LMFDB - Embedded newform 201.4.e.b.37.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.14
Character	$\chi$	$=$	201.37
Dual form			201.4.e.b.163.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63047 + 2.82406i) q^{2} -3.00000 q^{3} +(-1.31688 + 2.28090i) q^{4} -0.0205579 q^{5} +(-4.89142 - 8.47218i) q^{6} +(2.93590 - 5.08512i) q^{7} +17.4990 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(1.63047 + 2.82406i) q^{2} -3.00000 q^{3} +(-1.31688 + 2.28090i) q^{4} -0.0205579 q^{5} +(-4.89142 - 8.47218i) q^{6} +(2.93590 - 5.08512i) q^{7} +17.4990 q^{8} +9.00000 q^{9} +(-0.0335191 - 0.0580568i) q^{10} +(-33.0822 + 57.3000i) q^{11} +(3.95064 - 6.84270i) q^{12} +(32.8916 + 56.9699i) q^{13} +19.1476 q^{14} +0.0616738 q^{15} +(39.0667 + 67.6655i) q^{16} +(-42.9501 - 74.3917i) q^{17} +(14.6742 + 25.4165i) q^{18} +(64.6072 + 111.903i) q^{19} +(0.0270723 - 0.0468906i) q^{20} +(-8.80769 + 15.2554i) q^{21} -215.758 q^{22} +(23.7597 + 41.1529i) q^{23} -52.4970 q^{24} -125.000 q^{25} +(-107.258 + 185.776i) q^{26} -27.0000 q^{27} +(7.73244 + 13.3930i) q^{28} +(43.8763 - 75.9960i) q^{29} +(0.100557 + 0.174171i) q^{30} +(-61.3415 + 106.247i) q^{31} +(-57.3982 + 99.4167i) q^{32} +(99.2465 - 171.900i) q^{33} +(140.058 - 242.587i) q^{34} +(-0.0603560 + 0.104540i) q^{35} +(-11.8519 + 20.5281i) q^{36} +(44.9793 + 77.9064i) q^{37} +(-210.680 + 364.909i) q^{38} +(-98.6748 - 170.910i) q^{39} -0.359744 q^{40} +(8.37546 - 14.5067i) q^{41} -57.4428 q^{42} +313.793 q^{43} +(-87.1304 - 150.914i) q^{44} -0.185021 q^{45} +(-77.4789 + 134.197i) q^{46} +(88.8502 - 153.893i) q^{47} +(-117.200 - 202.996i) q^{48} +(154.261 + 267.188i) q^{49} +(-203.808 - 353.006i) q^{50} +(128.850 + 223.175i) q^{51} -173.257 q^{52} -543.089 q^{53} +(-44.0227 - 76.2496i) q^{54} +(0.680101 - 1.17797i) q^{55} +(51.3753 - 88.9847i) q^{56} +(-193.821 - 335.709i) q^{57} +286.156 q^{58} +191.454 q^{59} +(-0.0812169 + 0.140672i) q^{60} +(252.524 + 437.385i) q^{61} -400.063 q^{62} +(26.4231 - 45.7661i) q^{63} +250.722 q^{64} +(-0.676183 - 1.17118i) q^{65} +647.274 q^{66} +(-13.7086 - 548.247i) q^{67} +226.240 q^{68} +(-71.2790 - 123.459i) q^{69} -0.393635 q^{70} +(94.7817 - 164.167i) q^{71} +157.491 q^{72} +(-406.971 - 704.895i) q^{73} +(-146.675 + 254.048i) q^{74} +374.999 q^{75} -340.319 q^{76} +(194.252 + 336.454i) q^{77} +(321.773 - 557.327i) q^{78} +(510.856 - 884.829i) q^{79} +(-0.803130 - 1.39106i) q^{80} +81.0000 q^{81} +54.6238 q^{82} +(463.876 + 803.456i) q^{83} +(-23.1973 - 40.1790i) q^{84} +(0.882964 + 1.52934i) q^{85} +(511.631 + 886.172i) q^{86} +(-131.629 + 227.988i) q^{87} +(-578.905 + 1002.69i) q^{88} -1548.63 q^{89} +(-0.301672 - 0.522512i) q^{90} +386.265 q^{91} -125.154 q^{92} +(184.025 - 318.740i) q^{93} +579.471 q^{94} +(-1.32819 - 2.30049i) q^{95} +(172.195 - 298.250i) q^{96} +(929.306 + 1609.60i) q^{97} +(-503.037 + 871.285i) q^{98} +(-297.739 + 515.700i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9} + 14 q^{10} - 16 q^{11} + 270 q^{12} - 46 q^{13} + 14 q^{14} + 12 q^{15} - 346 q^{16} - 8 q^{17} + 18 q^{18} - 154 q^{19} - 180 q^{20} - 66 q^{21} + 214 q^{22} - 104 q^{23} - 144 q^{24} + 1032 q^{25} - 333 q^{26} - 972 q^{27} - 473 q^{28} + 76 q^{29} - 42 q^{30} + 498 q^{31} - 285 q^{32} + 48 q^{33} + 26 q^{34} - 392 q^{35} - 810 q^{36} - 124 q^{37} + 20 q^{38} + 138 q^{39} + 638 q^{40} - 508 q^{41} - 42 q^{42} - 1400 q^{43} - 333 q^{44} - 36 q^{45} - 1372 q^{46} + 18 q^{47} + 1038 q^{48} - 238 q^{49} - 337 q^{50} + 24 q^{51} + 3640 q^{52} + 724 q^{53} - 54 q^{54} - 178 q^{55} - 829 q^{56} + 462 q^{57} - 1472 q^{58} + 720 q^{59} + 540 q^{60} + 232 q^{61} - 3882 q^{62} + 198 q^{63} + 3628 q^{64} - 1428 q^{65} - 642 q^{66} - 1164 q^{67} + 1634 q^{68} + 312 q^{69} + 2550 q^{70} + 406 q^{71} + 432 q^{72} - 2120 q^{73} + 1375 q^{74} - 3096 q^{75} + 4190 q^{76} - 800 q^{77} + 999 q^{78} + 1306 q^{79} - 1927 q^{80} + 2916 q^{81} - 794 q^{82} - 1010 q^{83} + 1419 q^{84} + 472 q^{85} + 737 q^{86} - 228 q^{87} - 1838 q^{88} + 1904 q^{89} + 126 q^{90} + 7340 q^{91} + 7368 q^{92} - 1494 q^{93} - 9862 q^{94} + 1678 q^{95} + 855 q^{96} - 2358 q^{97} - 2610 q^{98} - 144 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9 + 14 * q^10 - 16 * q^11 + 270 * q^12 - 46 * q^13 + 14 * q^14 + 12 * q^15 - 346 * q^16 - 8 * q^17 + 18 * q^18 - 154 * q^19 - 180 * q^20 - 66 * q^21 + 214 * q^22 - 104 * q^23 - 144 * q^24 + 1032 * q^25 - 333 * q^26 - 972 * q^27 - 473 * q^28 + 76 * q^29 - 42 * q^30 + 498 * q^31 - 285 * q^32 + 48 * q^33 + 26 * q^34 - 392 * q^35 - 810 * q^36 - 124 * q^37 + 20 * q^38 + 138 * q^39 + 638 * q^40 - 508 * q^41 - 42 * q^42 - 1400 * q^43 - 333 * q^44 - 36 * q^45 - 1372 * q^46 + 18 * q^47 + 1038 * q^48 - 238 * q^49 - 337 * q^50 + 24 * q^51 + 3640 * q^52 + 724 * q^53 - 54 * q^54 - 178 * q^55 - 829 * q^56 + 462 * q^57 - 1472 * q^58 + 720 * q^59 + 540 * q^60 + 232 * q^61 - 3882 * q^62 + 198 * q^63 + 3628 * q^64 - 1428 * q^65 - 642 * q^66 - 1164 * q^67 + 1634 * q^68 + 312 * q^69 + 2550 * q^70 + 406 * q^71 + 432 * q^72 - 2120 * q^73 + 1375 * q^74 - 3096 * q^75 + 4190 * q^76 - 800 * q^77 + 999 * q^78 + 1306 * q^79 - 1927 * q^80 + 2916 * q^81 - 794 * q^82 - 1010 * q^83 + 1419 * q^84 + 472 * q^85 + 737 * q^86 - 228 * q^87 - 1838 * q^88 + 1904 * q^89 + 126 * q^90 + 7340 * q^91 + 7368 * q^92 - 1494 * q^93 - 9862 * q^94 + 1678 * q^95 + 855 * q^96 - 2358 * q^97 - 2610 * q^98 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.63047	+	2.82406i	0.576459	+	0.998456i	0.995881	+	0.0906651i	$0.0288993\pi$
$2$	1.63047	+	2.82406i	0.576459	+	0.998456i	−0.419422	+	0.907791i	$0.637767\pi$
$3$	−3.00000			−0.577350
$3$	−3.00000			−0.577350
$4$	−1.31688	+	2.28090i	−0.164610	+	0.285113i
$5$	−0.0205579			−0.00183876			−0.000919379	−	1.00000i	$-0.500293\pi$
$5$	−0.0205579			−0.00183876			−0.000919379		1.00000i	$0.500293\pi$
$6$	−4.89142	−	8.47218i	−0.332819	−	0.576459i
$7$	2.93590	−	5.08512i	0.158524	−	0.274571i	−0.775813	−	0.630963i	$-0.782660\pi$
$7$	2.93590	−	5.08512i	0.158524	−	0.274571i	0.934336	+	0.356392i	$0.115993\pi$
$8$	17.4990			0.773355
$9$	9.00000			0.333333
$10$	−0.0335191	−	0.0580568i	−0.00105997	−	0.00183592i
$11$	−33.0822	+	57.3000i	−0.906786	+	1.57060i	−0.0882841	+	0.996095i	$0.528138\pi$
$11$	−33.0822	+	57.3000i	−0.906786	+	1.57060i	−0.818502	+	0.574504i	$0.805195\pi$
$12$	3.95064	−	6.84270i	0.0950376	−	0.164610i
$13$	32.8916	+	56.9699i	0.701730	+	1.21543i	0.967859	+	0.251494i	$0.0809219\pi$
$13$	32.8916	+	56.9699i	0.701730	+	1.21543i	−0.266129	+	0.963937i	$0.585745\pi$
$14$	19.1476			0.365529
$15$	0.0616738			0.00106161
$16$	39.0667	+	67.6655i	0.610417	+	1.05727i
$17$	−42.9501	−	74.3917i	−0.612760	−	1.06133i	−0.990773	−	0.135531i	$-0.956726\pi$
$17$	−42.9501	−	74.3917i	−0.612760	−	1.06133i	0.378013	−	0.925800i	$-0.376607\pi$
$18$	14.6742	+	25.4165i	0.192153	+	0.332819i
$19$	64.6072	+	111.903i	0.780100	+	1.35117i	0.931883	+	0.362759i	$0.118165\pi$
$19$	64.6072	+	111.903i	0.780100	+	1.35117i	−0.151783	+	0.988414i	$0.548502\pi$
$20$	0.0270723	−	0.0468906i	0.000302678	−	0.000524253i
$21$	−8.80769	+	15.2554i	−0.0915236	+	0.158524i
$22$	−215.758			−2.09090
$23$	23.7597	+	41.1529i	0.215401	+	0.373086i	0.953397	−	0.301720i	$-0.0975607\pi$
$23$	23.7597	+	41.1529i	0.215401	+	0.373086i	−0.737995	+	0.674806i	$0.764227\pi$
$24$	−52.4970			−0.446496
$25$	−125.000			−0.999997
$26$	−107.258	+	185.776i	−0.809037	+	1.40129i
$27$	−27.0000			−0.192450
$28$	7.73244	+	13.3930i	0.0521891	+	0.0903942i
$29$	43.8763	−	75.9960i	0.280953	−	0.486624i	−0.690667	−	0.723173i	$-0.742683\pi$
$29$	43.8763	−	75.9960i	0.280953	−	0.486624i	0.971620	+	0.236549i	$0.0760163\pi$
$30$	0.100557	+	0.174171i	0.000611973	+	0.00105997i
$31$	−61.3415	+	106.247i	−0.355396	+	0.615563i	−0.987186	−	0.159576i	$-0.948987\pi$
$31$	−61.3415	+	106.247i	−0.355396	+	0.615563i	0.631790	+	0.775140i	$0.282321\pi$
$32$	−57.3982	+	99.4167i	−0.317084	+	0.549205i
$33$	99.2465	−	171.900i	0.523533	−	0.906786i
$34$	140.058	−	242.587i	0.706462	−	1.22363i
$35$	−0.0603560	+	0.104540i	−0.000291486	+	0.000504869i
$36$	−11.8519	+	20.5281i	−0.0548700	+	0.0950376i
$37$	44.9793	+	77.9064i	0.199853	+	0.346155i	0.948481	−	0.316835i	$-0.102620\pi$
$37$	44.9793	+	77.9064i	0.199853	+	0.346155i	−0.748628	+	0.662990i	$0.769287\pi$
$38$	−210.680	+	364.909i	−0.899391	+	1.55779i
$39$	−98.6748	−	170.910i	−0.405144	−	0.701730i
$40$	−0.359744			−0.00142201
$41$	8.37546	−	14.5067i	0.0319031	−	0.0552578i	−0.849633	−	0.527374i	$-0.823177\pi$
$41$	8.37546	−	14.5067i	0.0319031	−	0.0552578i	0.881536	+	0.472117i	$0.156510\pi$
$42$	−57.4428			−0.211038
$43$	313.793			1.11286			0.556431	−	0.830894i	$-0.312170\pi$
$43$	313.793			1.11286			0.556431	+	0.830894i	$0.312170\pi$
$44$	−87.1304	−	150.914i	−0.298532	−	0.517072i
$45$	−0.185021			−0.000612919
$46$	−77.4789	+	134.197i	−0.248340	+	0.430138i
$47$	88.8502	−	153.893i	0.275747	−	0.477609i	−0.694576	−	0.719419i	$-0.744408\pi$
