LMFDB - Embedded newform 200.4.f.d.149.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,4,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not 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:	$11.8003820011$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.23
Character	$\chi$	$=$	200.149
Dual form			200.4.f.d.149.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.79815 - 0.412714i) q^{2} +7.69300 q^{3} +(7.65933 - 2.30967i) q^{4} +(21.5262 - 3.17501i) q^{6} +15.6248i q^{7} +(20.4788 - 9.62394i) q^{8} +32.1823 q^{9} +O(q^{10})$	\(q+(2.79815 - 0.412714i) q^{2} +7.69300 q^{3} +(7.65933 - 2.30967i) q^{4} +(21.5262 - 3.17501i) q^{6} +15.6248i q^{7} +(20.4788 - 9.62394i) q^{8} +32.1823 q^{9} +46.7640i q^{11} +(58.9233 - 17.7683i) q^{12} -50.4964 q^{13} +(6.44855 + 43.7205i) q^{14} +(53.3308 - 35.3811i) q^{16} -111.080i q^{17} +(90.0511 - 13.2821i) q^{18} -84.9682i q^{19} +120.201i q^{21} +(19.3001 + 130.853i) q^{22} +53.2555i q^{23} +(157.543 - 74.0370i) q^{24} +(-141.297 + 20.8406i) q^{26} +39.8675 q^{27} +(36.0881 + 119.675i) q^{28} -229.789i q^{29} -338.615 q^{31} +(134.626 - 121.012i) q^{32} +359.755i q^{33} +(-45.8441 - 310.818i) q^{34} +(246.495 - 74.3307i) q^{36} +71.1508 q^{37} +(-35.0675 - 237.754i) q^{38} -388.469 q^{39} -3.06105 q^{41} +(49.6087 + 336.342i) q^{42} +115.970 q^{43} +(108.010 + 358.181i) q^{44} +(21.9793 + 149.017i) q^{46} +574.015i q^{47} +(410.274 - 272.187i) q^{48} +98.8671 q^{49} -854.536i q^{51} +(-386.769 + 116.630i) q^{52} +39.0500 q^{53} +(111.555 - 16.4539i) q^{54} +(150.372 + 319.976i) q^{56} -653.660i q^{57} +(-94.8372 - 642.985i) q^{58} +109.940i q^{59} +180.738i q^{61} +(-947.497 + 139.751i) q^{62} +502.841i q^{63} +(326.760 - 394.173i) q^{64} +(148.476 + 1006.65i) q^{66} +755.845 q^{67} +(-256.558 - 850.796i) q^{68} +409.695i q^{69} +127.821 q^{71} +(659.054 - 309.721i) q^{72} +347.937i q^{73} +(199.091 - 29.3649i) q^{74} +(-196.249 - 650.800i) q^{76} -730.676 q^{77} +(-1087.00 + 160.327i) q^{78} -456.703 q^{79} -562.221 q^{81} +(-8.56529 + 1.26334i) q^{82} +499.423 q^{83} +(277.626 + 920.662i) q^{84} +(324.502 - 47.8625i) q^{86} -1767.77i q^{87} +(450.054 + 957.669i) q^{88} -1301.32 q^{89} -788.995i q^{91} +(123.003 + 407.902i) q^{92} -2604.97 q^{93} +(236.904 + 1606.18i) q^{94} +(1035.67 - 930.948i) q^{96} +778.230i q^{97} +(276.645 - 40.8038i) q^{98} +1504.97i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} + 18 q^{6} + 216 q^{9}+O(q^{10}) $ 24 * q - 2 * q^4 + 18 * q^6 + 216 * q^9	$ 24 q - 2 q^{4} + 18 q^{6} + 216 q^{9} + 224 q^{14} + 338 q^{16} + 570 q^{24} - 376 q^{26} - 528 q^{31} - 930 q^{34} - 1400 q^{36} + 600 q^{39} - 40 q^{41} - 766 q^{44} + 824 q^{46} - 456 q^{49} + 1674 q^{54} + 1304 q^{56} + 1486 q^{64} - 1794 q^{66} + 1256 q^{71} - 2160 q^{74} - 1938 q^{76} - 2232 q^{79} + 2256 q^{81} - 5096 q^{84} + 5452 q^{86} + 848 q^{89} + 3736 q^{94} + 5470 q^{96}+O(q^{100}) $ 24 * q - 2 * q^4 + 18 * q^6 + 216 * q^9 + 224 * q^14 + 338 * q^16 + 570 * q^24 - 376 * q^26 - 528 * q^31 - 930 * q^34 - 1400 * q^36 + 600 * q^39 - 40 * q^41 - 766 * q^44 + 824 * q^46 - 456 * q^49 + 1674 * q^54 + 1304 * q^56 + 1486 * q^64 - 1794 * q^66 + 1256 * q^71 - 2160 * q^74 - 1938 * q^76 - 2232 * q^79 + 2256 * q^81 - 5096 * q^84 + 5452 * q^86 + 848 * q^89 + 3736 * q^94 + 5470 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	2.79815	−	0.412714i	0.989297	−	0.145916i
$2$	2.79815	−	0.412714i	0.989297	−	0.145916i
$3$	7.69300			1.48052			0.740260	−	0.672321i	$-0.234703\pi$
$3$	7.69300			1.48052			0.740260	+	0.672321i	$0.234703\pi$
$4$	7.65933	−	2.30967i	0.957417	−	0.288709i
$5$		0			0
$5$		0			0
$6$	21.5262	−	3.17501i	1.46467	−	0.216032i
$7$			15.6248i			0.843657i	0.906676	+	0.421829i	$0.138612\pi$
$7$			15.6248i			0.843657i	−0.906676	+	0.421829i	$0.861388\pi$
$8$	20.4788	−	9.62394i	0.905042	−	0.425322i
$9$	32.1823			1.19194
$10$		0			0
$11$			46.7640i			1.28181i	0.767622	+	0.640903i	$0.221440\pi$
$11$			46.7640i			1.28181i	−0.767622	+	0.640903i	$0.778560\pi$
$12$	58.9233	−	17.7683i	1.41747	−	0.427440i
$13$	−50.4964			−1.07732			−0.538661	−	0.842522i	$-0.681070\pi$
$13$	−50.4964			−1.07732			−0.538661	+	0.842522i	$0.681070\pi$
$14$	6.44855	+	43.7205i	0.123103	+	0.834628i
$15$		0			0
$16$	53.3308	−	35.3811i	0.833294	−	0.552830i
$17$		−	111.080i		−	1.58475i	−0.610034	−	0.792375i	$-0.708844\pi$
$17$		−	111.080i		−	1.58475i	0.610034	−	0.792375i	$-0.291156\pi$
$18$	90.0511	−	13.2821i	1.17918	−	0.173923i
$19$		−	84.9682i		−	1.02595i	−0.858404	−	0.512975i	$-0.828543\pi$
$19$		−	84.9682i		−	1.02595i	0.858404	−	0.512975i	$-0.171457\pi$
$20$		0			0
$21$			120.201i			1.24905i
$22$	19.3001	+	130.853i	0.187037	+	1.26809i
$23$			53.2555i			0.482806i	0.970425	+	0.241403i	$0.0776076\pi$
$23$			53.2555i			0.482806i	−0.970425	+	0.241403i	$0.922392\pi$
$24$	157.543	−	74.0370i	1.33993	−	0.629697i
$25$		0			0
$26$	−141.297	+	20.8406i	−1.06579	+	0.157199i
$27$	39.8675			0.284167
$28$	36.0881	+	119.675i	0.243572	+	0.807732i
$29$		−	229.789i		−	1.47141i	−0.677304	−	0.735703i	$-0.736852\pi$
$29$		−	229.789i		−	1.47141i	0.677304	−	0.735703i	$-0.263148\pi$
$30$		0			0
$31$	−338.615			−1.96184			−0.980920	−	0.194410i	$-0.937721\pi$
$31$	−338.615			−1.96184			−0.980920	+	0.194410i	$0.937721\pi$
$32$	134.626	−	121.012i	0.743708	−	0.668505i
$33$			359.755i			1.89774i
$34$	−45.8441	−	310.818i	−0.231241	−	1.56779i
$35$		0			0
$36$	246.495	−	74.3307i	1.14118	−	0.344123i
$37$	71.1508			0.316138			0.158069	−	0.987428i	$-0.449473\pi$
$37$	71.1508			0.316138			0.158069	+	0.987428i	$0.449473\pi$
$38$	−35.0675	−	237.754i	−0.149703	−	1.01497i
$39$	−388.469			−1.59500
$40$		0			0
$41$	−3.06105			−0.0116599			−0.00582995	−	0.999983i	$-0.501856\pi$
$41$	−3.06105			−0.0116599			−0.00582995	+	0.999983i	$0.501856\pi$
$42$	49.6087	+	336.342i	0.182257	+	1.23568i
$43$	115.970			0.411285			0.205643	−	0.978627i	$-0.434072\pi$
$43$	115.970			0.411285			0.205643	+	0.978627i	$0.434072\pi$
$44$	108.010	+	358.181i	0.370069	+	1.22722i
$45$		0			0
$46$	21.9793	+	149.017i	0.0704493	+	0.477638i
$47$			574.015i			1.78146i	0.454532	+	0.890730i	$0.349806\pi$
$47$			574.015i			1.78146i	−0.454532	+	0.890730i	$0.650194\pi$
$48$	410.274	−	272.187i	1.23371	−	0.818476i
$49$	98.8671			0.288242
$50$		0			0
$51$		−	854.536i		−	2.34625i
$52$	−386.769	+	116.630i	−1.03145	+	0.311033i
$53$	39.0500			0.101206			0.0506031	−	0.998719i	$-0.483886\pi$
$53$	39.0500			0.101206			0.0506031	+	0.998719i	$0.483886\pi$
$54$	111.555	−	16.4539i	0.281125	−	0.0414646i
$55$		0			0
$56$	150.372	+	319.976i	0.358826	+	0.763545i
$57$		−	653.660i		−	1.51894i
$58$	−94.8372	−	642.985i	−0.214702	−	1.45566i
$59$			109.940i			0.242593i	0.992616	+	0.121297i	$0.0387053\pi$
$59$			109.940i			0.242593i	−0.992616	+	0.121297i	$0.961295\pi$
$60$		0			0
$61$			180.738i			0.379363i	0.981846	+	0.189682i	$0.0607456\pi$
$61$			180.738i			0.379363i	−0.981846	+	0.189682i	$0.939254\pi$
$62$	−947.497	+	139.751i	−1.94084	+	0.286265i
$63$			502.841i			1.00559i
$64$	326.760	−	394.173i	0.638202	−	0.769869i
$65$		0			0
$66$	148.476	+	1006.65i	0.276911	+	1.87743i
$67$	755.845			1.37823			0.689113	−	0.724654i	$-0.258000\pi$
