LMFDB - Embedded newform 143.4.e.b.100.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(100,143)]

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([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("143.100");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.16
Character	$\chi$	$=$	143.100
Dual form			143.4.e.b.133.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.54066 - 4.40055i) q^{2} +(3.69680 - 6.40305i) q^{3} +(-8.90987 - 15.4324i) q^{4} +8.39690 q^{5} +(-18.7846 - 32.5359i) q^{6} +(7.09626 + 12.2911i) q^{7} -49.8972 q^{8} +(-13.8327 - 23.9589i) q^{9} +O(q^{10})$	\(q+(2.54066 - 4.40055i) q^{2} +(3.69680 - 6.40305i) q^{3} +(-8.90987 - 15.4324i) q^{4} +8.39690 q^{5} +(-18.7846 - 32.5359i) q^{6} +(7.09626 + 12.2911i) q^{7} -49.8972 q^{8} +(-13.8327 - 23.9589i) q^{9} +(21.3336 - 36.9509i) q^{10} +(-5.50000 + 9.52628i) q^{11} -131.752 q^{12} +(35.3970 + 30.7254i) q^{13} +72.1166 q^{14} +(31.0417 - 53.7657i) q^{15} +(-55.4927 + 96.1161i) q^{16} +(8.45781 + 14.6494i) q^{17} -140.576 q^{18} +(20.5587 + 35.6086i) q^{19} +(-74.8153 - 129.584i) q^{20} +104.934 q^{21} +(27.9472 + 48.4060i) q^{22} +(-65.8718 + 114.093i) q^{23} +(-184.460 + 319.494i) q^{24} -54.4921 q^{25} +(225.140 - 77.7033i) q^{26} -4.91923 q^{27} +(126.454 - 219.024i) q^{28} +(48.6894 - 84.3326i) q^{29} +(-157.732 - 273.201i) q^{30} -14.2202 q^{31} +(82.3868 + 142.698i) q^{32} +(40.6648 + 70.4335i) q^{33} +85.9535 q^{34} +(59.5866 + 103.207i) q^{35} +(-246.495 + 426.941i) q^{36} +(-182.315 + 315.779i) q^{37} +208.930 q^{38} +(327.592 - 113.063i) q^{39} -418.982 q^{40} +(57.2453 - 99.1517i) q^{41} +(266.601 - 461.766i) q^{42} +(-253.515 - 439.100i) q^{43} +196.017 q^{44} +(-116.152 - 201.180i) q^{45} +(334.715 + 579.744i) q^{46} -316.377 q^{47} +(410.291 + 710.644i) q^{48} +(70.7862 - 122.605i) q^{49} +(-138.446 + 239.795i) q^{50} +125.067 q^{51} +(158.783 - 820.019i) q^{52} -456.545 q^{53} +(-12.4981 + 21.6473i) q^{54} +(-46.1829 + 79.9912i) q^{55} +(-354.083 - 613.290i) q^{56} +304.005 q^{57} +(-247.406 - 428.520i) q^{58} +(300.452 + 520.397i) q^{59} -1106.31 q^{60} +(-332.902 - 576.603i) q^{61} +(-36.1286 + 62.5766i) q^{62} +(196.320 - 340.037i) q^{63} -50.6164 q^{64} +(297.225 + 257.998i) q^{65} +413.261 q^{66} +(404.206 - 700.105i) q^{67} +(150.716 - 261.048i) q^{68} +(487.030 + 843.560i) q^{69} +605.556 q^{70} +(247.698 + 429.025i) q^{71} +(690.211 + 1195.48i) q^{72} +494.502 q^{73} +(926.401 + 1604.57i) q^{74} +(-201.446 + 348.915i) q^{75} +(366.350 - 634.537i) q^{76} -156.118 q^{77} +(334.761 - 1728.84i) q^{78} -643.276 q^{79} +(-465.966 + 807.077i) q^{80} +(355.297 - 615.392i) q^{81} +(-290.881 - 503.821i) q^{82} +814.591 q^{83} +(-934.947 - 1619.38i) q^{84} +(71.0194 + 123.009i) q^{85} -2576.37 q^{86} +(-359.990 - 623.521i) q^{87} +(274.435 - 475.335i) q^{88} +(350.572 - 607.209i) q^{89} -1180.40 q^{90} +(-126.463 + 653.103i) q^{91} +2347.64 q^{92} +(-52.5692 + 91.0525i) q^{93} +(-803.805 + 1392.23i) q^{94} +(172.629 + 299.002i) q^{95} +1218.27 q^{96} +(405.147 + 701.735i) q^{97} +(-359.687 - 622.996i) q^{98} +304.319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) $ 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * 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 $

$2$	2.54066	−	4.40055i	0.898258	−	1.55583i	0.0685375	−	0.997649i	$-0.478167\pi$
$2$	2.54066	−	4.40055i	0.898258	−	1.55583i	0.829720	−	0.558180i	$-0.188500\pi$
$3$	3.69680	−	6.40305i	0.711450	−	1.23227i	−0.252863	−	0.967502i	$-0.581372\pi$
$3$	3.69680	−	6.40305i	0.711450	−	1.23227i	0.964313	−	0.264765i	$-0.0852943\pi$
$4$	−8.90987	−	15.4324i	−1.11373	−	1.92904i
$5$	8.39690			0.751042			0.375521	−	0.926814i	$-0.377464\pi$
$5$	8.39690			0.751042			0.375521	+	0.926814i	$0.377464\pi$
$6$	−18.7846	−	32.5359i	−1.27813	−	2.21379i
$7$	7.09626	+	12.2911i	0.383162	+	0.663656i	0.991512	−	0.130013i	$-0.0415018\pi$
$7$	7.09626	+	12.2911i	0.383162	+	0.663656i	−0.608350	+	0.793669i	$0.708168\pi$
$8$	−49.8972			−2.20517
$9$	−13.8327	−	23.9589i	−0.512321	−	0.887366i
$10$	21.3336	−	36.9509i	0.674629	−	1.16849i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$12$	−131.752			−3.16946
$13$	35.3970	+	30.7254i	0.755181	+	0.655516i
$13$	35.3970	+	30.7254i	0.755181	+	0.655516i
$14$	72.1166			1.37671
$15$	31.0417	−	53.7657i	0.534328	−	0.925484i
$16$	−55.4927	+	96.1161i	−0.867073	+	1.50181i
$17$	8.45781	+	14.6494i	0.120666	+	0.208999i	0.920030	−	0.391847i	$-0.128164\pi$
$17$	8.45781	+	14.6494i	0.120666	+	0.208999i	−0.799365	+	0.600846i	$0.794830\pi$
$18$	−140.576			−1.84079
$19$	20.5587	+	35.6086i	0.248236	+	0.429957i	0.963036	−	0.269371i	$-0.0868159\pi$
$19$	20.5587	+	35.6086i	0.248236	+	0.429957i	−0.714801	+	0.699328i	$0.753483\pi$
$20$	−74.8153	−	129.584i	−0.836460	−	1.44879i
$21$	104.934			1.09040
$22$	27.9472	+	48.4060i	0.270835	+	0.469100i
$23$	−65.8718	+	114.093i	−0.597183	+	1.03435i	0.396051	+	0.918228i	$0.370380\pi$
$23$	−65.8718	+	114.093i	−0.597183	+	1.03435i	−0.993235	+	0.116124i	$0.962953\pi$
$24$	−184.460	+	319.494i	−1.56886	+	2.71735i
$25$	−54.4921			−0.435937
$26$	225.140	−	77.7033i	1.69822	−	0.586110i
$27$	−4.91923			−0.0350632
$28$	126.454	−	219.024i	0.853481	−	1.47827i
$29$	48.6894	−	84.3326i	0.311772	−	0.540006i	−0.666974	−	0.745081i	$-0.732411\pi$
$29$	48.6894	−	84.3326i	0.311772	−	0.540006i	0.978746	+	0.205076i	$0.0657440\pi$
$30$	−157.732	−	273.201i	−0.959929	−	1.66265i
$31$	−14.2202			−0.0823878			−0.0411939	−	0.999151i	$-0.513116\pi$
$31$	−14.2202			−0.0823878			−0.0411939	+	0.999151i	$0.513116\pi$
$32$	82.3868	+	142.698i	0.455127	+	0.788303i
$33$	40.6648	+	70.4335i	0.214510	+	0.371542i
$34$	85.9535			0.433556
$35$	59.5866	+	103.207i	0.287771	+	0.498433i
$36$	−246.495	+	426.941i	−1.14118	+	1.97658i
$37$	−182.315	+	315.779i	−0.810066	+	1.40308i	0.102752	+	0.994707i	$0.467235\pi$
$37$	−182.315	+	315.779i	−0.810066	+	1.40308i	−0.912817	+	0.408368i	$0.866098\pi$
$38$	208.930			0.891919
$39$	327.592	−	113.063i	1.34504	−	0.464219i
$40$	−418.982			−1.65617
$41$	57.2453	−	99.1517i	0.218054	−	0.377680i	−0.736159	−	0.676809i	$-0.763362\pi$
$41$	57.2453	−	99.1517i	0.218054	−	0.377680i	0.954213	+	0.299128i	$0.0966958\pi$
$42$	266.601	−	461.766i	0.979462	−	1.69648i
$43$	−253.515	−	439.100i	−0.899084	−	1.55726i	−0.828667	−	0.559741i	$-0.810900\pi$
$43$	−253.515	−	439.100i	−0.899084	−	1.55726i	−0.0704166	−	0.997518i	$-0.522433\pi$
$44$	196.017			0.671607
$45$	−116.152	−	201.180i	−0.384774	−	0.666449i
$46$	334.715	+	579.744i	1.07285	+	1.85823i
$47$	−316.377			−0.981879			−0.490939	−	0.871194i	$-0.663346\pi$
$47$	−316.377			−0.981879			−0.490939	+	0.871194i	$0.663346\pi$
$48$	410.291	+	710.644i	1.23376	+	2.13693i
$49$	70.7862	−	122.605i	0.206374	−	0.357450i
$50$	−138.446	+	239.795i	−0.391583	+	0.678242i
$51$	125.067			0.343391
$52$	158.783	−	820.019i	0.423448	−	2.18685i
$53$	−456.545			−1.18323			−0.591616	−	0.806220i	$-0.701510\pi$
$53$	−456.545			−1.18323			−0.591616	+	0.806220i	$0.701510\pi$
$54$	−12.4981	+	21.6473i	−0.0314958	+	0.0545523i
$55$	−46.1829	+	79.9912i	−0.113224	+	0.196109i
$56$	−354.083	−	613.290i	−0.844935	−	1.46347i
$57$	304.005			0.706429
$58$	−247.406	−	428.520i	−0.560104	−	0.970129i
$59$	300.452	+	520.397i	0.662974	+	1.14830i	0.979830	+	0.199831i	$0.0640393\pi$
$59$	300.452	+	520.397i	0.662974	+	1.14830i	−0.316857	+	0.948473i	$0.602627\pi$
$60$	−1106.31			−2.38040
$61$	−332.902	−	576.603i	−0.698749	−	1.21027i	−0.968900	−	0.247451i	$-0.920407\pi$
$61$	−332.902	−	576.603i	−0.698749	−	1.21027i	0.270151	−	0.962818i	$-0.412926\pi$
$62$	−36.1286	+	62.5766i	−0.0740055	+	0.128181i
$63$	196.320	−	340.037i	0.392604	−	0.680010i
$64$	−50.6164			−0.0988601
$65$	297.225	+	257.998i	0.567173	+	0.492320i
$66$	413.261			0.770742
$67$	404.206	−	700.105i	0.737038	−	1.27659i	−0.216785	−	0.976219i	$-0.569557\pi$
$67$	404.206	−	700.105i	0.737038	−	1.27659i	0.953823	−	0.300369i	$-0.0971097\pi$
$68$	150.716	−	261.048i	0.268779	−	0.465539i
$69$	487.030	+	843.560i	0.849732	+	1.47178i
$70$	605.556			1.03397
$71$	247.698	+	429.025i	0.414033	+	0.717126i	0.995326	−	0.0965679i	$-0.0307865\pi$
$71$	247.698	+	429.025i	0.414033	+	0.717126i	−0.581293	+	0.813694i	$0.697453\pi$
$72$	690.211	+	1195.48i	1.12975	+	1.95679i
$73$	494.502			0.792837			0.396419	−	0.918070i	$-0.370253\pi$
