LMFDB - Embedded newform 164.5.d.f.163.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [164,5,Mod(163,164)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("164.163"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(164, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	164.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,6,0,-162,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$16.9526739458$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.4
Character	$\chi$	$=$	164.163
Dual form			164.5.d.f.163.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.71258 + 1.48887i) q^{2} +10.9113 q^{3} +(11.5666 - 11.0551i) q^{4} +8.39889 q^{5} +(-40.5091 + 16.2454i) q^{6} +64.7429 q^{7} +(-26.4823 + 58.2639i) q^{8} +38.0563 q^{9} +(-31.1816 + 12.5048i) q^{10} +53.4978 q^{11} +(126.206 - 120.625i) q^{12} +211.963i q^{13} +(-240.363 + 96.3934i) q^{14} +91.6427 q^{15} +(11.5707 - 255.738i) q^{16} +86.3903i q^{17} +(-141.287 + 56.6606i) q^{18} +370.107 q^{19} +(97.1462 - 92.8503i) q^{20} +706.428 q^{21} +(-198.615 + 79.6511i) q^{22} -759.854i q^{23} +(-288.956 + 635.735i) q^{24} -554.459 q^{25} +(-315.584 - 786.930i) q^{26} -468.572 q^{27} +(748.853 - 715.737i) q^{28} -1221.22i q^{29} +(-340.231 + 136.444i) q^{30} +1548.55i q^{31} +(337.803 + 966.677i) q^{32} +583.730 q^{33} +(-128.623 - 320.731i) q^{34} +543.768 q^{35} +(440.180 - 420.715i) q^{36} +1773.91 q^{37} +(-1374.05 + 551.040i) q^{38} +2312.79i q^{39} +(-222.422 + 489.352i) q^{40} +(1638.20 + 376.900i) q^{41} +(-2622.67 + 1051.78i) q^{42} +966.166i q^{43} +(618.786 - 591.423i) q^{44} +319.630 q^{45} +(1131.32 + 2821.02i) q^{46} +1379.97 q^{47} +(126.251 - 2790.44i) q^{48} +1790.64 q^{49} +(2058.47 - 825.514i) q^{50} +942.630i q^{51} +(2343.27 + 2451.68i) q^{52} +49.7786i q^{53} +(1739.61 - 697.640i) q^{54} +449.322 q^{55} +(-1714.54 + 3772.18i) q^{56} +4038.35 q^{57} +(1818.23 + 4533.89i) q^{58} +2186.63i q^{59} +(1059.99 - 1013.12i) q^{60} -1860.90 q^{61} +(-2305.58 - 5749.11i) q^{62} +2463.87 q^{63} +(-2693.37 - 3085.93i) q^{64} +1780.25i q^{65} +(-2167.15 + 869.096i) q^{66} -1144.73 q^{67} +(955.051 + 999.239i) q^{68} -8290.98i q^{69} +(-2018.78 + 809.597i) q^{70} -4669.47 q^{71} +(-1007.82 + 2217.31i) q^{72} +8288.70 q^{73} +(-6585.80 + 2641.12i) q^{74} -6049.86 q^{75} +(4280.87 - 4091.56i) q^{76} +3463.60 q^{77} +(-3443.43 - 8586.42i) q^{78} -5692.98 q^{79} +(97.1810 - 2147.92i) q^{80} -8195.28 q^{81} +(-6643.12 + 1039.79i) q^{82} -3047.28i q^{83} +(8170.95 - 7809.62i) q^{84} +725.582i q^{85} +(-1438.49 - 3586.97i) q^{86} -13325.1i q^{87} +(-1416.75 + 3116.99i) q^{88} -13007.7i q^{89} +(-1186.65 + 475.886i) q^{90} +13723.1i q^{91} +(-8400.24 - 8788.89i) q^{92} +16896.6i q^{93} +(-5123.24 + 2054.58i) q^{94} +3108.49 q^{95} +(3685.86 + 10547.7i) q^{96} +1202.68i q^{97} +(-6647.90 + 2666.02i) q^{98} +2035.93 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{2} - 162 q^{4} - 8 q^{5} + 162 q^{8} + 1728 q^{9} - 272 q^{10} - 2842 q^{16} - 298 q^{18} - 584 q^{20} + 280 q^{21} + 4264 q^{25} + 66 q^{32} + 3512 q^{33} - 11338 q^{36} + 5720 q^{37} - 4648 q^{40}+ \cdots + 2902 q^{98}+O(q^{100}) $ 72 * q + 6 * q^2 - 162 * q^4 - 8 * q^5 + 162 * q^8 + 1728 * q^9 - 272 * q^10 - 2842 * q^16 - 298 * q^18 - 584 * q^20 + 280 * q^21 + 4264 * q^25 + 66 * q^32 + 3512 * q^33 - 11338 * q^36 + 5720 * q^37 - 4648 * q^40 - 7928 * q^41 - 10140 * q^42 - 9528 * q^45 - 5680 * q^46 + 6624 * q^49 + 554 * q^50 + 29864 * q^57 + 11712 * q^61 - 3936 * q^62 - 34554 * q^64 + 24852 * q^66 - 12166 * q^72 + 16632 * q^73 - 11120 * q^74 + 84456 * q^77 - 20496 * q^78 - 12104 * q^80 + 13408 * q^81 - 51114 * q^82 - 948 * q^84 - 20400 * q^86 + 64976 * q^90 - 2784 * q^92 + 2902 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−3.71258	+	1.48887i	−0.928146	+	0.372216i
$2$	−3.71258	+	1.48887i	−0.928146	+	0.372216i
$3$	10.9113			1.21237			0.606183	−	0.795325i	$-0.292700\pi$
$3$	10.9113			1.21237			0.606183	+	0.795325i	$0.292700\pi$
$4$	11.5666	−	11.0551i	0.722910	−	0.690942i
$5$	8.39889			0.335955			0.167978	−	0.985791i	$-0.446276\pi$
$5$	8.39889			0.335955			0.167978	+	0.985791i	$0.446276\pi$
$6$	−40.5091	+	16.2454i	−1.12525	+	0.451262i
$7$	64.7429			1.32128			0.660642	−	0.750701i	$-0.270284\pi$
$7$	64.7429			1.32128			0.660642	+	0.750701i	$0.270284\pi$
$8$	−26.4823	+	58.2639i	−0.413786	+	0.910374i
$9$	38.0563			0.469830
$10$	−31.1816	+	12.5048i	−0.311816	+	0.125048i
$11$	53.4978			0.442131			0.221065	−	0.975259i	$-0.429047\pi$
$11$	53.4978			0.442131			0.221065	+	0.975259i	$0.429047\pi$
$12$	126.206	−	120.625i	0.876431	−	0.837674i
$13$			211.963i			1.25422i	0.778931	+	0.627109i	$0.215762\pi$
$13$			211.963i			1.25422i	−0.778931	+	0.627109i	$0.784238\pi$
$14$	−240.363	+	96.3934i	−1.22634	+	0.491803i
$15$	91.6427			0.407301
$16$	11.5707	−	255.738i	0.0451981	−	0.998978i
$17$			86.3903i			0.298928i	0.988767	+	0.149464i	$0.0477549\pi$
$17$			86.3903i			0.298928i	−0.988767	+	0.149464i	$0.952245\pi$
$18$	−141.287	+	56.6606i	−0.436071	+	0.174879i
$19$	370.107			1.02523			0.512614	−	0.858619i	$-0.328677\pi$
$19$	370.107			1.02523			0.512614	+	0.858619i	$0.328677\pi$
$20$	97.1462	−	92.8503i	0.242866	−	0.232126i
$21$	706.428			1.60188
$22$	−198.615	+	79.6511i	−0.410362	+	0.164568i
$23$		−	759.854i		−	1.43640i	−0.695839	−	0.718198i	$-0.744967\pi$
$23$		−	759.854i		−	1.43640i	0.695839	−	0.718198i	$-0.255033\pi$
$24$	−288.956	+	635.735i	−0.501660	+	1.10371i
$25$	−554.459			−0.887134
$26$	−315.584	−	786.930i	−0.466840	−	1.16410i
$27$	−468.572			−0.642759
$28$	748.853	−	715.737i	0.955169	−	0.912930i
$29$		−	1221.22i		−	1.45211i	−0.687638	−	0.726053i	$-0.741353\pi$
$29$		−	1221.22i		−	1.45211i	0.687638	−	0.726053i	$-0.258647\pi$
$30$	−340.231	+	136.444i	−0.378035	+	0.151604i
$31$			1548.55i			1.61139i	0.592330	+	0.805695i	$0.298208\pi$
$31$			1548.55i			1.61139i	−0.592330	+	0.805695i	$0.701792\pi$
$32$	337.803	+	966.677i	0.329885	+	0.944021i
$33$	583.730			0.536024
$34$	−128.623	−	320.731i	−0.111266	−	0.277449i
$35$	543.768			0.443892
$36$	440.180	−	420.715i	0.339645	−	0.324626i
$37$	1773.91			1.29577			0.647886	−	0.761737i	$-0.275653\pi$
$37$	1773.91			1.29577			0.647886	+	0.761737i	$0.275653\pi$
$38$	−1374.05	+	551.040i	−0.951561	+	0.381606i
$39$			2312.79i			1.52057i
$40$	−222.422	+	489.352i	−0.139014	+	0.305845i
$41$	1638.20	+	376.900i	0.974540	+	0.224212i
$41$	1638.20	+	376.900i	0.974540	+	0.224212i
$42$	−2622.67	+	1051.78i	−1.48678	+	0.596245i
$43$			966.166i			0.522534i	0.965267	+	0.261267i	$0.0841404\pi$
$43$			966.166i			0.522534i	−0.965267	+	0.261267i	$0.915860\pi$
$44$	618.786	−	591.423i	0.319621	−	0.305487i
$45$	319.630			0.157842
$46$	1131.32	+	2821.02i	0.534650	+	1.33319i
$47$	1379.97			0.624701			0.312351	−	0.949967i	$-0.398884\pi$
$47$	1379.97			0.624701			0.312351	+	0.949967i	$0.398884\pi$
$48$	126.251	−	2790.44i	0.0547966	−	1.21113i
$49$	1790.64			0.745790
$50$	2058.47	−	825.514i	0.823390	−	0.330206i
$51$			942.630i			0.362410i
$52$	2343.27	+	2451.68i	0.866592	+	0.906687i
$53$			49.7786i			0.0177211i	0.999961	+	0.00886056i	$0.00282044\pi$
$53$			49.7786i			0.0177211i	−0.999961	+	0.00886056i	$0.997180\pi$
$54$	1739.61	−	697.640i	0.596575	−	0.239246i
$55$	449.322			0.148536
$56$	−1714.54	+	3772.18i	−0.546729	+	1.20286i
$57$	4038.35			1.24295
$58$	1818.23	+	4533.89i	0.540498	+	1.34777i
$59$			2186.63i			0.628163i	0.949396	+	0.314081i	$0.101696\pi$
$59$			2186.63i			0.628163i	−0.949396	+	0.314081i	$0.898304\pi$
$60$	1059.99	−	1013.12i	0.294442	−	0.281421i
$61$	−1860.90			−0.500107			−0.250053	−	0.968232i	$-0.580448\pi$
$61$	−1860.90			−0.500107			−0.250053	+	0.968232i	$0.580448\pi$
$62$	−2305.58	−	5749.11i	−0.599786	−	1.49561i
$63$	2463.87			0.620779
$64$	−2693.37	−	3085.93i	−0.657562	−	0.753401i
$65$			1780.25i			0.421361i
$66$	−2167.15	+	869.096i	−0.497509	+	0.199517i
