LMFDB - Embedded newform 275.3.bk.c.82.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(82,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.82"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			82.14
Character	$\chi$	$=$	275.82
Dual form			275.3.bk.c.218.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35668 - 2.66263i) q^{2} +(5.64189 - 0.893588i) q^{3} +(-2.89790 - 3.98862i) q^{4} +(5.27495 - 16.2346i) q^{6} +(-7.26024 - 1.14991i) q^{7} +(-2.74554 + 0.434852i) q^{8} +(22.4730 - 7.30190i) q^{9} +(5.78433 + 9.35637i) q^{11} +(-19.9138 - 19.9138i) q^{12} +(-0.739658 - 0.376875i) q^{13} +(-12.9116 + 17.7713i) q^{14} +(3.52709 - 10.8553i) q^{16} +(-23.0319 + 11.7354i) q^{17} +(11.0463 - 69.7436i) q^{18} +(-6.24455 + 8.59489i) q^{19} -41.9890 q^{21} +(32.7601 - 2.70795i) q^{22} +(-15.1940 + 15.1940i) q^{23} +(-15.1015 + 4.90677i) q^{24} +(-2.00696 + 1.45814i) q^{26} +(74.4585 - 37.9385i) q^{27} +(16.4529 + 32.2906i) q^{28} +(-1.59333 - 2.19303i) q^{29} +(-2.08632 - 6.42102i) q^{31} +(-31.9809 - 31.9809i) q^{32} +(40.9953 + 47.6188i) q^{33} +77.2468i q^{34} +(-94.2489 - 68.4758i) q^{36} +(29.9976 + 4.75115i) q^{37} +(14.4132 + 28.2875i) q^{38} +(-4.50984 - 1.46534i) q^{39} +(47.7749 + 34.7105i) q^{41} +(-56.9657 + 111.801i) q^{42} +(-19.6393 + 19.6393i) q^{43} +(20.5566 - 50.1853i) q^{44} +(19.8426 + 61.0694i) q^{46} +(-14.1984 - 89.6453i) q^{47} +(10.1993 - 64.3961i) q^{48} +(4.78700 + 1.55539i) q^{49} +(-119.457 + 86.7907i) q^{51} +(0.640247 + 4.04236i) q^{52} +(3.94931 + 2.01228i) q^{53} -249.726i q^{54} +20.4333 q^{56} +(-27.5508 + 54.0715i) q^{57} +(-8.00088 + 1.26721i) q^{58} +(34.3182 + 47.2349i) q^{59} +(6.01985 - 18.5272i) q^{61} +(-19.9273 - 3.15617i) q^{62} +(-171.556 + 27.1717i) q^{63} +(-85.1200 + 27.6572i) q^{64} +(182.409 - 44.5520i) q^{66} +(15.8915 + 15.8915i) q^{67} +(113.552 + 57.8577i) q^{68} +(-72.1457 + 99.3000i) q^{69} +(-19.5314 + 60.1116i) q^{71} +(-58.5252 + 29.8201i) q^{72} +(-2.76193 + 17.4381i) q^{73} +(53.3477 - 73.4268i) q^{74} +52.3778 q^{76} +(-31.2366 - 74.5809i) q^{77} +(-10.0201 + 10.0201i) q^{78} +(21.7530 - 7.06797i) q^{79} +(214.136 - 155.579i) q^{81} +(157.236 - 80.1160i) q^{82} +(-38.0294 - 74.6368i) q^{83} +(121.680 + 167.478i) q^{84} +(25.6481 + 78.9367i) q^{86} +(-10.9491 - 10.9491i) q^{87} +(-19.9498 - 23.1730i) q^{88} -64.7104i q^{89} +(4.93672 + 3.58674i) q^{91} +(104.634 + 16.5723i) q^{92} +(-17.5085 - 34.3624i) q^{93} +(-257.956 - 83.8148i) q^{94} +(-209.010 - 151.855i) q^{96} +(-17.7536 + 34.8433i) q^{97} +(10.6359 - 10.6359i) q^{98} +(198.310 + 168.029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) $ 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.35668	−	2.66263i	0.678340	−	1.33132i	−0.253106	−	0.967438i	$-0.581452\pi$
$2$	1.35668	−	2.66263i	0.678340	−	1.33132i	0.931446	−	0.363879i	$-0.118548\pi$
$3$	5.64189	−	0.893588i	1.88063	−	0.297863i	0.892449	−	0.451148i	$-0.148985\pi$
$3$	5.64189	−	0.893588i	1.88063	−	0.297863i	0.988182	+	0.153285i	$0.0489854\pi$
$4$	−2.89790	−	3.98862i	−0.724475	−	0.997155i
$5$		0			0
$5$		0			0
$6$	5.27495	−	16.2346i	0.879158	−	2.70577i
$7$	−7.26024	−	1.14991i	−1.03718	−	0.164273i	−0.385452	−	0.922728i	$-0.625954\pi$
$7$	−7.26024	−	1.14991i	−1.03718	−	0.164273i	−0.651725	+	0.758455i	$0.725954\pi$
$8$	−2.74554	+	0.434852i	−0.343193	+	0.0543564i
$9$	22.4730	−	7.30190i	2.49699	−	0.811323i
$10$		0			0
$11$	5.78433	+	9.35637i	0.525848	+	0.850579i
$11$	5.78433	+	9.35637i	0.525848	+	0.850579i
$12$	−19.9138	−	19.9138i	−1.65949	−	1.65949i
$13$	−0.739658	−	0.376875i	−0.0568968	−	0.0289904i	0.425311	−	0.905047i	$-0.360165\pi$
$13$	−0.739658	−	0.376875i	−0.0568968	−	0.0289904i	−0.482207	+	0.876057i	$0.660165\pi$
$14$	−12.9116	+	17.7713i	−0.922258	+	1.26938i
$15$		0			0
$16$	3.52709	−	10.8553i	0.220443	−	0.678455i
$17$	−23.0319	+	11.7354i	−1.35482	+	0.690315i	−0.972323	−	0.233641i	$-0.924936\pi$
$17$	−23.0319	+	11.7354i	−1.35482	+	0.690315i	−0.382497	+	0.923957i	$0.624936\pi$
$18$	11.0463	−	69.7436i	0.613683	−	3.87464i
$19$	−6.24455	+	8.59489i	−0.328661	+	0.452363i	−0.941087	−	0.338165i	$-0.890194\pi$
$19$	−6.24455	+	8.59489i	−0.328661	+	0.452363i	0.612426	+	0.790528i	$0.290194\pi$
$20$		0			0
$21$	−41.9890			−1.99948
$22$	32.7601	−	2.70795i	1.48909	−	0.123089i
$23$	−15.1940	+	15.1940i	−0.660608	+	0.660608i	−0.955523	−	0.294915i	$-0.904709\pi$
$23$	−15.1940	+	15.1940i	−0.660608	+	0.660608i	0.294915	+	0.955523i	$0.404709\pi$
$24$	−15.1015	+	4.90677i	−0.629229	+	0.204449i
$25$		0			0
$26$	−2.00696	+	1.45814i	−0.0771907	+	0.0560823i
$27$	74.4585	−	37.9385i	2.75772	−	1.40513i
$28$	16.4529	+	32.2906i	0.587604	+	1.15324i
$29$	−1.59333	−	2.19303i	−0.0549424	−	0.0756218i	0.780662	−	0.624954i	$-0.214882\pi$
$29$	−1.59333	−	2.19303i	−0.0549424	−	0.0756218i	−0.835604	+	0.549332i	$0.814882\pi$
$30$		0			0
$31$	−2.08632	−	6.42102i	−0.0673005	−	0.207130i	0.911751	−	0.410744i	$-0.134731\pi$
$31$	−2.08632	−	6.42102i	−0.0673005	−	0.207130i	−0.979051	+	0.203614i	$0.934731\pi$
$32$	−31.9809	−	31.9809i	−0.999402	−	0.999402i
$33$	40.9953	+	47.6188i	1.24228	+	1.44299i
$34$			77.2468i			2.27196i
$35$		0			0
$36$	−94.2489	−	68.4758i	−2.61802	−	1.90211i
$37$	29.9976	+	4.75115i	0.810745	+	0.128409i	0.548024	−	0.836462i	$-0.315380\pi$
$37$	29.9976	+	4.75115i	0.810745	+	0.128409i	0.262721	+	0.964872i	$0.415380\pi$
$38$	14.4132	+	28.2875i	0.379294	+	0.744407i
$39$	−4.50984	−	1.46534i	−0.115637	−	0.0375727i
$40$		0			0
$41$	47.7749	+	34.7105i	1.16524	+	0.846597i	0.990431	−	0.138006i	$-0.0440693\pi$
$41$	47.7749	+	34.7105i	1.16524	+	0.846597i	0.174809	+	0.984602i	$0.444069\pi$
$42$	−56.9657	+	111.801i	−1.35633	+	2.66194i
$43$	−19.6393	+	19.6393i	−0.456729	+	0.456729i	−0.897580	−	0.440851i	$-0.854677\pi$
$43$	−19.6393	+	19.6393i	−0.456729	+	0.456729i	0.440851	+	0.897580i	$0.354677\pi$
$44$	20.5566	−	50.1853i	0.467195	−	1.14057i
$45$		0			0
$46$	19.8426	+	61.0694i	0.431362	+	1.32760i
$47$	−14.1984	−	89.6453i	−0.302094	−	1.90735i	−0.408019	−	0.912974i	$-0.633780\pi$
$47$	−14.1984	−	89.6453i	−0.302094	−	1.90735i	0.105924	−	0.994374i	$-0.466220\pi$
$48$	10.1993	−	64.3961i	0.212486	−	1.34158i
$49$	4.78700	+	1.55539i	0.0976940	+	0.0317427i
$50$		0			0
$51$	−119.457	+	86.7907i	−2.34230	+	1.70178i
$52$	0.640247	+	4.04236i	0.0123124	+	0.0777377i
$53$	3.94931	+	2.01228i	0.0745153	+	0.0379675i	0.490851	−	0.871243i	$-0.336686\pi$
$53$	3.94931	+	2.01228i	0.0745153	+	0.0379675i	−0.416336	+	0.909211i	$0.636686\pi$
$54$		−	249.726i		−	4.62456i
$55$		0			0
$56$	20.4333			0.364881
$57$	−27.5508	+	54.0715i	−0.483347	+	0.948623i
$58$	−8.00088	+	1.26721i	−0.137946	+	0.0218485i
$59$	34.3182	+	47.2349i	0.581664	+	0.800592i	0.993877	−	0.110496i	$-0.0352439\pi$
$59$	34.3182	+	47.2349i	0.581664	+	0.800592i	−0.412212	+	0.911088i	$0.635244\pi$
$60$		0			0
$61$	6.01985	−	18.5272i	0.0986861	−	0.303725i	−0.889511	−	0.456914i	$-0.848955\pi$
$61$	6.01985	−	18.5272i	0.0986861	−	0.303725i	0.988197	+	0.153190i	$0.0489546\pi$
$62$	−19.9273	−	3.15617i	−0.321408	−	0.0509060i
$63$	−171.556	+	27.1717i	−2.72310	+	0.431297i
$64$	−85.1200	+	27.6572i	−1.33000	+	0.432143i
$65$		0			0
$66$	182.409	−	44.5520i	2.76377	−	0.675030i
$67$	15.8915	+	15.8915i	0.237186	+	0.237186i	0.815684	−	0.578498i	$-0.196361\pi$
$67$	15.8915	+	15.8915i	0.237186	+	0.237186i	−0.578498	+	0.815684i	$0.696361\pi$
$68$	113.552	+	57.8577i	1.66988	+	0.850849i
$69$	−72.1457	+	99.3000i	−1.04559	+	1.43913i
$70$		0			0
$71$	−19.5314	+	60.1116i	−0.275091	+	0.846642i	0.714105	+	0.700039i	$0.246834\pi$
$71$	−19.5314	+	60.1116i	−0.275091	+	0.846642i	−0.989195	+	0.146603i	$0.953166\pi$
$72$	−58.5252	+	29.8201i	−0.812851	+	0.414168i
$73$	−2.76193	+	17.4381i	−0.0378346	+	0.238878i	−0.999357	−	0.0358472i	$-0.988587\pi$
$73$	−2.76193	+	17.4381i	−0.0378346	+	0.238878i	0.961523	+	0.274726i	$0.0885870\pi$
$74$	53.3477	−	73.4268i	0.720915	−	0.992254i
$75$		0			0
$76$	52.3778			0.689182
$77$	−31.2366	−	74.5809i	−0.405670	−	0.968583i
$78$	−10.0201	+	10.0201i	−0.128462	+	0.128462i
$79$	21.7530	−	7.06797i	0.275354	−	0.0894680i	−0.168085	−	0.985773i	$-0.553758\pi$
