LMFDB - Embedded newform 1110.2.ba.b.619.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.8
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.b.529.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.653296 - 2.13851i) q^{5} +1.00000i q^{6} +(3.20005 - 1.84755i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.653296 - 2.13851i) q^{5} +1.00000i q^{6} +(3.20005 - 1.84755i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.52535 - 1.63502i) q^{10} +4.44239 q^{11} +(0.866025 + 0.500000i) q^{12} +(3.09657 + 5.36341i) q^{13} -3.69510i q^{14} +(0.503482 + 2.17865i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.67263 + 2.89708i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(4.88936 - 2.82287i) q^{19} +(-2.17865 + 0.503482i) q^{20} +(-1.84755 + 3.20005i) q^{21} +(2.22120 - 3.84723i) q^{22} -3.31793 q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.14641 - 2.79415i) q^{25} +6.19314 q^{26} +1.00000i q^{27} +(-3.20005 - 1.84755i) q^{28} +0.108323i q^{29} +(2.13851 + 0.653296i) q^{30} +3.58380i q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.84723 + 2.22120i) q^{33} +(1.67263 + 2.89708i) q^{34} +(-1.86042 - 8.05033i) q^{35} -1.00000 q^{36} +(1.62326 - 5.86217i) q^{37} -5.64574i q^{38} +(-5.36341 - 3.09657i) q^{39} +(-0.653296 + 2.13851i) q^{40} +(0.667426 + 1.15602i) q^{41} +(1.84755 + 3.20005i) q^{42} +1.49655 q^{43} +(-2.22120 - 3.84723i) q^{44} +(-1.52535 - 1.63502i) q^{45} +(-1.65897 + 2.87341i) q^{46} -1.22763i q^{47} -1.00000i q^{48} +(3.32690 - 5.76236i) q^{49} +(-4.49301 + 2.19382i) q^{50} -3.34526i q^{51} +(3.09657 - 5.36341i) q^{52} +(-7.70341 - 4.44757i) q^{53} +(0.866025 + 0.500000i) q^{54} +(2.90220 - 9.50008i) q^{55} +(-3.20005 + 1.84755i) q^{56} +(-2.82287 + 4.88936i) q^{57} +(0.0938106 + 0.0541616i) q^{58} +(-0.292750 - 0.169019i) q^{59} +(1.63502 - 1.52535i) q^{60} +(11.4397 - 6.60469i) q^{61} +(3.10366 + 1.79190i) q^{62} -3.69510i q^{63} +1.00000 q^{64} +(13.4927 - 3.11813i) q^{65} +4.44239i q^{66} +(-12.7735 + 7.37478i) q^{67} +3.34526 q^{68} +(2.87341 - 1.65897i) q^{69} +(-7.90200 - 2.41400i) q^{70} +(2.66182 + 4.61040i) q^{71} +(-0.500000 + 0.866025i) q^{72} -2.67315i q^{73} +(-4.26515 - 4.33687i) q^{74} +(4.98797 + 0.346604i) q^{75} +(-4.88936 - 2.82287i) q^{76} +(14.2159 - 8.20755i) q^{77} +(-5.36341 + 3.09657i) q^{78} +(-4.87431 + 2.81418i) q^{79} +(1.52535 + 1.63502i) q^{80} +(-0.500000 - 0.866025i) q^{81} +1.33485 q^{82} +(5.20372 + 3.00437i) q^{83} +3.69510 q^{84} +(5.10271 + 5.46959i) q^{85} +(0.748273 - 1.29605i) q^{86} +(-0.0541616 - 0.0938106i) q^{87} -4.44239 q^{88} +(-13.9095 - 8.03066i) q^{89} +(-2.17865 + 0.503482i) q^{90} +(19.8184 + 11.4421i) q^{91} +(1.65897 + 2.87341i) q^{92} +(-1.79190 - 3.10366i) q^{93} +(-1.06316 - 0.613817i) q^{94} +(-2.84253 - 12.3001i) q^{95} +(-0.866025 - 0.500000i) q^{96} +12.8116 q^{97} +(-3.32690 - 5.76236i) q^{98} +(2.22120 - 3.84723i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.653296	−	2.13851i	0.292163	−	0.956369i
$5$	0.653296	−	2.13851i	0.292163	−	0.956369i
$6$			1.00000i			0.408248i
$7$	3.20005	−	1.84755i	1.20951	−	0.698309i	0.246855	−	0.969052i	$-0.420603\pi$
$7$	3.20005	−	1.84755i	1.20951	−	0.698309i	0.962652	+	0.270743i	$0.0872694\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.52535	−	1.63502i	−0.482359	−	0.517040i
$11$	4.44239			1.33943			0.669716	−	0.742617i	$-0.266416\pi$
$11$	4.44239			1.33943			0.669716	+	0.742617i	$0.266416\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	3.09657	+	5.36341i	0.858833	+	1.48754i	0.873043	+	0.487644i	$0.162144\pi$
$13$	3.09657	+	5.36341i	0.858833	+	1.48754i	−0.0142091	+	0.999899i	$0.504523\pi$
$14$		−	3.69510i		−	0.987558i
$15$	0.503482	+	2.17865i	0.129998	+	0.562524i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.67263	+	2.89708i	−0.405673	+	0.702646i	−0.994400	−	0.105686i	$-0.966296\pi$
$17$	−1.67263	+	2.89708i	−0.405673	+	0.702646i	0.588727	+	0.808332i	$0.299629\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	4.88936	−	2.82287i	1.12170	−	0.647611i	0.179862	−	0.983692i	$-0.442435\pi$
$19$	4.88936	−	2.82287i	1.12170	−	0.647611i	0.941833	+	0.336081i	$0.109101\pi$
$20$	−2.17865	+	0.503482i	−0.487160	+	0.112582i
$21$	−1.84755	+	3.20005i	−0.403169	+	0.698309i
$22$	2.22120	−	3.84723i	0.473561	−	0.820231i
$23$	−3.31793			−0.691837			−0.345918	−	0.938265i	$-0.612433\pi$
$23$	−3.31793			−0.691837			−0.345918	+	0.938265i	$0.612433\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−4.14641	−	2.79415i	−0.829282	−	0.558831i
$26$	6.19314			1.21457
$27$			1.00000i			0.192450i
$28$	−3.20005	−	1.84755i	−0.604753	−	0.349155i
$29$			0.108323i			0.0201151i	0.999949	+	0.0100575i	$0.00320147\pi$
$29$			0.108323i			0.0201151i	−0.999949	+	0.0100575i	$0.996799\pi$
$30$	2.13851	+	0.653296i	0.390436	+	0.119275i
$31$			3.58380i			0.643670i	0.946796	+	0.321835i	$0.104300\pi$
$31$			3.58380i			0.643670i	−0.946796	+	0.321835i	$0.895700\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.84723	+	2.22120i	−0.669716	+	0.386661i
$34$	1.67263	+	2.89708i	0.286854	+	0.496846i
$35$	−1.86042	−	8.05033i	−0.314468	−	1.36075i
$36$	−1.00000			−0.166667
$37$	1.62326	−	5.86217i	0.266863	−	0.963734i
$37$	1.62326	−	5.86217i	0.266863	−	0.963734i
$38$		−	5.64574i		−	0.915861i
$39$	−5.36341	−	3.09657i	−0.858833	−	0.495848i
$40$	−0.653296	+	2.13851i	−0.103295	+	0.338127i
$41$	0.667426	+	1.15602i	0.104234	+	0.180539i	0.913425	−	0.407007i	$-0.133427\pi$
$41$	0.667426	+	1.15602i	0.104234	+	0.180539i	−0.809191	+	0.587546i	$0.800094\pi$
$42$	1.84755	+	3.20005i	0.285084	+	0.493779i
$43$	1.49655			0.228221			0.114111	−	0.993468i	$-0.463598\pi$
$43$	1.49655			0.228221			0.114111	+	0.993468i	$0.463598\pi$
$44$	−2.22120	−	3.84723i	−0.334858	−	0.579991i
$45$	−1.52535	−	1.63502i	−0.227386	−	0.243735i
$46$	−1.65897	+	2.87341i	−0.244601	+	0.423662i
$47$		−	1.22763i		−	0.179069i	−0.995984	−	0.0895343i	$-0.971462\pi$
$47$		−	1.22763i		−	0.179069i	0.995984	−	0.0895343i	$-0.0285379\pi$
$48$		−	1.00000i		−	0.144338i
$49$	3.32690	−	5.76236i	0.475271	−	0.823194i
$50$	−4.49301	+	2.19382i	−0.635408	+	0.310253i
$51$		−	3.34526i		−	0.468431i
$52$	3.09657	−	5.36341i	0.429417	−	0.743772i
$53$	−7.70341	−	4.44757i	−1.05814	−	0.610920i	−0.133226	−	0.991086i	$-0.542534\pi$
$53$	−7.70341	−	4.44757i	−1.05814	−	0.610920i	−0.924919	+	0.380165i	$0.875867\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	2.90220	−	9.50008i	0.391332	−	1.28099i
$56$	−3.20005	+	1.84755i	−0.427625	+	0.246890i
$57$	−2.82287	+	4.88936i	−0.373899	+	0.647611i
$58$	0.0938106	+	0.0541616i	0.0123179	+	0.00711176i
$59$	−0.292750	−	0.169019i	−0.0381128	−	0.0220044i	0.480823	−	0.876818i	$-0.340338\pi$
$59$	−0.292750	−	0.169019i	−0.0381128	−	0.0220044i	−0.518935	+	0.854814i	$0.673671\pi$
$60$	1.63502	−	1.52535i	0.211081	−	0.196922i
$61$	11.4397	−	6.60469i	1.46470	−	0.845644i	0.465476	−	0.885060i	$-0.345883\pi$
$61$	11.4397	−	6.60469i	1.46470	−	0.845644i	0.999223	+	0.0394160i	$0.0125497\pi$
$62$	3.10366	+	1.79190i	0.394166	+	0.227572i
$63$		−	3.69510i		−	0.465539i
$64$	1.00000			0.125000
$65$	13.4927	−	3.11813i	1.67356	−	0.386756i
$66$			4.44239i			0.546821i
$67$	−12.7735	+	7.37478i	−1.56053	+	0.900972i	−0.563327	+	0.826234i	$0.690479\pi$
$67$	−12.7735	+	7.37478i	−1.56053	+	0.900972i	−0.997203	+	0.0747384i	$0.976188\pi$
$68$	3.34526			0.405673
$69$	2.87341	−	1.65897i	0.345918	−	0.199716i
$70$	−7.90200	−	2.41400i	−0.944470	−	0.288528i
$71$	2.66182	+	4.61040i	0.315899	+	0.547154i	0.979628	−	0.200819i	$-0.0643605\pi$
$71$	2.66182	+	4.61040i	0.315899	+	0.547154i	−0.663729	+	0.747973i	$0.731027\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$		−	2.67315i		−	0.312868i	−0.987688	−	0.156434i	$-0.950000\pi$
$73$		−	2.67315i		−	0.312868i	0.987688	−	0.156434i	$-0.0499999\pi$
$74$	−4.26515	−	4.33687i	−0.495814	−	0.504151i
$75$	4.98797	+	0.346604i	0.575961	+	0.0400224i
$76$	−4.88936	−	2.82287i	−0.560848	−	0.323806i
$77$	14.2159	−	8.20755i	1.62005	−	0.935338i
$78$	−5.36341	+	3.09657i	−0.607287	+	0.350617i
$79$	−4.87431	+	2.81418i	−0.548403	+	0.316620i	−0.748478	−	0.663160i	$-0.769215\pi$
$79$	−4.87431	+	2.81418i	−0.548403	+	0.316620i	0.200075	+	0.979781i	$0.435881\pi$
$80$	1.52535	+	1.63502i	0.170540	+	0.182801i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.33485			0.147410
$83$	5.20372	+	3.00437i	0.571182	+	0.329772i	0.757621	−	0.652694i	$-0.226361\pi$
$83$	5.20372	+	3.00437i	0.571182	+	0.329772i	−0.186439	+	0.982466i	$0.559695\pi$
$84$	3.69510			0.403169
