LMFDB - Embedded newform 950.2.bb.e.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.e.507.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(-0.186197 + 0.399301i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.414010 + 0.150687i) q^{6} +(-1.97694 - 0.529719i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.80359 + 2.14944i) q^{9} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.186197 + 0.399301i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.414010 + 0.150687i) q^{6} +(-1.97694 - 0.529719i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.80359 + 2.14944i) q^{9} +(-0.741552 + 1.28441i) q^{11} +(0.114031 - 0.425568i) q^{12} +(4.30347 - 2.00674i) q^{13} +(-0.355401 + 2.01558i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-7.79680 + 0.682131i) q^{17} +(1.98406 - 1.98406i) q^{18} +(-4.30701 - 0.670597i) q^{19} +(0.579617 - 0.690761i) q^{21} +(1.34415 + 0.626787i) q^{22} +(-3.96274 + 5.65938i) q^{23} +(-0.433887 - 0.0765060i) q^{24} +(-2.37418 - 4.11219i) q^{26} +(-2.47080 + 0.662049i) q^{27} +(2.03889 + 0.178380i) q^{28} +(-0.979963 + 0.822287i) q^{29} +(2.84525 - 1.64270i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-0.374790 - 0.535255i) q^{33} +(1.35907 + 7.70767i) q^{34} +(-2.14944 - 1.80359i) q^{36} +(7.59450 + 7.59450i) q^{37} +(-0.292664 + 4.34906i) q^{38} +2.09203i q^{39} +(1.53015 + 4.20406i) q^{41} +(-0.738650 - 0.517208i) q^{42} +(-9.48169 + 6.63915i) q^{43} +(0.507251 - 1.39366i) q^{44} +(5.98322 + 3.45441i) q^{46} +(-0.380772 + 4.35224i) q^{47} +(-0.0383991 + 0.438904i) q^{48} +(-2.43450 - 1.40556i) q^{49} +(1.17937 - 3.24028i) q^{51} +(-3.88962 + 2.72354i) q^{52} +(0.602564 + 0.421920i) q^{53} +(0.874874 + 2.40370i) q^{54} -2.04668i q^{56} +(1.06972 - 1.59493i) q^{57} +(0.904567 + 0.904567i) q^{58} +(10.1719 + 8.53523i) q^{59} +(0.0112403 + 0.0637470i) q^{61} +(-1.88443 - 2.69125i) q^{62} +(-2.42699 - 5.20469i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-0.500553 + 0.420014i) q^{66} +(-2.99318 - 0.261869i) q^{67} +(7.55989 - 2.02567i) q^{68} +(-1.52195 - 2.63609i) q^{69} +(1.10887 + 0.195524i) q^{71} +(-1.60939 + 2.29845i) q^{72} +(1.08185 + 0.504475i) q^{73} +(6.90370 - 8.22751i) q^{74} +(4.35802 - 0.0874950i) q^{76} +(2.14637 - 2.14637i) q^{77} +(2.08407 - 0.182332i) q^{78} +(-13.6309 + 4.96123i) q^{79} +(-1.26601 + 7.17992i) q^{81} +(4.05470 - 1.89074i) q^{82} +(1.21006 - 4.51600i) q^{83} +(-0.450862 + 0.780916i) q^{84} +(7.44027 + 8.86697i) q^{86} +(-0.145874 - 0.544408i) q^{87} +(-1.43257 - 0.383855i) q^{88} +(-10.2856 - 3.74366i) q^{89} +(-9.57069 + 1.68757i) q^{91} +(2.91980 - 6.26152i) q^{92} +(0.126157 + 1.44198i) q^{93} +4.36886 q^{94} +0.440580 q^{96} +(-0.599858 - 6.85641i) q^{97} +(-1.18803 + 2.54774i) q^{98} +(-4.09820 + 0.722624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$3$	−0.186197	+	0.399301i	−0.107501	+	0.230537i	−0.952698	−	0.303918i	$-0.901705\pi$
$3$	−0.186197	+	0.399301i	−0.107501	+	0.230537i	0.845197	+	0.534455i	$0.179483\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	0.414010	+	0.150687i	0.169019	+	0.0615178i
$7$	−1.97694	−	0.529719i	−0.747212	−	0.200215i	−0.134931	−	0.990855i	$-0.543081\pi$
$7$	−1.97694	−	0.529719i	−0.747212	−	0.200215i	−0.612281	+	0.790640i	$0.709748\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	1.80359	+	2.14944i	0.601197	+	0.716479i
$10$		0			0
$11$	−0.741552	+	1.28441i	−0.223586	+	0.387263i	−0.955894	−	0.293711i	$-0.905110\pi$
$11$	−0.741552	+	1.28441i	−0.223586	+	0.387263i	0.732308	+	0.680973i	$0.238443\pi$
$12$	0.114031	−	0.425568i	0.0329178	−	0.122851i
$13$	4.30347	−	2.00674i	1.19357	−	0.556570i	0.278721	−	0.960372i	$-0.410089\pi$
$13$	4.30347	−	2.00674i	1.19357	−	0.556570i	0.914846	+	0.403803i	$0.132312\pi$
$14$	−0.355401	+	2.01558i	−0.0949850	+	0.538687i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−7.79680	+	0.682131i	−1.89100	+	0.165441i	−0.972949	−	0.231020i	$-0.925794\pi$
$17$	−7.79680	+	0.682131i	−1.89100	+	0.165441i	−0.918052	+	0.396461i	$0.870238\pi$
$18$	1.98406	−	1.98406i	0.467648	−	0.467648i
$19$	−4.30701	−	0.670597i	−0.988095	−	0.153845i
$19$	−4.30701	−	0.670597i	−0.988095	−	0.153845i
$20$		0			0
$21$	0.579617	−	0.690761i	0.126483	−	0.150736i
$22$	1.34415	+	0.626787i	0.286573	+	0.133631i
$23$	−3.96274	+	5.65938i	−0.826288	+	1.18006i	0.155075	+	0.987903i	$0.450438\pi$
$23$	−3.96274	+	5.65938i	−0.826288	+	1.18006i	−0.981364	+	0.192160i	$0.938451\pi$
$24$	−0.433887	−	0.0765060i	−0.0885668	−	0.0156167i
$25$		0			0
$26$	−2.37418	−	4.11219i	−0.465614	−	0.806467i
$27$	−2.47080	+	0.662049i	−0.475506	+	0.127411i
$28$	2.03889	+	0.178380i	0.385313	+	0.0337106i
$29$	−0.979963	+	0.822287i	−0.181975	+	0.152695i	−0.729225	−	0.684274i	$-0.760119\pi$
$29$	−0.979963	+	0.822287i	−0.181975	+	0.152695i	0.547250	+	0.836969i	$0.315675\pi$
$30$		0			0
$31$	2.84525	−	1.64270i	0.511021	−	0.295038i	−0.222232	−	0.974994i	$-0.571334\pi$
$31$	2.84525	−	1.64270i	0.511021	−	0.295038i	0.733253	+	0.679956i	$0.238001\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$	−0.374790	−	0.535255i	−0.0652425	−	0.0931760i
$34$	1.35907	+	7.70767i	0.233079	+	1.32186i
$35$		0			0
$36$	−2.14944	−	1.80359i	−0.358239	−	0.300598i
$37$	7.59450	+	7.59450i	1.24853	+	1.24853i	0.956370	+	0.292159i	$0.0943737\pi$
$37$	7.59450	+	7.59450i	1.24853	+	1.24853i	0.292159	+	0.956370i	$0.405626\pi$
$38$	−0.292664	+	4.34906i	−0.0474764	+	0.705511i
$39$			2.09203i			0.334993i
$40$		0			0
$41$	1.53015	+	4.20406i	0.238970	+	0.656564i	0.999969	+	0.00781201i	$0.00248667\pi$
$41$	1.53015	+	4.20406i	0.238970	+	0.656564i	−0.761000	+	0.648752i	$0.775291\pi$
$42$	−0.738650	−	0.517208i	−0.113976	−	0.0798069i
$43$	−9.48169	+	6.63915i	−1.44594	+	1.01246i	−0.453304	+	0.891356i	$0.649755\pi$
$43$	−9.48169	+	6.63915i	−1.44594	+	1.01246i	−0.992640	+	0.121105i	$0.961356\pi$
$44$	0.507251	−	1.39366i	0.0764710	−	0.210102i
$45$		0			0
$46$	5.98322	+	3.45441i	0.882178	+	0.509325i
$47$	−0.380772	+	4.35224i	−0.0555412	+	0.634839i	0.916501	+	0.400033i	$0.131001\pi$
$47$	−0.380772	+	4.35224i	−0.0555412	+	0.634839i	−0.972042	+	0.234807i	$0.924554\pi$
$48$	−0.0383991	+	0.438904i	−0.00554243	+	0.0633503i
$49$	−2.43450	−	1.40556i	−0.347786	−	0.200794i
$50$		0			0
$51$	1.17937	−	3.24028i	0.165144	−	0.453730i
$52$	−3.88962	+	2.72354i	−0.539394	+	0.377687i
$53$	0.602564	+	0.421920i	0.0827686	+	0.0579552i	0.614228	−	0.789128i	$-0.289467\pi$
$53$	0.602564	+	0.421920i	0.0827686	+	0.0579552i	−0.531460	+	0.847084i	$0.678356\pi$
$54$	0.874874	+	2.40370i	0.119055	+	0.327102i
$55$		0			0
$56$		−	2.04668i		−	0.273498i
$57$	1.06972	−	1.59493i	0.141688	−	0.211254i
$58$	0.904567	+	0.904567i	0.118775	+	0.118775i
$59$	10.1719	+	8.53523i	1.32427	+	1.11119i	0.985381	+	0.170365i	$0.0544947\pi$
$59$	10.1719	+	8.53523i	1.32427	+	1.11119i	0.338886	+	0.940827i	$0.389950\pi$
$60$		0			0
$61$	0.0112403	+	0.0637470i	0.00143918	+	0.00816197i	0.985519	−	0.169566i	$-0.0542365\pi$
$61$	0.0112403	+	0.0637470i	0.00143918	+	0.00816197i	−0.984080	+	0.177728i	$0.943125\pi$
$62$	−1.88443	−	2.69125i	−0.239323	−	0.341789i
$63$	−2.42699	−	5.20469i	−0.305772	−	0.655730i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	−0.500553	+	0.420014i	−0.0616139	+	0.0517002i
$67$	−2.99318	−	0.261869i	−0.365675	−	0.0319924i	−0.0971624	−	0.995269i	$-0.530977\pi$
$67$	−2.99318	−	0.261869i	−0.365675	−	0.0319924i	−0.268513	+	0.963276i	$0.586532\pi$
$68$	7.55989	−	2.02567i	0.916772	−	0.245648i
$69$	−1.52195	−	2.63609i	−0.183221	−	0.317348i
$70$		0			0
$71$	1.10887	+	0.195524i	0.131599	+	0.0232045i	0.239060	−	0.971005i	$-0.423161\pi$
$71$	1.10887	+	0.195524i	0.131599	+	0.0232045i	−0.107461	+	0.994209i	$0.534272\pi$
$72$	−1.60939	+	2.29845i	−0.189669	+	0.270875i
$73$	1.08185	+	0.504475i	0.126621	+	0.0590443i	0.484896	−	0.874572i	$-0.338857\pi$
$73$	1.08185	+	0.504475i	0.126621	+	0.0590443i	−0.358275	+	0.933616i	$0.616635\pi$
$74$	6.90370	−	8.22751i	0.802539	−	0.956429i
$75$		0			0
$76$	4.35802	−	0.0874950i	0.499899	−	0.0100364i
$77$	2.14637	−	2.14637i	0.244602	−	0.244602i
$78$	2.08407	−	0.182332i	0.235974	−	0.0206451i
$79$	−13.6309	+	4.96123i	−1.53359	+	0.558182i	−0.964498	−	0.264090i	$-0.914929\pi$
$79$	−13.6309	+	4.96123i	−1.53359	+	0.558182i	−0.569095	+	0.822272i	$0.692706\pi$
$80$		0			0
$81$	−1.26601	+	7.17992i	−0.140668	+	0.797769i
$82$	4.05470	−	1.89074i	0.447767	−	0.208797i