$79$	21.7530	−	7.06797i	0.275354	−	0.0894680i	0.443439	+	0.896305i	$0.353758\pi$
$80$		0			0
$81$	214.136	−	155.579i	2.64365	−	1.92072i
$82$	157.236	−	80.1160i	1.91752	−	0.977024i
$83$	−38.0294	−	74.6368i	−0.458185	−	0.899239i	−0.998336	−	0.0576706i	$-0.981633\pi$
$83$	−38.0294	−	74.6368i	−0.458185	−	0.899239i	0.540151	−	0.841568i	$-0.318367\pi$
$84$	121.680	+	167.478i	1.44857	+	1.99379i
$85$		0			0
$86$	25.6481	+	78.9367i	0.298234	+	0.917869i
$87$	−10.9491	−	10.9491i	−0.125851	−	0.125851i
$88$	−19.9498	−	23.1730i	−0.226702	−	0.263329i
$89$		−	64.7104i		−	0.727083i	−0.931578	−	0.363542i	$-0.881567\pi$
$89$		−	64.7104i		−	0.727083i	0.931578	−	0.363542i	$-0.118433\pi$
$90$		0			0
$91$	4.93672	+	3.58674i	0.0542497	+	0.0394147i
$92$	104.634	+	16.5723i	1.13732	+	0.180134i
$93$	−17.5085	−	34.3624i	−0.188264	−	0.369488i
$94$	−257.956	−	83.8148i	−2.74421	−	0.891647i
$95$		0			0
$96$	−209.010	−	151.855i	−2.17719	−	1.58182i
$97$	−17.7536	+	34.8433i	−0.183026	+	0.359209i	−0.964230	−	0.265067i	$-0.914606\pi$
$97$	−17.7536	+	34.8433i	−0.183026	+	0.359209i	0.781204	+	0.624276i	$0.214606\pi$
$98$	10.6359	−	10.6359i	0.108529	−	0.108529i
$99$	198.310	+	168.029i	2.00313	+	1.69726i
$100$		0			0
$101$	5.90720	+	18.1805i	0.0584872	+	0.180005i	0.976032	−	0.217628i	$-0.0698319\pi$
$101$	5.90720	+	18.1805i	0.0584872	+	0.180005i	−0.917545	+	0.397633i	$0.869832\pi$
$102$	69.0268	+	435.818i	0.676733	+	4.27273i
$103$	21.3233	−	134.630i	0.207023	−	1.30709i	−0.637034	−	0.770836i	$-0.719839\pi$
$103$	21.3233	−	134.630i	0.207023	−	1.30709i	0.844056	−	0.536254i	$-0.180161\pi$
$104$	2.19465	+	0.713085i	0.0211024	+	0.00685658i
$105$		0			0
$106$	10.7159	−	7.78556i	0.101093	−	0.0734487i
$107$	5.97969	+	37.7543i	0.0558849	+	0.352844i	0.999747	+	0.0225031i	$0.00716357\pi$
$107$	5.97969	+	37.7543i	0.0558849	+	0.352844i	−0.943862	+	0.330340i	$0.892836\pi$
$108$	−367.095	−	187.044i	−3.39903	−	1.73189i
$109$		−	1.36826i		−	0.0125529i	−0.999980	−	0.00627643i	$-0.998002\pi$
$109$		−	1.36826i		−	0.0125529i	0.999980	−	0.00627643i	$-0.00199786\pi$
$110$		0			0
$111$	173.489			1.56296
$112$	−38.0901	+	74.7560i	−0.340090	+	0.667465i
$113$	1.21875	−	0.193031i	0.0107854	−	0.00170824i	−0.151039	−	0.988528i	$-0.548262\pi$
$113$	1.21875	−	0.193031i	0.0107854	−	0.00170824i	0.161825	+	0.986820i	$0.448262\pi$
$114$	106.595	+	146.715i	0.935044	+	1.28698i
$115$		0			0
$116$	−4.12985	+	12.7104i	−0.0356022	+	0.109572i
$117$	−19.3742	−	3.06857i	−0.165591	−	0.0262271i
$118$	172.328	−	27.2941i	1.46041	−	0.231306i
$119$	180.712	−	58.7169i	1.51859	−	0.493419i
$120$		0			0
$121$	−54.0831	+	108.241i	−0.446968	+	0.894550i
$122$	−41.1642	−	41.1642i	−0.337411	−	0.337411i
$123$	300.557	+	153.142i	2.44356	+	1.24505i
$124$	−19.5651	+	26.9290i	−0.157783	+	0.217169i
$125$		0			0
$126$	−160.398	+	493.653i	−1.27300	+	3.91788i
$127$	−97.3404	+	49.5974i	−0.766459	+	0.390531i	−0.793082	−	0.609115i	$-0.791525\pi$
$127$	−97.3404	+	49.5974i	−0.766459	+	0.390531i	0.0266225	+	0.999646i	$0.491525\pi$
$128$	−13.5390	+	85.4818i	−0.105773	+	0.667826i
$129$	−93.2536	+	128.353i	−0.722896	+	0.994981i
$130$		0			0
$131$	120.049			0.916404			0.458202	−	0.888848i	$-0.348494\pi$
$131$	120.049			0.916404			0.458202	+	0.888848i	$0.348494\pi$
$132$	71.1330	−	301.509i	0.538886	−	2.28416i
$133$	55.2203	−	55.2203i	0.415190	−	0.415190i
$134$	63.8728	−	20.7535i	0.476663	−	0.154877i
$135$		0			0
$136$	58.1321	−	42.2354i	0.427442	−	0.310555i
$137$	−171.881	+	87.5779i	−1.25461	+	0.639255i	−0.949710	−	0.313130i	$-0.898622\pi$
$137$	−171.881	+	87.5779i	−1.25461	+	0.639255i	−0.304898	+	0.952385i	$0.598622\pi$
$138$	166.521	+	326.816i	1.20667	+	2.36823i
$139$	−33.6518	−	46.3178i	−0.242100	−	0.333221i	0.670625	−	0.741796i	$-0.266026\pi$
$139$	−33.6518	−	46.3178i	−0.242100	−	0.333221i	−0.912725	+	0.408575i	$0.866026\pi$
$140$		0			0
$141$	−160.212	−	493.082i	−1.13626	−	3.49703i
$142$	133.557	+	133.557i	0.940545	+	0.940545i
$143$	−0.752247	−	9.10048i	−0.00526047	−	0.0636397i
$144$		−	269.704i		−	1.87295i
$145$		0			0
$146$	42.6843	+	31.0120i	0.292358	+	0.212411i
$147$	28.3976	+	4.49774i	0.193181	+	0.0305969i
$148$	−67.9795	−	133.417i	−0.459321	−	0.901468i
$149$	−167.106	−	54.2961i	−1.12152	−	0.364403i	−0.311172	−	0.950354i	$-0.600721\pi$
$149$	−167.106	−	54.2961i	−1.12152	−	0.364403i	−0.810347	+	0.585950i	$0.800721\pi$
$150$		0			0
$151$	−158.170	−	114.917i	−1.04748	−	0.761040i	−0.0757502	−	0.997127i	$-0.524135\pi$
$151$	−158.170	−	114.917i	−1.04748	−	0.761040i	−0.971732	+	0.236086i	$0.924135\pi$
$152$	13.4072	−	26.3131i	0.0882052	−	0.173112i
$153$	−431.905	+	431.905i	−2.82291	+	2.82291i
$154$	−240.960	−	18.0107i	−1.56467	−	0.116953i
$155$		0			0
$156$	7.22441	+	22.2344i	0.0463103	+	0.142528i
$157$	−17.8440	−	112.662i	−0.113656	−	0.717595i	−0.977041	−	0.213050i	$-0.931660\pi$
$157$	−17.8440	−	112.662i	−0.113656	−	0.717595i	0.863385	−	0.504545i	$-0.168340\pi$
$158$	10.6924	−	67.5092i	0.0676735	−	0.427274i
$159$	24.0797	+	7.82398i	0.151445	+	0.0492074i
$160$		0			0
$161$	127.784	−	92.8402i	0.793687	−	0.576647i
$162$	−123.736	−	781.235i	−0.763800	−	4.82244i
$163$	20.4791	+	10.4346i	0.125639	+	0.0640162i	0.515680	−	0.856781i	$-0.327539\pi$
$163$	20.4791	+	10.4346i	0.125639	+	0.0640162i	−0.390041	+	0.920797i	$0.627539\pi$
$164$		−	291.143i		−	1.77526i
$165$		0			0
$166$	−250.324			−1.50798
$167$	100.631	−	197.500i	0.602584	−	1.18264i	−0.365218	−	0.930922i	$-0.619005\pi$
$167$	100.631	−	197.500i	0.602584	−	1.18264i	0.967801	−	0.251715i	$-0.0809945\pi$
$168$	115.283	−	18.2590i	0.686207	−	0.108685i
$169$	−98.9306	−	136.166i	−0.585388	−	0.805718i
$170$		0			0
$171$	−77.5745	+	238.750i	−0.453652	+	1.39620i
$172$	135.247	+	21.4210i	0.786318	+	0.124541i
$173$	282.598	−	44.7592i	1.63352	−	0.258724i	0.728797	−	0.684730i	$-0.240080\pi$
$173$	282.598	−	44.7592i	1.63352	−	0.258724i	0.904720	+	0.426007i	$0.140080\pi$
$174$	−44.0077	+	14.2990i	−0.252918	+	0.0821781i
$175$		0			0
$176$	121.968	−	29.7897i	0.692999	−	0.169260i
$177$	235.828	+	235.828i	1.33236	+	1.33236i
$178$	−172.300	−	87.7913i	−0.967979	−	0.493210i
$179$	107.048	−	147.338i	0.598032	−	0.823120i	−0.397495	−	0.917604i	$-0.630120\pi$
$179$	107.048	−	147.338i	0.598032	−	0.823120i	0.995526	+	0.0944845i	$0.0301203\pi$
$180$		0			0
$181$	−26.7698	+	82.3891i	−0.147900	+	0.455188i	−0.997372	−	0.0724441i	$-0.976920\pi$
$181$	−26.7698	+	82.3891i	−0.147900	+	0.455188i	0.849473	+	0.527632i	$0.176920\pi$
$182$	16.2477	−	8.27863i	0.0892732	−	0.0454870i
$183$	17.4077	−	109.908i	0.0951240	−	0.600589i
$184$	35.1086	−	48.3229i	0.190808	−	0.262624i
$185$		0			0
$186$	−115.248			−0.619613
$187$	−243.025	−	147.614i	−1.29960	−	0.789380i
$188$	−316.415	+	316.415i	−1.68306	+	1.68306i
$189$	−584.212	+	189.822i	−3.09107	+	1.00435i
$190$		0			0
$191$	−89.7767	+	65.2266i	−0.470035	+	0.341501i	−0.797455	−	0.603378i	$-0.793821\pi$
$191$	−89.7767	+	65.2266i	−0.470035	+	0.341501i	0.327420	+	0.944879i	$0.393821\pi$
$192$	−455.524	+	232.101i	−2.37252	+	1.20886i
$193$	−141.689	−	278.079i	−0.734138	−	1.44083i	−0.891376	−	0.453265i	$-0.850259\pi$
$193$	−141.689	−	278.079i	−0.734138	−	1.44083i	0.157238	−	0.987561i	$-0.449741\pi$
$194$	68.6891	+	94.5425i	0.354068	+	0.487332i
$195$		0			0
$196$	−7.66840	−	23.6009i	−0.0391245	−	0.120413i
$197$	−185.550	−	185.550i	−0.941876	−	0.941876i	0.0565249	−	0.998401i	$-0.481998\pi$
$197$	−185.550	−	185.550i	−0.941876	−	0.941876i	−0.998401	+	0.0565249i	$0.981998\pi$
$198$	716.442	−	300.067i	3.61839	−	1.51549i
$199$			303.716i			1.52621i	0.646275	+	0.763105i	$0.276326\pi$
$199$			303.716i			1.52621i	−0.646275	+	0.763105i	$0.723674\pi$
$200$		0			0
$201$	103.858	+	75.4576i	0.516709	+	0.375411i
$202$	56.4222	+	8.93640i	0.279318	+	0.0442396i
$203$	9.04617	+	17.7541i	0.0445624	+	0.0874587i
$204$	692.350	+	224.958i	3.39387	+	1.10274i
$205$		0			0
$206$	−329.542	−	239.427i	−1.59972	−	1.16226i
$207$	−230.509	+	452.399i	−1.11357	+	2.18550i
$208$	−6.69992	+	6.69992i	−0.0322111	+	0.0322111i
$209$	−116.537	−	8.71067i	−0.557595	−	0.0416778i
$210$		0			0
$211$	81.0630	+	249.486i	0.384185	+	1.18240i	0.937070	+	0.349142i	$0.113527\pi$
