LMFDB - Embedded newform 1110.2.bb.d.1009.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.8
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.d.1099.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.40108 + 1.74269i) q^{5} +1.00000 q^{6} +(3.36459 - 1.94255i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.40108 + 1.74269i) q^{5} +1.00000 q^{6} +(3.36459 - 1.94255i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.342030 + 2.20975i) q^{10} -0.297359 q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.273612 + 0.157970i) q^{13} +3.88510 q^{14} +(2.08472 + 0.808671i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.766516 - 0.442548i) q^{17} +(0.866025 - 0.500000i) q^{18} +(1.55178 + 2.68777i) q^{19} +(-0.808671 + 2.08472i) q^{20} +(1.94255 - 3.36459i) q^{21} +(-0.257521 - 0.148680i) q^{22} -7.33518i q^{23} +(0.500000 + 0.866025i) q^{24} +(-1.07393 + 4.88331i) q^{25} -0.315940 q^{26} -1.00000i q^{27} +(3.36459 + 1.94255i) q^{28} -4.88510 q^{29} +(1.40108 + 1.74269i) q^{30} +1.38670 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.257521 + 0.148680i) q^{33} +(-0.442548 - 0.766516i) q^{34} +(8.09933 + 3.14176i) q^{35} +1.00000 q^{36} +(-1.88771 + 5.78243i) q^{37} +3.10357i q^{38} +(-0.157970 + 0.273612i) q^{39} +(-1.74269 + 1.40108i) q^{40} +(-6.17993 - 10.7040i) q^{41} +(3.36459 - 1.94255i) q^{42} +7.34477i q^{43} +(-0.148680 - 0.257521i) q^{44} +(2.20975 - 0.342030i) q^{45} +(3.66759 - 6.35245i) q^{46} -5.14536i q^{47} +1.00000i q^{48} +(4.04699 - 7.00959i) q^{49} +(-3.37170 + 3.69210i) q^{50} -0.885096 q^{51} +(-0.273612 - 0.157970i) q^{52} +(4.71160 + 2.72024i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.416625 - 0.518205i) q^{55} +(1.94255 + 3.36459i) q^{56} +(2.68777 + 1.55178i) q^{57} +(-4.23062 - 2.44255i) q^{58} +(-6.37254 + 11.0376i) q^{59} +(0.342030 + 2.20975i) q^{60} +(-1.26241 - 2.18655i) q^{61} +(1.20092 + 0.693350i) q^{62} -3.88510i q^{63} -1.00000 q^{64} +(-0.658645 - 0.255491i) q^{65} -0.297359 q^{66} +(0.512438 - 0.295856i) q^{67} -0.885096i q^{68} +(-3.66759 - 6.35245i) q^{69} +(5.44335 + 6.77051i) q^{70} +(-2.61853 - 4.53542i) q^{71} +(0.866025 + 0.500000i) q^{72} +14.4291i q^{73} +(-4.52602 + 4.06388i) q^{74} +(1.51161 + 4.76603i) q^{75} +(-1.55178 + 2.68777i) q^{76} +(-1.00049 + 0.577635i) q^{77} +(-0.273612 + 0.157970i) q^{78} +(1.22680 + 2.12488i) q^{79} +(-2.20975 + 0.342030i) q^{80} +(-0.500000 - 0.866025i) q^{81} -12.3599i q^{82} +(5.62000 + 3.24471i) q^{83} +3.88510 q^{84} +(-0.302730 - 1.95585i) q^{85} +(-3.67239 + 6.36076i) q^{86} +(-4.23062 + 2.44255i) q^{87} -0.297359i q^{88} +(2.65348 - 4.59596i) q^{89} +(2.08472 + 0.808671i) q^{90} +(-0.613728 + 1.06301i) q^{91} +(6.35245 - 3.66759i) q^{92} +(1.20092 - 0.693350i) q^{93} +(2.57268 - 4.45601i) q^{94} +(-2.50977 + 6.47007i) q^{95} +(-0.500000 + 0.866025i) q^{96} -8.87683i q^{97} +(7.00959 - 4.04699i) q^{98} +(-0.148680 + 0.257521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	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
$5$	1.40108	+	1.74269i	0.626584	+	0.779354i
$5$	1.40108	+	1.74269i	0.626584	+	0.779354i
$6$	1.00000			0.408248
$7$	3.36459	−	1.94255i	1.27170	−	0.734214i	0.296389	−	0.955067i	$-0.404217\pi$
$7$	3.36459	−	1.94255i	1.27170	−	0.734214i	0.975307	+	0.220853i	$0.0708841\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.342030	+	2.20975i	0.108159	+	0.698786i
$11$	−0.297359			−0.0896572			−0.0448286	−	0.998995i	$-0.514274\pi$
$11$	−0.297359			−0.0896572			−0.0448286	+	0.998995i	$0.514274\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−0.273612	+	0.157970i	−0.0758863	+	0.0438130i	−0.537463	−	0.843287i	$-0.680617\pi$
$13$	−0.273612	+	0.157970i	−0.0758863	+	0.0438130i	0.461577	+	0.887100i	$0.347284\pi$
$14$	3.88510			1.03834
$15$	2.08472	+	0.808671i	0.538272	+	0.208798i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.766516	−	0.442548i	−0.185907	−	0.107334i	0.404158	−	0.914689i	$-0.367565\pi$
$17$	−0.766516	−	0.442548i	−0.185907	−	0.107334i	−0.590065	+	0.807356i	$0.700898\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	1.55178	+	2.68777i	0.356004	+	0.616617i	0.987289	−	0.158934i	$-0.0508057\pi$
$19$	1.55178	+	2.68777i	0.356004	+	0.616617i	−0.631285	+	0.775551i	$0.717472\pi$
$20$	−0.808671	+	2.08472i	−0.180824	+	0.466157i
$21$	1.94255	−	3.36459i	0.423899	−	0.734214i
$22$	−0.257521	−	0.148680i	−0.0549036	−	0.0316986i
$23$		−	7.33518i		−	1.52949i	−0.644333	−	0.764745i	$-0.722865\pi$
$23$		−	7.33518i		−	1.52949i	0.644333	−	0.764745i	$-0.277135\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−1.07393	+	4.88331i	−0.214785	+	0.976661i
$26$	−0.315940			−0.0619609
$27$		−	1.00000i		−	0.192450i
$28$	3.36459	+	1.94255i	0.635848	+	0.367107i
$29$	−4.88510			−0.907140			−0.453570	−	0.891221i	$-0.649850\pi$
$29$	−4.88510			−0.907140			−0.453570	+	0.891221i	$0.649850\pi$
$30$	1.40108	+	1.74269i	0.255802	+	0.318170i
$31$	1.38670			0.249059			0.124529	−	0.992216i	$-0.460258\pi$
$31$	1.38670			0.249059			0.124529	+	0.992216i	$0.460258\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−0.257521	+	0.148680i	−0.0448286	+	0.0258818i
$34$	−0.442548	−	0.766516i	−0.0758964	−	0.131456i
$35$	8.09933	+	3.14176i	1.36904	+	0.531055i
$36$	1.00000			0.166667
$37$	−1.88771	+	5.78243i	−0.310338	+	0.950626i
$37$	−1.88771	+	5.78243i	−0.310338	+	0.950626i
$38$			3.10357i			0.503465i
$39$	−0.157970	+	0.273612i	−0.0252954	+	0.0438130i
$40$	−1.74269	+	1.40108i	−0.275543	+	0.221531i
$41$	−6.17993	−	10.7040i	−0.965143	−	1.67168i	−0.709231	−	0.704976i	$-0.750958\pi$
$41$	−6.17993	−	10.7040i	−0.965143	−	1.67168i	−0.255912	−	0.966700i	$-0.582376\pi$
$42$	3.36459	−	1.94255i	0.519168	−	0.299742i
$43$			7.34477i			1.12007i	0.828470	+	0.560034i	$0.189212\pi$
$43$			7.34477i			1.12007i	−0.828470	+	0.560034i	$0.810788\pi$
$44$	−0.148680	−	0.257521i	−0.0224143	−	0.0388227i
$45$	2.20975	−	0.342030i	0.329411	−	0.0509868i
$46$	3.66759	−	6.35245i	0.540756	−	0.936617i
$47$		−	5.14536i		−	0.750528i	−0.926918	−	0.375264i	$-0.877552\pi$
$47$		−	5.14536i		−	0.750528i	0.926918	−	0.375264i	$-0.122448\pi$
$48$			1.00000i			0.144338i
$49$	4.04699	−	7.00959i	0.578141	−	1.00137i
$50$	−3.37170	+	3.69210i	−0.476831	+	0.522142i
$51$	−0.885096			−0.123938
$52$	−0.273612	−	0.157970i	−0.0379431	−	0.0219065i
$53$	4.71160	+	2.72024i	0.647187	+	0.373654i	0.787378	−	0.616471i	$-0.211438\pi$
$53$	4.71160	+	2.72024i	0.647187	+	0.373654i	−0.140190	+	0.990125i	$0.544771\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−0.416625	−	0.518205i	−0.0561778	−	0.0698747i
$56$	1.94255	+	3.36459i	0.259584	+	0.449613i
$57$	2.68777	+	1.55178i	0.356004	+	0.205539i
$58$	−4.23062	−	2.44255i	−0.555507	−	0.320722i
$59$	−6.37254	+	11.0376i	−0.829634	+	1.43697i	0.0686908	+	0.997638i	$0.478118\pi$
$59$	−6.37254	+	11.0376i	−0.829634	+	1.43697i	−0.898325	+	0.439331i	$0.855216\pi$
$60$	0.342030	+	2.20975i	0.0441559	+	0.285278i
$61$	−1.26241	−	2.18655i	−0.161635	−	0.279960i	0.773820	−	0.633405i	$-0.218343\pi$
$61$	−1.26241	−	2.18655i	−0.161635	−	0.279960i	−0.935455	+	0.353446i	$0.885010\pi$
$62$	1.20092	+	0.693350i	0.152517	+	0.0880556i
$63$		−	3.88510i		−	0.489476i
$64$	−1.00000			−0.125000
$65$	−0.658645	−	0.255491i	−0.0816949	−	0.0316898i
$66$	−0.297359			−0.0366024
$67$	0.512438	−	0.295856i	0.0626042	−	0.0361446i	−0.468371	−	0.883532i	$-0.655159\pi$
$67$	0.512438	−	0.295856i	0.0626042	−	0.0361446i	0.530975	+	0.847387i	$0.321826\pi$
$68$		−	0.885096i		−	0.107334i
$69$	−3.66759	−	6.35245i	−0.441526	−	0.764745i
$70$	5.44335	+	6.77051i	0.650604	+	0.809231i
$71$	−2.61853	−	4.53542i	−0.310762	−	0.538256i	0.667766	−	0.744372i	$-0.267251\pi$
$71$	−2.61853	−	4.53542i	−0.310762	−	0.538256i	−0.978528	+	0.206116i	$0.933918\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			14.4291i			1.68880i	0.535710	+	0.844402i	$0.320044\pi$
$73$			14.4291i			1.68880i	−0.535710	+	0.844402i	$0.679956\pi$
$74$	−4.52602	+	4.06388i	−0.526139	+	0.472417i
$75$	1.51161	+	4.76603i	0.174545	+	0.550334i
$76$	−1.55178	+	2.68777i	−0.178002	+	0.308308i
$77$	−1.00049	+	0.577635i	−0.114017	+	0.0658276i
$78$	−0.273612	+	0.157970i	−0.0309804	+	0.0178866i
$79$	1.22680	+	2.12488i	0.138026	+	0.239067i	0.926749	−	0.375681i	$-0.122591\pi$
$79$	1.22680	+	2.12488i	0.138026	+	0.239067i	−0.788724	+	0.614748i	$0.789258\pi$
$80$	−2.20975	+	0.342030i	−0.247058	+	0.0382401i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	12.3599i		−	1.36492i
$83$	5.62000	+	3.24471i	0.616875	+	0.356153i	0.775651	−	0.631162i	$-0.217422\pi$