$47$	88.8502	−	153.893i	0.275747	−	0.477609i	0.970323	+	0.241811i	$0.0777413\pi$
$48$	−117.200	−	202.996i	−0.352424	−	0.610417i
$49$	154.261	+	267.188i	0.449741	+	0.778974i
$50$	−203.808	−	353.006i	−0.576457	−	0.998453i
$51$	128.850	+	223.175i	0.353777	+	0.612760i
$52$	−173.257			−0.462047
$53$	−543.089			−1.40753			−0.703765	−	0.710433i	$-0.748499\pi$
$53$	−543.089			−1.40753			−0.703765	+	0.710433i	$0.748499\pi$
$54$	−44.0227	−	76.2496i	−0.110940	−	0.192153i
$55$	0.680101	−	1.17797i	0.00166736	−	0.00288795i
$56$	51.3753	−	88.9847i	0.122595	−	0.212341i
$57$	−193.821	−	335.709i	−0.450391	−	0.780100i
$58$	286.156			0.647830
$59$	191.454			0.422461			0.211230	−	0.977436i	$-0.432253\pi$
$59$	191.454			0.422461			0.211230	+	0.977436i	$0.432253\pi$
$60$	−0.0812169	+	0.140672i	−0.000174751	+	0.000302678i
$61$	252.524	+	437.385i	0.530040	+	0.918056i	0.999386	+	0.0350420i	$0.0111565\pi$
$61$	252.524	+	437.385i	0.530040	+	0.918056i	−0.469346	+	0.883015i	$0.655510\pi$
$62$	−400.063			−0.819484
$63$	26.4231	−	45.7661i	0.0528412	−	0.0915236i
$64$	250.722			0.489692
$65$	−0.676183	−	1.17118i	−0.00129031	−	0.00223488i
$66$	647.274			1.20718
$67$	−13.7086	−	548.247i	−0.0249967	−	0.999688i
$67$	−13.7086	−	548.247i	−0.0249967	−	0.999688i
$68$	226.240			0.403465
$69$	−71.2790	−	123.459i	−0.124362	−	0.215401i
$70$	−0.393635			−0.000672120
$71$	94.7817	−	164.167i	0.158430	−	0.274408i	−0.775873	−	0.630889i	$-0.782690\pi$
$71$	94.7817	−	164.167i	0.158430	−	0.274408i	0.934303	+	0.356481i	$0.116024\pi$
$72$	157.491			0.257785
$73$	−406.971	−	704.895i	−0.652499	−	1.13016i	−0.982515	−	0.186186i	$-0.940387\pi$
$73$	−406.971	−	704.895i	−0.652499	−	1.13016i	0.330016	−	0.943975i	$-0.392946\pi$
$74$	−146.675	+	254.048i	−0.230414	+	0.399088i
$75$	374.999			0.577348
$76$	−340.319			−0.513649
$77$	194.252	+	336.454i	0.287494	+	0.497954i
$78$	321.773	−	557.327i	0.467098	−	0.809037i
$79$	510.856	−	884.829i	0.727542	−	1.26014i	−0.230377	−	0.973101i	$-0.573996\pi$
$79$	510.856	−	884.829i	0.727542	−	1.26014i	0.957919	−	0.287038i	$-0.0926706\pi$
$80$	−0.803130	−	1.39106i	−0.00112241	−	0.00194407i
$81$	81.0000			0.111111
$82$	54.6238			0.0735633
$83$	463.876	+	803.456i	0.613457	+	1.06254i	0.990653	+	0.136406i	$0.0435551\pi$
$83$	463.876	+	803.456i	0.613457	+	1.06254i	−0.377196	+	0.926134i	$0.623112\pi$
$84$	−23.1973	−	40.1790i	−0.0301314	−	0.0521891i
$85$	0.882964	+	1.52934i	0.00112672	+	0.00195153i
$86$	511.631	+	886.172i	0.641519	+	1.11114i
$87$	−131.629	+	227.988i	−0.162208	+	0.280953i
$88$	−578.905	+	1002.69i	−0.701267	+	1.21463i
$89$	−1548.63			−1.84443			−0.922217	−	0.386673i	$-0.873624\pi$
$89$	−1548.63			−1.84443			−0.922217	+	0.386673i	$0.873624\pi$
$90$	−0.301672	−	0.522512i	−0.000353323	−	0.000611973i
$91$	386.265			0.444963
$92$	−125.154			−0.141829
$93$	184.025	−	318.740i	0.205188	−	0.355396i
$94$	579.471			0.635828
$95$	−1.32819	−	2.30049i	−0.00143441	−	0.00248448i
$96$	172.195	−	298.250i	0.183068	−	0.317084i
$97$	929.306	+	1609.60i	0.972750	+	1.68485i	0.687170	+	0.726497i	$0.258853\pi$
$97$	929.306	+	1609.60i	0.972750	+	1.68485i	0.285580	+	0.958355i	$0.407814\pi$
$98$	−503.037	+	871.285i	−0.518514	+	0.898093i
$99$	−297.739	+	515.700i	−0.302262	+	0.523533i
$100$	164.609	−	285.112i	0.164609	−	0.285112i
$101$	903.274	−	1564.52i	0.889892	−	1.54134i	0.0498900	−	0.998755i	$-0.484113\pi$
$101$	903.274	−	1564.52i	0.889892	−	1.54134i	0.840002	−	0.542583i	$-0.182554\pi$
$102$	−420.173	+	727.761i	−0.407876	+	0.706462i
$103$	747.684	−	1295.03i	0.715257	−	1.23886i	−0.247603	−	0.968862i	$-0.579643\pi$
$103$	747.684	−	1295.03i	0.715257	−	1.23886i	0.962860	−	0.270001i	$-0.0870239\pi$
$104$	575.571	+	996.917i	0.542686	+	0.939960i
$105$	0.181068	−	0.313619i	0.000168290	−	0.000291486i
$106$	−885.492	−	1533.72i	−0.811383	−	1.40536i
$107$	−167.587			−0.151414			−0.0757070	−	0.997130i	$-0.524121\pi$
$107$	−167.587			−0.151414			−0.0757070	+	0.997130i	$0.524121\pi$
$108$	35.5557	−	61.5843i	0.0316792	−	0.0548700i
$109$	649.433			0.570682			0.285341	−	0.958426i	$-0.407893\pi$
$109$	649.433			0.570682			0.285341	+	0.958426i	$0.407893\pi$
$110$	4.43554			0.00384466
$111$	−134.938	−	233.719i	−0.115385	−	0.199853i
$112$	458.783			0.387062
$113$	362.545	−	627.947i	0.301818	−	0.522763i	−0.674730	−	0.738064i	$-0.735740\pi$
$113$	362.545	−	627.947i	0.301818	−	0.522763i	0.976548	+	0.215301i	$0.0690733\pi$
$114$	632.041	−	1094.73i	0.519264	−	0.899391i
$115$	−0.488449	−	0.846019i	−0.000396071	−	0.000686015i
$116$	115.560	+	200.155i	0.0924951	+	0.160206i
$117$	296.024	+	512.729i	0.233910	+	0.405144i
$118$	312.160	+	540.677i	0.243531	+	0.421808i
$119$	−504.388			−0.388547
$120$	1.07923			0.000820998
$121$	−1523.36	−	2638.53i	−1.14452	−	1.98237i
$122$	−823.468	+	1426.29i	−0.611093	+	1.05844i
$123$	−25.1264	+	43.5201i	−0.0184193	+	0.0319031i
$124$	−161.559	−	279.828i	−0.117003	−	0.202656i
$125$	5.13947			0.00367751
$126$	172.328			0.121843
$127$	1018.92	−	1764.82i	0.711925	−	1.23309i	−0.252209	−	0.967673i	$-0.581157\pi$
$127$	1018.92	−	1764.82i	0.711925	−	1.23309i	0.964134	−	0.265417i	$-0.0855096\pi$
$128$	867.981	+	1503.39i	0.599371	+	1.03814i
$129$	−941.380			−0.642511
$130$	2.20500	−	3.81916i	0.00148762	−	0.00257664i
$131$	−693.607			−0.462601			−0.231300	−	0.972882i	$-0.574298\pi$
$131$	−693.607			−0.462601			−0.231300	+	0.972882i	$0.574298\pi$
$132$	261.391	+	452.743i	0.172357	+	0.298532i
$133$	758.720			0.494657
$134$	1525.93	−	932.616i	0.983735	−	0.601237i
$135$	0.555064			0.000353869
$136$	−751.584	−	1301.78i	−0.473881	−	0.820785i
$137$	−1411.35			−0.880143			−0.440072	−	0.897963i	$-0.645047\pi$
$137$	−1411.35			−0.880143			−0.440072	+	0.897963i	$0.645047\pi$
$138$	232.437	−	402.592i	0.143379	−	0.248340i
$139$	−2809.63			−1.71446			−0.857230	−	0.514934i	$-0.827816\pi$
$139$	−2809.63			−1.71446			−0.857230	+	0.514934i	$0.827816\pi$
$140$	−0.158963	−	0.275332i	−9.59631e−5	−	0.000166213i
$141$	−266.551	+	461.679i	−0.159203	+	0.275747i
$142$	618.156			0.365313
$143$	−4352.50			−2.54527
$144$	351.600	+	608.989i	0.203472	+	0.352424i
$145$	−0.902006	+	1.56232i	−0.000516603	+	0.000894783i
$146$	1327.11	−	2298.62i	0.752278	−	1.30298i
$147$	−462.783	−	801.564i	−0.259658	−	0.449741i
$148$	−236.929			−0.131591
$149$	156.495			0.0860440			0.0430220	−	0.999074i	$-0.486301\pi$
$149$	156.495			0.0860440			0.0430220	+	0.999074i	$0.486301\pi$
$150$	611.425	+	1059.02i	0.332818	+	0.576457i
$151$	−900.278	−	1559.33i	−0.485189	−	0.840373i	0.514666	−	0.857391i	$-0.327916\pi$
$151$	−900.278	−	1559.33i	−0.485189	−	0.840373i	−0.999855	+	0.0170182i	$0.994583\pi$
$152$	1130.56	+	1958.19i	0.603294	+	1.04494i
$153$	−386.550	−	669.525i	−0.204253	−	0.353777i
$154$	−633.444	+	1097.16i	−0.331457	+	0.574100i
$155$	1.26105	−	2.18421i	0.000653486	−	0.00113187i
$156$	519.771			0.266763
$157$	−167.597	−	290.286i	−0.0851953	−	0.147563i	0.820279	−	0.571963i	$-0.193818\pi$
$157$	−167.597	−	290.286i	−0.0851953	−	0.147563i	−0.905474	+	0.424401i	$0.860485\pi$
$158$	3331.75			1.67759
$159$	1629.27			0.812637
$160$	1.17999	−	2.04380i	0.000583040	−	0.00100985i
$161$	279.024			0.136585
$162$	132.068	+	228.749i	0.0640510	+	0.110940i
$163$	−575.406	+	996.632i	−0.276499	+	0.478910i	−0.970512	−	0.241052i	$-0.922507\pi$
$163$	−575.406	+	996.632i	−0.276499	+	0.478910i	0.694014	+	0.719962i	$0.255841\pi$
$164$	22.0589	+	38.2072i	0.0105031	+	0.0181919i
$165$	−2.04030	+	3.53391i	−0.000962650	+	0.00166736i
$166$	−1512.67	+	2620.03i	−0.707266	+	1.22502i
$167$	−638.387	+	1105.72i	−0.295808	+	0.512354i	−0.975172	−	0.221447i	$-0.928922\pi$
$167$	−638.387	+	1105.72i	−0.295808	+	0.512354i	0.679365	+	0.733801i	$0.262255\pi$
$168$	−154.126	+	266.954i	−0.0707802	+	0.122595i
$169$	−1065.21	+	1845.00i	−0.484849	+	0.839784i
$170$	−2.87930	+	4.98709i	−0.00129901	+	0.00224995i
$171$	581.464	+	1007.13i	0.260033	+	0.450391i
$172$	−413.228	+	715.732i	−0.183188	+	0.317291i
$173$	−745.877	−	1291.90i	−0.327792	−	0.567752i	0.654282	−	0.756251i	$-0.272971\pi$
$173$	−745.877	−	1291.90i	−0.327792	−	0.567752i	−0.982073	+	0.188499i	$0.939638\pi$
$174$	−858.469			−0.374025
$175$	−366.986	+	635.638i	−0.158523	+	0.274570i
$176$	−5169.64			−2.21407
$177$	−574.362			−0.243908
$178$	−2525.00	−	4373.43i	−1.06324	−	1.84159i
$179$	4104.28			1.71379			0.856894	−	0.515493i	$-0.172391\pi$
$179$	4104.28			1.71379			0.856894	+	0.515493i	$0.172391\pi$
$180$	0.243651	−	0.422016i	0.000100893	−	0.000174751i
$181$	−1062.59	+	1840.46i	−0.436363	+	0.755802i	−0.997406	−	0.0719843i	$-0.977067\pi$
$181$	−1062.59	+	1840.46i	−0.436363	+	0.755802i	0.561043	+	0.827787i	$0.310400\pi$
$182$	629.795	+	1090.84i	0.256503	+	0.444276i
$183$	−757.573	−	1312.16i	−0.306019	−	0.530040i
$184$	415.771	+	720.136i	0.166582	+	0.288528i
$185$	−0.924681	−	1.60159i	−0.000367481	−	0.000636495i
$186$	1200.19			0.473129
$187$	5683.52			2.22257
$188$	234.010	+	405.317i	0.0907815	+	0.157238i
$189$	−79.2692	+	137.298i	−0.0305079	+	0.0528412i
