LMFDB - Embedded newform 150.3.i.a.119.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [150,3,Mod(29,150)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(150, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("150.29"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$N$	$=$	$150 = 2 \cdot 3 \cdot 5^{2}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	150.i (of order $10$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.08720396540$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			119.5
Character	$\chi$	$=$	150.119
Dual form			150.3.i.a.29.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.437016 - 1.34500i) q^{2} +(-0.0352727 + 2.99979i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(-4.11716 - 2.83707i) q^{5} +(4.05013 - 1.26352i) q^{6} -2.70868i q^{7} +(2.28825 + 1.66251i) q^{8} +(-8.99751 - 0.211621i) q^{9} +(-2.01659 + 6.77742i) q^{10} +(-1.51542 + 0.492390i) q^{11} +(-3.46940 - 4.89523i) q^{12} +(-15.0748 - 4.89810i) q^{13} +(-3.64317 + 1.18374i) q^{14} +(8.65585 - 12.2506i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-18.8231 - 13.6758i) q^{17} +(3.64743 + 12.1941i) q^{18} +(-19.4318 - 14.1180i) q^{19} +(9.99689 - 0.249534i) q^{20} +(8.12549 + 0.0955425i) q^{21} +(1.32453 + 1.82305i) q^{22} +(3.76161 + 11.5770i) q^{23} +(-5.06789 + 6.80562i) q^{24} +(8.90204 + 23.3614i) q^{25} +22.4161i q^{26} +(0.952187 - 26.9832i) q^{27} +(3.18425 + 4.38274i) q^{28} +(21.0025 + 28.9075i) q^{29} +(-20.2597 - 6.28841i) q^{30} +(17.8786 + 12.9896i) q^{31} -5.65685 q^{32} +(-1.42361 - 4.56331i) q^{33} +(-10.1679 + 31.2936i) q^{34} +(-7.68473 + 11.1521i) q^{35} +(14.8071 - 10.2348i) q^{36} +(-13.8928 - 4.51404i) q^{37} +(-10.4967 + 32.3055i) q^{38} +(15.2250 - 45.0485i) q^{39} +(-4.70442 - 13.3367i) q^{40} +(21.4020 + 6.95393i) q^{41} +(-3.42246 - 10.9705i) q^{42} -50.7907i q^{43} +(1.87316 - 2.57819i) q^{44} +(36.4438 + 26.3979i) q^{45} +(13.9272 - 10.1187i) q^{46} +(-37.9194 + 27.5500i) q^{47} +(11.3683 + 3.84213i) q^{48} +41.6630 q^{49} +(27.5306 - 22.1825i) q^{50} +(41.6885 - 55.9831i) q^{51} +(30.1496 - 9.79619i) q^{52} +(-40.8309 + 29.6654i) q^{53} +(-36.7085 + 10.5114i) q^{54} +(7.63617 + 2.27211i) q^{55} +(4.50321 - 6.19813i) q^{56} +(43.0366 - 57.7934i) q^{57} +(29.7020 - 40.8814i) q^{58} +(48.7840 + 15.8509i) q^{59} +(0.395933 + 29.9974i) q^{60} +(-12.9533 - 39.8662i) q^{61} +(9.65770 - 29.7234i) q^{62} +(-0.573216 + 24.3714i) q^{63} +(2.47214 + 7.60845i) q^{64} +(48.1691 + 62.9345i) q^{65} +(-5.51550 + 3.90900i) q^{66} +(29.7675 - 40.9714i) q^{67} +46.5334 q^{68} +(-34.8614 + 10.8757i) q^{69} +(18.3579 + 5.46230i) q^{70} +(-21.0491 - 28.9716i) q^{71} +(-20.2367 - 15.4427i) q^{72} +(-110.786 + 35.9965i) q^{73} +20.6585i q^{74} +(-70.3933 + 25.8803i) q^{75} +48.0381 q^{76} +(1.33373 + 4.10479i) q^{77} +(-67.2436 - 0.790676i) q^{78} +(-96.1429 + 69.8519i) q^{79} +(-15.8820 + 12.1558i) q^{80} +(80.9104 + 3.80813i) q^{81} -31.8246i q^{82} +(-102.618 - 74.5562i) q^{83} +(-13.2596 + 9.39750i) q^{84} +(38.6986 + 109.708i) q^{85} +(-68.3134 + 22.1964i) q^{86} +(-87.4573 + 61.9836i) q^{87} +(-4.28625 - 1.39269i) q^{88} +(101.736 - 33.0560i) q^{89} +(19.5785 - 60.5531i) q^{90} +(-13.2674 + 40.8328i) q^{91} +(-19.6961 - 14.3100i) q^{92} +(-39.5967 + 53.1740i) q^{93} +(53.6261 + 38.9616i) q^{94} +(39.9500 + 113.256i) q^{95} +(0.199532 - 16.9694i) q^{96} +(78.5564 + 108.124i) q^{97} +(-18.2074 - 56.0367i) q^{98} +(13.7392 - 4.10959i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$80 q - 40 q^{4} + 20 q^{9} + 16 q^{10} + 20 q^{12} + 32 q^{15} - 80 q^{16} + 60 q^{19} - 60 q^{21} + 40 q^{22} + 116 q^{25} - 210 q^{27} - 40 q^{28} - 68 q^{30} + 180 q^{31} - 50 q^{33} - 120 q^{34} + 40 q^{36}+ \cdots - 260 q^{99}+O(q^{100})$ 80 * q - 40 * q^4 + 20 * q^9 + 16 * q^10 + 20 * q^12 + 32 * q^15 - 80 * q^16 + 60 * q^19 - 60 * q^21 + 40 * q^22 + 116 * q^25 - 210 * q^27 - 40 * q^28 - 68 * q^30 + 180 * q^31 - 50 * q^33 - 120 * q^34 + 40 * q^36 - 40 * q^37 + 220 * q^39 + 32 * q^40 + 468 * q^45 + 120 * q^46 - 40 * q^48 - 680 * q^49 + 20 * q^51 - 120 * q^54 - 272 * q^55 - 156 * q^60 - 200 * q^61 - 830 * q^63 - 160 * q^64 + 160 * q^66 + 500 * q^67 - 280 * q^69 - 584 * q^70 + 120 * q^73 - 138 * q^75 - 80 * q^76 + 620 * q^78 + 400 * q^79 - 420 * q^81 + 180 * q^84 + 1632 * q^85 + 750 * q^87 + 160 * q^88 + 472 * q^90 - 340 * q^91 + 160 * q^94 + 20 * q^97 - 260 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$ .

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$

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

)

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

$2$	−0.437016	−	1.34500i	−0.218508	−	0.672499i
$2$	−0.437016	−	1.34500i	−0.218508	−	0.672499i
$3$	−0.0352727	+	2.99979i	−0.0117576	+	0.999931i
$3$	−0.0352727	+	2.99979i	−0.0117576	+	0.999931i
$4$	−1.61803	+	1.17557i	−0.404508	+	0.293893i
$5$	−4.11716	−	2.83707i	−0.823432	−	0.567415i
$5$	−4.11716	−	2.83707i	−0.823432	−	0.567415i
$6$	4.05013	−	1.26352i	0.675021	−	0.210586i
$7$		−	2.70868i		−	0.386955i	−0.981105	−	0.193477i	$-0.938023\pi$
$7$		−	2.70868i		−	0.386955i	0.981105	−	0.193477i	$-0.0619766\pi$
$8$	2.28825	+	1.66251i	0.286031	+	0.207813i
$9$	−8.99751	−	0.211621i	−0.999724	−	0.0235135i
$10$	−2.01659	+	6.77742i	−0.201659	+	0.677742i
$11$	−1.51542	+	0.492390i	−0.137765	+	0.0447627i	−0.377088	−	0.926177i	$-0.623075\pi$
$11$	−1.51542	+	0.492390i	−0.137765	+	0.0447627i	0.239323	+	0.970940i	$0.423075\pi$
$12$	−3.46940	−	4.89523i	−0.289116	−	0.407936i
$13$	−15.0748	−	4.89810i	−1.15960	−	0.376777i	−0.334848	−	0.942272i	$-0.608685\pi$
$13$	−15.0748	−	4.89810i	−1.15960	−	0.376777i	−0.824751	+	0.565495i	$0.808685\pi$
$14$	−3.64317	+	1.18374i	−0.260227	+	0.0845527i
$15$	8.65585	−	12.2506i	0.577057	−	0.816704i
$16$	1.23607	−	3.80423i	0.0772542	−	0.237764i
$17$	−18.8231	−	13.6758i	−1.10724	−	0.804460i	−0.125016	−	0.992155i	$-0.539898\pi$
$17$	−18.8231	−	13.6758i	−1.10724	−	0.804460i	−0.982227	+	0.187695i	$0.939898\pi$
$18$	3.64743	+	12.1941i	0.202635	+	0.677450i
$19$	−19.4318	−	14.1180i	−1.02273	−	0.743054i	−0.0558866	−	0.998437i	$-0.517799\pi$
$19$	−19.4318	−	14.1180i	−1.02273	−	0.743054i	−0.966840	+	0.255383i	$0.917799\pi$
$20$	9.99689	−	0.249534i	0.499844	−	0.0124767i
$21$	8.12549	+	0.0955425i	0.386928	+	0.00454964i
$22$	1.32453	+	1.82305i	0.0602057	+	0.0828660i
$23$	3.76161	+	11.5770i	0.163548	+	0.503350i	0.998926	−	0.0463259i	$-0.0147513\pi$
$23$	3.76161	+	11.5770i	0.163548	+	0.503350i	−0.835378	+	0.549676i	$0.814751\pi$
$24$	−5.06789	+	6.80562i	−0.211162	+	0.283568i
$25$	8.90204	+	23.3614i	0.356082	+	0.934455i
$26$			22.4161i			0.862158i
$27$	0.952187	−	26.9832i	0.0352662	−	0.999378i
$28$	3.18425	+	4.38274i	0.113723	+	0.156527i
$29$	21.0025	+	28.9075i	0.724225	+	0.996810i	0.999373	+	0.0354080i	$0.0112731\pi$
$29$	21.0025	+	28.9075i	0.724225	+	0.996810i	−0.275148	+	0.961402i	$0.588727\pi$
$30$	−20.2597	−	6.28841i	−0.675324	−	0.209614i
$31$	17.8786	+	12.9896i	0.576730	+	0.419019i	0.837544	−	0.546370i	$-0.183991\pi$
$31$	17.8786	+	12.9896i	0.576730	+	0.419019i	−0.260814	+	0.965389i	$0.583991\pi$
$32$	−5.65685			−0.176777
$33$	−1.42361	−	4.56331i	−0.0431398	−	0.138282i
$34$	−10.1679	+	31.2936i	−0.299056	+	0.920401i
$35$	−7.68473	+	11.1521i	−0.219564	+	0.318631i
$36$	14.8071	−	10.2348i	0.411307	−	0.284300i
$37$	−13.8928	−	4.51404i	−0.375481	−	0.122001i	0.115196	−	0.993343i	$-0.463250\pi$
$37$	−13.8928	−	4.51404i	−0.375481	−	0.122001i	−0.490677	+	0.871342i	$0.663250\pi$
$38$	−10.4967	+	32.3055i	−0.276229	+	0.850145i
$39$	15.2250	−	45.0485i	0.390385	−	1.15509i
$40$	−4.70442	−	13.3367i	−0.117611	−	0.333418i
$41$	21.4020	+	6.95393i	0.522000	+	0.169608i	0.558153	−	0.829738i	$-0.311510\pi$
$41$	21.4020	+	6.95393i	0.522000	+	0.169608i	−0.0361530	+	0.999346i	$0.511510\pi$
$42$	−3.42246	−	10.9705i	−0.0814873	−	0.261203i
$43$		−	50.7907i		−	1.18118i	−0.806972	−	0.590590i	$-0.798895\pi$
$43$		−	50.7907i		−	1.18118i	0.806972	−	0.590590i	$-0.201105\pi$
$44$	1.87316	−	2.57819i	0.0425718	−	0.0585951i
$45$	36.4438	+	26.3979i	0.809863	+	0.586619i
$46$	13.9272	−	10.1187i	0.302765	−	0.219972i
$47$	−37.9194	+	27.5500i	−0.806795	+	0.586171i	−0.912900	−	0.408184i	$-0.866162\pi$
$47$	−37.9194	+	27.5500i	−0.806795	+	0.586171i	0.106105	+	0.994355i	$0.466162\pi$
$48$	11.3683	+	3.84213i	0.236839	+	0.0800444i
$49$	41.6630			0.850266
$50$	27.5306	−	22.1825i	0.550613	−	0.443650i
$51$	41.6885	−	55.9831i	0.817422	−	1.09771i
$52$	30.1496	−	9.79619i	0.579800	−	0.188388i
$53$	−40.8309	+	29.6654i	−0.770395	+	0.559725i	−0.902081	−	0.431567i	$-0.857961\pi$
$53$	−40.8309	+	29.6654i	−0.770395	+	0.559725i	0.131686	+	0.991291i	$0.457961\pi$
$54$	−36.7085	+	10.5114i	−0.679786	+	0.194656i
$55$	7.63617	+	2.27211i	0.138839	+	0.0413110i
$56$	4.50321	−	6.19813i	0.0804144	−	0.110681i
$57$	43.0366	−	57.7934i	0.755028	−	1.01392i