$83$	5.62000	+	3.24471i	0.616875	+	0.356153i	−0.158777	+	0.987315i	$0.550755\pi$
$84$	3.88510			0.423899
$85$	−0.302730	−	1.95585i	−0.0328356	−	0.212141i
$86$	−3.67239	+	6.36076i	−0.396004	+	0.685898i
$87$	−4.23062	+	2.44255i	−0.453570	+	0.261869i
$88$		−	0.297359i		−	0.0316986i
$89$	2.65348	−	4.59596i	0.281268	−	0.487171i	−0.690429	−	0.723400i	$-0.742578\pi$
$89$	2.65348	−	4.59596i	0.281268	−	0.487171i	0.971697	+	0.236229i	$0.0759116\pi$
$90$	2.08472	+	0.808671i	0.219749	+	0.0852414i
$91$	−0.613728	+	1.06301i	−0.0643362	+	0.111434i
$92$	6.35245	−	3.66759i	0.662288	−	0.382372i
$93$	1.20092	−	0.693350i	0.124529	−	0.0718971i
$94$	2.57268	−	4.45601i	0.265352	−	0.459603i
$95$	−2.50977	+	6.47007i	−0.257496	+	0.663815i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	8.87683i		−	0.901306i	−0.892699	−	0.450653i	$-0.851191\pi$
$97$		−	8.87683i		−	0.901306i	0.892699	−	0.450653i	$-0.148809\pi$
$98$	7.00959	−	4.04699i	0.708075	−	0.408807i
$99$	−0.148680	+	0.257521i	−0.0149429	+	0.0258818i
$100$	−4.76603	+	1.51161i	−0.476603	+	0.151161i
$101$	−7.05378			−0.701877			−0.350939	−	0.936398i	$-0.614137\pi$
$101$	−7.05378			−0.701877			−0.350939	+	0.936398i	$0.614137\pi$
$102$	−0.766516	−	0.442548i	−0.0758964	−	0.0438188i
$103$			5.94035i			0.585320i	0.956217	+	0.292660i	$0.0945404\pi$
$103$			5.94035i			0.585320i	−0.956217	+	0.292660i	$0.905460\pi$
$104$	−0.157970	−	0.273612i	−0.0154902	−	0.0268298i
$105$	8.58511	−	1.32882i	0.837821	−	0.129680i
$106$	2.72024	+	4.71160i	0.264213	+	0.457631i
$107$	11.9668	−	6.90904i	1.15688	−	0.667922i	0.206322	−	0.978484i	$-0.433850\pi$
$107$	11.9668	−	6.90904i	1.15688	−	0.667922i	0.950553	+	0.310562i	$0.100517\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	3.08116	−	5.33672i	0.295121	−	0.511165i	−0.679892	−	0.733313i	$-0.737973\pi$
$109$	3.08116	−	5.33672i	0.295121	−	0.511165i	0.975013	+	0.222147i	$0.0713065\pi$
$110$	−0.101706	−	0.657091i	−0.00969727	−	0.0626512i
$111$	1.25641	+	5.95159i	0.119253	+	0.564900i
$112$			3.88510i			0.367107i
$113$	3.83100	+	2.21183i	0.360390	+	0.208071i	0.669252	−	0.743036i	$-0.266615\pi$
$113$	3.83100	+	2.21183i	0.360390	+	0.208071i	−0.308862	+	0.951107i	$0.599948\pi$
$114$	1.55178	+	2.68777i	0.145338	+	0.251733i
$115$	12.7829	−	10.2772i	1.19201	−	0.958354i
$116$	−2.44255	−	4.23062i	−0.226785	−	0.392803i
$117$			0.315940i			0.0292086i
$118$	−11.0376	+	6.37254i	−1.01609	+	0.586640i
$119$	−3.43868			−0.315224
$120$	−0.808671	+	2.08472i	−0.0738212	+	0.190308i
$121$	−10.9116			−0.991962
$122$		−	2.52482i		−	0.228586i
$123$	−10.7040	−	6.17993i	−0.965143	−	0.557225i
$124$	0.693350	+	1.20092i	0.0622647	+	0.107846i
$125$	−10.0147	+	4.97040i	−0.895746	+	0.444566i
$126$	1.94255	−	3.36459i	0.173056	−	0.299742i
$127$	−9.86467	−	5.69537i	−0.875348	−	0.505382i	−0.00622607	−	0.999981i	$-0.501982\pi$
$127$	−9.86467	−	5.69537i	−0.875348	−	0.505382i	−0.869122	+	0.494598i	$0.835315\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	3.67239	+	6.36076i	0.323336	+	0.560034i
$130$	−0.442658	−	0.550585i	−0.0388237	−	0.0482895i
$131$	−7.22034	+	12.5060i	−0.630844	+	1.09265i	0.356535	+	0.934282i	$0.383958\pi$
$131$	−7.22034	+	12.5060i	−0.630844	+	1.09265i	−0.987379	+	0.158372i	$0.949375\pi$
$132$	−0.257521	−	0.148680i	−0.0224143	−	0.0129409i
$133$	10.4422	+	6.02883i	0.905457	+	0.522766i
$134$	0.591712			0.0511161
$135$	1.74269	−	1.40108i	0.149987	−	0.120586i
$136$	0.442548	−	0.766516i	0.0379482	−	0.0657282i
$137$		−	14.0285i		−	1.19854i	−0.800548	−	0.599269i	$-0.795458\pi$
$137$		−	14.0285i		−	1.19854i	0.800548	−	0.599269i	$-0.204542\pi$
$138$		−	7.33518i		−	0.624412i
$139$	9.79333	−	16.9625i	0.830659	−	1.43874i	−0.0668571	−	0.997763i	$-0.521297\pi$
$139$	9.79333	−	16.9625i	0.830659	−	1.43874i	0.897516	−	0.440981i	$-0.145370\pi$
$140$	1.32882	+	8.58511i	0.112306	+	0.725574i
$141$	−2.57268	−	4.45601i	−0.216659	−	0.375264i
$142$		−	5.23705i		−	0.439484i
$143$	0.0813610	−	0.0469738i	0.00680375	−	0.00392815i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−6.84443	−	8.51320i	−0.568399	−	0.706983i
$146$	−7.21457	+	12.4960i	−0.597082	+	1.03418i
$147$		−	8.09397i		−	0.667580i
$148$	−5.95159	+	1.25641i	−0.489218	+	0.103277i
$149$	4.89601			0.401097			0.200548	−	0.979684i	$-0.435728\pi$
$149$	4.89601			0.401097			0.200548	+	0.979684i	$0.435728\pi$
$150$	−1.07393	+	4.88331i	−0.0876858	+	0.398720i
$151$	−2.85747	−	4.94928i	−0.232538	−	0.402767i	0.726017	−	0.687677i	$-0.241370\pi$
$151$	−2.85747	−	4.94928i	−0.232538	−	0.402767i	−0.958554	+	0.284910i	$0.908036\pi$
$152$	−2.68777	+	1.55178i	−0.218007	+	0.125866i
$153$	−0.766516	+	0.442548i	−0.0619691	+	0.0357779i
$154$	−1.15527			−0.0930943
$155$	1.94288	+	2.41659i	0.156056	+	0.194105i
$156$	−0.315940			−0.0252954
$157$	0.444121	+	0.256413i	0.0354447	+	0.0204640i	0.517618	−	0.855612i	$-0.326819\pi$
$157$	0.444121	+	0.256413i	0.0354447	+	0.0204640i	−0.482173	+	0.876076i	$0.660152\pi$
$158$			2.45360i			0.195198i
$159$	5.44048			0.431458
$160$	−2.08472	−	0.808671i	−0.164811	−	0.0639310i
$161$	−14.2489	−	24.6799i	−1.12297	−	1.94505i
$162$		−	1.00000i		−	0.0785674i
$163$	−4.81112	−	2.77770i	−0.376836	−	0.217566i	0.299605	−	0.954063i	$-0.403145\pi$
$163$	−4.81112	−	2.77770i	−0.376836	−	0.217566i	−0.676441	+	0.736497i	$0.736479\pi$
$164$	6.17993	−	10.7040i	0.482571	−	0.835838i
$165$	−0.619910	−	0.240466i	−0.0482600	−	0.0187202i
$166$	3.24471	+	5.62000i	0.251838	+	0.436196i
$167$	4.57289	−	2.64016i	0.353861	−	0.204302i	−0.312524	−	0.949910i	$-0.601174\pi$
$167$	4.57289	−	2.64016i	0.353861	−	0.204302i	0.666384	+	0.745608i	$0.267841\pi$
$168$	3.36459	+	1.94255i	0.259584	+	0.149871i
$169$	−6.45009	+	11.1719i	−0.496161	+	0.859376i
$170$	0.715751	−	1.84518i	0.0548956	−	0.141519i
$171$	3.10357			0.237336
$172$	−6.36076	+	3.67239i	−0.485003	+	0.280017i
$173$	−18.4308	−	10.6410i	−1.40127	−	0.809022i	−0.406745	−	0.913542i	$-0.633336\pi$
$173$	−18.4308	−	10.6410i	−1.40127	−	0.809022i	−0.994523	+	0.104520i	$0.966669\pi$
$174$	−4.88510			−0.370338
$175$	5.87273	+	18.5165i	0.443937	+	1.39971i
$176$	0.148680	−	0.257521i	0.0112071	−	0.0194114i
$177$			12.7451i			0.957979i
$178$	4.59596	−	2.65348i	0.344482	−	0.198887i
$179$	−18.3439			−1.37109			−0.685544	−	0.728032i	$-0.740435\pi$
$179$	−18.3439			−1.37109			−0.685544	+	0.728032i	$0.740435\pi$
$180$	1.40108	+	1.74269i	0.104431	+	0.129892i
$181$	7.21545	+	12.4975i	0.536320	+	0.928934i	0.999098	+	0.0424598i	$0.0135194\pi$
$181$	7.21545	+	12.4975i	0.536320	+	0.928934i	−0.462778	+	0.886474i	$0.653147\pi$
$182$	−1.06301	+	0.613728i	−0.0787954	+	0.0454926i
$183$	−2.18655	−	1.26241i	−0.161635	−	0.0933199i
$184$	7.33518			0.540756
$185$	−12.7218	+	4.81199i	−0.935327	+	0.353784i
$186$	1.38670			0.101678
$187$	0.227931	+	0.131596i	0.0166679	+	0.00962324i
$188$	4.45601	−	2.57268i	0.324988	−	0.187632i
$189$	−1.94255	−	3.36459i	−0.141300	−	0.244738i
$190$	−5.40855	+	4.34836i	−0.392378	+	0.315463i
$191$	6.95331			0.503124			0.251562	−	0.967841i	$-0.419056\pi$
$191$	6.95331			0.503124			0.251562	+	0.967841i	$0.419056\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$		−	24.4671i		−	1.76118i	−0.473877	−	0.880591i	$-0.657146\pi$
$193$		−	24.4671i		−	1.76118i	0.473877	−	0.880591i	$-0.342854\pi$
$194$	4.43842	−	7.68756i	0.318660	−	0.551935i
$195$	−0.698149	+	0.108061i	−0.0499955	+	0.00773840i
$196$	8.09397			0.578141
$197$	−18.9041	−	10.9143i	−1.34686	−	0.777609i	−0.359055	−	0.933317i	$-0.616901\pi$
$197$	−18.9041	−	10.9143i	−1.34686	−	0.777609i	−0.987803	+	0.155708i	$0.950234\pi$
$198$	−0.257521	+	0.148680i	−0.0183012	+	0.0105662i
$199$	−9.32319			−0.660903			−0.330452	−	0.943823i	$-0.607201\pi$
$199$	−9.32319			−0.660903			−0.330452	+	0.943823i	$0.607201\pi$
$200$	−4.88331	−	1.07393i	−0.345302	−	0.0759381i
$201$	0.295856	−	0.512438i	0.0208681	−	0.0361446i
$202$	−6.10875	−	3.52689i	−0.429810	−	0.248151i
$203$	−16.4364	+	9.48953i	−1.15361	+	0.666035i
$204$	−0.442548	−	0.766516i	−0.0309846	−	0.0536668i
$205$	9.99505	−	25.7668i	0.698085	−	1.79963i
$206$	−2.97017	+	5.14449i	−0.206942	+	0.358434i
$207$	−6.35245	−	3.66759i	−0.441526	−	0.254915i
$208$		−	0.315940i		−	0.0219065i
$209$	−0.461438	−	0.799233i	−0.0319183	−	0.0552841i
$210$	8.09933	+	3.14176i	0.558907	+	0.216802i
$211$	5.22728			0.359861			0.179930	−	0.983679i	$-0.442413\pi$
$211$	5.22728			0.359861			0.179930	+	0.983679i	$0.442413\pi$
$212$			5.44048i			0.373654i
$213$	−4.53542	−	2.61853i	−0.310762	−	0.179419i
$214$	13.8181			0.944585
$215$	−12.7997	+	10.2906i	−0.872929	+	0.701816i
$216$	1.00000			0.0680414
$217$	4.66568	−	2.69373i	0.316727	−	0.182863i