$67$	755.845			1.37823			0.689113	+	0.724654i	$0.258000\pi$
$68$	−256.558	−	850.796i	−0.457532	−	1.51727i
$69$			409.695i			0.714804i
$70$		0			0
$71$	127.821			0.213656			0.106828	−	0.994278i	$-0.465931\pi$
$71$	127.821			0.213656			0.106828	+	0.994278i	$0.465931\pi$
$72$	659.054	−	309.721i	1.07875	−	0.506957i
$73$			347.937i			0.557849i	0.960313	+	0.278924i	$0.0899779\pi$
$73$			347.937i			0.557849i	−0.960313	+	0.278924i	$0.910022\pi$
$74$	199.091	−	29.3649i	0.312755	−	0.0461297i
$75$		0			0
$76$	−196.249	−	650.800i	−0.296201	−	0.982261i
$77$	−730.676			−1.08141
$78$	−1087.00	+	160.327i	−1.57793	+	0.232736i
$79$	−456.703			−0.650419			−0.325210	−	0.945642i	$-0.605435\pi$
$79$	−456.703			−0.650419			−0.325210	+	0.945642i	$0.605435\pi$
$80$		0			0
$81$	−562.221			−0.771223
$82$	−8.56529	+	1.26334i	−0.0115351	+	0.00170137i
$83$	499.423			0.660467			0.330233	−	0.943899i	$-0.392873\pi$
$83$	499.423			0.660467			0.330233	+	0.943899i	$0.392873\pi$
$84$	277.626	+	920.662i	0.360613	+	1.19586i
$85$		0			0
$86$	324.502	−	47.8625i	0.406883	−	0.0600133i
$87$		−	1767.77i		−	2.17844i
$88$	450.054	+	957.669i	0.545181	+	1.16009i
$89$	−1301.32			−1.54989			−0.774944	−	0.632030i	$-0.782222\pi$
$89$	−1301.32			−1.54989			−0.774944	+	0.632030i	$0.782222\pi$
$90$		0			0
$91$		−	788.995i		−	0.908891i
$92$	123.003	+	407.902i	0.139391	+	0.462247i
$93$	−2604.97			−2.90454
$94$	236.904	+	1606.18i	0.259944	+	1.76239i
$95$		0			0
$96$	1035.67	−	930.948i	1.10107	−	0.989734i
$97$			778.230i			0.814611i	0.913292	+	0.407306i	$0.133532\pi$
$97$			778.230i			0.814611i	−0.913292	+	0.407306i	$0.866468\pi$
$98$	276.645	−	40.8038i	0.285157	−	0.0420593i
$99$			1504.97i			1.52783i
$100$		0			0
$101$			1147.12i			1.13012i	0.825048	+	0.565062i	$0.191148\pi$
$101$			1147.12i			1.13012i	−0.825048	+	0.565062i	$0.808852\pi$
$102$	−352.679	−	2391.12i	−0.342357	−	2.32114i
$103$			852.432i			0.815462i	0.913102	+	0.407731i	$0.133680\pi$
$103$			852.432i			0.815462i	−0.913102	+	0.407731i	$0.866320\pi$
$104$	−1034.10	+	485.975i	−0.975022	+	0.458209i
$105$		0			0
$106$	109.268	−	16.1165i	0.100123	−	0.0147676i
$107$	−42.6157			−0.0385030			−0.0192515	−	0.999815i	$-0.506128\pi$
$107$	−42.6157			−0.0385030			−0.0192515	+	0.999815i	$0.506128\pi$
$108$	305.359	−	92.0810i	0.272066	−	0.0820416i
$109$		−	1490.77i		−	1.31000i	−0.755628	−	0.655001i	$-0.772668\pi$
$109$		−	1490.77i		−	1.31000i	0.755628	−	0.655001i	$-0.227332\pi$
$110$		0			0
$111$	547.363			0.468049
$112$	552.822	+	833.281i	0.466399	+	0.703015i
$113$		−	846.817i		−	0.704972i	−0.935817	−	0.352486i	$-0.885336\pi$
$113$		−	846.817i		−	0.704972i	0.935817	−	0.352486i	$-0.114664\pi$
$114$	−269.775	−	1829.04i	−0.221638	−	1.50268i
$115$		0			0
$116$	−530.738	−	1760.03i	−0.424809	−	1.40875i
$117$	−1625.09			−1.28410
$118$	45.3739	+	307.630i	0.0353984	+	0.239997i
$119$	1735.59			1.33699
$120$		0			0
$121$	−855.870			−0.643028
$122$	74.5932	+	505.734i	0.0553553	+	0.375303i
$123$	−23.5487			−0.0172627
$124$	−2593.57	+	782.091i	−1.87830	+	0.566402i
$125$		0			0
$126$	207.529	+	1407.03i	0.146732	+	0.994824i
$127$		−	65.6584i		−	0.0458759i	−0.999737	−	0.0229380i	$-0.992698\pi$
$127$		−	65.6584i		−	0.0458759i	0.999737	−	0.0229380i	$-0.00730202\pi$
$128$	751.643	−	1237.81i	0.519035	−	0.854753i
$129$	892.158			0.608916
$130$		0			0
$131$		−	646.301i		−	0.431050i	−0.976498	−	0.215525i	$-0.930854\pi$
$131$		−	646.301i		−	0.431050i	0.976498	−	0.215525i	$-0.0691463\pi$
$132$	830.918	+	2755.49i	0.547895	+	1.81693i
$133$	1327.61			0.865550
$134$	2114.97	−	311.948i	1.36347	−	0.201106i
$135$		0			0
$136$	−1069.02	−	2274.77i	−0.674029	−	1.43427i
$137$			1794.01i			1.11878i	0.828906	+	0.559388i	$0.188964\pi$
$137$			1794.01i			1.11878i	−0.828906	+	0.559388i	$0.811036\pi$
$138$	169.087	+	1146.39i	0.104302	+	0.707153i
$139$			1.37996i			0.000842065i	1.00000		0.000421032i	$0.000134019\pi$
$139$			1.37996i			0.000842065i	−1.00000		0.000421032i	$0.999866\pi$
$140$		0			0
$141$			4415.90i			2.63749i
$142$	357.662	−	52.7534i	0.211369	−	0.0311758i
$143$		−	2361.41i		−	1.38092i
$144$	1716.31	−	1138.65i	0.993234	−	0.658939i
$145$		0			0
$146$	143.599	+	973.582i	0.0813993	+	0.551878i
$147$	760.585			0.426748
$148$	544.967	−	164.335i	0.302676	−	0.0912720i
$149$		−	743.959i		−	0.409044i	−0.978862	−	0.204522i	$-0.934436\pi$
$149$		−	743.959i		−	0.409044i	0.978862	−	0.204522i	$-0.0655640\pi$
$150$		0			0
$151$	2411.32			1.29954			0.649770	−	0.760131i	$-0.274865\pi$
$151$	2411.32			1.29954			0.649770	+	0.760131i	$0.274865\pi$
$152$	−817.729	−	1740.04i	−0.436359	−	0.928527i
$153$		−	3574.80i		−	1.88892i
$154$	−2044.54	+	301.560i	−1.06983	+	0.157795i
$155$		0			0
$156$	−2975.42	+	897.238i	−1.52708	+	0.460490i
$157$	−1497.53			−0.761249			−0.380624	−	0.924730i	$-0.624291\pi$
$157$	−1497.53			−0.761249			−0.380624	+	0.924730i	$0.624291\pi$
$158$	−1277.93	+	188.488i	−0.643458	+	0.0949068i
$159$	300.412			0.149838
$160$		0			0
$161$	−832.104			−0.407323
$162$	−1573.18	+	232.037i	−0.762968	+	0.112534i
$163$	2895.86			1.39154			0.695772	−	0.718263i	$-0.255063\pi$
$163$	2895.86			1.39154			0.695772	+	0.718263i	$0.255063\pi$
$164$	−23.4456	+	7.07003i	−0.0111634	+	0.00336632i
$165$		0			0
$166$	1397.46	−	206.119i	0.653398	−	0.0963729i
$167$			1923.39i			0.891237i	0.895223	+	0.445619i	$0.147016\pi$
$167$			1923.39i			0.891237i	−0.895223	+	0.445619i	$0.852984\pi$
$168$	1156.81	+	2461.57i	0.531249	+	1.13044i
$169$	352.891			0.160624
$170$		0			0
$171$		−	2734.47i		−	1.22287i
$172$	888.253	−	267.853i	0.393771	−	0.118742i
$173$	351.016			0.154262			0.0771309	−	0.997021i	$-0.475424\pi$
$173$	351.016			0.154262			0.0771309	+	0.997021i	$0.475424\pi$
$174$	−729.583	−	4946.49i	−0.317871	−	2.15513i
$175$		0			0
$176$	1654.56	+	2493.96i	0.708621	+	1.06812i
$177$			845.772i			0.359164i
$178$	−3641.30	+	537.074i	−1.53330	+	0.226154i
$179$		−	2001.39i		−	0.835705i	−0.908515	−	0.417853i	$-0.862783\pi$
$179$		−	2001.39i		−	0.835705i	0.908515	−	0.417853i	$-0.137217\pi$
$180$		0			0
$181$		−	4293.36i		−	1.76311i	−0.472082	−	0.881555i	$-0.656497\pi$
$181$		−	4293.36i		−	1.76311i	0.472082	−	0.881555i	$-0.343503\pi$
$182$	−325.629	−	2207.73i	−0.132622	−	0.899163i
$183$			1390.42i			0.561655i
$184$	512.528	+	1090.61i	0.205348	+	0.436960i
$185$		0			0
$186$	−7289.10	+	1075.11i	−2.87346	+	0.423821i
$187$	5194.52			2.03134
$188$	1325.79	+	4396.57i	0.514324	+	1.70560i
$189$			622.920i			0.239739i
$190$		0			0
$191$	442.947			0.167804			0.0839019	−	0.996474i	$-0.473262\pi$
$191$	442.947			0.167804			0.0839019	+	0.996474i	$0.473262\pi$
$192$	2513.76	−	3032.37i	0.944871	−	1.13981i
$193$			2844.03i			1.06071i	0.847775	+	0.530356i	$0.177942\pi$
$193$			2844.03i			1.06071i	−0.847775	+	0.530356i	$0.822058\pi$
$194$	321.186	+	2177.61i	0.118865	+	0.805892i
$195$		0			0
$196$	757.256	−	228.351i	0.275968	−	0.0832182i
$197$	4472.05			1.61736			0.808681	−	0.588247i	$-0.200182\pi$
$197$	4472.05			1.61736			0.808681	+	0.588247i	$0.200182\pi$
$198$	621.123	+	4211.15i	0.222936	+	1.51148i
$199$	1382.43			0.492452			0.246226	−	0.969212i	$-0.420809\pi$
$199$	1382.43			0.492452			0.246226	+	0.969212i	$0.420809\pi$
$200$		0			0
$201$	5814.72			2.04049
$202$	473.432	+	3209.81i	0.164904	+	1.11803i
