LMFDB - Embedded newform 1110.2.ba.a.529.6

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			529.6
Character	$\chi$	$=$	1110.529
Dual form			1110.2.ba.a.619.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.21345 - 0.317246i) q^{5} +1.00000i q^{6} +(-1.17143 - 0.676327i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.21345 - 0.317246i) q^{5} +1.00000i q^{6} +(-1.17143 - 0.676327i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.831981 + 2.07553i) q^{10} +3.00191 q^{11} +(0.866025 - 0.500000i) q^{12} +(-1.12218 + 1.94367i) q^{13} +1.35265i q^{14} +(1.75828 + 1.38147i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.19396 + 2.06800i) q^{17} +(0.500000 - 0.866025i) q^{18} +(4.57549 + 2.64166i) q^{19} +(1.38147 - 1.75828i) q^{20} +(0.676327 + 1.17143i) q^{21} +(-1.50095 - 2.59973i) q^{22} -6.77962 q^{23} +(-0.866025 - 0.500000i) q^{24} +(4.79871 + 1.40441i) q^{25} +2.24436 q^{26} -1.00000i q^{27} +(1.17143 - 0.676327i) q^{28} -4.07927i q^{29} +(0.317246 - 2.21345i) q^{30} +4.41998i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.59973 - 1.50095i) q^{33} +(1.19396 - 2.06800i) q^{34} +(2.37834 + 1.86865i) q^{35} -1.00000 q^{36} +(3.29819 - 5.11096i) q^{37} -5.28332i q^{38} +(1.94367 - 1.12218i) q^{39} +(-2.21345 - 0.317246i) q^{40} +(2.30168 - 3.98662i) q^{41} +(0.676327 - 1.17143i) q^{42} -3.19094 q^{43} +(-1.50095 + 2.59973i) q^{44} +(-0.831981 - 2.07553i) q^{45} +(3.38981 + 5.87132i) q^{46} -12.9161i q^{47} +1.00000i q^{48} +(-2.58516 - 4.47763i) q^{49} +(-1.18310 - 4.85801i) q^{50} -2.38792i q^{51} +(-1.12218 - 1.94367i) q^{52} +(5.39612 - 3.11545i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-6.64457 - 0.952343i) q^{55} +(-1.17143 - 0.676327i) q^{56} +(-2.64166 - 4.57549i) q^{57} +(-3.53275 + 2.03964i) q^{58} +(4.19055 - 2.41941i) q^{59} +(-2.07553 + 0.831981i) q^{60} +(9.20129 + 5.31237i) q^{61} +(3.82781 - 2.20999i) q^{62} -1.35265i q^{63} +1.00000 q^{64} +(3.10051 - 3.94621i) q^{65} +3.00191i q^{66} +(-3.05897 - 1.76610i) q^{67} -2.38792 q^{68} +(5.87132 + 3.38981i) q^{69} +(0.429124 - 2.99403i) q^{70} +(6.08437 - 10.5384i) q^{71} +(0.500000 + 0.866025i) q^{72} +7.06413i q^{73} +(-6.07532 - 0.300839i) q^{74} +(-3.45360 - 3.61561i) q^{75} +(-4.57549 + 2.64166i) q^{76} +(-3.51653 - 2.03027i) q^{77} +(-1.94367 - 1.12218i) q^{78} +(0.509669 + 0.294257i) q^{79} +(0.831981 + 2.07553i) q^{80} +(-0.500000 + 0.866025i) q^{81} -4.60335 q^{82} +(3.56360 - 2.05745i) q^{83} -1.35265 q^{84} +(-1.98671 - 4.95619i) q^{85} +(1.59547 + 2.76343i) q^{86} +(-2.03964 + 3.53275i) q^{87} +3.00191 q^{88} +(14.4684 - 8.35333i) q^{89} +(-1.38147 + 1.75828i) q^{90} +(2.62912 - 1.51792i) q^{91} +(3.38981 - 5.87132i) q^{92} +(2.20999 - 3.82781i) q^{93} +(-11.1857 + 6.45806i) q^{94} +(-9.28956 - 7.29873i) q^{95} +(0.866025 - 0.500000i) q^{96} +9.59790 q^{97} +(-2.58516 + 4.47763i) q^{98} +(1.50095 + 2.59973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 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} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 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} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	−2.21345	−	0.317246i	−0.989884	−	0.141877i
$5$	−2.21345	−	0.317246i	−0.989884	−	0.141877i
$6$			1.00000i			0.408248i
$7$	−1.17143	−	0.676327i	−0.442760	−	0.255628i	0.262008	−	0.965066i	$-0.415615\pi$
$7$	−1.17143	−	0.676327i	−0.442760	−	0.255628i	−0.704768	+	0.709438i	$0.748949\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.831981	+	2.07553i	0.263096	+	0.656339i
$11$	3.00191			0.905109			0.452555	−	0.891737i	$-0.350513\pi$
$11$	3.00191			0.905109			0.452555	+	0.891737i	$0.350513\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	−1.12218	+	1.94367i	−0.311237	+	0.539078i	−0.978630	−	0.205627i	$-0.934077\pi$
$13$	−1.12218	+	1.94367i	−0.311237	+	0.539078i	0.667394	+	0.744705i	$0.267410\pi$
$14$			1.35265i			0.361512i
$15$	1.75828	+	1.38147i	0.453986	+	0.356693i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.19396	+	2.06800i	0.289578	+	0.501564i	0.973709	−	0.227795i	$-0.0731517\pi$
$17$	1.19396	+	2.06800i	0.289578	+	0.501564i	−0.684131	+	0.729359i	$0.739818\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	4.57549	+	2.64166i	1.04969	+	0.606038i	0.922562	−	0.385848i	$-0.126091\pi$
$19$	4.57549	+	2.64166i	1.04969	+	0.606038i	0.127127	+	0.991886i	$0.459424\pi$
$20$	1.38147	−	1.75828i	0.308905	−	0.393163i
$21$	0.676327	+	1.17143i	0.147587	+	0.255628i
$22$	−1.50095	−	2.59973i	−0.320004	−	0.554264i
$23$	−6.77962			−1.41365			−0.706824	−	0.707390i	$-0.749873\pi$
$23$	−6.77962			−1.41365			−0.706824	+	0.707390i	$0.749873\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	4.79871	+	1.40441i	0.959742	+	0.280883i
$26$	2.24436			0.440155
$27$		−	1.00000i		−	0.192450i
$28$	1.17143	−	0.676327i	0.221380	−	0.127814i
$29$		−	4.07927i		−	0.757502i	−0.925499	−	0.378751i	$-0.876354\pi$
$29$		−	4.07927i		−	0.757502i	0.925499	−	0.378751i	$-0.123646\pi$
$30$	0.317246	−	2.21345i	0.0579209	−	0.404119i
$31$			4.41998i			0.793851i	0.917851	+	0.396926i	$0.129923\pi$
$31$			4.41998i			0.793851i	−0.917851	+	0.396926i	$0.870077\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.59973	−	1.50095i	−0.452555	−	0.261283i
$34$	1.19396	−	2.06800i	0.204763	−	0.354659i
$35$	2.37834	+	1.86865i	0.402014	+	0.315859i
$36$	−1.00000			−0.166667
$37$	3.29819	−	5.11096i	0.542220	−	0.840237i
$37$	3.29819	−	5.11096i	0.542220	−	0.840237i
$38$		−	5.28332i		−	0.857068i
$39$	1.94367	−	1.12218i	0.311237	−	0.179693i
$40$	−2.21345	−	0.317246i	−0.349977	−	0.0501610i
$41$	2.30168	−	3.98662i	0.359462	−	0.622606i	−0.628409	−	0.777883i	$-0.716294\pi$
$41$	2.30168	−	3.98662i	0.359462	−	0.622606i	0.987871	+	0.155277i	$0.0496271\pi$
$42$	0.676327	−	1.17143i	0.104360	−	0.180756i
$43$	−3.19094			−0.486614			−0.243307	−	0.969949i	$-0.578232\pi$
$43$	−3.19094			−0.486614			−0.243307	+	0.969949i	$0.578232\pi$
$44$	−1.50095	+	2.59973i	−0.226277	+	0.391924i
$45$	−0.831981	−	2.07553i	−0.124024	−	0.309401i
$46$	3.38981	+	5.87132i	0.499800	+	0.865679i
$47$		−	12.9161i		−	1.88401i	−0.335600	−	0.942005i	$-0.608939\pi$
$47$		−	12.9161i		−	1.88401i	0.335600	−	0.942005i	$-0.391061\pi$
$48$			1.00000i			0.144338i
$49$	−2.58516	−	4.47763i	−0.369309	−	0.639662i
$50$	−1.18310	−	4.85801i	−0.167315	−	0.687027i
$51$		−	2.38792i		−	0.334376i
$52$	−1.12218	−	1.94367i	−0.155618	−	0.269539i
$53$	5.39612	−	3.11545i	0.741213	−	0.427940i	−0.0812969	−	0.996690i	$-0.525906\pi$
$53$	5.39612	−	3.11545i	0.741213	−	0.427940i	0.822510	+	0.568750i	$0.192573\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−6.64457	−	0.952343i	−0.895954	−	0.128414i
$56$	−1.17143	−	0.676327i	−0.156539	−	0.0903780i
$57$	−2.64166	−	4.57549i	−0.349896	−	0.606038i
$58$	−3.53275	+	2.03964i	−0.463873	+	0.267817i
$59$	4.19055	−	2.41941i	0.545563	−	0.314981i	−0.201768	−	0.979433i	$-0.564669\pi$
$59$	4.19055	−	2.41941i	0.545563	−	0.314981i	0.747330	+	0.664453i	$0.231335\pi$
$60$	−2.07553	+	0.831981i	−0.267949	+	0.107408i
$61$	9.20129	+	5.31237i	1.17810	+	0.680179i	0.955575	−	0.294747i	$-0.0952355\pi$
$61$	9.20129	+	5.31237i	1.17810	+	0.680179i	0.222529	+	0.974926i	$0.428569\pi$
$62$	3.82781	−	2.20999i	0.486132	−	0.280669i
$63$		−	1.35265i		−	0.170418i
$64$	1.00000			0.125000
$65$	3.10051	−	3.94621i	0.384571	−	0.489467i
$66$			3.00191i			0.369509i
$67$	−3.05897	−	1.76610i	−0.373712	−	0.215763i	0.301367	−	0.953508i	$-0.402557\pi$
$67$	−3.05897	−	1.76610i	−0.373712	−	0.215763i	−0.675079	+	0.737745i	$0.735891\pi$
$68$	−2.38792			−0.289578
$69$	5.87132	+	3.38981i	0.706824	+	0.408085i
$70$	0.429124	−	2.99403i	0.0512901	−	0.357855i
$71$	6.08437	−	10.5384i	0.722082	−	1.25068i	−0.238081	−	0.971245i	$-0.576519\pi$
$71$	6.08437	−	10.5384i	0.722082	−	1.25068i	0.960164	−	0.279438i	$-0.0901481\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$			7.06413i			0.826794i	0.910551	+	0.413397i	$0.135658\pi$
$73$			7.06413i			0.826794i	−0.910551	+	0.413397i	$0.864342\pi$
$74$	−6.07532	−	0.300839i	−0.706241	−	0.0349718i
$75$	−3.45360	−	3.61561i	−0.398787	−	0.417495i
$76$	−4.57549	+	2.64166i	−0.524845	+	0.303019i
$77$	−3.51653	−	2.03027i	−0.400746	−	0.231371i
$78$	−1.94367	−	1.12218i	−0.220078	−	0.127062i
$79$	0.509669	+	0.294257i	0.0573422	+	0.0331066i	0.528397	−	0.848997i	$-0.322793\pi$
$79$	0.509669	+	0.294257i	0.0573422	+	0.0331066i	−0.471055	+	0.882104i	$0.656127\pi$
$80$	0.831981	+	2.07553i	0.0930184	+	0.232051i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.60335			−0.508355