$218$	5.33672	−	3.08116i	0.361449	−	0.208682i
$219$	7.21457	+	12.4960i	0.487516	+	0.844402i
$220$	0.240466	−	0.619910i	0.0162122	−	0.0417944i
$221$	0.279637			0.0188104
$222$	−1.88771	+	5.78243i	−0.126695	+	0.388092i
$223$			14.3590i			0.961551i	0.876844	+	0.480776i	$0.159645\pi$
$223$			14.3590i			0.961551i	−0.876844	+	0.480776i	$0.840355\pi$
$224$	−1.94255	+	3.36459i	−0.129792	+	0.224806i
$225$	3.69210	+	3.37170i	0.246140	+	0.224780i
$226$	2.21183	+	3.83100i	0.147129	+	0.254834i
$227$	−4.35717	+	2.51561i	−0.289195	+	0.166967i	−0.637579	−	0.770385i	$-0.720064\pi$
$227$	−4.35717	+	2.51561i	−0.289195	+	0.166967i	0.348384	+	0.937352i	$0.386731\pi$
$228$			3.10357i			0.205539i
$229$	1.24438	+	2.15533i	0.0822309	+	0.142428i	0.904208	−	0.427093i	$-0.140462\pi$
$229$	1.24438	+	2.15533i	0.0822309	+	0.142428i	−0.821977	+	0.569521i	$0.807129\pi$
$230$	16.2089	−	2.50885i	1.06879	−	0.165429i
$231$	−0.577635	+	1.00049i	−0.0380056	+	0.0658276i
$232$		−	4.88510i		−	0.320722i
$233$			23.9097i			1.56638i	0.621785	+	0.783188i	$0.286408\pi$
$233$			23.9097i			1.56638i	−0.621785	+	0.783188i	$0.713592\pi$
$234$	−0.157970	+	0.273612i	−0.0103268	+	0.0178866i
$235$	8.96676	−	7.20908i	0.584927	−	0.470269i
$236$	−12.7451			−0.829634
$237$	2.12488	+	1.22680i	0.138026	+	0.0796891i
$238$	−2.97799	−	1.71934i	−0.193034	−	0.111448i
$239$	−14.9600	+	25.9114i	−0.967679	+	1.67607i	−0.265442	+	0.964127i	$0.585518\pi$
$239$	−14.9600	+	25.9114i	−0.967679	+	1.67607i	−0.702237	+	0.711943i	$0.747815\pi$
$240$	−1.74269	+	1.40108i	−0.112490	+	0.0904396i
$241$	6.46707	+	11.2013i	0.416580	+	0.721538i	0.995593	−	0.0937802i	$-0.0298951\pi$
$241$	6.46707	+	11.2013i	0.416580	+	0.721538i	−0.579013	+	0.815319i	$0.696562\pi$
$242$	−9.44970	−	5.45579i	−0.607450	−	0.350711i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	1.26241	−	2.18655i	0.0808174	−	0.139980i
$245$	17.8857	−	2.76838i	1.14267	−	0.176865i
$246$	−6.17993	−	10.7040i	−0.394018	−	0.682459i
$247$	−0.849173	−	0.490270i	−0.0540316	−	0.0311952i
$248$			1.38670i			0.0880556i
$249$	6.48941			0.411250
$250$	−11.1582	−	0.702877i	−0.705708	−	0.0444538i
$251$	−11.5353			−0.728100			−0.364050	−	0.931379i	$-0.618606\pi$
$251$	−11.5353			−0.728100			−0.364050	+	0.931379i	$0.618606\pi$
$252$	3.36459	−	1.94255i	0.211949	−	0.122369i
$253$			2.18118i			0.137130i
$254$	−5.69537	−	9.86467i	−0.357359	−	0.618964i
$255$	−1.24009	−	1.54245i	−0.0776577	−	0.0965918i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.97268	−	5.18038i	−0.559701	−	0.323143i	0.193325	−	0.981135i	$-0.438073\pi$
$257$	−8.97268	−	5.18038i	−0.559701	−	0.323143i	−0.753025	+	0.657992i	$0.771406\pi$
$258$			7.34477i			0.457266i
$259$	4.88129	+	23.1225i	0.303308	+	1.43676i
$260$	−0.108061	−	0.698149i	−0.00670165	−	0.0432974i
$261$	−2.44255	+	4.23062i	−0.151190	+	0.261869i
$262$	−12.5060	+	7.22034i	−0.772623	+	0.446074i
$263$	−2.92053	+	1.68617i	−0.180088	+	0.103974i	−0.587334	−	0.809345i	$-0.699822\pi$
$263$	−2.92053	+	1.68617i	−0.180088	+	0.103974i	0.407246	+	0.913318i	$0.366489\pi$
$264$	−0.148680	−	0.257521i	−0.00915060	−	0.0158493i
$265$	1.86081	+	12.0221i	0.114309	+	0.738513i
$266$	6.02883	+	10.4422i	0.369651	+	0.640255i
$267$		−	5.30696i		−	0.324780i
$268$	0.512438	+	0.295856i	0.0313021	+	0.0180723i
$269$	13.5925			0.828752			0.414376	−	0.910106i	$-0.364000\pi$
$269$	13.5925			0.828752			0.414376	+	0.910106i	$0.364000\pi$
$270$	2.20975	−	0.342030i	0.134481	−	0.0208153i
$271$	5.79573	−	10.0385i	0.352066	−	0.609796i	−0.634546	−	0.772885i	$-0.718813\pi$
$271$	5.79573	−	10.0385i	0.352066	−	0.609796i	0.986611	+	0.163090i	$0.0521460\pi$
$272$	0.766516	−	0.442548i	0.0464768	−	0.0268334i
$273$			1.22746i			0.0742890i
$274$	7.01426	−	12.1491i	0.423747	−	0.733951i
$275$	0.319342	−	1.45210i	0.0192571	−	0.0875647i
$276$	3.66759	−	6.35245i	0.220763	−	0.382372i
$277$	13.0002	−	7.50570i	0.781109	−	0.450974i	−0.0557140	−	0.998447i	$-0.517743\pi$
$277$	13.0002	−	7.50570i	0.781109	−	0.450974i	0.836823	+	0.547473i	$0.184410\pi$
$278$	16.9625	−	9.79333i	1.01735	−	0.587365i
$279$	0.693350	−	1.20092i	0.0415098	−	0.0718971i
$280$	−3.14176	+	8.09933i	−0.187756	+	0.484028i
$281$	10.4127	−	18.0352i	0.621167	−	1.07589i	−0.368102	−	0.929785i	$-0.619992\pi$
$281$	10.4127	−	18.0352i	0.621167	−	1.07589i	0.989269	−	0.146107i	$-0.0466744\pi$
$282$		−	5.14536i		−	0.306402i
$283$	−6.88151	+	3.97304i	−0.409063	+	0.236173i	−0.690387	−	0.723440i	$-0.742560\pi$
$283$	−6.88151	+	3.97304i	−0.409063	+	0.236173i	0.281324	+	0.959613i	$0.409226\pi$
$284$	2.61853	−	4.53542i	0.155381	−	0.269128i
$285$	1.06151	+	6.85813i	0.0628787	+	0.406240i
$286$	0.0939476			0.00555524
$287$	−41.5859	−	24.0096i	−2.45474	−	1.41724i
$288$			1.00000i			0.0589256i
$289$	−8.10830	−	14.0440i	−0.476959	−	0.826117i
$290$	−1.67085	−	10.7949i	−0.0981157	−	0.633896i
$291$	−4.43842	−	7.68756i	−0.260185	−	0.450653i
$292$	−12.4960	+	7.21457i	−0.731274	+	0.422201i
$293$	16.9408	−	9.78077i	0.989692	−	0.571399i	0.0845098	−	0.996423i	$-0.473068\pi$
$293$	16.9408	−	9.78077i	0.989692	−	0.571399i	0.905182	+	0.425024i	$0.139734\pi$
$294$	4.04699	−	7.00959i	0.236025	−	0.408807i
$295$	−28.1635	+	4.35920i	−1.63974	+	0.253803i
$296$	−5.78243	−	1.88771i	−0.336097	−	0.109721i
$297$			0.297359i			0.0172545i
$298$	4.24007	+	2.44800i	0.245621	+	0.141809i
$299$	1.15874	+	2.00699i	0.0670115	+	0.116067i
$300$	−3.37170	+	3.69210i	−0.194665	+	0.213164i
$301$	14.2676	+	24.7122i	0.822369	+	1.42439i
$302$		−	5.71494i		−	0.328858i
$303$	−6.10875	+	3.52689i	−0.350939	+	0.202615i
$304$	−3.10357			−0.178002
$305$	2.04174	−	5.26353i	0.116910	−	0.301389i
$306$	−0.885096			−0.0505976
$307$			7.16588i			0.408978i	0.978869	+	0.204489i	$0.0655533\pi$
$307$			7.16588i			0.408978i	−0.978869	+	0.204489i	$0.934447\pi$
$308$	−1.00049	−	0.577635i	−0.0570084	−	0.0329138i
$309$	2.97017	+	5.14449i	0.168967	+	0.292660i
$310$	0.474294	+	3.06427i	0.0269381	+	0.174039i
$311$	12.7074	−	22.0099i	0.720571	−	1.24807i	−0.240200	−	0.970723i	$-0.577213\pi$
$311$	12.7074	−	22.0099i	0.720571	−	1.24807i	0.960771	−	0.277343i	$-0.0894537\pi$
$312$	−0.273612	−	0.157970i	−0.0154902	−	0.00894328i
$313$	2.73391	+	1.57843i	0.154530	+	0.0892179i	0.575271	−	0.817963i	$-0.304897\pi$
$313$	2.73391	+	1.57843i	0.154530	+	0.0892179i	−0.420741	+	0.907181i	$0.638230\pi$
$314$	0.256413	+	0.444121i	0.0144702	+	0.0250632i
$315$	6.77051	−	5.44335i	0.381475	−	0.306698i
$316$	−1.22680	+	2.12488i	−0.0690128	+	0.119534i
$317$	−4.88564	−	2.82073i	−0.274405	−	0.158428i	0.356483	−	0.934302i	$-0.383976\pi$
$317$	−4.88564	−	2.82073i	−0.274405	−	0.158428i	−0.630888	+	0.775874i	$0.717309\pi$
$318$	4.71160	+	2.72024i	0.264213	+	0.152544i
$319$	1.45263			0.0813316
$320$	−1.40108	−	1.74269i	−0.0783230	−	0.0974193i
$321$	6.90904	−	11.9668i	0.385625	−	0.667922i
$322$		−	28.4979i		−	1.58812i
$323$		−	2.74696i		−	0.152845i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−0.477576	−	1.50578i	−0.0264912	−	0.0835256i
$326$	−2.77770	−	4.81112i	−0.153843	−	0.266463i
$327$		−	6.16232i		−	0.340777i
$328$	10.7040	−	6.17993i	0.591027	−	0.341230i
$329$	−9.99511	−	17.3120i	−0.551048	−	0.954444i
$330$	−0.416625	−	0.518205i	−0.0229345	−	0.0285262i
$331$	−1.01400	+	1.75630i	−0.0557346	+	0.0965351i	−0.892547	−	0.450955i	$-0.851083\pi$
$331$	−1.01400	+	1.75630i	−0.0557346	+	0.0965351i	0.836812	+	0.547490i	$0.184417\pi$
$332$			6.48941i			0.356153i
$333$	4.06388	+	4.52602i	0.222699	+	0.248024i
$334$	5.28032			0.288926
$335$	1.23355	+	0.478500i	0.0673962	+	0.0261433i
$336$	1.94255	+	3.36459i	0.105975	+	0.183554i
$337$	27.6085	−	15.9398i	1.50393	−	0.868294i	0.503939	−	0.863739i	$-0.331884\pi$
$337$	27.6085	−	15.9398i	1.50393	−	0.868294i	0.999990	−	0.00455466i	$-0.00144980\pi$
$338$	−11.1719	+	6.45009i	−0.607670	+	0.350839i
$339$	4.42366			0.240260
$340$	1.54245	−	1.24009i	0.0836509	−	0.0672535i
$341$	−0.412348			−0.0223299
$342$	2.68777	+	1.55178i	0.145338	+	0.0839109i
$343$		−	4.25019i		−	0.229488i
$344$	−7.34477			−0.396004
$345$	5.93174	−	15.2918i	0.319354	−	0.823282i
$346$	−10.6410	−	18.4308i	−0.572065	−	0.990846i
$347$		−	8.51155i		−	0.456924i	−0.973553	−	0.228462i	$-0.926630\pi$
$347$		−	8.51155i		−	0.456924i	0.973553	−	0.228462i	$-0.0733696\pi$
$348$	−4.23062	−	2.44255i	−0.226785	−	0.130934i
$349$	−7.55902	+	13.0926i	−0.404625	+	0.700831i	−0.994278	−	0.106826i	$-0.965931\pi$
$349$	−7.55902	+	13.0926i	−0.404625	+	0.700831i	0.589653	+	0.807657i	$0.299265\pi$
$350$	−4.17231	+	18.9721i	−0.223019	+	1.01410i
$351$	0.157970	+	0.273612i	0.00843181	+	0.0146043i
