LMFDB - Embedded newform 200.5.g.h.51.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,5,Mod(51,200)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("200.51"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$N$	$=$	$200 = 2^{3} \cdot 5^{2}$
Weight:	$k$	$=$	$5$
Character orbit:	$[\chi]$	$=$	200.g (of order $2$ , degree $1$ , minimal)

Newform invariants

comment:select newform

sage:traces = [16,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$20.6739926168$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 6 x^{15} + 14 x^{14} - 84 x^{13} + 628 x^{12} - 1392 x^{11} + 2016 x^{10} - 18048 x^{9} + \cdots + 4294967296$ x^16 - 6x^15 + 14x^14 - 84x^13 + 628x^12 - 1392x^11 + 2016x^10 - 18048x^9 + 116992x^8 - 288768x^7 + 516096x^6 - 5701632x^5 + 41156608x^4 - 88080384x^3 + 234881024x^2 - 1610612736*x + 4294967296
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$2^{28}\cdot 3^{2}\cdot 5^{5}$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.4
Root			$-2.66926 + 2.97910i$ of defining polynomial
Character	$\chi$	$=$	200.51
Dual form			200.5.g.h.51.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66926 + 2.97910i) q^{2} +4.51805 q^{3} +(-1.75006 - 15.9040i) q^{4} +(-12.0599 + 13.4597i) q^{6} +50.0881i q^{7} +(52.0510 + 37.2384i) q^{8} -60.5872 q^{9} +158.856 q^{11} +(-7.90685 - 71.8551i) q^{12} -97.3070i q^{13} +(-149.217 - 133.698i) q^{14} +(-249.875 + 55.6658i) q^{16} -285.416 q^{17} +(161.723 - 180.495i) q^{18} +414.217 q^{19} +226.301i q^{21} +(-424.030 + 473.249i) q^{22} +546.228i q^{23} +(235.169 + 168.245i) q^{24} +(289.887 + 259.738i) q^{26} -639.698 q^{27} +(796.601 - 87.6570i) q^{28} +1162.39i q^{29} +369.759i q^{31} +(501.147 - 892.988i) q^{32} +717.721 q^{33} +(761.850 - 850.282i) q^{34} +(106.031 + 963.579i) q^{36} +1423.26i q^{37} +(-1105.65 + 1233.99i) q^{38} -439.638i q^{39} -2901.21 q^{41} +(-674.172 - 604.056i) q^{42} -905.493 q^{43} +(-278.008 - 2526.45i) q^{44} +(-1627.27 - 1458.03i) q^{46} +3025.75i q^{47} +(-1128.95 + 251.501i) q^{48} -107.819 q^{49} -1289.52 q^{51} +(-1547.57 + 170.293i) q^{52} -1605.79i q^{53} +(1707.52 - 1905.72i) q^{54} +(-1865.20 + 2607.13i) q^{56} +1871.45 q^{57} +(-3462.88 - 3102.73i) q^{58} -1809.93 q^{59} +1119.29i q^{61} +(-1101.55 - 986.984i) q^{62} -3034.70i q^{63} +(1322.60 + 3876.59i) q^{64} +(-1915.79 + 2138.16i) q^{66} -3916.26 q^{67} +(499.494 + 4539.25i) q^{68} +2467.89i q^{69} +4224.11i q^{71} +(-3153.62 - 2256.17i) q^{72} -4667.66 q^{73} +(-4240.03 - 3799.06i) q^{74} +(-724.902 - 6587.70i) q^{76} +7956.81i q^{77} +(1309.73 + 1173.51i) q^{78} +6812.31i q^{79} +2017.38 q^{81} +(7744.10 - 8642.99i) q^{82} +3166.94 q^{83} +(3599.09 - 396.039i) q^{84} +(2417.00 - 2697.55i) q^{86} +5251.74i q^{87} +(8268.62 + 5915.55i) q^{88} +10721.2 q^{89} +4873.93 q^{91} +(8687.22 - 955.931i) q^{92} +1670.59i q^{93} +(-9014.02 - 8076.54i) q^{94} +(2264.21 - 4034.56i) q^{96} -10051.4 q^{97} +(287.797 - 321.203i) q^{98} -9624.66 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 6 q^{2} + 8 q^{4} + 84 q^{6} + 216 q^{8} + 432 q^{9} + 192 q^{11} - 260 q^{12} + 972 q^{14} - 824 q^{16} + 806 q^{18} - 704 q^{19} + 1100 q^{22} - 1256 q^{24} + 108 q^{26} - 3648 q^{27} + 940 q^{28}+ \cdots + 2624 q^{99}+O(q^{100})$ 16 * q + 6 * q^2 + 8 * q^4 + 84 * q^6 + 216 * q^8 + 432 * q^9 + 192 * q^11 - 260 * q^12 + 972 * q^14 - 824 * q^16 + 806 * q^18 - 704 * q^19 + 1100 * q^22 - 1256 * q^24 + 108 * q^26 - 3648 * q^27 + 940 * q^28 - 4104 * q^32 + 992 * q^33 + 924 * q^34 - 2400 * q^36 + 420 * q^38 - 2208 * q^41 - 7820 * q^42 - 5568 * q^43 + 3816 * q^44 - 652 * q^46 - 4520 * q^48 - 2480 * q^49 - 17792 * q^51 + 4640 * q^52 + 6488 * q^54 - 12552 * q^56 - 8608 * q^57 - 1040 * q^58 + 14016 * q^59 - 12480 * q^62 - 3712 * q^64 - 13312 * q^66 + 18880 * q^67 - 12360 * q^68 + 16456 * q^72 + 7360 * q^73 - 11508 * q^74 + 9312 * q^76 + 26760 * q^78 + 10384 * q^81 + 16640 * q^82 - 10560 * q^83 - 12520 * q^84 + 25764 * q^86 - 41200 * q^88 + 6816 * q^89 + 24576 * q^91 - 30420 * q^92 - 28388 * q^94 + 6784 * q^96 - 448 * q^97 - 23934 * q^98 + 2624 * q^99

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

)

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

$2$	−2.66926	+	2.97910i	−0.667316	+	0.744775i
$2$	−2.66926	+	2.97910i	−0.667316	+	0.744775i
$3$	4.51805			0.502006			0.251003	−	0.967986i	$-0.419240\pi$
$3$	4.51805			0.502006			0.251003	+	0.967986i	$0.419240\pi$
$4$	−1.75006	−	15.9040i	−0.109379	−	0.994000i
$5$		0			0
$5$		0			0
$6$	−12.0599	+	13.4597i	−0.334996	+	0.373881i
$7$			50.0881i			1.02221i	0.859519	+	0.511103i	$0.170763\pi$
$7$			50.0881i			1.02221i	−0.859519	+	0.511103i	$0.829237\pi$
$8$	52.0510	+	37.2384i	0.813296	+	0.581850i
$9$	−60.5872			−0.747990
$10$		0			0
$11$	158.856			1.31286			0.656431	−	0.754386i	$-0.272065\pi$
$11$	158.856			1.31286			0.656431	+	0.754386i	$0.272065\pi$
$12$	−7.90685	−	71.8551i	−0.0549087	−	0.498994i
$13$		−	97.3070i		−	0.575781i	−0.957663	−	0.287891i	$-0.907046\pi$
$13$		−	97.3070i		−	0.575781i	0.957663	−	0.287891i	$-0.0929540\pi$
$14$	−149.217	−	133.698i	−0.761313	−	0.682135i
$15$		0			0
$16$	−249.875	+	55.6658i	−0.976073	+	0.217445i
$17$	−285.416			−0.987598			−0.493799	−	0.869576i	$-0.664392\pi$
$17$	−285.416			−0.987598			−0.493799	+	0.869576i	$0.664392\pi$
$18$	161.723	−	180.495i	0.499146	−	0.557084i
$19$	414.217			1.14741			0.573707	−	0.819061i	$-0.305505\pi$
$19$	414.217			1.14741			0.573707	+	0.819061i	$0.305505\pi$
$20$		0			0
$21$			226.301i			0.513153i
$22$	−424.030	+	473.249i	−0.876094	+	0.977787i
$23$			546.228i			1.03257i	0.856418	+	0.516284i	$0.172685\pi$
$23$			546.228i			1.03257i	−0.856418	+	0.516284i	$0.827315\pi$
$24$	235.169	+	168.245i	0.408279	+	0.292092i
$25$		0			0
$26$	289.887	+	259.738i	0.428827	+	0.384228i
$27$	−639.698			−0.877501
$28$	796.601	−	87.6570i	1.01607	−	0.111807i
$29$			1162.39i			1.38215i	0.722781	+	0.691077i	$0.242863\pi$
$29$			1162.39i			1.38215i	−0.722781	+	0.691077i	$0.757137\pi$
$30$		0			0
$31$			369.759i			0.384765i	0.981320	+	0.192382i	$0.0616214\pi$
$31$			369.759i			0.384765i	−0.981320	+	0.192382i	$0.938379\pi$
$32$	501.147	−	892.988i	0.489402	−	0.872058i
$33$	717.721			0.659064
$34$	761.850	−	850.282i	0.659040	−	0.735538i
$35$		0			0
$36$	106.031	+	963.579i	0.0818141	+	0.743502i
$37$			1423.26i			1.03964i	0.854277	+	0.519818i	$0.174000\pi$
$37$			1423.26i			1.03964i	−0.854277	+	0.519818i	$0.826000\pi$
$38$	−1105.65	+	1233.99i	−0.765688	+	0.854565i
$39$		−	439.638i		−	0.289045i
$40$		0			0
$41$	−2901.21			−1.72588			−0.862942	−	0.505303i	$-0.831381\pi$
$41$	−2901.21			−1.72588			−0.862942	+	0.505303i	$0.831381\pi$
$42$	−674.172	−	604.056i	−0.382184	−	0.342435i
$43$	−905.493			−0.489720			−0.244860	−	0.969558i	$-0.578742\pi$
$43$	−905.493			−0.489720			−0.244860	+	0.969558i	$0.578742\pi$
$44$	−278.008	−	2526.45i	−0.143599	−	1.30499i
$45$		0			0
$46$	−1627.27	−	1458.03i	−0.769030	−	0.689049i
$47$			3025.75i			1.36974i	0.728665	+	0.684870i	$0.240141\pi$