$83$	1.21006	−	4.51600i	0.132821	−	0.495696i	−0.867176	−	0.498002i	$-0.834067\pi$
$83$	1.21006	−	4.51600i	0.132821	−	0.495696i	0.999997	+	0.00230603i	$0.000734032\pi$
$84$	−0.450862	+	0.780916i	−0.0491931	+	0.0852050i
$85$		0			0
$86$	7.44027	+	8.86697i	0.802305	+	0.956150i
$87$	−0.145874	−	0.544408i	−0.0156393	−	0.0583667i
$88$	−1.43257	−	0.383855i	−0.152712	−	0.0409191i
$89$	−10.2856	−	3.74366i	−1.09027	−	0.396827i	−0.266551	−	0.963821i	$-0.585884\pi$
$89$	−10.2856	−	3.74366i	−1.09027	−	0.396827i	−0.823722	+	0.566994i	$0.808106\pi$
$90$		0			0
$91$	−9.57069	+	1.68757i	−1.00328	+	0.176906i
$92$	2.91980	−	6.26152i	0.304410	−	0.652809i
$93$	0.126157	+	1.44198i	0.0130818	+	0.149526i
$94$	4.36886			0.450614
$95$		0			0
$96$	0.440580			0.0449665
$97$	−0.599858	−	6.85641i	−0.0609063	−	0.696163i	−0.963857	−	0.266419i	$-0.914159\pi$
$97$	−0.599858	−	6.85641i	−0.0609063	−	0.696163i	0.902951	−	0.429744i	$-0.141396\pi$
$98$	−1.18803	+	2.54774i	−0.120009	+	0.257361i
$99$	−4.09820	+	0.722624i	−0.411885	+	0.0726264i
$100$		0			0
$101$	0.121740	+	0.0443096i	0.0121136	+	0.00440897i	0.348070	−	0.937469i	$-0.386837\pi$
$101$	0.121740	+	0.0443096i	0.0121136	+	0.00440897i	−0.335956	+	0.941878i	$0.609059\pi$
$102$	−3.33074	−	0.892469i	−0.329792	−	0.0883676i
$103$	−1.39817	−	5.21804i	−0.137766	−	0.514149i	−0.999971	−	0.00758999i	$-0.997584\pi$
$103$	−1.39817	−	5.21804i	−0.137766	−	0.514149i	0.862205	−	0.506559i	$-0.169083\pi$
$104$	3.05218	+	3.63745i	0.299291	+	0.356681i
$105$		0			0
$106$	0.367797	−	0.637044i	0.0357237	−	0.0618752i
$107$	−3.16154	+	11.7990i	−0.305637	+	1.14065i	0.626758	+	0.779214i	$0.284381\pi$
$107$	−3.16154	+	11.7990i	−0.305637	+	1.14065i	−0.932395	+	0.361440i	$0.882285\pi$
$108$	2.31830	−	1.08104i	0.223078	−	0.104023i
$109$	1.14089	−	6.47031i	0.109278	−	0.619744i	−0.880148	−	0.474700i	$-0.842557\pi$
$109$	1.14089	−	6.47031i	0.109278	−	0.619744i	0.989425	−	0.145044i	$-0.0463323\pi$
$110$		0			0
$111$	−4.44657	+	1.61842i	−0.422050	+	0.153614i
$112$	−2.03889	+	0.178380i	−0.192657	+	0.0168553i
$113$	5.06708	−	5.06708i	0.476670	−	0.476670i	−0.427395	−	0.904065i	$-0.640569\pi$
$113$	5.06708	−	5.06708i	0.476670	−	0.476670i	0.904065	+	0.427395i	$0.140569\pi$
$114$	−1.68209	−	0.926645i	−0.157542	−	0.0867882i
$115$		0			0
$116$	0.822287	−	0.979963i	0.0763474	−	0.0909873i
$117$	12.0751	+	5.63069i	1.11634	+	0.520558i
$118$	7.61621	−	10.8771i	0.701129	−	1.00132i
$119$	15.7751	+	2.78158i	1.44610	+	0.254987i
$120$		0			0
$121$	4.40020	+	7.62137i	0.400018	+	0.692852i
$122$	0.0625248	−	0.0167535i	0.00566073	−	0.00151679i
$123$	−1.96360	−	0.171793i	−0.177052	−	0.0154900i
$124$	−2.51677	+	2.11182i	−0.226012	+	0.189647i
$125$		0			0
$126$	−4.97336	+	2.87137i	−0.443062	+	0.255802i
$127$	0.277886	+	0.595928i	0.0246584	+	0.0528801i	0.918251	−	0.395998i	$-0.129601\pi$
$127$	0.277886	+	0.595928i	0.0246584	+	0.0528801i	−0.893593	+	0.448878i	$0.851824\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$	−0.885557	−	5.02224i	−0.0779689	−	0.442184i
$130$		0			0
$131$	−0.854946	−	0.717385i	−0.0746970	−	0.0626782i	0.604675	−	0.796473i	$-0.293303\pi$
$131$	−0.854946	−	0.717385i	−0.0746970	−	0.0626782i	−0.679372	+	0.733794i	$0.737748\pi$
$132$	0.462042	+	0.462042i	0.0402156	+	0.0402156i
$133$	8.15945	+	3.60723i	0.707514	+	0.312786i
$134$			3.00462i			0.259559i
$135$		0			0
$136$	−2.67685	−	7.35458i	−0.229538	−	0.630650i
$137$	4.65442	+	3.25906i	0.397654	+	0.278440i	0.755251	−	0.655436i	$-0.227515\pi$
$137$	4.65442	+	3.25906i	0.397654	+	0.278440i	−0.357597	+	0.933876i	$0.616404\pi$
$138$	−2.49341	+	1.74590i	−0.212253	+	0.148621i
$139$	6.13138	−	16.8458i	0.520057	−	1.42885i	−0.350400	−	0.936600i	$-0.613954\pi$
$139$	6.13138	−	16.8458i	0.520057	−	1.42885i	0.870457	−	0.492245i	$-0.163824\pi$
$140$		0			0
$141$	−1.66696	−	0.962418i	−0.140383	−	0.0810502i
$142$	0.0981356	−	1.12169i	0.00823536	−	0.0941305i
$143$	−0.613777	+	7.01550i	−0.0513266	+	0.586666i
$144$	2.42997	+	1.40294i	0.202498	+	0.116912i
$145$		0			0
$146$	0.408266	−	1.12170i	0.0337883	−	0.0928326i
$147$	1.01454	−	0.710388i	0.0836778	−	0.0585918i
$148$	−8.79790	−	6.16036i	−0.723183	−	0.506378i
$149$	1.30616	+	3.58864i	0.107005	+	0.293993i	0.981626	−	0.190813i	$-0.0611125\pi$
$149$	1.30616	+	3.58864i	0.107005	+	0.293993i	−0.874622	+	0.484806i	$0.838890\pi$
$150$		0			0
$151$		−	6.90330i		−	0.561782i	−0.959740	−	0.280891i	$-0.909370\pi$
$151$		−	6.90330i		−	0.561782i	0.959740	−	0.280891i	$-0.0906300\pi$
$152$	−0.466989	−	4.33381i	−0.0378778	−	0.351519i
$153$	−15.5284	−	15.5284i	−1.25540	−	1.25540i
$154$	−2.32528	−	1.95114i	−0.187376	−	0.157227i
$155$		0			0
$156$	−0.363277	−	2.06025i	−0.0290855	−	0.164952i
$157$	−3.83673	−	5.47942i	−0.306205	−	0.437305i	0.636329	−	0.771418i	$-0.280452\pi$
$157$	−3.83673	−	5.47942i	−0.306205	−	0.437305i	−0.942533	+	0.334113i	$0.891563\pi$
$158$	6.13036	+	13.1466i	0.487705	+	1.04589i
$159$	−0.280669	+	0.162044i	−0.0222585	+	0.0128509i
$160$		0			0
$161$	10.8320	−	9.08910i	0.853678	−	0.716321i
$162$	7.26294	+	0.635425i	0.570630	+	0.0499237i
$163$	4.11835	−	1.10351i	0.322574	−	0.0864334i	−0.0938985	−	0.995582i	$-0.529933\pi$
$163$	4.11835	−	1.10351i	0.322574	−	0.0864334i	0.416472	+	0.909148i	$0.363266\pi$
$164$	−2.23694	−	3.87449i	−0.174675	−	0.302546i
$165$		0			0
$166$	−4.60428	−	0.811859i	−0.357361	−	0.0630125i
$167$	6.98893	−	9.98122i	0.540820	−	0.772370i	−0.451997	−	0.892020i	$-0.649288\pi$
$167$	6.98893	−	9.98122i	0.540820	−	0.772370i	0.992816	+	0.119649i	$0.0381770\pi$
$168$	0.817240	+	0.381085i	0.0630514	+	0.0294014i
$169$	6.13659	−	7.31331i	0.472046	−	0.562562i
$170$		0			0
$171$	−6.32667	−	10.4671i	−0.483813	−	0.800440i
$172$	8.18476	−	8.18476i	0.624082	−	0.624082i
$173$	−17.3120	+	1.51460i	−1.31621	+	0.115153i	−0.723532	−	0.690290i	$-0.757483\pi$
$173$	−17.3120	+	1.51460i	−1.31621	+	0.115153i	−0.592673	+	0.805443i	$0.701927\pi$
$174$	−0.529623	+	0.192767i	−0.0401506	+	0.0146136i
$175$		0			0
$176$	−0.257538	+	1.46057i	−0.0194127	+	0.110095i
$177$	−5.30211	+	2.47241i	−0.398531	+	0.185838i
$178$	−2.83296	+	10.5728i	−0.212339	+	0.792462i
$179$	2.97818	−	5.15836i	0.222600	−	0.385554i	−0.732997	−	0.680232i	$-0.761879\pi$
$179$	2.97818	−	5.15836i	0.222600	−	0.385554i	0.955597	+	0.294678i	$0.0952123\pi$
$180$		0			0
$181$	1.32972	+	1.58470i	0.0988374	+	0.117790i	0.813196	−	0.581990i	$-0.197726\pi$
$181$	1.32972	+	1.58470i	0.0988374	+	0.117790i	−0.714358	+	0.699780i	$0.753281\pi$
$182$	2.51529	+	9.38719i	0.186446	+	0.695825i
$183$	−0.0275472	−	0.00738124i	−0.00203635	−	0.000545637i
$184$	−6.49217	−	2.36296i	−0.478609	−	0.174200i
$185$		0			0
$186$	1.42549	−	0.251353i	0.104522	−	0.0184301i
$187$	4.90559	−	10.5201i	0.358733	−	0.769305i
$188$	−0.380772	−	4.35224i	−0.0277706	−	0.317420i
$189$	5.23531			0.380813
$190$		0			0
$191$	−9.31472			−0.673989			−0.336995	−	0.941507i	$-0.609410\pi$
$191$	−9.31472			−0.673989			−0.336995	+	0.941507i	$0.609410\pi$
$192$	−0.0383991	−	0.438904i	−0.00277122	−	0.0316751i
$193$	1.26132	−	2.70491i	0.0907918	−	0.194704i	−0.855668	−	0.517525i	$-0.826853\pi$
$193$	1.26132	−	2.70491i	0.0907918	−	0.194704i	0.946460	+	0.322821i	$0.104631\pi$
$194$	−6.77804	+	1.19515i	−0.486635	+	0.0858068i
$195$		0			0
$196$	2.64159	+	0.961460i	0.188685	+	0.0686757i
$197$	20.3370	+	5.44928i	1.44895	+	0.388245i	0.895658	−	0.444743i	$-0.146705\pi$
$197$	20.3370	+	5.44928i	1.44895	+	0.388245i	0.553292	+	0.832988i	$0.313371\pi$
$198$	1.07706	+	4.01963i	0.0765430	+	0.285662i
$199$	−10.3621	−	12.3490i	−0.734547	−	0.875400i	0.261410	−	0.965228i	$-0.415813\pi$
$199$	−10.3621	−	12.3490i	−0.734547	−	0.875400i	−0.995957	+	0.0898283i	$0.971368\pi$
$200$		0			0
$201$	0.661887	−	1.14642i	0.0466859	−	0.0808624i
$202$	0.0335307	−	0.125138i	0.00235921	−	0.00880470i
$203$	2.37291	−	1.10650i	0.166545	−	0.0776614i
$204$	−0.598780	+	3.39585i	−0.0419230	+	0.237757i
$205$		0			0
$206$	−5.07632	+	1.84763i	−0.353684	+	0.128731i
$207$	−19.3116	+	1.68955i	−1.34225	+	0.117432i
$208$	3.35759	−	3.35759i	0.232807	−	0.232807i
$209$	4.05519	−	5.03466i	0.280503	−	0.348255i
$210$		0			0
$211$	10.7525	−	12.8144i	0.740236	−	0.882179i	−0.256192	−	0.966626i	$-0.582468\pi$
$211$	10.7525	−	12.8144i	0.740236	−	0.882179i	0.996428	+	0.0844472i	$0.0269124\pi$
$212$	−0.666675	−	0.310876i	−0.0457875	−	0.0213510i
$213$	−0.284542	+	0.406369i	−0.0194965	+	0.0278439i