$211$	81.0630	+	249.486i	0.384185	+	1.18240i	−0.552885	+	0.833258i	$0.686473\pi$
$212$	−3.41852	−	21.5837i	−0.0161251	−	0.101810i
$213$	−56.4793	+	356.596i	−0.265161	+	1.67416i
$214$	108.638	+	35.2987i	0.507656	+	0.164947i
$215$		0			0
$216$	−187.931	+	136.540i	−0.870053	+	0.632130i
$217$	7.76357	+	49.0172i	0.0357768	+	0.225886i
$218$	−3.64318	−	1.85629i	−0.0167119	−	0.00851511i
$219$			100.852i			0.460512i
$220$		0			0
$221$	21.4585			0.0970974
$222$	235.369	−	461.937i	1.06022	−	2.08080i
$223$	−392.047	+	62.0942i	−1.75806	+	0.278449i	−0.950362	−	0.311148i	$-0.899287\pi$
$223$	−392.047	+	62.0942i	−1.75806	+	0.278449i	−0.807698	+	0.589597i	$0.799287\pi$
$224$	195.414	+	268.964i	0.872382	+	1.20073i
$225$		0			0
$226$	1.13948	−	3.50696i	0.00504195	−	0.0155175i
$227$	168.118	+	26.6273i	0.740607	+	0.117301i	0.515327	−	0.856993i	$-0.327670\pi$
$227$	168.118	+	26.6273i	0.740607	+	0.117301i	0.225280	+	0.974294i	$0.427670\pi$
$228$	295.510	−	46.8042i	1.29610	−	0.205282i
$229$	253.887	−	82.4930i	1.10868	−	0.360231i	0.303242	−	0.952914i	$-0.401931\pi$
$229$	253.887	−	82.4930i	1.10868	−	0.360231i	0.805436	+	0.592682i	$0.201931\pi$
$230$		0			0
$231$	−242.878	−	392.865i	−1.05142	−	1.70071i
$232$	5.32820	+	5.32820i	0.0229664	+	0.0229664i
$233$	103.065	+	52.5144i	0.442340	+	0.225383i	0.660952	−	0.750428i	$-0.270153\pi$
$233$	103.065	+	52.5144i	0.442340	+	0.225383i	−0.218612	+	0.975812i	$0.570153\pi$
$234$	−34.4551	+	47.4233i	−0.147244	+	0.202664i
$235$		0			0
$236$	88.9514	−	273.764i	0.376913	−	1.16002i
$237$	116.412	−	59.3150i	0.491191	−	0.250274i
$238$	88.8267	−	560.830i	0.373222	−	2.35643i
$239$	3.00227	−	4.13227i	0.0125618	−	0.0172898i	−0.802690	−	0.596397i	$-0.796599\pi$
$239$	3.00227	−	4.13227i	0.0125618	−	0.0172898i	0.815252	+	0.579107i	$0.196599\pi$
$240$		0			0
$241$	−12.7150			−0.0527594			−0.0263797	−	0.999652i	$-0.508398\pi$
$241$	−12.7150			−0.0527594			−0.0263797	+	0.999652i	$0.508398\pi$
$242$	214.831	+	290.851i	0.887733	+	1.20187i
$243$	537.292	−	537.292i	2.21108	−	2.21108i
$244$	−91.3429	+	29.6791i	−0.374356	+	0.121636i
$245$		0			0
$246$	815.521	−	592.510i	3.31512	−	2.40858i
$247$	7.85803	−	4.00386i	0.0318139	−	0.0162100i
$248$	8.52027	+	16.7220i	0.0343559	+	0.0674273i
$249$	−281.252	−	387.110i	−1.12953	−	1.55466i
$250$		0			0
$251$	55.4542	+	170.671i	0.220933	+	0.679962i	0.998679	+	0.0513834i	$0.0163630\pi$
$251$	55.4542	+	170.671i	0.220933	+	0.679962i	−0.777746	+	0.628579i	$0.783637\pi$
$252$	605.528	+	605.528i	2.40289	+	2.40289i
$253$	−230.047	−	54.2735i	−0.909278	−	0.214520i
$254$			326.470i			1.28531i
$255$		0			0
$256$	−80.3911	−	58.4076i	−0.314028	−	0.228155i
$257$	116.416	+	18.4385i	0.452980	+	0.0717450i	0.378756	−	0.925497i	$-0.376352\pi$
$257$	116.416	+	18.4385i	0.452980	+	0.0717450i	0.0742243	+	0.997242i	$0.476352\pi$
$258$	215.241	+	422.434i	0.834266	+	1.63734i
$259$	−212.326	−	68.9889i	−0.819792	−	0.266367i
$260$		0			0
$261$	−51.8201	−	37.6495i	−0.198545	−	0.144251i
$262$	162.868	−	319.646i	0.621634	−	1.22002i
$263$	45.2638	−	45.2638i	0.172106	−	0.172106i	−0.615798	−	0.787904i	$-0.711166\pi$
$263$	45.2638	−	45.2638i	0.172106	−	0.172106i	0.787904	+	0.615798i	$0.211166\pi$
$264$	−133.261	−	112.913i	−0.504778	−	0.427700i
$265$		0			0
$266$	−72.1152	−	221.948i	−0.271110	−	0.834390i
$267$	−57.8245	−	365.089i	−0.216571	−	1.36738i
$268$	17.3331	−	109.437i	0.0646758	−	0.408347i
$269$	445.037	+	144.601i	1.65441	+	0.537551i	0.979690	−	0.200519i	$-0.0642629\pi$
$269$	445.037	+	144.601i	1.65441	+	0.537551i	0.674723	+	0.738071i	$0.264263\pi$
$270$		0			0
$271$	−273.448	+	198.672i	−1.00903	+	0.733107i	−0.964006	−	0.265879i	$-0.914338\pi$
$271$	−273.448	+	198.672i	−1.00903	+	0.733107i	−0.0450282	+	0.998986i	$0.514338\pi$
$272$	46.1548	+	291.410i	0.169687	+	1.07136i
$273$	31.0575	+	15.8246i	0.113764	+	0.0579656i
$274$			576.472i			2.10391i
$275$		0			0
$276$	605.141			2.19254
$277$	−2.53164	+	4.96863i	−0.00913951	+	0.0179373i	−0.895531	−	0.444999i	$-0.853204\pi$
$277$	−2.53164	+	4.96863i	−0.00913951	+	0.0179373i	0.886392	+	0.462936i	$0.153204\pi$
$278$	−168.982	+	26.7641i	−0.607849	+	0.0962739i
$279$	−93.7714	−	129.065i	−0.336098	−	0.462599i
$280$		0			0
$281$	42.3477	−	130.333i	0.150703	−	0.463817i	−0.846997	−	0.531598i	$-0.821592\pi$
$281$	42.3477	−	130.333i	0.150703	−	0.463817i	0.997700	+	0.0677806i	$0.0215918\pi$
$282$	−1530.25	−	242.368i	−5.42643	−	0.859462i
$283$	−307.975	+	48.7785i	−1.08825	+	0.172362i	−0.674681	−	0.738110i	$-0.735719\pi$
$283$	−307.975	+	48.7785i	−1.08825	+	0.172362i	−0.413571	+	0.910472i	$0.635719\pi$
$284$	296.362	−	96.2940i	1.04353	−	0.339063i
$285$		0			0
$286$	−25.2518	−	10.3435i	−0.0882930	−	0.0361660i
$287$	−306.943	−	306.943i	−1.06949	−	1.06949i
$288$	−952.225	−	485.183i	−3.30634	−	1.68466i
$289$	222.882	−	306.770i	0.771217	−	1.06149i
$290$		0			0
$291$	−69.0281	+	212.447i	−0.237210	+	0.730057i
$292$	77.5578	−	39.5177i	0.265609	−	0.135335i
$293$	−38.6619	+	244.101i	−0.131952	+	0.833111i	0.829574	+	0.558397i	$0.188583\pi$
$293$	−38.6619	+	244.101i	−0.131952	+	0.833111i	−0.961526	+	0.274714i	$0.911417\pi$
$294$	50.5024	−	69.5105i	0.171777	−	0.236430i
$295$		0			0
$296$	−84.4257			−0.285222
$297$	785.658	+	477.212i	2.64531	+	1.60677i
$298$	−371.280	+	371.280i	−1.24591	+	1.24591i
$299$	16.9646	−	5.51213i	0.0567377	−	0.0184352i
$300$		0			0
$301$	165.170	−	120.003i	0.548737	−	0.398681i
$302$	−520.568	+	265.243i	−1.72374	+	0.878287i
$303$	49.5737	+	97.2938i	0.163610	+	0.321102i
$304$	71.2747	+	98.1013i	0.234456	+	0.322702i
$305$		0			0
$306$	564.049	+	1735.96i	1.84330	+	5.67308i
$307$	117.293	+	117.293i	0.382063	+	0.382063i	0.871845	−	0.489782i	$-0.162924\pi$
$307$	117.293	+	117.293i	0.382063	+	0.382063i	−0.489782	+	0.871845i	$0.662924\pi$
$308$	−206.954	+	340.719i	−0.671929	+	1.10623i
$309$		−	778.624i		−	2.51982i
$310$		0			0
$311$	−11.7045	−	8.50380i	−0.0376350	−	0.0273434i	0.568809	−	0.822470i	$-0.307404\pi$
$311$	−11.7045	−	8.50380i	−0.0376350	−	0.0273434i	−0.606444	+	0.795126i	$0.707404\pi$
$312$	13.0192	+	2.06203i	0.0417281	+	0.00660909i
$313$	193.434	+	379.636i	0.618000	+	1.21289i	0.961775	+	0.273841i	$0.0882943\pi$
$313$	193.434	+	379.636i	0.618000	+	1.21289i	−0.343775	+	0.939052i	$0.611706\pi$
$314$	−324.187	−	105.335i	−1.03244	−	0.335461i
$315$		0			0
$316$	−91.2295	−	66.2821i	−0.288701	−	0.209753i
$317$	−171.173	+	335.946i	−0.539978	+	1.05977i	0.446333	+	0.894867i	$0.352730\pi$
$317$	−171.173	+	335.946i	−0.539978	+	1.05977i	−0.986310	+	0.164899i	$0.947270\pi$
$318$	53.5009	−	53.5009i	0.168242	−	0.168242i
$319$	11.3025	−	27.5930i	0.0354309	−	0.0864984i
$320$		0			0
$321$	67.4735	+	207.662i	0.210198	+	0.646923i
$322$	−73.8381	−	466.196i	−0.229311	−	1.44781i
$323$	42.9600	−	271.239i	0.133003	−	0.839749i
$324$	−1241.09	−	403.254i	−3.83052	−	1.24461i
$325$		0			0
$326$	55.5672	−	40.3720i	0.170452	−	0.123840i
$327$	−1.22266	−	7.71959i	−0.00373903	−	0.0236073i
$328$	−146.262	−	74.5241i	−0.445920	−	0.227208i
$329$			667.173i			2.02788i
$330$		0			0
$331$	177.839			0.537278			0.268639	−	0.963241i	$-0.413426\pi$
$331$	177.839			0.537278			0.268639	+	0.963241i	$0.413426\pi$
$332$	−187.493	+	367.975i	−0.564736	+	1.10836i
$333$	708.826	−	112.267i	2.12861	−	0.337138i
$334$	−389.347	−	535.890i	−1.16571	−	1.60446i
$335$		0			0
$336$	−148.099	+	455.802i	−0.440771	+	1.35655i
$337$	−176.531	−	27.9598i	−0.523831	−	0.0829666i	−0.111081	−	0.993811i	$-0.535431\pi$
$337$	−176.531	−	27.9598i	−0.523831	−	0.0829666i	−0.412749	+	0.910845i	$0.635431\pi$
$338$	−496.778	+	78.6820i	−1.46976	+	0.232787i
$339$	6.70356	−	2.17812i	0.0197745	−	0.00642513i
$340$		0			0
$341$	48.0095	−	56.6616i	0.140790	−	0.166163i
$342$	530.459	+	530.459i	1.55105	+	1.55105i
$343$	287.962	+	146.724i	0.839539	+	0.427767i
$344$	45.3805	−	62.4609i	0.131920	−	0.181572i
$345$		0			0
$346$	264.218	−	813.180i	0.763637	−	2.35023i
$347$	98.4313	−	50.1532i	0.283664	−	0.144534i	−0.306370	−	0.951912i	$-0.599114\pi$
$347$	98.4313	−	50.1532i	0.283664	−	0.144534i	0.590034	+	0.807379i	$0.299114\pi$
$348$	−11.9423	+	75.4010i	−0.0343171	+	0.216669i
$349$	179.109	−	246.522i	0.513206	−	0.706368i	−0.471250	−	0.882000i	$-0.656197\pi$