$58$	29.7020	−	40.8814i	0.512104	−	0.704851i
$59$	48.7840	+	15.8509i	0.826847	+	0.268659i	0.691717	−	0.722169i	$-0.256855\pi$
$59$	48.7840	+	15.8509i	0.826847	+	0.268659i	0.135130	+	0.990828i	$0.456855\pi$
$60$	0.395933	+	29.9974i	0.00659888	+	0.499956i
$61$	−12.9533	−	39.8662i	−0.212349	−	0.653544i	−0.999331	−	0.0365677i	$-0.988358\pi$
$61$	−12.9533	−	39.8662i	−0.212349	−	0.653544i	0.786982	−	0.616976i	$-0.211642\pi$
$62$	9.65770	−	29.7234i	0.155769	−	0.479409i
$63$	−0.573216	+	24.3714i	−0.00909866	+	0.386848i
$64$	2.47214	+	7.60845i	0.0386271	+	0.118882i
$65$	48.1691	+	62.9345i	0.741063	+	0.968224i
$66$	−5.51550	+	3.90900i	−0.0835682	+	0.0592272i
$67$	29.7675	−	40.9714i	0.444290	−	0.611513i	−0.526868	−	0.849947i	$-0.676634\pi$
$67$	29.7675	−	40.9714i	0.444290	−	0.611513i	0.971159	+	0.238434i	$0.0766339\pi$
$68$	46.5334			0.684314
$69$	−34.8614	+	10.8757i	−0.505238	+	0.157619i
$70$	18.3579	+	5.46230i	0.262255	+	0.0780329i
$71$	−21.0491	−	28.9716i	−0.296466	−	0.408050i	0.634635	−	0.772812i	$-0.281150\pi$
$71$	−21.0491	−	28.9716i	−0.296466	−	0.408050i	−0.931101	+	0.364762i	$0.881150\pi$
$72$	−20.2367	−	15.4427i	−0.281065	−	0.214482i
$73$	−110.786	+	35.9965i	−1.51761	+	0.493103i	−0.945097	−	0.326790i	$-0.894033\pi$
$73$	−110.786	+	35.9965i	−1.51761	+	0.493103i	−0.572517	+	0.819893i	$0.694033\pi$
$74$			20.6585i			0.279168i
$75$	−70.3933	+	25.8803i	−0.938577	+	0.345070i
$76$	48.0381			0.632080
$77$	1.33373	+	4.10479i	0.0173211	+	0.0533090i
$78$	−67.2436	−	0.790676i	−0.862098	−	0.0101369i
$79$	−96.1429	+	69.8519i	−1.21700	+	0.884201i	−0.995847	−	0.0910382i	$-0.970981\pi$
$79$	−96.1429	+	69.8519i	−1.21700	+	0.884201i	−0.221151	+	0.975240i	$0.570981\pi$
$80$	−15.8820	+	12.1558i	−0.198524	+	0.151947i
$81$	80.9104	+	3.80813i	0.998894	+	0.0470140i
$82$		−	31.8246i		−	0.388105i
$83$	−102.618	−	74.5562i	−1.23636	−	0.898267i	−0.239008	−	0.971017i	$-0.576822\pi$
$83$	−102.618	−	74.5562i	−1.23636	−	0.898267i	−0.997350	+	0.0727503i	$0.976822\pi$
$84$	−13.2596	+	9.39750i	−0.157853	+	0.111875i
$85$	38.6986	+	109.708i	0.455278	+	1.29068i
$86$	−68.3134	+	22.1964i	−0.794342	+	0.258097i
$87$	−87.4573	+	61.9836i	−1.00526	+	0.712455i
$88$	−4.28625	−	1.39269i	−0.0487074	−	0.0158260i
$89$	101.736	−	33.0560i	1.14310	−	0.371416i	0.324560	−	0.945865i	$-0.394784\pi$
$89$	101.736	−	33.0560i	1.14310	−	0.371416i	0.818540	+	0.574449i	$0.194784\pi$
$90$	19.5785	−	60.5531i	0.217539	−	0.672813i
$91$	−13.2674	+	40.8328i	−0.145796	+	0.448713i
$92$	−19.6961	−	14.3100i	−0.214088	−	0.155544i
$93$	−39.5967	+	53.1740i	−0.425771	+	0.571763i
$94$	53.6261	+	38.9616i	0.570490	+	0.414485i
$95$	39.9500	+	113.256i	0.420526	+	1.19216i
$96$	0.199532	−	16.9694i	0.00207846	−	0.176764i
$97$	78.5564	+	108.124i	0.809860	+	1.11468i	0.991345	+	0.131282i	$0.0419095\pi$
$97$	78.5564	+	108.124i	0.809860	+	1.11468i	−0.181485	+	0.983394i	$0.558091\pi$
$98$	−18.2074	−	56.0367i	−0.185790	−	0.571803i
$99$	13.7392	−	4.10959i	0.138780	−	0.0415110i
$100$	−41.8667	−	27.3345i	−0.418667	−	0.273345i
$101$		−	151.999i		−	1.50494i	−0.658629	−	0.752468i	$-0.728863\pi$
$101$		−	151.999i		−	1.50494i	0.658629	−	0.752468i	$-0.271137\pi$
$102$	−93.5157	−	31.6054i	−0.916821	−	0.309857i
$103$	−95.1578	−	130.973i	−0.923862	−	1.27159i	−0.962206	−	0.272322i	$-0.912208\pi$
$103$	−95.1578	−	130.973i	−0.923862	−	1.27159i	0.0383445	−	0.999265i	$-0.487792\pi$
$104$	−26.3517	−	36.2700i	−0.253382	−	0.348750i
$105$	−33.1829	−	23.4460i	−0.316028	−	0.223295i
$106$	57.7436	+	41.9532i	0.544751	+	0.395785i
$107$	−59.9911			−0.560664			−0.280332	−	0.959903i	$-0.590445\pi$
$107$	−59.9911			−0.560664			−0.280332	+	0.959903i	$0.590445\pi$
$108$	30.1800	+	44.7791i	0.279444	+	0.414621i
$109$	−58.3698	+	179.644i	−0.535503	+	1.64811i	0.207057	+	0.978329i	$0.433611\pi$
$109$	−58.3698	+	179.644i	−0.535503	+	1.64811i	−0.742560	+	0.669779i	$0.766389\pi$
$110$	−0.281152	−	11.2636i	−0.00255593	−	0.102396i
$111$	14.0312	−	41.5162i	0.126407	−	0.374020i
$112$	−10.3044	−	3.34812i	−0.0920040	−	0.0298939i
$113$	29.8088	−	91.7419i	0.263794	−	0.811875i	−0.728174	−	0.685392i	$-0.759631\pi$
$113$	29.8088	−	91.7419i	0.263794	−	0.811875i	0.991969	−	0.126484i	$-0.0403691\pi$
$114$	−96.5396	−	32.6274i	−0.846839	−	0.286206i
$115$	17.3578	−	58.3365i	0.150937	−	0.507274i
$116$	−67.9656	−	22.0834i	−0.585910	−	0.190374i
$117$	134.599	+	47.2608i	1.15042	+	0.403939i
$118$		−	72.5414i		−	0.614758i
$119$	−37.0435	+	50.9859i	−0.311290	+	0.428453i
$120$	40.1734	−	13.6419i	0.334778	−	0.113682i
$121$	−95.8370	+	69.6297i	−0.792041	+	0.575452i
$122$	−47.9591	+	34.8443i	−0.393107	+	0.285609i
$123$	−21.6152	+	63.9562i	−0.175734	+	0.519969i
$124$	−44.1984			−0.356439
$125$	29.6268	−	121.438i	0.237014	−	0.971506i
$126$	33.0300	−	9.87973i	0.262143	−	0.0784105i
$127$	182.392	−	59.2626i	1.43615	−	0.466635i	0.515458	−	0.856915i	$-0.327622\pi$
$127$	182.392	−	59.2626i	1.43615	−	0.466635i	0.920696	+	0.390280i	$0.127622\pi$
$128$	9.15298	−	6.65003i	0.0715077	−	0.0519534i
$129$	152.362	+	1.79153i	1.18110	+	0.0138878i
$130$	63.5961	−	92.2907i	0.489201	−	0.709928i
$131$	−3.28137	+	4.51642i	−0.0250486	+	0.0344765i	−0.821358	−	0.570414i	$-0.806783\pi$
$131$	−3.28137	+	4.51642i	−0.0250486	+	0.0344765i	0.796309	+	0.604890i	$0.206783\pi$
$132$	7.66795	+	5.71003i	0.0580905	+	0.0432578i
$133$	−38.2413	+	52.6346i	−0.287528	+	0.395749i
$134$	−68.1153	−	22.1320i	−0.508323	−	0.165164i
$135$	−80.4736	+	108.393i	−0.596101	+	0.802910i
$136$	−20.3358	−	62.5872i	−0.149528	−	0.460200i
$137$	35.5756	−	109.490i	0.259676	−	0.799199i	−0.733197	−	0.680017i	$-0.761973\pi$
$137$	35.5756	−	109.490i	0.259676	−	0.799199i	0.992872	−	0.119183i	$-0.0380274\pi$
$138$	29.8628	+	42.1357i	0.216397	+	0.305331i
$139$	−47.6998	−	146.805i	−0.343164	−	1.05615i	−0.962559	−	0.271071i	$-0.912622\pi$
$139$	−47.6998	−	146.805i	−0.343164	−	1.05615i	0.619395	−	0.785079i	$-0.287378\pi$
$140$	−0.675908	−	27.0784i	−0.00482792	−	0.193417i
$141$	−81.3069	−	114.722i	−0.576644	−	0.813631i
$142$	−29.7679	+	40.9720i	−0.209633	+	0.288535i
$143$	25.2564			0.176618
$144$	−11.9266	+	33.9670i	−0.0828236	+	0.235882i
$145$	−4.45812	−	178.602i	−0.0307457	−	1.23174i
$146$	96.8304	+	133.276i	0.663222	+	0.912847i
$147$	−1.46957	+	124.980i	−0.00999705	+	0.850207i
$148$	27.7856	−	9.02808i	0.187740	−	0.0610005i
$149$			58.3792i			0.391807i	0.980623	+	0.195903i	$0.0627639\pi$
$149$			58.3792i			0.391807i	−0.980623	+	0.195903i	$0.937236\pi$
$150$	65.5718	+	83.3687i	0.437146	+	0.555791i
$151$	−189.288			−1.25356			−0.626782	−	0.779194i	$-0.715628\pi$
$151$	−189.288			−1.25356			−0.626782	+	0.779194i	$0.715628\pi$
$152$	−20.9934	−	64.6111i	−0.138115	−	0.425073i
$153$	166.467	+	127.032i	1.08802	+	0.830272i
$154$	4.93807	−	3.58772i	0.0320654	−	0.0232969i
$155$	−36.7568	−	104.203i	−0.237141	−	0.672279i
$156$	28.3231	+	90.7880i	0.181558	+	0.581975i
$157$		−	76.5160i		−	0.487363i	−0.969855	−	0.243682i	$-0.921645\pi$
$157$		−	76.5160i		−	0.487363i	0.969855	−	0.243682i	$-0.0783552\pi$
$158$	135.967	+	98.7855i	0.860548	+	0.625225i
$159$	−87.5498	−	123.531i	−0.550628	−	0.776923i
$160$	23.2902	+	16.0489i	0.145564	+	0.100306i
$161$	31.3586	−	10.1890i	0.194774	−	0.0632858i
$162$	−30.2372	−	110.489i	−0.186650	−	0.682028i
$163$	117.667	+	38.2322i	0.721882	+	0.234554i	0.646839	−	0.762627i	$-0.276091\pi$
$163$	117.667	+	38.2322i	0.721882	+	0.234554i	0.0750430	+	0.997180i	$0.476091\pi$
$164$	−42.8040	+	13.9079i	−0.261000	+	0.0848040i
$165$	−7.08520	+	22.8268i	−0.0429406	+	0.138344i
$166$	−55.4322	+	170.603i	−0.333929	+	1.02773i
$167$	142.341	+	103.417i	0.852340	+	0.619261i	0.925790	−	0.378038i	$-0.123401\pi$
$167$	142.341	+	103.417i	0.852340	+	0.619261i	−0.0734503	+	0.997299i	$0.523401\pi$
$168$	18.4343	+	13.7273i	0.109728	+	0.0817102i
$169$	66.5341	+	48.3399i	0.393693	+	0.286035i
$170$	130.645	−	99.9938i	0.768501	−	0.588199i
$171$	171.850	+	131.139i	1.00497	+	0.766897i
$172$	59.7081	+	82.1811i	0.347140	+	0.477797i
$173$	2.25010	+	6.92508i	0.0130063	+	0.0400294i	0.957349	−	0.288934i	$-0.0933008\pi$
$173$	2.25010	+	6.92508i	0.0130063	+	0.0400294i	−0.944343	+	0.328963i	$0.893301\pi$
$174$	121.588	+	90.5420i	0.698781	+	0.520356i
$175$	63.2786	−	24.1128i	0.361592	−	0.137787i
$176$			6.37362i			0.0362138i
$177$	−49.2701	+	145.783i	−0.278362	+	0.823631i
$178$	−88.9205	−	122.389i	−0.499553	−	0.687576i
$179$	−69.5699	−	95.7547i	−0.388659	−	0.534943i	0.569194	−	0.822203i	$-0.307255\pi$
$179$	−69.5699	−	95.7547i	−0.388659	−	0.534943i	−0.957852	+	0.287261i	$0.907255\pi$
$180$	−89.9999	+	0.129628i	−0.499999	+	0.000720157i
$181$	−104.425	−	75.8689i	−0.576932	−	0.419165i	0.260685	−	0.965424i	$-0.416052\pi$
$181$	−104.425	−	75.8689i	−0.576932	−	0.419165i	−0.837617	+	0.546258i	$0.816052\pi$
$182$	60.7181			0.333616
$183$	120.047	−	37.4510i	0.655995	−	0.204650i