$73$	494.502			0.792837			0.396419	+	0.918070i	$0.370253\pi$
$74$	926.401	+	1604.57i	1.45530	+	2.52065i
$75$	−201.446	+	348.915i	−0.310147	+	0.537190i
$76$	366.350	−	634.537i	0.552937	−	0.957715i
$77$	−156.118			−0.231055
$78$	334.761	−	1728.84i	0.485952	−	2.50965i
$79$	−643.276			−0.916130			−0.458065	−	0.888919i	$-0.651457\pi$
$79$	−643.276			−0.916130			−0.458065	+	0.888919i	$0.651457\pi$
$80$	−465.966	+	807.077i	−0.651208	+	1.12792i
$81$	355.297	−	615.392i	0.487375	−	0.844159i
$82$	−290.881	−	503.821i	−0.391737	−	0.678509i
$83$	814.591			1.07727			0.538633	−	0.842541i	$-0.318941\pi$
$83$	814.591			1.07727			0.538633	+	0.842541i	$0.318941\pi$
$84$	−934.947	−	1619.38i	−1.21442	−	2.10343i
$85$	71.0194	+	123.009i	0.0906251	+	0.156967i
$86$	−2576.37			−3.23044
$87$	−359.990	−	623.521i	−0.443621	−	0.768374i
$88$	274.435	−	475.335i	0.332441	−	0.575805i
$89$	350.572	−	607.209i	0.417535	−	0.723191i	−0.578156	−	0.815926i	$-0.696228\pi$
$89$	350.572	−	607.209i	0.417535	−	0.723191i	0.995691	+	0.0927349i	$0.0295609\pi$
$90$	−1180.40			−1.38251
$91$	−126.463	+	653.103i	−0.145680	+	0.752349i
$92$	2347.64			2.66041
$93$	−52.5692	+	91.0525i	−0.0586148	+	0.101524i
$94$	−803.805	+	1392.23i	−0.881980	+	1.52763i
$95$	172.629	+	299.002i	0.186435	+	0.322915i
$96$	1218.27			1.29520
$97$	405.147	+	701.735i	0.424087	+	0.734540i	0.996335	−	0.0855408i	$-0.0272618\pi$
$97$	405.147	+	701.735i	0.424087	+	0.734540i	−0.572248	+	0.820081i	$0.693928\pi$
$98$	−359.687	−	622.996i	−0.370754	−	0.642164i
$99$	304.319			0.308941
$100$	485.517	+	840.941i	0.485517	+	0.840941i
$101$	−353.670	+	612.574i	−0.348430	+	0.603499i	−0.985971	−	0.166918i	$-0.946619\pi$
$101$	−353.670	+	612.574i	−0.348430	+	0.603499i	0.637540	+	0.770417i	$0.279952\pi$
$102$	317.753	−	550.364i	0.308453	−	0.534257i
$103$	1849.13			1.76893			0.884467	−	0.466602i	$-0.154522\pi$
$103$	1849.13			1.76893			0.884467	+	0.466602i	$0.154522\pi$
$104$	−1766.21	−	1533.11i	−1.66530	−	1.44552i
$105$	881.119			0.818937
$106$	−1159.92	+	2009.05i	−1.06285	+	1.84091i
$107$	−1005.03	+	1740.76i	−0.908036	+	1.57276i	−0.0912464	+	0.995828i	$0.529085\pi$
$107$	−1005.03	+	1740.76i	−0.908036	+	1.57276i	−0.816789	+	0.576936i	$0.804248\pi$
$108$	43.8297	+	75.9152i	0.0390510	+	0.0676384i
$109$	−1655.72			−1.45495			−0.727475	−	0.686134i	$-0.759307\pi$
$109$	−1655.72			−1.45495			−0.727475	+	0.686134i	$0.759307\pi$
$110$	234.670	+	406.460i	0.203408	+	0.352313i
$111$	1347.97	+	2334.75i	1.15264	+	1.99643i
$112$	−1575.16			−1.32892
$113$	−84.6179	−	146.563i	−0.0704441	−	0.122013i	0.828652	−	0.559764i	$-0.189108\pi$
$113$	−84.6179	−	146.563i	−0.0704441	−	0.122013i	−0.899096	+	0.437751i	$0.855775\pi$
$114$	772.372	−	1337.79i	0.634555	−	1.09908i
$115$	−553.119	+	958.030i	−0.448509	+	0.776841i
$116$	−1735.27			−1.38893
$117$	246.513	−	1273.09i	0.194787	−	1.00596i
$118$	3053.38			2.38209
$119$	−120.038	+	207.911i	−0.0924691	+	0.160161i
$120$	−1548.89	+	2682.76i	−1.17828	+	2.04084i
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$	−3383.16			−2.51063
$123$	−423.249	−	733.088i	−0.310269	−	0.537401i
$124$	126.700	+	219.451i	0.0917581	+	0.158930i
$125$	−1507.18			−1.07845
$126$	−997.565	−	1727.83i	−0.705319	−	1.22165i
$127$	−299.009	+	517.899i	−0.208919	+	0.361859i	−0.951374	−	0.308037i	$-0.900328\pi$
$127$	−299.009	+	517.899i	−0.208919	+	0.361859i	0.742455	+	0.669896i	$0.233661\pi$
$128$	−787.693	+	1364.32i	−0.543929	+	0.942112i
$129$	−3748.77			−2.55861
$130$	1890.48	−	652.467i	1.27543	−	0.440193i
$131$	2576.77			1.71858			0.859288	−	0.511493i	$-0.170907\pi$
$131$	2576.77			1.71858			0.859288	+	0.511493i	$0.170907\pi$
$132$	724.636	−	1255.11i	0.477814	−	0.827599i
$133$	−291.779	+	505.376i	−0.190229	+	0.329486i
$134$	−2053.90	−	3557.45i	−1.32410	−	2.29341i
$135$	−41.3063			−0.0263339
$136$	−422.021	−	730.961i	−0.266088	−	0.460878i
$137$	−1073.27	−	1858.96i	−0.669312	−	1.15928i	−0.978097	−	0.208150i	$-0.933256\pi$
$137$	−1073.27	−	1858.96i	−0.669312	−	1.15928i	0.308785	−	0.951132i	$-0.400078\pi$
$138$	4949.50			3.05311
$139$	−86.0733	−	149.083i	−0.0525226	−	0.0909718i	0.838569	−	0.544796i	$-0.183393\pi$
$139$	−86.0733	−	149.083i	−0.0525226	−	0.0909718i	−0.891091	+	0.453824i	$0.850059\pi$
$140$	1061.82	−	1839.12i	0.641000	−	1.11024i
$141$	−1169.58	+	2025.77i	−0.698557	+	1.20994i
$142$	2517.26			1.48763
$143$	−487.383	+	168.212i	−0.285014	+	0.0983676i
$144$	3070.45			1.77688
$145$	408.840	−	708.132i	0.234154	−	0.405567i
$146$	1256.36	−	2176.08i	0.712172	−	1.23352i
$147$	−523.365	−	906.495i	−0.293649	−	0.508615i
$148$	6497.62			3.60879
$149$	−1001.02	−	1733.81i	−0.550379	−	0.953284i	−0.998247	−	0.0591847i	$-0.981150\pi$
$149$	−1001.02	−	1733.81i	−0.550379	−	0.953284i	0.447868	−	0.894100i	$-0.352183\pi$
$150$	1023.61	+	1772.95i	0.557184	+	0.965071i
$151$	805.224			0.433962			0.216981	−	0.976176i	$-0.430379\pi$
$151$	805.224			0.433962			0.216981	+	0.976176i	$0.430379\pi$
$152$	−1025.82	−	1776.77i	−0.547401	−	0.948126i
$153$	233.988	−	405.279i	0.123639	−	0.214150i
$154$	−396.641	+	687.003i	−0.207547	+	0.359482i
$155$	−119.405			−0.0618766
$156$	−4663.63	−	4048.14i	−2.39352	−	2.07763i
$157$	−868.349			−0.441413			−0.220706	−	0.975340i	$-0.570836\pi$
$157$	−868.349			−0.441413			−0.220706	+	0.975340i	$0.570836\pi$
$158$	−1634.34	+	2830.77i	−0.822920	+	1.42534i
$159$	−1687.76	+	2923.28i	−0.841810	+	1.45806i
$160$	691.794	+	1198.22i	0.341819	+	0.592048i
$161$	−1869.77			−0.915272
$162$	−1805.37	−	3127.00i	−0.875577	−	1.51654i
$163$	693.856	+	1201.79i	0.333417	+	0.577496i	0.983180	−	0.182642i	$-0.0584649\pi$
$163$	693.856	+	1201.79i	0.333417	+	0.577496i	−0.649762	+	0.760138i	$0.725132\pi$
$164$	−2040.19			−0.971416
$165$	341.458	+	591.423i	0.161106	+	0.279044i
$166$	2069.60	−	3584.65i	0.967662	−	1.67604i
$167$	−176.629	+	305.931i	−0.0818443	+	0.141758i	−0.904042	−	0.427443i	$-0.859414\pi$
$167$	−176.629	+	305.931i	−0.0818443	+	0.141758i	0.822198	+	0.569202i	$0.192748\pi$
$168$	−5235.90			−2.40452
$169$	308.894	+	2175.18i	0.140598	+	0.990067i
$170$	721.743			0.325619
$171$	568.762	−	985.125i	0.254353	−	0.440552i
$172$	−4517.56	+	7824.65i	−2.00268	+	3.46874i
$173$	427.033	+	739.643i	0.187669	+	0.325052i	0.944473	−	0.328590i	$-0.106573\pi$
$173$	427.033	+	739.643i	0.187669	+	0.325052i	−0.756804	+	0.653642i	$0.773240\pi$
$174$	−3658.45			−1.59394
$175$	−386.690	−	669.767i	−0.167034	−	0.289312i
$176$	−610.419	−	1057.28i	−0.261432	−	0.452814i
$177$	4442.84			1.88669
$178$	−1781.37	−	3085.42i	−0.750107	−	1.29922i
$179$	−1019.09	+	1765.12i	−0.425534	+	0.737047i	−0.996470	−	0.0839477i	$-0.973247\pi$
$179$	−1019.09	+	1765.12i	−0.425534	+	0.737047i	0.570936	+	0.820995i	$0.306580\pi$
$180$	−2069.79	+	3584.98i	−0.857073	+	1.48449i
$181$	3743.92			1.53748			0.768738	−	0.639564i	$-0.220885\pi$
$181$	3743.92			1.53748			0.768738	+	0.639564i	$0.220885\pi$
$182$	2552.71	+	2215.82i	1.03967	+	0.902457i
$183$	−4922.69			−1.98850
$184$	3286.82	−	5692.93i	1.31689	−	2.28092i
$185$	−1530.88	+	2651.57i	−0.608393	+	1.05377i
$186$	267.121	+	462.666i	0.105302	+	0.182389i
$187$	−186.072			−0.0727642
$188$	2818.88	+	4882.44i	1.09355	+	1.89409i
$189$	−34.9081	−	60.4626i	−0.0134349	−	0.0232699i
$190$	1754.36			0.669868
$191$	577.361	+	1000.02i	0.218725	+	0.378842i	0.954418	−	0.298472i	$-0.0964770\pi$
$191$	577.361	+	1000.02i	0.218725	+	0.378842i	−0.735694	+	0.677314i	$0.763144\pi$
$192$	−187.119	+	324.099i	−0.0703340	+	0.121822i
$193$	2123.95	−	3678.79i	0.792151	−	1.37205i	−0.132481	−	0.991186i	$-0.542294\pi$
$193$	2123.95	−	3678.79i	0.792151	−	1.37205i	0.924632	−	0.380861i	$-0.124372\pi$
$194$	4117.36			1.52376
$195$	2750.76	−	949.376i	1.01018	−	0.348647i
$196$	−2522.78			−0.919382
$197$	265.179	−	459.304i	0.0959048	−	0.166112i	−0.814081	−	0.580751i	$-0.802759\pi$
$197$	265.179	−	459.304i	0.0959048	−	0.166112i	0.909986	+	0.414639i	$0.136092\pi$
$198$	773.169	−	1339.17i	0.277509	−	0.480659i
$199$	1313.65	+	2275.31i	0.467951	+	0.810515i	0.999329	−	0.0366197i	$-0.0116590\pi$
$199$	1313.65	+	2275.31i	0.467951	+	0.810515i	−0.531378	+	0.847135i	$0.678326\pi$
$200$	2719.00			0.961312
$201$	−2988.53	−	5176.29i	−1.04873	−	1.81646i
$202$	1797.11	+	3112.68i	0.625960	+	1.08420i
$203$	1382.05			0.477837
$204$	−1114.33	−	1930.08i	−0.382446	−	0.662416i
$205$	480.683	−	832.567i	0.163768	−	0.283654i