$85$	5.10271	+	5.46959i	0.553466	+	0.593260i
$86$	0.748273	−	1.29605i	0.0806884	−	0.139756i
$87$	−0.0541616	−	0.0938106i	−0.00580673	−	0.0100575i
$88$	−4.44239			−0.473561
$89$	−13.9095	−	8.03066i	−1.47440	−	0.851248i	−0.474820	−	0.880083i	$-0.657487\pi$
$89$	−13.9095	−	8.03066i	−1.47440	−	0.851248i	−0.999584	+	0.0288348i	$0.990820\pi$
$90$	−2.17865	+	0.503482i	−0.229650	+	0.0530716i
$91$	19.8184	+	11.4421i	2.07753	+	1.19946i
$92$	1.65897	+	2.87341i	0.172959	+	0.299574i
$93$	−1.79190	−	3.10366i	−0.185811	−	0.321835i
$94$	−1.06316	−	0.613817i	−0.109657	−	0.0633103i
$95$	−2.84253	−	12.3001i	−0.291637	−	1.26196i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	12.8116			1.30082			0.650410	−	0.759583i	$-0.274597\pi$
$97$	12.8116			1.30082			0.650410	+	0.759583i	$0.274597\pi$
$98$	−3.32690	−	5.76236i	−0.336068	−	0.582086i
$99$	2.22120	−	3.84723i	0.223239	−	0.386661i
$100$	−0.346604	+	4.98797i	−0.0346604	+	0.498797i
$101$	−10.2462			−1.01953			−0.509766	−	0.860313i	$-0.670268\pi$
$101$	−10.2462			−1.01953			−0.509766	+	0.860313i	$0.670268\pi$
$102$	−2.89708	−	1.67263i	−0.286854	−	0.165615i
$103$	−5.94305			−0.585586			−0.292793	−	0.956176i	$-0.594585\pi$
$103$	−5.94305			−0.585586			−0.292793	+	0.956176i	$0.594585\pi$
$104$	−3.09657	−	5.36341i	−0.303643	−	0.525926i
$105$	5.63633	+	6.04158i	0.550050	+	0.589598i
$106$	−7.70341	+	4.44757i	−0.748221	+	0.431986i
$107$	−9.10060	+	5.25423i	−0.879788	+	0.507946i	−0.870588	−	0.492012i	$-0.836262\pi$
$107$	−9.10060	+	5.25423i	−0.879788	+	0.507946i	−0.00919937	+	0.999958i	$0.502928\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−1.27969	−	0.738832i	−0.122573	−	0.0707673i	0.437460	−	0.899238i	$-0.355878\pi$
$109$	−1.27969	−	0.738832i	−0.122573	−	0.0707673i	−0.560033	+	0.828471i	$0.689211\pi$
$110$	−6.77621	−	7.26342i	−0.646087	−	0.692540i
$111$	1.52530	+	5.88842i	0.144775	+	0.558904i
$112$			3.69510i			0.349155i
$113$	3.19271	−	5.52994i	0.300345	−	0.520213i	−0.675869	−	0.737022i	$-0.736231\pi$
$113$	3.19271	−	5.52994i	0.300345	−	0.520213i	0.976214	+	0.216809i	$0.0695647\pi$
$114$	2.82287	+	4.88936i	0.264386	+	0.457930i
$115$	−2.16759	+	7.09542i	−0.202129	+	0.661651i
$116$	0.0938106	−	0.0541616i	0.00871009	−	0.00502877i
$117$	6.19314			0.572556
$118$	−0.292750	+	0.169019i	−0.0269498	+	0.0155595i
$119$			12.3611i			1.13314i
$120$	−0.503482	−	2.17865i	−0.0459614	−	0.198882i
$121$	8.73486			0.794078
$122$		−	13.2094i		−	1.19592i
$123$	−1.15602	−	0.667426i	−0.104234	−	0.0601797i
$124$	3.10366	−	1.79190i	0.278717	−	0.160917i
$125$	−8.68414	+	7.04171i	−0.776734	+	0.629829i
$126$	−3.20005	−	1.84755i	−0.285084	−	0.164593i
$127$	−15.2469	−	8.80279i	−1.35294	−	0.781122i	−0.364282	−	0.931289i	$-0.618685\pi$
$127$	−15.2469	−	8.80279i	−1.35294	−	0.781122i	−0.988661	+	0.150167i	$0.952019\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.29605	+	0.748273i	−0.114111	+	0.0658818i
$130$	4.04595	−	13.2441i	0.354853	−	1.16158i
$131$	−18.6551	−	10.7705i	−1.62990	−	0.941025i	−0.984120	−	0.177504i	$-0.943198\pi$
$131$	−18.6551	−	10.7705i	−1.62990	−	0.941025i	−0.645783	−	0.763521i	$-0.723469\pi$
$132$	3.84723	+	2.22120i	0.334858	+	0.193330i
$133$	10.4308	−	18.0667i	0.904466	−	1.56658i
$134$			14.7496i			1.27417i
$135$	2.13851	+	0.653296i	0.184053	+	0.0562268i
$136$	1.67263	−	2.89708i	0.143427	−	0.248423i
$137$			10.1403i			0.866343i	0.901312	+	0.433171i	$0.142606\pi$
$137$			10.1403i			0.866343i	−0.901312	+	0.433171i	$0.857394\pi$
$138$		−	3.31793i		−	0.282441i
$139$	−3.23928	+	5.61060i	−0.274752	+	0.475885i	−0.970073	−	0.242815i	$-0.921929\pi$
$139$	−3.23928	+	5.61060i	−0.274752	+	0.475885i	0.695320	+	0.718700i	$0.255263\pi$
$140$	−6.04158	+	5.63633i	−0.510607	+	0.476357i
$141$	0.613817	+	1.06316i	0.0516927	+	0.0895343i
$142$	5.32363			0.446749
$143$	13.7562	+	23.8264i	1.15035	+	1.99246i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	0.231650	+	0.0707671i	0.0192374	+	0.00587689i
$146$	−2.31501	−	1.33657i	−0.191592	−	0.110616i
$147$			6.65380i			0.548796i
$148$	−5.88842	+	1.52530i	−0.484025	+	0.125378i
$149$	1.79951			0.147421			0.0737107	−	0.997280i	$-0.476516\pi$
$149$	1.79951			0.147421			0.0737107	+	0.997280i	$0.476516\pi$
$150$	2.79415	−	4.14641i	0.228142	−	0.338553i
$151$	5.78284	+	10.0162i	0.470601	+	0.815104i	0.999435	−	0.0336210i	$-0.0107039\pi$
$151$	5.78284	+	10.0162i	0.470601	+	0.815104i	−0.528834	+	0.848725i	$0.677371\pi$
$152$	−4.88936	+	2.82287i	−0.396579	+	0.228965i
$153$	1.67263	+	2.89708i	0.135224	+	0.234215i
$154$		−	16.4151i		−	1.32277i
$155$	7.66398	+	2.34128i	0.615586	+	0.188056i
$156$			6.19314i			0.495848i
$157$	17.0546	+	9.84650i	1.36111	+	0.785836i	0.989771	−	0.142662i	$-0.0455661\pi$
$157$	17.0546	+	9.84650i	1.36111	+	0.785836i	0.371337	+	0.928498i	$0.378899\pi$
$158$			5.62837i			0.447769i
$159$	8.89513			0.705430
$160$	2.17865	−	0.503482i	0.172237	−	0.0398037i
$161$	−10.6176	+	6.13005i	−0.836781	+	0.483116i
$162$	−1.00000			−0.0785674
$163$	−8.25810	+	14.3034i	−0.646824	+	1.12033i	0.337053	+	0.941486i	$0.390570\pi$
$163$	−8.25810	+	14.3034i	−0.646824	+	1.12033i	−0.983877	+	0.178847i	$0.942763\pi$
$164$	0.667426	−	1.15602i	0.0521172	−	0.0902696i
$165$	2.23666	+	9.67841i	0.174124	+	0.753463i
$166$	5.20372	−	3.00437i	0.403887	−	0.233184i
$167$	−5.60293	−	9.70456i	−0.433568	−	0.750961i	0.563610	−	0.826041i	$-0.309412\pi$
$167$	−5.60293	−	9.70456i	−0.433568	−	0.750961i	−0.997178	+	0.0750799i	$0.976079\pi$
$168$	1.84755	−	3.20005i	0.142542	−	0.246890i
$169$	−12.6775	+	21.9580i	−0.975190	+	1.68908i
$170$	7.28815	−	1.68428i	0.558976	−	0.129178i
$171$		−	5.64574i		−	0.431741i
$172$	−0.748273	−	1.29605i	−0.0570553	−	0.0988227i
$173$	−12.4041	−	7.16151i	−0.943066	−	0.544480i	−0.0521462	−	0.998639i	$-0.516606\pi$
$173$	−12.4041	−	7.16151i	−0.943066	−	0.544480i	−0.890920	+	0.454160i	$0.849940\pi$
$174$	−0.108323			−0.00821195
$175$	−18.4311	−	1.28074i	−1.39326	−	0.0968147i
$176$	−2.22120	+	3.84723i	−0.167429	+	0.289996i
$177$	0.338038			0.0254085
$178$	−13.9095	+	8.03066i	−1.04256	+	0.601923i
$179$		−	6.16211i		−	0.460578i	−0.973122	−	0.230289i	$-0.926033\pi$
$179$		−	6.16211i		−	0.460578i	0.973122	−	0.230289i	$-0.0739671\pi$
$180$	−0.653296	+	2.13851i	−0.0486938	+	0.159395i
$181$	−1.83239	−	3.17379i	−0.136200	−	0.235906i	0.789855	−	0.613294i	$-0.210156\pi$
$181$	−1.83239	−	3.17379i	−0.136200	−	0.235906i	−0.926055	+	0.377388i	$0.876822\pi$
$182$	19.8184	−	11.4421i	1.46904	−	0.848148i
$183$	−6.60469	+	11.4397i	−0.488233	+	0.845644i
$184$	3.31793			0.244601
$185$	−11.4758	−	7.30109i	−0.843718	−	0.536787i
$186$	−3.58380			−0.262777
$187$	−7.43049	+	12.8700i	−0.543371	+	0.941147i
$188$	−1.06316	+	0.613817i	−0.0775390	+	0.0447672i
$189$	1.84755	+	3.20005i	0.134390	+	0.232770i
$190$	−12.0735	−	3.68834i	−0.875900	−	0.267580i
$191$			17.0867i			1.23635i	0.786040	+	0.618176i	$0.212128\pi$
$191$			17.0867i			1.23635i	−0.786040	+	0.618176i	$0.787872\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	24.1866			1.74099			0.870495	−	0.492177i	$-0.163799\pi$
$193$	24.1866			1.74099			0.870495	+	0.492177i	$0.163799\pi$
$194$	6.40580	−	11.0952i	0.459910	−	0.796587i
$195$	−10.1259	+	9.44671i	−0.725132	+	0.676493i
$196$	−6.65380			−0.475271
$197$	8.50118	+	4.90816i	0.605684	+	0.349692i	0.771274	−	0.636503i	$-0.219620\pi$
$197$	8.50118	+	4.90816i	0.605684	+	0.349692i	−0.165591	+	0.986195i	$0.552953\pi$
$198$	−2.22120	−	3.84723i	−0.157854	−	0.273410i
$199$			22.0251i			1.56132i	0.624958	+	0.780659i	$0.285116\pi$
$199$			22.0251i			1.56132i	−0.624958	+	0.780659i	$0.714884\pi$
$200$	4.14641	+	2.79415i	0.293195	+	0.197577i
$201$	7.37478	−	12.7735i	0.520177	−	0.900972i
$202$	−5.12308	+	8.87344i	−0.360459	+	0.624333i
$203$	0.200133	+	0.346640i	0.0140466	+	0.0243294i
$204$	−2.89708	+	1.67263i	−0.202836	+	0.117108i
$205$	2.90817	−	0.672073i	0.203115	−	0.0469396i
$206$	−2.97152	+	5.14683i	−0.207036	+	0.358597i
$207$	−1.65897	+	2.87341i	−0.115306	+	0.199716i
$208$	−6.19314			−0.429417
$209$	21.7205	−	12.5403i	1.50244	−	0.867431i
$210$	8.05033	−	1.86042i	0.555526	−	0.128381i
$211$	−7.17457			−0.493918			−0.246959	−	0.969026i	$-0.579431\pi$
$211$	−7.17457			−0.493918			−0.246959	+	0.969026i	$0.579431\pi$
$212$			8.89513i			0.610920i
$213$	−4.61040	−	2.66182i	−0.315899	−	0.182385i
$214$			10.5085i			0.718344i
$215$	0.977688	−	3.20037i	0.0666777	−	0.218264i
$216$		−	1.00000i		−	0.0680414i
$217$	6.62126	+	11.4684i	0.449481	+	0.778523i
$218$	−1.27969	+	0.738832i	−0.0866719	+	0.0500400i
