LMFDB - Embedded newform 143.3.k.a.87.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,3,Mod(87,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("143.87");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	143.k (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:	$3.89646778035$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			87.17
Character	$\chi$	$=$	143.87
Dual form			143.3.k.a.120.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01194 + 0.584243i) q^{2} +(1.93953 - 3.35937i) q^{3} +(-1.31732 - 2.28166i) q^{4} +7.51869 q^{5} +(3.92538 - 2.26632i) q^{6} +(-6.54691 + 3.77986i) q^{7} -7.75249i q^{8} +(-3.02358 - 5.23700i) q^{9} +O(q^{10})$	\(q+(1.01194 + 0.584243i) q^{2} +(1.93953 - 3.35937i) q^{3} +(-1.31732 - 2.28166i) q^{4} +7.51869 q^{5} +(3.92538 - 2.26632i) q^{6} +(-6.54691 + 3.77986i) q^{7} -7.75249i q^{8} +(-3.02358 - 5.23700i) q^{9} +(7.60845 + 4.39274i) q^{10} +(-10.8835 - 1.59642i) q^{11} -10.2199 q^{12} +(10.9163 + 7.05937i) q^{13} -8.83344 q^{14} +(14.5827 - 25.2581i) q^{15} +(-0.739936 + 1.28161i) q^{16} +(7.62136 - 4.40020i) q^{17} -7.06603i q^{18} +(9.11585 - 5.26304i) q^{19} +(-9.90451 - 17.1551i) q^{20} +29.3247i q^{21} +(-10.0808 - 7.97412i) q^{22} +(-13.3212 + 23.0731i) q^{23} +(-26.0435 - 15.0362i) q^{24} +31.5306 q^{25} +(6.92223 + 13.5214i) q^{26} +11.4542 q^{27} +(17.2487 + 9.95857i) q^{28} +(29.9239 + 17.2766i) q^{29} +(29.5137 - 17.0397i) q^{30} +0.387374 q^{31} +(-28.3529 + 16.3696i) q^{32} +(-26.4720 + 33.4655i) q^{33} +10.2831 q^{34} +(-49.2242 + 28.4196i) q^{35} +(-7.96605 + 13.7976i) q^{36} +(-19.3710 + 33.5516i) q^{37} +12.2996 q^{38} +(44.8876 - 22.9800i) q^{39} -58.2885i q^{40} +(-43.7000 - 25.2302i) q^{41} +(-17.1328 + 29.6748i) q^{42} +(35.4591 - 20.4723i) q^{43} +(10.6946 + 26.9356i) q^{44} +(-22.7334 - 39.3753i) q^{45} +(-26.9606 + 15.5657i) q^{46} -55.3426 q^{47} +(2.87026 + 4.97144i) q^{48} +(4.07471 - 7.05761i) q^{49} +(31.9071 + 18.4216i) q^{50} -34.1373i q^{51} +(1.72688 - 34.2067i) q^{52} +77.8755 q^{53} +(11.5910 + 6.69207i) q^{54} +(-81.8299 - 12.0030i) q^{55} +(29.3033 + 50.7549i) q^{56} -40.8314i q^{57} +(20.1875 + 34.9657i) q^{58} +(-18.1014 - 31.3525i) q^{59} -76.8405 q^{60} +(-79.3783 + 45.8291i) q^{61} +(0.391999 + 0.226321i) q^{62} +(39.5903 + 22.8575i) q^{63} -32.3358 q^{64} +(82.0761 + 53.0772i) q^{65} +(-46.3400 + 18.3990i) q^{66} +(-22.2515 + 38.5407i) q^{67} +(-20.0795 - 11.5929i) q^{68} +(51.6740 + 89.5020i) q^{69} -66.4158 q^{70} +(-2.13879 - 3.70449i) q^{71} +(-40.5998 + 23.4403i) q^{72} -29.6882i q^{73} +(-39.2046 + 22.6348i) q^{74} +(61.1547 - 105.923i) q^{75} +(-24.0170 - 13.8662i) q^{76} +(77.2878 - 30.6866i) q^{77} +(58.8494 + 2.97093i) q^{78} +80.4745i q^{79} +(-5.56335 + 9.63600i) q^{80} +(49.4281 - 85.6120i) q^{81} +(-29.4812 - 51.0629i) q^{82} +93.1097i q^{83} +(66.9091 - 38.6300i) q^{84} +(57.3026 - 33.0837i) q^{85} +47.8433 q^{86} +(116.077 - 67.0170i) q^{87} +(-12.3762 + 84.3745i) q^{88} +(79.7947 - 138.209i) q^{89} -53.1273i q^{90} +(-98.1514 - 4.95504i) q^{91} +70.1933 q^{92} +(0.751326 - 1.30133i) q^{93} +(-56.0033 - 32.3335i) q^{94} +(68.5392 - 39.5711i) q^{95} +126.997i q^{96} +(-69.1520 - 119.775i) q^{97} +(8.24673 - 4.76125i) q^{98} +(24.5468 + 61.8240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{3} + 46 q^{4} - 8 q^{5} - 64 q^{9}+O(q^{10}) $ 52 * q - 2 * q^3 + 46 * q^4 - 8 * q^5 - 64 * q^9	$ 52 q - 2 q^{3} + 46 q^{4} - 8 q^{5} - 64 q^{9} + 14 q^{11} - 36 q^{12} - 16 q^{14} - 28 q^{15} - 102 q^{16} - 50 q^{20} - 70 q^{22} - 20 q^{23} + 116 q^{25} - 252 q^{26} + 40 q^{27} - 52 q^{31} + 2 q^{33} + 476 q^{34} + 218 q^{36} - 38 q^{37} + 192 q^{38} - 394 q^{42} + 528 q^{44} - 278 q^{45} + 36 q^{47} + 80 q^{48} + 80 q^{49} + 120 q^{53} - 150 q^{55} + 94 q^{56} + 130 q^{58} - 176 q^{59} - 468 q^{60} + 128 q^{64} + 704 q^{66} + 74 q^{67} + 74 q^{69} - 652 q^{70} - 220 q^{71} - 546 q^{75} - 204 q^{77} - 256 q^{78} + 628 q^{80} + 106 q^{81} + 154 q^{82} - 960 q^{86} + 170 q^{88} + 28 q^{89} + 418 q^{91} - 272 q^{92} + 422 q^{93} + 36 q^{97} - 272 q^{99}+O(q^{100}) $ 52 * q - 2 * q^3 + 46 * q^4 - 8 * q^5 - 64 * q^9 + 14 * q^11 - 36 * q^12 - 16 * q^14 - 28 * q^15 - 102 * q^16 - 50 * q^20 - 70 * q^22 - 20 * q^23 + 116 * q^25 - 252 * q^26 + 40 * q^27 - 52 * q^31 + 2 * q^33 + 476 * q^34 + 218 * q^36 - 38 * q^37 + 192 * q^38 - 394 * q^42 + 528 * q^44 - 278 * q^45 + 36 * q^47 + 80 * q^48 + 80 * q^49 + 120 * q^53 - 150 * q^55 + 94 * q^56 + 130 * q^58 - 176 * q^59 - 468 * q^60 + 128 * q^64 + 704 * q^66 + 74 * q^67 + 74 * q^69 - 652 * q^70 - 220 * q^71 - 546 * q^75 - 204 * q^77 - 256 * q^78 + 628 * q^80 + 106 * q^81 + 154 * q^82 - 960 * q^86 + 170 * q^88 + 28 * q^89 + 418 * q^91 - 272 * q^92 + 422 * q^93 + 36 * q^97 - 272 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.01194	+	0.584243i	0.505970	+	0.292122i	0.731175	−	0.682190i	$-0.238972\pi$
$2$	1.01194	+	0.584243i	0.505970	+	0.292122i	−0.225206	+	0.974311i	$0.572305\pi$
$3$	1.93953	−	3.35937i	0.646511	−	1.11979i	−0.337439	−	0.941347i	$-0.609561\pi$
$3$	1.93953	−	3.35937i	0.646511	−	1.11979i	0.983950	−	0.178443i	$-0.0571060\pi$
$4$	−1.31732	−	2.28166i	−0.329330	−	0.570416i
$5$	7.51869			1.50374			0.751869	−	0.659313i	$-0.229153\pi$
$5$	7.51869			1.50374			0.751869	+	0.659313i	$0.229153\pi$
$6$	3.92538	−	2.26632i	0.654230	−	0.377720i
$7$	−6.54691	+	3.77986i	−0.935273	+	0.539980i	−0.888475	−	0.458924i	$-0.848235\pi$
$7$	−6.54691	+	3.77986i	−0.935273	+	0.539980i	−0.0467978	+	0.998904i	$0.514902\pi$
$8$		−	7.75249i		−	0.969061i
$9$	−3.02358	−	5.23700i	−0.335954	−	0.581889i
$10$	7.60845	+	4.39274i	0.760845	+	0.439274i
$11$	−10.8835	−	1.59642i	−0.989413	−	0.145129i
$11$	−10.8835	−	1.59642i	−0.989413	−	0.145129i
$12$	−10.2199			−0.851662
$13$	10.9163	+	7.05937i	0.839714	+	0.543029i
$13$	10.9163	+	7.05937i	0.839714	+	0.543029i
$14$	−8.83344			−0.630960
$15$	14.5827	−	25.2581i	0.972183	−	1.68387i
$16$	−0.739936	+	1.28161i	−0.0462460	+	0.0801005i
$17$	7.62136	−	4.40020i	0.448315	−	0.258835i	−0.258803	−	0.965930i	$-0.583328\pi$
$17$	7.62136	−	4.40020i	0.448315	−	0.258835i	0.707118	+	0.707095i	$0.249995\pi$
$18$		−	7.06603i		−	0.392557i
$19$	9.11585	−	5.26304i	0.479782	−	0.277002i	−0.240544	−	0.970638i	$-0.577326\pi$
$19$	9.11585	−	5.26304i	0.479782	−	0.277002i	0.720325	+	0.693636i	$0.243992\pi$
$20$	−9.90451	−	17.1551i	−0.495225	−	0.857756i
$21$			29.3247i			1.39641i
$22$	−10.0808	−	7.97412i	−0.458217	−	0.362460i
$23$	−13.3212	+	23.0731i	−0.579185	+	1.00318i	0.416389	+	0.909187i	$0.363296\pi$
$23$	−13.3212	+	23.0731i	−0.579185	+	1.00318i	−0.995573	+	0.0939902i	$0.970038\pi$
$24$	−26.0435	−	15.0362i	−1.08515	−	0.626509i
$25$	31.5306			1.26123
$26$	6.92223	+	13.5214i	0.266239	+	0.520055i
$27$	11.4542			0.424231
$28$	17.2487	+	9.95857i	0.616027	+	0.355663i
$29$	29.9239	+	17.2766i	1.03186	+	0.595744i	0.917517	−	0.397697i	$-0.130191\pi$
$29$	29.9239	+	17.2766i	1.03186	+	0.595744i	0.114342	+	0.993441i	$0.463524\pi$
$30$	29.5137	−	17.0397i	0.983790	−	0.567992i
$31$	0.387374			0.0124959			0.00624797	−	0.999980i	$-0.498011\pi$
$31$	0.387374			0.0124959			0.00624797	+	0.999980i	$0.498011\pi$
$32$	−28.3529	+	16.3696i	−0.886030	+	0.511549i
$33$	−26.4720	+	33.4655i	−0.802181	+	1.01411i
$34$	10.2831			0.302445
$35$	−49.2242	+	28.4196i	−1.40641	+	0.811988i
$36$	−7.96605	+	13.7976i	−0.221279	+	0.383267i
$37$	−19.3710	+	33.5516i	−0.523541	+	0.906800i	0.476083	+	0.879400i	$0.342056\pi$
$37$	−19.3710	+	33.5516i	−0.523541	+	0.906800i	−0.999625	+	0.0273999i	$0.991277\pi$
$38$	12.2996			0.323673
$39$	44.8876	−	22.9800i	1.15096	−	0.589230i
$40$		−	58.2885i		−	1.45721i
$41$	−43.7000	−	25.2302i	−1.06585	−	0.615371i	−0.138808	−	0.990319i	$-0.544327\pi$
$41$	−43.7000	−	25.2302i	−1.06585	−	0.615371i	−0.927046	+	0.374948i	$0.877661\pi$
$42$	−17.1328	+	29.6748i	−0.407923	+	0.706543i
$43$	35.4591	−	20.4723i	0.824631	−	0.476101i	−0.0273801	−	0.999625i	$-0.508716\pi$
$43$	35.4591	−	20.4723i	0.824631	−	0.476101i	0.852011	+	0.523524i	$0.175383\pi$
$44$	10.6946	+	26.9356i	0.243059	+	0.612172i
$45$	−22.7334	−	39.3753i	−0.505186	−	0.875008i
$46$	−26.9606	+	15.5657i	−0.586100	+	0.338385i
$47$	−55.3426			−1.17750			−0.588751	−	0.808315i	$-0.700380\pi$
$47$	−55.3426			−1.17750			−0.588751	+	0.808315i	$0.700380\pi$
$48$	2.87026	+	4.97144i	0.0597972	+	0.103572i
$49$	4.07471	−	7.05761i	0.0831574	−	0.144033i
$50$	31.9071	+	18.4216i	0.638142	+	0.368431i
$51$		−	34.1373i		−	0.669359i
$52$	1.72688	−	34.2067i	0.0332092	−	0.657822i
$53$	77.8755			1.46935			0.734674	−	0.678420i	$-0.237335\pi$
$53$	77.8755			1.46935			0.734674	+	0.678420i	$0.237335\pi$
$54$	11.5910	+	6.69207i	0.214648	+	0.123927i
$55$	−81.8299	−	12.0030i	−1.48782	−	0.218236i
$56$	29.3033	+	50.7549i	0.523274	+	0.906337i
$57$		−	40.8314i		−	0.716340i
$58$	20.1875	+	34.9657i	0.348059	+	0.602857i
$59$	−18.1014	−	31.3525i	−0.306803	−	0.531399i	0.670858	−	0.741586i	$-0.265926\pi$
