LMFDB - Embedded newform 1110.2.bb.d.1009.7

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			1009.7
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.d.1099.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.808671 + 2.08472i) q^{5} +1.00000 q^{6} +(-3.36459 + 1.94255i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.808671 + 2.08472i) 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} +(-1.74269 - 1.40108i) 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} +(-1.40108 + 1.74269i) q^{20} +(1.94255 - 3.36459i) q^{21} +(0.257521 + 0.148680i) q^{22} +7.33518i q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.69210 + 3.37170i) q^{25} -0.315940 q^{26} +1.00000i q^{27} +(-3.36459 - 1.94255i) q^{28} -4.88510 q^{29} +(0.808671 + 2.08472i) q^{30} +1.38670 q^{31} +(0.866025 - 0.500000i) q^{32} +(0.257521 - 0.148680i) q^{33} +(-0.442548 - 0.766516i) q^{34} +(-6.77051 - 5.44335i) q^{35} +1.00000 q^{36} +(1.88771 - 5.78243i) q^{37} -3.10357i q^{38} +(-0.157970 + 0.273612i) q^{39} +(2.08472 - 0.808671i) 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} +(4.88331 - 1.07393i) q^{50} -0.885096 q^{51} +(0.273612 + 0.157970i) q^{52} +(-4.71160 - 2.72024i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.240466 - 0.619910i) 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} +(0.550585 + 0.442658i) q^{65} -0.297359 q^{66} +(-0.512438 + 0.295856i) q^{67} +0.885096i q^{68} +(-3.66759 - 6.35245i) q^{69} +(3.14176 + 8.09933i) 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} +(-1.74269 - 1.40108i) 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} +(-4.34836 + 5.40855i) 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
$5$	0.808671	+	2.08472i	0.361648	+	0.932315i
$5$	0.808671	+	2.08472i	0.361648	+	0.932315i
$6$	1.00000			0.408248
$7$	−3.36459	+	1.94255i	−1.27170	+	0.734214i	−0.975307	−	0.220853i	$-0.929116\pi$
$7$	−3.36459	+	1.94255i	−1.27170	+	0.734214i	−0.296389	+	0.955067i	$0.595783\pi$
$8$		−	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	−0.461577	−	0.887100i	$-0.652716\pi$
$13$	0.273612	−	0.157970i	0.0758863	−	0.0438130i	0.537463	+	0.843287i	$0.319383\pi$
$14$	3.88510			1.03834
$15$	−1.74269	−	1.40108i	−0.449960	−	0.361758i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.766516	+	0.442548i	0.185907	+	0.107334i	0.590065	−	0.807356i	$-0.299102\pi$
$17$	0.766516	+	0.442548i	0.185907	+	0.107334i	−0.404158	+	0.914689i	$0.632435\pi$
$18$	−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	$0.717472\pi$
$20$	−1.40108	+	1.74269i	−0.313292	+	0.389677i
$21$	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	$0.277135\pi$
$23$			7.33518i			1.52949i	−0.644333	+	0.764745i	$0.722865\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−3.69210	+	3.37170i	−0.738421	+	0.674340i
$26$	−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	$0.649850\pi$
$30$	0.808671	+	2.08472i	0.147642	+	0.380616i
$31$	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
$35$	−6.77051	−	5.44335i	−1.14443	−	0.920093i
$36$	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
$40$	2.08472	−	0.808671i	0.329623	−	0.127862i
$41$	−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	$-0.810788\pi$
$43$		−	7.34477i		−	1.12007i	0.828470	−	0.560034i	$-0.189212\pi$
$44$	−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	$0.122448\pi$
$47$			5.14536i			0.750528i	−0.926918	+	0.375264i	$0.877552\pi$
$48$		−	1.00000i		−	0.144338i
$49$	4.04699	−	7.00959i	0.578141	−	1.00137i
$50$	4.88331	−	1.07393i	0.690604	−	0.151876i
$51$	−0.885096			−0.123938
$52$	0.273612	+	0.157970i	0.0379431	+	0.0219065i
$53$	−4.71160	−	2.72024i	−0.647187	−	0.373654i	0.140190	−	0.990125i	$-0.455229\pi$
$53$	−4.71160	−	2.72024i	−0.647187	−	0.373654i	−0.787378	+	0.616471i	$0.788562\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−0.240466	−	0.619910i	−0.0324244	−	0.0835887i
$56$	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
$65$	0.550585	+	0.442658i	0.0682916	+	0.0549050i
$66$	−0.297359			−0.0366024
$67$	−0.512438	+	0.295856i	−0.0626042	+	0.0361446i	−0.530975	−	0.847387i	$-0.678174\pi$
$67$	−0.512438	+	0.295856i	−0.0626042	+	0.0361446i	0.468371	+	0.883532i	$0.344841\pi$
$68$			0.885096i			0.107334i
$69$	−3.66759	−	6.35245i	−0.441526	−	0.764745i
$70$	3.14176	+	8.09933i	0.375512	+	0.968055i
$71$	−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	$-0.679956\pi$
$73$		−	14.4291i		−	1.68880i	0.535710	−	0.844402i	$-0.320044\pi$