$349$	179.109	−	246.522i	0.513206	−	0.706368i	0.984456	+	0.175632i	$0.0561969\pi$
$350$		0			0
$351$	−69.3719			−0.197641
$352$	114.237	−	484.212i	0.324537	−	1.37560i
$353$	275.060	−	275.060i	0.779207	−	0.779207i	−0.200489	−	0.979696i	$-0.564253\pi$
$353$	275.060	−	275.060i	0.779207	−	0.779207i	0.979696	+	0.200489i	$0.0642530\pi$
$354$	947.867	−	307.981i	2.67759	−	0.870002i
$355$		0			0
$356$	−258.105	+	187.524i	−0.725015	+	0.526754i
$357$	967.089	−	492.756i	2.70893	−	1.38027i
$358$	−247.079	−	484.920i	−0.690165	−	1.35453i
$359$	−325.640	−	448.205i	−0.907075	−	1.24848i	−0.968156	−	0.250349i	$-0.919455\pi$
$359$	−325.640	−	448.205i	−0.907075	−	1.24848i	0.0610804	−	0.998133i	$-0.480545\pi$
$360$		0			0
$361$	76.6775	+	235.989i	0.212403	+	0.653709i
$362$	183.054	+	183.054i	0.505674	+	0.505674i
$363$	−208.409	+	659.010i	−0.574129	+	1.81545i
$364$		−	30.0847i		−	0.0826503i
$365$		0			0
$366$	−269.028	−	195.460i	−0.735048	−	0.534044i
$367$	13.0718	+	2.07038i	0.0356181	+	0.00564135i	0.174218	−	0.984707i	$-0.444260\pi$
$367$	13.0718	+	2.07038i	0.0356181	+	0.00564135i	−0.138600	+	0.990348i	$0.544260\pi$
$368$	111.344	+	218.525i	0.302566	+	0.593819i
$369$	1327.09	+	431.199i	3.59646	+	1.16856i
$370$		0			0
$371$	−26.3590	−	19.1509i	−0.0710486	−	0.0516198i
$372$	−86.3206	+	169.414i	−0.232045	+	0.455413i
$373$	−11.0292	+	11.0292i	−0.0295689	+	0.0295689i	−0.721737	−	0.692168i	$-0.756656\pi$
$373$	−11.0292	+	11.0292i	−0.0295689	+	0.0295689i	0.692168	+	0.721737i	$0.256656\pi$
$374$	−722.749	+	446.821i	−1.93248	+	1.19471i
$375$		0			0
$376$	77.9648	+	239.951i	0.207353	+	0.638168i
$377$	0.352022	+	2.22258i	0.000933745	+	0.00589543i
$378$	−287.162	+	1813.07i	−0.759688	+	4.79648i
$379$	−162.869	−	52.9193i	−0.429733	−	0.139629i	0.0861607	−	0.996281i	$-0.472540\pi$
$379$	−162.869	−	52.9193i	−0.429733	−	0.139629i	−0.515894	+	0.856652i	$0.672540\pi$
$380$		0			0
$381$	−504.864	+	366.805i	−1.32510	+	0.962744i
$382$	51.8763	+	327.534i	0.135802	+	0.857420i
$383$	−498.019	−	253.753i	−1.30031	−	0.662541i	−0.339725	−	0.940525i	$-0.610334\pi$
$383$	−498.019	−	253.753i	−1.30031	−	0.662541i	−0.960586	+	0.277984i	$0.910334\pi$
$384$			494.377i			1.28744i
$385$		0			0
$386$	−932.650			−2.41619
$387$	−297.949	+	584.759i	−0.769895	+	1.51100i
$388$	190.425	−	30.1603i	0.490785	−	0.0777328i
$389$	183.509	+	252.578i	0.471744	+	0.649300i	0.976892	−	0.213733i	$-0.0685621\pi$
$389$	183.509	+	252.578i	0.471744	+	0.649300i	−0.505148	+	0.863033i	$0.668562\pi$
$390$		0			0
$391$	171.640	−	528.254i	0.438977	−	1.35103i
$392$	−13.8193	−	2.18876i	−0.0352533	−	0.00558358i
$393$	677.303	−	107.274i	1.72342	−	0.272963i
$394$	−745.782	+	242.319i	−1.89285	+	0.615024i
$395$		0			0
$396$	95.5185	−	1277.91i	0.241208	−	3.22705i
$397$	223.200	+	223.200i	0.562215	+	0.562215i	0.929936	−	0.367721i	$-0.119862\pi$
$397$	223.200	+	223.200i	0.562215	+	0.562215i	−0.367721	+	0.929936i	$0.619862\pi$
$398$	808.684	+	412.045i	2.03187	+	1.03529i
$399$	262.203	−	360.891i	0.657150	−	0.904489i
$400$		0			0
$401$	175.008	−	538.619i	0.436429	−	1.34319i	−0.455186	−	0.890396i	$-0.650427\pi$
$401$	175.008	−	538.619i	0.436429	−	1.34319i	0.891615	−	0.452794i	$-0.149573\pi$
$402$	341.819	−	174.165i	0.850295	−	0.433247i
$403$	−0.876759	+	5.53564i	−0.00217558	+	0.0137361i
$404$	55.3966	−	76.2469i	0.137120	−	0.188730i
$405$		0			0
$406$	59.5455			0.146664
$407$	129.062	+	308.150i	0.317106	+	0.757126i
$408$	290.234	−	290.234i	0.711358	−	0.711358i
$409$	51.3176	−	16.6741i	0.125471	−	0.0407679i	−0.245609	−	0.969369i	$-0.578988\pi$
$409$	51.3176	−	16.6741i	0.125471	−	0.0407679i	0.371079	+	0.928601i	$0.378988\pi$
$410$		0			0
$411$	−891.477	+	647.696i	−2.16904	+	1.57590i
$412$	−598.782	+	305.095i	−1.45335	+	0.740521i
$413$	−194.842	−	382.400i	−0.471773	−	0.925907i
$414$	891.846	+	1227.52i	2.15422	+	2.96503i
$415$		0			0
$416$	11.6021	+	35.7077i	0.0278897	+	0.0858357i
$417$	−231.249	−	231.249i	−0.554554	−	0.554554i
$418$	−181.297	+	298.479i	−0.433726	+	0.714065i
$419$			571.037i			1.36286i	0.731885	+	0.681428i	$0.238641\pi$
$419$			571.037i			1.36286i	−0.731885	+	0.681428i	$0.761359\pi$
$420$		0			0
$421$	537.862	+	390.780i	1.27758	+	0.928218i	0.999477	−	0.0323321i	$-0.0102934\pi$
$421$	537.862	+	390.780i	1.27758	+	0.928218i	0.278106	+	0.960550i	$0.410293\pi$
$422$	774.267	+	122.632i	1.83476	+	0.290597i
$423$	−973.662	−	1910.92i	−2.30180	−	4.51754i
$424$	−11.7181	−	3.80743i	−0.0276369	−	0.00897978i
$425$		0			0
$426$	872.861	+	634.171i	2.04897	+	1.48866i
$427$	−65.0102	+	127.590i	−0.152249	+	0.298805i
$428$	133.259	−	133.259i	0.311352	−	0.311352i
$429$	−12.3762	−	50.6717i	−0.0288489	−	0.118116i
$430$		0			0
$431$	−111.781	−	344.025i	−0.259352	−	0.798202i	−0.992941	−	0.118609i	$-0.962156\pi$
$431$	−111.781	−	344.025i	−0.259352	−	0.798202i	0.733589	−	0.679593i	$-0.237844\pi$
$432$	−149.211	−	942.079i	−0.345395	−	2.18074i
$433$	58.2731	−	367.922i	0.134580	−	0.849705i	−0.824354	−	0.566075i	$-0.808461\pi$
$433$	58.2731	−	367.922i	0.134580	−	0.849705i	0.958934	−	0.283630i	$-0.0915387\pi$
$434$	141.048	+	45.8292i	0.324995	+	0.105597i
$435$		0			0
$436$	−5.45748	+	3.96509i	−0.0125172	+	0.00909424i
$437$	−35.7110	−	225.470i	−0.0817185	−	0.515950i
$438$	268.532	+	136.824i	0.613087	+	0.312384i
$439$		−	731.071i		−	1.66531i	−0.553792	−	0.832655i	$-0.686820\pi$
$439$		−	731.071i		−	1.66531i	0.553792	−	0.832655i	$-0.313180\pi$
$440$		0			0
$441$	118.935			0.269695
$442$	29.1123	−	57.1362i	0.0658650	−	0.129267i
$443$	674.027	−	106.755i	1.52151	−	0.240983i	0.660986	−	0.750398i	$-0.270138\pi$
$443$	674.027	−	106.755i	1.52151	−	0.240983i	0.860521	+	0.509415i	$0.170138\pi$
$444$	−502.753	−	691.980i	−1.13233	−	1.55851i
$445$		0			0
$446$	−366.549	+	1128.12i	−0.821858	+	2.52942i
$447$	−991.314	−	157.009i	−2.21770	−	0.351250i
$448$	649.795	−	102.917i	1.45044	−	0.229726i
$449$	−172.805	+	56.1477i	−0.384866	+	0.125051i	−0.495058	−	0.868860i	$-0.664853\pi$
$449$	−172.805	+	56.1477i	−0.384866	+	0.125051i	0.110192	+	0.993910i	$0.464853\pi$
$450$		0			0
$451$	−48.4184	+	647.776i	−0.107358	+	1.43631i
$452$	−4.30174	−	4.30174i	−0.00951712	−	0.00951712i
$453$	−995.066	−	507.011i	−2.19661	−	1.11923i
$454$	298.981	−	411.512i	0.658548	−	0.906413i
$455$		0			0
$456$	52.1289	−	160.436i	0.114318	−	0.351834i
$457$	734.574	−	374.284i	1.60738	−	0.819002i	0.607691	−	0.794174i	$-0.292096\pi$
$457$	734.574	−	374.284i	1.60738	−	0.819002i	0.999692	−	0.0248284i	$-0.00790394\pi$
$458$	124.795	−	787.926i	0.272479	−	1.72036i
$459$	−1269.70	+	1747.59i	−2.76623	+	3.80739i
$460$		0			0
$461$	719.958			1.56173			0.780866	−	0.624699i	$-0.214778\pi$
$461$	719.958			1.56173			0.780866	+	0.624699i	$0.214778\pi$
$462$	−1375.56	+	113.704i	−2.97741	+	0.246113i
$463$	−501.863	+	501.863i	−1.08394	+	1.08394i	−0.0877980	+	0.996138i	$0.527983\pi$
$463$	−501.863	+	501.863i	−1.08394	+	1.08394i	−0.996138	+	0.0877980i	$0.972017\pi$
$464$	−29.4258	+	9.56101i	−0.0634176	+	0.0206056i
$465$		0			0
$466$	279.653	−	203.180i	0.600114	−	0.436008i
$467$	−45.4172	+	23.1412i	−0.0972531	+	0.0495529i	−0.501940	−	0.864902i	$-0.667380\pi$
$467$	−45.4172	+	23.1412i	−0.0972531	+	0.0495529i	0.404687	+	0.914455i	$0.367380\pi$
$468$	43.9051	+	86.1687i	0.0938144	+	0.184121i
$469$	−97.1022	−	133.650i	−0.207041	−	0.284967i
$470$		0			0
$471$	−201.348	−	619.684i	−0.427489	−	1.31568i
$472$	−114.762	−	114.762i	−0.243140	−	0.243140i
$473$	−297.353	−	70.1525i	−0.628654	−	0.148314i
$474$		−	390.435i		−	0.823702i
$475$		0			0
$476$	−757.885	−	550.635i	−1.59219	−	1.15680i
$477$	103.446	+	16.3843i	0.216868	+	0.0343486i
$478$	−6.92960	−	13.6001i	−0.0144971	−	0.0284521i
$479$	−27.4370	−	8.91483i	−0.0572798	−	0.0186113i	0.280237	−	0.959931i	$-0.409587\pi$
$479$	−27.4370	−	8.91483i	−0.0572798	−	0.0186113i	−0.337517	+	0.941320i	$0.609587\pi$
$480$		0			0
$481$	−20.3974	−	14.8195i	−0.0424061	−	0.0308099i
$482$	−17.2502	+	33.8554i	−0.0357888	+	0.0702395i
$483$	637.981	−	637.981i	1.32087	−	1.32087i
$484$	588.458	−	97.9533i	1.21582	−	0.202383i
$485$		0			0
$486$	−701.679	−	2159.55i	−1.44378	−	4.44351i