$219$	1.33657	+	2.31501i	0.0903173	+	0.156434i
$220$	−9.67841	+	2.23666i	−0.652518	+	0.150796i
$221$	−20.7177			−1.39362
$222$	5.86217	+	1.62326i	0.393443	+	0.108946i
$223$		−	0.219842i		−	0.0147217i	−0.999973	−	0.00736087i	$-0.997657\pi$
$223$		−	0.219842i		−	0.0147217i	0.999973	−	0.00736087i	$-0.00234306\pi$
$224$	3.20005	+	1.84755i	0.213813	+	0.123445i
$225$	−4.49301	+	2.19382i	−0.299534	+	0.146255i
$226$	−3.19271	−	5.52994i	−0.212376	−	0.367846i
$227$	12.3956	+	21.4699i	0.822728	+	1.42501i	0.903644	+	0.428285i	$0.140882\pi$
$227$	12.3956	+	21.4699i	0.822728	+	1.42501i	−0.0809161	+	0.996721i	$0.525785\pi$
$228$	5.64574			0.373899
$229$	−5.65301	−	9.79129i	−0.373561	−	0.647027i	0.616549	−	0.787316i	$-0.288530\pi$
$229$	−5.65301	−	9.79129i	−0.373561	−	0.647027i	−0.990111	+	0.140289i	$0.955197\pi$
$230$	5.06101	+	5.42490i	0.333713	+	0.357707i
$231$	−8.20755	+	14.2159i	−0.540017	+	0.935338i
$232$		−	0.108323i		−	0.00711176i
$233$		−	14.3078i		−	0.937337i	−0.883374	−	0.468669i	$-0.844734\pi$
$233$		−	14.3078i		−	0.937337i	0.883374	−	0.468669i	$-0.155266\pi$
$234$	3.09657	−	5.36341i	0.202429	−	0.350617i
$235$	−2.62530	−	0.802008i	−0.171256	−	0.0523172i
$236$			0.338038i			0.0220044i
$237$	2.81418	−	4.87431i	0.182801	−	0.316620i
$238$	10.7050	+	6.18055i	0.693904	+	0.400626i
$239$	5.88745	+	3.39912i	0.380828	+	0.219871i	0.678178	−	0.734897i	$-0.262770\pi$
$239$	5.88745	+	3.39912i	0.380828	+	0.219871i	−0.297351	+	0.954768i	$0.596103\pi$
$240$	−2.13851	−	0.653296i	−0.138040	−	0.0421701i
$241$	−4.79812	+	2.77020i	−0.309074	+	0.178444i	−0.646512	−	0.762904i	$-0.723773\pi$
$241$	−4.79812	+	2.77020i	−0.309074	+	0.178444i	0.337438	+	0.941348i	$0.390440\pi$
$242$	4.36743	−	7.56461i	0.280749	−	0.486272i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−11.4397	−	6.60469i	−0.732350	−	0.422822i
$245$	−10.1494	−	10.8791i	−0.648420	−	0.695041i
$246$	−1.15602	+	0.667426i	−0.0737048	+	0.0425535i
$247$	30.2805	+	17.4824i	1.92670	+	1.11238i
$248$		−	3.58380i		−	0.227572i
$249$	−6.00873			−0.380788
$250$	1.75622	+	11.0415i	0.111073	+	0.698329i
$251$		−	30.0814i		−	1.89872i	−0.314193	−	0.949359i	$-0.601734\pi$
$251$		−	30.0814i		−	1.89872i	0.314193	−	0.949359i	$-0.398266\pi$
$252$	−3.20005	+	1.84755i	−0.201584	+	0.116385i
$253$	−14.7396			−0.926668
$254$	−15.2469	+	8.80279i	−0.956675	+	0.552336i
$255$	−7.15387	−	2.18545i	−0.447992	−	0.136858i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.7565	−	20.3629i	0.733350	−	1.27020i	−0.222093	−	0.975025i	$-0.571289\pi$
$257$	11.7565	−	20.3629i	0.733350	−	1.27020i	0.955443	−	0.295174i	$-0.0953777\pi$
$258$			1.49655i			0.0931709i
$259$	−5.63613	−	21.7583i	−0.350212	−	1.35200i
$260$	−9.44671	−	10.1259i	−0.585860	−	0.627983i
$261$	0.0938106	+	0.0541616i	0.00580673	+	0.00335252i
$262$	−18.6551	+	10.7705i	−1.15252	+	0.665405i
$263$	23.8858	−	13.7905i	1.47286	−	0.850357i	0.473327	−	0.880887i	$-0.343053\pi$
$263$	23.8858	−	13.7905i	1.47286	−	0.850357i	0.999534	+	0.0305303i	$0.00971960\pi$
$264$	3.84723	−	2.22120i	0.236780	−	0.136705i
$265$	−14.5438	+	13.5682i	−0.893416	+	0.833488i
$266$	−10.4308	−	18.0667i	−0.639554	−	1.10774i
$267$	16.0613			0.982936
$268$	12.7735	+	7.37478i	0.780265	+	0.450486i
$269$	−13.5863			−0.828370			−0.414185	−	0.910193i	$-0.635933\pi$
$269$	−13.5863			−0.828370			−0.414185	+	0.910193i	$0.635933\pi$
$270$	1.63502	−	1.52535i	0.0995044	−	0.0928300i
$271$	4.97694	−	8.62031i	0.302327	−	0.523646i	−0.674335	−	0.738425i	$-0.735570\pi$
$271$	4.97694	−	8.62031i	0.302327	−	0.523646i	0.976663	+	0.214779i	$0.0689031\pi$
$272$	−1.67263	−	2.89708i	−0.101418	−	0.175662i
$273$	−22.8843			−1.38502
$274$	8.78174	+	5.07014i	0.530525	+	0.306299i
$275$	−18.4200	−	12.4127i	−1.11077	−	0.748516i
$276$	−2.87341	−	1.65897i	−0.172959	−	0.0998580i
$277$	13.3467	+	23.1172i	0.801926	+	1.38898i	0.918347	+	0.395777i	$0.129525\pi$
$277$	13.3467	+	23.1172i	0.801926	+	1.38898i	−0.116421	+	0.993200i	$0.537142\pi$
$278$	3.23928	+	5.61060i	0.194279	+	0.336502i
$279$	3.10366	+	1.79190i	0.185811	+	0.107278i
$280$	1.86042	+	8.05033i	0.111181	+	0.481099i
$281$	−0.674004	−	0.389137i	−0.0402077	−	0.0232139i	0.479761	−	0.877399i	$-0.340723\pi$
$281$	−0.674004	−	0.389137i	−0.0402077	−	0.0232139i	−0.519969	+	0.854185i	$0.674057\pi$
$282$	1.22763			0.0731045
$283$	−5.81231	−	10.0672i	−0.345506	−	0.598434i	0.639940	−	0.768425i	$-0.278959\pi$
$283$	−5.81231	−	10.0672i	−0.345506	−	0.598434i	−0.985446	+	0.169991i	$0.945626\pi$
$284$	2.66182	−	4.61040i	0.157950	−	0.273577i
$285$	8.61175	+	9.23092i	0.510116	+	0.546793i
$286$	27.5123			1.62684
$287$	4.27160	+	2.46621i	0.252144	+	0.145576i
$288$	1.00000			0.0589256
$289$	2.90460	+	5.03092i	0.170859	+	0.295936i
$290$	0.177111	−	0.165231i	0.0104003	−	0.00970269i
$291$	−11.0952	+	6.40580i	−0.650410	+	0.375515i
$292$	−2.31501	+	1.33657i	−0.135476	+	0.0782170i
$293$	−9.00934	+	5.20154i	−0.526331	+	0.303877i	−0.739521	−	0.673133i	$-0.764948\pi$
$293$	−9.00934	+	5.20154i	−0.526331	+	0.303877i	0.213190	+	0.977011i	$0.431615\pi$
$294$	5.76236	+	3.32690i	0.336068	+	0.194029i
$295$	−0.552700	+	0.515627i	−0.0321795	+	0.0300210i
$296$	−1.62326	+	5.86217i	−0.0943504	+	0.340732i
$297$			4.44239i			0.257774i
$298$	0.899754	−	1.55842i	0.0521213	−	0.0902768i
$299$	−10.2742	−	17.7954i	−0.594173	−	1.02914i
$300$	−2.19382	−	4.49301i	−0.126660	−	0.259404i
$301$	4.78903	−	2.76495i	0.276035	−	0.159369i
$302$	11.5657			0.665530
$303$	8.87344	−	5.12308i	0.509766	−	0.294313i
$304$			5.64574i			0.323806i
$305$	−6.65068	−	28.7786i	−0.380817	−	1.64786i
$306$	3.34526			0.191236
$307$			18.4064i			1.05051i	0.850945	+	0.525254i	$0.176030\pi$
$307$			18.4064i			1.05051i	−0.850945	+	0.525254i	$0.823970\pi$
$308$	−14.2159	−	8.20755i	−0.810026	−	0.467669i
$309$	5.14683	−	2.97152i	0.292793	−	0.169044i
$310$	5.85960	−	5.46656i	0.332803	−	0.310480i
$311$	16.0430	+	9.26245i	0.909717	+	0.525225i	0.880340	−	0.474343i	$-0.157314\pi$
$311$	16.0430	+	9.26245i	0.909717	+	0.525225i	0.0293771	+	0.999568i	$0.490648\pi$
$312$	5.36341	+	3.09657i	0.303643	+	0.175309i
$313$	10.9094	−	18.8956i	0.616634	−	1.06804i	−0.373461	−	0.927646i	$-0.621829\pi$
$313$	10.9094	−	18.8956i	0.616634	−	1.06804i	0.990095	−	0.140396i	$-0.0448376\pi$
$314$	17.0546	−	9.84650i	0.962449	−	0.555670i
$315$	−7.90200	−	2.41400i	−0.445227	−	0.136013i
$316$	4.87431	+	2.81418i	0.274201	+	0.158310i
$317$	24.1836	+	13.9624i	1.35829	+	0.784207i	0.989393	−	0.145264i	$-0.0464033\pi$
$317$	24.1836	+	13.9624i	1.35829	+	0.784207i	0.368894	+	0.929472i	$0.379737\pi$
$318$	4.44757	−	7.70341i	0.249407	−	0.431986i
$319$			0.481214i			0.0269428i
$320$	0.653296	−	2.13851i	0.0365204	−	0.119546i
$321$	5.25423	−	9.10060i	0.293263	−	0.507946i
$322$			12.2601i			0.683229i
$323$			18.8865i			1.05087i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	2.14656	−	30.8912i	0.119070	−	1.71353i
$326$	8.25810	+	14.3034i	0.457374	+	0.792195i
$327$	1.47766			0.0817150
$328$	−0.667426	−	1.15602i	−0.0368524	−	0.0638303i
$329$	−2.26812	−	3.92849i	−0.125045	−	0.216585i
$330$	9.50008	+	2.90220i	0.522962	+	0.159761i
$331$	28.7591	+	16.6041i	1.58074	+	0.912642i	0.994751	+	0.102324i	$0.0326278\pi$
$331$	28.7591	+	16.6041i	1.58074	+	0.912642i	0.585991	+	0.810318i	$0.300706\pi$
$332$		−	6.00873i		−	0.329772i
$333$	−4.26515	−	4.33687i	−0.233729	−	0.237659i
$334$	−11.2059			−0.613157
$335$	7.42613	+	32.1341i	0.405733	+	1.75567i
$336$	−1.84755	−	3.20005i	−0.100792	−	0.174577i
$337$	−5.47768	+	3.16254i	−0.298388	+	0.172275i	−0.641719	−	0.766940i	$-0.721778\pi$
$337$	−5.47768	+	3.16254i	−0.298388	+	0.172275i	0.343330	+	0.939215i	$0.388445\pi$
$338$	12.6775	+	21.9580i	0.689563	+	1.19436i
$339$			6.38543i			0.346809i
$340$	2.18545	−	7.15387i	0.118523	−	0.387973i
$341$			15.9207i			0.862152i
$342$	−4.88936	−	2.82287i	−0.264386	−	0.152643i
$343$			1.27925i			0.0690733i
$344$	−1.49655			−0.0806884
$345$	−1.67052	−	7.22861i	−0.0899377	−	0.389175i
$346$	−12.4041	+	7.16151i	−0.666849	+	0.385005i
$347$	−26.7305			−1.43497			−0.717483	−	0.696576i	$-0.754706\pi$
$347$	−26.7305			−1.43497			−0.717483	+	0.696576i	$0.754706\pi$
$348$	−0.0541616	+	0.0938106i	−0.00290336	+	0.00502877i
$349$	−9.72032	+	16.8361i	−0.520317	+	0.901215i	0.479404	+	0.877594i	$0.340853\pi$
$349$	−9.72032	+	16.8361i	−0.520317	+	0.901215i	−0.999721	+	0.0236209i	$0.992481\pi$
$350$	−10.3247	+	15.3214i	−0.551878	+	0.818964i
$351$	−5.36341	+	3.09657i	−0.286278	+	0.165283i
$352$	2.22120	+	3.84723i	0.118390	+	0.205058i
