i) q^{25} +(-8.49200 + 4.57974i) q^{26} +(-2.82336 - 2.82336i) q^{27} +0.781186i q^{29} +(-2.02428 + 5.99583i) q^{30} +3.69737i q^{31} +(-5.61834 + 0.659012i) q^{32} +(8.04183 + 8.04183i) q^{33} +(-2.54094 - 4.71154i) q^{34} +(-1.10399 + 1.67913i) q^{36} +(-2.43078 + 2.43078i) q^{37} +(0.457736 - 1.52940i) q^{38} -13.6528 q^{39} +(-6.27769 - 0.768519i) q^{40} +0.451387 q^{41} +(0.613245 - 0.613245i) q^{43} +(-6.24422 + 9.49725i) q^{44} +(-1.64298 + 1.53246i) q^{45} +(3.27031 + 6.06399i) q^{46} +(3.03222 + 3.03222i) q^{47} +(-7.44018 - 2.95298i) q^{48} +(-6.61681 - 2.49355i) q^{50} -7.57485i q^{51} +(-2.76137 - 13.3623i) q^{52} +(1.48677 + 1.48677i) q^{53} +(4.97004 - 2.68034i) q^{54} +(-9.29282 + 8.66767i) q^{55} +(1.59738 - 1.59738i) q^{57} +(-1.05838 - 0.316763i) q^{58} -9.27479 q^{59} +(-7.30253 - 5.17382i) q^{60} -1.51948 q^{61} +(-5.00933 - 1.49925i) q^{62} +(1.38533 - 7.87914i) q^{64} +(0.530664 - 15.2459i) q^{65} +(-14.1562 + 7.63447i) q^{66} +(9.65994 + 9.65994i) q^{67} +(7.41369 - 1.53206i) q^{68} +9.74921i q^{69} +11.8314i q^{71} +(-1.82728 - 2.17659i) q^{72} +(1.21746 + 1.21746i) q^{73} +(-2.30765 - 4.27896i) q^{74} +(-6.56622 - 7.55010i) q^{75} +(1.88647 + 1.24031i) q^{76} +(5.53607 - 18.4973i) q^{78} -5.46209 q^{79} +(3.58676 - 8.19360i) q^{80} +11.0047 q^{81} +(-0.183033 + 0.611555i) q^{82} +(0.968508 - 0.968508i) q^{83} +(8.45877 + 0.294423i) q^{85} +(0.582180 + 1.07951i) q^{86} +(-1.10542 - 1.10542i) q^{87} +(-10.3352 - 12.3109i) q^{88} +9.42358i q^{89} +(-1.41001 - 2.84737i) q^{90} +(-9.54179 + 1.97184i) q^{92} +(-5.23199 - 5.23199i) q^{93} +(-5.33770 + 2.87862i) q^{94} +(1.72169 + 1.84587i) q^{95} +(7.01772 - 8.88280i) q^{96} +(-6.77428 + 6.77428i) q^{97} -5.71016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{2} - 16 q^{8} + 32 q^{16} + 20 q^{22} + 32 q^{25} - 28 q^{30} - 64 q^{32} + 16 q^{36} - 8 q^{37} - 184 q^{46} - 12 q^{50} + 96 q^{53} - 8 q^{57} + 124 q^{58} + 8 q^{60} - 120 q^{65} - 80 q^{72}+ \cdots - 176 q^{93}+O(q^{100}) $ 56 * q - 4 * q^2 - 16 * q^8 + 32 * q^16 + 20 * q^22 + 32 * q^25 - 28 * q^30 - 64 * q^32 + 16 * q^36 - 8 * q^37 - 184 * q^46 - 12 * q^50 + 96 * q^53 - 8 * q^57 + 124 * q^58 + 8 * q^60 - 120 * q^65 - 80 * q^72 - 36 * q^78 - 72 * q^81 + 96 * q^85 + 104 * q^86 + 48 * q^88 - 152 * q^92 - 176 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.405491	+	1.35483i	−0.286725	+	0.958013i
$2$	−0.405491	+	1.35483i	−0.286725	+	0.958013i
$3$	−1.41506	+	1.41506i	−0.816983	+	0.816983i	−0.985670	−	0.168686i	$-0.946047\pi$
$3$	−1.41506	+	1.41506i	−0.816983	+	0.816983i	0.168686	+	0.985670i	$0.446047\pi$
$4$	−1.67115	−	1.09875i	−0.835577	−	0.549373i
$5$	−1.52518	−	1.63518i	−0.682082	−	0.731276i
$5$	−1.52518	−	1.63518i	−0.682082	−	0.731276i
$6$	−1.34338	−	2.49096i	−0.548431	−	1.01693i
$7$		0			0
$7$		0			0
$8$	2.16626	−	1.81861i	0.765887	−	0.642975i
$9$		−	1.00477i		−	0.334924i
$10$	2.83385	−	1.40332i	0.896142	−	0.443768i
$11$		−	5.68305i		−	1.71350i	−0.515730	−	0.856751i	$-0.672479\pi$
$11$		−	5.68305i		−	1.71350i	0.515730	−	0.856751i	$-0.327521\pi$
$12$	3.91957	−	0.809992i	1.13148	−	0.233825i
$13$	4.82411	+	4.82411i	1.33797	+	1.33797i	0.898027	+	0.439939i	$0.145000\pi$
$13$	4.82411	+	4.82411i	1.33797	+	1.33797i	0.439939	+	0.898027i	$0.355000\pi$
$14$		0			0
$15$	4.47209	+	0.155660i	1.15469	+	0.0401912i
$16$	1.58552	+	3.67235i	0.396379	+	0.918087i
$17$	−2.67652	+	2.67652i	−0.649151	+	0.649151i	−0.952788	−	0.303637i	$-0.901799\pi$
$17$	−2.67652	+	2.67652i	−0.649151	+	0.649151i	0.303637	+	0.952788i	$0.401799\pi$
$18$	1.36130	+	0.407425i	0.320861	+	0.0960310i
$19$	−1.12884			−0.258975			−0.129487	−	0.991581i	$-0.541333\pi$
$19$	−1.12884			−0.258975			−0.129487	+	0.991581i	$0.541333\pi$
$20$	0.752163	+	4.40843i	0.168189	+	0.985755i
$21$		0			0
$22$	7.69959	+	2.30442i	1.64156	+	0.491304i
$23$	3.44481	−	3.44481i	0.718293	−	0.718293i	−0.249962	−	0.968256i	$-0.580418\pi$
$23$	3.44481	−	3.44481i	0.718293	−	0.718293i	0.968256	+	0.249962i	$0.0804182\pi$
$24$	−0.491941	+	5.63881i	−0.100417	+	1.15102i
$25$	−0.347648	+	4.98790i	−0.0695296	+	0.997580i
$26$	−8.49200	+	4.57974i	−1.66542	+	0.898161i
$27$	−2.82336	−	2.82336i	−0.543356	−	0.543356i
$28$		0			0
$29$			0.781186i			0.145063i	0.997366	+	0.0725313i	$0.0231077\pi$
$29$			0.781186i			0.145063i	−0.997366	+	0.0725313i	$0.976892\pi$
$30$	−2.02428	+	5.99583i	−0.369582	+	1.09468i
$31$			3.69737i			0.664068i	0.943267	+	0.332034i	$0.107735\pi$
$31$			3.69737i			0.664068i	−0.943267	+	0.332034i	$0.892265\pi$
$32$	−5.61834	+	0.659012i	−0.993191	+	0.116498i
$33$	8.04183	+	8.04183i	1.39990	+	1.39990i
$34$	−2.54094	−	4.71154i	−0.435767	−	0.808023i
$35$		0			0
$36$	−1.10399	+	1.67913i	−0.183998	+	0.279855i
$37$	−2.43078	+	2.43078i	−0.399618	+	0.399618i	−0.878098	−	0.478480i	$-0.841188\pi$
$37$	−2.43078	+	2.43078i	−0.399618	+	0.399618i	0.478480	+	0.878098i	$0.341188\pi$
$38$	0.457736	−	1.52940i	0.0742546	−	0.248101i
$39$	−13.6528			−2.18619
$40$	−6.27769	−	0.768519i	−0.992590	−	0.121514i
$41$	0.451387			0.0704948			0.0352474	−	0.999379i	$-0.488778\pi$
$41$	0.451387			0.0704948			0.0352474	+	0.999379i	$0.488778\pi$
$42$		0			0
$43$	0.613245	−	0.613245i	0.0935189	−	0.0935189i	−0.658800	−	0.752319i	$-0.728935\pi$
$43$	0.613245	−	0.613245i	0.0935189	−	0.0935189i	0.752319	+	0.658800i	$0.228935\pi$
$44$	−6.24422	+	9.49725i	−0.941352	+	1.43176i
$45$	−1.64298	+	1.53246i	−0.244922	+	0.228445i
$46$	3.27031	+	6.06399i	0.482182	+	0.894087i
$47$	3.03222	+	3.03222i	0.442295	+	0.442295i	0.892783	−	0.450488i	$-0.148750\pi$
$47$	3.03222	+	3.03222i	0.442295	+	0.442295i	−0.450488	+	0.892783i	$0.648750\pi$
$48$	−7.44018	−	2.95298i	−1.07390	−	0.426226i
$49$		0			0
$50$	−6.61681	−	2.49355i	−0.935759	−	0.352641i
$51$		−	7.57485i		−	1.06069i
$52$	−2.76137	−	13.3623i	−0.382933	−	1.85302i
$53$	1.48677	+	1.48677i	0.204224	+	0.204224i	0.801807	−	0.597583i	$-0.203872\pi$
$53$	1.48677	+	1.48677i	0.204224	+	0.204224i	−0.597583	+	0.801807i	$0.703872\pi$
$54$	4.97004	−	2.68034i	0.676336	−	0.364748i
$55$	−9.29282	+	8.66767i	−1.25304	+	1.16875i
$56$		0			0
$57$	1.59738	−	1.59738i	0.211578	−	0.211578i
$58$	−1.05838	−	0.316763i	−0.138972	−	0.0415931i
$59$	−9.27479			−1.20748			−0.603738	−	0.797183i	$-0.706323\pi$
$59$	−9.27479			−1.20748			−0.603738	+	0.797183i	$0.706323\pi$
$60$	−7.30253	−	5.17382i	−0.942753	−	0.667938i
$61$	−1.51948			−0.194550			−0.0972751	−	0.995258i	$-0.531013\pi$
$61$	−1.51948			−0.194550			−0.0972751	+	0.995258i	$0.531013\pi$
$62$	−5.00933	−	1.49925i	−0.636185	−	0.190405i
$63$		0			0
$64$	1.38533	−	7.87914i	0.173166	−	0.984893i
$65$	0.530664	−	15.2459i	0.0658207	−	1.89103i
$66$	−14.1562	+	7.63447i	−1.74251	+	0.939738i
$67$	9.65994	+	9.65994i	1.18015	+	1.18015i	0.979705	+	0.200444i	$0.0642384\pi$
$67$	9.65994	+	9.65994i	1.18015	+	1.18015i	0.200444	+	0.979705i	$0.435762\pi$
$68$	7.41369	−	1.53206i	0.899041	−	0.185790i
$69$			9.74921i			1.17367i
$70$		0			0
$71$			11.8314i			1.40413i	0.712112	+	0.702066i	$0.247739\pi$
$71$			11.8314i			1.40413i	−0.712112	+	0.702066i	$0.752261\pi$
$72$	−1.82728	−	2.17659i	−0.215348	−	0.256514i
$73$	1.21746	+	1.21746i	0.142493	+	0.142493i	0.774755	−	0.632262i	$-0.217873\pi$
$73$	1.21746	+	1.21746i	0.142493	+	0.142493i	−0.632262	+	0.774755i	$0.717873\pi$
$74$	−2.30765	−	4.27896i	−0.268259	−	0.497419i
$75$	−6.56622	−	7.55010i	−0.758202	−	0.871811i
$76$	1.88647	+	1.24031i	0.216393	+	0.142274i
$77$		0			0
$78$	5.53607	−	18.4973i	0.626837	−	2.09440i
$79$	−5.46209			−0.614533			−0.307267	−	0.951623i	$-0.599414\pi$
$79$	−5.46209			−0.614533			−0.307267	+	0.951623i	$0.599414\pi$
$80$	3.58676	−	8.19360i	0.401012	−	0.916073i
$81$	11.0047			1.22275
$82$	−0.183033	+	0.611555i	−0.0202126	+	0.0675350i
$83$	0.968508	−	0.968508i	0.106308	−	0.106308i	−0.651952	−	0.758260i	$-0.726050\pi$
$83$	0.968508	−	0.968508i	0.106308	−	0.106308i	0.758260	+	0.651952i	$0.226050\pi$
$84$		0			0
$85$	8.45877	+	0.294423i	0.917482	+	0.0319347i
$86$	0.582180	+	1.07951i	0.0627781	+	0.116407i
$87$	−1.10542	−	1.10542i	−0.118514	−	0.118514i
$88$	−10.3352	−	12.3109i	−1.10174	−	1.31235i
$89$			9.42358i			0.998898i	0.866343	+	0.499449i	$0.166464\pi$