$206$	4698.01	−	8137.18i	1.58896	−	2.75216i
$207$	3644.73			1.22380
$208$	−4917.48	+	1697.18i	−1.63926	+	0.565762i
$209$	−452.290			−0.149692
$210$	2238.62	−	3877.40i	0.735616	−	1.27413i
$211$	−74.7655	+	129.498i	−0.0243937	+	0.0422511i	−0.877965	−	0.478726i	$-0.841099\pi$
$211$	−74.7655	+	129.498i	−0.0243937	+	0.0422511i	0.853571	+	0.520977i	$0.174432\pi$
$212$	4067.76	+	7045.57i	1.31781	+	2.28251i
$213$	3662.76			1.17825
$214$	5106.87	+	8845.35i	1.63130	+	2.82550i
$215$	−2128.74	−	3687.08i	−0.675249	−	1.16957i
$216$	245.456			0.0773201
$217$	−100.910	−	174.781i	−0.0315679	−	0.0546771i
$218$	−4206.63	+	7286.09i	−1.30692	+	2.26365i
$219$	1828.08	−	3166.32i	0.564064	−	0.976987i
$220$	1645.94			0.504405
$221$	−150.727	+	778.413i	−0.0458778	+	0.236931i
$222$	13698.9			4.14148
$223$	258.241	−	447.287i	0.0775475	−	0.134316i	−0.824644	−	0.565652i	$-0.808624\pi$
$223$	258.241	−	447.287i	0.0775475	−	0.134316i	0.902191	+	0.431336i	$0.141958\pi$
$224$	−1169.28	+	2025.25i	−0.348775	+	0.604095i
$225$	753.771	+	1305.57i	0.223339	+	0.386835i
$226$	−859.940			−0.253108
$227$	−2606.63	−	4514.81i	−0.762150	−	1.32008i	−0.941740	−	0.336341i	$-0.890811\pi$
$227$	−2606.63	−	4514.81i	−0.762150	−	1.32008i	0.179590	−	0.983741i	$-0.442523\pi$
$228$	−2708.64	−	4691.51i	−0.786774	−	1.36273i
$229$	879.485			0.253790			0.126895	−	0.991916i	$-0.459499\pi$
$229$	879.485			0.253790			0.126895	+	0.991916i	$0.459499\pi$
$230$	2810.57	+	4868.05i	0.805754	+	1.39561i
$231$	−577.136	+	999.629i	−0.164384	+	0.284722i
$232$	−2429.47	+	4207.96i	−0.687510	+	1.19080i
$233$	5310.87			1.49325			0.746624	−	0.665246i	$-0.231673\pi$
$233$	5310.87			1.49325			0.746624	+	0.665246i	$0.231673\pi$
$234$	−4975.98	−	4319.27i	−1.39013	−	1.20666i
$235$	−2656.58			−0.737432
$236$	5353.97	−	9273.35i	1.47675	−	2.55781i
$237$	−2378.06	+	4118.93i	−0.651780	+	1.12892i
$238$	609.948	+	1056.46i	0.166122	+	0.287732i
$239$	−2999.57			−0.811825			−0.405913	−	0.913912i	$-0.633046\pi$
$239$	−2999.57			−0.811825			−0.405913	+	0.913912i	$0.633046\pi$
$240$	3445.17	+	5967.21i	0.926603	+	1.60492i
$241$	−181.564	−	314.478i	−0.0485294	−	0.0840553i	0.840740	−	0.541439i	$-0.182120\pi$
$241$	−181.564	−	314.478i	−0.0485294	−	0.0840553i	−0.889270	+	0.457383i	$0.848787\pi$
$242$	−614.839			−0.163320
$243$	−2693.33	−	4664.99i	−0.711018	−	1.23152i
$244$	−5932.22	+	10274.9i	−1.55644	+	2.69584i
$245$	594.385	−	1029.50i	0.154995	−	0.268460i
$246$	−4301.32			−1.11480
$247$	−366.377	+	1892.11i	−0.0943805	+	0.487418i
$248$	709.547			0.181679
$249$	3011.38	−	5215.87i	0.766420	−	1.32748i
$250$	−3829.22	+	6632.40i	−0.968724	+	1.67788i
$251$	−1333.12	−	2309.03i	−0.335242	−	0.580656i	0.648289	−	0.761394i	$-0.275485\pi$
$251$	−1333.12	−	2309.03i	−0.335242	−	0.580656i	−0.983531	+	0.180738i	$0.942151\pi$
$252$	−6996.76			−1.74903
$253$	−724.590	−	1255.03i	−0.180058	−	0.311869i
$254$	1519.36	+	2631.61i	0.375327	+	0.650085i
$255$	1050.18			0.257901
$256$	3800.05	+	6581.88i	0.927746	+	1.60690i
$257$	161.172	−	279.158i	0.0391191	−	0.0677563i	−0.845803	−	0.533495i	$-0.820878\pi$
$257$	161.172	−	279.158i	0.0391191	−	0.0677563i	0.884922	+	0.465739i	$0.154211\pi$
$258$	−9524.34	+	16496.6i	−2.29829	+	3.98076i
$259$	−5175.02			−1.24155
$260$	1333.29	−	6885.61i	0.318027	−	1.64241i
$261$	−2694.02			−0.638910
$262$	6546.69	−	11339.2i	1.54372	−	2.67381i
$263$	−1531.32	+	2652.33i	−0.359032	+	0.621862i	−0.987799	−	0.155732i	$-0.950226\pi$
$263$	−1531.32	+	2652.33i	−0.359032	+	0.621862i	0.628767	+	0.777594i	$0.283560\pi$
$264$	−2029.06	−	3514.43i	−0.473030	−	0.819312i
$265$	−3833.56			−0.888657
$266$	1482.62	+	2567.97i	0.341749	+	0.591927i
$267$	−2591.99	−	4489.46i	−0.594110	−	1.02903i
$268$	−14405.7			−3.28346
$269$	−1955.72	−	3387.40i	−0.443280	−	0.767783i	0.554651	−	0.832083i	$-0.312852\pi$
$269$	−1955.72	−	3387.40i	−0.443280	−	0.767783i	−0.997931	+	0.0643000i	$0.979519\pi$
$270$	−104.945	+	181.770i	−0.0236546	+	0.0409710i
$271$	1954.93	−	3386.04i	0.438205	−	0.758993i	−0.559346	−	0.828934i	$-0.688948\pi$
$271$	1954.93	−	3386.04i	0.438205	−	0.758993i	0.997551	+	0.0699409i	$0.0222811\pi$
$272$	−1877.38			−0.418504
$273$	3714.34	+	3224.14i	0.823451	+	0.714776i
$274$	−10907.3			−2.40486
$275$	299.706	−	519.107i	0.0657199	−	0.113830i
$276$	8678.74	−	15032.0i	1.89275	−	3.27834i
$277$	374.810	+	649.189i	0.0813001	+	0.140816i	0.903809	−	0.427937i	$-0.140759\pi$
$277$	374.810	+	649.189i	0.0813001	+	0.140816i	−0.822509	+	0.568753i	$0.807426\pi$
$278$	−874.731			−0.188715
$279$	196.703	+	340.700i	0.0422090	+	0.0731081i
$280$	−2973.20	−	5149.74i	−0.634582	−	1.09913i
$281$	4479.67			0.951014			0.475507	−	0.879712i	$-0.342265\pi$
$281$	4479.67			0.951014			0.475507	+	0.879712i	$0.342265\pi$
$282$	5943.01	+	10293.6i	1.25497	+	2.17367i
$283$	1344.78	−	2329.22i	0.282469	−	0.489251i	−0.689523	−	0.724264i	$-0.742180\pi$
$283$	1344.78	−	2329.22i	0.282469	−	0.489251i	0.971992	+	0.235013i	$0.0755132\pi$
$284$	4413.91	−	7645.12i	0.922245	−	1.59738i
$285$	2552.70			0.530557
$286$	−498.049	+	2572.12i	−0.102973	+	0.531792i
$287$	1624.91			0.334200
$288$	2279.26	−	3947.79i	0.466342	−	0.807728i
$289$	2313.43	−	4006.98i	0.470880	−	0.815587i
$290$	−2077.45	−	3598.24i	−0.420661	−	0.728607i
$291$	5990.99			1.20687
$292$	−4405.95	−	7631.33i	−0.883010	−	1.52942i
$293$	−782.878	−	1355.98i	−0.156096	−	0.270367i	0.777361	−	0.629054i	$-0.216558\pi$
$293$	−782.878	−	1355.98i	−0.156096	−	0.270367i	−0.933458	+	0.358688i	$0.883224\pi$
$294$	−5318.76			−1.05509
$295$	2522.86	+	4369.72i	0.497921	+	0.862424i
$296$	9097.02	−	15756.5i	1.78633	−	3.09401i
$297$	27.0558	−	46.8619i	0.00528597	−	0.00915557i
$298$	−10173.0			−1.97753
$299$	−5837.23	+	2014.62i	−1.12902	+	0.389660i
$300$	7179.44			1.38168
$301$	3598.01	−	6231.94i	0.688990	−	1.19336i
$302$	2045.80	−	3543.43i	0.389809	−	0.675170i
$303$	2614.89	+	4529.13i	0.495781	+	0.858718i
$304$	−4563.42			−0.860954
$305$	−2795.34	−	4841.68i	−0.524790	−	0.908962i
$306$	−1188.97	−	2059.35i	−0.222120	−	0.384723i
$307$	−4583.91			−0.852174			−0.426087	−	0.904682i	$-0.640108\pi$
$307$	−4583.91			−0.852174			−0.426087	+	0.904682i	$0.640108\pi$
$308$	1390.99	+	2409.26i	0.257334	+	0.445716i
$309$	6835.87	−	11840.1i	1.25851	−	2.17980i
$310$	−303.368	+	525.449i	−0.0555812	+	0.0962694i
$311$	−8238.96			−1.50221			−0.751107	−	0.660181i	$-0.770480\pi$
$311$	−8238.96			−1.50221			−0.751107	+	0.660181i	$0.770480\pi$
$312$	−16345.9	+	5641.51i	−2.96604	+	1.02368i
$313$	−768.625			−0.138803			−0.0694014	−	0.997589i	$-0.522109\pi$
$313$	−768.625			−0.138803			−0.0694014	+	0.997589i	$0.522109\pi$
$314$	−2206.18	+	3821.21i	−0.396502	+	0.686762i
$315$	1648.48	−	2855.26i	0.294862	−	0.510716i
$316$	5731.51	+	9927.26i	1.02032	+	1.76725i
$317$	−7760.24			−1.37495			−0.687474	−	0.726209i	$-0.741281\pi$
$317$	−7760.24			−1.37495			−0.687474	+	0.726209i	$0.741281\pi$
$318$	8576.02	+	14854.1i	1.51232	+	2.61942i
$319$	535.584	+	927.658i	0.0940029	+	0.162818i
$320$	−425.021			−0.0742480
$321$	7430.78	+	12870.5i	1.29204	+	2.23788i
$322$	−4750.45	+	8228.02i	−0.822150	+	1.42401i
$323$	−347.762	+	602.342i	−0.0599071	+	0.103762i
$324$	−12662.6			−2.17123
$325$	−1928.86	−	1674.29i	−0.329211	−	0.285763i
$326$	7051.40			1.19798
$327$	−6120.88	+	10601.7i	−1.03512	+	1.79289i
$328$	−2856.38	+	4947.39i	−0.480845	+	0.832848i
$329$	−2245.09	−	3888.61i	−0.376219	−	0.651630i
$330$	3470.11			0.578859
$331$	−3420.41	−	5924.32i	−0.567984	−	0.983777i	−0.996765	−	0.0803686i	$-0.974390\pi$
$331$	−3420.41	−	5924.32i	−0.567984	−	0.983777i	0.428781	−	0.903408i	$-0.358943\pi$
$332$	−7257.90	−	12571.1i	−1.19979	−	2.07809i
$333$	10087.6			1.66005
$334$	897.509	+	1554.53i	0.147034	+	0.254671i
$335$	3394.07	−	5878.71i	0.553546	−	0.958771i
$336$	−5823.06	+	10085.8i	−0.945458	+	1.63758i
$337$	−8919.67			−1.44180			−0.720898	−	0.693041i	$-0.756271\pi$
$337$	−8919.67			−1.44180			−0.720898	+	0.693041i	$0.756271\pi$
$338$	10356.8	+	4167.08i	1.66667	+	0.670589i
$339$	−1251.26			−0.200470
$340$	1265.55	−	2191.99i	0.201864	−	0.349639i
$341$	78.2110	−	135.465i	0.0124204	−	0.0215128i
$342$	−2890.06	−	5005.73i	−0.456949	−	0.791458i
$343$	6877.30			1.08262
$344$	12649.7	+	21909.9i	1.98263	+	3.43401i
$345$	4089.54	+	7083.29i	0.638184	+	1.10537i
$346$	4339.78			0.674300