$47$			3025.75i			1.36974i	−0.728665	+	0.684870i	$0.759859\pi$
$48$	−1128.95	+	251.501i	−0.489994	+	0.109158i
$49$	−107.819			−0.0449058
$50$		0			0
$51$	−1289.52			−0.495780
$52$	−1547.57	+	170.293i	−0.572327	+	0.0629781i
$53$		−	1605.79i		−	0.571661i	−0.958280	−	0.285830i	$-0.907731\pi$
$53$		−	1605.79i		−	0.571661i	0.958280	−	0.285830i	$-0.0922694\pi$
$54$	1707.52	−	1905.72i	0.585571	−	0.653541i
$55$		0			0
$56$	−1865.20	+	2607.13i	−0.594771	+	0.831357i
$57$	1871.45			0.576008
$58$	−3462.88	−	3102.73i	−1.02939	−	0.922333i
$59$	−1809.93			−0.519946			−0.259973	−	0.965616i	$-0.583714\pi$
$59$	−1809.93			−0.519946			−0.259973	+	0.965616i	$0.583714\pi$
$60$		0			0
$61$			1119.29i			0.300804i	0.988625	+	0.150402i	$0.0480567\pi$
$61$			1119.29i			0.300804i	−0.988625	+	0.150402i	$0.951943\pi$
$62$	−1101.55	−	986.984i	−0.286563	−	0.256760i
$63$		−	3034.70i		−	0.764600i
$64$	1322.60	+	3876.59i	0.322901	+	0.946433i
$65$		0			0
$66$	−1915.79	+	2138.16i	−0.439804	+	0.490854i
$67$	−3916.26			−0.872412			−0.436206	−	0.899847i	$-0.643678\pi$
$67$	−3916.26			−0.872412			−0.436206	+	0.899847i	$0.643678\pi$
$68$	499.494	+	4539.25i	0.108022	+	0.981672i
$69$			2467.89i			0.518355i
$70$		0			0
$71$			4224.11i			0.837951i	0.907998	+	0.418975i	$0.137611\pi$
$71$			4224.11i			0.837951i	−0.907998	+	0.418975i	$0.862389\pi$
$72$	−3153.62	−	2256.17i	−0.608338	−	0.435218i
$73$	−4667.66			−0.875897			−0.437949	−	0.899000i	$-0.644295\pi$
$73$	−4667.66			−0.875897			−0.437949	+	0.899000i	$0.644295\pi$
$74$	−4240.03	−	3799.06i	−0.774294	−	0.693765i
$75$		0			0
$76$	−724.902	−	6587.70i	−0.125503	−	1.14053i
$77$			7956.81i			1.34202i
$78$	1309.73	+	1173.51i	0.215274	+	0.192885i
$79$			6812.31i			1.09154i	0.837935	+	0.545771i	$0.183763\pi$
$79$			6812.31i			1.09154i	−0.837935	+	0.545771i	$0.816237\pi$
$80$		0			0
$81$	2017.38			0.307480
$82$	7744.10	−	8642.99i	1.15171	−	1.28539i
$83$	3166.94			0.459709			0.229855	−	0.973225i	$-0.426175\pi$
$83$	3166.94			0.459709			0.229855	+	0.973225i	$0.426175\pi$
$84$	3599.09	−	396.039i	0.510075	−	0.0561280i
$85$		0			0
$86$	2417.00	−	2697.55i	0.326798	−	0.364731i
$87$			5251.74i			0.693849i
$88$	8268.62	+	5915.55i	1.06775	+	0.763889i
$89$	10721.2			1.35351			0.676756	−	0.736207i	$-0.263385\pi$
$89$	10721.2			1.35351			0.676756	+	0.736207i	$0.263385\pi$
$90$		0			0
$91$	4873.93			0.588567
$92$	8687.22	−	955.931i	1.02637	−	0.112941i
$93$			1670.59i			0.193154i
$94$	−9014.02	−	8076.54i	−1.02015	−	0.914049i
$95$		0			0
$96$	2264.21	−	4034.56i	0.245682	−	0.437778i
$97$	−10051.4			−1.06828			−0.534140	−	0.845396i	$-0.679364\pi$
$97$	−10051.4			−1.06828			−0.534140	+	0.845396i	$0.679364\pi$
$98$	287.797	−	321.203i	0.0299663	−	0.0334447i
$99$	−9624.66			−0.982008
$100$		0			0
$101$		−	15016.7i		−	1.47208i	−0.676935	−	0.736042i	$-0.736692\pi$
$101$		−	15016.7i		−	1.47208i	0.676935	−	0.736042i	$-0.263308\pi$
$102$	3442.08	−	3841.62i	0.330842	−	0.369244i
$103$		−	13177.3i		−	1.24209i	−0.783775	−	0.621045i	$-0.786708\pi$
$103$		−	13177.3i		−	1.24209i	0.783775	−	0.621045i	$-0.213292\pi$
$104$	3623.56	−	5064.92i	0.335018	−	0.468281i
$105$		0			0
$106$	4783.82	+	4286.29i	0.425758	+	0.381478i
$107$	13284.8			1.16035			0.580173	−	0.814493i	$-0.302985\pi$
$107$	13284.8			1.16035			0.580173	+	0.814493i	$0.302985\pi$
$108$	1119.51	+	10173.8i	0.0959798	+	0.872236i
$109$			19211.6i			1.61700i	0.588493	+	0.808502i	$0.299721\pi$
$109$			19211.6i			1.61700i	−0.588493	+	0.808502i	$0.700279\pi$
$110$		0			0
$111$			6430.36i			0.521903i
$112$	−2788.20	−	12515.7i	−0.222273	−	0.997748i
$113$	20975.3			1.64268			0.821338	−	0.570442i	$-0.193228\pi$
$113$	20975.3			1.64268			0.821338	+	0.570442i	$0.193228\pi$
$114$	−4995.40	+	5575.24i	−0.384380	+	0.428996i
$115$		0			0
$116$	18486.7	−	2034.25i	1.37386	−	0.151178i
$117$			5895.56i			0.430679i
$118$	4831.18	−	5391.96i	0.346968	−	0.387242i
$119$		−	14295.9i		−	1.00953i
$120$		0			0
$121$	10594.3			0.723607
$122$	−3334.47	−	2987.68i	−0.224031	−	0.200731i
$123$	−13107.8			−0.866403
$124$	5880.65	−	647.099i	0.382456	−	0.0420850i
$125$		0			0
$126$	9040.67	+	8100.41i	0.569455	+	0.510230i
$127$		−	10769.3i		−	0.667696i	−0.942627	−	0.333848i	$-0.891653\pi$
$127$		−	10769.3i		−	0.667696i	0.942627	−	0.333848i	$-0.108347\pi$
$128$	−15079.1	−	6407.47i	−0.920356	−	0.391081i
$129$	−4091.06			−0.245842
$130$		0			0
$131$	15667.6			0.912975			0.456487	−	0.889730i	$-0.349107\pi$
$131$	15667.6			0.912975			0.456487	+	0.889730i	$0.349107\pi$
$132$	−1256.05	−	11414.6i	−0.0720875	−	0.655110i
$133$			20747.3i			1.17289i
$134$	10453.5	−	11666.9i	0.582175	−	0.649751i
$135$		0			0
$136$	−14856.2	−	10628.4i	−0.803210	−	0.574634i
$137$	25231.8			1.34433			0.672167	−	0.740399i	$-0.265364\pi$
$137$	25231.8			1.34433			0.672167	+	0.740399i	$0.265364\pi$
$138$	−7352.08	−	6587.44i	−0.386058	−	0.345906i
$139$	−21388.1			−1.10699			−0.553494	−	0.832853i	$-0.686706\pi$
$139$	−21388.1			−1.10699			−0.553494	+	0.832853i	$0.686706\pi$
$140$		0			0
$141$			13670.5i			0.687617i
$142$	−12584.0	−	11275.3i	−0.624084	−	0.559178i
$143$		−	15457.8i		−	0.755922i
$144$	15139.2	−	3372.64i	0.730093	−	0.162646i
$145$		0			0
$146$	12459.2	−	13905.4i	0.584500	−	0.652346i
$147$	−487.131			−0.0225429
$148$	22635.5	−	2490.79i	1.03340	−	0.113714i
$149$			40319.2i			1.81610i	0.418863	+	0.908049i	$0.362429\pi$
$149$			40319.2i			1.81610i	−0.418863	+	0.908049i	$0.637571\pi$
$150$		0			0
$151$		−	28388.2i		−	1.24504i	−0.782603	−	0.622521i	$-0.786109\pi$
$151$		−	28388.2i		−	1.24504i	0.782603	−	0.622521i	$-0.213891\pi$
$152$	21560.4	+	15424.8i	0.933188	+	0.667623i
$153$	17292.5			0.738714
$154$	−23704.1	−	21238.8i	−0.999500	−	0.895549i
$155$		0			0
$156$	−6992.01	+	769.392i	−0.287311	+	0.0316154i
$157$			4835.50i			0.196174i	0.995178	+	0.0980872i	$0.0312724\pi$
$157$			4835.50i			0.196174i	−0.995178	+	0.0980872i	$0.968728\pi$
$158$	−20294.5	−	18183.9i	−0.812952	−	0.728403i
$159$		−	7255.06i		−	0.286977i
$160$		0			0
$161$	−27359.5			−1.05550
$162$	−5384.91	+	6009.96i	−0.205186	+	0.229003i
$163$	−26938.1			−1.01389			−0.506947	−	0.861977i	$-0.669226\pi$
$163$	−26938.1			−1.01389			−0.506947	+	0.861977i	$0.669226\pi$
$164$	5077.28	+	46140.9i	0.188775	+	1.71553i
$165$		0			0
$166$	−8453.39	+	9434.62i	−0.306771	+	0.342380i
$167$			24228.8i			0.868760i	0.900730	+	0.434380i	$0.143032\pi$
$167$			24228.8i			0.868760i	−0.900730	+	0.434380i	$0.856968\pi$
$168$	−8427.07	+	11779.2i	−0.298578	+	0.417346i
$169$	19092.3			0.668476
$170$		0			0
$171$	−25096.2			−0.858255
$172$	1584.66	+	14401.0i	0.0535649	+	0.486782i
$173$			15853.9i			0.529716i	0.964287	+	0.264858i	$0.0853251\pi$
$173$			15853.9i			0.529716i	−0.964287	+	0.264858i	$0.914675\pi$
$174$	−15645.5	−	14018.3i	−0.516761	−	0.463017i
$175$		0			0
$176$	−39694.2	+	8842.87i	−1.28145	+	0.285475i
$177$	−8177.36			−0.261016
$178$	−28617.6	+	31939.4i	−0.903220	+	1.00806i
$179$	5340.06			0.166663			0.0833316	−	0.996522i	$-0.473444\pi$