$67$	−1144.73			−0.255008			−0.127504	−	0.991838i	$-0.540697\pi$
$67$	−1144.73			−0.255008			−0.127504	+	0.991838i	$0.540697\pi$
$68$	955.051	+	999.239i	0.206542	+	0.216098i
$69$		−	8290.98i		−	1.74144i
$70$	−2018.78	+	809.597i	−0.411997	+	0.165224i
$71$	−4669.47			−0.926298			−0.463149	−	0.886280i	$-0.653281\pi$
$71$	−4669.47			−0.926298			−0.463149	+	0.886280i	$0.653281\pi$
$72$	−1007.82	+	2217.31i	−0.194409	+	0.427721i
$73$	8288.70			1.55539			0.777697	−	0.628639i	$-0.216388\pi$
$73$	8288.70			1.55539			0.777697	+	0.628639i	$0.216388\pi$
$74$	−6585.80	+	2641.12i	−1.20267	+	0.482307i
$75$	−6049.86			−1.07553
$76$	4280.87	−	4091.56i	0.741147	−	0.708373i
$77$	3463.60			0.584180
$78$	−3443.43	−	8586.42i	−0.565981	−	1.41131i
$79$	−5692.98			−0.912191			−0.456095	−	0.889931i	$-0.650752\pi$
$79$	−5692.98			−0.912191			−0.456095	+	0.889931i	$0.650752\pi$
$80$	97.1810	−	2147.92i	0.0151845	−	0.335612i
$81$	−8195.28			−1.24909
$82$	−6643.12	+	1039.79i	−0.987971	+	0.154638i
$83$		−	3047.28i		−	0.442341i	−0.975235	−	0.221170i	$-0.929012\pi$
$83$		−	3047.28i		−	0.442341i	0.975235	−	0.221170i	$-0.0709877\pi$
$84$	8170.95	−	7809.62i	1.15801	−	1.10681i
$85$			725.582i			0.100427i
$86$	−1438.49	−	3586.97i	−0.194496	−	0.484988i
$87$		−	13325.1i		−	1.76048i
$88$	−1416.75	+	3116.99i	−0.182948	+	0.402505i
$89$		−	13007.7i		−	1.64218i	−0.570798	−	0.821090i	$-0.693366\pi$
$89$		−	13007.7i		−	1.64218i	0.570798	−	0.821090i	$-0.306634\pi$
$90$	−1186.65	+	475.886i	−0.146500	+	0.0587514i
$91$			13723.1i			1.65718i
$92$	−8400.24	−	8788.89i	−0.992467	−	1.03839i
$93$			16896.6i			1.95359i
$94$	−5123.24	+	2054.58i	−0.579814	+	0.232524i
$95$	3108.49			0.344431
$96$	3685.86	+	10547.7i	0.399942	+	1.14450i
$97$			1202.68i			0.127822i	0.997956	+	0.0639109i	$0.0203574\pi$
$97$			1202.68i			0.127822i	−0.997956	+	0.0639109i	$0.979643\pi$
$98$	−6647.90	+	2666.02i	−0.692202	+	0.277595i
$99$	2035.93			0.207727
$100$	−6413.18	+	6129.58i	−0.641318	+	0.612958i
$101$			5757.94i			0.564449i	0.959348	+	0.282225i	$0.0910723\pi$
$101$			5757.94i			0.564449i	−0.959348	+	0.282225i	$0.908928\pi$
$102$	−1403.45	−	3499.59i	−0.134895	−	0.336370i
$103$			3187.97i			0.300496i	0.988648	+	0.150248i	$0.0480073\pi$
$103$			3187.97i			0.300496i	−0.988648	+	0.150248i	$0.951993\pi$
$104$	−12349.8	−	5613.27i	−1.14181	−	0.518978i
$105$	5933.21			0.538160
$106$	−74.1137	−	184.807i	−0.00659609	−	0.0164478i
$107$		−	17012.0i		−	1.48589i	−0.669352	−	0.742945i	$-0.733428\pi$
$107$		−	17012.0i		−	1.48589i	0.669352	−	0.742945i	$-0.266572\pi$
$108$	−5419.76	+	5180.09i	−0.464657	+	0.444110i
$109$		−	17305.0i		−	1.45653i	−0.685296	−	0.728264i	$-0.740327\pi$
$109$		−	17305.0i		−	1.45653i	0.685296	−	0.728264i	$-0.259673\pi$
$110$	−1668.15	+	668.980i	−0.137863	+	0.0552876i
$111$	19355.7			1.57095
$112$	749.121	−	16557.2i	0.0597194	−	1.31993i
$113$	−7981.54			−0.625072			−0.312536	−	0.949906i	$-0.601178\pi$
$113$	−7981.54			−0.625072			−0.312536	+	0.949906i	$0.601178\pi$
$114$	−14992.7	+	6012.55i	−1.15364	+	0.462646i
$115$		−	6381.92i		−	0.482565i
$116$	−13500.7	−	14125.3i	−1.00332	−	1.04974i
$117$			8066.51i			0.589270i
$118$	−3255.60	−	8118.06i	−0.233812	−	0.583027i
$119$			5593.16i			0.394969i
$120$	−2426.91	+	5339.46i	−0.168535	+	0.370796i
$121$	−11779.0			−0.804520
$122$	6908.74	−	2770.63i	0.464172	−	0.186148i
$123$	17874.9	+	4112.47i	1.18150	+	0.271827i
$124$	17119.3	+	17911.4i	1.11338	+	1.16489i
$125$	−9906.14			−0.633993
$126$	−9147.33	+	3668.37i	−0.576174	+	0.231064i
$127$			12068.8i			0.748265i	0.927375	+	0.374132i	$0.122059\pi$
$127$			12068.8i			0.748265i	−0.927375	+	0.374132i	$0.877941\pi$
$128$	14593.9	+	7446.70i	0.890741	+	0.454511i
$129$			10542.1i			0.633503i
$130$	−2650.55	−	6609.34i	−0.156838	−	0.391085i
$131$		−	28203.8i		−	1.64348i	−0.569859	−	0.821742i	$-0.693002\pi$
$131$		−	28203.8i		−	1.64348i	0.569859	−	0.821742i	$-0.306998\pi$
$132$	6751.75	−	6453.18i	0.387497	−	0.370362i
$133$	23961.8			1.35462
$134$	4249.90	−	1704.35i	0.236684	−	0.0949180i
$135$	−3935.48			−0.215939
$136$	−5033.44	−	2287.82i	−0.272137	−	0.123692i
$137$			21965.2i			1.17029i	0.810928	+	0.585145i	$0.198963\pi$
$137$			21965.2i			1.17029i	−0.810928	+	0.585145i	$0.801037\pi$
$138$	12344.2	+	30781.0i	0.648191	+	1.61631i
$139$			7395.26i			0.382758i	0.981516	+	0.191379i	$0.0612959\pi$
$139$			7395.26i			0.382758i	−0.981516	+	0.191379i	$0.938704\pi$
$140$	6289.53	−	6011.40i	0.320894	−	0.306704i
$141$	15057.2			0.757366
$142$	17335.8	−	6952.21i	0.859740	−	0.344783i
$143$			11339.6i			0.554529i
$144$	440.338	−	9732.45i	0.0212354	−	0.469350i
$145$		−	10256.9i		−	0.487843i
$146$	−30772.5	+	12340.8i	−1.44363	+	0.578943i
$147$	19538.2			0.904170
$148$	20518.1	−	19610.7i	0.936727	−	0.895304i
$149$			33575.6i			1.51235i	0.654371	+	0.756173i	$0.272933\pi$
$149$			33575.6i			1.51235i	−0.654371	+	0.756173i	$0.727067\pi$
$150$	22460.6	−	9007.43i	0.998250	−	0.400330i
$151$	−26884.0			−1.17907			−0.589536	−	0.807742i	$-0.700689\pi$
$151$	−26884.0			−1.17907			−0.589536	+	0.807742i	$0.700689\pi$
$152$	−9801.30	+	21563.9i	−0.424225	+	0.933340i
$153$			3287.69i			0.140446i
$154$	−12858.9	+	5156.84i	−0.542205	+	0.217441i
$155$			13006.1i			0.541356i
$156$	25568.0	+	26751.0i	1.05063	+	1.09924i
$157$		−	31732.0i		−	1.28735i	−0.765298	−	0.643677i	$-0.777408\pi$
$157$		−	31732.0i		−	1.28735i	0.765298	−	0.643677i	$-0.222592\pi$
$158$	21135.7	−	8476.08i	0.846646	−	0.339532i
$159$			543.149i			0.0214845i
$160$	2837.17	+	8119.01i	0.110827	+	0.317149i
$161$		−	49195.1i		−	1.89789i
$162$	30425.7	−	12201.7i	1.15934	−	0.464932i
$163$			26471.0i			0.996313i	0.867087	+	0.498156i	$0.165989\pi$
$163$			26471.0i			0.996313i	−0.867087	+	0.498156i	$0.834011\pi$
$164$	23115.0	−	13751.0i	0.859423	−	0.511266i
$165$	4902.69			0.180080
$166$	4536.99	+	11313.3i	0.164646	+	0.410557i
$167$	−21454.0			−0.769264			−0.384632	−	0.923070i	$-0.625672\pi$
$167$	−21454.0			−0.769264			−0.384632	+	0.923070i	$0.625672\pi$
$168$	−18707.9	+	41159.3i	−0.662835	+	1.45831i
$169$	−16367.3			−0.573063
$170$	−1080.29	−	2693.78i	−0.0373804	−	0.0932106i
$171$	14084.9			0.481683
$172$	10681.0	+	11175.2i	0.361041	+	0.377745i
$173$	−40986.3			−1.36945			−0.684725	−	0.728802i	$-0.740078\pi$
$173$	−40986.3			−1.36945			−0.684725	+	0.728802i	$0.740078\pi$
$174$	19839.3	+	49470.6i	0.655281	+	1.63399i
$175$	−35897.3			−1.17216
$176$	619.008	−	13681.5i	0.0199835	−	0.441679i
$177$			23859.0i			0.761563i
$178$	19366.7	+	48292.2i	0.611246	+	1.52418i
$179$	418.430			0.0130592			0.00652960	−	0.999979i	$-0.497922\pi$
$179$	418.430			0.0130592			0.00652960	+	0.999979i	$0.497922\pi$
$180$	3697.02	−	3533.54i	0.114106	−	0.109060i
$181$		−	31402.8i		−	0.958542i	−0.877667	−	0.479271i	$-0.840901\pi$
$181$		−	31402.8i		−	0.958542i	0.877667	−	0.479271i	$-0.159099\pi$
$182$	−20431.8	−	50948.1i	−0.616828	−	1.53810i
$183$	−20304.8			−0.606312
$184$	44272.1	+	20122.7i	1.30766	+	0.594361i
$185$	14898.9			0.435322
$186$	−25156.8	−	62730.2i	−0.727160	−	1.81322i
$187$			4621.69i			0.132165i
$188$	15961.5	−	15255.6i	0.451603	−	0.431632i
$189$	−30336.7			−0.849267
$190$	−11540.5	+	4628.12i	−0.319682	+	0.128203i
$191$	−39525.7			−1.08346			−0.541729	−	0.840553i	$-0.682230\pi$
$191$	−39525.7			−1.08346			−0.541729	+	0.840553i	$0.682230\pi$
$192$	−29388.2	−	33671.5i	−0.797205	−	0.913397i
$193$		−	11715.0i		−	0.314505i	−0.987558	−	0.157253i	$-0.949736\pi$
$193$		−	11715.0i		−	0.314505i	0.987558	−	0.157253i	$-0.0502637\pi$
$194$	−1790.62	−	4465.03i	−0.0475774	−	0.118637i
$195$			19424.8i			0.510844i
$196$	20711.6	−	19795.7i	0.539139	−	0.515297i
$197$	−16057.4			−0.413755			−0.206877	−	0.978367i	$-0.566330\pi$
$197$	−16057.4			−0.413755			−0.206877	+	0.978367i	$0.566330\pi$
$198$	−7558.55	+	3031.22i	−0.192801	+	0.0773192i
$199$	−7311.67			−0.184633			−0.0923167	−	0.995730i	$-0.529427\pi$