$347$	561.521	+	972.583i	0.0868704	+	0.150464i	0.906187	−	0.422878i	$-0.138980\pi$
$347$	561.521	+	972.583i	0.0868704	+	0.150464i	−0.819316	+	0.573342i	$0.805647\pi$
$348$	−6414.93	+	11111.0i	−0.988151	+	1.71153i
$349$	4343.16	−	7522.57i	0.666143	−	1.15379i	−0.312831	−	0.949809i	$-0.601277\pi$
$349$	4343.16	−	7522.57i	0.666143	−	1.15379i	0.978974	−	0.203985i	$-0.0653893\pi$
$350$	−3929.78			−0.600160
$351$	−174.126	−	151.145i	−0.0264791	−	0.0229845i
$352$	−1812.51			−0.274452
$353$	−3521.04	+	6098.62i	−0.530895	+	0.919537i	0.468455	+	0.883487i	$0.344811\pi$
$353$	−3521.04	+	6098.62i	−0.530895	+	0.919537i	−0.999350	+	0.0360496i	$0.988523\pi$
$354$	11287.7	−	19550.9i	1.69473	−	2.93537i
$355$	2079.90	+	3602.48i	0.310956	+	0.538592i
$356$	−12494.2			−1.86009
$357$	887.510	+	1537.21i	0.131574	+	0.227893i
$358$	5178.33	+	8969.14i	0.764479	+	1.32412i
$359$	3511.01			0.516167			0.258083	−	0.966123i	$-0.416909\pi$
$359$	3511.01			0.516167			0.258083	+	0.966123i	$0.416909\pi$
$360$	5795.63	+	10038.3i	0.848491	+	1.46963i
$361$	2584.18	−	4475.94i	0.376758	−	0.652564i
$362$	9512.01	−	16475.3i	1.38105	−	2.39205i
$363$	−894.626			−0.129354
$364$	11205.7	−	3867.45i	1.61356	−	0.556894i
$365$	4152.29			0.595454
$366$	−12506.9	+	21662.5i	−1.78619	+	3.09376i
$367$	−4543.65	+	7869.83i	−0.646258	+	1.11935i	0.337752	+	0.941235i	$0.390334\pi$
$367$	−4543.65	+	7869.83i	−0.646258	+	1.11935i	−0.984010	+	0.178116i	$0.943000\pi$
$368$	−7310.80	−	12662.7i	−1.03560	−	1.79372i
$369$	−3167.42			−0.446854
$370$	7778.89	+	13473.4i	1.09299	+	1.89311i
$371$	−3239.76	−	5611.43i	−0.453370	−	0.785259i
$372$	1873.54			0.261125
$373$	−539.478	−	934.403i	−0.0748877	−	0.129709i	0.826150	−	0.563451i	$-0.190526\pi$
$373$	−539.478	−	934.403i	−0.0748877	−	0.129709i	−0.901037	+	0.433741i	$0.857193\pi$
$374$	−472.744	+	818.817i	−0.0653610	+	0.113209i
$375$	−5571.73	+	9650.52i	−0.767261	+	1.32894i
$376$	15786.3			2.16520
$377$	4314.62	−	1489.11i	0.589427	−	0.203431i
$378$	−354.758			−0.0482719
$379$	−3665.72	+	6349.22i	−0.496822	+	0.860521i	−0.999993	−	0.00366563i	$-0.998833\pi$
$379$	−3665.72	+	6349.22i	−0.496822	+	0.860521i	0.503171	+	0.864187i	$0.332167\pi$
$380$	3076.20	−	5328.14i	0.415279	−	0.719284i
$381$	2210.75	+	3829.14i	0.297271	+	0.514889i
$382$	5867.51			0.785884
$383$	6560.88	+	11363.8i	0.875314	+	1.51609i	0.856428	+	0.516267i	$0.172679\pi$
$383$	6560.88	+	11363.8i	0.875314	+	1.51609i	0.0188862	+	0.999822i	$0.493988\pi$
$384$	5823.89	+	10087.3i	0.773956	+	1.34053i
$385$	−1310.90			−0.173532
$386$	−10792.5	−	18693.1i	−1.42311	−	2.46490i
$387$	−7013.57	+	12147.9i	−0.921239	+	1.59563i
$388$	7219.61	−	12504.7i	0.944640	−	1.63616i
$389$	−10391.2			−1.35439			−0.677193	−	0.735805i	$-0.736804\pi$
$389$	−10391.2			−1.35439			−0.677193	+	0.735805i	$0.736804\pi$
$390$	2810.96	−	14516.9i	0.364970	−	1.88485i
$391$	−2228.52			−0.288239
$392$	−3532.03	+	6117.66i	−0.455088	+	0.788236i
$393$	9525.80	−	16499.2i	1.22268	−	2.11774i
$394$	−1347.46	−	2333.87i	−0.172294	−	0.298423i
$395$	−5401.53			−0.688051
$396$	−2711.44	−	4696.35i	−0.344078	−	0.595961i
$397$	908.287	+	1573.20i	0.114825	+	0.198883i	0.917710	−	0.397251i	$-0.130036\pi$
$397$	908.287	+	1573.20i	0.114825	+	0.198883i	−0.802885	+	0.596134i	$0.796703\pi$
$398$	13350.1			1.68136
$399$	2157.30	+	3736.55i	0.270677	+	0.468826i
$400$	3023.91	−	5237.57i	0.377989	−	0.654696i
$401$	−2158.42	+	3738.49i	−0.268794	+	0.465564i	−0.968551	−	0.248817i	$-0.919958\pi$
$401$	−2158.42	+	3738.49i	−0.268794	+	0.465564i	0.699757	+	0.714381i	$0.253292\pi$
$402$	−30371.4			−3.76812
$403$	−503.352	−	436.922i	−0.0622177	−	0.0540065i
$404$	12604.6			1.55223
$405$	2983.39	−	5167.38i	0.366039	−	0.633998i
$406$	3511.32	−	6081.78i	0.429221	−	0.743433i
$407$	−2005.47	−	3473.57i	−0.244244	−	0.423043i
$408$	−6240.51			−0.757233
$409$	2605.30	+	4512.52i	0.314973	+	0.545549i	0.979432	−	0.201776i	$-0.0646712\pi$
$409$	2605.30	+	4512.52i	0.314973	+	0.545549i	−0.664459	+	0.747325i	$0.731338\pi$
$410$	−2442.50	−	4230.53i	−0.294211	−	0.509588i
$411$	−15870.7			−1.90473
$412$	−16475.5	−	28536.4i	−1.97012	−	3.41235i
$413$	−4264.16	+	7385.75i	−0.508053	+	0.879973i
$414$	9260.01	−	16038.8i	1.09929	−	1.90402i
$415$	6840.04			0.809071
$416$	−1468.22	+	7582.45i	−0.173042	+	0.893655i
$417$	−1272.78			−0.149469
$418$	−1149.11	+	1990.32i	−0.134462	+	0.232895i
$419$	−7567.84	+	13107.9i	−0.882371	+	1.52831i	−0.0336726	+	0.999433i	$0.510720\pi$
$419$	−7567.84	+	13107.9i	−0.882371	+	1.52831i	−0.848698	+	0.528878i	$0.822613\pi$
$420$	−7850.65	−	13597.7i	−0.912078	−	1.57977i
$421$	9138.85			1.05796			0.528979	−	0.848635i	$-0.322575\pi$
$421$	9138.85			1.05796			0.528979	+	0.848635i	$0.322575\pi$
$422$	379.907	+	658.018i	0.0438237	+	0.0759048i
$423$	4376.33	+	7580.03i	0.503037	+	0.871286i
$424$	22780.3			2.60922
$425$	−460.883	−	798.273i	−0.0526027	−	0.0911105i
$426$	9305.82	−	16118.1i	1.05838	−	1.83316i
$427$	4724.71	−	8183.45i	0.535468	−	0.927458i
$428$	35818.7			4.04524
$429$	−724.689	+	3742.58i	−0.0815579	+	0.421197i
$430$	−21633.6			−2.42619
$431$	−8066.18	+	13971.0i	−0.901471	+	1.56139i	−0.0758862	+	0.997116i	$0.524179\pi$
$431$	−8066.18	+	13971.0i	−0.901471	+	1.56139i	−0.825585	+	0.564278i	$0.809155\pi$
$432$	272.981	−	472.817i	0.0304023	−	0.0526584i
$433$	6610.12	+	11449.1i	0.733631	+	1.27069i	0.955322	+	0.295568i	$0.0955090\pi$
$433$	6610.12	+	11449.1i	0.733631	+	1.27069i	−0.221691	+	0.975117i	$0.571158\pi$
$434$	−1025.51			−0.113424
$435$	−3022.80	−	5235.65i	−0.333178	−	0.577081i
$436$	14752.3	+	25551.7i	1.62043	+	2.80666i
$437$	−5416.94			−0.592969
$438$	−9289.03	−	16089.1i	−1.01335	−	1.75517i
$439$	−988.575	+	1712.26i	−0.107476	+	0.186154i	−0.914747	−	0.404027i	$-0.867610\pi$
$439$	−988.575	+	1712.26i	−0.107476	+	0.186154i	0.807271	+	0.590181i	$0.200944\pi$
$440$	2304.40	−	3991.34i	0.249677	−	0.432453i
$441$	−3916.65			−0.422919
$442$	3042.50	+	2640.96i	0.327414	+	0.284203i
$443$	−8193.35			−0.878731			−0.439366	−	0.898308i	$-0.644797\pi$
$443$	−8193.35			−0.878731			−0.439366	+	0.898308i	$0.644797\pi$
$444$	24020.4	−	41604.6i	2.56747	−	4.44699i
$445$	2943.72	−	5098.67i	0.313586	−	0.543147i
$446$	−1312.20	−	2272.80i	−0.139315	−	0.241301i
$447$	−14802.2			−1.56627
$448$	−359.187	−	622.130i	−0.0378794	−	0.0656091i
$449$	−4721.16	−	8177.28i	−0.496225	−	0.859488i	0.503765	−	0.863841i	$-0.331948\pi$
$449$	−4721.16	−	8177.28i	−0.496225	−	0.859488i	−0.999991	+	0.00435307i	$0.998614\pi$
$450$	7660.29			0.802466
$451$	629.698	+	1090.67i	0.0657457	+	0.113875i
$452$	−1507.87	+	2611.71i	−0.156912	+	0.271780i
$453$	2976.75	−	5155.89i	0.308742	−	0.534757i
$454$	−26490.2			−2.73843
$455$	−1061.90	+	5484.04i	−0.109412	+	0.565046i
$456$	−15169.0			−1.55779
$457$	6567.02	−	11374.4i	0.672193	−	1.16427i	−0.305088	−	0.952324i	$-0.598686\pi$
$457$	6567.02	−	11374.4i	0.672193	−	1.16427i	0.977281	−	0.211949i	$-0.0679809\pi$
$458$	2234.47	−	3870.22i	0.227969	−	0.394854i
$459$	−41.6059	−	72.0635i	−0.00423093	−	0.00732818i
$460$	19712.9			1.99808
$461$	−3896.22	−	6748.45i	−0.393634	−	0.681793i	0.599292	−	0.800530i	$-0.295449\pi$
$461$	−3896.22	−	6748.45i	−0.393634	−	0.681793i	−0.992926	+	0.118737i	$0.962115\pi$
$462$	2932.61	+	5079.43i	0.295319	+	0.511507i
$463$	4945.75			0.496433			0.248216	−	0.968705i	$-0.420156\pi$
$463$	4945.75			0.496433			0.248216	+	0.968705i	$0.420156\pi$
$464$	5403.81	+	9359.68i	0.540659	+	0.936448i
$465$	−441.418	+	764.559i	−0.0440221	+	0.0762485i
$466$	13493.1	−	23370.7i	1.34132	−	2.32324i
$467$	2325.45			0.230427			0.115213	−	0.993341i	$-0.463245\pi$
$467$	2325.45			0.230427			0.115213	+	0.993341i	$0.463245\pi$
$468$	−21843.1	+	7538.78i	−2.15748	+	0.744615i
$469$	11473.4			1.12962
$470$	−6749.47	+	11690.4i	−0.662404	+	1.14732i
$471$	−3210.11	+	5560.08i	−0.314043	+	0.543938i
$472$	−14991.7	−	25966.4i	−1.46197	−	2.53220i
$473$	5577.32			0.542168
$474$	12083.7	+	20929.6i	1.17093	+	2.02812i
$475$	−1120.28	−	1940.39i	−0.108215	−	0.187434i
$476$	4278.08			0.411944
$477$	6315.24	+	10938.3i	0.606195	+	1.04996i
$478$	−7620.89	+	13199.8i	−0.729228	+	1.26306i
$479$	−1088.94	+	1886.11i	−0.103873	+	0.179913i	−0.913277	−	0.407339i	$-0.866457\pi$
$479$	−1088.94	+	1886.11i	−0.103873	+	0.179913i	0.809404	+	0.587252i	$0.199790\pi$
$480$	10229.7			0.972749
$481$	−16155.9	+	5575.92i	−1.53148	+	0.528565i