$190$	4.33115	−	7.50177i	0.00165376	−	0.00286440i
$191$	844.211	+	1462.22i	0.319816	+	0.553938i	0.980450	−	0.196771i	$-0.0630454\pi$
$191$	844.211	+	1462.22i	0.319816	+	0.553938i	−0.660633	+	0.750709i	$0.729712\pi$
$192$	−752.166			−0.282724
$193$	−1895.85			−0.707079			−0.353539	−	0.935420i	$-0.615022\pi$
$193$	−1895.85			−0.707079			−0.353539	+	0.935420i	$0.615022\pi$
$194$	−3030.41	+	5248.83i	−1.12150	+	1.94250i
$195$	2.02855	+	3.51355i	0.000744961	+	0.00129031i
$196$	−812.572			−0.296127
$197$	358.363	−	620.704i	0.129606	−	0.224484i	−0.793918	−	0.608025i	$-0.791962\pi$
$197$	358.363	−	620.704i	0.129606	−	0.224484i	0.923524	+	0.383541i	$0.125295\pi$
$198$	−1941.82			−0.696966
$199$	171.585	+	297.194i	0.0611223	+	0.105867i	0.894967	−	0.446132i	$-0.147199\pi$
$199$	171.585	+	297.194i	0.0611223	+	0.105867i	−0.833845	+	0.551999i	$0.813865\pi$
$200$	−2187.37			−0.773352
$201$	41.1259	+	1644.74i	0.0144318	+	0.577170i
$202$	5891.05			2.05194
$203$	−257.633	−	446.233i	−0.0890752	−	0.154283i
$204$	−678.720			−0.232941
$205$	−0.172182	+	0.298228i	−5.86620e−5	+	0.000101606i
$206$	4876.31			1.64927
$207$	213.837	+	370.376i	0.0718005	+	0.124362i
$208$	−2569.93	+	4451.25i	−0.856696	+	1.48384i
$209$	−8549.37			−2.82953
$210$	1.18090			0.000388048
$211$	1331.23	+	2305.75i	0.434338	+	0.752296i	0.997241	−	0.0742267i	$-0.0236488\pi$
$211$	1331.23	+	2305.75i	0.434338	+	0.752296i	−0.562903	+	0.826523i	$0.690316\pi$
$212$	715.183	−	1238.73i	0.231693	−	0.401304i
$213$	−284.345	+	492.500i	−0.0914695	+	0.158430i
$214$	−273.247	−	473.277i	−0.0872839	−	0.151180i
$215$	−6.45094			−0.00204628
$216$	−472.473			−0.148832
$217$	360.185	+	623.859i	0.112677	+	0.195163i
$218$	1058.88	+	1834.04i	0.328975	+	0.569801i
$219$	1220.91	+	2114.69i	0.376720	+	0.652499i
$220$	1.79122	+	3.10248i	0.000548928	+	0.000950770i
$221$	2825.39	−	4893.72i	0.859984	−	1.48954i
$222$	440.025	−	762.145i	0.133029	−	0.230414i
$223$	2726.62			0.818781			0.409390	−	0.912359i	$-0.365741\pi$
$223$	2726.62			0.818781			0.409390	+	0.912359i	$0.365741\pi$
$224$	337.031	+	583.754i	0.100530	+	0.174124i
$225$	−1125.00			−0.333332
$226$	2364.48			0.695942
$227$	−49.5343	+	85.7959i	−0.0144833	+	0.0250858i	−0.873176	−	0.487405i	$-0.837944\pi$
$227$	−49.5343	+	85.7959i	−0.0144833	+	0.0250858i	0.858693	+	0.512490i	$0.171277\pi$
$228$	1020.96			0.296555
$229$	1472.01	+	2549.60i	0.424775	+	0.735731i	0.996399	−	0.0847838i	$-0.0270200\pi$
$229$	1472.01	+	2549.60i	0.424775	+	0.735731i	−0.571625	+	0.820515i	$0.693687\pi$
$230$	1.59281	−	2.75882i	0.000456637	−	0.000790919i
$231$	−582.755	−	1009.36i	−0.165985	−	0.287494i
$232$	767.792	−	1329.85i	0.217276	−	0.376333i
$233$	2174.89	−	3767.02i	0.611510	−	1.05917i	−0.379476	−	0.925202i	$-0.623896\pi$
$233$	2174.89	−	3767.02i	0.611510	−	1.05917i	0.990986	−	0.133965i	$-0.0427710\pi$
$234$	−965.319	+	1671.98i	−0.269679	+	0.467098i
$235$	−1.82658	+	3.16372i	−0.000507033	+	0.000878206i
$236$	−252.122	+	436.687i	−0.0695412	+	0.120449i
$237$	−1532.57	+	2654.49i	−0.420046	+	0.727542i
$238$	−822.390	−	1424.42i	−0.223982	−	0.387948i
$239$	−177.973	+	308.259i	−0.0481680	+	0.0834294i	−0.889104	−	0.457705i	$-0.848672\pi$
$239$	−177.973	+	308.259i	−0.0481680	+	0.0834294i	0.840936	+	0.541134i	$0.182005\pi$
$240$	2.40939	+	4.17319i	0.000648023	+	0.00112241i
$241$	−1297.40			−0.346776			−0.173388	−	0.984854i	$-0.555471\pi$
$241$	−1297.40			−0.346776			−0.173388	+	0.984854i	$0.555471\pi$
$242$	4967.59	−	8604.11i	1.31954	−	2.28551i
$243$	−243.000			−0.0641500
$244$	−1330.18			−0.348999
$245$	−3.17129	−	5.49283i	−0.000826964	−	0.00143234i
$246$	−163.871			−0.0424718
$247$	−4250.06	+	7361.33i	−1.09484	+	1.89632i
$248$	−1073.42	+	1859.21i	−0.274847	+	0.476049i
$249$	−1391.63	−	2410.37i	−0.354180	−	0.613457i
$250$	8.37977	+	14.5142i	0.00211993	+	0.00367183i
$251$	−3382.38	−	5858.46i	−0.850575	−	1.47324i	−0.880691	−	0.473692i	$-0.842921\pi$
$251$	−3382.38	−	5858.46i	−0.850575	−	1.47324i	0.0301161	−	0.999546i	$-0.490412\pi$
$252$	69.5920	+	120.537i	0.0173964	+	0.0301314i
$253$	−3144.08			−0.781292
$254$	6645.27			1.64158
$255$	−2.64889	−	4.58802i	−0.000650510	−	0.00112672i
$256$	−1827.55	+	3165.41i	−0.446179	+	0.772805i
$257$	−1744.77	+	3022.03i	−0.423485	+	0.733498i	−0.996278	−	0.0862024i	$-0.972527\pi$
$257$	−1744.77	+	3022.03i	−0.423485	+	0.733498i	0.572792	+	0.819701i	$0.305860\pi$
$258$	−1534.89	−	2658.51i	−0.370381	−	0.641519i
$259$	528.218			0.126725
$260$	3.56181			0.000849591
$261$	394.887	−	683.964i	0.0936508	−	0.162208i
$262$	−1130.91	−	1958.79i	−0.266670	−	0.461886i
$263$	7689.08			1.80277			0.901386	−	0.433017i	$-0.142551\pi$
$263$	7689.08			1.80277			0.901386	+	0.433017i	$0.142551\pi$
$264$	1736.72	−	3008.08i	0.404877	−	0.701267i
$265$	11.1648			0.00258810
$266$	1237.07	+	2142.67i	0.285149	+	0.493893i
$267$	4645.89			1.06488
$268$	1268.55	+	690.707i	0.289138	+	0.157432i
$269$	−8268.33			−1.87408			−0.937042	−	0.349216i	$-0.886448\pi$
$269$	−8268.33			−1.87408			−0.937042	+	0.349216i	$0.886448\pi$
$270$	0.905017	+	1.56753i	0.000203991	+	0.000353323i
$271$	7147.26			1.60208			0.801042	−	0.598608i	$-0.204279\pi$
$271$	7147.26			1.60208			0.801042	+	0.598608i	$0.204279\pi$
$272$	3355.83	−	5812.47i	0.748078	−	1.29571i
$273$	−1158.80			−0.256899
$274$	−2301.16	−	3985.73i	−0.507366	−	0.878784i
$275$	4135.26	−	7162.47i	0.906783	−	1.57059i
$276$	375.463			0.0818849
$277$	5973.35			1.29568			0.647841	−	0.761775i	$-0.275672\pi$
$277$	5973.35			1.29568			0.647841	+	0.761775i	$0.275672\pi$
$278$	−4581.03	−	7934.57i	−0.988316	−	1.71181i
$279$	−552.074	+	956.220i	−0.118465	+	0.205188i
$280$	−1.05617	+	1.82934i	−0.000225422	+	0.000390443i
$281$	−356.024	−	616.651i	−0.0755821	−	0.130912i	0.825757	−	0.564026i	$-0.190748\pi$
$281$	−356.024	−	616.651i	−0.0755821	−	0.130912i	−0.901339	+	0.433114i	$0.857415\pi$
$282$	−1738.41			−0.367096
$283$	−316.164			−0.0664098			−0.0332049	−	0.999449i	$-0.510571\pi$
$283$	−316.164			−0.0664098			−0.0332049	+	0.999449i	$0.510571\pi$
$284$	249.632	+	432.375i	0.0521582	+	0.0903407i
$285$	3.98457	+	6.90147i	0.000828159	+	0.00143441i
$286$	−7096.63	−	12291.7i	−1.46725	−	2.54135i
$287$	−49.1790	−	85.1805i	−0.0101148	−	0.0175193i
$288$	−516.584	+	894.750i	−0.105695	+	0.183068i
$289$	−1232.91	+	2135.47i	−0.250949	+	0.434657i
$290$	−5.88278			−0.00119120
$291$	−2787.92	−	4828.81i	−0.561617	−	0.972750i
$292$	2143.73			0.429631
$293$	6410.69			1.27821			0.639107	−	0.769118i	$-0.279304\pi$
$293$	6410.69			1.27821			0.639107	+	0.769118i	$0.279304\pi$
$294$	1509.11	−	2613.85i	0.299364	−	0.518514i
$295$	−3.93589			−0.000776802
$296$	787.093	+	1363.29i	0.154557	+	0.267701i
$297$	893.218	−	1547.10i	0.174511	−	0.302262i
$298$	255.160	+	441.951i	0.0496008	+	0.0859111i
$299$	−1562.99	+	2707.17i	−0.302307	+	0.523611i
$300$	−493.828	+	855.335i	−0.0950372	+	0.164609i
$301$	921.265	−	1595.68i	0.176415	−	0.305559i
$302$	2935.76	−	5084.88i	0.559384	−	0.968881i
$303$	−2709.82	+	4693.55i	−0.513779	+	0.889892i
$304$	−5047.98	+	8743.35i	−0.952372	+	1.64956i
$305$	−5.19138	−	8.99173i	−0.000974615	−	0.00168808i
$306$	1260.52	−	2183.28i	0.235487	−	0.407876i
$307$	758.114	+	1313.09i	0.140938	+	0.244111i	0.927850	−	0.372954i	$-0.121655\pi$
$307$	758.114	+	1313.09i	0.140938	+	0.244111i	−0.786912	+	0.617065i	$0.788322\pi$
$308$	−1023.22			−0.189297
$309$	−2243.05	+	3885.08i	−0.412954	+	0.715257i
$310$	8.22446			0.00150683
$311$	3230.92			0.589095			0.294547	−	0.955637i	$-0.404831\pi$
$311$	3230.92			0.589095			0.294547	+	0.955637i	$0.404831\pi$
$312$	−1726.71	−	2990.75i	−0.313320	−	0.542686i
$313$	4288.18			0.774384			0.387192	−	0.921999i	$-0.373445\pi$
$313$	4288.18			0.774384			0.387192	+	0.921999i	$0.373445\pi$
$314$	546.523	−	946.606i	0.0982232	−	0.170128i
$315$	−0.543204	+	0.940856i	−9.71621e−5	+	0.000168290i
$316$	1345.47	+	2330.42i	0.239521	+	0.414863i
$317$	894.890	+	1549.99i	0.158555	+	0.274626i	0.934348	−	0.356362i	$-0.115983\pi$
$317$	894.890	+	1549.99i	0.158555	+	0.274626i	−0.775793	+	0.630988i	$0.782650\pi$
$318$	2656.48	+	4601.15i	0.468452	+	0.811383i
$319$	2903.04	+	5028.22i	0.509528	+	0.882528i
$320$	−5.15433			−0.000900424
$321$	502.762			0.0874189
$322$	454.940	+	787.980i	0.0787355	+	0.136374i
$323$	5549.76	−	9612.47i	0.956028	−	1.65589i
$324$	−106.667	+	184.753i	−0.0182900	+	0.0316792i
$325$	−4111.44	−	7121.21i	−0.701727	−	1.21543i
$326$	−3752.73			−0.637560
$327$	−1948.30			−0.329484
$328$	146.562	−	253.853i	0.0246724	−	0.0427338i
$329$	−521.710	−	903.628i	−0.0874249	−	0.151424i
$330$	−13.3066			−0.00221971
$331$	−1329.18	+	2302.21i	−0.220720	+	0.382299i	−0.955027	−	0.296519i	$-0.904174\pi$
$331$	−1329.18	+	2302.21i	−0.220720	+	0.382299i	0.734307	+	0.678818i	$0.237507\pi$
$332$	−2443.47			−0.403925
$333$	404.814	+	701.158i	0.0666176	+	0.115385i
$334$	−4163.49			−0.682084
$335$	0.281821	+	11.2708i	4.59628e−5	+	0.00183818i
$336$	−1376.35			−0.223470
$337$	−1652.06	−	2861.45i	−0.267042	−	0.462531i	0.701054	−	0.713108i	$-0.252713\pi$