$184$	−10.6394	+	32.7448i	−0.0578231	+	0.177961i
$185$	44.3922	+	57.9998i	0.239958	+	0.313513i
$186$	88.8233	+	30.0195i	0.477544	+	0.161395i
$187$	35.2588	+	11.4563i	0.188550	+	0.0612635i
$188$	28.9678	−	89.1538i	0.154084	−	0.474222i
$189$	−73.0890	−	2.57917i	−0.386714	−	0.0136464i
$190$	134.870	−	103.227i	0.709841	−	0.543301i
$191$	−39.9390	−	12.9770i	−0.209105	−	0.0679422i	0.202592	−	0.979263i	$-0.435064\pi$
$191$	−39.9390	−	12.9770i	−0.209105	−	0.0679422i	−0.411696	+	0.911321i	$0.635064\pi$
$192$	−22.9110	+	7.14752i	−0.119328	+	0.0372267i
$193$			124.881i			0.647052i	0.946219	+	0.323526i	$0.104868\pi$
$193$			124.881i			0.647052i	−0.946219	+	0.323526i	$0.895132\pi$
$194$	111.095	−	152.910i	0.572657	−	0.788195i
$195$	−190.490	+	142.277i	−0.976870	+	0.729628i
$196$	−67.4122	+	48.9778i	−0.343940	+	0.249887i
$197$	−200.048	+	145.344i	−1.01547	+	0.737785i	−0.965350	−	0.260958i	$-0.915962\pi$
$197$	−200.048	+	145.344i	−1.01547	+	0.737785i	−0.0501237	+	0.998743i	$0.515962\pi$
$198$	−11.5316	−	16.6832i	−0.0582406	−	0.0842587i
$199$	132.790			0.667289			0.333644	−	0.942699i	$-0.391722\pi$
$199$	132.790			0.667289			0.333644	+	0.942699i	$0.391722\pi$
$200$	−18.4684	+	68.2563i	−0.0923421	+	0.341281i
$201$	121.856	+	90.7414i	0.606247	+	0.451450i
$202$	−204.438	+	66.4258i	−1.01207	+	0.328841i
$203$	78.3012	−	56.8892i	0.385720	−	0.280242i
$204$	−1.64136	+	139.590i	−0.00804586	+	0.684267i
$205$	−68.3866	−	89.3494i	−0.333593	−	0.435851i
$206$	−134.573	+	185.224i	−0.653269	+	0.899147i
$207$	−31.3952	−	104.961i	−0.151668	−	0.507056i
$208$	−37.2669	+	51.2935i	−0.179168	+	0.246604i
$209$	36.3989	+	11.8267i	0.174157	+	0.0565872i
$210$	−17.0333	+	54.8772i	−0.0811110	+	0.261320i
$211$	−96.6511	−	297.461i	−0.458062	−	1.40977i	−0.867502	−	0.497433i	$-0.834276\pi$
$211$	−96.6511	−	297.461i	−0.458062	−	1.40977i	0.409440	−	0.912337i	$-0.365724\pi$
$212$	31.1920	−	95.9993i	0.147132	−	0.452827i
$213$	87.6512	−	62.1210i	0.411508	−	0.291648i
$214$	26.2171	+	80.6878i	0.122510	+	0.377046i
$215$	−144.097	+	209.114i	−0.670219	+	0.972622i
$216$	47.0386	−	60.1612i	0.217771	−	0.278524i
$217$	35.1847	−	48.4276i	0.162141	−	0.223168i
$218$	267.129			1.22536
$219$	−104.074	−	333.604i	−0.475225	−	1.52331i
$220$	−15.0266	+	5.30051i	−0.0683028	+	0.0240932i
$221$	216.769	+	298.358i	0.980857	+	1.35003i
$222$	−61.9711	−	0.728679i	−0.279149	−	0.00328234i
$223$	135.646	−	44.0739i	0.608276	−	0.197641i	0.0113480	−	0.999936i	$-0.496388\pi$
$223$	135.646	−	44.0739i	0.608276	−	0.197641i	0.596928	+	0.802295i	$0.296388\pi$
$224$			15.3226i			0.0684046i
$225$	−75.1524	−	212.078i	−0.334011	−	0.942569i
$226$	−136.420			−0.603626
$227$	−79.3191	−	244.119i	−0.349423	−	1.07541i	−0.959173	−	0.282820i	$-0.908730\pi$
$227$	−79.3191	−	244.119i	−0.349423	−	1.07541i	0.609750	−	0.792594i	$-0.291270\pi$
$228$	−1.69443	+	144.104i	−0.00743171	+	0.632036i
$229$	187.232	−	136.032i	0.817609	−	0.594028i	−0.0984175	−	0.995145i	$-0.531378\pi$
$229$	187.232	−	136.032i	0.817609	−	0.594028i	0.916027	+	0.401117i	$0.131378\pi$
$230$	−86.0481	+	2.14786i	−0.374122	+	0.00933852i
$231$	−12.3606	+	3.85612i	−0.0535090	+	0.0166932i
$232$			101.064i			0.435622i
$233$	−268.204	−	194.861i	−1.15109	−	0.836315i	−0.162463	−	0.986715i	$-0.551944\pi$
$233$	−268.204	−	194.861i	−1.15109	−	0.836315i	−0.988625	+	0.150400i	$0.951944\pi$
$234$	4.74373	−	201.689i	0.0202723	−	0.861919i
$235$	234.282	−	5.84794i	0.996943	−	0.0248848i
$236$	−97.5680	+	31.7018i	−0.413424	+	0.134329i
$237$	−206.150	−	290.873i	−0.869831	−	1.22731i
$238$	84.7645	+	27.5417i	0.356153	+	0.115721i
$239$	154.833	−	50.3083i	0.647837	−	0.210495i	0.0333769	−	0.999443i	$-0.489374\pi$
$239$	154.833	−	50.3083i	0.647837	−	0.210495i	0.614460	+	0.788948i	$0.289374\pi$
$240$	−35.9047	−	48.0713i	−0.149603	−	0.200297i
$241$	−79.0724	+	243.360i	−0.328101	+	1.00979i	0.641920	+	0.766772i	$0.278138\pi$
$241$	−79.0724	+	243.360i	−0.328101	+	1.00979i	−0.970021	+	0.243020i	$0.921862\pi$
$242$	135.534	+	98.4712i	0.560058	+	0.406906i
$243$	−14.2775	+	242.580i	−0.0587553	+	0.998272i
$244$	67.8244	+	49.2773i	0.277969	+	0.201956i
$245$	−171.533	−	118.201i	−0.700136	−	0.482453i
$246$	95.4672	+	1.12254i	0.388078	+	0.00456316i
$247$	223.779	+	308.005i	0.905988	+	1.24698i
$248$	19.3154	+	59.4467i	0.0778847	+	0.239705i
$249$	227.273	−	305.202i	0.912742	−	1.22571i
$250$	−176.281	+	13.2225i	−0.705126	+	0.0528902i
$251$		−	370.225i		−	1.47500i	−0.675346	−	0.737501i	$-0.736006\pi$
$251$		−	370.225i		−	1.47500i	0.675346	−	0.737501i	$-0.263994\pi$
$252$	−27.7228	−	40.1076i	−0.110011	−	0.159157i
$253$	−11.4008	−	15.6919i	−0.0450626	−	0.0620233i
$254$	−159.416	−	219.417i	−0.627622	−	0.863848i
$255$	−330.467	+	112.218i	−1.29595	+	0.440071i
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	201.413			0.783707			0.391854	−	0.920028i	$-0.371834\pi$
$257$	201.413			0.783707			0.391854	+	0.920028i	$0.371834\pi$
$258$	−64.1749	−	205.709i	−0.248740	−	0.797322i
$259$	−12.2271	+	37.6312i	−0.0472089	+	0.145294i
$260$	−151.923	−	45.2040i	−0.584320	−	0.173862i
$261$	−182.853	−	264.540i	−0.700586	−	1.01356i
$262$	7.50858	+	2.43968i	0.0286587	+	0.00931177i
$263$	−31.2902	+	96.3012i	−0.118974	+	0.366164i	−0.992755	−	0.120155i	$-0.961661\pi$
$263$	−31.2902	+	96.3012i	−0.118974	+	0.366164i	0.873781	+	0.486319i	$0.161661\pi$
$264$	4.32896	−	12.8087i	0.0163976	−	0.0485180i
$265$	252.270	−	6.29696i	0.951964	−	0.0237621i
$266$	87.5055	+	28.4322i	0.328968	+	0.106888i
$267$	95.5727	+	306.353i	0.357950	+	1.14739i
$268$			101.287i			0.377936i
$269$	−176.811	+	243.360i	−0.657291	+	0.904684i	−0.999388	−	0.0349809i	$-0.988863\pi$
$269$	−176.811	+	243.360i	−0.657291	+	0.904684i	0.342097	+	0.939665i	$0.388863\pi$
$270$	180.956	+	60.8674i	0.670208	+	0.225435i
$271$	−105.894	+	76.9364i	−0.390752	+	0.283898i	−0.765764	−	0.643122i	$-0.777639\pi$
$271$	−105.894	+	76.9364i	−0.390752	+	0.283898i	0.375012	+	0.927020i	$0.377639\pi$
$272$	−75.2926	+	54.7032i	−0.276811	+	0.201115i
$273$	−122.022	−	41.2397i	−0.446967	−	0.151061i
$274$	−162.811			−0.594201
$275$	−24.9932	−	31.0190i	−0.0908844	−	0.112796i
$276$	43.6218	−	58.5793i	0.158050	−	0.212244i
$277$	−307.000	+	99.7505i	−1.10830	+	0.360110i	−0.805293	−	0.592877i	$-0.797992\pi$
$277$	−307.000	+	99.7505i	−1.10830	+	0.360110i	−0.303012	+	0.952987i	$0.597992\pi$
$278$	−176.607	+	128.312i	−0.635275	+	0.461555i
$279$	−158.114	−	120.657i	−0.566718	−	0.432464i
$280$	−36.1250	+	12.7428i	−0.129018	+	0.0455100i
$281$	−180.302	+	248.165i	−0.641646	+	0.883149i	−0.998702	−	0.0509334i	$-0.983780\pi$
$281$	−180.302	+	248.165i	−0.641646	+	0.883149i	0.357056	+	0.934083i	$0.383780\pi$
$282$	−118.768	+	159.493i	−0.421164	+	0.565577i
$283$	148.721	−	204.697i	0.525517	−	0.723313i	−0.460922	−	0.887441i	$-0.652481\pi$
$283$	148.721	−	204.697i	0.525517	−	0.723313i	0.986439	+	0.164128i	$0.0524811\pi$
$284$	68.1163	+	22.1323i	0.239846	+	0.0779307i
$285$	−341.153	+	115.847i	−1.19703	+	0.406480i
$286$	−11.0375	−	33.9698i	−0.0385925	−	0.118775i
$287$	18.8360	−	57.9712i	0.0656306	−	0.201990i
$288$	50.8976	+	1.19711i	0.176728	+	0.00415664i
$289$	77.9769	+	239.988i	0.269816	+	0.830409i
$290$	−238.271	+	84.0483i	−0.821626	+	0.289822i
$291$	−327.119	+	231.839i	−1.12412	+	0.796698i
$292$	136.939	−	188.480i	0.468969	−	0.645480i
$293$	−331.150			−1.13020			−0.565102	−	0.825021i	$-0.691163\pi$
$293$	−331.150			−1.13020			−0.565102	+	0.825021i	$0.691163\pi$
$294$	168.741	−	52.6419i	0.573947	−	0.179054i
$295$	−155.881	−	203.664i	−0.528412	−	0.690388i
$296$	−24.2855	−	33.4261i	−0.0820455	−	0.112926i
$297$	11.8433	+	41.3597i	0.0398764	+	0.139258i
$298$	78.5199	−	25.5127i	0.263489	−	0.0856129i
$299$		−	192.946i		−	0.645305i
$300$	83.4746	−	124.627i	0.278249	−	0.415425i
$301$	−137.576			−0.457063
$302$	82.7220	+	254.592i	0.273914	+	0.843020i
$303$	455.964	+	5.36140i	1.50483	+	0.0176944i
$304$	−77.7272	+	56.4721i	−0.255682	+	0.185764i
$305$	−59.7724	+	200.885i	−0.195975	+	0.658639i
$306$	98.1083	−	279.413i	0.320615	−	0.913114i
$307$			446.812i			1.45541i	0.685888	+	0.727707i	$0.259414\pi$
$307$			446.812i			1.45541i	−0.685888	+	0.727707i	$0.740586\pi$
$308$	−6.98349	−	5.07380i	−0.0226737	−	0.0164734i
$309$	396.250	−	280.834i	1.28236	−	0.908847i
$310$	−124.090	+	94.9763i	−0.400289	+	0.306375i
$311$	395.681	−	128.564i	1.27228	−	0.413390i	0.406428	−	0.913683i	$-0.366774\pi$
$311$	395.681	−	128.564i	1.27228	−	0.413390i	0.865857	+	0.500292i	$0.166774\pi$
$312$	109.732	−	77.7703i	0.351705	−	0.249264i
$313$	−26.0997	−	8.48032i	−0.0833857	−	0.0270937i	0.267027	−	0.963689i	$-0.413959\pi$
$313$	−26.0997	−	8.48032i	−0.0833857	−	0.0270937i	−0.350413	+	0.936595i	$0.613959\pi$
$314$	−102.914	+	33.4387i	−0.327751	+	0.106493i
$315$	71.5035	−	98.7148i	0.226995	−	0.313380i
$316$	73.4466	−	226.046i	0.232426	−	0.715334i
$317$	467.709	+	339.811i	1.47542	+	1.07196i	0.978996	+	0.203880i	$0.0653554\pi$