$482$	−1845.17			−0.174367
$483$	−6912.18	+	11972.2i	−0.651170	+	1.12786i
$484$	−1078.09	+	1867.31i	−0.101249	+	0.175368i
$485$	3401.98	+	5892.40i	0.318507	+	0.551670i
$486$	−27371.3			−2.55471
$487$	−4351.34	−	7536.74i	−0.404883	−	0.701278i	0.589425	−	0.807823i	$-0.299354\pi$
$487$	−4351.34	−	7536.74i	−0.404883	−	0.701278i	−0.994308	+	0.106545i	$0.966021\pi$
$488$	16610.9	+	28770.9i	1.54086	+	2.66884i
$489$	10260.2			0.948839
$490$	−3020.26	−	5231.24i	−0.278451	−	0.482292i
$491$	4904.13	−	8494.20i	0.450754	−	0.780728i	−0.547679	−	0.836688i	$-0.684489\pi$
$491$	4904.13	−	8494.20i	0.450754	−	0.780728i	0.998433	+	0.0559599i	$0.0178219\pi$
$492$	−7542.18	+	13063.4i	−0.691113	+	1.19704i
$493$	1647.22			0.150481
$494$	7395.49	+	6419.46i	0.673560	+	0.584667i
$495$	2555.33			0.232028
$496$	789.116	−	1366.79i	0.0714362	−	0.123731i
$497$	−3515.46	+	6088.95i	−0.317283	+	0.549551i
$498$	−15301.8	−	26503.4i	−1.37689	−	2.38484i
$499$	−38.4379			−0.00344833			−0.00172417	−	0.999999i	$-0.500549\pi$
$499$	−38.4379			−0.00344833			−0.00172417	+	0.999999i	$0.500549\pi$
$500$	13428.8	+	23259.3i	1.20110	+	2.08037i
$501$	1305.93	+	2261.93i	0.116456	+	0.201708i
$502$	−13548.0			−1.20453
$503$	−7252.71	−	12562.1i	−0.642907	−	1.11355i	−0.984781	−	0.173802i	$-0.944395\pi$
$503$	−7252.71	−	12562.1i	−0.642907	−	1.11355i	0.341874	−	0.939746i	$-0.388939\pi$
$504$	−9795.84	+	16966.9i	−0.865756	+	1.49953i
$505$	−2969.73	+	5143.72i	−0.261686	+	0.453253i
$506$	−7363.73			−0.646952
$507$	15069.7	+	6063.33i	1.32005	+	0.531128i
$508$	10656.5			0.930723
$509$	2283.78	−	3955.62i	0.198874	−	0.344460i	−0.749290	−	0.662242i	$-0.769605\pi$
$509$	2283.78	−	3955.62i	0.198874	−	0.344460i	0.948164	+	0.317783i	$0.102938\pi$
$510$	2668.14	−	4621.35i	0.231661	−	0.401249i
$511$	3509.12	+	6077.97i	0.303785	+	0.526171i
$512$	26015.4			2.24556
$513$	−101.133	−	175.167i	−0.00870393	−	0.0150757i
$514$	−818.964	−	1418.49i	−0.0702781	−	0.121725i
$515$	15527.0			1.32854
$516$	33401.1	+	57852.4i	2.84961	+	4.93567i
$517$	1740.07	−	3013.89i	0.148024	−	0.256385i
$518$	−13148.0	+	22772.9i	−1.11523	+	1.93163i
$519$	6314.62			0.534068
$520$	−14830.7	−	12873.4i	−1.25071	−	1.08565i
$521$	−15441.2			−1.29845			−0.649224	−	0.760597i	$-0.724906\pi$
$521$	−15441.2			−1.29845			−0.649224	+	0.760597i	$0.724906\pi$
$522$	−6844.58	+	11855.2i	−0.573906	+	0.994035i
$523$	7251.80	−	12560.5i	0.606308	−	1.05016i	−0.385535	−	0.922693i	$-0.625983\pi$
$523$	7251.80	−	12560.5i	0.606308	−	1.05016i	0.991843	−	0.127464i	$-0.0406836\pi$
$524$	−22958.7	−	39765.6i	−1.91404	−	3.31521i
$525$	−5718.06			−0.475346
$526$	7781.13	+	13477.3i	0.645007	+	1.11718i
$527$	−120.272	−	208.317i	−0.00994139	−	0.0172190i
$528$	−9026.39			−0.743983
$529$	−2594.68	−	4494.12i	−0.213256	−	0.369370i
$530$	−9739.77	+	16869.8i	−0.798243	+	1.38260i
$531$	8312.09	−	14397.0i	0.679311	−	1.17660i
$532$	10398.9			0.847458
$533$	5072.79	−	1750.79i	0.412246	−	0.142279i
$534$	−26341.4			−2.13465
$535$	−8439.13	+	14617.0i	−0.681973	+	1.18121i
$536$	−20168.7	+	34933.3i	−1.62529	+	2.81509i
$537$	7534.77	+	13050.6i	0.605492	+	1.04874i
$538$	−19875.2			−1.59272
$539$	778.648	+	1348.66i	0.0622240	+	0.107775i
$540$	368.033	+	637.453i	0.0293290	+	0.0507993i
$541$	4920.22			0.391010			0.195505	−	0.980703i	$-0.437365\pi$
$541$	4920.22			0.391010			0.195505	+	0.980703i	$0.437365\pi$
$542$	−9933.61	−	17205.5i	−0.787242	−	1.36354i
$543$	13840.5	−	23972.5i	1.09384	−	1.89458i
$544$	−1393.62	+	2413.83i	−0.109837	+	0.190242i
$545$	−13903.0			−1.09273
$546$	23624.8	−	8153.70i	1.85174	−	0.639096i
$547$	9165.27			0.716415			0.358207	−	0.933642i	$-0.383388\pi$
$547$	9165.27			0.716415			0.358207	+	0.933642i	$0.383388\pi$
$548$	−19125.4	+	33126.2i	−1.49087	+	2.58226i
$549$	−9209.84	+	15951.9i	−0.715968	+	1.24009i
$550$	−1522.90	−	2637.74i	−0.118067	−	0.204498i
$551$	4003.96			0.309572
$552$	−24301.4	−	42091.3i	−1.87380	−	3.24551i
$553$	−4564.86	−	7906.56i	−0.351026	−	0.607995i
$554$	3809.05			0.292114
$555$	11318.7	+	19604.6i	0.865682	+	1.49941i
$556$	−1533.80	+	2656.63i	−0.116992	+	0.202637i
$557$	5858.03	−	10146.4i	0.445624	−	0.771844i	−0.552471	−	0.833532i	$-0.686315\pi$
$557$	5858.03	−	10146.4i	0.445624	−	0.771844i	0.998095	+	0.0616881i	$0.0196484\pi$
$558$	1999.02			0.151658
$559$	4517.89	−	23332.2i	0.341836	−	1.76538i
$560$	−13226.5			−0.998072
$561$	−687.870	+	1191.43i	−0.0517681	+	0.0896650i
$562$	11381.3	−	19713.0i	0.854255	−	1.47961i
$563$	8963.22	+	15524.8i	0.670968	+	1.16215i	0.977630	+	0.210332i	$0.0674544\pi$
$563$	8963.22	+	15524.8i	0.670968	+	1.16215i	−0.306662	+	0.951818i	$0.599212\pi$
$564$	41683.3			3.11203
$565$	−710.528	−	1230.67i	−0.0529065	−	0.0916367i
$566$	−6833.24	−	11835.5i	−0.507460	−	0.878946i
$567$	10085.1			0.746975
$568$	−12359.4	−	21407.2i	−0.913011	−	1.58138i
$569$	8501.89	−	14725.7i	0.626394	−	1.08495i	−0.361876	−	0.932226i	$-0.617864\pi$
$569$	8501.89	−	14725.7i	0.626394	−	1.08495i	0.988270	−	0.152719i	$-0.0488030\pi$
$570$	6485.53	−	11233.3i	0.476577	−	0.825456i
$571$	17442.2			1.27834			0.639169	−	0.769066i	$-0.279278\pi$
$571$	17442.2			1.27834			0.639169	+	0.769066i	$0.279278\pi$
$572$	6938.42	+	6022.72i	0.507185	+	0.440249i
$573$	8537.56			0.622446
$574$	4128.34	−	7150.49i	0.300198	−	0.519957i
$575$	3589.49	−	6217.18i	0.260334	−	0.450912i
$576$	700.159	+	1212.71i	0.0506481	+	0.0877251i
$577$	−3667.47			−0.264608			−0.132304	−	0.991209i	$-0.542237\pi$
$577$	−3667.47			−0.264608			−0.132304	+	0.991209i	$0.542237\pi$
$578$	−11755.3	−	20360.7i	−0.845942	−	1.46522i
$579$	−15703.6	−	27199.5i	−1.12715	−	1.95228i
$580$	−14570.9			−1.04314
$581$	5780.55	+	10012.2i	0.412767	+	0.714934i
$582$	15221.0	−	26363.6i	1.08408	−	1.87768i
$583$	2511.00	−	4349.18i	0.178379	−	0.308961i
$584$	−24674.3			−1.74834
$585$	2069.94	−	10690.0i	0.146293	−	0.755515i
$586$	−7956.09			−0.560859
$587$	−8434.67	+	14609.3i	−0.593077	+	1.02724i	0.400739	+	0.916192i	$0.368754\pi$
$587$	−8434.67	+	14609.3i	−0.593077	+	1.02724i	−0.993815	+	0.111046i	$0.964580\pi$
$588$	−9326.23	+	16153.5i	−0.654094	+	1.13292i
$589$	−292.348	−	506.361i	−0.0204516	−	0.0354232i
$590$	25638.9			1.78905
$591$	−1960.63	−	3395.91i	−0.136463	−	0.236361i
$592$	−20234.3	−	35046.8i	−1.40477	−	2.43314i
$593$	−19768.3			−1.36895			−0.684475	−	0.729036i	$-0.739969\pi$
$593$	−19768.3			−1.36895			−0.684475	+	0.729036i	$0.739969\pi$
$594$	−137.479	−	238.120i	−0.00949633	−	0.0164481i
$595$	−1007.94	+	1745.81i	−0.0694482	+	0.120288i
$596$	−17837.9	+	30896.1i	−1.22595	+	2.12341i
$597$	19425.2			1.33169
$598$	−5964.97	+	30805.5i	−0.407903	+	2.10657i
$599$	6521.14			0.444819			0.222409	−	0.974953i	$-0.428608\pi$
$599$	6521.14			0.444819			0.222409	+	0.974953i	$0.428608\pi$
$600$	10051.6	−	17409.9i	0.683925	−	1.18459i
$601$	−3200.00	+	5542.56i	−0.217189	+	0.376182i	−0.953947	−	0.299974i	$-0.903022\pi$
$601$	−3200.00	+	5542.56i	−0.217189	+	0.376182i	0.736759	+	0.676156i	$0.236355\pi$
$602$	−18282.6	−	31666.4i	−1.23778	−	2.14390i
$603$	−22365.0			−1.51040
$604$	−7174.44	−	12426.5i	−0.483318	−	0.837131i
$605$	−508.012	−	879.903i	−0.0341383	−	0.0591292i
$606$	26574.2			1.78136
$607$	4681.53	+	8108.65i	0.313044	+	0.542207i	0.979020	−	0.203766i	$-0.0653181\pi$
$607$	4681.53	+	8108.65i	0.313044	+	0.542207i	−0.665976	+	0.745973i	$0.731985\pi$
$608$	−3387.52	+	5867.36i	−0.225958	+	0.391370i
$609$	5109.17	−	8849.34i	0.339957	−	0.588823i
$610$	−28408.0			−1.88559
$611$	−11198.8	−	9720.82i	−0.741496	−	0.643637i
$612$	−8339.21			−0.550805
$613$	7483.56	−	12961.9i	0.493080	−	0.854040i	−0.506888	−	0.862012i	$-0.669204\pi$
$613$	7483.56	−	12961.9i	0.493080	−	0.854040i	0.999968	+	0.00797197i	$0.00253758\pi$
$614$	−11646.1	+	20171.7i	−0.765472	+	1.32584i
$615$	−3553.98	−	6155.67i	−0.233025	−	0.403611i
$616$	7789.83			0.509515
$617$	7424.90	+	12860.3i	0.484465	+	0.839118i	0.999841	−	0.0178461i	$-0.00568090\pi$
$617$	7424.90	+	12860.3i	0.484465	+	0.839118i	−0.515376	+	0.856964i	$0.672348\pi$
$618$	−34735.2	−	60163.1i	−2.26093	−	3.91604i
$619$	−17698.2			−1.14919			−0.574597	−	0.818437i	$-0.694841\pi$
$619$	−17698.2			−1.14919			−0.574597	+	0.818437i	$0.694841\pi$
$620$	1063.89	+	1842.71i	0.0689141	+	0.119363i
$621$	324.038	−	561.251i	0.0209391	−	0.0362677i
$622$	−20932.4	+	36255.9i	−1.34938	+	2.33719i
$623$	9951.01			0.639934