$337$	−1652.06	−	2861.45i	−0.267042	−	0.462531i	−0.968097	+	0.250577i	$0.919380\pi$
$338$	−6947.21			−1.11798
$339$	−1087.64	+	1883.84i	−0.174254	+	0.301818i
$340$	−4.65103			−0.000741875
$341$	−4058.62	−	7029.74i	−0.644535	−	1.11637i
$342$	−1896.12	+	3284.18i	−0.299797	+	0.519264i
$343$	3825.60			0.602225
$344$	5491.08			0.860636
$345$	1.46535	+	2.53806i	0.000228672	+	0.000396071i
$346$	2432.26	−	4212.80i	0.377917	−	0.654571i
$347$	−3327.71	+	5763.76i	−0.514815	+	0.891686i	0.485037	+	0.874494i	$0.338806\pi$
$347$	−3327.71	+	5763.76i	−0.514815	+	0.891686i	−0.999852	+	0.0171924i	$0.994527\pi$
$348$	−346.679	−	600.465i	−0.0534021	−	0.0924951i
$349$	7059.41			1.08276			0.541378	−	0.840779i	$-0.317903\pi$
$349$	7059.41			1.08276			0.541378	+	0.840779i	$0.317903\pi$
$350$	−2393.44			−0.365528
$351$	−888.073	−	1538.19i	−0.135048	−	0.233910i
$352$	−3797.72	−	6577.84i	−0.575054	−	0.996022i
$353$	3770.08	+	6529.97i	0.568445	+	0.984576i	0.996720	+	0.0809275i	$0.0257882\pi$
$353$	3770.08	+	6529.97i	0.568445	+	0.984576i	−0.428275	+	0.903649i	$0.640878\pi$
$354$	−936.481	−	1622.03i	−0.140603	−	0.243531i
$355$	−1.94852	+	3.37493i	−0.000291314	+	0.000504571i
$356$	2039.36	−	3532.28i	0.303612	−	0.525871i
$357$	1513.16			0.224328
$358$	6691.91	+	11590.7i	0.987928	+	1.71114i
$359$	−2074.39			−0.304964			−0.152482	−	0.988306i	$-0.548727\pi$
$359$	−2074.39			−0.304964			−0.152482	+	0.988306i	$0.548727\pi$
$360$	−3.23769			−0.000474004
$361$	−4918.67	+	8519.38i	−0.717112	+	1.24207i
$362$	−6930.09			−1.00618
$363$	4570.07	+	7915.60i	0.660790	+	1.14452i
$364$	−508.665	+	881.033i	−0.0732453	+	0.126865i
$365$	8.36649	+	14.4912i	0.00119979	+	0.00207809i
$366$	2470.41	−	4278.87i	0.352815	−	0.611093i
$367$	320.133	−	554.487i	0.0455335	−	0.0788664i	−0.842360	−	0.538915i	$-0.818835\pi$
$367$	320.133	−	554.487i	0.0455335	−	0.0788664i	0.887894	+	0.460048i	$0.152168\pi$
$368$	−1856.42	+	3215.42i	−0.262969	+	0.455476i
$369$	75.3791	−	130.560i	0.0106344	−	0.0184193i
$370$	3.01533	−	5.22271i	0.000423675	−	0.000733826i
$371$	−1594.45	+	2761.68i	−0.223127	+	0.386467i
$372$	484.676	+	839.484i	0.0675519	+	0.117003i
$373$	3558.24	−	6163.05i	0.493937	−	0.855524i	−0.506039	−	0.862511i	$-0.668891\pi$
$373$	3558.24	−	6163.05i	0.493937	−	0.855524i	0.999976	+	0.00698693i	$0.00222403\pi$
$374$	9266.82	+	16050.6i	1.28122	+	2.21914i
$375$	−15.4184			−0.00212321
$376$	1554.79	−	2692.98i	0.213251	−	0.369361i
$377$	5772.64			0.788611
$378$	−516.985			−0.0703461
$379$	5394.12	+	9342.89i	0.731075	+	1.26626i	0.956424	+	0.291981i	$0.0943144\pi$
$379$	5394.12	+	9342.89i	0.731075	+	1.26626i	−0.225349	+	0.974278i	$0.572352\pi$
$380$	6.99626			0.000944475
$381$	−3056.76	+	5294.46i	−0.411030	+	0.711925i
$382$	−2752.92	+	4768.20i	−0.368722	+	0.638645i
$383$	4390.16	+	7603.98i	0.585710	+	1.01448i	0.994787	+	0.101979i	$0.0325174\pi$
$383$	4390.16	+	7603.98i	0.585710	+	1.01448i	−0.409077	+	0.912500i	$0.634149\pi$
$384$	−2603.94	−	4510.16i	−0.346047	−	0.599371i
$385$	−3.99341	−	6.91679i	−0.000528631	−	0.000915616i
$386$	−3091.13	−	5353.99i	−0.407602	−	0.705987i
$387$	2824.14			0.370954
$388$	−4895.13			−0.640497
$389$	997.362	+	1727.48i	0.129995	+	0.225159i	0.923675	−	0.383178i	$-0.125170\pi$
$389$	997.362	+	1727.48i	0.129995	+	0.225159i	−0.793679	+	0.608337i	$0.791837\pi$
$390$	−6.61499	+	11.4575i	−0.000858879	+	0.00148762i
$391$	2040.96	−	3535.04i	0.263979	−	0.457224i
$392$	2699.42	+	4675.53i	0.347809	+	0.602423i
$393$	2080.82			0.267083
$394$	2337.21			0.298850
$395$	−10.5021	+	18.1902i	−0.00133777	+	0.00231709i
$396$	−784.174	−	1358.23i	−0.0995106	−	0.172357i
$397$	−11342.8			−1.43395			−0.716976	−	0.697098i	$-0.754474\pi$
$397$	−11342.8			−1.43395			−0.716976	+	0.697098i	$0.754474\pi$
$398$	−559.529	+	969.133i	−0.0704690	+	0.122056i
$399$	−2276.16			−0.285590
$400$	−4883.32	−	8458.16i	−0.610415	−	1.05727i
$401$	715.308			0.0890792			0.0445396	−	0.999008i	$-0.485818\pi$
$401$	715.308			0.0890792			0.0445396	+	0.999008i	$0.485818\pi$
$402$	−4577.80	+	2797.85i	−0.567959	+	0.347124i
$403$	−8070.48			−0.997567
$404$	2379.00	+	4120.56i	0.292970	+	0.507439i
$405$	−1.66519			−0.000204306
$406$	840.126	−	1455.14i	0.102696	−	0.177875i
$407$	−5952.05			−0.724894
$408$	2254.75	+	3905.34i	0.273595	+	0.473881i
$409$	−1598.25	+	2768.26i	−0.193224	+	0.334674i	−0.946317	−	0.323240i	$-0.895228\pi$
$409$	−1598.25	+	2768.26i	−0.193224	+	0.334674i	0.753093	+	0.657914i	$0.228561\pi$
$410$	−1.12295			−0.000135265
$411$	4234.04			0.508151
$412$	1969.22	+	3410.79i	0.235477	+	0.407858i
$413$	562.089	−	973.567i	0.0669699	−	0.115995i
$414$	−697.310	+	1207.78i	−0.0827800	+	0.143379i
$415$	−9.53632	−	16.5174i	−0.00112800	−	0.00195375i
$416$	−7551.68			−0.890028
$417$	8428.90			0.989844
$418$	−13939.5	−	24144.0i	−1.63111	−	2.82517i
$419$	−1064.55	−	1843.85i	−0.124121	−	0.214983i	0.797268	−	0.603625i	$-0.206278\pi$
$419$	−1064.55	−	1843.85i	−0.124121	−	0.214983i	−0.921389	+	0.388642i	$0.872944\pi$
$420$	0.476889	+	0.825996i	5.54043e−5	+	9.59631e-5i
$421$	−5182.32	−	8976.04i	−0.599931	−	1.03911i	−0.992831	−	0.119529i	$-0.961862\pi$
$421$	−5182.32	−	8976.04i	−0.599931	−	1.03911i	0.392900	−	0.919581i	$-0.371472\pi$
$422$	−4341.06	+	7518.93i	−0.500757	+	0.867336i
$423$	799.652	−	1385.04i	0.0919158	−	0.159203i
$424$	−9503.53			−1.08852
$425$	5368.74	+	9298.93i	0.612758	+	1.06133i
$426$	−1854.47			−0.210914
$427$	2965.54			0.336095
$428$	220.692	−	382.250i	0.0249242	−	0.0431700i
$429$	13057.5			1.46951
$430$	−10.5181	−	18.2179i	−0.00117960	−	0.00204312i
$431$	838.323	−	1452.02i	0.0936905	−	0.162277i	−0.815371	−	0.578939i	$-0.803467\pi$
$431$	838.323	−	1452.02i	0.0936905	−	0.162277i	0.909061	+	0.416662i	$0.136800\pi$
$432$	−1054.80	−	1826.97i	−0.117475	−	0.203472i
$433$	−5401.72	+	9356.05i	−0.599515	+	1.03839i	0.393378	+	0.919377i	$0.371306\pi$
$433$	−5401.72	+	9356.05i	−0.599515	+	1.03839i	−0.992893	+	0.119013i	$0.962027\pi$
$434$	−1174.54	+	2034.37i	−0.129908	+	0.225006i
$435$	2.70602	−	4.68696i	0.000298261	−	0.000516603i
$436$	−855.225	+	1481.29i	−0.0939400	+	0.162709i
$437$	−3070.09	+	5317.55i	−0.336069	+	0.582089i
$438$	−3981.33	+	6895.87i	−0.434328	+	0.752278i
$439$	4440.16	+	7690.58i	0.482727	+	0.836108i	0.999803	−	0.0198315i	$-0.00631297\pi$
$439$	4440.16	+	7690.58i	0.482727	+	0.836108i	−0.517076	+	0.855939i	$0.672980\pi$
$440$	11.9011	−	20.6133i	0.00128946	−	0.00223341i
$441$	1388.35	+	2404.69i	0.149914	+	0.259658i
$442$	18426.9			1.98298
$443$	7656.12	−	13260.8i	0.821113	−	1.42221i	−0.0837410	−	0.996488i	$-0.526687\pi$
$443$	7656.12	−	13260.8i	0.821113	−	1.42221i	0.904854	−	0.425722i	$-0.139980\pi$
$444$	710.787			0.0759741
$445$	31.8367			0.00339147
$446$	4445.68	+	7700.14i	0.471993	+	0.817517i
$447$	−469.484			−0.0496775
$448$	736.094	−	1274.95i	0.0776277	−	0.134455i
$449$	587.881	−	1018.24i	0.0617902	−	0.107024i	−0.833475	−	0.552556i	$-0.813652\pi$
$449$	587.881	−	1018.24i	0.0617902	−	0.107024i	0.895266	+	0.445533i	$0.146986\pi$
$450$	−1834.28	−	3177.06i	−0.192152	−	0.332818i
$451$	554.156	+	959.827i	0.0578585	+	0.100214i
$452$	954.856	+	1653.86i	0.0993643	+	0.172104i
$453$	2700.83	+	4677.98i	0.280124	+	0.485189i
$454$	−323.057			−0.0333961
$455$	−7.94082			−0.000818178
$456$	−3391.68	−	5874.57i	−0.348312	−	0.603294i
$457$	3377.03	−	5849.19i	0.345669	−	0.598717i	−0.639806	−	0.768536i	$-0.720985\pi$
$457$	3377.03	−	5849.19i	0.345669	−	0.598717i	0.985475	+	0.169820i	$0.0543186\pi$
$458$	−4800.16	+	8314.11i	−0.489730	+	0.848238i
$459$	1159.65	+	2008.58i	0.117926	+	0.204253i
$460$	2.57292			0.000260789
$461$	−17937.3			−1.81219			−0.906097	−	0.423070i	$-0.860952\pi$
$461$	−17937.3			−1.81219			−0.906097	+	0.423070i	$0.860952\pi$
$462$	1900.33	−	3291.47i	0.191367	−	0.331457i
$463$	8182.72	+	14172.9i	0.821346	+	1.42261i	0.904680	+	0.426091i	$0.140110\pi$
$463$	8182.72	+	14172.9i	0.821346	+	1.42261i	−0.0833346	+	0.996522i	$0.526557\pi$
$464$	6856.41			0.685993
$465$	−3.78316	+	6.55263i	−0.000377290	+	0.000653486i
$466$	14184.4			1.41004
$467$	−3491.90	−	6048.14i	−0.346008	−	0.599303i	0.639529	−	0.768767i	$-0.279130\pi$
$467$	−3491.90	−	6048.14i	−0.346008	−	0.599303i	−0.985536	+	0.169464i	$0.945796\pi$
$468$	−1559.31			−0.154016
$469$	−2828.15	−	1539.89i	−0.278448	−	0.151611i
$470$	−11.9127			−0.00116913
$471$	502.790	+	870.857i	0.0491875	+	0.0851953i
$472$	3350.25			0.326712
$473$	−10381.0	+	17980.4i	−1.00913	+	1.74786i
$474$	−9995.24			−0.968558
$475$	−8075.87	−	13987.8i	−0.780097	−	1.35117i
$476$	664.218	−	1150.46i	0.0639588	−	0.110780i
$477$	−4887.80			−0.469176
$478$	−1160.72			−0.111067
$479$	−4442.49	−	7694.63i	−0.423764	−	0.733980i	0.572540	−	0.819876i	$-0.305958\pi$
$479$	−4442.49	−	7694.63i	−0.423764	−	0.733980i	−0.996304	+	0.0858964i	$0.972625\pi$
$480$	−3.53997	+	6.13140i	−0.000336618	+	0.000583040i
$481$	−2958.88	+	5124.93i	−0.280485	+	0.485815i
$482$	−2115.38	−	3663.94i	−0.199902	−	0.346241i
$483$	−837.071			−0.0788573