$179$	5340.06			0.166663			0.0833316	+	0.996522i	$0.473444\pi$
$180$		0			0
$181$		−	16455.4i		−	0.502286i	−0.967950	−	0.251143i	$-0.919193\pi$
$181$		−	16455.4i		−	0.502286i	0.967950	−	0.251143i	$-0.0808065\pi$
$182$	−13009.8	+	14519.9i	−0.392760	+	0.438350i
$183$			5057.01i			0.151005i
$184$	−20340.7	+	28431.7i	−0.600799	+	0.839783i
$185$		0			0
$186$	−4976.85	−	4459.25i	−0.143856	−	0.128895i
$187$	−45340.1			−1.29658
$188$	48121.6	−	5295.24i	1.36152	−	0.149820i
$189$		−	32041.3i		−	0.896987i
$190$		0			0
$191$			36286.3i			0.994663i	0.867561	+	0.497331i	$0.165687\pi$
$191$			36286.3i			0.994663i	−0.867561	+	0.497331i	$0.834313\pi$
$192$	5975.59	+	17514.6i	0.162098	+	0.475115i
$193$	−1934.56			−0.0519358			−0.0259679	−	0.999663i	$-0.508267\pi$
$193$	−1934.56			−0.0519358			−0.0259679	+	0.999663i	$0.508267\pi$
$194$	26830.0	−	29944.2i	0.712880	−	0.795628i
$195$		0			0
$196$	188.689	+	1714.75i	0.00491173	+	0.0446363i
$197$		−	72587.7i		−	1.87038i	−0.354142	−	0.935192i	$-0.615227\pi$
$197$		−	72587.7i		−	1.87038i	0.354142	−	0.935192i	$-0.384773\pi$
$198$	25690.8	−	28672.8i	0.655310	−	0.731375i
$199$		−	77717.2i		−	1.96251i	−0.192723	−	0.981253i	$-0.561732\pi$
$199$		−	77717.2i		−	1.96251i	0.192723	−	0.981253i	$-0.438268\pi$
$200$		0			0
$201$	−17693.9			−0.437956
$202$	44736.3	+	40083.6i	1.09637	+	0.982346i
$203$	−58222.0			−1.41285
$204$	2256.74	+	20508.6i	0.0542277	+	0.492805i
$205$		0			0
$206$	39256.6	+	35173.8i	0.925078	+	0.828867i
$207$		−	33094.5i		−	0.772351i
$208$	5416.68	+	24314.6i	0.125201	+	0.562004i
$209$	65800.9			1.50640
$210$		0			0
$211$	35806.9			0.804271			0.402135	−	0.915580i	$-0.368268\pi$
$211$	35806.9			0.804271			0.402135	+	0.915580i	$0.368268\pi$
$212$	−25538.6	+	2810.23i	−0.568231	+	0.0625274i
$213$			19084.7i			0.420656i
$214$	−35460.6	+	39576.7i	−0.774317	+	0.864196i
$215$		0			0
$216$	−33296.9	−	23821.3i	−0.713668	−	0.510574i
$217$	−18520.5			−0.393309
$218$	−57233.3	−	51280.9i	−1.20430	−	1.07905i
$219$	−21088.7			−0.439705
$220$		0			0
$221$			27773.0i			0.568640i
$222$	−19156.7	−	17164.3i	−0.388700	−	0.348274i
$223$		−	66087.5i		−	1.32895i	−0.747309	−	0.664477i	$-0.768655\pi$
$223$		−	66087.5i		−	1.32895i	0.747309	−	0.664477i	$-0.231345\pi$
$224$	44728.1	+	25101.5i	0.891424	+	0.500270i
$225$		0			0
$226$	−55988.7	+	62487.6i	−1.09618	+	1.22342i
$227$	6504.85			0.126237			0.0631184	−	0.998006i	$-0.479895\pi$
$227$	6504.85			0.126237			0.0631184	+	0.998006i	$0.479895\pi$
$228$	−3275.15	−	29763.6i	−0.0630030	−	0.572552i
$229$			5180.89i			0.0987946i	0.998779	+	0.0493973i	$0.0157301\pi$
$229$			5180.89i			0.0987946i	−0.998779	+	0.0493973i	$0.984270\pi$
$230$		0			0
$231$			35949.3i			0.673700i
$232$	−43285.6	+	60503.6i	−0.804206	+	1.12410i
$233$	45055.0			0.829910			0.414955	−	0.909842i	$-0.363797\pi$
$233$	45055.0			0.829910			0.414955	+	0.909842i	$0.363797\pi$
$234$	−17563.5	−	15736.8i	−0.320759	−	0.287399i
$235$		0			0
$236$	3167.48	+	28785.1i	0.0568709	+	0.516826i
$237$			30778.4i			0.547960i
$238$	42589.0	+	38159.6i	0.751871	+	0.673675i
$239$		−	71745.9i		−	1.25603i	−0.778200	−	0.628017i	$-0.783867\pi$
$239$		−	71745.9i		−	1.25603i	0.778200	−	0.628017i	$-0.216133\pi$
$240$		0			0
$241$	−13213.7			−0.227504			−0.113752	−	0.993509i	$-0.536287\pi$
$241$	−13213.7			−0.227504			−0.113752	+	0.993509i	$0.536287\pi$
$242$	−28279.1	+	31561.6i	−0.482875	+	0.538924i
$243$	60930.2			1.03186
$244$	17801.2	−	1958.82i	0.298999	−	0.0329015i
$245$		0			0
$246$	34988.2	−	39049.5i	0.578165	−	0.645275i
$247$		−	40306.2i		−	0.660660i
$248$	−13769.2	+	19246.3i	−0.223875	+	0.312928i
$249$	14308.4			0.230777
$250$		0			0
$251$	−9203.91			−0.146091			−0.0730457	−	0.997329i	$-0.523272\pi$
$251$	−9203.91			−0.146091			−0.0730457	+	0.997329i	$0.523272\pi$
$252$	−48263.9	+	5310.90i	−0.760013	+	0.0836309i
$253$			86771.8i			1.35562i
$254$	32082.7	+	28746.0i	0.497283	+	0.445564i
$255$		0			0
$256$	59338.6	−	27818.9i	0.905436	−	0.424483i
$257$	32215.5			0.487751			0.243876	−	0.969807i	$-0.421581\pi$
$257$	32215.5			0.487751			0.243876	+	0.969807i	$0.421581\pi$
$258$	10920.1	−	12187.7i	0.164055	−	0.183097i
$259$	−71288.4			−1.06272
$260$		0			0
$261$		−	70426.0i		−	1.03384i
$262$	−41820.9	+	46675.2i	−0.609243	+	0.679960i
$263$			90235.1i			1.30456i	0.757978	+	0.652280i	$0.226187\pi$
$263$			90235.1i			1.30456i	−0.757978	+	0.652280i	$0.773813\pi$
$264$	37358.1	+	26726.8i	0.536014	+	0.383476i
$265$		0			0
$266$	−61808.3	−	55380.1i	−0.873542	−	0.782691i
$267$	48438.8			0.679471
$268$	6853.68	+	62284.2i	0.0954232	+	0.867178i
$269$		−	10715.9i		−	0.148090i	−0.997255	−	0.0740448i	$-0.976409\pi$
$269$		−	10715.9i		−	0.148090i	0.997255	−	0.0740448i	$-0.0235908\pi$
$270$		0			0
$271$			40139.7i			0.546557i	0.961935	+	0.273278i	$0.0881080\pi$
$271$			40139.7i			0.546557i	−0.961935	+	0.273278i	$0.911892\pi$
$272$	71318.1	−	15887.9i	0.963967	−	0.214748i
$273$	22020.6			0.295464
$274$	−67350.4	+	75168.1i	−0.897096	+	1.00123i
$275$		0			0
$276$	39249.3	−	4318.94i	0.515245	−	0.0566969i
$277$			9941.96i			0.129572i	0.997899	+	0.0647862i	$0.0206365\pi$
$277$			9941.96i			0.129572i	−0.997899	+	0.0647862i	$0.979363\pi$
$278$	57090.5	−	63717.3i	0.738711	−	0.824456i
$279$		−	22402.7i		−	0.287800i
$280$		0			0
$281$	3041.90			0.0385241			0.0192621	−	0.999814i	$-0.493868\pi$
$281$	3041.90			0.0385241			0.0192621	+	0.999814i	$0.493868\pi$
$282$	−40725.8	−	36490.2i	−0.512120	−	0.458858i
$283$	63175.8			0.788821			0.394410	−	0.918934i	$-0.370949\pi$
$283$	63175.8			0.788821			0.394410	+	0.918934i	$0.370949\pi$
$284$	67180.2	−	7392.43i	0.832923	−	0.0916538i
$285$		0			0
$286$	46050.4	+	41261.1i	0.562991	+	0.504439i
$287$		−	145316.i		−	1.76421i
$288$	−30363.1	+	54103.6i	−0.366068	+	0.652291i
$289$	−2058.84			−0.0246506
$290$		0			0
$291$	−45412.9			−0.536282
$292$	8168.67	+	74234.4i	0.0958044	+	0.870642i
$293$		−	50125.3i		−	0.583877i	−0.956437	−	0.291939i	$-0.905700\pi$
$293$		−	50125.3i		−	0.583877i	0.956437	−	0.291939i	$-0.0943003\pi$
$294$	1300.28	−	1451.21i	0.0150433	−	0.0167894i
$295$		0			0
$296$	−52999.9	+	74082.1i	−0.604912	+	0.845531i
$297$	−101620.			−1.15204
$298$	−120115.	−	107623.i	−1.35258	−	1.21191i
$299$	53151.9			0.594533
$300$		0			0
$301$		−	45354.4i		−	0.500595i
$302$	84571.3	+	75775.6i	0.927276	+	0.830837i
$303$		−	67846.4i		−	0.738995i
$304$	−103502.	+	23057.7i	−1.11996	+	0.249499i
$305$		0			0
$306$	−46158.4	+	51516.2i	−0.492955	+	0.550175i
$307$	49587.2			0.526129			0.263065	−	0.964778i	$-0.415267\pi$
$307$	49587.2			0.526129			0.263065	+	0.964778i	$0.415267\pi$
$308$	126545.	−	13924.9i	1.33396	−	0.146788i
$309$		−	59535.9i		−	0.623537i
$310$		0			0
$311$		−	122692.i		−	1.26852i	−0.773120	−	0.634260i	$-0.781305\pi$
$311$		−	122692.i		−	1.26852i	0.773120	−	0.634260i	$-0.218695\pi$
$312$	16371.4	−	22883.6i	0.168181	−	0.235080i
$313$	−178246.			−1.81942			−0.909708	−	0.415248i	$-0.863695\pi$
$313$	−178246.			−1.81942			−0.909708	+	0.415248i	$0.863695\pi$
$314$	−14405.4	−	12907.2i	−0.146106	−	0.130910i