$83$	3.56360	−	2.05745i	0.391156	−	0.225834i	−0.291505	−	0.956569i	$-0.594156\pi$
$83$	3.56360	−	2.05745i	0.391156	−	0.225834i	0.682661	+	0.730735i	$0.260823\pi$
$84$	−1.35265			−0.147587
$85$	−1.98671	−	4.95619i	−0.215489	−	0.537575i
$86$	1.59547	+	2.76343i	0.172044	+	0.297989i
$87$	−2.03964	+	3.53275i	−0.218672	+	0.378751i
$88$	3.00191			0.320004
$89$	14.4684	−	8.35333i	1.53365	−	0.885451i	0.534457	−	0.845195i	$-0.320516\pi$
$89$	14.4684	−	8.35333i	1.53365	−	0.885451i	0.999189	−	0.0402561i	$-0.0128174\pi$
$90$	−1.38147	+	1.75828i	−0.145619	+	0.185339i
$91$	2.62912	−	1.51792i	0.275606	−	0.159121i
$92$	3.38981	−	5.87132i	0.353412	−	0.612127i
$93$	2.20999	−	3.82781i	0.229165	−	0.396926i
$94$	−11.1857	+	6.45806i	−1.15372	+	0.666098i
$95$	−9.28956	−	7.29873i	−0.953088	−	0.748834i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	9.59790			0.974519			0.487260	−	0.873257i	$-0.337997\pi$
$97$	9.59790			0.974519			0.487260	+	0.873257i	$0.337997\pi$
$98$	−2.58516	+	4.47763i	−0.261141	+	0.452309i
$99$	1.50095	+	2.59973i	0.150852	+	0.261283i
$100$	−3.61561	+	3.45360i	−0.361561	+	0.345360i
$101$	−16.6462			−1.65636			−0.828180	−	0.560462i	$-0.810624\pi$
$101$	−16.6462			−1.65636			−0.828180	+	0.560462i	$0.810624\pi$
$102$	−2.06800	+	1.19396i	−0.204763	+	0.118220i
$103$	6.71339			0.661490			0.330745	−	0.943720i	$-0.392700\pi$
$103$	6.71339			0.661490			0.330745	+	0.943720i	$0.392700\pi$
$104$	−1.12218	+	1.94367i	−0.110039	+	0.190593i
$105$	−1.12538	−	2.80747i	−0.109826	−	0.273981i
$106$	−5.39612	−	3.11545i	−0.524117	−	0.302599i
$107$	−0.170274	−	0.0983076i	−0.0164610	−	0.00950376i	0.491747	−	0.870738i	$-0.336359\pi$
$107$	−0.170274	−	0.0983076i	−0.0164610	−	0.00950376i	−0.508208	+	0.861234i	$0.669692\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−11.6161	+	6.70656i	−1.11262	+	0.642372i	−0.939507	−	0.342530i	$-0.888716\pi$
$109$	−11.6161	+	6.70656i	−1.11262	+	0.642372i	−0.173114	+	0.984902i	$0.555383\pi$
$110$	2.49753	+	6.23054i	0.238130	+	0.594058i
$111$	−5.41180	+	2.77713i	−0.513665	+	0.263593i
$112$			1.35265i			0.127814i
$113$	7.24481	+	12.5484i	0.681535	+	1.18045i	0.974512	+	0.224333i	$0.0720204\pi$
$113$	7.24481	+	12.5484i	0.681535	+	1.18045i	−0.292978	+	0.956119i	$0.594646\pi$
$114$	−2.64166	+	4.57549i	−0.247414	+	0.428534i
$115$	15.0063	+	2.15080i	1.39935	+	0.200564i
$116$	3.53275	+	2.03964i	0.328008	+	0.189375i
$117$	−2.24436			−0.207491
$118$	−4.19055	−	2.41941i	−0.385771	−	0.222725i
$119$		−	3.23003i		−	0.296096i
$120$	1.75828	+	1.38147i	0.160508	+	0.126110i
$121$	−1.98855			−0.180777
$122$		−	10.6247i		−	0.961918i
$123$	−3.98662	+	2.30168i	−0.359462	+	0.207535i
$124$	−3.82781	−	2.20999i	−0.343748	−	0.198463i
$125$	−10.1762	−	4.63097i	−0.910183	−	0.414207i
$126$	−1.17143	+	0.676327i	−0.104360	+	0.0602520i
$127$	8.91376	−	5.14636i	0.790968	−	0.456666i	−0.0493351	−	0.998782i	$-0.515710\pi$
$127$	8.91376	−	5.14636i	0.790968	−	0.456666i	0.840303	+	0.542117i	$0.182377\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.76343	+	1.59547i	0.243307	+	0.140473i
$130$	−4.96778	−	0.712014i	−0.435703	−	0.0624477i
$131$	3.29183	−	1.90054i	0.287608	−	0.166051i	−0.349255	−	0.937028i	$-0.613565\pi$
$131$	3.29183	−	1.90054i	0.287608	−	0.166051i	0.636863	+	0.770977i	$0.280232\pi$
$132$	2.59973	−	1.50095i	0.226277	−	0.130641i
$133$	−3.57325	−	6.18905i	−0.309840	−	0.536659i
$134$			3.53219i			0.305135i
$135$	−0.317246	+	2.21345i	−0.0273042	+	0.190503i
$136$	1.19396	+	2.06800i	0.102381	+	0.177330i
$137$			10.1698i			0.868862i	0.900705	+	0.434431i	$0.143050\pi$
$137$			10.1698i			0.868862i	−0.900705	+	0.434431i	$0.856950\pi$
$138$		−	6.77962i		−	0.577119i
$139$	0.463646	+	0.803059i	0.0393260	+	0.0681146i	0.885018	−	0.465556i	$-0.154146\pi$
$139$	0.463646	+	0.803059i	0.0393260	+	0.0681146i	−0.845692	+	0.533671i	$0.820812\pi$
$140$	−2.80747	+	1.12538i	−0.237274	+	0.0951122i
$141$	−6.45806	+	11.1857i	−0.543867	+	0.942005i
$142$	−12.1687			−1.02118
$143$	−3.36868	+	5.83473i	−0.281703	+	0.487924i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−1.29413	+	9.02926i	−0.107472	+	0.749839i
$146$	6.11771	−	3.53206i	0.506306	−	0.292316i
$147$			5.17033i			0.426441i
$148$	2.77713	+	5.41180i	0.228278	+	0.444847i
$149$	−9.05684			−0.741965			−0.370983	−	0.928640i	$-0.620979\pi$
$149$	−9.05684			−0.741965			−0.370983	+	0.928640i	$0.620979\pi$
$150$	−1.40441	+	4.79871i	−0.114670	+	0.391813i
$151$	5.73747	−	9.93758i	0.466908	−	0.808709i	−0.532377	−	0.846507i	$-0.678701\pi$
$151$	5.73747	−	9.93758i	0.466908	−	0.808709i	0.999285	+	0.0377983i	$0.0120344\pi$
$152$	4.57549	+	2.64166i	0.371121	+	0.214267i
$153$	−1.19396	+	2.06800i	−0.0965260	+	0.167188i
$154$			4.06054i			0.327208i
$155$	1.40222	−	9.78339i	0.112629	−	0.785821i
$156$			2.24436i			0.179693i
$157$	5.04062	−	2.91020i	0.402285	−	0.232259i	−0.285184	−	0.958473i	$-0.592055\pi$
$157$	5.04062	−	2.91020i	0.402285	−	0.232259i	0.687469	+	0.726213i	$0.258722\pi$
$158$		−	0.588515i		−	0.0468197i
$159$	−6.23090			−0.494142
$160$	1.38147	−	1.75828i	0.109215	−	0.139004i
$161$	7.94187	+	4.58524i	0.625907	+	0.361367i
$162$	1.00000			0.0785674
$163$	2.20296	+	3.81563i	0.172549	+	0.298863i	0.939310	−	0.343069i	$-0.111466\pi$
$163$	2.20296	+	3.81563i	0.172549	+	0.298863i	−0.766761	+	0.641932i	$0.778133\pi$
$164$	2.30168	+	3.98662i	0.179731	+	0.311303i
$165$	5.27819	+	4.14704i	0.410907	+	0.322846i
$166$	−3.56360	−	2.05745i	−0.276589	−	0.159689i
$167$	10.8349	−	18.7666i	0.838431	−	1.45221i	−0.0527743	−	0.998606i	$-0.516806\pi$
$167$	10.8349	−	18.7666i	0.838431	−	1.45221i	0.891206	−	0.453599i	$-0.149860\pi$
$168$	0.676327	+	1.17143i	0.0521798	+	0.0903780i
$169$	3.98142	+	6.89603i	0.306263	+	0.530464i
$170$	−3.29884	+	4.19863i	−0.253009	+	0.322021i
$171$			5.28332i			0.404026i
$172$	1.59547	−	2.76343i	0.121653	−	0.210710i
$173$	−14.2574	+	8.23149i	−1.08397	+	0.625829i	−0.931964	−	0.362551i	$-0.881906\pi$
$173$	−14.2574	+	8.23149i	−1.08397	+	0.625829i	−0.152003	+	0.988380i	$0.548572\pi$
$174$	4.07927			0.309249
$175$	−4.67152	−	4.89067i	−0.353134	−	0.369700i
$176$	−1.50095	−	2.59973i	−0.113139	−	0.195962i
$177$	−4.83883			−0.363709
$178$	−14.4684	−	8.35333i	−1.08445	−	0.626109i
$179$		−	21.2532i		−	1.58854i	−0.607566	−	0.794269i	$-0.707854\pi$
$179$		−	21.2532i		−	1.58854i	0.607566	−	0.794269i	$-0.292146\pi$
$180$	2.21345	+	0.317246i	0.164981	+	0.0236461i
$181$	9.22354	−	15.9756i	0.685580	−	1.18746i	−0.287674	−	0.957728i	$-0.592882\pi$
$181$	9.22354	−	15.9756i	0.685580	−	1.18746i	0.973254	−	0.229731i	$-0.0737847\pi$
$182$	−2.62912	−	1.51792i	−0.194883	−	0.112516i
$183$	−5.31237	−	9.20129i	−0.392701	−	0.680179i
$184$	−6.77962			−0.499800
$185$	−8.92181	+	10.2665i	−0.655945	+	0.754809i
$186$	−4.41998			−0.324088
$187$	3.58416	+	6.20795i	0.262100	+	0.453970i
$188$	11.1857	+	6.45806i	0.815800	+	0.471002i
$189$	−0.676327	+	1.17143i	−0.0491956	+	0.0852092i
$190$	−1.67611	+	11.6944i	−0.121598	+	0.848398i
$191$			8.76184i			0.633985i	0.948428	+	0.316992i	$0.102673\pi$
$191$			8.76184i			0.633985i	−0.948428	+	0.316992i	$0.897327\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	13.2262			0.952041			0.476020	−	0.879434i	$-0.342079\pi$
$193$	13.2262			0.952041			0.476020	+	0.879434i	$0.342079\pi$
$194$	−4.79895	−	8.31202i	−0.344545	−	0.596769i
$195$	−4.65823	+	1.86727i	−0.333583	+	0.133718i
$196$	5.17033			0.369309
$197$	7.32681	−	4.23013i	0.522013	−	0.301385i	−0.215745	−	0.976450i	$-0.569218\pi$
$197$	7.32681	−	4.23013i	0.522013	−	0.301385i	0.737758	+	0.675065i	$0.235885\pi$
$198$	1.50095	−	2.59973i	0.106668	−	0.184755i
$199$			7.72653i			0.547719i	0.961770	+	0.273860i	$0.0883004\pi$
$199$			7.72653i			0.547719i	−0.961770	+	0.273860i	$0.911700\pi$
$200$	4.79871	+	1.40441i	0.339320	+	0.0993071i
$201$	1.76610	+	3.05897i	0.124571	+	0.215763i
$202$	8.32311	+	14.4160i	0.585612	+	1.01431i
$203$	−2.75892	+	4.77859i	−0.193638	+	0.335391i
$204$	2.06800	+	1.19396i	0.144789	+	0.0835940i
$205$	−6.35938	+	8.09398i	−0.444159	+	0.565308i
$206$	−3.35670	−	5.81397i	−0.233872	−	0.405078i
$207$	−3.38981	−	5.87132i	−0.235608	−	0.408085i
$208$	2.24436			0.155618
$209$	13.7352	+	7.93002i	0.950084	+	0.548531i
$210$	−1.86865	+	2.37834i	−0.128949	+	0.164121i
$211$	−14.0101			−0.964494			−0.482247	−	0.876035i	$-0.660179\pi$
$211$	−14.0101			−0.964494			−0.482247	+	0.876035i	$0.660179\pi$
$212$			6.23090i			0.427940i
$213$	−10.5384	+	6.08437i	−0.722082	+	0.416894i
$214$			0.196615i			0.0134403i
$215$	7.06298	+	1.01231i	0.481691	+	0.0690391i