$89$			9.42358i			0.998898i	−0.866343	+	0.499449i	$0.833536\pi$
$90$	−1.41001	−	2.84737i	−0.148628	−	0.300139i
$91$		0			0
$92$	−9.54179	+	1.97184i	−0.994800	+	0.205579i
$93$	−5.23199	−	5.23199i	−0.542532	−	0.542532i
$94$	−5.33770	+	2.87862i	−0.550542	+	0.296907i
$95$	1.72169	+	1.84587i	0.176642	+	0.189382i
$96$	7.01772	−	8.88280i	0.716244	−	0.906597i
$97$	−6.77428	+	6.77428i	−0.687824	+	0.687824i	−0.961751	−	0.273927i	$-0.911677\pi$
$97$	−6.77428	+	6.77428i	−0.687824	+	0.687824i	0.273927	+	0.961751i	$0.411677\pi$
$98$		0			0
$99$	−5.71016			−0.573893
$100$	6.06140	−	7.95358i	0.606140	−	0.795358i
$101$	12.0610			1.20012			0.600059	−	0.799956i	$-0.295144\pi$
$101$	12.0610			1.20012			0.600059	+	0.799956i	$0.295144\pi$
$102$	10.2627	+	3.07153i	1.01616	+	0.304127i
$103$	−7.75896	+	7.75896i	−0.764513	+	0.764513i	−0.977135	−	0.212621i	$-0.931800\pi$
$103$	−7.75896	+	7.75896i	−0.764513	+	0.764513i	0.212621	+	0.977135i	$0.431800\pi$
$104$	19.2234	+	1.67709i	1.88501	+	0.164452i
$105$		0			0
$106$	−2.61720	+	1.41146i	−0.254205	+	0.137093i
$107$	6.96815	+	6.96815i	0.673637	+	0.673637i	0.958553	−	0.284916i	$-0.0919656\pi$
$107$	6.96815	+	6.96815i	0.673637	+	0.673637i	−0.284916	+	0.958553i	$0.591966\pi$
$108$	1.61612	+	7.82043i	0.155511	+	0.752521i
$109$			5.11637i			0.490060i	0.969516	+	0.245030i	$0.0787977\pi$
$109$			5.11637i			0.490060i	−0.969516	+	0.245030i	$0.921202\pi$
$110$	−7.97511	−	16.1049i	−0.760397	−	1.53554i
$111$		−	6.87938i		−	0.652962i
$112$		0			0
$113$	1.98553	+	1.98553i	0.186783	+	0.186783i	0.794304	−	0.607521i	$-0.207836\pi$
$113$	1.98553	+	1.98553i	0.186783	+	0.186783i	−0.607521	+	0.794304i	$0.707836\pi$
$114$	1.51646	+	2.81191i	0.142030	+	0.263359i
$115$	−10.8869	−	0.378938i	−1.01521	−	0.0353362i
$116$	0.858324	−	1.30548i	0.0796934	−	0.121211i
$117$	4.84712	−	4.84712i	0.448117	−	0.448117i
$118$	3.76084	−	12.5658i	0.346213	−	1.15678i
$119$		0			0
$120$	9.97078	−	7.79579i	0.910204	−	0.711655i
$121$	−21.2970			−1.93609
$122$	0.616137	−	2.05865i	0.0557824	−	0.186382i
$123$	−0.638739	+	0.638739i	−0.0575931	+	0.0575931i
$124$	4.06247	−	6.17888i	0.364821	−	0.554880i
$125$	8.68635	−	7.03898i	0.776931	−	0.629586i
$126$		0			0
$127$	−12.1710	−	12.1710i	−1.08000	−	1.08000i	−0.996509	−	0.0834907i	$-0.973393\pi$
$127$	−12.1710	−	12.1710i	−1.08000	−	1.08000i	−0.0834907	−	0.996509i	$-0.526607\pi$
$128$	10.1132	+	5.07181i	0.893889	+	0.448289i
$129$			1.73555i			0.152807i
$130$	20.4405	+	6.90104i	1.79275	+	0.605262i
$131$		−	3.22924i		−	0.282140i	−0.990000	−	0.141070i	$-0.954946\pi$
$131$		−	3.22924i		−	0.282140i	0.990000	−	0.141070i	$-0.0450542\pi$
$132$	−4.60322	−	22.2751i	−0.400659	−	1.93880i
$133$		0			0
$134$	−17.0046	+	9.17061i	−1.46898	+	0.792220i
$135$	−0.310577	+	8.92285i	−0.0267302	+	0.767957i
$136$	−0.930485	+	10.6656i	−0.0797885	+	0.914564i
$137$	−10.6422	+	10.6422i	−0.909221	+	0.909221i	−0.996209	−	0.0869887i	$-0.972276\pi$
$137$	−10.6422	+	10.6422i	−0.909221	+	0.909221i	0.0869887	+	0.996209i	$0.472276\pi$
$138$	−13.2086	−	3.95321i	−1.12439	−	0.336520i
$139$	−7.49343			−0.635584			−0.317792	−	0.948160i	$-0.602941\pi$
$139$	−7.49343			−0.635584			−0.317792	+	0.948160i	$0.602941\pi$
$140$		0			0
$141$	−8.58153			−0.722696
$142$	−16.0296	−	4.79753i	−1.34518	−	0.402600i
$143$	27.4156	−	27.4156i	2.29261	−	2.29261i
$144$	3.68987	−	1.59308i	0.307489	−	0.132757i
$145$	1.27738	−	1.19145i	0.106081	−	0.0989445i
$146$	−2.14313	+	1.15579i	−0.177367	+	0.0956539i
$147$		0			0
$148$	6.73302	−	1.39140i	0.553451	−	0.114373i
$149$			4.33552i			0.355180i	0.984105	+	0.177590i	$0.0568300\pi$
$149$			4.33552i			0.355180i	−0.984105	+	0.177590i	$0.943170\pi$
$150$	12.8917	−	5.83465i	1.05260	−	0.476397i
$151$			14.1691i			1.15307i	0.817074	+	0.576533i	$0.195595\pi$
$151$			14.1691i			1.15307i	−0.817074	+	0.576533i	$0.804405\pi$
$152$	−2.44537	+	2.05293i	−0.198345	+	0.166514i
$153$	2.68929	+	2.68929i	0.217416	+	0.217416i
$154$		0			0
$155$	6.04588	−	5.63916i	0.485617	−	0.452948i
$156$	22.8159	+	15.0009i	1.82673	+	1.20103i
$157$	−3.53257	+	3.53257i	−0.281929	+	0.281929i	−0.833878	−	0.551949i	$-0.813884\pi$
$157$	−3.53257	+	3.53257i	−0.281929	+	0.281929i	0.551949	+	0.833878i	$0.313884\pi$
$158$	2.21483	−	7.40023i	0.176202	−	0.588731i
$159$	−4.20773			−0.333695
$160$	9.64658	+	8.18190i	0.762629	+	0.646836i
$161$		0			0
$162$	−4.46232	+	14.9096i	−0.350593	+	1.17141i
$163$	11.4267	−	11.4267i	0.895006	−	0.895006i	−0.0999836	−	0.994989i	$-0.531879\pi$
$163$	11.4267	−	11.4267i	0.895006	−	0.895006i	0.994989	+	0.0999836i	$0.0318790\pi$
$164$	−0.754338	−	0.495960i	−0.0589039	−	0.0387279i
$165$	0.884621	−	25.4151i	0.0688677	−	1.97856i
$166$	0.919447	+	1.70489i	0.0713630	+	0.132325i
$167$	5.33030	+	5.33030i	0.412471	+	0.412471i	0.882599	−	0.470127i	$-0.155792\pi$
$167$	5.33030	+	5.33030i	0.412471	+	0.412471i	−0.470127	+	0.882599i	$0.655792\pi$
$168$		0			0
$169$			33.5440i			2.58031i
$170$	−3.82885	+	11.3408i	−0.293659	+	0.869803i
$171$			1.13423i			0.0867368i
$172$	−1.69863	+	0.351027i	−0.129519	+	0.0267656i
$173$	3.10667	+	3.10667i	0.236196	+	0.236196i	0.815273	−	0.579077i	$-0.196587\pi$
$173$	3.10667	+	3.10667i	0.236196	+	0.236196i	−0.579077	+	0.815273i	$0.696587\pi$
$174$	1.94590	−	1.04943i	0.147518	−	0.0795568i
$175$		0			0
$176$	20.8701	−	9.01057i	1.57314	−	0.679197i
$177$	13.1244	−	13.1244i	0.986487	−	0.986487i
$178$	−12.7674	−	3.82117i	−0.956957	−	0.286409i
$179$	0.679087			0.0507573			0.0253787	−	0.999678i	$-0.491921\pi$
$179$	0.679087			0.0507573			0.0253787	+	0.999678i	$0.491921\pi$
$180$	4.42946	−	0.755752i	0.330153	−	0.0563304i
$181$	7.86696			0.584746			0.292373	−	0.956304i	$-0.405555\pi$
$181$	7.86696			0.584746			0.292373	+	0.956304i	$0.405555\pi$
$182$		0			0
$183$	2.15016	−	2.15016i	0.158944	−	0.158944i
$184$	1.19758	−	13.7271i	0.0882869	−	1.01198i
$185$	7.68215	+	0.267392i	0.564803	+	0.0196590i
$186$	9.21001	−	4.96696i	0.675311	−	0.364195i
$187$	15.2108	+	15.2108i	1.11232	+	1.11232i
$188$	−1.73567	−	8.39895i	−0.126587	−	0.612557i
$189$		0			0
$190$	−3.19898	+	1.58413i	−0.232078	+	0.114925i
$191$			10.6830i			0.772998i	0.922290	+	0.386499i	$0.126316\pi$
$191$			10.6830i			0.772998i	−0.922290	+	0.386499i	$0.873684\pi$
$192$	9.18911	+	13.1098i	0.663167	+	0.946115i
$193$	7.97938	+	7.97938i	0.574369	+	0.574369i	0.933346	−	0.358978i	$-0.116875\pi$
$193$	7.97938	+	7.97938i	0.574369	+	0.574369i	−0.358978	+	0.933346i	$0.616875\pi$
$194$	−6.43113	−	11.9249i	−0.461728	−	0.856161i
$195$	20.8229	+	22.3248i	1.49116	+	1.59871i
$196$		0			0
$197$	3.29596	−	3.29596i	0.234827	−	0.234827i	−0.579877	−	0.814704i	$-0.696899\pi$
$197$	3.29596	−	3.29596i	0.234827	−	0.234827i	0.814704	+	0.579877i	$0.196899\pi$
$198$	2.31542	−	7.73632i	0.164549	−	0.549797i
$199$	9.57804			0.678969			0.339484	−	0.940612i	$-0.389747\pi$
$199$	9.57804			0.678969			0.339484	+	0.940612i	$0.389747\pi$
$200$	8.31794	+	11.4373i	0.588167	+	0.808739i
$201$	−27.3387			−1.92832
$202$	−4.89064	+	16.3407i	−0.344104	+	1.14973i
$203$		0			0
$204$	−8.32283	+	12.6587i	−0.582714	+	0.886289i
$205$	−0.688447	−	0.738101i	−0.0480832	−	0.0515512i
$206$	−7.36593	−	13.6583i	−0.513208	−	0.951619i
$207$	−3.46125	−	3.46125i	−0.240573	−	0.240573i
$208$	−10.0671	+	25.3645i	−0.698027	+	1.75871i
$209$			6.41528i			0.443754i
$210$		0			0
$211$			19.2356i			1.32424i	0.749400	+	0.662118i	$0.230342\pi$
$211$			19.2356i			1.32424i	−0.749400	+	0.662118i	$0.769658\pi$
$212$	−0.851043	−	4.11821i	−0.0584498	−	0.282840i
$213$	−16.7421	−	16.7421i	−1.14715	−	1.14715i
$214$	−12.2662	+	6.61518i	−0.838501	+	0.452204i
$215$	−1.93808	−	0.0674584i	−0.132176	−	0.00460063i
$216$	−11.2507	−	0.981536i	−0.765514	−	0.0667850i
$217$		0			0
$218$	−6.93184	−	2.07464i	−0.469483	−	0.140512i
$219$	−3.44556			−0.232829
$220$	25.0533	−	4.27458i	1.68909	−	0.288192i
$221$	−25.8236			−1.73708
$222$	9.32043	+	2.78952i	0.625546	+	0.187221i
$223$	−6.67775	+	6.67775i	−0.447175	+	0.447175i	−0.894414	−	0.447239i	$-0.852407\pi$
$223$	−6.67775	+	6.67775i	−0.447175	+	0.447175i	0.447239	+	0.894414i	$0.352407\pi$
$224$		0			0
$225$	5.01170	+	0.349306i	0.334113	+	0.0232871i
$226$	−3.49517	+	1.88495i	−0.232495	+	0.125385i