$353$	−2.02075	+	3.50004i	−0.107554	+	0.186288i	−0.914779	−	0.403955i	$-0.867635\pi$
$353$	−2.02075	+	3.50004i	−0.107554	+	0.186288i	0.807225	+	0.590244i	$0.200968\pi$
$354$	0.169019	−	0.292750i	0.00898326	−	0.0155595i
$355$	11.5983	−	2.68035i	0.615575	−	0.142258i
$356$			16.0613i			0.851248i
$357$	−6.18055	−	10.7050i	−0.327109	−	0.566570i
$358$	−5.33654	−	3.08106i	−0.282045	−	0.162839i
$359$	−0.449208			−0.0237083			−0.0118542	−	0.999930i	$-0.503773\pi$
$359$	−0.449208			−0.0237083			−0.0118542	+	0.999930i	$0.503773\pi$
$360$	1.52535	+	1.63502i	0.0803931	+	0.0861733i
$361$	6.43721	−	11.1496i	0.338801	−	0.586820i
$362$	−3.66478			−0.192617
$363$	−7.56461	+	4.36743i	−0.397039	+	0.229231i
$364$		−	22.8843i		−	1.19946i
$365$	−5.71654	−	1.74636i	−0.299217	−	0.0914085i
$366$	6.60469	+	11.4397i	0.345233	+	0.597961i
$367$	28.8599	−	16.6623i	1.50647	−	0.869763i	0.506502	−	0.862239i	$-0.330938\pi$
$367$	28.8599	−	16.6623i	1.50647	−	0.869763i	0.999972	−	0.00752386i	$-0.00239494\pi$
$368$	1.65897	−	2.87341i	0.0864796	−	0.149787i
$369$	1.33485			0.0694896
$370$	−12.0608	+	6.28779i	−0.627013	+	0.326887i
$371$	−32.8684			−1.70644
$372$	−1.79190	+	3.10366i	−0.0929057	+	0.160917i
$373$	0.921169	−	0.531837i	0.0476963	−	0.0275375i	−0.475962	−	0.879466i	$-0.657900\pi$
$373$	0.921169	−	0.531837i	0.0476963	−	0.0275375i	0.523659	+	0.851928i	$0.324567\pi$
$374$	7.43049	+	12.8700i	0.384222	+	0.665491i
$375$	3.99984	−	10.4404i	0.206551	−	0.539138i
$376$			1.22763i			0.0633103i
$377$	−0.580982	+	0.335430i	−0.0299221	+	0.0172755i
$378$	3.69510			0.190056
$379$	−11.9117	+	20.6317i	−0.611863	+	1.05978i	0.379063	+	0.925371i	$0.376246\pi$
$379$	−11.9117	+	20.6317i	−0.611863	+	1.05978i	−0.990926	+	0.134407i	$0.957087\pi$
$380$	−9.23092	+	8.61175i	−0.473536	+	0.441773i
$381$	17.6056			0.901962
$382$	14.7975	+	8.54336i	0.757107	+	0.437116i
$383$	12.3247	+	21.3470i	0.629762	+	1.09078i	0.987599	+	0.156995i	$0.0501807\pi$
$383$	12.3247	+	21.3470i	0.629762	+	1.09078i	−0.357838	+	0.933784i	$0.616486\pi$
$384$			1.00000i			0.0510310i
$385$	−8.26471	−	35.7627i	−0.421208	−	1.82264i
$386$	12.0933	−	20.9462i	0.615533	−	1.06613i
$387$	0.748273	−	1.29605i	0.0380369	−	0.0658818i
$388$	−6.40580	−	11.0952i	−0.325205	−	0.563272i
$389$	3.99858	−	2.30858i	0.202736	−	0.117050i	−0.395195	−	0.918597i	$-0.629323\pi$
$389$	3.99858	−	2.30858i	0.202736	−	0.117050i	0.597931	+	0.801548i	$0.295990\pi$
$390$	3.11813	+	13.4927i	0.157893	+	0.683228i
$391$	5.54968	−	9.61233i	0.280659	−	0.486116i
$392$	−3.32690	+	5.76236i	−0.168034	+	0.291043i
$393$	21.5410			1.08660
$394$	8.50118	−	4.90816i	0.428283	−	0.247269i
$395$	2.83378	+	12.2622i	0.142583	+	0.616980i
$396$	−4.44239			−0.223239
$397$		−	11.6194i		−	0.583162i	−0.956546	−	0.291581i	$-0.905819\pi$
$397$		−	11.6194i		−	0.583162i	0.956546	−	0.291581i	$-0.0941813\pi$
$398$	19.0743	+	11.0125i	0.956108	+	0.552009i
$399$			20.8616i			1.04439i
$400$	4.49301	−	2.19382i	0.224651	−	0.109691i
$401$		−	6.31885i		−	0.315548i	−0.987475	−	0.157774i	$-0.949568\pi$
$401$		−	6.31885i		−	0.315548i	0.987475	−	0.157774i	$-0.0504318\pi$
$402$	−7.37478	−	12.7735i	−0.367820	−	0.637084i
$403$	−19.2214	+	11.0975i	−0.957487	+	0.552805i
$404$	5.12308	+	8.87344i	0.254883	+	0.441470i
$405$	−2.17865	+	0.503482i	−0.108258	+	0.0250182i
$406$	0.400265			0.0198648
$407$	7.21118	−	26.0421i	0.357445	−	1.29086i
$408$			3.34526i			0.165615i
$409$	−12.2422	−	7.06806i	−0.605340	−	0.349493i	0.165799	−	0.986159i	$-0.446980\pi$
$409$	−12.2422	−	7.06806i	−0.605340	−	0.349493i	−0.771139	+	0.636666i	$0.780313\pi$
$410$	0.872053	−	2.85459i	0.0430676	−	0.140978i
$411$	−5.07014	−	8.78174i	−0.250092	−	0.433171i
$412$	2.97152	+	5.14683i	0.146396	+	0.253566i
$413$	−1.24909			−0.0614635
$414$	1.65897	+	2.87341i	0.0815337	+	0.141221i
$415$	9.82442	−	9.16543i	0.482262	−	0.449913i
$416$	−3.09657	+	5.36341i	−0.151822	+	0.262963i
$417$		−	6.47856i		−	0.317257i
$418$		−	25.0806i		−	1.22673i
$419$	−19.8015	+	34.2972i	−0.967366	+	1.67553i	−0.264248	+	0.964455i	$0.585124\pi$
$419$	−19.8015	+	34.2972i	−0.967366	+	1.67553i	−0.703119	+	0.711073i	$0.748210\pi$
$420$	2.41400	−	7.90200i	0.117791	−	0.385578i
$421$			7.95090i			0.387503i	0.981051	+	0.193752i	$0.0620656\pi$
$421$			7.95090i			0.387503i	−0.981051	+	0.193752i	$0.937934\pi$
$422$	−3.58728	+	6.21336i	−0.174626	+	0.302462i
$423$	−1.06316	−	0.613817i	−0.0516927	−	0.0298448i
$424$	7.70341	+	4.44757i	0.374111	+	0.215993i
$425$	15.0303	−	7.33890i	0.729077	−	0.355989i
$426$	−4.61040	+	2.66182i	−0.223375	+	0.128965i
$427$	24.4050	−	42.2708i	1.18104	−	2.04563i
$428$	9.10060	+	5.25423i	0.439894	+	0.253973i
$429$	−23.8264	−	13.7562i	−1.15035	−	0.664154i
$430$	−2.28276	−	2.44689i	−0.110084	−	0.117999i
$431$	9.99522	−	5.77074i	0.481453	−	0.277967i	−0.239569	−	0.970879i	$-0.577006\pi$
$431$	9.99522	−	5.77074i	0.481453	−	0.277967i	0.721022	+	0.692912i	$0.243673\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$		−	14.0193i		−	0.673725i	−0.941554	−	0.336862i	$-0.890634\pi$
$433$		−	14.0193i		−	0.673725i	0.941554	−	0.336862i	$-0.109366\pi$
$434$	13.2425			0.635661
$435$	−0.235998	+	0.0545387i	−0.0113152	+	0.00261493i
$436$			1.47766i			0.0707673i
$437$	−16.2226	+	9.36610i	−0.776030	+	0.448041i
$438$	2.67315			0.127728
$439$	−20.7334	+	11.9704i	−0.989551	+	0.571317i	−0.905140	−	0.425114i	$-0.860234\pi$
$439$	−20.7334	+	11.9704i	−0.989551	+	0.571317i	−0.0844108	+	0.996431i	$0.526901\pi$
$440$	−2.90220	+	9.50008i	−0.138357	+	0.452899i
$441$	−3.32690	−	5.76236i	−0.158424	−	0.274398i
$442$	−10.3588	+	17.9420i	−0.492720	+	0.853416i
$443$		−	26.2329i		−	1.24636i	−0.782077	−	0.623182i	$-0.785840\pi$
$443$		−	26.2329i		−	1.24636i	0.782077	−	0.623182i	$-0.214160\pi$
$444$	4.33687	−	4.26515i	0.205819	−	0.202415i
$445$	−26.2606	+	24.4992i	−1.24487	+	1.16137i
$446$	−0.190389	−	0.109921i	−0.00901519	−	0.00520492i
$447$	−1.55842	+	0.899754i	−0.0737107	+	0.0425569i
$448$	3.20005	−	1.84755i	0.151188	−	0.0872886i
$449$	16.5697	−	9.56655i	0.781974	−	0.451473i	−0.0551551	−	0.998478i	$-0.517565\pi$
$449$	16.5697	−	9.56655i	0.781974	−	0.451473i	0.837130	+	0.547005i	$0.184232\pi$
$450$	−0.346604	+	4.98797i	−0.0163391	+	0.235135i
$451$	2.96497	+	5.13547i	0.139615	+	0.241820i
$452$	−6.38543			−0.300345
$453$	−10.0162	−	5.78284i	−0.470601	−	0.271701i
$454$	24.7913			1.16351
$455$	37.4163	−	34.9066i	1.75411	−	1.63645i
$456$	2.82287	−	4.88936i	0.132193	−	0.228965i
$457$	−20.5198	−	35.5413i	−0.959875	−	1.66255i	−0.722794	−	0.691063i	$-0.757143\pi$
$457$	−20.5198	−	35.5413i	−0.959875	−	1.66255i	−0.237081	−	0.971490i	$-0.576191\pi$
$458$	−11.3060			−0.528295
$459$	−2.89708	−	1.67263i	−0.135224	−	0.0780718i
$460$	7.22861	−	1.67052i	0.337036	−	0.0778883i
$461$	−9.56724	−	5.52365i	−0.445591	−	0.257262i	0.260375	−	0.965507i	$-0.416154\pi$
$461$	−9.56724	−	5.52365i	−0.445591	−	0.257262i	−0.705966	+	0.708245i	$0.749487\pi$
$462$	8.20755	+	14.2159i	0.381850	+	0.661384i
$463$	−4.02668	−	6.97442i	−0.187136	−	0.324129i	0.757158	−	0.653231i	$-0.226587\pi$
$463$	−4.02668	−	6.97442i	−0.187136	−	0.324129i	−0.944294	+	0.329103i	$0.893254\pi$
$464$	−0.0938106	−	0.0541616i	−0.00435505	−	0.00251439i
$465$	−7.80784	+	1.80438i	−0.362080	+	0.0836761i
$466$	−12.3909	−	7.15391i	−0.573999	−	0.331399i
$467$	−9.63792			−0.445990			−0.222995	−	0.974820i	$-0.571583\pi$
$467$	−9.63792			−0.445990			−0.222995	+	0.974820i	$0.571583\pi$
$468$	−3.09657	−	5.36341i	−0.143139	−	0.247924i
$469$	−27.2506	+	47.1994i	−1.25831	+	2.17946i
$470$	−2.00721	+	1.87257i	−0.0925856	+	0.0863753i
$471$	−19.6930			−0.907406
$472$	0.292750	+	0.169019i	0.0134749	+	0.00777973i
$473$	6.64825			0.305687
$474$	−2.81418	−	4.87431i	−0.129260	−	0.223884i
$475$	−28.1608	−	1.95684i	−1.29211	−	0.0897858i
$476$	10.7050	−	6.18055i	0.490664	−	0.283285i
$477$	−7.70341	+	4.44757i	−0.352715	+	0.203640i
$478$	5.88745	−	3.39912i	0.269286	−	0.155472i
$479$	−27.4842	−	15.8680i	−1.25578	−	0.725027i	−0.283532	−	0.958963i	$-0.591506\pi$
$479$	−27.4842	−	15.8680i	−1.25578	−	0.725027i	−0.972252	+	0.233936i	$0.924840\pi$
$480$	−1.63502	+	1.52535i	−0.0746283	+	0.0696225i
$481$	36.4678	−	9.44636i	1.66279	−	0.430717i
$482$			5.54039i			0.252358i
$483$	6.13005	−	10.6176i	0.278927	−	0.483116i
$484$	−4.36743	−	7.56461i	−0.198520	−	0.343846i
$485$	8.36977	−	27.3977i	0.380052	−	1.24406i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−4.48336			−0.203161			−0.101580	−	0.994827i	$-0.532390\pi$
$487$	−4.48336			−0.203161			−0.101580	+	0.994827i	$0.532390\pi$
$488$	−11.4397	+	6.60469i	−0.517849	+	0.298980i