$216$		−	1.00000i		−	0.0680414i
$217$	2.98935	−	5.17770i	0.202930	−	0.351485i
$218$	11.6161	+	6.70656i	0.786742	+	0.454226i
$219$	3.53206	−	6.11771i	0.238675	−	0.413397i
$220$	4.14704	−	5.27819i	0.279593	−	0.355856i
$221$	−5.35935			−0.360509
$222$	5.11096	+	3.29819i	0.343025	+	0.221360i
$223$			3.10337i			0.207817i	0.994587	+	0.103908i	$0.0331349\pi$
$223$			3.10337i			0.207817i	−0.994587	+	0.103908i	$0.966865\pi$
$224$	1.17143	−	0.676327i	0.0782696	−	0.0451890i
$225$	1.18310	+	4.85801i	0.0788731	+	0.323867i
$226$	7.24481	−	12.5484i	0.481918	−	0.834706i
$227$	7.97179	−	13.8076i	0.529107	−	0.916439i	−0.470317	−	0.882497i	$-0.655860\pi$
$227$	7.97179	−	13.8076i	0.529107	−	0.916439i	0.999424	−	0.0339421i	$-0.0108062\pi$
$228$	5.28332			0.349896
$229$	−6.73382	+	11.6633i	−0.444983	+	0.770733i	−0.998051	−	0.0624027i	$-0.980124\pi$
$229$	−6.73382	+	11.6633i	−0.444983	+	0.770733i	0.553068	+	0.833136i	$0.313457\pi$
$230$	−5.64052	−	14.0713i	−0.371925	−	0.927832i
$231$	2.03027	+	3.51653i	0.133582	+	0.231371i
$232$		−	4.07927i		−	0.267817i
$233$			27.6386i			1.81067i	0.424703	+	0.905333i	$0.360378\pi$
$233$			27.6386i			1.81067i	−0.424703	+	0.905333i	$0.639622\pi$
$234$	1.12218	+	1.94367i	0.0733592	+	0.127062i
$235$	−4.09758	+	28.5892i	−0.267297	+	1.86495i
$236$			4.83883i			0.314981i
$237$	−0.294257	−	0.509669i	−0.0191141	−	0.0331066i
$238$	−2.79729	+	1.61502i	−0.181321	+	0.104686i
$239$	11.3747	−	6.56719i	0.735768	−	0.424796i	−0.0847604	−	0.996401i	$-0.527012\pi$
$239$	11.3747	−	6.56719i	0.735768	−	0.424796i	0.820529	+	0.571605i	$0.193679\pi$
$240$	0.317246	−	2.21345i	0.0204781	−	0.142877i
$241$	24.8544	+	14.3497i	1.60101	+	0.924346i	0.991285	+	0.131736i	$0.0420553\pi$
$241$	24.8544	+	14.3497i	1.60101	+	0.924346i	0.609730	+	0.792610i	$0.291278\pi$
$242$	0.994274	+	1.72213i	0.0639143	+	0.110703i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−9.20129	+	5.31237i	−0.589052	+	0.340089i
$245$	4.30162	+	10.7311i	0.274820	+	0.685588i
$246$	3.98662	+	2.30168i	0.254178	+	0.146750i
$247$	−10.2690	+	5.92884i	−0.653404	+	0.377243i
$248$			4.41998i			0.280669i
$249$	−4.11489			−0.260771
$250$	1.07754	+	11.1283i	0.0681496	+	0.703815i
$251$		−	7.61640i		−	0.480743i	−0.970681	−	0.240372i	$-0.922731\pi$
$251$		−	7.61640i		−	0.480743i	0.970681	−	0.240372i	$-0.0772693\pi$
$252$	1.17143	+	0.676327i	0.0737933	+	0.0426046i
$253$	−20.3518			−1.27951
$254$	−8.91376	−	5.14636i	−0.559299	−	0.322911i
$255$	−0.757558	+	5.28554i	−0.0474401	+	0.330993i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.86850	+	10.1645i	0.366067	+	0.634046i	0.988947	−	0.148271i	$-0.0473708\pi$
$257$	5.86850	+	10.1645i	0.366067	+	0.634046i	−0.622880	+	0.782317i	$0.714037\pi$
$258$		−	3.19094i		−	0.198659i
$259$	−7.32029	+	3.75649i	−0.454861	+	0.233417i
$260$	1.86727	+	4.65823i	0.115803	+	0.288891i
$261$	3.53275	−	2.03964i	0.218672	−	0.126250i
$262$	−3.29183	−	1.90054i	−0.203370	−	0.117416i
$263$	12.8963	+	7.44568i	0.795219	+	0.459120i	0.841797	−	0.539795i	$-0.181498\pi$
$263$	12.8963	+	7.44568i	0.795219	+	0.459120i	−0.0465775	+	0.998915i	$0.514831\pi$
$264$	−2.59973	−	1.50095i	−0.160002	−	0.0923773i
$265$	−12.9324	+	5.18399i	−0.794430	+	0.318450i
$266$	−3.57325	+	6.18905i	−0.219090	+	0.379475i
$267$	−16.7067			−1.02243
$268$	3.05897	−	1.76610i	0.186856	−	0.107881i
$269$	11.5433			0.703807			0.351904	−	0.936036i	$-0.385534\pi$
$269$	11.5433			0.703807			0.351904	+	0.936036i	$0.385534\pi$
$270$	2.07553	−	0.831981i	0.126312	−	0.0506328i
$271$	0.336417	+	0.582692i	0.0204359	+	0.0353960i	0.876062	−	0.482198i	$-0.160161\pi$
$271$	0.336417	+	0.582692i	0.0204359	+	0.0353960i	−0.855627	+	0.517594i	$0.826828\pi$
$272$	1.19396	−	2.06800i	0.0723945	−	0.125391i
$273$	−3.03584			−0.183738
$274$	8.80728	−	5.08488i	0.532067	−	0.307189i
$275$	14.4053	+	4.21592i	0.868672	+	0.254230i
$276$	−5.87132	+	3.38981i	−0.353412	+	0.204042i
$277$	14.1902	−	24.5782i	0.852607	−	1.47676i	−0.0262400	−	0.999656i	$-0.508353\pi$
$277$	14.1902	−	24.5782i	0.852607	−	1.47676i	0.878847	−	0.477103i	$-0.158313\pi$
$278$	0.463646	−	0.803059i	0.0278077	−	0.0481643i
$279$	−3.82781	+	2.20999i	−0.229165	+	0.132309i
$280$	2.37834	+	1.86865i	0.142133	+	0.111673i
$281$	−17.3856	+	10.0376i	−1.03714	+	0.598791i	−0.919021	−	0.394209i	$-0.871018\pi$
$281$	−17.3856	+	10.0376i	−1.03714	+	0.598791i	−0.118115	+	0.993000i	$0.537685\pi$
$282$	12.9161			0.769144
$283$	4.39309	−	7.60906i	0.261142	−	0.452312i	−0.705404	−	0.708806i	$-0.749234\pi$
$283$	4.39309	−	7.60906i	0.261142	−	0.452312i	0.966546	+	0.256494i	$0.0825675\pi$
$284$	6.08437	+	10.5384i	0.361041	+	0.625342i
$285$	4.39562	+	10.9657i	0.260374	+	0.649550i
$286$	6.73736			0.398389
$287$	−5.39252	+	3.11337i	−0.318310	+	0.183777i
$288$	−1.00000			−0.0589256
$289$	5.64892	−	9.78421i	0.332289	−	0.575542i
$290$	8.46663	−	3.39388i	0.497178	−	0.199295i
$291$	−8.31202	−	4.79895i	−0.487260	−	0.281319i
$292$	−6.11771	−	3.53206i	−0.358012	−	0.206698i
$293$	18.1855	+	10.4994i	1.06241	+	0.613380i	0.926097	−	0.377286i	$-0.123143\pi$
$293$	18.1855	+	10.4994i	1.06241	+	0.613380i	0.136309	+	0.990666i	$0.456476\pi$
$294$	4.47763	−	2.58516i	0.261141	−	0.150770i
$295$	−10.0431	+	4.02582i	−0.584733	+	0.234392i
$296$	3.29819	−	5.11096i	0.191704	−	0.297069i
$297$		−	3.00191i		−	0.174188i
$298$	4.52842	+	7.84345i	0.262324	+	0.454359i
$299$	7.60795	−	13.1774i	0.439979	−	0.762066i
$300$	4.85801	−	1.18310i	0.280477	−	0.0683061i
$301$	3.73797	+	2.15812i	0.215453	+	0.124392i
$302$	−11.4749			−0.660308
$303$	14.4160	+	8.32311i	0.828180	+	0.478150i
$304$		−	5.28332i		−	0.303019i
$305$	−18.6813	−	14.6777i	−1.06969	−	0.840444i
$306$	2.38792			0.136508
$307$		−	16.2086i		−	0.925073i	−0.886600	−	0.462537i	$-0.846939\pi$
$307$		−	16.2086i		−	0.925073i	0.886600	−	0.462537i	$-0.153061\pi$
$308$	3.51653	−	2.03027i	0.200373	−	0.115685i
$309$	−5.81397	−	3.35670i	−0.330745	−	0.190956i
$310$	−9.17377	+	3.67734i	−0.521035	+	0.208859i
$311$	2.58380	−	1.49176i	0.146514	−	0.0845899i	−0.424951	−	0.905216i	$-0.639709\pi$
$311$	2.58380	−	1.49176i	0.146514	−	0.0845899i	0.571465	+	0.820626i	$0.306375\pi$
$312$	1.94367	−	1.12218i	0.110039	−	0.0635309i
$313$	2.25748	+	3.91006i	0.127600	+	0.221010i	0.922746	−	0.385408i	$-0.125939\pi$
$313$	2.25748	+	3.91006i	0.127600	+	0.221010i	−0.795146	+	0.606418i	$0.792606\pi$
$314$	−5.04062	−	2.91020i	−0.284458	−	0.164232i
$315$	−0.429124	+	2.99403i	−0.0241784	+	0.168694i
$316$	−0.509669	+	0.294257i	−0.0286711	+	0.0165533i
$317$	5.91704	−	3.41620i	0.332334	−	0.191873i	−0.324543	−	0.945871i	$-0.605210\pi$
$317$	5.91704	−	3.41620i	0.332334	−	0.191873i	0.656877	+	0.753998i	$0.271877\pi$
$318$	3.11545	+	5.39612i	0.174706	+	0.302599i
$319$		−	12.2456i		−	0.685622i
$320$	−2.21345	−	0.317246i	−0.123736	−	0.0177346i
$321$	0.0983076	+	0.170274i	0.00548700	+	0.00950376i
$322$		−	9.17048i		−	0.511051i
$323$			12.6162i			0.701982i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−8.11474	+	7.75112i	−0.450125	+	0.429955i
$326$	2.20296	−	3.81563i	0.122010	−	0.211328i
$327$	13.4131			0.741747
$328$	2.30168	−	3.98662i	0.127089	−	0.220124i
$329$	−8.73552	+	15.1304i	−0.481605	+	0.834164i
$330$	0.952343	−	6.64457i	0.0524247	−	0.365772i
$331$	−8.89801	+	5.13727i	−0.489079	+	0.282370i	−0.724192	−	0.689598i	$-0.757787\pi$
$331$	−8.89801	+	5.13727i	−0.489079	+	0.282370i	0.235113	+	0.971968i	$0.424454\pi$
$332$			4.11489i			0.225834i
$333$	6.07532	+	0.300839i	0.332925	+	0.0164859i
$334$	−21.6698			−1.18572
$335$	6.21058	+	4.87961i	0.339320	+	0.266601i
$336$	0.676327	−	1.17143i	0.0368967	−	0.0639069i
$337$	−17.6489	−	10.1896i	−0.961395	−	0.555062i	−0.0647931	−	0.997899i	$-0.520639\pi$
$337$	−17.6489	−	10.1896i	−0.961395	−	0.555062i	−0.896602	+	0.442837i	$0.853972\pi$
$338$	3.98142	−	6.89603i	0.216561	−	0.375095i
$339$		−	14.4896i		−	0.786968i
$340$	5.28554	+	0.757558i	0.286649	+	0.0410843i
$341$			13.2684i			0.718522i
$342$	4.57549	−	2.64166i	0.247414	−	0.142845i
$343$			16.4622i			0.888878i
$344$	−3.19094			−0.172044
$345$	−11.9205	−	9.36582i	−0.641776	−	0.504239i
$346$	14.2574	+	8.23149i	0.766480	+	0.442528i
$347$	2.73199			0.146661			0.0733304	−	0.997308i	$-0.476637\pi$
$347$	2.73199			0.146661			0.0733304	+	0.997308i	$0.476637\pi$
$348$	−2.03964	−	3.53275i	−0.109336	−	0.189375i
$349$	6.08918	+	10.5468i	0.325946	+	0.564556i	0.981703	−	0.190416i	$-0.0609838\pi$
$349$	6.08918	+	10.5468i	0.325946	+	0.564556i	−0.655757	+	0.754972i	$0.727650\pi$
$350$	−1.89969	+	6.49099i	−0.101543	+	0.346958i