$487$	4.27107	+	26.9665i	0.00877017	+	0.0553727i	0.991685	−	0.128687i	$-0.0410761\pi$
$487$	4.27107	+	26.9665i	0.00877017	+	0.0553727i	−0.982915	+	0.184059i	$0.941076\pi$
$488$	−8.47119	+	53.4850i	−0.0173590	+	0.109600i
$489$	124.865	+	40.5712i	0.255348	+	0.0829677i
$490$		0			0
$491$	313.154	−	227.520i	0.637788	−	0.463380i	−0.221301	−	0.975205i	$-0.571030\pi$
$491$	313.154	−	227.520i	0.637788	−	0.463380i	0.859090	+	0.511825i	$0.171030\pi$
$492$	−260.162	−	1642.60i	−0.528785	−	3.33861i
$493$	62.4335	+	31.8115i	0.126640	+	0.0645263i
$494$		−	26.3550i		−	0.0533502i
$495$		0			0
$496$	−77.0606			−0.155364
$497$	210.926	−	413.965i	0.424398	−	0.832928i
$498$	−1412.30	+	223.687i	−2.83595	+	0.449170i
$499$	−245.444	−	337.825i	−0.491872	−	0.677003i	0.488860	−	0.872362i	$-0.337413\pi$
$499$	−245.444	−	337.825i	−0.491872	−	0.677003i	−0.980732	+	0.195359i	$0.937413\pi$
$500$		0			0
$501$	391.268	−	1204.20i	0.780974	−	2.40359i
$502$	529.667	+	83.8910i	1.05511	+	0.167114i
$503$	817.154	−	129.425i	1.62456	−	0.257305i	0.723285	−	0.690550i	$-0.242631\pi$
$503$	817.154	−	129.425i	1.62456	−	0.257305i	0.901276	+	0.433245i	$0.142631\pi$
$504$	459.198	−	149.202i	0.911106	−	0.296036i
$505$		0			0
$506$	−456.611	+	538.900i	−0.902394	+	1.06502i
$507$	−679.833	−	679.833i	−1.34089	−	1.34089i
$508$	479.908	+	244.525i	0.944700	+	0.481349i
$509$	−316.476	+	435.592i	−0.621760	+	0.855780i	−0.997480	−	0.0709537i	$-0.977396\pi$
$509$	−316.476	+	435.592i	−0.621760	+	0.855780i	0.375719	+	0.926734i	$0.377396\pi$
$510$		0			0
$511$	40.1045	−	123.429i	0.0784824	−	0.241544i
$512$	−573.040	+	291.978i	−1.11922	+	0.570270i
$513$	−138.883	+	876.871i	−0.270727	+	1.70930i
$514$	207.034	−	284.958i	0.402790	−	0.554393i
$515$		0			0
$516$	782.189			1.51587
$517$	756.626	−	651.384i	1.46349	−	1.25993i
$518$	−471.751	+	471.751i	−0.910716	+	0.910716i
$519$	1554.39	−	505.053i	2.99498	−	0.973127i
$520$		0			0
$521$	236.468	−	171.804i	0.453874	−	0.329759i	−0.337249	−	0.941415i	$-0.609497\pi$
$521$	236.468	−	171.804i	0.453874	−	0.329759i	0.791123	+	0.611657i	$0.209497\pi$
$522$	−170.550	+	86.8997i	−0.326725	+	0.166475i
$523$	393.098	+	771.497i	0.751621	+	1.47514i	0.875694	+	0.482866i	$0.160404\pi$
$523$	393.098	+	771.497i	0.751621	+	1.47514i	−0.124074	+	0.992273i	$0.539596\pi$
$524$	−347.890	−	478.829i	−0.663912	−	0.913797i
$525$		0			0
$526$	−59.1125	−	181.930i	−0.112381	−	0.345874i
$527$	123.405	+	123.405i	0.234165	+	0.234165i
$528$	661.509	−	277.059i	1.25286	−	0.524733i
$529$			67.2858i			0.127194i
$530$		0			0
$531$	1116.14	+	810.920i	2.10195	+	1.52716i
$532$	−380.275	−	60.2297i	−0.714803	−	0.113214i
$533$	−22.2556	−	43.6790i	−0.0417553	−	0.0819493i
$534$	−1050.55	−	341.344i	−1.96732	−	0.639221i
$535$		0			0
$536$	−50.5412	−	36.7203i	−0.0942933	−	0.0685081i
$537$	472.292	−	926.924i	0.879500	−	1.72612i
$538$	988.794	−	988.794i	1.83791	−	1.83791i
$539$	13.1368	+	53.7858i	0.0243725	+	0.0997882i
$540$		0			0
$541$	33.2984	+	102.482i	0.0615496	+	0.189430i	0.977103	−	0.212766i	$-0.0682471\pi$
$541$	33.2984	+	102.482i	0.0615496	+	0.189430i	−0.915554	+	0.402196i	$0.868247\pi$
$542$	158.009	+	997.627i	0.291529	+	1.84064i
$543$	−77.4106	+	488.751i	−0.142561	+	0.900095i
$544$	1111.89	+	361.274i	2.04391	+	0.664107i
$545$		0			0
$546$	84.2703	−	61.2259i	0.154341	−	0.112135i
$547$	50.9150	+	321.465i	0.0930805	+	0.587687i	0.989506	+	0.144492i	$0.0461549\pi$
$547$	50.9150	+	321.465i	0.0930805	+	0.587687i	−0.896425	+	0.443195i	$0.853845\pi$
$548$	847.410	+	431.777i	1.54637	+	0.787914i
$549$		−	460.317i		−	0.838465i
$550$		0			0
$551$	28.7985			0.0522659
$552$	154.898	−	304.005i	0.280613	−	0.550734i
$553$	−166.059	+	26.3012i	−0.300288	+	0.0475610i
$554$	9.79502	+	13.4817i	0.0176805	+	0.0243352i
$555$		0			0
$556$	−87.2242	+	268.449i	−0.156878	+	0.482821i
$557$	711.735	+	112.728i	1.27780	+	0.202384i	0.758198	−	0.652024i	$-0.226080\pi$
$557$	711.735	+	112.728i	1.27780	+	0.202384i	0.519603	+	0.854408i	$0.326080\pi$
$558$	−470.871	+	74.5787i	−0.843855	+	0.133654i
$559$	21.9280	−	7.12483i	0.0392271	−	0.0127457i
$560$		0			0
$561$	−1503.02	−	615.659i	−2.67919	−	1.09743i
$562$	−289.576	−	289.576i	−0.515260	−	0.515260i
$563$	590.171	+	300.707i	1.04826	+	0.534116i	0.891265	−	0.453484i	$-0.149819\pi$
$563$	590.171	+	300.707i	1.04826	+	0.534116i	0.156996	+	0.987599i	$0.449819\pi$
$564$	−1502.44	+	2067.93i	−2.66390	+	3.66654i
$565$		0			0
$566$	−287.944	+	886.202i	−0.508736	+	1.56573i
$567$	−1733.58	+	883.302i	−3.05746	+	1.55785i
$568$	27.4848	−	173.532i	0.0483888	−	0.305515i
$569$	298.438	−	410.765i	0.524496	−	0.721907i	−0.461783	−	0.886993i	$-0.652790\pi$
$569$	298.438	−	410.765i	0.524496	−	0.721907i	0.986279	+	0.165086i	$0.0527902\pi$
$570$		0			0
$571$	−447.072			−0.782963			−0.391482	−	0.920186i	$-0.628037\pi$
$571$	−447.072			−0.782963			−0.391482	+	0.920186i	$0.628037\pi$
$572$	−34.1184	+	29.3727i	−0.0596475	+	0.0513509i
$573$	−448.225	+	448.225i	−0.782243	+	0.782243i
$574$	−1233.70	+	400.854i	−2.14930	+	0.698351i
$575$		0			0
$576$	−1710.95	+	1243.08i	−2.97040	+	2.15812i
$577$	−488.958	+	249.136i	−0.847414	+	0.431779i	−0.823080	−	0.567925i	$-0.807746\pi$
$577$	−488.958	+	249.136i	−0.847414	+	0.431779i	−0.0243334	+	0.999704i	$0.507746\pi$
$578$	−514.438	−	1009.64i	−0.890031	−	1.74678i
$579$	−1047.88	−	1442.28i	−1.80981	−	2.49099i
$580$		0			0
$581$	190.277	+	585.612i	0.327499	+	1.00794i
$582$	472.019	+	472.019i	0.811029	+	0.811029i
$583$	4.01653	+	48.5909i	0.00688942	+	0.0833463i
$584$		−	49.0782i		−	0.0840380i
$585$		0			0
$586$	597.501	+	434.110i	1.01963	+	0.740802i
$587$	321.206	+	50.8740i	0.547199	+	0.0866678i	0.423912	−	0.905703i	$-0.360657\pi$
$587$	321.206	+	50.8740i	0.547199	+	0.0866678i	0.123287	+	0.992371i	$0.460657\pi$
$588$	−64.3538	−	126.301i	−0.109445	−	0.214798i
$589$	68.2161	+	22.1647i	0.115817	+	0.0376311i
$590$		0			0
$591$	−1212.66	−	881.046i	−2.05187	−	1.49077i
$592$	157.379	−	308.874i	0.265843	−	0.521747i
$593$	−5.55830	+	5.55830i	−0.00937318	+	0.00937318i	−0.711778	−	0.702405i	$-0.752110\pi$
$593$	−5.55830	+	5.55830i	−0.00937318	+	0.00937318i	0.702405	+	0.711778i	$0.252110\pi$
$594$	2336.53	−	1444.50i	3.93355	−	2.43181i
$595$		0			0
$596$	267.691	+	823.868i	0.449146	+	1.38233i
$597$	271.397	+	1713.53i	0.454601	+	2.87024i
$598$	8.33873	−	52.6487i	0.0139444	−	0.0880412i
$599$	35.3715	+	11.4929i	0.0590509	+	0.0191868i	0.338393	−	0.941005i	$-0.390117\pi$
$599$	35.3715	+	11.4929i	0.0590509	+	0.0191868i	−0.279343	+	0.960191i	$0.590117\pi$
$600$		0			0
$601$	−166.472	+	120.949i	−0.276992	+	0.201247i	−0.717604	−	0.696451i	$-0.754761\pi$
$601$	−166.472	+	120.949i	−0.276992	+	0.201247i	0.440612	+	0.897698i	$0.354761\pi$
$602$	−95.4413	−	602.592i	−0.158540	−	1.00098i
$603$	473.166	+	241.090i	0.784687	+	0.399818i
$604$			963.897i			1.59586i
$605$		0			0
$606$	326.314			0.538471
$607$	−410.353	+	805.363i	−0.676034	+	1.32679i	0.256793	+	0.966467i	$0.417334\pi$
$607$	−410.353	+	805.363i	−0.676034	+	1.32679i	−0.932827	+	0.360325i	$0.882666\pi$
$608$	474.578	−	75.1658i	0.780556	−	0.123628i
$609$	66.9024	+	92.0833i	0.109856	+	0.151204i
$610$		0			0
$611$	−23.2831	+	71.6579i	−0.0381065	+	0.117280i
$612$	2974.32	+	471.087i	4.86001	+	0.769749i
$613$	−487.431	+	77.2015i	−0.795156	+	0.125940i	−0.540779	−	0.841165i	$-0.681870\pi$
$613$	−487.431	+	77.2015i	−0.795156	+	0.125940i	−0.254377	+	0.967105i	$0.581870\pi$
$614$	471.439	−	153.180i	0.767815	−	0.249478i
$615$		0			0
$616$	118.193	+	191.182i	0.191872	+	0.310360i
$617$	−614.016	−	614.016i	−0.995164	−	0.995164i	0.00482401	−	0.999988i	$-0.498464\pi$
$617$	−614.016	−	614.016i	−0.995164	−	0.995164i	−0.999988	+	0.00482401i	$0.998464\pi$
$618$	−2073.19	−	1056.34i	−3.35468	−	1.70929i
$619$	138.286	−	190.335i	0.223403	−	0.307487i	−0.682573	−	0.730818i	$-0.739139\pi$
$619$	138.286	−	190.335i	0.223403	−	0.307487i	0.905975	+	0.423330i	$0.139139\pi$
$620$		0			0
$621$	−554.884	+	1707.76i	−0.893533	+	2.75001i
$622$	−38.5218	+	19.6278i	−0.0619321	+	0.0315560i
$623$	−74.4111	+	469.813i	−0.119440	+	0.754114i
$624$	−31.8133	+	43.7872i	−0.0509828	+	0.0701718i
$625$		0			0
$626$	1273.26			2.03396