$484$	8024.31			0.753598
$485$	−19.1046	−	33.0901i	−0.00178865	−	0.00309803i
$486$	−396.205	−	686.247i	−0.0369799	−	0.0640510i
$487$	−3423.08	−	5928.95i	−0.318511	−	0.551676i	0.661667	−	0.749798i	$-0.269849\pi$
$487$	−3423.08	−	5928.95i	−0.318511	−	0.551676i	−0.980177	+	0.198121i	$0.936516\pi$
$488$	4418.93	+	7653.81i	0.409909	+	0.709983i
$489$	1726.22	−	2989.90i	0.159637	−	0.276499i
$490$	10.3414	−	17.9118i	0.000953421	−	0.00165137i
$491$	−714.919			−0.0657105			−0.0328553	−	0.999460i	$-0.510460\pi$
$491$	−714.919			−0.0657105			−0.0328553	+	0.999460i	$0.510460\pi$
$492$	−66.1768	−	114.622i	−0.00606398	−	0.0105031i
$493$	−7537.96			−0.688626
$494$	−27718.4			−2.52452
$495$	6.12091	−	10.6017i	0.000555786	−	0.000962650i
$496$	−9585.64			−0.867758
$497$	−556.539	−	963.953i	−0.0502297	−	0.0870004i
$498$	4538.02	−	7860.08i	0.408340	−	0.707266i
$499$	−8248.88	−	14287.5i	−0.740021	−	1.28175i	−0.952485	−	0.304585i	$-0.901482\pi$
$499$	−8248.88	−	14287.5i	−0.740021	−	1.28175i	0.212464	−	0.977169i	$-0.431851\pi$
$500$	−6.76807	+	11.7226i	−0.000605354	+	0.00104850i
$501$	1915.16	−	3317.16i	0.170785	−	0.295808i
$502$	11029.8	−	19104.1i	0.980643	−	1.69852i
$503$	−105.706	+	183.088i	−0.00937016	+	0.0162296i	−0.870672	−	0.491863i	$-0.836316\pi$
$503$	−105.706	+	183.088i	−0.00937016	+	0.0162296i	0.861302	+	0.508093i	$0.169649\pi$
$504$	462.378	−	800.862i	0.0408650	−	0.0707802i
$505$	−18.5694	+	32.1632i	−0.00163630	+	0.00283415i
$506$	−5126.34	−	8879.08i	−0.450383	−	0.780086i
$507$	3195.64	−	5535.01i	0.279928	−	0.484849i
$508$	2683.59	+	4648.11i	0.234380	+	0.405957i
$509$	3790.06			0.330043			0.165021	−	0.986290i	$-0.447231\pi$
$509$	3790.06			0.330043			0.165021	+	0.986290i	$0.447231\pi$
$510$	8.63789	−	14.9613i	0.000749985	−	0.00129901i
$511$	−4779.31			−0.413746
$512$	1968.62			0.169925
$513$	−1744.39	−	3021.38i	−0.150130	−	0.260033i
$514$	−11379.2			−0.976488
$515$	−15.3708	+	26.6231i	−0.00131518	+	0.00227797i
$516$	1239.68	−	2147.20i	0.105764	−	0.183188i
$517$	5878.71	+	10182.2i	0.500088	+	0.866178i
$518$	861.245	+	1491.72i	0.0730520	+	0.126530i
$519$	2237.63	+	3875.69i	0.189251	+	0.327792i
$520$	−11.8325	−	20.4946i	−0.000997867	−	0.00172836i
$521$	−6659.42			−0.559990			−0.279995	−	0.960002i	$-0.590333\pi$
$521$	−6659.42			−0.559990			−0.279995	+	0.960002i	$0.590333\pi$
$522$	2575.41			0.215943
$523$	−657.033	−	1138.01i	−0.0549332	−	0.0951470i	0.837251	−	0.546819i	$-0.184161\pi$
$523$	−657.033	−	1138.01i	−0.0549332	−	0.0951470i	−0.892184	+	0.451671i	$0.850828\pi$
$524$	913.396	−	1582.05i	0.0761486	−	0.131893i
$525$	1100.96	−	1906.91i	0.0915233	−	0.158523i
$526$	12536.8	+	21714.4i	1.03922	+	1.79999i
$527$	10538.5			0.871089
$528$	15508.9			1.27829
$529$	4954.46	−	8581.37i	0.407204	−	0.705299i
$530$	18.2039	+	31.5300i	0.00149194	+	0.00258411i
$531$	1723.08			0.140820
$532$	−999.142	+	1730.57i	−0.0814254	+	0.141033i
$533$	1101.93			0.0895494
$534$	7575.00	+	13120.3i	0.613862	+	1.06324i
$535$	3.44525			0.000278413
$536$	−239.888	−	9593.79i	−0.0193313	−	0.773113i
$537$	−12312.8			−0.989456
$538$	−13481.3	−	23350.3i	−1.08033	−	1.87119i
$539$	−20413.1			−1.63127
$540$	−0.730952	+	1.26605i	−5.82503e−5	+	0.000100893i
$541$	−18165.7			−1.44363			−0.721817	−	0.692084i	$-0.756693\pi$
$541$	−18165.7			−1.44363			−0.721817	+	0.692084i	$0.756693\pi$
$542$	11653.4	+	20184.3i	0.923536	+	1.59961i
$543$	3187.77	−	5521.38i	0.251934	−	0.436363i
$544$	9861.03			0.777184
$545$	−13.3510			−0.00104935
$546$	−1889.38	−	3272.51i	−0.148092	−	0.256503i
$547$	5941.48	−	10291.0i	0.464423	−	0.804405i	−0.534752	−	0.845009i	$-0.679595\pi$
$547$	5941.48	−	10291.0i	0.464423	−	0.804405i	0.999175	+	0.0406044i	$0.0129283\pi$
$548$	1858.57	−	3219.15i	0.144880	−	0.250940i
$549$	2272.72	+	3936.47i	0.176680	+	0.306019i
$550$	26969.7			2.09089
$551$	11338.9			0.876684
$552$	−1247.31	−	2160.41i	−0.0961760	−	0.166582i
$553$	−2999.64	−	5195.53i	−0.230665	−	0.399524i
$554$	9739.39	+	16869.1i	0.746908	+	1.29368i
$555$	2.77404	+	4.80478i	0.000212165	+	0.000367481i
$556$	3699.95	−	6408.49i	0.282217	−	0.488814i
$557$	4711.48	−	8160.53i	0.358406	−	0.620777i	−0.629289	−	0.777171i	$-0.716654\pi$
$557$	4711.48	−	8160.53i	0.358406	−	0.620777i	0.987695	+	0.156395i	$0.0499872\pi$
$558$	−3600.56			−0.273161
$559$	10321.2	+	17876.8i	0.780928	+	1.35261i
$560$	−9.43163			−0.000711713
$561$	−17050.6			−1.28320
$562$	1160.97	−	2010.86i	0.0871400	−	0.150931i
$563$	−3262.45			−0.244220			−0.122110	−	0.992517i	$-0.538966\pi$
$563$	−3262.45			−0.244220			−0.122110	+	0.992517i	$0.538966\pi$
$564$	−702.030	−	1215.95i	−0.0524127	−	0.0907815i
$565$	−7.45318	+	12.9093i	−0.000554969	+	0.000961235i
$566$	−515.496	−	892.865i	−0.0382825	−	0.0663073i
$567$	237.808	−	411.895i	0.0176137	−	0.0305079i
$568$	1658.59	−	2872.76i	0.122522	−	0.212215i
$569$	8218.73	−	14235.3i	0.605531	−	1.04881i	−0.386437	−	0.922316i	$-0.626294\pi$
$569$	8218.73	−	14235.3i	0.605531	−	1.04881i	0.991967	−	0.126494i	$-0.0403724\pi$
$570$	−12.9935	+	22.5053i	−0.000954800	+	0.00165376i
$571$	142.882	−	247.480i	0.0104719	−	0.0181378i	−0.860742	−	0.509041i	$-0.830000\pi$
$571$	142.882	−	247.480i	0.0104719	−	0.0181378i	0.871214	+	0.490904i	$0.163333\pi$
$572$	5731.72	−	9927.62i	0.418977	−	0.725690i
$573$	−2532.63	−	4386.65i	−0.184646	−	0.319816i
$574$	160.370	−	277.769i	0.0116615	−	0.0201983i
$575$	−2969.95	−	5144.10i	−0.215401	−	0.373085i
$576$	2256.50			0.163231
$577$	1463.25	−	2534.43i	0.105574	−	0.182859i	−0.808399	−	0.588635i	$-0.799665\pi$
$577$	1463.25	−	2534.43i	0.105574	−	0.182859i	0.913972	+	0.405776i	$0.132999\pi$
$578$	−8040.93			−0.578648
$579$	5687.55			0.408232
$580$	−2.37567	−	4.11477i	−0.000170076	−	0.000294580i
$581$	5447.57			0.388990
$582$	9091.24	−	15746.5i	0.647499	−	1.12150i
$583$	17966.6	−	31119.0i	1.27633	−	2.21066i
$584$	−7121.60	−	12335.0i	−0.504613	−	0.874015i
$585$	−6.08565	−	10.5407i	−0.000430103	−	0.000744961i
$586$	10452.5	+	18104.2i	0.736838	+	1.27624i
$587$	11294.7	+	19563.1i	0.794180	+	1.37556i	0.923358	+	0.383939i	$0.125433\pi$
$587$	11294.7	+	19563.1i	0.794180	+	1.37556i	−0.129178	+	0.991621i	$0.541234\pi$
$588$	2437.72			0.170969
$589$	−15852.4			−1.10898
$590$	−6.41737	−	11.1152i	−0.000447795	−	0.000775603i
$591$	−1075.09	+	1862.11i	−0.0748279	+	0.129606i
$592$	−3514.38	+	6087.09i	−0.243987	+	0.422598i
$593$	8927.29	+	15462.5i	0.618212	+	1.07077i	0.989812	+	0.142382i	$0.0454760\pi$
$593$	8927.29	+	15462.5i	0.618212	+	1.07077i	−0.371600	+	0.928393i	$0.621191\pi$
$594$	5825.47			0.402394
$595$	10.3692			0.000714444
$596$	−206.085	+	356.949i	−0.0141637	+	0.0245322i
$597$	−514.755	−	891.582i	−0.0352890	−	0.0611223i
$598$	−10193.6			−0.697071
$599$	−12370.6	+	21426.5i	−0.843821	+	1.46154i	0.0428195	+	0.999083i	$0.486366\pi$
$599$	−12370.6	+	21426.5i	−0.843821	+	1.46154i	−0.886641	+	0.462459i	$0.846967\pi$
$600$	6562.11			0.446495
$601$	−11726.7	−	20311.2i	−0.795908	−	1.37855i	−0.922261	−	0.386567i	$-0.873661\pi$
$601$	−11726.7	−	20311.2i	−0.795908	−	1.37855i	0.126354	−	0.991985i	$-0.459673\pi$
$602$	6008.39			0.406783
$603$	−123.378	−	4934.23i	−0.00833222	−	0.333229i
$604$	4742.23			0.319468
$605$	31.3171	+	54.2428i	0.00210450	+	0.00364510i
$606$	−17673.2			−1.18469
$607$	−6987.38	+	12102.5i	−0.467231	+	0.809268i	−0.999299	−	0.0374338i	$-0.988082\pi$
$607$	−6987.38	+	12102.5i	−0.467231	+	0.809268i	0.532068	+	0.846702i	$0.321415\pi$
$608$	−14833.3			−0.989427
$609$	772.898	+	1338.70i	0.0514276	+	0.0890752i
$610$	16.9288	−	29.3215i	0.00112365	−	0.00194622i
$611$	11689.7			0.774001
$612$	2036.16			0.134488
$613$	5636.98	+	9763.54i	0.371412	+	0.643304i	0.989783	−	0.142582i	$-0.0455405\pi$
$613$	5636.98	+	9763.54i	0.371412	+	0.643304i	−0.618371	+	0.785886i	$0.712207\pi$
$614$	−2472.17	+	4281.92i	−0.162490	+	0.281440i
$615$	0.516546	−	0.894684i	3.38685e−5	−	5.86620e-5i
$616$	3399.21	+	5887.61i	0.222335	+	0.385095i
$617$	3654.45			0.238448			0.119224	−	0.992867i	$-0.461959\pi$
$617$	3654.45			0.238448			0.119224	+	0.992867i	$0.461959\pi$
$618$	−14628.9			−0.952204
$619$	11647.4	+	20173.9i	0.756299	+	1.30995i	0.944726	+	0.327861i	$0.106328\pi$
$619$	11647.4	+	20173.9i	0.756299	+	1.30995i	−0.188427	+	0.982087i	$0.560339\pi$
$620$	3.32131	+	5.75268i	0.000215141	+	0.000372634i
$621$	−641.511	−	1111.13i	−0.0414540	−	0.0718005i
$622$	5267.92	+	9124.30i	0.339589	+	0.588185i
$623$	−4546.62	+	7874.98i	−0.292386	+	0.506428i
$624$	7709.79	−	13353.8i	0.494613	−	0.856696i
$625$	15624.8			0.999990
$626$	6991.76	+	12110.1i	0.446401	+	0.773188i
$627$	25648.1			1.63363
$628$	882.818			0.0560960
$629$	3863.73	−	6692.17i	0.244923	−	0.424220i
$630$	−3.54271			−0.000224040
$631$	2312.10	+	4004.67i	0.145869	+	0.252652i	0.929697	−	0.368326i	$-0.120069\pi$
$631$	2312.10	+	4004.67i	0.145869	+	0.252652i	−0.783828	+	0.620978i	$0.786736\pi$
$632$	8939.48	−	15483.6i	0.562648	−	0.974534i
$633$	−3993.68	−	6917.26i	−0.250765	−	0.434338i
$634$	−2918.19	+	5054.45i	−0.182801	+	0.316621i