$351$	1.94367	+	1.12218i	0.103746	+	0.0598975i
$352$	−1.50095	+	2.59973i	−0.0800011	+	0.138566i
$353$	−12.4776	−	21.6118i	−0.664115	−	1.15028i	−0.979525	−	0.201325i	$-0.935475\pi$
$353$	−12.4776	−	21.6118i	−0.664115	−	1.15028i	0.315410	−	0.948956i	$-0.397858\pi$
$354$	2.41941	+	4.19055i	0.128590	+	0.222725i
$355$	−16.8107	+	21.3961i	−0.892221	+	1.13559i
$356$			16.7067i			0.885451i
$357$	−1.61502	+	2.79729i	−0.0854757	+	0.148048i
$358$	−18.4058	+	10.6266i	−0.972777	+	0.561633i
$359$	−32.9716			−1.74018			−0.870088	−	0.492897i	$-0.835938\pi$
$359$	−32.9716			−1.74018			−0.870088	+	0.492897i	$0.835938\pi$
$360$	−0.831981	−	2.07553i	−0.0438493	−	0.109390i
$361$	4.45674	+	7.71930i	0.234565	+	0.406279i
$362$	−18.4471			−0.969557
$363$	1.72213	+	0.994274i	0.0903885	+	0.0521858i
$364$			3.03584i			0.159121i
$365$	2.24106	−	15.6361i	0.117303	−	0.818430i
$366$	−5.31237	+	9.20129i	−0.277682	+	0.480959i
$367$	25.6297	+	14.7973i	1.33786	+	0.772413i	0.986490	−	0.163824i	$-0.0523830\pi$
$367$	25.6297	+	14.7973i	1.33786	+	0.772413i	0.351369	+	0.936237i	$0.385716\pi$
$368$	3.38981	+	5.87132i	0.176706	+	0.306064i
$369$	4.60335			0.239641
$370$	13.3520	+	2.59326i	0.694136	+	0.134817i
$371$	−8.42825			−0.437573
$372$	2.20999	+	3.82781i	0.114583	+	0.198463i
$373$	1.28458	+	0.741651i	0.0665129	+	0.0384012i	0.532888	−	0.846186i	$-0.321107\pi$
$373$	1.28458	+	0.741651i	0.0665129	+	0.0384012i	−0.466375	+	0.884587i	$0.654440\pi$
$374$	3.58416	−	6.20795i	0.185333	−	0.321005i
$375$	6.49732	+	9.09861i	0.335520	+	0.469850i
$376$		−	12.9161i		−	0.666098i
$377$	7.92877	+	4.57768i	0.408352	+	0.235762i
$378$	1.35265			0.0695730
$379$	−6.13208	−	10.6211i	−0.314984	−	0.545568i	0.664450	−	0.747333i	$-0.268666\pi$
$379$	−6.13208	−	10.6211i	−0.314984	−	0.545568i	−0.979434	+	0.201764i	$0.935332\pi$
$380$	10.9657	−	4.39562i	0.562527	−	0.225491i
$381$	−10.2927			−0.527312
$382$	7.58798	−	4.38092i	0.388235	−	0.224147i
$383$	−6.12268	+	10.6048i	−0.312855	+	0.541880i	−0.978979	−	0.203961i	$-0.934619\pi$
$383$	−6.12268	+	10.6048i	−0.312855	+	0.541880i	0.666125	+	0.745841i	$0.267952\pi$
$384$			1.00000i			0.0510310i
$385$	7.13957	+	5.60951i	0.363866	+	0.285887i
$386$	−6.61309	−	11.4542i	−0.336597	−	0.583003i
$387$	−1.59547	−	2.76343i	−0.0811023	−	0.140473i
$388$	−4.79895	+	8.31202i	−0.243630	+	0.421979i
$389$	3.72965	+	2.15332i	0.189101	+	0.109177i	0.591562	−	0.806260i	$-0.298512\pi$
$389$	3.72965	+	2.15332i	0.189101	+	0.109177i	−0.402461	+	0.915437i	$0.631845\pi$
$390$	3.94621	+	3.10051i	0.199824	+	0.157000i
$391$	−8.09460	−	14.0203i	−0.409361	−	0.709035i
$392$	−2.58516	−	4.47763i	−0.130570	−	0.226155i
$393$	−3.80107			−0.191739
$394$	−7.32681	−	4.23013i	−0.369119	−	0.213111i
$395$	−1.03477	−	0.813014i	−0.0520651	−	0.0409072i
$396$	−3.00191			−0.150852
$397$			3.36805i			0.169038i	0.996422	+	0.0845189i	$0.0269353\pi$
$397$			3.36805i			0.169038i	−0.996422	+	0.0845189i	$0.973065\pi$
$398$	6.69137	−	3.86326i	0.335408	−	0.193648i
$399$			7.14651i			0.357773i
$400$	−1.18310	−	4.85801i	−0.0591548	−	0.242901i
$401$			23.8277i			1.18990i	0.803763	+	0.594950i	$0.202828\pi$
$401$			23.8277i			1.18990i	−0.803763	+	0.594950i	$0.797172\pi$
$402$	1.76610	−	3.05897i	0.0880849	−	0.152567i
$403$	−8.59099	−	4.96001i	−0.427947	−	0.247076i
$404$	8.32311	−	14.4160i	0.414090	−	0.717225i
$405$	1.38147	−	1.75828i	0.0686457	−	0.0873696i
$406$	5.51784			0.273846
$407$	9.90087	−	15.3426i	0.490768	−	0.760506i
$408$		−	2.38792i		−	0.118220i
$409$	29.8037	−	17.2072i	1.47370	−	0.850840i	0.474136	−	0.880452i	$-0.342761\pi$
$409$	29.8037	−	17.2072i	1.47370	−	0.850840i	0.999561	+	0.0296121i	$0.00942722\pi$
$410$	10.1893	+	1.46039i	0.503213	+	0.0721237i
$411$	5.08488	−	8.80728i	0.250819	−	0.434431i
$412$	−3.35670	+	5.81397i	−0.165373	+	0.286434i
$413$	−6.54526			−0.322071
$414$	−3.38981	+	5.87132i	−0.166600	+	0.288560i
$415$	−8.54057	+	3.42351i	−0.419240	+	0.168054i
$416$	−1.12218	−	1.94367i	−0.0550194	−	0.0952964i
$417$		−	0.927293i		−	0.0454097i
$418$		−	15.8600i		−	0.775740i
$419$	8.20896	+	14.2183i	0.401034	+	0.694611i	0.993851	−	0.110726i	$-0.0353176\pi$
$419$	8.20896	+	14.2183i	0.401034	+	0.694611i	−0.592817	+	0.805337i	$0.701984\pi$
$420$	2.99403	+	0.429124i	0.146094	+	0.0209391i
$421$		−	16.8650i		−	0.821952i	−0.911646	−	0.410976i	$-0.865188\pi$
$421$		−	16.8650i		−	0.821952i	0.911646	−	0.410976i	$-0.134812\pi$
$422$	7.00504	+	12.1331i	0.341000	+	0.590630i
$423$	11.1857	−	6.45806i	0.543867	−	0.314002i
$424$	5.39612	−	3.11545i	0.262059	−	0.151300i
$425$	2.82514	+	11.6006i	0.137039	+	0.562709i
$426$	10.5384	+	6.08437i	0.510589	+	0.294789i
$427$	−7.18579	−	12.4462i	−0.347745	−	0.602312i
$428$	0.170274	−	0.0983076i	0.00823049	−	0.00475188i
$429$	5.83473	−	3.36868i	0.281703	−	0.162641i
$430$	−2.65480	−	6.62288i	−0.128026	−	0.319384i
$431$	−20.9618	−	12.1023i	−1.00969	−	0.582946i	−0.0985911	−	0.995128i	$-0.531434\pi$
$431$	−20.9618	−	12.1023i	−1.00969	−	0.582946i	−0.911102	+	0.412182i	$0.864767\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$		−	27.2175i		−	1.30799i	−0.756499	−	0.653995i	$-0.773092\pi$
$433$		−	27.2175i		−	1.30799i	0.756499	−	0.653995i	$-0.226908\pi$
$434$	−5.97870			−0.286987
$435$	5.63538	−	7.17250i	0.270196	−	0.343895i
$436$		−	13.4131i		−	0.642372i
$437$	−31.0201	−	17.9094i	−1.48389	−	0.856725i
$438$	−7.06413			−0.337537
$439$	−0.303940	−	0.175480i	−0.0145063	−	0.00837519i	0.492729	−	0.870183i	$-0.335999\pi$
$439$	−0.303940	−	0.175480i	−0.0145063	−	0.00837519i	−0.507236	+	0.861807i	$0.669333\pi$
$440$	−6.64457	−	0.952343i	−0.316767	−	0.0454012i
$441$	2.58516	−	4.47763i	0.123103	−	0.213221i
$442$	2.67968	+	4.64134i	0.127459	+	0.220766i
$443$		−	29.6858i		−	1.41042i	−0.709001	−	0.705208i	$-0.750854\pi$
$443$		−	29.6858i		−	1.41042i	0.709001	−	0.705208i	$-0.249146\pi$
$444$	0.300839	−	6.07532i	0.0142772	−	0.288322i
$445$	−34.6751	+	13.8996i	−1.64376	+	0.658906i
$446$	2.68760	−	1.55168i	0.127261	−	0.0734744i
$447$	7.84345	+	4.52842i	0.370983	+	0.214187i
$448$	−1.17143	−	0.676327i	−0.0553450	−	0.0319534i
$449$	17.7164	+	10.2286i	0.836090	+	0.482717i	0.855933	−	0.517086i	$-0.172983\pi$
$449$	17.7164	+	10.2286i	0.836090	+	0.482717i	−0.0198434	+	0.999803i	$0.506317\pi$
$450$	3.61561	−	3.45360i	0.170442	−	0.162804i
$451$	6.90942	−	11.9675i	0.325352	−	0.563526i
$452$	−14.4896			−0.681535
$453$	−9.93758	+	5.73747i	−0.466908	+	0.269570i
$454$	−15.9436			−0.748270
$455$	−6.30097	+	2.52576i	−0.295394	+	0.118410i
$456$	−2.64166	−	4.57549i	−0.123707	−	0.214267i
$457$	−16.1935	+	28.0480i	−0.757502	+	1.31203i	0.186619	+	0.982432i	$0.440247\pi$
$457$	−16.1935	+	28.0480i	−0.757502	+	1.31203i	−0.944121	+	0.329599i	$0.893086\pi$
$458$	13.4676			0.629301
$459$	2.06800	−	1.19396i	0.0965260	−	0.0557293i
$460$	−9.36582	+	11.9205i	−0.436684	+	0.555795i
$461$	−16.5318	+	9.54466i	−0.769964	+	0.444539i	−0.832862	−	0.553481i	$-0.813299\pi$
$461$	−16.5318	+	9.54466i	−0.769964	+	0.444539i	0.0628977	+	0.998020i	$0.479966\pi$
$462$	2.03027	−	3.51653i	0.0944568	−	0.163604i
$463$	9.39427	−	16.2714i	0.436589	−	0.756194i	−0.560835	−	0.827928i	$-0.689520\pi$
$463$	9.39427	−	16.2714i	0.436589	−	0.756194i	0.997424	+	0.0717334i	$0.0228531\pi$
$464$	−3.53275	+	2.03964i	−0.164004	+	0.0946877i
$465$	−6.10605	+	7.77155i	−0.283161	+	0.360397i
$466$	23.9357	−	13.8193i	1.10880	−	0.640167i
$467$	−2.97790			−0.137801			−0.0689004	−	0.997624i	$-0.521949\pi$
$467$	−2.97790			−0.137801			−0.0689004	+	0.997624i	$0.521949\pi$
$468$	1.12218	−	1.94367i	0.0518728	−	0.0898463i
$469$	2.38892	+	4.13773i	0.110310	+	0.191062i
$470$	26.8077	−	10.7460i	1.23655	−	0.495675i
$471$	−5.82040			−0.268190
$472$	4.19055	−	2.41941i	0.192886	−	0.111363i
$473$	−9.57891			−0.440439
$474$	−0.294257	+	0.509669i	−0.0135157	+	0.0234099i
$475$	18.2465	+	19.1024i	0.837205	+	0.876480i
$476$	2.79729	+	1.61502i	0.128214	+	0.0740241i
$477$	5.39612	+	3.11545i	0.247071	+	0.142647i
$478$	−11.3747	−	6.56719i	−0.520267	−	0.300376i
$479$	28.9748	−	16.7286i	1.32389	−	0.764350i	0.339546	−	0.940589i	$-0.389727\pi$
$479$	28.9748	−	16.7286i	1.32389	−	0.764350i	0.984347	+	0.176239i	$0.0563932\pi$
$480$	−2.07553	+	0.831981i	−0.0947344	+	0.0379746i
$481$	6.23287	+	12.1460i	0.284194	+	0.553811i
$482$		−	28.6994i		−	1.30722i
$483$	−4.58524	−	7.94187i	−0.208636	−	0.361367i
$484$	0.994274	−	1.72213i	0.0451943	−	0.0782788i
$485$	−21.2445	−	3.04489i	−0.964661	−	0.138261i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−3.98263			−0.180470			−0.0902350	−	0.995920i	$-0.528762\pi$