$59$	−18.1014	−	31.3525i	−0.306803	−	0.531399i	−0.977661	+	0.210187i	$0.932593\pi$
$60$	−76.8405			−1.28068
$61$	−79.3783	+	45.8291i	−1.30128	+	0.751296i	−0.980624	−	0.195898i	$-0.937238\pi$
$61$	−79.3783	+	45.8291i	−1.30128	+	0.751296i	−0.320659	+	0.947195i	$0.603904\pi$
$62$	0.391999	+	0.226321i	0.00632257	+	0.00365034i
$63$	39.5903	+	22.8575i	0.628417	+	0.362817i
$64$	−32.3358			−0.505247
$65$	82.0761	+	53.0772i	1.26271	+	0.816572i
$66$	−46.3400	+	18.3990i	−0.702122	+	0.278773i
$67$	−22.2515	+	38.5407i	−0.332112	+	0.575234i	−0.982926	−	0.184003i	$-0.941094\pi$
$67$	−22.2515	+	38.5407i	−0.332112	+	0.575234i	0.650814	+	0.759237i	$0.274428\pi$
$68$	−20.0795	−	11.5929i	−0.295287	−	0.170484i
$69$	51.6740	+	89.5020i	0.748899	+	1.29713i
$70$	−66.4158			−0.948798
$71$	−2.13879	−	3.70449i	−0.0301238	−	0.0521759i	0.850571	−	0.525861i	$-0.176257\pi$
$71$	−2.13879	−	3.70449i	−0.0301238	−	0.0521759i	−0.880694	+	0.473685i	$0.842923\pi$
$72$	−40.5998	+	23.4403i	−0.563886	+	0.325560i
$73$		−	29.6882i		−	0.406687i	−0.979107	−	0.203344i	$-0.934819\pi$
$73$		−	29.6882i		−	0.406687i	0.979107	−	0.203344i	$-0.0651808\pi$
$74$	−39.2046	+	22.6348i	−0.529792	+	0.305876i
$75$	61.1547	−	105.923i	0.815396	−	1.41231i
$76$	−24.0170	−	13.8662i	−0.316013	−	0.182450i
$77$	77.2878	−	30.6866i	1.00374	−	0.398528i
$78$	58.8494	+	2.97093i	0.754479	+	0.0380888i
$79$			80.4745i			1.01866i	0.860570	+	0.509332i	$0.170108\pi$
$79$			80.4745i			1.01866i	−0.860570	+	0.509332i	$0.829892\pi$
$80$	−5.56335	+	9.63600i	−0.0695419	+	0.120450i
$81$	49.4281	−	85.6120i	0.610224	−	1.05694i
$82$	−29.4812	−	51.0629i	−0.359527	−	0.622718i
$83$			93.1097i			1.12180i	0.827882	+	0.560902i	$0.189546\pi$
$83$			93.1097i			1.12180i	−0.827882	+	0.560902i	$0.810454\pi$
$84$	66.9091	−	38.6300i	0.796536	−	0.459881i
$85$	57.3026	−	33.0837i	0.674148	−	0.389220i
$86$	47.8433			0.556317
$87$	116.077	−	67.0170i	1.33422	−	0.770310i
$88$	−12.3762	+	84.3745i	−0.140639	+	0.958801i
$89$	79.7947	−	138.209i	0.896570	−	1.55291i	0.0647210	−	0.997903i	$-0.479384\pi$
$89$	79.7947	−	138.209i	0.896570	−	1.55291i	0.831849	−	0.555002i	$-0.187282\pi$
$90$		−	53.1273i		−	0.590303i
$91$	−98.1514	−	4.95504i	−1.07859	−	0.0544510i
$92$	70.1933			0.762971
$93$	0.751326	−	1.30133i	0.00807877	−	0.0139928i
$94$	−56.0033	−	32.3335i	−0.595780	−	0.343974i
$95$	68.5392	−	39.5711i	0.721465	−	0.416538i
$96$			126.997i			1.32289i
$97$	−69.1520	−	119.775i	−0.712908	−	1.23479i	−0.963761	−	0.266767i	$-0.914045\pi$
$97$	−69.1520	−	119.775i	−0.712908	−	1.23479i	0.250853	−	0.968025i	$-0.419289\pi$
$98$	8.24673	−	4.76125i	0.0841503	−	0.0485842i
$99$	24.5468	+	61.8240i	0.247948	+	0.624485i
$100$	−41.5359	−	71.9423i	−0.415359	−	0.719423i
$101$	30.2582	+	17.4696i	0.299586	+	0.172966i	0.642257	−	0.766489i	$-0.277998\pi$
$101$	30.2582	+	17.4696i	0.299586	+	0.172966i	−0.342671	+	0.939456i	$0.611332\pi$
$102$	19.9445	−	34.5449i	0.195534	−	0.338675i
$103$	−20.8436			−0.202365			−0.101183	−	0.994868i	$-0.532263\pi$
$103$	−20.8436			−0.202365			−0.101183	+	0.994868i	$0.532263\pi$
$104$	54.7277	−	84.6284i	0.526228	−	0.813734i
$105$			220.483i			2.09984i
$106$	78.8052	+	45.4982i	0.743446	+	0.429229i
$107$	−79.8959	−	46.1279i	−0.746690	−	0.431102i	0.0778065	−	0.996968i	$-0.475208\pi$
$107$	−79.8959	−	46.1279i	−0.746690	−	0.431102i	−0.824497	+	0.565867i	$0.808542\pi$
$108$	−15.0889	−	26.1347i	−0.139712	−	0.241988i
$109$		−	99.9387i		−	0.916869i	−0.888728	−	0.458434i	$-0.848410\pi$
$109$		−	99.9387i		−	0.916869i	0.888728	−	0.458434i	$-0.151590\pi$
$110$	−75.7942	−	59.9549i	−0.689039	−	0.545044i
$111$	75.1415	+	130.149i	0.676951	+	1.17251i
$112$		−	11.1874i		−	0.0998878i
$113$	−54.7173	−	94.7731i	−0.484224	−	0.838700i	0.515612	−	0.856822i	$-0.327565\pi$
$113$	−54.7173	−	94.7731i	−0.484224	−	0.838700i	−0.999836	+	0.0181220i	$0.994231\pi$
$114$	23.8555	−	41.3189i	0.209258	−	0.362446i
$115$	−100.158	+	173.479i	−0.870941	+	1.50851i
$116$		−	91.0351i		−	0.784785i
$117$	3.96363	−	78.5132i	0.0338772	−	0.671053i
$118$		−	42.3025i		−	0.358496i
$119$	−33.2643	+	57.6154i	−0.279532	+	0.484163i
$120$	−195.813	−	113.053i	−1.63177	−	0.942105i
$121$	115.903	+	34.7494i	0.957875	+	0.287185i
$122$	−107.101			−0.877880
$123$	−169.515	+	97.8697i	−1.37817	+	0.795689i
$124$	−0.510296	−	0.883858i	−0.00411529	−	0.00712789i
$125$	49.1018			0.392814
$126$	26.7086	+	46.2607i	0.211973	+	0.367148i
$127$	−99.5947	−	57.5010i	−0.784210	−	0.452764i	0.0537099	−	0.998557i	$-0.482895\pi$
$127$	−99.5947	−	57.5010i	−0.784210	−	0.452764i	−0.837920	+	0.545792i	$0.816229\pi$
$128$	80.6899	+	46.5864i	0.630390	+	0.363956i
$129$		−	158.827i		−	1.23122i
$130$	52.0460	+	101.663i	0.400354	+	0.782026i
$131$		−	165.295i		−	1.26179i	−0.775867	−	0.630897i	$-0.782687\pi$
$131$		−	165.295i		−	1.26179i	0.775867	−	0.630897i	$-0.217313\pi$
$132$	111.229	+	16.3153i	0.842645	+	0.123601i
$133$	−39.7871	+	68.9133i	−0.299151	+	0.518145i
$134$	−45.0343	+	26.0006i	−0.336077	+	0.194034i
$135$	86.1209			0.637932
$136$	−34.1125	−	59.0845i	−0.250827	−	0.434445i
$137$	73.8659	+	127.940i	0.539167	+	0.933865i	0.998949	+	0.0458332i	$0.0145943\pi$
$137$	73.8659	+	127.940i	0.539167	+	0.933865i	−0.459782	+	0.888032i	$0.652072\pi$
$138$			120.761i			0.875078i
$139$	91.6236	−	52.8989i	0.659163	−	0.380568i	−0.132795	−	0.991144i	$-0.542395\pi$
$139$	91.6236	−	52.8989i	0.659163	−	0.380568i	0.791958	+	0.610576i	$0.209062\pi$
$140$	129.688	+	74.8754i	0.926342	+	0.534824i
$141$	−107.339	+	185.916i	−0.761268	+	1.31856i
$142$		−	4.99829i		−	0.0351992i
$143$	−107.538	−	94.2579i	−0.752015	−	0.659146i
$144$	8.94904			0.0621461
$145$	224.988	+	129.897i	1.55164	+	0.895842i
$146$	17.3451	−	30.0426i	0.118802	−	0.205771i
$147$	−15.8061	−	27.3770i	−0.107524	−	0.186238i
$148$	102.071			0.689671
$149$	−230.233	+	132.925i	−1.54519	+	0.892114i	−0.546688	+	0.837337i	$0.684112\pi$
$149$	−230.233	+	132.925i	−1.54519	+	0.892114i	−0.998499	+	0.0547773i	$0.982555\pi$
$150$	123.770	−	71.4585i	0.825132	−	0.476390i
$151$		−	126.291i		−	0.836367i	−0.908363	−	0.418183i	$-0.862667\pi$
$151$		−	126.291i		−	0.836367i	0.908363	−	0.418183i	$-0.137333\pi$
$152$	−40.8016	−	70.6705i	−0.268432	−	0.464938i
$153$	−46.0876	−	26.6087i	−0.301226	−	0.173913i
$154$	96.1391	+	14.1019i	0.624280	+	0.0915708i
$155$	2.91255			0.0187906
$156$	−111.564	−	72.1464i	−0.715152	−	0.462477i
$157$	−161.269			−1.02719			−0.513597	−	0.858032i	$-0.671687\pi$
$157$	−161.269			−1.02719			−0.513597	+	0.858032i	$0.671687\pi$
$158$	−47.0167	+	81.4353i	−0.297574	+	0.515413i
$159$	151.042	−	261.613i	0.949950	−	1.64536i
$160$	−213.177	+	123.078i	−1.33236	+	0.769236i
$161$		−	201.410i		−	1.25099i
$162$	100.037	−	57.7561i	0.617510	−	0.356519i
$163$	−113.343	−	196.315i	−0.695353	−	1.20439i	−0.970061	−	0.242859i	$-0.921915\pi$
$163$	−113.343	−	196.315i	−0.695353	−	1.20439i	0.274708	−	0.961528i	$-0.411419\pi$
$164$			132.945i			0.810640i
$165$	−199.034	+	251.617i	−1.20627	+	1.52495i
$166$	−54.3987	+	94.2214i	−0.327703	+	0.567599i
$167$	182.488	+	105.359i	1.09274	+	0.630894i	0.934305	−	0.356475i	$-0.116021\pi$
$167$	182.488	+	105.359i	1.09274	+	0.630894i	0.158436	+	0.987369i	$0.449355\pi$
$168$	227.339			1.35321
$169$	69.3306	+	154.124i	0.410240	+	0.911978i
$170$	77.3157			0.454798
$171$	−55.1251	−	31.8265i	−0.322369	−	0.186120i
$172$	−93.4219	−	53.9372i	−0.543151	−	0.313588i
$173$	42.4667	−	24.5181i	0.245472	−	0.141723i	−0.372217	−	0.928146i	$-0.621402\pi$
$173$	42.4667	−	24.5181i	0.245472	−	0.141723i	0.617689	+	0.786422i	$0.288069\pi$
$174$	156.617			0.900098
$175$	−206.428	+	119.181i	−1.17959	+	0.681037i
$176$	10.0991	−	12.7672i	0.0573813	−	0.0725408i
$177$	−140.433			−0.793407
$178$	161.495	−	93.2391i	0.907275	−	0.523815i
$179$	−108.184	+	187.380i	−0.604379	+	1.04682i	0.387770	+	0.921756i	$0.373246\pi$
$179$	−108.184	+	187.380i	−0.604379	+	1.04682i	−0.992149	+	0.125060i	$0.960088\pi$
$180$	−59.8942	+	103.740i	−0.332746	+	0.576332i
$181$	−14.6391			−0.0808790			−0.0404395	−	0.999182i	$-0.512876\pi$
$181$	−14.6391			−0.0808790			−0.0404395	+	0.999182i	$0.512876\pi$
$182$	−96.4283	−	62.3585i	−0.529826	−	0.342629i
$183$			355.548i			1.94289i
$184$	178.874	+	103.273i	0.972140	+	0.561265i
$185$	−145.645	+	252.264i	−0.787268	+	1.36359i
$186$	1.52059	−	0.877914i	0.00817523	−	0.00471997i
$187$	−89.9720	+	35.7228i	−0.481133	+	0.191031i
$188$	72.9038	+	126.273i	0.387786	+	0.671666i
$189$	−74.9900	+	43.2955i	−0.396772	+	0.229077i
$190$	92.4767			0.486719
$191$	90.5152	+	156.777i	0.473901	+	0.820821i	0.999554	−	0.0298783i	$-0.00951196\pi$
$191$	90.5152	+	156.777i	0.473901	+	0.820821i	−0.525652	+	0.850700i	$0.676179\pi$
$192$	−62.7164	+	108.628i	−0.326648	+	0.565770i
$193$	−194.743	−	112.435i	−1.00903	−	0.582565i	−0.0981240	−	0.995174i	$-0.531284\pi$
$193$	−194.743	−	112.435i	−1.00903	−	0.582565i	−0.910908	+	0.412609i	$0.864618\pi$
$194$		−	161.606i		−	0.833023i