$199$	−7311.67			−0.184633			−0.0923167	+	0.995730i	$0.529427\pi$
$200$	14683.4	−	32304.9i	0.367084	−	0.807624i
$201$	−12490.5			−0.309163
$202$	−8572.80	−	21376.9i	−0.210097	−	0.523891i
$203$		−	79065.4i		−	1.91864i
$204$	10420.8	+	10903.0i	0.250405	+	0.261990i
$205$	13759.1	+	3165.54i	0.327402	+	0.0753252i
$206$	−4746.45	−	11835.6i	−0.111850	−	0.278905i
$207$		−	28917.2i		−	0.674863i
$208$	54207.0	+	2452.56i	1.25294	+	0.0566882i
$209$	19799.9			0.453285
$210$	−22027.5	+	8833.75i	−0.499491	+	0.200312i
$211$	33084.4			0.743120			0.371560	−	0.928409i	$-0.378823\pi$
$211$	33084.4			0.743120			0.371560	+	0.928409i	$0.378823\pi$
$212$	550.306	+	575.768i	0.0122443	+	0.0128108i
$213$	−50949.9			−1.12301
$214$	25328.5	+	63158.3i	0.553073	+	1.37912i
$215$			8114.72i			0.175548i
$216$	12408.9	−	27300.8i	0.265965	−	0.585152i
$217$			100257.i			2.12910i
$218$	25764.8	+	64246.3i	0.542144	+	1.35187i
$219$	90440.4			1.88571
$220$	5197.11	−	4967.29i	0.107378	−	0.102630i
$221$	−18311.5			−0.374921
$222$	−71859.6	+	28818.0i	−1.45807	+	0.584733i
$223$		−	67686.9i		−	1.36111i	−0.732695	−	0.680557i	$-0.761738\pi$
$223$		−	67686.9i		−	1.36111i	0.732695	−	0.680557i	$-0.238262\pi$
$224$	21870.3	+	62585.5i	0.435872	+	1.24732i
$225$	−21100.6			−0.416802
$226$	29632.1	−	11883.4i	0.580158	−	0.232662i
$227$	−25028.0			−0.485707			−0.242854	−	0.970063i	$-0.578083\pi$
$227$	−25028.0			−0.485707			−0.242854	+	0.970063i	$0.578083\pi$
$228$	46709.8	−	44644.2i	0.898541	−	0.858807i
$229$			94720.5i			1.80623i	0.429399	+	0.903115i	$0.358725\pi$
$229$			94720.5i			1.80623i	−0.429399	+	0.903115i	$0.641275\pi$
$230$	9501.82	+	23693.4i	0.179619	+	0.447891i
$231$	37792.4			0.708240
$232$	71153.2	+	32340.8i	1.32196	+	0.600862i
$233$		−	43248.7i		−	0.796638i	−0.917247	−	0.398319i	$-0.869594\pi$
$233$		−	43248.7i		−	0.796638i	0.917247	−	0.398319i	$-0.130406\pi$
$234$	−12010.0	−	29947.6i	−0.219336	−	0.546928i
$235$	11590.2			0.209872
$236$	24173.4	+	25291.8i	0.434024	+	0.454105i
$237$	−62117.8			−1.10591
$238$	−8327.46	−	20765.1i	−0.147014	−	0.366589i
$239$	−45302.7			−0.793101			−0.396550	−	0.918013i	$-0.629793\pi$
$239$	−45302.7			−0.793101			−0.396550	+	0.918013i	$0.629793\pi$
$240$	1060.37	−	23436.6i	0.0184092	−	0.406885i
$241$	41114.1			0.707875			0.353937	−	0.935269i	$-0.384843\pi$
$241$	41114.1			0.707875			0.353937	+	0.935269i	$0.384843\pi$
$242$	43730.5	−	17537.3i	0.746712	−	0.299456i
$243$	−51466.8			−0.871594
$244$	−21524.2	+	20572.4i	−0.361532	+	0.345545i
$245$	15039.4			0.250552
$246$	−72485.0	+	11345.4i	−1.19778	+	0.187478i
$247$			78449.0i			1.28586i
$248$	−90224.4	−	41009.1i	−1.46697	−	0.666771i
$249$		−	33249.8i		−	0.536278i
$250$	36777.4	−	14748.9i	0.588438	−	0.235982i
$251$			31230.5i			0.495714i	0.968797	+	0.247857i	$0.0797262\pi$
$251$			31230.5i			0.495714i	−0.968797	+	0.247857i	$0.920274\pi$
$252$	28498.5	−	27238.3i	0.448767	−	0.428922i
$253$		−	40650.5i		−	0.635075i
$254$	−17968.8	−	44806.3i	−0.278516	−	0.694499i
$255$			7917.04i			0.121754i
$256$	−65268.2	−	5918.15i	−0.995914	−	0.0903038i
$257$		−	108313.i		−	1.63989i	−0.572441	−	0.819946i	$-0.694003\pi$
$257$		−	108313.i		−	1.63989i	0.572441	−	0.819946i	$-0.305997\pi$
$258$	−15695.8	−	39138.5i	−0.235800	−	0.587983i
$259$	114848.			1.71208
$260$	19680.8	+	20591.4i	0.291136	+	0.304606i
$261$		−	46475.1i		−	0.682244i
$262$	41991.7	+	104709.i	0.611732	+	1.52539i
$263$	−79971.4			−1.15617			−0.578087	−	0.815975i	$-0.696201\pi$
$263$	−79971.4			−1.15617			−0.578087	+	0.815975i	$0.696201\pi$
$264$	−15458.5	+	34010.4i	−0.221800	+	0.487983i
$265$			418.085i			0.00595351i
$266$	−88960.2	+	35675.9i	−1.25728	+	0.504210i
$267$		−	141931.i		−	1.99092i
$268$	−13240.6	+	12655.1i	−0.184348	+	0.176196i
$269$	−31997.5			−0.442192			−0.221096	−	0.975252i	$-0.570963\pi$
$269$	−31997.5			−0.442192			−0.221096	+	0.975252i	$0.570963\pi$
$270$	14610.8	−	5859.40i	0.200422	−	0.0803758i
$271$		−	697.687i		−	0.00949997i	−0.999989	−	0.00474999i	$-0.998488\pi$
$271$		−	697.687i		−	0.00949997i	0.999989	−	0.00474999i	$-0.00151197\pi$
$272$	22093.3	+	999.597i	0.298623	+	0.0135110i
$273$			149737.i			2.00911i
$274$	−32703.2	−	81547.6i	−0.435601	−	1.08620i
$275$	−29662.3			−0.392229
$276$	−91657.4	−	95898.2i	−1.20323	−	1.25890i
$277$	−24514.1			−0.319489			−0.159744	−	0.987158i	$-0.551067\pi$
$277$	−24514.1			−0.319489			−0.159744	+	0.987158i	$0.551067\pi$
$278$	−11010.5	−	27455.5i	−0.142469	−	0.355255i
$279$			58931.9i			0.757080i
$280$	−14400.2	+	31682.1i	−0.183677	+	0.404108i
$281$			98113.6i			1.24256i	0.783589	+	0.621279i	$0.213387\pi$
$281$			98113.6i			1.24256i	−0.783589	+	0.621279i	$0.786613\pi$
$282$	−55901.1	+	22418.1i	−0.702947	+	0.281904i
$283$		−	18480.4i		−	0.230748i	−0.993322	−	0.115374i	$-0.963193\pi$
$283$		−	18480.4i		−	0.230748i	0.993322	−	0.115374i	$-0.0368067\pi$
$284$	−54009.7	+	51621.3i	−0.669630	+	0.640018i
$285$	33917.6			0.417576
$286$	−16883.1	−	42099.1i	−0.206405	−	0.514684i
$287$	106062.	+	24401.6i	1.28764	+	0.296247i
$288$	12855.5	+	36788.1i	0.154990	+	0.443530i
$289$	76057.7			0.910642
$290$	15271.1	+	38079.6i	0.181583	+	0.452790i
$291$			13122.7i			0.154967i
$292$	95871.8	−	91632.2i	1.12441	−	1.07469i
$293$		−	13202.8i		−	0.153791i	−0.997039	−	0.0768953i	$-0.975499\pi$
$293$		−	13202.8i		−	0.153791i	0.997039	−	0.0768953i	$-0.0245007\pi$
$294$	−72537.2	+	29089.7i	−0.839201	+	0.336547i
$295$			18365.3i			0.211035i
$296$	−46977.3	+	103355.i	−0.536173	+	1.17964i
$297$	−25067.6			−0.284184
$298$	−49989.6	−	124652.i	−0.562920	−	1.40368i
$299$	161061.			1.80155
$300$	−69976.1	+	66881.6i	−0.777512	+	0.743129i
$301$			62552.4i			0.690416i
$302$	99809.1	−	40026.7i	1.09435	−	0.438870i
$303$			62826.6i			0.684319i
$304$	4282.40	−	94650.6i	0.0463383	−	1.02418i
$305$	−15629.5			−0.168014
$306$	−4894.93	−	12205.8i	−0.0522761	−	0.130354i
$307$			22851.6i			0.242460i	0.992624	+	0.121230i	$0.0386839\pi$
$307$			22851.6i			0.242460i	−0.992624	+	0.121230i	$0.961316\pi$
$308$	40062.0	−	38290.4i	0.422310	−	0.403635i
$309$			34784.8i			0.364311i
$310$	−19364.3	−	48286.1i	−0.201501	−	0.502457i
$311$	−158073.			−1.63432			−0.817159	−	0.576412i	$-0.804452\pi$
$311$	−158073.			−1.63432			−0.817159	+	0.576412i	$0.804452\pi$
$312$	−134752.	−	61248.0i	−1.38429	−	0.629191i
$313$		−	62359.7i		−	0.636525i	−0.948003	−	0.318263i	$-0.896901\pi$
$313$		−	62359.7i		−	0.636525i	0.948003	−	0.318263i	$-0.103099\pi$
$314$	47244.6	+	117808.i	0.479174	+	1.19485i
$315$	20693.8			0.208554
$316$	−65848.2	+	62936.3i	−0.659432	+	0.630271i
$317$			12742.6i			0.126806i	0.997988	+	0.0634030i	$0.0201953\pi$
$317$			12742.6i			0.126806i	−0.997988	+	0.0634030i	$0.979805\pi$
$318$	−808.676	−	2016.49i	−0.00799687	−	0.0199407i
$319$		−	65332.7i		−	0.642021i
$320$	−22621.3	−	25918.4i	−0.220911	−	0.253109i
$321$		−	185622.i		−	1.80144i
$322$	73244.9	+	182641.i	0.706424	+	1.76152i
$323$			31973.7i			0.306470i
$324$	−94791.2	+	90599.4i	−0.902980	+	0.863049i
$325$		−	117525.i		−	1.11266i
$326$	−39411.8	−	98276.0i	−0.370844	−	0.924724i
$327$		−	188820.i		−	1.76585i
$328$	−65343.1	+	85466.9i	−0.607368	+	0.794420i
$329$	89342.9			0.825407
$330$	−18201.6	+	7299.44i	−0.167141	+	0.0670288i
$331$	−4782.50			−0.0436514			−0.0218257	−	0.999762i	$-0.506948\pi$
$331$	−4782.50			−0.0436514			−0.0218257	+	0.999762i	$0.506948\pi$
$332$	−33687.9	−	35246.6i	−0.305632	−	0.319772i
$333$	67508.5			0.608793
$334$	79649.8	−	31942.1i	0.713989	−	0.286333i
$335$	−9614.45			−0.0856712
$336$	8173.87	−	180661.i	0.0724018	−	1.60024i
$337$	179723.			1.58250			0.791251	−	0.611492i	$-0.209430\pi$
$337$	179723.			1.58250			0.791251	+	0.611492i	$0.209430\pi$
$338$	60764.8	−	24368.6i	0.531886	−	0.213303i
$339$	−87088.9			−0.757816
$340$	8021.36	+	8392.49i	0.0693890	+	0.0725994i
$341$			82843.9i			0.712446i
$342$	−52291.3	+	20970.5i	−0.447072	+	0.179290i