$487$	−3.98263			−0.180470			−0.0902350	+	0.995920i	$0.528762\pi$
$488$	9.20129	+	5.31237i	0.416523	+	0.240479i
$489$		−	4.40591i		−	0.199242i
$490$	7.14264	−	9.09088i	0.322671	−	0.410684i
$491$	−39.2680			−1.77214			−0.886070	−	0.463551i	$-0.846575\pi$
$491$	−39.2680			−1.77214			−0.886070	+	0.463551i	$0.846575\pi$
$492$		−	4.60335i		−	0.207535i
$493$	8.43593	−	4.87049i	0.379935	−	0.219356i
$494$	10.2690	+	5.92884i	0.462026	+	0.266751i
$495$	−2.49753	−	6.23054i	−0.112256	−	0.280042i
$496$	3.82781	−	2.20999i	0.171874	−	0.0992314i
$497$	−14.2549	+	8.23005i	−0.639418	+	0.369168i
$498$	2.05745	+	3.56360i	0.0921964	+	0.159689i
$499$	−11.2105	−	6.47239i	−0.501851	−	0.289744i	0.227627	−	0.973749i	$-0.426903\pi$
$499$	−11.2105	−	6.47239i	−0.501851	−	0.289744i	−0.729478	+	0.684005i	$0.760237\pi$
$500$	9.09861	−	6.49732i	0.406902	−	0.290569i
$501$	−18.7666	+	10.8349i	−0.838431	+	0.484069i
$502$	−6.59600	+	3.80820i	−0.294394	+	0.169968i
$503$	−3.46336	−	5.99871i	−0.154424	−	0.267469i	0.778425	−	0.627737i	$-0.216019\pi$
$503$	−3.46336	−	5.99871i	−0.154424	−	0.267469i	−0.932849	+	0.360268i	$0.882685\pi$
$504$		−	1.35265i		−	0.0602520i
$505$	36.8455	+	5.28094i	1.63961	+	0.234999i
$506$	10.1759	+	17.6252i	0.452374	+	0.783534i
$507$		−	7.96285i		−	0.353643i
$508$			10.2927i			0.456666i
$509$	−11.5336	−	19.9767i	−0.511216	−	0.885452i	−0.999916	−	0.0129996i	$-0.995862\pi$
$509$	−11.5336	−	19.9767i	−0.511216	−	0.885452i	0.488700	−	0.872452i	$-0.337471\pi$
$510$	4.95619	−	1.98671i	0.219464	−	0.0879728i
$511$	4.77766	−	8.27515i	0.211351	−	0.366071i
$512$	1.00000			0.0441942
$513$	2.64166	−	4.57549i	0.116632	−	0.202013i
$514$	5.86850	−	10.1645i	0.258848	−	0.448338i
$515$	−14.8598	−	2.12980i	−0.654799	−	0.0938500i
$516$	−2.76343	+	1.59547i	−0.121653	+	0.0702366i
$517$		−	38.7730i		−	1.70523i
$518$	6.91336	+	4.46131i	0.303756	+	0.196019i
$519$	16.4630			0.722645
$520$	3.10051	−	3.94621i	0.135966	−	0.173053i
$521$	−14.6787	+	25.4242i	−0.643084	+	1.11385i	0.341657	+	0.939825i	$0.389012\pi$
$521$	−14.6787	+	25.4242i	−0.643084	+	1.11385i	−0.984741	+	0.174029i	$0.944321\pi$
$522$	−3.53275	−	2.03964i	−0.154624	−	0.0892724i
$523$	3.65507	−	6.33077i	0.159825	−	0.276825i	−0.774980	−	0.631985i	$-0.782240\pi$
$523$	3.65507	−	6.33077i	0.159825	−	0.276825i	0.934806	+	0.355160i	$0.115574\pi$
$524$			3.80107i			0.166051i
$525$	1.60032	+	6.57121i	0.0698437	+	0.286791i
$526$		−	14.8914i		−	0.649294i
$527$	−9.14051	+	5.27728i	−0.398167	+	0.229882i
$528$			3.00191i			0.130641i
$529$	22.9632			0.998400
$530$	10.9557	+	8.60778i	0.475884	+	0.373898i
$531$	4.19055	+	2.41941i	0.181854	+	0.104994i
$532$	7.14651			0.309840
$533$	5.16579	+	8.94741i	0.223755	+	0.387555i
$534$	8.35333	+	14.4684i	0.361484	+	0.626109i
$535$	0.345705	+	0.271618i	0.0149461	+	0.0117430i
$536$	−3.05897	−	1.76610i	−0.132127	−	0.0762837i
$537$	−10.6266	+	18.4058i	−0.458571	+	0.794269i
$538$	−5.77165	−	9.99679i	−0.248833	−	0.430992i
$539$	−7.76042	−	13.4414i	−0.334265	−	0.578964i
$540$	−1.75828	−	1.38147i	−0.0756643	−	0.0594489i
$541$			20.4675i			0.879965i	0.898006	+	0.439982i	$0.145015\pi$
$541$			20.4675i			0.879965i	−0.898006	+	0.439982i	$0.854985\pi$
$542$	0.336417	−	0.582692i	0.0144504	−	0.0250288i
$543$	−15.9756	+	9.22354i	−0.685580	+	0.395820i
$544$	−2.38792			−0.102381
$545$	27.8393	−	11.1595i	1.19250	−	0.478019i
$546$	1.51792	+	2.62912i	0.0649610	+	0.112516i
$547$	−11.7724			−0.503352			−0.251676	−	0.967812i	$-0.580982\pi$
$547$	−11.7724			−0.503352			−0.251676	+	0.967812i	$0.580982\pi$
$548$	−8.80728	−	5.08488i	−0.376228	−	0.217215i
$549$			10.6247i			0.453452i
$550$	−3.55155	−	14.5833i	−0.151438	−	0.621834i
$551$	10.7760	−	18.6647i	0.459075	−	0.795141i
$552$	5.87132	+	3.38981i	0.249900	+	0.144280i
$553$	−0.398029	−	0.689406i	−0.0169259	−	0.0293165i
$554$	−28.3804			−1.20577
$555$	12.8598	−	4.43015i	0.545867	−	0.188050i
$556$	−0.927293			−0.0393260
$557$	2.72821	+	4.72539i	0.115598	+	0.200221i	0.918019	−	0.396537i	$-0.129788\pi$
$557$	2.72821	+	4.72539i	0.115598	+	0.200221i	−0.802421	+	0.596759i	$0.796455\pi$
$558$	3.82781	+	2.20999i	0.162044	+	0.0935562i
$559$	3.58081	−	6.20214i	0.151452	−	0.262323i
$560$	0.429124	−	2.99403i	0.0181338	−	0.126521i
$561$		−	7.16832i		−	0.302647i
$562$	17.3856	+	10.0376i	0.733366	+	0.423409i
$563$	−14.7884			−0.623255			−0.311627	−	0.950204i	$-0.600874\pi$
$563$	−14.7884			−0.623255			−0.311627	+	0.950204i	$0.600874\pi$
$564$	−6.45806	−	11.1857i	−0.271933	−	0.471002i
$565$	−12.0551	−	30.0736i	−0.507162	−	1.26521i
$566$	−8.78618			−0.369311
$567$	1.17143	−	0.676327i	0.0491956	−	0.0284031i
$568$	6.08437	−	10.5384i	0.255295	−	0.442183i
$569$		−	7.17981i		−	0.300993i	−0.988611	−	0.150497i	$-0.951913\pi$
$569$		−	7.17981i		−	0.300993i	0.988611	−	0.150497i	$-0.0480873\pi$
$570$	7.29873	−	9.28956i	0.305710	−	0.389097i
$571$	−7.05703	−	12.2231i	−0.295328	−	0.511523i	0.679733	−	0.733459i	$-0.262096\pi$
$571$	−7.05703	−	12.2231i	−0.295328	−	0.511523i	−0.975061	+	0.221937i	$0.928762\pi$
$572$	−3.36868	−	5.83473i	−0.140852	−	0.243962i
$573$	4.38092	−	7.58798i	0.183016	−	0.316992i
$574$	5.39252	+	3.11337i	0.225079	+	0.129950i
$575$	−32.5334	−	9.52139i	−1.35674	−	0.397070i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−6.70480	−	11.6130i	−0.279124	−	0.483458i	0.692043	−	0.721856i	$-0.256711\pi$
$577$	−6.70480	−	11.6130i	−0.279124	−	0.483458i	−0.971167	+	0.238399i	$0.923378\pi$
$578$	−11.2978			−0.469928
$579$	−11.4542	−	6.61309i	−0.476020	−	0.274830i
$580$	−7.17250	−	5.63538i	−0.297822	−	0.233996i
$581$	−5.56603			−0.230918
$582$			9.59790i			0.397846i
$583$	16.1986	−	9.35229i	0.670879	−	0.387332i
$584$			7.06413i			0.292316i
$585$	4.96778	+	0.712014i	0.205392	+	0.0294381i
$586$		−	20.9988i		−	0.867451i
$587$	11.2829	−	19.5426i	0.465697	−	0.806611i	−0.533536	−	0.845777i	$-0.679137\pi$
$587$	11.2829	−	19.5426i	0.465697	−	0.806611i	0.999233	+	0.0391668i	$0.0124704\pi$
$588$	−4.47763	−	2.58516i	−0.184655	−	0.106610i
$589$	−11.6761	+	20.2236i	−0.481104	+	0.833297i
$590$	8.50801	+	6.68468i	0.350269	+	0.275204i
$591$	−8.46027			−0.348009
$592$	−6.07532	−	0.300839i	−0.249694	−	0.0123644i
$593$		−	1.74844i		−	0.0717997i	−0.999355	−	0.0358998i	$-0.988570\pi$
$593$		−	1.74844i		−	0.0717997i	0.999355	−	0.0358998i	$-0.0114297\pi$
$594$	−2.59973	+	1.50095i	−0.106668	+	0.0615849i
$595$	−1.02471	+	7.14951i	−0.0420092	+	0.293101i
$596$	4.52842	−	7.84345i	0.185491	−	0.321280i
$597$	3.86326	−	6.69137i	0.158113	−	0.273860i
$598$	−15.2159			−0.622224
$599$	−14.3049	+	24.7768i	−0.584481	+	1.01235i	0.410459	+	0.911879i	$0.365369\pi$
$599$	−14.3049	+	24.7768i	−0.584481	+	1.01235i	−0.994940	+	0.100472i	$0.967965\pi$
$600$	−3.45360	−	3.61561i	−0.140993	−	0.147607i
$601$	−6.17497	−	10.6954i	−0.251882	−	0.436273i	0.712162	−	0.702015i	$-0.247716\pi$
$601$	−6.17497	−	10.6954i	−0.251882	−	0.436273i	−0.964044	+	0.265743i	$0.914383\pi$
$602$		−	4.31624i		−	0.175917i
$603$		−	3.53219i		−	0.143842i
$604$	5.73747	+	9.93758i	0.233454	+	0.404355i
$605$	4.40155	+	0.630858i	0.178948	+	0.0256480i
$606$		−	16.6462i		−	0.676206i
$607$	−18.1702	−	31.4717i	−0.737505	−	1.27740i	−0.953616	−	0.301027i	$-0.902671\pi$
$607$	−18.1702	−	31.4717i	−0.737505	−	1.27740i	0.216111	−	0.976369i	$-0.430663\pi$
$608$	−4.57549	+	2.64166i	−0.185561	+	0.107133i
$609$	4.77859	−	2.75892i	0.193638	−	0.111797i
$610$	−3.37065	+	23.5173i	−0.136474	+	0.952187i
$611$	25.1047	+	14.4942i	1.01563	+	0.586373i
$612$	−1.19396	−	2.06800i	−0.0482630	−	0.0835940i
$613$	0.816507	−	0.471410i	0.0329784	−	0.0190401i	−0.483420	−	0.875388i	$-0.660606\pi$
$613$	0.816507	−	0.471410i	0.0329784	−	0.0190401i	0.516399	+	0.856348i	$0.327272\pi$
$614$	−14.0371	+	8.10430i	−0.566489	+	0.327063i
$615$	9.55438	−	3.82990i	0.385270	−	0.154437i
$616$	−3.51653	−	2.03027i	−0.141685	−	0.0818020i
$617$	8.06384	−	4.65566i	0.324638	−	0.187430i	−0.328820	−	0.944393i	$-0.606651\pi$
$617$	8.06384	−	4.65566i	0.324638	−	0.187430i	0.653458	+	0.756963i	$0.273318\pi$
$618$			6.71339i			0.270052i
$619$	−0.187571			−0.00753912			−0.00376956	−	0.999993i	$-0.501200\pi$
$619$	−0.187571			−0.00753912			−0.00376956	+	0.999993i	$0.501200\pi$
$620$	7.77155	+	6.10605i	0.312113	+	0.245225i
$621$			6.77962i			0.272057i
$622$	−2.58380	−	1.49176i	−0.103601	−	0.0598141i
$623$	−22.5983			−0.905383
$624$	−1.94367	−	1.12218i	−0.0778092	−	0.0449232i
$625$	21.0552	+	13.4788i	0.842210	+	0.539150i
$626$	2.25748	−	3.91006i	0.0902269	−	0.156278i
$627$	−7.93002	−	13.7352i	−0.316695	−	0.548531i