$635$	−20.9469	+	36.2810i	−0.00130906	+	0.00226735i
$636$	−2145.55	+	3716.20i	−0.133768	+	0.231693i
$637$	−10147.8	+	17576.5i	−0.631193	+	1.09326i
$638$	−9466.67	+	16396.7i	−0.587443	+	1.01748i
$639$	853.035	−	1477.50i	0.0528099	−	0.0914695i
$640$	−17.8439	−	30.9065i	−0.00110210	−	0.00190889i
$641$	12490.8	−	21634.7i	0.769669	−	1.33310i	−0.168074	−	0.985774i	$-0.553755\pi$
$641$	12490.8	−	21634.7i	0.769669	−	1.33310i	0.937743	−	0.347331i	$-0.112912\pi$
$642$	819.740	+	1419.83i	0.0503934	+	0.0872839i
$643$	8745.91			0.536399			0.268200	−	0.963363i	$-0.413571\pi$
$643$	8745.91			0.536399			0.268200	+	0.963363i	$0.413571\pi$
$644$	−367.441	+	636.426i	−0.0224832	+	0.0389421i
$645$	19.3528			0.00118142
$646$	36194.9			2.20444
$647$	−10995.9	−	19045.5i	−0.668151	−	1.15727i	−0.978421	−	0.206623i	$-0.933753\pi$
$647$	−10995.9	−	19045.5i	−0.668151	−	1.15727i	0.310270	−	0.950649i	$-0.399581\pi$
$648$	1417.42			0.0859283
$649$	−6333.71	+	10970.3i	−0.383081	+	0.663516i
$650$	13407.2	−	23221.9i	0.809034	−	1.40129i
$651$	−1080.55	−	1871.58i	−0.0650542	−	0.112677i
$652$	−1515.48	−	2624.89i	−0.0910288	−	0.157666i
$653$	−11018.7	−	19084.9i	−0.660329	−	1.14372i	−0.980529	−	0.196374i	$-0.937083\pi$
$653$	−11018.7	−	19084.9i	−0.660329	−	1.14372i	0.320200	−	0.947350i	$-0.396250\pi$
$654$	−3176.65	−	5502.11i	−0.189934	−	0.328975i
$655$	14.2591			0.000850610
$656$	1308.81			0.0778967
$657$	−3662.74	−	6344.06i	−0.217500	−	0.376720i
$658$	1701.27	−	2946.68i	0.100794	−	0.174580i
$659$	−8070.48	+	13978.5i	−0.477058	+	0.826289i	−0.999654	−	0.0262913i	$-0.991630\pi$
$659$	−8070.48	+	13978.5i	−0.477058	+	0.826289i	0.522596	+	0.852580i	$0.324964\pi$
$660$	−5.37366	−	9.30745i	−0.000316923	−	0.000548928i
$661$	3451.77			0.203114			0.101557	−	0.994830i	$-0.467618\pi$
$661$	3451.77			0.203114			0.101557	+	0.994830i	$0.467618\pi$
$662$	−8668.77			−0.508945
$663$	−8476.17	+	14681.2i	−0.496512	+	0.859984i
$664$	8117.37	+	14059.7i	0.474420	+	0.821720i
$665$	−15.5977			−0.000909554
$666$	−1320.07	+	2286.44i	−0.0768046	+	0.133029i
$667$	4169.94			0.242070
$668$	−1681.36	−	2912.20i	−0.0973857	−	0.168677i
$669$	−8179.86			−0.472723
$670$	−31.3700	+	19.1727i	−0.00180885	+	0.00110553i
$671$	−33416.2			−1.92253
$672$	−1011.09	−	1751.26i	−0.0580413	−	0.100530i
$673$	−25230.3			−1.44511			−0.722553	−	0.691316i	$-0.757031\pi$
$673$	−25230.3			−1.44511			−0.722553	+	0.691316i	$0.757031\pi$
$674$	5387.26	−	9331.02i	0.307878	−	0.533260i
$675$	3374.99			0.192449
$676$	−2805.52	−	4859.30i	−0.159622	−	0.276473i
$677$	2718.17	−	4708.00i	0.154310	−	0.267272i	−0.778498	−	0.627647i	$-0.784018\pi$
$677$	2718.17	−	4708.00i	0.154310	−	0.267272i	0.932807	+	0.360375i	$0.117351\pi$
$678$	−7093.44			−0.401802
$679$	10913.4			0.616815
$680$	15.4510	+	26.7619i	0.000871351	+	0.00150922i
$681$	148.603	−	257.388i	0.00836193	−	0.0144833i
$682$	13234.9	−	22923.6i	0.743097	−	1.28708i
$683$	11445.6	+	19824.3i	0.641220	+	1.11062i	0.985161	+	0.171634i	$0.0549046\pi$
$683$	11445.6	+	19824.3i	0.641220	+	1.11062i	−0.343941	+	0.938991i	$0.611762\pi$
$684$	−3062.87			−0.171216
$685$	29.0144			0.00161837
$686$	6237.54	+	10803.7i	0.347158	+	0.601295i
$687$	−4416.04	−	7648.81i	−0.245244	−	0.424775i
$688$	12258.9	+	21233.0i	0.679310	+	1.17660i
$689$	−17863.1	−	30939.7i	−0.987705	−	1.71076i
$690$	−4.77842	+	8.27646i	−0.000263640	+	0.000456637i
$691$	−9918.93	+	17180.1i	−0.546069	+	0.945820i	0.452469	+	0.891780i	$0.350543\pi$
$691$	−9918.93	+	17180.1i	−0.546069	+	0.945820i	−0.998539	+	0.0540400i	$0.982790\pi$
$692$	3928.92			0.215831
$693$	1748.26	+	3028.08i	0.0958313	+	0.165985i
$694$	−21703.0			−1.18708
$695$	57.7602			0.00315247
$696$	−2303.38	+	3989.56i	−0.125444	+	0.217276i
$697$	−1438.90			−0.0781957
$698$	11510.2	+	19936.2i	0.624164	+	1.08108i
$699$	−6524.67	+	11301.1i	−0.353056	+	0.611510i
$700$	−966.552	−	1674.12i	−0.0521889	−	0.0903939i
$701$	12987.2	−	22494.4i	0.699740	−	1.21199i	−0.268816	−	0.963192i	$-0.586632\pi$
$701$	12987.2	−	22494.4i	0.699740	−	1.21199i	0.968556	−	0.248794i	$-0.0800343\pi$
$702$	2895.96	−	5015.94i	0.155699	−	0.269679i
$703$	−5811.97	+	10066.6i	−0.311810	+	0.540071i
$704$	−8294.43	+	14366.4i	−0.444045	+	0.769109i
$705$	5.47973	−	9.49117i	0.000292735	−	0.000507033i
$706$	−12294.0	+	21293.9i	−0.655371	+	1.13514i
$707$	−5303.84	−	9186.52i	−0.282138	−	0.488677i
$708$	756.365	−	1310.06i	0.0401496	−	0.0695412i
$709$	−6517.93	−	11289.4i	−0.345255	−	0.598000i	0.640145	−	0.768254i	$-0.278874\pi$
$709$	−6517.93	−	11289.4i	−0.345255	−	0.598000i	−0.985400	+	0.170254i	$0.945541\pi$
$710$	−12.7080			−0.000671722
$711$	4597.70	−	7963.46i	0.242514	−	0.420046i
$712$	−27099.5			−1.42640
$713$	−5829.82			−0.306211
$714$	2467.17	+	4273.27i	0.129316	+	0.223982i
$715$	89.4784			0.00468014
$716$	−5404.83	+	9361.45i	−0.282106	+	0.488623i
$717$	533.920	−	924.777i	0.0278098	−	0.0481680i
$718$	−3382.23	−	5858.20i	−0.175799	−	0.304493i
$719$	−9219.07	−	15967.9i	−0.478183	−	0.828236i	0.521505	−	0.853248i	$-0.325371\pi$
$719$	−9219.07	−	15967.9i	−0.478183	−	0.828236i	−0.999687	+	0.0250120i	$0.992038\pi$
$720$	−7.22817	−	12.5196i	−0.000374136	−	0.000648023i
$721$	−4390.25	−	7604.13i	−0.226770	−	0.392778i
$722$	−32079.0			−1.65354
$723$	3892.20			0.200211
$724$	−2798.60	−	4847.32i	−0.143659	−	0.248825i
$725$	−5484.52	+	9499.46i	−0.280952	+	0.486622i
$726$	−14902.8	+	25812.3i	−0.761836	+	1.31954i
$727$	−8217.41	−	14233.0i	−0.419212	−	0.726096i	0.576649	−	0.816992i	$-0.304360\pi$
$727$	−8217.41	−	14233.0i	−0.419212	−	0.726096i	−0.995860	+	0.0908963i	$0.971027\pi$
$728$	6759.26			0.344114
$729$	729.000			0.0370370
$730$	−27.2827	+	47.2550i	−0.00138326	+	0.00239587i
$731$	−13477.4	−	23343.6i	−0.681917	−	1.18111i
$732$	3990.53			0.201495
$733$	4410.78	−	7639.69i	0.222259	−	0.384964i	−0.733235	−	0.679976i	$-0.761990\pi$
$733$	4410.78	−	7639.69i	0.222259	−	0.384964i	0.955494	+	0.295012i	$0.0953236\pi$
$734$	2087.87			0.104993
$735$	9.51386	+	16.4785i	0.000477448	+	0.000826964i
$736$	−5455.05			−0.273201
$737$	31868.1	+	17351.7i	1.59278	+	0.867243i
$738$	491.614			0.0245211
$739$	−11219.5	−	19432.8i	−0.558480	−	0.967316i	−0.997624	−	0.0688992i	$-0.978051\pi$
$739$	−11219.5	−	19432.8i	−0.558480	−	0.967316i	0.439143	−	0.898417i	$-0.355282\pi$
$740$	4.87077			0.000241964
$741$	12750.2	−	22084.0i	0.632105	−	1.09484i
$742$	−10398.9			−0.514493
$743$	−257.991	−	446.853i	−0.0127386	−	0.0220638i	0.859586	−	0.510991i	$-0.170722\pi$
$743$	−257.991	−	446.853i	−0.0127386	−	0.0220638i	−0.872324	+	0.488928i	$0.837388\pi$
$744$	3220.25	−	5577.64i	0.158683	−	0.274847i
$745$	−3.21721			−0.000158214
$746$	23206.4			1.13894
$747$	4174.88	+	7231.11i	0.204486	+	0.354180i
$748$	−7484.51	+	12963.6i	−0.365857	+	0.633682i
$749$	−492.020	+	852.203i	−0.0240027	+	0.0415739i
$750$	−25.1393	−	43.5426i	−0.00122394	−	0.00211993i
$751$	6712.80			0.326170			0.163085	−	0.986612i	$-0.447856\pi$
$751$	6712.80			0.326170			0.163085	+	0.986612i	$0.447856\pi$
$752$	13884.3			0.673284
$753$	10147.2	+	17575.4i	0.491079	+	0.850575i
$754$	9412.14	+	16302.3i	0.454602	+	0.787394i
$755$	18.5079	+	32.0565i	0.000892145	+	0.00154524i
$756$	−208.776	−	361.611i	−0.0100438	−	0.0173964i
$757$	11467.7	−	19862.7i	0.550596	−	0.953660i	−0.447636	−	0.894216i	$-0.647734\pi$
$757$	11467.7	−	19862.7i	0.550596	−	0.953660i	0.998232	−	0.0594443i	$-0.0189329\pi$
$758$	−17589.9	+	30466.7i	−0.842869	+	1.45989i
$759$	9432.25			0.451079
$760$	−23.2420	−	40.2563i	−0.00110931	−	0.00192138i
$761$	−9015.03			−0.429428			−0.214714	−	0.976677i	$-0.568882\pi$
$761$	−9015.03			−0.429428			−0.214714	+	0.976677i	$0.568882\pi$
$762$	−19935.8			−0.947767
$763$	1906.67	−	3302.45i	0.0904666	−	0.156693i
$764$	−4446.89			−0.210580
$765$	7.94668	+	13.7640i	0.000375572	+	0.000650510i
$766$	−14316.1	+	24796.2i	−0.675275	+	1.16961i
$767$	6297.22	+	10907.1i	0.296453	+	0.513472i
$768$	5482.65	−	9496.23i	0.257602	−	0.446179i
$769$	14596.4	−	25281.8i	0.684475	−	1.18554i	−0.289127	−	0.957291i	$-0.593365\pi$
$769$	14596.4	−	25281.8i	0.684475	−	1.18554i	0.973602	−	0.228254i	$-0.0733017\pi$
$770$	13.0223	−	22.5553i	0.000609469	−	0.00105563i
$771$	5234.31	−	9066.09i	0.244499	−	0.423485i
$772$	2496.60	−	4324.25i	0.116392	−	0.201597i
$773$	−18110.4	+	31368.1i	−0.842671	+	1.45955i	0.0449574	+	0.998989i	$0.485685\pi$
$773$	−18110.4	+	31368.1i	−0.842671	+	1.45955i	−0.887628	+	0.460560i	$0.847649\pi$
$774$	4604.68	+	7975.54i	0.213840	+	0.370381i
$775$	7667.67	−	13280.8i	0.355394	−	0.615561i
$776$	16261.9	+	28166.5i	0.752280	+	1.30299i
$777$	−1584.66			−0.0731650
$778$	−3252.34	+	5633.22i	−0.149874	+	0.259590i
$779$	2164.46			0.0995504
$780$	−10.6854			−0.000490512
$781$	6271.16	+	10862.0i	0.287324	+	0.497659i
$782$	13310.9			0.608691
$783$	−1184.66	+	2051.89i	−0.0540693	+	0.0936508i
$784$	−12052.9	+	20876.3i	−0.549059	+	0.950997i
$785$	3.44544	+	5.96767i	0.000156653	+	0.000271332i
$786$	3392.72	+	5876.36i	0.153962	+	0.266670i