$203$	3590.40			1.24136
$204$	−1973.70	−	6545.17i	−0.677385	−	2.24634i
$205$		0			0
$206$	351.811	+	2385.24i	0.118989	+	0.806734i
$207$			1713.88i			0.575474i
$208$	−2693.02	+	1786.62i	−0.897726	+	0.595577i
$209$	3973.45			1.31507
$210$		0			0
$211$			350.255i			0.114278i	0.998366	+	0.0571388i	$0.0181978\pi$
$211$			350.255i			0.114278i	−0.998366	+	0.0571388i	$0.981802\pi$
$212$	299.097	−	90.1928i	0.0968965	−	0.0292192i
$213$	983.326			0.316321
$214$	−119.245	+	17.5881i	−0.0380909	+	0.00561821i
$215$		0			0
$216$	816.437	−	383.682i	0.257183	−	0.120862i
$217$		−	5290.78i		−	1.65512i
$218$	−615.263	−	4171.42i	−0.191151	−	1.29598i
$219$			2676.68i			0.825906i
$220$		0			0
$221$			5609.12i			1.70729i
$222$	1531.61	−	225.904i	0.463039	−	0.0682960i
$223$		−	4547.35i		−	1.36553i	−0.730638	−	0.682765i	$-0.760777\pi$
$223$		−	4547.35i		−	1.36553i	0.730638	−	0.682765i	$-0.239223\pi$
$224$	1890.79	+	2103.49i	0.563989	+	0.627435i
$225$		0			0
$226$	−349.493	−	2369.53i	−0.102867	−	0.697427i
$227$	−3747.56			−1.09575			−0.547873	−	0.836561i	$-0.684562\pi$
$227$	−3747.56			−1.09575			−0.547873	+	0.836561i	$0.684562\pi$
$228$	−1509.74	−	5006.60i	−0.438531	−	1.45426i
$229$			2061.75i			0.594954i	0.954729	+	0.297477i	$0.0961451\pi$
$229$			2061.75i			0.594954i	−0.954729	+	0.297477i	$0.903855\pi$
$230$		0			0
$231$	−5621.09			−1.60104
$232$	−2211.48	−	4705.80i	−0.625821	−	1.33168i
$233$			809.747i			0.227675i	0.993499	+	0.113837i	$0.0363143\pi$
$233$			809.747i			0.227675i	−0.993499	+	0.113837i	$0.963686\pi$
$234$	−4547.26	+	670.698i	−1.27036	+	0.187371i
$235$		0			0
$236$	253.926	+	842.070i	0.0700390	+	0.232263i
$237$	−3513.42			−0.962958
$238$	4856.45	−	716.303i	1.32268	−	0.195088i
$239$	−1159.14			−0.313717			−0.156858	−	0.987621i	$-0.550137\pi$
$239$	−1159.14			−0.313717			−0.156858	+	0.987621i	$0.550137\pi$
$240$		0			0
$241$	3732.40			0.997615			0.498807	−	0.866713i	$-0.333772\pi$
$241$	3732.40			0.997615			0.498807	+	0.866713i	$0.333772\pi$
$242$	−2394.86	+	353.229i	−0.636145	+	0.0938283i
$243$	−5401.59			−1.42598
$244$	417.447	+	1384.34i	0.109526	+	0.363209i
$245$		0			0
$246$	−65.8928	+	9.71887i	−0.0170779	+	0.00251891i
$247$			4290.59i			1.10528i
$248$	−6934.42	+	3258.81i	−1.77555	+	0.834414i
$249$	3842.06			0.977834
$250$		0			0
$251$			3609.63i			0.907719i	0.891073	+	0.453860i	$0.149953\pi$
$251$			3609.63i			0.907719i	−0.891073	+	0.453860i	$0.850047\pi$
$252$	1161.40	+	3851.42i	0.290322	+	0.962766i
$253$	−2490.44			−0.618864
$254$	−27.0981	−	183.722i	−0.00669405	−	0.0453849i
$255$		0			0
$256$	1592.35	−	3773.81i	0.388757	−	0.921340i
$257$		−	2378.19i		−	0.577226i	−0.957446	−	0.288613i	$-0.906806\pi$
$257$		−	2378.19i		−	0.577226i	0.957446	−	0.288613i	$-0.0931941\pi$
$258$	2496.40	−	368.206i	0.602399	−	0.0888508i
$259$			1111.71i			0.266712i
$260$		0			0
$261$		−	7395.14i		−	1.75382i
$262$	−266.737	−	1808.45i	−0.0628973	−	0.426437i
$263$		−	3933.72i		−	0.922296i	−0.887323	−	0.461148i	$-0.847438\pi$
$263$		−	3933.72i		−	0.922296i	0.887323	−	0.461148i	$-0.152562\pi$
$264$	3462.27	+	7367.35i	0.807150	+	1.71753i
$265$		0			0
$266$	3714.85	−	547.922i	0.856286	−	0.126298i
$267$	−10011.1			−2.29464
$268$	5789.27	−	1745.76i	1.31954	−	0.397907i
$269$		−	3629.38i		−	0.822628i	−0.911494	−	0.411314i	$-0.865070\pi$
$269$		−	3629.38i		−	0.822628i	0.911494	−	0.411314i	$-0.134930\pi$
$270$		0			0
$271$	4019.80			0.901054			0.450527	−	0.892763i	$-0.351236\pi$
$271$	4019.80			0.901054			0.450527	+	0.892763i	$0.351236\pi$
$272$	−3930.12	−	5923.96i	−0.876098	−	1.32056i
$273$		−	6069.74i		−	1.34563i
$274$	740.412	+	5019.91i	0.163248	+	1.10680i
$275$		0			0
$276$	946.261	+	3137.99i	0.206370	+	0.684365i
$277$	5566.24			1.20737			0.603687	−	0.797221i	$-0.293698\pi$
$277$	5566.24			1.20737			0.603687	+	0.797221i	$0.293698\pi$
$278$	0.569530	+	3.86135i	0.000122871	+	0.000833052i
$279$	−10897.4			−2.33839
$280$		0			0
$281$	−8293.84			−1.76074			−0.880372	−	0.474284i	$-0.842707\pi$
$281$	−8293.84			−1.76074			−0.880372	+	0.474284i	$0.842707\pi$
$282$	1822.50	+	12356.4i	0.384853	+	2.60926i
$283$	−2632.57			−0.552968			−0.276484	−	0.961018i	$-0.589169\pi$
$283$	−2632.57			−0.552968			−0.276484	+	0.961018i	$0.589169\pi$
$284$	979.023	−	295.225i	0.204557	−	0.0616843i
$285$		0			0
$286$	−974.589	−	6607.60i	−0.201499	−	1.36614i
$287$		−	47.8282i		−	0.00983696i
$288$	4332.56	−	3894.45i	0.886453	−	0.796816i
$289$	−7425.67			−1.51143
$290$		0			0
$291$			5986.93i			1.20605i
$292$	803.622	+	2664.97i	0.161056	+	0.534094i
$293$	569.395			0.113530			0.0567652	−	0.998388i	$-0.481921\pi$
$293$	569.395			0.113530			0.0567652	+	0.998388i	$0.481921\pi$
$294$	2128.23	−	313.904i	0.422181	−	0.0622696i
$295$		0			0
$296$	1457.08	−	684.751i	0.286118	−	0.134461i
$297$			1864.36i			0.364247i
$298$	−307.042	−	2081.71i	−0.0596862	−	0.404666i
$299$		−	2689.21i		−	0.520138i
$300$		0			0
$301$			1812.00i			0.346984i
$302$	6747.24	−	995.185i	1.28563	−	0.189624i
$303$			8824.79i			1.67317i
$304$	−3006.27	−	4531.42i	−0.567176	−	0.854917i
$305$		0			0
$306$	−1475.37	−	10002.8i	−0.275625	−	1.86871i
$307$	527.093			0.0979895			0.0489947	−	0.998799i	$-0.484398\pi$
$307$	527.093			0.0979895			0.0489947	+	0.998799i	$0.484398\pi$
$308$	−5596.49	+	1687.62i	−1.03536	+	0.312212i
$309$			6557.76i			1.20731i
$310$		0			0
$311$	−6798.16			−1.23951			−0.619756	−	0.784795i	$-0.712768\pi$
$311$	−6798.16			−1.23951			−0.619756	+	0.784795i	$0.712768\pi$
$312$	−7955.37	+	3738.61i	−1.44354	+	0.678387i
$313$			9479.08i			1.71179i	0.517153	+	0.855893i	$0.326992\pi$
$313$			9479.08i			1.71179i	−0.517153	+	0.855893i	$0.673008\pi$
$314$	−4190.32	+	618.052i	−0.753101	+	0.111079i
$315$		0			0
$316$	−3498.04	+	1054.84i	−0.622722	+	0.187782i
$317$	−9286.72			−1.64541			−0.822704	−	0.568471i	$-0.807535\pi$
$317$	−9286.72			−1.64541			−0.822704	+	0.568471i	$0.807535\pi$
$318$	840.599	−	123.984i	0.148234	−	0.0218638i
$319$	10745.9			1.88606
$320$		0			0
$321$	−327.843			−0.0570044
$322$	−2328.36	+	343.421i	−0.402963	+	0.0594351i
$323$	−9438.23			−1.62587
$324$	−4306.24	+	1298.55i	−0.738382	+	0.222659i
$325$		0			0
$326$	8103.07	−	1195.16i	1.37665	−	0.203049i
$327$		−	11468.5i		−	1.93948i
$328$	−62.6865	+	29.4594i	−0.0105527	+	0.00495921i
$329$	−8968.84			−1.50294
$330$		0			0
$331$			559.492i			0.0929078i	0.998920	+	0.0464539i	$0.0147921\pi$
$331$			559.492i			0.0929078i	−0.998920	+	0.0464539i	$0.985208\pi$
$332$	3825.24	−	1153.50i	0.632342	−	0.190683i
$333$	2289.80			0.376817
$334$	793.811	+	5381.95i	0.130046	+	0.881698i
$335$		0			0
$336$	4252.86	+	6410.43i	0.690513	+	1.04083i
$337$		−	62.1362i		−	0.0100438i	−0.999987	−	0.00502192i	$-0.998401\pi$
$337$		−	62.1362i		−	0.0100438i	0.999987	−	0.00502192i	$-0.00159853\pi$
$338$	987.444	−	145.643i	0.158905	−	0.0234377i
$339$		−	6514.57i		−	1.04372i
$340$		0			0
$341$		−	15835.0i		−	2.51470i
$342$	−1128.55	−	7651.47i	−0.178436	−	1.20978i
$343$			6904.06i			1.08684i
$344$	2374.92	−	1116.09i	0.372230	−	0.174929i
$345$		0			0
$346$	982.198	−	144.869i	0.152611	−	0.0225093i
$347$	2384.20			0.368849			0.184424	−	0.982847i	$-0.440958\pi$
$347$	2384.20			0.368849			0.184424	+	0.982847i	$0.440958\pi$