$195$	337.495	−	172.779i	1.73075	−	0.886047i
$196$	−21.4708			−0.109545
$197$	249.803	+	144.224i	1.26803	+	0.732100i	0.974616	−	0.223884i	$-0.0718736\pi$
$197$	249.803	+	144.224i	1.26803	+	0.732100i	0.293419	+	0.955984i	$0.405207\pi$
$198$	−11.2804	+	76.9035i	−0.0569716	+	0.388401i
$199$	−142.580	−	246.955i	−0.716481	−	1.24098i	−0.962386	−	0.271687i	$-0.912419\pi$
$199$	−142.580	−	246.955i	−0.716481	−	1.24098i	0.245905	−	0.969294i	$-0.420915\pi$
$200$		−	244.441i		−	1.22220i
$201$	86.3150	+	149.502i	0.429428	+	0.743791i
$202$	20.4130	+	35.3563i	0.101054	+	0.175031i
$203$	−261.212			−1.28676
$204$	−77.8899	+	44.9697i	−0.381813	+	0.220440i
$205$	−328.567	−	189.698i	−1.60276	−	0.925356i
$206$	−21.0925	−	12.1778i	−0.102391	−	0.0591153i
$207$	161.112			0.778317
$208$	−17.1247	+	8.76691i	−0.0823303	+	0.0421486i
$209$	−107.615	+	42.7277i	−0.514903	+	0.204439i
$210$	−128.816	+	223.115i	−0.613408	+	1.06245i
$211$	7.77062	+	4.48637i	0.0368276	+	0.0212624i	0.518301	−	0.855198i	$-0.326565\pi$
$211$	7.77062	+	4.48637i	0.0368276	+	0.0212624i	−0.481473	+	0.876461i	$0.659898\pi$
$212$	−102.587	−	177.686i	−0.483900	−	0.838140i
$213$	−16.5930			−0.0779014
$214$	−53.8998	−	93.3573i	−0.251868	−	0.436249i
$215$	266.606	−	153.925i	1.24003	−	0.715930i
$216$		−	88.7989i		−	0.411106i
$217$	−2.53611	+	1.46422i	−0.0116871	+	0.00674757i
$218$	58.3885	−	101.132i	0.267837	−	0.463908i
$219$	−99.7336	−	57.5812i	−0.455404	−	0.262928i
$220$	80.4093	+	202.520i	0.365497	+	0.920546i
$221$	114.260	+	5.76824i	0.517012	+	0.0261006i
$222$			175.604i			0.791008i
$223$	114.677	−	198.626i	0.514246	−	0.890700i	−0.485618	−	0.874171i	$-0.661405\pi$
$223$	114.677	−	198.626i	0.514246	−	0.890700i	0.999863	−	0.0165284i	$-0.00526139\pi$
$224$	123.750	−	214.340i	0.552453	−	0.956877i
$225$	−95.3355	−	165.126i	−0.423713	−	0.733893i
$226$		−	127.873i		−	0.565809i
$227$	65.8541	−	38.0209i	0.290106	−	0.167493i	−0.347883	−	0.937538i	$-0.613100\pi$
$227$	65.8541	−	38.0209i	0.290106	−	0.167493i	0.637990	+	0.770045i	$0.279766\pi$
$228$	−93.1634	+	53.7879i	−0.408612	+	0.235912i
$229$	72.1966			0.315269			0.157635	−	0.987498i	$-0.449613\pi$
$229$	72.1966			0.315269			0.157635	+	0.987498i	$0.449613\pi$
$230$	−202.708	+	117.034i	−0.881340	+	0.508842i
$231$	46.8146	−	319.156i	0.202660	−	1.38163i
$232$	133.936	−	231.985i	0.577312	−	0.999934i
$233$			48.2431i			0.207052i	0.994627	+	0.103526i	$0.0330125\pi$
$233$			48.2431i			0.207052i	−0.994627	+	0.103526i	$0.966988\pi$
$234$	49.8818	−	77.1348i	0.213170	−	0.329636i
$235$	−416.103			−1.77065
$236$	−47.6906	+	82.6026i	−0.202079	+	0.350011i
$237$	270.344	+	156.083i	1.14069	+	0.658578i
$238$	−67.3228	+	38.8689i	−0.282869	+	0.163315i
$239$		−	204.675i		−	0.856382i	−0.903688	−	0.428191i	$-0.859151\pi$
$239$		−	204.675i		−	0.856382i	0.903688	−	0.428191i	$-0.140849\pi$
$240$	21.5806	+	37.3787i	0.0899192	+	0.155745i
$241$	−295.142	+	170.400i	−1.22465	+	0.707054i	−0.965907	−	0.258891i	$-0.916643\pi$
$241$	−295.142	+	170.400i	−1.22465	+	0.707054i	−0.258747	+	0.965945i	$0.583310\pi$
$242$	96.9845	+	102.880i	0.400763	+	0.425123i
$243$	−140.191	−	242.818i	−0.576918	−	0.999251i
$244$	209.133	+	120.743i	0.857103	+	0.494848i
$245$	30.6365	−	53.0640i	0.125047	−	0.216588i
$246$	−228.719			−0.929752
$247$	136.665	+	6.89934i	0.553299	+	0.0279326i
$248$		−	3.00312i		−	0.0121093i
$249$	312.790	+	180.589i	1.25619	+	0.725259i
$250$	49.6880	+	28.6874i	0.198752	+	0.114750i
$251$	150.605	+	260.856i	0.600020	+	1.03927i	0.992817	+	0.119640i	$0.0381741\pi$
$251$	150.605	+	260.856i	0.600020	+	1.03927i	−0.392797	+	0.919625i	$0.628493\pi$
$252$		−	120.442i		−	0.477945i
$253$	181.817	−	229.850i	0.718643	−	0.908499i
$254$	−67.1892	−	116.375i	−0.264524	−	0.458170i
$255$		−	256.668i		−	1.00654i
$256$	119.107	+	206.300i	0.465262	+	0.805858i
$257$	165.094	−	285.951i	0.642388	−	1.11265i	−0.342510	−	0.939514i	$-0.611277\pi$
$257$	165.094	−	285.951i	0.642388	−	1.11265i	0.984898	−	0.173135i	$-0.0553895\pi$
$258$	92.7937	−	160.723i	0.359665	−	0.622959i
$259$		−	292.879i		−	1.13081i
$260$	12.9839	−	257.190i	0.0499380	−	0.989191i
$261$		−	208.949i		−	0.800569i
$262$	96.5725	−	167.268i	0.368597	−	0.638429i
$263$	186.943	+	107.931i	0.710808	+	0.410385i	0.811360	−	0.584546i	$-0.198728\pi$
$263$	186.943	+	107.931i	0.710808	+	0.410385i	−0.100552	+	0.994932i	$0.532061\pi$
$264$	259.441	+	205.224i	0.982732	+	0.777362i
$265$	585.521			2.20951
$266$	−80.5243	+	46.4907i	−0.302723	+	0.174777i
$267$	−309.529	−	536.120i	−1.15929	−	2.00794i
$268$	117.249			0.437497
$269$	24.9092	+	43.1440i	0.0925992	+	0.160387i	0.908604	−	0.417658i	$-0.137149\pi$
$269$	24.9092	+	43.1440i	0.0925992	+	0.160387i	−0.816005	+	0.578045i	$0.803816\pi$
$270$	87.1491	+	50.3156i	0.322774	+	0.186354i
$271$	217.246	+	125.427i	0.801644	+	0.462829i	0.844046	−	0.536271i	$-0.180168\pi$
$271$	217.246	+	125.427i	0.801644	+	0.462829i	−0.0424017	+	0.999101i	$0.513501\pi$
$272$			13.0235i			0.0478804i
$273$	−207.014	+	320.117i	−0.758292	+	1.17259i
$274$			172.623i			0.630010i
$275$	−343.165	−	50.3362i	−1.24787	−	0.183041i
$276$	136.142	−	235.805i	0.493269	−	0.854367i
$277$	−307.151	+	177.334i	−1.10885	+	0.640194i	−0.938531	−	0.345195i	$-0.887813\pi$
$277$	−307.151	+	177.334i	−1.10885	+	0.640194i	−0.170318	+	0.985389i	$0.554480\pi$
$278$	123.623			0.444689
$279$	−1.17126	−	2.02868i	−0.00419806	−	0.00727125i
$280$	220.323	+	381.610i	0.786866	+	1.36289i
$281$			297.701i			1.05943i	0.848174	+	0.529717i	$0.177702\pi$
$281$			297.701i			1.05943i	−0.848174	+	0.529717i	$0.822298\pi$
$282$	−217.241	+	125.424i	−0.770357	+	0.444766i
$283$	194.104	+	112.066i	0.685878	+	0.395992i	0.802066	−	0.597235i	$-0.203734\pi$
$283$	194.104	+	112.066i	0.685878	+	0.395992i	−0.116188	+	0.993227i	$0.537067\pi$
$284$	−5.63493	+	9.75998i	−0.0198413	+	0.0343661i
$285$		−	306.998i		−	1.07719i
$286$	−53.7524	−	158.212i	−0.187946	−	0.553188i
$287$	381.467			1.32915
$288$	171.455	+	98.9896i	0.595330	+	0.343714i
$289$	−105.777	+	183.210i	−0.366009	+	0.633946i
$290$	151.783	+	262.896i	0.523390	+	0.906538i
$291$	−536.491			−1.84361
$292$	−67.7384	+	39.1088i	−0.231981	+	0.133934i
$293$	−6.42334	+	3.70852i	−0.0219227	+	0.0126571i	−0.510921	−	0.859628i	$-0.670696\pi$
$293$	−6.42334	+	3.70852i	−0.0219227	+	0.0126571i	0.488999	+	0.872285i	$0.337362\pi$
$294$		−	36.9384i		−	0.125641i
$295$	−136.099	−	235.730i	−0.461351	−	0.799084i
$296$	260.108	+	150.174i	0.878745	+	0.507343i
$297$	−124.663	−	18.2858i	−0.419740	−	0.0615684i
$298$	−310.642			−1.04242
$299$	−308.300	+	157.833i	−1.03110	+	0.527868i
$300$	−322.241			−1.07414
$301$	−154.765	+	268.061i	−0.514170	+	0.890568i
$302$	73.7849	−	127.799i	0.244321	−	0.423176i
$303$	117.374	−	67.7657i	0.387372	−	0.223649i
$304$			15.5773i			0.0512410i
$305$	−596.820	+	344.574i	−1.95679	+	1.12975i
$306$	−31.0919	−	53.8528i	−0.101608	−	0.175990i
$307$			232.976i			0.758879i	0.925217	+	0.379439i	$0.123883\pi$
$307$			232.976i			0.758879i	−0.925217	+	0.379439i	$0.876117\pi$
$308$	−171.829	−	135.921i	−0.557888	−	0.441301i
$309$	−40.4269	+	70.0215i	−0.130831	+	0.226607i
$310$	2.94732	+	1.70164i	0.00950748	+	0.00548915i
$311$	118.412			0.380746			0.190373	−	0.981712i	$-0.439030\pi$
$311$	118.412			0.380746			0.190373	+	0.981712i	$0.439030\pi$
$312$	−178.152	−	347.990i	−0.571000	−	1.11535i
$313$	155.580			0.497061			0.248531	−	0.968624i	$-0.420052\pi$
$313$	155.580			0.497061			0.248531	+	0.968624i	$0.420052\pi$
$314$	−163.195	−	94.2206i	−0.519729	−	0.300066i
$315$	297.667	+	171.858i	0.944974	+	0.545581i
$316$	183.616	−	106.011i	0.581062	−	0.335477i
$317$	507.379			1.60056			0.800282	−	0.599624i	$-0.204683\pi$
$317$	507.379			1.60056			0.800282	+	0.599624i	$0.204683\pi$
$318$	305.691	−	176.491i	0.961292	−	0.555002i
$319$	−298.097	−	235.801i	−0.934474	−	0.739190i
$320$	−243.123			−0.759758
$321$	−309.921	+	178.933i	−0.965487	+	0.557424i
$322$	117.672	−	203.815i	0.365442	−	0.632964i
$323$	46.3168	−	80.2230i	0.143396	−	0.248369i
$324$	−260.451			−0.803860
$325$	344.197	+	222.586i	1.05907	+	0.684881i
$326$		−	264.879i		−	0.812511i
$327$	−335.731	−	193.834i	−1.02670	−	0.592766i
$328$	−195.597	+	338.784i	−0.596332	+	1.03288i
$329$	362.323	−	209.187i	1.10129	−	0.635828i
$330$	−348.416	+	138.336i	−1.05581	+	0.419201i
$331$	196.624	+	340.562i	0.594029	+	1.02889i	0.993683	+	0.112222i	$0.0357969\pi$
$331$	196.624	+	340.562i	0.594029	+	1.02889i	−0.399654	+	0.916666i	$0.630870\pi$
$332$	212.445	−	122.655i	0.639895	−	0.369443i
$333$	234.280			0.703542
$334$	123.111	+	213.235i	0.368596	+	0.638427i
$335$	−167.302	+	289.775i	−0.499409	+	0.865001i
$336$	−37.5827	−	21.6984i	−0.111853	−	0.0645786i
$337$		−	353.644i		−	1.04939i	−0.851291	−	0.524694i	$-0.824180\pi$
$337$		−	353.644i		−	1.04939i	0.851291	−	0.524694i	$-0.175820\pi$
$338$	−19.8878	+	196.470i	−0.0588395	+	0.581273i
$339$	−424.504			−1.25222
$340$	−150.972	−	87.1635i	−0.444034	−	0.256363i