$628$			5.82040i			0.232259i
$629$	14.5074	+	0.718380i	0.578447	+	0.0286437i
$630$	2.80747	−	1.12538i	0.111852	−	0.0448363i
$631$	24.8688	−	14.3580i	0.990013	−	0.571584i	0.0847345	−	0.996404i	$-0.472996\pi$
$631$	24.8688	−	14.3580i	0.990013	−	0.571584i	0.905278	+	0.424820i	$0.139662\pi$
$632$	0.509669	+	0.294257i	0.0202735	+	0.0117049i
$633$	12.1331	+	7.00504i	0.482247	+	0.278425i
$634$	−5.91704	−	3.41620i	−0.234995	−	0.135675i
$635$	−21.3628	+	8.56335i	−0.847757	+	0.339826i
$636$	3.11545	−	5.39612i	0.123536	−	0.213970i
$637$	11.6041			0.459770
$638$	−10.6050	+	6.12280i	−0.419856	+	0.242404i
$639$	12.1687			0.481388
$640$	0.831981	+	2.07553i	0.0328870	+	0.0820424i
$641$	4.13811	+	7.16743i	0.163446	+	0.283096i	0.936102	−	0.351728i	$-0.114406\pi$
$641$	4.13811	+	7.16743i	0.163446	+	0.283096i	−0.772657	+	0.634824i	$0.781072\pi$
$642$	0.0983076	−	0.170274i	0.00387989	−	0.00672017i
$643$	14.4839			0.571189			0.285595	−	0.958351i	$-0.407809\pi$
$643$	14.4839			0.571189			0.285595	+	0.958351i	$0.407809\pi$
$644$	−7.94187	+	4.58524i	−0.312953	+	0.180684i
$645$	−5.61057	−	4.40818i	−0.220916	−	0.173572i
$646$	10.9259	−	6.30808i	0.429874	−	0.248188i
$647$	17.3434	−	30.0396i	0.681839	−	1.18098i	−0.292581	−	0.956241i	$-0.594514\pi$
$647$	17.3434	−	30.0396i	0.681839	−	1.18098i	0.974419	−	0.224738i	$-0.0721527\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	12.5796	−	7.26286i	0.493794	−	0.285092i
$650$	10.7700	+	3.15201i	0.422435	+	0.123632i
$651$	−5.17770	+	2.98935i	−0.202930	+	0.117162i
$652$	−4.40591			−0.172549
$653$	−11.4681	+	19.8634i	−0.448783	+	0.777315i	−0.998307	−	0.0581630i	$-0.981476\pi$
$653$	−11.4681	+	19.8634i	−0.448783	+	0.777315i	0.549524	+	0.835478i	$0.314809\pi$
$654$	−6.70656	−	11.6161i	−0.262247	−	0.454226i
$655$	−7.88922	+	3.16242i	−0.308257	+	0.123566i
$656$	−4.60335			−0.179731
$657$	−6.11771	+	3.53206i	−0.238675	+	0.137799i
$658$	17.4710			0.681092
$659$	−19.8771	+	34.4282i	−0.774303	+	1.34113i	0.160883	+	0.986974i	$0.448566\pi$
$659$	−19.8771	+	34.4282i	−0.774303	+	1.34113i	−0.935186	+	0.354158i	$0.884767\pi$
$660$	−6.23054	+	2.49753i	−0.242523	+	0.0972163i
$661$	−24.3780	−	14.0746i	−0.948194	−	0.547440i	−0.0556746	−	0.998449i	$-0.517731\pi$
$661$	−24.3780	−	14.0746i	−0.948194	−	0.547440i	−0.892519	+	0.451009i	$0.851064\pi$
$662$	8.89801	+	5.13727i	0.345831	+	0.199666i
$663$	4.64134	+	2.67968i	0.180255	+	0.104070i
$664$	3.56360	−	2.05745i	0.138295	−	0.0798444i
$665$	5.94576	+	14.8328i	0.230567	+	0.575190i
$666$	−2.77713	−	5.41180i	−0.107611	−	0.209703i
$667$			27.6559i			1.07084i
$668$	10.8349	+	18.7666i	0.419216	+	0.726103i
$669$	1.55168	−	2.68760i	0.0599916	−	0.103908i
$670$	1.12057	−	7.81833i	0.0432915	−	0.302048i
$671$	27.6214	+	15.9472i	1.06631	+	0.615636i
$672$	−1.35265			−0.0521798
$673$	−10.4568	−	6.03721i	−0.403078	−	0.232717i	0.284733	−	0.958607i	$-0.408095\pi$
$673$	−10.4568	−	6.03721i	−0.403078	−	0.232717i	−0.687811	+	0.725890i	$0.741428\pi$
$674$			20.3792i			0.784976i
$675$	1.40441	−	4.79871i	0.0540559	−	0.184702i
$676$	−7.96285			−0.306263
$677$			32.2867i			1.24088i	0.784254	+	0.620440i	$0.213046\pi$
$677$			32.2867i			1.24088i	−0.784254	+	0.620440i	$0.786954\pi$
$678$	−12.5484	+	7.24481i	−0.481918	+	0.278235i
$679$	−11.2433	−	6.49132i	−0.431478	−	0.249114i
$680$	−1.98671	−	4.95619i	−0.0761867	−	0.190061i
$681$	−13.8076	+	7.97179i	−0.529107	+	0.305480i
$682$	11.4907	−	6.63418i	0.440003	−	0.254036i
$683$	12.6798	+	21.9620i	0.485178	+	0.840353i	0.999855	−	0.0170311i	$-0.00542143\pi$
$683$	12.6798	+	21.9620i	0.485178	+	0.840353i	−0.514677	+	0.857384i	$0.672088\pi$
$684$	−4.57549	−	2.64166i	−0.174948	−	0.101006i
$685$	3.22632	−	22.5103i	0.123271	−	0.860073i
$686$	14.2567	−	8.23112i	0.544324	−	0.314266i
$687$	11.6633	−	6.73382i	0.444983	−	0.256911i
$688$	1.59547	+	2.76343i	0.0608267	+	0.105355i
$689$			13.9844i			0.532762i
$690$	−2.15080	+	15.0063i	−0.0818797	+	0.571281i
$691$	−17.4719	−	30.2623i	−0.664664	−	1.15123i	−0.979376	−	0.202045i	$-0.935241\pi$
$691$	−17.4719	−	30.2623i	−0.664664	−	1.15123i	0.314712	−	0.949187i	$-0.398092\pi$
$692$		−	16.4630i		−	0.625829i
$693$		−	4.06054i		−	0.154247i
$694$	−1.36599	−	2.36597i	−0.0518524	−	0.0898110i
$695$	−0.771490	−	1.92462i	−0.0292643	−	0.0730050i
$696$	−2.03964	+	3.53275i	−0.0773122	+	0.133909i
$697$	10.9924			0.416369
$698$	6.08918	−	10.5468i	0.230479	−	0.399201i
$699$	13.8193	−	23.9357i	0.522694	−	0.905333i
$700$	6.57121	−	1.60032i	0.248368	−	0.0604864i
$701$	−18.2155	+	10.5167i	−0.687990	+	0.397211i	−0.802859	−	0.596169i	$-0.796689\pi$
$701$	−18.2155	+	10.5167i	−0.687990	+	0.397211i	0.114868	+	0.993381i	$0.463355\pi$
$702$		−	2.24436i		−	0.0847079i
$703$	28.5923	−	14.6724i	1.07838	−	0.553382i
$704$	3.00191			0.113139
$705$	17.8432	−	22.7101i	0.672013	−	0.855314i
$706$	−12.4776	+	21.6118i	−0.469600	+	0.813371i
$707$	19.4999	+	11.2583i	0.733370	+	0.423411i
$708$	2.41941	−	4.19055i	0.0909271	−	0.157490i
$709$			40.1656i			1.50845i	0.656615	+	0.754226i	$0.271988\pi$
$709$			40.1656i			1.50845i	−0.656615	+	0.754226i	$0.728012\pi$
$710$	26.9349	+	3.86048i	1.01085	+	0.144881i
$711$			0.588515i			0.0220710i
$712$	14.4684	−	8.35333i	0.542226	−	0.313054i
$713$		−	29.9657i		−	1.12223i
$714$	3.23003			0.120881
$715$	9.30745	−	11.8462i	0.348079	−	0.443022i
$716$	18.4058	+	10.6266i	0.687857	+	0.397134i
$717$	−13.1344			−0.490512
$718$	16.4858	+	28.5543i	0.615245	+	1.06564i
$719$	26.0199	+	45.0677i	0.970377	+	1.68074i	0.694416	+	0.719574i	$0.255663\pi$
$719$	26.0199	+	45.0677i	0.970377	+	1.68074i	0.275962	+	0.961169i	$0.411004\pi$
$720$	−1.38147	+	1.75828i	−0.0514842	+	0.0655272i
$721$	−7.86429	−	4.54045i	−0.292881	−	0.169095i
$722$	4.45674	−	7.71930i	0.165863	−	0.287283i
$723$	−14.3497	−	24.8544i	−0.533671	−	0.924346i
$724$	9.22354	+	15.9756i	0.342790	+	0.593730i
$725$	5.72899	−	19.5752i	0.212769	−	0.727006i
$726$		−	1.98855i		−	0.0738019i
$727$	−11.3516	+	19.6615i	−0.421008	+	0.729206i	−0.996038	−	0.0889253i	$-0.971657\pi$
$727$	−11.3516	+	19.6615i	−0.421008	+	0.729206i	0.575031	+	0.818132i	$0.304990\pi$
$728$	2.62912	−	1.51792i	0.0974415	−	0.0562579i
$729$	−1.00000			−0.0370370
$730$	−14.6618	+	5.87722i	−0.542657	+	0.217526i
$731$	−3.80986	−	6.59887i	−0.140913	−	0.244068i
$732$	10.6247			0.392701
$733$	−26.1668	−	15.1074i	−0.966494	−	0.558005i	−0.0683283	−	0.997663i	$-0.521767\pi$
$733$	−26.1668	−	15.1074i	−0.966494	−	0.558005i	−0.898166	+	0.439657i	$0.855100\pi$
$734$		−	29.5946i		−	1.09236i
$735$	1.64026	−	11.4443i	0.0605021	−	0.422128i
$736$	3.38981	−	5.87132i	0.124950	−	0.216420i
$737$	−9.18274	−	5.30166i	−0.338251	−	0.195289i
$738$	−2.30168	−	3.98662i	−0.0847259	−	0.146750i
$739$	−20.1078			−0.739676			−0.369838	−	0.929096i	$-0.620587\pi$
$739$	−20.1078			−0.739676			−0.369838	+	0.929096i	$0.620587\pi$
$740$	−4.43015	−	12.8598i	−0.162856	−	0.472735i
$741$	11.8577			0.435602
$742$	4.21412	+	7.29908i	0.154705	+	0.267958i
$743$	−8.93959	−	5.16128i	−0.327962	−	0.189349i	0.326974	−	0.945033i	$-0.393971\pi$
$743$	−8.93959	−	5.16128i	−0.327962	−	0.189349i	−0.654936	+	0.755684i	$0.727304\pi$
$744$	2.20999	−	3.82781i	0.0810221	−	0.140334i
$745$	20.0468	+	2.87324i	0.734460	+	0.105268i
$746$		−	1.48330i		−	0.0543075i
$747$	3.56360	+	2.05745i	0.130385	+	0.0752780i
$748$	−7.16832			−0.262100
$749$	0.132976	+	0.230322i	0.00485884	+	0.00841577i
$750$	4.63097	−	10.1762i	0.169099	−	0.371581i
$751$	15.2700			0.557208			0.278604	−	0.960406i	$-0.410128\pi$
$751$	15.2700			0.557208			0.278604	+	0.960406i	$0.410128\pi$
$752$	−11.1857	+	6.45806i	−0.407900	+	0.235501i
$753$	−3.80820	+	6.59600i	−0.138779	+	0.240372i
$754$		−	9.15535i		−	0.333418i
$755$	−15.8522	+	20.1761i	−0.576922	+	0.734285i
$756$	−0.676327	−	1.17143i	−0.0245978	−	0.0426046i
$757$	2.93517	+	5.08386i	0.106680	+	0.184776i	0.914424	−	0.404759i	$-0.132644\pi$
$757$	2.93517	+	5.08386i	0.106680	+	0.184776i	−0.807743	+	0.589535i	$0.799311\pi$
$758$	−6.13208	+	10.6211i	−0.222727	+	0.385775i
$759$	17.6252	+	10.1759i	0.639753	+	0.369362i
$760$	−9.28956	−	7.29873i	−0.336968	−	0.264753i
$761$	−13.7631	−	23.8384i	−0.498911	−	0.864140i	0.501088	−	0.865396i	$-0.332933\pi$
$761$	−13.7631	−	23.8384i	−0.498911	−	0.864140i	−0.999999	+	0.00125666i	$0.999600\pi$
$762$	5.14636	+	8.91376i	0.186433	+	0.322911i
$763$	18.1433			0.656832
$764$	−7.58798	−	4.38092i	−0.274523	−	0.158496i
$765$	3.29884	−	4.19863i	0.119270	−	0.151802i
$766$	12.2454			0.442443
$767$			10.8601i			0.392134i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$			27.2786i			0.983692i	0.870682	+	0.491846i	$0.163678\pi$