$317$	467.709	+	339.811i	1.47542	+	1.07196i	0.496428	+	0.868078i	$0.334645\pi$
$318$	−127.888	+	171.739i	−0.402163	+	0.540060i
$319$	−46.0614	−	33.4655i	−0.144393	−	0.104908i
$320$	11.4075	−	38.3389i	0.0356486	−	0.119809i
$321$	2.11605	−	179.961i	0.00659204	−	0.560626i
$322$	−27.4084	−	37.7244i	−0.0851192	−	0.117157i
$323$	172.692	+	531.491i	0.534650	+	1.64548i
$324$	−135.393	+	88.9542i	−0.417878	+	0.274550i
$325$	−19.7701	−	395.771i	−0.0608311	−	1.21776i
$326$		−	174.970i		−	0.536716i
$327$	−536.835	−	181.434i	−1.64170	−	0.554844i
$328$	37.4120	+	51.4933i	0.114061	+	0.156992i
$329$	74.6243	+	102.712i	0.226822	+	0.312193i
$330$	33.7983	−	0.446101i	0.102419	−	0.00135182i
$331$	256.384	+	186.274i	0.774575	+	0.562762i	0.903346	−	0.428913i	$-0.141103\pi$
$331$	256.384	+	186.274i	0.774575	+	0.562762i	−0.128771	+	0.991674i	$0.541103\pi$
$332$	253.685			0.764112
$333$	124.045	+	43.5551i	0.372508	+	0.130796i
$334$	76.8898	−	236.643i	0.230209	−	0.708511i
$335$	−238.796	+	84.2334i	−0.712825	+	0.251443i
$336$	10.4071	−	30.7931i	0.0309736	−	0.0916461i
$337$	27.3492	+	8.88630i	0.0811550	+	0.0263689i	0.349313	−	0.937006i	$-0.386415\pi$
$337$	27.3492	+	8.88630i	0.0811550	+	0.0263689i	−0.268158	+	0.963375i	$0.586415\pi$
$338$	35.9405	−	110.613i	0.106333	−	0.327259i
$339$	274.155	+	92.6561i	0.808718	+	0.273322i
$340$	−191.585	−	132.019i	−0.563486	−	0.388290i
$341$	−33.4896	−	10.8814i	−0.0982098	−	0.0319103i
$342$	101.281	−	288.448i	0.296143	−	0.843415i
$343$		−	245.577i		−	0.715969i
$344$	84.4400	−	116.222i	0.245465	−	0.337854i
$345$	174.385	+	54.1274i	0.505465	+	0.156891i
$346$	8.33089	−	6.05274i	0.0240777	−	0.0174935i
$347$	−182.296	+	132.446i	−0.525349	+	0.381688i	−0.818615	−	0.574343i	$-0.805258\pi$
$347$	−182.296	+	132.446i	−0.525349	+	0.381688i	0.293266	+	0.956031i	$0.405258\pi$
$348$	68.6428	−	203.104i	0.197249	−	0.583631i
$349$	−155.674			−0.446058			−0.223029	−	0.974812i	$-0.571594\pi$
$349$	−155.674			−0.446058			−0.223029	+	0.974812i	$0.571594\pi$
$350$	−60.0854	−	74.5718i	−0.171673	−	0.213062i
$351$	−146.520	+	402.102i	−0.417437	+	1.14559i
$352$	8.57251	−	2.78538i	0.0243537	−	0.00791300i
$353$	−51.2709	+	37.2505i	−0.145243	+	0.105525i	−0.658034	−	0.752988i	$-0.728612\pi$
$353$	−51.2709	+	37.2505i	−0.145243	+	0.105525i	0.512791	+	0.858514i	$0.328612\pi$
$354$	217.609	+	2.55873i	0.614715	+	0.00722805i
$355$	4.46801	+	178.998i	0.0125859	+	0.504221i
$356$	−125.753	+	173.084i	−0.353237	+	0.486190i
$357$	−151.641	−	112.921i	−0.424764	−	0.316306i
$358$	−98.3867	+	135.418i	−0.274823	+	0.378262i
$359$	38.8547	+	12.6247i	0.108230	+	0.0351662i	0.362632	−	0.931933i	$-0.381878\pi$
$359$	38.8547	+	12.6247i	0.108230	+	0.0351662i	−0.254401	+	0.967099i	$0.581878\pi$
$360$	39.5058	+	120.993i	0.109738	+	0.336092i
$361$	66.7211	+	205.346i	0.184823	+	0.568826i
$362$	−56.4083	+	173.607i	−0.155824	+	0.479577i
$363$	−205.494	−	289.947i	−0.566100	−	0.798753i
$364$	−26.5348	−	81.6657i	−0.0728978	−	0.224356i
$365$	558.248	+	166.104i	1.52945	+	0.455080i
$366$	−102.834	−	145.096i	−0.280967	−	0.396438i
$367$	204.108	−	280.930i	0.556152	−	0.765478i	−0.434679	−	0.900586i	$-0.643138\pi$
$367$	204.108	−	280.930i	0.556152	−	0.765478i	0.990831	+	0.135108i	$0.0431381\pi$
$368$	48.6913			0.132313
$369$	−191.093	−	67.0972i	−0.517867	−	0.181835i
$370$	58.6095	−	85.0542i	0.158404	−	0.229876i
$371$	80.3542	+	110.598i	0.216588	+	0.298108i
$372$	1.55900	−	132.586i	0.00419085	−	0.356414i
$373$	−180.806	+	58.7475i	−0.484735	+	0.157500i	−0.541182	−	0.840906i	$-0.682023\pi$
$373$	−180.806	+	58.7475i	−0.484735	+	0.157500i	0.0564465	+	0.998406i	$0.482023\pi$
$374$		−	52.4295i		−	0.140186i
$375$	363.245	+	93.1576i	0.968652	+	0.248420i
$376$	−132.571			−0.352582
$377$	−175.017	−	538.647i	−0.464236	−	1.42877i
$378$	28.4721	+	99.4316i	0.0753229	+	0.263047i
$379$	194.948	−	141.638i	0.514374	−	0.373715i	−0.300106	−	0.953906i	$-0.597022\pi$
$379$	194.948	−	141.638i	0.514374	−	0.373715i	0.814480	+	0.580191i	$0.197022\pi$
$380$	−197.780	−	136.287i	−0.520475	−	0.358651i
$381$	171.342	+	549.227i	0.449717	+	1.44154i
$382$			59.3890i			0.155469i
$383$	343.680	+	249.698i	0.897337	+	0.651953i	0.937780	−	0.347229i	$-0.112877\pi$
$383$	343.680	+	249.698i	0.897337	+	0.651953i	−0.0404440	+	0.999182i	$0.512877\pi$
$384$	19.6259	+	27.6916i	0.0511090	+	0.0721136i
$385$	6.15442	−	20.6840i	0.0159855	−	0.0537246i
$386$	167.965	−	54.5750i	0.435142	−	0.141386i
$387$	−10.7484	+	456.990i	−0.0277737	+	1.18085i
$388$	−254.214	−	82.5991i	−0.655190	−	0.212884i
$389$	−559.973	+	181.946i	−1.43952	+	0.467728i	−0.921747	−	0.387791i	$-0.873238\pi$
$389$	−559.973	+	181.946i	−1.43952	+	0.467728i	−0.517771	+	0.855519i	$0.673238\pi$
$390$	274.610	+	194.030i	0.704128	+	0.497514i
$391$	87.5202	−	269.359i	0.223837	−	0.688899i
$392$	95.3352	+	69.2651i	0.243202	+	0.176697i
$393$	−13.4326	−	10.0027i	−0.0341796	−	0.0254522i
$394$	282.911	+	205.547i	0.718048	+	0.521693i
$395$	594.011	−	14.8272i	1.50382	−	0.0375372i
$396$	−17.3994	+	22.8009i	−0.0439379	+	0.0575779i
$397$	45.1315	+	62.1182i	0.113681	+	0.156469i	0.862066	−	0.506796i	$-0.169170\pi$
$397$	45.1315	+	62.1182i	0.113681	+	0.156469i	−0.748385	+	0.663265i	$0.769170\pi$
$398$	−58.0316	−	178.603i	−0.145808	−	0.448751i
$399$	−156.544	−	116.573i	−0.392341	−	0.292162i
$400$	99.8755	−	4.98912i	0.249689	−	0.0124728i
$401$		−	220.661i		−	0.550276i	−0.961405	−	0.275138i	$-0.911276\pi$
$401$		−	220.661i		−	0.550276i	0.961405	−	0.275138i	$-0.0887235\pi$
$402$	68.7940	−	203.551i	0.171129	−	0.506346i
$403$	−205.892	−	283.387i	−0.510899	−	0.703192i
$404$	178.685	+	245.939i	0.442290	+	0.608759i
$405$	−322.317	−	245.227i	−0.795845	−	0.605500i
$406$	−110.735	−	80.4535i	−0.272746	−	0.198161i
$407$	23.2761			0.0571893
$408$	188.466	−	58.7956i	0.461927	−	0.144107i
$409$	−32.8392	+	101.069i	−0.0802914	+	0.247111i	−0.983142	−	0.182842i	$-0.941470\pi$
$409$	−32.8392	+	101.069i	−0.0802914	+	0.247111i	0.902851	+	0.429954i	$0.141470\pi$
$410$	−90.2887	+	131.027i	−0.220216	+	0.319578i
$411$	327.193	+	110.581i	0.796091	+	0.269054i
$412$	307.937	+	100.055i	0.747420	+	0.242851i
$413$	42.9350	−	132.140i	0.103959	−	0.319953i
$414$	−127.452	+	88.0959i	−0.307854	+	0.212792i
$415$	210.973	+	598.094i	0.508368	+	1.44119i
$416$	85.2759	+	27.7078i	0.204990	+	0.0666053i
$417$	442.067	−	137.911i	1.06011	−	0.330723i
$418$		−	54.1249i		−	0.129485i
$419$	−388.137	+	534.225i	−0.926342	+	1.27500i	0.0349274	+	0.999390i	$0.488880\pi$
$419$	−388.137	+	534.225i	−0.926342	+	1.27500i	−0.961269	+	0.275611i	$0.911120\pi$
$420$	81.2534	−	1.07246i	0.193461	−	0.00255347i
$421$	319.900	−	232.421i	0.759857	−	0.552068i	−0.139010	−	0.990291i	$-0.544392\pi$
$421$	319.900	−	232.421i	0.759857	−	0.552068i	0.898866	+	0.438223i	$0.144392\pi$
$422$	−357.847	+	259.991i	−0.847978	+	0.616092i
$423$	347.010	−	239.857i	0.820355	−	0.567038i
$424$	−142.750			−0.336675
$425$	151.921	−	561.477i	0.357462	−	1.32112i
$426$	−121.858	−	90.7427i	−0.286051	−	0.213011i
$427$	−107.985	+	35.0864i	−0.252892	+	0.0821696i
$428$	97.0676	−	70.5237i	0.226793	−	0.164775i
$429$	−0.890861	+	75.7640i	−0.00207660	+	0.176606i
$430$	344.230	+	102.424i	0.800535	+	0.238195i
$431$	91.4244	−	125.835i	0.212122	−	0.291960i	−0.689677	−	0.724117i	$-0.742247\pi$
$431$	91.4244	−	125.835i	0.212122	−	0.291960i	0.901798	+	0.432157i	$0.142247\pi$
$432$	−101.473	−	36.9754i	−0.234892	−	0.0855912i
$433$	−315.463	+	434.197i	−0.728551	+	1.00276i	0.270645	+	0.962679i	$0.412763\pi$
$433$	−315.463	+	434.197i	−0.728551	+	1.00276i	−0.999196	+	0.0400854i	$0.987237\pi$
$434$	−80.5112	−	26.1597i	−0.185510	−	0.0602757i
$435$	535.928	−	7.07366i	1.23202	−	0.0162613i
$436$	−116.740	−	359.288i	−0.267751	−	0.824054i
$437$	90.3503	−	278.069i	0.206751	−	0.636315i
$438$	−403.215	+	285.770i	−0.920581	+	0.652443i
$439$	177.231	+	545.460i	0.403714	+	1.24251i	0.921964	+	0.387276i	$0.126584\pi$
$439$	177.231	+	545.460i	0.403714	+	1.24251i	−0.518249	+	0.855230i	$0.673416\pi$
$440$	13.6960	+	17.8943i	0.0311274	+	0.0406689i
$441$	−374.864	−	8.81679i	−0.850031	−	0.0199927i
$442$	306.558	−	421.941i	0.693571	−	0.954618i
$443$	339.491			0.766344			0.383172	−	0.923677i	$-0.374832\pi$
$443$	339.491			0.766344			0.383172	+	0.923677i	$0.374832\pi$
$444$	26.1023	+	83.6694i	0.0587889	+	0.188445i
$445$	−512.646	−	152.535i	−1.15201	−	0.342776i
$446$	−118.559	−	163.182i	−0.265826	−	0.365879i
$447$	−175.126	−	2.05919i	−0.391780	−	0.00460669i
$448$	20.6089	−	6.69623i	0.0460020	−	0.0149470i
$449$			283.865i			0.632216i	0.948723	+	0.316108i	$0.102376\pi$
$449$			283.865i			0.632216i	−0.948723	+	0.316108i	$0.897624\pi$
$450$	−252.402	+	193.761i	−0.560892	+	0.430581i
$451$	−35.8570			−0.0795056
$452$	59.6175	+	183.484i	0.131897	+	0.405938i
$453$	6.67670	−	567.826i	0.0147389	−	1.25348i
$454$	−293.676	+	213.368i	−0.646863	+	0.469973i