$343$	−39516.4			−0.335884
$344$	−56292.6	−	25586.3i	−0.475702	−	0.216218i
$345$		−	69635.0i		−	0.585045i
$346$	152165.	−	61023.0i	1.27105	−	0.509732i
$347$	−30157.9			−0.250462			−0.125231	−	0.992128i	$-0.539967\pi$
$347$	−30157.9			−0.250462			−0.125231	+	0.992128i	$0.539967\pi$
$348$	−147310.	−	154126.i	−1.21639	−	1.27267i
$349$	−205819.			−1.68979			−0.844897	−	0.534929i	$-0.820338\pi$
$349$	−205819.			−1.68979			−0.844897	+	0.534929i	$0.820338\pi$
$350$	133272.	−	53446.2i	1.08793	−	0.436295i
$351$		−	99319.8i		−	0.806161i
$352$	18071.7	+	51715.2i	0.145853	+	0.417381i
$353$	37308.9			0.299408			0.149704	−	0.988731i	$-0.452168\pi$
$353$	37308.9			0.299408			0.149704	+	0.988731i	$0.452168\pi$
$354$	−35522.8	−	88578.6i	−0.283466	−	0.706842i
$355$	−39218.3			−0.311195
$356$	−143801.	−	150455.i	−1.13465	−	1.18715i
$357$			61028.6i			0.478847i
$358$	−1553.46	+	622.986i	−0.0121208	+	0.00486085i
$359$			157948.i			1.22553i	0.790265	+	0.612766i	$0.209943\pi$
$359$			157948.i			1.22553i	−0.790265	+	0.612766i	$0.790057\pi$
$360$	−8464.55	+	18622.9i	−0.0653129	+	0.143695i
$361$	6658.27			0.0510913
$362$	46754.5	+	116586.i	0.356785	+	0.889667i
$363$	−128524.			−0.975373
$364$	151710.	+	158729.i	1.14501	+	1.19799i
$365$	69615.8			0.522543
$366$	75383.3	−	30231.1i	0.562746	−	0.225679i
$367$			123736.i			0.918678i	0.888261	+	0.459339i	$0.151914\pi$
$367$			123736.i			0.918678i	−0.888261	+	0.459339i	$0.848086\pi$
$368$	−194324.	−	8792.04i	−1.43493	−	0.0649223i
$369$	62343.9	+	14343.4i	0.457869	+	0.105342i
$370$	−55313.4	+	22182.4i	−0.404042	+	0.162034i
$371$			3222.81i			0.0234146i
$372$	186794.	+	195436.i	1.34982	+	1.41227i
$373$	−167782.			−1.20595			−0.602974	−	0.797761i	$-0.706018\pi$
$373$	−167782.			−1.20595			−0.602974	+	0.797761i	$0.706018\pi$
$374$	−6881.08	−	17158.4i	−0.0491941	−	0.122669i
$375$	−108089.			−0.768631
$376$	−36544.7	+	80402.2i	−0.258493	+	0.568712i
$377$	258854.			1.82126
$378$	112627.	−	45167.2i	0.788244	−	0.316111i
$379$			238729.i			1.66198i	0.556285	+	0.830992i	$0.312226\pi$
$379$			238729.i			1.66198i	−0.556285	+	0.830992i	$0.687774\pi$
$380$	35954.5	−	34364.6i	0.248992	−	0.237982i
$381$			131686.i			0.907170i
$382$	146742.	−	58848.4i	1.00561	−	0.403281i
$383$	237079.			1.61620			0.808100	−	0.589045i	$-0.200496\pi$
$383$	237079.			1.61620			0.808100	+	0.589045i	$0.200496\pi$
$384$	159238.	+	81253.1i	1.07990	+	0.551033i
$385$	29090.4			0.196258
$386$	17442.1	+	43492.9i	0.117064	+	0.291907i
$387$			36768.7i			0.245503i
$388$	13295.7	+	13910.8i	0.0883175	+	0.0924037i
$389$	219696.			1.45185			0.725927	−	0.687772i	$-0.241411\pi$
$389$	219696.			1.45185			0.725927	+	0.687772i	$0.241411\pi$
$390$	−28921.0	−	72116.4i	−0.190144	−	0.474138i
$391$	65644.0			0.429380
$392$	−47420.3	+	104330.i	−0.308597	+	0.678947i
$393$		−	307740.i		−	1.99250i
$394$	59614.5	−	23907.3i	0.384025	−	0.154006i
$395$	−47814.7			−0.306455
$396$	23548.7	−	22507.3i	0.150168	−	0.143527i
$397$		−	11360.1i		−	0.0720778i	−0.999350	−	0.0360389i	$-0.988526\pi$
$397$		−	11360.1i		−	0.0720778i	0.999350	−	0.0360389i	$-0.0114740\pi$
$398$	27145.2	−	10886.1i	0.171367	−	0.0687236i
$399$	261454.			1.64229
$400$	−6415.48	+	141796.i	−0.0400967	+	0.886227i
$401$	−5772.18			−0.0358964			−0.0179482	−	0.999839i	$-0.505713\pi$
$401$	−5772.18			−0.0358964			−0.0179482	+	0.999839i	$0.505713\pi$
$402$	46371.9	−	18596.6i	0.286948	−	0.115075i
$403$	−328234.			−2.02104
$404$	63654.5	+	66599.6i	0.390002	+	0.408046i
$405$	−68831.2			−0.419638
$406$	117718.	+	293537.i	0.714150	+	1.78078i
$407$	94900.5			0.572901
$408$	−54921.3	−	24963.0i	−0.329929	−	0.149960i
$409$	242850.			1.45175			0.725874	−	0.687828i	$-0.241436\pi$
$409$	242850.			1.45175			0.725874	+	0.687828i	$0.241436\pi$
$410$	−55794.8	+	8733.06i	−0.331914	+	0.0519516i
$411$			239669.i			1.41882i
$412$	35243.2	+	36873.8i	0.207626	+	0.217232i
$413$			141569.i			0.829981i
$414$	43053.8	+	107357.i	0.251195	+	0.626371i
$415$		−	25593.8i		−	0.148607i
$416$	−204900.	+	71601.6i	−1.18401	+	0.413748i
$417$			80691.8i			0.464042i
$418$	−73508.9	+	29479.4i	−0.420714	+	0.168720i
$419$			112368.i			0.640050i	0.947409	+	0.320025i	$0.103691\pi$
$419$			112368.i			0.640050i	−0.947409	+	0.320025i	$0.896309\pi$
$420$	68626.9	−	65592.1i	0.389041	−	0.371837i
$421$		−	115877.i		−	0.653780i	−0.945062	−	0.326890i	$-0.893999\pi$
$421$		−	115877.i		−	0.653780i	0.945062	−	0.326890i	$-0.106001\pi$
$422$	−122829.	+	49258.3i	−0.689724	+	0.276601i
$423$	52516.3			0.293504
$424$	−2900.30	−	1318.25i	−0.0161328	−	0.00733276i
$425$		−	47899.9i		−	0.265190i
$426$	189156.	−	75857.6i	1.04232	−	0.418003i
$427$	−120480.			−0.660783
$428$	−188068.	−	196770.i	−1.02666	−	1.07417i
$429$			123729.i			0.672291i
$430$	−12081.7	−	30126.6i	−0.0653419	−	0.162934i
$431$		−	241005.i		−	1.29739i	−0.761048	−	0.648695i	$-0.775315\pi$
$431$		−	241005.i		−	1.29739i	0.761048	−	0.648695i	$-0.224685\pi$
$432$	−5421.70	+	119832.i	−0.0290515	+	0.642103i
$433$	49875.4			0.266018			0.133009	−	0.991115i	$-0.457536\pi$
$433$	49875.4			0.266018			0.133009	+	0.991115i	$0.457536\pi$
$434$	−149270.	−	372214.i	−0.792487	−	1.97612i
$435$		−	111916.i		−	0.591444i
$436$	−191308.	−	200160.i	−1.00638	−	1.05294i
$437$		−	281227.i		−	1.47263i
$438$	−335768.	+	134654.i	−1.75021	+	0.701891i
$439$	130984.			0.679658			0.339829	−	0.940487i	$-0.389631\pi$
$439$	130984.			0.679658			0.339829	+	0.940487i	$0.389631\pi$
$440$	−11899.1	+	26179.3i	−0.0614623	+	0.135224i
$441$	68145.1			0.350395
$442$	67983.1	−	27263.4i	0.347982	−	0.139552i
$443$			20713.2i			0.105546i	0.998607	+	0.0527729i	$0.0168059\pi$
$443$			20713.2i			0.105546i	−0.998607	+	0.0527729i	$0.983194\pi$
$444$	223879.	−	213978.i	1.13566	−	1.08544i
$445$		−	109250.i		−	0.551700i
$446$	100777.	+	251293.i	0.506629	+	1.26331i
$447$			366353.i			1.83352i
$448$	−174377.	−	199792.i	−0.868825	−	0.995456i
$449$	131041.			0.650003			0.325002	−	0.945713i	$-0.394635\pi$
$449$	131041.			0.650003			0.325002	+	0.945713i	$0.394635\pi$
$450$	78337.8	−	31416.0i	0.386854	−	0.155141i
$451$	87640.3	+	20163.4i	0.430874	+	0.0991310i
$452$	−92319.0	+	88236.5i	−0.451871	+	0.431888i
$453$	−293339.			−1.42947
$454$	92918.6	−	37263.3i	0.450807	−	0.180788i
$455$			115259.i			0.556738i
$456$	−106945.	+	235290.i	−0.514316	+	1.13155i
$457$		−	95912.4i		−	0.459243i	−0.973280	−	0.229621i	$-0.926251\pi$
$457$		−	95912.4i		−	0.459243i	0.973280	−	0.229621i	$-0.0737488\pi$
$458$	−141026.	−	351658.i	−0.672308	−	1.67644i
$459$		−	40480.0i		−	0.192139i
$460$	−70552.6	−	73816.9i	−0.333425	−	0.348851i
$461$	101343.			0.476860			0.238430	−	0.971160i	$-0.423367\pi$
$461$	101343.			0.476860			0.238430	+	0.971160i	$0.423367\pi$
$462$	−140307.	+	56267.8i	−0.657350	+	0.263618i
$463$	307663.			1.43520			0.717601	−	0.696454i	$-0.245240\pi$
$463$	307663.			1.43520			0.717601	+	0.696454i	$0.245240\pi$
$464$	−312313.	−	14130.4i	−1.45062	−	0.0656324i
$465$			141913.i			0.656321i
$466$	64391.5	+	160564.i	0.296522	+	0.739397i
$467$			15893.5i			0.0728761i	0.999336	+	0.0364380i	$0.0116012\pi$
$467$			15893.5i			0.0728761i	−0.999336	+	0.0364380i	$0.988399\pi$
$468$	89175.9	+	93301.8i	0.407151	+	0.425989i
$469$	−74113.1			−0.336937
$470$	−43029.5	+	17256.2i	−0.194792	+	0.0781177i
$471$		−	346237.i		−	1.56074i
$472$	−127402.	−	57907.2i	−0.571863	−	0.259925i
$473$			51687.8i			0.231029i
$474$	230617.	−	92485.0i	1.02644	−	0.411637i
$475$	−205209.			−0.909514
$476$	61832.8	+	64693.6i	0.272901	+	0.285527i
$477$			1894.39i			0.00832592i
$478$	168190.	−	67449.6i	0.736113	−	0.295205i
$479$	326388.			1.42254			0.711268	−	0.702921i	$-0.248121\pi$
$479$	326388.			1.42254			0.711268	+	0.702921i	$0.248121\pi$
$480$	30957.1	+	88588.9i	0.134363	+	0.384500i
$481$			376004.i			1.62518i
$482$	−152639.	+	61213.3i	−0.657011	+	0.263483i
$483$		−	536782.i		−	2.30093i