$348$	−4082.97	−	13539.9i	−0.628937	−	2.08568i
$349$			7940.30i			1.21786i	0.793223	+	0.608932i	$0.208402\pi$
$349$			7940.30i			1.21786i	−0.793223	+	0.608932i	$0.791598\pi$
$350$		0			0
$351$	−2013.17			−0.306139
$352$	5659.01	+	6295.63i	0.856893	+	0.953290i
$353$			8718.60i			1.31457i	0.753641	+	0.657286i	$0.228296\pi$
$353$			8718.60i			1.31457i	−0.753641	+	0.657286i	$0.771704\pi$
$354$	349.062	+	2366.60i	0.0524080	+	0.355320i
$355$		0			0
$356$	−9967.27	+	3005.63i	−1.48389	+	0.447467i
$357$	13351.9			1.97943
$358$	−826.003	−	5600.21i	−0.121943	−	0.826761i
$359$	−5920.09			−0.870336			−0.435168	−	0.900349i	$-0.643311\pi$
$359$	−5920.09			−0.870336			−0.435168	+	0.900349i	$0.643311\pi$
$360$		0			0
$361$	−360.591			−0.0525719
$362$	−1771.93	−	12013.5i	−0.257267	−	1.74424i
$363$	−6584.21			−0.952015
$364$	−1822.32	−	6043.17i	−0.262405	−	0.870188i
$365$		0			0
$366$	573.846	+	3890.61i	0.0819547	+	0.555643i
$367$		−	8779.02i		−	1.24867i	−0.781158	−	0.624334i	$-0.785371\pi$
$367$		−	8779.02i		−	1.24867i	0.781158	−	0.624334i	$-0.214629\pi$
$368$	1884.24	+	2840.16i	0.266910	+	0.402319i
$369$	−98.5117			−0.0138979
$370$		0			0
$371$			610.147i			0.0853834i
$372$	−19952.3	+	6016.63i	−2.78086	+	0.838569i
$373$	10346.8			1.43629			0.718145	−	0.695893i	$-0.244991\pi$
$373$	10346.8			1.43629			0.718145	+	0.695893i	$0.244991\pi$
$374$	14535.1	−	2143.85i	2.00960	−	0.296406i
$375$		0			0
$376$	5524.28	+	11755.1i	0.757694	+	1.61230i
$377$			11603.5i			1.58518i
$378$	257.088	+	1743.03i	0.0349819	+	0.237174i
$379$		−	5650.98i		−	0.765888i	−0.923772	−	0.382944i	$-0.874910\pi$
$379$		−	5650.98i		−	0.765888i	0.923772	−	0.382944i	$-0.125090\pi$
$380$		0			0
$381$		−	505.110i		−	0.0679202i
$382$	1239.43	−	182.810i	0.166008	−	0.0244853i
$383$		−	4349.97i		−	0.580348i	−0.956974	−	0.290174i	$-0.906287\pi$
$383$		−	4349.97i		−	0.580348i	0.956974	−	0.290174i	$-0.0937132\pi$
$384$	5782.39	−	9522.51i	0.768441	−	1.26548i
$385$		0			0
$386$	1173.77	+	7958.02i	0.154775	+	1.04936i
$387$	3732.18			0.490226
$388$	1797.46	+	5960.72i	0.235186	+	0.779922i
$389$		−	3876.59i		−	0.505273i	−0.967561	−	0.252636i	$-0.918702\pi$
$389$		−	3876.59i		−	0.505273i	0.967561	−	0.252636i	$-0.0812976\pi$
$390$		0			0
$391$	5915.60			0.765127
$392$	2024.68	−	951.491i	0.260871	−	0.122596i
$393$		−	4972.00i		−	0.638178i
$394$	12513.5	−	1845.68i	1.60005	−	0.236000i
$395$		0			0
$396$	3476.00	+	11527.1i	0.441100	+	1.46277i
$397$	10301.1			1.30226			0.651130	−	0.758966i	$-0.274295\pi$
$397$	10301.1			1.30226			0.651130	+	0.758966i	$0.274295\pi$
$398$	3868.26	−	570.549i	0.487182	−	0.0718569i
$399$	10213.3			1.28146
$400$		0			0
$401$	−7296.55			−0.908660			−0.454330	−	0.890834i	$-0.650121\pi$
$401$	−7296.55			−0.908660			−0.454330	+	0.890834i	$0.650121\pi$
$402$	16270.5	−	2399.81i	2.01865	−	0.297741i
$403$	17098.9			2.11354
$404$	2649.47	+	8786.16i	0.326277	+	1.08200i
$405$		0			0
$406$	10046.5	−	1481.81i	1.22808	−	0.181135i
$407$			3327.29i			0.405228i
$408$	−8224.00	−	17499.8i	−0.997913	−	2.12346i
$409$	4045.02			0.489031			0.244515	−	0.969645i	$-0.421371\pi$
$409$	4045.02			0.489031			0.244515	+	0.969645i	$0.421371\pi$
$410$		0			0
$411$			13801.3i			1.65637i
$412$	1968.84	+	6529.06i	0.235432	+	0.780737i
$413$	−1717.79			−0.204666
$414$	707.344	+	4795.71i	0.0839712	+	0.569315i
$415$		0			0
$416$	−6798.11	+	6110.69i	−0.801214	+	0.720195i
$417$			10.6161i			0.00124669i
$418$	11118.3	−	1639.90i	1.30099	−	0.191890i
$419$			10923.6i			1.27363i	0.771016	+	0.636815i	$0.219749\pi$
$419$			10923.6i			1.27363i	−0.771016	+	0.636815i	$0.780251\pi$
$420$		0			0
$421$		−	14877.4i		−	1.72228i	−0.508368	−	0.861140i	$-0.669751\pi$
$421$		−	14877.4i		−	1.72228i	0.508368	−	0.861140i	$-0.330249\pi$
$422$	144.555	+	980.069i	0.0166750	+	0.113054i
$423$			18473.1i			2.12339i
$424$	799.696	−	375.815i	0.0915959	−	0.0430452i
$425$		0			0
$426$	2751.50	−	405.832i	0.312936	−	0.0461564i
$427$	−2823.99			−0.320053
$428$	−326.408	+	98.4285i	−0.0368634	+	0.0111162i
$429$		−	18166.4i		−	2.04448i
$430$		0			0
$431$	9899.13			1.10632			0.553161	−	0.833075i	$-0.313422\pi$
$431$	9899.13			1.10632			0.553161	+	0.833075i	$0.313422\pi$
$432$	2126.17	−	1410.56i	0.236795	−	0.157096i
$433$		−	4671.88i		−	0.518513i	−0.965808	−	0.259257i	$-0.916522\pi$
$433$		−	4671.88i		−	0.518513i	0.965808	−	0.259257i	$-0.0834775\pi$
$434$	−2183.58	−	14804.4i	−0.241509	−	1.63741i
$435$		0			0
$436$	−3443.20	−	11418.3i	−0.378210	−	1.25422i
$437$	4525.02			0.495334
$438$	1104.70	+	7489.77i	0.120513	+	0.817066i
$439$	1304.49			0.141823			0.0709113	−	0.997483i	$-0.477409\pi$
$439$	1304.49			0.141823			0.0709113	+	0.997483i	$0.477409\pi$
$440$		0			0
$441$	3181.77			0.343567
$442$	2314.96	+	15695.2i	0.249121	+	1.68901i
$443$	−8613.52			−0.923794			−0.461897	−	0.886934i	$-0.652831\pi$
$443$	−8613.52			−0.923794			−0.461897	+	0.886934i	$0.652831\pi$
$444$	4192.44	−	1264.23i	0.448118	−	0.135130i
$445$		0			0
$446$	−1876.76	−	12724.2i	−0.199253	−	1.35091i
$447$		−	5723.28i		−	0.605597i
$448$	6158.85	+	5105.54i	0.649505	+	0.538424i
$449$	−16155.3			−1.69803			−0.849016	−	0.528367i	$-0.822805\pi$
$449$	−16155.3			−1.69803			−0.849016	+	0.528367i	$0.822805\pi$
$450$		0			0
$451$		−	143.147i		−	0.0149457i
$452$	−1955.87	−	6486.06i	−0.203532	−	0.674952i
$453$	18550.3			1.92399
$454$	−10486.3	+	1546.67i	−1.08402	+	0.159887i
$455$		0			0
$456$	−6290.79	−	13386.2i	−0.646038	−	1.37470i
$457$			1325.32i			0.135659i	0.997697	+	0.0678293i	$0.0216073\pi$
$457$			1325.32i			0.135659i	−0.997697	+	0.0678293i	$0.978393\pi$
$458$	850.914	+	5769.10i	0.0868135	+	0.588586i
$459$		−	4428.47i		−	0.450334i
$460$		0			0
$461$			4357.31i			0.440217i	0.975475	+	0.220109i	$0.0706412\pi$
$461$			4357.31i			0.440217i	−0.975475	+	0.220109i	$0.929359\pi$
$462$	−15728.7	+	2319.90i	−1.58391	+	0.233618i
$463$		−	12348.5i		−	1.23949i	−0.784805	−	0.619743i	$-0.787237\pi$
$463$		−	12348.5i		−	1.23949i	0.784805	−	0.619743i	$-0.212763\pi$
$464$	−8130.20	−	12254.8i	−0.813438	−	1.22611i
$465$		0			0
$466$	334.194	+	2265.80i	0.0332215	+	0.225238i
$467$	−11587.9			−1.14823			−0.574113	−	0.818776i	$-0.694653\pi$
$467$	−11587.9			−1.14823			−0.574113	+	0.818776i	$0.694653\pi$
$468$	−12447.1	+	3753.43i	−1.22942	+	0.370732i
$469$			11809.9i			1.16275i
$470$		0			0
$471$	−11520.5			−1.12704
$472$	1058.06	+	2251.44i	0.103180	+	0.219557i
$473$			5423.22i			0.527188i
$474$	−9831.09	+	1450.04i	−0.952651	+	0.140511i
$475$		0			0
$476$	13293.5	−	4008.65i	1.28005	−	0.386000i
$477$	1256.72			0.120631
$478$	−3243.44	+	478.392i	−0.310359	+	0.0457764i
$479$	−7554.03			−0.720568			−0.360284	−	0.932843i	$-0.617320\pi$
$479$	−7554.03			−0.720568			−0.360284	+	0.932843i	$0.617320\pi$
$480$		0			0
$481$	−3592.86			−0.340583
$482$	10443.8	−	1540.41i	0.986937	−	0.145568i
$483$	−6401.38			−0.603049
$484$	−6555.39	+	1976.78i	−0.615646	+	0.185648i
$485$		0			0
$486$	−15114.5	+	2229.31i	−1.41071	+	0.208073i
$487$			1536.22i			0.142942i	0.997443	+	0.0714710i	$0.0227693\pi$
$487$			1536.22i			0.142942i	−0.997443	+	0.0714710i	$0.977231\pi$
$488$	1739.41	+	3701.30i	0.161352	+	0.343340i
$489$	22277.9			2.06021
$490$		0			0
$491$			1242.72i			0.114223i	0.998368	+	0.0571113i	$0.0181890\pi$