$214$	12.0297	+	2.12115i	0.822330	+	0.144999i
$215$		0			0
$216$	−1.27898	−	2.21526i	−0.0870236	−	0.150729i
$217$	−6.49504	+	1.74034i	−0.440912	+	0.118142i
$218$	−6.54513	−	0.572624i	−0.443292	−	0.0387830i
$219$	−0.402875	+	0.338052i	−0.0272238	+	0.0228434i
$220$		0			0
$221$	−32.1844	+	18.5817i	−2.16496	+	1.24994i
$222$	1.99981	+	4.28860i	0.134218	+	0.287832i
$223$	14.9250	+	21.3151i	0.999450	+	1.42736i	0.901806	+	0.432141i	$0.142242\pi$
$223$	14.9250	+	21.3151i	0.999450	+	1.42736i	0.0976438	+	0.995221i	$0.468869\pi$
$224$	0.355401	+	2.01558i	0.0237463	+	0.134672i
$225$		0			0
$226$	−5.48942	−	4.60617i	−0.365151	−	0.306398i
$227$	−7.27359	−	7.27359i	−0.482765	−	0.482765i	0.423249	−	0.906014i	$-0.360890\pi$
$227$	−7.27359	−	7.27359i	−0.482765	−	0.482765i	−0.906014	+	0.423249i	$0.860890\pi$
$228$	−0.776515	+	1.75645i	−0.0514259	+	0.116324i
$229$			16.0296i			1.05927i	0.848226	+	0.529634i	$0.177671\pi$
$229$			16.0296i			1.05927i	−0.848226	+	0.529634i	$0.822329\pi$
$230$		0			0
$231$	0.457401	+	1.25670i	0.0300948	+	0.0826847i
$232$	−1.04790	−	0.733748i	−0.0687981	−	0.0481729i
$233$	−7.60498	+	5.32506i	−0.498219	+	0.348856i	−0.795520	−	0.605927i	$-0.792802\pi$
$233$	−7.60498	+	5.32506i	−0.498219	+	0.348856i	0.297301	+	0.954784i	$0.403913\pi$
$234$	4.55685	−	12.5199i	0.297891	−	0.818448i
$235$		0			0
$236$	−11.4995	−	6.63923i	−0.748553	−	0.432177i
$237$	0.557005	−	6.36659i	0.0361813	−	0.413555i
$238$	1.39610	−	15.9575i	0.0904958	−	1.03437i
$239$	−15.9340	−	9.19951i	−1.03069	−	0.595067i	−0.113505	−	0.993537i	$-0.536208\pi$
$239$	−15.9340	−	9.19951i	−1.03069	−	0.595067i	−0.917181	+	0.398470i	$0.869541\pi$
$240$		0			0
$241$	3.48221	−	9.56729i	0.224309	−	0.616284i	−0.775579	−	0.631250i	$-0.782542\pi$
$241$	3.48221	−	9.56729i	0.224309	−	0.616284i	0.999888	+	0.0149668i	$0.00476425\pi$
$242$	7.20887	−	5.04770i	0.463404	−	0.324479i
$243$	−8.91730	−	6.24396i	−0.572045	−	0.400550i
$244$	−0.0221391	−	0.0608267i	−0.00141731	−	0.00389403i
$245$		0			0
$246$			1.97110i			0.125673i
$247$	−19.8808	+	5.75715i	−1.26498	+	0.366319i
$248$	2.32313	+	2.32313i	0.147519	+	0.147519i
$249$	1.57794	+	1.32405i	0.0999976	+	0.0839080i
$250$		0			0
$251$	1.05835	+	6.00222i	0.0668026	+	0.378857i	0.999819	+	0.0190227i	$0.00605549\pi$
$251$	1.05835	+	6.00222i	0.0668026	+	0.378857i	−0.933016	+	0.359834i	$0.882833\pi$
$252$	3.29390	+	4.70418i	0.207496	+	0.296336i
$253$	−4.33036	−	9.28649i	−0.272247	−	0.583836i
$254$	0.569441	−	0.328767i	0.0357299	−	0.0206287i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	11.7437	+	1.02744i	0.732549	+	0.0640898i	0.447326	−	0.894371i	$-0.352377\pi$
$257$	11.7437	+	1.02744i	0.732549	+	0.0640898i	0.285224	+	0.958461i	$0.407932\pi$
$258$	−4.92595	+	1.31990i	−0.306676	+	0.0821736i
$259$	−10.9909	−	19.0368i	−0.682942	−	1.18289i
$260$		0			0
$261$	−3.53490	−	0.623299i	−0.218805	−	0.0385812i
$262$	−0.640141	+	0.914217i	−0.0395481	+	0.0564805i
$263$	−0.793713	−	0.370115i	−0.0489425	−	0.0228222i	0.397993	−	0.917388i	$-0.369707\pi$
$263$	−0.793713	−	0.370115i	−0.0489425	−	0.0228222i	−0.446935	+	0.894566i	$0.647485\pi$
$264$	0.420014	−	0.500553i	0.0258501	−	0.0308069i
$265$		0			0
$266$	2.88236	−	8.44279i	0.176729	−	0.517661i
$267$	3.41000	−	3.41000i	0.208689	−	0.208689i
$268$	2.99318	−	0.261869i	0.182838	−	0.0159962i
$269$	−13.4434	+	4.89298i	−0.819656	+	0.298330i	−0.717606	−	0.696449i	$-0.754762\pi$
$269$	−13.4434	+	4.89298i	−0.819656	+	0.298330i	−0.102050	+	0.994779i	$0.532540\pi$
$270$		0			0
$271$	−4.04329	+	22.9306i	−0.245612	+	1.39294i	0.573454	+	0.819238i	$0.305603\pi$
$271$	−4.04329	+	22.9306i	−0.245612	+	1.39294i	−0.819066	+	0.573699i	$0.805508\pi$
$272$	−7.09329	+	3.30765i	−0.430094	+	0.200556i
$273$	1.10819	−	4.13581i	0.0670705	−	0.250311i
$274$	2.84100	−	4.92076i	0.171631	−	0.297274i
$275$		0			0
$276$	1.95658	+	2.33176i	0.117772	+	0.140355i
$277$	−4.67404	−	17.4438i	−0.280836	−	1.04809i	−0.951829	−	0.306630i	$-0.900798\pi$
$277$	−4.67404	−	17.4438i	−0.280836	−	1.04809i	0.670993	−	0.741464i	$-0.265868\pi$
$278$	−17.3161	−	4.63984i	−1.03855	−	0.278279i
$279$	8.66254	+	3.15291i	0.518613	+	0.188760i
$280$		0			0
$281$	2.30637	−	0.406675i	0.137586	−	0.0242602i	−0.104431	−	0.994532i	$-0.533302\pi$
$281$	2.30637	−	0.406675i	0.137586	−	0.0242602i	0.242017	+	0.970272i	$0.422191\pi$
$282$	−0.813470	+	1.74449i	−0.0484415	+	0.103883i
$283$	−0.176920	−	2.02221i	−0.0105168	−	0.120208i	0.989122	−	0.147101i	$-0.0469942\pi$
$283$	−0.176920	−	2.02221i	−0.0105168	−	0.120208i	−0.999638	+	0.0268931i	$0.991439\pi$
$284$	−1.12598			−0.0668146
$285$		0			0
$286$	7.04230			0.416420
$287$	−0.798047	−	9.12172i	−0.0471072	−	0.538438i
$288$	1.18582	−	2.54300i	0.0698751	−	0.149848i
$289$	43.5830	−	7.68486i	2.56371	−	0.452050i
$290$		0			0
$291$	2.84946	+	1.03712i	0.167039	+	0.0607971i
$292$	−1.15302	−	0.308949i	−0.0674751	−	0.0180799i
$293$	−3.96704	−	14.8052i	−0.231757	−	0.864930i	−0.979584	−	0.201036i	$-0.935569\pi$
$293$	−3.96704	−	14.8052i	−0.231757	−	0.864930i	0.747827	−	0.663894i	$-0.231097\pi$
$294$	−0.796108	−	0.948764i	−0.0464300	−	0.0553331i
$295$		0			0
$296$	−5.37013	+	9.30133i	−0.312132	+	0.540629i
$297$	0.981887	−	3.66445i	0.0569749	−	0.212633i
$298$	3.46114	−	1.61396i	0.200499	−	0.0934940i
$299$	−5.69662	+	32.3071i	−0.329444	+	1.86837i
$300$		0			0
$301$	22.2616	−	8.10255i	1.28314	−	0.467023i
$302$	−6.87703	+	0.601662i	−0.395729	+	0.0346218i
$303$	−0.0403605	+	0.0403605i	−0.00231865	+	0.00231865i
$304$	−4.27662	+	0.842928i	−0.245281	+	0.0483452i
$305$		0			0
$306$	−14.1159	+	16.8227i	−0.806955	+	0.961691i
$307$	−4.42067	−	2.06139i	−0.252301	−	0.117650i	0.292354	−	0.956310i	$-0.405561\pi$
$307$	−4.42067	−	2.06139i	−0.252301	−	0.117650i	−0.544655	+	0.838660i	$0.683339\pi$
$308$	−1.74105	+	2.48648i	−0.0992056	+	0.141680i
$309$	2.34391	+	0.413294i	0.133340	+	0.0235115i
$310$		0			0
$311$	6.10041	+	10.5662i	0.345923	+	0.599156i	0.985521	−	0.169554i	$-0.0542326\pi$
$311$	6.10041	+	10.5662i	0.345923	+	0.599156i	−0.639598	+	0.768709i	$0.720899\pi$
$312$	−2.02075	+	0.541457i	−0.114402	+	0.0306540i
$313$	18.4390	+	1.61321i	1.04224	+	0.0911839i	0.595398	−	0.803431i	$-0.296994\pi$
$313$	18.4390	+	1.61321i	1.04224	+	0.0911839i	0.446838	+	0.894615i	$0.352550\pi$
$314$	−5.12418	+	4.29970i	−0.289174	+	0.242646i
$315$		0			0
$316$	12.5623	−	7.25284i	0.706684	−	0.408004i
$317$	6.58755	+	14.1271i	0.369994	+	0.793454i	0.999860	+	0.0167503i	$0.00533205\pi$
$317$	6.58755	+	14.1271i	0.369994	+	0.793454i	−0.629866	+	0.776704i	$0.716890\pi$
$318$	0.185890	+	0.265478i	0.0104242	+	0.0148873i
$319$	−0.329456	−	1.86844i	−0.0184460	−	0.104612i
$320$		0			0
$321$	−4.12269	−	3.45935i	−0.230106	−	0.193082i
$322$	−9.99858	−	9.99858i	−0.557199	−	0.557199i
$323$	34.0383	+	2.29056i	1.89394	+	0.127450i
$324$		−	7.29068i		−	0.405038i
$325$		0			0
$326$	−1.45825	−	4.00650i	−0.0807648	−	0.221899i
$327$	2.37117	+	1.66031i	0.131126	+	0.0918155i
$328$	−3.66478	+	2.56611i	−0.202354	+	0.141690i
$329$	3.05822	−	8.40240i	0.168605	−	0.463239i
$330$		0			0
$331$	−31.0987	−	17.9548i	−1.70934	−	0.986888i	−0.935374	−	0.353660i	$-0.884937\pi$
$331$	−31.0987	−	17.9548i	−1.70934	−	0.986888i	−0.773965	−	0.633228i	$-0.781730\pi$
$332$	−0.407480	+	4.65752i	−0.0223634	+	0.255615i
$333$	−2.62652	+	30.0213i	−0.143932	+	1.64516i
$334$	−10.5524	−	6.09241i	−0.577400	−	0.333362i
$335$		0			0
$336$	0.308408	−	0.847344i	0.0168250	−	0.0462264i
$337$	10.0463	−	7.03450i	0.547257	−	0.383193i	−0.267001	−	0.963696i	$-0.586033\pi$
$337$	10.0463	−	7.03450i	0.547257	−	0.383193i	0.814258	+	0.580503i	$0.197144\pi$
$338$	−7.82032	−	5.47584i	−0.425369	−	0.297847i
$339$	1.07981	+	2.96677i	0.0586475	+	0.161133i
$340$		0			0
$341$			4.87260i			0.263866i
$342$	−9.87588	+	7.21487i	−0.534026	+	0.390135i
$343$	14.1988	+	14.1988i	0.766665	+	0.766665i
$344$	−8.86697	−	7.44027i	−0.478075	−	0.401152i
$345$		0			0
$346$	3.01768	+	17.1141i	0.162231	+	0.920059i
$347$	15.2100	+	21.7222i	0.816518	+	1.16611i	0.983635	+	0.180172i	$0.0576653\pi$
$347$	15.2100	+	21.7222i	0.816518	+	1.16611i	−0.167117	+	0.985937i	$0.553446\pi$
$348$	0.238193	+	0.510807i	0.0127685	+	0.0273821i
$349$	−3.23153	+	1.86572i	−0.172980	+	0.0998700i	−0.583990	−	0.811761i	$-0.698509\pi$
$349$	−3.23153	+	1.86572i	−0.172980	+	0.0998700i	0.411010	+	0.911631i	$0.365176\pi$
$350$		0			0
$351$	−9.30445	+	7.80736i	−0.496635	+	0.416726i