$455$	170.470	−	130.475i	0.374659	−	0.286758i
$456$	194.560	−	60.6969i	0.426667	−	0.133107i
$457$		−	628.493i		−	1.37526i	−0.726062	−	0.687630i	$-0.758651\pi$
$457$		−	628.493i		−	1.37526i	0.726062	−	0.687630i	$-0.241349\pi$
$458$	−264.787	−	192.379i	−0.578137	−	0.420041i
$459$	−386.940	+	494.887i	−0.843007	+	1.07818i
$460$	40.4933	+	114.796i	0.0880288	+	0.249556i
$461$	−462.891	+	150.402i	−1.00410	+	0.326252i	−0.764503	−	0.644620i	$-0.777016\pi$
$461$	−462.891	+	150.402i	−1.00410	+	0.326252i	−0.239598	+	0.970872i	$0.577016\pi$
$462$	10.5882	+	14.9397i	0.0229183	+	0.0323371i
$463$	394.728	+	128.255i	0.852545	+	0.277009i	0.702512	−	0.711672i	$-0.252062\pi$
$463$	394.728	+	128.255i	0.852545	+	0.277009i	0.150033	+	0.988681i	$0.452062\pi$
$464$	135.931	−	44.1667i	0.292955	−	0.0951869i
$465$	313.884	−	106.587i	0.675020	−	0.229220i
$466$	−144.879	+	445.890i	−0.310898	+	0.956847i
$467$	−642.975	−	467.149i	−1.37682	−	1.00032i	−0.997169	−	0.0751884i	$-0.976044\pi$
$467$	−642.975	−	467.149i	−1.37682	−	1.00032i	−0.379651	−	0.925130i	$-0.623956\pi$
$468$	−273.344	+	81.7611i	−0.584069	+	0.174703i
$469$	−110.979	−	80.6306i	−0.236628	−	0.171920i
$470$	−110.250	−	312.552i	−0.234575	−	0.665005i
$471$	229.532	+	2.69892i	0.487329	+	0.00573020i
$472$	85.2775	+	117.374i	0.180673	+	0.248675i
$473$	25.0088	+	76.9693i	0.0528728	+	0.162726i
$474$	−301.132	+	404.387i	−0.635299	+	0.853137i
$475$	156.834	−	579.633i	0.330177	−	1.22028i
$476$		−	126.044i		−	0.264799i
$477$	373.655	−	258.274i	0.783343	−	0.541455i
$478$	−135.329	−	186.265i	−0.283115	−	0.389675i
$479$	−177.966	−	244.949i	−0.371536	−	0.511376i	0.581781	−	0.813345i	$-0.302356\pi$
$479$	−177.966	−	244.949i	−0.371536	−	0.511376i	−0.953318	+	0.301970i	$0.902356\pi$
$480$	−48.9649	+	69.2996i	−0.102010	+	0.144374i
$481$	187.321	+	136.096i	0.389440	+	0.282945i
$482$	361.874			0.750776
$483$	29.4588	+	94.4286i	0.0609914	+	0.195504i
$484$	73.2130	−	225.326i	0.151266	−	0.465550i
$485$	−16.6749	−	668.032i	−0.0343812	−	1.37739i
$486$	332.509	−	86.8082i	0.684175	−	0.178618i
$487$	−768.396	−	249.667i	−1.57781	−	0.512663i	−0.616322	−	0.787494i	$-0.711378\pi$
$487$	−768.396	−	249.667i	−1.57781	−	0.512663i	−0.961493	+	0.274831i	$0.911378\pi$
$488$	36.6375	−	112.759i	0.0750768	−	0.231063i
$489$	−118.839	+	351.627i	−0.243025	+	0.719074i
$490$	−84.0172	+	282.368i	−0.171464	+	0.576261i
$491$	341.484	+	110.955i	0.695486	+	0.225977i	0.635363	−	0.772214i	$-0.280851\pi$
$491$	341.484	+	110.955i	0.695486	+	0.225977i	0.0601234	+	0.998191i	$0.480851\pi$
$492$	−40.2109	−	128.894i	−0.0817294	−	0.261979i
$493$		−	831.356i		−	1.68632i
$494$	316.471	−	435.585i	0.640630	−	0.881751i
$495$	−68.2257	−	22.0593i	−0.137830	−	0.0445642i
$496$	71.5145	−	51.9583i	0.144182	−	0.104755i
$497$	−78.4749	+	57.0153i	−0.157897	+	0.114719i
$498$	−509.818	−	172.303i	−1.02373	−	0.345990i
$499$	−688.464			−1.37969			−0.689844	−	0.723958i	$-0.742321\pi$
$499$	−688.464			−1.37969			−0.689844	+	0.723958i	$0.742321\pi$
$500$	94.8221	+	231.320i	0.189644	+	0.462639i
$501$	−315.249	+	423.345i	−0.629240	+	0.845000i
$502$	−497.952	+	161.794i	−0.991937	+	0.322300i
$503$	−596.829	+	433.621i	−1.18654	+	0.862071i	−0.992894	−	0.119001i	$-0.962031\pi$
$503$	−596.829	+	433.621i	−1.18654	+	0.862071i	−0.193644	+	0.981072i	$0.562031\pi$
$504$	−41.8293	+	54.8148i	−0.0829947	+	0.108760i
$505$	−431.231	+	625.803i	−0.853923	+	1.23921i
$506$	−16.1232	+	22.1917i	−0.0318641	+	0.0438571i
$507$	−147.356	+	197.883i	−0.290644	+	0.390303i
$508$	−225.448	+	310.303i	−0.443796	+	0.610833i
$509$	91.6916	+	29.7924i	0.180141	+	0.0585313i	0.397698	−	0.917516i	$-0.369809\pi$
$509$	91.6916	+	29.7924i	0.180141	+	0.0585313i	−0.217558	+	0.976047i	$0.569809\pi$
$510$	295.352	+	395.436i	0.579122	+	0.775364i
$511$	97.5032	+	300.084i	0.190809	+	0.587248i
$512$	−6.99226	+	21.5200i	−0.0136568	+	0.0420312i
$513$	−399.452	+	510.889i	−0.778660	+	0.995886i
$514$	−88.0206	−	270.900i	−0.171246	−	0.527042i
$515$	20.1988	+	809.208i	0.0392209	+	1.57128i
$516$	−248.632	+	176.213i	−0.481846	+	0.341498i
$517$	43.8984	−	60.4209i	0.0849098	−	0.116868i
$518$	55.9572			0.108026
$519$	−20.8532	+	6.50555i	−0.0401795	+	0.0125348i
$520$	5.59357	+	224.091i	0.0107569	+	0.430945i
$521$	−406.508	−	559.510i	−0.780246	−	1.07392i	−0.995255	−	0.0973043i	$-0.968978\pi$
$521$	−406.508	−	559.510i	−0.780246	−	1.07392i	0.215009	−	0.976612i	$-0.431022\pi$
$522$	−275.896	+	361.545i	−0.528536	+	0.692615i
$523$	−194.437	+	63.1763i	−0.371772	+	0.120796i	−0.488943	−	0.872316i	$-0.662617\pi$
$523$	−194.437	+	63.1763i	−0.371772	+	0.120796i	0.117171	+	0.993112i	$0.462617\pi$
$524$		−	11.1652i		−	0.0213076i
$525$	70.1014	+	190.673i	0.133527	+	0.363187i
$526$	143.199			0.272242
$527$	−158.889	−	489.010i	−0.301497	−	0.927912i
$528$	−19.1196	−	0.224815i	−0.0362113	−	0.000425786i
$529$	308.092	−	223.842i	0.582404	−	0.423141i
$530$	−118.716	−	336.551i	−0.223992	−	0.635002i
$531$	−435.580	−	152.942i	−0.820302	−	0.288027i
$532$		−	130.120i		−	0.244586i
$533$	−288.569	−	209.658i	−0.541406	−	0.393355i
$534$	370.277	−	262.426i	0.693402	−	0.491435i
$535$	246.993	+	170.199i	0.461669	+	0.318129i
$536$	136.231	−	44.2640i	0.254161	−	0.0825821i
$537$	289.698	−	205.318i	0.539475	−	0.382342i
$538$	404.588	+	131.459i	0.752022	+	0.244347i
$539$	−63.1370	+	20.5144i	−0.117137	+	0.0380602i
$540$	2.78568	−	269.986i	0.00515867	−	0.499973i
$541$	−123.230	+	379.264i	−0.227782	+	0.701042i	0.770215	+	0.637784i	$0.220149\pi$
$541$	−123.230	+	379.264i	−0.227782	+	0.701042i	−0.997997	+	0.0632575i	$0.979851\pi$
$542$	149.756	+	108.804i	0.276303	+	0.200746i
$543$	231.274	−	310.576i	0.425920	−	0.571964i
$544$	106.480	+	77.3621i	0.195735	+	0.142210i
$545$	749.980	−	574.023i	1.37611	−	1.05325i
$546$	−2.14169	+	182.142i	−0.00392251	+	0.333593i
$547$	98.1369	+	135.074i	0.179409	+	0.246936i	0.889245	−	0.457432i	$-0.151231\pi$
$547$	98.1369	+	135.074i	0.179409	+	0.246936i	−0.709835	+	0.704368i	$0.751231\pi$
$548$	71.1511	+	218.981i	0.129838	+	0.399600i
$549$	108.111	+	361.438i	0.196923	+	0.658356i
$550$	−30.7980	+	47.1716i	−0.0559964	+	0.0857666i
$551$		−	858.239i		−	1.55760i
$552$	−97.8524	−	33.0711i	−0.177269	−	0.0599114i
$553$	189.207	+	260.421i	0.342146	+	0.470924i
$554$	268.328	+	369.322i	0.484347	+	0.666646i
$555$	−175.553	+	131.121i	−0.316312	+	0.236255i
$556$	249.759	+	181.461i	0.449208	+	0.326368i
$557$	−939.086			−1.68597			−0.842985	−	0.537936i	$-0.819204\pi$
$557$	−939.086			−1.68597			−0.842985	+	0.537936i	$0.819204\pi$
$558$	−93.1854	+	265.392i	−0.166999	+	0.475614i
$559$	−248.778	+	765.660i	−0.445041	+	1.36970i
$560$	32.9262	+	43.0192i	0.0587968	+	0.0768200i
$561$	−35.6101	+	105.365i	−0.0634761	+	0.187816i
$562$	412.576	+	134.054i	0.734121	+	0.238530i
$563$	2.66316	−	8.19635i	0.00473030	−	0.0145584i	−0.948664	−	0.316287i	$-0.897564\pi$
$563$	2.66316	−	8.19635i	0.00473030	−	0.0145584i	0.953394	+	0.301729i	$0.0975637\pi$
$564$	266.421	+	90.0421i	0.472378	+	0.159649i
$565$	−383.006	+	293.147i	−0.677887	+	0.518844i
$566$	−340.311	−	110.574i	−0.601256	−	0.195360i
$567$	10.3150	−	219.161i	0.0181923	−	0.386527i
$568$		−	101.288i		−	0.178325i
$569$	130.006	−	178.937i	0.228481	−	0.314477i	−0.679349	−	0.733815i	$-0.737738\pi$
$569$	130.006	−	178.937i	0.228481	−	0.314477i	0.907830	+	0.419338i	$0.137738\pi$
$570$	304.903	+	408.222i	0.534917	+	0.716180i
$571$	804.112	−	584.222i	1.40825	−	1.02316i	0.414678	−	0.909968i	$-0.363894\pi$
$571$	804.112	−	584.222i	1.40825	−	1.02316i	0.993574	−	0.113187i	$-0.0361059\pi$
$572$	−40.8657	+	29.6907i	−0.0714436	+	0.0519068i
$573$	40.3370	−	119.351i	0.0703961	−	0.208291i
$574$	−86.2027			−0.150179
$575$	−236.970	+	190.936i	−0.412121	+	0.332062i
$576$	−20.6330	−	68.9803i	−0.0358211	−	0.119757i
$577$	599.210	−	194.695i	1.03849	−	0.337426i	0.260350	−	0.965514i	$-0.416162\pi$
$577$	599.210	−	194.695i	1.03849	−	0.337426i	0.778142	+	0.628088i	$0.216162\pi$
$578$	288.706	−	209.757i	0.499492	−	0.362902i
$579$	−374.617	−	4.40489i	−0.647008	−	0.00760776i
$580$	217.173	+	283.744i	0.374437	+	0.489214i
$581$	−201.949	+	277.959i	−0.347589	+	0.478415i
$582$	454.779	+	338.657i	0.781407	+	0.581885i
$583$	47.2690	−	65.0602i	0.0810790	−	0.111596i
$584$	−313.350	−	101.813i	−0.536558	−	0.174338i
$585$	−420.084	−	576.448i	−0.718092	−	0.985381i
$586$	144.718	+	445.396i	0.246959	+	0.760061i
$587$	60.7330	−	186.917i	0.103463	−	0.318428i	−0.885903	−	0.463870i	$-0.846461\pi$
$587$	60.7330	−	186.917i	0.103463	−	0.318428i	0.989367	+	0.145442i	$0.0464605\pi$
$588$	−144.546	−	203.950i	−0.245826	−	0.346854i
$589$	−164.027	−	504.822i	−0.278483	−	0.857083i
$590$	−205.805	+	298.665i	−0.348822	+	0.506211i
$591$	−428.945	−	605.230i	−0.725794	−	1.02408i
$592$	−34.3448	+	47.2716i	−0.0580149	+	0.0798507i
$593$	−424.765			−0.716298			−0.358149	−	0.933664i	$-0.616592\pi$