$341$	−4.21600	−	0.618413i	−0.0123637	−	0.00181353i
$342$	−37.1888	−	64.4129i	−0.108739	−	0.188342i
$343$		−	308.819i		−	0.900347i
$344$	−158.711	−	274.896i	−0.461371	−	0.799117i
$345$	388.521	+	672.937i	1.12615	+	1.95054i
$346$	57.2983			0.165602
$347$	538.660	−	310.995i	1.55233	−	0.896240i	0.554382	−	0.832262i	$-0.312955\pi$
$347$	538.660	−	310.995i	1.55233	−	0.896240i	0.997951	−	0.0639782i	$-0.0203788\pi$
$348$	−305.821	−	176.566i	−0.878795	−	0.507372i
$349$	183.326	+	105.843i	0.525289	+	0.303276i	0.739096	−	0.673600i	$-0.235253\pi$
$349$	183.326	+	105.843i	0.525289	+	0.303276i	−0.213807	+	0.976876i	$0.568586\pi$
$350$	−278.524			−0.795783
$351$	125.038	+	80.8598i	0.356233	+	0.230370i
$352$	334.713	−	132.896i	0.950890	−	0.377545i
$353$	−166.763	+	288.842i	−0.472416	+	0.818249i	−0.999502	−	0.0315633i	$-0.989951\pi$
$353$	−166.763	+	288.842i	−0.472416	+	0.818249i	0.527086	+	0.849812i	$0.323285\pi$
$354$	−142.110	−	82.0471i	−0.401440	−	0.231771i
$355$	−16.0809	−	27.8529i	−0.0452982	−	0.0784588i
$356$	−420.461			−1.18107
$357$	129.034	+	223.494i	0.361441	+	0.626034i
$358$	−218.951	+	126.412i	−0.611595	+	0.353105i
$359$			347.019i			0.966627i	0.875447	+	0.483313i	$0.160567\pi$
$359$			347.019i			0.966627i	−0.875447	+	0.483313i	$0.839433\pi$
$360$	−305.257	+	176.240i	−0.847936	+	0.489556i
$361$	−125.101	+	216.681i	−0.346540	+	0.600224i
$362$	−14.8139	−	8.55279i	−0.0409223	−	0.0236265i
$363$	341.534	−	321.963i	0.940865	−	0.886951i
$364$	117.991	+	230.476i	0.324151	+	0.633176i
$365$		−	223.216i		−	0.611551i
$366$	−207.727	+	359.793i	−0.567559	+	0.983041i
$367$	168.829	−	292.421i	0.460025	−	0.796787i	−0.538936	−	0.842347i	$-0.681174\pi$
$367$	168.829	−	292.421i	0.460025	−	0.796787i	0.998962	+	0.0455592i	$0.0145070\pi$
$368$	−19.7137	−	34.1452i	−0.0535700	−	0.0927859i
$369$			305.143i			0.826945i
$370$	−294.767	+	170.184i	−0.796668	+	0.459956i
$371$	−509.844	+	294.359i	−1.37424	+	0.793419i
$372$	−3.95894			−0.0106423
$373$	531.385	−	306.795i	1.42463	−	0.822508i	0.427936	−	0.903809i	$-0.359241\pi$
$373$	531.385	−	306.795i	1.42463	−	0.822508i	0.996690	+	0.0813015i	$0.0259077\pi$
$374$	−111.917	−	16.4162i	−0.299243	−	0.0438937i
$375$	95.2345	−	164.951i	0.253959	−	0.439869i
$376$			429.043i			1.14107i
$377$	204.696	+	399.840i	0.542960	+	1.06058i
$378$	−101.180			−0.267673
$379$	139.219	−	241.134i	0.367331	−	0.636236i	−0.621816	−	0.783163i	$-0.713605\pi$
$379$	139.219	−	241.134i	0.367331	−	0.636236i	0.989147	+	0.146927i	$0.0469382\pi$
$380$	−180.576	−	104.256i	−0.475200	−	0.274357i
$381$	−386.335	+	223.050i	−1.01400	+	0.585434i
$382$			211.532i			0.553748i
$383$	−31.3238	−	54.2544i	−0.0817853	−	0.141656i	0.822232	−	0.569153i	$-0.192729\pi$
$383$	−31.3238	−	54.2544i	−0.0817853	−	0.141656i	−0.904017	+	0.427497i	$0.859396\pi$
$384$	313.002	−	180.712i	0.815109	−	0.470603i
$385$	581.103	−	230.723i	1.50936	−	0.599281i
$386$	−131.379	−	227.555i	−0.340360	−	0.589520i
$387$	−214.427	−	123.800i	−0.554075	−	0.319895i
$388$	−182.191	+	315.563i	−0.469563	+	0.813308i
$389$	225.680			0.580155			0.290078	−	0.957003i	$-0.406319\pi$
$389$	225.680			0.580155			0.290078	+	0.957003i	$0.406319\pi$
$390$	442.470	+	22.3375i	1.13454	+	0.0572756i
$391$			234.464i			0.599653i
$392$	−54.7141	−	31.5892i	−0.139577	−	0.0805846i
$393$	−555.287	−	320.595i	−1.41294	−	0.815764i
$394$	168.524	+	291.891i	0.427725	+	0.740841i
$395$			605.062i			1.53180i
$396$	108.726	−	137.450i	0.274560	−	0.347095i
$397$	−44.6531	−	77.3415i	−0.112476	−	0.194815i	0.804292	−	0.594235i	$-0.202545\pi$
$397$	−44.6531	−	77.3415i	−0.112476	−	0.194815i	−0.916768	+	0.399420i	$0.869212\pi$
$398$		−	333.205i		−	0.837198i
$399$	154.337	+	267.319i	0.386809	+	0.669973i
$400$	−23.3307	+	40.4099i	−0.0583267	+	0.101025i
$401$	−12.3573	+	21.4035i	−0.0308163	+	0.0533753i	−0.881022	−	0.473075i	$-0.843144\pi$
$401$	−12.3573	+	21.4035i	−0.0308163	+	0.0533753i	0.850206	+	0.526450i	$0.176477\pi$
$402$			201.716i			0.501781i
$403$	4.22869	+	2.73462i	0.0104930	+	0.00678566i
$404$		−	92.0521i		−	0.227852i
$405$	371.635	−	643.690i	0.917616	−	1.58936i
$406$	−264.331	−	152.612i	−0.651062	−	0.375891i
$407$	264.388	−	334.236i	0.649602	−	0.821218i
$408$	−264.649			−0.648650
$409$	−0.403228	+	0.232804i	−0.000985888	+	0.000569203i	−0.500493	−	0.865741i	$-0.666848\pi$
$409$	−0.403228	+	0.232804i	−0.000985888	+	0.000569203i	0.499507	+	0.866310i	$0.333515\pi$
$410$	−221.660	−	383.926i	−0.540633	−	0.936405i
$411$	573.062			1.39431
$412$	27.4577	+	47.5582i	0.0666449	+	0.115432i
$413$	237.016	+	136.842i	0.573890	+	0.331335i
$414$	163.035	+	94.1284i	0.393805	+	0.227363i
$415$			700.063i			1.68690i
$416$	−425.068	−	21.4590i	−1.02180	−	0.0515841i
$417$		−	410.397i		−	0.984166i
$418$	−133.863	−	19.6353i	−0.320246	−	0.0469745i
$419$	−259.389	+	449.275i	−0.619068	+	1.07226i	0.370589	+	0.928797i	$0.379156\pi$
$419$	−259.389	+	449.275i	−0.619068	+	1.07226i	−0.989656	+	0.143459i	$0.954177\pi$
$420$	503.068	−	290.447i	1.19778	−	0.691539i
$421$	−587.768			−1.39612			−0.698062	−	0.716038i	$-0.745954\pi$
$421$	−587.768			−1.39612			−0.698062	+	0.716038i	$0.745954\pi$
$422$	5.24227	+	9.07987i	0.0124224	+	0.0215163i
$423$	167.333	+	289.829i	0.395586	+	0.685175i
$424$		−	603.729i		−	1.42389i
$425$	240.306	−	138.741i	0.565427	−	0.326449i
$426$	−16.7911	−	9.69435i	−0.0394157	−	0.0227567i
$427$	346.455	−	600.078i	0.811370	−	1.40533i
$428$			243.061i			0.567899i
$429$	−525.221	+	178.444i	−1.22429	+	0.415953i
$430$	359.719			0.836555
$431$	−487.737	−	281.595i	−1.13164	−	0.653353i	−0.187294	−	0.982304i	$-0.559972\pi$
$431$	−487.737	−	281.595i	−1.13164	−	0.653353i	−0.944347	+	0.328951i	$0.893305\pi$
$432$	−8.47541	+	14.6798i	−0.0196190	+	0.0339811i
$433$	−285.872	−	495.145i	−0.660213	−	1.14352i	−0.980560	−	0.196221i	$-0.937133\pi$
$433$	−285.872	−	495.145i	−0.660213	−	1.14352i	0.320347	−	0.947300i	$-0.396200\pi$
$434$	−3.42185			−0.00788444
$435$	872.745	−	503.880i	2.00631	−	1.15834i
$436$	−228.026	+	131.651i	−0.522996	+	0.301952i
$437$			280.441i			0.641741i
$438$	−67.2829	−	116.537i	−0.153614	−	0.266067i
$439$	−223.853	−	129.242i	−0.509917	−	0.294401i	0.222883	−	0.974845i	$-0.428453\pi$
$439$	−223.853	−	129.242i	−0.509917	−	0.294401i	−0.732799	+	0.680445i	$0.761787\pi$
$440$	−93.0531	+	634.385i	−0.211484	+	1.44179i
$441$	−49.2809			−0.111748
$442$	112.254	+	72.5925i	0.253968	+	0.164236i
$443$	563.029			1.27095			0.635473	−	0.772123i	$-0.280805\pi$
$443$	563.029			1.27095			0.635473	+	0.772123i	$0.280805\pi$
$444$	197.971	−	342.895i	0.445880	−	0.772287i
$445$	599.952	−	1039.15i	1.34821	−	2.33516i
$446$	232.092	−	133.998i	0.520385	−	0.300445i
$447$			1031.25i			2.30705i
$448$	211.700	−	122.225i	0.472544	−	0.272823i
$449$	−129.355	−	224.049i	−0.288095	−	0.498996i	0.685260	−	0.728299i	$-0.259689\pi$
$449$	−129.355	−	224.049i	−0.288095	−	0.498996i	−0.973355	+	0.229303i	$0.926355\pi$
$450$		−	222.796i		−	0.495103i
$451$	435.333	+	344.358i	0.965261	+	0.763543i
$452$	−144.160	+	249.693i	−0.318939	+	0.552418i
$453$	−424.260	−	244.946i	−0.936556	−	0.540721i
$454$	88.8538			0.195713
$455$	−737.970	−	37.2554i	−1.62191	−	0.0818800i
$456$	−316.545			−0.694177
$457$	510.555	+	294.769i	1.11719	+	0.645009i	0.940682	−	0.339290i	$-0.110187\pi$
$457$	510.555	+	294.769i	1.11719	+	0.645009i	0.176507	+	0.984299i	$0.443520\pi$
$458$	73.0586	+	42.1804i	0.159517	+	0.0920970i
$459$	87.2969	−	50.4009i	0.190189	−	0.109806i
$460$	527.761			1.14731
$461$	−224.681	+	129.719i	−0.487377	+	0.281387i	−0.723486	−	0.690339i	$-0.757461\pi$
$461$	−224.681	+	129.719i	−0.487377	+	0.281387i	0.236109	+	0.971727i	$0.424128\pi$
$462$	233.838	−	295.616i	0.506144	−	0.639861i
$463$	−638.625			−1.37932			−0.689660	−	0.724133i	$-0.742240\pi$
$463$	−638.625			−1.37932			−0.689660	+	0.724133i	$0.742240\pi$
$464$	−44.2836	+	25.5671i	−0.0954387	+	0.0551016i
$465$	5.64898	−	9.78432i	0.0121483	−	0.0210416i
$466$	−28.1857	+	48.8191i	−0.0604844	+	0.104762i
$467$	−251.519			−0.538585			−0.269293	−	0.963058i	$-0.586790\pi$
$467$	−251.519			−0.538585			−0.269293	+	0.963058i	$0.586790\pi$
$468$	−184.362	+	94.3832i	−0.393936	+	0.201674i
$469$		−	336.430i		−	0.717335i
$470$	−421.071	−	243.106i	−0.895897	−	0.517246i
$471$	−312.787	+	541.764i	−0.664092	+	1.15024i
$472$	−243.060	+	140.331i	−0.514958	+	0.297311i
$473$	−418.603	+	166.204i	−0.884996	+	0.351382i
$474$	182.381	+	315.893i	0.384770	+	0.666441i
$475$	287.429	−	165.947i	0.605113	−	0.349362i
$476$	175.279			0.368232
$477$	−235.463	−	407.834i	−0.493633	−	0.854997i
$478$	119.580	−	207.119i	0.250168	−	0.433303i
$479$	−514.812	−	297.227i	−1.07476	−	0.620515i	−0.145284	−	0.989390i	$-0.546410\pi$
$479$	−514.812	−	297.227i	−1.07476	−	0.620515i	−0.929479	+	0.368875i	$0.879743\pi$
$480$			954.854i			1.98928i
$481$	−448.313	+	229.512i	−0.932043	+	0.477155i
$482$	−398.220			−0.826183
$483$	−676.610	−	390.641i	−1.40085	−	0.808781i