$227$	19.3121	+	19.3121i	1.28179	+	1.28179i	0.939648	+	0.342143i	$0.111153\pi$
$227$	19.3121	+	19.3121i	1.28179	+	1.28179i	0.342143	+	0.939648i	$0.388847\pi$
$228$	−4.42458	+	0.914355i	−0.293025	+	0.0605547i
$229$		−	12.6547i		−	0.836246i	−0.908390	−	0.418123i	$-0.862688\pi$
$229$		−	12.6547i		−	0.836246i	0.908390	−	0.418123i	$-0.137312\pi$
$230$	4.92792	−	14.5962i	0.324937	−	0.962448i
$231$		0			0
$232$	1.42067	+	1.69225i	0.0932716	+	0.111102i
$233$	12.2544	+	12.2544i	0.802814	+	0.802814i	0.983535	−	0.180720i	$-0.0578429\pi$
$233$	12.2544	+	12.2544i	0.802814	+	0.802814i	−0.180720	+	0.983535i	$0.557843\pi$
$234$	4.60159	+	8.53252i	0.300815	+	0.557788i
$235$	0.333552	−	9.58293i	0.0217585	−	0.625121i
$236$	15.4996	+	10.1906i	1.00894	+	0.663354i
$237$	7.72917	−	7.72917i	0.502064	−	0.502064i
$238$		0			0
$239$	−21.7639			−1.40779			−0.703893	−	0.710306i	$-0.748557\pi$
$239$	−21.7639			−1.40779			−0.703893	+	0.710306i	$0.748557\pi$
$240$	6.51895	+	16.6699i	0.420796	+	1.07604i
$241$	20.8514			1.34316			0.671579	−	0.740933i	$-0.265616\pi$
$241$	20.8514			1.34316			0.671579	+	0.740933i	$0.265616\pi$
$242$	8.63573	−	28.8539i	0.555126	−	1.85480i
$243$	−7.10226	+	7.10226i	−0.455610	+	0.455610i
$244$	2.53929	+	1.66953i	0.162562	+	0.106881i
$245$		0			0
$246$	−0.606383	−	1.12439i	−0.0386616	−	0.0716883i
$247$	−5.44567	−	5.44567i	−0.346500	−	0.346500i
$248$	6.72407	+	8.00945i	0.426979	+	0.508601i
$249$			2.74099i			0.173703i
$250$	6.01442	+	14.6228i	0.380385	+	0.924828i
$251$		−	14.6586i		−	0.925243i	−0.886556	−	0.462621i	$-0.846909\pi$
$251$		−	14.6586i		−	0.925243i	0.886556	−	0.462621i	$-0.153091\pi$
$252$		0			0
$253$	−19.5770	−	19.5770i	−1.23080	−	1.23080i
$254$	21.4249	−	11.5544i	1.34432	−	0.724990i
$255$	−12.3863	+	11.5530i	−0.775658	+	0.723478i
$256$	−10.9723	+	11.6451i	−0.685767	+	0.727821i
$257$	9.69389	−	9.69389i	0.604688	−	0.604688i	−0.336865	−	0.941553i	$-0.609367\pi$
$257$	9.69389	−	9.69389i	0.604688	−	0.604688i	0.941553	+	0.336865i	$0.109367\pi$
$258$	−2.35139	−	0.703750i	−0.146391	−	0.0438136i
$259$		0			0
$260$	−17.6382	+	24.8953i	−1.09388	+	1.54394i
$261$	0.784913			0.0485849
$262$	4.37508	+	1.30942i	0.270293	+	0.0808965i
$263$	16.2797	−	16.2797i	1.00385	−	1.00385i	0.00385576	−	0.999993i	$-0.498773\pi$
$263$	16.2797	−	16.2797i	1.00385	−	1.00385i	0.999993	−	0.00385576i	$-0.00122733\pi$
$264$	32.0456	+	2.79573i	1.97227	+	0.172065i
$265$	0.163549	−	4.69874i	0.0100467	−	0.288641i
$266$		0			0
$267$	−13.3349	−	13.3349i	−0.816083	−	0.816083i
$268$	−5.52944	−	26.7571i	−0.337764	−	1.63445i
$269$		−	30.2134i		−	1.84214i	−0.389396	−	0.921070i	$-0.627316\pi$
$269$		−	30.2134i		−	1.84214i	0.389396	−	0.921070i	$-0.372684\pi$
$270$	−11.9631	−	4.03891i	−0.728048	−	0.245800i
$271$		−	10.7605i		−	0.653656i	−0.945084	−	0.326828i	$-0.894020\pi$
$271$		−	10.7605i		−	0.653656i	0.945084	−	0.326828i	$-0.105980\pi$
$272$	−14.0728	−	5.58544i	−0.853287	−	0.338667i
$273$		0			0
$274$	−10.1031	−	18.7337i	−0.610349	−	1.13174i
$275$	28.3465	+	1.97570i	1.70936	+	0.119139i
$276$	10.7119	−	16.2924i	0.644781	−	0.980690i
$277$	22.8225	−	22.8225i	1.37127	−	1.37127i	0.512709	−	0.858562i	$-0.328642\pi$
$277$	22.8225	−	22.8225i	1.37127	−	1.37127i	0.858562	−	0.512709i	$-0.171358\pi$
$278$	3.03851	−	10.1524i	0.182238	−	0.608898i
$279$	3.71501			0.222412
$280$		0			0
$281$	1.05159			0.0627325			0.0313663	−	0.999508i	$-0.490014\pi$
$281$	1.05159			0.0627325			0.0313663	+	0.999508i	$0.490014\pi$
$282$	3.47973	−	11.6266i	0.207215	−	0.692352i
$283$	−7.60096	+	7.60096i	−0.451830	+	0.451830i	−0.895962	−	0.444132i	$-0.853512\pi$
$283$	−7.60096	+	7.60096i	−0.451830	+	0.451830i	0.444132	+	0.895962i	$0.353512\pi$
$284$	12.9997	−	19.7722i	0.771392	−	1.17326i
$285$	−5.04830	−	0.175716i	−0.299036	−	0.0104085i
$286$	26.0269	+	48.2604i	1.53900	+	2.85370i
$287$		0			0
$288$	0.662156	+	5.64514i	0.0390179	+	0.332643i
$289$			2.67251i			0.157207i
$290$	1.09625	+	2.21376i	0.0643741	+	0.129997i
$291$		−	19.1720i		−	1.12388i
$292$	−0.696887	−	3.37225i	−0.0407822	−	0.197346i
$293$	−19.1160	−	19.1160i	−1.11677	−	1.11677i	−0.992213	−	0.124555i	$-0.960250\pi$
$293$	−19.1160	−	19.1160i	−1.11677	−	1.11677i	−0.124555	−	0.992213i	$-0.539750\pi$
$294$		0			0
$295$	14.1457	+	15.1660i	0.823597	+	0.882998i
$296$	−0.845055	+	9.68633i	−0.0491178	+	0.563006i
$297$	−16.0453	+	16.0453i	−0.931043	+	0.931043i
$298$	−5.87392	−	1.75801i	−0.340267	−	0.101839i
$299$	33.2363			1.92211
$300$	2.67753	+	19.8320i	0.154587	+	1.14500i
$301$		0			0
$302$	−19.1968	−	5.74544i	−1.10465	−	0.330613i
$303$	−17.0671	+	17.0671i	−0.980477	+	0.980477i
$304$	−1.78980	−	4.14551i	−0.102652	−	0.237761i
$305$	2.31749	+	2.48464i	0.132699	+	0.142270i
$306$	−4.73402	+	2.55306i	−0.270626	+	0.145949i
$307$	−0.726484	−	0.726484i	−0.0414626	−	0.0414626i	0.686071	−	0.727534i	$-0.259334\pi$
$307$	−0.726484	−	0.726484i	−0.0414626	−	0.0414626i	−0.727534	+	0.686071i	$0.759334\pi$
$308$		0			0
$309$		−	21.9587i		−	1.24919i
$310$	5.18858	+	10.4778i	0.294692	+	0.595099i
$311$			13.3115i			0.754824i	0.926045	+	0.377412i	$0.123186\pi$
$311$			13.3115i			0.754824i	−0.926045	+	0.377412i	$0.876814\pi$
$312$	−29.5754	+	24.8290i	−1.67438	+	1.40567i
$313$	15.3769	+	15.3769i	0.869155	+	0.869155i	0.992379	−	0.123224i	$-0.0393234\pi$
$313$	15.3769	+	15.3769i	0.869155	+	0.869155i	−0.123224	+	0.992379i	$0.539323\pi$
$314$	−3.35362	−	6.21847i	−0.189256	−	0.350928i
$315$		0			0
$316$	9.12800	+	6.00145i	0.513490	+	0.337608i
$317$	−10.9153	+	10.9153i	−0.613063	+	0.613063i	−0.943743	−	0.330680i	$-0.892722\pi$
$317$	−10.9153	+	10.9153i	−0.613063	+	0.613063i	0.330680	+	0.943743i	$0.392722\pi$
$318$	1.70620	−	5.70078i	0.0956787	−	0.319684i
$319$	4.43951			0.248565
$320$	−14.9967	+	9.75185i	−0.838342	+	0.545145i
$321$	−19.7207			−1.10070
$322$		0			0
$323$	3.02137	−	3.02137i	0.168114	−	0.168114i
$324$	−18.3906	−	12.0914i	−1.02170	−	0.671745i
$325$	−25.7393	+	22.3851i	−1.42776	+	1.24170i
$326$	10.8478	+	20.1146i	0.600806	+	1.11405i
$327$	−7.23996	−	7.23996i	−0.400370	−	0.400370i
$328$	0.977820	−	0.820897i	0.0539911	−	0.0453264i
$329$		0			0
$330$	34.0746	+	11.5041i	1.87574	+	0.633280i
$331$		−	26.4652i		−	1.45466i	−0.686287	−	0.727330i	$-0.740761\pi$
$331$		−	26.4652i		−	1.45466i	0.686287	−	0.727330i	$-0.259239\pi$
$332$	−2.68267	+	0.554383i	−0.147231	+	0.0304257i
$333$	2.44238	+	2.44238i	0.133841	+	0.133841i
$334$	−9.38307	+	5.06029i	−0.513418	+	0.276887i
$335$	1.06262	−	30.5289i	0.0580570	−	1.66797i
$336$		0			0
$337$	−10.6349	+	10.6349i	−0.579322	+	0.579322i	−0.934717	−	0.355394i	$-0.884347\pi$
$337$	−10.6349	+	10.6349i	−0.579322	+	0.579322i	0.355394	+	0.934717i	$0.384347\pi$
$338$	−45.4466	−	13.6018i	−2.47197	−	0.739840i
$339$	−5.61926			−0.305196
$340$	−13.8124	−	9.78606i	−0.749083	−	0.530724i
$341$	21.0123			1.13788
$342$	−1.53670	−	0.459920i	−0.0830950	−	0.0248696i
$343$		0			0
$344$	0.213193	−	2.44370i	0.0114946	−	0.131755i
$345$	15.9417	−	14.8693i	0.858275	−	0.800537i
$346$	−5.46874	+	2.94930i	−0.294002	+	0.158555i
$347$	−3.70208	−	3.70208i	−0.198738	−	0.198738i	0.600721	−	0.799459i	$-0.294880\pi$
$347$	−3.70208	−	3.70208i	−0.198738	−	0.198738i	−0.799459	+	0.600721i	$0.794880\pi$
$348$	0.632754	+	3.06191i	0.0339192	+	0.164136i
$349$		−	27.3545i		−	1.46426i	−0.681168	−	0.732128i	$-0.738527\pi$
$349$		−	27.3545i		−	1.46426i	0.681168	−	0.732128i	$-0.261473\pi$
$350$		0			0
$351$		−	27.2404i		−	1.45399i
$352$	3.74520	+	31.9293i	0.199620	+	1.70184i
$353$	−10.5919	−	10.5919i	−0.563748	−	0.563748i	0.366622	−	0.930370i	$-0.380514\pi$
$353$	−10.5919	−	10.5919i	−0.563748	−	0.563748i	−0.930370	+	0.366622i	$0.880514\pi$
$354$	12.4595	+	23.1031i	0.662217	+	1.22792i
$355$	19.3466	−	18.0451i	1.02681	−	0.957733i
$356$	10.3541	−	15.7483i	0.548767	−	0.834656i
$357$		0			0
$358$	−0.275363	+	0.920050i	−0.0145534	+	0.0486262i
$359$	−23.9822			−1.26573			−0.632867	−	0.774260i	$-0.718122\pi$
$359$	−23.9822			−1.26573			−0.632867	+	0.774260i	$0.718122\pi$
$360$	−0.772186	+	6.30764i	−0.0406978	+	0.332442i
$361$	−17.7257			−0.932932
$362$	−3.18998	+	10.6584i	−0.167661	+	0.560194i
$363$	30.1365	−	30.1365i	1.58175	−	1.58175i
$364$		0			0
$365$	0.133924	−	3.84762i	0.00700989	−	0.201394i