$352$	0.257521	−	0.148680i	0.0137259	−	0.00792465i
$353$	22.8657	+	13.2015i	1.21702	+	0.702645i	0.964279	−	0.264890i	$-0.0853358\pi$
$353$	22.8657	+	13.2015i	1.21702	+	0.702645i	0.252738	+	0.967535i	$0.418669\pi$
$354$	−6.37254	+	11.0376i	−0.338697	+	0.586640i
$355$	4.23505	−	10.9178i	0.224773	−	0.579456i
$356$	5.30696			0.281268
$357$	−2.97799	+	1.71934i	−0.157612	+	0.0909972i
$358$	−15.8863	−	9.17195i	−0.839616	−	0.484752i
$359$	−15.8538			−0.836730			−0.418365	−	0.908279i	$-0.637397\pi$
$359$	−15.8538			−0.836730			−0.418365	+	0.908279i	$0.637397\pi$
$360$	0.342030	+	2.20975i	0.0180266	+	0.116464i
$361$	4.68393	−	8.11280i	0.246523	−	0.426990i
$362$			14.4309i			0.758472i
$363$	−9.44970	+	5.45579i	−0.495981	+	0.286355i
$364$	−1.22746			−0.0643362
$365$	−25.1455	+	20.2164i	−1.31618	+	1.05818i
$366$	−1.26241	−	2.18655i	−0.0659871	−	0.114293i
$367$	24.6085	−	14.2077i	1.28455	−	0.741637i	0.306876	−	0.951749i	$-0.400716\pi$
$367$	24.6085	−	14.2077i	1.28455	−	0.741637i	0.977677	+	0.210112i	$0.0673828\pi$
$368$	6.35245	+	3.66759i	0.331144	+	0.191186i
$369$	−12.3599			−0.643429
$370$	−13.4234	−	2.19361i	−0.697850	−	0.114040i
$371$	21.1368			1.09737
$372$	1.20092	+	0.693350i	0.0622647	+	0.0359485i
$373$	−4.25045	+	2.45400i	−0.220080	+	0.127063i	−0.605987	−	0.795474i	$-0.707222\pi$
$373$	−4.25045	+	2.45400i	−0.220080	+	0.127063i	0.385907	+	0.922538i	$0.373888\pi$
$374$	0.131596	+	0.227931i	0.00680466	+	0.0117860i
$375$	−6.18782	+	9.31187i	−0.319538	+	0.480863i
$376$	5.14536			0.265352
$377$	1.33662	−	0.771698i	0.0688394	−	0.0397445i
$378$		−	3.88510i		−	0.199828i
$379$	−10.9001	+	18.8795i	−0.559899	+	0.969773i	0.437605	+	0.899167i	$0.355827\pi$
$379$	−10.9001	+	18.8795i	−0.559899	+	0.969773i	−0.997504	+	0.0706062i	$0.977507\pi$
$380$	−6.85813	+	1.06151i	−0.351814	+	0.0544545i
$381$	−11.3907			−0.583565
$382$	6.02174	+	3.47665i	0.308099	+	0.177881i
$383$	18.7573	−	10.8295i	0.958453	−	0.553363i	0.0627565	−	0.998029i	$-0.480011\pi$
$383$	18.7573	−	10.8295i	0.958453	−	0.553363i	0.895697	+	0.444666i	$0.146678\pi$
$384$	−1.00000			−0.0510310
$385$	−2.40841	−	0.934232i	−0.122744	−	0.0476129i
$386$	12.2336	−	21.1891i	0.622672	−	1.07850i
$387$	6.36076	+	3.67239i	0.323336	+	0.186678i
$388$	7.68756	−	4.43842i	0.390277	−	0.225326i
$389$	10.1405	+	17.5639i	0.514144	+	0.890524i	0.999865	+	0.0164099i	$0.00522367\pi$
$389$	10.1405	+	17.5639i	0.514144	+	0.890524i	−0.485721	+	0.874114i	$0.661443\pi$
$390$	−0.658645	−	0.255491i	−0.0333518	−	0.0129373i
$391$	−3.24617	+	5.62253i	−0.164166	+	0.284343i
$392$	7.00959	+	4.04699i	0.354038	+	0.204404i
$393$			14.4407i			0.728436i
$394$	−10.9143	−	18.9041i	−0.549852	−	0.952372i
$395$	−1.98415	+	5.11506i	−0.0998335	+	0.257367i
$396$	−0.297359			−0.0149429
$397$		−	12.4857i		−	0.626638i	−0.949648	−	0.313319i	$-0.898559\pi$
$397$		−	12.4857i		−	0.626638i	0.949648	−	0.313319i	$-0.101441\pi$
$398$	−8.07412	−	4.66159i	−0.404719	−	0.233665i
$399$	12.0577			0.603638
$400$	−3.69210	−	3.37170i	−0.184605	−	0.168585i
$401$	−4.29869			−0.214667			−0.107333	−	0.994223i	$-0.534231\pi$
$401$	−4.29869			−0.214667			−0.107333	+	0.994223i	$0.534231\pi$
$402$	0.512438	−	0.295856i	0.0255581	−	0.0147560i
$403$	−0.379418	+	0.219057i	−0.0189001	+	0.0109120i
$404$	−3.52689	−	6.10875i	−0.175469	−	0.303922i
$405$	0.808671	−	2.08472i	0.0401832	−	0.103591i
$406$	−18.9791			−0.941915
$407$	0.561328	−	1.71946i	0.0278240	−	0.0852305i
$408$		−	0.885096i		−	0.0438188i
$409$	2.94848	−	5.10692i	0.145793	−	0.252521i	−0.783876	−	0.620918i	$-0.786760\pi$
$409$	2.94848	−	5.10692i	0.145793	−	0.252521i	0.929668	+	0.368397i	$0.120093\pi$
$410$	21.5394	−	17.3172i	1.06375	−	0.855236i
$411$	−7.01426	−	12.1491i	−0.345988	−	0.599269i
$412$	−5.14449	+	2.97017i	−0.253451	+	0.146330i
$413$			49.5159i			2.43652i
$414$	−3.66759	−	6.35245i	−0.180252	−	0.312206i
$415$	2.21957	+	14.3400i	0.108955	+	0.703923i
$416$	0.157970	−	0.273612i	0.00774511	−	0.0134149i
$417$		−	19.5867i		−	0.959163i
$418$		−	0.922875i		−	0.0451393i
$419$	5.97334	−	10.3461i	0.291817	−	0.505441i	−0.682423	−	0.730958i	$-0.739074\pi$
$419$	5.97334	−	10.3461i	0.291817	−	0.505441i	0.974239	+	0.225517i	$0.0724070\pi$
$420$	5.44335	+	6.77051i	0.265608	+	0.330367i
$421$	30.2064			1.47217			0.736086	−	0.676888i	$-0.236672\pi$
$421$	30.2064			1.47217			0.736086	+	0.676888i	$0.236672\pi$
$422$	4.52695	+	2.61364i	0.220369	+	0.127230i
$423$	−4.45601	−	2.57268i	−0.216659	−	0.125088i
$424$	−2.72024	+	4.71160i	−0.132107	+	0.228815i
$425$	2.98428	−	3.26787i	0.144759	−	0.158515i
$426$	−2.61853	−	4.53542i	−0.126868	−	0.219742i
$427$	−8.49497	−	4.90458i	−0.411101	−	0.237349i
$428$	11.9668	+	6.90904i	0.578438	+	0.333961i
$429$	0.0469738	−	0.0813610i	0.00226792	−	0.00392815i
$430$	−16.2301	+	2.51213i	−0.782687	+	0.121146i
$431$	10.9678	+	18.9968i	0.528300	+	0.915042i	0.999456	+	0.0329922i	$0.0105037\pi$
$431$	10.9678	+	18.9968i	0.528300	+	0.915042i	−0.471156	+	0.882050i	$0.656163\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$		−	41.5595i		−	1.99722i	−0.0526686	−	0.998612i	$-0.516773\pi$
$433$		−	41.5595i		−	1.99722i	0.0526686	−	0.998612i	$-0.483227\pi$
$434$	5.38747			0.258607
$435$	−10.1841	−	3.95043i	−0.488288	−	0.189409i
$436$	6.16232			0.295121
$437$	19.7153	−	11.3826i	0.943109	−	0.544504i
$438$			14.4291i			0.689451i
$439$	11.2929	+	19.5599i	0.538982	+	0.933543i	0.998959	+	0.0456130i	$0.0145241\pi$
$439$	11.2929	+	19.5599i	0.538982	+	0.933543i	−0.459978	+	0.887931i	$0.652143\pi$
$440$	0.518205	−	0.416625i	0.0247044	−	0.0198618i
$441$	−4.04699	−	7.00959i	−0.192714	−	0.333790i
$442$	0.242173	+	0.139819i	0.0115190	+	0.00665049i
$443$		−	4.84155i		−	0.230029i	−0.993364	−	0.115014i	$-0.963309\pi$
$443$		−	4.84155i		−	0.230029i	0.993364	−	0.115014i	$-0.0366914\pi$
$444$	−4.52602	+	4.06388i	−0.214795	+	0.192863i
$445$	11.7271	−	1.81514i	0.555917	−	0.0860458i
$446$	−7.17951	+	12.4353i	−0.339960	+	0.588828i
$447$	4.24007	−	2.44800i	0.200548	−	0.115787i
$448$	−3.36459	+	1.94255i	−0.158962	+	0.0917768i
$449$	17.8372	+	30.8949i	0.841789	+	1.45802i	0.888381	+	0.459107i	$0.151830\pi$
$449$	17.8372	+	30.8949i	0.841789	+	1.45802i	−0.0465924	+	0.998914i	$0.514836\pi$
$450$	1.51161	+	4.76603i	0.0712578	+	0.224673i
$451$	1.83766	+	3.18292i	0.0865320	+	0.149878i
$452$			4.42366i			0.208071i
$453$	−4.94928	−	2.85747i	−0.232538	−	0.134256i
$454$	−5.03122			−0.236127
$455$	−2.71238	+	0.419827i	−0.127158	+	0.0196818i
$456$	−1.55178	+	2.68777i	−0.0726690	+	0.125866i
$457$	−7.99977	+	4.61867i	−0.374213	+	0.216052i	−0.675298	−	0.737545i	$-0.735985\pi$
$457$	−7.99977	+	4.61867i	−0.374213	+	0.216052i	0.301084	+	0.953598i	$0.402651\pi$
$458$			2.48876i			0.116292i
$459$	−0.442548	+	0.766516i	−0.0206564	+	0.0357779i
$460$	15.2918	+	5.93174i	0.712983	+	0.276569i
$461$	−2.17760	+	3.77172i	−0.101421	+	0.175666i	−0.912270	−	0.409589i	$-0.865672\pi$
$461$	−2.17760	+	3.77172i	−0.101421	+	0.175666i	0.810849	+	0.585255i	$0.199006\pi$
$462$	−1.00049	+	0.577635i	−0.0465471	+	0.0268740i
$463$	−4.84239	+	2.79576i	−0.225045	+	0.129930i	−0.608284	−	0.793719i	$-0.708142\pi$
$463$	−4.84239	+	2.79576i	−0.225045	+	0.129930i	0.383239	+	0.923649i	$0.374809\pi$
$464$	2.44255	−	4.23062i	0.113392	−	0.196401i
$465$	2.89088	+	1.12138i	0.134061	+	0.0520029i
$466$	−11.9548	+	20.7064i	−0.553797	+	0.959205i
$467$			13.0932i			0.605881i	0.953009	+	0.302941i	$0.0979684\pi$
$467$			13.0932i			0.605881i	−0.953009	+	0.302941i	$0.902032\pi$
$468$	−0.273612	+	0.157970i	−0.0126477	+	0.00730216i
$469$	1.14943	−	1.99087i	0.0530757	−	0.0919298i
$470$	11.3700	−	1.75987i	0.524458	−	0.0811767i
$471$	0.512826			0.0236298
$472$	−11.0376	−	6.37254i	−0.508045	−	0.293320i
$473$		−	2.18404i		−	0.100422i
$474$	1.22680	+	2.12488i	0.0563487	+	0.0975989i
$475$	−14.7917	+	4.69137i	−0.678690	+	0.215255i
$476$	−1.71934	−	2.97799i	−0.0788059	−	0.136496i
$477$	4.71160	−	2.72024i	0.215729	−	0.124551i
$478$	−25.9114	+	14.9600i	−1.18516	+	0.684253i
$479$	−12.5645	+	21.7624i	−0.574088	+	0.994349i	0.422052	+	0.906572i	$0.361310\pi$
$479$	−12.5645	+	21.7624i	−0.574088	+	0.994349i	−0.996140	+	0.0877779i	$0.972023\pi$
$480$	−2.20975	+	0.342030i	−0.100861	+	0.0156115i
$481$	−0.396951	−	1.88034i	−0.0180994	−	0.0857363i
$482$			12.9341i			0.589134i
$483$	−24.6799	−	14.2489i	−1.12297	−	0.648349i
$484$	−5.45579	−	9.44970i	−0.247990	−	0.429532i
$485$	15.4696	−	12.4372i	0.702436	−	0.564744i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$		−	4.67830i		−	0.211994i	−0.994366	−	0.105997i	$-0.966197\pi$
$487$		−	4.67830i		−	0.211994i	0.994366	−	0.105997i	$-0.0338034\pi$