$489$		−	16.5162i		−	0.746888i
$490$	−14.4963	+	3.35006i	−0.654875	+	0.151341i
$491$	−8.90853			−0.402037			−0.201018	−	0.979587i	$-0.564425\pi$
$491$	−8.90853			−0.402037			−0.201018	+	0.979587i	$0.564425\pi$
$492$			1.33485i			0.0601797i
$493$	−0.313821	−	0.181185i	−0.0141338	−	0.00816015i
$494$	30.2805	−	17.4824i	1.36238	−	0.786572i
$495$	−6.77621	−	7.26342i	−0.304568	−	0.326466i
$496$	−3.10366	−	1.79190i	−0.139359	−	0.0804587i
$497$	17.0359	+	9.83569i	0.764165	+	0.441191i
$498$	−3.00437	+	5.20372i	−0.134629	+	0.233184i
$499$	31.6688	−	18.2840i	1.41769	−	0.818503i	0.421594	−	0.906785i	$-0.361471\pi$
$499$	31.6688	−	18.2840i	1.41769	−	0.818503i	0.996096	+	0.0882814i	$0.0281375\pi$
$500$	10.4404	+	3.99984i	0.466908	+	0.178878i
$501$	9.70456	+	5.60293i	0.433568	+	0.250320i
$502$	−26.0512	−	15.0407i	−1.16272	−	0.671298i
$503$	−4.13426	+	7.16075i	−0.184338	+	0.319282i	−0.943353	−	0.331790i	$-0.892347\pi$
$503$	−4.13426	+	7.16075i	−0.184338	+	0.319282i	0.759016	+	0.651073i	$0.225681\pi$
$504$			3.69510i			0.164593i
$505$	−6.69378	+	21.9115i	−0.297869	+	0.975048i
$506$	−7.36978	+	12.7648i	−0.327627	+	0.567466i
$507$		−	25.3549i		−	1.12605i
$508$			17.6056i			0.781122i
$509$	−18.6383	+	32.2825i	−0.826129	+	1.43090i	0.0749237	+	0.997189i	$0.476129\pi$
$509$	−18.6383	+	32.2825i	−0.826129	+	1.43090i	−0.901053	+	0.433709i	$0.857205\pi$
$510$	−5.46959	+	5.10271i	−0.242197	+	0.225952i
$511$	−4.93878	−	8.55421i	−0.218479	−	0.378416i
$512$	−1.00000			−0.0441942
$513$	2.82287	+	4.88936i	0.124633	+	0.215870i
$514$	−11.7565	−	20.3629i	−0.518557	−	0.898167i
$515$	−3.88257	+	12.7092i	−0.171086	+	0.560036i
$516$	1.29605	+	0.748273i	0.0570553	+	0.0329409i
$517$		−	5.45363i		−	0.239850i
$518$	−21.6613	−	5.99813i	−0.951744	−	0.263543i
$519$	14.3230			0.628711
$520$	−13.4927	+	3.11813i	−0.591692	+	0.136739i
$521$	−2.11581	−	3.66469i	−0.0926953	−	0.160553i	0.815949	−	0.578124i	$-0.196215\pi$
$521$	−2.11581	−	3.66469i	−0.0926953	−	0.160553i	−0.908644	+	0.417571i	$0.862882\pi$
$522$	0.0938106	−	0.0541616i	0.00410598	−	0.00237059i
$523$	6.66483	+	11.5438i	0.291433	+	0.504776i	0.974149	−	0.225908i	$-0.0725348\pi$
$523$	6.66483	+	11.5438i	0.291433	+	0.504776i	−0.682716	+	0.730684i	$0.739201\pi$
$524$			21.5410i			0.941025i
$525$	16.6022	−	8.10639i	0.724577	−	0.353792i
$526$		−	27.5809i		−	1.20259i
$527$	−10.3826	−	5.99438i	−0.452272	−	0.261119i
$528$		−	4.44239i		−	0.193330i
$529$	−11.9913			−0.521362
$530$	4.47854	+	19.3794i	0.194535	+	0.841786i
$531$	−0.292750	+	0.169019i	−0.0127043	+	0.00733480i
$532$	−20.8616			−0.904466
$533$	−4.13346	+	7.15936i	−0.179040	+	0.310106i
$534$	8.03066	−	13.9095i	0.347521	−	0.601923i
$535$	5.29082	+	22.8942i	0.228742	+	0.989804i
$536$	12.7735	−	7.37478i	0.551731	−	0.318542i
$537$	3.08106	+	5.33654i	0.132957	+	0.230289i
$538$	−6.79314	+	11.7661i	−0.292873	+	0.507271i
$539$	14.7794	−	25.5987i	0.636594	−	1.10261i
$540$	−0.503482	−	2.17865i	−0.0216664	−	0.0937541i
$541$		−	8.60984i		−	0.370166i	−0.982723	−	0.185083i	$-0.940745\pi$
$541$		−	8.60984i		−	0.370166i	0.982723	−	0.185083i	$-0.0592554\pi$
$542$	−4.97694	−	8.62031i	−0.213778	−	0.370274i
$543$	3.17379	+	1.83239i	0.136200	+	0.0786354i
$544$	−3.34526			−0.143427
$545$	−2.41602	+	2.25396i	−0.103491	+	0.0965489i
$546$	−11.4421	+	19.8184i	−0.489678	+	0.848148i
$547$	−16.9211			−0.723496			−0.361748	−	0.932276i	$-0.617820\pi$
$547$	−16.9211			−0.723496			−0.361748	+	0.932276i	$0.617820\pi$
$548$	8.78174	−	5.07014i	0.375138	−	0.216586i
$549$		−	13.2094i		−	0.563763i
$550$	−19.9597	+	9.74580i	−0.851086	+	0.415563i
$551$	0.305782	+	0.529631i	0.0130268	+	0.0225630i
$552$	−2.87341	+	1.65897i	−0.122301	+	0.0706103i
$553$	−10.3987	+	18.0111i	−0.442198	+	0.765909i
$554$	26.6934			1.13409
$555$	13.5889	+	0.585029i	0.576816	+	0.0248331i
$556$	6.47856			0.274752
$557$	−17.5570	+	30.4096i	−0.743914	+	1.28850i	0.206787	+	0.978386i	$0.433699\pi$
$557$	−17.5570	+	30.4096i	−0.743914	+	1.28850i	−0.950701	+	0.310110i	$0.899634\pi$
$558$	3.10366	−	1.79190i	0.131389	−	0.0758572i
$559$	4.63416	+	8.02659i	0.196004	+	0.339489i
$560$	7.90200	+	2.41400i	0.333920	+	0.102010i
$561$		−	14.8610i		−	0.627431i
$562$	−0.674004	+	0.389137i	−0.0284312	+	0.0164147i
$563$	13.6442			0.575035			0.287518	−	0.957775i	$-0.407170\pi$
$563$	13.6442			0.575035			0.287518	+	0.957775i	$0.407170\pi$
$564$	0.613817	−	1.06316i	0.0258463	−	0.0447672i
$565$	−9.74003	−	10.4403i	−0.409766	−	0.439228i
$566$	−11.6246			−0.488619
$567$	−3.20005	−	1.84755i	−0.134390	−	0.0775899i
$568$	−2.66182	−	4.61040i	−0.111687	−	0.193448i
$569$			32.8741i			1.37815i	0.724689	+	0.689076i	$0.241984\pi$
$569$			32.8741i			1.37815i	−0.724689	+	0.689076i	$0.758016\pi$
$570$	12.3001	−	2.84253i	0.515194	−	0.119060i
$571$	15.5801	−	26.9856i	0.652008	−	1.12931i	−0.330627	−	0.943762i	$-0.607260\pi$
$571$	15.5801	−	26.9856i	0.652008	−	1.12931i	0.982635	−	0.185550i	$-0.0594066\pi$
$572$	13.7562	−	23.8264i	0.575175	−	0.996232i
$573$	−8.54336	−	14.7975i	−0.356904	−	0.618176i
$574$	4.27160	−	2.46621i	0.178293	−	0.102938i
$575$	13.7575	+	9.27081i	0.573728	+	0.386620i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	5.44050	−	9.42322i	0.226491	−	0.392294i	−0.730275	−	0.683154i	$-0.760608\pi$
$577$	5.44050	−	9.42322i	0.226491	−	0.392294i	0.956766	+	0.290860i	$0.0939413\pi$
$578$	5.80920			0.241631
$579$	−20.9462	+	12.0933i	−0.870495	+	0.502581i
$580$	−0.0545387	−	0.235998i	−0.00226460	−	0.00979928i
$581$	22.2029			0.921131
$582$			12.8116i			0.531058i
$583$	−34.2216	−	19.7578i	−1.41731	−	0.818286i
$584$			2.67315i			0.110616i
$585$	4.04595	−	13.2441i	0.167279	−	0.547574i
$586$			10.4031i			0.429748i
$587$	−12.4630	−	21.5865i	−0.514403	−	0.890971i	−0.999860	−	0.0167112i	$-0.994680\pi$
$587$	−12.4630	−	21.5865i	−0.514403	−	0.890971i	0.485458	−	0.874260i	$-0.338653\pi$
$588$	5.76236	−	3.32690i	0.237636	−	0.137199i
$589$	10.1166	+	17.5225i	0.416848	+	0.722002i
$590$	0.170196	+	0.736466i	0.00700686	+	0.0303198i
$591$	−9.81631			−0.403789
$592$	4.26515	+	4.33687i	0.175297	+	0.178244i
$593$		−	14.2693i		−	0.585969i	−0.956117	−	0.292984i	$-0.905352\pi$
$593$		−	14.2693i		−	0.585969i	0.956117	−	0.292984i	$-0.0946484\pi$
$594$	3.84723	+	2.22120i	0.157854	+	0.0911368i
$595$	26.4343	+	8.07546i	1.08370	+	0.331062i
$596$	−0.899754	−	1.55842i	−0.0368554	−	0.0638354i
$597$	−11.0125	−	19.0743i	−0.450714	−	0.780659i
$598$	−20.5484			−0.840287
$599$	10.1315	+	17.5483i	0.413962	+	0.717003i	0.995319	−	0.0966459i	$-0.0308114\pi$
$599$	10.1315	+	17.5483i	0.413962	+	0.717003i	−0.581357	+	0.813648i	$0.697478\pi$
$600$	−4.98797	−	0.346604i	−0.203633	−	0.0141500i
$601$	−6.63186	+	11.4867i	−0.270519	+	0.468553i	−0.968995	−	0.247081i	$-0.920529\pi$
$601$	−6.63186	+	11.4867i	−0.270519	+	0.468553i	0.698476	+	0.715634i	$0.253862\pi$
$602$		−	5.52989i		−	0.225382i
$603$			14.7496i			0.600648i
$604$	5.78284	−	10.0162i	0.235300	−	0.407552i
$605$	5.70645	−	18.6795i	0.232000	−	0.759432i
$606$		−	10.2462i		−	0.416222i
$607$	1.63728	−	2.83585i	0.0664552	−	0.115104i	−0.830883	−	0.556447i	$-0.812164\pi$
$607$	1.63728	−	2.83585i	0.0664552	−	0.115104i	0.897339	+	0.441343i	$0.145498\pi$
$608$	4.88936	+	2.82287i	0.198290	+	0.114483i
$609$	−0.346640	−	0.200133i	−0.0140466	−	0.00810978i
$610$	−28.2483	−	8.62964i	−1.14374	−	0.349404i
$611$	6.58430	−	3.80145i	0.266372	−	0.153790i
$612$	1.67263	−	2.89708i	0.0676122	−	0.117108i
$613$	−26.8039	−	15.4752i	−1.08260	−	0.625039i	−0.151003	−	0.988533i	$-0.548250\pi$
$613$	−26.8039	−	15.4752i	−1.08260	−	0.625039i	−0.931597	+	0.363494i	$0.881584\pi$
$614$	15.9404	+	9.20320i	0.643302	+	0.371411i
$615$	−2.18251	+	2.03612i	−0.0880074	+	0.0821042i
$616$	−14.2159	+	8.20755i	−0.572775	+	0.330692i
$617$	0.416548	+	0.240494i	0.0167696	+	0.00968194i	0.508361	−	0.861144i	$-0.330251\pi$
$617$	0.416548	+	0.240494i	0.0167696	+	0.00968194i	−0.491592	+	0.870826i	$0.663585\pi$
$618$		−	5.94305i		−	0.239064i
$619$	−0.362624			−0.0145751			−0.00728754	−	0.999973i	$-0.502320\pi$
$619$	−0.362624			−0.0145751			−0.00728754	+	0.999973i	$0.502320\pi$
$620$	−1.80438	−	7.80784i	−0.0724656	−	0.313571i
$621$		−	3.31793i		−	0.133144i
$622$	16.0430	−	9.26245i	0.643267	−	0.371391i
$623$	−59.3482			−2.37774
$624$	5.36341	−	3.09657i	0.214708	−	0.123962i
$625$	9.38541	+	23.1714i	0.375416	+	0.926856i
$626$	−10.9094	−	18.8956i	−0.436026	−	0.755220i
$627$	−12.5403	+	21.7205i	−0.500812	+	0.867431i
$628$		−	19.6930i		−	0.785836i
$629$	14.2681	+	14.5080i	0.568905	+	0.578471i