$491$			1242.72i			0.114223i	−0.998368	+	0.0571113i	$0.981811\pi$
$492$	−180.367	+	54.3898i	−0.0165276	+	0.00498390i
$493$	−25524.9			−2.33181
$494$	1770.79	+	12005.7i	0.161278	+	1.09345i
$495$		0			0
$496$	−18058.6	+	11980.6i	−1.63479	+	1.08457i
$497$			1997.17i			0.180252i
$498$	10750.7	−	1585.67i	0.967368	−	0.142682i
$499$		−	17543.4i		−	1.57385i	−0.617049	−	0.786925i	$-0.711672\pi$
$499$		−	17543.4i		−	1.57385i	0.617049	−	0.786925i	$-0.288328\pi$
$500$		0			0
$501$			14796.7i			1.31949i
$502$	1489.74	+	10100.3i	0.132451	+	0.898004i
$503$		−	3452.08i		−	0.306005i	−0.988226	−	0.153002i	$-0.951106\pi$
$503$		−	3452.08i		−	0.306005i	0.988226	−	0.153002i	$-0.0488942\pi$
$504$	4839.31	+	10297.6i	0.427698	+	0.910098i
$505$		0			0
$506$	−6968.63	+	1027.84i	−0.612240	+	0.0903024i
$507$	2714.79			0.237807
$508$	−151.650	−	502.900i	−0.0132448	−	0.0439224i
$509$		−	2687.40i		−	0.234021i	−0.993131	−	0.117011i	$-0.962669\pi$
$509$		−	2687.40i		−	0.234021i	0.993131	−	0.117011i	$-0.0373311\pi$
$510$		0			0
$511$	−5436.43			−0.470633
$512$	2898.14	−	11216.9i	0.250158	−	0.968205i
$513$		−	3387.47i		−	0.291541i
$514$	−981.510	−	6654.53i	−0.0842268	−	0.571048i
$515$		0			0
$516$	6833.34	−	2060.59i	0.582986	−	0.175800i
$517$	−26843.2			−2.28349
$518$	458.819	+	3110.74i	0.0389177	+	0.263858i
$519$	2700.37			0.228387
$520$		0			0
$521$	−1131.78			−0.0951711			−0.0475855	−	0.998867i	$-0.515153\pi$
$521$	−1131.78			−0.0951711			−0.0475855	+	0.998867i	$0.515153\pi$
$522$	−3052.08	−	20692.8i	−0.255912	−	1.73505i
$523$	−1002.24			−0.0837952			−0.0418976	−	0.999122i	$-0.513340\pi$
$523$	−1002.24			−0.0837952			−0.0418976	+	0.999122i	$0.513340\pi$
$524$	−1492.74	−	4950.23i	−0.124448	−	0.412695i
$525$		0			0
$526$	−1623.50	−	11007.2i	−0.134578	−	0.912424i
$527$			37613.2i			3.10903i
$528$	12728.6	+	19186.1i	1.04913	+	1.58137i
$529$	9330.85			0.766898
$530$		0			0
$531$			3538.13i			0.289156i
$532$	10168.6	−	3066.34i	0.828692	−	0.249892i
$533$	154.572			0.0125615
$534$	−28012.6	+	4131.71i	−2.27008	+	0.334825i
$535$		0			0
$536$	15478.8	−	7274.20i	1.24735	−	0.586190i
$537$		−	15396.7i		−	1.23728i
$538$	−1497.89	−	10155.6i	−0.120035	−	0.813824i
$539$			4623.42i			0.369471i
$540$		0			0
$541$			6785.77i			0.539266i	0.962963	+	0.269633i	$0.0869024\pi$
$541$			6785.77i			0.539266i	−0.962963	+	0.269633i	$0.913098\pi$
$542$	11248.0	−	1659.03i	0.891410	−	0.131479i
$543$		−	33028.8i		−	2.61032i
$544$	−13442.0	−	14954.1i	−1.05941	−	1.17859i
$545$		0			0
$546$	−2505.07	−	16984.1i	−0.196350	−	1.33123i
$547$	−1675.49			−0.130967			−0.0654833	−	0.997854i	$-0.520859\pi$
$547$	−1675.49			−0.130967			−0.0654833	+	0.997854i	$0.520859\pi$
$548$	4143.57	+	13740.9i	0.323001	+	1.07114i
$549$			5816.58i			0.452177i
$550$		0			0
$551$	−19524.8			−1.50959
$552$	3942.88	+	8390.04i	0.304022	+	0.646927i
$553$		−	7135.87i		−	0.548731i
$554$	15575.2	−	2297.26i	1.19445	−	0.176176i
$555$		0			0
$556$	3.18727	+	10.5696i	0.000243112	+	0.000806207i
$557$	−6407.34			−0.487411			−0.243705	−	0.969849i	$-0.578363\pi$
$557$	−6407.34			−0.487411			−0.243705	+	0.969849i	$0.578363\pi$
$558$	−30492.6	+	4497.51i	−2.31336	+	0.341210i
$559$	−5856.08			−0.443087
$560$		0			0
$561$	39961.5			3.00744
$562$	−23207.4	+	3422.98i	−1.74190	+	0.256921i
$563$	5627.44			0.421258			0.210629	−	0.977566i	$-0.432449\pi$
$563$	5627.44			0.421258			0.210629	+	0.977566i	$0.432449\pi$
$564$	10199.3	+	33822.8i	0.761467	+	2.52517i
$565$		0			0
$566$	−7366.33	+	1086.50i	−0.547050	+	0.0806871i
$567$		−	8784.57i		−	0.650648i
$568$	2617.61	−	1230.14i	0.193367	−	0.0908724i
$569$	−8395.02			−0.618520			−0.309260	−	0.950978i	$-0.600081\pi$
$569$	−8395.02			−0.618520			−0.309260	+	0.950978i	$0.600081\pi$
$570$		0			0
$571$		−	2784.73i		−	0.204093i	−0.994780	−	0.102047i	$-0.967461\pi$
$571$		−	2784.73i		−	0.204093i	0.994780	−	0.102047i	$-0.0325391\pi$
$572$	−5454.10	−	18086.9i	−0.398684	−	1.32212i
$573$	3407.59			0.248437
$574$	−19.7394	−	133.831i	−0.00143537	−	0.00973167i
$575$		0			0
$576$	10515.9	−	12685.4i	0.760697	−	0.917635i
$577$		−	19751.5i		−	1.42507i	−0.701635	−	0.712537i	$-0.747546\pi$
$577$		−	19751.5i		−	1.42507i	0.701635	−	0.712537i	$-0.252454\pi$
$578$	−20778.2	+	3064.68i	−1.49526	+	0.220543i
$579$			21879.1i			1.57041i
$580$		0			0
$581$			7803.35i			0.557208i
$582$	2470.89	+	16752.3i	0.175982	+	1.19314i
$583$			1826.13i			0.129727i
$584$	3348.53	+	7125.32i	0.237265	+	0.504877i
$585$		0			0
$586$	1593.26	−	234.997i	0.112315	−	0.0165660i
$587$	−8029.42			−0.564582			−0.282291	−	0.959329i	$-0.591094\pi$
$587$	−8029.42			−0.564582			−0.282291	+	0.959329i	$0.591094\pi$
$588$	5825.57	−	1756.70i	0.408576	−	0.123206i
$589$			28771.5i			2.01275i
$590$		0			0
$591$	34403.5			2.39454
$592$	3794.53	−	2517.39i	0.263436	−	0.174771i
$593$		−	18749.1i		−	1.29837i	−0.760629	−	0.649186i	$-0.775110\pi$
$593$		−	18749.1i		−	1.29837i	0.760629	−	0.649186i	$-0.224890\pi$
$594$	769.449	+	5216.78i	0.0531496	+	0.360348i
$595$		0			0
$596$	−1718.30	−	5698.23i	−0.118095	−	0.391625i
$597$	10635.1			0.729085
$598$	−1109.88	−	7524.83i	−0.0758966	−	0.514571i
$599$	2130.81			0.145346			0.0726732	−	0.997356i	$-0.476847\pi$
$599$	2130.81			0.145346			0.0726732	+	0.997356i	$0.476847\pi$
$600$		0			0
$601$	14697.1			0.997517			0.498759	−	0.866741i	$-0.333789\pi$
$601$	14697.1			0.997517			0.498759	+	0.866741i	$0.333789\pi$
$602$	747.839	+	5070.27i	0.0506306	+	0.343270i
$603$	24324.8			1.64276
$604$	18469.1	−	5569.36i	1.24420	−	0.375189i
$605$		0			0
$606$	3642.11	+	24693.1i	0.244143	+	1.65526i
$607$			5643.07i			0.377340i	0.982041	+	0.188670i	$0.0604176\pi$
$607$			5643.07i			0.377340i	−0.982041	+	0.188670i	$0.939582\pi$
$608$	−10282.2	−	11438.9i	−0.685852	−	0.763007i
$609$	27620.9			1.83786
$610$		0			0
$611$		−	28985.7i		−	1.91921i
$612$	−8256.62	−	27380.6i	−0.545350	−	1.80849i
$613$	−11519.3			−0.758988			−0.379494	−	0.925194i	$-0.623902\pi$
$613$	−11519.3			−0.758988			−0.379494	+	0.925194i	$0.623902\pi$
$614$	1474.89	−	217.538i	0.0969407	−	0.0142983i
$615$		0			0
$616$	−14963.3	+	7031.98i	−0.978717	+	0.459946i
$617$			1610.86i			0.105107i	0.998618	+	0.0525534i	$0.0167360\pi$
$617$			1610.86i			0.105107i	−0.998618	+	0.0525534i	$0.983264\pi$
$618$	2706.48	+	18349.6i	0.176166	+	1.19439i
$619$			17227.9i			1.11866i	0.828946	+	0.559328i	$0.188941\pi$
$619$			17227.9i			1.11866i	−0.828946	+	0.559328i	$0.811059\pi$
$620$		0			0
$621$			2123.16i			0.137197i
$622$	−19022.3	+	2805.69i	−1.22625	+	0.180865i
$623$		−	20332.9i		−	1.30757i
$624$	−20717.4	+	13744.5i	−1.32910	+	0.881763i
$625$		0			0
$626$	3912.15	+	26523.9i	0.249778	+	1.69346i
$627$	30567.8			1.94698
$628$	−11470.1	+	3458.81i	−0.728832	+	0.219780i
$629$		−	7903.40i		−	0.501000i
$630$		0			0
$631$	22325.0			1.40847			0.704236	−	0.709966i	$-0.251290\pi$
$631$	22325.0			1.40847			0.704236	+	0.709966i	$0.251290\pi$
$632$	−9352.71	+	4395.28i	−0.588657	+	0.276638i
$633$			2694.52i			0.169190i
$634$	−25985.7	+	3832.76i	−1.62780	+	0.240092i
$635$		0			0
$636$	2300.95	−	693.853i	0.143457	−	0.0432596i
$637$	−4992.44			−0.310530
$638$	30068.6	−	4434.96i	1.86587	−	0.275207i
$639$	4113.57			0.254664
$640$		0			0