$484$	−73.3945	−	310.227i	−0.151642	−	0.640966i
$485$	−519.932	−	900.549i	−1.07203	−	1.85680i
$486$		−	327.623i		−	0.674121i
$487$	98.4591	+	170.536i	0.202175	+	0.350177i	0.949229	−	0.314586i	$-0.101866\pi$
$487$	98.4591	+	170.536i	0.202175	+	0.350177i	−0.747054	+	0.664763i	$0.768532\pi$
$488$	355.289	+	615.379i	0.728052	+	1.26102i
$489$	−879.327			−1.79821
$490$	62.0046	−	35.7983i	0.126540	−	0.0730578i
$491$	215.587	+	124.469i	0.439077	+	0.253501i	0.703206	−	0.710986i	$-0.251751\pi$
$491$	215.587	+	124.469i	0.439077	+	0.253501i	−0.264129	+	0.964487i	$0.585084\pi$
$492$	446.612	+	257.851i	0.907747	+	0.524088i
$493$	304.081			0.616798
$494$	134.266	+	86.8273i	0.271793	+	0.175764i
$495$	184.560	+	464.835i	0.372848	+	0.939061i
$496$	−0.286632	+	0.496462i	−0.000577888	+	0.00100093i
$497$	28.0049	+	16.1686i	0.0563479	+	0.0325325i
$498$	211.016	+	365.491i	0.423728	+	0.733918i
$499$	46.5422			0.0932709			0.0466355	−	0.998912i	$-0.485150\pi$
$499$	46.5422			0.0932709			0.0466355	+	0.998912i	$0.485150\pi$
$500$	−64.6827	−	112.034i	−0.129365	−	0.224067i
$501$	707.882	−	408.696i	1.41294	−	0.815761i
$502$			351.960i			0.701116i
$503$	188.674	−	108.931i	0.375096	−	0.216562i	−0.300586	−	0.953755i	$-0.597182\pi$
$503$	188.674	−	108.931i	0.375096	−	0.216562i	0.675683	+	0.737193i	$0.263849\pi$
$504$	177.202	−	306.923i	0.351591	−	0.608974i
$505$	227.502	+	131.348i	0.450499	+	0.260096i
$506$	318.276	−	126.369i	0.629004	−	0.249742i
$507$	652.229	+	66.0221i	1.28645	+	0.130221i
$508$			302.989i			0.596435i
$509$	334.852	−	579.980i	0.657862	−	1.13945i	−0.323307	−	0.946294i	$-0.604795\pi$
$509$	334.852	−	579.980i	0.657862	−	1.13945i	0.981168	−	0.193155i	$-0.0618721\pi$
$510$	149.956	−	259.732i	0.294032	−	0.509279i
$511$	112.217	+	194.366i	0.219603	+	0.380364i
$512$		−	94.3406i		−	0.184259i
$513$	104.415	−	60.2841i	0.203538	−	0.117513i
$514$	334.130	−	192.910i	0.650058	−	0.375311i
$515$	−156.717			−0.304304
$516$	−362.390	+	209.226i	−0.702306	+	0.405477i
$517$	602.323	+	88.3501i	1.16504	+	0.170890i
$518$	171.113	−	296.376i	0.330334	−	0.572154i
$519$		−	190.215i		−	0.366503i
$520$	411.480	−	636.294i	0.791308	−	1.22364i
$521$	143.425			0.275287			0.137644	−	0.990482i	$-0.456047\pi$
$521$	143.425			0.275287			0.137644	+	0.990482i	$0.456047\pi$
$522$	122.077	−	211.443i	0.233864	−	0.405064i
$523$	186.585	+	107.725i	0.356759	+	0.205975i	0.667658	−	0.744468i	$-0.267297\pi$
$523$	186.585	+	107.725i	0.356759	+	0.205975i	−0.310899	+	0.950443i	$0.600630\pi$
$524$	−377.147	+	217.746i	−0.719747	+	0.415546i
$525$			924.626i			1.76119i
$526$	126.116	+	218.440i	0.239765	+	0.415285i
$527$	2.95232	−	1.70452i	0.00560213	−	0.00323439i
$528$	−23.3021	−	58.6890i	−0.0441328	−	0.111153i
$529$	−90.4111	−	156.597i	−0.170909	−	0.296024i
$530$	592.512	+	342.087i	1.11795	+	0.645447i
$531$	−109.462	+	189.594i	−0.206143	+	0.357051i
$532$	209.649			0.394078
$533$	−298.932	−	583.915i	−0.560849	−	1.09553i
$534$		−	723.362i		−	1.35461i
$535$	−600.712	−	346.821i	−1.12283	−	0.648264i
$536$	298.786	+	172.504i	0.557437	+	0.321837i
$537$	419.653	+	726.860i	0.781476	+	1.35356i
$538$			58.2121i			0.108201i
$539$	−55.6142	+	70.3068i	−0.103180	+	0.130439i
$540$	−113.449	−	196.499i	−0.210090	−	0.363887i
$541$			301.380i			0.557079i	0.960425	+	0.278539i	$0.0898502\pi$
$541$			301.380i			0.557079i	−0.960425	+	0.278539i	$0.910150\pi$
$542$	146.560	+	253.849i	0.270405	+	0.468355i
$543$	−28.3930	+	49.1781i	−0.0522892	+	0.0905675i
$544$	−144.059	+	249.517i	−0.264814	+	0.458671i
$545$		−	751.407i		−	1.37873i
$546$	−396.511	+	202.992i	−0.726211	+	0.371780i
$547$		−	666.861i		−	1.21912i	−0.792739	−	0.609562i	$-0.791345\pi$
$547$		−	666.861i		−	1.21912i	0.792739	−	0.609562i	$-0.208655\pi$
$548$	194.610	−	337.074i	0.355128	−	0.615099i
$549$	480.014	+	277.136i	0.874342	+	0.504801i
$550$	−317.853	−	251.429i	−0.577915	−	0.457144i
$551$	363.709			0.660089
$552$	693.863	−	400.602i	1.25700	−	0.725728i
$553$	−304.182	−	526.859i	−0.550059	−	0.952730i
$554$	−414.425			−0.748059
$555$	564.965	+	978.549i	1.01796	+	1.76315i
$556$	−241.395	−	139.370i	−0.434164	−	0.250665i
$557$	−735.721	−	424.769i	−1.32086	−	0.762601i	−0.336997	−	0.941506i	$-0.609411\pi$
$557$	−735.721	−	424.769i	−1.32086	−	0.762601i	−0.983866	+	0.178905i	$0.942745\pi$
$558$		−	2.73720i		−	0.00490538i
$559$	531.604	+	26.8373i	0.950990	+	0.0480094i
$560$		−	84.1148i		−	0.150205i
$561$	−54.4976	+	371.535i	−0.0971436	+	0.662272i
$562$	−173.930	+	301.255i	−0.309484	+	0.536041i
$563$	138.091	−	79.7269i	0.245277	−	0.141611i	−0.372323	−	0.928103i	$-0.621438\pi$
$563$	138.091	−	79.7269i	0.245277	−	0.141611i	0.617600	+	0.786493i	$0.288105\pi$
$564$	565.598			1.00283
$565$	−411.402	−	712.569i	−0.728145	−	1.26118i
$566$	130.947	+	226.807i	0.231356	+	0.400720i
$567$			747.326i			1.31804i
$568$	−28.7190	+	16.5809i	−0.0505616	+	0.0291918i
$569$	−611.720	−	353.177i	−1.07508	−	0.620697i	−0.145514	−	0.989356i	$-0.546484\pi$
$569$	−611.720	−	353.177i	−1.07508	−	0.620697i	−0.929565	+	0.368659i	$0.879817\pi$
$570$	179.362	−	310.664i	0.314670	−	0.545024i
$571$			515.964i			0.903614i	0.892116	+	0.451807i	$0.149220\pi$
$571$			515.964i			0.903614i	−0.892116	+	0.451807i	$0.850780\pi$
$572$	−73.4030	+	369.534i	−0.128327	+	0.646038i
$573$	702.229			1.22553
$574$	386.021	+	222.870i	0.672511	+	0.388274i
$575$	−420.027	+	727.508i	−0.730482	+	1.26523i
$576$	97.7699	+	169.343i	0.169739	+	0.293997i
$577$	−5.53717			−0.00959648			−0.00479824	−	0.999988i	$-0.501527\pi$
$577$	−5.53717			−0.00959648			−0.00479824	+	0.999988i	$0.501527\pi$
$578$	−214.079	+	123.599i	−0.370379	+	0.213838i
$579$	−755.422	+	436.143i	−1.30470	+	0.753270i
$580$		−	684.464i		−	1.18011i
$581$	−351.942	−	609.581i	−0.605752	−	1.04919i
$582$	−542.896	−	313.441i	−0.932811	−	0.538559i
$583$	−847.561	−	124.322i	−1.45379	−	0.213245i
$584$	−230.157			−0.394105
$585$	29.8013	−	590.316i	0.0509424	−	1.00909i
$586$	−8.66671			−0.0147896
$587$	195.188	−	338.075i	0.332517	−	0.575937i	−0.650487	−	0.759517i	$-0.725435\pi$
$587$	195.188	−	338.075i	0.332517	−	0.575937i	0.983005	+	0.183580i	$0.0587687\pi$
$588$	−41.6433	+	72.1284i	−0.0708220	+	0.122667i
$589$	3.53125	−	2.03877i	0.00599533	−	0.00346140i
$590$		−	318.059i		−	0.539083i
$591$	969.002	−	559.454i	1.63960	−	0.946622i
$592$	−28.6667	−	49.6521i	−0.0484234	−	0.0838718i
$593$		−	88.4317i		−	0.149126i	−0.997216	−	0.0745630i	$-0.976244\pi$
$593$		−	88.4317i		−	0.149126i	0.997216	−	0.0745630i	$-0.0237562\pi$
$594$	−115.468	−	91.3375i	−0.194390	−	0.153767i
$595$	−250.104	+	433.192i	−0.420342	+	0.728054i
$596$	606.580	+	350.209i	1.01775	+	0.587599i
$597$	−1106.15			−1.85285
$598$	−404.193	−	20.4052i	−0.675909	−	0.0341223i
$599$	47.7985			0.0797972			0.0398986	−	0.999204i	$-0.487297\pi$
$599$	47.7985			0.0797972			0.0398986	+	0.999204i	$0.487297\pi$
$600$	−821.168	−	474.101i	−1.36861	−	0.790169i
$601$	35.8908	+	20.7216i	0.0597184	+	0.0344785i	0.529562	−	0.848271i	$-0.322356\pi$
$601$	35.8908	+	20.7216i	0.0597184	+	0.0344785i	−0.469843	+	0.882750i	$0.655690\pi$
$602$	−313.226	+	180.841i	−0.520309	+	0.300400i
$603$	269.117			0.446297
$604$	−288.155	+	166.366i	−0.477077	+	0.275441i
$605$	871.437	+	261.270i	1.44039	+	0.431851i
$606$	158.367			0.261331
$607$	371.320	−	214.381i	0.611729	−	0.353182i	−0.161913	−	0.986805i	$-0.551766\pi$
$607$	371.320	−	214.381i	0.611729	−	0.353182i	0.773642	+	0.633623i	$0.218433\pi$
$608$	−172.307	+	298.445i	−0.283400	+	0.490864i
$609$	−506.630	+	877.509i	−0.831905	+	1.44090i
$610$	−805.261			−1.32010
$611$	−604.135	−	390.684i	−0.988765	−	0.639417i
$612$			140.209i			0.229099i
$613$	831.548	+	480.094i	1.35652	+	0.783188i	0.989153	−	0.146887i	$-0.0469254\pi$
$613$	831.548	+	480.094i	1.35652	+	0.783188i	0.367369	+	0.930075i	$0.380259\pi$
$614$	−136.115	+	235.757i	−0.221685	+	0.383970i
$615$	−1274.53	+	735.852i	−2.07241	+	1.19651i
$616$	−237.898	−	599.173i	−0.386198	−	0.972684i
$617$	132.716	+	229.872i	0.215100	+	0.372563i	0.953303	−	0.302014i	$-0.0976591\pi$
$617$	132.716	+	229.872i	0.215100	+	0.372563i	−0.738204	+	0.674578i	$0.764326\pi$
$618$	−81.8192	+	47.2383i	−0.132394	+	0.0764374i
$619$	−1042.99			−1.68497			−0.842483	−	0.538723i	$-0.818907\pi$
$619$	−1042.99			−1.68497			−0.842483	+	0.538723i	$0.818907\pi$
$620$	−3.83675	−	6.64545i	−0.00618831	−	0.0107185i
$621$	−152.585	+	264.285i	−0.245708	+	0.425579i
$622$	119.826	+	69.1814i	0.192646	+	0.111224i
$623$			1206.45i			1.93652i
$624$	−3.76264	+	74.5319i	−0.00602988	+	0.119442i
$625$	−419.085			−0.670536
$626$	157.438	+	90.8967i	0.251498	+	0.145202i
$627$	−65.1841	+	444.390i	−0.103962	+	0.708756i
$628$	212.443	+	367.963i	0.338285	+	0.585928i
$629$			340.945i			0.542043i
$630$	200.814	+	347.820i	0.318752	+	0.552095i
$631$	338.178	+	585.742i	0.535940	+	0.928276i	0.999117	+	0.0420102i	$0.0133762\pi$
$631$	338.178	+	585.742i	0.535940	+	0.928276i	−0.463177	+	0.886266i	$0.653290\pi$