$630$	−6.04158	+	5.63633i	−0.240702	+	0.224557i
$631$	−16.6855	−	9.63338i	−0.664239	−	0.383499i	0.129651	−	0.991560i	$-0.458614\pi$
$631$	−16.6855	−	9.63338i	−0.664239	−	0.383499i	−0.793890	+	0.608061i	$0.791948\pi$
$632$	4.87431	−	2.81418i	0.193890	−	0.111942i
$633$	6.21336	−	3.58728i	0.246959	−	0.142582i
$634$	24.1836	−	13.9624i	0.960454	−	0.554518i
$635$	−28.7856	+	26.8547i	−1.14232	+	1.06570i
$636$	−4.44757	−	7.70341i	−0.176357	−	0.305460i
$637$	41.2079			1.63272
$638$	0.416744	+	0.240607i	0.0164990	+	0.00952572i
$639$	5.32363			0.210600
$640$	−1.52535	−	1.63502i	−0.0602948	−	0.0646300i
$641$	−6.93767	+	12.0164i	−0.274021	+	0.474619i	−0.969888	−	0.243552i	$-0.921687\pi$
$641$	−6.93767	+	12.0164i	−0.274021	+	0.474619i	0.695866	+	0.718171i	$0.255021\pi$
$642$	−5.25423	−	9.10060i	−0.207368	−	0.359172i
$643$	−32.7410			−1.29118			−0.645589	−	0.763685i	$-0.723388\pi$
$643$	−32.7410			−1.29118			−0.645589	+	0.763685i	$0.723388\pi$
$644$	10.6176	+	6.13005i	0.418391	+	0.241558i
$645$	0.753483	+	3.26045i	0.0296684	+	0.128380i
$646$	16.3562	+	9.44325i	0.643526	+	0.371540i
$647$	10.0075	+	17.3335i	0.393435	+	0.681449i	0.992900	−	0.118952i	$-0.0379533\pi$
$647$	10.0075	+	17.3335i	0.393435	+	0.681449i	−0.599465	+	0.800401i	$0.704620\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−1.30051	−	0.750849i	−0.0510495	−	0.0294734i
$650$	−25.6793	−	17.3046i	−1.00722	−	0.678741i
$651$	−11.4684	−	6.62126i	−0.449481	−	0.259508i
$652$	16.5162			0.646824
$653$	12.6958	+	21.9898i	0.496825	+	0.860526i	0.999993	−	0.00366254i	$-0.00116582\pi$
$653$	12.6958	+	21.9898i	0.496825	+	0.860526i	−0.503168	+	0.864188i	$0.667832\pi$
$654$	0.738832	−	1.27969i	0.0288906	−	0.0500400i
$655$	−35.2201	+	32.8577i	−1.37616	+	1.28386i
$656$	−1.33485			−0.0521172
$657$	−2.31501	−	1.33657i	−0.0903173	−	0.0521447i
$658$	−4.53623			−0.176841
$659$	10.2268	+	17.7134i	0.398381	+	0.690016i	0.993526	−	0.113602i	$-0.0362388\pi$
$659$	10.2268	+	17.7134i	0.398381	+	0.690016i	−0.595145	+	0.803618i	$0.702906\pi$
$660$	7.26342	−	6.77621i	0.282728	−	0.263764i
$661$	0.419280	−	0.242071i	0.0163081	−	0.00941548i	−0.491824	−	0.870695i	$-0.663670\pi$
$661$	0.419280	−	0.242071i	0.0163081	−	0.00941548i	0.508132	+	0.861279i	$0.330336\pi$
$662$	28.7591	−	16.6041i	1.11775	−	0.645335i
$663$	17.9420	−	10.3588i	0.696811	−	0.402304i
$664$	−5.20372	−	3.00437i	−0.201943	−	0.116592i
$665$	−31.8213	−	34.1092i	−1.23398	−	1.32270i
$666$	−5.88842	+	1.52530i	−0.228172	+	0.0591040i
$667$		−	0.359409i		−	0.0139164i
$668$	−5.60293	+	9.70456i	−0.216784	+	0.375481i
$669$	0.109921	+	0.190389i	0.00424980	+	0.00736087i
$670$	31.5420	+	9.63583i	1.21857	+	0.372264i
$671$	50.8195	−	29.3407i	1.96187	−	1.13268i
$672$	−3.69510			−0.142542
$673$	−35.6479	+	20.5813i	−1.37413	+	0.793352i	−0.991445	−	0.130529i	$-0.958333\pi$
$673$	−35.6479	+	20.5813i	−1.37413	+	0.793352i	−0.382681	+	0.923880i	$0.624999\pi$
$674$			6.32508i			0.243633i
$675$	2.79415	−	4.14641i	0.107547	−	0.159595i
$676$	25.3549			0.975190
$677$			15.4030i			0.591984i	0.955190	+	0.295992i	$0.0956501\pi$
$677$			15.4030i			0.591984i	−0.955190	+	0.295992i	$0.904350\pi$
$678$	5.52994	+	3.19271i	0.212376	+	0.122615i
$679$	40.9978	−	23.6701i	1.57335	−	0.908375i
$680$	−5.10271	−	5.46959i	−0.195680	−	0.209749i
$681$	−21.4699	−	12.3956i	−0.822728	−	0.475002i
$682$	13.7877	+	7.96033i	0.527958	+	0.304817i
$683$	7.89432	−	13.6734i	0.302068	−	0.523197i	−0.674536	−	0.738242i	$-0.735656\pi$
$683$	7.89432	−	13.6734i	0.302068	−	0.523197i	0.976604	+	0.215045i	$0.0689897\pi$
$684$	−4.88936	+	2.82287i	−0.186949	+	0.107935i
$685$	21.6851	+	6.62461i	0.828543	+	0.253113i
$686$	1.10787	+	0.639627i	0.0422986	+	0.0244211i
$687$	9.79129	+	5.65301i	0.373561	+	0.215676i
$688$	−0.748273	+	1.29605i	−0.0285276	+	0.0494113i
$689$		−	55.0888i		−	2.09871i
$690$	−7.09542	−	2.16759i	−0.270118	−	0.0825188i
$691$	13.8305	−	23.9551i	0.526137	−	0.911297i	−0.473399	−	0.880848i	$-0.656973\pi$
$691$	13.8305	−	23.9551i	0.526137	−	0.911297i	0.999536	−	0.0304486i	$-0.00969358\pi$
$692$			14.3230i			0.544480i
$693$		−	16.4151i		−	0.623558i
$694$	−13.3652	+	23.1493i	−0.507337	+	0.878734i
$695$	9.88209	+	10.5926i	0.374849	+	0.401800i
$696$	0.0541616	+	0.0938106i	0.00205299	+	0.00355588i
$697$	−4.46543			−0.169140
$698$	9.72032	+	16.8361i	0.367920	+	0.637255i
$699$	7.15391	+	12.3909i	0.270586	+	0.468669i
$700$	8.10639	+	16.6022i	0.306393	+	0.627502i
$701$	−10.6850	−	6.16897i	−0.403566	−	0.232999i	0.284456	−	0.958689i	$-0.408187\pi$
$701$	−10.6850	−	6.16897i	−0.403566	−	0.232999i	−0.688021	+	0.725690i	$0.741521\pi$
$702$			6.19314i			0.233745i
$703$	−8.61143	−	33.2445i	−0.324786	−	1.25384i
$704$	4.44239			0.167429
$705$	2.67458	−	0.618091i	0.100731	−	0.0232786i
$706$	2.02075	+	3.50004i	0.0760519	+	0.131726i
$707$	−32.7883	+	18.9303i	−1.23313	+	0.711948i
$708$	−0.169019	−	0.292750i	−0.00635213	−	0.0110022i
$709$		−	40.5310i		−	1.52217i	−0.648651	−	0.761086i	$-0.724666\pi$
$709$		−	40.5310i		−	1.52217i	0.648651	−	0.761086i	$-0.275334\pi$
$710$	3.47791	−	11.3846i	0.130524	−	0.427257i
$711$			5.62837i			0.211080i
$712$	13.9095	+	8.03066i	0.521281	+	0.300962i
$713$		−	11.8908i		−	0.445314i
$714$	−12.3611			−0.462603
$715$	59.9397	−	13.8520i	2.24162	−	0.518034i
$716$	−5.33654	+	3.08106i	−0.199436	+	0.115144i
$717$	−6.79825			−0.253885
$718$	−0.224604	+	0.389026i	−0.00838216	+	0.0145183i
$719$	−2.47337	+	4.28400i	−0.0922412	+	0.159766i	−0.908454	−	0.417985i	$-0.862736\pi$
$719$	−2.47337	+	4.28400i	−0.0922412	+	0.159766i	0.816213	+	0.577752i	$0.196070\pi$
$720$	2.17865	−	0.503482i	0.0811934	−	0.0187637i
$721$	−19.0181	+	10.9801i	−0.708270	+	0.408920i
$722$	−6.43721	−	11.1496i	−0.239568	−	0.414944i
$723$	2.77020	−	4.79812i	0.103025	−	0.178444i
$724$	−1.83239	+	3.17379i	−0.0681002	+	0.117953i
$725$	0.302671	−	0.449152i	0.0112409	−	0.0166811i
$726$			8.73486i			0.324181i
$727$	−17.2930	−	29.9524i	−0.641363	−	1.11087i	−0.985129	−	0.171817i	$-0.945036\pi$
$727$	−17.2930	−	29.9524i	−0.641363	−	1.11087i	0.343766	−	0.939055i	$-0.388297\pi$
$728$	−19.8184	−	11.4421i	−0.734518	−	0.424074i
$729$	−1.00000			−0.0370370
$730$	−4.37066	+	4.07749i	−0.161765	+	0.150915i
$731$	−2.50317	+	4.33562i	−0.0925831	+	0.160359i
$732$	13.2094			0.488233
$733$	34.9113	−	20.1561i	1.28948	−	0.744481i	0.310917	−	0.950437i	$-0.399364\pi$
$733$	34.9113	−	20.1561i	1.28948	−	0.744481i	0.978561	+	0.205956i	$0.0660304\pi$
$734$		−	33.3245i		−	1.23003i
$735$	14.2292	+	4.34690i	0.524851	+	0.160338i
$736$	−1.65897	−	2.87341i	−0.0611503	−	0.105915i
$737$	−56.7449	+	32.7617i	−2.09022	+	1.20679i
$738$	0.667426	−	1.15602i	0.0245683	−	0.0425535i
$739$	−15.1392			−0.556904			−0.278452	−	0.960450i	$-0.589821\pi$
$739$	−15.1392			−0.556904			−0.278452	+	0.960450i	$0.589821\pi$
$740$	−0.585029	+	13.5889i	−0.0215061	+	0.499537i
$741$	−34.9649			−1.28447
$742$	−16.4342	+	28.4649i	−0.603319	+	1.04498i
$743$	13.4411	−	7.76020i	0.493105	−	0.284694i	−0.232757	−	0.972535i	$-0.574775\pi$
$743$	13.4411	−	7.76020i	0.493105	−	0.284694i	0.725862	+	0.687841i	$0.241441\pi$
$744$	1.79190	+	3.10366i	0.0656943	+	0.113786i
$745$	1.17561	−	3.84826i	0.0430711	−	0.140989i
$746$		−	1.06367i		−	0.0389439i
$747$	5.20372	−	3.00437i	0.190394	−	0.109924i
$748$	14.8610			0.543371
$749$	−19.4149	+	33.6277i	−0.709406	+	1.22873i
$750$	−7.04171	−	8.68414i	−0.257127	−	0.317100i
$751$	17.8620			0.651793			0.325896	−	0.945406i	$-0.394334\pi$
$751$	17.8620			0.651793			0.325896	+	0.945406i	$0.394334\pi$
$752$	1.06316	+	0.613817i	0.0387695	+	0.0223836i
$753$	15.0407	+	26.0512i	0.548113	+	0.949359i
$754$			0.670860i			0.0244313i
$755$	25.1975	−	5.82311i	0.917032	−	0.211925i
$756$	1.84755	−	3.20005i	0.0671948	−	0.116385i
$757$	5.03804	−	8.72614i	0.183111	−	0.317157i	−0.759828	−	0.650125i	$-0.774717\pi$
$757$	5.03804	−	8.72614i	0.183111	−	0.317157i	0.942938	+	0.332968i	$0.108050\pi$
$758$	11.9117	+	20.6317i	0.432652	+	0.749376i
$759$	12.7648	−	7.36978i	0.463334	−	0.267506i
$760$	2.84253	+	12.3001i	0.103109	+	0.446171i
$761$	14.5679	−	25.2324i	0.528086	−	0.914672i	−0.471378	−	0.881931i	$-0.656243\pi$
$761$	14.5679	−	25.2324i	0.528086	−	0.914672i	0.999464	−	0.0327408i	$-0.0104236\pi$
$762$	8.80279	−	15.2469i	0.318892	−	0.552336i
$763$	−5.46012			−0.197670
$764$	14.7975	−	8.54336i	0.535356	−	0.309088i
$765$	7.28815	−	1.68428i	0.263504	−	0.0608952i
$766$	24.6494			0.890617
$767$		−	2.09352i		−	0.0755925i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$		−	48.5732i		−	1.75160i	−0.482678	−	0.875798i	$-0.660336\pi$