$484$	−136242.	+	130218.i	−0.581596	+	0.555877i
$485$			10101.1i			0.0429424i
$486$	191075.	−	76627.1i	0.808967	−	0.324421i
$487$			95282.0i			0.401747i	0.979617	+	0.200874i	$0.0643781\pi$
$487$			95282.0i			0.401747i	−0.979617	+	0.200874i	$0.935622\pi$
$488$	49280.9	−	108423.i	0.206937	−	0.455284i
$489$			288833.i			1.20790i
$490$	−55835.0	+	22391.6i	−0.232549	+	0.0932595i
$491$			166293.i			0.689782i	0.938643	+	0.344891i	$0.112084\pi$
$491$			166293.i			0.689782i	−0.938643	+	0.344891i	$0.887916\pi$
$492$	252215.	−	150041.i	1.04193	−	0.619841i
$493$	105502.			0.434076
$494$	−116800.	−	291248.i	−0.478618	−	1.19346i
$495$	17099.5			0.0697869
$496$	396023.	+	17917.8i	1.60974	+	0.0728318i
$497$	−302315.			−1.22390
$498$	49504.5	+	123443.i	0.199612	+	0.497745i
$499$	18690.1			0.0750605			0.0375302	−	0.999295i	$-0.488051\pi$
$499$	18690.1			0.0750605			0.0375302	+	0.999295i	$0.488051\pi$
$500$	−114580.	+	109513.i	−0.458320	+	0.438052i
$501$	−234091.			−0.932629
$502$	−46497.9	−	115946.i	−0.184513	−	0.460095i
$503$	−155261.			−0.613660			−0.306830	−	0.951764i	$-0.599268\pi$
$503$	−155261.			−0.613660			−0.306830	+	0.951764i	$0.599268\pi$
$504$	−65249.0	+	143555.i	−0.256870	+	0.565141i
$505$			48360.3i			0.189630i
$506$	60523.2	+	150919.i	0.236385	+	0.589443i
$507$	−178588.			−0.694762
$508$	133421.	+	139594.i	0.517007	+	0.540928i
$509$			22301.9i			0.0860810i	0.999073	+	0.0430405i	$0.0137044\pi$
$509$			22301.9i			0.0860810i	−0.999073	+	0.0430405i	$0.986296\pi$
$510$	−11787.4	−	29392.7i	−0.0453187	−	0.113005i
$511$	536634.			2.05512
$512$	251125.	−	75204.0i	0.957966	−	0.286880i
$513$	−173422.			−0.658975
$514$	161264.	+	402122.i	0.610395	+	1.52206i
$515$			26775.4i			0.100953i
$516$	116544.	+	121936.i	0.437714	+	0.457966i
$517$	73825.2			0.276200
$518$	−426384.	+	170993.i	−1.58906	+	0.637265i
$519$	−447213.			−1.66027
$520$	−103724.	−	47145.2i	−0.383596	−	0.174354i
$521$		−	160459.i		−	0.591136i	−0.955322	−	0.295568i	$-0.904491\pi$
$521$		−	160459.i		−	0.591136i	0.955322	−	0.295568i	$-0.0955089\pi$
$522$	69195.2	+	172543.i	0.253942	+	0.633222i
$523$		−	439631.i		−	1.60725i	−0.595133	−	0.803627i	$-0.702900\pi$
$523$		−	439631.i		−	1.60725i	0.595133	−	0.803627i	$-0.297100\pi$
$524$	−311795.	−	326221.i	−1.13555	−	1.18809i
$525$	−391685.			−1.42108
$526$	296900.	−	119067.i	1.07310	−	0.430347i
$527$	−133779.			−0.481690
$528$	6754.17	−	149282.i	0.0242273	−	0.535477i
$529$	−297537.			−1.06323
$530$	−622.472	−	1552.18i	−0.00221599	−	0.00552572i
$531$			83215.1i			0.295130i
$532$	277156.	−	264899.i	0.979266	−	0.935961i
$533$	−79888.9	+	347238.i	−0.281211	+	1.22229i
$534$	211316.	+	526931.i	0.741054	+	1.84787i
$535$		−	142882.i		−	0.499193i
$536$	30315.1	−	66696.4i	0.105519	−	0.232152i
$537$	4565.61			0.0158325
$538$	118793.	−	47639.9i	0.410419	−	0.164591i
$539$	95795.4			0.329737
$540$	−45520.0	+	43507.0i	−0.156104	+	0.149201i
$541$	−456987.			−1.56138			−0.780691	−	0.624917i	$-0.785133\pi$
$541$	−456987.			−1.56138			−0.780691	+	0.624917i	$0.785133\pi$
$542$	1038.76	+	2590.22i	0.00353604	+	0.00881736i
$543$		−	342645.i		−	1.16210i
$544$	−83511.6	+	29182.9i	−0.282195	+	0.0986121i
$545$		−	145343.i		−	0.489329i
$546$	−222938.	−	555910.i	−0.747822	−	1.86474i
$547$	−223278.			−0.746226			−0.373113	−	0.927786i	$-0.621710\pi$
$547$	−223278.			−0.746226			−0.373113	+	0.927786i	$0.621710\pi$
$548$	242827.	+	254062.i	0.808603	+	0.846015i
$549$	−70818.8			−0.234965
$550$	110124.	−	44163.2i	0.364046	−	0.145994i
$551$		−	451983.i		−	1.48874i
$552$	483065.	+	219565.i	1.58536	+	0.720583i
$553$	−368580.			−1.20526
$554$	91010.5	−	36498.1i	0.296532	−	0.118919i
$555$	162566.			0.527769
$556$	81755.1	+	85537.7i	0.264463	+	0.276699i
$557$		−	501110.i		−	1.61519i	−0.589740	−	0.807593i	$-0.700770\pi$
$557$		−	501110.i		−	1.61519i	0.589740	−	0.807593i	$-0.299230\pi$
$558$	−87741.6	−	218790.i	−0.281798	−	0.702681i
$559$	−204791.			−0.655372
$560$	6291.78	−	139062.i	0.0200631	−	0.443439i
$561$			50428.6i			0.160233i
$562$	−146078.	−	364255.i	−0.462500	−	1.15328i
$563$	364685.			1.15054			0.575269	−	0.817965i	$-0.304898\pi$
$563$	364685.			1.15054			0.575269	+	0.817965i	$0.304898\pi$
$564$	174160.	−	166458.i	0.547508	−	0.523296i
$565$	−67036.1			−0.209996
$566$	27514.8	+	68610.0i	0.0858883	+	0.214168i
$567$	−530586.			−1.65040
$568$	123658.	−	272062.i	0.383289	−	0.843278i
$569$	593925.			1.83445			0.917227	−	0.398365i	$-0.130422\pi$
$569$	593925.			1.83445			0.917227	+	0.398365i	$0.130422\pi$
$570$	−125922.	+	50498.7i	−0.387571	+	0.155429i
$571$	−323291.			−0.991565			−0.495783	−	0.868447i	$-0.665119\pi$
$571$	−323291.			−0.991565			−0.495783	+	0.868447i	$0.665119\pi$
$572$	125360.	+	131160.i	0.383147	+	0.400874i
$573$	−431276.			−1.31355
$574$	−430095.	+	67318.9i	−1.30539	+	0.204321i
$575$			421307.i			1.27428i
$576$	−102500.	−	117439.i	−0.308943	−	0.353970i
$577$			60102.3i			0.180526i	0.995918	+	0.0902630i	$0.0287707\pi$
$577$			60102.3i			0.180526i	−0.995918	+	0.0902630i	$0.971229\pi$
$578$	−282371.	+	113240.i	−0.845209	+	0.338956i
$579$		−	127826.i		−	0.381295i
$580$	−113391.	−	118637.i	−0.337071	−	0.352667i
$581$		−	197290.i		−	0.584457i
$582$	−19538.0	−	48719.3i	−0.0576812	−	0.143832i
$583$			2663.05i			0.00783505i
$584$	−219504.	+	482932.i	−0.643601	+	1.41599i
$585$			67749.7i			0.197968i
$586$	19657.2	+	49016.4i	0.0572434	+	0.142740i
$587$	−350288.			−1.01660			−0.508298	−	0.861181i	$-0.669725\pi$
$587$	−350288.			−1.01660			−0.508298	+	0.861181i	$0.669725\pi$
$588$	225990.	−	215996.i	0.653633	−	0.624729i
$589$			573128.i			1.65204i
$590$	−27343.4	−	68182.7i	−0.0785505	−	0.195871i
$591$	−175207.			−0.501622
$592$	20525.4	−	453657.i	0.0585664	−	1.29445i
$593$			519422.i			1.47710i	0.674197	+	0.738552i	$0.264490\pi$
$593$			519422.i			1.47710i	−0.674197	+	0.738552i	$0.735510\pi$
$594$	93065.5	−	37322.2i	0.263764	−	0.105778i
$595$			46976.3i			0.132692i
$596$	371181.	+	388354.i	1.04494	+	1.09329i
$597$	−79779.8			−0.223843
$598$	−597952.	+	239798.i	−1.67211	+	0.670568i
$599$			306566.i			0.854419i	0.904153	+	0.427210i	$0.140503\pi$
$599$			306566.i			0.854419i	−0.904153	+	0.427210i	$0.859497\pi$
$600$	160214.	−	352489.i	0.445040	−	0.979135i
$601$		−	539204.i		−	1.49281i	−0.665492	−	0.746405i	$-0.731778\pi$
$601$		−	539204.i		−	1.49281i	0.665492	−	0.746405i	$-0.268222\pi$
$602$	−93132.0	−	232231.i	−0.256984	−	0.640807i
$603$	−43564.1			−0.119810
$604$	−310956.	+	297205.i	−0.852363	+	0.814670i
$605$	−98930.3			−0.270283
$606$	−93540.3	−	233249.i	−0.254715	−	0.635148i
$607$		−	565998.i		−	1.53616i	−0.640352	−	0.768081i	$-0.721212\pi$
$607$		−	565998.i		−	1.53616i	0.640352	−	0.768081i	$-0.278788\pi$
$608$	125023.	+	357774.i	0.338208	+	0.967836i
$609$		−	862706.i		−	2.32610i
$610$	58025.7	−	23270.2i	0.155941	−	0.0625374i
$611$			292501.i			0.783512i
$612$	36345.7	+	38027.3i	0.0970398	+	0.101530i
$613$	−434334.			−1.15585			−0.577927	−	0.816089i	$-0.696138\pi$
$613$	−434334.			−1.15585			−0.577927	+	0.816089i	$0.696138\pi$
$614$	−34023.0	−	84838.6i	−0.0902476	−	0.225038i
$615$	150129.	+	34540.1i	0.396931	+	0.0913217i
$616$	−91724.3	+	201803.i	−0.241726	+	0.531822i
$617$	−94005.0			−0.246934			−0.123467	−	0.992349i	$-0.539401\pi$
$617$	−94005.0			−0.246934			−0.123467	+	0.992349i	$0.539401\pi$
$618$	−51789.9	−	129142.i	−0.135603	−	0.338134i
$619$		−	503623.i		−	1.31439i	−0.753721	−	0.657194i	$-0.771743\pi$
$619$		−	503623.i		−	1.31439i	0.753721	−	0.657194i	$-0.228257\pi$
$620$	143783.	+	150435.i	0.374045	+	0.391351i
$621$			356046.i			0.923257i
$622$	586859.	−	235349.i	1.51689	−	0.608320i
$623$		−	842157.i		−	2.16979i
$624$	591469.	+	26760.6i	1.51902	+	0.0687269i
$625$	263336.			0.674141
$626$	92845.2	+	231516.i	0.236925	+	0.590788i
$627$	216043.			0.549547
$628$	−350799.	−	367030.i	−0.889487	−	0.930641i
$629$			153249.i			0.387343i