$74$	−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	0.158777	−	0.987315i	$-0.449245\pi$
$83$	−5.62000	−	3.24471i	−0.616875	−	0.356153i	−0.775651	+	0.631162i	$0.782578\pi$
$84$	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	$0.0759116\pi$
$90$	−1.74269	−	1.40108i	−0.183696	−	0.147687i
$91$	−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
$95$	−4.34836	+	5.40855i	−0.446133	+	0.554906i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$			8.87683i			0.901306i	0.892699	+	0.450653i	$0.148809\pi$
$97$			8.87683i			0.901306i	−0.892699	+	0.450653i	$0.851191\pi$
$98$	−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	$-0.905460\pi$
$103$		−	5.94035i		−	0.585320i	0.956217	−	0.292660i	$-0.0945404\pi$
$104$	−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	−0.950553	−	0.310562i	$-0.899483\pi$
$107$	−11.9668	+	6.90904i	−1.15688	+	0.667922i	−0.206322	+	0.978484i	$0.566150\pi$
$108$	−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	0.308862	−	0.951107i	$-0.400052\pi$
$113$	−3.83100	−	2.21183i	−0.360390	−	0.208071i	−0.669252	+	0.743036i	$0.733385\pi$
$114$	1.55178	+	2.68777i	0.145338	+	0.251733i
$115$	−15.2918	+	5.93174i	−1.42597	+	0.553138i
$116$	−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
$120$	−1.40108	+	1.74269i	−0.127901	+	0.159085i
$121$	−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	0.869122	−	0.494598i	$-0.164685\pi$
$127$	9.86467	+	5.69537i	0.875348	+	0.505382i	0.00622607	+	0.999981i	$0.498018\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	3.67239	+	6.36076i	0.323336	+	0.560034i
$130$	−0.255491	−	0.658645i	−0.0224081	−	0.0577670i
$131$	−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
$135$	−2.08472	+	0.808671i	−0.179424	+	0.0695993i
$136$	0.442548	−	0.766516i	0.0379482	−	0.0657282i
$137$			14.0285i			1.19854i	0.800548	+	0.599269i	$0.204542\pi$
$137$			14.0285i			1.19854i	−0.800548	+	0.599269i	$0.795458\pi$
$138$			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
$145$	−3.95043	−	10.1841i	−0.328066	−	0.845739i
$146$	−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	$0.435728\pi$
$150$	−3.69210	+	3.37170i	−0.301459	+	0.275298i
$151$	−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
$155$	1.12138	+	2.89088i	0.0900717	+	0.232201i
$156$	−0.315940			−0.0252954
$157$	−0.444121	−	0.256413i	−0.0354447	−	0.0204640i	0.482173	−	0.876076i	$-0.339848\pi$
$157$	−0.444121	−	0.256413i	−0.0354447	−	0.0204640i	−0.517618	+	0.855612i	$0.673181\pi$
$158$		−	2.45360i		−	0.195198i
$159$	5.44048			0.431458
$160$	1.74269	+	1.40108i	0.137772	+	0.110765i
$161$	−14.2489	−	24.6799i	−1.12297	−	1.94505i
$162$			1.00000i			0.0785674i
$163$	4.81112	+	2.77770i	0.376836	+	0.217566i	0.676441	−	0.736497i	$-0.263521\pi$
$163$	4.81112	+	2.77770i	0.376836	+	0.217566i	−0.299605	+	0.954063i	$0.596855\pi$
$164$	6.17993	−	10.7040i	0.482571	−	0.835838i
$165$	0.518205	+	0.416625i	0.0403422	+	0.0324342i
$166$	3.24471	+	5.62000i	0.251838	+	0.436196i
$167$	−4.57289	+	2.64016i	−0.353861	+	0.204302i	−0.666384	−	0.745608i	$-0.732159\pi$
$167$	−4.57289	+	2.64016i	−0.353861	+	0.204302i	0.312524	+	0.949910i	$0.398826\pi$
$168$	−3.36459	−	1.94255i	−0.259584	−	0.149871i
$169$	−6.45009	+	11.1719i	−0.496161	+	0.859376i
$170$	1.24009	−	1.54245i	0.0951109	−	0.118300i
$171$	3.10357			0.237336
$172$	6.36076	−	3.67239i	0.485003	−	0.280017i
$173$	18.4308	+	10.6410i	1.40127	+	0.809022i	0.994523	−	0.104520i	$-0.0333306\pi$
$173$	18.4308	+	10.6410i	1.40127	+	0.809022i	0.406745	+	0.913542i	$0.366664\pi$
$174$	−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	$0.740435\pi$
$180$	0.808671	+	2.08472i	0.0602747	+	0.155386i
$181$	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
$185$	13.5813	−	0.740741i	0.998516	−	0.0544604i
$186$	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
$190$	6.47007	−	2.50977i	0.469388	−	0.182077i
$191$	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	$0.342854\pi$
$193$			24.4671i			1.76118i	−0.473877	+	0.880591i	$0.657146\pi$
$194$	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	0.987803	−	0.155708i	$-0.0497658\pi$
$197$	18.9041	+	10.9143i	1.34686	+	0.777609i	0.359055	+	0.933317i	$0.383099\pi$
$198$	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	$0.607201\pi$
$200$	3.37170	+	3.69210i	0.238415	+	0.261071i
$201$	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
$205$	17.3172	−	21.5394i	1.20949	−	1.50438i
$206$	−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
