LMFDB - Embedded newform 201.4.e.a.37.8

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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	201.37
Dual form			201.4.e.a.163.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.252285 + 0.436970i) q^{2} +3.00000 q^{3} +(3.87271 - 6.70772i) q^{4} -15.4844 q^{5} +(0.756854 + 1.31091i) q^{6} +(10.1103 - 17.5115i) q^{7} +7.94465 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(0.252285 + 0.436970i) q^{2} +3.00000 q^{3} +(3.87271 - 6.70772i) q^{4} -15.4844 q^{5} +(0.756854 + 1.31091i) q^{6} +(10.1103 - 17.5115i) q^{7} +7.94465 q^{8} +9.00000 q^{9} +(-3.90648 - 6.76622i) q^{10} +(-17.8751 + 30.9605i) q^{11} +(11.6181 - 20.1232i) q^{12} +(-9.46987 - 16.4023i) q^{13} +10.2026 q^{14} -46.4533 q^{15} +(-28.9773 - 50.1902i) q^{16} +(-31.8535 - 55.1718i) q^{17} +(2.27056 + 3.93273i) q^{18} +(-70.8658 - 122.743i) q^{19} +(-59.9666 + 103.865i) q^{20} +(30.3308 - 52.5344i) q^{21} -18.0384 q^{22} +(6.22118 + 10.7754i) q^{23} +23.8339 q^{24} +114.767 q^{25} +(4.77820 - 8.27609i) q^{26} +27.0000 q^{27} +(-78.3080 - 135.634i) q^{28} +(16.5369 - 28.6428i) q^{29} +(-11.7194 - 20.2987i) q^{30} +(-34.6603 + 60.0334i) q^{31} +(46.3997 - 80.3666i) q^{32} +(-53.6252 + 92.8815i) q^{33} +(16.0723 - 27.8380i) q^{34} +(-156.551 + 271.155i) q^{35} +(34.8543 - 60.3695i) q^{36} +(54.8115 + 94.9362i) q^{37} +(35.7567 - 61.9324i) q^{38} +(-28.4096 - 49.2069i) q^{39} -123.018 q^{40} +(80.4119 - 139.277i) q^{41} +30.6079 q^{42} +187.612 q^{43} +(138.450 + 239.802i) q^{44} -139.360 q^{45} +(-3.13902 + 5.43694i) q^{46} +(303.525 - 525.720i) q^{47} +(-86.9320 - 150.571i) q^{48} +(-32.9344 - 57.0440i) q^{49} +(28.9540 + 50.1498i) q^{50} +(-95.5604 - 165.515i) q^{51} -146.696 q^{52} -599.835 q^{53} +(6.81168 + 11.7982i) q^{54} +(276.785 - 479.405i) q^{55} +(80.3224 - 139.122i) q^{56} +(-212.597 - 368.229i) q^{57} +16.6880 q^{58} +574.014 q^{59} +(-179.900 + 311.596i) q^{60} +(154.537 + 267.665i) q^{61} -34.9770 q^{62} +(90.9923 - 157.603i) q^{63} -416.814 q^{64} +(146.635 + 253.980i) q^{65} -54.1152 q^{66} +(468.049 - 285.819i) q^{67} -493.436 q^{68} +(18.6636 + 32.3262i) q^{69} -157.982 q^{70} +(-289.439 + 501.322i) q^{71} +71.5018 q^{72} +(482.440 + 835.610i) q^{73} +(-27.6562 + 47.9019i) q^{74} +344.302 q^{75} -1097.77 q^{76} +(361.443 + 626.037i) q^{77} +(14.3346 - 24.8283i) q^{78} +(-347.275 + 601.498i) q^{79} +(448.697 + 777.166i) q^{80} +81.0000 q^{81} +81.1467 q^{82} +(242.739 + 420.436i) q^{83} +(-234.924 - 406.901i) q^{84} +(493.232 + 854.303i) q^{85} +(47.3317 + 81.9809i) q^{86} +(49.6107 - 85.9283i) q^{87} +(-142.011 + 245.970i) q^{88} +2.01453 q^{89} +(-35.1583 - 60.8960i) q^{90} -382.971 q^{91} +96.3712 q^{92} +(-103.981 + 180.100i) q^{93} +306.298 q^{94} +(1097.32 + 1900.61i) q^{95} +(139.199 - 241.100i) q^{96} +(-673.281 - 1166.16i) q^{97} +(16.6177 - 28.7826i) q^{98} +(-160.876 + 278.645i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * 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 $

$2$	0.252285	+	0.436970i	0.0891961	+	0.154492i	0.907172	−	0.420761i	$-0.138237\pi$
$2$	0.252285	+	0.436970i	0.0891961	+	0.154492i	−0.817975	+	0.575253i	$0.804904\pi$
$3$	3.00000			0.577350
$3$	3.00000			0.577350
$4$	3.87271	−	6.70772i	0.484088	−	0.838465i
$5$	−15.4844			−1.38497			−0.692484	−	0.721433i	$-0.743484\pi$
$5$	−15.4844			−1.38497			−0.692484	+	0.721433i	$0.743484\pi$
$6$	0.756854	+	1.31091i	0.0514974	+	0.0891961i
$7$	10.1103	−	17.5115i	0.545902	−	0.945530i	−0.452647	−	0.891690i	$-0.649520\pi$
$7$	10.1103	−	17.5115i	0.545902	−	0.945530i	0.998550	−	0.0538408i	$-0.0171463\pi$
$8$	7.94465			0.351107
$9$	9.00000			0.333333
$10$	−3.90648	−	6.76622i	−0.123534	−	0.213967i
$11$	−17.8751	+	30.9605i	−0.489958	+	0.848631i	−0.999933	−	0.0115575i	$-0.996321\pi$
$11$	−17.8751	+	30.9605i	−0.489958	+	0.848631i	0.509976	+	0.860189i	$0.329654\pi$
$12$	11.6181	−	20.1232i	0.279488	−	0.484088i
$13$	−9.46987	−	16.4023i	−0.202036	−	0.349937i	0.747148	−	0.664657i	$-0.231422\pi$
$13$	−9.46987	−	16.4023i	−0.202036	−	0.349937i	−0.949184	+	0.314721i	$0.898089\pi$
$14$	10.2026			0.194769
$15$	−46.4533			−0.799612
$16$	−28.9773	−	50.1902i	−0.452771	−	0.784222i
$17$	−31.8535	−	55.1718i	−0.454447	−	0.787125i	0.544209	−	0.838949i	$-0.316830\pi$
$17$	−31.8535	−	55.1718i	−0.454447	−	0.787125i	−0.998656	+	0.0518244i	$0.983496\pi$
$18$	2.27056	+	3.93273i	0.0297320	+	0.0514974i
$19$	−70.8658	−	122.743i	−0.855670	−	1.48206i	−0.876022	−	0.482270i	$-0.839812\pi$
$19$	−70.8658	−	122.743i	−0.855670	−	1.48206i	0.0203529	−	0.999793i	$-0.493521\pi$
$20$	−59.9666	+	103.865i	−0.670447	+	1.16125i
$21$	30.3308	−	52.5344i	0.315177	−	0.545902i
$22$	−18.0384			−0.174809
$23$	6.22118	+	10.7754i	0.0564003	+	0.0976882i	0.892847	−	0.450360i	$-0.148704\pi$
$23$	6.22118	+	10.7754i	0.0564003	+	0.0976882i	−0.836447	+	0.548048i	$0.815371\pi$
$24$	23.8339			0.202712
$25$	114.767			0.918138
$26$	4.77820	−	8.27609i	0.0360416	−	0.0624259i
$27$	27.0000			0.192450
$28$	−78.3080	−	135.634i	−0.528530	−	0.915440i
$29$	16.5369	−	28.6428i	0.105891	−	0.183408i	−0.808211	−	0.588893i	$-0.799564\pi$
$29$	16.5369	−	28.6428i	0.105891	−	0.183408i	0.914102	+	0.405485i	$0.132897\pi$
$30$	−11.7194	−	20.2987i	−0.0713222	−	0.123534i
$31$	−34.6603	+	60.0334i	−0.200812	+	0.347817i	−0.948790	−	0.315907i	$-0.897691\pi$
$31$	−34.6603	+	60.0334i	−0.200812	+	0.347817i	0.747978	+	0.663723i	$0.231025\pi$
$32$	46.3997	−	80.3666i	0.256324	−	0.443967i
$33$	−53.6252	+	92.8815i	−0.282877	+	0.489958i
$34$	16.0723	−	27.8380i	0.0810697	−	0.140417i
$35$	−156.551	+	271.155i	−0.756057	+	1.30953i
$36$	34.8543	−	60.3695i	0.161363	−	0.279488i
$37$	54.8115	+	94.9362i	0.243539	+	0.421822i	0.961720	−	0.274034i	$-0.0883582\pi$
$37$	54.8115	+	94.9362i	0.243539	+	0.421822i	−0.718181	+	0.695857i	$0.755025\pi$
$38$	35.7567	−	61.9324i	0.152645	−	0.264388i
$39$	−28.4096	−	49.2069i	−0.116646	−	0.202036i
$40$	−123.018			−0.486272
$41$	80.4119	−	139.277i	0.306298	−	0.530524i	−0.671251	−	0.741230i	$-0.734243\pi$
$41$	80.4119	−	139.277i	0.306298	−	0.530524i	0.977550	+	0.210706i	$0.0675762\pi$
$42$	30.6079			0.112450
$43$	187.612			0.665363			0.332682	−	0.943039i	$-0.392047\pi$
$43$	187.612			0.665363			0.332682	+	0.943039i	$0.392047\pi$
$44$	138.450	+	239.802i	0.474365	+	0.821625i
$45$	−139.360			−0.461656
$46$	−3.13902	+	5.43694i	−0.0100614	+	0.0174268i
$47$	303.525	−	525.720i	0.941992	−	1.63158i	0.180328	−	0.983606i	$-0.442284\pi$
$47$	303.525	−	525.720i	0.941992	−	1.63158i	0.761664	−	0.647972i	$-0.224383\pi$
$48$	−86.9320	−	150.571i	−0.261407	−	0.452771i
$49$	−32.9344	−	57.0440i	−0.0960185	−	0.166309i
$50$	28.9540	+	50.1498i	0.0818943	+	0.141845i
$51$	−95.5604	−	165.515i	−0.262375	−	0.454447i
$52$	−146.696			−0.391213
$53$	−599.835			−1.55460			−0.777298	−	0.629132i	$-0.783410\pi$
$53$	−599.835			−1.55460			−0.777298	+	0.629132i	$0.783410\pi$
$54$	6.81168	+	11.7982i	0.0171658	+	0.0297320i
$55$	276.785	−	479.405i	0.678576	−	1.17533i
$56$	80.3224	−	139.122i	0.191670	−	0.331982i
$57$	−212.597	−	368.229i	−0.494021	−	0.855670i
$58$	16.6880			0.0377801
$59$	574.014			1.26661			0.633307	−	0.773900i	$-0.281697\pi$
$59$	574.014			1.26661			0.633307	+	0.773900i	$0.281697\pi$
$60$	−179.900	+	311.596i	−0.387083	+	0.670447i
$61$	154.537	+	267.665i	0.324367	+	0.561820i	0.981384	−	0.192055i	$-0.0615153\pi$
$61$	154.537	+	267.665i	0.324367	+	0.561820i	−0.657017	+	0.753876i	$0.728182\pi$
$62$	−34.9770			−0.0716466
$63$	90.9923	−	157.603i	0.181967	−	0.315177i
$64$	−416.814			−0.814089
$65$	146.635	+	253.980i	0.279814	+	0.484651i
$66$	−54.1152			−0.100926
$67$	468.049	−	285.819i	0.853453	−	0.521170i
$67$	468.049	−	285.819i	0.853453	−	0.521170i
$68$	−493.436			−0.879969
$69$	18.6636	+	32.3262i	0.0325627	+	0.0564003i
$70$	−157.982			−0.269749
$71$	−289.439	+	501.322i	−0.483803	+	0.837972i	−0.999827	−	0.0186023i	$-0.994078\pi$
$71$	−289.439	+	501.322i	−0.483803	+	0.837972i	0.516024	+	0.856574i	$0.327412\pi$
$72$	71.5018			0.117036
$73$	482.440	+	835.610i	0.773497	+	1.33974i	0.935635	+	0.352969i	$0.114828\pi$
$73$	482.440	+	835.610i	0.773497	+	1.33974i	−0.162138	+	0.986768i	$0.551839\pi$
$74$	−27.6562	+	47.9019i	−0.0434455	+	0.0752497i
$75$	344.302			0.530087
$76$	−1097.77			−1.65688