$315$		0			0
$316$	108343.	−	11921.9i	1.08499	−	0.119391i
$317$		−	9020.39i		−	0.0897650i	−0.998992	−	0.0448825i	$-0.985709\pi$
$317$		−	9020.39i		−	0.0897650i	0.998992	−	0.0448825i	$-0.0142913\pi$
$318$	21613.5	+	19365.7i	0.213733	+	0.191504i
$319$			184653.i			1.81458i
$320$		0			0
$321$	60021.4			0.582500
$322$	73029.8	−	81506.8i	0.704350	−	0.786108i
$323$	−118224.			−1.13318
$324$	−3530.52	−	32084.3i	−0.0336317	−	0.305635i
$325$		0			0
$326$	71905.0	−	80251.4i	0.676587	−	0.755122i
$327$			86799.1i			0.811745i
$328$	−151011.	−	108036.i	−1.40365	−	1.00421i
$329$	−151554.			−1.40016
$330$		0			0
$331$	70357.4			0.642175			0.321088	−	0.947049i	$-0.395952\pi$
$331$	70357.4			0.642175			0.321088	+	0.947049i	$0.395952\pi$
$332$	−5542.32	−	50367.0i	−0.0502823	−	0.456951i
$333$		−	86231.4i		−	0.777637i
$334$	−72180.1	−	64673.2i	−0.647030	−	0.579737i
$335$		0			0
$336$	−12597.2	−	56546.8i	−0.111582	−	0.500875i
$337$	148629.			1.30871			0.654356	−	0.756186i	$-0.272940\pi$
$337$	148629.			1.30871			0.654356	+	0.756186i	$0.272940\pi$
$338$	−50962.5	+	56878.0i	−0.446085	+	0.497864i
$339$	94767.6			0.824633
$340$		0			0
$341$			58738.5i			0.505143i
$342$	66988.5	−	74764.1i	0.572727	−	0.639206i
$343$			114861.i			0.976303i
$344$	−47131.8	−	33719.1i	−0.398288	−	0.284944i
$345$		0			0
$346$	−47230.2	−	42318.2i	−0.394519	−	0.353488i
$347$	−94414.8			−0.784117			−0.392059	−	0.919940i	$-0.628237\pi$
$347$	−94414.8			−0.784117			−0.392059	+	0.919940i	$0.628237\pi$
$348$	83523.7	−	9190.85i	0.689686	−	0.0758922i
$349$			72082.1i			0.591802i	0.955219	+	0.295901i	$0.0956198\pi$
$349$			72082.1i			0.591802i	−0.955219	+	0.295901i	$0.904380\pi$
$350$		0			0
$351$			62247.1i			0.505249i
$352$	79610.4	−	141857.i	0.642517	−	1.14489i
$353$	31879.4			0.255836			0.127918	−	0.991785i	$-0.459171\pi$
$353$	31879.4			0.255836			0.127918	+	0.991785i	$0.459171\pi$
$354$	21827.5	−	24361.2i	0.174180	−	0.194398i
$355$		0			0
$356$	−18762.7	−	170509.i	−0.148045	−	1.34539i
$357$		−	64589.8i		−	0.506789i
$358$	−14254.0	+	15908.6i	−0.111217	+	0.124127i
$359$		−	34649.8i		−	0.268851i	−0.990924	−	0.134426i	$-0.957081\pi$
$359$		−	34649.8i		−	0.268851i	0.990924	−	0.134426i	$-0.0429189\pi$
$360$		0			0
$361$	41254.3			0.316559
$362$	49022.3	+	43923.8i	0.374090	+	0.335184i
$363$	47865.7			0.363255
$364$	−8529.65	−	77514.9i	−0.0643766	−	0.585036i
$365$		0			0
$366$	−15065.3	−	13498.5i	−0.112465	−	0.100768i
$367$			90234.4i			0.669946i	0.942228	+	0.334973i	$0.108727\pi$
$367$			90234.4i			0.669946i	−0.942228	+	0.334973i	$0.891273\pi$
$368$	−30406.2	−	136489.i	−0.224526	−	1.00786i
$369$	175776.			1.29094
$370$		0			0
$371$	80431.2			0.584355
$372$	26569.1	−	2923.63i	0.191995	−	0.0211269i
$373$		−	18934.5i		−	0.136093i	−0.997682	−	0.0680466i	$-0.978323\pi$
$373$		−	18934.5i		−	0.136093i	0.997682	−	0.0680466i	$-0.0216767\pi$
$374$	121025.	−	135073.i	0.865229	−	0.965660i
$375$		0			0
$376$	−112674.	+	157493.i	−0.796983	+	1.11400i
$377$	113109.			0.795818
$378$	95454.1	+	85526.6i	0.668053	+	0.598574i
$379$	−146129.			−1.01732			−0.508661	−	0.860967i	$-0.669859\pi$
$379$	−146129.			−1.01732			−0.508661	+	0.860967i	$0.669859\pi$
$380$		0			0
$381$		−	48656.1i		−	0.335187i
$382$	−108100.	−	96857.7i	−0.740800	−	0.663755i
$383$			63738.0i			0.434511i	0.976115	+	0.217255i	$0.0697104\pi$
$383$			63738.0i			0.434511i	−0.976115	+	0.217255i	$0.930290\pi$
$384$	−68128.2	−	28949.3i	−0.462024	−	0.196325i
$385$		0			0
$386$	5163.84	−	5763.23i	0.0346576	−	0.0386804i
$387$	54861.3			0.366306
$388$	17590.6	+	159858.i	0.116847	+	1.06187i
$389$			73071.2i			0.482889i	0.970415	+	0.241444i	$0.0776212\pi$
$389$			73071.2i			0.482889i	−0.970415	+	0.241444i	$0.922379\pi$
$390$		0			0
$391$		−	155902.i		−	1.01976i
$392$	−5612.07	−	4015.00i	−0.0365217	−	0.0261284i
$393$	70786.8			0.458318
$394$	216246.	+	193756.i	1.39301	+	1.24814i
$395$		0			0
$396$	16843.7	+	153071.i	0.107411	+	0.976116i
$397$		−	17918.3i		−	0.113689i	−0.998383	−	0.0568443i	$-0.981896\pi$
$397$		−	17918.3i		−	0.113689i	0.998383	−	0.0568443i	$-0.0181038\pi$
$398$	231527.	+	207448.i	1.46162	+	1.30961i
$399$			93737.5i			0.588799i
$400$		0			0
$401$	−66769.8			−0.415232			−0.207616	−	0.978210i	$-0.566570\pi$
$401$	−66769.8			−0.415232			−0.207616	+	0.978210i	$0.566570\pi$
$402$	47229.6	−	52711.7i	0.292255	−	0.326178i
$403$	35980.1			0.221540
$404$	−238826.	+	26280.1i	−1.46325	+	0.161015i
$405$		0			0
$406$	155410.	−	173449.i	0.942815	−	1.05225i
$407$			226094.i			1.36490i
$408$	−67120.9	−	48019.8i	−0.403216	−	0.288469i
$409$	−291009.			−1.73964			−0.869822	−	0.493366i	$-0.835766\pi$
$409$	−291009.			−1.73964			−0.869822	+	0.493366i	$0.835766\pi$
$410$		0			0
$411$	113999.			0.674863
$412$	−209572.	+	23061.1i	−1.23464	+	0.135858i
$413$		−	90656.0i		−	0.531492i
$414$	98591.6	+	88337.8i	0.575227	+	0.515402i
$415$		0			0
$416$	−86894.0	−	48765.2i	−0.502115	−	0.281788i
$417$	−96632.6			−0.555714
$418$	−175640.	+	196027.i	−1.00524	+	1.12193i
$419$	199703.			1.13751			0.568757	−	0.822506i	$-0.307424\pi$
$419$	199703.			1.13751			0.568757	+	0.822506i	$0.307424\pi$
$420$		0			0
$421$			116540.i			0.657525i	0.944413	+	0.328763i	$0.106632\pi$
$421$			116540.i			0.657525i	−0.944413	+	0.328763i	$0.893368\pi$
$422$	−95578.2	+	106672.i	−0.536703	+	0.599001i
$423$		−	183322.i		−	1.02455i
$424$	59797.2	−	83583.1i	0.332621	−	0.464929i
$425$		0			0
$426$	−56855.3	−	50942.2i	−0.313294	−	0.280710i
$427$	−56063.1			−0.307483
$428$	−23249.1	−	211281.i	−0.126917	−	1.15338i
$429$		−	69839.3i		−	0.379477i
$430$		0			0
$431$			57475.2i			0.309404i	0.987961	+	0.154702i	$0.0494417\pi$
$431$			57475.2i			0.309404i	−0.987961	+	0.154702i	$0.950558\pi$
$432$	159844.	−	35609.3i	0.856505	−	0.190808i
$433$	78282.3			0.417530			0.208765	−	0.977966i	$-0.433056\pi$
$433$	78282.3			0.417530			0.208765	+	0.977966i	$0.433056\pi$
$434$	49436.2	−	55174.5i	0.262461	−	0.292927i
$435$		0			0
$436$	305542.	−	33621.4i	1.60730	−	0.176866i
$437$			226257.i			1.18478i
$438$	56291.3	−	62825.4i	0.293423	−	0.327481i
$439$			248919.i			1.29160i	0.763506	+	0.645801i	$0.223476\pi$
$439$			248919.i			1.29160i	−0.763506	+	0.645801i	$0.776524\pi$
$440$		0			0
$441$	6532.44			0.0335891
$442$	−82738.4	−	74133.4i	−0.423509	−	0.379463i
$443$	305178.			1.55505			0.777527	−	0.628849i	$-0.216474\pi$
$443$	305178.			1.55505			0.777527	+	0.628849i	$0.216474\pi$
$444$	102269.	−	11253.5i	0.518771	−	0.0570850i
$445$		0			0
$446$	196881.	+	176405.i	0.989771	+	0.886832i
$447$			182164.i			0.911692i
$448$	−194171.	+	66246.7i	−0.967449	+	0.330072i
$449$	−106754.			−0.529529			−0.264765	−	0.964313i	$-0.585294\pi$
$449$	−106754.			−0.529529			−0.264765	+	0.964313i	$0.585294\pi$
$450$		0			0
$451$	−460876.			−2.26585
$452$	−36708.0	−	333592.i	−0.179673	−	1.63282i
$453$		−	128259.i		−	0.625018i
$454$	−17363.2	+	19378.6i	−0.0842398	+	0.0940179i
$455$		0			0
$456$	97410.8	+	69689.8i	0.468465	+	0.335150i
$457$	−212418.			−1.01709			−0.508543	−	0.861036i	$-0.669816\pi$