$352$	1.47746	+	0.129261i	0.0787489	+	0.00688963i
$353$	11.9016	−	3.18902i	0.633458	−	0.169734i	0.0722194	−	0.997389i	$-0.476992\pi$
$353$	11.9016	−	3.18902i	0.633458	−	0.169734i	0.561238	+	0.827654i	$0.310325\pi$
$354$	2.92511	+	5.06645i	0.155468	+	0.269279i
$355$		0			0
$356$	10.7794	+	1.90070i	0.571309	+	0.100737i
$357$	−4.04797	+	5.78110i	−0.214241	+	0.305968i
$358$	−5.39830	−	2.51727i	−0.285309	−	0.133042i
$359$	−11.3915	+	13.5759i	−0.601220	+	0.716507i	−0.977721	−	0.209910i	$-0.932683\pi$
$359$	−11.3915	+	13.5759i	−0.601220	+	0.716507i	0.376500	+	0.926416i	$0.377127\pi$
$360$		0			0
$361$	18.1006	+	5.77653i	0.952663	+	0.304028i
$362$	1.46278	−	1.46278i	0.0768818	−	0.0768818i
$363$	−3.86253	+	0.337928i	−0.202730	+	0.0177366i
$364$	9.13225	−	3.32387i	0.478660	−	0.174218i
$365$		0			0
$366$	−0.00495226	+	0.0280857i	−0.000258859	+	0.00146806i
$367$	24.7098	−	11.5224i	1.28984	−	0.601464i	0.347993	−	0.937497i	$-0.386863\pi$
$367$	24.7098	−	11.5224i	1.28984	−	0.601464i	0.941850	+	0.336033i	$0.109085\pi$
$368$	−1.78814	+	6.67341i	−0.0932130	+	0.347876i
$369$	−6.27659	+	10.8714i	−0.326746	+	0.565941i
$370$		0			0
$371$	−0.967732	−	1.15330i	−0.0502422	−	0.0598763i
$372$	−0.374637	−	1.39816i	−0.0194240	−	0.0724914i
$373$	−23.4649	−	6.28739i	−1.21497	−	0.325549i	−0.406257	−	0.913759i	$-0.633166\pi$
$373$	−23.4649	−	6.28739i	−1.21497	−	0.325549i	−0.808708	+	0.588210i	$0.799833\pi$
$374$	−10.9076	−	3.97004i	−0.564019	−	0.205286i
$375$		0			0
$376$	−4.30249	+	0.758645i	−0.221884	+	0.0391241i
$377$	−2.56712	+	5.50522i	−0.132214	+	0.283533i
$378$	−0.456288	−	5.21539i	−0.0234689	−	0.268251i
$379$	−10.5542			−0.542133			−0.271067	−	0.962561i	$-0.587376\pi$
$379$	−10.5542			−0.542133			−0.271067	+	0.962561i	$0.587376\pi$
$380$		0			0
$381$	−0.289696			−0.0148416
$382$	0.811831	+	9.27927i	0.0415369	+	0.474769i
$383$	−0.648082	+	1.38982i	−0.0331155	+	0.0710163i	−0.922170	−	0.386786i	$-0.873585\pi$
$383$	−0.648082	+	1.38982i	−0.0331155	+	0.0710163i	0.889054	+	0.457802i	$0.151363\pi$
$384$	−0.433887	+	0.0765060i	−0.0221417	+	0.00390418i
$385$		0			0
$386$	−2.80455	−	1.02077i	−0.142748	−	0.0519559i
$387$	−31.3715	−	8.40597i	−1.59470	−	0.427299i
$388$	1.78135	+	6.64808i	0.0904342	+	0.337505i
$389$	−6.83297	−	8.14322i	−0.346446	−	0.412878i	0.564481	−	0.825446i	$-0.309076\pi$
$389$	−6.83297	−	8.14322i	−0.346446	−	0.412878i	−0.910927	+	0.412568i	$0.864632\pi$
$390$		0			0
$391$	27.0362	−	46.8281i	1.36728	−	2.36820i
$392$	0.727571	−	2.71533i	0.0367479	−	0.137145i
$393$	0.445641	−	0.207806i	0.0224796	−	0.0104824i
$394$	3.65606	−	20.7345i	0.184190	−	1.04459i
$395$		0			0
$396$	3.91046	−	1.42329i	0.196508	−	0.0715231i
$397$	20.7547	−	1.81580i	1.04165	−	0.0911323i	0.446528	−	0.894770i	$-0.352660\pi$
$397$	20.7547	−	1.81580i	1.04165	−	0.0911323i	0.595119	+	0.803637i	$0.297105\pi$
$398$	−11.3989	+	11.3989i	−0.571377	+	0.571377i
$399$	−2.95964	+	2.58642i	−0.148167	+	0.129483i
$400$		0			0
$401$	18.8139	−	22.4216i	0.939522	−	1.11968i	−0.0531191	−	0.998588i	$-0.516916\pi$
$401$	18.8139	−	22.4216i	0.939522	−	1.11968i	0.992641	−	0.121091i	$-0.0386393\pi$
$402$	−1.19975	−	0.559451i	−0.0598379	−	0.0279029i
$403$	8.94795	−	12.7790i	0.445729	−	0.636567i
$404$	−0.127584	−	0.0224966i	−0.00634756	−	0.00111925i
$405$		0			0
$406$	−1.30911	−	2.26744i	−0.0649698	−	0.112531i
$407$	−15.3861	+	4.12270i	−0.762663	+	0.204355i
$408$	3.43511	+	0.300534i	0.170063	+	0.0148786i
$409$	7.92614	−	6.65082i	0.391922	−	0.328862i	−0.425439	−	0.904987i	$-0.639880\pi$
$409$	7.92614	−	6.65082i	0.391922	−	0.328862i	0.817361	+	0.576125i	$0.195436\pi$
$410$		0			0
$411$	−2.16799	+	1.25169i	−0.106939	+	0.0617412i
$412$	2.28303	+	4.89598i	0.112477	+	0.241207i
$413$	−15.5879	−	22.2618i	−0.767031	−	1.09543i
$414$	3.36624	+	19.0909i	0.165442	+	0.938266i
$415$		0			0
$416$	−3.63745	−	3.05218i	−0.178341	−	0.149646i
$417$	5.58492	+	5.58492i	0.273495	+	0.273495i
$418$	−5.36893	−	3.60096i	−0.262603	−	0.176128i
$419$			27.0637i			1.32215i	0.750321	+	0.661073i	$0.229899\pi$
$419$			27.0637i			1.32215i	−0.750321	+	0.661073i	$0.770101\pi$
$420$		0			0
$421$	−4.11274	−	11.2997i	−0.200443	−	0.550712i	0.798222	−	0.602363i	$-0.205774\pi$
$421$	−4.11274	−	11.2997i	−0.200443	−	0.550712i	−0.998665	+	0.0516506i	$0.983552\pi$
$422$	−13.7028	−	9.59478i	−0.667040	−	0.467067i
$423$	−10.0416	+	7.03121i	−0.488240	+	0.341869i
$424$	−0.251588	+	0.691233i	−0.0122182	+	0.0335693i
$425$		0			0
$426$	0.429622	+	0.248042i	0.0208152	+	0.0120177i
$427$	0.0115466	−	0.131978i	0.000558778	−	0.00638686i
$428$	1.06463	−	12.1688i	0.0514607	−	0.588199i
$429$	−2.68701	−	1.55135i	−0.129730	−	0.0748998i
$430$		0			0
$431$	−5.84092	+	16.0478i	−0.281347	+	0.772995i	0.715855	+	0.698249i	$0.246037\pi$
$431$	−5.84092	+	16.0478i	−0.281347	+	0.772995i	−0.997203	+	0.0747466i	$0.976185\pi$
$432$	−2.09536	+	1.46719i	−0.100813	+	0.0705900i
$433$	22.2823	+	15.6022i	1.07082	+	0.749796i	0.969508	−	0.245059i	$-0.0788074\pi$
$433$	22.2823	+	15.6022i	1.07082	+	0.749796i	0.101311	+	0.994855i	$0.467696\pi$
$434$	2.29980	+	6.31864i	0.110394	+	0.303305i
$435$		0			0
$436$			6.57013i			0.314652i
$437$	20.8627	−	21.7176i	0.997999	−	1.03889i
$438$	0.371879	+	0.371879i	0.0177690	+	0.0177690i
$439$	16.7852	+	14.0844i	0.801112	+	0.672213i	0.948469	−	0.316871i	$-0.102632\pi$
$439$	16.7852	+	14.0844i	0.801112	+	0.672213i	−0.147357	+	0.989083i	$0.547077\pi$
$440$		0			0
$441$	−1.36968	−	7.76786i	−0.0652230	−	0.369898i
$442$	21.3160	+	30.4424i	1.01390	+	1.44800i
$443$	4.27616	+	9.17026i	0.203167	+	0.435692i	0.981320	−	0.192382i	$-0.0616213\pi$
$443$	4.27616	+	9.17026i	0.203167	+	0.435692i	−0.778154	+	0.628074i	$0.783843\pi$
$444$	4.09798	−	2.36597i	0.194482	−	0.112284i
$445$		0			0
$446$	19.9332	−	16.7259i	0.943862	−	0.791995i
$447$	−1.67615	−	0.146644i	−0.0792792	−	0.00693603i
$448$	1.97694	−	0.529719i	0.0934015	−	0.0250268i
$449$	17.4460	+	30.2174i	0.823329	+	1.42605i	0.903190	+	0.429242i	$0.141219\pi$
$449$	17.4460	+	30.2174i	0.823329	+	1.42605i	−0.0798608	+	0.996806i	$0.525448\pi$
$450$		0			0
$451$	−6.53441	−	1.15219i	−0.307693	−	0.0542546i
$452$	−4.11021	+	5.86999i	−0.193328	+	0.276101i
$453$	2.75650	+	1.28538i	0.129511	+	0.0603922i
$454$	−6.61197	+	7.87984i	−0.310315	+	0.369819i
$455$		0			0
$456$	1.81745	+	0.620475i	0.0851098	+	0.0290564i
$457$	−5.93949	+	5.93949i	−0.277838	+	0.277838i	−0.832245	−	0.554408i	$-0.812945\pi$
$457$	−5.93949	+	5.93949i	−0.277838	+	0.277838i	0.554408	+	0.832245i	$0.312945\pi$
$458$	15.9686	−	1.39707i	0.746165	−	0.0652810i
$459$	18.8127	−	6.84727i	0.878102	−	0.319603i
$460$		0			0
$461$	−3.75525	+	21.2971i	−0.174899	+	0.991904i	0.763360	+	0.645973i	$0.223548\pi$
$461$	−3.75525	+	21.2971i	−0.174899	+	0.991904i	−0.938260	+	0.345931i	$0.887563\pi$
$462$	1.21205	−	0.565189i	0.0563897	−	0.0262950i
$463$	1.44183	−	5.38097i	0.0670074	−	0.250075i	−0.924295	−	0.381679i	$-0.875346\pi$
$463$	1.44183	−	5.38097i	0.0670074	−	0.250075i	0.991302	+	0.131604i	$0.0420127\pi$
$464$	−0.639625	+	1.10786i	−0.0296939	+	0.0514313i
$465$		0			0
$466$	5.96762	+	7.11193i	0.276444	+	0.329454i
$467$	−1.02970	−	3.84289i	−0.0476487	−	0.177828i	0.938000	−	0.346634i	$-0.112675\pi$
$467$	−1.02970	−	3.84289i	−0.0476487	−	0.177828i	−0.985649	+	0.168806i	$0.946009\pi$
$468$	−12.8694	−	3.44834i	−0.594887	−	0.159399i
$469$	5.77861	+	2.10324i	0.266832	+	0.0971187i
$470$		0			0
$471$	2.90233	−	0.511759i	0.133732	−	0.0235806i
$472$	−5.61172	+	12.0344i	−0.258300	+	0.553927i
$473$	−1.49620	−	17.1016i	−0.0687952	−	0.786333i
$474$	−6.39091			−0.293544
$475$		0			0
$476$	−16.0185			−0.734205
$477$	0.179889	+	2.05614i	0.00823656	+	0.0941444i
$478$	−7.77576	+	16.6752i	−0.355655	+	0.762705i
$479$	11.3821	−	2.00697i	0.520060	−	0.0917007i	0.0925445	−	0.995709i	$-0.470500\pi$
$479$	11.3821	−	2.00697i	0.520060	−	0.0917007i	0.427516	+	0.904008i	$0.359389\pi$
$480$		0			0
$481$	47.9229	+	17.4425i	2.18510	+	0.795310i
$482$	−9.83438	−	2.63511i	−0.447944	−	0.120026i
$483$	1.61241	+	6.01758i	0.0733670	+	0.273809i
$484$	−5.65679	−	6.74150i	−0.257127	−	0.306432i
$485$		0			0
$486$	−5.44300	+	9.42756i	−0.246900	+	0.427643i
$487$	−5.26129	+	19.6354i	−0.238412	+	0.889764i	0.738170	+	0.674615i	$0.235690\pi$
$487$	−5.26129	+	19.6354i	−0.238412	+	0.889764i	−0.976581	+	0.215149i	$0.930976\pi$
$488$	−0.0586657	+	0.0273563i	−0.00265567	+	0.00123836i