$366$	2.04124	+	3.78498i	0.106697	+	0.197844i
$367$	−9.57685	−	9.57685i	−0.499908	−	0.499908i	0.411501	−	0.911409i	$-0.365005\pi$
$367$	−9.57685	−	9.57685i	−0.499908	−	0.499908i	−0.911409	+	0.411501i	$0.865005\pi$
$368$	18.1124	+	7.18874i	0.944172	+	0.374739i
$369$		−	0.453541i		−	0.0236104i
$370$	−3.47731	+	10.2996i	−0.180777	+	0.535452i
$371$		0			0
$372$	2.99484	+	14.4921i	0.155275	+	0.751380i
$373$	13.0073	+	13.0073i	0.673494	+	0.673494i	0.958520	−	0.285026i	$-0.0920022\pi$
$373$	13.0073	+	13.0073i	0.673494	+	0.673494i	−0.285026	+	0.958520i	$0.592002\pi$
$374$	−26.7759	+	14.4403i	−1.38455	+	0.746688i
$375$	−2.33113	+	22.2522i	−0.120379	+	1.14910i
$376$	12.0830	+	1.05415i	0.623133	+	0.0543634i
$377$	−3.76852	+	3.76852i	−0.194089	+	0.194089i
$378$		0			0
$379$	27.8562			1.43088			0.715440	−	0.698675i	$-0.246226\pi$
$379$	27.8562			1.43088			0.715440	+	0.698675i	$0.246226\pi$
$380$	−0.849076	−	4.97643i	−0.0435567	−	0.255286i
$381$	34.4452			1.76468
$382$	−14.4738	−	4.33187i	−0.740542	−	0.221638i
$383$	−9.34843	+	9.34843i	−0.477683	+	0.477683i	−0.904390	−	0.426707i	$-0.859673\pi$
$383$	−9.34843	+	9.34843i	−0.477683	+	0.477683i	0.426707	+	0.904390i	$0.359673\pi$
$384$	−21.4876	+	7.13385i	−1.09654	+	0.364048i
$385$		0			0
$386$	−14.0463	+	7.57518i	−0.714938	+	0.385567i
$387$	−0.616170	−	0.616170i	−0.0313217	−	0.0313217i
$388$	18.7641	−	3.87766i	0.952602	−	0.196859i
$389$			16.8299i			0.853308i	0.904415	+	0.426654i	$0.140308\pi$
$389$			16.8299i			0.853308i	−0.904415	+	0.426654i	$0.859692\pi$
$390$	−38.6899	+	19.1592i	−1.95914	+	0.970162i
$391$			18.4402i			0.932561i
$392$		0			0
$393$	4.56955	+	4.56955i	0.230503	+	0.230503i
$394$	3.12900	+	5.80195i	0.157637	+	0.292298i
$395$	8.33068	+	8.93152i	0.419162	+	0.449394i
$396$	9.54256	+	6.27401i	0.479532	+	0.315281i
$397$	−7.34767	+	7.34767i	−0.368769	+	0.368769i	−0.867028	−	0.498259i	$-0.833973\pi$
$397$	−7.34767	+	7.34767i	−0.368769	+	0.368769i	0.498259	+	0.867028i	$0.333973\pi$
$398$	−3.88380	+	12.9767i	−0.194677	+	0.650461i
$399$		0			0
$400$	−18.8685	+	6.63172i	−0.943425	+	0.331586i
$401$	22.1972			1.10848			0.554239	−	0.832358i	$-0.313009\pi$
$401$	22.1972			1.10848			0.554239	+	0.832358i	$0.313009\pi$
$402$	11.0856	−	37.0394i	0.552899	−	1.84736i
$403$	−17.8365	+	17.8365i	−0.888501	+	0.888501i
$404$	−20.1559	−	13.2520i	−1.00279	−	0.659312i
$405$	−16.7842	−	17.9948i	−0.834015	−	0.894168i
$406$		0			0
$407$	13.8142	+	13.8142i	0.684746	+	0.684746i
$408$	−13.7757	−	16.4091i	−0.681998	−	0.812369i
$409$		−	9.21458i		−	0.455632i	−0.973704	−	0.227816i	$-0.926842\pi$
$409$		−	9.21458i		−	0.455632i	0.973704	−	0.227816i	$-0.0731585\pi$
$410$	1.27916	−	0.633439i	0.0631734	−	0.0312833i
$411$		−	30.1185i		−	1.48564i
$412$	21.4916	−	4.44130i	1.05881	−	0.218807i
$413$		0			0
$414$	6.09292	−	3.28592i	0.299451	−	0.161494i
$415$	−3.06084	−	0.106538i	−0.150251	−	0.00522976i
$416$	−30.2826	−	23.9243i	−1.48473	−	1.17299i
$417$	10.6036	−	10.6036i	0.519262	−	0.519262i
$418$	−8.69164	−	2.60133i	−0.425122	−	0.127235i
$419$	−18.5156			−0.904546			−0.452273	−	0.891880i	$-0.649387\pi$
$419$	−18.5156			−0.904546			−0.452273	+	0.891880i	$0.649387\pi$
$420$		0			0
$421$	25.5501			1.24524			0.622619	−	0.782525i	$-0.286069\pi$
$421$	25.5501			1.24524			0.622619	+	0.782525i	$0.286069\pi$
$422$	−26.0611	−	7.79987i	−1.26864	−	0.379692i
$423$	3.04669	−	3.04669i	0.148135	−	0.148135i
$424$	5.92458	+	0.516873i	0.287723	+	0.0251016i
$425$	−12.4197	−	14.2807i	−0.602445	−	0.692715i
$426$	29.4716	−	15.8941i	1.42790	−	0.770070i
$427$		0			0
$428$	−3.98864	−	19.3011i	−0.192798	−	0.932953i
$429$			77.5893i			3.74605i
$430$	0.877267	−	2.59842i	0.0423056	−	0.125307i
$431$		−	10.4213i		−	0.501978i	−0.967990	−	0.250989i	$-0.919244\pi$
$431$		−	10.4213i		−	0.501978i	0.967990	−	0.250989i	$-0.0807559\pi$
$432$	5.89188	−	14.8449i	0.283473	−	0.714223i
$433$	20.3802	+	20.3802i	0.979412	+	0.979412i	0.999792	−	0.0203805i	$-0.00648777\pi$
$433$	20.3802	+	20.3802i	0.979412	+	0.979412i	−0.0203805	+	0.999792i	$0.506488\pi$
$434$		0			0
$435$	−0.121599	+	3.49354i	−0.00583023	+	0.167502i
$436$	5.62159	−	8.55025i	0.269225	−	0.409483i
$437$	−3.88866	+	3.88866i	−0.186020	+	0.186020i
$438$	1.39714	−	4.66816i	0.0667579	−	0.223053i
$439$	−20.8364			−0.994466			−0.497233	−	0.867617i	$-0.665651\pi$
$439$	−20.8364			−0.994466			−0.497233	+	0.867617i	$0.665651\pi$
$440$	−4.36753	+	35.6764i	−0.208214	+	1.70081i
$441$		0			0
$442$	10.4712	−	34.9867i	0.498066	−	1.66415i
$443$	−18.8907	+	18.8907i	−0.897525	+	0.897525i	−0.995217	−	0.0976921i	$-0.968854\pi$
$443$	−18.8907	+	18.8907i	−0.897525	+	0.897525i	0.0976921	+	0.995217i	$0.468854\pi$
$444$	−7.55869	+	11.4965i	−0.358720	+	0.545600i
$445$	15.4093	−	14.3727i	0.730470	−	0.681330i
$446$	−6.33948	−	11.7550i	−0.300183	−	0.556616i
$447$	−6.13501	−	6.13501i	−0.290176	−	0.290176i
$448$		0			0
$449$		−	27.5815i		−	1.30165i	−0.759227	−	0.650826i	$-0.774423\pi$
$449$		−	27.5815i		−	1.30165i	0.759227	−	0.650826i	$-0.225577\pi$
$450$	−2.50545	+	6.64838i	−0.118108	+	0.313408i
$451$		−	2.56525i		−	0.120793i
$452$	−1.13653	−	5.49971i	−0.0534580	−	0.258684i
$453$	−20.0501	−	20.0501i	−0.942035	−	0.942035i
$454$	−33.9956	+	18.3339i	−1.59549	+	0.860451i
$455$		0			0
$456$	0.555326	−	6.36534i	0.0260055	−	0.298084i
$457$	0.972763	−	0.972763i	0.0455040	−	0.0455040i	−0.683989	−	0.729493i	$-0.739756\pi$
$457$	0.972763	−	0.972763i	0.0455040	−	0.0455040i	0.729493	+	0.683989i	$0.239756\pi$
$458$	17.1450	+	5.13136i	0.801134	+	0.239773i
$459$	15.1136			0.705440
$460$	17.7773	+	12.5952i	0.828870	+	0.587252i
$461$	−17.6688			−0.822918			−0.411459	−	0.911428i	$-0.634981\pi$
$461$	−17.6688			−0.822918			−0.411459	+	0.911428i	$0.634981\pi$
$462$		0			0
$463$	5.55471	−	5.55471i	0.258149	−	0.258149i	−0.566152	−	0.824301i	$-0.691568\pi$
$463$	5.55471	−	5.55471i	0.258149	−	0.258149i	0.824301	+	0.566152i	$0.191568\pi$
$464$	−2.86878	+	1.23858i	−0.133180	+	0.0574998i
$465$	−0.575532	+	16.5350i	−0.0266897	+	0.766792i
$466$	−21.5718	+	11.6337i	−0.999293	+	0.538919i
$467$	−9.27108	−	9.27108i	−0.429014	−	0.429014i	0.459278	−	0.888293i	$-0.348108\pi$
$467$	−9.27108	−	9.27108i	−0.429014	−	0.429014i	−0.888293	+	0.459278i	$0.848108\pi$
$468$	−13.4261	+	2.77454i	−0.620619	+	0.128253i
$469$		0			0
$470$	12.8480	+	4.33769i	0.592635	+	0.200083i
$471$		−	9.99756i		−	0.460663i
$472$	−20.0916	+	16.8672i	−0.924790	+	0.776376i
$473$	−3.48510	−	3.48510i	−0.160245	−	0.160245i
$474$	7.33764	+	13.6059i	0.337029	+	0.624938i
$475$	0.392441	−	5.63057i	0.0180064	−	0.258348i
$476$		0			0
$477$	1.49387	−	1.49387i	0.0683994	−	0.0683994i
$478$	8.82504	−	29.4864i	0.403648	−	1.34868i
$479$	2.54348			0.116214			0.0581072	−	0.998310i	$-0.481493\pi$
$479$	2.54348			0.116214			0.0581072	+	0.998310i	$0.481493\pi$
$480$	−25.2283	+	2.07262i	−1.15151	+	0.0946015i
$481$	−23.4527			−1.06935
$482$	−8.45506	+	28.2502i	−0.385117	+	1.28676i
$483$		0			0
$484$	35.5906	+	23.4000i	1.61775	+	1.06364i
$485$	21.4092	+	0.745188i	0.972141	+	0.0338372i
$486$	−6.74249	−	12.5023i	−0.305845	−	0.567115i
$487$	2.60265	+	2.60265i	0.117937	+	0.117937i	0.763612	−	0.645675i	$-0.223424\pi$
$487$	2.60265	+	2.60265i	0.117937	+	0.117937i	−0.645675	+	0.763612i	$0.723424\pi$
$488$	−3.29159	+	2.76335i	−0.149003	+	0.125091i
$489$			32.3388i			1.46241i
$490$		0			0
$491$		−	22.3410i		−	1.00823i	−0.863635	−	0.504117i	$-0.831818\pi$
$491$		−	22.3410i		−	1.00823i	0.863635	−	0.504117i	$-0.168182\pi$
$492$	1.76924	−	0.365620i	0.0797636	−	0.0164834i
$493$	−2.09086	−	2.09086i	−0.0941674	−	0.0941674i
$494$	9.58615	−	5.16982i	0.431301	−	0.232601i
$495$	8.70902	+	9.33716i	0.391442	+	0.419674i
$496$	−13.5780	+	5.86225i	−0.609672	+	0.263223i
$497$		0			0
$498$	−3.71358	−	1.11144i	−0.166410	−	0.0498050i
$499$	−9.95656			−0.445717			−0.222858	−	0.974851i	$-0.571539\pi$
$499$	−9.95656			−0.445717			−0.222858	+	0.974851i	$0.571539\pi$
$500$	−22.2503	+	2.21913i	−0.995063	+	0.0992427i
$501$	−15.0854			−0.673964
$502$	19.8600	+	5.94392i	0.886394	+	0.265290i
$503$	−8.22634	+	8.22634i	−0.366794	+	0.366794i	−0.866307	−	0.499512i	$-0.833513\pi$
$503$	−8.22634	+	8.22634i	−0.366794	+	0.366794i	0.499512	+	0.866307i	$0.333513\pi$