$641$	−17545.4			−1.08113			−0.540564	−	0.841303i	$-0.681789\pi$
$641$	−17545.4			−1.08113			−0.540564	+	0.841303i	$0.681789\pi$
$642$	−917.355	+	135.305i	−0.0563943	+	0.00831788i
$643$	−17840.2			−1.09417			−0.547083	−	0.837078i	$-0.684262\pi$
$643$	−17840.2			−1.09417			−0.547083	+	0.837078i	$0.684262\pi$
$644$	−6373.36	+	1921.89i	−0.389978	+	0.117598i
$645$		0			0
$646$	−26409.6	+	3895.29i	−1.60847	+	0.237242i
$647$		−	3785.71i		−	0.230033i	−0.993364	−	0.115017i	$-0.963308\pi$
$647$		−	3785.71i		−	0.230033i	0.993364	−	0.115017i	$-0.0366921\pi$
$648$	−11513.6	+	5410.78i	−0.697989	+	0.328018i
$649$	−5141.25			−0.310958
$650$		0			0
$651$		−	40702.0i		−	2.45044i
$652$	22180.4	−	6688.50i	1.33229	−	0.401751i
$653$	17813.4			1.06752			0.533761	−	0.845636i	$-0.320778\pi$
$653$	17813.4			1.06752			0.533761	+	0.845636i	$0.320778\pi$
$654$	−4733.22	−	32090.7i	−0.283003	−	1.91873i
$655$		0			0
$656$	−163.248	+	108.303i	−0.00971612	+	0.00644594i
$657$			11197.4i			0.664921i
$658$	−25096.2	+	3701.56i	−1.48686	+	0.219304i
$659$			5929.18i			0.350483i	0.984525	+	0.175241i	$0.0560706\pi$
$659$			5929.18i			0.350483i	−0.984525	+	0.175241i	$0.943929\pi$
$660$		0			0
$661$			13203.3i			0.776927i	0.921464	+	0.388464i	$0.126994\pi$
$661$			13203.3i			0.776927i	−0.921464	+	0.388464i	$0.873006\pi$
$662$	230.910	+	1565.55i	0.0135568	+	0.0919134i
$663$			43151.0i			2.52767i
$664$	10227.6	−	4806.41i	0.597750	−	0.280911i
$665$		0			0
$666$	6407.20	−	945.031i	0.372784	−	0.0549838i
$667$	12237.5			0.710404
$668$	4442.41	+	14731.9i	0.257308	+	0.853285i
$669$		−	34982.8i		−	2.02169i
$670$		0			0
$671$	−8452.04			−0.486270
$672$	14545.8	+	16182.2i	0.834996	+	0.928929i
$673$			12240.5i			0.701094i	0.936545	+	0.350547i	$0.114004\pi$
$673$			12240.5i			0.701094i	−0.936545	+	0.350547i	$0.885996\pi$
$674$	−25.6445	−	173.867i	−0.00146556	−	0.00993633i
$675$		0			0
$676$	2702.91	−	815.064i	0.153784	−	0.0463737i
$677$	3035.77			0.172340			0.0861701	−	0.996280i	$-0.472537\pi$
$677$	3035.77			0.172340			0.0861701	+	0.996280i	$0.472537\pi$
$678$	−2688.65	−	18228.8i	−0.152297	−	1.03255i
$679$	−12159.7			−0.687253
$680$		0			0
$681$	−28830.0			−1.62227
$682$	−6535.32	−	44308.7i	−0.366936	−	2.48779i
$683$	18824.7			1.05462			0.527311	−	0.849673i	$-0.323200\pi$
$683$	18824.7			1.05462			0.527311	+	0.849673i	$0.323200\pi$
$684$	−6315.74	−	20944.2i	−0.353053	−	1.17079i
$685$		0			0
$686$	2849.40	+	19318.6i	0.158587	+	1.07520i
$687$			15861.1i			0.880841i
$688$	6184.78	−	4103.15i	0.342722	−	0.227371i
$689$	−1971.89			−0.109032
$690$		0			0
$691$			22287.6i			1.22700i	0.789694	+	0.613502i	$0.210240\pi$
$691$			22287.6i			1.22700i	−0.789694	+	0.613502i	$0.789760\pi$
$692$	2688.55	−	810.733i	0.147693	−	0.0445368i
$693$	−23514.8			−1.28897
$694$	6671.36	−	983.992i	0.364901	−	0.0538211i
$695$		0			0
$696$	−17012.9	−	36201.7i	−0.926541	−	1.97158i
$697$			340.020i			0.0184780i
$698$	3277.07	+	22218.2i	0.177706	+	1.20483i
$699$			6229.38i			0.337077i
$700$		0			0
$701$		−	12975.8i		−	0.699129i	−0.936912	−	0.349565i	$-0.886330\pi$
$701$		−	12975.8i		−	0.699129i	0.936912	−	0.349565i	$-0.113670\pi$
$702$	−5633.15	+	830.862i	−0.302863	+	0.0446708i
$703$		−	6045.55i		−	0.324342i
$704$	18433.1	+	15280.6i	0.986823	+	0.818052i
$705$		0			0
$706$	3598.29	+	24396.0i	0.191818	+	1.30050i
$707$	−17923.4			−0.953438
$708$	1953.46	+	6478.05i	0.103694	+	0.343870i
$709$		−	10236.0i		−	0.542200i	−0.962551	−	0.271100i	$-0.912613\pi$
$709$		−	10236.0i		−	0.542200i	0.962551	−	0.271100i	$-0.0873874\pi$
$710$		0			0
$711$	−14697.8			−0.775259
$712$	−26649.5	+	12523.9i	−1.40271	+	0.659201i
$713$		−	18033.1i		−	0.947189i
$714$	37360.7	−	5510.52i	1.95825	−	0.288832i
$715$		0			0
$716$	−4622.57	−	15329.4i	−0.241276	−	0.800118i
$717$	−8917.24			−0.464464
$718$	−16565.3	+	2443.30i	−0.861021	+	0.126996i
$719$	17107.9			0.887367			0.443684	−	0.896184i	$-0.353671\pi$
$719$	17107.9			0.887367			0.443684	+	0.896184i	$0.353671\pi$
$720$		0			0
$721$	−13319.0			−0.687971
$722$	−1008.99	+	148.821i	−0.0520092	+	0.00767110i
$723$	28713.4			1.47699
$724$	−9916.26	−	32884.3i	−0.509026	−	1.68803i
$725$		0			0
$726$	−18423.6	+	2717.40i	−0.941825	+	0.138915i
$727$		−	29399.2i		−	1.49980i	−0.661549	−	0.749902i	$-0.730101\pi$
$727$		−	29399.2i		−	1.49980i	0.661549	−	0.749902i	$-0.269899\pi$
$728$	−7593.24	−	16157.6i	−0.386571	−	0.822585i
$729$	−26374.5			−1.33996
$730$		0			0
$731$		−	12881.9i		−	0.651785i
$732$	3211.42	+	10649.7i	0.162155	+	0.537738i
$733$	−17312.7			−0.872386			−0.436193	−	0.899853i	$-0.643673\pi$
$733$	−17312.7			−0.872386			−0.436193	+	0.899853i	$0.643673\pi$
$734$	−3623.22	−	24565.0i	−0.182201	−	1.23530i
$735$		0			0
$736$	6444.57	+	7169.55i	0.322758	+	0.359067i
$737$			35346.3i			1.76662i
$738$	−275.651	+	40.6571i	−0.0137491	+	0.00202793i
$739$		−	20459.6i		−	1.01843i	−0.860639	−	0.509215i	$-0.829936\pi$
$739$		−	20459.6i		−	1.01843i	0.860639	−	0.509215i	$-0.170064\pi$
$740$		0			0
$741$			33007.5i			1.63639i
$742$	251.816	+	1707.28i	0.0124588	+	0.0844695i
$743$			15382.4i			0.759524i	0.925084	+	0.379762i	$0.123994\pi$
$743$			15382.4i			0.759524i	−0.925084	+	0.379762i	$0.876006\pi$
$744$	−53346.5	+	25070.0i	−2.62873	+	1.23537i
$745$		0			0
$746$	28951.9	−	4270.26i	1.42092	−	0.209578i
$747$	16072.6			0.787235
$748$	39786.6	−	11997.7i	1.94484	−	0.586468i
$749$		−	665.860i		−	0.0324833i
$750$		0			0
$751$	−16396.7			−0.796705			−0.398352	−	0.917232i	$-0.630418\pi$
$751$	−16396.7			−0.796705			−0.398352	+	0.917232i	$0.630418\pi$
$752$	20309.3	+	30612.7i	0.984845	+	1.48448i
$753$			27768.9i			1.34390i
$754$	4788.94	+	32468.5i	0.231304	+	1.56821i
$755$		0			0
$756$	1438.74	+	4771.15i	0.0692150	+	0.229531i
$757$	−30322.2			−1.45585			−0.727924	−	0.685657i	$-0.759515\pi$
$757$	−30322.2			−1.45585			−0.727924	+	0.685657i	$0.759515\pi$
$758$	−2332.24	−	15812.3i	−0.111756	−	0.757691i
$759$	−19159.0			−0.916240
$760$		0			0
$761$	29611.4			1.41053			0.705264	−	0.708944i	$-0.250828\pi$
$761$	29611.4			1.41053			0.705264	+	0.708944i	$0.250828\pi$
$762$	−208.466	−	1413.38i	−0.00991067	−	0.0671932i
$763$	23293.0			1.10519
$764$	3392.68	−	1023.06i	0.160658	−	0.0484465i
$765$		0			0
$766$	−1795.29	−	12171.9i	−0.0846823	−	0.574136i
$767$		−	5551.60i		−	0.261351i
$768$	12250.0	−	29031.9i	0.575563	−	1.36406i
$769$	−18385.0			−0.862131			−0.431066	−	0.902321i	$-0.641862\pi$
$769$	−18385.0			−0.862131			−0.431066	+	0.902321i	$0.641862\pi$
$770$		0			0
$771$		−	18295.4i		−	0.854594i
$772$	6568.77	+	21783.3i	0.306238	+	1.01554i
$773$	−16712.1			−0.777609			−0.388804	−	0.921320i	$-0.627112\pi$
$773$	−16712.1			−0.777609			−0.388804	+	0.921320i	$0.627112\pi$
$774$	10443.2	−	1540.32i	0.484979	−	0.0715321i
$775$		0			0
$776$	7489.64	+	15937.2i	0.346472	+	0.737257i
$777$			8552.41i			0.394873i
$778$	−1599.92	−	10847.3i	−0.0737276	−	0.499865i
$779$			260.092i			0.0119625i
$780$		0			0
$781$			5977.41i			0.273865i
$782$	16552.8	−	2441.45i	0.756938	−	0.111645i
$783$		−	9161.12i		−	0.418125i
$784$	5272.66	−	3498.03i	0.240190	−	0.159349i
$785$		0			0
$786$	−2052.01	−	13912.4i	−0.0931207	−	0.631348i
$787$	33805.6			1.53118			0.765591	−	0.643328i	$-0.222447\pi$