$77$	361.443	+	626.037i	0.534938	+	0.926539i
$78$	14.3346	−	24.8283i	0.0208086	−	0.0360416i
$79$	−347.275	+	601.498i	−0.494576	+	0.856630i	−0.999980	−	0.00625206i	$-0.998010\pi$
$79$	−347.275	+	601.498i	−0.494576	+	0.856630i	0.505405	+	0.862882i	$0.331343\pi$
$80$	448.697	+	777.166i	0.627073	+	1.08612i
$81$	81.0000			0.111111
$82$	81.1467			0.109282
$83$	242.739	+	420.436i	0.321013	+	0.556011i	0.980697	−	0.195532i	$-0.0626434\pi$
$83$	242.739	+	420.436i	0.321013	+	0.556011i	−0.659684	+	0.751543i	$0.729310\pi$
$84$	−234.924	−	406.901i	−0.305147	−	0.528530i
$85$	493.232	+	854.303i	0.629395	+	1.09014i
$86$	47.3317	+	81.9809i	0.0593478	+	0.102793i
$87$	49.6107	−	85.9283i	0.0611360	−	0.105891i
$88$	−142.011	+	245.970i	−0.172028	+	0.297960i
$89$	2.01453			0.00239932			0.00119966	−	0.999999i	$-0.499618\pi$
$89$	2.01453			0.00239932			0.00119966	+	0.999999i	$0.499618\pi$
$90$	−35.1583	−	60.8960i	−0.0411779	−	0.0713222i
$91$	−382.971			−0.441168
$92$	96.3712			0.109211
$93$	−103.981	+	180.100i	−0.115939	+	0.200812i
$94$	306.298			0.336088
$95$	1097.32	+	1900.61i	1.18508	+	2.05261i
$96$	139.199	−	241.100i	0.147989	−	0.256324i
$97$	−673.281	−	1166.16i	−0.704756	−	1.22067i	−0.966779	−	0.255612i	$-0.917723\pi$
$97$	−673.281	−	1166.16i	−0.704756	−	1.22067i	0.262023	−	0.965062i	$-0.415610\pi$
$98$	16.6177	−	28.7826i	0.0171289	−	0.0296682i
$99$	−160.876	+	278.645i	−0.163319	+	0.282877i
$100$	444.460	−	769.827i	0.444460	−	0.769827i
$101$	−119.035	+	206.175i	−0.117272	+	0.203121i	−0.918686	−	0.394990i	$-0.870748\pi$
$101$	−119.035	+	206.175i	−0.117272	+	0.203121i	0.801414	+	0.598110i	$0.204082\pi$
$102$	48.2168	−	83.5139i	0.0468056	−	0.0810697i
$103$	956.505	−	1656.71i	0.915021	−	1.58486i	0.108151	−	0.994134i	$-0.465507\pi$
$103$	956.505	−	1656.71i	0.915021	−	1.58486i	0.806870	−	0.590729i	$-0.201160\pi$
$104$	−75.2347	−	130.310i	−0.0709363	−	0.122865i
$105$	−469.654	+	813.465i	−0.436510	+	0.756057i
$106$	−151.329	−	262.109i	−0.138664	−	0.240173i
$107$	1699.37			1.53537			0.767684	−	0.640829i	$-0.221409\pi$
$107$	1699.37			1.53537			0.767684	+	0.640829i	$0.221409\pi$
$108$	104.563	−	181.108i	0.0931628	−	0.161363i
$109$	705.309			0.619783			0.309891	−	0.950772i	$-0.399707\pi$
$109$	705.309			0.619783			0.309891	+	0.950772i	$0.399707\pi$
$110$	279.314			0.242105
$111$	164.434	+	284.809i	0.140607	+	0.243539i
$112$	−1171.87			−0.988674
$113$	−638.610	+	1106.10i	−0.531640	+	0.920828i	0.467677	+	0.883899i	$0.345091\pi$
$113$	−638.610	+	1106.10i	−0.531640	+	0.920828i	−0.999318	+	0.0369290i	$0.988242\pi$
$114$	107.270	−	185.797i	0.0881295	−	0.152645i
$115$	−96.3314	−	166.851i	−0.0781126	−	0.135295i
$116$	−128.085	−	221.850i	−0.102521	−	0.177571i
$117$	−85.2288	−	147.621i	−0.0673453	−	0.116646i
$118$	144.815	+	250.827i	0.112977	+	0.195682i
$119$	−1288.19			−0.992334
$120$	−369.055			−0.280749
$121$	26.4646	+	45.8381i	0.0198833	+	0.0344389i
$122$	−77.9744	+	135.056i	−0.0578645	+	0.100224i
$123$	241.236	−	417.832i	0.176841	−	0.306298i
$124$	268.458	+	464.983i	0.194421	+	0.336748i
$125$	158.448			0.113376
$126$	91.8238			0.0649231
$127$	1280.75	−	2218.33i	0.894868	−	1.54996i	0.0609002	−	0.998144i	$-0.480603\pi$
$127$	1280.75	−	2218.33i	0.894868	−	1.54996i	0.833968	−	0.551813i	$-0.186064\pi$
$128$	−476.353	−	825.067i	−0.328938	−	0.569737i
$129$	562.837			0.384148
$130$	−73.9877	+	128.150i	−0.0499165	+	0.0864580i
$131$	595.092			0.396896			0.198448	−	0.980111i	$-0.436410\pi$
$131$	595.092			0.396896			0.198448	+	0.980111i	$0.436410\pi$
$132$	415.349	+	719.405i	0.273875	+	0.474365i
$133$	−2865.88			−1.86845
$134$	242.976	+	132.416i	0.156641	+	0.0853654i
$135$	−418.079			−0.266537
$136$	−253.064	−	438.320i	−0.159560	−	0.276365i
$137$	−1979.47			−1.23444			−0.617218	−	0.786792i	$-0.711740\pi$
$137$	−1979.47			−1.23444			−0.617218	+	0.786792i	$0.711740\pi$
$138$	−9.41705	+	16.3108i	−0.00580893	+	0.0100614i
$139$	−510.906			−0.311759			−0.155880	−	0.987776i	$-0.549821\pi$
$139$	−510.906			−0.311759			−0.155880	+	0.987776i	$0.549821\pi$
$140$	1212.55	+	2100.21i	0.731997	+	1.26786i
$141$	910.574	−	1577.16i	0.543860	−	0.941992i
$142$	−292.084			−0.172613
$143$	677.098			0.395956
$144$	−260.796	−	451.712i	−0.150924	−	0.261407i
$145$	−256.065	+	443.517i	−0.146655	+	0.254014i
$146$	−243.424	+	421.623i	−0.137986	+	0.238998i
$147$	−98.8031	−	171.132i	−0.0554363	−	0.0960185i
$148$	849.074			0.471578
$149$	97.6525			0.0536913			0.0268456	−	0.999640i	$-0.491454\pi$
$149$	97.6525			0.0536913			0.0268456	+	0.999640i	$0.491454\pi$
$150$	86.8620	+	150.449i	0.0472817	+	0.0818943i
$151$	396.144	+	686.141i	0.213495	+	0.369784i	0.952806	−	0.303580i	$-0.0981820\pi$
$151$	396.144	+	686.141i	0.213495	+	0.369784i	−0.739311	+	0.673364i	$0.764849\pi$
$152$	−563.003	−	975.151i	−0.300432	−	0.520363i
$153$	−286.681	−	496.546i	−0.151482	−	0.262375i
$154$	−182.373	+	315.879i	−0.0954287	+	0.165287i
$155$	536.695	−	929.582i	0.278118	−	0.481715i
$156$	−440.088			−0.225867
$157$	739.196	+	1280.32i	0.375760	+	0.650835i	0.990440	−	0.137941i	$-0.0440485\pi$
$157$	739.196	+	1280.32i	0.375760	+	0.650835i	−0.614681	+	0.788776i	$0.710715\pi$
$158$	−350.448			−0.176457
$159$	−1799.50			−0.897547
$160$	−718.472	+	1244.43i	−0.355001	+	0.614880i
$161$	251.591			0.123156
$162$	20.4350	+	35.3945i	0.00991067	+	0.0171658i
$163$	−1671.65	+	2895.39i	−0.803275	+	1.39131i	0.114174	+	0.993461i	$0.463578\pi$
$163$	−1671.65	+	2895.39i	−0.803275	+	1.39131i	−0.917449	+	0.397853i	$0.869755\pi$
$164$	−622.823	−	1078.76i	−0.296551	−	0.513641i
$165$	830.355	−	1438.22i	0.391776	−	0.678576i
$166$	−122.479	+	212.139i	−0.0572662	+	0.0991879i
$167$	−373.282	+	646.543i	−0.172967	+	0.299587i	−0.939456	−	0.342670i	$-0.888669\pi$
$167$	−373.282	+	646.543i	−0.172967	+	0.299587i	0.766489	+	0.642257i	$0.222002\pi$
$168$	240.967	−	417.367i	0.110661	−	0.191670i
$169$	919.143	−	1592.00i	0.418363	−	0.724626i
$170$	−248.870	+	431.055i	−0.112279	+	0.194473i
$171$	−637.792	−	1104.69i	−0.285223	−	0.494021i
$172$	726.568	−	1258.45i	0.322095	−	0.557884i
$173$	−755.067	−	1307.81i	−0.331830	−	0.574747i	0.651040	−	0.759043i	$-0.274333\pi$
$173$	−755.067	−	1307.81i	−0.331830	−	0.574747i	−0.982871	+	0.184296i	$0.941000\pi$
$174$	50.0641			0.0218124
$175$	1160.33	−	2009.74i	0.501214	−	0.868127i
$176$	2071.89			0.887354
$177$	1722.04			0.731280
$178$	0.508235	+	0.880288i	0.000214010	+	0.000370676i
$179$	−114.949			−0.0479982			−0.0239991	−	0.999712i	$-0.507640\pi$
$179$	−114.949			−0.0479982			−0.0239991	+	0.999712i	$0.507640\pi$
$180$	−539.699	+	934.787i	−0.223482	+	0.387083i
$181$	1129.25	−	1955.92i	0.463737	−	0.803217i	−0.535406	−	0.844595i	$-0.679841\pi$
$181$	1129.25	−	1955.92i	0.463737	−	0.803217i	0.999144	+	0.0413779i	$0.0131748\pi$
$182$	−96.6176	−	167.347i	−0.0393504	−	0.0681569i
$183$	463.610	+	802.996i	0.187273	+	0.324367i
$184$	49.4251	+	85.6068i	0.0198025	+	0.0342990i
$185$	−848.724	−	1470.03i	−0.337294	−	0.584210i
$186$	−104.931			−0.0413652
$187$	2277.53			0.890639
$188$	−2350.92	−	4071.92i	−0.912015	−	1.57966i
$189$	272.977	−	472.810i	0.105059	−	0.181967i
$190$	−553.671	+	958.987i	−0.211408	+	0.366170i
$191$	−2387.94	−	4136.02i	−0.904633	−	1.56687i	−0.821409	−	0.570340i	$-0.806812\pi$
$191$	−2387.94	−	4136.02i	−0.904633	−	1.56687i	−0.0832241	−	0.996531i	$-0.526522\pi$
$192$	−1250.44			−0.470015
$193$	1622.72			0.605213			0.302606	−	0.953116i	$-0.402143\pi$
$193$	1622.72			0.605213			0.302606	+	0.953116i	$0.402143\pi$
$194$	339.717	−	588.407i	0.125723	−	0.217759i
$195$	439.906	+	761.940i	0.161550	+	0.279814i
$196$	−510.180			−0.185926
$197$	−560.789	+	971.314i	−0.202815	+	0.351286i	−0.949434	−	0.313966i	$-0.898342\pi$
$197$	−560.789	+	971.314i	−0.202815	+	0.351286i	0.746619	+	0.665251i	$0.231676\pi$
$198$	−162.346			−0.0582697
$199$	−2002.81	−	3468.97i	−0.713444	−	1.23572i	−0.963556	−	0.267505i	$-0.913801\pi$
$199$	−2002.81	−	3468.97i	−0.713444	−	1.23572i	0.250112	−	0.968217i	$-0.419533\pi$
$200$	911.785			0.322365
$201$	1404.15	−	857.458i	0.492741	−	0.300898i
$202$	−120.123			−0.0418407
$203$	−334.385	−	579.171i	−0.115612	−	0.200246i
$204$	−1480.31			−0.508051
$205$	−1245.13	+	2156.63i	−0.424213	+	0.734759i
$206$	965.245			0.326465
$207$	55.9907	+	96.9787i	0.0188001	+	0.0325627i
$208$	−548.823	+	950.589i	−0.182952	+	0.316882i