$787$	−7036.54	−	12187.7i	−0.318711	−	0.552024i	0.661508	−	0.749938i	$-0.269917\pi$
$787$	−7036.54	−	12187.7i	−0.318711	−	0.552024i	−0.980219	+	0.197914i	$0.936583\pi$
$788$	943.843	+	1634.78i	0.0426688	+	0.0739045i
$789$	−23067.2			−1.04083
$790$	−68.4938			−0.00308468
$791$	−2128.79	−	3687.17i	−0.0956904	−	0.165741i
$792$	−5210.15	+	9024.24i	−0.233756	+	0.404877i
$793$	−16611.9	+	28772.6i	−0.743890	+	1.28846i
$794$	−18494.1	−	32032.7i	−0.826614	−	1.43174i
$795$	−33.4944			−0.00149424
$796$	−903.827			−0.0402453
$797$	4528.52	−	7843.63i	0.201265	−	0.348602i	−0.747671	−	0.664069i	$-0.768828\pi$
$797$	4528.52	−	7843.63i	0.201265	−	0.348602i	0.948936	+	0.315468i	$0.102161\pi$
$798$	−3711.21	−	6428.01i	−0.164631	−	0.285149i
$799$	−15264.5			−0.675868
$800$	7174.76	−	12427.0i	0.317082	−	0.549203i
$801$	−13937.7			−0.614811
$802$	1166.29	+	2020.07i	0.0513505	+	0.0889417i
$803$	53854.0			2.36671
$804$	−3805.65	−	2072.12i	−0.166934	−	0.0908932i
$805$	−5.73615			−0.000251146
$806$	−13158.7	−	22791.5i	−0.575056	−	0.996027i
$807$	24805.0			1.08200
$808$	15806.4	−	27377.5i	0.688202	−	1.19200i
$809$	−18821.3			−0.817952			−0.408976	−	0.912545i	$-0.634114\pi$
$809$	−18821.3			−0.817952			−0.408976	+	0.912545i	$0.634114\pi$
$810$	−2.71505	−	4.70260i	−0.000117774	−	0.000203991i
$811$	10414.2	−	18038.0i	0.450916	−	0.781009i	−0.547527	−	0.836788i	$-0.684431\pi$
$811$	10414.2	−	18038.0i	0.450916	−	0.781009i	0.998443	+	0.0557785i	$0.0177641\pi$
$812$	1357.08			0.0586506
$813$	−21441.8			−0.924964
$814$	−9704.65	−	16808.9i	−0.417872	−	0.723775i
$815$	11.8292	−	20.4887i	0.000508414	−	0.000880598i
$816$	−10067.5	+	17437.4i	−0.431903	+	0.748078i
$817$	20273.3	+	35114.4i	0.868143	+	1.50367i
$818$	−10423.6			−0.445543
$819$	3476.39			0.148321
$820$	−0.453486	−	0.785460i	−1.93127e−5	−	3.34506e-5i
$821$	−13486.4	−	23359.1i	−0.573298	−	0.992982i	−0.996224	−	0.0868174i	$-0.972330\pi$
$821$	−13486.4	−	23359.1i	−0.573298	−	0.992982i	0.422926	−	0.906164i	$-0.361003\pi$
$822$	6903.49	+	11957.2i	0.292928	+	0.507366i
$823$	−12352.6	−	21395.4i	−0.523191	−	0.906193i	−0.999636	−	0.0269884i	$-0.991408\pi$
$823$	−12352.6	−	21395.4i	−0.523191	−	0.906193i	0.476445	−	0.879204i	$-0.341925\pi$
$824$	13083.7	−	22661.7i	0.553148	−	0.958080i
$825$	−12405.8	+	21487.4i	−0.523531	+	0.906783i
$826$	3665.88			0.154422
$827$	507.015	+	878.176i	0.0213188	+	0.0369253i	0.876488	−	0.481424i	$-0.159880\pi$
$827$	507.015	+	878.176i	0.0213188	+	0.0369253i	−0.855169	+	0.518349i	$0.826547\pi$
$828$	−1126.39			−0.0472763
$829$	−18547.3			−0.777049			−0.388525	−	0.921438i	$-0.627015\pi$
$829$	−18547.3			−0.777049			−0.388525	+	0.921438i	$0.627015\pi$
$830$	31.0974	−	53.8623i	0.00130049	−	0.00225252i
$831$	−17920.1			−0.748063
$832$	8246.65	+	14283.6i	0.343631	+	0.595187i
$833$	13251.0	−	22951.5i	0.551166	−	0.954647i
$834$	13743.1	+	23803.7i	0.570604	+	0.988316i
$835$	13.1239	−	22.7313i	0.000543918	−	0.000942094i
$836$	11258.5	−	19500.3i	0.465769	−	0.806736i
$837$	1656.22	−	2868.66i	0.0683959	−	0.118465i
$838$	3471.43	−	6012.70i	0.143101	−	0.247858i
$839$	−14975.9	+	25939.0i	−0.616240	+	1.06736i	0.373925	+	0.927459i	$0.378012\pi$
$839$	−14975.9	+	25939.0i	−0.616240	+	1.06736i	−0.990166	+	0.139901i	$0.955322\pi$
$840$	3.16851	−	5.48802i	0.000130148	−	0.000225422i
$841$	8344.24	+	14452.7i	0.342131	+	0.592589i
$842$	16899.3	−	29270.4i	0.691671	−	1.19801i
$843$	1068.07	+	1849.95i	0.0436374	+	0.0755821i
$844$	−7012.26			−0.285986
$845$	21.8986	−	37.9295i	0.000891520	−	0.00154416i
$846$	5215.24			0.211943
$847$	−17889.7			−0.725734
$848$	−21216.7	−	36748.4i	−0.859180	−	1.48814i
$849$	948.491			0.0383417
$850$	−17507.2	+	30323.3i	−0.706459	+	1.22362i
$851$	−2137.39	+	3702.06i	−0.0860971	+	0.149125i
$852$	−748.896	−	1297.13i	−0.0301136	−	0.0521582i
$853$	9539.62	+	16523.1i	0.382919	+	0.663236i	0.991478	−	0.130273i	$-0.0415854\pi$
$853$	9539.62	+	16523.1i	0.382919	+	0.663236i	−0.608559	+	0.793509i	$0.708252\pi$
$854$	4835.24	+	8374.88i	0.193745	+	0.335577i
$855$	−11.9537	−	20.7044i	−0.000478138	−	0.000828159i
$856$	−2932.62			−0.117097
$857$	5671.06			0.226044			0.113022	−	0.993592i	$-0.463947\pi$
$857$	5671.06			0.226044			0.113022	+	0.993592i	$0.463947\pi$
$858$	21289.9	+	36875.2i	0.847115	+	1.46725i
$859$	−8128.22	+	14078.5i	−0.322853	+	0.559199i	−0.981076	−	0.193625i	$-0.937975\pi$
$859$	−8128.22	+	14078.5i	−0.322853	+	0.559199i	0.658222	+	0.752824i	$0.271309\pi$
$860$	8.49511	−	14.7140i	0.000336838	−	0.000583421i
$861$	147.537	+	255.541i	0.00583977	+	0.0101148i
$862$	5467.45			0.216035
$863$	18346.2			0.723651			0.361825	−	0.932246i	$-0.382154\pi$
$863$	18346.2			0.723651			0.361825	+	0.932246i	$0.382154\pi$
$864$	1549.75	−	2684.25i	0.0610227	−	0.105695i
$865$	15.3337	+	26.5587i	0.000602729	+	0.00104396i
$866$	−35229.4			−1.38238
$867$	3698.74	−	6406.41i	0.144886	−	0.250949i
$868$	−1897.28			−0.0741911
$869$	33800.4	+	58544.1i	1.31945	+	2.28535i
$870$	17.6483			0.000687741
$871$	30782.7	−	18813.7i	1.19751	−	0.731892i
$872$	11364.4			0.441340
$873$	8363.75	+	14486.4i	0.324250	+	0.561617i
$874$	−20022.8			−0.774920
$875$	15.0890	−	26.1349i	0.000582972	−	0.00100974i
$876$	−6431.19			−0.248048
$877$	−16935.7	−	29333.5i	−0.652085	−	1.12944i	−0.982616	−	0.185649i	$-0.940561\pi$
$877$	−16935.7	−	29333.5i	−0.652085	−	1.12944i	0.330531	−	0.943795i	$-0.392772\pi$
$878$	−14479.1	+	25078.6i	−0.556545	+	0.963964i
$879$	−19232.1			−0.737977
$880$	106.277			0.00407114
$881$	13388.4	+	23189.5i	0.511995	+	0.886802i	0.999903	+	0.0139070i	$0.00442687\pi$
$881$	13388.4	+	23189.5i	0.511995	+	0.886802i	−0.487908	+	0.872895i	$0.662240\pi$
$882$	−4527.33	+	7841.56i	−0.172838	+	0.299364i
$883$	717.333	−	1242.46i	0.0273388	−	0.0473522i	−0.852032	−	0.523489i	$-0.824630\pi$
$883$	717.333	−	1242.46i	0.0273388	−	0.0473522i	0.879371	+	0.476137i	$0.157963\pi$
$884$	7441.40	+	12888.9i	0.283124	+	0.490384i
$885$	11.8077			0.000448487
$886$	49932.3			1.89335
$887$	−8047.82	−	13939.2i	−0.304644	−	0.527659i	0.672538	−	0.740063i	$-0.265204\pi$
$887$	−8047.82	−	13939.2i	−0.304644	−	0.527659i	−0.977182	+	0.212404i	$0.931871\pi$
$888$	−2361.28	−	4089.86i	−0.0892335	−	0.154557i
$889$	−5982.88	−	10362.7i	−0.225714	−	0.390947i
$890$	51.9088	+	89.9086i	0.00195504	+	0.00338623i
$891$	−2679.65	+	4641.30i	−0.100754	+	0.174511i
$892$	−3590.63	+	6219.15i	−0.134779	+	0.233445i
$893$	22961.4			0.860442
$894$	−765.481	−	1325.85i	−0.0286370	−	0.0496008i
$895$	−84.3754			−0.00315124
$896$	10193.2			0.380057
$897$	4688.96	−	8121.51i	0.174537	−	0.302307i
$898$	3834.09			0.142478
$899$	5382.88	+	9323.42i	0.199699	+	0.345888i
$900$	1481.48	−	2566.01i	0.0548698	−	0.0950372i
$901$	23325.7	+	40401.3i	0.862477	+	1.49385i
$902$	−1807.07	+	3129.94i	−0.0667061	+	0.115538i
$903$	−2763.80	+	4787.03i	−0.101853	+	0.176415i
$904$	6344.18	−	10988.4i	0.233412	−	0.404281i
$905$	21.8446	−	37.8360i	0.000802365	−	0.00138974i
$906$	−8807.27	+	15254.6i	−0.322960	+	0.559384i
$907$	3647.68	−	6317.97i	0.133538	−	0.231295i	−0.791500	−	0.611169i	$-0.790699\pi$
$907$	3647.68	−	6317.97i	0.133538	−	0.231295i	0.925038	+	0.379874i	$0.124033\pi$
$908$	−130.461	−	225.966i	−0.00476819	−	0.00825874i
$909$	8129.46	−	14080.6i	0.296631	−	0.513779i
$910$	−12.9473	−	22.4253i	−0.000471646	−	0.000816915i
$911$	15105.6			0.549364			0.274682	−	0.961535i	$-0.411427\pi$
$911$	15105.6			0.549364			0.274682	+	0.961535i	$0.411427\pi$
$912$	15143.9	−	26230.0i	0.549853	−	0.952372i
$913$	−61384.0			−2.22510
$914$	22024.6			0.797056
$915$	15.5741	+	26.9752i	0.000562694	+	0.000974615i
$916$	−7753.86			−0.279689
$917$	−2036.36	+	3527.07i	−0.0733331	+	0.127017i
$918$	−3781.56	+	6549.85i	−0.135959	+	0.235487i
$919$	12728.5	+	22046.4i	0.456882	+	0.791343i	0.998794	−	0.0490924i	$-0.0156329\pi$
$919$	12728.5	+	22046.4i	0.456882	+	0.791343i	−0.541912	+	0.840435i	$0.682300\pi$
$920$	−8.54738	−	14.8045i	−0.000306303	−	0.000530533i
$921$	−2274.34	−	3939.28i	−0.0813704	−	0.140938i
$922$	−29246.2	−	50655.9i	−1.04466	−	1.80940i
$923$	12470.1			0.444700
$924$	3069.67			0.109291
$925$	−5622.39	−	9738.27i	−0.199852	−	0.346154i
$926$	−26683.4	+	46217.0i	−0.946944	+	1.64016i
$927$	6729.16	−	11655.2i	0.238419	−	0.412954i
$928$	5036.84	+	8724.07i	0.178171	+	0.308601i
$929$	−5374.04			−0.189792			−0.0948959	−	0.995487i	$-0.530252\pi$
$929$	−5374.04			−0.189792			−0.0948959	+	0.995487i	$0.530252\pi$
$930$	−24.6734			−0.000869970
$931$	−19932.7	+	34524.5i	−0.701685	+	1.21535i
$932$	5728.14	+	9921.43i	0.201321	+	0.348699i
$933$	−9692.75			−0.340114
$934$	11386.9	−	19722.6i	0.398919	−	0.690947i
$935$	−116.841			−0.00408676
$936$	5180.13	+	8972.26i	0.180895	+	0.313320i
$937$	197.435			0.00688358			0.00344179	−	0.999994i	$-0.498904\pi$
$937$	197.435			0.00688358			0.00344179	+	0.999994i	$0.498904\pi$
$938$	−262.487	−	10497.6i	−0.00913701	−	0.365415i
$939$	−12864.5			−0.447091
$940$	−4.81076	−	8.33248i	−0.000166925	−	0.000289123i