$630$	−76827.4	+	30810.2i	−0.193569	+	0.0776272i
$631$			547080.i			1.37402i	0.726649	+	0.687009i	$0.241077\pi$
$631$			547080.i			1.37402i	−0.726649	+	0.687009i	$0.758923\pi$
$632$	150763.	−	331696.i	0.377452	−	0.830435i
$633$	360994.			0.900933
$634$	−18972.0	−	47308.0i	−0.0471992	−	0.117694i
$635$			101364.i			0.251384i
$636$	6004.55	+	6282.37i	0.0148445	+	0.0155313i
$637$			379549.i			0.935383i
$638$	97271.6	+	242553.i	0.238971	+	0.595889i
$639$	−177703.			−0.435203
$640$	122573.	+	62544.0i	0.299249	+	0.152695i
$641$		−	396706.i		−	0.965500i	−0.875758	−	0.482750i	$-0.839638\pi$
$641$		−	396706.i		−	0.965500i	0.875758	−	0.482750i	$-0.160362\pi$
$642$	276367.	+	689139.i	0.670526	+	1.67200i
$643$	638459.			1.54423			0.772113	−	0.635485i	$-0.219200\pi$
$643$	638459.			1.54423			0.772113	+	0.635485i	$0.219200\pi$
$644$	−543856.	−	569018.i	−1.31133	−	1.37200i
$645$			88542.1i			0.212829i
$646$	−47604.5	−	118705.i	−0.114073	−	0.284449i
$647$			573811.i			1.37076i	0.728187	+	0.685378i	$0.240363\pi$
$647$			573811.i			1.37076i	−0.728187	+	0.685378i	$0.759637\pi$
$648$	217030.	−	477489.i	0.516856	−	1.13714i
$649$			116980.i			0.277730i
$650$	174978.	+	436320.i	0.414150	+	1.03271i
$651$			1.09394e6i			2.58125i
$652$	292639.	+	306179.i	0.688395	+	0.720245i
$653$			61153.9i			0.143416i	0.997426	+	0.0717080i	$0.0228450\pi$
$653$			61153.9i			0.143416i	−0.997426	+	0.0717080i	$0.977155\pi$
$654$	281128.	+	701011.i	0.657276	+	1.63896i
$655$		−	236881.i		−	0.552137i
$656$	115343.	−	414590.i	0.268030	−	0.963411i
$657$	315437.			0.730772
$658$	−331693.	+	133020.i	−0.766099	+	0.307230i
$659$	749776.			1.72648			0.863238	−	0.504797i	$-0.168433\pi$
$659$	749776.			1.72648			0.863238	+	0.504797i	$0.168433\pi$
$660$	56707.2	−	54199.5i	0.130182	−	0.124425i
$661$	343879.			0.787051			0.393525	−	0.919314i	$-0.371255\pi$
$661$	343879.			0.787051			0.393525	+	0.919314i	$0.371255\pi$
$662$	17755.4	−	7120.49i	0.0405149	−	0.0162478i
$663$	−199802.			−0.454542
$664$	177547.	+	80699.2i	0.402695	+	0.183034i
$665$	201252.			0.455091
$666$	−250631.	+	100511.i	−0.565049	+	0.226603i
$667$	−927950.			−2.08580
$668$	−248149.	+	237176.i	−0.556109	+	0.531517i
$669$		−	738551.i		−	1.65017i
$670$	35694.5	−	14314.6i	0.0795154	−	0.0318882i
$671$	−99554.0			−0.221113
$672$	238633.	+	682888.i	0.528436	+	1.51221i
$673$		−	154257.i		−	0.340576i	−0.985394	−	0.170288i	$-0.945530\pi$
$673$		−	154257.i		−	0.340576i	0.985394	−	0.170288i	$-0.0544698\pi$
$674$	−667237.	+	267584.i	−1.46879	+	0.589033i
$675$	259804.			0.570214
$676$	−189313.	+	180941.i	−0.414273	+	0.395954i
$677$	108868.			0.237531			0.118766	−	0.992922i	$-0.462106\pi$
$677$	108868.			0.237531			0.118766	+	0.992922i	$0.462106\pi$
$678$	323325.	−	129664.i	0.703363	−	0.282071i
$679$			77864.7i			0.168889i
$680$	−42275.3	−	19215.1i	−0.0914258	−	0.0415552i
$681$	−273088.			−0.588855
$682$	−123343.	−	307565.i	−0.265184	−	0.661254i
$683$	−193799.			−0.415443			−0.207721	−	0.978188i	$-0.566605\pi$
$683$	−193799.			−0.415443			−0.207721	+	0.978188i	$0.566605\pi$
$684$	162914.	−	155710.i	0.348214	−	0.332815i
$685$			184483.i			0.393166i
$686$	146708.	−	58834.6i	0.311749	−	0.125022i
$687$			1.03352e6i			2.18981i
$688$	247086.	+	11179.2i	0.522000	+	0.0236175i
$689$	−10551.2			−0.0222262
$690$	103677.	+	258526.i	0.217763	+	0.543008i
$691$	−105395.			−0.220732			−0.110366	−	0.993891i	$-0.535202\pi$
$691$	−105395.			−0.220732			−0.110366	+	0.993891i	$0.535202\pi$
$692$	−474070.	+	453106.i	−0.989989	+	0.946211i
$693$	131812.			0.274466
$694$	111964.	−	44901.1i	0.232466	−	0.0932262i
$695$			62111.9i			0.128589i
$696$	776373.	+	352880.i	1.60270	+	0.728464i
$697$	−32560.5	+	141525.i	−0.0670233	+	0.291318i
$698$	764119.	−	306436.i	1.56838	−	0.628969i
$699$		−	471899.i		−	0.965817i
$700$	−415208.	+	396847.i	−0.847363	+	0.809891i
$701$	534922.			1.08857			0.544283	−	0.838902i	$-0.316802\pi$
$701$	534922.			1.08857			0.544283	+	0.838902i	$0.316802\pi$
$702$	147874.	+	368733.i	0.300066	+	0.748235i
$703$	656537.			1.32846
$704$	−144090.	−	165091.i	−0.290728	−	0.333102i
$705$	126464.			0.254441
$706$	−138512.	+	55547.9i	−0.277894	+	0.111444i
$707$			372786.i			0.745797i
$708$	263763.	+	275967.i	0.526196	+	0.550542i
$709$		−	154782.i		−	0.307913i	−0.988078	−	0.153957i	$-0.950798\pi$
$709$		−	154782.i		−	0.307913i	0.988078	−	0.153957i	$-0.0492016\pi$
$710$	145601.	−	58390.8i	0.288834	−	0.115832i
$711$	−216654.			−0.428575
$712$	757881.	+	344474.i	1.49500	+	0.679512i
$713$	1.17667e6			2.31460
$714$	−90863.3	−	226574.i	−0.178235	−	0.444440i
$715$			95239.6i			0.186297i
$716$	4839.79	−	4625.77i	0.00944063	−	0.00902315i
$717$	−494311.			−0.961528
$718$	−235163.	−	586394.i	−0.456163	−	1.13747i
$719$	158146.			0.305915			0.152957	−	0.988233i	$-0.451120\pi$
$719$	158146.			0.305915			0.152957	+	0.988233i	$0.451120\pi$
$720$	3698.35	−	81741.7i	0.00713416	−	0.157681i
$721$			206398.i			0.397041i
$722$	−24719.4	+	9913.27i	−0.0474202	+	0.0190170i
$723$	448608.			0.858203
$724$	−347160.	−	363222.i	−0.662297	−	0.692940i
$725$			677117.i			1.28821i
$726$	477156.	−	191355.i	0.905288	−	0.363050i
$727$	903429.			1.70933			0.854664	−	0.519182i	$-0.173763\pi$
$727$	903429.			1.70933			0.854664	+	0.519182i	$0.173763\pi$
$728$	−799561.	−	363419.i	−1.50865	−	0.685717i
$729$	102249.			0.192399
$730$	−258455.	+	103649.i	−0.484997	+	0.194499i
$731$	−83467.4			−0.156200
$732$	−234857.	+	224471.i	−0.438309	+	0.418927i
$733$	−454267.			−0.845479			−0.422740	−	0.906251i	$-0.638931\pi$
$733$	−454267.			−0.845479			−0.422740	+	0.906251i	$0.638931\pi$
$734$	−184226.	−	459380.i	−0.341947	−	0.852667i
$735$	164099.			0.303761
$736$	734533.	−	256681.i	1.35599	−	0.473846i
$737$	−61240.5			−0.112747
$738$	−252812.	+	39570.5i	−0.464179	+	0.0726538i
$739$			23069.1i			0.0422417i	0.999777	+	0.0211208i	$0.00672347\pi$
$739$			23069.1i			0.0422417i	−0.999777	+	0.0211208i	$0.993277\pi$
$740$	172329.	−	164708.i	0.314698	−	0.300782i
$741$			855979.i			1.55893i
$742$	−4798.33	−	11965.0i	−0.00871530	−	0.0217322i
$743$			418800.i			0.758629i	0.925268	+	0.379314i	$0.123840\pi$
$743$			418800.i			0.758629i	−0.925268	+	0.379314i	$0.876160\pi$
$744$	−984465.	−	447462.i	−1.77850	−	0.808371i
$745$			281998.i			0.508081i
$746$	622906.	−	249805.i	1.11930	−	0.448874i
$747$		−	115968.i		−	0.207825i
$748$	51093.2	+	53457.1i	0.0913187	+	0.0955438i
$749$		−	1.10140e6i		−	1.96328i
$750$	401289.	−	160930.i	0.713402	−	0.286097i
$751$	530569.			0.940723			0.470362	−	0.882474i	$-0.344123\pi$
$751$	530569.			0.940723			0.470362	+	0.882474i	$0.344123\pi$
$752$	15967.2	−	352910.i	0.0282353	−	0.624063i
$753$			340765.i			0.600986i
$754$	−961016.	+	385398.i	−1.69039	+	0.677902i
$755$	−225796.			−0.396115
$756$	−350891.	+	335374.i	−0.613944	+	0.586795i
$757$		−	861681.i		−	1.50368i	−0.659347	−	0.751839i	$-0.729167\pi$
$757$		−	861681.i		−	1.50368i	0.659347	−	0.751839i	$-0.270833\pi$
$758$	−355435.	−	886301.i	−0.618617	−	1.54256i
$759$		−	443550.i		−	0.769943i
$760$	−82320.0	+	181113.i	−0.142521	+	0.313561i
$761$	541732.			0.935438			0.467719	−	0.883877i	$-0.345076\pi$
$761$	541732.			0.935438			0.467719	+	0.883877i	$0.345076\pi$
$762$	−196062.	−	488894.i	−0.337663	−	0.841986i
$763$		−	1.12038e6i		−	1.92449i
$764$	−457176.	+	436959.i	−0.783243	+	0.748607i
$765$			27612.9i			0.0471835i
$766$	−880175.	+	352978.i	−1.50007	+	0.601576i
$767$	−463485.			−0.787853
$768$	−712161.	−	64574.6i	−1.20741	−	0.109481i
$769$	616831.			1.04307			0.521535	−	0.853230i	$-0.325359\pi$
$769$	616831.			1.04307			0.521535	+	0.853230i	$0.325359\pi$
$770$	−108001.	+	43311.7i	−0.182157	+	0.0730506i
$771$		−	1.18184e6i		−	1.98815i
$772$	−129510.	−	135502.i	−0.217305	−	0.227359i
$773$			977948.i			1.63665i	0.574753	+	0.818327i	$0.305098\pi$
$773$			977948.i			1.63665i	−0.574753	+	0.818327i	$0.694902\pi$