$489$	−0.326193	+	1.84993i	−0.0147509	+	0.0836568i
$490$		0			0
$491$	−7.37683	+	2.68495i	−0.332912	+	0.121170i	−0.503067	−	0.864247i	$-0.667795\pi$
$491$	−7.37683	+	2.68495i	−0.332912	+	0.121170i	0.170156	+	0.985417i	$0.445573\pi$
$492$	1.96360	−	0.171793i	0.0885258	−	0.00774501i
$493$	7.07966	−	7.07966i	0.318852	−	0.318852i
$494$	7.46797	+	19.3034i	0.336000	+	0.868499i
$495$		0			0
$496$	2.11182	−	2.51677i	0.0948235	−	0.113006i
$497$	−2.08860	−	0.973930i	−0.0936865	−	0.0436867i
$498$	1.18148	−	1.68733i	0.0529434	−	0.0756110i
$499$	−33.7144	−	5.94476i	−1.50927	−	0.266124i	−0.643061	−	0.765815i	$-0.722336\pi$
$499$	−33.7144	−	5.94476i	−1.50927	−	0.266124i	−0.866204	+	0.499691i	$0.833447\pi$
$500$		0			0
$501$	2.68420	+	4.64916i	0.119921	+	0.207709i
$502$	5.88713	−	1.57745i	0.262756	−	0.0704052i
$503$	0.528316	+	0.0462216i	0.0235564	+	0.00206092i	0.0989279	−	0.995095i	$-0.468459\pi$
$503$	0.528316	+	0.0462216i	0.0235564	+	0.00206092i	−0.0753714	+	0.997156i	$0.524014\pi$
$504$	4.39920	−	3.69136i	0.195956	−	0.164426i
$505$		0			0
$506$	−8.87373	+	5.12325i	−0.394486	+	0.227756i
$507$	1.77760	+	3.81207i	0.0789458	+	0.169300i
$508$	−0.377146	−	0.538620i	−0.0167331	−	0.0238974i
$509$	5.59450	+	31.7280i	0.247972	+	1.40632i	0.813489	+	0.581581i	$0.197566\pi$
$509$	5.59450	+	31.7280i	0.247972	+	1.40632i	−0.565517	+	0.824737i	$0.691323\pi$
$510$		0			0
$511$	−1.87152	−	1.57039i	−0.0827911	−	0.0694700i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	11.0857	−	1.19454i	0.489446	−	0.0527401i
$514$		−	11.7885i		−	0.519969i
$515$		0			0
$516$	1.74421	+	4.79217i	0.0767844	+	0.210963i
$517$	−5.30768	−	3.71648i	−0.233431	−	0.163450i
$518$	−18.0064	+	12.6082i	−0.791158	+	0.553975i
$519$	2.61866	−	7.19471i	0.114946	−	0.315813i
$520$		0			0
$521$	23.4211	+	13.5222i	1.02610	+	0.592416i	0.915864	−	0.401489i	$-0.131507\pi$
$521$	23.4211	+	13.5222i	1.02610	+	0.592416i	0.110232	+	0.993906i	$0.464841\pi$
$522$	−0.312840	+	3.57578i	−0.0136926	+	0.156508i
$523$	−1.75556	+	20.0661i	−0.0767652	+	0.877430i	0.856007	+	0.516964i	$0.172938\pi$
$523$	−1.75556	+	20.0661i	−0.0767652	+	0.877430i	−0.932772	+	0.360466i	$0.882618\pi$
$524$	0.966530	+	0.558026i	0.0422231	+	0.0243775i
$525$		0			0
$526$	−0.299529	+	0.822951i	−0.0130601	+	0.0358823i
$527$	−21.0633	+	14.7487i	−0.917530	+	0.642461i
$528$	−0.535255	−	0.374790i	−0.0232940	−	0.0163106i
$529$	−8.45880	−	23.2404i	−0.367774	−	1.01045i
$530$		0			0
$531$			37.2579i			1.61685i
$532$	−8.66188	−	2.13555i	−0.375540	−	0.0925879i
$533$	15.0214	+	15.0214i	0.650650	+	0.650650i
$534$	−3.69423	−	3.09982i	−0.159865	−	0.134142i
$535$		0			0
$536$	−0.521746	−	2.95897i	−0.0225360	−	0.127808i
$537$	1.50521	+	2.14967i	0.0649547	+	0.0927649i
$538$	6.04603	+	12.9657i	0.260663	+	0.558993i
$539$	3.61062	−	2.08459i	0.155520	−	0.0897897i
$540$		0			0
$541$	−0.119323	+	0.100124i	−0.00513008	+	0.00430465i	−0.645349	−	0.763888i	$-0.723288\pi$
$541$	−0.119323	+	0.100124i	−0.00513008	+	0.00430465i	0.640219	+	0.768192i	$0.278844\pi$
$542$	23.1958	+	2.02937i	0.996343	+	0.0871688i
$543$	−0.880363	+	0.235893i	−0.0377800	+	0.0101231i
$544$	3.91329	+	6.77802i	0.167781	+	0.290605i
$545$		0			0
$546$	−4.21666	−	0.743510i	−0.180456	−	0.0318193i
$547$	−7.75652	+	11.0775i	−0.331645	+	0.473638i	−0.949995	−	0.312265i	$-0.898912\pi$
$547$	−7.75652	+	11.0775i	−0.331645	+	0.473638i	0.618350	+	0.785903i	$0.287801\pi$
$548$	−5.14964	−	2.40132i	−0.219982	−	0.102579i
$549$	−0.116747	+	0.139134i	−0.00498265	+	0.00593809i
$550$		0			0
$551$	4.77213	−	2.88443i	0.203300	−	0.122881i
$552$	2.15236	−	2.15236i	0.0916104	−	0.0916104i
$553$	29.5754	−	2.58751i	1.25768	−	0.110032i
$554$	−16.9700	+	6.17658i	−0.720987	+	0.262418i
$555$		0			0
$556$	−3.11298	+	17.6546i	−0.132020	+	0.748722i
$557$	−7.46961	+	3.48314i	−0.316498	+	0.147585i	−0.574375	−	0.818592i	$-0.694755\pi$
$557$	−7.46961	+	3.48314i	−0.316498	+	0.147585i	0.257877	+	0.966178i	$0.416977\pi$
$558$	2.38592	−	8.90437i	0.101004	−	0.376952i
$559$	−27.4811	+	47.5986i	−1.16233	+	2.01321i
$560$		0			0
$561$	3.28727	+	3.91762i	0.138789	+	0.165402i
$562$	−0.606140	−	2.26215i	−0.0255685	−	0.0954229i
$563$	5.50560	+	1.47522i	0.232034	+	0.0621732i	0.372962	−	0.927847i	$-0.378342\pi$
$563$	5.50560	+	1.47522i	0.232034	+	0.0621732i	−0.140929	+	0.990020i	$0.545009\pi$
$564$	1.80875	+	0.658332i	0.0761623	+	0.0277208i
$565$		0			0
$566$	−1.99909	+	0.352494i	−0.0840281	+	0.0148164i
$567$	6.30616	−	13.5236i	0.264834	−	0.567938i
$568$	0.0981356	+	1.12169i	0.00411768	+	0.0470653i
$569$	39.5404			1.65762			0.828810	−	0.559531i	$-0.189019\pi$
$569$	39.5404			1.65762			0.828810	+	0.559531i	$0.189019\pi$
$570$		0			0
$571$	28.7433			1.20287			0.601434	−	0.798922i	$-0.294596\pi$
$571$	28.7433			1.20287			0.601434	+	0.798922i	$0.294596\pi$
$572$	−0.613777	−	7.01550i	−0.0256633	−	0.293333i
$573$	1.73437	−	3.71938i	0.0724545	−	0.155379i
$574$	−9.01745	+	1.59002i	−0.376381	+	0.0663662i
$575$		0			0
$576$	−2.63667	−	0.959671i	−0.109861	−	0.0399863i
$577$	−29.3603	−	7.86706i	−1.22228	−	0.327510i	−0.410713	−	0.911765i	$-0.634720\pi$
$577$	−29.3603	−	7.86706i	−1.22228	−	0.327510i	−0.811570	+	0.584255i	$0.801387\pi$
$578$	−11.4541	−	42.7474i	−0.476429	−	1.77806i
$579$	0.845220	+	1.00729i	0.0351261	+	0.0418617i
$580$		0			0
$581$	−4.78442	+	8.28686i	−0.198491	+	0.343797i
$582$	0.784826	−	2.92901i	0.0325321	−	0.121411i
$583$	−0.988749	+	0.461061i	−0.0409498	+	0.0190952i
$584$	−0.207282	+	1.17555i	−0.00857739	+	0.0486448i
$585$		0			0
$586$	−14.4031	+	5.24231i	−0.594988	+	0.216558i
$587$	−10.1334	+	0.886556i	−0.418249	+	0.0365921i	−0.294338	−	0.955701i	$-0.595099\pi$
$587$	−10.1334	+	0.886556i	−0.418249	+	0.0365921i	−0.123911	+	0.992293i	$0.539544\pi$
$588$	−0.875769	+	0.875769i	−0.0361161	+	0.0361161i
$589$	−13.3561	+	5.16712i	−0.550328	+	0.212908i
$590$		0			0
$591$	−5.96259	+	7.10594i	−0.245268	+	0.292299i
$592$	9.73397	+	4.53903i	0.400064	+	0.186553i
$593$	6.37841	−	9.10931i	0.261930	−	0.374075i	−0.666548	−	0.745462i	$-0.732229\pi$
$593$	6.37841	−	9.10931i	0.261930	−	0.374075i	0.928478	+	0.371387i	$0.121118\pi$
$594$	−3.73608	−	0.658772i	−0.153293	−	0.0270298i
$595$		0			0
$596$	−1.90947	−	3.30731i	−0.0782151	−	0.135473i
$597$	6.86037	−	1.83823i	0.280776	−	0.0752338i
$598$	32.6807	+	2.85919i	1.33641	+	0.116921i
$599$	26.2171	−	21.9988i	1.07120	−	0.898845i	0.0760409	−	0.997105i	$-0.475772\pi$
$599$	26.2171	−	21.9988i	1.07120	−	0.898845i	0.995161	+	0.0982598i	$0.0313276\pi$
$600$		0			0
$601$	−24.3618	+	14.0653i	−0.993737	+	0.573735i	−0.906389	−	0.422443i	$-0.861173\pi$
$601$	−24.3618	+	14.0653i	−0.993737	+	0.573735i	−0.0873480	+	0.996178i	$0.527839\pi$
$602$	−10.0119	−	21.4707i	−0.408056	−	0.875079i
$603$	−4.83560	−	6.90596i	−0.196921	−	0.281232i
$604$	1.19875	+	6.79842i	0.0487762	+	0.276624i
$605$		0			0
$606$	0.0437245	+	0.0366893i	0.00177619	+	0.00149040i
$607$	−11.1486	−	11.1486i	−0.452506	−	0.452506i	0.443680	−	0.896185i	$-0.353673\pi$
$607$	−11.1486	−	11.1486i	−0.452506	−	0.452506i	−0.896185	+	0.443680i	$0.853673\pi$
$608$	1.21245	+	4.18688i	0.0491714	+	0.169800i
$609$			1.15353i			0.0467435i
$610$		0			0
$611$	7.09517	+	19.4938i	0.287040	+	0.788636i
$612$	17.9890	+	12.5960i	0.727162	+	0.509164i
$613$	−31.0863	+	21.7668i	−1.25556	+	0.879155i	−0.996240	−	0.0866359i	$-0.972388\pi$
$613$	−31.0863	+	21.7668i	−1.25556	+	0.879155i	−0.259323	+	0.965791i	$0.583499\pi$
$614$	−1.66826	+	4.58351i	−0.0673255	+	0.184975i
$615$		0			0
$616$	2.62876	+	1.51772i	0.105916	+	0.0611505i
$617$	2.82275	−	32.2641i	0.113639	−	1.29891i	−0.698571	−	0.715541i	$-0.746180\pi$
$617$	2.82275	−	32.2641i	0.113639	−	1.29891i	0.812210	−	0.583365i	$-0.198264\pi$
$618$	0.207436	−	2.37101i	0.00834431	−	0.0953759i
$619$	27.5924	+	15.9305i	1.10903	+	0.640300i	0.938578	−	0.345066i	$-0.112143\pi$
$619$	27.5924	+	15.9305i	1.10903	+	0.640300i	0.170453	+	0.985366i	$0.445477\pi$
$620$		0			0
$621$	6.04435	−	16.6067i	0.242551	−	0.666405i
$622$	9.99433	−	6.99811i	0.400736	−	0.280598i
$623$	18.3509	+	12.8495i	0.735214	+	0.514803i
$624$	0.715516	+	1.96586i	0.0286436	+	0.0786976i
$625$		0			0
$626$		−	18.5095i		−	0.739787i
$627$	1.25528	+	2.55668i	0.0501311	+	0.102104i
$628$	4.72994	+	4.72994i	0.188745	+	0.188745i
$629$	−64.3932	−	54.0324i	−2.56753	−	2.15441i
$630$		0			0
$631$	−6.72813	−	38.1571i	−0.267843	−	1.51901i	−0.760816	−	0.648968i	$-0.775201\pi$