$504$		0			0
$505$	−18.3953	−	19.7220i	−0.818579	−	0.877618i
$506$	34.4619	−	18.5853i	1.53202	−	0.826219i
$507$	−47.4667	−	47.4667i	−2.10807	−	2.10807i
$508$	6.96678	+	33.7124i	0.309101	+	1.49575i
$509$		−	32.8461i		−	1.45588i	−0.685643	−	0.727938i	$-0.740479\pi$
$509$		−	32.8461i		−	1.45588i	0.685643	−	0.727938i	$-0.259521\pi$
$510$	−10.6299	−	21.4660i	−0.470700	−	0.950529i
$511$		0			0
$512$	−11.3281	−	19.5876i	−0.500636	−	0.865658i
$513$	3.18714	+	3.18714i	0.140716	+	0.140716i
$514$	9.20284	+	17.0644i	0.405920	+	0.752678i
$515$	24.5211	+	0.853505i	1.08053	+	0.0376099i
$516$	1.90693	−	2.90038i	0.0839479	−	0.127682i
$517$	17.2323	−	17.2323i	0.757874	−	0.757874i
$518$		0			0
$519$	−8.79222			−0.385936
$520$	−26.5768	−	33.9917i	−1.16547	−	1.49063i
$521$	−1.79803			−0.0787730			−0.0393865	−	0.999224i	$-0.512540\pi$
$521$	−1.79803			−0.0787730			−0.0393865	+	0.999224i	$0.512540\pi$
$522$	−0.318275	+	1.06343i	−0.0139305	+	0.0465449i
$523$	−18.1484	+	18.1484i	−0.793574	+	0.793574i	−0.982073	−	0.188499i	$-0.939638\pi$
$523$	−18.1484	+	18.1484i	−0.793574	+	0.793574i	0.188499	+	0.982073i	$0.439638\pi$
$524$	−3.54811	+	5.39655i	−0.155000	+	0.235750i
$525$		0			0
$526$	15.4550	+	28.6575i	0.673871	+	1.24953i
$527$	−9.89608	−	9.89608i	−0.431080	−	0.431080i
$528$	−16.7819	+	42.2829i	−0.730340	+	1.84013i
$529$		−	0.733480i		−	0.0318905i
$530$	6.29970	+	2.12688i	0.273641	+	0.0923856i
$531$			9.31904i			0.404412i
$532$		0			0
$533$	2.17754	+	2.17754i	0.0943198	+	0.0943198i
$534$	23.4738	−	12.6594i	1.01581	−	0.547826i
$535$	0.766514	−	22.0219i	0.0331393	−	0.952090i
$536$	38.4935	+	3.35826i	1.66267	+	0.145055i
$537$	−0.960946	+	0.960946i	−0.0414679	+	0.0414679i
$538$	40.9341	+	12.2512i	1.76479	+	0.528188i
$539$		0			0
$540$	10.3230	−	14.5702i	0.444230	−	0.627003i
$541$	−25.3319			−1.08910			−0.544552	−	0.838727i	$-0.683300\pi$
$541$	−25.3319			−1.08910			−0.544552	+	0.838727i	$0.683300\pi$
$542$	14.5787	+	4.36330i	0.626211	+	0.187420i
$543$	−11.1322	+	11.1322i	−0.477728	+	0.477728i
$544$	13.2737	−	16.8014i	0.569106	−	0.720355i
$545$	8.36620	−	7.80339i	0.358369	−	0.334261i
$546$		0			0
$547$	17.3594	+	17.3594i	0.742233	+	0.742233i	0.973007	−	0.230774i	$-0.0741260\pi$
$547$	17.3594	+	17.3594i	0.742233	+	0.742233i	−0.230774	+	0.973007i	$0.574126\pi$
$548$	29.4777	−	6.09167i	1.25923	−	0.260223i
$549$			1.52673i			0.0651594i
$550$	−14.1710	+	37.6036i	−0.604252	+	1.60342i
$551$		−	0.881837i		−	0.0375675i
$552$	17.7300	+	21.1193i	0.754639	+	0.898897i
$553$		0			0
$554$	21.6664	+	40.1750i	0.920518	+	1.70687i
$555$	−11.2490	+	10.4923i	−0.477496	+	0.445373i
$556$	12.5227	+	8.23337i	0.531080	+	0.349173i
$557$	−19.9014	+	19.9014i	−0.843247	+	0.843247i	−0.989280	−	0.146032i	$-0.953350\pi$
$557$	−19.9014	+	19.9014i	−0.843247	+	0.843247i	0.146032	+	0.989280i	$0.453350\pi$
$558$	−1.50640	+	5.03323i	−0.0637711	+	0.213074i
$559$	5.91672			0.250250
$560$		0			0
$561$	−43.0482			−1.81750
$562$	−0.426409	+	1.42473i	−0.0179870	+	0.0600986i
$563$	−17.2935	+	17.2935i	−0.728833	+	0.728833i	−0.970387	−	0.241554i	$-0.922343\pi$
$563$	−17.2935	+	17.2935i	−0.728833	+	0.728833i	0.241554	+	0.970387i	$0.422343\pi$
$564$	14.3411	+	9.42892i	0.603868	+	0.397029i
$565$	0.218413	−	6.27498i	0.00918869	−	0.263990i
$566$	−7.21592	−	13.3802i	−0.303308	−	0.562410i
$567$		0			0
$568$	21.5167	+	25.6299i	0.902822	+	1.07541i
$569$		−	40.4108i		−	1.69411i	−0.531505	−	0.847055i	$-0.678373\pi$
$569$		−	40.4108i		−	1.69411i	0.531505	−	0.847055i	$-0.321627\pi$
$570$	2.28510	−	6.76836i	0.0957125	−	0.283496i
$571$		−	15.6638i		−	0.655512i	−0.944762	−	0.327756i	$-0.893708\pi$
$571$		−	15.6638i		−	0.655512i	0.944762	−	0.327756i	$-0.106292\pi$
$572$	−75.9386	+	15.6930i	−3.17515	+	0.656156i
$573$	−15.1171	−	15.1171i	−0.631526	−	0.631526i
$574$		0			0
$575$	15.9848	+	18.3800i	0.666612	+	0.766498i
$576$	−7.91673	−	1.39194i	−0.329864	−	0.0579974i
$577$	−8.05576	+	8.05576i	−0.335365	+	0.335365i	−0.854620	−	0.519254i	$-0.826210\pi$
$577$	−8.05576	+	8.05576i	−0.335365	+	0.335365i	0.519254	+	0.854620i	$0.326210\pi$
$578$	−3.62081	−	1.08368i	−0.150606	−	0.0450751i
$579$	−22.5826			−0.938499
$580$	−3.44380	+	0.587579i	−0.142996	+	0.0243979i
$581$		0			0
$582$	25.9749	+	7.77406i	1.07669	+	0.322245i
$583$	8.44939	−	8.44939i	0.349938	−	0.349938i
$584$	4.85142	+	0.423248i	0.200753	+	0.0175141i
$585$	−15.3187	−	0.533196i	−0.633349	−	0.0220449i
$586$	33.6503	−	18.1476i	1.39008	−	0.749672i
$587$	10.0769	+	10.0769i	0.415916	+	0.415916i	0.883794	−	0.467877i	$-0.154981\pi$
$587$	10.0769	+	10.0769i	0.415916	+	0.415916i	−0.467877	+	0.883794i	$0.654981\pi$
$588$		0			0
$589$		−	4.17376i		−	0.171977i
$590$	−26.2834	+	13.0155i	−1.08207	+	0.535839i
$591$			9.32793i			0.383700i
$592$	−12.7807	−	5.07262i	−0.525284	−	0.208484i
$593$	7.85987	+	7.85987i	0.322766	+	0.322766i	0.849827	−	0.527061i	$-0.176706\pi$
$593$	7.85987	+	7.85987i	0.322766	+	0.322766i	−0.527061	+	0.849827i	$0.676706\pi$
$594$	−15.2325	−	28.2449i	−0.624997	−	1.15890i
$595$		0			0
$596$	4.76363	−	7.24533i	0.195126	−	0.296780i
$597$	−13.5535	+	13.5535i	−0.554706	+	0.554706i
$598$	−13.4770	+	45.0297i	−0.551116	+	1.84140i
$599$	−11.3067			−0.461978			−0.230989	−	0.972956i	$-0.574196\pi$
$599$	−11.3067			−0.461978			−0.230989	+	0.972956i	$0.574196\pi$
$600$	−27.9548	−	4.41407i	−1.14125	−	0.180204i
$601$	−37.1086			−1.51369			−0.756846	−	0.653593i	$-0.773261\pi$
$601$	−37.1086			−1.51369			−0.756846	+	0.653593i	$0.773261\pi$
$602$		0			0
$603$	9.70602	−	9.70602i	0.395260	−	0.395260i
$604$	15.5682	−	23.6788i	0.633462	−	0.963475i
$605$	32.4818	+	34.8245i	1.32057	+	1.41582i
$606$	−16.2025	−	30.0436i	−0.658182	−	1.22044i
$607$	20.9421	+	20.9421i	0.850015	+	0.850015i	0.990135	−	0.140120i	$-0.0447487\pi$
$607$	20.9421	+	20.9421i	0.850015	+	0.850015i	−0.140120	+	0.990135i	$0.544749\pi$
$608$	6.34223	−	0.743923i	0.257211	−	0.0301700i
$609$		0			0
$610$	−4.30599	+	2.13232i	−0.174345	+	0.0863351i
$611$			29.2555i			1.18355i
$612$	−1.53937	−	7.44906i	−0.0622255	−	0.301110i
$613$	−3.30886	−	3.30886i	−0.133643	−	0.133643i	0.637121	−	0.770764i	$-0.280125\pi$
$613$	−3.30886	−	3.30886i	−0.133643	−	0.133643i	−0.770764	+	0.637121i	$0.780125\pi$
$614$	1.27885	−	0.689683i	0.0516101	−	0.0278334i
$615$	2.01865	+	0.0702628i	0.0813997	+	0.00283327i
$616$		0			0
$617$	7.18275	−	7.18275i	0.289167	−	0.289167i	−0.547584	−	0.836751i	$-0.684452\pi$
$617$	7.18275	−	7.18275i	0.289167	−	0.289167i	0.836751	+	0.547584i	$0.184452\pi$
$618$	29.7505	+	8.90406i	1.19674	+	0.358174i
$619$	32.0811			1.28945			0.644725	−	0.764415i	$-0.276972\pi$
$619$	32.0811			1.28945			0.644725	+	0.764415i	$0.276972\pi$
$620$	−16.2996	+	2.78103i	−0.654608	+	0.111689i
$621$	−19.4519			−0.780578
$622$	−18.0348	−	5.39767i	−0.723131	−	0.216427i
$623$		0			0
$624$	−21.6467	−	50.1377i	−0.866562	−	2.00712i
$625$	−24.7583	−	3.46806i	−0.990331	−	0.138723i
$626$	−27.0684	+	14.5980i	−1.08187	+	0.583453i
$627$	−9.07798	−	9.07798i	−0.362540	−	0.362540i
$628$	9.78486	−	2.02207i	0.390458	−	0.0806896i
$629$		−	13.0120i		−	0.518824i
$630$		0			0
$631$		−	18.7069i		−	0.744710i	−0.928090	−	0.372355i	$-0.878550\pi$
$631$		−	18.7069i		−	0.744710i	0.928090	−	0.372355i	$-0.121450\pi$
$632$	−11.8323	+	9.93340i	−0.470663	+	0.395130i
$633$	−27.2195	−	27.2195i	−1.08188	−	1.08188i
$634$	−10.3624	−	19.2144i	−0.411542	−	0.763103i
$635$	−1.33884	+	38.4647i	−0.0531301	+	1.52643i
$636$	7.03177	+	4.62323i	0.278828	+	0.183323i
$637$		0			0
$638$	−1.80018	+	6.01481i	−0.0712698	+	0.238129i
$639$	11.8879			0.470277
$640$	−7.13112	−	24.2724i	−0.281882	−	0.959449i
$641$	−29.6087			−1.16947			−0.584736	−	0.811224i	$-0.698802\pi$
$641$	−29.6087			−1.16947			−0.584736	+	0.811224i	$0.698802\pi$
$642$	7.99654	−	26.7182i	0.315598	−	1.05449i
$643$	−15.8819	+	15.8819i	−0.626323	+	0.626323i	−0.947141	−	0.320818i	$-0.896042\pi$
$643$	−15.8819	+	15.8819i	−0.626323	+	0.626323i	0.320818	+	0.947141i	$0.396042\pi$
$644$		0			0
$645$	2.83795	−	2.64703i	0.111744	−	0.104227i
$646$	2.86832	+	5.31860i	0.112853	+	0.209257i
$647$	−17.6813	−	17.6813i	−0.695124	−	0.695124i	0.268231	−	0.963355i	$-0.413561\pi$