$624$	−7311.81	+	37761.0i	−0.469081	+	2.42252i
$625$	−5844.10			−0.374023
$626$	−1952.81	+	3382.37i	−0.124681	+	0.215953i
$627$	−1672.03	+	2896.04i	−0.106498	+	0.184460i
$628$	7736.88	+	13400.7i	0.491616	+	0.851504i
$629$	−6167.95			−0.390989
$630$	−8376.46	−	14508.4i	−0.529724	−	0.917509i
$631$	4215.23	+	7300.99i	0.265936	+	0.460615i	0.967808	−	0.251688i	$-0.0809856\pi$
$631$	4215.23	+	7300.99i	0.265936	+	0.460615i	−0.701872	+	0.712303i	$0.747652\pi$
$632$	32097.7			2.02022
$633$	552.786	+	957.454i	0.0347098	+	0.0601191i
$634$	−19716.1	+	34149.3i	−1.23506	+	2.13918i
$635$	−2510.75	+	4348.75i	−0.156907	+	0.271771i
$636$	60150.8			3.75021
$637$	6272.72	−	2164.92i	0.390164	−	0.134658i
$638$	5442.94			0.337755
$639$	6852.65	−	11869.1i	0.424236	−	0.734798i
$640$	−6614.18	+	11456.1i	−0.408513	+	0.707566i
$641$	9789.54	+	16956.0i	0.603219	+	1.04481i	0.992330	+	0.123615i	$0.0394489\pi$
$641$	9789.54	+	16956.0i	0.603219	+	1.04481i	−0.389111	+	0.921191i	$0.627218\pi$
$642$	75516.3			4.64235
$643$	259.439	+	449.362i	0.0159118	+	0.0275601i	0.873872	−	0.486157i	$-0.161602\pi$
$643$	259.439	+	449.362i	0.0159118	+	0.0275601i	−0.857960	+	0.513717i	$0.828268\pi$
$644$	16659.4	+	28855.0i	1.01937	+	1.76560i
$645$	−31478.1			−1.92162
$646$	1767.09	+	3060.69i	0.107624	+	0.186410i
$647$	8330.50	−	14428.9i	0.506192	−	0.876749i	−0.493783	−	0.869585i	$-0.664386\pi$
$647$	8330.50	−	14428.9i	0.506192	−	0.876749i	0.999974	−	0.00716418i	$-0.00228045\pi$
$648$	−17728.3	+	30706.3i	−1.07474	+	1.86151i
$649$	−6609.93			−0.399788
$650$	−12268.4	+	4234.21i	−0.740315	+	0.255507i
$651$	−1492.18			−0.0898358
$652$	12364.3	−	21415.7i	0.742676	−	1.28635i
$653$	3403.98	−	5895.87i	0.203994	−	0.353328i	−0.745818	−	0.666150i	$-0.767941\pi$
$653$	3403.98	−	5895.87i	0.203994	−	0.353328i	0.949812	+	0.312822i	$0.101274\pi$
$654$	31102.1	+	53870.5i	1.85962	+	3.22095i
$655$	21636.9			1.29072
$656$	6353.38	+	11004.4i	0.378137	+	0.654953i
$657$	−6840.29	−	11847.7i	−0.406187	−	0.703537i
$658$	−22816.0			−1.35176
$659$	9587.75	+	16606.5i	0.566746	+	0.981633i	0.996885	+	0.0788700i	$0.0251312\pi$
$659$	9587.75	+	16606.5i	0.566746	+	0.981633i	−0.430139	+	0.902763i	$0.641535\pi$
$660$	6084.70	−	10539.0i	0.358858	−	0.621561i
$661$	7149.14	−	12382.7i	0.420680	−	0.728639i	−0.575326	−	0.817924i	$-0.695125\pi$
$661$	7149.14	−	12382.7i	0.420680	−	0.728639i	0.996006	+	0.0892853i	$0.0284583\pi$
$662$	−34760.3			−2.04078
$663$	4427.01	+	3842.75i	0.259322	+	0.225098i
$664$	−40645.8			−2.37555
$665$	−2450.04	+	4243.59i	−0.142870	+	0.247458i
$666$	25629.2	−	44391.0i	1.49116	−	2.58276i
$667$	6414.52	+	11110.3i	0.372371	+	0.644965i
$668$	6294.98			0.364611
$669$	−1909.33	−	3307.06i	−0.110342	−	0.191118i
$670$	−17246.4	−	29871.6i	−0.994455	−	1.72245i
$671$	7323.84			0.421362
$672$	8645.16	+	14973.9i	0.496271	+	0.859567i
$673$	8734.36	−	15128.3i	0.500274	−	0.866501i	−0.499726	−	0.866184i	$-0.666566\pi$
$673$	8734.36	−	15128.3i	0.500274	−	0.866501i	1.00000		0.000316880i	$-0.000100866\pi$
$674$	−22661.8	+	39251.4i	−1.29511	+	2.24319i
$675$	268.059			0.0152853
$676$	30815.9	−	24147.5i	1.75329	−	1.37389i
$677$	−6157.18			−0.349542			−0.174771	−	0.984609i	$-0.555918\pi$
$677$	−6157.18			−0.349542			−0.174771	+	0.984609i	$0.555918\pi$
$678$	−3179.03	+	5506.24i	−0.180073	+	0.311896i
$679$	−5750.05	+	9959.38i	−0.324988	+	0.562896i
$680$	−3543.67	−	6137.81i	−0.199843	−	0.346139i
$681$	−38544.7			−2.16892
$682$	−397.415	−	688.343i	−0.0223135	−	0.0386481i
$683$	−1266.40	−	2193.47i	−0.0709479	−	0.122885i	0.828369	−	0.560183i	$-0.189269\pi$
$683$	−1266.40	−	2193.47i	−0.0709479	−	0.122885i	−0.899317	+	0.437297i	$0.855936\pi$
$684$	−20270.4			−1.13313
$685$	−9012.15	−	15609.5i	−0.502681	−	0.870669i
$686$	17472.9	−	30263.9i	0.972474	−	1.68437i
$687$	3251.28	−	5631.38i	0.180559	−	0.312738i
$688$	56272.8			3.11828
$689$	−16160.3	−	14027.6i	−0.893555	−	0.775628i
$690$	41560.5			2.29301
$691$	−860.791	+	1490.93i	−0.0473894	+	0.0820808i	−0.888747	−	0.458398i	$-0.848423\pi$
$691$	−860.791	+	1490.93i	−0.0473894	+	0.0820808i	0.841358	+	0.540479i	$0.181757\pi$
$692$	7609.62	−	13180.2i	0.418026	−	0.724043i
$693$	2159.52	+	3740.41i	0.118375	+	0.205031i
$694$	5706.53			0.312128
$695$	−722.749	−	1251.84i	−0.0394467	−	0.0683236i
$696$	17962.5	+	31112.0i	0.978257	+	1.69439i
$697$	1936.68			0.105247
$698$	−22068.9	−	38224.5i	−1.19674	−	2.07281i
$699$	19633.2	−	34005.8i	1.06237	−	1.84008i
$700$	−6890.71	+	11935.1i	−0.372064	+	0.644433i
$701$	−4583.86			−0.246976			−0.123488	−	0.992346i	$-0.539408\pi$
$701$	−4583.86			−0.246976			−0.123488	+	0.992346i	$0.539408\pi$
$702$	−1107.52	+	382.240i	−0.0595449	+	0.0205509i
$703$	−14992.6			−0.804349
$704$	278.390	−	482.186i	0.0149037	−	0.0258140i
$705$	−9820.86	+	17010.2i	−0.524645	+	0.908712i
$706$	17891.5	+	30989.0i	0.953761	+	1.65196i
$707$	−10038.9			−0.534021
$708$	−39585.1	−	68563.4i	−2.10127	−	3.63951i
$709$	11771.3	+	20388.5i	0.623528	+	1.07998i	0.988824	+	0.149091i	$0.0476347\pi$
$709$	11771.3	+	20388.5i	0.623528	+	1.07998i	−0.365295	+	0.930892i	$0.619032\pi$
$710$	21137.2			1.11727
$711$	8898.23	+	15412.2i	0.469352	+	0.812942i
$712$	−17492.6	+	30298.0i	−0.920733	+	1.59476i
$713$	936.709	−	1622.43i	0.0492006	−	0.0852180i
$714$	9019.43			0.472750
$715$	−4092.50	+	1412.46i	−0.214057	+	0.0738781i
$716$	36320.0			1.89573
$717$	−11088.8	+	19206.4i	−0.577573	+	1.00039i
$718$	8920.26	−	15450.3i	0.463651	−	0.803066i
$719$	13960.9	+	24181.0i	0.724135	+	1.25424i	0.959329	+	0.282290i	$0.0910940\pi$
$719$	13960.9	+	24181.0i	0.724135	+	1.25424i	−0.235194	+	0.971948i	$0.575573\pi$
$720$	25782.2			1.33451
$721$	13121.9	+	22727.8i	0.677788	+	1.17396i
$722$	−13131.0	−	22743.6i	−0.676852	−	1.17234i
$723$	−2684.83			−0.138105
$724$	−33357.8	−	57777.4i	−1.71234	−	2.96586i
$725$	−2653.19	+	4595.46i	−0.135913	+	0.235408i
$726$	−2272.94	+	3936.84i	−0.116194	+	0.201253i
$727$	−13436.0			−0.685440			−0.342720	−	0.939438i	$-0.611348\pi$
$727$	−13436.0			−0.685440			−0.342720	+	0.939438i	$0.611348\pi$
$728$	6310.14	−	32588.0i	0.321249	−	1.65905i
$729$	−20640.8			−1.04866
$730$	10549.5	−	18272.3i	0.534871	−	0.926424i
$731$	4288.35	−	7427.65i	0.216977	−	0.375816i
$732$	43860.5	+	75968.6i	2.21466	+	3.83590i
$733$	31785.9			1.60169			0.800846	−	0.598871i	$-0.204384\pi$
$733$	31785.9			1.60169			0.800846	+	0.598871i	$0.204384\pi$
$734$	23087.7	+	39989.1i	1.16101	+	2.01093i
$735$	−4394.64	−	7611.75i	−0.220543	−	0.381991i
$736$	−21707.9			−1.08718
$737$	4446.26	+	7701.15i	0.222225	+	0.384906i
$738$	−8047.32	+	13938.4i	−0.401390	+	0.695228i
$739$	18723.1	−	32429.4i	0.931992	−	1.61426i	0.152079	−	0.988368i	$-0.451403\pi$
$739$	18723.1	−	32429.4i	0.931992	−	1.61426i	0.779912	−	0.625889i	$-0.215264\pi$
$740$	54559.9			2.71035
$741$	10760.9	+	9340.69i	0.533482	+	0.463075i
$742$	−32924.5			−1.62897
$743$	11239.2	−	19466.9i	0.554949	−	0.961200i	−0.442958	−	0.896542i	$-0.646071\pi$
$743$	11239.2	−	19466.9i	0.554949	−	0.961200i	0.997907	−	0.0646580i	$-0.0205957\pi$
$744$	2623.06	−	4543.27i	0.129255	−	0.223877i
$745$	−8405.43	−	14558.6i	−0.413357	−	0.715956i
$746$	−5482.51			−0.269074
$747$	−11268.0	−	19516.7i	−0.551906	−	0.955929i
$748$	1657.88	+	2871.52i	0.0810400	+	0.140365i
$749$	−28527.8			−1.39170
$750$	28311.7	+	49037.3i	1.37840	+	2.38745i
$751$	−19145.2	+	33160.4i	−0.930250	+	1.61124i	−0.147358	+	0.989083i	$0.547077\pi$
$751$	−19145.2	+	33160.4i	−0.930250	+	1.61124i	−0.782892	+	0.622157i	$0.786256\pi$
$752$	17556.6	−	30408.9i	0.851360	−	1.47460i
$753$	−19713.1			−0.954031
$754$	4409.04	−	22770.0i	0.212955	−	1.09978i
$755$	6761.39			0.325923
$756$	−622.054	+	1077.43i	−0.0299258	+	0.0518329i
$757$	−15581.4	+	26987.8i	−0.748105	+	1.29576i	0.200625	+	0.979668i	$0.435703\pi$
$757$	−15581.4	+	26987.8i	−0.748105	+	1.29576i	−0.948730	+	0.316087i	$0.897631\pi$
$758$	18626.7	+	32262.4i	0.892549	+	1.54594i
$759$	−10714.7			−0.512407
$760$	−8613.70	−	14919.4i	−0.411121	−	0.712082i
$761$	3470.49	+	6011.07i	0.165316	+	0.286335i	0.936767	−	0.349953i	$-0.113802\pi$
$761$	3470.49	+	6011.07i	0.165316	+	0.286335i	−0.771452	+	0.636288i	$0.780469\pi$
$762$	22467.1			1.06811
$763$	−11749.5	−	20350.6i	−0.557482	−	0.965587i
$764$	10288.4	−	17820.1i	0.487202	−	0.843859i
$765$	1964.77	−	3403.09i	0.0928582	−	0.160835i
$766$	66675.8			3.14503