$209$	5066.92			1.67697
$210$	−473.946			−0.155740
$211$	−859.927	−	1489.44i	−0.280568	−	0.485958i	0.690957	−	0.722896i	$-0.257189\pi$
$211$	−859.927	−	1489.44i	−0.280568	−	0.485958i	−0.971525	+	0.236938i	$0.923856\pi$
$212$	−2322.98	+	4023.52i	−0.752562	+	1.30348i
$213$	−868.316	+	1503.97i	−0.279324	+	0.483803i
$214$	428.725	+	742.573i	0.136949	+	0.237202i
$215$	−2905.07			−0.921507
$216$	214.505			0.0675706
$217$	700.849	+	1213.91i	0.219248	+	0.379748i
$218$	177.938	+	308.198i	0.0552822	+	0.0957515i
$219$	1447.32	+	2506.83i	0.446579	+	0.773497i
$220$	−2143.81	−	3713.19i	−0.656981	−	1.13792i
$221$	−603.296	+	1044.94i	−0.183629	+	0.318055i
$222$	−82.9685	+	143.706i	−0.0250832	+	0.0434455i
$223$	−225.324			−0.0676627			−0.0338313	−	0.999428i	$-0.510771\pi$
$223$	−225.324			−0.0676627			−0.0338313	+	0.999428i	$0.510771\pi$
$224$	−938.224	−	1625.05i	−0.279856	−	0.484725i
$225$	1032.91			0.306046
$226$	−644.446			−0.189681
$227$	−238.567	+	413.210i	−0.0697544	+	0.120818i	−0.898793	−	0.438373i	$-0.855555\pi$
$227$	−238.567	+	413.210i	−0.0697544	+	0.120818i	0.829039	+	0.559191i	$0.188888\pi$
$228$	−3293.31			−0.956599
$229$	745.358	+	1291.00i	0.215086	+	0.372539i	0.953299	−	0.302028i	$-0.0976636\pi$
$229$	745.358	+	1291.00i	0.215086	+	0.372539i	−0.738213	+	0.674567i	$0.764330\pi$
$230$	48.6059	−	84.1878i	0.0139347	−	0.0241356i
$231$	1084.33	+	1878.11i	0.308846	+	0.534938i
$232$	131.380	−	227.557i	0.0371789	−	0.0643958i
$233$	2178.27	−	3772.88i	0.612461	−	1.06081i	−0.378363	−	0.925657i	$-0.623513\pi$
$233$	2178.27	−	3772.88i	0.612461	−	1.06081i	0.990824	−	0.135157i	$-0.0431538\pi$
$234$	43.0038	−	74.4848i	0.0120139	−	0.0208086i
$235$	−4699.91	+	8140.47i	−1.30463	+	2.25969i
$236$	2222.99	−	3850.33i	0.613153	−	1.06201i
$237$	−1041.82	+	1804.49i	−0.285543	+	0.494576i
$238$	−324.989	−	562.898i	−0.0885123	−	0.153308i
$239$	1214.47	−	2103.52i	0.328692	−	0.569311i	−0.653561	−	0.756874i	$-0.726726\pi$
$239$	1214.47	−	2103.52i	0.328692	−	0.569311i	0.982253	+	0.187563i	$0.0600589\pi$
$240$	1346.09	+	2331.50i	0.362041	+	0.627073i
$241$	2239.72			0.598643			0.299322	−	0.954152i	$-0.403240\pi$
$241$	2239.72			0.598643			0.299322	+	0.954152i	$0.403240\pi$
$242$	−13.3532	+	23.1285i	−0.00354702	+	0.00614362i
$243$	243.000			0.0641500
$244$	2393.90			0.628089
$245$	509.969	+	883.293i	0.132983	+	0.230333i
$246$	243.440			0.0630942
$247$	−1342.18	+	2324.72i	−0.345752	+	0.598860i
$248$	−275.364	+	476.944i	−0.0705065	+	0.122121i
$249$	728.217	+	1261.31i	0.185337	+	0.321013i
$250$	39.9740	+	69.2371i	0.0101127	+	0.0175157i
$251$	1584.48	+	2744.41i	0.398453	+	0.690141i	0.993535	−	0.113524i	$-0.0362138\pi$
$251$	1584.48	+	2744.41i	0.398453	+	0.690141i	−0.595082	+	0.803665i	$0.702880\pi$
$252$	−704.772	−	1220.70i	−0.176177	−	0.305147i
$253$	−444.816			−0.110535
$254$	1292.45			0.319275
$255$	1479.70	+	2562.91i	0.363381	+	0.629395i
$256$	−1426.90	+	2471.47i	−0.348365	+	0.603385i
$257$	1935.38	−	3352.18i	0.469750	−	0.813631i	−0.529652	−	0.848215i	$-0.677677\pi$
$257$	1935.38	−	3352.18i	0.469750	−	0.813631i	0.999402	+	0.0345843i	$0.0110107\pi$
$258$	141.995	+	245.943i	0.0342645	+	0.0593478i
$259$	2216.63			0.531794
$260$	2271.50			0.541818
$261$	148.832	−	257.785i	0.0352969	−	0.0611360i
$262$	150.132	+	260.037i	0.0354016	+	0.0613173i
$263$	−5395.45			−1.26501			−0.632505	−	0.774557i	$-0.717973\pi$
$263$	−5395.45			−1.26501			−0.632505	+	0.774557i	$0.717973\pi$
$264$	−426.033	+	737.911i	−0.0993202	+	0.172028i
$265$	9288.09			2.15307
$266$	−723.018	−	1252.30i	−0.166658	−	0.288660i
$267$	6.04359			0.00138525
$268$	−104.579	−	4246.44i	−0.0238365	−	0.967883i
$269$	−3214.18			−0.728520			−0.364260	−	0.931297i	$-0.618678\pi$
$269$	−3214.18			−0.728520			−0.364260	+	0.931297i	$0.618678\pi$
$270$	−105.475	−	182.688i	−0.0237741	−	0.0411779i
$271$	6854.13			1.53638			0.768189	−	0.640223i	$-0.221158\pi$
$271$	6854.13			1.53638			0.768189	+	0.640223i	$0.221158\pi$
$272$	−1846.06	+	3197.46i	−0.411521	+	0.712774i
$273$	−1148.91			−0.254708
$274$	−499.390	−	864.969i	−0.110107	−	0.190711i
$275$	−2051.47	+	3553.25i	−0.449849	+	0.779161i
$276$	289.114			0.0630529
$277$	−6574.66			−1.42611			−0.713056	−	0.701107i	$-0.752690\pi$
$277$	−6574.66			−1.42611			−0.713056	+	0.701107i	$0.752690\pi$
$278$	−128.894	−	223.251i	−0.0278077	−	0.0481643i
$279$	−311.943	+	540.301i	−0.0669374	+	0.115939i
$280$	−1243.75	+	2154.23i	−0.265457	+	0.459785i
$281$	−2710.76	−	4695.17i	−0.575482	−	0.996764i	−0.995989	−	0.0894746i	$-0.971481\pi$
$281$	−2710.76	−	4695.17i	−0.575482	−	0.996764i	0.420507	−	0.907289i	$-0.361852\pi$
$282$	918.895			0.194040
$283$	−4518.40			−0.949084			−0.474542	−	0.880233i	$-0.657386\pi$
$283$	−4518.40			−0.949084			−0.474542	+	0.880233i	$0.657386\pi$
$284$	2241.82	+	3882.95i	0.468407	+	0.811305i
$285$	3291.95	+	5701.82i	0.684204	+	1.18508i
$286$	170.821	+	295.871i	0.0353177	+	0.0611721i
$287$	−1625.97	−	2816.26i	−0.334418	−	0.579229i
$288$	417.597	−	723.299i	0.0854414	−	0.147989i
$289$	427.215	−	739.958i	0.0869561	−	0.150612i
$290$	−258.404			−0.0523243
$291$	−2019.84	−	3498.47i	−0.406891	−	0.704756i
$292$	7473.39			1.49776
$293$	1931.15			0.385048			0.192524	−	0.981292i	$-0.438333\pi$
$293$	1931.15			0.385048			0.192524	+	0.981292i	$0.438333\pi$
$294$	49.8530	−	86.3479i	0.00988940	−	0.0171289i
$295$	−8888.27			−1.75422
$296$	435.458	+	754.235i	0.0855083	+	0.148105i
$297$	−482.627	+	835.934i	−0.0942924	+	0.163319i
$298$	24.6362	+	42.6712i	0.00478905	+	0.00829488i
$299$	117.828	−	204.083i	0.0227898	−	0.0394731i
$300$	1333.38	−	2309.48i	0.256609	−	0.444460i
$301$	1896.81	−	3285.37i	0.363223	−	0.629121i
$302$	−199.882	+	346.206i	−0.0380858	+	0.0659666i
$303$	−357.106	+	618.525i	−0.0677069	+	0.117272i
$304$	−4107.00	+	7113.53i	−0.774844	+	1.34207i
$305$	−2392.91	−	4144.64i	−0.449238	−	0.778104i
$306$	144.650	−	250.542i	0.0270232	−	0.0468056i
$307$	4295.80	+	7440.54i	0.798612	+	1.38324i	0.920520	+	0.390696i	$0.127766\pi$
$307$	4295.80	+	7440.54i	0.798612	+	1.38324i	−0.121907	+	0.992541i	$0.538901\pi$
$308$	5599.04			1.03583
$309$	2869.51	−	4970.14i	0.528288	−	0.915021i
$310$	541.599			0.0992283
$311$	−223.650			−0.0407782			−0.0203891	−	0.999792i	$-0.506491\pi$
$311$	−223.650			−0.0407782			−0.0203891	+	0.999792i	$0.506491\pi$
$312$	−225.704	−	390.931i	−0.0409551	−	0.0709363i
$313$	5322.74			0.961210			0.480605	−	0.876937i	$-0.340417\pi$
$313$	5322.74			0.961210			0.480605	+	0.876937i	$0.340417\pi$
$314$	−372.975	+	646.012i	−0.0670325	+	0.116104i
$315$	−1408.96	+	2440.39i	−0.252019	+	0.436510i
$316$	2689.79	+	4658.85i	0.478837	+	0.829369i
$317$	1934.29	+	3350.28i	0.342714	+	0.593598i	0.984936	−	0.172921i	$-0.0553205\pi$
$317$	1934.29	+	3350.28i	0.342714	+	0.593598i	−0.642222	+	0.766519i	$0.721987\pi$
$318$	−453.987	−	786.328i	−0.0800576	−	0.138664i
$319$	591.197	+	1023.98i	0.103764	+	0.179724i
$320$	6454.12			1.12749
$321$	5098.11			0.886445
$322$	63.4725	+	109.938i	0.0109850	+	0.0190267i
$323$	−4514.64	+	7819.58i	−0.777713	+	1.34704i
$324$	313.689	−	543.325i	0.0537876	−	0.0931628i
$325$	−1086.83	−	1882.45i	−0.185497	−	0.321290i
$326$	−1686.93			−0.286596
$327$	2115.93			0.357832
$328$	638.844	−	1106.51i	0.107543	−	0.186271i
$329$	−6137.42	−	10630.3i	−1.02847	−	1.78136i
$330$	837.943			0.139779
$331$	2201.31	−	3812.78i	0.365543	−	0.633140i	−0.623320	−	0.781967i	$-0.714217\pi$
$331$	2201.31	−	3812.78i	0.365543	−	0.633140i	0.988863	+	0.148827i	$0.0475499\pi$
$332$	3760.23			0.621594
$333$	493.303	+	854.426i	0.0811797	+	0.140607i
$334$	−376.693			−0.0617117
$335$	−7247.47	+	4425.75i	−1.18201	+	0.721804i
$336$	−3515.62			−0.570811
$337$	−1968.21	−	3409.04i	−0.318146	−	0.551045i	0.661955	−	0.749543i	$-0.269727\pi$
$337$	−1968.21	−	3409.04i	−0.318146	−	0.551045i	−0.980101	+	0.198499i	$0.936393\pi$
$338$	927.543			0.149265
$339$	−1915.83	+	3318.31i	−0.306943	+	0.531640i
$340$	7640.57			1.21873
$341$	−1239.11	−	2146.20i	−0.196779	−	0.340831i
$342$	321.810	−	557.391i	0.0508816	−	0.0881295i
$343$	5603.73			0.882138
$344$	1490.51			0.233614
$345$	−288.994	−	500.553i	−0.0450983	−	0.0781126i
$346$	380.983	−	659.883i	0.0591959	−	0.102530i
$347$	−3519.64	+	6096.20i	−0.544508	+	0.943116i	0.454130	+	0.890936i	$0.349950\pi$
$347$	−3519.64	+	6096.20i	−0.544508	+	0.943116i	−0.998638	+	0.0521802i	$0.983383\pi$