$488$	2.18655	−	1.26241i	0.0989807	−	0.0571465i
$489$	−5.55541			−0.251224
$490$	16.8737	+	6.54536i	0.762274	+	0.295689i
$491$	−8.10382			−0.365720			−0.182860	−	0.983139i	$-0.558536\pi$
$491$	−8.10382			−0.365720			−0.182860	+	0.983139i	$0.558536\pi$
$492$		−	12.3599i		−	0.557225i
$493$	3.74450	+	2.16189i	0.168644	+	0.0973666i
$494$	−0.490270	−	0.849173i	−0.0220583	−	0.0382061i
$495$	−0.657091	+	0.101706i	−0.0295340	+	0.00457134i
$496$	−0.693350	+	1.20092i	−0.0311324	+	0.0539228i
$497$	−17.6205	−	10.1732i	−0.790390	−	0.456332i
$498$	5.62000	+	3.24471i	0.251838	+	0.145399i
$499$	6.68241	+	11.5743i	0.299146	+	0.518136i	0.975941	−	0.218036i	$-0.0699649\pi$
$499$	6.68241	+	11.5743i	0.299146	+	0.518136i	−0.676795	+	0.736172i	$0.736632\pi$
$500$	−9.31187	−	6.18782i	−0.416439	−	0.276728i
$501$	2.64016	−	4.57289i	0.117954	−	0.204302i
$502$	−9.98983	−	5.76763i	−0.445868	−	0.257422i
$503$	21.1165	+	12.1916i	0.941539	+	0.543598i	0.890443	−	0.455096i	$-0.150395\pi$
$503$	21.1165	+	12.1916i	0.941539	+	0.543598i	0.0510969	+	0.998694i	$0.483728\pi$
$504$	3.88510			0.173056
$505$	−9.88294	−	12.2925i	−0.439785	−	0.547011i
$506$	−1.09059	+	1.88896i	−0.0484827	+	0.0839745i
$507$			12.9002i			0.572917i
$508$		−	11.3907i		−	0.505382i
$509$	−5.64271	+	9.77345i	−0.250109	+	0.433201i	−0.963555	−	0.267509i	$-0.913800\pi$
$509$	−5.64271	+	9.77345i	−0.250109	+	0.433201i	0.713447	+	0.700709i	$0.247133\pi$
$510$	−0.302730	−	1.95585i	−0.0134051	−	0.0866063i
$511$	28.0293	+	48.5482i	1.23994	+	2.14765i
$512$		−	1.00000i		−	0.0441942i
$513$	2.68777	−	1.55178i	0.118668	−	0.0685130i
$514$	−5.18038	−	8.97268i	−0.228497	−	0.395768i
$515$	−10.3522	+	8.32293i	−0.456172	+	0.366752i
$516$	−3.67239	+	6.36076i	−0.161668	+	0.280017i
$517$			1.53002i			0.0672902i
$518$	−7.33393	+	22.4653i	−0.322234	+	0.987069i
$519$	−21.2820			−0.934178
$520$	0.255491	−	0.658645i	0.0112040	−	0.0288835i
$521$	−8.10569	−	14.0395i	−0.355117	−	0.615080i	0.632021	−	0.774951i	$-0.282225\pi$
$521$	−8.10569	−	14.0395i	−0.355117	−	0.615080i	−0.987138	+	0.159871i	$0.948892\pi$
$522$	−4.23062	+	2.44255i	−0.185169	+	0.106907i
$523$	19.3660	−	11.1810i	0.846817	−	0.488910i	−0.0127588	−	0.999919i	$-0.504061\pi$
$523$	19.3660	−	11.1810i	0.846817	−	0.488910i	0.859575	+	0.511009i	$0.170728\pi$
$524$	−14.4407			−0.630844
$525$	14.3442	+	13.0994i	0.626031	+	0.571704i
$526$	−3.37234			−0.147041
$527$	−1.06293	−	0.613682i	−0.0463019	−	0.0267324i
$528$		−	0.297359i		−	0.0129409i
$529$	−30.8048			−1.33934
$530$	−4.39956	+	11.3419i	−0.191105	+	0.492659i
$531$	6.37254	+	11.0376i	0.276545	+	0.478990i
$532$			12.0577i			0.522766i
$533$	3.38180	+	1.95249i	0.146482	+	0.0845715i
$534$	2.65348	−	4.59596i	0.114827	−	0.198887i
$535$	28.8068	+	11.1743i	1.24543	+	0.483106i
$536$	0.295856	+	0.512438i	0.0127790	+	0.0221339i
$537$	−15.8863	+	9.17195i	−0.685544	+	0.395799i
$538$	11.7715	+	6.79627i	0.507505	+	0.293008i
$539$	−1.20341	+	2.08437i	−0.0518345	+	0.0897800i
$540$	2.08472	+	0.808671i	0.0897120	+	0.0347996i
$541$	19.8953			0.855368			0.427684	−	0.903928i	$-0.359330\pi$
$541$	19.8953			0.855368			0.427684	+	0.903928i	$0.359330\pi$
$542$	10.0385	−	5.79573i	0.431191	−	0.248948i
$543$	12.4975	+	7.21545i	0.536320	+	0.309645i
$544$	0.885096			0.0379482
$545$	13.6172	−	2.10770i	0.583297	−	0.0902839i
$546$	−0.613728	+	1.06301i	−0.0262651	+	0.0454926i
$547$			36.1842i			1.54712i	0.633721	+	0.773562i	$0.281527\pi$
$547$			36.1842i			1.54712i	−0.633721	+	0.773562i	$0.718473\pi$
$548$	12.1491	−	7.01426i	0.518982	−	0.299634i
$549$	−2.52482			−0.107757
$550$	1.00261	−	1.09788i	0.0427513	−	0.0468138i
$551$	−7.58062	−	13.1300i	−0.322945	−	0.559357i
$552$	6.35245	−	3.66759i	0.270378	−	0.156103i
$553$	8.25535	+	4.76623i	0.351053	+	0.202681i
$554$	15.0114			0.637773
$555$	−8.61143	+	10.5282i	−0.365535	+	0.446898i
$556$	19.5867			0.830659
$557$	−7.64850	−	4.41586i	−0.324077	−	0.187106i	0.329131	−	0.944284i	$-0.393244\pi$
$557$	−7.64850	−	4.41586i	−0.324077	−	0.187106i	−0.653209	+	0.757178i	$0.726578\pi$
$558$	1.20092	−	0.693350i	0.0508389	−	0.0293519i
$559$	−1.16025	−	2.00962i	−0.0490735	−	0.0849977i
$560$	−6.77051	+	5.44335i	−0.286106	+	0.230023i
$561$	0.263192			0.0111120
$562$	18.0352	−	10.4127i	0.760771	−	0.439231i
$563$			23.4622i			0.988815i	0.869230	+	0.494407i	$0.164615\pi$
$563$			23.4622i			0.988815i	−0.869230	+	0.494407i	$0.835385\pi$
$564$	2.57268	−	4.45601i	0.108329	−	0.187632i
$565$	1.51302	+	9.77520i	0.0636534	+	0.411246i
$566$	−7.94608			−0.333999
$567$	−3.36459	−	1.94255i	−0.141300	−	0.0815794i
$568$	4.53542	−	2.61853i	0.190302	−	0.109871i
$569$	22.5086			0.943612			0.471806	−	0.881702i	$-0.343602\pi$
$569$	22.5086			0.943612			0.471806	+	0.881702i	$0.343602\pi$
$570$	−2.50977	+	6.47007i	−0.105122	+	0.271001i
$571$	7.70572	−	13.3467i	0.322474	−	0.558542i	−0.658524	−	0.752560i	$-0.728819\pi$
$571$	7.70572	−	13.3467i	0.322474	−	0.558542i	0.980998	+	0.194018i	$0.0621520\pi$
$572$	0.0813610	+	0.0469738i	0.00340188	+	0.00196407i
$573$	6.02174	−	3.47665i	0.251562	−	0.145239i
$574$	−24.0096	−	41.5859i	−1.00214	−	1.73576i
$575$	35.8199	+	7.87744i	1.49379	+	0.328512i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	8.01405	+	4.62692i	0.333629	+	0.192621i	0.657451	−	0.753497i	$-0.271635\pi$
$577$	8.01405	+	4.62692i	0.333629	+	0.192621i	−0.323822	+	0.946118i	$0.604968\pi$
$578$		−	16.2166i		−	0.674522i
$579$	−12.2336	−	21.1891i	−0.508409	−	0.880591i
$580$	3.95043	−	10.1841i	0.164033	−	0.422870i
$581$	25.2120			1.04597
$582$		−	8.87683i		−	0.367957i
$583$	−1.40104	−	0.808889i	−0.0580250	−	0.0335008i
$584$	−14.4291			−0.597082
$585$	−0.550585	+	0.442658i	−0.0227639	+	0.0183017i
$586$	19.5615			0.808080
$587$	15.3642	−	8.87053i	0.634149	−	0.366126i	−0.148208	−	0.988956i	$-0.547351\pi$
$587$	15.3642	−	8.87053i	0.634149	−	0.366126i	0.782357	+	0.622830i	$0.214017\pi$
$588$	7.00959	−	4.04699i	0.289070	−	0.166895i
$589$	2.15186	+	3.72713i	0.0886659	+	0.153574i
$590$	−26.5699	−	10.3066i	−1.09387	−	0.424315i
$591$	−21.8285			−0.897905
$592$	−4.06388	−	4.52602i	−0.167024	−	0.186018i
$593$		−	0.121693i		−	0.00499735i	−0.999997	−	0.00249867i	$-0.999205\pi$
$593$		−	0.121693i		−	0.00499735i	0.999997	−	0.00249867i	$-0.000795353\pi$
$594$	−0.148680	+	0.257521i	−0.00610040	+	0.0105662i
$595$	−4.81788	−	5.99255i	−0.197514	−	0.245671i
$596$	2.44800	+	4.24007i	0.100274	+	0.173680i
$597$	−8.07412	+	4.66159i	−0.330452	+	0.190786i
$598$			2.31747i			0.0947685i
$599$	18.4792	+	32.0069i	0.755039	+	1.30777i	0.945355	+	0.326042i	$0.105715\pi$
$599$	18.4792	+	32.0069i	0.755039	+	1.30777i	−0.190317	+	0.981723i	$0.560951\pi$
$600$	−4.76603	+	1.51161i	−0.194572	+	0.0617110i
$601$	−6.53316	+	11.3158i	−0.266493	+	0.461580i	−0.967954	−	0.251129i	$-0.919198\pi$
$601$	−6.53316	+	11.3158i	−0.266493	+	0.461580i	0.701461	+	0.712708i	$0.252532\pi$
$602$			28.5351i			1.16301i
$603$		−	0.591712i		−	0.0240964i
$604$	2.85747	−	4.94928i	0.116269	−	0.201383i
$605$	−15.2880	−	19.0155i	−0.621547	−	0.773089i
$606$	−7.05378			−0.286540
$607$	32.7606	+	18.9143i	1.32971	+	0.767710i	0.985255	−	0.171093i	$-0.0547297\pi$
$607$	32.7606	+	18.9143i	1.32971	+	0.767710i	0.344457	+	0.938802i	$0.388063\pi$
$608$	−2.68777	−	1.55178i	−0.109003	−	0.0629332i
$609$	−9.48953	+	16.4364i	−0.384535	+	0.666035i
$610$	4.39997	−	3.53748i	0.178149	−	0.143228i
$611$	0.812812	+	1.40783i	0.0328829	+	0.0569548i
$612$	−0.766516	−	0.442548i	−0.0309846	−	0.0178889i
$613$	15.6579	+	9.04011i	0.632418	+	0.365127i	0.781688	−	0.623670i	$-0.214359\pi$
$613$	15.6579	+	9.04011i	0.632418	+	0.365127i	−0.149270	+	0.988796i	$0.547692\pi$
$614$	−3.58294	+	6.20583i	−0.144596	+	0.250447i
$615$	−4.22744	−	27.3123i	−0.170467	−	1.10134i
$616$	−0.577635	−	1.00049i	−0.0232736	−	0.0403110i
$617$	24.4225	+	14.1003i	0.983213	+	0.567658i	0.903239	−	0.429139i	$-0.141183\pi$
$617$	24.4225	+	14.1003i	0.983213	+	0.567658i	0.0799744	+	0.996797i	$0.474516\pi$
$618$			5.94035i			0.238956i
$619$	−28.9547			−1.16379			−0.581894	−	0.813264i	$-0.697688\pi$
$619$	−28.9547			−1.16379			−0.581894	+	0.813264i	$0.697688\pi$
$620$	−1.12138	+	2.89088i	−0.0450359	+	0.116101i
$621$	−7.33518			−0.294350
$622$	22.0099	−	12.7074i	0.882516	−	0.509521i
$623$		−	20.6180i		−	0.826044i
$624$	−0.157970	−	0.273612i	−0.00632386	−	0.0109532i
$625$	−22.6934	−	10.4886i	−0.907735	−	0.419545i
$626$	1.57843	+	2.73391i	0.0630866	+	0.109269i
$627$	−0.799233	−	0.461438i	−0.0319183	−	0.0184280i
$628$			0.512826i			0.0204640i
$629$	4.00596	−	3.59693i	0.159728	−	0.143419i