$627$	−665.276	+	54.9918i	−1.06105	+	0.0877062i
$628$	−397.657	+	397.657i	−0.633212	+	0.633212i
$629$	−746.659	+	242.604i	−1.18706	+	0.385698i
$630$		0			0
$631$	−531.837	+	386.402i	−0.842848	+	0.612365i	−0.923165	−	0.384404i	$-0.874407\pi$
$631$	−531.837	+	386.402i	−0.842848	+	0.612365i	0.0803166	+	0.996769i	$0.474407\pi$
$632$	−56.6503	+	28.8648i	−0.0896365	+	0.0456721i
$633$	680.287	+	1335.14i	1.07470	+	2.10922i
$634$	662.274	+	911.542i	1.04460	+	1.43776i
$635$		0			0
$636$	−38.5738	−	118.718i	−0.0606507	−	0.186664i
$637$	−2.95456	−	2.95456i	−0.00463824	−	0.00463824i
$638$	−58.1362	−	67.5292i	−0.0911226	−	0.105845i
$639$			1493.50i			2.33725i
$640$		0			0
$641$	−613.451	−	445.698i	−0.957022	−	0.695317i	−0.00456459	−	0.999990i	$-0.501453\pi$
$641$	−613.451	−	445.698i	−0.957022	−	0.695317i	−0.952457	+	0.304673i	$0.901453\pi$
$642$	644.468	+	102.074i	1.00384	+	0.158993i
$643$	−129.076	−	253.326i	−0.200740	−	0.393974i	0.768588	−	0.639744i	$-0.220959\pi$
$643$	−129.076	−	253.326i	−0.200740	−	0.393974i	−0.969328	+	0.245769i	$0.920959\pi$
$644$	−740.609	−	240.638i	−1.15001	−	0.373662i
$645$		0			0
$646$	−663.927	−	482.371i	−1.02775	−	0.746705i
$647$	−162.807	+	319.527i	−0.251634	+	0.493860i	−0.981924	−	0.189278i	$-0.939385\pi$
$647$	−162.807	+	319.527i	−0.251634	+	0.493860i	0.730289	+	0.683138i	$0.239385\pi$
$648$	−520.265	+	520.265i	−0.802879	+	0.802879i
$649$	−243.440	+	594.316i	−0.375100	+	0.915741i
$650$		0			0
$651$	87.6024	+	269.613i	0.134566	+	0.414151i
$652$	−17.7267	−	111.922i	−0.0271882	−	0.171659i
$653$	−6.13452	+	38.7318i	−0.00939436	+	0.0593137i	−0.991940	−	0.126707i	$-0.959559\pi$
$653$	−6.13452	+	38.7318i	−0.00939436	+	0.0593137i	0.982546	+	0.186021i	$0.0595592\pi$
$654$	−22.2132	−	7.21751i	−0.0339652	−	0.0110360i
$655$		0			0
$656$	545.298	−	396.182i	0.831247	−	0.603936i
$657$	65.2629	+	412.053i	0.0993346	+	0.627174i
$658$	1776.44	+	905.141i	2.69976	+	1.37559i
$659$		−	693.150i		−	1.05182i	−0.850540	−	0.525911i	$-0.823725\pi$
$659$		−	693.150i		−	1.05182i	0.850540	−	0.525911i	$-0.176275\pi$
$660$		0			0
$661$	1020.90			1.54448			0.772238	−	0.635334i	$-0.219137\pi$
$661$	1020.90			1.54448			0.772238	+	0.635334i	$0.219137\pi$
$662$	241.270	−	473.520i	0.364457	−	0.715287i
$663$	121.067	−	19.1751i	0.182604	−	0.0289217i
$664$	136.867	+	188.382i	0.206125	+	0.283707i
$665$		0			0
$666$	662.724	−	2039.66i	0.995082	−	3.06255i
$667$	57.5299	+	9.11184i	0.0862517	+	0.0136609i
$668$	−1079.37	+	170.956i	−1.61583	+	0.255922i
$669$	−2156.40	+	700.658i	−3.22332	+	1.04732i
$670$		0			0
$671$	208.168	−	50.8434i	0.310236	−	0.0757727i
$672$	1342.85	+	1342.85i	1.99828	+	1.99828i
$673$	553.128	+	281.833i	0.821885	+	0.418771i	0.813764	−	0.581196i	$-0.197415\pi$
$673$	553.128	+	281.833i	0.821885	+	0.418771i	0.00812090	+	0.999967i	$0.497415\pi$
$674$	−313.943	+	432.105i	−0.465790	+	0.641105i
$675$		0			0
$676$	−256.424	+	789.193i	−0.379326	+	1.16745i
$677$	368.236	−	187.626i	0.543923	−	0.277143i	−0.160364	−	0.987058i	$-0.551267\pi$
$677$	368.236	−	187.626i	0.543923	−	0.277143i	0.704287	+	0.709915i	$0.251267\pi$
$678$	3.29505	−	20.8041i	0.00485996	−	0.0306846i
$679$	168.962	−	232.556i	0.248839	−	0.342498i
$680$		0			0
$681$	972.297			1.42775
$682$	−85.7357	−	204.703i	−0.125712	−	0.300152i
$683$	−862.593	+	862.593i	−1.26295	+	1.26295i	−0.313289	+	0.949658i	$0.601431\pi$
$683$	−862.593	+	862.593i	−1.26295	+	1.26295i	−0.949658	+	0.313289i	$0.898569\pi$
$684$	1177.08	−	382.458i	1.72088	−	0.559149i
$685$		0			0
$686$	781.345	−	567.680i	1.13899	−	0.827522i
$687$	1358.69	−	692.288i	1.97772	−	1.00770i
$688$	143.921	+	282.460i	0.209187	+	0.410553i
$689$	−2.16277	−	2.97679i	−0.00313899	−	0.00432045i
$690$		0			0
$691$	−189.856	−	584.318i	−0.274756	−	0.845612i	−0.989284	−	0.146005i	$-0.953358\pi$
$691$	−189.856	−	584.318i	−0.274756	−	0.845612i	0.714528	−	0.699607i	$-0.246642\pi$
$692$	−997.469	−	997.469i	−1.44143	−	1.44143i
$693$	−1246.56	−	1447.97i	−1.79879	−	2.08942i
$694$		−	330.128i		−	0.475689i
$695$		0			0
$696$	34.8224	+	25.2999i	0.0500321	+	0.0363505i
$697$	−1507.69	−	238.794i	−2.16311	−	0.342603i
$698$	−413.405	−	811.354i	−0.592271	−	1.16240i
$699$	628.409	+	204.183i	0.899012	+	0.292107i
$700$		0			0
$701$	675.948	+	491.105i	0.964262	+	0.700578i	0.954137	−	0.299371i	$-0.0967769\pi$
$701$	675.948	+	491.105i	0.964262	+	0.700578i	0.0101256	+	0.999949i	$0.496777\pi$
$702$	−94.1154	+	184.712i	−0.134068	+	0.263122i
$703$	−228.157	+	228.157i	−0.324548	+	0.324548i
$704$	−751.133	−	636.436i	−1.06695	−	0.904028i
$705$		0			0
$706$	−359.216	−	1105.55i	−0.508805	−	1.56594i
$707$	−21.9818	−	138.788i	−0.0310916	−	0.196305i
$708$	257.222	−	1624.03i	0.363308	−	2.29383i
$709$	913.184	+	296.711i	1.28799	+	0.418493i	0.871387	−	0.490597i	$-0.163221\pi$
$709$	913.184	+	296.711i	1.28799	+	0.418493i	0.416601	+	0.909089i	$0.363221\pi$
$710$		0			0
$711$	437.244	−	317.676i	0.614971	−	0.446802i
$712$	28.1394	+	177.665i	0.0395217	+	0.249530i
$713$	129.260	+	65.8614i	0.181291	+	0.0923723i
$714$		−	3243.52i		−	4.54274i
$715$		0			0
$716$	−897.890			−1.25404
$717$	13.2459	−	25.9966i	0.0184741	−	0.0362575i
$718$	−1635.20	+	258.990i	−2.27743	+	0.360710i
$719$	72.4505	+	99.7196i	0.100766	+	0.138692i	0.856422	−	0.516276i	$-0.172682\pi$
$719$	72.4505	+	99.7196i	0.100766	+	0.138692i	−0.755657	+	0.654968i	$0.772682\pi$
$720$		0			0
$721$	−309.625	+	952.928i	−0.429439	+	1.32168i
$722$	732.379	+	115.997i	1.01438	+	0.160661i
$723$	−71.7368	+	11.3620i	−0.0992210	+	0.0157151i
$724$	406.195	−	131.981i	0.561043	−	0.182294i
$725$		0			0
$726$	1471.96	+	1448.98i	2.02749	+	1.99584i
$727$	595.052	+	595.052i	0.818504	+	0.818504i	0.985891	−	0.167388i	$-0.0535331\pi$
$727$	595.052	+	595.052i	0.818504	+	0.818504i	−0.167388	+	0.985891i	$0.553533\pi$
$728$	−15.1137	−	7.70081i	−0.0207606	−	0.0105780i
$729$	1151.02	−	1584.24i	1.57890	−	2.17317i
$730$		0			0
$731$	221.857	−	682.807i	0.303499	−	0.934073i
$732$	−488.826	+	249.069i	−0.667795	+	0.340259i
$733$	94.5709	−	597.097i	0.129019	−	0.814594i	−0.835289	−	0.549811i	$-0.814700\pi$
$733$	94.5709	−	597.097i	0.129019	−	0.814594i	0.964308	−	0.264783i	$-0.0853003\pi$
$734$	23.2470	−	31.9967i	0.0316716	−	0.0435922i
$735$		0			0
$736$	971.833			1.32043
$737$	−56.7650	+	240.608i	−0.0770217	+	0.326469i
$738$	2948.57	−	2948.57i	3.99535	−	3.99535i
$739$	−1039.94	+	337.898i	−1.40723	+	0.457237i	−0.911522	−	0.411251i	$-0.865092\pi$
$739$	−1039.94	+	337.898i	−1.40723	+	0.457237i	−0.495710	+	0.868488i	$0.665092\pi$
$740$		0			0
$741$	40.7563	−	29.6112i	0.0550018	−	0.0399612i
$742$	−86.7527	+	44.2027i	−0.116917	+	0.0595724i
$743$	−145.464	−	285.489i	−0.195779	−	0.384238i	0.772158	−	0.635431i	$-0.219177\pi$
$743$	−145.464	−	285.489i	−0.195779	−	0.384238i	−0.967937	+	0.251192i	$0.919177\pi$
$744$	63.0130	+	86.7299i	0.0846949	+	0.116572i
$745$		0			0
$746$	14.4036	+	44.3298i	0.0193078	+	0.0594234i
$747$	−1399.62	−	1399.62i	−1.87366	−	1.87366i
$748$	115.485	+	1397.10i	0.154391	+	1.86779i
$749$		−	280.981i		−	0.375142i
$750$		0			0
$751$	−377.847	−	274.522i	−0.503125	−	0.365542i	0.307084	−	0.951682i	$-0.400647\pi$
$751$	−377.847	−	274.522i	−0.503125	−	0.365542i	−0.810209	+	0.586141i	$0.800647\pi$
$752$	−1023.20	−	162.060i	−1.36064	−	0.215505i
$753$	465.376	+	913.352i	0.618029	+	1.21295i
$754$	6.39550	+	2.07802i	0.00848209	+	0.00275600i
$755$		0			0
$756$	2450.12	+	1780.11i	3.24089	+	2.35465i
$757$	−643.359	+	1262.66i	−0.849880	+	1.66798i	−0.111330	+	0.993783i	$0.535511\pi$
$757$	−643.359	+	1262.66i	−0.849880	+	1.66798i	−0.738549	+	0.674199i	$0.764489\pi$
$758$	−361.866	+	361.866i	−0.477396	+	0.477396i
$759$	−1346.40	−	100.638i	−1.77391	−	0.132592i
$760$		0			0
$761$	−46.2283	−	142.276i	−0.0607468	−	0.186959i	0.916078	−	0.401000i	$-0.131337\pi$
$761$	−46.2283	−	142.276i	−0.0607468	−	0.186959i	−0.976825	+	0.214041i	$0.931337\pi$
$762$	291.729	+	1841.91i	0.382847	+	2.41720i
$763$	−1.57338	+	9.93391i	−0.00206209	+	0.0130195i
$764$	520.328	+	169.065i	0.681058	+	0.221289i
$765$		0			0
$766$	−1351.30	+	981.780i	−1.76411	+	1.28170i
$767$	−7.58208	−	47.8713i	−0.00988537	−	0.0624137i
$768$	−505.750	−	257.693i	−0.658529	−	0.335537i