$647$	−17.6813	−	17.6813i	−0.695124	−	0.695124i	−0.963355	+	0.268231i	$0.913561\pi$
$648$	23.8391	−	20.0133i	0.936488	−	0.786198i
$649$			52.7091i			2.06901i
$650$	−19.8911	−	43.9494i	−0.780191	−	1.72384i
$651$		0			0
$652$	−31.6507	+	6.54073i	−1.23954	+	0.256155i
$653$	29.2577	+	29.2577i	1.14494	+	1.14494i	0.987533	+	0.157411i	$0.0503147\pi$
$653$	29.2577	+	29.2577i	1.14494	+	1.14494i	0.157411	+	0.987533i	$0.449685\pi$
$654$	12.7447	−	6.87321i	0.498356	−	0.268764i
$655$	−5.28039	+	4.92517i	−0.206322	+	0.192442i
$656$	0.715682	+	1.65765i	0.0279427	+	0.0647204i
$657$	1.22327	−	1.22327i	0.0477243	−	0.0477243i
$658$		0			0
$659$	32.9086			1.28194			0.640968	−	0.767568i	$-0.278533\pi$
$659$	32.9086			1.28194			0.640968	+	0.767568i	$0.278533\pi$
$660$	−29.4031	+	41.5006i	−1.14451	+	1.61541i
$661$	−17.9700			−0.698953			−0.349477	−	0.936945i	$-0.613641\pi$
$661$	−17.9700			−0.698953			−0.349477	+	0.936945i	$0.613641\pi$
$662$	35.8560	+	10.7314i	1.39358	+	0.417088i
$663$	36.5419	−	36.5419i	1.41917	−	1.41917i
$664$	0.336700	−	3.85937i	0.0130665	−	0.149773i
$665$		0			0
$666$	−4.29938	+	2.31866i	−0.166598	+	0.0898461i
$667$	2.69104	+	2.69104i	0.104197	+	0.104197i
$668$	−3.05112	−	14.7644i	−0.118051	−	0.571252i
$669$		−	18.8988i		−	0.730669i
$670$	40.9308	+	13.8189i	1.58129	+	0.533869i
$671$			8.63530i			0.333362i
$672$		0			0
$673$	6.28219	+	6.28219i	0.242161	+	0.242161i	0.817744	−	0.575583i	$-0.195225\pi$
$673$	6.28219	+	6.28219i	0.242161	+	0.242161i	−0.575583	+	0.817744i	$0.695225\pi$
$674$	−10.0962	−	18.7210i	−0.388892	−	0.721105i
$675$	15.0642	−	13.1011i	0.579821	−	0.504262i
$676$	36.8564	−	56.0573i	1.41755	−	2.15605i
$677$	19.2113	−	19.2113i	0.738351	−	0.738351i	−0.233908	−	0.972259i	$-0.575151\pi$
$677$	19.2113	−	19.2113i	0.738351	−	0.738351i	0.972259	+	0.233908i	$0.0751513\pi$
$678$	2.27856	−	7.61317i	0.0875075	−	0.292382i
$679$		0			0
$680$	18.8593	−	14.7454i	0.723221	−	0.565460i
$681$	−54.6555			−2.09440
$682$	−8.52030	+	28.4682i	−0.326259	+	1.09011i
$683$	−15.9151	+	15.9151i	−0.608975	+	0.608975i	−0.942678	−	0.333703i	$-0.891702\pi$
$683$	−15.9151	+	15.9151i	−0.608975	+	0.608975i	0.333703	+	0.942678i	$0.391702\pi$
$684$	1.24623	−	1.89548i	0.0476508	−	0.0724753i
$685$	33.6331	+	1.17066i	1.28505	+	0.0447287i
$686$		0			0
$687$	17.9071	+	17.9071i	0.683199	+	0.683199i
$688$	3.22436	+	1.27974i	0.122927	+	0.0487895i
$689$			14.3447i			0.546489i
$690$	13.6812	+	27.6278i	0.520836	+	1.05177i
$691$		−	11.4960i		−	0.437327i	−0.975800	−	0.218663i	$-0.929830\pi$
$691$		−	11.4960i		−	0.437327i	0.975800	−	0.218663i	$-0.0701697\pi$
$692$	−1.77829	−	8.60516i	−0.0676003	−	0.327119i
$693$		0			0
$694$	6.51686	−	3.51455i	0.247377	−	0.133410i
$695$	11.4288	+	12.2531i	0.433520	+	0.464788i
$696$	−4.40496	−	0.384298i	−0.166969	−	0.0145668i
$697$	−1.20815	+	1.20815i	−0.0457618	+	0.0457618i
$698$	37.0609	+	11.0920i	1.40278	+	0.419839i
$699$	−34.6814			−1.31177
$700$		0			0
$701$	−2.54230			−0.0960214			−0.0480107	−	0.998847i	$-0.515288\pi$
$701$	−2.54230			−0.0960214			−0.0480107	+	0.998847i	$0.515288\pi$
$702$	36.9063	+	11.0457i	1.39294	+	0.416894i
$703$	2.74397	−	2.74397i	0.103491	−	0.103491i
$704$	−44.7775	−	7.87289i	−1.68762	−	0.296721i
$705$	13.0884	+	14.0324i	0.492937	+	0.528490i
$706$	18.6451	−	10.0553i	0.701719	−	0.378437i
$707$		0			0
$708$	−36.3532	+	7.51251i	−1.36624	+	0.282337i
$709$			10.1545i			0.381362i	0.981652	+	0.190681i	$0.0610696\pi$
$709$			10.1545i			0.381362i	−0.981652	+	0.190681i	$0.938930\pi$
$710$	16.6032	+	33.5285i	0.623109	+	1.25830i
$711$			5.48815i			0.205822i
$712$	17.1378	+	20.4139i	0.642266	+	0.765043i
$713$	12.7368	+	12.7368i	0.476995	+	0.476995i
$714$		0			0
$715$	−86.6434	−	3.01579i	−3.24028	−	0.112784i
$716$	−1.13486	−	0.746143i	−0.0424117	−	0.0278847i
$717$	30.7971	−	30.7971i	1.15014	−	1.15014i
$718$	9.72457	−	32.4920i	0.362918	−	1.21259i
$719$	37.4085			1.39510			0.697550	−	0.716536i	$-0.254273\pi$
$719$	37.4085			1.39510			0.697550	+	0.716536i	$0.254273\pi$
$720$	−8.23270	−	3.60387i	−0.306814	−	0.134308i
$721$		0			0
$722$	7.18761	−	24.0154i	0.267495	−	0.893761i
$723$	−29.5060	+	29.5060i	−1.09734	+	1.09734i
$724$	−13.1469	−	8.64378i	−0.488601	−	0.321244i
$725$	−3.89648	−	0.271577i	−0.144711	−	0.0100861i
$726$	28.6099	+	53.0500i	1.06181	+	1.96887i
$727$	8.42845	+	8.42845i	0.312594	+	0.312594i	0.845914	−	0.533320i	$-0.179056\pi$
$727$	8.42845	+	8.42845i	0.312594	+	0.312594i	−0.533320	+	0.845914i	$0.679056\pi$
$728$		0			0
$729$			12.9141i			0.478298i
$730$	5.15859	+	1.74162i	0.190928	+	0.0644602i
$731$			3.28272i			0.121416i
$732$	−5.95572	+	1.23077i	−0.220130	+	0.0454906i
$733$	−5.28196	−	5.28196i	−0.195093	−	0.195093i	0.602799	−	0.797893i	$-0.294052\pi$
$733$	−5.28196	−	5.28196i	−0.195093	−	0.195093i	−0.797893	+	0.602799i	$0.794052\pi$
$734$	16.8584	−	9.09173i	0.622254	−	0.335582i
$735$		0			0
$736$	−17.0839	+	21.6243i	−0.629723	+	0.797082i
$737$	54.8979	−	54.8979i	2.02219	−	2.02219i
$738$	0.614473	+	0.183907i	0.0226191	+	0.00676969i
$739$	2.38865			0.0878677			0.0439339	−	0.999034i	$-0.486011\pi$
$739$	2.38865			0.0878677			0.0439339	+	0.999034i	$0.486011\pi$
$740$	−12.5443	−	8.88758i	−0.461136	−	0.326714i
$741$	15.4119			0.566169
$742$		0			0
$743$	−14.6605	+	14.6605i	−0.537841	+	0.537841i	−0.922894	−	0.385053i	$-0.874183\pi$
$743$	−14.6605	+	14.6605i	−0.537841	+	0.537841i	0.385053	+	0.922894i	$0.374183\pi$
$744$	−20.8488	−	1.81889i	−0.764353	−	0.0666838i
$745$	7.08937	−	6.61245i	0.259734	−	0.242262i
$746$	−22.8971	+	12.3484i	−0.838324	+	0.452108i
$747$	−0.973129	−	0.973129i	−0.0356049	−	0.0356049i
$748$	−8.70679	−	42.1323i	−0.318352	−	1.54051i
$749$		0			0
$750$	−29.2029	−	12.1814i	−1.06634	−	0.444801i
$751$			0.813636i			0.0296900i	0.999890	+	0.0148450i	$0.00472549\pi$
$751$			0.813636i			0.0296900i	−0.999890	+	0.0148450i	$0.995275\pi$
$752$	−6.32773	+	15.9430i	−0.230749	+	0.581382i
$753$	20.7427	+	20.7427i	0.755908	+	0.755908i
$754$	−3.57763	−	6.63383i	−0.130289	−	0.241590i
$755$	23.1691	−	21.6104i	0.843209	−	0.786484i
$756$		0			0
$757$	11.0046	−	11.0046i	0.399968	−	0.399968i	−0.478254	−	0.878222i	$-0.658730\pi$
$757$	11.0046	−	11.0046i	0.399968	−	0.399968i	0.878222	+	0.478254i	$0.158730\pi$
$758$	−11.2954	+	37.7406i	−0.410269	+	1.37080i
$759$	55.4052			2.01108
$760$	7.08654	+	0.867539i	0.257056	+	0.0314690i
$761$	−2.31392			−0.0838795			−0.0419397	−	0.999120i	$-0.513354\pi$
$761$	−2.31392			−0.0838795			−0.0419397	+	0.999120i	$0.513354\pi$
$762$	−13.9672	+	46.6676i	−0.505979	+	1.69059i
$763$		0			0
$764$	11.7379	−	17.8530i	0.424664	−	0.645900i
$765$	0.295828	−	8.49912i	0.0106957	−	0.307286i
$766$	−8.87488	−	16.4563i	−0.320662	−	0.594590i
$767$	−44.7426	−	44.7426i	−1.61556	−	1.61556i
$768$	−0.952151	−	32.0049i	−0.0343578	−	1.15488i
$769$			18.4165i			0.664117i	0.943259	+	0.332059i	$0.107743\pi$
$769$			18.4165i			0.664117i	−0.943259	+	0.332059i	$0.892257\pi$
$770$		0			0
$771$			27.4348i			0.988040i
$772$	−4.56748	−	22.1021i	−0.164387	−	0.795472i
$773$	12.3700	+	12.3700i	0.444919	+	0.444919i	0.893661	−	0.448743i	$-0.148128\pi$
$773$	12.3700	+	12.3700i	0.444919	+	0.444919i	−0.448743	+	0.893661i	$0.648128\pi$
$774$	1.08466	−	0.584958i	0.0389873	−	0.0210259i
$775$	−18.4421	−	1.28538i	−0.662461	−	0.0461723i
$776$	−2.35506	+	26.9946i	−0.0845419	+	0.969049i
$777$		0			0
$778$	−22.8017	−	6.82435i	−0.817480	−	0.244665i
$779$	−0.509546			−0.0182564
$780$	−10.2691	−	60.1873i	−0.367693	−	2.15505i
$781$	67.2386			2.40598
$782$	−24.9834	−	7.47733i	−0.893406	−	0.267389i
$783$	2.20557	−	2.20557i	0.0788206	−	0.0788206i
$784$		0			0
$785$	11.1642	+	0.388591i	0.398467	+	0.0138694i
$786$	−8.04390	+	4.33808i	−0.286916	+	0.154734i
$787$	16.2361	+	16.2361i	0.578754	+	0.578754i	0.934560	−	0.355806i	$-0.115794\pi$
$787$	16.2361	+	16.2361i	0.578754	+	0.578754i	−0.355806	+	0.934560i	$0.615794\pi$
$788$	−9.12947	+	1.88664i	−0.325224	+	0.0672086i
$789$			46.0734i			1.64025i
$790$	−15.4787	+	7.66504i	−0.550709	+	0.272710i
$791$		0			0
$792$	−12.3697	+	10.3845i	−0.439537	+	0.368999i
$793$	−7.33016	−	7.33016i	−0.260302	−	0.260302i
$794$	−6.97547	−	12.9343i	−0.247550	−	0.459021i
$795$	6.41755	+	6.88041i	0.227607	+	0.244023i