$210$	−6.77051	−	5.44335i	−0.467210	−	0.375627i
$211$	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
$215$	15.3118	−	5.93950i	1.04426	−	0.405071i
$216$	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
$220$	0.416625	−	0.518205i	0.0280889	−	0.0349373i
$221$	0.279637			0.0188104
$222$	1.88771	−	5.78243i	0.126695	−	0.388092i
$223$		−	14.3590i		−	0.961551i	−0.876844	−	0.480776i	$-0.840355\pi$
$223$		−	14.3590i		−	0.961551i	0.876844	−	0.480776i	$-0.159645\pi$
$224$	−1.94255	+	3.36459i	−0.129792	+	0.224806i
$225$	1.07393	+	4.88331i	0.0715951	+	0.325554i
$226$	2.21183	+	3.83100i	0.147129	+	0.254834i
$227$	4.35717	−	2.51561i	0.289195	−	0.166967i	−0.348384	−	0.937352i	$-0.613269\pi$
$227$	4.35717	−	2.51561i	0.289195	−	0.166967i	0.637579	+	0.770385i	$0.279936\pi$
$228$		−	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	$-0.713592\pi$
$233$		−	23.9097i		−	1.56638i	0.621785	−	0.783188i	$-0.286408\pi$
$234$	−0.157970	+	0.273612i	−0.0103268	+	0.0178866i
$235$	−10.7266	+	4.16090i	−0.699728	+	0.271427i
$236$	−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	$0.747815\pi$
$240$	2.08472	−	0.808671i	0.134568	−	0.0521995i
$241$	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
$250$	6.18782	+	9.31187i	0.391352	+	0.588934i
$251$	−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
$255$	−0.715751	−	1.84518i	−0.0448221	−	0.115549i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.97268	+	5.18038i	0.559701	+	0.323143i	0.753025	−	0.657992i	$-0.228594\pi$
$257$	8.97268	+	5.18038i	0.559701	+	0.323143i	−0.193325	+	0.981135i	$0.561927\pi$
$258$		−	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	−0.407246	−	0.913318i	$-0.633511\pi$
$263$	2.92053	−	1.68617i	0.180088	−	0.103974i	0.587334	+	0.809345i	$0.300178\pi$
$264$	−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
$275$	1.09788	−	1.00261i	0.0662047	−	0.0604595i
$276$	3.66759	−	6.35245i	0.220763	−	0.382372i
$277$	−13.0002	+	7.50570i	−0.781109	+	0.450974i	−0.836823	−	0.547473i	$-0.815590\pi$
$277$	−13.0002	+	7.50570i	−0.781109	+	0.450974i	0.0557140	+	0.998447i	$0.482257\pi$
$278$	−16.9625	+	9.79333i	−1.01735	+	0.587365i
$279$	0.693350	−	1.20092i	0.0415098	−	0.0718971i
$280$	−5.44335	+	6.77051i	−0.325302	+	0.404616i
$281$	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	−0.281324	−	0.959613i	$-0.590774\pi$
$283$	6.88151	−	3.97304i	0.409063	−	0.236173i	0.690387	+	0.723440i	$0.257440\pi$
$284$	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	−0.905182	−	0.425024i	$-0.860266\pi$
$293$	−16.9408	+	9.78077i	−0.989692	+	0.571399i	−0.0845098	+	0.996423i	$0.526932\pi$
$294$	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
$300$	4.88331	−	1.07393i	0.281938	−	0.0620032i
$301$	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
$305$	3.53748	−	4.39997i	0.202555	−	0.251941i
$306$	−0.885096			−0.0505976
$307$		−	7.16588i		−	0.408978i	−0.978869	−	0.204489i	$-0.934447\pi$
$307$		−	7.16588i		−	0.408978i	0.978869	−	0.204489i	$-0.0655533\pi$
$308$	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	0.420741	−	0.907181i	$-0.361770\pi$
$313$	−2.73391	−	1.57843i	−0.154530	−	0.0892179i	−0.575271	+	0.817963i	$0.695103\pi$
$314$	0.256413	+	0.444121i	0.0144702	+	0.0250632i
$315$	−8.09933	+	3.14176i	−0.456346	+	0.177018i
$316$	−1.22680	+	2.12488i	−0.0690128	+	0.119534i
$317$	4.88564	+	2.82073i	0.274405	+	0.158428i	0.630888	−	0.775874i	$-0.282691\pi$
$317$	4.88564	+	2.82073i	0.274405	+	0.158428i	−0.356483	+	0.934302i	$0.616024\pi$
$318$	−4.71160	−	2.72024i	−0.264213	−	0.152544i
$319$	1.45263			0.0813316
$320$	−0.808671	−	2.08472i	−0.0452061	−	0.116539i
$321$	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
$330$	−0.240466	−	0.619910i	−0.0132372	−	0.0341249i
$331$	−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
$335$	−1.03117	−	0.829039i	−0.0563388	−	0.0452952i
$336$	1.94255	+	3.36459i	0.105975	+	0.183554i
$337$	−27.6085	+	15.9398i	−1.50393	+	0.868294i	−0.503939	+	0.863739i	$0.668116\pi$
$337$	−27.6085	+	15.9398i	−1.50393	+	0.868294i	−0.999990	+	0.00455466i	$0.998550\pi$
$338$	11.1719	−	6.45009i	0.607670	−	0.350839i
$339$	4.42366			0.240260
$340$	−1.84518	+	0.715751i	−0.100069	+	0.0388171i
$341$	−0.412348			−0.0223299
$342$	−2.68777	−	1.55178i	−0.145338	−	0.0839109i
$343$			4.25019i			0.229488i
$344$	−7.34477			−0.396004
$345$	10.2772	−	12.7829i	0.553306	−	0.688210i
$346$	−10.6410	−	18.4308i	−0.572065	−	0.990846i