$348$	−384.256	−	665.550i	−0.0591904	−	0.102521i
$349$	176.004			0.0269951			0.0134975	−	0.999909i	$-0.495703\pi$
$349$	176.004			0.0269951			0.0134975	+	0.999909i	$0.495703\pi$
$350$	1170.93			0.178825
$351$	−255.686	−	442.862i	−0.0388818	−	0.0673453i
$352$	1658.79	+	2873.11i	0.251176	+	0.435050i
$353$	5387.28	+	9331.05i	0.812284	+	1.40692i	0.911262	+	0.411827i	$0.135109\pi$
$353$	5387.28	+	9331.05i	0.812284	+	1.40692i	−0.0989786	+	0.995090i	$0.531558\pi$
$354$	434.445	+	752.480i	0.0652273	+	0.112977i
$355$	4481.79	−	7762.69i	0.670053	−	1.16057i
$356$	7.80168	−	13.5129i	0.00116148	−	0.00201175i
$357$	−3864.56			−0.572924
$358$	−28.9998	−	50.2291i	−0.00428125	−	0.00741534i
$359$	−10480.4			−1.54076			−0.770379	−	0.637586i	$-0.779933\pi$
$359$	−10480.4			−1.54076			−0.770379	+	0.637586i	$0.779933\pi$
$360$	−1107.16			−0.162091
$361$	−6614.41	+	11456.5i	−0.964341	+	1.67029i
$362$	1139.57			0.165454
$363$	79.3939	+	137.514i	0.0114796	+	0.0198833i
$364$	−1483.13	+	2568.86i	−0.213564	+	0.369904i
$365$	−7470.30	−	12938.9i	−1.07127	−	1.85549i
$366$	−233.923	+	405.167i	−0.0334081	+	0.0578645i
$367$	−1719.02	+	2977.43i	−0.244501	+	0.423489i	−0.961991	−	0.273080i	$-0.911958\pi$
$367$	−1719.02	+	2977.43i	−0.244501	+	0.423489i	0.717490	+	0.696569i	$0.245291\pi$
$368$	360.547	−	624.485i	0.0510728	−	0.0884607i
$369$	723.707	−	1253.50i	0.102099	−	0.176841i
$370$	428.240	−	741.733i	0.0601706	−	0.104219i
$371$	−6064.48	+	10504.0i	−0.848658	+	1.46992i
$372$	805.375	+	1394.95i	0.112249	+	0.194421i
$373$	−5491.87	+	9512.20i	−0.762354	+	1.32044i	0.179280	+	0.983798i	$0.442623\pi$
$373$	−5491.87	+	9512.20i	−0.762354	+	1.32044i	−0.941634	+	0.336638i	$0.890710\pi$
$374$	574.585	+	995.211i	0.0794415	+	0.137597i
$375$	475.345			0.0654578
$376$	2411.40	−	4176.66i	0.330740	−	0.572859i
$377$	−626.409			−0.0855749
$378$	275.471			0.0374834
$379$	4782.83	+	8284.10i	0.648225	+	1.12276i	0.983547	+	0.180655i	$0.0578218\pi$
$379$	4782.83	+	8284.10i	0.648225	+	1.12276i	−0.335321	+	0.942104i	$0.608845\pi$
$380$	16998.3			2.29472
$381$	3842.25	−	6654.98i	0.516652	−	0.894868i
$382$	1204.88	−	2086.91i	0.161379	−	0.279517i
$383$	−3079.49	−	5333.83i	−0.410847	−	0.711608i	0.584135	−	0.811656i	$-0.301434\pi$
$383$	−3079.49	−	5333.83i	−0.410847	−	0.711608i	−0.994983	+	0.100048i	$0.968100\pi$
$384$	−1429.06	−	2475.20i	−0.189912	−	0.328938i
$385$	−5596.73	−	9693.82i	−0.740872	−	1.28323i
$386$	409.388	+	709.080i	0.0539826	+	0.0935006i
$387$	1688.51			0.221788
$388$	−10429.7			−1.36466
$389$	−6723.63	−	11645.7i	−0.876353	−	1.51789i	−0.855314	−	0.518110i	$-0.826636\pi$
$389$	−6723.63	−	11645.7i	−0.876353	−	1.51789i	−0.0210392	−	0.999779i	$-0.506697\pi$
$390$	−221.963	+	384.451i	−0.0288193	+	0.0499165i
$391$	396.332	−	686.468i	0.0512619	−	0.0887882i
$392$	−261.652	−	453.194i	−0.0337128	−	0.0583923i
$393$	1785.28			0.229148
$394$	−565.913			−0.0723612
$395$	5377.35	−	9313.85i	0.684972	−	1.18641i
$396$	1246.05	+	2158.22i	0.158122	+	0.273875i
$397$	−3446.76			−0.435738			−0.217869	−	0.975978i	$-0.569910\pi$
$397$	−3446.76			−0.435738			−0.217869	+	0.975978i	$0.569910\pi$
$398$	1010.56	−	1750.33i	0.127273	−	0.220443i
$399$	−8597.65			−1.07875
$400$	−3325.65	−	5760.19i	−0.415706	−	0.720024i
$401$	2423.89			0.301854			0.150927	−	0.988545i	$-0.451774\pi$
$401$	2423.89			0.301854			0.150927	+	0.988545i	$0.451774\pi$
$402$	728.928	+	397.247i	0.0904369	+	0.0492857i
$403$	1312.91			0.162285
$404$	921.977	+	1596.91i	0.113540	+	0.196657i
$405$	−1254.24			−0.153885
$406$	168.720	−	292.232i	0.0206242	−	0.0357222i
$407$	−3919.03			−0.477295
$408$	−759.193	−	1314.96i	−0.0921217	−	0.159560i
$409$	−4354.37	+	7541.99i	−0.526430	+	0.911803i	0.473096	+	0.881011i	$0.343136\pi$
$409$	−4354.37	+	7541.99i	−0.526430	+	0.911803i	−0.999526	+	0.0307920i	$0.990197\pi$
$410$	−1256.51			−0.151353
$411$	−5938.41			−0.712702
$412$	−7408.52	−	12831.9i	−0.885902	−	1.53443i
$413$	5803.43	−	10051.8i	0.691448	−	1.19762i
$414$	−28.2512	+	48.9324i	−0.00335379	+	0.00580893i
$415$	−3758.67	−	6510.21i	−0.444593	−	0.770057i
$416$	−1757.59			−0.207147
$417$	−1532.72			−0.179994
$418$	1278.31	+	2214.09i	0.149579	+	0.259078i
$419$	2842.80	+	4923.87i	0.331455	+	0.574097i	0.982797	−	0.184687i	$-0.0591272\pi$
$419$	2842.80	+	4923.87i	0.331455	+	0.574097i	−0.651342	+	0.758784i	$0.725794\pi$
$420$	3637.66	+	6300.62i	0.422619	+	0.731997i
$421$	−4310.77	−	7466.47i	−0.499036	−	0.864355i	0.500964	−	0.865468i	$-0.332979\pi$
$421$	−4310.77	−	7466.47i	−0.499036	−	0.864355i	−0.999999	+	0.00111296i	$0.999646\pi$
$422$	433.893	−	751.524i	0.0500511	−	0.0866910i
$423$	2731.72	−	4731.48i	0.313997	−	0.543860i
$424$	−4765.47			−0.545830
$425$	−3655.73	−	6331.92i	−0.417245	−	0.722689i
$426$	−876.251			−0.0996584
$427$	6249.62			0.708291
$428$	6581.16	−	11398.9i	0.743253	−	1.28735i
$429$	2031.29			0.228605
$430$	−732.904	−	1269.43i	−0.0821948	−	0.142366i
$431$	−2987.62	+	5174.71i	−0.333895	+	0.578323i	−0.983272	−	0.182144i	$-0.941696\pi$
$431$	−2987.62	+	5174.71i	−0.333895	+	0.578323i	0.649377	+	0.760467i	$0.275030\pi$
$432$	−782.388	−	1355.14i	−0.0871358	−	0.150924i
$433$	3371.22	−	5839.12i	0.374158	−	0.648060i	−0.616043	−	0.787713i	$-0.711265\pi$
$433$	3371.22	−	5839.12i	0.374158	−	0.648060i	0.990201	+	0.139652i	$0.0445985\pi$
$434$	−353.627	+	612.499i	−0.0391120	+	0.0677440i
$435$	−768.194	+	1330.55i	−0.0846714	+	0.146655i
$436$	2731.45	−	4731.01i	0.300029	−	0.519666i
$437$	881.738	−	1527.21i	0.0965200	−	0.167178i
$438$	−730.273	+	1264.87i	−0.0796661	+	0.137986i
$439$	−5820.85	−	10082.0i	−0.632834	−	1.09610i	−0.986970	−	0.160906i	$-0.948558\pi$
$439$	−5820.85	−	10082.0i	−0.632834	−	1.09610i	0.354136	−	0.935194i	$-0.384775\pi$
$440$	2198.96	−	3808.71i	0.238253	−	0.412666i
$441$	−296.409	−	513.396i	−0.0320062	−	0.0554363i
$442$	−608.809			−0.0655160
$443$	5408.52	−	9367.82i	0.580059	−	1.00469i	−0.415412	−	0.909633i	$-0.636363\pi$
$443$	5408.52	−	9367.82i	0.580059	−	1.00469i	0.995472	−	0.0950591i	$-0.0303040\pi$
$444$	2547.22			0.272265
$445$	−31.1938			−0.00332299
$446$	−56.8456	−	98.4596i	−0.00603525	−	0.0104534i
$447$	292.957			0.0309987
$448$	−4214.09	+	7299.02i	−0.444413	+	0.769746i
$449$	2648.50	−	4587.33i	0.278375	−	0.482160i	−0.692606	−	0.721316i	$-0.743538\pi$
$449$	2648.50	−	4587.33i	0.278375	−	0.482160i	0.970981	+	0.239156i	$0.0768709\pi$
$450$	260.586	+	451.348i	0.0272981	+	0.0472817i
$451$	2874.73	+	4979.19i	0.300146	+	0.519869i
$452$	4946.30	+	8567.24i	0.514722	+	0.891524i
$453$	1188.43	+	2058.42i	0.123261	+	0.213495i
$454$	−240.747			−0.0248873
$455$	5930.08			0.611003
$456$	−1689.01	−	2925.45i	−0.173454	−	0.300432i
$457$	112.824	−	195.418i	0.0115486	−	0.0200028i	−0.860193	−	0.509968i	$-0.829657\pi$
$457$	112.824	−	195.418i	0.0115486	−	0.0200028i	0.871742	+	0.489965i	$0.162991\pi$
$458$	−376.084	+	651.397i	−0.0383696	+	0.0664581i
$459$	−860.043	−	1489.64i	−0.0874583	−	0.151482i
$460$	−1492.25			−0.151254
$461$	7268.37			0.734321			0.367160	−	0.930158i	$-0.380330\pi$
$461$	7268.37			0.734321			0.367160	+	0.930158i	$0.380330\pi$
$462$	−547.118	+	947.637i	−0.0550958	+	0.0954287i
$463$	−1387.09	−	2402.52i	−0.139231	−	0.241154i	0.787975	−	0.615707i	$-0.211130\pi$
$463$	−1387.09	−	2402.52i	−0.139231	−	0.241154i	−0.927206	+	0.374553i	$0.877796\pi$
$464$	−1916.78			−0.191777
$465$	1610.08	−	2788.75i	0.160572	−	0.278118i
$466$	2198.18			0.218517
$467$	9911.45	+	17167.1i	0.982114	+	1.70107i	0.654120	+	0.756391i	$0.273039\pi$
$467$	9911.45	+	17167.1i	0.982114	+	1.70107i	0.327994	+	0.944680i	$0.393627\pi$
$468$	−1320.26			−0.130404
$469$	−273.019	−	11085.9i	−0.0268802	−	1.09147i
$470$	−4742.85			−0.465471
$471$	2217.59	+	3840.97i	0.216945	+	0.375760i
$472$	4560.34			0.444717
$473$	−3353.58	+	5808.58i	−0.326000	+	0.564648i
$474$	−1051.35			−0.101877
$475$	−8133.07	−	14086.9i	−0.785623	−	1.36074i
$476$	−4988.76	+	8640.79i	−0.480377	+	0.832038i
$477$	−5398.51			−0.518199
$478$	1225.56			0.117272
$479$	−704.594	−	1220.39i	−0.0672103	−	0.116412i	0.830462	−	0.557075i	$-0.188077\pi$
$479$	−704.594	−	1220.39i	−0.0672103	−	0.116412i	−0.897672	+	0.440664i	$0.854743\pi$
$480$	−2155.41	+	3733.29i	−0.204960	+	0.355001i
$481$	1038.11	−	1798.07i	0.0984073	−	0.170447i