$631$	−6.72813	−	38.1571i	−0.267843	−	1.51901i	0.492973	−	0.870044i	$-0.335910\pi$
$632$	−8.32011	−	11.8824i	−0.330956	−	0.472655i
$633$	3.11471	+	6.67951i	0.123798	+	0.265487i
$634$	13.4991	−	7.79374i	0.536120	−	0.309529i
$635$		0			0
$636$	0.248266	−	0.208320i	0.00984440	−	0.00826043i
$637$	−13.2974	−	1.16337i	−0.526862	−	0.0460944i
$638$	−1.83261	+	0.491047i	−0.0725539	+	0.0194408i
$639$	1.57969	+	2.73610i	0.0624915	+	0.108238i
$640$		0			0
$641$	−30.0967	−	5.30686i	−1.18875	−	0.209608i	−0.455919	−	0.890021i	$-0.650689\pi$
$641$	−30.0967	−	5.30686i	−1.18875	−	0.209608i	−0.732829	+	0.680413i	$0.761801\pi$
$642$	−3.08687	+	4.40850i	−0.121829	+	0.173990i
$643$	−8.14300	−	3.79714i	−0.321129	−	0.149745i	0.255369	−	0.966844i	$-0.417803\pi$
$643$	−8.14300	−	3.79714i	−0.321129	−	0.149745i	−0.576497	+	0.817099i	$0.695581\pi$
$644$	−9.08910	+	10.8320i	−0.358161	+	0.426839i
$645$		0			0
$646$	−0.684787	−	34.1084i	−0.0269426	−	1.34198i
$647$	−15.4658	+	15.4658i	−0.608024	+	0.608024i	−0.942429	−	0.334405i	$-0.891465\pi$
$647$	−15.4658	+	15.4658i	−0.608024	+	0.608024i	0.334405	+	0.942429i	$0.391465\pi$
$648$	−7.26294	+	0.635425i	−0.285315	+	0.0249618i
$649$	−18.5057	+	6.73552i	−0.726412	+	0.264392i
$650$		0			0
$651$	0.514438	−	2.91752i	0.0201624	−	0.114347i
$652$	−3.86416	+	1.80189i	−0.151332	+	0.0705673i
$653$	4.41282	−	16.4689i	0.172687	−	0.644476i	−0.824247	−	0.566230i	$-0.808401\pi$
$653$	4.41282	−	16.4689i	0.172687	−	0.644476i	0.996934	−	0.0782460i	$-0.0249319\pi$
$654$	1.44733	−	2.50686i	0.0565952	−	0.0980258i
$655$		0			0
$656$	2.87575	+	3.42718i	0.112279	+	0.133809i
$657$	0.866878	+	3.23523i	0.0338201	+	0.126218i
$658$	−8.63697	−	2.31427i	−0.336704	−	0.0902196i
$659$	9.41754	+	3.42770i	0.366855	+	0.133524i	0.518869	−	0.854854i	$-0.326353\pi$
$659$	9.41754	+	3.42770i	0.366855	+	0.133524i	−0.152013	+	0.988378i	$0.548576\pi$
$660$		0			0
$661$	2.38949	−	0.421332i	0.0929406	−	0.0163879i	−0.126984	−	0.991905i	$-0.540530\pi$
$661$	2.38949	−	0.421332i	0.0929406	−	0.0163879i	0.219925	+	0.975517i	$0.429419\pi$
$662$	−15.1761	+	32.5452i	−0.589836	+	1.26491i
$663$	−1.42704	−	16.3111i	−0.0554216	−	0.633472i
$664$	4.67531			0.181437
$665$		0			0
$666$	30.1360			1.16774
$667$	−0.770293	−	8.80449i	−0.0298259	−	0.340911i
$668$	−5.14953	+	11.0432i	−0.199241	+	0.427274i
$669$	−11.2901	+	1.99075i	−0.436501	+	0.0769670i
$670$		0			0
$671$	−0.0902123	−	0.0328346i	−0.00348261	−	0.00126757i
$672$	−0.870999	−	0.233384i	−0.0335995	−	0.00900296i
$673$	−3.06530	−	11.4399i	−0.118159	−	0.440974i	0.881345	−	0.472473i	$-0.156639\pi$
$673$	−3.06530	−	11.4399i	−0.118159	−	0.440974i	−0.999504	+	0.0314990i	$0.989972\pi$
$674$	−7.88332	−	9.39497i	−0.303654	−	0.361881i
$675$		0			0
$676$	−4.77342	+	8.26781i	−0.183593	+	0.317993i
$677$	−9.64922	+	36.0114i	−0.370850	+	1.38403i	0.488465	+	0.872583i	$0.337557\pi$
$677$	−9.64922	+	36.0114i	−0.370850	+	1.38403i	−0.859315	+	0.511447i	$0.829110\pi$
$678$	2.86136	−	1.33428i	0.109890	−	0.0512426i
$679$	−2.44609	+	13.8724i	−0.0938721	+	0.532375i
$680$		0			0
$681$	4.25867	−	1.55003i	0.163193	−	0.0593973i
$682$	4.85406	−	0.424675i	0.185871	−	0.0162616i
$683$	−25.8108	+	25.8108i	−0.987623	+	0.987623i	−0.999924	−	0.0123014i	$-0.996084\pi$
$683$	−25.8108	+	25.8108i	−0.987623	+	0.987623i	0.0123014	+	0.999924i	$0.496084\pi$
$684$	8.04815	+	9.20948i	0.307729	+	0.352133i
$685$		0			0
$686$	12.9073	−	15.3823i	0.492803	−	0.587299i
$687$	−6.40065	−	2.98467i	−0.244200	−	0.113872i
$688$	−6.63915	+	9.48169i	−0.253115	+	0.361486i
$689$	3.43980	+	0.606529i	0.131046	+	0.0231069i
$690$		0			0
$691$	−9.09764	−	15.7576i	−0.346091	−	0.599446i	0.639461	−	0.768824i	$-0.279158\pi$
$691$	−9.09764	−	15.7576i	−0.346091	−	0.599446i	−0.985551	+	0.169377i	$0.945824\pi$
$692$	16.7860	−	4.49778i	0.638106	−	0.170980i
$693$	8.48467	+	0.742313i	0.322306	+	0.0281981i
$694$	20.3139	−	17.0454i	0.771105	−	0.647034i
$695$		0			0
$696$	0.488103	−	0.281806i	0.0185015	−	0.0106818i
$697$	−14.7980	−	31.7345i	−0.560515	−	1.20203i
$698$	2.14027	+	3.05662i	0.0810105	+	0.115695i
$699$	−0.710278	−	4.02819i	−0.0268652	−	0.152360i
$700$		0			0
$701$	−27.6397	−	23.1925i	−1.04394	−	0.875968i	−0.0514954	−	0.998673i	$-0.516399\pi$
$701$	−27.6397	−	23.1925i	−1.04394	−	0.875968i	−0.992443	+	0.122705i	$0.960843\pi$
$702$	8.58858	+	8.58858i	0.324155	+	0.324155i
$703$	−27.6167	−	37.8024i	−1.04158	−	1.42575i
$704$		−	1.48310i		−	0.0558966i
$705$		0			0
$706$	−4.21418	−	11.5784i	−0.158603	−	0.435757i
$707$	−0.217200	−	0.152085i	−0.00816865	−	0.00571975i
$708$	4.79223	−	3.35555i	0.180103	−	0.126109i
$709$	0.631353	−	1.73463i	0.0237110	−	0.0651454i	−0.927272	−	0.374387i	$-0.877853\pi$
$709$	0.631353	−	1.73463i	0.0237110	−	0.0651454i	0.950983	+	0.309242i	$0.100075\pi$
$710$		0			0
$711$	−35.2484	−	20.3507i	−1.32192	−	0.763209i
$712$	0.953983	−	10.9041i	0.0357520	−	0.408647i
$713$	−1.97829	+	22.6119i	−0.0740875	+	0.846823i
$714$	6.11190	+	3.52871i	0.228732	+	0.132059i
$715$		0			0
$716$	−2.03720	+	5.59715i	−0.0761336	+	0.209175i
$717$	6.64025	−	4.64955i	0.247985	−	0.173641i
$718$	14.5170	+	10.1649i	0.541771	+	0.379352i
$719$	−0.692519	−	1.90268i	−0.0258266	−	0.0709580i	0.926109	−	0.377255i	$-0.123132\pi$
$719$	−0.692519	−	1.90268i	−0.0258266	−	0.0709580i	−0.951936	+	0.306297i	$0.900910\pi$
$720$		0			0
$721$			11.0564i			0.411761i
$722$	4.17697	−	18.5352i	0.155451	−	0.689808i
$723$	3.17185	+	3.17185i	0.117963	+	0.117963i
$724$	−1.58470	−	1.32972i	−0.0588949	−	0.0494187i
$725$		0			0
$726$	0.673283	+	3.81838i	0.0249879	+	0.141713i
$727$	10.4415	+	14.9120i	0.387254	+	0.553055i	0.964693	−	0.263378i	$-0.0848368\pi$
$727$	10.4415	+	14.9120i	0.387254	+	0.553055i	−0.577439	+	0.816434i	$0.695948\pi$
$728$	−4.10715	−	8.80780i	−0.152221	−	0.326439i
$729$	−14.7881	+	8.53794i	−0.547709	+	0.316220i
$730$		0			0
$731$	69.3980	−	58.2318i	2.56678	−	2.15378i
$732$	0.0284104	+	0.00248559i	0.00105008	+	9.18700e-5i
$733$	−21.0325	+	5.63564i	−0.776853	+	0.208157i	−0.625397	−	0.780307i	$-0.715063\pi$
$733$	−21.0325	+	5.63564i	−0.776853	+	0.208157i	−0.151456	+	0.988464i	$0.548396\pi$
$734$	−13.6321	−	23.6116i	−0.503172	−	0.871519i
$735$		0			0
$736$	6.80387	+	1.19971i	0.250794	+	0.0442217i
$737$	2.55595	−	3.65027i	0.0941495	−	0.134459i
$738$	11.3770	+	5.30521i	0.418795	+	0.195287i
$739$	−13.1966	+	15.7271i	−0.485445	+	0.578531i	−0.952053	−	0.305934i	$-0.901031\pi$
$739$	−13.1966	+	15.7271i	−0.485445	+	0.578531i	0.466608	+	0.884464i	$0.345476\pi$
$740$		0			0
$741$	1.40291	−	9.01038i	0.0515371	−	0.331005i
$742$	−1.06457	+	1.06457i	−0.0390815	+	0.0390815i
$743$	−18.8393	+	1.64822i	−0.691146	+	0.0604675i	−0.427317	−	0.904102i	$-0.640541\pi$
$743$	−18.8393	+	1.64822i	−0.691146	+	0.0604675i	−0.263829	+	0.964569i	$0.584986\pi$
$744$	−1.36019	+	0.495069i	−0.0498670	+	0.0181501i
$745$		0			0
$746$	−4.21837	+	23.9236i	−0.154445	+	0.875904i
$747$	11.8893	−	5.54407i	0.435007	−	0.202847i
$748$	−3.00427	+	11.2121i	−0.109847	+	0.409955i
$749$	12.5003	−	21.6512i	0.456751	−	0.791117i
$750$		0			0
$751$	13.9590	+	16.6356i	0.509370	+	0.607043i	0.958033	−	0.286658i	$-0.0925443\pi$
$751$	13.9590	+	16.6356i	0.509370	+	0.607043i	−0.448663	+	0.893701i	$0.648100\pi$
$752$	1.13075	+	4.22000i	0.0412340	+	0.153888i
$753$	−2.59375	−	0.694995i	−0.0945217	−	0.0253270i
$754$	5.70801	+	2.07754i	0.207873	+	0.0756597i
$755$		0			0
$756$	−5.15578	+	0.909103i	−0.187514	+	0.0330637i
$757$	−4.09421	+	8.78006i	−0.148806	+	0.319117i	−0.966555	−	0.256459i	$-0.917444\pi$
$757$	−4.09421	+	8.78006i	−0.148806	+	0.319117i	0.817749	+	0.575576i	$0.195222\pi$
$758$	0.919860	+	10.5140i	0.0334108	+	0.381887i
$759$	4.51441			0.163863
$760$		0			0
$761$	−38.7090			−1.40320			−0.701600	−	0.712571i	$-0.747530\pi$
$761$	−38.7090			−1.40320			−0.701600	+	0.712571i	$0.747530\pi$
$762$	0.0252487	+	0.288594i	0.000914664	+	0.0104547i
$763$	−5.68291	+	12.1870i	−0.205735	+	0.441201i
$764$	9.17320	−	1.61748i	0.331875	−	0.0585185i
$765$		0			0
$766$	1.44101	+	0.524486i	0.0520659	+	0.0189504i
$767$	60.9024	+	16.3187i	2.19906	+	0.589236i
$768$	0.114031	+	0.425568i	0.00411472	+	0.0153564i
$769$	−21.0130	−	25.0423i	−0.757747	−	0.903048i	0.239956	−	0.970784i	$-0.422867\pi$
$769$	−21.0130	−	25.0423i	−0.757747	−	0.903048i	−0.997703	+	0.0677358i	$0.978422\pi$
$770$		0			0
$771$	−2.59689	+	4.49795i	−0.0935248	+	0.161990i