$347$			8.51155i			0.456924i	0.973553	+	0.228462i	$0.0733696\pi$
$347$			8.51155i			0.456924i	−0.973553	+	0.228462i	$0.926630\pi$
$348$	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	$0.299265\pi$
$350$	−14.3442	+	13.0994i	−0.766729	+	0.700191i
$351$	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	−0.252738	−	0.967535i	$-0.581331\pi$
$353$	−22.8657	−	13.2015i	−1.21702	−	0.702645i	−0.964279	+	0.264890i	$0.914664\pi$
$354$	−6.37254	+	11.0376i	−0.338697	+	0.586640i
$355$	7.33755	−	9.12655i	0.389437	−	0.484387i
$356$	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
$365$	30.0807	−	11.6684i	1.57450	−	0.610753i
$366$	−1.26241	−	2.18655i	−0.0659871	−	0.114293i
$367$	−24.6085	+	14.2077i	−1.28455	+	0.741637i	−0.977677	−	0.210112i	$-0.932617\pi$
$367$	−24.6085	+	14.2077i	−1.28455	+	0.741637i	−0.306876	+	0.951749i	$0.599284\pi$
$368$	−6.35245	−	3.66759i	−0.331144	−	0.191186i
$369$	−12.3599			−0.643429
$370$	−12.1321	−	6.14914i	−0.630718	−	0.319679i
$371$	21.1368			1.09737
$372$	−1.20092	−	0.693350i	−0.0622647	−	0.0359485i
$373$	4.25045	−	2.45400i	0.220080	−	0.127063i	−0.385907	−	0.922538i	$-0.626112\pi$
$373$	4.25045	−	2.45400i	0.220080	−	0.127063i	0.605987	+	0.795474i	$0.292778\pi$
$374$	0.131596	+	0.227931i	0.00680466	+	0.0117860i
$375$	11.1582	−	0.702877i	0.576208	−	0.0362964i
$376$	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	−0.895697	−	0.444666i	$-0.853322\pi$
$383$	−18.7573	+	10.8295i	−0.958453	+	0.553363i	−0.0627565	+	0.998029i	$0.519989\pi$
$384$	−1.00000			−0.0510310
$385$	2.01327	+	1.61863i	0.102606	+	0.0824930i
$386$	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	$0.661443\pi$
$390$	0.550585	+	0.442658i	0.0278799	+	0.0224149i
$391$	−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
$395$	−3.43770	+	4.27586i	−0.172969	+	0.215142i
$396$	−0.297359			−0.0149429
$397$			12.4857i			0.626638i	0.949648	+	0.313319i	$0.101441\pi$
$397$			12.4857i			0.626638i	−0.949648	+	0.313319i	$0.898559\pi$
$398$	8.07412	+	4.66159i	0.404719	+	0.233665i
$399$	12.0577			0.603638
$400$	−1.07393	−	4.88331i	−0.0536963	−	0.244165i
$401$	−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
$405$	1.40108	−	1.74269i	0.0696204	−	0.0865949i
$406$	−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	$0.120093\pi$
$410$	−25.7668	+	9.99505i	−1.27253	+	0.493620i
$411$	−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	$0.0724070\pi$
$420$	3.14176	+	8.09933i	0.153302	+	0.395207i
$421$	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
$425$	−4.32220	+	0.950528i	−0.209657	+	0.0461074i
$426$	−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	$0.483227\pi$
$433$			41.5595i			1.99722i	−0.0526686	+	0.998612i	$0.516773\pi$
$434$	5.38747			0.258607
$435$	8.51320	+	6.84443i	0.408177	+	0.328165i
$436$	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	$0.652143\pi$
$440$	−0.619910	+	0.240466i	−0.0295531	+	0.0114638i
$441$	−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	$0.0366914\pi$
$443$			4.84155i			0.230029i	−0.993364	+	0.115014i	$0.963309\pi$
$444$	−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	−0.301084	−	0.953598i	$-0.597349\pi$
$457$	7.99977	−	4.61867i	0.374213	−	0.216052i	0.675298	+	0.737545i	$0.264015\pi$
$458$		−	2.48876i		−	0.116292i
$459$	−0.442548	+	0.766516i	−0.0206564	+	0.0357779i
$460$	−12.7829	−	10.2772i	−0.596007	−	0.479177i
$461$	−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	−0.383239	−	0.923649i	$-0.625191\pi$
$463$	4.84239	−	2.79576i	0.225045	−	0.129930i	0.608284	+	0.793719i	$0.291858\pi$
$464$	2.44255	−	4.23062i	0.113392	−	0.196401i
$465$	−2.41659	−	1.94288i	−0.112067	−	0.0900991i
$466$	−11.9548	+	20.7064i	−0.553797	+	0.959205i
$467$		−	13.0932i		−	0.605881i	−0.953009	−	0.302941i	$-0.902032\pi$
$467$		−	13.0932i		−	0.605881i	0.953009	−	0.302941i	$-0.0979684\pi$
$468$	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
$485$	−18.5057	+	7.17843i	−0.840301	+	0.325956i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$			4.67830i			0.211994i	0.994366	+	0.105997i	$0.0338034\pi$
$487$			4.67830i			0.211994i	−0.994366	+	0.105997i	$0.966197\pi$
$488$	−2.18655	+	1.26241i	−0.0989807	+	0.0571465i
$489$	−5.55541			−0.251224
$490$	−14.1053	−	11.3403i	−0.637211	−	0.512304i
$491$	−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	$0.736632\pi$
$500$	−0.702877	−	11.1582i	−0.0314336	−	0.499011i
$501$	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	−0.0510969	−	0.998694i	$-0.516272\pi$