$769$			866.331i			1.12657i	0.826263	+	0.563284i	$0.190462\pi$
$769$			866.331i			1.12657i	−0.826263	+	0.563284i	$0.809538\pi$
$770$		0			0
$771$	673.283			0.873259
$772$	−698.553	+	1370.99i	−0.904862	+	1.77589i
$773$	236.050	−	37.3867i	0.305369	−	0.0483657i	−0.00186958	−	0.999998i	$-0.500595\pi$
$773$	236.050	−	37.3867i	0.305369	−	0.0483657i	0.307238	+	0.951633i	$0.400595\pi$
$774$	1152.78	+	1586.66i	1.48938	+	2.04995i
$775$		0			0
$776$	33.5915	−	103.384i	0.0432880	−	0.133227i
$777$	−1259.57	−	199.496i	−1.62107	−	0.256752i
$778$	921.485	−	145.949i	1.18443	−	0.187595i
$779$	−596.665	+	193.868i	−0.765937	+	0.248868i
$780$		0			0
$781$	−675.402	+	164.962i	−0.864792	+	0.211219i
$782$	−1173.69	−	1173.69i	−1.50088	−	1.50088i
$783$	−201.837	−	102.841i	−0.257774	−	0.131343i
$784$	33.7684	−	46.4782i	0.0430719	−	0.0592834i
$785$		0			0
$786$	633.252	−	1948.95i	0.805664	−	2.47958i
$787$	−958.967	+	488.618i	−1.21851	+	0.620862i	−0.940525	−	0.339724i	$-0.889666\pi$
$787$	−958.967	+	488.618i	−1.21851	+	0.620862i	−0.277984	+	0.960586i	$0.589666\pi$
$788$	−202.382	+	1277.79i	−0.256830	+	1.62156i
$789$	214.926	−	295.821i	0.272404	−	0.374931i
$790$		0			0
$791$	−9.07037			−0.0114670
$792$	−617.537	−	375.094i	−0.779718	−	0.473604i
$793$	−11.4351	+	11.4351i	−0.0144200	+	0.0144200i
$794$	897.109	−	291.488i	1.12986	−	0.367114i
$795$		0			0
$796$	1211.41	−	880.138i	1.52187	−	1.10570i
$797$	1166.61	−	594.417i	1.46375	−	0.745817i	0.472941	−	0.881094i	$-0.343192\pi$
$797$	1166.61	−	594.417i	1.46375	−	0.745817i	0.990808	+	0.135276i	$0.0431922\pi$
$798$	−605.196	−	1187.76i	−0.758391	−	1.48843i
$799$	1379.04	+	1898.08i	1.72595	+	2.37557i
$800$		0			0
$801$	−472.509	−	1454.23i	−0.589899	−	1.81552i
$802$	−1196.72	−	1196.72i	−1.49217	−	1.49217i
$803$	−179.133	+	75.0262i	−0.223080	+	0.0934324i
$804$		−	632.920i		−	0.787214i
$805$		0			0
$806$	13.5499	+	9.84458i	0.0168113	+	0.0122141i
$807$	2640.07	+	418.145i	3.27146	+	0.518148i
$808$	−24.1243	−	47.3466i	−0.0298568	−	0.0585973i
$809$	938.088	+	304.803i	1.15956	+	0.376765i	0.824738	−	0.565514i	$-0.191322\pi$
$809$	938.088	+	304.803i	1.15956	+	0.376765i	0.334826	+	0.942280i	$0.391322\pi$
$810$		0			0
$811$	1031.12	+	749.155i	1.27142	+	0.923742i	0.999258	−	0.0385091i	$-0.0122609\pi$
$811$	1031.12	+	749.155i	1.27142	+	0.923742i	0.272163	+	0.962251i	$0.412261\pi$
$812$	44.5995	−	87.5314i	0.0549255	−	0.107797i
$813$	−1365.24	+	1365.24i	−1.67926	+	1.67926i
$814$	995.588	+	74.4159i	1.22308	+	0.0914200i
$815$		0			0
$816$	520.800	+	1602.86i	0.638236	+	1.96429i
$817$	−46.1591	−	291.437i	−0.0564983	−	0.356716i
$818$	25.2245	−	159.261i	0.0308368	−	0.194696i
$819$	137.133	+	44.5571i	0.167439	+	0.0544043i
$820$		0			0
$821$	1061.13	−	770.954i	1.29248	−	0.939043i	0.292629	−	0.956226i	$-0.405470\pi$
$821$	1061.13	−	770.954i	1.29248	−	0.939043i	0.999852	+	0.0171835i	$0.00546994\pi$
$822$	515.129	+	3252.40i	0.626677	+	3.95669i
$823$	−1416.42	−	721.703i	−1.72105	−	0.876918i	−0.978258	−	0.207393i	$-0.933502\pi$
$823$	−1416.42	−	721.703i	−1.72105	−	0.876918i	−0.742790	−	0.669524i	$-0.766498\pi$
$824$			378.906i			0.459837i
$825$		0			0
$826$	−1282.53			−1.55270
$827$	531.696	−	1043.51i	0.642921	−	1.26180i	−0.307710	−	0.951480i	$-0.599563\pi$
$827$	531.696	−	1043.51i	0.642921	−	1.26180i	0.950631	−	0.310324i	$-0.100437\pi$
$828$	2472.44	−	391.595i	2.98603	−	0.472941i
$829$	−570.758	−	785.581i	−0.688490	−	0.947625i	0.311507	−	0.950244i	$-0.399166\pi$
$829$	−570.758	−	785.581i	−0.688490	−	0.947625i	−0.999997	+	0.00261906i	$0.999166\pi$
$830$		0			0
$831$	−9.84336	+	30.2947i	−0.0118452	+	0.0364558i
$832$	73.3830	+	11.6227i	0.0882007	+	0.0139696i
$833$	−128.507	+	20.3535i	−0.154270	+	0.0244340i
$834$	−929.463	+	302.001i	−1.11446	+	0.362111i
$835$		0			0
$836$	302.970	+	490.066i	0.362405	+	0.586203i
$837$	−398.948	−	398.948i	−0.476640	−	0.476640i
$838$	1520.46	+	774.714i	1.81439	+	0.924480i
$839$	282.214	−	388.434i	0.336369	−	0.462973i	−0.607007	−	0.794696i	$-0.707630\pi$
$839$	282.214	−	388.434i	0.336369	−	0.462973i	0.943377	+	0.331724i	$0.107630\pi$
$840$		0			0
$841$	257.613	−	792.850i	0.306317	−	0.942747i
$842$	1770.21	−	901.968i	2.10239	−	1.07122i
$843$	122.457	−	773.164i	0.145264	−	0.917158i
$844$	760.193	−	1046.32i	0.900703	−	1.23971i
$845$		0			0
$846$	−6409.03			−7.57569
$847$	517.123	−	723.661i	0.610535	−	0.854382i
$848$	35.7734	−	35.7734i	0.0421856	−	0.0421856i
$849$	−1693.98	+	550.406i	−1.99526	+	0.648299i
$850$		0			0
$851$	−527.971	+	383.594i	−0.620413	+	0.450756i
$852$	1586.00	−	808.106i	1.86150	−	0.948482i
$853$	112.057	+	219.925i	0.131369	+	0.257825i	0.947316	−	0.320301i	$-0.103784\pi$
$853$	112.057	+	219.925i	0.131369	+	0.257825i	−0.815947	+	0.578126i	$0.803784\pi$
$854$	251.527	+	346.197i	0.294528	+	0.405383i
$855$		0			0
$856$	−32.8350	−	101.056i	−0.0383586	−	0.118056i
$857$	93.0660	+	93.0660i	0.108595	+	0.108595i	0.759317	−	0.650721i	$-0.225533\pi$
$857$	93.0660	+	93.0660i	0.108595	+	0.108595i	−0.650721	+	0.759317i	$0.725533\pi$
$858$	−151.711	−	35.7921i	−0.176819	−	0.0417157i
$859$			265.184i			0.308713i	0.988015	+	0.154356i	$0.0493304\pi$
$859$			265.184i			0.308713i	−0.988015	+	0.154356i	$0.950670\pi$
$860$		0			0
$861$	−2006.02	−	1457.46i	−2.32987	−	1.69275i
$862$	−1067.66	−	169.101i	−1.23859	−	0.196173i
$863$	−350.143	−	687.194i	−0.405727	−	0.796285i	0.594241	−	0.804287i	$-0.297453\pi$
$863$	−350.143	−	687.194i	−0.405727	−	0.796285i	−0.999968	+	0.00800259i	$0.997453\pi$
$864$	−3594.55	−	1167.94i	−4.16036	−	1.35178i
$865$		0			0
$866$	−900.584	−	654.313i	−1.03994	−	0.755557i
$867$	983.348	−	1929.93i	1.13420	−	2.22599i
$868$	173.013	−	173.013i	0.199324	−	0.199324i
$869$	191.957	+	162.645i	0.220894	+	0.187164i
$870$		0			0
$871$	−5.76516	−	17.7434i	−0.00661902	−	0.0203712i
$872$	0.594991	+	3.75663i	0.000682329	+	0.00430806i
$873$	−144.552	+	912.667i	−0.165581	+	1.04544i
$874$	−648.793	−	210.806i	−0.742326	−	0.241196i
$875$		0			0
$876$	402.260	−	292.259i	0.459201	−	0.333629i
$877$	156.734	+	989.583i	0.178717	+	1.12837i	0.900051	+	0.435785i	$0.143529\pi$
$877$	156.734	+	989.583i	0.178717	+	1.12837i	−0.721334	+	0.692587i	$0.756471\pi$
$878$	−1946.58	−	991.830i	−2.21706	−	1.12965i
$879$			1411.74i			1.60608i
$880$		0			0
$881$	−629.188			−0.714175			−0.357087	−	0.934071i	$-0.616230\pi$
$881$	−629.188			−0.714175			−0.357087	+	0.934071i	$0.616230\pi$
$882$	161.357	−	316.682i	0.182945	−	0.359049i
$883$	643.428	−	101.909i	0.728685	−	0.115412i	0.218940	−	0.975738i	$-0.429740\pi$
$883$	643.428	−	101.909i	0.728685	−	0.115412i	0.509744	+	0.860326i	$0.329740\pi$
$884$	−62.1847	−	85.5898i	−0.0703446	−	0.0968211i
$885$		0			0
$886$	630.189	−	1939.52i	0.711274	−	2.18908i
$887$	−812.165	−	128.634i	−0.915632	−	0.145022i	−0.319202	−	0.947687i	$-0.603415\pi$
$887$	−812.165	−	128.634i	−0.915632	−	0.145022i	−0.596430	+	0.802665i	$0.703415\pi$
$888$	−476.321	+	75.4418i	−0.536397	+	0.0849570i
$889$	763.747	−	248.156i	0.859108	−	0.279141i
$890$		0			0
$891$	2694.28	+	1103.61i	3.02388	+	1.23862i
$892$	1383.78	+	1383.78i	1.55133	+	1.55133i
$893$	859.155	+	437.761i	0.962099	+	0.490214i
$894$	−1762.95	+	2426.50i	−1.97198	+	2.71420i
$895$		0			0
$896$	196.592	−	605.049i	0.219411	−	0.675278i
$897$	90.7868	−	46.2582i	0.101212	−	0.0515699i
$898$	−84.9401	+	536.290i	−0.0945880	+	0.597205i
$899$	−10.7573	+	14.8062i	−0.0119659	+	0.0164696i
$900$		0			0
$901$	−114.575			−0.127164
$902$	1659.10	+	1007.74i	1.83936	+	1.11723i
$903$	824.637	−	824.637i	0.913220	−	0.913220i
$904$	−3.26219	+	1.05995i	−0.00360862	+	0.00117251i
$905$		0			0
$906$	−2699.97	+	1961.64i	−2.98010	+	2.16517i
$907$	−175.306	+	89.3227i	−0.193281	+	0.0984815i	−0.547953	−	0.836509i	$-0.684593\pi$
$907$	−175.306	+	89.3227i	−0.193281	+	0.0984815i	0.354672	+	0.934991i	$0.384593\pi$
$908$	−380.983	−	747.721i	−0.419585	−	0.823481i
$909$	265.505	+	365.436i	0.292084	+	0.402019i
$910$		0			0
$911$	474.334	+	1459.85i	0.520674	+	1.60247i	0.772715	+	0.634754i	$0.218898\pi$
$911$	474.334	+	1459.85i	0.520674	+	1.60247i	−0.252040	+	0.967717i	$0.581102\pi$
$912$	489.787	+	489.787i	0.537047	+	0.537047i