$767$	−5354.36	+	27652.0i	−0.252066	+	1.30177i
$768$	56192.1			2.64018
$769$	14821.4	−	25671.4i	0.695024	−	1.20382i	−0.275149	−	0.961402i	$-0.588727\pi$
$769$	14821.4	−	25671.4i	0.695024	−	1.20382i	0.970173	−	0.242415i	$-0.0779396\pi$
$770$	−3330.56	+	5768.70i	−0.155877	+	0.269986i
$771$	−1191.64	−	2063.98i	−0.0556626	−	0.0964104i
$772$	−75696.5			−3.52898
$773$	6129.92	+	10617.3i	0.285224	+	0.494022i	0.972663	−	0.232220i	$-0.0745988\pi$
$773$	6129.92	+	10617.3i	0.285224	+	0.494022i	−0.687440	+	0.726241i	$0.741265\pi$
$774$	35638.1	+	61727.0i	1.65502	+	2.86658i
$775$	774.888			0.0359158
$776$	−20215.7	−	35014.6i	−0.935182	−	1.61978i
$777$	−19131.0	+	33135.9i	−0.883297	+	1.52992i
$778$	−26400.5	+	45727.1i	−1.21659	+	2.10719i
$779$	4707.54			0.216515
$780$	−39160.0	−	33991.8i	−1.79763	−	1.56039i
$781$	−5449.36			−0.249671
$782$	−5661.91	+	9806.72i	−0.258912	+	0.448450i
$783$	−239.514	+	414.851i	−0.0109317	+	0.0189343i
$784$	7856.23	+	13607.4i	0.357882	+	0.619870i
$785$	−7291.44			−0.331519
$786$	−48403.6	−	83837.5i	−2.19656	−	3.80456i
$787$	14565.7	+	25228.6i	0.659737	+	1.14270i	0.980684	+	0.195600i	$0.0626655\pi$
$787$	14565.7	+	25228.6i	0.659737	+	1.14270i	−0.320947	+	0.947097i	$0.604001\pi$
$788$	−9450.86			−0.427250
$789$	11322.0	+	19610.3i	0.510867	+	0.884847i
$790$	−13723.4	+	23769.7i	−0.618047	+	1.07049i
$791$	1200.94	−	2080.09i	0.0539830	−	0.0935013i
$792$	−15184.6			−0.681266
$793$	5932.66	−	30638.6i	0.265668	−	1.37201i
$794$	9230.58			0.412571
$795$	−14171.9	+	24546.5i	−0.632234	+	1.09506i
$796$	23408.9	−	40545.5i	1.04235	−	1.80540i
$797$	4894.21	+	8477.03i	0.217518	+	0.376752i	0.954049	−	0.299652i	$-0.0968705\pi$
$797$	4894.21	+	8477.03i	0.217518	+	0.376752i	−0.736530	+	0.676404i	$0.763537\pi$
$798$	21923.8			0.972549
$799$	−2675.85	−	4634.71i	−0.118479	−	0.205212i
$800$	−4489.43	−	7775.91i	−0.198406	−	0.343650i
$801$	−19397.4			−0.855647
$802$	10967.6	+	18996.4i	0.482892	+	0.836393i
$803$	−2719.76	+	4710.77i	−0.119525	+	0.207023i
$804$	−53254.9	+	92240.2i	−2.33602	+	4.04610i
$805$	−15700.3			−0.687407
$806$	−3201.54	+	1104.96i	−0.139912	+	0.0482883i
$807$	−28919.6			−1.26149
$808$	17647.1	−	30565.7i	0.768346	−	1.33081i
$809$	−16755.4	+	29021.2i	−0.728169	+	1.26122i	0.229488	+	0.973312i	$0.426295\pi$
$809$	−16755.4	+	29021.2i	−0.728169	+	1.26122i	−0.957656	+	0.287913i	$0.907038\pi$
$810$	−15159.5	−	26257.1i	−0.657595	−	1.13899i
$811$	−25368.7			−1.09842			−0.549208	−	0.835686i	$-0.685070\pi$
$811$	−25368.7			−1.09842			−0.549208	+	0.835686i	$0.685070\pi$
$812$	−12313.9	−	21328.3i	−0.532184	−	0.921769i
$813$	−14454.0	−	25035.0i	−0.623521	−	1.07997i
$814$	−20380.8			−0.877576
$815$	5826.24	+	10091.3i	0.250410	+	0.433723i
$816$	−6940.32	+	12021.0i	−0.297745	+	0.515709i
$817$	10423.8	−	18054.6i	0.446369	−	0.773135i
$818$	26476.7			1.13171
$819$	17396.9	−	6004.25i	0.742244	−	0.256173i
$820$	−17131.3			−0.729574
$821$	−3432.85	+	5945.88i	−0.145929	+	0.252756i	−0.929719	−	0.368270i	$-0.879950\pi$
$821$	−3432.85	+	5945.88i	−0.145929	+	0.252756i	0.783790	+	0.621025i	$0.213284\pi$
$822$	−40321.9	+	69839.7i	−1.71094	+	2.96343i
$823$	−11816.4	−	20466.6i	−0.500478	−	0.866853i	−1.00000		0.000551524i	$-0.999824\pi$
$823$	−11816.4	−	20466.6i	−0.500478	−	0.866853i	0.499522	−	0.866301i	$-0.333509\pi$
$824$	−92266.4			−3.90079
$825$	−2215.91	−	3838.07i	−0.0935128	−	0.161969i
$826$	21667.6	+	37529.3i	0.912725	+	1.58089i
$827$	16496.1			0.693621			0.346810	−	0.937935i	$-0.387265\pi$
$827$	16496.1			0.693621			0.346810	+	0.937935i	$0.387265\pi$
$828$	−32474.1	−	56246.8i	−1.36299	−	2.36076i
$829$	7457.17	−	12916.2i	0.312422	−	0.541131i	−0.666464	−	0.745537i	$-0.732193\pi$
$829$	7457.17	−	12916.2i	0.312422	−	0.541131i	0.978886	+	0.204406i	$0.0655263\pi$
$830$	17378.2	−	30099.9i	0.726754	−	1.25878i
$831$	5542.38			0.231364
$832$	−1791.67	−	1555.21i	−0.0746573	−	0.0648044i
$833$	2394.78			0.0996091
$834$	−3233.71	+	5600.94i	−0.134261	+	0.232548i
$835$	−1483.14	+	2568.87i	−0.0614684	+	0.106466i
$836$	4029.85	+	6979.90i	0.166717	+	0.288762i
$837$	69.9523			0.00288878
$838$	38454.6	+	66605.3i	1.58519	+	2.74563i
$839$	15824.0	+	27408.1i	0.651140	+	1.12781i	0.982847	+	0.184425i	$0.0590424\pi$
$839$	15824.0	+	27408.1i	0.651140	+	1.12781i	−0.331706	+	0.943383i	$0.607624\pi$
$840$	−43965.3			−1.80589
$841$	7453.18	+	12909.3i	0.305596	+	0.529308i
$842$	23218.7	−	40215.9i	0.950319	−	1.64600i
$843$	16560.5	−	28683.5i	0.676598	−	1.17190i
$844$	2664.60			0.108672
$845$	2593.75	+	18264.7i	0.105595	+	0.743581i
$846$	44475.1			1.80743
$847$	858.647	−	1487.22i	0.0348329	−	0.0603324i
$848$	25334.9	−	43881.3i	1.02595	−	1.77699i
$849$	−9942.75	−	17221.3i	−0.401925	−	0.696154i
$850$	−4683.79			−0.189003
$851$	−24018.9	−	41601.9i	−0.967516	−	1.67579i
$852$	−32634.7	−	56525.0i	−1.31226	−	2.27290i
$853$	−18058.9			−0.724883			−0.362442	−	0.932006i	$-0.618057\pi$
$853$	−18058.9			−0.724883			−0.362442	+	0.932006i	$0.618057\pi$
$854$	−24007.8	−	41582.7i	−0.961977	−	1.66619i
$855$	4775.84	−	8271.99i	0.191029	−	0.330873i
$856$	50148.1	−	86859.1i	2.00237	−	3.46820i
$857$	−1170.83			−0.0466682			−0.0233341	−	0.999728i	$-0.507428\pi$
$857$	−1170.83			−0.0466682			−0.0233341	+	0.999728i	$0.507428\pi$
$858$	14628.2	+	12697.6i	0.582050	+	0.505233i
$859$	29295.1			1.16360			0.581802	−	0.813330i	$-0.302348\pi$
$859$	29295.1			1.16360			0.581802	+	0.813330i	$0.302348\pi$
$860$	−37933.5	+	65702.8i	−1.50410	+	2.60517i
$861$	6006.96	−	10404.4i	0.237766	−	0.411823i
$862$	40986.8	+	70991.2i	1.61951	+	2.80507i
$863$	40519.5			1.59826			0.799131	−	0.601156i	$-0.205293\pi$
$863$	40519.5			1.59826			0.799131	+	0.601156i	$0.205293\pi$
$864$	−405.279	−	701.964i	−0.0159582	−	0.0276404i
$865$	3585.75	+	6210.71i	0.140947	+	0.244128i
$866$	67176.2			2.63596
$867$	−17104.6	−	29626.0i	−0.670014	−	1.16050i
$868$	−1798.19	+	3114.56i	−0.0703164	+	0.121792i
$869$	3538.02	−	6128.03i	0.138112	−	0.239217i
$870$	−30719.6			−1.19712
$871$	35818.7	−	12362.2i	1.39342	−	0.480915i
$872$	82616.0			3.20841
$873$	11208.5	−	19413.7i	0.434537	−	0.752641i
$874$	−13762.6	+	23837.5i	−0.532639	+	0.922558i
$875$	−10695.3	−	18524.8i	−0.413220	−	0.715719i
$876$	−65151.7			−2.51287
$877$	−7442.80	−	12891.3i	−0.286574	−	0.496361i	0.686415	−	0.727210i	$-0.259183\pi$
$877$	−7442.80	−	12891.3i	−0.286574	−	0.496361i	−0.972990	+	0.230848i	$0.925850\pi$
$878$	5023.26	+	8700.54i	0.193083	+	0.334429i
$879$	−11576.6			−0.444218
$880$	−5125.63	−	8877.85i	−0.196346	−	0.340082i
$881$	24277.8	−	42050.3i	0.928421	−	1.60807i	0.142456	−	0.989801i	$-0.454500\pi$
$881$	24277.8	−	42050.3i	0.928421	−	1.60807i	0.785965	−	0.618271i	$-0.212167\pi$
$882$	−9950.86	+	17235.4i	−0.379890	+	0.657989i
$883$	44627.8			1.70084			0.850422	−	0.526101i	$-0.176346\pi$
$883$	44627.8			1.70084			0.850422	+	0.526101i	$0.176346\pi$
$884$	13355.7	−	4609.49i	0.508146	−	0.175378i
$885$	37306.1			1.41698
$886$	−20816.5	+	36055.2i	−0.789327	+	1.36715i
$887$	−196.547	+	340.430i	−0.00744015	+	0.0128867i	−0.869722	−	0.493543i	$-0.835702\pi$
$887$	−196.547	+	340.430i	−0.00744015	+	0.0128867i	0.862281	+	0.506430i	$0.169035\pi$
$888$	−67259.7	−	116497.i	−2.54177	−	4.40247i
$889$	−8487.39			−0.320200
$890$	−14958.0	−	25908.0i	−0.563362	−	0.975771i
$891$	3908.26	+	6769.31i	0.146949	+	0.254523i
$892$	−9203.58			−0.345469
$893$	−6504.28	−	11265.7i	−0.243737	−	0.422165i
$894$	−37607.4	+	65137.9i	−1.40691	+	2.43684i
$895$	−8557.23	+	14821.6i	−0.319594	+	0.553553i
$896$	−22358.7			−0.833651
$897$	−8679.38	+	44823.7i	−0.323072	+	1.66847i
$898$	−47979.4			−1.78295
$899$	−692.373	+	1199.23i	−0.0256862	+	0.0444899i
$900$	13432.0	−	23264.9i	0.497482	−	0.861663i
$901$	−3861.37	−	6688.09i	−0.142776	−	0.247295i
$902$	6399.38			0.236226
$903$	−26602.3	−	46076.5i	−0.980363	−	1.69804i
$904$	4222.20	+	7313.06i	0.155341	+	0.269058i
$905$	31437.3			1.15471
$906$	−15125.8	−	26198.7i	−0.554659	−	0.960698i
$907$	−18922.2	+	32774.2i	−0.692725	+	1.19984i	0.278216	+	0.960519i	$0.410257\pi$
$907$	−18922.2	+	32774.2i	−0.692725	+	1.19984i	−0.970941	+	0.239317i	$0.923076\pi$
$908$	−46449.5	+	80452.8i	−1.69766	+	2.94044i
$909$	19568.8			0.714033
$910$	21434.9	+	18606.0i	0.780834	+	0.677783i
$911$	−18091.5			−0.657957			−0.328978	−	0.944337i	$-0.606704\pi$
$911$	−18091.5			−0.657957			−0.328978	+	0.944337i	$0.606704\pi$