$632$	623.877			0.987148
$633$	30.1428	−	17.4029i	0.0476189	−	0.0274928i
$634$	513.437	+	296.433i	0.809837	+	0.467560i
$635$	−748.821	−	432.332i	−1.17925	−	0.680838i
$636$	−795.883			−1.25139
$637$	94.3030	−	48.2780i	0.148042	−	0.0757896i
$638$	−163.891	−	412.778i	−0.256882	−	0.646988i
$639$	−12.9336	+	22.4016i	−0.0202404	+	0.0350574i
$640$	606.682	+	350.268i	0.947941	+	0.547294i
$641$	426.652	+	738.983i	0.665604	+	1.15286i	0.979121	+	0.203278i	$0.0651594\pi$
$641$	426.652	+	738.983i	0.665604	+	1.15286i	−0.313517	+	0.949583i	$0.601507\pi$
$642$	−418.162			−0.651343
$643$	206.377	+	357.455i	0.320959	+	0.555917i	0.980686	−	0.195588i	$-0.0626615\pi$
$643$	206.377	+	357.455i	0.320959	+	0.555917i	−0.659727	+	0.751505i	$0.729328\pi$
$644$	−459.550	+	265.321i	−0.713586	+	0.411989i
$645$		−	1194.17i		−	1.85143i
$646$	93.7396	−	54.1206i	0.145108	−	0.0837780i
$647$	188.228	−	326.021i	0.290925	−	0.503897i	−0.683104	−	0.730321i	$-0.739370\pi$
$647$	188.228	−	326.021i	0.290925	−	0.503897i	0.974029	+	0.226425i	$0.0727037\pi$
$648$	−663.706	−	383.191i	−1.02424	−	0.591344i
$649$	146.955	+	370.124i	0.226434	+	0.570299i
$650$	218.262	+	426.339i	0.335788	+	0.655906i
$651$			11.3596i			0.0174495i
$652$	−298.617	+	517.219i	−0.458001	+	0.793281i
$653$	366.429	−	634.674i	0.561147	−	0.971935i	−0.436249	−	0.899826i	$-0.643693\pi$
$653$	366.429	−	634.674i	0.561147	−	0.971935i	0.997397	−	0.0721097i	$-0.0229732\pi$
$654$	−226.493	−	392.297i	−0.346320	−	0.599843i
$655$		−	1242.80i		−	1.89741i
$656$	64.6705	−	37.3375i	0.0985830	−	0.0569169i
$657$	−155.477	+	89.7646i	−0.236647	+	0.136628i
$658$	488.865			0.742956
$659$	321.086	−	185.379i	0.487232	−	0.281303i	−0.236194	−	0.971706i	$-0.575900\pi$
$659$	321.086	−	185.379i	0.487232	−	0.281303i	0.723425	+	0.690403i	$0.242567\pi$
$660$	836.297	+	122.670i	1.26712	+	0.185863i
$661$	372.245	−	644.747i	0.563154	−	0.975411i	−0.434065	−	0.900881i	$-0.642921\pi$
$661$	372.245	−	644.747i	0.563154	−	0.975411i	0.997219	−	0.0745293i	$-0.0237454\pi$
$662$			459.504i			0.694115i
$663$	240.988	−	372.653i	0.363481	−	0.562070i
$664$	721.832			1.08710
$665$	−299.147	+	518.138i	−0.449845	+	0.779154i
$666$	237.077	+	136.876i	0.355971	+	0.205520i
$667$	−797.247	+	460.291i	−1.19527	+	0.690091i
$668$		−	555.168i		−	0.831089i
$669$	−444.839	−	770.484i	−0.664931	−	1.15169i
$670$	−338.599	+	195.490i	−0.505371	+	0.291776i
$671$	937.079	−	372.061i	1.39654	−	0.554488i
$672$	−480.033	−	831.441i	−0.714334	−	1.23726i
$673$	−520.710	−	300.632i	−0.773715	−	0.446704i	0.0604835	−	0.998169i	$-0.480736\pi$
$673$	−520.710	−	300.632i	−0.773715	−	0.446704i	−0.834198	+	0.551465i	$0.814069\pi$
$674$	206.614	−	357.866i	0.306549	−	0.530958i
$675$	361.160			0.535051
$676$	260.329	−	361.220i	0.385102	−	0.534349i
$677$			402.474i			0.594497i	0.954800	+	0.297248i	$0.0960690\pi$
$677$			402.474i			0.594497i	−0.954800	+	0.297248i	$0.903931\pi$
$678$	−429.572	−	248.014i	−0.633588	−	0.365802i
$679$	905.465	+	522.770i	1.33353	+	0.769912i
$680$	−256.481	−	444.238i	−0.377178	−	0.653291i
$681$		−	294.971i		−	0.433144i
$682$	−3.90504	−	3.08897i	−0.00572586	−	0.00452928i
$683$	244.404	+	423.321i	0.357839	+	0.619796i	0.987600	−	0.156994i	$-0.0501802\pi$
$683$	244.404	+	423.321i	0.357839	+	0.619796i	−0.629760	+	0.776790i	$0.716847\pi$
$684$			167.702i			0.245179i
$685$	555.375	+	961.937i	0.810766	+	1.40429i
$686$	180.426	−	312.506i	0.263011	−	0.455548i
$687$	140.028	−	242.535i	0.203825	−	0.353035i
$688$			60.5929i			0.0880711i
$689$	850.111	+	549.752i	1.23383	+	0.797898i
$690$			907.962i			1.31589i
$691$	−386.010	+	668.590i	−0.558626	+	0.967568i	0.438986	+	0.898494i	$0.355338\pi$
$691$	−386.010	+	668.590i	−0.558626	+	0.967568i	−0.997612	+	0.0690741i	$0.977995\pi$
$692$	−111.884	−	64.5964i	−0.161683	−	0.0933475i
$693$	−394.392	−	311.973i	−0.569108	−	0.450177i
$694$	726.788			1.04724
$695$	688.889	−	397.730i	0.991208	−	0.572274i
$696$	−519.548	−	899.884i	−0.746478	−	1.29294i
$697$	−444.071			−0.637118
$698$	123.676	+	214.214i	0.177187	+	0.306897i
$699$	162.067	+	93.5691i	0.231855	+	0.133861i
$700$	543.864	+	314.000i	0.776948	+	0.448571i
$701$			816.623i			1.16494i	0.812852	+	0.582470i	$0.197914\pi$
$701$			816.623i			1.16494i	−0.812852	+	0.582470i	$0.802086\pi$
$702$	79.2889	+	154.878i	0.112947	+	0.220624i
$703$			407.802i			0.580088i
$704$	351.928	+	51.6216i	0.499898	+	0.0733261i
$705$	−807.047	+	1397.85i	−1.14475	+	1.98276i
$706$	−337.508	+	194.860i	−0.478057	+	0.276006i
$707$	−264.131			−0.373593
$708$	184.995	+	320.421i	0.261293	+	0.452572i
$709$	−189.926	−	328.961i	−0.267879	−	0.463979i	0.700435	−	0.713716i	$-0.252989\pi$
$709$	−189.926	−	328.961i	−0.267879	−	0.463979i	−0.968314	+	0.249737i	$0.919656\pi$
$710$		−	37.5806i		−	0.0529304i
$711$	421.445	−	243.321i	0.592749	−	0.342224i
$712$	−1071.46	−	618.608i	−1.50486	−	0.868831i
$713$	−5.16031	+	8.93792i	−0.00723746	+	0.0125356i
$714$			301.550i			0.422339i
$715$	−808.545	−	708.696i	−1.13083	−	0.991183i
$716$	570.051			0.796161
$717$	−687.580	−	396.975i	−0.958968	−	0.553661i
$718$	−202.744	+	351.162i	−0.282373	+	0.489084i
$719$	265.146	+	459.246i	0.368770	+	0.638728i	0.989374	−	0.145396i	$-0.0464456\pi$
$719$	265.146	+	459.246i	0.368770	+	0.638728i	−0.620603	+	0.784125i	$0.713112\pi$
$720$	67.2850			0.0934514
$721$	136.461	−	78.7861i	0.189267	−	0.109273i
$722$	−253.189	+	146.179i	−0.350677	+	0.202464i
$723$			1321.99i			1.82847i
$724$	19.2844	+	33.4015i	0.0266359	+	0.0461346i
$725$	943.520	+	544.741i	1.30141	+	0.751367i
$726$	533.716	−	126.268i	0.735146	−	0.173923i
$727$	−512.696			−0.705222			−0.352611	−	0.935770i	$-0.614706\pi$
$727$	−512.696			−0.705222			−0.352611	+	0.935770i	$0.614706\pi$
$728$	−38.4139	+	760.918i	−0.0527663	+	1.04522i
$729$	−197.914			−0.271487
$730$	130.412	−	225.881i	0.178647	−	0.309426i
$731$	180.164	−	312.054i	0.246463	−	0.426886i
$732$	811.241	−	468.370i	1.10825	−	0.639850i
$733$		−	835.352i		−	1.13963i	−0.821772	−	0.569817i	$-0.807014\pi$
$733$		−	835.352i		−	1.13963i	0.821772	−	0.569817i	$-0.192986\pi$
$734$	341.690	−	197.275i	0.465518	−	0.268767i
$735$	−118.841	−	205.839i	−0.161688	−	0.280053i
$736$		−	872.253i		−	1.18513i
$737$	303.702	−	383.937i	0.412079	−	0.520945i
$738$	−178.278	+	308.786i	−0.241568	+	0.418409i
$739$	−690.329	−	398.562i	−0.934139	−	0.539326i	−0.0460210	−	0.998940i	$-0.514654\pi$
$739$	−690.329	−	398.562i	−0.934139	−	0.539326i	−0.888118	+	0.459615i	$0.847987\pi$
$740$	767.442			1.03708
$741$	288.244	−	445.727i	0.388993	−	0.601521i
$742$	−687.908			−0.927100
$743$	−50.6333	−	29.2331i	−0.0681471	−	0.0393447i	0.465539	−	0.885027i	$-0.345860\pi$
$743$	−50.6333	−	29.2331i	−0.0681471	−	0.0393447i	−0.533686	+	0.845682i	$0.679194\pi$
$744$	−10.0886	−	5.82464i	−0.0135599	−	0.00782882i
$745$	−1731.05	+	999.421i	−2.32355	+	1.34150i
$746$	716.973			0.961089
$747$	487.615	−	281.525i	0.652765	−	0.376874i
$748$	200.029	+	158.227i	0.267419	+	0.211534i
$749$	697.428			0.931146
$750$	192.743	−	111.280i	0.256991	−	0.148374i
$751$	−39.2604	+	68.0010i	−0.0522775	+	0.0905472i	−0.890980	−	0.454043i	$-0.849981\pi$
$751$	−39.2604	+	68.0010i	−0.0522775	+	0.0905472i	0.838702	+	0.544590i	$0.183315\pi$
$752$	40.9500	−	70.9275i	0.0544548	−	0.0943184i
$753$	1168.41			1.55168
$754$	−26.4638	+	524.206i	−0.0350979	+	0.695234i
$755$		−	949.545i		−	1.25768i
$756$	197.571	+	114.068i	0.261338	+	0.150883i
$757$	−239.209	+	414.322i	−0.315996	+	0.547321i	−0.979649	−	0.200720i	$-0.935672\pi$
$757$	−239.209	+	414.322i	−0.315996	+	0.547321i	0.663653	+	0.748041i	$0.269005\pi$
$758$	281.761	−	162.675i	0.371717	−	0.214611i
$759$	−419.513	−	1056.59i	−0.552718	−	1.39208i
$760$	−306.775	−	531.349i	−0.403651	−	0.699144i
$761$	203.199	−	117.317i	0.267016	−	0.154162i	−0.360515	−	0.932754i	$-0.617399\pi$
$761$	203.199	−	117.317i	0.267016	−	0.154162i	0.627531	+	0.778592i	$0.284066\pi$
$762$	−521.263			−0.684072
$763$	377.754	+	654.290i	0.495091	+	0.857523i
$764$	238.475	−	413.050i	0.312140	−	0.540642i
$765$	−346.518	−	200.063i	−0.452965	−	0.261520i
$766$		−	73.2029i		−	0.0955651i
$767$	23.7292	−	470.038i	0.0309377	−	0.612826i
$768$	924.049			1.20319
$769$	103.576	+	59.7997i	0.134689	+	0.0777629i	0.565831	−	0.824522i	$-0.308556\pi$
$769$	103.576	+	59.7997i	0.134689	+	0.0777629i	−0.431141	+	0.902284i	$0.641889\pi$
$770$	722.840	+	106.028i	0.938753	+	0.137698i
$771$	−640.410	−	1109.22i	−0.830622	−	1.43868i
$772$			592.451i			0.767424i
$773$	−356.628	−	617.698i	−0.461356	−	0.799092i	0.537673	−	0.843154i	$-0.319304\pi$
$773$	−356.628	−	617.698i	−0.461356	−	0.799092i	−0.999029	+	0.0440616i	$0.985970\pi$
$774$	−144.658	−	250.555i	−0.186897	−	0.323715i
$775$	12.2142			0.0157602
$776$	−928.553	+	536.100i	−1.19659	+	0.690851i
$777$	−983.890	−	568.049i	−1.26627	−	0.731080i
$778$	228.375	+	131.852i	0.293541	+	0.169476i
$779$	−531.150			−0.681836
$780$	−838.813	−	542.446i	−1.07540	−	0.695443i