$913$	478.355	−	787.540i	0.523938	−	0.862585i
$914$		−	2463.69i		−	2.69550i
$915$		0			0
$916$	−1064.77	−	773.603i	−1.16242	−	0.844545i
$917$	−871.584	−	138.045i	−0.950473	−	0.150540i
$918$	2930.63	+	5751.68i	3.19240	+	6.26544i
$919$	−525.464	−	170.734i	−0.571778	−	0.185782i	0.00883567	−	0.999961i	$-0.497187\pi$
$919$	−525.464	−	170.734i	−0.571778	−	0.185782i	−0.580614	+	0.814179i	$0.697187\pi$
$920$		0			0
$921$	766.568	+	556.944i	0.832322	+	0.604717i
$922$	976.753	−	1916.99i	1.05938	−	2.07916i
$923$	37.1011	−	37.1011i	0.0401962	−	0.0401962i
$924$	−863.150	+	2107.23i	−0.934145	+	2.28055i
$925$		0			0
$926$	655.410	+	2017.14i	0.707786	+	2.17834i
$927$	−503.859	−	3181.24i	−0.543537	−	3.43176i
$928$	−19.1789	+	121.091i	−0.0206670	+	0.130486i
$929$	−408.527	−	132.739i	−0.439749	−	0.142883i	0.0807706	−	0.996733i	$-0.474262\pi$
$929$	−408.527	−	132.739i	−0.439749	−	0.142883i	−0.520520	+	0.853849i	$0.674262\pi$
$930$		0			0
$931$	−43.2611	+	31.4310i	−0.0464674	+	0.0337605i
$932$	−89.2131	−	563.269i	−0.0957222	−	0.604366i
$933$	−73.6343	−	37.5186i	−0.0789221	−	0.0402128i
$934$			152.325i			0.163088i
$935$		0			0
$936$	54.5271			0.0582555
$937$	−337.934	+	663.233i	−0.360655	+	0.707826i	−0.998031	−	0.0627275i	$-0.980020\pi$
$937$	−337.934	+	663.233i	−0.360655	+	0.707826i	0.637375	+	0.770554i	$0.280020\pi$
$938$	−487.597	+	77.2277i	−0.519826	+	0.0823323i
$939$	1430.57	+	1969.01i	1.52351	+	2.09693i
$940$		0			0
$941$	−240.721	+	740.864i	−0.255814	+	0.787315i	0.737854	+	0.674960i	$0.235839\pi$
$941$	−240.721	+	740.864i	−0.255814	+	0.787315i	−0.993668	+	0.112355i	$0.964161\pi$
$942$	−1923.16	−	304.598i	−2.04157	−	0.323352i
$943$	−1253.28	+	198.500i	−1.32904	+	0.210499i
$944$	633.791	−	205.931i	0.671389	−	0.218148i
$945$		0			0
$946$	−590.204	+	696.569i	−0.623894	+	0.736331i
$947$	−358.441	−	358.441i	−0.378502	−	0.378502i	0.492060	−	0.870561i	$-0.336244\pi$
$947$	−358.441	−	358.441i	−0.378502	−	0.378502i	−0.870561	+	0.492060i	$0.836244\pi$
$948$	−573.936	−	292.435i	−0.605417	−	0.308476i
$949$	8.61487	−	11.8573i	0.00907784	−	0.0124946i
$950$		0			0
$951$	−665.542	+	2048.33i	−0.699834	+	2.15387i
$952$	−470.620	+	239.793i	−0.494348	+	0.251883i
$953$	195.205	−	1232.48i	0.204832	−	1.29326i	−0.644174	−	0.764879i	$-0.722799\pi$
$953$	195.205	−	1232.48i	0.204832	−	1.29326i	0.849006	−	0.528382i	$-0.177201\pi$
$954$	183.969	−	253.211i	0.192839	−	0.265420i
$955$		0			0
$956$	−25.1823			−0.0263413
$957$	39.1105	−	165.776i	0.0408678	−	0.173225i
$958$	−60.9602	+	60.9602i	−0.0636327	+	0.0636327i
$959$	1348.61	−	438.189i	1.40626	−	0.456922i
$960$		0			0
$961$	740.589	−	538.069i	0.770644	−	0.559905i
$962$	−67.1317	+	34.2053i	−0.0697835	+	0.0355565i
$963$	410.059	+	804.787i	0.425814	+	0.835708i
$964$	36.8468	+	50.7153i	0.0382229	+	0.0526093i
$965$		0			0
$966$	−833.174	−	2564.25i	−0.862499	−	2.65450i
$967$	996.526	+	996.526i	1.03053	+	1.03053i	0.999519	+	0.0310143i	$0.00987374\pi$
$967$	996.526	+	996.526i	1.03053	+	1.03053i	0.0310143	+	0.999519i	$0.490126\pi$
$968$	101.419	−	320.697i	0.104772	−	0.331299i
$969$		−	1568.69i		−	1.61888i
$970$		0			0
$971$	−907.621	−	659.425i	−0.934728	−	0.679120i	0.0124175	−	0.999923i	$-0.496047\pi$
$971$	−907.621	−	659.425i	−0.934728	−	0.679120i	−0.947146	+	0.320803i	$0.896047\pi$
$972$	−3700.07	−	586.034i	−3.80666	−	0.602915i
$973$	191.059	+	374.975i	0.196361	+	0.385380i
$974$	77.5964	+	25.2126i	0.0796678	+	0.0258856i
$975$		0			0
$976$	−179.885	−	130.694i	−0.184309	−	0.133908i
$977$	−635.126	+	1246.51i	−0.650078	+	1.27585i	0.297009	+	0.954875i	$0.404011\pi$
$977$	−635.126	+	1246.51i	−0.650078	+	1.27585i	−0.947087	+	0.320976i	$0.895989\pi$
$978$	277.428	−	277.428i	0.283669	−	0.283669i
$979$	605.454	−	374.306i	0.618442	−	0.382335i
$980$		0			0
$981$	−9.99092	−	30.7489i	−0.0101844	−	0.0313444i
$982$	−180.952	−	1142.49i	−0.184269	−	1.16343i
$983$	66.9091	−	422.448i	0.0680663	−	0.429754i	−0.929998	−	0.367564i	$-0.880192\pi$
$983$	66.9091	−	422.448i	0.0680663	−	0.429754i	0.998064	−	0.0621892i	$-0.0198082\pi$
$984$	−891.788	−	289.759i	−0.906288	−	0.294471i
$985$		0			0
$986$	169.405	−	123.080i	0.171810	−	0.124827i
$987$	596.178	+	3764.12i	0.604031	+	3.81370i
$988$	−38.7417	−	19.7399i	−0.0392122	−	0.0199796i
$989$		−	596.800i		−	0.603438i
$990$		0			0
$991$	−1760.99			−1.77699			−0.888493	−	0.458890i	$-0.848247\pi$
$991$	−1760.99			−1.77699			−0.888493	+	0.458890i	$0.848247\pi$
$992$	−138.628	+	272.072i	−0.139746	+	0.274266i
$993$	1003.35	−	158.915i	1.01042	−	0.160035i
$994$	−816.079	−	1123.24i	−0.821005	−	1.13002i
$995$		0			0
$996$	−728.995	+	2243.62i	−0.731923	+	2.25263i
$997$	116.575	+	18.4636i	0.116925	+	0.0185191i	0.214623	−	0.976697i	$-0.431148\pi$
$997$	116.575	+	18.4636i	0.116925	+	0.0185191i	−0.0976975	+	0.995216i	$0.531148\pi$
$998$	−1232.49	+	195.208i	−1.23496	+	0.195599i
$999$	2413.82	−	784.299i	2.41624	−	0.785084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.bk.c.82.14	yes	128
5.2	odd	4	inner	275.3.bk.c.93.14	yes	128
5.3	odd	4	inner	275.3.bk.c.93.3	yes	128
5.4	even	2	inner	275.3.bk.c.82.3	✓	128
11.9	even	5	inner	275.3.bk.c.207.3	yes	128
55.9	even	10	inner	275.3.bk.c.207.14	yes	128
55.42	odd	20	inner	275.3.bk.c.218.3	yes	128
55.53	odd	20	inner	275.3.bk.c.218.14	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.3	✓	128	5.4	even	2	inner
275.3.bk.c.82.14	yes	128	1.1	even	1	trivial
275.3.bk.c.93.3	yes	128	5.3	odd	4	inner
275.3.bk.c.93.14	yes	128	5.2	odd	4	inner
275.3.bk.c.207.3	yes	128	11.9	even	5	inner
275.3.bk.c.207.14	yes	128	55.9	even	10	inner
275.3.bk.c.218.3	yes	128	55.42	odd	20	inner
275.3.bk.c.218.14	yes	128	55.53	odd	20	inner

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35668 - 2.66263i) q^{2} +(5.64189 - 0.893588i) q^{3} +(-2.89790 - 3.98862i) q^{4} +(5.27495 - 16.2346i) q^{6} +(-7.26024 - 1.14991i) q^{7} +(-2.74554 + 0.434852i) q^{8} +(22.4730 - 7.30190i) q^{9} +(5.78433 + 9.35637i) q^{11} +(-19.9138 - 19.9138i) q^{12} +(-0.739658 - 0.376875i) q^{13} +(-12.9116 + 17.7713i) q^{14} +(3.52709 - 10.8553i) q^{16} +(-23.0319 + 11.7354i) q^{17} +(11.0463 - 69.7436i) q^{18} +(-6.24455 + 8.59489i) q^{19} -41.9890 q^{21} +(32.7601 - 2.70795i) q^{22} +(-15.1940 + 15.1940i) q^{23} +(-15.1015 + 4.90677i) q^{24} +(-2.00696 + 1.45814i) q^{26} +(74.4585 - 37.9385i) q^{27} +(16.4529 + 32.2906i) q^{28} +(-1.59333 - 2.19303i) q^{29} +(-2.08632 - 6.42102i) q^{31} +(-31.9809 - 31.9809i) q^{32} +(40.9953 + 47.6188i) q^{33} +77.2468i q^{34} +(-94.2489 - 68.4758i) q^{36} +(29.9976 + 4.75115i) q^{37} +(14.4132 + 28.2875i) q^{38} +(-4.50984 - 1.46534i) q^{39} +(47.7749 + 34.7105i) q^{41} +(-56.9657 + 111.801i) q^{42} +(-19.6393 + 19.6393i) q^{43} +(20.5566 - 50.1853i) q^{44} +(19.8426 + 61.0694i) q^{46} +(-14.1984 - 89.6453i) q^{47} +(10.1993 - 64.3961i) q^{48} +(4.78700 + 1.55539i) q^{49} +(-119.457 + 86.7907i) q^{51} +(0.640247 + 4.04236i) q^{52} +(3.94931 + 2.01228i) q^{53} -249.726i q^{54} +20.4333 q^{56} +(-27.5508 + 54.0715i) q^{57} +(-8.00088 + 1.26721i) q^{58} +(34.3182 + 47.2349i) q^{59} +(6.01985 - 18.5272i) q^{61} +(-19.9273 - 3.15617i) q^{62} +(-171.556 + 27.1717i) q^{63} +(-85.1200 + 27.6572i) q^{64} +(182.409 - 44.5520i) q^{66} +(15.8915 + 15.8915i) q^{67} +(113.552 + 57.8577i) q^{68} +(-72.1457 + 99.3000i) q^{69} +(-19.5314 + 60.1116i) q^{71} +(-58.5252 + 29.8201i) q^{72} +(-2.76193 + 17.4381i) q^{73} +(53.3477 - 73.4268i) q^{74} +52.3778 q^{76} +(-31.2366 - 74.5809i) q^{77} +(-10.0201 + 10.0201i) q^{78} +(21.7530 - 7.06797i) q^{79} +(214.136 - 155.579i) q^{81} +(157.236 - 80.1160i) q^{82} +(-38.0294 - 74.6368i) q^{83} +(121.680 + 167.478i) q^{84} +(25.6481 + 78.9367i) q^{86} +(-10.9491 - 10.9491i) q^{87} +(-19.9498 - 23.1730i) q^{88} -64.7104i q^{89} +(4.93672 + 3.58674i) q^{91} +(104.634 + 16.5723i) q^{92} +(-17.5085 - 34.3624i) q^{93} +(-257.956 - 83.8148i) q^{94} +(-209.010 - 151.855i) q^{96} +(-17.7536 + 34.8433i) q^{97} +(10.6359 - 10.6359i) q^{98} +(198.310 + 168.029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) \) 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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