$503$	−21.1165	−	12.1916i	−0.941539	−	0.543598i	−0.890443	+	0.455096i	$0.849605\pi$
$504$	3.88510			0.173056
$505$	−5.70418	−	14.7051i	−0.253833	−	0.654370i
$506$	−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
$515$	12.3840	−	4.80379i	0.545702	−	0.211680i
$516$	−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
$520$	0.442658	−	0.550585i	0.0194118	−	0.0241447i
$521$	−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	−0.859575	−	0.511009i	$-0.829272\pi$
$523$	−19.3660	+	11.1810i	−0.846817	+	0.488910i	0.0127588	+	0.999919i	$0.495939\pi$
$524$	−14.4407			−0.630844
$525$	4.17231	+	18.9721i	0.182094	+	0.828011i
$526$	−3.37234			−0.147041
$527$	1.06293	+	0.613682i	0.0463019	+	0.0267324i
$528$			0.297359i			0.0129409i
$529$	−30.8048			−1.33934
$530$	−7.62257	+	9.48106i	−0.331103	+	0.411831i
$531$	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
$535$	−24.0806	−	19.3603i	−1.04110	−	0.837019i
$536$	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
$540$	−1.74269	−	1.40108i	−0.0749934	−	0.0602931i
$541$	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	$-0.718473\pi$
$547$		−	36.1842i		−	1.54712i	0.633721	−	0.773562i	$-0.281527\pi$
$548$	−12.1491	+	7.01426i	−0.518982	+	0.299634i
$549$	−2.52482			−0.107757
$550$	−1.45210	+	0.319342i	−0.0619176	+	0.0136168i
$551$	−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
$555$	−11.3914	+	7.43214i	−0.483537	+	0.315477i
$556$	19.5867			0.830659
$557$	7.64850	+	4.41586i	0.324077	+	0.187106i	0.653209	−	0.757178i	$-0.273422\pi$
$557$	7.64850	+	4.41586i	0.324077	+	0.187106i	−0.329131	+	0.944284i	$0.606756\pi$
$558$	−1.20092	+	0.693350i	−0.0508389	+	0.0293519i
$559$	−1.16025	−	2.00962i	−0.0490735	−	0.0849977i
$560$	8.09933	−	3.14176i	0.342259	−	0.132764i
$561$	0.263192			0.0111120
$562$	−18.0352	+	10.4127i	−0.760771	+	0.439231i
$563$		−	23.4622i		−	0.988815i	−0.869230	−	0.494407i	$-0.835385\pi$
$563$		−	23.4622i		−	0.988815i	0.869230	−	0.494407i	$-0.164615\pi$
$564$	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	$0.343602\pi$
$570$	−4.34836	+	5.40855i	−0.182133	+	0.226539i
$571$	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
$575$	−24.7320	−	27.0822i	−1.03140	−	1.12941i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−8.01405	−	4.62692i	−0.333629	−	0.192621i	0.323822	−	0.946118i	$-0.395032\pi$
$577$	−8.01405	−	4.62692i	−0.333629	−	0.192621i	−0.657451	+	0.753497i	$0.728365\pi$
$578$			16.2166i			0.674522i
$579$	−12.2336	−	21.1891i	−0.508409	−	0.880591i
$580$	6.84443	−	8.51320i	0.284200	−	0.353491i
$581$	25.2120			1.04597
$582$			8.87683i			0.367957i
$583$	1.40104	+	0.808889i	0.0580250	+	0.0335008i
$584$	−14.4291			−0.597082
$585$	0.658645	−	0.255491i	0.0272316	−	0.0105633i
$586$	19.5615			0.808080
$587$	−15.3642	+	8.87053i	−0.634149	+	0.366126i	−0.782357	−	0.622830i	$-0.785983\pi$
$587$	−15.3642	+	8.87053i	−0.634149	+	0.366126i	0.148208	+	0.988956i	$0.452649\pi$
$588$	−7.00959	+	4.04699i	−0.289070	+	0.166895i
$589$	2.15186	+	3.72713i	0.0886659	+	0.153574i
$590$	22.2107	+	17.8569i	0.914401	+	0.735159i
$591$	−21.8285			−0.897905
$592$	4.06388	+	4.52602i	0.167024	+	0.186018i
$593$			0.121693i			0.00499735i	0.999997	+	0.00249867i	$0.000795353\pi$
$593$			0.121693i			0.00499735i	−0.999997	+	0.00249867i	$0.999205\pi$
$594$	−0.148680	+	0.257521i	−0.00610040	+	0.0105662i
$595$	−2.78076	−	7.16869i	−0.114000	−	0.293888i
$596$	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
$605$	−8.82387	−	22.7476i	−0.358741	−	0.924820i
$606$	−7.05378			−0.286540
$607$	−32.7606	−	18.9143i	−1.32971	−	0.767710i	−0.344457	−	0.938802i	$-0.611937\pi$
$607$	−32.7606	−	18.9143i	−1.32971	−	0.767710i	−0.985255	+	0.171093i	$0.945270\pi$
$608$	2.68777	+	1.55178i	0.109003	+	0.0629332i
$609$	−9.48953	+	16.4364i	−0.384535	+	0.666035i
$610$	−5.26353	+	2.04174i	−0.213114	+	0.0826678i
$611$	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	0.149270	−	0.988796i	$-0.452308\pi$
$613$	−15.6579	−	9.04011i	−0.632418	−	0.365127i	−0.781688	+	0.623670i	$0.785641\pi$
$614$	−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	−0.0799744	−	0.996797i	$-0.525484\pi$
$617$	−24.4225	−	14.1003i	−0.983213	−	0.567658i	−0.903239	+	0.429139i	$0.858817\pi$
$618$		−	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	$0.697688\pi$
$620$	−1.94288	+	2.41659i	−0.0780281	+	0.0970525i
$621$	−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
$625$	2.26326	−	24.8973i	0.0905306	−	0.995894i