$781$	17.3636	+	43.7323i	0.0222326	+	0.0559953i
$782$	−136.984	+	237.264i	−0.175172	+	0.303406i
$783$	342.756	+	197.890i	0.437747	+	0.252733i
$784$	6.03006	+	10.4444i	0.00769140	+	0.0133219i
$785$	−1212.53			−1.54463
$786$	−374.611	−	648.846i	−0.476605	−	0.825503i
$787$	1055.73	−	609.529i	1.34147	−	0.774497i	0.354445	−	0.935077i	$-0.384670\pi$
$787$	1055.73	−	609.529i	1.34147	−	0.774497i	0.987023	+	0.160581i	$0.0513366\pi$
$788$		−	759.955i		−	0.964410i
$789$	725.163	−	418.673i	0.919091	−	0.530637i
$790$	−353.504	+	612.286i	−0.447473	+	0.775046i
$791$	716.459	+	413.648i	0.905763	+	0.522943i
$792$	479.290	−	190.299i	0.605164	−	0.240276i
$793$	−1190.04	−	60.0776i	−1.50068	−	0.0757599i
$794$		−	104.353i		−	0.131427i
$795$	1135.64	−	1966.98i	1.42848	−	2.47419i
$796$	−375.646	+	650.638i	−0.471917	+	0.817384i
$797$	−68.3934	−	118.461i	−0.0858135	−	0.148633i	0.819924	−	0.572472i	$-0.194016\pi$
$797$	−68.3934	−	118.461i	−0.0858135	−	0.148633i	−0.905738	+	0.423839i	$0.860682\pi$
$798$			360.681i			0.451982i
$799$	−421.786	+	243.518i	−0.527892	+	0.304779i
$800$	−893.986	+	516.143i	−1.11748	+	0.645179i
$801$	−965.064			−1.20482
$802$	−25.0097	+	14.4394i	−0.0311842	+	0.0180042i
$803$	−47.3948	+	323.112i	−0.0590222	+	0.402381i
$804$	227.409	−	393.884i	0.282847	−	0.489905i
$805$		−	1514.34i		−	1.88116i
$806$	2.68149	+	5.23785i	0.00332691	+	0.00649858i
$807$	193.249			0.239466
$808$	135.433	−	234.576i	0.167615	−	0.290317i
$809$	−675.676	−	390.102i	−0.835199	−	0.482202i	0.0204303	−	0.999791i	$-0.493496\pi$
$809$	−675.676	−	390.102i	−0.835199	−	0.482202i	−0.855629	+	0.517589i	$0.826830\pi$
$810$	752.143	−	434.250i	0.928572	−	0.536111i
$811$		−	561.314i		−	0.692125i	−0.938211	−	0.346063i	$-0.887518\pi$
$811$		−	561.314i		−	0.692125i	0.938211	−	0.346063i	$-0.112482\pi$
$812$	344.100	+	595.999i	0.423768	+	0.733988i
$813$	842.710	−	486.539i	1.03654	−	0.598449i
$814$	462.820	−	183.760i	0.568574	−	0.225749i
$815$	−852.187	−	1476.03i	−1.04563	−	1.81108i
$816$	43.7506	+	25.2594i	0.0536160	+	0.0309552i
$817$	215.493	−	373.245i	0.263762	−	0.456849i
$818$	−0.544057			−0.000665106
$819$	270.819	+	529.001i	0.330671	+	0.645911i
$820$			999.572i			1.21899i
$821$	736.304	+	425.105i	0.896838	+	0.517790i	0.876173	−	0.481997i	$-0.160088\pi$
$821$	736.304	+	425.105i	0.896838	+	0.517790i	0.0206651	+	0.999786i	$0.493422\pi$
$822$	579.904	+	334.808i	0.705479	+	0.407309i
$823$	−539.924	−	935.175i	−0.656043	−	1.13630i	−0.981631	−	0.190789i	$-0.938895\pi$
$823$	−539.924	−	935.175i	−0.656043	−	1.13630i	0.325588	−	0.945512i	$-0.394438\pi$
$824$			161.590i			0.196104i
$825$	−834.678	+	1055.19i	−1.01173	+	1.27902i
$826$	159.898	+	276.951i	0.193581	+	0.335291i
$827$			788.781i			0.953786i	0.878961	+	0.476893i	$0.158237\pi$
$827$			788.781i			0.953786i	−0.878961	+	0.476893i	$0.841763\pi$
$828$	−212.235	−	367.602i	−0.256323	−	0.443964i
$829$	537.474	−	930.932i	0.648340	−	1.12296i	−0.335179	−	0.942154i	$-0.608797\pi$
$829$	537.474	−	930.932i	0.648340	−	1.12296i	0.983519	−	0.180803i	$-0.0578697\pi$
$830$	−409.007	+	708.421i	−0.492780	+	0.853519i
$831$			1375.78i			1.65557i
$832$	−352.987	−	228.270i	−0.424263	−	0.274363i
$833$		−	71.7182i		−	0.0860962i
$834$	239.772	−	415.297i	0.287496	−	0.497958i
$835$	1372.07	+	792.164i	1.64320	+	0.948699i
$836$	239.253	+	189.255i	0.286188	+	0.226381i
$837$	4.43708			0.00530117
$838$	−524.972	+	303.093i	−0.626459	+	0.361686i
$839$	515.592	+	893.031i	0.614531	+	1.06440i	0.990467	+	0.137754i	$0.0439882\pi$
$839$	515.592	+	893.031i	0.614531	+	1.06440i	−0.375935	+	0.926646i	$0.622678\pi$
$840$	1709.29			2.03487
$841$	176.460	+	305.638i	0.209822	+	0.363422i
$842$	−594.786	−	343.400i	−0.706396	−	0.407838i
$843$	1000.09	+	577.401i	1.18634	+	0.684936i
$844$		−	23.6399i		−	0.0280094i
$845$	521.275	+	1158.81i	0.616893	+	1.37137i
$846$			391.053i			0.462237i
$847$	−890.154	+	210.595i	−1.05095	+	0.248637i
$848$	−57.6229	+	99.8058i	−0.0679515	+	0.117695i
$849$	752.941	−	434.710i	0.886856	−	0.512026i
$850$	324.234			0.381452
$851$	−516.092	−	893.898i	−0.606454	−	1.05041i
$852$	21.8583	+	37.8596i	0.0256552	+	0.0444362i
$853$		−	17.6592i		−	0.0207025i	−0.999946	−	0.0103513i	$-0.996705\pi$
$853$		−	17.6592i		−	0.0207025i	0.999946	−	0.0103513i	$-0.00329496\pi$
$854$	701.183	−	404.828i	0.821058	−	0.474038i
$855$	−414.468	−	239.293i	−0.484758	−	0.279875i
$856$	−357.606	+	619.392i	−0.417764	+	0.723588i
$857$		−	1063.50i		−	1.24096i	−0.784222	−	0.620480i	$-0.786938\pi$
$857$		−	1063.50i		−	1.24096i	0.784222	−	0.620480i	$-0.213062\pi$
$858$	−635.747	−	126.283i	−0.740963	−	0.147183i
$859$	−116.802			−0.135975			−0.0679874	−	0.997686i	$-0.521658\pi$
$859$	−116.802			−0.135975			−0.0679874	+	0.997686i	$0.521658\pi$
$860$	−702.410	−	405.537i	−0.816756	−	0.471554i
$861$	739.868	−	1281.49i	0.859312	−	1.48837i
$862$	−329.040	−	569.914i	−0.381717	−	0.661154i
$863$	−54.9368			−0.0636579			−0.0318290	−	0.999493i	$-0.510133\pi$
$863$	−54.9368			−0.0636579			−0.0318290	+	0.999493i	$0.510133\pi$
$864$	−324.762	+	187.501i	−0.375882	+	0.217015i
$865$	319.294	−	184.344i	0.369125	−	0.213115i
$866$		−	668.075i		−	0.771450i
$867$	410.314	+	710.685i	0.473258	+	0.819706i
$868$	6.68172	+	3.85769i	0.00769784	+	0.00444435i
$869$	128.471	−	875.847i	0.147838	−	1.00788i
$870$	1177.55			1.35351
$871$	−514.977	+	263.640i	−0.591248	+	0.302686i
$872$	−774.773			−0.888502
$873$	−418.174	+	724.298i	−0.479008	+	0.829666i
$874$	−163.846	+	283.789i	−0.187467	+	0.324702i
$875$	−321.465	+	185.598i	−0.367389	+	0.212112i
$876$			303.411i			0.346360i
$877$	−686.722	+	396.479i	−0.783036	+	0.452086i	−0.837505	−	0.546430i	$-0.815987\pi$
$877$	−686.722	+	396.479i	−0.783036	+	0.452086i	0.0544693	+	0.998515i	$0.482653\pi$
$878$	−151.017	−	261.570i	−0.172002	−	0.297915i
$879$			28.7712i			0.0327317i
$880$	75.9321	−	95.9924i	0.0862864	−	0.109082i
$881$	197.381	−	341.875i	0.224043	−	0.388053i	−0.731989	−	0.681316i	$-0.761408\pi$
$881$	197.381	−	341.875i	0.224043	−	0.388053i	0.956032	+	0.293263i	$0.0947412\pi$
$882$	−49.8693	−	28.7921i	−0.0565412	−	0.0326441i
$883$	712.484			0.806890			0.403445	−	0.915004i	$-0.367813\pi$
$883$	712.484			0.806890			0.403445	+	0.915004i	$0.367813\pi$
$884$	−137.355	−	268.301i	−0.155379	−	0.303507i
$885$	−1055.87			−1.19308
$886$	569.751	+	328.946i	0.643060	+	0.371271i
$887$	−1035.51	−	597.851i	−1.16743	−	0.674014i	−0.214354	−	0.976756i	$-0.568765\pi$
$887$	−1035.51	−	597.851i	−1.16743	−	0.674014i	−0.953073	+	0.302742i	$0.902098\pi$
$888$	1008.98	−	582.534i	1.13624	−	0.656006i
$889$	869.384			0.977935
$890$	1214.23	−	701.036i	1.36430	−	0.787680i
$891$	−674.626	+	852.854i	−0.757156	+	0.957187i
$892$	−604.264			−0.677426
$893$	−504.495	+	291.270i	−0.564944	+	0.326170i
$894$	−602.501	+	1043.56i	−0.673938	+	1.16730i
$895$	−813.401	+	1408.85i	−0.908828	+	1.57414i
$896$	−704.360			−0.786116
$897$	−67.7397	+	1341.82i	−0.0755181	+	1.49589i
$898$		−	302.299i		−	0.336636i
$899$	11.5918	+	6.69250i	0.0128941	+	0.00744439i
$900$	−251.174	+	435.047i	−0.279083	+	0.483386i
$901$	593.517	−	342.667i	0.658732	−	0.380319i
$902$	239.342	+	602.809i	0.265345	+	0.668303i
$903$	600.344	+	1039.83i	0.664833	+	1.15153i
$904$	−734.727	+	424.195i	−0.812752	+	0.469242i
$905$	−110.067			−0.121621
$906$	−286.217	−	495.742i	−0.315912	−	0.547176i
$907$	503.596	−	872.254i	0.555233	−	0.961692i	−0.442652	−	0.896693i	$-0.645962\pi$
$907$	503.596	−	872.254i	0.555233	−	0.961692i	0.997885	−	0.0649984i	$-0.0207042\pi$
$908$	−173.502	−	100.171i	−0.191081	−	0.110321i
$909$		−	211.283i		−	0.232435i
$910$	−725.014	−	468.854i	−0.796719	−	0.515224i
$911$	1000.18			1.09790			0.548948	−	0.835857i	$-0.315029\pi$
$911$	1000.18			1.09790			0.548948	+	0.835857i	$0.315029\pi$
$912$	52.3298	+	30.2126i	0.0573791	+	0.0331279i
$913$	148.642	−	1013.36i	0.162807	−	1.10993i
$914$	344.434	+	596.577i	0.376843	+	0.652710i
$915$			2673.25i			2.92159i
$916$	−95.1060	−	164.728i	−0.103828	−	0.179835i
$917$	624.792	+	1082.17i	0.681344	+	1.18012i
$918$	117.786			0.128307
$919$	373.770	−	215.796i	0.406714	−	0.234816i	−0.282663	−	0.959219i	$-0.591218\pi$
$919$	373.770	−	215.796i	0.406714	−	0.234816i	0.689377	+	0.724403i	$0.257885\pi$
$920$	1344.90	+	776.476i	1.46184	+	0.843995i
$921$	782.652	+	451.865i	0.849785	+	0.490624i
$922$	−303.151			−0.328797
$923$	2.80375	−	55.5377i	0.00303765	−	0.0601709i
$924$	−789.877	+	313.616i	−0.854845	+	0.339411i
$925$	−610.781	+	1057.90i	−0.660303	+	1.14368i
$926$	−646.250	−	373.113i	−0.697894	−	0.402929i
$927$	63.0224	+	109.158i	0.0679854	+	0.117754i
$928$	−1131.24			−1.21901
$929$	360.242	+	623.957i	0.387774	+	0.671644i	0.992150	−	0.125055i	$-0.0399108\pi$
$929$	360.242	+	623.957i	0.387774	+	0.671644i	−0.604376	+	0.796699i	$0.706577\pi$
$930$	11.4329	−	6.60076i	0.0122934	−	0.00709759i
$931$		−	85.7815i		−	0.0921391i
$932$	110.075	−	63.5516i	0.118106	−	0.0681884i
$933$	229.664	−	397.790i	0.246156	−	0.426356i