$593$	−424.765			−0.716298			−0.358149	+	0.933664i	$0.616592\pi$
$594$	50.4530	−	34.0040i	0.0849377	−	0.0572459i
$595$	297.165	−	104.822i	0.499436	−	0.176172i
$596$	−68.6289	−	94.4596i	−0.115149	−	0.158489i
$597$	−4.68388	+	398.344i	−0.00784569	+	0.667243i
$598$	−259.512	+	84.3206i	−0.433967	+	0.141004i
$599$		−	334.573i		−	0.558552i	−0.960211	−	0.279276i	$-0.909906\pi$
$599$		−	334.573i		−	0.558552i	0.960211	−	0.279276i	$-0.0900945\pi$
$600$	−204.103	−	57.8090i	−0.340172	−	0.0963483i
$601$	893.199			1.48619			0.743094	−	0.669187i	$-0.233358\pi$
$601$	893.199			1.48619			0.743094	+	0.669187i	$0.233358\pi$
$602$	60.1229	+	185.039i	0.0998720	+	0.307374i
$603$	−276.504	+	362.341i	−0.458546	+	0.600897i
$604$	306.275	−	222.522i	0.507078	−	0.368413i
$605$	592.121	−	14.7800i	0.978712	−	0.0244298i
$606$	−192.053	−	615.613i	−0.316918	−	1.01586i
$607$		−	361.640i		−	0.595783i	−0.954600	−	0.297891i	$-0.903717\pi$
$607$		−	361.640i		−	0.595783i	0.954600	−	0.297891i	$-0.0962833\pi$
$608$	109.923	+	79.8637i	0.180794	+	0.131355i
$609$	167.894	+	236.894i	0.275688	+	0.388989i
$610$	296.311	−	7.39627i	0.485756	−	0.0121250i
$611$	706.569	−	229.578i	1.15641	−	0.375742i
$612$	−418.684	−	9.84746i	−0.684125	−	0.0160906i
$613$	−150.413	−	48.8722i	−0.245372	−	0.0797263i	0.183749	−	0.982973i	$-0.441177\pi$
$613$	−150.413	−	48.8722i	−0.245372	−	0.0797263i	−0.429121	+	0.903247i	$0.641177\pi$
$614$	600.961	−	195.264i	0.978764	−	0.318020i
$615$	270.442	−	201.994i	0.439743	−	0.328446i
$616$	−3.77235	+	11.6101i	−0.00612395	+	0.0188476i
$617$	902.981	+	656.054i	1.46350	+	1.06330i	0.982433	+	0.186614i	$0.0597514\pi$
$617$	902.981	+	656.054i	1.46350	+	1.06330i	0.481069	+	0.876683i	$0.340249\pi$
$618$	−550.888	−	410.226i	−0.891404	−	0.663795i
$619$	−422.883	−	307.242i	−0.683171	−	0.496353i	0.191237	−	0.981544i	$-0.438750\pi$
$619$	−422.883	−	307.242i	−0.683171	−	0.496353i	−0.874408	+	0.485191i	$0.838750\pi$
$620$	181.972	+	125.394i	0.293503	+	0.202249i
$621$	315.968	−	90.4768i	0.508805	−	0.145695i
$622$	−345.838	−	476.005i	−0.556009	−	0.765281i
$623$	−89.5383	−	275.571i	−0.143721	−	0.442328i
$624$	−152.555	−	113.602i	−0.244480	−	0.182055i
$625$	−466.507	+	415.928i	−0.746412	+	0.665484i
$626$			38.8101i			0.0619969i
$627$	−36.7616	+	108.772i	−0.0586309	+	0.173480i
$628$	89.9500	+	123.805i	0.143232	+	0.197143i
$629$	199.773	+	274.963i	0.317604	+	0.437144i
$630$	−164.019	−	53.0320i	−0.260348	−	0.0841778i
$631$	−307.273	−	223.247i	−0.486963	−	0.353799i	0.317052	−	0.948408i	$-0.397307\pi$
$631$	−307.273	−	223.247i	−0.486963	−	0.353799i	−0.804015	+	0.594609i	$0.797307\pi$
$632$	−336.128			−0.531848
$633$	895.732	−	279.441i	1.41506	−	0.441455i
$634$	252.648	−	777.570i	0.398498	−	1.22645i
$635$	−919.068	−	273.464i	−1.44735	−	0.430653i
$636$	286.878	+	96.9558i	0.451065	+	0.152446i
$637$	−628.062	−	204.070i	−0.985968	−	0.320360i
$638$	−24.8815	+	76.5774i	−0.0389992	+	0.120027i
$639$	183.258	+	265.127i	0.286789	+	0.414909i
$640$	−56.5509	+	1.41158i	−0.0883608	+	0.00220559i
$641$	978.556	+	317.952i	1.52661	+	0.496025i	0.947644	−	0.319328i	$-0.103457\pi$
$641$	978.556	+	317.952i	1.52661	+	0.496025i	0.578964	+	0.815353i	$0.303457\pi$
$642$	−242.971	+	75.7997i	−0.378460	+	0.118068i
$643$			664.252i			1.03305i	0.856272	+	0.516526i	$0.172775\pi$
$643$			664.252i			1.03305i	−0.856272	+	0.516526i	$0.827225\pi$
$644$	−38.7613	+	53.3504i	−0.0601884	+	0.0828422i
$645$	−622.215	−	439.637i	−0.964674	−	0.681608i
$646$	639.385	−	464.541i	0.989760	−	0.719103i
$647$	534.360	−	388.235i	0.825904	−	0.600054i	−0.0924936	−	0.995713i	$-0.529484\pi$
$647$	534.360	−	388.235i	0.825904	−	0.600054i	0.918397	+	0.395659i	$0.129484\pi$
$648$	178.812	+	143.228i	0.275944	+	0.221031i
$649$	−81.7330			−0.125937
$650$	−523.671	+	199.549i	−0.805647	+	0.306998i
$651$	144.032	+	107.255i	0.221247	+	0.164754i
$652$	−235.334	+	76.4645i	−0.360941	+	0.117277i
$653$	−344.343	+	250.180i	−0.527325	+	0.383124i	−0.819356	−	0.573285i	$-0.805669\pi$
$653$	−344.343	+	250.180i	−0.527325	+	0.383124i	0.292031	+	0.956409i	$0.405669\pi$
$654$	−9.42235	+	801.331i	−0.0144073	+	1.22528i
$655$	26.3233	−	9.28534i	0.0401883	−	0.0141761i
$656$	52.9086	−	72.8225i	0.0806534	−	0.111010i
$657$	1004.41	−	300.434i	1.52879	−	0.457282i
$658$	105.535	−	145.256i	0.160387	−	0.220754i
$659$	567.227	+	184.303i	0.860738	+	0.279671i	0.705937	−	0.708275i	$-0.250526\pi$
$659$	567.227	+	184.303i	0.860738	+	0.279671i	0.154802	+	0.987946i	$0.450526\pi$
$660$	−15.3704	−	45.2637i	−0.0232885	−	0.0685813i
$661$	104.063	+	320.274i	0.157433	+	0.484529i	0.998399	−	0.0565584i	$-0.0180127\pi$
$661$	104.063	+	320.274i	0.157433	+	0.484529i	−0.840966	+	0.541088i	$0.818013\pi$
$662$	138.494	−	426.241i	0.209206	−	0.643868i
$663$	−902.657	+	639.740i	−1.36147	+	0.964916i
$664$	−110.864	−	341.206i	−0.166965	−	0.513864i
$665$	306.774	−	108.212i	0.461314	−	0.162725i
$666$	4.37177	−	185.875i	0.00656422	−	0.279091i
$667$	−255.660	+	351.886i	−0.383298	+	0.527565i
$668$	−351.886			−0.526775
$669$	127.428	+	408.463i	0.190475	+	0.610558i
$670$	217.651	+	284.369i	0.324853	+	0.424431i
$671$	39.2594	+	54.0359i	0.0585088	+	0.0805304i
$672$	−45.9647	−	0.540470i	−0.0683999	−	0.000804271i
$673$	1113.47	−	361.788i	1.65449	−	0.537576i	0.674782	−	0.738017i	$-0.264238\pi$
$673$	1113.47	−	361.788i	1.65449	−	0.537576i	0.979706	+	0.200442i	$0.0642377\pi$
$674$		−	40.6681i		−	0.0603384i
$675$	638.841	−	217.961i	0.946431	−	0.322905i
$676$	−164.481			−0.243316
$677$	−17.9307	−	55.1849i	−0.0264855	−	0.0815139i	0.936940	−	0.349490i	$-0.113645\pi$
$677$	−17.9307	−	55.1849i	−0.0264855	−	0.0815139i	−0.963426	+	0.267976i	$0.913645\pi$
$678$	4.81188	−	409.230i	0.00709717	−	0.603584i
$679$	292.873	−	212.784i	0.431329	−	0.313379i
$680$	−93.8386	+	315.376i	−0.137998	+	0.463788i
$681$	735.104	−	229.330i	1.07945	−	0.336755i
$682$			49.7987i			0.0730186i
$683$	241.858	+	175.720i	0.354111	+	0.257277i	0.750592	−	0.660766i	$-0.229769\pi$
$683$	241.858	+	175.720i	0.354111	+	0.257277i	−0.396481	+	0.918043i	$0.629769\pi$
$684$	−432.223	−	10.1659i	−0.631905	−	0.0148624i
$685$	−457.102	+	349.859i	−0.667302	+	0.510743i
$686$	−330.301	+	107.321i	−0.481488	+	0.156445i
$687$	401.465	+	566.457i	0.584374	+	0.824537i
$688$	−193.219	−	62.7808i	−0.280842	−	0.0912512i
$689$	760.822	−	247.206i	1.10424	−	0.358789i
$690$	−3.40799	−	258.202i	−0.00493911	−	0.374206i
$691$	357.640	−	1100.70i	0.517568	−	1.59291i	−0.260992	−	0.965341i	$-0.584050\pi$
$691$	357.640	−	1100.70i	0.517568	−	1.59291i	0.778560	−	0.627570i	$-0.215950\pi$
$692$	−11.7817	−	8.55987i	−0.0170255	−	0.0123698i
$693$	−11.1316	−	37.2152i	−0.0160629	−	0.0537015i
$694$	257.806	+	187.307i	0.371478	+	0.269894i
$695$	−220.108	+	739.747i	−0.316703	+	1.06438i
$696$	−303.172	−	3.56481i	−0.435592	−	0.00512185i
$697$	−307.752	−	423.584i	−0.441538	−	0.607725i
$698$	68.0321	+	209.381i	0.0974672	+	0.299973i
$699$	594.004	−	797.682i	0.849791	−	1.14118i
$700$	−74.0406	+	113.404i	−0.105772	+	0.162005i
$701$			309.274i			0.441190i	0.975366	+	0.220595i	$0.0707998\pi$
$701$			309.274i			0.441190i	−0.975366	+	0.220595i	$0.929200\pi$
$702$	604.858	+	21.3443i	0.861621	+	0.0304050i
$703$	206.232	+	283.855i	0.293361	+	0.403776i
$704$	−7.49265	−	10.3127i	−0.0106430	−	0.0146488i
$705$	9.27886	+	703.002i	0.0131615	+	0.997166i
$706$	72.5080	+	52.6801i	0.102703	+	0.0746178i
$707$	−411.716			−0.582342
$708$	−91.6572	−	293.802i	−0.129459	−	0.414974i
$709$	−152.491	+	469.319i	−0.215079	+	0.661944i	0.784069	+	0.620673i	$0.213141\pi$
$709$	−152.491	+	469.319i	−0.215079	+	0.661944i	−0.999148	+	0.0412710i	$0.986859\pi$
$710$	238.800	−	84.2347i	0.336338	−	0.118640i
$711$	879.829	−	608.147i	1.23745	−	0.855341i
$712$	287.753	+	93.4965i	0.404147	+	0.131315i
$713$	−83.1286	+	255.844i	−0.116590	+	0.358827i
$714$	−85.6091	+	253.305i	−0.119901	+	0.354768i
$715$	−103.985	−	71.6542i	−0.145433	−	0.100216i
$716$	225.133	+	73.1501i	0.314431	+	0.102165i
$717$	145.453	+	466.242i	0.202864	+	0.650267i
$718$		−	57.7767i		−	0.0804689i
$719$	−249.465	+	343.359i	−0.346961	+	0.477550i	−0.946458	−	0.322826i	$-0.895367\pi$
$719$	−249.465	+	343.359i	−0.346961	+	0.477550i	0.599498	+	0.800377i	$0.295367\pi$
$720$	145.471	−	106.011i	0.202042	−	0.147237i
$721$	−354.766	+	257.752i	−0.492047	+	0.357493i
$722$	247.032	−	179.479i	0.342150	−	0.248586i
$723$	−727.240	−	245.785i	−1.00586	−	0.339951i
$724$	258.152			0.356563
$725$	−488.353	+	747.983i	−0.673591	+	1.03170i
$726$	−300.174	+	403.101i	−0.413463	+	0.555235i
$727$	−651.165	+	211.576i	−0.895688	+	0.291027i	−0.720456	−	0.693501i	$-0.756067\pi$
$727$	−651.165	+	211.576i	−0.895688	+	0.291027i	−0.175232	+	0.984527i	$0.556067\pi$
$728$	−98.2440	+	71.3784i	−0.134951	+	0.0980473i
$729$	−727.187	−	51.3861i	−0.997513	−	0.0704885i
$730$	−20.5538	−	823.432i	−0.0281559	−	1.12799i
$731$	−694.605	+	956.041i	−0.950212	+	1.30785i