$626$	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	$0.167608\pi$
$643$			25.4872i			1.00512i	−0.864544	+	0.502558i	$0.832392\pi$
$644$	14.2489	−	24.6799i	0.561487	−	0.972523i
$645$	−10.2906	+	12.7997i	−0.405194	+	0.503986i
$646$	1.37348	−	2.37893i	0.0540388	−	0.0935979i
$647$	−12.9156	+	7.45681i	−0.507764	+	0.293158i	−0.731914	−	0.681397i	$-0.761373\pi$
$647$	−12.9156	+	7.45681i	−0.507764	+	0.293158i	0.224150	+	0.974555i	$0.428039\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	1.89493	−	3.28212i	0.0743827	−	0.128835i
$650$	1.16648	−	1.06525i	0.0457532	−	0.0417827i
$651$	2.69373	−	4.66568i	0.105576	−	0.182863i
$652$			5.55541i			0.217566i
$653$	19.5857	−	11.3078i	0.766449	−	0.442510i	−0.0651574	−	0.997875i	$-0.520755\pi$
$653$	19.5857	−	11.3078i	0.766449	−	0.442510i	0.831606	+	0.555365i	$0.187422\pi$
$654$	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
$670$	0.478500	+	1.23355i	0.0184861	+	0.0476563i
$671$	0.375389	+	0.650192i	0.0144917	+	0.0251004i
$672$		−	3.88510i		−	0.149871i
$673$	4.54995	−	2.62692i	0.175388	−	0.101260i	−0.409736	−	0.912204i	$-0.634379\pi$
$673$	4.54995	−	2.62692i	0.175388	−	0.101260i	0.585124	+	0.810944i	$0.301046\pi$
$674$	31.8795			1.22795
$675$	−3.37170	−	3.69210i	−0.129777	−	0.142109i
$676$	−12.9002			−0.496161
$677$			32.3513i			1.24336i	0.783271	+	0.621680i	$0.213550\pi$
$677$			32.3513i			1.24336i	−0.783271	+	0.621680i	$0.786450\pi$
$678$	−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	0.680728	−	0.732537i	$-0.261664\pi$
$683$	10.1060	+	5.83471i	0.386696	+	0.223259i	−0.294032	+	0.955796i	$0.594997\pi$
$684$	1.55178	+	2.68777i	0.0593340	+	0.102769i
$685$	−29.2455	+	11.3445i	−1.11741	+	0.433449i
$686$	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
$690$	−15.2918	+	5.93174i	−0.582148	+	0.225817i
$691$	−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
$700$	18.9721	−	4.17231i	0.717079	−	0.157698i
$701$	−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
$705$	7.20908	−	8.96676i	0.271510	−	0.337708i
$706$	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	$0.209512\pi$
$710$	−10.9178	+	4.23505i	−0.409737	+	0.158939i
$711$	2.45360			0.0920171
$712$	−4.59596	−	2.65348i	−0.172241	−	0.0994433i
$713$			10.1717i			0.380933i
$714$	−3.43868			−0.128689
$715$	−0.163721	−	0.131629i	−0.00612283	−	0.00492263i
$716$	−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	$-0.104833\pi$
$720$	−1.40108	+	1.74269i	−0.0522153	+	0.0649462i
$721$	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
$725$	18.0363	−	16.4711i	0.669851	−	0.611721i
$726$	−10.9116			−0.404967
$727$	37.6222	−	21.7212i	1.39533	−	0.805594i	0.401430	−	0.915890i	$-0.368513\pi$
$727$	37.6222	−	21.7212i	1.39533	−	0.805594i	0.993899	+	0.110296i	$0.0351799\pi$
$728$	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	−0.371484	−	0.928440i	$-0.621151\pi$
$733$	6.68259	−	3.85819i	0.246827	−	0.142506i	0.618310	+	0.785934i	$0.287817\pi$
$734$	28.4155			1.04883
$735$	−16.8737	+	6.54536i	−0.622394	+	0.241429i
$736$	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	$0.773735\pi$
$740$	7.43214	+	11.3914i	0.273211	+	0.418755i
$741$	−0.980541			−0.0360211
$742$	−18.3050	−	10.5684i	−0.671998	−	0.387978i
$743$	−15.5183	+	8.95952i	−0.569313	+	0.328693i	−0.756875	−	0.653560i	$-0.773275\pi$
$743$	−15.5183	+	8.95952i	−0.569313	+	0.328693i	0.187562	+	0.982253i	$0.439941\pi$
$744$	0.693350	+	1.20092i	0.0254195	+	0.0440278i
$745$	3.95926	+	10.2068i	0.145056	+	0.373948i
$746$	−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
$755$	8.00711	−	9.95936i	0.291409	−	0.362458i
$756$	1.94255	−	3.36459i	0.0706498	−	0.122369i
$757$	4.64047	+	2.67918i	0.168661	+	0.0973763i	0.581954	−	0.813222i	$-0.302288\pi$
$757$	4.64047	+	2.67918i	0.168661	+	0.0973763i	−0.413293	+	0.910598i	$0.635622\pi$
$758$	18.8795	−	10.9001i	0.685733	−	0.395908i
$759$	1.09059	+	1.88896i	0.0395860	+	0.0685649i
$760$	5.40855	+	4.34836i	0.196189	+	0.157732i
$761$	−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
$765$	1.54245	+	1.24009i	0.0557673	+	0.0448357i
$766$	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	$0.603282\pi$
$770$	−0.934232	−	2.40841i	−0.0336674	−	0.0867931i
$771$	−10.3608			−0.373134
$772$	−21.1891	+	12.2336i	−0.762614	+	0.440295i
$773$	−16.7129	+	9.64917i	−0.601120	+	0.347057i	−0.769482	−	0.638669i	$-0.779486\pi$
$773$	−16.7129	+	9.64917i	−0.601120	+	0.347057i	0.168362	+	0.985725i	$0.446152\pi$