$912$	−16870.0	+	29219.8i	−0.612525	+	1.06092i
$913$	−4480.25	+	7760.02i	−0.162404	+	0.281292i
$914$	−33369.1	−	57797.0i	−1.20761	−	2.09163i
$915$	−41335.3			−1.49345
$916$	−7836.10	−	13572.5i	−0.282655	−	0.489573i
$917$	18285.4	+	31671.3i	0.658493	+	1.14054i
$918$	−422.825			−0.0152019
$919$	3004.21	+	5203.45i	0.107834	+	0.186775i	0.914893	−	0.403697i	$-0.132275\pi$
$919$	3004.21	+	5203.45i	0.107834	+	0.186775i	−0.807058	+	0.590472i	$0.798942\pi$
$920$	27599.1	−	47803.0i	0.989037	−	1.71306i
$921$	−16945.8	+	29351.0i	−0.606279	+	1.05011i
$922$	−39595.8			−1.41434
$923$	−4414.24	+	22796.8i	−0.157418	+	0.812966i
$924$	20568.8			0.732321
$925$	9934.73	−	17207.5i	0.353137	−	0.611652i
$926$	12565.4	−	21764.0i	0.445925	−	0.772364i
$927$	−25578.4	−	44303.1i	−0.906262	−	1.56969i
$928$	16045.5			0.567584
$929$	−23738.4	−	41116.1i	−0.838354	−	1.45207i	−0.891271	−	0.453472i	$-0.850185\pi$
$929$	−23738.4	−	41116.1i	−0.838354	−	1.45207i	0.0529170	−	0.998599i	$-0.483148\pi$
$930$	2242.98	+	3884.96i	0.0790864	+	0.136982i
$931$	5821.08			0.204917
$932$	−47319.2	−	81959.2i	−1.66308	−	2.88054i
$933$	−30457.8	+	52754.4i	−1.06875	+	1.85113i
$934$	5908.18	−	10233.3i	0.206982	−	0.358504i
$935$	−1562.43			−0.0546490
$936$	−12300.3	+	63523.5i	−0.429538	+	2.21830i
$937$	−21379.3			−0.745390			−0.372695	−	0.927954i	$-0.621566\pi$
$937$	−21379.3			−0.745390			−0.372695	+	0.927954i	$0.621566\pi$
$938$	29149.9	−	50489.2i	1.01469	−	1.75750i
$939$	−2841.45	+	4921.54i	−0.0987512	+	0.171042i
$940$	23669.8	+	40997.3i	0.821303	+	1.42254i
$941$	−348.879			−0.0120862			−0.00604312	−	0.999982i	$-0.501924\pi$
$941$	−348.879			−0.0120862			−0.00604312	+	0.999982i	$0.501924\pi$
$942$	16311.6	+	28252.5i	0.564183	+	0.977193i
$943$	7541.69	+	13062.6i	0.260436	+	0.451089i
$944$	−66691.4			−2.29939
$945$	−293.120	−	507.699i	−0.0100901	−	0.0174767i
$946$	14170.1	−	24543.3i	0.487007	−	0.843520i
$947$	5164.14	−	8944.56i	0.177204	−	0.306926i	−0.763718	−	0.645550i	$-0.776628\pi$
$947$	5164.14	−	8944.56i	0.177204	−	0.306926i	0.940922	+	0.338624i	$0.109961\pi$
$948$	84753.0			2.90364
$949$	17503.9	+	15193.8i	0.598736	+	0.519717i
$950$	−11385.0			−0.388820
$951$	−28688.1	+	49689.2i	−0.978206	+	1.69430i
$952$	5989.54	−	10374.2i	0.203910	−	0.353182i
$953$	−2775.55	−	4807.40i	−0.0943431	−	0.163407i	0.814991	−	0.579473i	$-0.196742\pi$
$953$	−2775.55	−	4807.40i	−0.0943431	−	0.163407i	−0.909334	+	0.416066i	$0.863408\pi$
$954$	64179.4			2.17808
$955$	4848.04	+	8397.06i	0.164271	+	0.284526i
$956$	26725.8	+	46290.5i	0.904158	+	1.56605i
$957$	7919.79			0.267513
$958$	5533.27	+	9583.90i	0.186609	+	0.323217i
$959$	15232.4	−	26383.3i	0.512910	−	0.888386i
$960$	−1571.22	+	2721.43i	−0.0528237	+	0.0914934i
$961$	−29588.8			−0.993212
$962$	−16509.4	+	85261.1i	−0.553311	+	2.85751i
$963$	55608.9			1.86082
$964$	−3235.43	+	5603.92i	−0.108098	+	0.187230i
$965$	17834.6	−	30890.4i	0.594939	−	1.03046i
$966$	35122.9	+	60834.7i	1.16984	+	2.02622i
$967$	37547.1			1.24864			0.624320	−	0.781169i	$-0.285376\pi$
$967$	37547.1			1.24864			0.624320	+	0.781169i	$0.285376\pi$
$968$	3018.78	+	5228.68i	0.100235	+	0.173612i
$969$	2571.21	+	4453.47i	0.0852418	+	0.147643i
$970$	34573.0			1.14441
$971$	−15291.7	−	26486.0i	−0.505390	−	0.875361i	−0.999981	−	0.00623487i	$-0.998015\pi$
$971$	−15291.7	−	26486.0i	−0.505390	−	0.875361i	0.494591	−	0.869126i	$-0.335318\pi$
$972$	−47994.5	+	83128.9i	−1.58377	+	2.74317i
$973$	1221.60	−	2115.87i	0.0402493	−	0.0697139i
$974$	−44221.1			−1.45476
$975$	−17851.2	+	6161.02i	−0.586354	+	0.202370i
$976$	73894.4			2.42347
$977$	−4509.41	+	7810.53i	−0.147665	+	0.255764i	−0.930364	−	0.366637i	$-0.880509\pi$
$977$	−4509.41	+	7810.53i	−0.147665	+	0.255764i	0.782699	+	0.622401i	$0.213842\pi$
$978$	26067.6	−	45150.5i	0.852302	−	1.47623i
$979$	3856.29	+	6679.30i	0.125891	+	0.218050i
$980$	−21183.6			−0.690494
$981$	22903.1	+	39669.3i	0.745402	+	1.29107i
$982$	−24919.4	−	43161.7i	−0.809786	−	1.40259i
$983$	−31169.0			−1.01133			−0.505665	−	0.862730i	$-0.668753\pi$
$983$	−31169.0			−1.01133			−0.505665	+	0.862730i	$0.668753\pi$
$984$	21118.9	+	36579.0i	0.684194	+	1.18506i
$985$	2226.68	−	3856.73i	0.0720285	−	0.124757i
$986$	4185.03	−	7248.68i	0.135171	−	0.234123i
$987$	−33198.6			−1.07064
$988$	32464.1	−	11204.4i	1.04537	−	0.360790i
$989$	66797.8			2.14767
$990$	6492.23	−	11244.9i	0.208421	−	0.360995i
$991$	27697.7	−	47973.9i	0.887838	−	1.53778i	0.0454111	−	0.998968i	$-0.485540\pi$
$991$	27697.7	−	47973.9i	0.887838	−	1.53778i	0.842426	−	0.538811i	$-0.181126\pi$
$992$	−1171.56	−	2029.19i	−0.0374969	−	0.0649465i
$993$	−50578.3			−1.61637
$994$	17863.1	+	30939.9i	0.570005	+	0.987277i
$995$	11030.6	+	19105.6i	0.351451	+	0.608730i
$996$	−107324.			−3.41435
$997$	21242.8	+	36793.7i	0.674792	+	1.16877i	0.976530	+	0.215383i	$0.0691001\pi$
$997$	21242.8	+	36793.7i	0.674792	+	1.16877i	−0.301737	+	0.953391i	$0.597567\pi$
$998$	−97.6575	+	169.148i	−0.00309749	+	0.00536501i
$999$	896.850	−	1553.39i	0.0284035	−	0.0491963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.b.100.16	✓	34
13.3	even	3	inner	143.4.e.b.133.16	yes	34
13.4	even	6		1859.4.a.h.1.16		17
13.9	even	3		1859.4.a.g.1.2		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.16	✓	34	1.1	even	1	trivial
143.4.e.b.133.16	yes	34	13.3	even	3	inner
1859.4.a.g.1.2		17	13.9	even	3
1859.4.a.h.1.16		17	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.54066 - 4.40055i) q^{2} +(3.69680 - 6.40305i) q^{3} +(-8.90987 - 15.4324i) q^{4} +8.39690 q^{5} +(-18.7846 - 32.5359i) q^{6} +(7.09626 + 12.2911i) q^{7} -49.8972 q^{8} +(-13.8327 - 23.9589i) q^{9} +O(q^{10})\)	\(q+(2.54066 - 4.40055i) q^{2} +(3.69680 - 6.40305i) q^{3} +(-8.90987 - 15.4324i) q^{4} +8.39690 q^{5} +(-18.7846 - 32.5359i) q^{6} +(7.09626 + 12.2911i) q^{7} -49.8972 q^{8} +(-13.8327 - 23.9589i) q^{9} +(21.3336 - 36.9509i) q^{10} +(-5.50000 + 9.52628i) q^{11} -131.752 q^{12} +(35.3970 + 30.7254i) q^{13} +72.1166 q^{14} +(31.0417 - 53.7657i) q^{15} +(-55.4927 + 96.1161i) q^{16} +(8.45781 + 14.6494i) q^{17} -140.576 q^{18} +(20.5587 + 35.6086i) q^{19} +(-74.8153 - 129.584i) q^{20} +104.934 q^{21} +(27.9472 + 48.4060i) q^{22} +(-65.8718 + 114.093i) q^{23} +(-184.460 + 319.494i) q^{24} -54.4921 q^{25} +(225.140 - 77.7033i) q^{26} -4.91923 q^{27} +(126.454 - 219.024i) q^{28} +(48.6894 - 84.3326i) q^{29} +(-157.732 - 273.201i) q^{30} -14.2202 q^{31} +(82.3868 + 142.698i) q^{32} +(40.6648 + 70.4335i) q^{33} +85.9535 q^{34} +(59.5866 + 103.207i) q^{35} +(-246.495 + 426.941i) q^{36} +(-182.315 + 315.779i) q^{37} +208.930 q^{38} +(327.592 - 113.063i) q^{39} -418.982 q^{40} +(57.2453 - 99.1517i) q^{41} +(266.601 - 461.766i) q^{42} +(-253.515 - 439.100i) q^{43} +196.017 q^{44} +(-116.152 - 201.180i) q^{45} +(334.715 + 579.744i) q^{46} -316.377 q^{47} +(410.291 + 710.644i) q^{48} +(70.7862 - 122.605i) q^{49} +(-138.446 + 239.795i) q^{50} +125.067 q^{51} +(158.783 - 820.019i) q^{52} -456.545 q^{53} +(-12.4981 + 21.6473i) q^{54} +(-46.1829 + 79.9912i) q^{55} +(-354.083 - 613.290i) q^{56} +304.005 q^{57} +(-247.406 - 428.520i) q^{58} +(300.452 + 520.397i) q^{59} -1106.31 q^{60} +(-332.902 - 576.603i) q^{61} +(-36.1286 + 62.5766i) q^{62} +(196.320 - 340.037i) q^{63} -50.6164 q^{64} +(297.225 + 257.998i) q^{65} +413.261 q^{66} +(404.206 - 700.105i) q^{67} +(150.716 - 261.048i) q^{68} +(487.030 + 843.560i) q^{69} +605.556 q^{70} +(247.698 + 429.025i) q^{71} +(690.211 + 1195.48i) q^{72} +494.502 q^{73} +(926.401 + 1604.57i) q^{74} +(-201.446 + 348.915i) q^{75} +(366.350 - 634.537i) q^{76} -156.118 q^{77} +(334.761 - 1728.84i) q^{78} -643.276 q^{79} +(-465.966 + 807.077i) q^{80} +(355.297 - 615.392i) q^{81} +(-290.881 - 503.821i) q^{82} +814.591 q^{83} +(-934.947 - 1619.38i) q^{84} +(71.0194 + 123.009i) q^{85} -2576.37 q^{86} +(-359.990 - 623.521i) q^{87} +(274.435 - 475.335i) q^{88} +(350.572 - 607.209i) q^{89} -1180.40 q^{90} +(-126.463 + 653.103i) q^{91} +2347.64 q^{92} +(-52.5692 + 91.0525i) q^{93} +(-803.805 + 1392.23i) q^{94} +(172.629 + 299.002i) q^{95} +1218.27 q^{96} +(405.147 + 701.735i) q^{97} +(-359.687 - 622.996i) q^{98} +304.319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * q^99

Introduction

L-functions

Modular forms

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