$482$	565.046	+	978.689i	0.0533966	+	0.0924856i
$483$	754.773			0.0711042
$484$	409.959			0.0385010
$485$	10425.4	+	18057.3i	0.976066	+	1.69060i
$486$	61.3051	+	106.184i	0.00572193	+	0.00991067i
$487$	4813.78	+	8337.71i	0.447912	+	0.775806i	0.998250	−	0.0591358i	$-0.0188345\pi$
$487$	4813.78	+	8337.71i	0.447912	+	0.775806i	−0.550338	+	0.834942i	$0.685501\pi$
$488$	1227.74	+	2126.51i	0.113888	+	0.197259i
$489$	−5014.96	+	8686.16i	−0.463771	+	0.803275i
$490$	−257.315	+	445.682i	−0.0237231	+	0.0410895i
$491$	−13985.4			−1.28545			−0.642723	−	0.766099i	$-0.722195\pi$
$491$	−13985.4			−1.28545			−0.642723	+	0.766099i	$0.722195\pi$
$492$	−1868.47	−	3236.28i	−0.171214	−	0.296551i
$493$	−2107.03			−0.192487
$494$	−1354.44			−0.123359
$495$	2491.06	−	4314.65i	0.226192	−	0.391776i
$496$	4017.45			0.363687
$497$	5852.59	+	10137.0i	0.528219	+	0.914902i
$498$	−367.436	+	636.417i	−0.0330626	+	0.0572662i
$499$	7576.67	+	13123.2i	0.679716	+	1.17730i	0.975066	+	0.221914i	$0.0712303\pi$
$499$	7576.67	+	13123.2i	0.679716	+	1.17730i	−0.295350	+	0.955389i	$0.595436\pi$
$500$	613.623	−	1062.83i	0.0548841	−	0.0950621i
$501$	−1119.85	+	1939.63i	−0.0998623	+	0.172967i
$502$	−799.482	+	1384.74i	−0.0710809	+	0.123116i
$503$	−3253.47	+	5635.18i	−0.288400	+	0.499523i	−0.973428	−	0.228993i	$-0.926457\pi$
$503$	−3253.47	+	5635.18i	−0.288400	+	0.499523i	0.685028	+	0.728517i	$0.259790\pi$
$504$	722.901	−	1252.10i	0.0638901	−	0.110661i
$505$	1843.19	−	3192.50i	0.162418	−	0.281316i
$506$	−112.220	−	194.371i	−0.00985928	−	0.0170768i
$507$	2757.43	−	4776.01i	0.241542	−	0.418363i
$508$	−9919.94	−	17181.8i	−0.866390	−	1.50063i
$509$	16390.0			1.42726			0.713630	−	0.700522i	$-0.247050\pi$
$509$	16390.0			1.42726			0.713630	+	0.700522i	$0.247050\pi$
$510$	−746.609	+	1293.17i	−0.0648243	+	0.112279i
$511$	19510.3			1.68902
$512$	−9061.59			−0.782167
$513$	−1913.38	−	3314.06i	−0.164674	−	0.285223i
$514$	1953.07			0.167599
$515$	−14810.9	+	25653.3i	−1.26728	+	2.19499i
$516$	2179.70	−	3775.36i	0.185961	−	0.322095i
$517$	10851.0	+	18794.6i	0.923072	+	1.59881i
$518$	559.222	+	968.600i	0.0474339	+	0.0821580i
$519$	−2265.20	−	3923.44i	−0.191582	−	0.331830i
$520$	1164.97	+	2017.78i	0.0982445	+	0.170164i
$521$	−9344.84			−0.785806			−0.392903	−	0.919580i	$-0.628529\pi$
$521$	−9344.84			−0.785806			−0.392903	+	0.919580i	$0.628529\pi$
$522$	150.192			0.0125934
$523$	−7487.17	−	12968.2i	−0.625987	−	1.08424i	−0.988349	−	0.152204i	$-0.951363\pi$
$523$	−7487.17	−	12968.2i	−0.625987	−	1.08424i	0.362362	−	0.932037i	$-0.381970\pi$
$524$	2304.62	−	3991.71i	0.192133	−	0.332784i
$525$	3480.98	−	6029.23i	0.289376	−	0.501214i
$526$	−1361.19	−	2357.65i	−0.112834	−	0.195434i
$527$	4416.20			0.365034
$528$	6215.66			0.512314
$529$	6006.09	−	10402.9i	0.493638	−	0.855006i
$530$	2343.24	+	4058.61i	0.192045	+	0.332632i
$531$	5166.13			0.422205
$532$	−11098.7	+	19223.5i	−0.904493	+	1.56663i
$533$	−3045.96			−0.247533
$534$	1.52470	+	2.64087i	0.000123559	+	0.000214010i
$535$	−26313.8			−2.12644
$536$	3718.49	−	2270.73i	0.299653	−	0.182986i
$537$	−344.846			−0.0277117
$538$	−810.887	−	1404.50i	−0.0649811	−	0.112551i
$539$	2354.81			0.188180
$540$	−1619.10	+	2804.36i	−0.129028	+	0.223482i
$541$	3761.01			0.298888			0.149444	−	0.988770i	$-0.452252\pi$
$541$	3761.01			0.298888			0.149444	+	0.988770i	$0.452252\pi$
$542$	1729.19	+	2995.04i	0.137039	+	0.237358i
$543$	3387.75	−	5867.75i	0.267739	−	0.463737i
$544$	−5911.96			−0.465943
$545$	−10921.3			−0.858380
$546$	−289.853	−	502.040i	−0.0227190	−	0.0393504i
$547$	−6523.48	+	11299.0i	−0.509916	+	0.883200i	0.490018	+	0.871712i	$0.336990\pi$
$547$	−6523.48	+	11299.0i	−0.509916	+	0.883200i	−0.999934	+	0.0114878i	$0.996343\pi$
$548$	−7665.91	+	13277.7i	−0.597576	+	1.03503i
$549$	1390.83	+	2408.99i	0.108122	+	0.187273i
$550$	−2070.22			−0.160499
$551$	−4687.60			−0.362430
$552$	148.275	+	256.820i	0.0114330	+	0.0198025i
$553$	7022.07	+	12162.6i	0.539980	+	0.935273i
$554$	−1658.69	−	2872.93i	−0.127204	−	0.220323i
$555$	−2546.17	−	4410.10i	−0.194737	−	0.337294i
$556$	−1978.59	+	3427.02i	−0.150919	+	0.261399i
$557$	−514.893	+	891.821i	−0.0391683	+	0.0678414i	−0.884945	−	0.465696i	$-0.845804\pi$
$557$	−514.893	+	891.821i	−0.0391683	+	0.0678414i	0.845777	+	0.533537i	$0.179137\pi$
$558$	−314.793			−0.0238822
$559$	−1776.66	−	3077.27i	−0.134427	−	0.232835i
$560$	18145.8			1.36928
$561$	6832.59			0.514210
$562$	1367.77	−	2369.04i	0.102661	−	0.177815i
$563$	1717.75			0.128587			0.0642934	−	0.997931i	$-0.479521\pi$
$563$	1717.75			0.128587			0.0642934	+	0.997931i	$0.479521\pi$
$564$	−7052.77	−	12215.8i	−0.526552	−	0.912015i
$565$	9888.50	−	17127.4i	0.736305	−	1.27532i
$566$	−1139.92	−	1974.40i	−0.0846545	−	0.146626i
$567$	818.930	−	1418.43i	0.0606558	−	0.105059i
$568$	−2299.49	+	3982.83i	−0.169867	+	0.294218i
$569$	−251.078	+	434.880i	−0.0184987	+	0.0320406i	−0.875127	−	0.483894i	$-0.839222\pi$
$569$	−251.078	+	434.880i	−0.0184987	+	0.0320406i	0.856628	+	0.515935i	$0.172555\pi$
$570$	−1661.01	+	2876.96i	−0.122057	+	0.211408i
$571$	−9527.71	+	16502.5i	−0.698288	+	1.20947i	0.270772	+	0.962643i	$0.412721\pi$
$571$	−9527.71	+	16502.5i	−0.698288	+	1.20947i	−0.969060	+	0.246826i	$0.920612\pi$
$572$	2622.20	−	4541.78i	0.191678	−	0.331996i
$573$	−7163.81	−	12408.1i	−0.522290	−	0.904633i
$574$	820.414	−	1421.00i	0.0596575	−	0.103330i
$575$	713.988	+	1236.66i	0.0517832	+	0.0896912i
$576$	−3751.32			−0.271363
$577$	1790.70	−	3101.59i	0.129199	−	0.223779i	−0.794167	−	0.607699i	$-0.792093\pi$
$577$	1790.70	−	3101.59i	0.129199	−	0.223779i	0.923366	+	0.383920i	$0.125426\pi$
$578$	431.119			0.0310245
$579$	4868.17			0.349420
$580$	1983.32	+	3435.22i	0.141988	+	0.245931i
$581$	9816.61			0.700967
$582$	1019.15	−	1765.22i	0.0725862	−	0.125723i
$583$	10722.1	−	18571.2i	0.761686	−	1.31928i
$584$	3832.81	+	6638.63i	0.271580	+	0.470391i
$585$	1319.72	+	2285.82i	0.0932712	+	0.161550i
$586$	487.199	+	843.854i	0.0343447	+	0.0594868i
$587$	9753.17	+	16893.0i	0.685786	+	1.18782i	0.973189	+	0.230007i	$0.0738748\pi$
$587$	9753.17	+	16893.0i	0.685786	+	1.18782i	−0.287403	+	0.957810i	$0.592792\pi$
$588$	−1530.54			−0.107344
$589$	9824.92			0.687315
$590$	−2242.37	−	3883.91i	−0.156470	−	0.271013i
$591$	−1682.37	+	2913.94i	−0.117095	+	0.202815i
$592$	3176.58	−	5502.00i	0.220535	−	0.381977i
$593$	4243.17	+	7349.38i	0.293838	+	0.508942i	0.974714	−	0.223456i	$-0.0717341\pi$
$593$	4243.17	+	7349.38i	0.293838	+	0.508942i	−0.680876	+	0.732399i	$0.738401\pi$
$594$	−487.037			−0.0336420
$595$	19946.8			1.37435
$596$	378.179	−	655.026i	0.0259913	−	0.0450183i
$597$	−6008.43	−	10406.9i	−0.411907	−	0.713444i
$598$	118.904			0.00813103
$599$	10058.0	−	17420.9i	0.686074	−	1.18831i	−0.287024	−	0.957923i	$-0.592666\pi$
$599$	10058.0	−	17420.9i	0.686074	−	1.18831i	0.973098	−	0.230391i	$-0.0740006\pi$
$600$	2735.36			0.186117
$601$	−3460.99	−	5994.61i	−0.234903	−	0.406864i	0.724342	−	0.689441i	$-0.242144\pi$
$601$	−3460.99	−	5994.61i	−0.234903	−	0.406864i	−0.959244	+	0.282577i	$0.908811\pi$
$602$	1914.14			0.129592
$603$	4212.45	−	2572.37i	0.284484	−	0.173723i
$604$	6136.59			0.413401
$605$	−409.790	−	709.777i	−0.0275377	−	0.0476967i
$606$	−360.369			−0.0241568
$607$	−1523.43	+	2638.66i	−0.101868	+	0.176441i	−0.912454	−	0.409178i	$-0.865815\pi$
$607$	−1523.43	+	2638.66i	−0.101868	+	0.176441i	0.810586	+	0.585619i	$0.199149\pi$
$608$	−13152.6			−0.877316
$609$	−1003.15	−	1737.51i	−0.0667485	−	0.115612i
$610$	1207.39	−	2091.26i	0.0801406	−	0.138808i
$611$	−11497.4			−0.761266
$612$	−4440.92			−0.293323
$613$	9954.53	+	17241.8i	0.655889	+	1.13603i	0.981670	+	0.190588i	$0.0610393\pi$
$613$	9954.53	+	17241.8i	0.655889	+	1.13603i	−0.325781	+	0.945445i	$0.605627\pi$
$614$	−2167.53	+	3754.26i	−0.142466	+	0.246759i
$615$	−3735.39	+	6469.89i	−0.244920	+	0.424213i
$616$	2871.53	+	4973.64i	0.187820	+	0.325315i
$617$	8655.06			0.564732			0.282366	−	0.959307i	$-0.408881\pi$
$617$	8655.06			0.564732			0.282366	+	0.959307i	$0.408881\pi$
$618$	2895.74			0.188485
$619$	−13256.0	−	22960.1i	−0.860750	−	1.49086i	−0.871206	−	0.490918i	$-0.836661\pi$
$619$	−13256.0	−	22960.1i	−0.860750	−	1.49086i	0.0104552	−	0.999945i	$-0.496672\pi$
$620$	−4156.92	−	7200.00i	−0.269268	−	0.466385i
$621$	167.972	+	290.936i	0.0108542	+	0.0188001i