$769$		−	48.5732i		−	1.75160i	0.482678	−	0.875798i	$-0.339664\pi$
$770$	−35.1038	−	10.7239i	−1.26505	−	0.386463i
$771$			23.5130i			0.846800i
$772$	−12.0933	−	20.9462i	−0.435248	−	0.753871i
$773$	−24.3124	+	14.0368i	−0.874458	+	0.504868i	−0.868827	−	0.495116i	$-0.835126\pi$
$773$	−24.3124	+	14.0368i	−0.874458	+	0.504868i	−0.00563072	+	0.999984i	$0.501792\pi$
$774$	−0.748273	−	1.29605i	−0.0268961	−	0.0465854i
$775$	10.0137	−	14.8599i	0.359703	−	0.533784i
$776$	−12.8116			−0.459910
$777$	15.7602	+	16.0252i	0.565394	+	0.574901i
$778$		−	4.61716i		−	0.165533i
$779$	6.52657	+	3.76811i	0.233838	+	0.135007i
$780$	13.2441	+	4.04595i	0.474213	+	0.144868i
$781$	11.8248	+	20.4812i	0.423126	+	0.732875i
$782$	−5.54968	−	9.61233i	−0.198456	−	0.343736i
$783$	−0.108323			−0.00387115
$784$	3.32690	+	5.76236i	0.118818	+	0.205798i
$785$	32.1985	−	30.0388i	1.14921	−	1.07213i
$786$	10.7705	−	18.6551i	0.384172	−	0.665405i
$787$		−	18.8436i		−	0.671702i	−0.941915	−	0.335851i	$-0.890976\pi$
$787$		−	18.8436i		−	0.671702i	0.941915	−	0.335851i	$-0.109024\pi$
$788$		−	9.81631i		−	0.349692i
$789$	−13.7905	+	23.8858i	−0.490954	+	0.850357i
$790$	12.0363	+	3.67699i	0.428232	+	0.130821i
$791$		−	23.5948i		−	0.838936i
$792$	−2.22120	+	3.84723i	−0.0789268	+	0.136705i
$793$	70.8474	+	40.9038i	2.51587	+	1.45254i
$794$	−10.0627	−	5.80971i	−0.357113	−	0.206179i
$795$	5.81115	−	19.0223i	0.206100	−	0.674651i
$796$	19.0743	−	11.0125i	0.676070	−	0.390329i
$797$	14.8187	−	25.6667i	0.524905	−	0.909163i	−0.474674	−	0.880162i	$-0.657434\pi$
$797$	14.8187	−	25.6667i	0.524905	−	0.909163i	0.999579	−	0.0290012i	$-0.00923265\pi$
$798$	18.0667	+	10.4308i	0.639554	+	0.369247i
$799$	3.55656	+	2.05338i	0.125822	+	0.0726433i
$800$	0.346604	−	4.98797i	0.0122543	−	0.176351i
$801$	−13.9095	+	8.03066i	−0.491468	+	0.283749i
$802$	−5.47228	−	3.15942i	−0.193233	−	0.111563i
$803$		−	11.8752i		−	0.419066i
$804$	−14.7496			−0.520177
$805$	6.17274	+	26.7105i	0.217560	+	0.941420i
$806$			22.1950i			0.781785i
$807$	11.7661	−	6.79314i	0.414185	−	0.239130i
$808$	10.2462			0.360459
$809$	32.2806	−	18.6372i	1.13493	−	0.655251i	0.189758	−	0.981831i	$-0.439230\pi$
$809$	32.2806	−	18.6372i	1.13493	−	0.655251i	0.945169	+	0.326580i	$0.105896\pi$
$810$	−0.653296	+	2.13851i	−0.0229545	+	0.0751394i
$811$	8.33056	+	14.4289i	0.292525	+	0.506669i	0.974406	−	0.224794i	$-0.0721711\pi$
$811$	8.33056	+	14.4289i	0.292525	+	0.506669i	−0.681881	+	0.731463i	$0.738838\pi$
$812$	0.200133	−	0.346640i	0.00702328	−	0.0121647i
$813$			9.95387i			0.349098i
$814$	−18.9475	−	19.2661i	−0.664109	−	0.675276i
$815$	25.1930	+	27.0044i	0.882473	+	0.945922i
$816$	2.89708	+	1.67263i	0.101418	+	0.0585538i
$817$	7.31715	−	4.22456i	0.255995	−	0.147799i
$818$	−12.2422	+	7.06806i	−0.428040	+	0.247129i
$819$	19.8184	−	11.4421i	0.692510	−	0.399821i
$820$	−2.03612	−	2.18251i	−0.0711043	−	0.0762167i
$821$	−10.5880	−	18.3390i	−0.369525	−	0.640037i	0.619966	−	0.784629i	$-0.287146\pi$
$821$	−10.5880	−	18.3390i	−0.369525	−	0.640037i	−0.989491	+	0.144592i	$0.953813\pi$
$822$	−10.1403			−0.353683
$823$	17.6753	+	10.2048i	0.616121	+	0.355717i	0.775357	−	0.631523i	$-0.217570\pi$
$823$	17.6753	+	10.2048i	0.616121	+	0.355717i	−0.159236	+	0.987240i	$0.550903\pi$
$824$	5.94305			0.207036
$825$	22.1585	+	1.53975i	0.771461	+	0.0536072i
$826$	−0.624543	+	1.08174i	−0.0217306	+	0.0376386i
$827$	9.94714	+	17.2290i	0.345896	+	0.599110i	0.985516	−	0.169582i	$-0.0542416\pi$
$827$	9.94714	+	17.2290i	0.345896	+	0.599110i	−0.639620	+	0.768691i	$0.720908\pi$
$828$	3.31793			0.115306
$829$	−33.0369	−	19.0739i	−1.14742	−	0.662463i	−0.199163	−	0.979966i	$-0.563822\pi$
$829$	−33.0369	−	19.0739i	−1.14742	−	0.662463i	−0.948257	+	0.317503i	$0.897156\pi$
$830$	−3.02529	−	13.0909i	−0.105009	−	0.454392i
$831$	−23.1172	−	13.3467i	−0.801926	−	0.462992i
$832$	3.09657	+	5.36341i	0.107354	+	0.185943i
$833$	11.1294	+	19.2766i	0.385609	+	0.667895i
$834$	−5.61060	−	3.23928i	−0.194279	−	0.112167i
$835$	−24.4136	+	5.64194i	−0.844868	+	0.195247i
$836$	−21.7205	−	12.5403i	−0.751218	−	0.433716i
$837$	−3.58380			−0.123874
$838$	19.8015	+	34.2972i	0.684031	+	1.18478i
$839$	−24.9103	+	43.1458i	−0.859998	+	1.48956i	0.0119323	+	0.999929i	$0.496202\pi$
$839$	−24.9103	+	43.1458i	−0.859998	+	1.48956i	−0.871930	+	0.489631i	$0.837132\pi$
$840$	−5.63633	−	6.04158i	−0.194472	−	0.208454i
$841$	28.9883			0.999595
$842$	6.88568	+	3.97545i	0.237296	+	0.137003i
$843$	0.778273			0.0268051
$844$	3.58728	+	6.21336i	0.123479	+	0.213873i
$845$	38.6752	+	41.4559i	1.33047	+	1.42613i
$846$	−1.06316	+	0.613817i	−0.0365522	+	0.0211034i
$847$	27.9520	−	16.1381i	0.960443	−	0.554512i
$848$	7.70341	−	4.44757i	0.264536	−	0.152730i
$849$	10.0672	+	5.81231i	0.345506	+	0.199478i
$850$	1.15948	−	16.6861i	0.0397699	−	0.572328i
$851$	−5.38588	+	19.4503i	−0.184626	+	0.666747i
$852$			5.32363i			0.182385i
$853$	15.7852	−	27.3408i	0.540475	−	0.936130i	−0.458402	−	0.888745i	$-0.651578\pi$
$853$	15.7852	−	27.3408i	0.540475	−	0.936130i	0.998877	−	0.0473848i	$-0.0150887\pi$
$854$	−24.4050	−	42.2708i	−0.835123	−	1.44648i
$855$	−12.0735	−	3.68834i	−0.412903	−	0.126139i
$856$	9.10060	−	5.25423i	0.311052	−	0.179586i
$857$	51.4712			1.75822			0.879112	−	0.476615i	$-0.158137\pi$
$857$	51.4712			1.75822			0.879112	+	0.476615i	$0.158137\pi$
$858$	−23.8264	+	13.7562i	−0.813420	+	0.469628i
$859$			8.76509i			0.299061i	0.988757	+	0.149531i	$0.0477762\pi$
$859$			8.76509i			0.299061i	−0.988757	+	0.149531i	$0.952224\pi$
$860$	−3.26045	+	0.753483i	−0.111180	+	0.0256936i
$861$	−4.93242			−0.168096
$862$		−	11.5415i		−	0.393104i
$863$	42.3921	+	24.4751i	1.44305	+	0.833143i	0.998052	−	0.0623913i	$-0.0198727\pi$
$863$	42.3921	+	24.4751i	1.44305	+	0.833143i	0.444993	+	0.895534i	$0.353206\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−23.4185	+	21.8476i	−0.796252	+	0.742842i
$866$	−12.1411	−	7.00965i	−0.412571	−	0.238198i
$867$	−5.03092	−	2.90460i	−0.170859	−	0.0986455i
$868$	6.62126	−	11.4684i	0.224740	−	0.389262i
$869$	−21.6536	+	12.5017i	−0.734548	+	0.424092i
$870$	−0.0707671	+	0.231650i	−0.00239923	+	0.00785366i
$871$	−79.1080	−	45.6730i	−2.68047	−	1.54757i
$872$	1.27969	+	0.738832i	0.0433359	+	0.0250200i
$873$	6.40580	−	11.0952i	0.216803	−	0.375515i
$874$			18.7322i			0.633626i
$875$	−14.7798	+	38.5783i	−0.499649	+	1.30418i
$876$	1.33657	−	2.31501i	0.0451586	−	0.0782170i
$877$			36.6528i			1.23768i	0.785518	+	0.618839i	$0.212397\pi$
$877$			36.6528i			1.23768i	−0.785518	+	0.618839i	$0.787603\pi$
$878$			23.9409i			0.807965i
$879$	5.20154	−	9.00934i	0.175444	−	0.303877i
$880$	6.77621	+	7.26342i	0.228426	+	0.244850i
$881$	13.2691	+	22.9828i	0.447048	+	0.774310i	0.998192	−	0.0600998i	$-0.0191419\pi$
$881$	13.2691	+	22.9828i	0.447048	+	0.774310i	−0.551144	+	0.834410i	$0.685809\pi$
$882$	−6.65380			−0.224045
$883$	−19.8327	−	34.3512i	−0.667422	−	1.15601i	−0.978623	−	0.205665i	$-0.934064\pi$
$883$	−19.8327	−	34.3512i	−0.667422	−	1.15601i	0.311201	−	0.950344i	$-0.399269\pi$
$884$	10.3588	+	17.9420i	0.348405	+	0.603456i
$885$	0.220839	−	0.722896i	0.00742342	−	0.0242999i
$886$	−22.7184	−	13.1165i	−0.763239	−	0.440656i
$887$			0.635075i			0.0213237i	0.999943	+	0.0106619i	$0.00339384\pi$
$887$			0.635075i			0.0213237i	−0.999943	+	0.0106619i	$0.996606\pi$
$888$	−1.52530	−	5.88842i	−0.0511856	−	0.197602i
$889$	−65.0545			−2.18186
$890$	8.08658	+	34.9919i	0.271063	+	1.17293i
$891$	−2.22120	−	3.84723i	−0.0744129	−	0.128887i
$892$	−0.190389	+	0.109921i	−0.00637470	+	0.00368044i
$893$	−3.46545	−	6.00234i	−0.115967	−	0.200861i
$894$			1.79951i			0.0601845i
$895$	−13.1777	−	4.02568i	−0.440482	−	0.134564i
$896$		−	3.69510i		−	0.123445i
$897$	17.7954	+	10.2742i	0.594173	+	0.343046i
$898$		−	19.1331i		−	0.638479i
$899$	−0.388209			−0.0129475
$900$	4.14641	+	2.79415i	0.138214	+	0.0931385i
$901$	25.7699	−	14.8783i	0.858521	−	0.495668i
$902$	5.92994			0.197445
$903$	−2.76495	+	4.78903i	−0.0920117	+	0.159369i
$904$	−3.19271	+	5.52994i	−0.106188	+	0.183923i
$905$	−7.98426	+	1.84515i	−0.265406	+	0.0613348i
$906$	−10.0162	+	5.78284i	−0.332765	+	0.192122i
$907$	−6.74363	−	11.6803i	−0.223919	−	0.387838i	0.732076	−	0.681223i	$-0.238552\pi$
$907$	−6.74363	−	11.6803i	−0.223919	−	0.387838i	−0.955994	+	0.293385i	$0.905218\pi$
$908$	12.3956	−	21.4699i	0.411364	−	0.712503i
$909$	−5.12308	+	8.87344i	−0.169922	+	0.294313i
$910$	−11.5218	−	49.8568i	−0.381945	−	1.65274i
$911$			1.13010i			0.0374418i	0.999825	+	0.0187209i	$0.00595939\pi$