$630$	8.58511	−	1.32882i	0.342039	−	0.0529415i
$631$	−24.6501	+	42.6952i	−0.981304	+	1.69967i	−0.323974	+	0.946066i	$0.605019\pi$
$631$	−24.6501	+	42.6952i	−0.981304	+	1.69967i	−0.657330	+	0.753603i	$0.728314\pi$
$632$	−2.12488	+	1.22680i	−0.0845231	+	0.0487994i
$633$	4.52695	−	2.61364i	0.179930	−	0.103883i
$634$	−2.82073	−	4.88564i	−0.112025	−	0.194034i
$635$	−3.89598	−	25.1707i	−0.154607	−	0.998870i
$636$	2.72024	+	4.71160i	0.107865	+	0.186827i
$637$			2.55721i			0.101320i
$638$	1.25801	+	0.726314i	0.0498052	+	0.0287551i
$639$	−5.23705			−0.207175
$640$	−0.342030	−	2.20975i	−0.0135199	−	0.0873482i
$641$	−6.83132	+	11.8322i	−0.269821	+	0.467344i	−0.968815	−	0.247783i	$-0.920298\pi$
$641$	−6.83132	+	11.8322i	−0.269821	+	0.467344i	0.698995	+	0.715127i	$0.253631\pi$
$642$	11.9668	−	6.90904i	0.472292	−	0.272678i
$643$		−	25.4872i		−	1.00512i	−0.864544	−	0.502558i	$-0.832392\pi$
$643$		−	25.4872i		−	1.00512i	0.864544	−	0.502558i	$-0.167608\pi$
$644$	14.2489	−	24.6799i	0.561487	−	0.972523i
$645$	−5.93950	+	15.3118i	−0.233868	+	0.602901i
$646$	1.37348	−	2.37893i	0.0540388	−	0.0935979i
$647$	12.9156	−	7.45681i	0.507764	−	0.293158i	−0.224150	−	0.974555i	$-0.571961\pi$
$647$	12.9156	−	7.45681i	0.507764	−	0.293158i	0.731914	+	0.681397i	$0.238627\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	1.89493	−	3.28212i	0.0743827	−	0.128835i
$650$	0.339296	−	1.54283i	0.0133083	−	0.0605148i
$651$	2.69373	−	4.66568i	0.105576	−	0.182863i
$652$		−	5.55541i		−	0.217566i
$653$	−19.5857	+	11.3078i	−0.766449	+	0.442510i	−0.831606	−	0.555365i	$-0.812578\pi$
$653$	−19.5857	+	11.3078i	−0.766449	+	0.442510i	0.0651574	+	0.997875i	$0.479245\pi$
$654$	3.08116	−	5.33672i	0.120483	−	0.208682i
$655$	−31.9104	+	4.93915i	−1.24684	+	0.192988i
$656$	12.3599			0.482571
$657$	12.4960	+	7.21457i	0.487516	+	0.281467i
$658$		−	19.9902i		−	0.779300i
$659$	15.3180	+	26.5316i	0.596705	+	1.03352i	0.993304	+	0.115531i	$0.0368569\pi$
$659$	15.3180	+	26.5316i	0.596705	+	1.03352i	−0.396599	+	0.917992i	$0.629810\pi$
$660$	−0.101706	−	0.657091i	−0.00395889	−	0.0255772i
$661$	−21.5266	−	37.2852i	−0.837289	−	1.45023i	−0.892153	−	0.451733i	$-0.850806\pi$
$661$	−21.5266	−	37.2852i	−0.837289	−	1.45023i	0.0548648	−	0.998494i	$-0.482527\pi$
$662$	−1.75630	+	1.01400i	−0.0682607	+	0.0394103i
$663$	0.242173	−	0.139819i	0.00940521	−	0.00543010i
$664$	−3.24471	+	5.62000i	−0.125919	+	0.218098i
$665$	4.12409	+	26.6445i	0.159925	+	1.03323i
$666$	1.25641	+	5.95159i	0.0486850	+	0.230619i
$667$			35.8330i			1.38746i
$668$	4.57289	+	2.64016i	0.176930	+	0.102151i
$669$	7.17951	+	12.4353i	0.277576	+	0.480776i
$670$	0.829039	+	1.03117i	0.0320286	+	0.0398376i
$671$	0.375389	+	0.650192i	0.0144917	+	0.0251004i
$672$			3.88510i			0.149871i
$673$	−4.54995	+	2.62692i	−0.175388	+	0.101260i	−0.585124	−	0.810944i	$-0.698954\pi$
$673$	−4.54995	+	2.62692i	−0.175388	+	0.101260i	0.409736	+	0.912204i	$0.365621\pi$
$674$	31.8795			1.22795
$675$	4.88331	+	1.07393i	0.187959	+	0.0413355i
$676$	−12.9002			−0.496161
$677$		−	32.3513i		−	1.24336i	−0.783271	−	0.621680i	$-0.786450\pi$
$677$		−	32.3513i		−	1.24336i	0.783271	−	0.621680i	$-0.213550\pi$
$678$	3.83100	+	2.21183i	0.147129	+	0.0849448i
$679$	−17.2437	−	29.8669i	−0.661752	−	1.14619i
$680$	1.95585	−	0.302730i	0.0750032	−	0.0116091i
$681$	−2.51561	+	4.35717i	−0.0963985	+	0.166967i
$682$	−0.357104	−	0.206174i	−0.0136742	−	0.00789482i
$683$	−10.1060	−	5.83471i	−0.386696	−	0.223259i	0.294032	−	0.955796i	$-0.405003\pi$
$683$	−10.1060	−	5.83471i	−0.386696	−	0.223259i	−0.680728	+	0.732537i	$0.738336\pi$
$684$	1.55178	+	2.68777i	0.0593340	+	0.102769i
$685$	24.4473	−	19.6551i	0.934085	−	0.750984i
$686$	2.12509	−	3.68077i	0.0811364	−	0.140532i
$687$	2.15533	+	1.24438i	0.0822309	+	0.0474760i
$688$	−6.36076	−	3.67239i	−0.242502	−	0.140008i
$689$	−1.71886			−0.0654835
$690$	12.7829	−	10.2772i	0.486638	−	0.391246i
$691$	−12.3043	+	21.3117i	−0.468077	+	0.810734i	−0.999334	−	0.0364770i	$-0.988386\pi$
$691$	−12.3043	+	21.3117i	−0.468077	+	0.810734i	0.531257	+	0.847211i	$0.321720\pi$
$692$		−	21.2820i		−	0.809022i
$693$			1.15527i			0.0438851i
$694$	4.25577	−	7.37122i	0.161547	−	0.279807i
$695$	43.2817	−	6.69923i	1.64177	−	0.254116i
$696$	−2.44255	−	4.23062i	−0.0925845	−	0.160361i
$697$			10.9397i			0.414369i
$698$	−13.0926	+	7.55902i	−0.495562	+	0.286113i
$699$	11.9548	+	20.7064i	0.452174	+	0.783188i
$700$	−13.0994	+	14.3442i	−0.495110	+	0.542159i
$701$	−4.03627	+	6.99102i	−0.152448	+	0.264047i	−0.932127	−	0.362132i	$-0.882049\pi$
$701$	−4.03627	+	6.99102i	−0.152448	+	0.264047i	0.779679	+	0.626179i	$0.215382\pi$
$702$			0.315940i			0.0119244i
$703$	−18.4712	+	3.89937i	−0.696654	+	0.147067i
$704$	0.297359			0.0112071
$705$	4.16090	−	10.7266i	0.156709	−	0.403988i
$706$	13.2015	+	22.8657i	0.496845	+	0.860560i
$707$	−23.7331	+	13.7023i	−0.892575	+	0.515328i
$708$	−11.0376	+	6.37254i	−0.414817	+	0.239495i
$709$	42.1290			1.58219			0.791094	−	0.611694i	$-0.209512\pi$
$709$	42.1290			1.58219			0.791094	+	0.611694i	$0.209512\pi$
$710$	9.12655	−	7.33755i	0.342513	−	0.275373i
$711$	2.45360			0.0920171
$712$	4.59596	+	2.65348i	0.172241	+	0.0994433i
$713$		−	10.1717i		−	0.380933i
$714$	−3.43868			−0.128689
$715$	0.195854	+	0.0759727i	0.00732454	+	0.00284122i
$716$	−9.17195	−	15.8863i	−0.342772	−	0.593698i
$717$			29.9199i			1.11738i
$718$	−13.7298	−	7.92689i	−0.512391	−	0.295829i
$719$	20.1969	−	34.9821i	0.753218	−	1.30461i	−0.193037	−	0.981192i	$-0.561834\pi$
$719$	20.1969	−	34.9821i	0.753218	−	1.30461i	0.946255	−	0.323421i	$-0.104833\pi$
$720$	−0.808671	+	2.08472i	−0.0301374	+	0.0776929i
$721$	11.5394	+	19.9869i	0.429750	+	0.744349i
$722$	8.11280	−	4.68393i	0.301927	−	0.174318i
$723$	11.2013	+	6.46707i	0.416580	+	0.240513i
$724$	−7.21545	+	12.4975i	−0.268160	+	0.464467i
$725$	5.24624	−	23.8554i	0.194840	−	0.885968i
$726$	−10.9116			−0.404967
$727$	−37.6222	+	21.7212i	−1.39533	+	0.805594i	−0.993899	−	0.110296i	$-0.964820\pi$
$727$	−37.6222	+	21.7212i	−1.39533	+	0.805594i	−0.401430	+	0.915890i	$0.631487\pi$
$728$	−1.06301	−	0.613728i	−0.0393977	−	0.0227463i
$729$	−1.00000			−0.0370370
$730$	−31.8849	+	4.93520i	−1.18011	+	0.182660i
$731$	3.25041	−	5.62988i	0.120221	−	0.208229i
$732$		−	2.52482i		−	0.0933199i
$733$	−6.68259	+	3.85819i	−0.246827	+	0.142506i	−0.618310	−	0.785934i	$-0.712183\pi$
$733$	−6.68259	+	3.85819i	−0.246827	+	0.142506i	0.371484	+	0.928440i	$0.378849\pi$
$734$	28.4155			1.04883
$735$	14.1053	−	11.3403i	0.520281	−	0.418295i
$736$	3.66759	+	6.35245i	0.135189	+	0.234154i
$737$	−0.152378	+	0.0879756i	−0.00561292	+	0.00324062i
$738$	−10.7040	−	6.17993i	−0.394018	−	0.227486i
$739$	−41.2019			−1.51564			−0.757818	−	0.652466i	$-0.773735\pi$
$739$	−41.2019			−1.51564			−0.757818	+	0.652466i	$0.773735\pi$
$740$	−10.5282	−	8.61143i	−0.387025	−	0.316562i
$741$	−0.980541			−0.0360211
$742$	18.3050	+	10.5684i	0.671998	+	0.387978i
$743$	15.5183	−	8.95952i	0.569313	−	0.328693i	−0.187562	−	0.982253i	$-0.560059\pi$
$743$	15.5183	−	8.95952i	0.569313	−	0.328693i	0.756875	+	0.653560i	$0.226725\pi$
$744$	0.693350	+	1.20092i	0.0254195	+	0.0440278i
$745$	6.85972	+	8.53222i	0.251321	+	0.312596i
$746$	−4.90800			−0.179695
$747$	5.62000	−	3.24471i	0.205625	−	0.118718i
$748$			0.263192i			0.00962324i
$749$	26.8423	−	46.4922i	0.980796	−	1.69879i
$750$	−10.0147	+	4.97040i	−0.365687	+	0.181493i
$751$	25.5716			0.933120			0.466560	−	0.884490i	$-0.345493\pi$
$751$	25.5716			0.933120			0.466560	+	0.884490i	$0.345493\pi$
$752$	4.45601	+	2.57268i	0.162494	+	0.0938160i
$753$	−9.98983	+	5.76763i	−0.364050	+	0.210184i
$754$	1.54340			0.0562072
$755$	4.62150	−	11.9140i	0.168194	−	0.433596i
$756$	1.94255	−	3.36459i	0.0706498	−	0.122369i
$757$	−4.64047	−	2.67918i	−0.168661	−	0.0973763i	0.413293	−	0.910598i	$-0.364378\pi$
$757$	−4.64047	−	2.67918i	−0.168661	−	0.0973763i	−0.581954	+	0.813222i	$0.697712\pi$
$758$	−18.8795	+	10.9001i	−0.685733	+	0.395908i
$759$	1.09059	+	1.88896i	0.0395860	+	0.0685649i
$760$	−6.47007	−	2.50977i	−0.234694	−	0.0910387i
$761$	−26.4595	+	45.8292i	−0.959156	+	1.66131i	−0.234598	+	0.972092i	$0.575377\pi$
$761$	−26.4595	+	45.8292i	−0.959156	+	1.66131i	−0.724558	+	0.689214i	$0.757956\pi$
$762$	−9.86467	−	5.69537i	−0.357359	−	0.206321i
$763$		−	23.9412i		−	0.866729i
$764$	3.47665	+	6.02174i	0.125781	+	0.217859i
$765$	−1.84518	−	0.715751i	−0.0667125	−	0.0258780i
$766$	21.6591			0.782574
$767$		−	4.02668i		−	0.145395i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−17.6816			−0.637615			−0.318808	−	0.947819i	$-0.603282\pi$