$787$	33805.6			1.53118			0.765591	+	0.643328i	$0.222447\pi$
$788$	34252.9	−	10329.0i	1.54849	−	0.466947i
$789$		−	30262.1i		−	1.36548i
$790$		0			0
$791$	13231.3			0.594755
$792$	14483.8	+	30820.0i	0.649821	+	1.38275i
$793$		−	9126.64i		−	0.408697i
$794$	28824.1	−	4251.41i	1.28832	−	0.190021i
$795$		0			0
$796$	10588.5	−	3192.97i	0.471482	−	0.142176i
$797$	8399.83			0.373321			0.186661	−	0.982424i	$-0.440234\pi$
$797$	8399.83			0.373321			0.186661	+	0.982424i	$0.440234\pi$
$798$	28578.3	−	4215.16i	1.26775	−	0.186986i
$799$	63761.3			2.82317
$800$		0			0
$801$	−41879.6			−1.84737
$802$	−20416.9	+	3011.39i	−0.898934	+	0.132588i
$803$	−16270.9			−0.715054
$804$	44536.9	−	13430.1i	1.95360	−	0.589108i
$805$		0			0
$806$	47845.2	−	7056.94i	2.09091	−	0.308400i
$807$		−	27920.8i		−	1.21792i
$808$	11039.8	+	23491.6i	0.480667	+	1.02281i
$809$	12503.9			0.543402			0.271701	−	0.962382i	$-0.412414\pi$
$809$	12503.9			0.543402			0.271701	+	0.962382i	$0.412414\pi$
$810$		0			0
$811$			31097.9i			1.34648i	0.739425	+	0.673239i	$0.235098\pi$
$811$			31097.9i			1.34648i	−0.739425	+	0.673239i	$0.764902\pi$
$812$	27500.1	−	8292.65i	1.18850	−	0.358393i
$813$	30924.3			1.33403
$814$	1373.22	+	9310.28i	0.0591294	+	0.400891i
$815$		0			0
$816$	−30234.4	−	45573.1i	−1.29708	−	1.95512i
$817$		−	9853.76i		−	0.421958i
$818$	11318.6	−	1669.44i	0.483797	−	0.0713576i
$819$		−	25391.7i		−	1.08334i
$820$		0			0
$821$			38043.1i			1.61719i	0.588367	+	0.808594i	$0.299771\pi$
$821$			38043.1i			1.61719i	−0.588367	+	0.808594i	$0.700229\pi$
$822$	5695.99	+	38618.2i	0.241692	+	1.63864i
$823$			39096.4i			1.65591i	0.560794	+	0.827955i	$0.310496\pi$
$823$			39096.4i			1.65591i	−0.560794	+	0.827955i	$0.689504\pi$
$824$	8203.75	+	17456.8i	0.346834	+	0.738028i
$825$		0			0
$826$	−4806.64	+	708.956i	−0.202475	+	0.0298641i
$827$	24525.7			1.03125			0.515625	−	0.856815i	$-0.327560\pi$
$827$	24525.7			1.03125			0.515625	+	0.856815i	$0.327560\pi$
$828$	3958.52	+	13127.2i	0.166145	+	0.550969i
$829$			22818.8i			0.956007i	0.878358	+	0.478004i	$0.158639\pi$
$829$			22818.8i			0.956007i	−0.878358	+	0.478004i	$0.841361\pi$
$830$		0			0
$831$	42821.1			1.78754
$832$	−16500.2	+	19904.3i	−0.687550	+	0.829397i
$833$		−	10982.1i		−	0.456792i
$834$	4.38140	+	29.7054i	0.000181913	+	0.00123335i
$835$		0			0
$836$	30434.0	−	9177.38i	1.25907	−	0.379672i
$837$	−13499.7			−0.557490
$838$	4508.31	+	30565.8i	0.185844	+	1.26000i
$839$	−43262.8			−1.78021			−0.890107	−	0.455752i	$-0.849370\pi$
$839$	−43262.8			−1.78021			−0.890107	+	0.455752i	$0.849370\pi$
$840$		0			0
$841$	−28414.0			−1.16503
$842$	−6140.11	−	41629.2i	−0.251309	−	1.70385i
$843$	−63804.6			−2.60682
$844$	808.976	+	2682.72i	0.0329930	+	0.109411i
$845$		0			0
$846$	7624.11	+	51690.6i	0.309837	+	2.10066i
$847$		−	13372.8i		−	0.542495i
$848$	2082.57	−	1381.63i	0.0843345	−	0.0559499i
$849$	−20252.4			−0.818680
$850$		0			0
$851$			3789.17i			0.152633i
$852$	7531.62	−	2271.16i	0.302851	−	0.0913249i
$853$	−36605.3			−1.46933			−0.734666	−	0.678429i	$-0.762661\pi$
$853$	−36605.3			−1.46933			−0.734666	+	0.678429i	$0.762661\pi$
$854$	−7901.96	+	1165.50i	−0.316627	+	0.0467009i
$855$		0			0
$856$	−872.717	+	410.131i	−0.0348468	+	0.0163762i
$857$		−	145.647i		−	0.00580539i	−0.999996	−	0.00290269i	$-0.999076\pi$
$857$		−	145.647i		−	0.00580539i	0.999996	−	0.00290269i	$-0.000923958\pi$
$858$	−7497.52	−	50832.3i	−0.298323	−	2.02260i
$859$		−	48187.2i		−	1.91400i	−0.290088	−	0.957000i	$-0.593685\pi$
$859$		−	48187.2i		−	1.91400i	0.290088	−	0.957000i	$-0.406315\pi$
$860$		0			0
$861$		−	367.942i		−	0.0145638i
$862$	27699.3	−	4085.51i	1.09448	−	0.161430i
$863$			13624.8i			0.537419i	0.963221	+	0.268710i	$0.0865972\pi$
$863$			13624.8i			0.537419i	−0.963221	+	0.268710i	$0.913403\pi$
$864$	5367.18	−	4824.46i	0.211337	−	0.189967i
$865$		0			0
$866$	−1928.15	−	13072.6i	−0.0756596	−	0.512964i
$867$	−57125.7			−2.23771
$868$	−12220.0	−	40523.8i	−0.477849	−	1.58464i
$869$		−	21357.3i		−	0.833711i
$870$		0			0
$871$	−38167.5			−1.48479
$872$	−14347.1	−	30529.2i	−0.557173	−	1.18561i
$873$			25045.2i			0.970965i
$874$	12661.7	−	1867.54i	0.490033	−	0.0722774i
$875$		0			0
$876$	6182.26	+	20501.6i	0.238447	+	0.790736i
$877$	−7517.05			−0.289433			−0.144716	−	0.989473i	$-0.546227\pi$
$877$	−7517.05			−0.289433			−0.144716	+	0.989473i	$0.546227\pi$
$878$	3650.18	−	538.383i	0.140305	−	0.0206943i
$879$	4380.36			0.168084
$880$		0			0
$881$	−28282.2			−1.08156			−0.540778	−	0.841165i	$-0.681870\pi$
$881$	−28282.2			−1.08156			−0.540778	+	0.841165i	$0.681870\pi$
$882$	8903.09	−	1313.16i	0.339889	−	0.0501320i
$883$	18051.5			0.687974			0.343987	−	0.938974i	$-0.388222\pi$
$883$	18051.5			0.687974			0.343987	+	0.938974i	$0.388222\pi$
$884$	12955.3	+	42962.2i	0.492910	+	1.63459i
$885$		0			0
$886$	−24102.0	+	3554.92i	−0.913907	+	0.134797i
$887$		−	11236.4i		−	0.425345i	−0.977123	−	0.212673i	$-0.931783\pi$
$887$		−	11236.4i		−	0.425345i	0.977123	−	0.212673i	$-0.0682168\pi$
$888$	11209.3	−	5267.79i	0.423604	−	0.199071i
$889$	1025.90			0.0387036
$890$		0			0
$891$		−	26291.7i		−	0.988558i
$892$	−10502.9	−	34829.7i	−0.394241	−	1.30738i
$893$	48773.0			1.82769
$894$	−2362.08	−	16014.6i	−0.0883666	−	0.599116i
$895$		0			0
$896$	19340.5	+	11744.2i	0.721119	+	0.437888i
$897$		−	20688.1i		−	0.770074i
$898$	−45205.1	+	6667.53i	−1.67986	+	0.247771i
$899$			77810.1i			2.88666i
$900$		0			0
$901$		−	4337.66i		−	0.160387i
$902$	−59.0787	−	400.547i	−0.00218083	−	0.0147858i
$903$			13939.7i			0.513716i
$904$	−8149.72	−	17341.8i	−0.299840	−	0.638029i
$905$		0			0
$906$	51906.6	−	7655.96i	1.90340	−	0.280742i
$907$	12021.6			0.440100			0.220050	−	0.975489i	$-0.429378\pi$
$907$	12021.6			0.440100			0.220050	+	0.975489i	$0.429378\pi$
$908$	−28703.8	+	8655.65i	−1.04909	+	0.316352i
$909$			36916.9i			1.34704i
$910$		0			0
$911$	15718.1			0.571642			0.285821	−	0.958283i	$-0.407734\pi$
$911$	15718.1			0.571642			0.285821	+	0.958283i	$0.407734\pi$
$912$	−23127.3	−	34860.2i	−0.839715	−	1.26572i
$913$			23355.0i			0.846591i
$914$	546.979	+	3708.46i	0.0197948	+	0.134207i
$915$		0			0
$916$	4761.98	+	15791.6i	0.171769	+	0.569619i
$917$	10098.3			0.363659
$918$	−1827.69	−	12391.5i	−0.0657111	−	0.445514i
$919$	−29706.9			−1.06631			−0.533156	−	0.846017i	$-0.678994\pi$
$919$	−29706.9			−1.06631			−0.533156	+	0.846017i	$0.678994\pi$
$920$		0			0
$921$	4054.93			0.145075
$922$	1798.32	+	12192.4i	0.0642349	+	0.435506i
$923$	−6454.50			−0.230176
$924$	−43053.8	+	12982.9i	−1.53286	+	0.462236i
$925$		0			0
$926$	−5096.38	−	34552.9i	−0.180861	−	1.22622i
$927$			27433.2i			0.971980i
$928$	−27807.3	−	30935.5i	−0.983641	−	1.09430i
$929$	32926.5			1.16285			0.581423	−	0.813602i	$-0.302496\pi$
$929$	32926.5			1.16285			0.581423	+	0.813602i	$0.302496\pi$
$930$		0			0
$931$		−	8400.56i		−	0.295722i
$932$	1870.25	+	6202.12i	0.0657319	+	0.217980i
$933$	−52298.3			−1.83512
$934$	−32424.6	+	4782.47i	−1.13594	+	0.167545i
$935$		0			0
$936$	−33279.9	+	15639.8i	−1.16217	+	0.546157i
$937$		−	31490.5i		−	1.09792i	−0.835849	−	0.548960i	$-0.815024\pi$
$937$		−	31490.5i		−	1.09792i	0.835849	−	0.548960i	$-0.184976\pi$
$938$	4874.11	+	33045.9i	0.169664	+	1.15031i
$939$			72922.6i			2.53433i