$774$	3.67239	+	6.36076i	0.132001	+	0.228633i
$775$	−5.11984	+	4.67554i	−0.183910	+	0.167950i
$776$	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
$780$	−0.255491	−	0.658645i	−0.00914805	−	0.0235833i
$781$	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	$0.176670\pi$
$787$			29.5664i			1.05393i	−0.849888	+	0.526963i	$0.823330\pi$
$788$			21.8285i			0.777609i
$789$	−1.68617	+	2.92053i	−0.0600292	+	0.103974i
$790$	5.11506	−	1.98415i	0.181986	−	0.0705930i
$791$	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
$795$	4.39956	+	11.3419i	0.156036	+	0.402255i
$796$	−4.66159	−	8.07412i	−0.165226	−	0.286179i
$797$	−47.5797	−	27.4702i	−1.68536	−	0.973043i	−0.957992	−	0.286795i	$-0.907410\pi$
$797$	−47.5797	−	27.4702i	−1.68536	−	0.973043i	−0.727368	−	0.686248i	$-0.759257\pi$
$798$	−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
$805$	39.9279	−	49.6629i	1.40727	−	1.75039i
$806$	−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	$0.691947\pi$
$810$	−2.08472	+	0.808671i	−0.0732495	+	0.0284138i
$811$	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	−0.213485	−	0.976946i	$-0.568481\pi$
$823$	−33.4584	−	19.3172i	−1.16629	−	0.673356i	−0.952803	+	0.303590i	$0.901815\pi$
$824$	−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	0.120498	−	0.992714i	$-0.461551\pi$
$827$	29.9212	−	17.2750i	1.04046	−	0.600711i	0.919964	+	0.392003i	$0.128218\pi$
$828$			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	$-0.195402\pi$
$830$	−9.09221	+	11.3090i	−0.315595	+	0.392542i
$831$	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
$835$	−9.20195	−	7.39817i	−0.318447	−	0.256024i
$836$	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	0.815679	−	0.578505i	$-0.196364\pi$
$853$	21.1020	+	12.1832i	0.722518	+	0.417146i	−0.0931608	+	0.995651i	$0.529697\pi$
$854$	−4.90458	−	8.49497i	−0.167831	−	0.290692i
$855$	2.50977	+	6.47007i	0.0858322	+	0.221272i
$856$	6.90904	+	11.9668i	0.236146	+	0.409017i
$857$		−	0.352479i		−	0.0120404i	−0.999982	−	0.00602022i	$-0.998084\pi$
$857$		−	0.352479i		−	0.0120404i	0.999982	−	0.00602022i	$-0.00191631\pi$
$858$	−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	$0.530111\pi$
$860$	12.7997	+	10.2906i	0.436464	+	0.350908i
$861$	−48.0192			−1.63649
$862$		−	21.9356i		−	0.747129i
$863$	−1.01152	−	0.584003i	−0.0344326	−	0.0198797i	0.482685	−	0.875794i	$-0.339662\pi$
$863$	−1.01152	−	0.584003i	−0.0344326	−	0.0198797i	−0.517118	+	0.855914i	$0.672995\pi$
$864$	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
$870$	−3.95043	−	10.1841i	−0.133932	−	0.345272i
$871$	−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
$875$	43.3508	−	2.73074i	1.46552	−	0.0923160i
$876$	−7.21457	+	12.4960i	−0.243758	+	0.422201i
$877$		−	34.1036i		−	1.15160i	−0.817592	−	0.575799i	$-0.804691\pi$
$877$		−	34.1036i		−	1.15160i	0.817592	−	0.575799i	$-0.195309\pi$
$878$		−	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	−0.182474	−	0.983211i	$-0.558411\pi$
$883$	17.1687	−	9.91237i	0.577774	−	0.333578i	0.760248	+	0.649633i	$0.225077\pi$
$884$	0.139819	+	0.242173i	0.00470261	+	0.00814515i
$885$	26.5699	−	10.3066i	0.893138	−	0.346452i
$886$	2.42077	−	4.19290i	0.0813275	−	0.140863i
$887$			57.3569i			1.92586i	0.269759	+	0.962928i	$0.413056\pi$
$887$			57.3569i			1.92586i	−0.269759	+	0.962928i	$0.586944\pi$
$888$	5.95159	−	1.25641i	0.199722	−	0.0421625i
$889$	−44.2541			−1.48424
$890$	−9.24837	−	7.43549i	−0.310006	−	0.249238i
$891$	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
$895$	−14.8342	−	38.2419i	−0.495851	−	1.27828i
$896$	−3.88510			−0.129792
$897$	−2.00699	−	1.15874i	−0.0670115	−	0.0386891i
$898$		−	35.6744i		−	1.19047i
$899$	−6.77417			−0.225931
$900$	−3.69210	+	3.37170i	−0.123070	+	0.112390i
$901$	−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
$905$	−20.2189	+	25.1486i	−0.672099	+	0.835967i
$906$	−2.85747	−	4.94928i	−0.0949331	−	0.164429i
$907$	21.9044	−	12.6465i	0.727324	−	0.419921i	−0.0901186	−	0.995931i	$-0.528725\pi$
$907$	21.9044	−	12.6465i	0.727324	−	0.419921i	0.817442	+	0.576010i	$0.195391\pi$
$908$	4.35717	+	2.51561i	0.144598	+	0.0834835i
$909$	−3.52689	+	6.10875i	−0.116980	+	0.202615i
$910$	2.13907	+	1.71977i	0.0709096	+	0.0570098i
$911$	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	$0.626331\pi$
$920$	5.93174	+	15.2918i	0.195564	+	0.504155i
$921$	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
$925$	12.5270	+	27.7141i	0.411886	+	0.911235i