$622$	−56.4234	−	97.7282i	−0.00363726	−	0.00629991i
$623$	20.3674	−	35.2774i	0.00130980	−	0.00226863i
$624$	−1646.47	+	2851.77i	−0.105627	+	0.182952i
$625$	−16799.4			−1.07516
$626$	1342.84	+	2325.87i	0.0857362	+	0.148499i
$627$	15200.8			0.968197
$628$	11450.7			0.727603
$629$	3491.87	−	6048.09i	0.221351	−	0.383392i
$630$	−1421.84			−0.0899165
$631$	14746.6	+	25541.9i	0.930356	+	1.61142i	0.782713	+	0.622383i	$0.213836\pi$
$631$	14746.6	+	25541.9i	0.930356	+	1.61142i	0.147644	+	0.989041i	$0.452831\pi$
$632$	−2758.98	+	4778.69i	−0.173649	+	0.300769i
$633$	−2579.78	−	4468.31i	−0.161986	−	0.280568i
$634$	−975.981	+	1690.45i	−0.0611375	+	0.105893i
$635$	−19831.7	+	34349.5i	−1.23936	+	2.14664i
$636$	−6968.95	+	12070.6i	−0.434492	+	0.752562i
$637$	−623.768	+	1080.40i	−0.0387984	+	0.0672008i
$638$	−298.300	+	516.670i	−0.0185106	+	0.0320614i
$639$	−2604.95	+	4511.90i	−0.161268	+	0.279324i
$640$	7376.05	+	12775.7i	0.455569	+	0.789068i
$641$	−13634.3	+	23615.3i	−0.840128	+	1.45514i	0.0496579	+	0.998766i	$0.484187\pi$
$641$	−13634.3	+	23615.3i	−0.840128	+	1.45514i	−0.889786	+	0.456378i	$0.849146\pi$
$642$	1286.17	+	2227.72i	0.0790674	+	0.136949i
$643$	−4247.96			−0.260534			−0.130267	−	0.991479i	$-0.541583\pi$
$643$	−4247.96			−0.260534			−0.130267	+	0.991479i	$0.541583\pi$
$644$	974.337	−	1687.60i	0.0596184	−	0.103262i
$645$	−8715.21			−0.532033
$646$	−4555.89			−0.277476
$647$	−2749.08	−	4761.54i	−0.167044	−	0.289329i	0.770335	−	0.637639i	$-0.220089\pi$
$647$	−2749.08	−	4761.54i	−0.167044	−	0.289329i	−0.937379	+	0.348310i	$0.886755\pi$
$648$	643.516			0.0390119
$649$	−10260.5	+	17771.8i	−0.620587	+	1.07489i
$650$	548.381	−	949.824i	0.0330912	−	0.0573156i
$651$	2102.55	+	3641.72i	0.126583	+	0.219248i
$652$	12947.6	+	22426.0i	0.777712	+	1.34704i
$653$	−5904.84	−	10227.5i	−0.353866	−	0.612913i	0.633058	−	0.774105i	$-0.281800\pi$
$653$	−5904.84	−	10227.5i	−0.353866	−	0.612913i	−0.986923	+	0.161192i	$0.948466\pi$
$654$	533.815	+	924.595i	0.0319172	+	0.0552822i
$655$	−9214.65			−0.549689
$656$	−9320.49			−0.554732
$657$	4341.96	+	7520.49i	0.257832	+	0.446579i
$658$	3096.75	−	5363.74i	0.183471	−	0.317781i
$659$	13475.1	−	23339.6i	0.796536	−	1.37964i	−0.125324	−	0.992116i	$-0.539997\pi$
$659$	13475.1	−	23339.6i	0.796536	−	1.37964i	0.921859	−	0.387525i	$-0.126670\pi$
$660$	−6431.44	−	11139.6i	−0.379308	−	0.656981i
$661$	−7712.56			−0.453833			−0.226917	−	0.973914i	$-0.572864\pi$
$661$	−7712.56			−0.453833			−0.226917	+	0.973914i	$0.572864\pi$
$662$	2221.42			0.130420
$663$	−1809.89	+	3134.82i	−0.106018	+	0.183629i
$664$	1928.48	+	3340.22i	0.112710	+	0.195219i
$665$	44376.5			2.58774
$666$	−248.905	+	431.117i	−0.0144818	+	0.0250832i
$667$	411.517			0.0238890
$668$	2891.22	+	5007.74i	0.167462	+	0.290053i
$669$	−675.971			−0.0390651
$670$	−3762.34	−	2050.38i	−0.216943	−	0.118228i
$671$	−11049.4			−0.635705
$672$	−2814.67	−	4875.16i	−0.161575	−	0.279856i
$673$	21230.2			1.21599			0.607997	−	0.793939i	$-0.291973\pi$
$673$	21230.2			1.21599			0.607997	+	0.793939i	$0.291973\pi$
$674$	993.097	−	1720.09i	0.0567547	−	0.0983020i
$675$	3098.72			0.176696
$676$	−7119.14	−	12330.7i	−0.405049	−	0.701565i
$677$	2916.18	−	5050.97i	0.165551	−	0.286742i	−0.771300	−	0.636472i	$-0.780393\pi$
$677$	2916.18	−	5050.97i	0.165551	−	0.286742i	0.936851	+	0.349729i	$0.113727\pi$
$678$	−1933.34			−0.109512
$679$	−27228.2			−1.53891
$680$	3918.56	+	6787.14i	0.220985	+	0.382757i
$681$	−715.701	+	1239.63i	−0.0402727	+	0.0697544i
$682$	625.216	−	1082.91i	0.0351038	−	0.0608015i
$683$	−8189.63	−	14184.9i	−0.458810	−	0.794683i	0.540088	−	0.841609i	$-0.318391\pi$
$683$	−8189.63	−	14184.9i	−0.458810	−	0.794683i	−0.998898	+	0.0469256i	$0.985058\pi$
$684$	−9879.92			−0.552293
$685$	30651.0			1.70965
$686$	1413.74	+	2448.66i	0.0786832	+	0.136283i
$687$	2236.07	+	3872.99i	0.124180	+	0.215086i
$688$	−5436.51	−	9416.31i	−0.301257	−	0.521793i
$689$	5680.35	+	9838.66i	0.314084	+	0.544010i
$690$	145.818	−	252.563i	0.00804519	−	0.0139347i
$691$	−7817.13	+	13539.7i	−0.430358	+	0.745403i	−0.996904	−	0.0786278i	$-0.974946\pi$
$691$	−7817.13	+	13539.7i	−0.430358	+	0.745403i	0.566546	+	0.824030i	$0.308279\pi$
$692$	−11696.6			−0.642541
$693$	3252.98	+	5634.33i	0.178313	+	0.308846i
$694$	−3551.81			−0.194272
$695$	7911.09			0.431777
$696$	394.140	−	682.670i	0.0214653	−	0.0371789i
$697$	−10245.6			−0.556785
$698$	44.4031	+	76.9085i	0.00240785	+	0.00417053i
$699$	6534.82	−	11318.6i	0.353605	−	0.612461i
$700$	−8987.20	−	15566.3i	−0.485263	−	0.840500i
$701$	14339.4	−	24836.6i	0.772601	−	1.33818i	−0.163532	−	0.986538i	$-0.552289\pi$
$701$	14339.4	−	24836.6i	0.772601	−	1.33818i	0.936133	−	0.351646i	$-0.114378\pi$
$702$	129.011	−	223.454i	0.00693621	−	0.0120139i
$703$	7768.51	−	13455.5i	0.416778	−	0.721881i
$704$	7450.57	−	12904.8i	0.398869	−	0.690861i
$705$	−14099.7	+	24421.4i	−0.753228	+	1.30463i
$706$	−2718.26	+	4708.16i	−0.144905	+	0.250983i
$707$	2406.95	+	4168.97i	0.128038	+	0.221768i
$708$	6668.96	−	11551.0i	0.354004	−	0.613153i
$709$	−13993.4	−	24237.3i	−0.741232	−	1.28385i	−0.951935	−	0.306301i	$-0.900909\pi$
$709$	−13993.4	−	24237.3i	−0.741232	−	1.28385i	0.210703	−	0.977550i	$-0.432425\pi$
$710$	4522.74			0.239064
$711$	−3125.47	+	5413.48i	−0.164859	+	0.285543i
$712$	16.0047			0.000842419
$713$	−862.513			−0.0453034
$714$	−974.968	−	1688.69i	−0.0511026	−	0.0885123i
$715$	−10484.5			−0.548387
$716$	−445.162	+	771.044i	−0.0232353	+	0.0402448i
$717$	3643.40	−	6310.56i	0.189770	−	0.328692i
$718$	−2644.03	−	4579.60i	−0.137429	−	0.238035i
$719$	−5092.40	−	8820.30i	−0.264137	−	0.457499i	0.703200	−	0.710992i	$-0.251754\pi$
$719$	−5092.40	−	8820.30i	−0.264137	−	0.457499i	−0.967337	+	0.253493i	$0.918420\pi$
$720$	4038.27	+	6994.50i	0.209024	+	0.362041i
$721$	−19341.0	−	33499.6i	−0.999024	−	1.73036i
$722$	−6674.86			−0.344062
$723$	6719.16			0.345627
$724$	−8746.50	−	15149.4i	−0.448980	−	0.777656i
$725$	1897.90	−	3287.25i	0.0972222	−	0.168394i
$726$	−40.0597	+	69.3855i	−0.00204787	+	0.00354702i
$727$	7570.34	+	13112.2i	0.386201	+	0.668920i	0.991935	−	0.126747i	$-0.0404537\pi$
$727$	7570.34	+	13112.2i	0.386201	+	0.668920i	−0.605734	+	0.795667i	$0.707120\pi$
$728$	−3042.57			−0.154897
$729$	729.000			0.0370370
$730$	3769.28	−	6528.59i	0.191106	−	0.331005i
$731$	−5976.10	−	10350.9i	−0.302372	−	0.523724i
$732$	7181.70			0.362627
$733$	−5191.28	+	8991.56i	−0.261588	+	0.453084i	−0.966664	−	0.256048i	$-0.917580\pi$
$733$	−5191.28	+	8991.56i	−0.261588	+	0.453084i	0.705076	+	0.709132i	$0.250913\pi$
$734$	−1734.73			−0.0872342
$735$	1529.91	+	2649.88i	0.0767776	+	0.132983i
$736$	1154.64			0.0578271
$737$	482.701	+	19600.1i	0.0241255	+	0.979618i
$738$	730.320			0.0364275
$739$	8891.92	+	15401.3i	0.442618	+	0.766637i	0.997883	−	0.0650367i	$-0.0207164\pi$
$739$	8891.92	+	15401.3i	0.442618	+	0.766637i	−0.555265	+	0.831674i	$0.687383\pi$
$740$	−13147.4			−0.653120
$741$	−4026.54	+	6974.16i	−0.199620	+	0.345752i
$742$	−6119.90			−0.302788
$743$	8082.06	+	13998.5i	0.399061	+	0.691193i	0.993610	−	0.112866i	$-0.0360030\pi$
$743$	8082.06	+	13998.5i	0.399061	+	0.691193i	−0.594550	+	0.804059i	$0.702670\pi$
$744$	−826.092	+	1430.83i	−0.0407070	+	0.0705065i
$745$	−1512.09			−0.0743607
$746$	−5542.05			−0.271996
$747$	2184.65	+	3783.93i	0.107004	+	0.185337i
$748$	8820.20	−	15277.0i	0.431148	−	0.746770i
$749$	17181.1	−	29758.5i	0.838161	−	1.45174i
$750$	119.922	+	207.711i	0.00583858	+	0.0101127i
$751$	32411.8			1.57486			0.787432	−	0.616401i	$-0.211410\pi$
$751$	32411.8			1.57486			0.787432	+	0.616401i	$0.211410\pi$
$752$	−35181.3			−1.70603
$753$	4753.45	+	8233.22i	0.230047	+	0.398453i
$754$	−158.033	−	273.722i	−0.00763294	−	0.0132206i
$755$	−6134.06	−	10624.5i	−0.295684	−	0.512139i
$756$	−2114.32	−	3662.10i	−0.101716	−	0.176177i
$757$	−1887.00	+	3268.39i	−0.0906002	+	0.156924i	−0.907764	−	0.419482i	$-0.862212\pi$
$757$	−1887.00	+	3268.39i	−0.0906002	+	0.156924i	0.817164	+	0.576406i	$0.195545\pi$
$758$	−2413.27	+	4179.90i	−0.115638	+	0.200291i
$759$	−1334.45			−0.0638174
$760$	8717.78	+	15099.6i	0.416088	+	0.720686i
$761$	17543.6			0.835685			0.417842	−	0.908520i	$-0.362786\pi$
$761$	17543.6			0.835685			0.417842	+	0.908520i	$0.362786\pi$
$762$	3877.36			0.184333
$763$	7130.85	−	12351.0i	0.338341	−	0.586023i