$934$	−254.522	−	146.949i	−0.272508	−	0.157332i
$935$	−676.471	+	268.588i	−0.723498	+	0.287260i
$936$	−608.672	−	30.7280i	−0.650291	−	0.0328291i
$937$		−	111.112i		−	0.118583i	−0.998241	−	0.0592915i	$-0.981116\pi$
$937$		−	111.112i		−	0.118583i	0.998241	−	0.0592915i	$-0.0188841\pi$
$938$	196.557	−	340.447i	0.209549	−	0.362950i
$939$	301.753	−	522.652i	0.321356	−	0.556605i
$940$	548.141	+	949.408i	0.583129	+	1.01001i
$941$			459.936i			0.488774i	0.969678	+	0.244387i	$0.0785867\pi$
$941$			459.936i			0.488774i	−0.969678	+	0.244387i	$0.921413\pi$
$942$	−633.044	+	365.488i	−0.672021	+	0.387992i
$943$	1164.28	−	672.196i	1.23465	−	0.712827i
$944$	53.5755			0.0567537
$945$	−563.826	+	325.525i	−0.596641	+	0.344471i
$946$	−520.704	−	76.3781i	−0.550427	−	0.0807379i
$947$	462.952	−	801.857i	0.488862	−	0.846734i	−0.511056	−	0.859547i	$-0.670745\pi$
$947$	462.952	−	801.857i	0.488862	−	0.846734i	0.999918	+	0.0128137i	$0.00407882\pi$
$948$		−	822.444i		−	0.867557i
$949$	209.580	−	324.084i	0.220843	−	0.341501i
$950$	387.814			0.408225
$951$	984.079	−	1704.47i	1.03478	−	1.79230i
$952$	446.663	+	257.881i	0.469183	+	0.270883i
$953$	617.783	−	356.677i	0.648251	−	0.374268i	−0.139535	−	0.990217i	$-0.544561\pi$
$953$	617.783	−	356.677i	0.648251	−	0.374268i	0.787786	+	0.615949i	$0.211227\pi$
$954$		−	550.271i		−	0.576804i
$955$	680.555	+	1178.76i	0.712623	+	1.23430i
$956$	−467.000	+	269.623i	−0.488494	+	0.282032i
$957$	−1370.31	+	544.075i	−1.43189	+	0.568521i
$958$	−347.305	−	601.551i	−0.362532	−	0.627924i
$959$	−967.188	−	558.406i	−1.00854	−	0.582279i
$960$	−471.545	+	816.739i	−0.491192	+	0.850770i
$961$	−960.850			−0.999844
$962$	−587.756	−	29.6721i	−0.610973	−	0.0308441i
$963$			557.886i			0.579321i
$964$	777.591	+	448.942i	0.806630	+	0.465708i
$965$	−1464.21	−	845.364i	−1.51732	−	0.876025i
$966$	−456.459	−	790.610i	−0.472525	−	0.818437i
$967$		−	272.748i		−	0.282056i	−0.990006	−	0.141028i	$-0.954959\pi$
$967$		−	272.748i		−	0.282056i	0.990006	−	0.141028i	$-0.0450408\pi$
$968$	269.395	−	898.536i	0.278300	−	0.928239i
$969$	−179.666	−	311.191i	−0.185414	−	0.321146i
$970$		−	1215.07i		−	1.25265i
$971$	309.633	+	536.301i	0.318881	+	0.552318i	0.980255	−	0.197738i	$-0.0633596\pi$
$971$	309.633	+	536.301i	0.318881	+	0.552318i	−0.661374	+	0.750056i	$0.730026\pi$
$972$	−369.353	+	639.737i	−0.379992	+	0.658166i
$973$	−399.901	+	692.649i	−0.410998	+	0.711870i
$974$			230.096i			0.236239i
$975$	1415.33	−	724.573i	1.45162	−	0.743152i
$976$		−	135.642i		−	0.138978i
$977$	−770.894	+	1335.23i	−0.789042	+	1.36666i	0.137512	+	0.990500i	$0.456090\pi$
$977$	−770.894	+	1335.23i	−0.789042	+	1.36666i	−0.926554	+	0.376161i	$0.877244\pi$
$978$	−889.826	−	513.741i	−0.909842	−	0.525298i
$979$	−1089.09	+	1376.81i	−1.11245	+	1.40635i
$980$	−161.432			−0.164727
$981$	−523.379	+	302.173i	−0.533515	+	0.308025i
$982$	145.441	+	251.910i	0.148106	+	0.256528i
$983$	306.768			0.312073			0.156037	−	0.987751i	$-0.450128\pi$
$983$	306.768			0.312073			0.156037	+	0.987751i	$0.450128\pi$
$984$	758.734	+	1314.17i	0.771071	+	1.33553i
$985$	1878.19	+	1084.37i	1.90679	+	1.10089i
$986$	307.712	+	177.657i	0.312081	+	0.180180i
$987$		−	1622.90i		−	1.64428i
$988$	−164.289	−	320.912i	−0.166285	−	0.324810i
$989$			1090.87i			1.10300i
$990$	−84.8136	+	578.213i	−0.0856703	+	0.584053i
$991$	15.6246	−	27.0626i	0.0157665	−	0.0273083i	−0.858035	−	0.513592i	$-0.828315\pi$
$991$	15.6246	−	27.0626i	0.0157665	−	0.0273083i	0.873801	+	0.486284i	$0.161648\pi$
$992$	−10.9832	+	6.34116i	−0.0110718	+	0.00639230i
$993$	1525.43			1.53619
$994$	18.8928	+	32.7234i	0.0190069	+	0.0329209i
$995$	−1072.01	−	1856.78i	−1.07740	−	1.86611i
$996$		−	951.576i		−	0.955397i
$997$	−364.153	+	210.244i	−0.365249	+	0.210877i	−0.671381	−	0.741112i	$-0.734299\pi$
$997$	−364.153	+	210.244i	−0.365249	+	0.210877i	0.306132	+	0.951989i	$0.400965\pi$
$998$	47.0979	+	27.1920i	0.0471922	+	0.0272465i
$999$	−221.880	+	384.308i	−0.222103	+	0.384693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.3.k.a.87.17	yes	52
11.10	odd	2	inner	143.3.k.a.87.10	✓	52
13.3	even	3	inner	143.3.k.a.120.10	yes	52
143.120	odd	6	inner	143.3.k.a.120.17	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.3.k.a.87.10	✓	52	11.10	odd	2	inner
143.3.k.a.87.17	yes	52	1.1	even	1	trivial
143.3.k.a.120.10	yes	52	13.3	even	3	inner
143.3.k.a.120.17	yes	52	143.120	odd	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	143.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.01194 + 0.584243i) q^{2} +(1.93953 - 3.35937i) q^{3} +(-1.31732 - 2.28166i) q^{4} +7.51869 q^{5} +(3.92538 - 2.26632i) q^{6} +(-6.54691 + 3.77986i) q^{7} -7.75249i q^{8} +(-3.02358 - 5.23700i) q^{9} +O(q^{10})\)	\(q+(1.01194 + 0.584243i) q^{2} +(1.93953 - 3.35937i) q^{3} +(-1.31732 - 2.28166i) q^{4} +7.51869 q^{5} +(3.92538 - 2.26632i) q^{6} +(-6.54691 + 3.77986i) q^{7} -7.75249i q^{8} +(-3.02358 - 5.23700i) q^{9} +(7.60845 + 4.39274i) q^{10} +(-10.8835 - 1.59642i) q^{11} -10.2199 q^{12} +(10.9163 + 7.05937i) q^{13} -8.83344 q^{14} +(14.5827 - 25.2581i) q^{15} +(-0.739936 + 1.28161i) q^{16} +(7.62136 - 4.40020i) q^{17} -7.06603i q^{18} +(9.11585 - 5.26304i) q^{19} +(-9.90451 - 17.1551i) q^{20} +29.3247i q^{21} +(-10.0808 - 7.97412i) q^{22} +(-13.3212 + 23.0731i) q^{23} +(-26.0435 - 15.0362i) q^{24} +31.5306 q^{25} +(6.92223 + 13.5214i) q^{26} +11.4542 q^{27} +(17.2487 + 9.95857i) q^{28} +(29.9239 + 17.2766i) q^{29} +(29.5137 - 17.0397i) q^{30} +0.387374 q^{31} +(-28.3529 + 16.3696i) q^{32} +(-26.4720 + 33.4655i) q^{33} +10.2831 q^{34} +(-49.2242 + 28.4196i) q^{35} +(-7.96605 + 13.7976i) q^{36} +(-19.3710 + 33.5516i) q^{37} +12.2996 q^{38} +(44.8876 - 22.9800i) q^{39} -58.2885i q^{40} +(-43.7000 - 25.2302i) q^{41} +(-17.1328 + 29.6748i) q^{42} +(35.4591 - 20.4723i) q^{43} +(10.6946 + 26.9356i) q^{44} +(-22.7334 - 39.3753i) q^{45} +(-26.9606 + 15.5657i) q^{46} -55.3426 q^{47} +(2.87026 + 4.97144i) q^{48} +(4.07471 - 7.05761i) q^{49} +(31.9071 + 18.4216i) q^{50} -34.1373i q^{51} +(1.72688 - 34.2067i) q^{52} +77.8755 q^{53} +(11.5910 + 6.69207i) q^{54} +(-81.8299 - 12.0030i) q^{55} +(29.3033 + 50.7549i) q^{56} -40.8314i q^{57} +(20.1875 + 34.9657i) q^{58} +(-18.1014 - 31.3525i) q^{59} -76.8405 q^{60} +(-79.3783 + 45.8291i) q^{61} +(0.391999 + 0.226321i) q^{62} +(39.5903 + 22.8575i) q^{63} -32.3358 q^{64} +(82.0761 + 53.0772i) q^{65} +(-46.3400 + 18.3990i) q^{66} +(-22.2515 + 38.5407i) q^{67} +(-20.0795 - 11.5929i) q^{68} +(51.6740 + 89.5020i) q^{69} -66.4158 q^{70} +(-2.13879 - 3.70449i) q^{71} +(-40.5998 + 23.4403i) q^{72} -29.6882i q^{73} +(-39.2046 + 22.6348i) q^{74} +(61.1547 - 105.923i) q^{75} +(-24.0170 - 13.8662i) q^{76} +(77.2878 - 30.6866i) q^{77} +(58.8494 + 2.97093i) q^{78} +80.4745i q^{79} +(-5.56335 + 9.63600i) q^{80} +(49.4281 - 85.6120i) q^{81} +(-29.4812 - 51.0629i) q^{82} +93.1097i q^{83} +(66.9091 - 38.6300i) q^{84} +(57.3026 - 33.0837i) q^{85} +47.8433 q^{86} +(116.077 - 67.0170i) q^{87} +(-12.3762 + 84.3745i) q^{88} +(79.7947 - 138.209i) q^{89} -53.1273i q^{90} +(-98.1514 - 4.95504i) q^{91} +70.1933 q^{92} +(0.751326 - 1.30133i) q^{93} +(-56.0033 - 32.3335i) q^{94} +(68.5392 - 39.5711i) q^{95} +126.997i q^{96} +(-69.1520 - 119.775i) q^{97} +(8.24673 - 4.76125i) q^{98} +(24.5468 + 61.8240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{3} + 46 q^{4} - 8 q^{5} - 64 q^{9}+O(q^{10}) \) 52 * q - 2 * q^3 + 46 * q^4 - 8 * q^5 - 64 * q^9	\( 52 q - 2 q^{3} + 46 q^{4} - 8 q^{5} - 64 q^{9} + 14 q^{11} - 36 q^{12} - 16 q^{14} - 28 q^{15} - 102 q^{16} - 50 q^{20} - 70 q^{22} - 20 q^{23} + 116 q^{25} - 252 q^{26} + 40 q^{27} - 52 q^{31} + 2 q^{33} + 476 q^{34} + 218 q^{36} - 38 q^{37} + 192 q^{38} - 394 q^{42} + 528 q^{44} - 278 q^{45} + 36 q^{47} + 80 q^{48} + 80 q^{49} + 120 q^{53} - 150 q^{55} + 94 q^{56} + 130 q^{58} - 176 q^{59} - 468 q^{60} + 128 q^{64} + 704 q^{66} + 74 q^{67} + 74 q^{69} - 652 q^{70} - 220 q^{71} - 546 q^{75} - 204 q^{77} - 256 q^{78} + 628 q^{80} + 106 q^{81} + 154 q^{82} - 960 q^{86} + 170 q^{88} + 28 q^{89} + 418 q^{91} - 272 q^{92} + 422 q^{93} + 36 q^{97} - 272 q^{99}+O(q^{100}) \) 52 * q - 2 * q^3 + 46 * q^4 - 8 * q^5 - 64 * q^9 + 14 * q^11 - 36 * q^12 - 16 * q^14 - 28 * q^15 - 102 * q^16 - 50 * q^20 - 70 * q^22 - 20 * q^23 + 116 * q^25 - 252 * q^26 + 40 * q^27 - 52 * q^31 + 2 * q^33 + 476 * q^34 + 218 * q^36 - 38 * q^37 + 192 * q^38 - 394 * q^42 + 528 * q^44 - 278 * q^45 + 36 * q^47 + 80 * q^48 + 80 * q^49 + 120 * q^53 - 150 * q^55 + 94 * q^56 + 130 * q^58 - 176 * q^59 - 468 * q^60 + 128 * q^64 + 704 * q^66 + 74 * q^67 + 74 * q^69 - 652 * q^70 - 220 * q^71 - 546 * q^75 - 204 * q^77 - 256 * q^78 + 628 * q^80 + 106 * q^81 + 154 * q^82 - 960 * q^86 + 170 * q^88 + 28 * q^89 + 418 * q^91 - 272 * q^92 + 422 * q^93 + 36 * q^97 - 272 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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