$457$	−212418.			−1.01709			−0.508543	+	0.861036i	$0.669816\pi$
$458$	−15434.4	−	13829.2i	−0.0735797	−	0.0659272i
$459$	182580.			0.866618
$460$		0			0
$461$			377548.i			1.77652i	0.459340	+	0.888261i	$0.348086\pi$
$461$			377548.i			1.77652i	−0.459340	+	0.888261i	$0.651914\pi$
$462$	−107096.	−	95958.2i	−0.501754	−	0.449571i
$463$			64579.0i			0.301252i	0.988591	+	0.150626i	$0.0481288\pi$
$463$			64579.0i			0.301252i	−0.988591	+	0.150626i	$0.951871\pi$
$464$	−64705.5	−	290452.i	−0.300542	−	1.34908i
$465$		0			0
$466$	−120264.	+	134223.i	−0.553812	+	0.618096i
$467$	−100635.			−0.461439			−0.230720	−	0.973020i	$-0.574108\pi$
$467$	−100635.			−0.461439			−0.230720	+	0.973020i	$0.574108\pi$
$468$	93763.1	−	10317.6i	0.428095	−	0.0471070i
$469$		−	196158.i		−	0.891785i
$470$		0			0
$471$			21847.0i			0.0984806i
$472$	−94208.6	−	67398.9i	−0.422870	−	0.302530i
$473$	−143843.			−0.642936
$474$	−91691.8	−	82155.6i	−0.408107	−	0.365662i
$475$		0			0
$476$	−227363.	+	25018.7i	−1.00347	+	0.110421i
$477$			97290.6i			0.427597i
$478$	213738.	+	191509.i	0.935462	+	0.838171i
$479$			188868.i			0.823168i	0.911372	+	0.411584i	$0.135024\pi$
$479$			188868.i			0.823168i	−0.911372	+	0.411584i	$0.864976\pi$
$480$		0			0
$481$	138493.			0.598603
$482$	35270.7	−	39364.8i	0.151817	−	0.169439i
$483$	−123612.			−0.529866
$484$	−18540.7	−	168492.i	−0.0791471	−	0.719266i
$485$		0			0
$486$	−162639.	+	181517.i	−0.688575	+	0.768501i
$487$		−	105446.i		−	0.444604i	−0.974978	−	0.222302i	$-0.928643\pi$
$487$		−	105446.i		−	0.444604i	0.974978	−	0.222302i	$-0.0713571\pi$
$488$	−41680.6	+	58260.1i	−0.175022	+	0.244642i
$489$	−121708.			−0.508980
$490$		0			0
$491$	−248385.			−1.03030			−0.515149	−	0.857101i	$-0.672263\pi$
$491$	−248385.			−1.03030			−0.515149	+	0.857101i	$0.672263\pi$
$492$	22939.4	+	208467.i	0.0947659	+	0.861205i
$493$		−	331765.i		−	1.36501i
$494$	120076.	+	107588.i	0.492043	+	0.440869i
$495$		0			0
$496$	−20582.9	−	92393.4i	−0.0836650	−	0.375558i
$497$	−211578.			−0.856558
$498$	−38192.8	+	42626.1i	−0.154001	+	0.171877i
$499$	194138.			0.779668			0.389834	−	0.920885i	$-0.372532\pi$
$499$	194138.			0.779668			0.389834	+	0.920885i	$0.372532\pi$
$500$		0			0
$501$			109467.i			0.436122i
$502$	24567.7	−	27419.4i	0.0974892	−	0.108805i
$503$			323180.i			1.27735i	0.769478	+	0.638673i	$0.220516\pi$
$503$			323180.i			1.27735i	−0.769478	+	0.638673i	$0.779484\pi$
$504$	113007.	−	157959.i	0.444883	−	0.621847i
$505$		0			0
$506$	−258502.	−	231617.i	−1.00963	−	0.904626i
$507$	86260.2			0.335579
$508$	−171275.	+	18846.8i	−0.663690	+	0.0730317i
$509$		−	148319.i		−	0.572481i	−0.958158	−	0.286240i	$-0.907594\pi$
$509$		−	148319.i		−	0.572481i	0.958158	−	0.286240i	$-0.0924056\pi$
$510$		0			0
$511$		−	233794.i		−	0.895348i
$512$	−75515.1	+	251032.i	−0.288067	+	0.957610i
$513$	−264974.			−1.00686
$514$	−85991.7	+	95973.1i	−0.325484	+	0.363265i
$515$		0			0
$516$	7159.59	+	65064.3i	0.0268899	+	0.244367i
$517$			480660.i			1.79828i
$518$	190288.	−	212375.i	0.709171	−	0.791488i
$519$			71628.6i			0.265920i
$520$		0			0
$521$	88345.8			0.325470			0.162735	−	0.986670i	$-0.447969\pi$
$521$	88345.8			0.325470			0.162735	+	0.986670i	$0.447969\pi$
$522$	209806.	+	187986.i	0.769976	+	0.689896i
$523$	−116531.			−0.426028			−0.213014	−	0.977049i	$-0.568328\pi$
$523$	−116531.			−0.426028			−0.213014	+	0.977049i	$0.568328\pi$
$524$	−27419.1	−	249177.i	−0.0998598	−	0.907497i
$525$		0			0
$526$	−268819.	−	240861.i	−0.971603	−	0.870554i
$527$		−	105535.i		−	0.379993i
$528$	−179340.	+	39952.5i	−0.643295	+	0.143310i
$529$	−18524.3			−0.0661959
$530$		0			0
$531$	109659.			0.388914
$532$	329965.	−	36309.0i	1.16586	−	0.128289i
$533$			282308.i			0.993732i
$534$	−129296.	+	144304.i	−0.453422	+	0.506053i
$535$		0			0
$536$	−203845.	−	145835.i	−0.709530	−	0.507613i
$537$	24126.7			0.0836659
$538$	31923.8	+	28603.6i	0.110293	+	0.0988226i
$539$	−17127.7			−0.0589551
$540$		0			0
$541$		−	468624.i		−	1.60114i	−0.599237	−	0.800572i	$-0.704529\pi$
$541$		−	468624.i		−	1.60114i	0.599237	−	0.800572i	$-0.295471\pi$
$542$	−119580.	−	107143.i	−0.407062	−	0.364726i
$543$		−	74346.4i		−	0.252151i
$544$	−143035.	+	254873.i	−0.483332	+	0.861243i
$545$		0			0
$546$	−58778.9	+	65601.7i	−0.197168	+	0.220054i
$547$	362111.			1.21023			0.605114	−	0.796139i	$-0.293128\pi$
$547$	362111.			1.21023			0.605114	+	0.796139i	$0.293128\pi$
$548$	−44157.1	−	401287.i	−0.147041	−	1.33627i
$549$		−	67814.7i		−	0.224998i
$550$		0			0
$551$			481482.i			1.58590i
$552$	−91900.2	+	128456.i	−0.301605	+	0.421576i
$553$	−341216.			−1.11578
$554$	−29618.1	−	26537.7i	−0.0965022	−	0.0864657i
$555$		0			0
$556$	37430.4	+	340157.i	0.121081	+	1.10035i
$557$		−	498265.i		−	1.60602i	−0.595968	−	0.803008i	$-0.703231\pi$
$557$		−	498265.i		−	1.60602i	0.595968	−	0.803008i	$-0.296769\pi$
$558$	66739.7	+	59798.6i	0.214346	+	0.192054i
$559$			88110.9i			0.281972i
$560$		0			0
$561$	−204849.			−0.650890
$562$	−8119.65	+	9062.13i	−0.0257078	+	0.0286918i
$563$	245981.			0.776041			0.388021	−	0.921651i	$-0.373159\pi$
$563$	245981.			0.776041			0.388021	+	0.921651i	$0.373159\pi$
$564$	217416.	−	23924.2i	0.683491	−	0.0752106i
$565$		0			0
$566$	−168633.	+	188207.i	−0.526393	+	0.587494i
$567$			101047.i			0.314308i
$568$	−157299.	+	219869.i	−0.487561	+	0.681502i
$569$	385802.			1.19163			0.595813	−	0.803123i	$-0.296830\pi$
$569$	385802.			1.19163			0.595813	+	0.803123i	$0.296830\pi$
$570$		0			0
$571$	−14171.0			−0.0434640			−0.0217320	−	0.999764i	$-0.506918\pi$
$571$	−14171.0			−0.0434640			−0.0217320	+	0.999764i	$0.506918\pi$
$572$	−245842.	+	27052.1i	−0.751386	+	0.0826816i
$573$			163943.i			0.499326i
$574$	432911.	+	387887.i	1.31394	+	1.17729i
$575$		0			0
$576$	−80132.9	−	234872.i	−0.241527	−	0.707922i
$577$	109691.			0.329474			0.164737	−	0.986338i	$-0.447323\pi$
$577$	109691.			0.329474			0.164737	+	0.986338i	$0.447323\pi$
$578$	5495.60	−	6133.50i	0.0164497	−	0.0183591i
$579$	−8740.42			−0.0260720
$580$		0			0
$581$			158626.i			0.469918i
$582$	121219.	−	135290.i	0.357870	−	0.399410i
$583$		−	255091.i		−	0.750512i
$584$	−242956.	−	173816.i	−0.712364	−	0.509641i
$585$		0			0
$586$	149328.	+	133798.i	0.434857	+	0.389631i
$587$	−377043.			−1.09425			−0.547123	−	0.837052i	$-0.684277\pi$
$587$	−377043.			−1.09425			−0.547123	+	0.837052i	$0.684277\pi$
$588$	852.506	+	7747.32i	0.00246571	+	0.0224077i
$589$			153160.i			0.441485i
$590$		0			0
$591$		−	327955.i		−	0.938943i
$592$	−79227.0	−	355637.i	−0.226063	−	1.01476i
$593$	27615.5			0.0785314			0.0392657	−	0.999229i	$-0.487498\pi$
$593$	27615.5			0.0785314			0.0392657	+	0.999229i	$0.487498\pi$
$594$	271251.	−	302736.i	0.768773	−	0.858009i
$595$		0			0
$596$	641237.	−	70560.9i	1.80520	−	0.198642i
$597$		−	351130.i		−	0.985189i
$598$	−141876.	+	158345.i	−0.396742	+	0.442793i
$599$			170000.i			0.473802i	0.971534	+	0.236901i	$0.0761316\pi$
$599$			170000.i			0.473802i	−0.971534	+	0.236901i	$0.923868\pi$