$769$	−17.6816			−0.637615			−0.318808	+	0.947819i	$0.603282\pi$
$770$	−1.61863	−	2.01327i	−0.0583314	−	0.0725534i
$771$	−10.3608			−0.373134
$772$	21.1891	−	12.2336i	0.762614	−	0.440295i
$773$	16.7129	−	9.64917i	0.601120	−	0.347057i	−0.168362	−	0.985725i	$-0.553848\pi$
$773$	16.7129	−	9.64917i	0.601120	−	0.347057i	0.769482	+	0.638669i	$0.220514\pi$
$774$	3.67239	+	6.36076i	0.132001	+	0.228633i
$775$	−1.48922	+	6.77169i	−0.0534942	+	0.243246i
$776$	8.87683			0.318660
$777$	15.7886	+	17.5840i	0.566412	+	0.630824i
$778$			20.2810i			0.727110i
$779$	19.1798	−	33.2205i	0.687189	−	1.19025i
$780$	−0.442658	−	0.550585i	−0.0158497	−	0.0197141i
$781$	0.778643	+	1.34865i	0.0278620	+	0.0482585i
$782$	−5.62253	+	3.24617i	−0.201061	+	0.116083i
$783$			4.88510i			0.174579i
$784$	4.04699	+	7.00959i	0.144535	+	0.250342i
$785$	0.175402	+	1.13322i	0.00626037	+	0.0404464i
$786$	−7.22034	+	12.5060i	−0.257541	+	0.446074i
$787$		−	29.5664i		−	1.05393i	−0.849888	−	0.526963i	$-0.823330\pi$
$787$		−	29.5664i		−	1.05393i	0.849888	−	0.526963i	$-0.176670\pi$
$788$		−	21.8285i		−	0.777609i
$789$	−1.68617	+	2.92053i	−0.0600292	+	0.103974i
$790$	−4.27586	+	3.43770i	−0.152128	+	0.122308i
$791$	17.1863			0.611076
$792$	−0.257521	−	0.148680i	−0.00915060	−	0.00528310i
$793$	0.690819	+	0.398845i	0.0245317	+	0.0141634i
$794$	6.24284	−	10.8129i	0.221550	−	0.383736i
$795$	7.62257	+	9.48106i	0.270345	+	0.336259i
$796$	−4.66159	−	8.07412i	−0.165226	−	0.286179i
$797$	47.5797	+	27.4702i	1.68536	+	0.973043i	0.957992	+	0.286795i	$0.0925899\pi$
$797$	47.5797	+	27.4702i	1.68536	+	0.973043i	0.727368	+	0.686248i	$0.240743\pi$
$798$	10.4422	+	6.02883i	0.369651	+	0.213418i
$799$	−2.27707	+	3.94400i	−0.0805569	+	0.139529i
$800$	−1.51161	−	4.76603i	−0.0534433	−	0.168505i
$801$	−2.65348	−	4.59596i	−0.0937561	−	0.162390i
$802$	−3.72278	−	2.14935i	−0.131456	−	0.0758961i
$803$		−	4.29064i		−	0.151413i
$804$	0.591712			0.0208681
$805$	23.0454	−	59.4100i	0.812243	−	2.09393i
$806$	−0.438114			−0.0154319
$807$	11.7715	−	6.79627i	0.414376	−	0.239240i
$808$		−	7.05378i		−	0.248151i
$809$	12.2224	+	21.1698i	0.429716	+	0.744289i	0.996848	−	0.0793374i	$-0.0252805\pi$
$809$	12.2224	+	21.1698i	0.429716	+	0.744289i	−0.567132	+	0.823627i	$0.691947\pi$
$810$	1.74269	−	1.40108i	0.0612318	−	0.0492291i
$811$	15.4561	+	26.7707i	0.542737	+	0.940048i	0.998746	+	0.0500725i	$0.0159452\pi$
$811$	15.4561	+	26.7707i	0.542737	+	0.940048i	−0.456009	+	0.889975i	$0.650721\pi$
$812$	−16.4364	−	9.48953i	−0.576803	−	0.333017i
$813$		−	11.5915i		−	0.406530i
$814$	1.34585	−	1.20843i	0.0471722	−	0.0423555i
$815$	−1.90012	−	12.2761i	−0.0665582	−	0.430012i
$816$	0.442548	−	0.766516i	0.0154923	−	0.0268334i
$817$	−19.7411	+	11.3975i	−0.690652	+	0.398748i
$818$	5.10692	−	2.94848i	0.178559	−	0.103091i
$819$	0.613728	+	1.06301i	0.0214454	+	0.0371445i
$820$	27.3123	−	4.22744i	0.953785	−	0.147629i
$821$	−16.4835	−	28.5503i	−0.575279	−	0.996412i	−0.996011	−	0.0892274i	$-0.971560\pi$
$821$	−16.4835	−	28.5503i	−0.575279	−	0.996412i	0.420732	−	0.907185i	$-0.361773\pi$
$822$		−	14.0285i		−	0.489301i
$823$	33.4584	+	19.3172i	1.16629	+	0.673356i	0.952803	−	0.303590i	$-0.0981854\pi$
$823$	33.4584	+	19.3172i	1.16629	+	0.673356i	0.213485	+	0.976946i	$0.431519\pi$
$824$	−5.94035			−0.206942
$825$	−0.449490	−	1.41722i	−0.0156492	−	0.0493414i
$826$	−24.7579	+	42.8820i	−0.861439	+	1.49206i
$827$	−29.9212	+	17.2750i	−1.04046	+	0.600711i	−0.919964	−	0.392003i	$-0.871782\pi$
$827$	−29.9212	+	17.2750i	−1.04046	+	0.600711i	−0.120498	+	0.992714i	$0.538449\pi$
$828$		−	7.33518i		−	0.254915i
$829$	26.1312	−	45.2606i	0.907575	−	1.57197i	0.0901510	−	0.995928i	$-0.471265\pi$
$829$	26.1312	−	45.2606i	0.907575	−	1.57197i	0.817424	−	0.576037i	$-0.195402\pi$
$830$	−5.24780	+	13.5286i	−0.182154	+	0.469585i
$831$	7.50570	−	13.0002i	0.260370	−	0.450974i
$832$	0.273612	−	0.157970i	0.00948578	−	0.00547662i
$833$	−6.20416	+	3.58197i	−0.214961	+	0.124108i
$834$	9.79333	−	16.9625i	0.339115	−	0.587365i
$835$	11.0080	+	4.27004i	0.380947	+	0.147771i
$836$	0.461438	−	0.799233i	0.0159592	−	0.0276421i
$837$		−	1.38670i		−	0.0479314i
$838$	10.3461	−	5.97334i	0.357401	−	0.206345i
$839$	−13.3565	+	23.1341i	−0.461117	+	0.798679i	−0.999017	−	0.0443302i	$-0.985885\pi$
$839$	−13.3565	+	23.1341i	−0.461117	+	0.798679i	0.537900	+	0.843009i	$0.319218\pi$
$840$	1.32882	+	8.58511i	0.0458486	+	0.296214i
$841$	−5.13584			−0.177098
$842$	26.1596	+	15.1032i	0.901518	+	0.520491i
$843$		−	20.8253i		−	0.717262i
$844$	2.61364	+	4.52695i	0.0899652	+	0.155824i
$845$	−28.5062	+	4.41225i	−0.980644	+	0.151786i
$846$	−2.57268	−	4.45601i	−0.0884506	−	0.153201i
$847$	−36.7130	+	21.1963i	−1.26147	+	0.728312i
$848$	−4.71160	+	2.72024i	−0.161797	+	0.0934134i
$849$	−3.97304	+	6.88151i	−0.136354	+	0.236173i
$850$	4.21840	−	1.33792i	0.144690	−	0.0458901i
$851$	42.4152	+	13.8467i	1.45397	+	0.474658i
$852$		−	5.23705i		−	0.179419i
$853$	−21.1020	−	12.1832i	−0.722518	−	0.417146i	0.0931608	−	0.995651i	$-0.470303\pi$
$853$	−21.1020	−	12.1832i	−0.722518	−	0.417146i	−0.815679	+	0.578505i	$0.803636\pi$
$854$	−4.90458	−	8.49497i	−0.167831	−	0.290692i
$855$	4.34836	+	5.40855i	0.148711	+	0.184969i
$856$	6.90904	+	11.9668i	0.236146	+	0.409017i
$857$			0.352479i			0.0120404i	0.999982	+	0.00602022i	$0.00191631\pi$
$857$			0.352479i			0.0120404i	−0.999982	+	0.00602022i	$0.998084\pi$
$858$	0.0813610	−	0.0469738i	0.00277762	−	0.00160366i
$859$	−5.53671			−0.188910			−0.0944551	−	0.995529i	$-0.530111\pi$
$859$	−5.53671			−0.188910			−0.0944551	+	0.995529i	$0.530111\pi$
$860$	−15.3118	−	5.93950i	−0.522128	−	0.202535i
$861$	−48.0192			−1.63649
$862$			21.9356i			0.747129i
$863$	1.01152	+	0.584003i	0.0344326	+	0.0198797i	0.517118	−	0.855914i	$-0.327005\pi$
$863$	1.01152	+	0.584003i	0.0344326	+	0.0198797i	−0.482685	+	0.875794i	$0.660338\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−7.27910	−	47.0281i	−0.247497	−	1.59900i
$866$	20.7798	−	35.9916i	0.706125	−	1.22304i
$867$	−14.0440	−	8.10830i	−0.476959	−	0.275372i
$868$	4.66568	+	2.69373i	0.158364	+	0.0914313i
$869$	−0.364800	−	0.631852i	−0.0123750	−	0.0214341i
$870$	−6.84443	−	8.51320i	−0.232048	−	0.288625i
$871$	−0.0934727	+	0.161899i	−0.00316720	+	0.00548575i
$872$	5.33672	+	3.08116i	0.180724	+	0.104341i
$873$	−7.68756	−	4.43842i	−0.260185	−	0.150218i
$874$	22.7652			0.770045
$875$	−24.0403	+	36.1775i	−0.812710	+	1.22302i
$876$	−7.21457	+	12.4960i	−0.243758	+	0.422201i
$877$			34.1036i			1.15160i	0.817592	+	0.575799i	$0.195309\pi$
$877$			34.1036i			1.15160i	−0.817592	+	0.575799i	$0.804691\pi$
$878$			22.5858i			0.762235i
$879$	9.78077	−	16.9408i	0.329897	−	0.571399i
$880$	0.657091	−	0.101706i	0.0221505	−	0.00342850i
$881$	9.15065	+	15.8494i	0.308293	+	0.533980i	0.977989	−	0.208656i	$-0.0669088\pi$
$881$	9.15065	+	15.8494i	0.308293	+	0.533980i	−0.669696	+	0.742636i	$0.733576\pi$
$882$		−	8.09397i		−	0.272538i
$883$	−17.1687	+	9.91237i	−0.577774	+	0.333578i	−0.760248	−	0.649633i	$-0.774923\pi$
$883$	−17.1687	+	9.91237i	−0.577774	+	0.333578i	0.182474	+	0.983211i	$0.441589\pi$
$884$	0.139819	+	0.242173i	0.00470261	+	0.00814515i
$885$	−22.2107	+	17.8569i	−0.746605	+	0.600254i
$886$	2.42077	−	4.19290i	0.0813275	−	0.140863i
$887$		−	57.3569i		−	1.92586i	−0.269759	−	0.962928i	$-0.586944\pi$
$887$		−	57.3569i		−	1.92586i	0.269759	−	0.962928i	$-0.413056\pi$
$888$	−5.95159	+	1.25641i	−0.199722	+	0.0421625i
$889$	−44.2541			−1.48424
$890$	11.0635	+	4.29158i	0.370850	+	0.143854i
$891$	0.148680	+	0.257521i	0.00498096	+	0.00862727i
$892$	−12.4353	+	7.17951i	−0.416364	+	0.240388i
$893$	13.8295	−	7.98449i	0.462788	−	0.267191i
$894$	4.89601			0.163747
$895$	−25.7013	−	31.9677i	−0.859101	−	1.06856i
$896$	−3.88510			−0.129792
$897$	2.00699	+	1.15874i	0.0670115	+	0.0386891i
$898$			35.6744i			1.19047i
$899$	−6.77417			−0.225931
$900$	−1.07393	+	4.88331i	−0.0357976	+	0.162777i
$901$	−2.40767	−	4.17021i	−0.0802113	−	0.138930i
$902$			3.67532i			0.122375i
$903$	24.7122	+	14.2676i	0.822369	+	0.474795i
$904$	−2.21183	+	3.83100i	−0.0735643	+	0.127417i
$905$	−11.6698	+	30.0844i	−0.387919	+	1.00004i
$906$	−2.85747	−	4.94928i	−0.0949331	−	0.164429i
$907$	−21.9044	+	12.6465i	−0.727324	+	0.419921i	−0.817442	−	0.576010i	$-0.804609\pi$
$907$	−21.9044	+	12.6465i	−0.727324	+	0.419921i	0.0901186	+	0.995931i	$0.471275\pi$
$908$	−4.35717	−	2.51561i	−0.144598	−	0.0834835i
$909$	−3.52689	+	6.10875i	−0.116980	+	0.202615i
$910$	−2.55890	−	0.992608i	−0.0848267	−	0.0329046i
$911$	43.5990			1.44450			0.722250	−	0.691632i	$-0.243108\pi$