$911$			1.13010i			0.0374418i	−0.999825	+	0.0187209i	$0.994041\pi$
$912$	−2.82287	−	4.88936i	−0.0934746	−	0.161903i
$913$	23.1170	+	13.3466i	0.765059	+	0.441707i
$914$	−41.0396			−1.35747
$915$	20.1490	+	21.5977i	0.666104	+	0.713997i
$916$	−5.65301	+	9.79129i	−0.186781	+	0.323513i
$917$	−79.5964			−2.62851
$918$	−2.89708	+	1.67263i	−0.0956180	+	0.0552051i
$919$			32.5408i			1.07342i	0.843766	+	0.536712i	$0.180334\pi$
$919$			32.5408i			1.07342i	−0.843766	+	0.536712i	$0.819666\pi$
$920$	2.16759	−	7.09542i	0.0714634	−	0.233929i
$921$	−9.20320	−	15.9404i	−0.303256	−	0.525254i
$922$	−9.56724	+	5.52365i	−0.315080	+	0.181912i
$923$	−16.4850	+	28.5528i	−0.542610	+	0.939828i
$924$	16.4151			0.540017
$925$	−23.1105	+	19.7713i	−0.759869	+	0.650076i
$926$	−8.05337			−0.264650
$927$	−2.97152	+	5.14683i	−0.0975976	+	0.169044i
$928$	−0.0938106	+	0.0541616i	−0.00307948	+	0.00177794i
$929$	0.825374	+	1.42959i	0.0270797	+	0.0469033i	0.879248	−	0.476365i	$-0.158046\pi$
$929$	0.825374	+	1.42959i	0.0270797	+	0.0469033i	−0.852168	+	0.523268i	$0.824713\pi$
$930$	−2.34128	+	7.66398i	−0.0767737	+	0.251312i
$931$		−	37.5656i		−	1.23116i
$932$	−12.3909	+	7.15391i	−0.405879	+	0.234334i
$933$	−18.5249			−0.606478
$934$	−4.81896	+	8.34668i	−0.157681	+	0.273112i
$935$	22.6682	+	24.2981i	0.741330	+	0.794631i
$936$	−6.19314			−0.202429
$937$	−47.2940	−	27.3052i	−1.54503	−	0.892022i	−0.998510	−	0.0545738i	$-0.982620\pi$
$937$	−47.2940	−	27.3052i	−1.54503	−	0.892022i	−0.546517	−	0.837448i	$-0.684047\pi$
$938$	27.2506	+	47.1994i	0.889763	+	1.54111i
$939$			21.8188i			0.712028i
$940$	0.618091	+	2.67458i	0.0201599	+	0.0872352i
$941$	5.39829	−	9.35012i	0.175979	−	0.304805i	−0.764520	−	0.644599i	$-0.777024\pi$
$941$	5.39829	−	9.35012i	0.175979	−	0.304805i	0.940500	+	0.339794i	$0.110357\pi$
$942$	−9.84650	+	17.0546i	−0.320816	+	0.555670i
$943$	−2.21447	−	3.83558i	−0.0721132	−	0.124904i
$944$	0.292750	−	0.169019i	0.00952819	−	0.00550110i
$945$	8.05033	−	1.86042i	0.261877	−	0.0605194i
$946$	3.32412	−	5.75755i	0.108077	−	0.187194i
$947$	−26.1293	+	45.2573i	−0.849089	+	1.47067i	0.0329334	+	0.999458i	$0.489515\pi$
$947$	−26.1293	+	45.2573i	−0.849089	+	1.47067i	−0.882022	+	0.471208i	$0.843818\pi$
$948$	−5.62837			−0.182801
$949$	14.3372	−	8.27758i	0.465405	−	0.268702i
$950$	−15.7751	+	23.4096i	−0.511811	+	0.759506i
$951$	−27.9248			−0.905524
$952$		−	12.3611i		−	0.400626i
$953$	44.8260	+	25.8803i	1.45206	+	0.838345i	0.998598	−	0.0529333i	$-0.0168571\pi$
$953$	44.8260	+	25.8803i	1.45206	+	0.838345i	0.453457	+	0.891278i	$0.350190\pi$
$954$			8.89513i			0.287991i
$955$	36.5400	+	11.1627i	1.18241	+	0.361216i
$956$		−	6.79825i		−	0.219871i
$957$	−0.240607	−	0.416744i	−0.00777772	−	0.0134714i
$958$	−27.4842	+	15.8680i	−0.887973	+	0.512672i
$959$	18.7347	+	32.4495i	0.604975	+	1.04785i
$960$	0.503482	+	2.17865i	0.0162498	+	0.0703156i
$961$	18.1564			0.585689
$962$	10.0531	−	36.3052i	0.324125	−	1.17053i
$963$			10.5085i			0.338630i
$964$	4.79812	+	2.77020i	0.154537	+	0.0892220i
$965$	15.8010	−	51.7232i	0.508653	−	1.66503i
$966$	−6.13005	−	10.6176i	−0.197231	−	0.341615i
$967$	−6.57419	−	11.3868i	−0.211412	−	0.366176i	0.740745	−	0.671787i	$-0.234473\pi$
$967$	−6.57419	−	11.3868i	−0.211412	−	0.366176i	−0.952157	+	0.305611i	$0.901139\pi$
$968$	−8.73486			−0.280749
$969$	−9.44325	−	16.3562i	−0.303361	−	0.525437i
$970$	−19.5422	−	20.9473i	−0.627462	−	0.672576i
$971$	−15.3443	+	26.5771i	−0.492423	+	0.852901i	−0.999962	−	0.00872744i	$-0.997222\pi$
$971$	−15.3443	+	26.5771i	−0.492423	+	0.852901i	0.507539	+	0.861629i	$0.330555\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			23.9390i			0.767448i
$974$	−2.24168	+	3.88271i	−0.0718281	+	0.124410i
$975$	13.5866	+	27.8258i	0.435120	+	0.891140i
$976$			13.2094i			0.422822i
$977$	2.65295	−	4.59505i	0.0848755	−	0.147009i	−0.820463	−	0.571700i	$-0.806284\pi$
$977$	2.65295	−	4.59505i	0.0848755	−	0.147009i	0.905338	+	0.424691i	$0.139617\pi$
$978$	−14.3034	−	8.25810i	−0.457374	−	0.264065i
$979$	−61.7915	−	35.6753i	−1.97486	−	1.14019i
$980$	−4.34690	+	14.2292i	−0.138857	+	0.454534i
$981$	−1.27969	+	0.738832i	−0.0408575	+	0.0235891i
$982$	−4.45427	+	7.71502i	−0.142141	+	0.246196i
$983$	6.62158	+	3.82297i	0.211196	+	0.121934i	0.601867	−	0.798596i	$-0.294424\pi$
$983$	6.62158	+	3.82297i	0.211196	+	0.121934i	−0.390671	+	0.920530i	$0.627757\pi$
$984$	1.15602	+	0.667426i	0.0368524	+	0.0212768i
$985$	16.0499	−	14.9733i	0.511392	−	0.477090i
$986$	−0.313821	+	0.181185i	−0.00999410	+	0.00577010i
$987$	3.92849	+	2.26812i	0.125045	+	0.0721949i
$988$		−	34.9649i		−	1.11238i
$989$	−4.96544			−0.157892
$990$	−9.67841	+	2.23666i	−0.307600	+	0.0710858i
$991$			5.76561i			0.183151i	0.995798	+	0.0915753i	$0.0291902\pi$
$991$			5.76561i			0.183151i	−0.995798	+	0.0915753i	$0.970810\pi$
$992$	−3.10366	+	1.79190i	−0.0985414	+	0.0568929i
$993$	−33.2081			−1.05383
$994$	17.0359	−	9.83569i	0.540346	−	0.311969i
$995$	47.1008	+	14.3889i	1.49319	+	0.456159i
$996$	3.00437	+	5.20372i	0.0951970	+	0.164886i
$997$	−8.96717	+	15.5316i	−0.283993	+	0.491891i	−0.972365	−	0.233468i	$-0.924993\pi$
$997$	−8.96717	+	15.5316i	−0.283993	+	0.491891i	0.688371	+	0.725358i	$0.258326\pi$
$998$		−	36.5680i		−	1.15754i
$999$	5.86217	+	1.62326i	0.185471	+	0.0513578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.b.619.8	yes	36
5.4	even	2		1110.2.ba.a.619.11	yes	36
37.11	even	6		1110.2.ba.a.529.11	✓	36
185.159	even	6	inner	1110.2.ba.b.529.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.11	✓	36	37.11	even	6
1110.2.ba.a.619.11	yes	36	5.4	even	2
1110.2.ba.b.529.8	yes	36	185.159	even	6	inner
1110.2.ba.b.619.8	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.653296 - 2.13851i) q^{5} +1.00000i q^{6} +(3.20005 - 1.84755i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.653296 - 2.13851i) q^{5} +1.00000i q^{6} +(3.20005 - 1.84755i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.52535 - 1.63502i) q^{10} +4.44239 q^{11} +(0.866025 + 0.500000i) q^{12} +(3.09657 + 5.36341i) q^{13} -3.69510i q^{14} +(0.503482 + 2.17865i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.67263 + 2.89708i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(4.88936 - 2.82287i) q^{19} +(-2.17865 + 0.503482i) q^{20} +(-1.84755 + 3.20005i) q^{21} +(2.22120 - 3.84723i) q^{22} -3.31793 q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.14641 - 2.79415i) q^{25} +6.19314 q^{26} +1.00000i q^{27} +(-3.20005 - 1.84755i) q^{28} +0.108323i q^{29} +(2.13851 + 0.653296i) q^{30} +3.58380i q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.84723 + 2.22120i) q^{33} +(1.67263 + 2.89708i) q^{34} +(-1.86042 - 8.05033i) q^{35} -1.00000 q^{36} +(1.62326 - 5.86217i) q^{37} -5.64574i q^{38} +(-5.36341 - 3.09657i) q^{39} +(-0.653296 + 2.13851i) q^{40} +(0.667426 + 1.15602i) q^{41} +(1.84755 + 3.20005i) q^{42} +1.49655 q^{43} +(-2.22120 - 3.84723i) q^{44} +(-1.52535 - 1.63502i) q^{45} +(-1.65897 + 2.87341i) q^{46} -1.22763i q^{47} -1.00000i q^{48} +(3.32690 - 5.76236i) q^{49} +(-4.49301 + 2.19382i) q^{50} -3.34526i q^{51} +(3.09657 - 5.36341i) q^{52} +(-7.70341 - 4.44757i) q^{53} +(0.866025 + 0.500000i) q^{54} +(2.90220 - 9.50008i) q^{55} +(-3.20005 + 1.84755i) q^{56} +(-2.82287 + 4.88936i) q^{57} +(0.0938106 + 0.0541616i) q^{58} +(-0.292750 - 0.169019i) q^{59} +(1.63502 - 1.52535i) q^{60} +(11.4397 - 6.60469i) q^{61} +(3.10366 + 1.79190i) q^{62} -3.69510i q^{63} +1.00000 q^{64} +(13.4927 - 3.11813i) q^{65} +4.44239i q^{66} +(-12.7735 + 7.37478i) q^{67} +3.34526 q^{68} +(2.87341 - 1.65897i) q^{69} +(-7.90200 - 2.41400i) q^{70} +(2.66182 + 4.61040i) q^{71} +(-0.500000 + 0.866025i) q^{72} -2.67315i q^{73} +(-4.26515 - 4.33687i) q^{74} +(4.98797 + 0.346604i) q^{75} +(-4.88936 - 2.82287i) q^{76} +(14.2159 - 8.20755i) q^{77} +(-5.36341 + 3.09657i) q^{78} +(-4.87431 + 2.81418i) q^{79} +(1.52535 + 1.63502i) q^{80} +(-0.500000 - 0.866025i) q^{81} +1.33485 q^{82} +(5.20372 + 3.00437i) q^{83} +3.69510 q^{84} +(5.10271 + 5.46959i) q^{85} +(0.748273 - 1.29605i) q^{86} +(-0.0541616 - 0.0938106i) q^{87} -4.44239 q^{88} +(-13.9095 - 8.03066i) q^{89} +(-2.17865 + 0.503482i) q^{90} +(19.8184 + 11.4421i) q^{91} +(1.65897 + 2.87341i) q^{92} +(-1.79190 - 3.10366i) q^{93} +(-1.06316 - 0.613817i) q^{94} +(-2.84253 - 12.3001i) q^{95} +(-0.866025 - 0.500000i) q^{96} +12.8116 q^{97} +(-3.32690 - 5.76236i) q^{98} +(2.22120 - 3.84723i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

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