$600$		0			0
$601$	297213.			0.822846			0.411423	−	0.911445i	$-0.365032\pi$
$601$	297213.			0.822846			0.411423	+	0.911445i	$0.365032\pi$
$602$	135115.	+	121063.i	0.372831	+	0.334055i
$603$	237275.			0.652556
$604$	−451486.	+	49681.0i	−1.23757	+	0.136181i
$605$		0			0
$606$	202121.	+	181100.i	0.550385	+	0.493143i
$607$		−	23984.9i		−	0.0650969i	−0.999470	−	0.0325485i	$-0.989638\pi$
$607$		−	23984.9i		−	0.0650969i	0.999470	−	0.0325485i	$-0.0103623\pi$
$608$	207584.	−	369890.i	0.561547	−	1.00061i
$609$	−263050.			−0.709257
$610$		0			0
$611$	294427.			0.788671
$612$	−30262.9	−	275021.i	−0.0807994	−	0.734281i
$613$		−	291516.i		−	0.775785i	−0.921705	−	0.387893i	$-0.873203\pi$
$613$		−	291516.i		−	0.775785i	0.921705	−	0.387893i	$-0.126797\pi$
$614$	−132361.	+	147725.i	−0.351094	+	0.391848i
$615$		0			0
$616$	−296299.	+	414160.i	−0.780852	+	1.09146i
$617$	111058.			0.291729			0.145864	−	0.989305i	$-0.453404\pi$
$617$	111058.			0.291729			0.145864	+	0.989305i	$0.453404\pi$
$618$	177363.	+	158917.i	0.464394	+	0.416096i
$619$	−300205.			−0.783496			−0.391748	−	0.920073i	$-0.628129\pi$
$619$	−300205.			−0.783496			−0.391748	+	0.920073i	$0.628129\pi$
$620$		0			0
$621$		−	349421.i		−	0.906079i
$622$	365513.	+	327499.i	0.944761	+	0.846503i
$623$			537003.i			1.38357i
$624$	24472.8	+	109854.i	0.0628514	+	0.282129i
$625$		0			0
$626$	475787.	−	531014.i	1.21413	−	1.35506i
$627$	297292.			0.756220
$628$	76903.8	−	8462.40i	0.194997	−	0.0214573i
$629$		−	406221.i		−	1.02674i
$630$		0			0
$631$		−	150496.i		−	0.377979i	−0.981979	−	0.188989i	$-0.939479\pi$
$631$		−	150496.i		−	0.377979i	0.981979	−	0.188989i	$-0.0605212\pi$
$632$	−253679.	+	354587.i	−0.635113	+	0.887746i
$633$	161778.			0.403749
$634$	26872.6	+	24077.8i	0.0668547	+	0.0599016i
$635$		0			0
$636$	−115385.	+	12696.8i	−0.285255	+	0.0313891i
$637$			10491.5i			0.0258559i
$638$	−550100.	−	492888.i	−1.35145	−	1.21090i
$639$		−	255927.i		−	0.626779i
$640$		0			0
$641$	−341612.			−0.831414			−0.415707	−	0.909499i	$-0.636466\pi$
$641$	−341612.			−0.831414			−0.415707	+	0.909499i	$0.636466\pi$
$642$	−160213.	+	178810.i	−0.388712	+	0.433831i
$643$	−89782.7			−0.217156			−0.108578	−	0.994088i	$-0.534630\pi$
$643$	−89782.7			−0.217156			−0.108578	+	0.994088i	$0.534630\pi$
$644$	47880.8	+	435126.i	0.115449	+	1.04916i
$645$		0			0
$646$	315571.	−	352201.i	0.756192	−	0.843967i
$647$		−	569707.i		−	1.36095i	−0.732770	−	0.680477i	$-0.761773\pi$
$647$		−	569707.i		−	1.36095i	0.732770	−	0.680477i	$-0.238227\pi$
$648$	105006.	+	75123.8i	0.250072	+	0.178907i
$649$	−287519.			−0.682617
$650$		0			0
$651$	−83676.7			−0.197443
$652$	47143.3	+	428424.i	0.110898	+	1.00781i
$653$			258929.i			0.607233i	0.952794	+	0.303616i	$0.0981941\pi$
$653$			258929.i			0.607233i	−0.952794	+	0.303616i	$0.901806\pi$
$654$	−258583.	−	231690.i	−0.604567	−	0.541691i
$655$		0			0
$656$	724939.	−	161498.i	1.68459	−	0.375284i
$657$	282800.			0.655163
$658$	404539.	−	451495.i	0.934347	−	1.04280i
$659$	−43971.3			−0.101251			−0.0506255	−	0.998718i	$-0.516121\pi$
$659$	−43971.3			−0.101251			−0.0506255	+	0.998718i	$0.516121\pi$
$660$		0			0
$661$			216610.i			0.495765i	0.968790	+	0.247882i	$0.0797347\pi$
$661$			216610.i			0.495765i	−0.968790	+	0.247882i	$0.920265\pi$
$662$	−187802.	+	209602.i	−0.428534	+	0.478276i
$663$			125480.i			0.285461i
$664$	164842.	+	117932.i	0.373880	+	0.267482i
$665$		0			0
$666$	256892.	+	230174.i	0.579164	+	0.518930i
$667$	−634931.			−1.42717
$668$	385336.	−	42401.8i	0.863547	−	0.0950237i
$669$		−	298587.i		−	0.667142i
$670$		0			0
$671$			177806.i			0.394914i
$672$	202084.	+	113410.i	0.447500	+	0.251138i
$673$	614134.			1.35592			0.677958	−	0.735101i	$-0.262865\pi$
$673$	614134.			1.35592			0.677958	+	0.735101i	$0.262865\pi$
$674$	−396730.	+	442781.i	−0.873325	+	0.974696i
$675$		0			0
$676$	−33412.7	−	303645.i	−0.0731169	−	0.664465i
$677$		−	710586.i		−	1.55038i	−0.631725	−	0.775192i	$-0.717653\pi$
$677$		−	710586.i		−	1.55038i	0.631725	−	0.775192i	$-0.282347\pi$
$678$	−252960.	+	282322.i	−0.550291	+	0.614165i
$679$		−	503458.i		−	1.09200i
$680$		0			0
$681$	29389.3			0.0633716
$682$	−174988.	−	156789.i	−0.376218	−	0.337090i
$683$	187636.			0.402231			0.201116	−	0.979568i	$-0.435543\pi$
$683$	187636.			0.402231			0.201116	+	0.979568i	$0.435543\pi$
$684$	43919.8	+	399130.i	0.0938747	+	0.853105i
$685$		0			0
$686$	−342183.	−	306595.i	−0.727126	−	0.651503i
$687$			23407.5i			0.0495955i
$688$	226260.	−	50405.0i	0.478003	−	0.106487i
$689$	−156255.			−0.329151
$690$		0			0
$691$	628570.			1.31643			0.658215	−	0.752830i	$-0.271312\pi$
$691$	628570.			1.31643			0.658215	+	0.752830i	$0.271312\pi$
$692$	252140.	−	27745.2i	0.526538	−	0.0579396i
$693$		−	482081.i		−	1.00382i
$694$	252018.	−	281271.i	0.523254	−	0.583991i
$695$		0			0
$696$	−195566.	+	273358.i	−0.403716	+	0.564305i
$697$	828051.			1.70448
$698$	−214740.	−	192406.i	−0.440759	−	0.394919i
$699$	203561.			0.416619
$700$		0			0
$701$		−	149078.i		−	0.303374i	−0.988429	−	0.151687i	$-0.951529\pi$
$701$		−	149078.i		−	0.303374i	0.988429	−	0.151687i	$-0.0484705\pi$
$702$	−185440.	−	166154.i	−0.376296	−	0.337161i
$703$			589538.i			1.19289i
$704$	210104.	+	615821.i	0.423925	+	1.24254i
$705$		0			0
$706$	−85094.7	+	94972.0i	−0.170723	+	0.190540i
$707$	752160.			1.50477
$708$	14310.8	+	130053.i	0.0285495	+	0.259450i
$709$			47510.9i			0.0945151i	0.998883	+	0.0472575i	$0.0150481\pi$
$709$			47510.9i			0.0945151i	−0.998883	+	0.0472575i	$0.984952\pi$
$710$		0			0
$711$		−	412739.i		−	0.816462i
$712$	558047.	+	399239.i	1.10081	+	0.787541i
$713$	−201973.			−0.397296
$714$	192419.	+	172407.i	0.377444	+	0.338189i
$715$		0			0
$716$	−9345.40	−	84928.3i	−0.0182294	−	0.165663i
$717$		−	324152.i		−	0.630536i
$718$	103225.	+	92489.5i	0.200234	+	0.179409i
$719$		−	843806.i		−	1.63224i	−0.577880	−	0.816122i	$-0.696120\pi$
$719$		−	843806.i		−	1.63224i	0.577880	−	0.816122i	$-0.303880\pi$
$720$		0			0
$721$	660028.			1.26967
$722$	−110119.	+	122901.i	−0.211245	+	0.235765i
$723$	−59700.0			−0.114208
$724$	−261707.	+	28797.9i	−0.499273	+	0.0549394i
$725$		0			0
$726$	−127766.	+	142597.i	−0.242406	+	0.270543i
$727$		−	792065.i		−	1.49862i	−0.662218	−	0.749311i	$-0.730385\pi$
$727$		−	792065.i		−	1.49862i	0.662218	−	0.749311i	$-0.269615\pi$
$728$	253693.	+	181497.i	0.478680	+	0.342458i
$729$	111878.			0.210519
$730$		0			0
$731$	258442.			0.483647
$732$	80426.7	−	8850.05i	0.150099	−	0.0165167i
$733$		−	4047.83i		−	0.00753380i	−0.999993	−	0.00376690i	$-0.998801\pi$
$733$		−	4047.83i		−	0.00753380i	0.999993	−	0.00376690i	$-0.00119904\pi$
$734$	−268817.	−	240859.i	−0.498959	−	0.447066i
$735$		0			0
$736$	487775.	+	273741.i	0.900459	+	0.505340i
$737$	−622123.			−1.14536
$738$	−469193.	+	523655.i	−0.861468	+	0.961463i
$739$	895023.			1.63887			0.819437	−	0.573170i	$-0.194286\pi$
$739$	895023.			1.63887			0.819437	+	0.573170i	$0.194286\pi$
$740$		0			0
$741$		−	182105.i		−	0.331655i
$742$	−214692.	+	239613.i	−0.389950	+	0.435213i