$911$	43.5990			1.44450			0.722250	+	0.691632i	$0.243108\pi$
$912$	−2.68777	+	1.55178i	−0.0890010	+	0.0513847i
$913$	−1.67116	−	0.964843i	−0.0553073	−	0.0319317i
$914$	−9.23734			−0.305544
$915$	−0.863563	−	5.57922i	−0.0285485	−	0.184443i
$916$	−1.24438	+	2.15533i	−0.0411154	+	0.0712140i
$917$			56.1034i			1.85270i
$918$	−0.766516	+	0.442548i	−0.0252988	+	0.0146063i
$919$	−23.4361			−0.773086			−0.386543	−	0.922271i	$-0.626331\pi$
$919$	−23.4361			−0.773086			−0.386543	+	0.922271i	$0.626331\pi$
$920$	10.2772	+	12.7829i	0.338829	+	0.421441i
$921$	3.58294	+	6.20583i	0.118062	+	0.204489i
$922$	−3.77172	+	2.17760i	−0.124215	+	0.0717155i
$923$	1.43292	+	0.827297i	0.0471651	+	0.0272308i
$924$	−1.15527			−0.0380056
$925$	−26.2101	−	15.4282i	−0.861784	−	0.507275i
$926$	−5.59151			−0.183749
$927$	5.14449	+	2.97017i	0.168967	+	0.0975533i
$928$	4.23062	−	2.44255i	0.138877	−	0.0801806i
$929$	−21.8232	−	37.7989i	−0.715996	−	1.24014i	−0.962574	−	0.271019i	$-0.912639\pi$
$929$	−21.8232	−	37.7989i	−0.715996	−	1.24014i	0.246578	−	0.969123i	$-0.420694\pi$
$930$	1.94288	+	2.41659i	0.0637097	+	0.0792430i
$931$	25.1202			0.823281
$932$	−20.7064	+	11.9548i	−0.678260	+	0.391594i
$933$		−	25.4148i		−	0.832044i
$934$	−6.54660	+	11.3390i	−0.214211	+	0.371025i
$935$	0.0900194	+	0.581589i	0.00294395	+	0.0190200i
$936$	−0.315940			−0.0103268
$937$	25.9384	+	14.9756i	0.847371	+	0.489230i	0.859763	−	0.510693i	$-0.170611\pi$
$937$	25.9384	+	14.9756i	0.847371	+	0.489230i	−0.0123919	+	0.999923i	$0.503945\pi$
$938$	1.99087	−	1.14943i	0.0650042	−	0.0375302i
$939$	3.15685			0.103020
$940$	10.7266	+	4.16090i	0.349864	+	0.135714i
$941$	15.7396	−	27.2617i	0.513095	−	0.888707i	−0.486789	−	0.873519i	$-0.661832\pi$
$941$	15.7396	−	27.2617i	0.513095	−	0.888707i	0.999885	−	0.0151878i	$-0.00483460\pi$
$942$	0.444121	+	0.256413i	0.0144702	+	0.00835439i
$943$	−78.5154	+	45.3309i	−2.55681	+	1.47618i
$944$	−6.37254	−	11.0376i	−0.207409	−	0.359242i
$945$	3.14176	−	8.09933i	0.102202	−	0.263471i
$946$	1.09202	−	1.89143i	0.0355046	−	0.0614957i
$947$	−13.9000	−	8.02515i	−0.451688	−	0.260782i	0.256855	−	0.966450i	$-0.417314\pi$
$947$	−13.9000	−	8.02515i	−0.451688	−	0.260782i	−0.708543	+	0.705668i	$0.750647\pi$
$948$			2.45360i			0.0796891i
$949$	−2.27937	−	3.94799i	−0.0739915	−	0.128157i
$950$	−15.1557	−	3.33301i	−0.491715	−	0.108137i
$951$	−5.64145			−0.182937
$952$		−	3.43868i		−	0.111448i
$953$	−48.1223	−	27.7834i	−1.55883	−	0.899994i	−0.997369	−	0.0724935i	$-0.976904\pi$
$953$	−48.1223	−	27.7834i	−1.55883	−	0.899994i	−0.561466	−	0.827500i	$-0.689762\pi$
$954$	5.44048			0.176142
$955$	9.74217	+	12.1174i	0.315249	+	0.392111i
$956$	−29.9199			−0.967679
$957$	1.25801	−	0.726314i	0.0406658	−	0.0234784i
$958$	−21.7624	+	12.5645i	−0.703111	+	0.405941i
$959$	−27.2511	−	47.2003i	−0.879983	−	1.52418i
$960$	−2.08472	−	0.808671i	−0.0672840	−	0.0260997i
$961$	−29.0771			−0.937970
$962$	0.596402	−	1.82690i	0.0192288	−	0.0589016i
$963$		−	13.8181i		−	0.445282i
$964$	−6.46707	+	11.2013i	−0.208290	+	0.360769i
$965$	42.6386	−	34.2805i	1.37258	−	1.10353i
$966$	−14.2489	−	24.6799i	−0.458452	−	0.794062i
$967$	28.9931	−	16.7392i	0.932354	−	0.538295i	0.0447986	−	0.998996i	$-0.485735\pi$
$967$	28.9931	−	16.7392i	0.932354	−	0.538295i	0.887555	+	0.460701i	$0.152402\pi$
$968$		−	10.9116i		−	0.350711i
$969$	−1.37348	−	2.37893i	−0.0441225	−	0.0764224i
$970$	19.6156	−	3.03614i	0.629820	−	0.0974847i
$971$	14.1086	−	24.4368i	0.452766	−	0.784213i	−0.545791	−	0.837921i	$-0.683771\pi$
$971$	14.1086	−	24.4368i	0.452766	−	0.784213i	0.998557	+	0.0537083i	$0.0171041\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	76.0960i		−	2.43953i
$974$	2.33915	−	4.05153i	0.0749512	−	0.129819i
$975$	−1.16648	−	1.06525i	−0.0373573	−	0.0341154i
$976$	2.52482			0.0808174
$977$	42.6720	+	24.6367i	1.36520	+	0.788197i	0.990310	−	0.138873i	$-0.0443480\pi$
$977$	42.6720	+	24.6367i	1.36520	+	0.788197i	0.374888	+	0.927070i	$0.377681\pi$
$978$	−4.81112	−	2.77770i	−0.153843	−	0.0888211i
$979$	−0.789036	+	1.36665i	−0.0252177	+	0.0436784i
$980$	11.3403	+	14.1053i	0.362254	+	0.450576i
$981$	−3.08116	−	5.33672i	−0.0983738	−	0.170388i
$982$	−7.01811	−	4.05191i	−0.223957	−	0.129302i
$983$	21.2400	+	12.2629i	0.677451	+	0.391126i	0.798894	−	0.601472i	$-0.205419\pi$
$983$	21.2400	+	12.2629i	0.677451	+	0.391126i	−0.121443	+	0.992598i	$0.538752\pi$
$984$	6.17993	−	10.7040i	0.197009	−	0.341230i
$985$	−7.46601	−	48.2357i	−0.237887	−	1.53692i
$986$	2.16189	+	3.74450i	0.0688486	+	0.119249i
$987$	−17.3120	−	9.99511i	−0.551048	−	0.318148i
$988$		−	0.980541i		−	0.0311952i
$989$	53.8752			1.71313
$990$	−0.619910	−	0.240466i	−0.0197020	−	0.00764250i
$991$	30.8951			0.981416			0.490708	−	0.871324i	$-0.336738\pi$
$991$	30.8951			0.981416			0.490708	+	0.871324i	$0.336738\pi$
$992$	−1.20092	+	0.693350i	−0.0381292	+	0.0220139i
$993$			2.02800i			0.0643568i
$994$	−10.1732	−	17.6205i	−0.322675	−	0.558890i
$995$	−13.0626	−	16.2474i	−0.414111	−	0.515077i
$996$	3.24471	+	5.62000i	0.102812	+	0.178076i
$997$	−44.2485	−	25.5469i	−1.40137	−	0.809079i	−0.406832	−	0.913503i	$-0.633367\pi$
$997$	−44.2485	−	25.5469i	−1.40137	−	0.809079i	−0.994533	+	0.104424i	$0.966700\pi$
$998$			13.3648i			0.423056i
$999$	5.78243	+	1.88771i	0.182948	+	0.0597245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.d.1009.8	yes	28
5.4	even	2	inner	1110.2.bb.d.1009.7	✓	28
37.26	even	3	inner	1110.2.bb.d.1099.7	yes	28
185.174	even	6	inner	1110.2.bb.d.1099.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.d.1009.7	✓	28	5.4	even	2	inner
1110.2.bb.d.1009.8	yes	28	1.1	even	1	trivial
1110.2.bb.d.1099.7	yes	28	37.26	even	3	inner
1110.2.bb.d.1099.8	yes	28	185.174	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.40108 + 1.74269i) q^{5} +1.00000 q^{6} +(3.36459 - 1.94255i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.40108 + 1.74269i) q^{5} +1.00000 q^{6} +(3.36459 - 1.94255i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.342030 + 2.20975i) q^{10} -0.297359 q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.273612 + 0.157970i) q^{13} +3.88510 q^{14} +(2.08472 + 0.808671i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.766516 - 0.442548i) q^{17} +(0.866025 - 0.500000i) q^{18} +(1.55178 + 2.68777i) q^{19} +(-0.808671 + 2.08472i) q^{20} +(1.94255 - 3.36459i) q^{21} +(-0.257521 - 0.148680i) q^{22} -7.33518i q^{23} +(0.500000 + 0.866025i) q^{24} +(-1.07393 + 4.88331i) q^{25} -0.315940 q^{26} -1.00000i q^{27} +(3.36459 + 1.94255i) q^{28} -4.88510 q^{29} +(1.40108 + 1.74269i) q^{30} +1.38670 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.257521 + 0.148680i) q^{33} +(-0.442548 - 0.766516i) q^{34} +(8.09933 + 3.14176i) q^{35} +1.00000 q^{36} +(-1.88771 + 5.78243i) q^{37} +3.10357i q^{38} +(-0.157970 + 0.273612i) q^{39} +(-1.74269 + 1.40108i) q^{40} +(-6.17993 - 10.7040i) q^{41} +(3.36459 - 1.94255i) q^{42} +7.34477i q^{43} +(-0.148680 - 0.257521i) q^{44} +(2.20975 - 0.342030i) q^{45} +(3.66759 - 6.35245i) q^{46} -5.14536i q^{47} +1.00000i q^{48} +(4.04699 - 7.00959i) q^{49} +(-3.37170 + 3.69210i) q^{50} -0.885096 q^{51} +(-0.273612 - 0.157970i) q^{52} +(4.71160 + 2.72024i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.416625 - 0.518205i) q^{55} +(1.94255 + 3.36459i) q^{56} +(2.68777 + 1.55178i) q^{57} +(-4.23062 - 2.44255i) q^{58} +(-6.37254 + 11.0376i) q^{59} +(0.342030 + 2.20975i) q^{60} +(-1.26241 - 2.18655i) q^{61} +(1.20092 + 0.693350i) q^{62} -3.88510i q^{63} -1.00000 q^{64} +(-0.658645 - 0.255491i) q^{65} -0.297359 q^{66} +(0.512438 - 0.295856i) q^{67} -0.885096i q^{68} +(-3.66759 - 6.35245i) q^{69} +(5.44335 + 6.77051i) q^{70} +(-2.61853 - 4.53542i) q^{71} +(0.866025 + 0.500000i) q^{72} +14.4291i q^{73} +(-4.52602 + 4.06388i) q^{74} +(1.51161 + 4.76603i) q^{75} +(-1.55178 + 2.68777i) q^{76} +(-1.00049 + 0.577635i) q^{77} +(-0.273612 + 0.157970i) q^{78} +(1.22680 + 2.12488i) q^{79} +(-2.20975 + 0.342030i) q^{80} +(-0.500000 - 0.866025i) q^{81} -12.3599i q^{82} +(5.62000 + 3.24471i) q^{83} +3.88510 q^{84} +(-0.302730 - 1.95585i) q^{85} +(-3.67239 + 6.36076i) q^{86} +(-4.23062 + 2.44255i) q^{87} -0.297359i q^{88} +(2.65348 - 4.59596i) q^{89} +(2.08472 + 0.808671i) q^{90} +(-0.613728 + 1.06301i) q^{91} +(6.35245 - 3.66759i) q^{92} +(1.20092 - 0.693350i) q^{93} +(2.57268 - 4.45601i) q^{94} +(-2.50977 + 6.47007i) q^{95} +(-0.500000 + 0.866025i) q^{96} -8.87683i q^{97} +(7.00959 - 4.04699i) q^{98} +(-0.148680 + 0.257521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

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