$772$	−0.772455	+	2.88284i	−0.0278013	+	0.103756i
$773$	−23.2023	+	10.8194i	−0.834530	+	0.389148i	−0.792428	−	0.609966i	$-0.791183\pi$
$773$	−23.2023	+	10.8194i	−0.834530	+	0.389148i	−0.0421020	+	0.999113i	$0.513405\pi$
$774$	−5.63978	+	31.9848i	−0.202718	+	1.14967i
$775$		0			0
$776$	6.46753	−	2.35399i	0.232171	−	0.0845032i
$777$	9.64790	−	0.844082i	0.346116	−	0.0302813i
$778$	−7.51670	+	7.51670i	−0.269487	+	0.269487i
$779$	−3.77115	−	19.1330i	−0.135116	−	0.685512i
$780$		0			0
$781$	−1.07342	+	1.27925i	−0.0384100	+	0.0457752i
$782$	−49.0063	−	22.8520i	−1.75246	−	0.817186i
$783$	1.87690	−	2.68049i	0.0670749	−	0.0957929i
$784$	−2.76841	−	0.488146i	−0.0988719	−	0.0174338i
$785$		0			0
$786$	−0.245855	−	0.425834i	−0.00876937	−	0.0151890i
$787$	19.7658	−	5.29623i	0.704574	−	0.188790i	0.111296	−	0.993787i	$-0.464500\pi$
$787$	19.7658	−	5.29623i	0.704574	−	0.188790i	0.593279	+	0.804997i	$0.297833\pi$
$788$	−20.9743	−	1.83501i	−0.747178	−	0.0653696i
$789$	0.295574	−	0.248016i	0.0105227	−	0.00882962i
$790$		0			0
$791$	−12.7014	+	7.33316i	−0.451610	+	0.260737i
$792$	−1.75869	−	3.77153i	−0.0624925	−	0.134016i
$793$	0.176296	+	0.251777i	0.00626046	+	0.00894086i
$794$	−3.61778	−	20.5174i	−0.128390	−	0.728136i
$795$		0			0
$796$	12.3490	+	10.3621i	0.437700	+	0.367274i
$797$	35.1928	+	35.1928i	1.24659	+	1.24659i	0.957215	+	0.289377i	$0.0934483\pi$
$797$	35.1928	+	35.1928i	1.24659	+	1.24659i	0.289377	+	0.957215i	$0.406552\pi$
$798$	2.83453	+	2.72295i	0.100341	+	0.0963915i
$799$		−	34.1933i		−	1.20967i
$800$		0			0
$801$	−10.5043	−	28.8603i	−0.371151	−	1.01973i
$802$	−23.9760	−	16.7882i	−0.846621	−	0.592811i
$803$	−1.45020	+	1.01544i	−0.0511764	+	0.0358341i
$804$	−0.452757	+	1.24394i	−0.0159675	+	0.0438704i
$805$		0			0
$806$	−13.5102	−	7.80013i	−0.475877	−	0.274748i
$807$	0.549342	−	6.27901i	0.0193378	−	0.221032i
$808$	−0.0112913	+	0.129060i	−0.000397225	+	0.00454030i
$809$	21.5375	+	12.4347i	0.757217	+	0.437179i	0.828296	−	0.560291i	$-0.189311\pi$
$809$	21.5375	+	12.4347i	0.757217	+	0.437179i	−0.0710788	+	0.997471i	$0.522644\pi$
$810$		0			0
$811$	8.23112	−	22.6148i	0.289034	−	0.794113i	−0.707169	−	0.707045i	$-0.750028\pi$
$811$	8.23112	−	22.6148i	0.289034	−	0.794113i	0.996202	−	0.0870684i	$-0.0277499\pi$
$812$	−2.14471	+	1.50174i	−0.0752647	+	0.0527009i
$813$	−8.40338	−	5.88411i	−0.294719	−	0.206365i
$814$	5.44801	+	14.9683i	0.190953	+	0.524638i
$815$		0			0
$816$		−	3.44824i		−	0.120712i
$817$	45.2899	−	22.2365i	1.58449	−	0.777955i
$818$	−7.31632	−	7.31632i	−0.255809	−	0.255809i
$819$	−20.8889	−	17.5279i	−0.729918	−	0.612474i
$820$		0			0
$821$	8.40091	+	47.6439i	0.293194	+	1.66278i	0.674454	+	0.738317i	$0.264379\pi$
$821$	8.40091	+	47.6439i	0.293194	+	1.66278i	−0.381260	+	0.924468i	$0.624510\pi$
$822$	1.43588	+	2.05065i	0.0500820	+	0.0715245i
$823$	12.7706	+	27.3867i	0.445156	+	0.954639i	0.993006	+	0.118063i	$0.0376685\pi$
$823$	12.7706	+	27.3867i	0.445156	+	0.954639i	−0.547850	+	0.836576i	$0.684554\pi$
$824$	4.67837	−	2.70106i	0.162979	−	0.0940957i
$825$		0			0
$826$	−20.8186	+	17.4688i	−0.724370	+	0.607819i
$827$	−51.3267	−	4.49051i	−1.78480	−	0.156150i	−0.853667	−	0.520818i	$-0.825627\pi$
$827$	−51.3267	−	4.49051i	−1.78480	−	0.156150i	−0.931138	+	0.364668i	$0.881182\pi$
$828$	18.7249	−	5.01731i	0.650734	−	0.174364i
$829$	5.98724	+	10.3702i	0.207946	+	0.360172i	0.951067	−	0.308984i	$-0.0999890\pi$
$829$	5.98724	+	10.3702i	0.207946	+	0.360172i	−0.743122	+	0.669156i	$0.766656\pi$
$830$		0			0
$831$	7.83561	+	1.38163i	0.271814	+	0.0479282i
$832$	−2.72354	+	3.88962i	−0.0944219	+	0.134848i
$833$	19.9401	+	9.29822i	0.690883	+	0.322164i
$834$	5.07691	−	6.05042i	0.175799	−	0.209509i
$835$		0			0
$836$	−3.11932	+	5.66235i	−0.107884	+	0.195836i
$837$	−5.94248	+	5.94248i	−0.205402	+	0.205402i
$838$	26.9607	−	2.35875i	0.931341	−	0.0814818i
$839$	35.5528	−	12.9402i	1.22742	−	0.446744i	0.354706	−	0.934978i	$-0.384581\pi$
$839$	35.5528	−	12.9402i	1.22742	−	0.446744i	0.872713	+	0.488234i	$0.162359\pi$
$840$		0			0
$841$	−4.75162	+	26.9478i	−0.163849	+	0.929235i
$842$	−10.8982	+	5.08193i	−0.375578	+	0.175135i
$843$	−0.267053	+	0.996657i	−0.00919781	+	0.0343267i
$844$	−8.36400	+	14.4869i	−0.287901	+	0.498659i
$845$		0			0
$846$	7.87964	+	9.39059i	0.270908	+	0.322855i
$847$	−4.66174	−	17.3978i	−0.160179	−	0.597797i
$848$	0.710530	+	0.190386i	0.0243997	+	0.00653788i
$849$	0.840412	+	0.305885i	0.0288429	+	0.0104979i
$850$		0			0
$851$	−73.0752	+	12.8851i	−2.50499	+	0.441697i
$852$	0.209654	−	0.449605i	0.00718264	−	0.0154032i
$853$	−3.61755	−	41.3488i	−0.123862	−	1.41575i	−0.762869	−	0.646553i	$-0.776210\pi$
$853$	−3.61755	−	41.3488i	−0.123862	−	1.41575i	0.639007	−	0.769201i	$-0.279346\pi$
$854$	−0.132482			−0.00453345
$855$		0			0
$856$	−12.2152			−0.417508
$857$	3.94642	+	45.1077i	0.134807	+	1.54085i	0.698948	+	0.715173i	$0.253652\pi$
$857$	3.94642	+	45.1077i	0.134807	+	1.54085i	−0.564141	+	0.825679i	$0.690792\pi$
$858$	−1.31126	+	2.81200i	−0.0447656	+	0.0960000i
$859$	1.09507	−	0.193090i	0.0373633	−	0.00658815i	−0.154935	−	0.987925i	$-0.549517\pi$
$859$	1.09507	−	0.193090i	0.0373633	−	0.00658815i	0.192299	+	0.981336i	$0.438406\pi$
$860$		0			0
$861$	3.79091	+	1.37978i	0.129194	+	0.0470227i
$862$	16.4958	+	4.42004i	0.561849	+	0.150547i
$863$	−9.44218	−	35.2387i	−0.321416	−	1.19954i	−0.917866	−	0.396890i	$-0.870089\pi$
$863$	−9.44218	−	35.2387i	−0.321416	−	1.19954i	0.596451	−	0.802650i	$-0.296577\pi$
$864$	1.64422	+	1.95951i	0.0559377	+	0.0666639i
$865$		0			0
$866$	13.6008	−	23.5573i	0.462175	−	0.800511i
$867$	−5.04646	+	18.8336i	−0.171387	+	0.639624i
$868$	6.09416	−	2.84175i	0.206849	−	0.0964554i
$869$	3.73577	−	21.1866i	0.126727	−	0.718705i
$870$		0			0
$871$	−13.4066	+	4.87959i	−0.454264	+	0.165339i
$872$	6.54513	−	0.572624i	0.221646	−	0.0193915i
$873$	13.6555	−	13.6555i	0.462169	−	0.462169i
$874$	−23.4532	−	18.8905i	−0.793318	−	0.638981i
$875$		0			0
$876$	0.338052	−	0.402875i	0.0114217	−	0.0136119i
$877$	8.64420	+	4.03085i	0.291894	+	0.136112i	0.563049	−	0.826423i	$-0.309628\pi$
$877$	8.64420	+	4.03085i	0.291894	+	0.136112i	−0.271156	+	0.962535i	$0.587406\pi$
$878$	12.5679	−	17.9488i	0.424146	−	0.605743i
$879$	6.65039	+	1.17264i	0.224312	+	0.0395523i
$880$		0			0
$881$	−3.76827	−	6.52684i	−0.126956	−	0.219895i	0.795540	−	0.605902i	$-0.207187\pi$
$881$	−3.76827	−	6.52684i	−0.126956	−	0.219895i	−0.922496	+	0.386007i	$0.873854\pi$
$882$	−7.61892	+	2.04148i	−0.256543	+	0.0687404i
$883$	34.4459	+	3.01363i	1.15920	+	0.101417i	0.650485	−	0.759519i	$-0.274566\pi$
$883$	34.4459	+	3.01363i	1.15920	+	0.101417i	0.508713	+	0.860936i	$0.330121\pi$
$884$	28.4688	−	23.8881i	0.957509	−	0.803445i
$885$		0			0
$886$	8.76267	−	5.05913i	0.294388	−	0.169965i
$887$	−10.2035	−	21.8815i	−0.342600	−	0.734707i	0.657220	−	0.753699i	$-0.271732\pi$
$887$	−10.2035	−	21.8815i	−0.342600	−	0.734707i	−0.999820	+	0.0189915i	$0.993954\pi$
$888$	−2.71413	−	3.87618i	−0.0910803	−	0.130076i
$889$	−0.233688	−	1.32531i	−0.00783766	−	0.0444496i
$890$		0			0
$891$	−8.28311	−	6.95036i	−0.277495	−	0.232846i
$892$	−18.3995	−	18.3995i	−0.616062	−	0.616062i
$893$	4.55858	−	18.4898i	0.152547	−	0.618737i
$894$			1.68255i			0.0562730i
$895$		0			0
$896$	−0.700004	−	1.92325i	−0.0233855	−	0.0642511i
$897$	−11.8396	−	8.29017i	−0.395312	−	0.276801i
$898$	28.5819	−	20.0133i	0.953790	−	0.667851i
$899$	−1.43746	+	3.94940i	−0.0479421	+	0.131720i
$900$		0			0
$901$	−4.98587	−	2.87860i	−0.166104	−	0.0958999i
$902$	−0.578297	+	6.60996i	−0.0192552	+	0.220088i
$903$	−0.909685	+	10.3977i	−0.0302724	+	0.346015i
$904$	6.20588	+	3.58296i	0.206404	+	0.119168i
$905$		0			0
$906$	1.04024	−	2.85803i	0.0345596	−	0.0949518i
$907$	29.2516	−	20.4822i	0.971284	−	0.680100i	0.0237376	−	0.999718i	$-0.492443\pi$
$907$	29.2516	−	20.4822i	0.971284	−	0.680100i	0.947547	+	0.319618i	$0.103554\pi$
$908$	8.42613	+	5.90004i	0.279631	+	0.195800i
$909$	0.124328	+	0.341588i	0.00412370	+	0.0113298i
$910$		0			0
$911$			0.847344i			0.0280738i	0.999901	+	0.0140369i	$0.00446823\pi$
$911$			0.847344i			0.0280738i	−0.999901	+	0.0140369i	$0.995532\pi$
$912$	0.459712	−	1.86461i	0.0152226	−	0.0617434i
$913$	4.90306	+	4.90306i	0.162267	+	0.162267i
$914$	6.43455	+	5.39923i	0.212836	+	0.178591i
$915$		0			0
$916$	−2.78352	−	15.7861i	−0.0919700	−	0.521588i
$917$	1.31016	+	1.87110i	0.0432654	+	0.0617893i