$743$		−	616018.i		−	1.11588i	−0.829883	−	0.557938i	$-0.811593\pi$
$743$		−	616018.i		−	1.11588i	0.829883	−	0.557938i	$-0.188407\pi$
$744$	−62210.1	+	86955.8i	−0.112387	+	0.157091i
$745$		0			0
$746$	56407.8	+	50541.2i	0.101359	+	0.0908172i
$747$	−191876.			−0.343858
$748$	79347.8	+	721089.i	0.141818	+	1.28880i
$749$			665410.i			1.18611i
$750$		0			0
$751$		−	232448.i		−	0.412141i	−0.978537	−	0.206071i	$-0.933932\pi$
$751$		−	232448.i		−	0.412141i	0.978537	−	0.206071i	$-0.0660677\pi$
$752$	−168431.	−	756059.i	−0.297842	−	1.33697i
$753$	−41583.7			−0.0733387
$754$	−301917.	+	336962.i	−0.531062	+	0.592705i
$755$		0			0
$756$	−509585.	+	56074.1i	−0.891605	+	0.0981111i
$757$			431771.i			0.753462i	0.926323	+	0.376731i	$0.122952\pi$
$757$			431771.i			0.753462i	−0.926323	+	0.376731i	$0.877048\pi$
$758$	390057.	−	435333.i	0.678875	−	0.757675i
$759$			392040.i			0.680528i
$760$		0			0
$761$	−368807.			−0.636840			−0.318420	−	0.947950i	$-0.603152\pi$
$761$	−368807.			−0.636840			−0.318420	+	0.947950i	$0.603152\pi$
$762$	144951.	+	129876.i	0.249639	+	0.223676i
$763$	−962274.			−1.65291
$764$	577097.	−	63503.1i	0.988695	−	0.108795i
$765$		0			0
$766$	−189882.	−	170133.i	−0.323613	−	0.289956i
$767$			176119.i			0.299375i
$768$	268095.	−	125687.i	0.454534	−	0.213093i
$769$	850748.			1.43863			0.719313	−	0.694686i	$-0.244456\pi$
$769$	850748.			1.43863			0.719313	+	0.694686i	$0.244456\pi$
$770$		0			0
$771$	145551.			0.244854
$772$	3385.58	+	30767.2i	0.00568066	+	0.0516242i
$773$			967445.i			1.61908i	0.587067	+	0.809538i	$0.300282\pi$
$773$			967445.i			1.61908i	−0.587067	+	0.809538i	$0.699718\pi$
$774$	−146439.	+	163437.i	−0.244442	+	0.272816i
$775$		0			0
$776$	−523187.	−	374300.i	−0.868828	−	0.621578i
$777$	−322085.			−0.533492
$778$	−217686.	−	195046.i	−0.359643	−	0.322240i
$779$	−1.20173e6			−1.98030
$780$		0			0
$781$			671026.i			1.10011i
$782$	464448.	+	416144.i	0.759493	+	0.680503i
$783$		−	743580.i		−	1.21284i
$784$	26941.2	−	6001.82i	0.0438313	−	0.00976451i
$785$		0			0
$786$	−188949.	+	210881.i	−0.305843	+	0.341344i
$787$	−434908.			−0.702178			−0.351089	−	0.936342i	$-0.614189\pi$
$787$	−434908.			−0.702178			−0.351089	+	0.936342i	$0.614189\pi$
$788$	−1.15443e6	+	127033.i	−1.85916	+	0.204580i
$789$			407687.i			0.654896i
$790$		0			0
$791$			1.05061e6i			1.67915i
$792$	−500973.	−	358407.i	−0.798664	−	0.571381i
$793$	108915.			0.173197
$794$	53380.5	+	47828.8i	0.0846723	+	0.0758662i
$795$		0			0
$796$	−1.23601e6	+	136010.i	−1.95073	+	0.214656i
$797$			648541.i			1.02099i	0.859881	+	0.510494i	$0.170537\pi$
$797$			648541.i			1.02099i	−0.859881	+	0.510494i	$0.829463\pi$
$798$	−279253.	−	250210.i	−0.438523	−	0.392915i
$799$		−	863598.i		−	1.35275i
$800$		0			0
$801$	−649566.			−1.01241
$802$	178226.	−	198914.i	0.277091	−	0.309255i
$803$	−741487.			−1.14993
$804$	30965.3	+	281403.i	0.0479030	+	0.435328i
$805$		0			0
$806$	−96040.5	+	107188.i	−0.147837	+	0.164998i
$807$		−	48415.0i		−	0.0743418i
$808$	559199.	−	781636.i	0.856532	−	1.19724i
$809$	338083.			0.516567			0.258284	−	0.966069i	$-0.416843\pi$
$809$	338083.			0.516567			0.258284	+	0.966069i	$0.416843\pi$
$810$		0			0
$811$	−941405.			−1.43131			−0.715657	−	0.698452i	$-0.753872\pi$
$811$	−941405.			−1.43131			−0.715657	+	0.698452i	$0.753872\pi$
$812$	101892.	+	925962.i	0.154535	+	1.40437i
$813$			181353.i			0.274375i
$814$	−673556.	−	603505.i	−1.01654	−	0.910818i
$815$		0			0
$816$	322219.	−	71782.3i	0.483917	−	0.107805i
$817$	−375070.			−0.561912
$818$	776781.	−	866945.i	1.16089	−	1.29564i
$819$	−295298.			−0.440243
$820$		0			0
$821$		−	702066.i		−	1.04158i	−0.853686	−	0.520789i	$-0.825638\pi$
$821$		−	702066.i		−	1.04158i	0.853686	−	0.520789i	$-0.174362\pi$
$822$	−304292.	+	339613.i	−0.450347	+	0.502621i
$823$		−	736652.i		−	1.08758i	−0.839220	−	0.543792i	$-0.816988\pi$
$823$		−	736652.i		−	1.08758i	0.839220	−	0.543792i	$-0.183012\pi$
$824$	490703.	−	685893.i	0.722710	−	1.01019i
$825$		0			0
$826$	270073.	+	241985.i	0.395842	+	0.354673i
$827$	698186.			1.02085			0.510423	−	0.859923i	$-0.329489\pi$
$827$	698186.			1.02085			0.510423	+	0.859923i	$0.329489\pi$
$828$	−526334.	+	57917.2i	−0.767717	+	0.0844786i
$829$		−	609784.i		−	0.887293i	−0.896202	−	0.443647i	$-0.853685\pi$
$829$		−	609784.i		−	0.887293i	0.896202	−	0.443647i	$-0.146315\pi$
$830$		0			0
$831$			44918.3i			0.0650461i
$832$	377219.	−	128699.i	0.544938	−	0.185921i
$833$	30773.2			0.0443488
$834$	257938.	−	287878.i	0.370837	−	0.413882i
$835$		0			0
$836$	−115155.	−	1.04650e6i	−0.164767	−	1.49736i
$837$		−	236534.i		−	0.337631i
$838$	−533060.	+	594935.i	−0.759081	+	0.847192i
$839$		−	245795.i		−	0.349179i	−0.984641	−	0.174590i	$-0.944140\pi$
$839$		−	245795.i		−	0.349179i	0.984641	−	0.174590i	$-0.0558599\pi$
$840$		0			0
$841$	−643872.			−0.910348
$842$	−347185.	−	311077.i	−0.489708	−	0.438777i
$843$	13743.5			0.0193393
$844$	−62664.2	−	569474.i	−0.0879700	−	0.799445i
$845$		0			0
$846$	546135.	+	489335.i	0.763060	+	0.683700i
$847$			530650.i			0.739676i
$848$	89387.9	+	401247.i	0.124304	+	0.557982i
$849$	285432.			0.395992
$850$		0			0
$851$	−777425.			−1.07349
$852$	303524.	−	33399.4i	0.418132	−	0.0460107i
$853$			482861.i			0.663627i	0.943345	+	0.331813i	$0.107660\pi$
$853$			482861.i			0.663627i	−0.943345	+	0.331813i	$0.892340\pi$
$854$	149647.	−	167018.i	0.205189	−	0.229006i
$855$		0			0
$856$	691486.	+	494704.i	0.943705	+	0.675147i
$857$	−275704.			−0.375389			−0.187695	−	0.982227i	$-0.560102\pi$
$857$	−275704.			−0.375389			−0.187695	+	0.982227i	$0.560102\pi$
$858$	208058.	+	186420.i	0.282625	+	0.253231i
$859$	−874456.			−1.18509			−0.592546	−	0.805537i	$-0.701877\pi$
$859$	−874456.			−1.18509			−0.592546	+	0.805537i	$0.701877\pi$
$860$		0			0
$861$		−	656546.i		−	0.885643i
$862$	−171224.	−	153416.i	−0.230436	−	0.206470i
$863$			207383.i			0.278453i	0.990261	+	0.139227i	$0.0444616\pi$
$863$			207383.i			0.278453i	−0.990261	+	0.139227i	$0.955538\pi$
$864$	−320583.	+	571243.i	−0.429451	+	0.765232i
$865$		0			0
$866$	−208956.	+	233211.i	−0.278624	+	0.310966i
$867$	−9301.96			−0.0123747
$868$	32412.0	+	294550.i	0.0430196	+	0.390949i
$869$			1.08218e6i			1.43304i
$870$		0			0
$871$			381080.i			0.502319i
$872$	−715410.	+	999984.i	−0.940854	+	1.31510i
$873$	608989.			0.799063
$874$	−674041.	−	603939.i	−0.882396	−	0.790625i
$875$		0			0
$876$	36906.4	+	335395.i	0.0480943	+	0.437067i
$877$			287580.i			0.373903i	0.982369	+	0.186952i	$0.0598607\pi$
$877$			287580.i			0.373903i	−0.982369	+	0.186952i	$0.940139\pi$
$878$	−741553.	−	664430.i	−0.961952	−	0.861906i
$879$		−	226468.i		−	0.293110i
$880$		0			0
$881$	72878.9			0.0938966			0.0469483	−	0.998897i	$-0.485050\pi$
$881$	72878.9			0.0938966			0.0469483	+	0.998897i	$0.485050\pi$
$882$	−17436.8	+	19460.8i	−0.0224145	+	0.0250163i
$883$	587119.			0.753017			0.376509	−	0.926413i	$-0.377125\pi$
$883$	587119.			0.753017			0.376509	+	0.926413i	$0.377125\pi$
$884$	441701.	−	48604.3i	0.565229	−	0.0621971i