$732$	−150.214	+	201.721i	−0.205210	+	0.275575i
$733$	−736.608	+	1013.85i	−1.00492	+	1.38316i	−0.0826661	+	0.996577i	$0.526344\pi$
$733$	−736.608	+	1013.85i	−1.00492	+	1.38316i	−0.922256	+	0.386579i	$0.873656\pi$
$734$	−467.049	−	151.753i	−0.636306	−	0.206748i
$735$	360.629	−	510.395i	0.490652	−	0.694416i
$736$	−21.2789	−	65.4897i	−0.0289115	−	0.0889805i
$737$	−24.9363	+	76.7460i	−0.0338349	+	0.104133i
$738$	−6.73476	+	286.342i	−0.00912570	+	0.387997i
$739$	−332.312	−	1022.75i	−0.449677	−	1.38397i	−0.877272	−	0.479994i	$-0.840639\pi$
$739$	−332.312	−	1022.75i	−0.449677	−	1.38397i	0.427594	−	0.903971i	$-0.359361\pi$
$740$	−140.011	−	41.6596i	−0.189204	−	0.0562968i
$741$	−931.845	+	660.426i	−1.25755	+	0.891263i
$742$	113.638	−	156.409i	0.153151	−	0.210794i
$743$	1177.21			1.58440			0.792202	−	0.610258i	$-0.208934\pi$
$743$	1177.21			1.58440			0.792202	+	0.610258i	$0.208934\pi$
$744$	−179.009	+	55.8454i	−0.240604	+	0.0750610i
$745$	165.626	−	240.357i	0.222317	−	0.322626i
$746$	158.030	+	217.510i	0.211837	+	0.291569i
$747$	907.527	+	692.536i	1.21490	+	0.927090i
$748$	−70.5176	+	22.9125i	−0.0942748	+	0.0306317i
$749$			162.497i			0.216952i
$750$	−33.4470	−	529.274i	−0.0445960	−	0.705699i
$751$	−1113.51			−1.48270			−0.741349	−	0.671119i	$-0.765814\pi$
$751$	−1113.51			−1.48270			−0.741349	+	0.671119i	$0.765814\pi$
$752$	57.9356	+	178.308i	0.0770421	+	0.237111i
$753$	1110.60	+	13.0588i	1.47490	+	0.0173424i
$754$	−647.993	+	470.794i	−0.859407	+	0.624396i
$755$	779.330	+	537.025i	1.03223	+	0.711291i
$756$	121.292	−	81.7481i	0.160440	−	0.108132i
$757$			390.313i			0.515606i	0.966198	+	0.257803i	$0.0829985\pi$
$757$			390.313i			0.515606i	−0.966198	+	0.257803i	$0.917002\pi$
$758$	−275.698	−	200.306i	−0.363718	−	0.264256i
$759$	47.4746	−	33.6466i	0.0625489	−	0.0443302i
$760$	−96.8730	+	325.574i	−0.127464	+	0.428387i
$761$	−1070.12	+	347.702i	−1.40620	+	0.456901i	−0.911190	−	0.411987i	$-0.864835\pi$
$761$	−1070.12	+	347.702i	−1.40620	+	0.456901i	−0.495008	+	0.868889i	$0.664835\pi$
$762$	663.830	−	470.476i	0.871168	−	0.617422i
$763$	486.598	+	158.105i	0.637743	+	0.207215i
$764$	79.8780	−	25.9539i	0.104552	−	0.0339711i
$765$	−324.975	−	995.290i	−0.424804	−	1.30103i
$766$	185.650	−	571.370i	0.242362	−	0.745914i
$767$	−657.769	−	477.897i	−0.857587	−	0.623073i
$768$	28.6683	−	38.4984i	0.0373285	−	0.0501281i
$769$	−532.417	−	386.824i	−0.692350	−	0.503022i	0.185082	−	0.982723i	$-0.440745\pi$
$769$	−532.417	−	386.824i	−0.692350	−	0.503022i	−0.877432	+	0.479701i	$0.840745\pi$
$770$	−30.5095	+	0.761551i	−0.0396227	+	0.000989028i
$771$	−7.10437	+	604.196i	−0.00921448	+	0.783653i
$772$	−146.807	−	202.062i	−0.190164	−	0.261738i
$773$	−184.504	−	567.843i	−0.238685	−	0.734597i	−0.996611	−	0.0822566i	$-0.973787\pi$
$773$	−184.504	−	567.843i	−0.238685	−	0.734597i	0.757926	−	0.652340i	$-0.226213\pi$
$774$	619.348	−	185.256i	0.800191	−	0.239348i
$775$	−144.298	+	533.303i	−0.186191	+	0.688133i
$776$			378.014i			0.487131i
$777$	−112.454	−	38.0061i	−0.144729	−	0.0489139i
$778$	489.434	+	673.648i	0.629092	+	0.865872i
$779$	−317.703	−	437.281i	−0.407835	−	0.561337i
$780$	140.961	−	454.144i	0.180720	−	0.582235i
$781$	46.1635	+	33.5397i	0.0591082	+	0.0429446i
$782$	−400.535			−0.512194
$783$	800.015	−	539.190i	1.02173	−	0.688621i
$784$	51.4983	−	158.496i	0.0656867	−	0.202163i
$785$	−217.081	+	315.029i	−0.276537	+	0.401310i
$786$	−7.58340	+	22.4381i	−0.00964809	+	0.0285472i
$787$	−892.259	−	289.913i	−1.13375	−	0.368377i	−0.318748	−	0.947839i	$-0.603262\pi$
$787$	−892.259	−	289.913i	−1.13375	−	0.368377i	−0.814999	+	0.579463i	$0.803262\pi$
$788$	152.823	−	470.342i	0.193938	−	0.596881i
$789$	−287.780	−	97.2608i	−0.364740	−	0.123271i
$790$	−279.535	−	792.463i	−0.353841	−	1.00312i
$791$	−248.500	−	80.7425i	−0.314159	−	0.102076i
$792$	38.2709	+	13.4378i	0.0483218	+	0.0169669i
$793$			664.421i			0.837857i
$794$	63.8256	−	87.8484i	0.0803848	−	0.110640i
$795$	9.99132	+	756.981i	0.0125677	+	0.952177i
$796$	−214.860	+	156.105i	−0.269924	+	0.196111i
$797$	−128.891	+	93.6449i	−0.161720	+	0.117497i	−0.665702	−	0.746218i	$-0.731868\pi$
$797$	−128.891	+	93.6449i	−0.161720	+	0.117497i	0.503982	+	0.863714i	$0.331868\pi$
$798$	−88.3774	+	261.495i	−0.110749	+	0.327688i
$799$	1090.53			1.36487
$800$	−50.3575	−	132.152i	−0.0629469	−	0.165190i
$801$	−922.366	+	275.892i	−1.15152	+	0.344435i
$802$	−296.788	+	96.4322i	−0.370060	+	0.120240i
$803$	150.163	−	109.100i	0.187002	−	0.135865i
$804$	−303.840	−	3.57266i	−0.377910	−	0.00444360i
$805$	−158.015	−	47.0167i	−0.196292	−	0.0584058i
$806$	−291.176	+	400.769i	−0.361260	+	0.497232i
$807$	−723.793	−	538.981i	−0.896893	−	0.667883i
$808$	252.699	−	347.810i	0.312746	−	0.430458i
$809$	264.577	+	85.9661i	0.327042	+	0.106262i	0.467936	−	0.883762i	$-0.344998\pi$
$809$	264.577	+	85.9661i	0.327042	+	0.106262i	−0.140894	+	0.990025i	$0.544998\pi$
$810$	−188.972	+	540.684i	−0.233299	+	0.667511i
$811$	163.579	+	503.443i	0.201700	+	0.620769i	0.999833	+	0.0182871i	$0.00582130\pi$
$811$	163.579	+	503.443i	0.201700	+	0.620769i	−0.798133	+	0.602482i	$0.794179\pi$
$812$	−59.8168	+	184.097i	−0.0736660	+	0.226721i
$813$	−227.058	−	320.373i	−0.279284	−	0.394063i
$814$	−10.1720	−	31.3062i	−0.0124963	−	0.0384597i
$815$	−375.985	−	491.237i	−0.461332	−	0.602745i
$816$	−161.443	−	227.792i	−0.197846	−	0.279156i
$817$	−717.065	+	986.956i	−0.877681	+	1.20802i
$818$	150.288			0.183726
$819$	128.015	−	364.586i	0.156306	−	0.445160i
$820$	215.688	+	64.1771i	0.263035	+	0.0782648i
$821$	341.419	+	469.923i	0.415858	+	0.572379i	0.964635	−	0.263590i	$-0.0849065\pi$
$821$	341.419	+	469.923i	0.415858	+	0.572379i	−0.548777	+	0.835969i	$0.684906\pi$
$822$	5.74279	−	488.400i	0.00698636	−	0.594160i
$823$	369.062	−	119.916i	0.448435	−	0.145705i	−0.0760888	−	0.997101i	$-0.524243\pi$
$823$	369.062	−	119.916i	0.448435	−	0.145705i	0.524524	+	0.851396i	$0.324243\pi$
$824$		−	457.900i		−	0.555704i
$825$	93.9322	−	73.8803i	0.113857	−	0.0895519i
$826$	−196.492			−0.237883
$827$	120.659	+	371.350i	0.145900	+	0.449032i	0.997126	−	0.0757667i	$-0.0241404\pi$
$827$	120.659	+	371.350i	0.145900	+	0.449032i	−0.851226	+	0.524799i	$0.824140\pi$
$828$	174.187	+	132.923i	0.210371	+	0.160535i
$829$	838.932	−	609.519i	1.01198	−	0.735247i	0.0473567	−	0.998878i	$-0.484920\pi$
$829$	838.932	−	609.519i	1.01198	−	0.735247i	0.964623	+	0.263631i	$0.0849203\pi$
$830$	712.236	−	545.134i	0.858116	−	0.656788i
$831$	−288.402	−	924.456i	−0.347054	−	1.11246i
$832$		−	126.805i		−	0.152409i
$833$	−784.229	−	569.776i	−0.941452	−	0.684005i
$834$	−378.681	−	534.309i	−0.454053	−	0.640658i
$835$	−292.639	−	829.614i	−0.350466	−	0.993550i
$836$	−72.7978	+	23.6534i	−0.0870787	+	0.0282936i
$837$	367.524	−	470.054i	0.439097	−	0.561594i
$838$	888.153	+	288.579i	1.05985	+	0.344366i
$839$	−677.194	+	220.034i	−0.807144	+	0.262257i	−0.683388	−	0.730056i	$-0.739494\pi$
$839$	−677.194	+	220.034i	−0.807144	+	0.262257i	−0.123756	+	0.992313i	$0.539494\pi$
$840$	−36.9515	−	108.817i	−0.0439899	−	0.129544i
$841$	−134.654	+	414.421i	−0.160111	+	0.492772i
$842$	−452.407	−	328.693i	−0.537300	−	0.390371i
$843$	−738.084	−	549.623i	−0.875544	−	0.651985i
$844$	506.072	+	367.683i	0.599611	+	0.435643i
$845$	−136.788	−	387.785i	−0.161879	−	0.458917i
$846$	−474.256	−	361.906i	−0.560586	−	0.427785i
$847$	188.605	+	259.592i	0.222674	+	0.306484i
$848$	62.3841	+	191.999i	0.0735662	+	0.226413i
$849$	608.804	+	453.354i	0.717084	+	0.533985i
$850$	−821.577	+	41.0406i	−0.966561	+	0.0482830i
$851$		−	177.817i		−	0.208951i
$852$	−68.7950	+	203.554i	−0.0807453	+	0.238913i
$853$	116.328	+	160.112i	0.136375	+	0.187704i	0.871742	−	0.489965i	$-0.162990\pi$
$853$	116.328	+	160.112i	0.136375	+	0.187704i	−0.735367	+	0.677669i	$0.762990\pi$
$854$	94.3822	+	129.906i	0.110518	+	0.152115i
$855$	−335.483	−	1027.47i	−0.392378	−	1.20172i
$856$	−137.274	−	99.7356i	−0.160367	−	0.116514i
$857$	584.566			0.682107			0.341054	−	0.940044i	$-0.389216\pi$
$857$	584.566			0.682107			0.341054	+	0.940044i	$0.389216\pi$
$858$	102.292	−	31.9119i	0.119221	−	0.0371933i
$859$	186.893	−	575.198i	0.217571	−	0.669614i	−0.781390	−	0.624042i	$-0.785489\pi$
$859$	186.893	−	575.198i	0.217571	−	0.669614i	0.998961	−	0.0455712i	$-0.0145108\pi$
$860$	−12.6740	−	507.749i	−0.0147372	−	0.590406i
$861$	173.237	+	58.5489i	0.201205	+	0.0680010i
$862$	−209.202	−	67.9737i	−0.242693	−	0.0788558i
$863$	263.066	−	809.635i	0.304828	−	0.938164i	−0.674914	−	0.737897i	$-0.735819\pi$
$863$	263.066	−	809.635i	0.304828	−	0.938164i	0.979741	−	0.200267i	$-0.0641809\pi$
$864$	−5.38638	+	152.640i	−0.00623424	+	0.176667i
$865$	10.3830	−	34.8954i	0.0120034	−	0.0403415i
$866$	721.856	+	234.545i	0.833552	+	0.270837i
$867$	−722.665	+	225.449i	−0.833524	+	0.260034i
$868$			119.720i			0.137926i
$869$	111.302	−	153.195i	0.128081	−	0.176288i
$870$	−243.723	−	717.730i	−0.280141	−	0.824977i