$764$	−36991.1			−1.75169
$765$	4439.09	+	7688.73i	0.209798	+	0.363381i
$766$	1553.81	−	2691.29i	0.0732919	−	0.126945i
$767$	−5435.84	−	9415.14i	−0.255902	−	0.443235i
$768$	−4280.70	+	7414.40i	−0.201128	+	0.348365i
$769$	2848.65	−	4934.01i	0.133583	−	0.231372i	−0.791472	−	0.611205i	$-0.790685\pi$
$769$	2848.65	−	4934.01i	0.133583	−	0.231372i	0.925055	+	0.379833i	$0.124018\pi$
$770$	2823.94	−	4891.20i	0.132166	−	0.228918i
$771$	5806.14	−	10056.5i	0.271210	−	0.469750i
$772$	6284.32	−	10884.8i	0.292976	−	0.507450i
$773$	17232.2	−	29847.0i	0.801808	−	1.38877i	−0.116617	−	0.993177i	$-0.537205\pi$
$773$	17232.2	−	29847.0i	0.801808	−	1.38877i	0.918425	−	0.395596i	$-0.129462\pi$
$774$	425.985	+	737.828i	0.0197826	+	0.0342645i
$775$	−3977.87	+	6889.87i	−0.184373	+	0.319344i
$776$	−5348.98	−	9264.71i	−0.247445	−	0.428587i
$777$	6649.89			0.307032
$778$	3392.53	−	5876.04i	0.156335	−	0.270779i
$779$	−22793.8			−1.04836
$780$	6814.51			0.312819
$781$	−10347.5	−	17922.3i	−0.474086	−	0.821141i
$782$	399.954			0.0182894
$783$	446.497	−	773.355i	0.0203787	−	0.0352969i
$784$	−1908.70	+	3305.96i	−0.0869488	+	0.150600i
$785$	−11446.0	−	19825.1i	−0.520415	−	0.901385i
$786$	450.397	+	780.111i	0.0204391	+	0.0354016i
$787$	13562.2	+	23490.3i	0.614280	+	1.06396i	0.990510	+	0.137438i	$0.0438869\pi$
$787$	13562.2	+	23490.3i	0.614280	+	1.06396i	−0.376230	+	0.926526i	$0.622780\pi$
$788$	4343.54	+	7523.23i	0.196361	+	0.340106i
$789$	−16186.3			−0.730353
$790$	5426.49			0.244387
$791$	12913.0	+	22366.0i	0.580447	+	1.00536i
$792$	−1278.10	+	2213.73i	−0.0573425	+	0.0993202i
$793$	2926.88	−	5069.51i	0.131068	−	0.227016i
$794$	−869.564	−	1506.13i	−0.0388661	−	0.0673180i
$795$	27864.3			1.24307
$796$	−31025.2			−1.38148
$797$	−8938.11	+	15481.3i	−0.397245	+	0.688048i	−0.993385	−	0.114832i	$-0.963367\pi$
$797$	−8938.11	+	15481.3i	−0.397245	+	0.688048i	0.596140	+	0.802880i	$0.296700\pi$
$798$	−2169.05	−	3756.91i	−0.0962201	−	0.166658i
$799$	−38673.2			−1.71234
$800$	5325.16	−	9223.45i	0.235341	−	0.407623i
$801$	18.1308			0.000799774
$802$	611.510	+	1059.17i	0.0269242	+	0.0466340i
$803$	−34494.6			−1.51592
$804$	−313.737	−	12739.3i	−0.0137620	−	0.558807i
$805$	−3895.74			−0.170567
$806$	331.228	+	573.703i	0.0144752	+	0.0250718i
$807$	−9642.53			−0.420611
$808$	−945.693	+	1637.99i	−0.0411750	+	0.0713171i
$809$	33452.9			1.45382			0.726911	−	0.686731i	$-0.240955\pi$
$809$	33452.9			1.45382			0.726911	+	0.686731i	$0.240955\pi$
$810$	−316.425	−	548.064i	−0.0137260	−	0.0237741i
$811$	−8831.79	+	15297.1i	−0.382399	+	0.662335i	−0.991405	−	0.130831i	$-0.958235\pi$
$811$	−8831.79	+	15297.1i	−0.382399	+	0.662335i	0.609005	+	0.793166i	$0.291569\pi$
$812$	−5179.89			−0.223865
$813$	20562.4			0.887028
$814$	−988.711	−	1712.50i	−0.0425729	−	0.0737383i
$815$	25884.6	−	44833.4i	1.11251	−	1.92693i
$816$	−5538.17	+	9592.39i	−0.237591	+	0.411521i
$817$	−13295.3	−	23028.1i	−0.569331	−	0.986111i
$818$	−4394.16			−0.187822
$819$	−3446.74			−0.147056
$820$	9644.05	+	16704.0i	0.410713	+	0.711376i
$821$	−8351.35	−	14465.0i	−0.355011	−	0.614898i	0.632109	−	0.774880i	$-0.282190\pi$
$821$	−8351.35	−	14465.0i	−0.355011	−	0.614898i	−0.987120	+	0.159982i	$0.948856\pi$
$822$	−1498.17	−	2594.91i	−0.0635702	−	0.110107i
$823$	6727.65	+	11652.6i	0.284947	+	0.493542i	0.972596	−	0.232501i	$-0.0746908\pi$
$823$	6727.65	+	11652.6i	0.284947	+	0.493542i	−0.687650	+	0.726043i	$0.741357\pi$
$824$	7599.09	−	13162.0i	0.321270	−	0.556457i
$825$	−6154.41	+	10659.8i	−0.259720	+	0.449849i
$826$	5856.46			0.246698
$827$	−6798.91	−	11776.1i	−0.285878	−	0.495155i	0.686944	−	0.726711i	$-0.258952\pi$
$827$	−6798.91	−	11776.1i	−0.285878	−	0.495155i	−0.972822	+	0.231555i	$0.925619\pi$
$828$	867.341			0.0364036
$829$	23422.9			0.981318			0.490659	−	0.871352i	$-0.336756\pi$
$829$	23422.9			0.981318			0.490659	+	0.871352i	$0.336756\pi$
$830$	1896.51	−	3284.85i	0.0793118	−	0.137372i
$831$	−19724.0			−0.823366
$832$	3947.17	+	6836.70i	0.164475	+	0.284880i
$833$	−2098.15	+	3634.10i	−0.0872706	+	0.151157i
$834$	−386.681	−	669.752i	−0.0160548	−	0.0278077i
$835$	5780.05	−	10011.3i	0.239553	−	0.414918i
$836$	19622.7	−	33987.5i	0.811800	−	1.40608i
$837$	−935.828	+	1620.90i	−0.0386463	+	0.0669374i
$838$	−1434.39	+	2484.43i	−0.0591290	+	0.102414i
$839$	11655.9	−	20188.6i	0.479626	−	0.830737i	−0.520101	−	0.854105i	$-0.674106\pi$
$839$	11655.9	−	20188.6i	0.479626	−	0.830737i	0.999727	+	0.0233678i	$0.00743886\pi$
$840$	−3731.24	+	6462.69i	−0.153262	+	0.265457i
$841$	11647.6	+	20174.2i	0.477574	+	0.827183i
$842$	2175.08	−	3767.35i	0.0890241	−	0.154194i
$843$	−8132.28	−	14085.5i	−0.332255	−	0.575482i
$844$	−13321.0			−0.543278
$845$	−14232.4	+	24651.2i	−0.579419	+	1.00358i
$846$	2756.69			0.112029
$847$	1070.26			0.0434173
$848$	17381.6	+	30105.8i	0.703876	+	1.21915i
$849$	−13555.2			−0.547954
$850$	1844.57	−	3194.89i	0.0744332	−	0.128922i
$851$	−681.984	+	1181.23i	−0.0274714	+	0.0475818i
$852$	6725.46	+	11648.8i	0.270435	+	0.468407i
$853$	−4476.75	−	7753.96i	−0.179696	−	0.311243i	0.762080	−	0.647483i	$-0.224178\pi$
$853$	−4476.75	−	7753.96i	−0.179696	−	0.311243i	−0.941777	+	0.336239i	$0.890845\pi$
$854$	1576.68	+	2730.89i	0.0631768	+	0.109425i
$855$	9875.84	+	17105.5i	0.395025	+	0.684204i
$856$	13500.9			0.539078
$857$	39535.7			1.57586			0.787932	−	0.615762i	$-0.211152\pi$
$857$	39535.7			1.57586			0.787932	+	0.615762i	$0.211152\pi$
$858$	512.464	+	887.613i	0.0203907	+	0.0353177i
$859$	17019.5	−	29478.6i	0.676015	−	1.17089i	−0.300156	−	0.953890i	$-0.597039\pi$
$859$	17019.5	−	29478.6i	0.676015	−	1.17089i	0.976171	−	0.217003i	$-0.0696281\pi$
$860$	−11250.5	+	19486.4i	−0.446091	+	0.772652i
$861$	−4877.91	−	8448.78i	−0.193076	−	0.334418i
$862$	−3014.92			−0.119128
$863$	−17570.7			−0.693065			−0.346532	−	0.938038i	$-0.612641\pi$
$863$	−17570.7			−0.693065			−0.346532	+	0.938038i	$0.612641\pi$
$864$	1252.79	−	2169.90i	0.0493296	−	0.0854414i
$865$	11691.8	+	20250.7i	0.459575	+	0.796007i
$866$	3402.02			0.133494
$867$	1281.65	−	2219.87i	0.0502041	−	0.0869561i
$868$	10856.7			0.424541
$869$	−12415.1	−	21503.6i	−0.484642	−	0.839425i
$870$	−775.213			−0.0302094
$871$	−9120.46	−	4970.41i	−0.354805	−	0.193359i
$872$	5603.43			0.217610
$873$	−6059.53	−	10495.4i	−0.234919	−	0.406891i
$874$	889.795			0.0344368
$875$	1601.95	−	2774.66i	0.0618924	−	0.107201i
$876$	22420.2			0.864734
$877$	16623.4	+	28792.6i	0.640060	+	1.10862i	0.985419	+	0.170146i	$0.0544238\pi$
$877$	16623.4	+	28792.6i	0.640060	+	1.10862i	−0.345359	+	0.938471i	$0.612243\pi$
$878$	2937.02	−	5087.07i	0.112893	−	0.195536i
$879$	5793.45			0.222307
$880$	−32081.9			−1.22896
$881$	−21214.6	−	36744.8i	−0.811282	−	1.40518i	−0.911967	−	0.410263i	$-0.865437\pi$
$881$	−21214.6	−	36744.8i	−0.811282	−	1.40518i	0.100686	−	0.994918i	$-0.467896\pi$
$882$	149.559	−	259.044i	0.00570965	−	0.00988940i
$883$	−23975.0	+	41525.9i	−0.913728	+	1.58262i	−0.104975	+	0.994475i	$0.533476\pi$
$883$	−23975.0	+	41525.9i	−0.913728	+	1.58262i	−0.808753	+	0.588148i	$0.799857\pi$
$884$	4672.77	+	8093.48i	0.177786	+	0.307934i
$885$	−26664.8			−1.01280
$886$	5457.94			0.206956
$887$	9141.25	+	15833.1i	0.346035	+	0.599350i	0.985541	−	0.169436i	$-0.0541945\pi$
$887$	9141.25	+	15833.1i	0.346035	+	0.599350i	−0.639506	+	0.768786i	$0.720861\pi$
$888$	1306.37	+	2262.70i	0.0493682	+	0.0855083i
$889$	−25897.4	−	44855.6i	−0.977021	−	1.69225i
$890$	−7.86972	−	13.6308i	−0.000296397	−	0.000513375i
$891$	−1447.88	+	2507.80i	−0.0544397	+	0.0942924i
$892$	−872.612	+	1511.41i	−0.0327547	+	0.0567328i
$893$	−86038.1			−3.22414
$894$	73.9086	+	128.013i	0.00276496	+	0.00478905i
$895$	1779.91			0.0664759
$896$	−19264.2			−0.718272
$897$	353.483	−	612.250i	0.0131577	−	0.0227898i
$898$	2672.70			0.0993198
$899$	1146.35	+	1985.53i	0.0425282	+	0.0736611i
$900$	4000.14	−	6928.44i	0.148153	−	0.256609i
$901$	19106.8	+	33094.0i	0.706482	+	1.22366i
$902$	−1450.50	+	2512.34i	−0.0535437	+	0.0927404i
$903$	5690.43	−	9856.11i	0.209707	−	0.363223i
$904$	−5073.53	+	8787.61i	−0.186663	+	0.323309i
$905$	−17485.8	+	30286.3i	−0.642262	+	1.11243i
$906$	−599.646	+	1038.62i	−0.0219889	+	0.0380858i
$907$	−11681.0	+	20232.0i	−0.427629	+	0.740676i	−0.996662	−	0.0816391i	$-0.973985\pi$
$907$	−11681.0	+	20232.0i	−0.427629	+	0.740676i	0.569033	+	0.822315i	$0.307318\pi$