$774$	−54743.6	−	136507.i	−0.0913800	−	0.227862i
$775$		−	858605.i		−	1.42952i
$776$	−70072.6	−	31849.6i	−0.116366	−	0.0528909i
$777$	1.25314e6			2.07567
$778$	−815640.	+	327098.i	−1.34753	+	0.540404i
$779$	606310.	+	139493.i	0.999126	+	0.229868i
$780$	214743.	+	224679.i	0.352964	+	0.369294i
$781$	−249806.			−0.409545
$782$	−243709.	+	97735.0i	−0.398527	+	0.159822i
$783$			572230.i			0.933355i
$784$	20719.0	−	457936.i	0.0337082	−	0.745027i
$785$		−	266513.i		−	0.432493i
$786$	458184.	+	1.14251e6i	0.741642	+	1.84933i
$787$			872525.i			1.40873i	0.709837	+	0.704366i	$0.248768\pi$
$787$			872525.i			1.40873i	−0.709837	+	0.704366i	$0.751232\pi$
$788$	−185729.	+	177516.i	−0.299108	+	0.285881i
$789$	−872591.			−1.40171
$790$	177516.	−	71189.6i	0.284435	−	0.114068i
$791$	−516748.			−0.825897
$792$	−53916.1	+	118621.i	−0.0859544	+	0.189109i
$793$		−	394441.i		−	0.627243i
$794$	16913.7	+	42175.4i	0.0268285	+	0.0668987i
$795$			4561.85i			0.00721783i
$796$	−84570.9	+	80831.0i	−0.133473	+	0.127571i
$797$	670191.			1.05507			0.527536	−	0.849533i	$-0.323116\pi$
$797$	670191.			1.05507			0.527536	+	0.849533i	$0.323116\pi$
$798$	−970671.	+	389270.i	−1.52428	+	0.611287i
$799$			119216.i			0.186741i
$800$	−187298.	−	535983.i	−0.292653	−	0.837473i
$801$		−	495025.i		−	0.771546i
$802$	21429.7	−	8594.00i	0.0333171	−	0.0133612i
$803$	443428.			0.687688
$804$	−144472.	+	138083.i	−0.223497	+	0.213613i
$805$		−	413184.i		−	0.637605i
$806$	1.21860e6	−	488697.i	1.87582	−	0.752262i
$807$	−349134.			−0.536098
$808$	−335481.	−	152484.i	−0.513860	−	0.233561i
$809$		−	527423.i		−	0.805864i	−0.915230	−	0.402932i	$-0.867991\pi$
$809$		−	527423.i		−	0.805864i	0.915230	−	0.402932i	$-0.132009\pi$
$810$	255542.	−	102480.i	0.389486	−	0.156196i
$811$			403394.i			0.613321i	0.951819	+	0.306661i	$0.0992117\pi$
$811$			403394.i			0.613321i	−0.951819	+	0.306661i	$0.900788\pi$
$812$	−874074.	−	914515.i	−1.32567	−	1.38701i
$813$		−	7612.67i		−	0.0115174i
$814$	−352326.	+	141294.i	−0.531736	+	0.213243i
$815$			222327.i			0.334717i
$816$	241067.	+	10906.9i	0.362040	+	0.0163803i
$817$			357585.i			0.535717i
$818$	−901600.	+	361571.i	−1.34743	+	0.540364i
$819$			522249.i			0.778592i
$820$	194140.	−	115493.i	0.288728	−	0.171763i
$821$	302174.			0.448303			0.224151	−	0.974554i	$-0.428039\pi$
$821$	302174.			0.448303			0.224151	+	0.974554i	$0.428039\pi$
$822$	−356834.	−	889790.i	−0.528108	−	1.31687i
$823$	396407.			0.585251			0.292625	−	0.956227i	$-0.405471\pi$
$823$	396407.			0.585251			0.292625	+	0.956227i	$0.405471\pi$
$824$	−185743.	−	84424.7i	−0.273564	−	0.124341i
$825$	−323654.			−0.475525
$826$	−210777.	−	525587.i	−0.308932	−	0.770343i
$827$	−1.19767e6			−1.75115			−0.875577	−	0.483078i	$-0.839519\pi$
$827$	−1.19767e6			−1.75115			−0.875577	+	0.483078i	$0.839519\pi$
$828$	−319682.	−	334472.i	−0.466291	−	0.487865i
$829$	464722.			0.676215			0.338107	−	0.941108i	$-0.390213\pi$
$829$	464722.			0.676215			0.338107	+	0.941108i	$0.390213\pi$
$830$	38105.7	+	95019.1i	0.0553138	+	0.137929i
$831$	−267480.			−0.387337
$832$	654102.	−	570895.i	0.944929	−	0.824726i
$833$			154694.i			0.222938i
$834$	−120139.	−	299575.i	−0.172724	−	0.430699i
$835$	−180190.			−0.258438
$836$	229017.	−	218890.i	0.327684	−	0.313194i
$837$		−	725605.i		−	1.03574i
$838$	−167301.	−	417175.i	−0.238237	−	0.594060i
$839$	−311715.			−0.442827			−0.221413	−	0.975180i	$-0.571067\pi$
$839$	−311715.			−0.442827			−0.221413	+	0.975180i	$0.571067\pi$
$840$	−157125.	+	345692.i	−0.222683	+	0.489927i
$841$	−784101.			−1.10861
$842$	172525.	+	430202.i	0.243348	+	0.606803i
$843$			1.07055e6i			1.50643i
$844$	382673.	−	365751.i	0.537209	−	0.513453i
$845$	−137467.			−0.192524
$846$	−194971.	+	78189.7i	−0.272414	+	0.109247i
$847$	−762605.			−1.06300
$848$	12730.3	+	575.974i	0.0177030	+	0.000800960i
$849$		−	201645.i		−	0.279751i
$850$	71316.4	+	177832.i	0.0987078	+	0.246135i
$851$		−	1.34791e6i		−	1.86124i
$852$	−589316.	+	563255.i	−0.811837	+	0.775936i
$853$	−1.31916e6			−1.81301			−0.906506	−	0.422193i	$-0.861260\pi$
$853$	−1.31916e6			−1.81301			−0.906506	+	0.422193i	$0.861260\pi$
$854$	447292.	−	179378.i	0.613303	−	0.245954i
$855$	118297.			0.161824
$856$	991184.	+	450516.i	1.35272	+	0.614841i
$857$	−281386.			−0.383125			−0.191563	−	0.981480i	$-0.561356\pi$
$857$	−281386.			−0.383125			−0.191563	+	0.981480i	$0.561356\pi$
$858$	−184216.	−	459355.i	−0.250238	−	0.623985i
$859$			1.39446e6i			1.88982i	0.327328	+	0.944911i	$0.393852\pi$
$859$			1.39446e6i			1.88982i	−0.327328	+	0.944911i	$0.606148\pi$
$860$	89708.8	+	93859.4i	0.121294	+	0.126906i
$861$	1.15727e6	+	266253.i	1.56110	+	0.359160i
$862$	358823.	+	894750.i	0.482910	+	1.20417i
$863$		−	1.15180e6i		−	1.54652i	−0.634089	−	0.773260i	$-0.718625\pi$
$863$		−	1.15180e6i		−	1.54652i	0.634089	−	0.773260i	$-0.281375\pi$
$864$	−158285.	−	452958.i	−0.212037	−	0.606778i
$865$	−344239.			−0.460074
$866$	−185167.	+	74257.8i	−0.246903	+	0.0990162i
$867$	829888.			1.10403
$868$	1.10835e6	+	1.15963e6i	1.47109	+	1.53915i
$869$	−304562.			−0.403308
$870$	166628.	+	415498.i	0.220145	+	0.548947i
$871$		−	242640.i		−	0.319835i
$872$	1.00826e6	+	458277.i	1.32599	+	0.602692i
$873$			45769.3i			0.0600546i
$874$	418709.	+	1.04408e6i	0.548138	+	1.36682i
$875$	−641352.			−0.837684
$876$	1.04608e6	−	999825.i	1.36320	−	1.30291i
$877$	602111.			0.782848			0.391424	−	0.920210i	$-0.371983\pi$
$877$	602111.			0.782848			0.391424	+	0.920210i	$0.371983\pi$
$878$	−486291.	+	195018.i	−0.630822	+	0.252980i
$879$		−	144059.i		−	0.186451i
$880$	5198.97	−	114909.i	0.00671355	−	0.148384i
$881$	167820.			0.216218			0.108109	−	0.994139i	$-0.465520\pi$
$881$	167820.			0.216218			0.108109	+	0.994139i	$0.465520\pi$
$882$	−252994.	+	101459.i	−0.325217	+	0.130423i
$883$	−1.43605e6			−1.84182			−0.920910	−	0.389776i	$-0.872552\pi$
$883$	−1.43605e6			−1.84182			−0.920910	+	0.389776i	$0.872552\pi$
$884$	−211802.	+	202435.i	−0.271034	+	0.259049i
$885$			200389.i			0.255851i
$886$	−30839.2	−	76899.7i	−0.0392858	−	0.0979619i
$887$	−497062.			−0.631776			−0.315888	−	0.948796i	$-0.602302\pi$
$887$	−497062.			−0.631776			−0.315888	+	0.948796i	$0.602302\pi$
$888$	−512583.	+	1.12774e6i	−0.650037	+	1.43015i
$889$			781366.i			0.988669i
$890$	162659.	+	405601.i	0.205352	+	0.512058i
$891$	−438430.			−0.552261
$892$	−748283.	−	782904.i	−0.940451	−	0.983963i
$893$	510735.			0.640461
$894$	−545451.	−	1.36012e6i	−0.682465	−	1.70177i
$895$	3514.34			0.00438731
$896$	944852.	+	482121.i	1.17692	+	0.600537i
$897$	1.75738e6			2.18414
$898$	−486502.	+	195103.i	−0.603298	+	0.241942i
$899$	1.89112e6			2.33991
$900$	−244062.	+	233269.i	−0.301311	+	0.287986i
$901$	−4300.39			−0.00529735
$902$	−355392.	+	55626.4i	−0.436813	+	0.0683704i
$903$			682527.i			0.837037i
$904$	211370.	−	465036.i	0.258646	−	0.569049i
$905$		−	263749.i		−	0.322027i
$906$	1.08905e6	−	436742.i	1.32675	−	0.532070i
$907$			744074.i			0.904485i	0.891895	+	0.452242i	$0.149376\pi$
$907$			744074.i			0.904485i	−0.891895	+	0.452242i	$0.850624\pi$
$908$	−289488.	+	276686.i	−0.351123	+	0.335596i
$909$			219126.i			0.265195i
$910$	−171605.	−	427907.i	−0.207227	−	0.516734i
$911$			1.05100e6i			1.26639i	0.773992	+	0.633196i	$0.218257\pi$
$911$			1.05100e6i			1.26639i	−0.773992	+	0.633196i	$0.781743\pi$
$912$	46726.5	−	1.03276e6i	0.0561790	−	1.24168i
$913$		−	163023.i		−	0.195572i
$914$	142801.	+	356083.i	0.170938	+	0.426244i
$915$	−170538.			−0.203694
$916$	1.04714e6	+	1.09559e6i	1.24800	+	1.30574i
$917$		−	1.82600e6i		−	2.17151i
$918$	60269.3	+	150286.i	0.0715173	+	0.178333i
$919$	−528431.			−0.625688			−0.312844	−	0.949805i	$-0.601282\pi$
$919$	−528431.			−0.625688			−0.312844	+	0.949805i	$0.601282\pi$
$920$	371836.	+	169008.i	0.439315	+	0.199679i
$921$			249341.i			0.293950i
$922$	−376244.	+	150886.i	−0.442596	+	0.177495i