$926$	−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	$-0.420694\pi$
$930$	1.12138	+	2.89088i	0.0367716	+	0.0947957i
$931$	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	0.0123919	−	0.999923i	$-0.496055\pi$
$937$	−25.9384	−	14.9756i	−0.847371	−	0.489230i	−0.859763	+	0.510693i	$0.829389\pi$
$938$	−1.99087	+	1.14943i	−0.0650042	+	0.0375302i
$939$	3.15685			0.103020
$940$	−8.96676	−	7.20908i	−0.292463	−	0.235134i
$941$	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
$945$	5.44335	−	6.77051i	0.177072	−	0.220245i
$946$	1.09202	−	1.89143i	0.0355046	−	0.0614957i
$947$	13.9000	+	8.02515i	0.451688	+	0.260782i	0.708543	−	0.705668i	$-0.249353\pi$
$947$	13.9000	+	8.02515i	0.451688	+	0.260782i	−0.256855	+	0.966450i	$0.582686\pi$
$948$		−	2.45360i		−	0.0796891i
$949$	−2.27937	−	3.94799i	−0.0739915	−	0.128157i
$950$	10.4643	+	11.4587i	0.339507	+	0.371769i
$951$	−5.64145			−0.182937
$952$			3.43868i			0.111448i
$953$	48.1223	+	27.7834i	1.55883	+	0.899994i	0.997369	+	0.0724935i	$0.0230957\pi$
$953$	48.1223	+	27.7834i	1.55883	+	0.899994i	0.561466	+	0.827500i	$0.310238\pi$
$954$	5.44048			0.176142
$955$	5.62293	+	14.4957i	0.181954	+	0.469070i
$956$	−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
$960$	1.74269	+	1.40108i	0.0562450	+	0.0452198i
$961$	−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
$965$	−51.0071	+	19.7858i	−1.64198	+	0.636929i
$966$	−14.2489	−	24.6799i	−0.458452	−	0.794062i
$967$	−28.9931	+	16.7392i	−0.932354	+	0.538295i	−0.887555	−	0.460701i	$-0.847598\pi$
$967$	−28.9931	+	16.7392i	−0.932354	+	0.538295i	−0.0447986	+	0.998996i	$0.514265\pi$
$968$			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
$975$	−0.339296	−	1.54283i	−0.0108662	−	0.0494101i
$976$	2.52482			0.0808174
$977$	−42.6720	−	24.6367i	−1.36520	−	0.788197i	−0.374888	−	0.927070i	$-0.622319\pi$
$977$	−42.6720	−	24.6367i	−1.36520	−	0.788197i	−0.990310	+	0.138873i	$0.955652\pi$
$978$	4.81112	+	2.77770i	0.153843	+	0.0888211i
$979$	−0.789036	+	1.36665i	−0.0252177	+	0.0436784i
$980$	6.54536	+	16.8737i	0.209084	+	0.539009i
$981$	−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	0.121443	−	0.992598i	$-0.461248\pi$
$983$	−21.2400	−	12.2629i	−0.677451	−	0.391126i	−0.798894	+	0.601472i	$0.794581\pi$
$984$	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
$990$	0.518205	+	0.416625i	0.0164696	+	0.0132412i
$991$	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
$995$	−7.53939	−	19.4362i	−0.239015	−	0.616170i
$996$	3.24471	+	5.62000i	0.102812	+	0.178076i
$997$	44.2485	+	25.5469i	1.40137	+	0.809079i	0.994533	−	0.104424i	$-0.0333000\pi$
$997$	44.2485	+	25.5469i	1.40137	+	0.809079i	0.406832	+	0.913503i	$0.366633\pi$
$998$		−	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.1009.7	✓	28
5.4	even	2	inner	1110.2.bb.d.1009.8	yes	28
37.26	even	3	inner	1110.2.bb.d.1099.8	yes	28
185.174	even	6	inner	1110.2.bb.d.1099.7	yes	28

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.808671 + 2.08472i) q^{5} +1.00000 q^{6} +(-3.36459 + 1.94255i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.808671 + 2.08472i) 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} +(-1.74269 - 1.40108i) 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} +(-1.40108 + 1.74269i) q^{20} +(1.94255 - 3.36459i) q^{21} +(0.257521 + 0.148680i) q^{22} +7.33518i q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.69210 + 3.37170i) q^{25} -0.315940 q^{26} +1.00000i q^{27} +(-3.36459 - 1.94255i) q^{28} -4.88510 q^{29} +(0.808671 + 2.08472i) q^{30} +1.38670 q^{31} +(0.866025 - 0.500000i) q^{32} +(0.257521 - 0.148680i) q^{33} +(-0.442548 - 0.766516i) q^{34} +(-6.77051 - 5.44335i) q^{35} +1.00000 q^{36} +(1.88771 - 5.78243i) q^{37} -3.10357i q^{38} +(-0.157970 + 0.273612i) q^{39} +(2.08472 - 0.808671i) 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} +(4.88331 - 1.07393i) q^{50} -0.885096 q^{51} +(0.273612 + 0.157970i) q^{52} +(-4.71160 - 2.72024i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.240466 - 0.619910i) 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} +(0.550585 + 0.442658i) q^{65} -0.297359 q^{66} +(-0.512438 + 0.295856i) q^{67} +0.885096i q^{68} +(-3.66759 - 6.35245i) q^{69} +(3.14176 + 8.09933i) 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} +(-1.74269 - 1.40108i) 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} +(-4.34836 + 5.40855i) 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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