$871$	−649.420	+	471.831i	−0.745603	+	0.541712i
$872$	−432.224	+	314.029i	−0.495669	+	0.360125i
$873$	−683.931	−	989.467i	−0.783426	−	1.13341i
$874$	−413.487			−0.473097
$875$	−328.938	−	80.2496i	−0.375929	−	0.0917138i
$876$	560.571	+	417.436i	0.639921	+	0.476525i
$877$	1245.95	−	404.834i	1.42070	−	0.461612i	0.504873	−	0.863193i	$-0.331539\pi$
$877$	1245.95	−	404.834i	1.42070	−	0.461612i	0.915824	+	0.401581i	$0.131539\pi$
$878$	656.189	−	476.749i	0.747368	−	0.542995i
$879$	11.6805	−	993.381i	0.0132884	−	1.13013i
$880$	18.0824	−	26.2412i	0.0205482	−	0.0298196i
$881$	−348.486	+	479.650i	−0.395558	+	0.544438i	−0.959622	−	0.281292i	$-0.909237\pi$
$881$	−348.486	+	479.650i	−0.395558	+	0.544438i	0.564065	+	0.825731i	$0.309237\pi$
$882$	151.963	+	508.044i	0.172293	+	0.576013i
$883$	−393.287	+	541.314i	−0.445399	+	0.613039i	−0.971401	−	0.237444i	$-0.923690\pi$
$883$	−393.287	+	541.314i	−0.445399	+	0.613039i	0.526002	+	0.850483i	$0.323690\pi$
$884$	−701.481	−	227.925i	−0.793530	−	0.257834i
$885$	616.449	−	460.428i	0.696553	−	0.520258i
$886$	−148.363	−	456.614i	−0.167452	−	0.515365i
$887$	−384.779	+	1184.23i	−0.433798	+	1.33509i	0.460515	+	0.887652i	$0.347665\pi$
$887$	−384.779	+	1184.23i	−0.433798	+	1.33509i	−0.894313	+	0.447442i	$0.852335\pi$
$888$	101.128	−	71.6723i	0.113883	−	0.0807121i
$889$	−160.524	−	494.041i	−0.180567	−	0.555727i
$890$	18.8748	+	756.167i	0.0212076	+	0.849626i
$891$	−124.488	+	34.0685i	−0.139718	+	0.0382363i
$892$	−167.667	+	230.774i	−0.187968	+	0.258715i
$893$	1125.79			1.26069
$894$	73.7631	+	236.443i	0.0825090	+	0.264478i
$895$	14.7673	+	591.612i	0.0164998	+	0.661019i
$896$	−18.0128	−	24.7925i	−0.0201036	−	0.0276702i
$897$	578.799	+	6.80573i	0.645261	+	0.00758722i
$898$	381.798	−	124.054i	0.425165	−	0.138144i
$899$			789.640i			0.878354i
$900$	370.912	+	254.803i	0.412124	+	0.283114i
$901$	1174.26			1.30329
$902$	15.6701	+	48.2276i	0.0173726	+	0.0534674i
$903$	4.85268	−	412.700i	0.00537395	−	0.457032i
$904$	220.731	−	160.371i	0.244172	−	0.177401i
$905$	214.687	+	608.625i	0.237224	+	0.672514i
$906$	−766.641	+	239.169i	−0.846183	+	0.263983i
$907$			60.8076i			0.0670425i	0.999438	+	0.0335213i	$0.0106721\pi$
$907$			60.8076i			0.0670425i	−0.999438	+	0.0335213i	$0.989328\pi$
$908$	415.320	+	301.748i	0.457401	+	0.332321i
$909$	−32.1661	+	1367.61i	−0.0353863	+	1.50452i
$910$	−249.986	−	172.262i	−0.274710	−	0.189299i
$911$	−288.931	+	93.8793i	−0.317158	+	0.103051i	−0.463270	−	0.886217i	$-0.653324\pi$
$911$	−288.931	+	93.8793i	−0.317158	+	0.103051i	0.146112	+	0.989268i	$0.453324\pi$
$912$	−166.663	−	235.157i	−0.182745	−	0.257848i
$913$	192.220	+	62.4559i	0.210536	+	0.0684074i
$914$	−845.322	+	274.662i	−0.924860	+	0.300505i
$915$	−600.505	−	186.390i	−0.656289	−	0.203705i
$916$	−143.033	+	440.210i	−0.156149	+	0.480579i
$917$	12.2335	+	8.88819i	0.0133408	+	0.00969268i
$918$	834.720	+	304.160i	0.909281	+	0.331329i
$919$	72.1242	+	52.4013i	0.0784812	+	0.0570199i	0.626334	−	0.779555i	$-0.284555\pi$
$919$	72.1242	+	52.4013i	0.0784812	+	0.0570199i	−0.547853	+	0.836575i	$0.684555\pi$
$920$	136.704	−	104.631i	0.148591	−	0.113729i
$921$	−1340.34	−	15.7603i	−1.45531	−	0.0171121i
$922$	404.581	+	556.859i	0.438808	+	0.603968i
$923$	175.405	+	539.841i	0.190038	+	0.584876i
$924$	15.4667	−	20.7701i	0.0167388	−	0.0224784i
$925$	−18.2199	−	364.739i	−0.0196972	−	0.394312i
$926$		−	586.958i		−	0.633864i
$927$	828.466	+	1198.57i	0.893707	+	1.29296i
$928$	−118.808	−	163.525i	−0.128026	−	0.176213i
$929$	−576.140	−	792.988i	−0.620172	−	0.853594i	0.377193	−	0.926135i	$-0.376889\pi$
$929$	−576.140	−	792.988i	−0.620172	−	0.853594i	−0.997365	+	0.0725410i	$0.976889\pi$
$930$	−280.532	−	375.593i	−0.301647	−	0.403864i
$931$	−809.588	−	588.200i	−0.869590	−	0.631794i
$932$	663.036			0.711412
$933$	371.710	+	1191.49i	0.398403	+	1.27706i
$934$	−347.323	+	1068.95i	−0.371866	+	1.14449i
$935$	−112.664	−	147.199i	−0.120496	−	0.157432i
$936$	229.424	+	331.916i	0.245111	+	0.354612i
$937$	511.887	+	166.322i	0.546304	+	0.177505i	0.569149	−	0.822234i	$-0.307273\pi$
$937$	511.887	+	166.322i	0.546304	+	0.177505i	−0.0228455	+	0.999739i	$0.507273\pi$
$938$	−59.9486	+	184.503i	−0.0639111	+	0.196698i
$939$	26.3598	−	77.9946i	0.0280722	−	0.0830614i
$940$	−372.201	+	284.877i	−0.395958	+	0.303060i
$941$	1460.60	+	474.577i	1.55218	+	0.504333i	0.954704	−	0.297556i	$-0.0961714\pi$
$941$	1460.60	+	474.577i	1.55218	+	0.504333i	0.597473	+	0.801889i	$0.296171\pi$
$942$	−96.6792	−	309.900i	−0.102632	−	0.328980i
$943$			273.930i			0.290488i
$944$	120.601	−	165.993i	0.127755	−	0.175840i
$945$	293.602	+	217.978i	0.310690	+	0.230664i
$946$	92.5942	−	67.2736i	0.0978797	−	0.0711138i
$947$	627.137	−	455.641i	0.662235	−	0.481142i	−0.205182	−	0.978724i	$-0.565779\pi$
$947$	627.137	−	455.641i	0.662235	−	0.481142i	0.867417	+	0.497582i	$0.165779\pi$
$948$	675.499	+	228.298i	0.712552	+	0.240821i
$949$	1846.39			1.94561
$950$	−848.143	+	42.3677i	−0.892783	+	0.0445976i
$951$	−1035.86	+	1391.05i	−1.08923	+	1.46272i
$952$	−169.529	+	55.0833i	−0.178077	+	0.0578606i
$953$	−340.354	+	247.282i	−0.357140	+	0.259477i	−0.751858	−	0.659325i	$-0.770842\pi$
$953$	−340.354	+	247.282i	−0.357140	+	0.259477i	0.394718	+	0.918802i	$0.370842\pi$
$954$	−510.671	−	389.694i	−0.535294	−	0.408485i
$955$	127.619	+	166.738i	0.133632	+	0.174595i
$956$	−191.384	+	263.418i	−0.200193	+	0.275542i
$957$	102.014	−	136.994i	0.106598	−	0.143150i
$958$	−251.682	+	346.410i	−0.262716	+	0.361597i
$959$	−296.575	−	96.3629i	−0.309254	−	0.100483i
$960$	114.606	+	35.5726i	0.119382	+	0.0370548i
$961$	−146.049	−	449.493i	−0.151976	−	0.467735i
$962$	101.187	−	311.422i	0.105184	−	0.323723i
$963$	539.770	+	12.6954i	0.560509	+	0.0131832i
$964$	−158.145	−	486.720i	−0.164051	−	0.504896i
$965$	354.297	−	514.156i	0.367147	−	0.532804i
$966$	114.132	−	80.8888i	0.118149	−	0.0837359i
$967$	−466.301	+	641.808i	−0.482214	+	0.663710i	−0.978928	−	0.204204i	$-0.934540\pi$
$967$	−466.301	+	641.808i	−0.482214	+	0.663710i	0.496715	+	0.867914i	$0.334540\pi$
$968$	−335.058			−0.346135
$969$	−1600.46	+	499.293i	−1.65166	+	0.515266i
$970$	−891.214	+	314.368i	−0.918778	+	0.324091i
$971$	−792.099	−	1090.23i	−0.815756	−	1.12279i	−0.990410	−	0.138162i	$-0.955880\pi$
$971$	−792.099	−	1090.23i	−0.815756	−	1.12279i	0.174653	−	0.984630i	$-0.444120\pi$
$972$	−262.069	−	409.287i	−0.269618	−	0.421077i
$973$	−397.648	+	129.204i	−0.408683	+	0.132789i
$974$			1142.60i			1.17310i
$975$	1187.93	−	45.3463i	1.21839	−	0.0465091i
$976$	−167.671			−0.171794
$977$	298.849	+	919.762i	0.305884	+	0.941414i	0.979346	+	0.202192i	$0.0648066\pi$
$977$	298.849	+	919.762i	0.305884	+	0.941414i	−0.673462	+	0.739222i	$0.735193\pi$
$978$	524.872	+	6.17164i	0.536679	+	0.00631047i
$979$	−137.896	+	100.187i	−0.140854	+	0.102337i
$980$	416.501	−	10.3963i	0.425001	−	0.0106085i
$981$	563.199	−	1603.99i	0.574108	−	1.63506i
$982$		−	507.784i		−	0.517091i
$983$	−633.042	−	459.932i	−0.643990	−	0.467886i	0.217229	−	0.976121i	$-0.430298\pi$
$983$	−633.042	−	459.932i	−0.643990	−	0.467886i	−0.861219	+	0.508234i	$0.830298\pi$
$984$	−155.789	+	110.412i	−0.158322	+	0.112207i
$985$	1235.98	−	30.8515i	1.25480	−	0.0313214i
$986$	−1118.17	+	363.316i	−1.13405	+	0.368475i
$987$	−310.746	+	220.235i	−0.314838	+	0.223135i
$988$	−724.164	−	235.295i	−0.732959	−	0.238153i
$989$	588.007	−	191.055i	0.594547	−	0.193180i
$990$	0.146053	+	101.404i	0.000147529	+	0.102428i
$991$	146.977	−	452.348i	0.148312	−	0.456456i	−0.849110	−	0.528216i	$-0.822861\pi$
$991$	146.977	−	452.348i	0.148312	−	0.456456i	0.997422	+	0.0717592i	$0.0228613\pi$
$992$	−101.137	−	73.4802i	−0.101952	−	0.0740728i
$993$	−567.827	+	762.529i	−0.571830	+	0.767905i
$994$	110.980	+	80.6318i	0.111650	+	0.0811186i
$995$	−546.720	−	376.736i	−0.549467	−	0.378629i
$996$	−8.94815	+	761.003i	−0.00898409	+	0.764059i
$997$	−408.159	−	561.782i	−0.409387	−	0.563473i	0.553682	−	0.832728i	$-0.313222\pi$
$997$	−408.159	−	561.782i	−0.409387	−	0.563473i	−0.963069	+	0.269256i	$0.913222\pi$
$998$	300.870	+	925.982i	0.301473	+	0.927838i
$999$	−135.032	+	370.574i	−0.135167	+	0.370944i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.3.i.a.119.5	yes	80
3.2	odd	2	inner	150.3.i.a.119.20	yes	80
25.4	even	10	inner	150.3.i.a.29.20	yes	80
75.29	odd	10	inner	150.3.i.a.29.5	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.3.i.a.29.5	✓	80	75.29	odd	10	inner
150.3.i.a.29.20	yes	80	25.4	even	10	inner
150.3.i.a.119.5	yes	80	1.1	even	1	trivial
150.3.i.a.119.20	yes	80	3.2	odd	2	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 $\F_{q}$
Belyi maps

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Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	150.3.i.a.119.5

Level	$150$
Weight	$3$
Character	150.119
Analytic conductor	$4.087$
Analytic rank	$0$
Dimension	$80$
Inner twists	$4$