$923$		−	989754.i		−	1.16178i
$924$	437128.	−	417798.i	0.511994	−	0.489353i
$925$	−983561.			−1.14952
$926$	−1.14222e6	+	458069.i	−1.33208	+	0.534206i
$927$			121322.i			0.141182i
$928$	1.18053e6	−	412532.i	1.37082	−	0.479029i
$929$			1.54286e6i			1.78770i	0.448366	+	0.893850i	$0.352006\pi$
$929$			1.54286e6i			1.78770i	−0.448366	+	0.893850i	$0.647994\pi$
$930$	−211289.	−	526864.i	−0.244293	−	0.609162i
$931$	662729.			0.764604
$932$	−478118.	−	500239.i	−0.550431	−	0.575898i
$933$	−1.72478e6			−1.98139
$934$	−23663.2	−	59005.8i	−0.0271257	−	0.0676396i
$935$			38817.1i			0.0444017i
$936$	−469987.	−	213620.i	−0.536456	−	0.243832i
$937$		−	554710.i		−	0.631811i	−0.948791	−	0.315905i	$-0.897692\pi$
$937$		−	554710.i		−	0.631811i	0.948791	−	0.315905i	$-0.102308\pi$
$938$	275151.	−	110344.i	0.312727	−	0.125414i
$939$		−	680425.i		−	0.771701i
$940$	134058.	−	128130.i	0.151718	−	0.145009i
$941$	379562.			0.428651			0.214326	−	0.976762i	$-0.431245\pi$
$941$	379562.			0.428651			0.214326	+	0.976762i	$0.431245\pi$
$942$	515500.	+	1.28543e6i	0.580934	+	1.44860i
$943$	286389.	−	1.24479e6i	0.322057	−	1.39983i
$944$	559206.	+	25300.9i	0.627521	+	0.0283917i
$945$	−254794.			−0.285316
$946$	−76956.2	−	191895.i	−0.0859926	−	0.214428i
$947$		−	223175.i		−	0.248855i	−0.992229	−	0.124427i	$-0.960291\pi$
$947$		−	223175.i		−	0.248855i	0.992229	−	0.124427i	$-0.0397094\pi$
$948$	−718489.	+	686717.i	−0.799472	+	0.764119i
$949$			1.75690e6i			1.95080i
$950$	761856.	−	305529.i	0.844162	−	0.338536i
$951$			139038.i			0.153735i
$952$	−325879.	−	148120.i	−0.359570	−	0.163433i
$953$	−262226.			−0.288729			−0.144364	−	0.989525i	$-0.546114\pi$
$953$	−262226.			−0.288729			−0.144364	+	0.989525i	$0.546114\pi$
$954$	−2820.49	−	7033.08i	−0.00309904	−	0.00772767i
$955$	−331972.			−0.363994
$956$	−523997.	+	500825.i	−0.573341	+	0.547987i
$957$		−	712864.i		−	0.778364i
$958$	−1.21174e6	+	485947.i	−1.32032	+	0.529491i
$959$			1.42209e6i			1.54629i
$960$	−246828.	−	282803.i	−0.267825	−	0.306861i
$961$	−1.47448e6			−1.59658
$962$	−559818.	−	1.39594e6i	−0.604919	−	1.50841i
$963$		−	647412.i		−	0.698117i
$964$	475549.	−	454519.i	0.511730	−	0.489101i
$965$		−	98393.0i		−	0.105660i
$966$	799196.	+	1.99285e6i	0.856444	+	2.13560i
$967$	1.33860e6			1.43152			0.715759	−	0.698348i	$-0.246081\pi$
$967$	1.33860e6			1.43152			0.715759	+	0.698348i	$0.246081\pi$
$968$	311935.	−	686290.i	0.332899	−	0.732414i
$969$			348874.i			0.371553i
$970$	−15039.2	−	37501.3i	−0.0159839	−	0.0398569i
$971$	1.12869e6			1.19712			0.598558	−	0.801079i	$-0.295740\pi$
$971$	1.12869e6			1.19712			0.598558	+	0.801079i	$0.295740\pi$
$972$	−595293.	+	568969.i	−0.630084	+	0.602221i
$973$			478790.i			0.505731i
$974$	−141862.	−	353743.i	−0.149537	−	0.372880i
$975$		−	1.28235e6i		−	1.34895i
$976$	−21531.9	+	475903.i	−0.0226039	+	0.499596i
$977$		−	1.67211e6i		−	1.75177i	−0.482520	−	0.875885i	$-0.660279\pi$
$977$		−	1.67211e6i		−	1.75177i	0.482520	−	0.875885i	$-0.339721\pi$
$978$	−430034.	−	1.07232e6i	−0.449598	−	1.12110i
$979$		−	695885.i		−	0.726059i
$980$	173954.	−	166262.i	0.181127	−	0.173117i
$981$		−	658564.i		−	0.684322i
$982$	−247588.	−	617378.i	−0.256748	−	0.640219i
$983$		−	39813.3i		−	0.0412022i	−0.999788	−	0.0206011i	$-0.993442\pi$
$983$		−	39813.3i		−	0.0412022i	0.999788	−	0.0206011i	$-0.00655801\pi$
$984$	−712978.	+	932555.i	−0.736352	+	0.963128i
$985$	−134864.			−0.139003
$986$	−391684.	+	157078.i	−0.402886	+	0.161570i
$987$	974847.			1.00070
$988$	867259.	+	907385.i	0.888454	+	0.929560i
$989$	734145.			0.750566
$990$	−63483.4	+	25458.9i	−0.0647724	+	0.0259758i
$991$	−1.86660e6			−1.90065			−0.950327	−	0.311253i	$-0.899251\pi$
$991$	−1.86660e6			−1.90065			−0.950327	+	0.311253i	$0.899251\pi$
$992$	−1.49695e6	+	523103.i	−1.52119	+	0.531574i
$993$	−52183.2			−0.0529215
$994$	1.12237e6	−	450106.i	1.13596	−	0.455556i
$995$	−61409.9			−0.0620286
$996$	−367579.	−	384586.i	−0.370537	−	0.387681i
$997$			1.59801e6i			1.60764i	0.594874	+	0.803819i	$0.297202\pi$
$997$			1.59801e6i			1.60764i	−0.594874	+	0.803819i	$0.702798\pi$
$998$	−69388.7	+	27827.1i	−0.0696671	+	0.0279387i
$999$	−831205.			−0.832870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.5.d.f.163.4	yes	72
4.3	odd	2	inner	164.5.d.f.163.1	✓	72
41.40	even	2	inner	164.5.d.f.163.3	yes	72
164.163	odd	2	inner	164.5.d.f.163.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.5.d.f.163.1	✓	72	4.3	odd	2	inner
164.5.d.f.163.2	yes	72	164.163	odd	2	inner
164.5.d.f.163.3	yes	72	41.40	even	2	inner
164.5.d.f.163.4	yes	72	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	164.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.71258 + 1.48887i) q^{2} +10.9113 q^{3} +(11.5666 - 11.0551i) q^{4} +8.39889 q^{5} +(-40.5091 + 16.2454i) q^{6} +64.7429 q^{7} +(-26.4823 + 58.2639i) q^{8} +38.0563 q^{9} +(-31.1816 + 12.5048i) q^{10} +53.4978 q^{11} +(126.206 - 120.625i) q^{12} +211.963i q^{13} +(-240.363 + 96.3934i) q^{14} +91.6427 q^{15} +(11.5707 - 255.738i) q^{16} +86.3903i q^{17} +(-141.287 + 56.6606i) q^{18} +370.107 q^{19} +(97.1462 - 92.8503i) q^{20} +706.428 q^{21} +(-198.615 + 79.6511i) q^{22} -759.854i q^{23} +(-288.956 + 635.735i) q^{24} -554.459 q^{25} +(-315.584 - 786.930i) q^{26} -468.572 q^{27} +(748.853 - 715.737i) q^{28} -1221.22i q^{29} +(-340.231 + 136.444i) q^{30} +1548.55i q^{31} +(337.803 + 966.677i) q^{32} +583.730 q^{33} +(-128.623 - 320.731i) q^{34} +543.768 q^{35} +(440.180 - 420.715i) q^{36} +1773.91 q^{37} +(-1374.05 + 551.040i) q^{38} +2312.79i q^{39} +(-222.422 + 489.352i) q^{40} +(1638.20 + 376.900i) q^{41} +(-2622.67 + 1051.78i) q^{42} +966.166i q^{43} +(618.786 - 591.423i) q^{44} +319.630 q^{45} +(1131.32 + 2821.02i) q^{46} +1379.97 q^{47} +(126.251 - 2790.44i) q^{48} +1790.64 q^{49} +(2058.47 - 825.514i) q^{50} +942.630i q^{51} +(2343.27 + 2451.68i) q^{52} +49.7786i q^{53} +(1739.61 - 697.640i) q^{54} +449.322 q^{55} +(-1714.54 + 3772.18i) q^{56} +4038.35 q^{57} +(1818.23 + 4533.89i) q^{58} +2186.63i q^{59} +(1059.99 - 1013.12i) q^{60} -1860.90 q^{61} +(-2305.58 - 5749.11i) q^{62} +2463.87 q^{63} +(-2693.37 - 3085.93i) q^{64} +1780.25i q^{65} +(-2167.15 + 869.096i) q^{66} -1144.73 q^{67} +(955.051 + 999.239i) q^{68} -8290.98i q^{69} +(-2018.78 + 809.597i) q^{70} -4669.47 q^{71} +(-1007.82 + 2217.31i) q^{72} +8288.70 q^{73} +(-6585.80 + 2641.12i) q^{74} -6049.86 q^{75} +(4280.87 - 4091.56i) q^{76} +3463.60 q^{77} +(-3443.43 - 8586.42i) q^{78} -5692.98 q^{79} +(97.1810 - 2147.92i) q^{80} -8195.28 q^{81} +(-6643.12 + 1039.79i) q^{82} -3047.28i q^{83} +(8170.95 - 7809.62i) q^{84} +725.582i q^{85} +(-1438.49 - 3586.97i) q^{86} -13325.1i q^{87} +(-1416.75 + 3116.99i) q^{88} -13007.7i q^{89} +(-1186.65 + 475.886i) q^{90} +13723.1i q^{91} +(-8400.24 - 8788.89i) q^{92} +16896.6i q^{93} +(-5123.24 + 2054.58i) q^{94} +3108.49 q^{95} +(3685.86 + 10547.7i) q^{96} +1202.68i q^{97} +(-6647.90 + 2666.02i) q^{98} +2035.93 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{2} - 162 q^{4} - 8 q^{5} + 162 q^{8} + 1728 q^{9} - 272 q^{10} - 2842 q^{16} - 298 q^{18} - 584 q^{20} + 280 q^{21} + 4264 q^{25} + 66 q^{32} + 3512 q^{33} - 11338 q^{36} + 5720 q^{37} - 4648 q^{40}+ \cdots + 2902 q^{98}+O(q^{100}) \) 72 * q + 6 * q^2 - 162 * q^4 - 8 * q^5 + 162 * q^8 + 1728 * q^9 - 272 * q^10 - 2842 * q^16 - 298 * q^18 - 584 * q^20 + 280 * q^21 + 4264 * q^25 + 66 * q^32 + 3512 * q^33 - 11338 * q^36 + 5720 * q^37 - 4648 * q^40 - 7928 * q^41 - 10140 * q^42 - 9528 * q^45 - 5680 * q^46 + 6624 * q^49 + 554 * q^50 + 29864 * q^57 + 11712 * q^61 - 3936 * q^62 - 34554 * q^64 + 24852 * q^66 - 12166 * q^72 + 16632 * q^73 - 11120 * q^74 + 84456 * q^77 - 20496 * q^78 - 12104 * q^80 + 13408 * q^81 - 51114 * q^82 - 948 * q^84 - 20400 * q^86 + 64976 * q^90 - 2784 * q^92 + 2902 * q^98

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