$796$	−16.0064	−	10.5238i	−0.567331	−	0.373007i
$797$	−2.27256	+	2.27256i	−0.0804981	+	0.0804981i	−0.746209	−	0.665711i	$-0.768128\pi$
$797$	−2.27256	+	2.27256i	−0.0804981	+	0.0804981i	0.665711	+	0.746209i	$0.268128\pi$
$798$		0			0
$799$	−16.2316			−0.574232
$800$	−1.33388	−	28.2528i	−0.0471599	−	0.998887i
$801$	9.46854			0.334554
$802$	−9.00077	+	30.0736i	−0.317828	+	1.06194i
$803$	6.91889	−	6.91889i	0.244162	−	0.244162i
$804$	45.6872	+	30.0383i	1.61126	+	1.05937i
$805$		0			0
$806$	−16.9330	−	31.3981i	−0.596440	−	1.10595i
$807$	42.7536	+	42.7536i	1.50500	+	1.50500i
$808$	26.1273	−	21.9343i	0.919155	−	0.771646i
$809$			10.4295i			0.366680i	0.983050	+	0.183340i	$0.0586910\pi$
$809$			10.4295i			0.366680i	−0.983050	+	0.183340i	$0.941309\pi$
$810$	31.1858	−	15.4431i	1.09576	−	0.542617i
$811$		−	13.6718i		−	0.480081i	−0.970763	−	0.240040i	$-0.922839\pi$
$811$		−	13.6718i		−	0.480081i	0.970763	−	0.240040i	$-0.0771607\pi$
$812$		0			0
$813$	15.2268	+	15.2268i	0.534026	+	0.534026i
$814$	−24.3175	+	13.1145i	−0.852329	+	0.459662i
$815$	−36.1124	−	1.25696i	−1.26496	−	0.0440294i
$816$	27.8175	−	12.0101i	0.973806	−	0.420436i
$817$	−0.692258	+	0.692258i	−0.0242190	+	0.0242190i
$818$	12.4842	+	3.73643i	0.436501	+	0.130641i
$819$		0			0
$820$	0.339517	+	1.98991i	0.0118564	+	0.0694906i
$821$	−31.4980			−1.09929			−0.549645	−	0.835399i	$-0.685237\pi$
$821$	−31.4980			−1.09929			−0.549645	+	0.835399i	$0.685237\pi$
$822$	40.8056	+	12.2128i	1.42326	+	0.425969i
$823$	5.62138	−	5.62138i	0.195949	−	0.195949i	−0.602312	−	0.798261i	$-0.705754\pi$
$823$	5.62138	−	5.62138i	0.195949	−	0.195949i	0.798261	+	0.602312i	$0.205754\pi$
$824$	−2.69739	+	30.9184i	−0.0939679	+	1.07709i
$825$	−42.9076	+	37.3161i	−1.49385	+	1.29918i
$826$		0			0
$827$	−4.54203	−	4.54203i	−0.157942	−	0.157942i	0.623712	−	0.781654i	$-0.285624\pi$
$827$	−4.54203	−	4.54203i	−0.157942	−	0.157942i	−0.781654	+	0.623712i	$0.785624\pi$
$828$	1.98125	+	9.58731i	0.0688533	+	0.333182i
$829$		−	11.9204i		−	0.414012i	−0.978340	−	0.207006i	$-0.933628\pi$
$829$		−	11.9204i		−	0.414012i	0.978340	−	0.207006i	$-0.0663720\pi$
$830$	1.38548	−	4.10373i	0.0480908	−	0.142442i
$831$			64.5903i			2.24061i
$832$	44.6928	−	31.3269i	1.54944	−	1.08606i
$833$		0			0
$834$	10.0665	+	18.6658i	0.348574	+	0.646345i
$835$	0.586346	−	16.8457i	0.0202914	−	0.582969i
$836$	7.04876	−	10.7209i	0.243786	−	0.370791i
$837$	10.4390	−	10.4390i	0.360825	−	0.360825i
$838$	7.50789	−	25.0856i	0.259356	−	0.866566i
$839$	26.9117			0.929095			0.464548	−	0.885548i	$-0.346217\pi$
$839$	26.9117			0.929095			0.464548	+	0.885548i	$0.346217\pi$
$840$		0			0
$841$	28.3897			0.978957
$842$	−10.3603	+	34.6162i	−0.357041	+	1.19295i
$843$	−1.48806	+	1.48806i	−0.0512514	+	0.0512514i
$844$	21.1351	−	32.1457i	0.727499	−	1.10650i
$845$	54.8507	−	51.1607i	1.88692	−	1.75998i
$846$	2.89236	+	5.36316i	0.0994413	+	0.184389i
$847$		0			0
$848$	−3.10264	+	7.81725i	−0.106545	+	0.268445i
$849$		−	21.5116i		−	0.738275i
$850$	24.3840	−	11.0360i	0.836366	−	0.378531i
$851$			16.7472i			0.574085i
$852$	9.58336	+	46.3741i	0.328321	+	1.58875i
$853$	−17.1543	−	17.1543i	−0.587353	−	0.587353i	0.349561	−	0.936914i	$-0.386331\pi$
$853$	−17.1543	−	17.1543i	−0.587353	−	0.587353i	−0.936914	+	0.349561i	$0.886331\pi$
$854$		0			0
$855$	1.85467	−	1.72991i	0.0634285	−	0.0591616i
$856$	27.7671	+	2.42246i	0.949062	+	0.0827981i
$857$	25.9527	−	25.9527i	0.886526	−	0.886526i	−0.107662	−	0.994188i	$-0.534336\pi$
$857$	25.9527	−	25.9527i	0.886526	−	0.886526i	0.994188	+	0.107662i	$0.0343363\pi$
$858$	−105.121	−	31.4617i	−3.58876	−	1.07409i
$859$	−33.8055			−1.15343			−0.576714	−	0.816946i	$-0.695665\pi$
$859$	−33.8055			−1.15343			−0.576714	+	0.816946i	$0.695665\pi$
$860$	3.16471	+	2.24219i	0.107916	+	0.0764579i
$861$		0			0
$862$	14.1192	+	4.22576i	0.480902	+	0.143930i
$863$	22.7989	−	22.7989i	0.776084	−	0.776084i	−0.203078	−	0.979163i	$-0.565095\pi$
$863$	22.7989	−	22.7989i	0.776084	−	0.776084i	0.979163	+	0.203078i	$0.0650946\pi$
$864$	17.7232	+	14.0020i	0.602956	+	0.476357i
$865$	0.341741	−	9.81820i	0.0116195	−	0.333829i
$866$	−35.8759	+	19.3479i	−1.21911	+	0.657467i
$867$	−3.78176	−	3.78176i	−0.128435	−	0.128435i
$868$		0			0
$869$			31.0413i			1.05300i
$870$	−4.68386	−	1.58134i	−0.158798	−	0.0536125i
$871$			93.2012i			3.15800i
$872$	9.30467	+	11.0834i	0.315096	+	0.375330i
$873$	6.80660	+	6.80660i	0.230369	+	0.230369i
$874$	−3.69168	−	6.84531i	−0.124873	−	0.231546i
$875$		0			0
$876$	5.75806	+	3.78579i	0.194547	+	0.127910i
$877$	11.3149	−	11.3149i	0.382078	−	0.382078i	−0.489772	−	0.871850i	$-0.662920\pi$
$877$	11.3149	−	11.3149i	0.382078	−	0.382078i	0.871850	+	0.489772i	$0.162920\pi$
$878$	8.44895	−	28.2299i	0.285138	−	0.952711i
$879$	54.1004			1.82476
$880$	−46.5646	−	20.3837i	−1.56969	−	0.687135i
$881$	52.7104			1.77586			0.887929	−	0.459981i	$-0.152144\pi$
$881$	52.7104			1.77586			0.887929	+	0.459981i	$0.152144\pi$
$882$		0			0
$883$	5.34754	−	5.34754i	0.179959	−	0.179959i	−0.611379	−	0.791338i	$-0.709385\pi$
$883$	5.34754	−	5.34754i	0.179959	−	0.179959i	0.791338	+	0.611379i	$0.209385\pi$
$884$	43.1553	+	28.3736i	1.45147	+	0.954307i
$885$	−41.4777	−	1.44371i	−1.39426	−	0.0485298i
$886$	−17.9338	−	33.2538i	−0.602497	−	1.11718i
$887$	−32.6754	−	32.6754i	−1.09713	−	1.09713i	−0.994745	−	0.102387i	$-0.967352\pi$
$887$	−32.6754	−	32.6754i	−1.09713	−	1.09713i	−0.102387	−	0.994745i	$-0.532648\pi$
$888$	−12.5109	−	14.9025i	−0.419838	−	0.500095i
$889$		0			0
$890$	13.2243	+	26.7050i	0.443279	+	0.895154i
$891$		−	62.5405i		−	2.09519i
$892$	18.4967	−	3.82241i	0.619315	−	0.127984i
$893$	−3.42291	−	3.42291i	−0.114543	−	0.114543i
$894$	10.7996	−	5.82424i	0.361193	−	0.194792i
$895$	−1.03573	−	1.11043i	−0.0346206	−	0.0371176i
$896$		0			0
$897$	−47.0313	+	47.0313i	−1.57033	+	1.57033i
$898$	37.3684	+	11.1840i	1.24700	+	0.373216i
$899$	−2.88833			−0.0963313
$900$	−7.99152	−	6.09032i	−0.266384	−	0.203011i
$901$	−7.95874			−0.265144
$902$	3.47550	+	1.04019i	0.115721	+	0.0346344i
$903$		0			0
$904$	7.91205	+	0.690264i	0.263151	+	0.0229578i
$905$	−11.9985	−	12.8639i	−0.398845	−	0.427611i
$906$	35.2947	−	19.0344i	1.17259	−	0.632377i
$907$	42.1199	+	42.1199i	1.39857	+	1.39857i	0.804177	+	0.594390i	$0.202606\pi$
$907$	42.1199	+	42.1199i	1.39857	+	1.39857i	0.594390	+	0.804177i	$0.297394\pi$
$908$	−11.0544	−	53.4927i	−0.366855	−	1.77522i
$909$		−	12.1186i		−	0.401948i
$910$		0			0
$911$		−	45.5865i		−	1.51035i	−0.655524	−	0.755174i	$-0.727552\pi$
$911$		−	45.5865i		−	1.51035i	0.655524	−	0.755174i	$-0.272448\pi$
$912$	8.39881	+	3.33346i	0.278112	+	0.110382i
$913$	−5.50407	−	5.50407i	−0.182158	−	0.182158i
$914$	0.923488	+	1.71238i	0.0305463	+	0.0566405i
$915$	−6.79528	−	0.236523i	−0.224645	−	0.00781920i
$916$	−13.9043	+	21.1480i	−0.459411	+	0.698748i
$917$		0			0
$918$	−6.12840	+	20.4764i	−0.202267	+	0.675821i
$919$	48.7511			1.60815			0.804076	−	0.594527i	$-0.202661\pi$
$919$	48.7511			1.60815			0.804076	+	0.594527i	$0.202661\pi$
$920$	−24.2729	+	18.9781i	−0.800253	+	0.625688i
$921$	2.05603			0.0677486
$922$	7.16453	−	23.9383i	0.235951	−	0.788366i
$923$	−57.0761	+	57.0761i	−1.87868	+	1.87868i
$924$		0			0
$925$	−11.2794	−	12.9695i	−0.370865	−	0.426436i
$926$	5.27333	+	9.77810i	0.173293	+	0.321328i
$927$	7.79598	+	7.79598i	0.256054	+	0.256054i
$928$	−0.514811	−	4.38896i	−0.0168995	−	0.144075i
$929$		−	14.1656i		−	0.464759i	−0.972625	−	0.232379i	$-0.925349\pi$
$929$		−	14.1656i		−	0.464759i	0.972625	−	0.232379i	$-0.0746511\pi$
$930$	−22.1688	−	7.48454i	−0.726944	−	0.245428i
$931$		0			0
$932$	−7.01455	−	33.9435i	−0.229769	−	1.11186i
$933$	−18.8365	−	18.8365i	−0.616678	−	0.616678i
$934$	16.3201	−	8.80145i	0.534011	−	0.287992i
$935$	1.67322	−	48.0716i	0.0547202	−	1.57211i
$936$	1.68509	−	19.3151i	0.0550790	−	0.631335i
$937$	−10.0190	+	10.0190i	−0.327306	+	0.327306i	−0.851561	−	0.524255i	$-0.824344\pi$
$937$	−10.0190	+	10.0190i	−0.327306	+	0.327306i	0.524255	+	0.851561i	$0.324344\pi$
$938$		0			0
$939$	−43.5184			−1.42017
$940$	−11.0866	+	15.6481i	−0.361605	+	0.510384i
$941$	−27.8056			−0.906437			−0.453219	−	0.891399i	$-0.649724\pi$
$941$	−27.8056			−0.906437			−0.453219	+	0.891399i	$0.649724\pi$