$769$			27.2786i			0.983692i	−0.870682	+	0.491846i	$0.836322\pi$
$770$	1.28819	−	8.98780i	0.0464232	−	0.323898i
$771$		−	11.7370i		−	0.422698i
$772$	−6.61309	+	11.4542i	−0.238010	+	0.412246i
$773$	−34.4624	−	19.8969i	−1.23953	−	0.715642i	−0.270530	−	0.962711i	$-0.587199\pi$
$773$	−34.4624	−	19.8969i	−1.23953	−	0.715642i	−0.968998	+	0.247070i	$0.920532\pi$
$774$	−1.59547	+	2.76343i	−0.0573480	+	0.0993296i
$775$	−6.20748	+	21.2102i	−0.222979	+	0.761892i
$776$	9.59790			0.344545
$777$	8.21780	+	0.406931i	0.294812	+	0.0145986i
$778$		−	4.30663i		−	0.154400i
$779$	21.0626	−	12.1605i	0.754646	−	0.435695i
$780$	0.712014	−	4.96778i	0.0254942	−	0.177875i
$781$	18.2647	−	31.6354i	0.653563	−	1.13201i
$782$	−8.09460	+	14.0203i	−0.289462	+	0.501363i
$783$	−4.07927			−0.145781
$784$	−2.58516	+	4.47763i	−0.0923273	+	0.159916i
$785$	−12.0804	+	4.84247i	−0.431168	+	0.172835i
$786$	1.90054	+	3.29183i	0.0677899	+	0.117416i
$787$			15.7678i			0.562061i	0.959699	+	0.281031i	$0.0906763\pi$
$787$			15.7678i			0.562061i	−0.959699	+	0.281031i	$0.909324\pi$
$788$			8.46027i			0.301385i
$789$	−7.44568	−	12.8963i	−0.265073	−	0.459120i
$790$	−0.186704	+	1.30265i	−0.00664263	+	0.0463461i
$791$		−	19.5994i		−	0.696876i
$792$	1.50095	+	2.59973i	0.0533341	+	0.0923773i
$793$	−20.6510	+	11.9229i	−0.733338	+	0.423393i
$794$	2.91682	−	1.68403i	0.103514	−	0.0597639i
$795$	13.7918	+	1.97673i	0.489144	+	0.0701072i
$796$	−6.69137	−	3.86326i	−0.237169	−	0.136930i
$797$	−7.06082	−	12.2297i	−0.250107	−	0.433198i	0.713448	−	0.700708i	$-0.247132\pi$
$797$	−7.06082	−	12.2297i	−0.250107	−	0.433198i	−0.963555	+	0.267510i	$0.913799\pi$
$798$	6.18905	−	3.57325i	0.219090	−	0.126492i
$799$	26.7105	−	15.4213i	0.944951	−	0.545568i
$800$	−3.61561	+	3.45360i	−0.127831	+	0.122103i
$801$	14.4684	+	8.35333i	0.511216	+	0.295150i
$802$	20.6354	−	11.9139i	0.728661	−	0.420693i
$803$			21.2059i			0.748339i
$804$	−3.53219			−0.124571
$805$	−16.1243	−	12.6687i	−0.568306	−	0.446513i
$806$			9.92002i			0.349418i
$807$	−9.99679	−	5.77165i	−0.351904	−	0.203172i
$808$	−16.6462			−0.585612
$809$	−24.2202	−	13.9835i	−0.851537	−	0.491635i	0.00963235	−	0.999954i	$-0.496934\pi$
$809$	−24.2202	−	13.9835i	−0.851537	−	0.491635i	−0.861169	+	0.508319i	$0.830267\pi$
$810$	−2.21345	−	0.317246i	−0.0777727	−	0.0111469i
$811$	24.4604	−	42.3666i	0.858919	−	1.48769i	−0.0140411	−	0.999901i	$-0.504470\pi$
$811$	24.4604	−	42.3666i	0.858919	−	1.48769i	0.872961	−	0.487791i	$-0.162197\pi$
$812$	−2.75892	−	4.77859i	−0.0968192	−	0.167696i
$813$		−	0.672835i		−	0.0235973i
$814$	−18.2375	−	0.903091i	−0.639226	−	0.0316533i
$815$	−3.66564	−	9.14458i	−0.128402	−	0.320321i
$816$	−2.06800	+	1.19396i	−0.0723945	+	0.0417970i
$817$	−14.6001	−	8.42938i	−0.510793	−	0.294907i
$818$	−29.8037	−	17.2072i	−1.04206	−	0.601634i
$819$	2.62912	+	1.51792i	0.0918688	+	0.0530405i
$820$	−3.82990	−	9.55438i	−0.133746	−	0.333653i
$821$	−7.27927	+	12.6081i	−0.254048	+	0.440025i	−0.964637	−	0.263583i	$-0.915096\pi$
$821$	−7.27927	+	12.6081i	−0.254048	+	0.440025i	0.710588	+	0.703608i	$0.248429\pi$
$822$	−10.1698			−0.354711
$823$	13.1840	−	7.61181i	0.459567	−	0.265331i	−0.252295	−	0.967650i	$-0.581185\pi$
$823$	13.1840	−	7.61181i	0.459567	−	0.265331i	0.711862	+	0.702319i	$0.247852\pi$
$824$	6.71339			0.233872
$825$	−10.3674	−	10.8537i	−0.360946	−	0.377879i
$826$	3.27263	+	5.66836i	0.113869	+	0.197228i
$827$	−6.92772	+	11.9992i	−0.240900	+	0.417252i	−0.960971	−	0.276649i	$-0.910776\pi$
$827$	−6.92772	+	11.9992i	−0.240900	+	0.417252i	0.720071	+	0.693901i	$0.244109\pi$
$828$	6.77962			0.235608
$829$	18.9388	−	10.9343i	0.657770	−	0.379764i	−0.133657	−	0.991028i	$-0.542672\pi$
$829$	18.9388	−	10.9343i	0.657770	−	0.379764i	0.791427	+	0.611264i	$0.209339\pi$
$830$	7.23513	+	5.68459i	0.251135	+	0.197315i
$831$	−24.5782	+	14.1902i	−0.852607	+	0.492253i
$832$	−1.12218	+	1.94367i	−0.0389046	+	0.0673847i
$833$	6.17317	−	10.6922i	0.213888	−	0.370464i
$834$	−0.803059	+	0.463646i	−0.0278077	+	0.0160548i
$835$	−29.9362	+	38.1017i	−1.03598	+	1.31856i
$836$	−13.7352	+	7.93002i	−0.475042	+	0.274266i
$837$	4.41998			0.152777
$838$	8.20896	−	14.2183i	0.283574	−	0.491164i
$839$	14.0966	+	24.4161i	0.486669	+	0.842936i	0.999883	−	0.0153252i	$-0.00487836\pi$
$839$	14.0966	+	24.4161i	0.486669	+	0.842936i	−0.513213	+	0.858261i	$0.671545\pi$
$840$	−1.12538	−	2.80747i	−0.0388294	−	0.0968669i
$841$	12.3595			0.426191
$842$	−14.6055	+	8.43252i	−0.503340	+	0.290604i
$843$	20.0751			0.691424
$844$	7.00504	−	12.1331i	0.241124	−	0.417638i
$845$	−6.62494	−	16.5271i	−0.227905	−	0.568549i
$846$	−11.1857	−	6.45806i	−0.384572	−	0.222033i
$847$	2.32945	+	1.34491i	0.0800408	+	0.0462116i
$848$	−5.39612	−	3.11545i	−0.185303	−	0.106985i
$849$	−7.60906	+	4.39309i	−0.261142	+	0.150771i
$850$	8.63380	−	8.24692i	0.296137	−	0.282867i
$851$	−22.3605	+	34.6504i	−0.766508	+	1.18780i
$852$		−	12.1687i		−	0.416894i
$853$	12.4816	+	21.6188i	0.427362	+	0.740213i	0.996638	−	0.0819335i	$-0.0261095\pi$
$853$	12.4816	+	21.6188i	0.427362	+	0.740213i	−0.569275	+	0.822147i	$0.692776\pi$
$854$	−7.18579	+	12.4462i	−0.245893	+	0.425899i
$855$	1.67611	−	11.6944i	0.0573218	−	0.399939i
$856$	−0.170274	−	0.0983076i	−0.00581984	−	0.00336009i
$857$	25.5581			0.873047			0.436524	−	0.899693i	$-0.356210\pi$
$857$	25.5581			0.873047			0.436524	+	0.899693i	$0.356210\pi$
$858$	−5.83473	−	3.36868i	−0.199194	−	0.115005i
$859$			26.1665i			0.892789i	0.894836	+	0.446395i	$0.147292\pi$
$859$			26.1665i			0.892789i	−0.894836	+	0.446395i	$0.852708\pi$
$860$	−4.40818	+	5.61057i	−0.150318	+	0.191319i
$861$	6.22675			0.212207
$862$			24.2046i			0.824411i
$863$	−21.4938	+	12.4095i	−0.731658	+	0.422423i	−0.819029	−	0.573753i	$-0.805487\pi$
$863$	−21.4938	+	12.4095i	−0.731658	+	0.422423i	0.0873702	+	0.996176i	$0.472154\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	34.1693	−	13.6969i	1.16179	−	0.465708i
$866$	−23.5710	+	13.6087i	−0.800977	+	0.462444i
$867$	−9.78421	+	5.64892i	−0.332289	+	0.191847i
$868$	2.98935	+	5.17770i	0.101465	+	0.175743i
$869$	1.52998	+	0.883334i	0.0519010	+	0.0299651i
$870$	−9.02926	−	1.29413i	−0.306120	−	0.0438752i
$871$	6.86543	−	3.96376i	0.232626	−	0.134307i
$872$	−11.6161	+	6.70656i	−0.393371	+	0.227113i
$873$	4.79895	+	8.31202i	0.162420	+	0.281319i
$874$			35.8189i			1.21159i
$875$	8.78863	+	12.3073i	0.297110	+	0.416062i
$876$	3.53206	+	6.11771i	0.119337	+	0.206698i
$877$			18.9348i			0.639384i	0.947522	+	0.319692i	$0.103579\pi$
$877$			18.9348i			0.639384i	−0.947522	+	0.319692i	$0.896421\pi$
$878$			0.350960i			0.0118443i
$879$	−10.4994	−	18.1855i	−0.354135	−	0.613380i
$880$	2.49753	+	6.23054i	0.0841918	+	0.210031i
$881$	0.835883	−	1.44779i	0.0281616	−	0.0487773i	−0.851601	−	0.524190i	$-0.824368\pi$
$881$	0.835883	−	1.44779i	0.0281616	−	0.0487773i	0.879763	+	0.475413i	$0.157701\pi$
$882$	−5.17033			−0.174094
$883$	−19.4113	+	33.6214i	−0.653242	+	1.13145i	0.329089	+	0.944299i	$0.393258\pi$
$883$	−19.4113	+	33.6214i	−0.653242	+	1.13145i	−0.982331	+	0.187150i	$0.940075\pi$
$884$	2.67968	−	4.64134i	0.0901273	−	0.156105i
$885$	10.7105	+	1.53510i	0.360029	+	0.0516017i
$886$	−25.7087	+	14.8429i	−0.863700	+	0.498657i
$887$			54.2705i			1.82222i	0.412159	+	0.911112i	$0.364775\pi$
$887$			54.2705i			1.82222i	−0.412159	+	0.911112i	$0.635225\pi$
$888$	−5.41180	+	2.77713i	−0.181608	+	0.0931942i
$889$	−13.9225			−0.466945
$890$	29.3750	+	23.0797i	0.984652	+	0.773634i
$891$	−1.50095	+	2.59973i	−0.0502839	+	0.0870942i
$892$	−2.68760	−	1.55168i	−0.0899874	−	0.0519542i
$893$	34.1200	−	59.0976i	1.14178	−	1.97762i
$894$		−	9.05684i		−	0.302906i
$895$	−6.74248	+	47.0428i	−0.225376	+	1.57247i
$896$			1.35265i			0.0451890i
$897$	−13.1774	+	7.60795i	−0.439979	+	0.254022i
$898$		−	20.4572i		−	0.682664i
$899$	18.0303			0.601343
$900$	−4.79871	−	1.40441i	−0.159957	−	0.0468138i
$901$	12.8855	+	7.43945i	0.429278	+	0.247844i
$902$	−13.8188			−0.460117
$903$	−2.15812	−	3.73797i	−0.0718177	−	0.124392i
$904$	7.24481	+	12.5484i	0.240959	+	0.417353i
$905$	−25.4840	+	32.4351i	−0.847118	+	1.07818i
$906$	9.93758	+	5.73747i	0.330154	+	0.190615i
$907$	−7.93667	+	13.7467i	−0.263533	+	0.456452i	−0.967178	−	0.254099i	$-0.918221\pi$
$907$	−7.93667	+	13.7467i	−0.263533	+	0.456452i	0.703645	+	0.710551i	$0.251554\pi$
$908$	7.97179	+	13.8076i	0.264553	+	0.458220i
$909$	−8.32311	−	14.4160i	−0.276060	−	0.478150i
$910$	5.33786	+	4.19392i	0.176948	+	0.139027i
$911$		−	54.2419i		−	1.79712i	−0.438855	−	0.898558i	$-0.644616\pi$