$885$		0			0
$886$	−814601.	+	909155.i	−1.03771	+	1.15817i
$887$			525528.i			0.667958i	0.942581	+	0.333979i	$0.108391\pi$
$887$			525528.i			0.667958i	−0.942581	+	0.333979i	$0.891609\pi$
$888$	−239456.	+	334707.i	−0.303669	+	0.424462i
$889$	539413.			0.682523
$890$		0			0
$891$	320473.			0.403679
$892$	−1.05106e6	+	115657.i	−1.32098	+	0.145359i
$893$			1.25332e6i			1.57166i
$894$	−542685.	−	486244.i	−0.679005	−	0.608387i
$895$		0			0
$896$	320938.	−	755284.i	0.399765	−	0.940794i
$897$	240143.			0.298459
$898$	284954.	−	318030.i	0.353363	−	0.394380i
$899$	−429804.			−0.531804
$900$		0			0
$901$			458319.i			0.564571i
$902$	1.23020e6	−	1.37299e6i	1.51204	−	1.68755i
$903$		−	204914.i		−	0.251302i
$904$	1.09179e6	+	781088.i	1.33598	+	0.955791i
$905$		0			0
$906$	382097.	+	342358.i	0.465498	+	0.417085i
$907$	−1.45695e6			−1.77105			−0.885523	−	0.464596i	$-0.846199\pi$
$907$	−1.45695e6			−1.77105			−0.885523	+	0.464596i	$0.846199\pi$
$908$	−11383.9	−	103453.i	−0.0138076	−	0.125479i
$909$			909822.i			1.10111i
$910$		0			0
$911$			546104.i			0.658020i	0.944326	+	0.329010i	$0.106715\pi$
$911$			546104.i			0.658020i	−0.944326	+	0.329010i	$0.893285\pi$
$912$	−467628.	+	104176.i	−0.562226	+	0.125250i
$913$	503088.			0.603535
$914$	566999.	−	632813.i	0.678718	−	0.757500i
$915$		0			0
$916$	82396.9	−	9066.85i	0.0982019	−	0.0108060i
$917$			784758.i			0.933248i
$918$	−487354.	+	543924.i	−0.578308	+	0.645435i
$919$			1.30937e6i			1.55036i	0.631740	+	0.775180i	$0.282341\pi$
$919$			1.30937e6i			1.55036i	−0.631740	+	0.775180i	$0.717659\pi$
$920$		0			0
$921$	224037.			0.264120
$922$	−1.12475e6	−	1.00778e6i	−1.32311	−	1.18550i
$923$	411036.			0.482476
$924$	571738.	−	62913.3i	0.669658	−	0.0736883i
$925$		0			0
$926$	−192387.	−	172378.i	−0.224364	−	0.201030i
$927$			798378.i			0.929072i
$928$	1.03800e6	+	582529.i	1.20532	+	0.676428i
$929$	731556.			0.847649			0.423824	−	0.905744i	$-0.360687\pi$
$929$	731556.			0.847649			0.423824	+	0.905744i	$0.360687\pi$
$930$		0			0
$931$	−44660.3			−0.0515255
$932$	−78848.8	−	716554.i	−0.0907743	−	0.824930i
$933$		−	554331.i		−	0.636804i
$934$	268621.	−	299801.i	0.307926	−	0.343668i
$935$		0			0
$936$	−219541.	+	306870.i	−0.250590	+	0.350269i
$937$	−368844.			−0.420111			−0.210055	−	0.977690i	$-0.567364\pi$
$937$	−368844.			−0.420111			−0.210055	+	0.977690i	$0.567364\pi$
$938$	584374.	+	523598.i	0.664179	+	0.595103i
$939$	−805327.			−0.913358
$940$		0			0
$941$			1.05710e6i			1.19381i	0.802310	+	0.596907i	$0.203604\pi$
$941$			1.05710e6i			1.19381i	−0.802310	+	0.596907i	$0.796396\pi$
$942$	−65084.5	−	58315.5i	−0.0733459	−	0.0657177i
$943$		−	1.58472e6i		−	1.78209i
$944$	452256.	−	100751.i	0.507505	−	0.113059i
$945$		0			0
$946$	383956.	−	428523.i	0.429041	−	0.478842i
$947$	1.05246e6			1.17356			0.586778	−	0.809748i	$-0.300396\pi$
$947$	1.05246e6			1.17356			0.586778	+	0.809748i	$0.300396\pi$
$948$	489499.	−	53863.9i	0.544672	−	0.0599351i
$949$			454196.i			0.504325i
$950$		0			0
$951$		−	40754.6i		−	0.0450625i
$952$	532358.	−	744117.i	0.587394	−	0.821046i
$953$	−65088.8			−0.0716672			−0.0358336	−	0.999358i	$-0.511409\pi$
$953$	−65088.8			−0.0716672			−0.0358336	+	0.999358i	$0.511409\pi$
$954$	−289838.	−	259694.i	−0.318463	−	0.285342i
$955$		0			0
$956$	−1.14105e6	+	125559.i	−1.24850	+	0.137383i
$957$			834273.i			0.910928i
$958$	−562658.	−	504140.i	−0.613074	−	0.549313i
$959$			1.26381e6i			1.37419i
$960$		0			0
$961$	786799.			0.851956
$962$	−369675.	+	412585.i	−0.399457	+	0.445824i
$963$	−804889.			−0.867927
$964$	23124.6	+	210150.i	0.0248840	+	0.226139i
$965$		0			0
$966$	329953.	−	368252.i	0.353588	−	0.394630i
$967$			481804.i			0.515250i	0.966245	+	0.257625i	$0.0829399\pi$
$967$			481804.i			0.515250i	−0.966245	+	0.257625i	$0.917060\pi$
$968$	551445.	+	394516.i	0.588507	+	0.421031i
$969$	−534142.			−0.568865
$970$		0			0
$971$	439500.			0.466144			0.233072	−	0.972459i	$-0.425122\pi$
$971$	439500.			0.466144			0.233072	+	0.972459i	$0.425122\pi$
$972$	−106631.	−	969033.i	−0.112863	−	1.02567i
$973$		−	1.07129e6i		−	1.13157i
$974$	314135.	+	281464.i	0.331130	+	0.296691i
$975$		0			0
$976$	−62306.2	−	279682.i	−0.0654081	−	0.293606i
$977$	1.37613e6			1.44169			0.720844	−	0.693098i	$-0.243755\pi$
$977$	1.37613e6			1.44169			0.720844	+	0.693098i	$0.243755\pi$
$978$	324870.	−	362580.i	0.339651	−	0.379076i
$979$	1.70313e6			1.77697
$980$		0			0
$981$		−	1.16398e6i		−	1.20950i
$982$	663005.	−	739964.i	0.687534	−	0.767339i
$983$			767551.i			0.794328i	0.917748	+	0.397164i	$0.130006\pi$
$983$			767551.i			0.794328i	−0.917748	+	0.397164i	$0.869994\pi$
$984$	−682274.	−	488114.i	−0.704643	−	0.504117i
$985$		0			0
$986$	988360.	+	885568.i	1.01663	+	0.910894i
$987$	−684730.			−0.702887
$988$	−641030.	+	70538.1i	−0.656696	+	0.0722620i
$989$		−	494606.i		−	0.505670i
$990$		0			0
$991$		−	1.85016e6i		−	1.88392i	−0.335722	−	0.941961i	$-0.608980\pi$
$991$		−	1.85016e6i		−	1.88392i	0.335722	−	0.941961i	$-0.391020\pi$
$992$	330190.	+	185304.i	0.335537	+	0.188305i
$993$	317878.			0.322376
$994$	564757.	−	630311.i	0.571595	−	0.637943i
$995$		0			0
$996$	−25040.5	−	227561.i	−0.0252420	−	0.229392i
$997$		−	337598.i		−	0.339633i	−0.985476	−	0.169816i	$-0.945683\pi$
$997$		−	337598.i		−	0.339633i	0.985476	−	0.169816i	$-0.0543175\pi$
$998$	−518206.	+	578356.i	−0.520285	+	0.580677i
$999$		−	910457.i		−	0.912281i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.5.g.h.51.4		16
4.3	odd	2		800.5.g.h.751.7		16
5.2	odd	4		200.5.e.e.99.7		32
5.3	odd	4		200.5.e.e.99.26		32
5.4	even	2		40.5.g.a.11.13	✓	16
8.3	odd	2	inner	200.5.g.h.51.3		16
8.5	even	2		800.5.g.h.751.8		16
15.14	odd	2		360.5.g.a.91.4		16
20.3	even	4		800.5.e.e.399.11		32
20.7	even	4		800.5.e.e.399.22		32
20.19	odd	2		160.5.g.a.111.9		16
40.3	even	4		200.5.e.e.99.8		32
40.13	odd	4		800.5.e.e.399.21		32
40.19	odd	2		40.5.g.a.11.14	yes	16
40.27	even	4		200.5.e.e.99.25		32
40.29	even	2		160.5.g.a.111.10		16
40.37	odd	4		800.5.e.e.399.12		32
60.59	even	2		1440.5.g.a.271.15		16
120.29	odd	2		1440.5.g.a.271.2		16
120.59	even	2		360.5.g.a.91.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.5.g.a.11.13	✓	16	5.4	even	2
40.5.g.a.11.14	yes	16	40.19	odd	2
160.5.g.a.111.9		16	20.19	odd	2
160.5.g.a.111.10		16	40.29	even	2
200.5.e.e.99.7		32	5.2	odd	4
200.5.e.e.99.8		32	40.3	even	4
200.5.e.e.99.25		32	40.27	even	4
200.5.e.e.99.26		32	5.3	odd	4
200.5.g.h.51.3		16	8.3	odd	2	inner
200.5.g.h.51.4		16	1.1	even	1	trivial
360.5.g.a.91.3		16	120.59	even	2
360.5.g.a.91.4		16	15.14	odd	2
800.5.e.e.399.11		32	20.3	even	4
800.5.e.e.399.12		32	40.37	odd	4
800.5.e.e.399.21		32	40.13	odd	4
800.5.e.e.399.22		32	20.7	even	4
800.5.g.h.751.7		16	4.3	odd	2
800.5.g.h.751.8		16	8.5	even	2
1440.5.g.a.271.2		16	120.29	odd	2
1440.5.g.a.271.15		16	60.59	even	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	200.5.g.h.51.4

Level	$200$
Weight	$5$
Character	200.51
Analytic conductor	$20.674$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$