$918$	−8.46085	−	18.1443i	−0.279250	−	0.598853i
$919$	32.0833	−	18.5233i	1.05833	−	0.611027i	0.133360	−	0.991068i	$-0.457423\pi$
$919$	32.0833	−	18.5233i	1.05833	−	0.611027i	0.924970	+	0.380041i	$0.124090\pi$
$920$		0			0
$921$	1.64623	−	1.38135i	0.0542452	−	0.0455171i
$922$	21.5433	+	1.88480i	0.709492	+	0.0620725i
$923$	5.16437	−	1.38379i	0.169987	−	0.0455479i
$924$	−0.668676	−	1.15818i	−0.0219978	−	0.0381013i
$925$		0			0
$926$	−5.48616	−	0.967358i	−0.180286	−	0.0317893i
$927$	8.69411	−	12.4165i	0.285552	−	0.407811i
$928$	1.15940	+	0.540635i	0.0380590	+	0.0177472i
$929$	−14.6216	+	17.4253i	−0.479719	+	0.571706i	−0.950572	−	0.310505i	$-0.899502\pi$
$929$	−14.6216	+	17.4253i	−0.479719	+	0.571706i	0.470853	+	0.882212i	$0.343946\pi$
$930$		0			0
$931$	9.54285	+	7.68632i	0.312754	+	0.251909i
$932$	6.56475	−	6.56475i	0.215036	−	0.215036i
$933$	−5.35499	+	0.468501i	−0.175314	+	0.0153380i
$934$	−3.73852	+	1.36071i	−0.122328	+	0.0445238i
$935$		0			0
$936$	−2.31358	+	13.1209i	−0.0756216	+	0.428871i
$937$	24.2435	−	11.3049i	0.792001	−	0.369316i	0.0158589	−	0.999874i	$-0.494952\pi$
$937$	24.2435	−	11.3049i	0.792001	−	0.369316i	0.776142	+	0.630558i	$0.217174\pi$
$938$	1.59160	−	5.93993i	0.0519676	−	0.193946i
$939$	−4.07745	+	7.06236i	−0.133063	+	0.230471i
$940$		0			0
$941$	28.1950	+	33.6015i	0.919132	+	1.09538i	0.995159	+	0.0982731i	$0.0313319\pi$
$941$	28.1950	+	33.6015i	0.919132	+	1.09538i	−0.0760275	+	0.997106i	$0.524224\pi$
$942$	−0.762766	−	2.84668i	−0.0248523	−	0.0927499i
$943$	−29.8560	−	7.99989i	−0.972245	−	0.260512i
$944$	12.4777	+	4.54150i	0.406114	+	0.147813i
$945$		0			0
$946$	−16.9061	+	2.98101i	−0.549665	+	0.0969209i
$947$	19.7669	−	42.3903i	0.642339	−	1.37750i	−0.267912	−	0.963443i	$-0.586334\pi$
$947$	19.7669	−	42.3903i	0.642339	−	1.37750i	0.910251	−	0.414057i	$-0.135889\pi$
$948$	0.557005	+	6.36659i	0.0180907	+	0.206777i
$949$	5.66806			0.183993
$950$		0			0
$951$	−6.86753			−0.222695
$952$	1.39610	+	15.9575i	0.0452479	+	0.517186i
$953$	9.29452	−	19.9322i	0.301079	−	0.645666i	−0.696321	−	0.717731i	$-0.745181\pi$
$953$	9.29452	−	19.9322i	0.301079	−	0.645666i	0.997400	+	0.0720645i	$0.0229587\pi$
$954$	2.03264	−	0.358409i	0.0658092	−	0.0116039i
$955$		0			0
$956$	17.2894	+	6.29284i	0.559180	+	0.203525i
$957$	0.807414	+	0.216346i	0.0261000	+	0.00699347i
$958$	−2.99134	−	11.1638i	−0.0966459	−	0.360687i
$959$	−7.47511	−	8.90849i	−0.241384	−	0.287670i
$960$		0			0
$961$	−10.1031	+	17.4990i	−0.325905	+	0.564484i
$962$	13.1994	−	49.2608i	0.425565	−	1.58823i
$963$	−31.0633	+	14.4851i	−1.00100	+	0.466775i
$964$	−1.76796	+	10.0266i	−0.0569423	+	0.322936i
$965$		0			0
$966$	5.85415	−	2.13074i	0.188354	−	0.0685553i
$967$	7.85294	−	0.687044i	0.252534	−	0.0220938i	0.0398140	−	0.999207i	$-0.487323\pi$
$967$	7.85294	−	0.687044i	0.252534	−	0.0220938i	0.212720	+	0.977113i	$0.431768\pi$
$968$	−6.22283	+	6.22283i	−0.200009	+	0.200009i
$969$	−7.25246	+	13.1650i	−0.232983	+	0.422922i
$970$		0			0
$971$	−30.6024	+	36.4705i	−0.982077	+	1.17039i	0.00329777	+	0.999995i	$0.498950\pi$
$971$	−30.6024	+	36.4705i	−0.982077	+	1.17039i	−0.985375	+	0.170400i	$0.945494\pi$
$972$	9.86607	+	4.60063i	0.316455	+	0.147565i
$973$	−21.0449	+	30.0552i	−0.674669	+	0.963527i
$974$	20.0192	+	3.52993i	0.641457	+	0.113106i
$975$		0			0
$976$	0.0323652	+	0.0560582i	0.00103598	+	0.00179438i
$977$	−37.7506	+	10.1152i	−1.20775	+	0.323615i	−0.805878	−	0.592081i	$-0.798307\pi$
$977$	−37.7506	+	10.1152i	−1.20775	+	0.323615i	−0.401871	+	0.915696i	$0.631640\pi$
$978$	1.87132	+	0.163719i	0.0598383	+	0.00523517i
$979$	12.4357	−	10.4348i	0.397446	−	0.333497i
$980$		0			0
$981$	15.9652	−	9.21752i	0.509730	−	0.294293i
$982$	3.31766	+	7.11475i	0.105871	+	0.227041i
$983$	−4.86152	−	6.94296i	−0.155058	−	0.221446i	0.734105	−	0.679036i	$-0.237602\pi$
$983$	−4.86152	−	6.94296i	−0.155058	−	0.221446i	−0.889164	+	0.457589i	$0.848713\pi$
$984$	−0.342278	−	1.94115i	−0.0109114	−	0.0618817i
$985$		0			0
$986$	−7.66976	−	6.43569i	−0.244255	−	0.204954i
$987$	2.78566	+	2.78566i	0.0886684	+	0.0886684i
$988$	18.5790	−	9.12195i	0.591077	−	0.290208i
$989$		−	79.9697i		−	2.54289i
$990$		0			0
$991$	4.72876	+	12.9922i	0.150214	+	0.412710i	0.991862	−	0.127317i	$-0.0406364\pi$
$991$	4.72876	+	12.9922i	0.150214	+	0.412710i	−0.841648	+	0.540027i	$0.818414\pi$
$992$	−2.69125	−	1.88443i	−0.0854472	−	0.0598308i
$993$	12.9599	−	9.07461i	0.411270	−	0.287974i
$994$	−0.788190	+	2.16554i	−0.0249999	+	0.0686866i
$995$		0			0
$996$	−1.78388	−	1.02992i	−0.0565244	−	0.0326344i
$997$	2.18952	−	25.0263i	0.0693427	−	0.792590i	−0.879306	−	0.476258i	$-0.841993\pi$
$997$	2.18952	−	25.0263i	0.0693427	−	0.792590i	0.948648	−	0.316333i	$-0.102452\pi$
$998$	−2.98374	+	34.1043i	−0.0944485	+	1.07955i
$999$	−23.7924	−	13.7366i	−0.752759	−	0.434606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.193.3		120
5.2	odd	4	inner	950.2.bb.e.307.8		120
5.3	odd	4		190.2.r.a.117.3	yes	120
5.4	even	2		190.2.r.a.3.8	✓	120
19.13	odd	18	inner	950.2.bb.e.393.8		120
95.13	even	36		190.2.r.a.127.8	yes	120
95.32	even	36	inner	950.2.bb.e.507.3		120
95.89	odd	18		190.2.r.a.13.3	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.3.8	✓	120	5.4	even	2
190.2.r.a.13.3	yes	120	95.89	odd	18
190.2.r.a.117.3	yes	120	5.3	odd	4
190.2.r.a.127.8	yes	120	95.13	even	36
950.2.bb.e.193.3		120	1.1	even	1	trivial
950.2.bb.e.307.8		120	5.2	odd	4	inner
950.2.bb.e.393.8		120	19.13	odd	18	inner
950.2.bb.e.507.3		120	95.32	even	36	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.186197 + 0.399301i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.414010 + 0.150687i) q^{6} +(-1.97694 - 0.529719i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.80359 + 2.14944i) q^{9} +O(q^{10})\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.186197 + 0.399301i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.414010 + 0.150687i) q^{6} +(-1.97694 - 0.529719i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.80359 + 2.14944i) q^{9} +(-0.741552 + 1.28441i) q^{11} +(0.114031 - 0.425568i) q^{12} +(4.30347 - 2.00674i) q^{13} +(-0.355401 + 2.01558i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-7.79680 + 0.682131i) q^{17} +(1.98406 - 1.98406i) q^{18} +(-4.30701 - 0.670597i) q^{19} +(0.579617 - 0.690761i) q^{21} +(1.34415 + 0.626787i) q^{22} +(-3.96274 + 5.65938i) q^{23} +(-0.433887 - 0.0765060i) q^{24} +(-2.37418 - 4.11219i) q^{26} +(-2.47080 + 0.662049i) q^{27} +(2.03889 + 0.178380i) q^{28} +(-0.979963 + 0.822287i) q^{29} +(2.84525 - 1.64270i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-0.374790 - 0.535255i) q^{33} +(1.35907 + 7.70767i) q^{34} +(-2.14944 - 1.80359i) q^{36} +(7.59450 + 7.59450i) q^{37} +(-0.292664 + 4.34906i) q^{38} +2.09203i q^{39} +(1.53015 + 4.20406i) q^{41} +(-0.738650 - 0.517208i) q^{42} +(-9.48169 + 6.63915i) q^{43} +(0.507251 - 1.39366i) q^{44} +(5.98322 + 3.45441i) q^{46} +(-0.380772 + 4.35224i) q^{47} +(-0.0383991 + 0.438904i) q^{48} +(-2.43450 - 1.40556i) q^{49} +(1.17937 - 3.24028i) q^{51} +(-3.88962 + 2.72354i) q^{52} +(0.602564 + 0.421920i) q^{53} +(0.874874 + 2.40370i) q^{54} -2.04668i q^{56} +(1.06972 - 1.59493i) q^{57} +(0.904567 + 0.904567i) q^{58} +(10.1719 + 8.53523i) q^{59} +(0.0112403 + 0.0637470i) q^{61} +(-1.88443 - 2.69125i) q^{62} +(-2.42699 - 5.20469i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-0.500553 + 0.420014i) q^{66} +(-2.99318 - 0.261869i) q^{67} +(7.55989 - 2.02567i) q^{68} +(-1.52195 - 2.63609i) q^{69} +(1.10887 + 0.195524i) q^{71} +(-1.60939 + 2.29845i) q^{72} +(1.08185 + 0.504475i) q^{73} +(6.90370 - 8.22751i) q^{74} +(4.35802 - 0.0874950i) q^{76} +(2.14637 - 2.14637i) q^{77} +(2.08407 - 0.182332i) q^{78} +(-13.6309 + 4.96123i) q^{79} +(-1.26601 + 7.17992i) q^{81} +(4.05470 - 1.89074i) q^{82} +(1.21006 - 4.51600i) q^{83} +(-0.450862 + 0.780916i) q^{84} +(7.44027 + 8.86697i) q^{86} +(-0.145874 - 0.544408i) q^{87} +(-1.43257 - 0.383855i) q^{88} +(-10.2856 - 3.74366i) q^{89} +(-9.57069 + 1.68757i) q^{91} +(2.91980 - 6.26152i) q^{92} +(0.126157 + 1.44198i) q^{93} +4.36886 q^{94} +0.440580 q^{96} +(-0.599858 - 6.85641i) q^{97} +(-1.18803 + 2.54774i) q^{98} +(-4.09820 + 0.722624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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Database

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