$911$		−	54.2419i		−	1.79712i	0.438855	−	0.898558i	$-0.355384\pi$
$912$	−2.64166	+	4.57549i	−0.0874741	+	0.151510i
$913$	10.6976	−	6.17626i	0.354039	−	0.204405i
$914$	32.3871			1.07127
$915$	8.83958	+	22.0519i	0.292227	+	0.729013i
$916$	−6.73382	−	11.6633i	−0.222492	−	0.385367i
$917$	−5.14154			−0.169788
$918$	−2.06800	−	1.19396i	−0.0682542	−	0.0394066i
$919$		−	11.6006i		−	0.382667i	−0.981525	−	0.191333i	$-0.938719\pi$
$919$		−	11.6006i		−	0.382667i	0.981525	−	0.191333i	$-0.0612812\pi$
$920$	15.0063	+	2.15080i	0.494744	+	0.0709099i
$921$	−8.10430	+	14.0371i	−0.267046	+	0.462537i
$922$	16.5318	+	9.54466i	0.544447	+	0.314337i
$923$	13.6555	+	23.6521i	0.449477	+	0.778517i
$924$	−4.06054			−0.133582
$925$	23.0050	−	19.8940i	0.756399	−	0.654110i
$926$	−18.7885			−0.617430
$927$	3.35670	+	5.81397i	0.110248	+	0.190956i
$928$	3.53275	+	2.03964i	0.115968	+	0.0669543i
$929$	22.6937	−	39.3066i	0.744555	−	1.28961i	−0.205847	−	0.978584i	$-0.565995\pi$
$929$	22.6937	−	39.3066i	0.744555	−	1.28961i	0.950402	−	0.311023i	$-0.100672\pi$
$930$	9.78339	+	1.40222i	0.320810	+	0.0459806i
$931$		−	27.3165i		−	0.895262i
$932$	−23.9357	−	13.8193i	−0.784041	−	0.452666i
$933$	−2.98352			−0.0976760
$934$	1.48895	+	2.57894i	0.0487200	+	0.0843854i
$935$	−5.96391	−	14.8780i	−0.195041	−	0.486564i
$936$	−2.24436			−0.0733592
$937$	−3.30744	+	1.90955i	−0.108049	+	0.0623823i	−0.553051	−	0.833148i	$-0.686536\pi$
$937$	−3.30744	+	1.90955i	−0.108049	+	0.0623823i	0.445002	+	0.895530i	$0.353203\pi$
$938$	2.38892	−	4.13773i	0.0780009	−	0.135102i
$939$		−	4.51495i		−	0.147340i
$940$	−22.7101	−	17.8432i	−0.740723	−	0.581981i
$941$	13.6763	+	23.6880i	0.445833	+	0.772206i	0.998110	−	0.0614552i	$-0.0195741\pi$
$941$	13.6763	+	23.6880i	0.445833	+	0.772206i	−0.552277	+	0.833661i	$0.686241\pi$
$942$	2.91020	+	5.04062i	0.0948195	+	0.164232i
$943$	−15.6045	+	27.0278i	−0.508152	+	0.880145i
$944$	−4.19055	−	2.41941i	−0.136391	−	0.0787452i
$945$	1.86865	−	2.37834i	0.0607871	−	0.0773676i
$946$	4.78945	+	8.29558i	0.155719	+	0.269712i
$947$	−17.8892	−	30.9851i	−0.581322	−	1.00688i	−0.995323	−	0.0966032i	$-0.969202\pi$
$947$	−17.8892	−	30.9851i	−0.581322	−	1.00688i	0.414001	−	0.910277i	$-0.364131\pi$
$948$	0.588515			0.0191141
$949$	−13.7304	−	7.92722i	−0.445706	−	0.257328i
$950$	7.41997	−	25.3531i	0.240736	−	0.822564i
$951$	−6.83240			−0.221556
$952$		−	3.23003i		−	0.104686i
$953$	−2.51306	+	1.45091i	−0.0814059	+	0.0469997i	−0.540150	−	0.841568i	$-0.681633\pi$
$953$	−2.51306	+	1.45091i	−0.0814059	+	0.0469997i	0.458744	+	0.888568i	$0.348299\pi$
$954$		−	6.23090i		−	0.201733i
$955$	2.77966	−	19.3939i	0.0899476	−	0.627572i
$956$			13.1344i			0.424796i
$957$	−6.12280	+	10.6050i	−0.197922	+	0.342811i
$958$	−28.9748	−	16.7286i	−0.936134	−	0.540477i
$959$	6.87809	−	11.9132i	0.222105	−	0.384697i
$960$	1.75828	+	1.38147i	0.0567482	+	0.0445867i
$961$	11.4638			0.369801
$962$	7.40233	−	11.4708i	0.238661	−	0.369835i
$963$		−	0.196615i		−	0.00633584i
$964$	−24.8544	+	14.3497i	−0.800507	+	0.462173i
$965$	−29.2755	−	4.19595i	−0.942410	−	0.135072i
$966$	−4.58524	+	7.94187i	−0.147528	+	0.255525i
$967$	−26.9414	+	46.6639i	−0.866377	+	1.50061i	−0.000703986		1.00000i	$0.500224\pi$
$967$	−26.9414	+	46.6639i	−0.866377	+	1.50061i	−0.865673	+	0.500610i	$0.833109\pi$
$968$	−1.98855			−0.0639143
$969$	6.30808	−	10.9259i	0.202645	−	0.350991i
$970$	7.98527	+	19.9207i	0.256392	+	0.639615i
$971$	−12.2032	−	21.1365i	−0.391618	−	0.678302i	0.601045	−	0.799215i	$-0.294751\pi$
$971$	−12.2032	−	21.1365i	−0.391618	−	0.678302i	−0.992663	+	0.120913i	$0.961418\pi$
$972$			1.00000i			0.0320750i
$973$		−	1.25431i		−	0.0402112i
$974$	1.99131	+	3.44906i	0.0638058	+	0.110515i
$975$	10.9031	−	2.65529i	0.349180	−	0.0850375i
$976$		−	10.6247i		−	0.340089i
$977$	20.8789	+	36.1634i	0.667976	+	1.15697i	0.978469	+	0.206393i	$0.0661725\pi$
$977$	20.8789	+	36.1634i	0.667976	+	1.15697i	−0.310493	+	0.950576i	$0.600494\pi$
$978$	−3.81563	+	2.20296i	−0.122010	+	0.0704427i
$979$	43.4328	−	25.0759i	1.38812	−	0.801430i
$980$	−11.4443	−	1.64026i	−0.365573	−	0.0523963i
$981$	−11.6161	−	6.70656i	−0.370874	−	0.214124i
$982$	19.6340	+	34.0071i	0.626546	+	1.08521i
$983$	−0.756705	+	0.436884i	−0.0241352	+	0.0139344i	−0.512019	−	0.858974i	$-0.671102\pi$
$983$	−0.756705	+	0.436884i	−0.0241352	+	0.0139344i	0.487884	+	0.872909i	$0.337769\pi$
$984$	−3.98662	+	2.30168i	−0.127089	+	0.0733748i
$985$	−17.5595	+	7.03879i	−0.559492	+	0.224274i
$986$	−8.43593	−	4.87049i	−0.268655	−	0.155108i
$987$	15.1304	−	8.73552i	0.481605	−	0.278055i
$988$		−	11.8577i		−	0.377243i
$989$	21.6333			0.687900
$990$	−4.14704	+	5.27819i	−0.131802	+	0.167752i
$991$		−	23.5804i		−	0.749055i	−0.927216	−	0.374527i	$-0.877805\pi$
$991$		−	23.5804i		−	0.749055i	0.927216	−	0.374527i	$-0.122195\pi$
$992$	−3.82781	−	2.20999i	−0.121533	−	0.0701672i
$993$	10.2745			0.326053
$994$	14.2549	+	8.23005i	0.452137	+	0.261041i
$995$	2.45121	−	17.1023i	0.0777085	−	0.542179i
$996$	2.05745	−	3.56360i	0.0651927	−	0.112917i
$997$	30.1315	+	52.1894i	0.954276	+	1.65285i	0.736017	+	0.676963i	$0.236704\pi$
$997$	30.1315	+	52.1894i	0.954276	+	1.65285i	0.218258	+	0.975891i	$0.429963\pi$
$998$			12.9448i			0.409760i
$999$	−5.11096	−	3.29819i	−0.161704	−	0.104350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.a.529.6	✓	36
5.4	even	2		1110.2.ba.b.529.13	yes	36
37.27	even	6		1110.2.ba.b.619.13	yes	36
185.64	even	6	inner	1110.2.ba.a.619.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.6	✓	36	1.1	even	1	trivial
1110.2.ba.a.619.6	yes	36	185.64	even	6	inner
1110.2.ba.b.529.13	yes	36	5.4	even	2
1110.2.ba.b.619.13	yes	36	37.27	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.21345 - 0.317246i) q^{5} +1.00000i q^{6} +(-1.17143 - 0.676327i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.21345 - 0.317246i) q^{5} +1.00000i q^{6} +(-1.17143 - 0.676327i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.831981 + 2.07553i) q^{10} +3.00191 q^{11} +(0.866025 - 0.500000i) q^{12} +(-1.12218 + 1.94367i) q^{13} +1.35265i q^{14} +(1.75828 + 1.38147i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.19396 + 2.06800i) q^{17} +(0.500000 - 0.866025i) q^{18} +(4.57549 + 2.64166i) q^{19} +(1.38147 - 1.75828i) q^{20} +(0.676327 + 1.17143i) q^{21} +(-1.50095 - 2.59973i) q^{22} -6.77962 q^{23} +(-0.866025 - 0.500000i) q^{24} +(4.79871 + 1.40441i) q^{25} +2.24436 q^{26} -1.00000i q^{27} +(1.17143 - 0.676327i) q^{28} -4.07927i q^{29} +(0.317246 - 2.21345i) q^{30} +4.41998i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.59973 - 1.50095i) q^{33} +(1.19396 - 2.06800i) q^{34} +(2.37834 + 1.86865i) q^{35} -1.00000 q^{36} +(3.29819 - 5.11096i) q^{37} -5.28332i q^{38} +(1.94367 - 1.12218i) q^{39} +(-2.21345 - 0.317246i) q^{40} +(2.30168 - 3.98662i) q^{41} +(0.676327 - 1.17143i) q^{42} -3.19094 q^{43} +(-1.50095 + 2.59973i) q^{44} +(-0.831981 - 2.07553i) q^{45} +(3.38981 + 5.87132i) q^{46} -12.9161i q^{47} +1.00000i q^{48} +(-2.58516 - 4.47763i) q^{49} +(-1.18310 - 4.85801i) q^{50} -2.38792i q^{51} +(-1.12218 - 1.94367i) q^{52} +(5.39612 - 3.11545i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-6.64457 - 0.952343i) q^{55} +(-1.17143 - 0.676327i) q^{56} +(-2.64166 - 4.57549i) q^{57} +(-3.53275 + 2.03964i) q^{58} +(4.19055 - 2.41941i) q^{59} +(-2.07553 + 0.831981i) q^{60} +(9.20129 + 5.31237i) q^{61} +(3.82781 - 2.20999i) q^{62} -1.35265i q^{63} +1.00000 q^{64} +(3.10051 - 3.94621i) q^{65} +3.00191i q^{66} +(-3.05897 - 1.76610i) q^{67} -2.38792 q^{68} +(5.87132 + 3.38981i) q^{69} +(0.429124 - 2.99403i) q^{70} +(6.08437 - 10.5384i) q^{71} +(0.500000 + 0.866025i) q^{72} +7.06413i q^{73} +(-6.07532 - 0.300839i) q^{74} +(-3.45360 - 3.61561i) q^{75} +(-4.57549 + 2.64166i) q^{76} +(-3.51653 - 2.03027i) q^{77} +(-1.94367 - 1.12218i) q^{78} +(0.509669 + 0.294257i) q^{79} +(0.831981 + 2.07553i) q^{80} +(-0.500000 + 0.866025i) q^{81} -4.60335 q^{82} +(3.56360 - 2.05745i) q^{83} -1.35265 q^{84} +(-1.98671 - 4.95619i) q^{85} +(1.59547 + 2.76343i) q^{86} +(-2.03964 + 3.53275i) q^{87} +3.00191 q^{88} +(14.4684 - 8.35333i) q^{89} +(-1.38147 + 1.75828i) q^{90} +(2.62912 - 1.51792i) q^{91} +(3.38981 - 5.87132i) q^{92} +(2.20999 - 3.82781i) q^{93} +(-11.1857 + 6.45806i) q^{94} +(-9.28956 - 7.29873i) q^{95} +(0.866025 - 0.500000i) q^{96} +9.59790 q^{97} +(-2.58516 + 4.47763i) q^{98} +(1.50095 + 2.59973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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