$908$	1847.80	+	3200.48i	0.0675346	+	0.116973i
$909$	−1071.32	+	1855.58i	−0.0390906	+	0.0677069i
$910$	1496.07	+	2591.27i	0.0544991	+	0.0943952i
$911$	28215.8			1.02616			0.513079	−	0.858341i	$-0.328505\pi$
$911$	28215.8			1.02616			0.513079	+	0.858341i	$0.328505\pi$
$912$	−12321.0	+	21340.6i	−0.447357	+	0.774844i
$913$	−17355.9			−0.629131
$914$	113.855			0.00412036
$915$	−7178.73	−	12433.9i	−0.259368	−	0.449238i
$916$	11546.2			0.416482
$917$	6016.53	−	10420.9i	0.216667	−	0.375278i
$918$	433.951	−	751.626i	0.0156019	−	0.0270232i
$919$	−5182.13	−	8975.71i	−0.186009	−	0.322178i	0.757907	−	0.652363i	$-0.226222\pi$
$919$	−5182.13	−	8975.71i	−0.186009	−	0.322178i	−0.943916	+	0.330185i	$0.892889\pi$
$920$	−765.319	−	1325.57i	−0.0274259	−	0.0475030i
$921$	12887.4	+	22321.6i	0.461079	+	0.798612i
$922$	1833.70	+	3176.06i	0.0654985	+	0.113447i
$923$	10963.8			0.390983
$924$	16797.1			0.598036
$925$	6290.56	+	10895.6i	0.223603	+	0.387291i
$926$	699.885	−	1212.24i	0.0248376	−	0.0430200i
$927$	8608.54	−	14910.4i	0.305007	−	0.528288i
$928$	−1534.61	−	2658.03i	−0.0542847	−	0.0940238i
$929$	−37819.8			−1.33566			−0.667830	−	0.744313i	$-0.732777\pi$
$929$	−37819.8			−1.33566			−0.667830	+	0.744313i	$0.732777\pi$
$930$	1624.80			0.0572895
$931$	−4667.84	+	8084.93i	−0.164320	+	0.284611i
$932$	−16871.6	−	29222.5i	−0.592971	−	1.02706i
$933$	−670.950			−0.0235433
$934$	−5001.01	+	8662.00i	−0.175201	+	0.303458i
$935$	−35266.2			−1.23351
$936$	−677.113	−	1172.79i	−0.0236454	−	0.0409551i
$937$	38339.2			1.33670			0.668350	−	0.743847i	$-0.267001\pi$
$937$	38339.2			1.33670			0.668350	+	0.743847i	$0.267001\pi$
$938$	4775.34	−	2916.11i	0.166226	−	0.101508i
$939$	15968.2			0.554955
$940$	36402.7	+	63051.3i	1.26311	+	2.18777i
$941$	29538.6			1.02331			0.511653	−	0.859192i	$-0.329033\pi$
$941$	29538.6			1.02331			0.511653	+	0.859192i	$0.329033\pi$
$942$	−1118.93	+	1938.04i	−0.0387013	+	0.0670325i
$943$	2001.03			0.0691012
$944$	−16633.4	−	28809.9i	−0.573486	−	0.993307i
$945$	−4226.89	+	7321.18i	−0.145503	+	0.252019i
$946$	−3384.23			−0.116312
$947$	46241.6			1.58675			0.793374	−	0.608734i	$-0.208323\pi$
$947$	46241.6			1.58675			0.793374	+	0.608734i	$0.208323\pi$
$948$	8069.36	+	13976.5i	0.276456	+	0.478837i
$949$	9137.28	−	15826.2i	0.312549	−	0.541350i
$950$	4103.69	−	7107.81i	0.140149	−	0.242745i
$951$	5802.86	+	10050.8i	0.197866	+	0.342714i
$952$	−10234.2			−0.348416
$953$	28459.6			0.967364			0.483682	−	0.875244i	$-0.339299\pi$
$953$	28459.6			0.967364			0.483682	+	0.875244i	$0.339299\pi$
$954$	−1361.96	−	2358.99i	−0.0462213	−	0.0800576i
$955$	36975.8	+	64043.9i	1.25289	+	2.17007i
$956$	−9406.54	−	16292.6i	−0.318232	−	0.551193i
$957$	1773.59	+	3071.95i	0.0599081	+	0.103764i
$958$	355.517	−	615.773i	0.0119898	−	0.0207669i
$959$	−20013.0	+	34663.5i	−0.673881	+	1.16720i
$960$	19362.4			0.650955
$961$	12492.8	+	21638.2i	0.419349	+	0.726334i
$962$	1047.60			0.0351102
$963$	15294.3			0.511789
$964$	8673.77	−	15023.4i	0.289796	−	0.501941i
$965$	−25126.9			−0.838201
$966$	190.418	+	329.813i	0.00634222	+	0.0109850i
$967$	27526.4	−	47677.1i	0.915398	−	1.58552i	0.109079	−	0.994033i	$-0.465210\pi$
$967$	27526.4	−	47677.1i	0.915398	−	1.58552i	0.806318	−	0.591482i	$-0.201457\pi$
$968$	210.252	+	364.168i	0.00698116	+	0.0120917i
$969$	−13543.9	+	23458.8i	−0.449013	+	0.777713i
$970$	−5260.32	+	9111.14i	−0.174122	+	0.301589i
$971$	−21358.9	+	36994.6i	−0.705910	+	1.22267i	0.260452	+	0.965487i	$0.416128\pi$
$971$	−21358.9	+	36994.6i	−0.705910	+	1.22267i	−0.966362	+	0.257185i	$0.917205\pi$
$972$	941.067	−	1629.98i	0.0310543	−	0.0537876i
$973$	−5165.39	+	8946.72i	−0.170190	+	0.294778i
$974$	−2428.88	+	4206.95i	−0.0799039	+	0.138398i
$975$	−3260.49	−	5647.34i	−0.107097	−	0.185497i
$976$	8956.12	−	15512.5i	0.293728	−	0.508752i
$977$	21355.9	+	36989.6i	0.699321	+	1.21126i	0.968702	+	0.248226i	$0.0798475\pi$
$977$	21355.9	+	36989.6i	0.699321	+	1.21126i	−0.269381	+	0.963034i	$0.586819\pi$
$978$	−5060.78			−0.165466
$979$	−36.0098	+	62.3709i	−0.00117557	+	0.00203614i
$980$	7899.84			0.257501
$981$	6347.78			0.206594
$982$	−3528.31	−	6111.21i	−0.114657	−	0.198591i
$983$	−24205.0			−0.785372			−0.392686	−	0.919673i	$-0.628454\pi$
$983$	−24205.0			−0.785372			−0.392686	+	0.919673i	$0.628454\pi$
$984$	1916.53	−	3319.53i	0.0620903	−	0.107543i
$985$	8683.49	−	15040.2i	0.280892	−	0.486520i
$986$	−531.571	−	920.709i	−0.0171690	−	0.0297377i
$987$	−18412.3	−	31891.0i	−0.593788	−	1.02847i
$988$	10395.7	+	18005.9i	0.334749	+	0.579802i
$989$	1167.17	+	2021.60i	0.0375267	+	0.0649981i
$990$	2513.83			0.0807017
$991$	−39874.0			−1.27814			−0.639071	−	0.769148i	$-0.720681\pi$
$991$	−39874.0			−1.27814			−0.639071	+	0.769148i	$0.720681\pi$
$992$	3216.45	+	5571.06i	0.102946	+	0.178308i
$993$	6603.93	−	11438.3i	0.211047	−	0.365543i
$994$	−2953.04	+	5114.81i	−0.0942301	+	0.163211i
$995$	31012.3	+	53715.0i	0.988098	+	1.71144i
$996$	11280.7			0.358878
$997$	−2956.35			−0.0939104			−0.0469552	−	0.998897i	$-0.514952\pi$
$997$	−2956.35			−0.0939104			−0.0469552	+	0.998897i	$0.514952\pi$
$998$	−3822.95	+	6621.55i	−0.121256	+	0.210021i
$999$	1479.91	+	2563.28i	0.0468691	+	0.0811797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.a.37.8	✓	32
67.29	even	3	inner	201.4.e.a.163.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.a.37.8	✓	32	1.1	even	1	trivial
201.4.e.a.163.8	yes	32	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)

\(f(q)\)	\(=\)	\(q+(0.252285 + 0.436970i) q^{2} +3.00000 q^{3} +(3.87271 - 6.70772i) q^{4} -15.4844 q^{5} +(0.756854 + 1.31091i) q^{6} +(10.1103 - 17.5115i) q^{7} +7.94465 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(0.252285 + 0.436970i) q^{2} +3.00000 q^{3} +(3.87271 - 6.70772i) q^{4} -15.4844 q^{5} +(0.756854 + 1.31091i) q^{6} +(10.1103 - 17.5115i) q^{7} +7.94465 q^{8} +9.00000 q^{9} +(-3.90648 - 6.76622i) q^{10} +(-17.8751 + 30.9605i) q^{11} +(11.6181 - 20.1232i) q^{12} +(-9.46987 - 16.4023i) q^{13} +10.2026 q^{14} -46.4533 q^{15} +(-28.9773 - 50.1902i) q^{16} +(-31.8535 - 55.1718i) q^{17} +(2.27056 + 3.93273i) q^{18} +(-70.8658 - 122.743i) q^{19} +(-59.9666 + 103.865i) q^{20} +(30.3308 - 52.5344i) q^{21} -18.0384 q^{22} +(6.22118 + 10.7754i) q^{23} +23.8339 q^{24} +114.767 q^{25} +(4.77820 - 8.27609i) q^{26} +27.0000 q^{27} +(-78.3080 - 135.634i) q^{28} +(16.5369 - 28.6428i) q^{29} +(-11.7194 - 20.2987i) q^{30} +(-34.6603 + 60.0334i) q^{31} +(46.3997 - 80.3666i) q^{32} +(-53.6252 + 92.8815i) q^{33} +(16.0723 - 27.8380i) q^{34} +(-156.551 + 271.155i) q^{35} +(34.8543 - 60.3695i) q^{36} +(54.8115 + 94.9362i) q^{37} +(35.7567 - 61.9324i) q^{38} +(-28.4096 - 49.2069i) q^{39} -123.018 q^{40} +(80.4119 - 139.277i) q^{41} +30.6079 q^{42} +187.612 q^{43} +(138.450 + 239.802i) q^{44} -139.360 q^{45} +(-3.13902 + 5.43694i) q^{46} +(303.525 - 525.720i) q^{47} +(-86.9320 - 150.571i) q^{48} +(-32.9344 - 57.0440i) q^{49} +(28.9540 + 50.1498i) q^{50} +(-95.5604 - 165.515i) q^{51} -146.696 q^{52} -599.835 q^{53} +(6.81168 + 11.7982i) q^{54} +(276.785 - 479.405i) q^{55} +(80.3224 - 139.122i) q^{56} +(-212.597 - 368.229i) q^{57} +16.6880 q^{58} +574.014 q^{59} +(-179.900 + 311.596i) q^{60} +(154.537 + 267.665i) q^{61} -34.9770 q^{62} +(90.9923 - 157.603i) q^{63} -416.814 q^{64} +(146.635 + 253.980i) q^{65} -54.1152 q^{66} +(468.049 - 285.819i) q^{67} -493.436 q^{68} +(18.6636 + 32.3262i) q^{69} -157.982 q^{70} +(-289.439 + 501.322i) q^{71} +71.5018 q^{72} +(482.440 + 835.610i) q^{73} +(-27.6562 + 47.9019i) q^{74} +344.302 q^{75} -1097.77 q^{76} +(361.443 + 626.037i) q^{77} +(14.3346 - 24.8283i) q^{78} +(-347.275 + 601.498i) q^{79} +(448.697 + 777.166i) q^{80} +81.0000 q^{81} +81.1467 q^{82} +(242.739 + 420.436i) q^{83} +(-234.924 - 406.901i) q^{84} +(493.232 + 854.303i) q^{85} +(47.3317 + 81.9809i) q^{86} +(49.6107 - 85.9283i) q^{87} +(-142.011 + 245.970i) q^{88} +2.01453 q^{89} +(-35.1583 - 60.8960i) q^{90} -382.971 q^{91} +96.3712 q^{92} +(-103.981 + 180.100i) q^{93} +306.298 q^{94} +(1097.32 + 1900.61i) q^{95} +(139.199 - 241.100i) q^{96} +(-673.281 - 1166.16i) q^{97} +(16.6177 - 28.7826i) q^{98} +(-160.876 + 278.645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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