$940$		0			0
$941$		−	51748.0i		−	1.79271i	−0.443340	−	0.896353i	$-0.646207\pi$
$941$		−	51748.0i		−	1.79271i	0.443340	−	0.896353i	$-0.353793\pi$
$942$	−32236.2	+	4754.68i	−1.11498	+	0.164454i
$943$		−	163.018i		−	0.00562947i
$944$	3889.82	+	5863.21i	0.134113	+	0.202152i
$945$		0			0
$946$	2238.24	+	15175.0i	0.0769254	+	0.521546i
$947$	17708.2			0.607644			0.303822	−	0.952729i	$-0.401737\pi$
$947$	17708.2			0.607644			0.303822	+	0.952729i	$0.401737\pi$
$948$	−26910.4	+	8114.85i	−0.921952	+	0.278015i
$949$		−	17569.6i		−	0.600983i
$950$		0			0
$951$	−71442.8			−2.43606
$952$	35542.8	−	16703.2i	1.21003	−	0.568650i
$953$			26224.3i			0.891382i	0.895187	+	0.445691i	$0.147042\pi$
$953$			26224.3i			0.891382i	−0.895187	+	0.445691i	$0.852958\pi$
$954$	3516.49	−	518.665i	0.119340	−	0.0176021i
$955$		0			0
$956$	−8878.21	+	2677.23i	−0.300358	+	0.0905729i
$957$	82667.9			2.79234
$958$	−21137.3	+	3117.65i	−0.712856	+	0.105143i
$959$	−28030.9			−0.943864
$960$		0			0
$961$	84869.2			2.84882
$962$	−10053.4	+	1482.82i	−0.336938	+	0.0496966i
$963$	−1371.47			−0.0458931
$964$	28587.7	−	8620.63i	0.955133	−	0.288021i
$965$		0			0
$966$	−17912.0	+	2641.94i	−0.596595	+	0.0879948i
$967$			28936.2i			0.962282i	0.876643	+	0.481141i	$0.159777\pi$
$967$			28936.2i			0.962282i	−0.876643	+	0.481141i	$0.840223\pi$
$968$	−17527.2	+	8236.84i	−0.581967	+	0.273494i
$969$	−72608.3			−2.40714
$970$		0			0
$971$		−	3747.04i		−	0.123840i	−0.998081	−	0.0619198i	$-0.980278\pi$
$971$		−	3747.04i		−	0.123840i	0.998081	−	0.0619198i	$-0.0197223\pi$
$972$	−41372.6	+	12475.9i	−1.36525	+	0.411693i
$973$	−21.5616			−0.000710414
$974$	634.019	+	4298.58i	0.0208576	+	0.141412i
$975$		0			0
$976$	6394.73	+	9638.92i	0.209724	+	0.316121i
$977$		−	10231.8i		−	0.335050i	−0.985868	−	0.167525i	$-0.946422\pi$
$977$		−	10231.8i		−	0.335050i	0.985868	−	0.167525i	$-0.0535775\pi$
$978$	62337.0	−	9194.40i	2.03816	−	0.300618i
$979$		−	60855.1i		−	1.98666i
$980$		0			0
$981$		−	47976.6i		−	1.56144i
$982$	512.889	+	3477.33i	0.0166669	+	0.113000i
$983$			913.463i			0.0296388i	0.999890	+	0.0148194i	$0.00471733\pi$
$983$			913.463i			0.0296388i	−0.999890	+	0.0148194i	$0.995283\pi$
$984$	−482.248	+	226.631i	−0.0156235	+	0.00734221i
$985$		0			0
$986$	−71422.6	+	10534.5i	−2.30685	+	0.340249i
$987$	−68997.3			−2.22514
$988$	9909.87	+	32863.1i	0.319104	+	1.05821i
$989$			6176.04i			0.198571i
$990$		0			0
$991$	20267.9			0.649677			0.324838	−	0.945770i	$-0.394690\pi$
$991$	20267.9			0.649677			0.324838	+	0.945770i	$0.394690\pi$
$992$	−45586.2	+	40976.6i	−1.45904	+	1.31150i
$993$			4304.18i			0.137552i
$994$	824.260	+	5588.39i	0.0263017	+	0.178323i
$995$		0			0
$996$	29427.6	−	8873.91i	0.936195	−	0.282310i
$997$	−34081.1			−1.08261			−0.541304	−	0.840827i	$-0.682069\pi$
$997$	−34081.1			−1.08261			−0.541304	+	0.840827i	$0.682069\pi$
$998$	−7240.41	−	49089.2i	−0.229650	−	1.55700i
$999$	2836.60			0.0898360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.4.f.d.149.23		24
4.3	odd	2		800.4.f.d.49.3		24
5.2	odd	4		200.4.d.c.101.8	yes	12
5.3	odd	4		200.4.d.d.101.5	yes	12
5.4	even	2	inner	200.4.f.d.149.2		24
8.3	odd	2		800.4.f.d.49.21		24
8.5	even	2	inner	200.4.f.d.149.1		24
20.3	even	4		800.4.d.c.401.2		12
20.7	even	4		800.4.d.b.401.11		12
20.19	odd	2		800.4.f.d.49.22		24
40.3	even	4		800.4.d.c.401.11		12
40.13	odd	4		200.4.d.d.101.6	yes	12
40.19	odd	2		800.4.f.d.49.4		24
40.27	even	4		800.4.d.b.401.2		12
40.29	even	2	inner	200.4.f.d.149.24		24
40.37	odd	4		200.4.d.c.101.7	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.4.d.c.101.7	✓	12	40.37	odd	4
200.4.d.c.101.8	yes	12	5.2	odd	4
200.4.d.d.101.5	yes	12	5.3	odd	4
200.4.d.d.101.6	yes	12	40.13	odd	4
200.4.f.d.149.1		24	8.5	even	2	inner
200.4.f.d.149.2		24	5.4	even	2	inner
200.4.f.d.149.23		24	1.1	even	1	trivial
200.4.f.d.149.24		24	40.29	even	2	inner
800.4.d.b.401.2		12	40.27	even	4
800.4.d.b.401.11		12	20.7	even	4
800.4.d.c.401.2		12	20.3	even	4
800.4.d.c.401.11		12	40.3	even	4
800.4.f.d.49.3		24	4.3	odd	2
800.4.f.d.49.4		24	40.19	odd	2
800.4.f.d.49.21		24	8.3	odd	2
800.4.f.d.49.22		24	20.19	odd	2

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.79815 - 0.412714i) q^{2} +7.69300 q^{3} +(7.65933 - 2.30967i) q^{4} +(21.5262 - 3.17501i) q^{6} +15.6248i q^{7} +(20.4788 - 9.62394i) q^{8} +32.1823 q^{9} +O(q^{10})\)	\(q+(2.79815 - 0.412714i) q^{2} +7.69300 q^{3} +(7.65933 - 2.30967i) q^{4} +(21.5262 - 3.17501i) q^{6} +15.6248i q^{7} +(20.4788 - 9.62394i) q^{8} +32.1823 q^{9} +46.7640i q^{11} +(58.9233 - 17.7683i) q^{12} -50.4964 q^{13} +(6.44855 + 43.7205i) q^{14} +(53.3308 - 35.3811i) q^{16} -111.080i q^{17} +(90.0511 - 13.2821i) q^{18} -84.9682i q^{19} +120.201i q^{21} +(19.3001 + 130.853i) q^{22} +53.2555i q^{23} +(157.543 - 74.0370i) q^{24} +(-141.297 + 20.8406i) q^{26} +39.8675 q^{27} +(36.0881 + 119.675i) q^{28} -229.789i q^{29} -338.615 q^{31} +(134.626 - 121.012i) q^{32} +359.755i q^{33} +(-45.8441 - 310.818i) q^{34} +(246.495 - 74.3307i) q^{36} +71.1508 q^{37} +(-35.0675 - 237.754i) q^{38} -388.469 q^{39} -3.06105 q^{41} +(49.6087 + 336.342i) q^{42} +115.970 q^{43} +(108.010 + 358.181i) q^{44} +(21.9793 + 149.017i) q^{46} +574.015i q^{47} +(410.274 - 272.187i) q^{48} +98.8671 q^{49} -854.536i q^{51} +(-386.769 + 116.630i) q^{52} +39.0500 q^{53} +(111.555 - 16.4539i) q^{54} +(150.372 + 319.976i) q^{56} -653.660i q^{57} +(-94.8372 - 642.985i) q^{58} +109.940i q^{59} +180.738i q^{61} +(-947.497 + 139.751i) q^{62} +502.841i q^{63} +(326.760 - 394.173i) q^{64} +(148.476 + 1006.65i) q^{66} +755.845 q^{67} +(-256.558 - 850.796i) q^{68} +409.695i q^{69} +127.821 q^{71} +(659.054 - 309.721i) q^{72} +347.937i q^{73} +(199.091 - 29.3649i) q^{74} +(-196.249 - 650.800i) q^{76} -730.676 q^{77} +(-1087.00 + 160.327i) q^{78} -456.703 q^{79} -562.221 q^{81} +(-8.56529 + 1.26334i) q^{82} +499.423 q^{83} +(277.626 + 920.662i) q^{84} +(324.502 - 47.8625i) q^{86} -1767.77i q^{87} +(450.054 + 957.669i) q^{88} -1301.32 q^{89} -788.995i q^{91} +(123.003 + 407.902i) q^{92} -2604.97 q^{93} +(236.904 + 1606.18i) q^{94} +(1035.67 - 930.948i) q^{96} +778.230i q^{97} +(276.645 - 40.8038i) q^{98} +1504.97i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} + 18 q^{6} + 216 q^{9}+O(q^{10}) \) 24 * q - 2 * q^4 + 18 * q^6 + 216 * q^9	\( 24 q - 2 q^{4} + 18 q^{6} + 216 q^{9} + 224 q^{14} + 338 q^{16} + 570 q^{24} - 376 q^{26} - 528 q^{31} - 930 q^{34} - 1400 q^{36} + 600 q^{39} - 40 q^{41} - 766 q^{44} + 824 q^{46} - 456 q^{49} + 1674 q^{54} + 1304 q^{56} + 1486 q^{64} - 1794 q^{66} + 1256 q^{71} - 2160 q^{74} - 1938 q^{76} - 2232 q^{79} + 2256 q^{81} - 5096 q^{84} + 5452 q^{86} + 848 q^{89} + 3736 q^{94} + 5470 q^{96}+O(q^{100}) \) 24 * q - 2 * q^4 + 18 * q^6 + 216 * q^9 + 224 * q^14 + 338 * q^16 + 570 * q^24 - 376 * q^26 - 528 * q^31 - 930 * q^34 - 1400 * q^36 + 600 * q^39 - 40 * q^41 - 766 * q^44 + 824 * q^46 - 456 * q^49 + 1674 * q^54 + 1304 * q^56 + 1486 * q^64 - 1794 * q^66 + 1256 * q^71 - 2160 * q^74 - 1938 * q^76 - 2232 * q^79 + 2256 * q^81 - 5096 * q^84 + 5452 * q^86 + 848 * q^89 + 3736 * q^94 + 5470 * q^96

Introduction

L-functions

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