$941$	35508.2			1.23011			0.615055	−	0.788484i	$-0.289134\pi$
$941$	35508.2			1.23011			0.615055	+	0.788484i	$0.289134\pi$
$942$	−1639.57	+	2839.82i	−0.0567092	+	0.0982232i
$943$	795.992			0.0274879
$944$	7479.47	+	12954.8i	0.257877	+	0.446656i
$945$	1.62961	−	2.82257i	5.60966e−5	−	9.71621e-5i
$946$	−67703.5			−2.32688
$947$	36736.4			1.26058			0.630292	−	0.776358i	$-0.282935\pi$
$947$	36736.4			1.26058			0.630292	+	0.776358i	$0.282935\pi$
$948$	−4036.41	−	6991.27i	−0.138288	−	0.239521i
$949$	26771.9	−	46370.3i	0.915756	−	1.58614i
$950$	26335.0	−	45613.5i	0.899388	−	1.55779i
$951$	−2684.67	−	4649.98i	−0.0915419	−	0.158555i
$952$	−8826.29			−0.300485
$953$	1859.60			0.0632091			0.0316046	−	0.999500i	$-0.489938\pi$
$953$	1859.60			0.0632091			0.0316046	+	0.999500i	$0.489938\pi$
$954$	−7969.43	−	13803.5i	−0.270461	−	0.468452i
$955$	−17.3552	−	30.0601i	−0.000588065	−	0.00101856i
$956$	−468.739	−	811.880i	−0.0158579	−	0.0274666i
$957$	−8709.13	−	15084.7i	−0.294176	−	0.509528i
$958$	14486.7	−	25091.7i	0.488565	−	0.846219i
$959$	−4143.57	+	7176.88i	−0.139523	+	0.241662i
$960$	15.4630			0.000519860
$961$	7369.93	+	12765.1i	0.247388	+	0.428488i
$962$	−19297.5			−0.646753
$963$	−1508.29			−0.0504713
$964$	1708.52	−	2959.25i	0.0570827	−	0.0988702i
$965$	38.9747			0.00130015
$966$	−1364.82	−	2363.94i	−0.0454580	−	0.0787355i
$967$	−21404.7	+	37074.0i	−0.711819	+	1.23291i	0.252355	+	0.967635i	$0.418795\pi$
$967$	−21404.7	+	37074.0i	−0.711819	+	1.23291i	−0.964174	+	0.265272i	$0.914538\pi$
$968$	−26657.3	−	46171.7i	−0.885121	−	1.53307i
$969$	−16649.3	+	28837.4i	−0.551963	+	0.956028i
$970$	62.2990	−	107.905i	0.00206217	−	0.00357178i
$971$	13468.0	−	23327.3i	0.445118	−	0.770967i	−0.552942	−	0.833220i	$-0.686495\pi$
$971$	13468.0	−	23327.3i	0.445118	−	0.770967i	0.998060	+	0.0622523i	$0.0198283\pi$
$972$	320.002	−	554.259i	0.0105597	−	0.0182900i
$973$	−8248.79	+	14287.3i	−0.271782	+	0.470741i
$974$	11162.5	−	19334.0i	0.367216	−	0.636038i
$975$	12334.3	+	21363.6i	0.405142	+	0.701727i
$976$	−19730.6	+	34174.4i	−0.647091	+	1.12079i
$977$	13398.4	+	23206.8i	0.438745	+	0.759928i	0.997593	−	0.0693418i	$-0.0220899\pi$
$977$	13398.4	+	23206.8i	0.438745	+	0.759928i	−0.558848	+	0.829270i	$0.688757\pi$
$978$	11258.2			0.368096
$979$	51232.1	−	88736.5i	1.67251	−	2.89687i
$980$	16.7048			0.000544506
$981$	5844.90			0.190227
$982$	−1165.66	−	2018.98i	−0.0378794	−	0.0656091i
$983$	15851.6			0.514332			0.257166	−	0.966367i	$-0.417211\pi$
$983$	15851.6			0.514332			0.257166	+	0.966367i	$0.417211\pi$
$984$	−439.687	+	761.560i	−0.0142446	+	0.0246724i
$985$	−7.36721	+	12.7604i	−0.000238314	+	0.000412771i
$986$	−12290.4	−	21287.6i	−0.396964	−	0.687563i
$987$	1565.13	+	2710.88i	0.0504748	+	0.0874249i
$988$	−11193.6	−	19388.0i	−0.360442	−	0.624305i
$989$	7455.62	+	12913.5i	0.239712	+	0.415193i
$990$	39.9199			0.00128155
$991$	20622.1			0.661032			0.330516	−	0.943800i	$-0.392777\pi$
$991$	20622.1			0.661032			0.330516	+	0.943800i	$0.392777\pi$
$992$	−7041.79	−	12196.7i	−0.225380	−	0.390370i
$993$	3987.54	−	6906.63i	0.127433	−	0.220720i
$994$	1814.84	−	3143.40i	0.0579107	−	0.100304i
$995$	−3.52743	−	6.10969i	−0.000112389	−	0.000194664i
$996$	7330.42			0.233206
$997$	38273.8			1.21579			0.607896	−	0.794017i	$-0.292014\pi$
$997$	38273.8			1.21579			0.607896	+	0.794017i	$0.292014\pi$
$998$	26899.1	−	46590.7i	0.853184	−	1.47776i
$999$	−1214.44	−	2103.47i	−0.0384617	−	0.0666176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.b.37.14	✓	36
67.29	even	3	inner	201.4.e.b.163.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.b.37.14	✓	36	1.1	even	1	trivial
201.4.e.b.163.14	yes	36	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63047 + 2.82406i) q^{2} -3.00000 q^{3} +(-1.31688 + 2.28090i) q^{4} -0.0205579 q^{5} +(-4.89142 - 8.47218i) q^{6} +(2.93590 - 5.08512i) q^{7} +17.4990 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(1.63047 + 2.82406i) q^{2} -3.00000 q^{3} +(-1.31688 + 2.28090i) q^{4} -0.0205579 q^{5} +(-4.89142 - 8.47218i) q^{6} +(2.93590 - 5.08512i) q^{7} +17.4990 q^{8} +9.00000 q^{9} +(-0.0335191 - 0.0580568i) q^{10} +(-33.0822 + 57.3000i) q^{11} +(3.95064 - 6.84270i) q^{12} +(32.8916 + 56.9699i) q^{13} +19.1476 q^{14} +0.0616738 q^{15} +(39.0667 + 67.6655i) q^{16} +(-42.9501 - 74.3917i) q^{17} +(14.6742 + 25.4165i) q^{18} +(64.6072 + 111.903i) q^{19} +(0.0270723 - 0.0468906i) q^{20} +(-8.80769 + 15.2554i) q^{21} -215.758 q^{22} +(23.7597 + 41.1529i) q^{23} -52.4970 q^{24} -125.000 q^{25} +(-107.258 + 185.776i) q^{26} -27.0000 q^{27} +(7.73244 + 13.3930i) q^{28} +(43.8763 - 75.9960i) q^{29} +(0.100557 + 0.174171i) q^{30} +(-61.3415 + 106.247i) q^{31} +(-57.3982 + 99.4167i) q^{32} +(99.2465 - 171.900i) q^{33} +(140.058 - 242.587i) q^{34} +(-0.0603560 + 0.104540i) q^{35} +(-11.8519 + 20.5281i) q^{36} +(44.9793 + 77.9064i) q^{37} +(-210.680 + 364.909i) q^{38} +(-98.6748 - 170.910i) q^{39} -0.359744 q^{40} +(8.37546 - 14.5067i) q^{41} -57.4428 q^{42} +313.793 q^{43} +(-87.1304 - 150.914i) q^{44} -0.185021 q^{45} +(-77.4789 + 134.197i) q^{46} +(88.8502 - 153.893i) q^{47} +(-117.200 - 202.996i) q^{48} +(154.261 + 267.188i) q^{49} +(-203.808 - 353.006i) q^{50} +(128.850 + 223.175i) q^{51} -173.257 q^{52} -543.089 q^{53} +(-44.0227 - 76.2496i) q^{54} +(0.680101 - 1.17797i) q^{55} +(51.3753 - 88.9847i) q^{56} +(-193.821 - 335.709i) q^{57} +286.156 q^{58} +191.454 q^{59} +(-0.0812169 + 0.140672i) q^{60} +(252.524 + 437.385i) q^{61} -400.063 q^{62} +(26.4231 - 45.7661i) q^{63} +250.722 q^{64} +(-0.676183 - 1.17118i) q^{65} +647.274 q^{66} +(-13.7086 - 548.247i) q^{67} +226.240 q^{68} +(-71.2790 - 123.459i) q^{69} -0.393635 q^{70} +(94.7817 - 164.167i) q^{71} +157.491 q^{72} +(-406.971 - 704.895i) q^{73} +(-146.675 + 254.048i) q^{74} +374.999 q^{75} -340.319 q^{76} +(194.252 + 336.454i) q^{77} +(321.773 - 557.327i) q^{78} +(510.856 - 884.829i) q^{79} +(-0.803130 - 1.39106i) q^{80} +81.0000 q^{81} +54.6238 q^{82} +(463.876 + 803.456i) q^{83} +(-23.1973 - 40.1790i) q^{84} +(0.882964 + 1.52934i) q^{85} +(511.631 + 886.172i) q^{86} +(-131.629 + 227.988i) q^{87} +(-578.905 + 1002.69i) q^{88} -1548.63 q^{89} +(-0.301672 - 0.522512i) q^{90} +386.265 q^{91} -125.154 q^{92} +(184.025 - 318.740i) q^{93} +579.471 q^{94} +(-1.32819 - 2.30049i) q^{95} +(172.195 - 298.250i) q^{96} +(929.306 + 1609.60i) q^{97} +(-503.037 + 871.285i) q^{98} +(-297.739 + 515.700i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9} + 14 q^{10} - 16 q^{11} + 270 q^{12} - 46 q^{13} + 14 q^{14} + 12 q^{15} - 346 q^{16} - 8 q^{17} + 18 q^{18} - 154 q^{19} - 180 q^{20} - 66 q^{21} + 214 q^{22} - 104 q^{23} - 144 q^{24} + 1032 q^{25} - 333 q^{26} - 972 q^{27} - 473 q^{28} + 76 q^{29} - 42 q^{30} + 498 q^{31} - 285 q^{32} + 48 q^{33} + 26 q^{34} - 392 q^{35} - 810 q^{36} - 124 q^{37} + 20 q^{38} + 138 q^{39} + 638 q^{40} - 508 q^{41} - 42 q^{42} - 1400 q^{43} - 333 q^{44} - 36 q^{45} - 1372 q^{46} + 18 q^{47} + 1038 q^{48} - 238 q^{49} - 337 q^{50} + 24 q^{51} + 3640 q^{52} + 724 q^{53} - 54 q^{54} - 178 q^{55} - 829 q^{56} + 462 q^{57} - 1472 q^{58} + 720 q^{59} + 540 q^{60} + 232 q^{61} - 3882 q^{62} + 198 q^{63} + 3628 q^{64} - 1428 q^{65} - 642 q^{66} - 1164 q^{67} + 1634 q^{68} + 312 q^{69} + 2550 q^{70} + 406 q^{71} + 432 q^{72} - 2120 q^{73} + 1375 q^{74} - 3096 q^{75} + 4190 q^{76} - 800 q^{77} + 999 q^{78} + 1306 q^{79} - 1927 q^{80} + 2916 q^{81} - 794 q^{82} - 1010 q^{83} + 1419 q^{84} + 472 q^{85} + 737 q^{86} - 228 q^{87} - 1838 q^{88} + 1904 q^{89} + 126 q^{90} + 7340 q^{91} + 7368 q^{92} - 1494 q^{93} - 9862 q^{94} + 1678 q^{95} + 855 q^{96} - 2358 q^{97} - 2610 q^{98} - 144 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9 + 14 * q^10 - 16 * q^11 + 270 * q^12 - 46 * q^13 + 14 * q^14 + 12 * q^15 - 346 * q^16 - 8 * q^17 + 18 * q^18 - 154 * q^19 - 180 * q^20 - 66 * q^21 + 214 * q^22 - 104 * q^23 - 144 * q^24 + 1032 * q^25 - 333 * q^26 - 972 * q^27 - 473 * q^28 + 76 * q^29 - 42 * q^30 + 498 * q^31 - 285 * q^32 + 48 * q^33 + 26 * q^34 - 392 * q^35 - 810 * q^36 - 124 * q^37 + 20 * q^38 + 138 * q^39 + 638 * q^40 - 508 * q^41 - 42 * q^42 - 1400 * q^43 - 333 * q^44 - 36 * q^45 - 1372 * q^46 + 18 * q^47 + 1038 * q^48 - 238 * q^49 - 337 * q^50 + 24 * q^51 + 3640 * q^52 + 724 * q^53 - 54 * q^54 - 178 * q^55 - 829 * q^56 + 462 * q^57 - 1472 * q^58 + 720 * q^59 + 540 * q^60 + 232 * q^61 - 3882 * q^62 + 198 * q^63 + 3628 * q^64 - 1428 * q^65 - 642 * q^66 - 1164 * q^67 + 1634 * q^68 + 312 * q^69 + 2550 * q^70 + 406 * q^71 + 432 * q^72 - 2120 * q^73 + 1375 * q^74 - 3096 * q^75 + 4190 * q^76 - 800 * q^77 + 999 * q^78 + 1306 * q^79 - 1927 * q^80 + 2916 * q^81 - 794 * q^82 - 1010 * q^83 + 1419 * q^84 + 472 * q^85 + 737 * q^86 - 228 * q^87 - 1838 * q^88 + 1904 * q^89 + 126 * q^90 + 7340 * q^91 + 7368 * q^92 - 1494 * q^93 - 9862 * q^94 + 1678 * q^95 + 855 * q^96 - 2358 * q^97 - 2610 * q^98 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more