$942$	13.5450	+	4.05392i	0.441321	+	0.132084i
$943$	1.55494	−	1.55494i	0.0506360	−	0.0506360i
$944$	−14.7053	−	34.0603i	−0.478618	−	1.10857i
$945$		0			0
$946$	6.13491	−	3.30856i	0.199463	−	0.107570i
$947$	−20.5281	−	20.5281i	−0.667073	−	0.667073i	0.289964	−	0.957038i	$-0.406357\pi$
$947$	−20.5281	−	20.5281i	−0.667073	−	0.667073i	−0.957038	+	0.289964i	$0.906357\pi$
$948$	−21.4090	+	4.42425i	−0.695333	+	0.143693i
$949$			11.7463i			0.381302i
$950$	7.46935	+	2.81483i	0.242338	+	0.0913252i
$951$		−	30.8915i		−	1.00172i
$952$		0			0
$953$	33.2622	+	33.2622i	1.07747	+	1.07747i	0.996736	+	0.0807336i	$0.0257263\pi$
$953$	33.2622	+	33.2622i	1.07747	+	1.07747i	0.0807336	+	0.996736i	$0.474274\pi$
$954$	1.41819	+	2.62969i	0.0459157	+	0.0851393i
$955$	17.4687	−	16.2936i	0.565275	−	0.527248i
$956$	36.3708	+	23.9129i	1.17631	+	0.773400i
$957$	−6.28216	+	6.28216i	−0.203074	+	0.203074i
$958$	−1.03136	+	3.44599i	−0.0333216	+	0.111335i
$959$		0			0
$960$	7.42179	−	35.0206i	0.239537	−	1.13029i
$961$	17.3294			0.559014
$962$	9.50984	−	31.7745i	0.306610	−	1.02445i
$963$	7.00140	−	7.00140i	0.225617	−	0.225617i
$964$	−34.8460	−	22.9104i	−1.12231	−	0.737895i
$965$	0.877752	−	25.2178i	0.0282558	−	0.811788i
$966$		0			0
$967$	8.70456	+	8.70456i	0.279920	+	0.279920i	0.833077	−	0.553157i	$-0.186577\pi$
$967$	8.70456	+	8.70456i	0.279920	+	0.279920i	−0.553157	+	0.833077i	$0.686577\pi$
$968$	−46.1348	+	38.7309i	−1.48283	+	1.24486i
$969$			8.55083i			0.274692i
$970$	−9.69083	+	28.7038i	−0.311154	+	0.921622i
$971$			50.7450i			1.62849i	0.580525	+	0.814243i	$0.302848\pi$
$971$			50.7450i			1.62849i	−0.580525	+	0.814243i	$0.697152\pi$
$972$	19.6725	−	4.06540i	0.630997	−	0.130398i
$973$		0			0
$974$	−4.58151	+	2.47081i	−0.146801	+	0.0791698i
$975$	4.74636	−	68.0987i	0.152005	−	2.18090i
$976$	−2.40917	−	5.58008i	−0.0771156	−	0.178614i
$977$	−0.120416	+	0.120416i	−0.00385245	+	0.00385245i	−0.709030	−	0.705178i	$-0.750867\pi$
$977$	−0.120416	+	0.120416i	−0.00385245	+	0.00385245i	0.705178	+	0.709030i	$0.250867\pi$
$978$	−43.8137	−	13.1131i	−1.40101	−	0.419309i
$979$	53.5546			1.71161
$980$		0			0
$981$	5.14078			0.164133
$982$	30.2683	+	9.05905i	0.965901	+	0.289086i
$983$	−15.8935	+	15.8935i	−0.506922	+	0.506922i	−0.913580	−	0.406658i	$-0.866694\pi$
$983$	−15.8935	+	15.8935i	−0.506922	+	0.506922i	0.406658	+	0.913580i	$0.366694\pi$
$984$	−0.222056	+	2.54529i	−0.00707889	+	0.0811408i
$985$	−10.4164	−	0.362563i	−0.331895	−	0.0115522i
$986$	3.68059	−	1.98494i	0.117214	−	0.0632135i
$987$		0			0
$988$	3.11715	+	15.0840i	0.0991699	+	0.479885i
$989$		−	4.22503i		−	0.134348i
$990$	−16.1817	+	8.01316i	−0.514289	+	0.254675i
$991$			13.8742i			0.440727i	0.975418	+	0.220364i	$0.0707244\pi$
$991$			13.8742i			0.440727i	−0.975418	+	0.220364i	$0.929276\pi$
$992$	−2.43661	−	20.7731i	−0.0773626	−	0.659546i
$993$	37.4498	+	37.4498i	1.18843	+	1.18843i
$994$		0			0
$995$	−14.6082	−	15.6618i	−0.463112	−	0.496514i
$996$	3.01165	−	4.58061i	0.0954277	−	0.145142i
$997$	−11.1566	+	11.1566i	−0.353334	+	0.353334i	−0.861348	−	0.508015i	$-0.830380\pi$
$997$	−11.1566	+	11.1566i	−0.353334	+	0.353334i	0.508015	+	0.861348i	$0.330380\pi$
$998$	4.03729	−	13.4895i	0.127798	−	0.427002i
$999$	13.7259			0.434270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.k.m.883.11	yes	56
4.3	odd	2	inner	980.2.k.m.883.6	yes	56
5.2	odd	4	inner	980.2.k.m.687.6	yes	56
7.2	even	3		980.2.x.n.263.27		112
7.3	odd	6		980.2.x.n.863.9		112
7.4	even	3		980.2.x.n.863.10		112
7.5	odd	6		980.2.x.n.263.28		112
7.6	odd	2	inner	980.2.k.m.883.12	yes	56
20.7	even	4	inner	980.2.k.m.687.11	yes	56
28.3	even	6		980.2.x.n.863.16		112
28.11	odd	6		980.2.x.n.863.15		112
28.19	even	6		980.2.x.n.263.21		112
28.23	odd	6		980.2.x.n.263.22		112
28.27	even	2	inner	980.2.k.m.883.5	yes	56
35.2	odd	12		980.2.x.n.67.15		112
35.12	even	12		980.2.x.n.67.16		112
35.17	even	12		980.2.x.n.667.21		112
35.27	even	4	inner	980.2.k.m.687.5	✓	56
35.32	odd	12		980.2.x.n.667.22		112
140.27	odd	4	inner	980.2.k.m.687.12	yes	56
140.47	odd	12		980.2.x.n.67.9		112
140.67	even	12		980.2.x.n.667.27		112
140.87	odd	12		980.2.x.n.667.28		112
140.107	even	12		980.2.x.n.67.10		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.m.687.5	✓	56	35.27	even	4	inner
980.2.k.m.687.6	yes	56	5.2	odd	4	inner
980.2.k.m.687.11	yes	56	20.7	even	4	inner
980.2.k.m.687.12	yes	56	140.27	odd	4	inner
980.2.k.m.883.5	yes	56	28.27	even	2	inner
980.2.k.m.883.6	yes	56	4.3	odd	2	inner
980.2.k.m.883.11	yes	56	1.1	even	1	trivial
980.2.k.m.883.12	yes	56	7.6	odd	2	inner
980.2.x.n.67.9		112	140.47	odd	12
980.2.x.n.67.10		112	140.107	even	12
980.2.x.n.67.15		112	35.2	odd	12
980.2.x.n.67.16		112	35.12	even	12
980.2.x.n.263.21		112	28.19	even	6
980.2.x.n.263.22		112	28.23	odd	6
980.2.x.n.263.27		112	7.2	even	3
980.2.x.n.263.28		112	7.5	odd	6
980.2.x.n.667.21		112	35.17	even	12
980.2.x.n.667.22		112	35.32	odd	12
980.2.x.n.667.27		112	140.67	even	12
980.2.x.n.667.28		112	140.87	odd	12
980.2.x.n.863.9		112	7.3	odd	6
980.2.x.n.863.10		112	7.4	even	3
980.2.x.n.863.15		112	28.11	odd	6
980.2.x.n.863.16		112	28.3	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.405491 + 1.35483i) q^{2} +(-1.41506 + 1.41506i) q^{3} +(-1.67115 - 1.09875i) q^{4} +(-1.52518 - 1.63518i) q^{5} +(-1.34338 - 2.49096i) q^{6} +(2.16626 - 1.81861i) q^{8} -1.00477i q^{9} +(2.83385 - 1.40332i) q^{10} -5.68305i q^{11} +(3.91957 - 0.809992i) q^{12} +(4.82411 + 4.82411i) q^{13} +(4.47209 + 0.155660i) q^{15} +(1.58552 + 3.67235i) q^{16} +(-2.67652 + 2.67652i) q^{17} +(1.36130 + 0.407425i) q^{18} -1.12884 q^{19} +(0.752163 + 4.40843i) q^{20} +(7.69959 + 2.30442i) q^{22} +(3.44481 - 3.44481i) q^{23} +(-0.491941 + 5.63881i) q^{24} +(-0.347648 + 4.98790i) q^{25} +(-8.49200 + 4.57974i) q^{26} +(-2.82336 - 2.82336i) q^{27} +0.781186i q^{29} +(-2.02428 + 5.99583i) q^{30} +3.69737i q^{31} +(-5.61834 + 0.659012i) q^{32} +(8.04183 + 8.04183i) q^{33} +(-2.54094 - 4.71154i) q^{34} +(-1.10399 + 1.67913i) q^{36} +(-2.43078 + 2.43078i) q^{37} +(0.457736 - 1.52940i) q^{38} -13.6528 q^{39} +(-6.27769 - 0.768519i) q^{40} +0.451387 q^{41} +(0.613245 - 0.613245i) q^{43} +(-6.24422 + 9.49725i) q^{44} +(-1.64298 + 1.53246i) q^{45} +(3.27031 + 6.06399i) q^{46} +(3.03222 + 3.03222i) q^{47} +(-7.44018 - 2.95298i) q^{48} +(-6.61681 - 2.49355i) q^{50} -7.57485i q^{51} +(-2.76137 - 13.3623i) q^{52} +(1.48677 + 1.48677i) q^{53} +(4.97004 - 2.68034i) q^{54} +(-9.29282 + 8.66767i) q^{55} +(1.59738 - 1.59738i) q^{57} +(-1.05838 - 0.316763i) q^{58} -9.27479 q^{59} +(-7.30253 - 5.17382i) q^{60} -1.51948 q^{61} +(-5.00933 - 1.49925i) q^{62} +(1.38533 - 7.87914i) q^{64} +(0.530664 - 15.2459i) q^{65} +(-14.1562 + 7.63447i) q^{66} +(9.65994 + 9.65994i) q^{67} +(7.41369 - 1.53206i) q^{68} +9.74921i q^{69} +11.8314i q^{71} +(-1.82728 - 2.17659i) q^{72} +(1.21746 + 1.21746i) q^{73} +(-2.30765 - 4.27896i) q^{74} +(-6.56622 - 7.55010i) q^{75} +(1.88647 + 1.24031i) q^{76} +(5.53607 - 18.4973i) q^{78} -5.46209 q^{79} +(3.58676 - 8.19360i) q^{80} +11.0047 q^{81} +(-0.183033 + 0.611555i) q^{82} +(0.968508 - 0.968508i) q^{83} +(8.45877 + 0.294423i) q^{85} +(0.582180 + 1.07951i) q^{86} +(-1.10542 - 1.10542i) q^{87} +(-10.3352 - 12.3109i) q^{88} +9.42358i q^{89} +(-1.41001 - 2.84737i) q^{90} +(-9.54179 + 1.97184i) q^{92} +(-5.23199 - 5.23199i) q^{93} +(-5.33770 + 2.87862i) q^{94} +(1.72169 + 1.84587i) q^{95} +(7.01772 - 8.88280i) q^{96} +(-6.77428 + 6.77428i) q^{97} -5.71016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{2} - 16 q^{8} + 32 q^{16} + 20 q^{22} + 32 q^{25} - 28 q^{30} - 64 q^{32} + 16 q^{36} - 8 q^{37} - 184 q^{46} - 12 q^{50} + 96 q^{53} - 8 q^{57} + 124 q^{58} + 8 q^{60} - 120 q^{65} - 80 q^{72}+ \cdots - 176 q^{93}+O(q^{100}) \) 56 * q - 4 * q^2 - 16 * q^8 + 32 * q^16 + 20 * q^22 + 32 * q^25 - 28 * q^30 - 64 * q^32 + 16 * q^36 - 8 * q^37 - 184 * q^46 - 12 * q^50 + 96 * q^53 - 8 * q^57 + 124 * q^58 + 8 * q^60 - 120 * q^65 - 80 * q^72 - 36 * q^78 - 72 * q^81 + 96 * q^85 + 104 * q^86 + 48 * q^88 - 152 * q^92 - 176 * q^93

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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