LMFDB - Embedded newform 81.5.h.a.2.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,5,Mod(2,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.2"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	81.h (of order $54$, degree $18$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$8.37296700979$
Analytic rank:	$0$
Dimension:	$630$
Relative dimension:	$35$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			2.9
Character	$\chi$	$=$	81.2
Dual form			81.5.h.a.41.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.33543 - 0.252510i) q^{2} +(-8.98142 + 0.578015i) q^{3} +(2.84035 + 0.331989i) q^{4} +(-9.04763 - 38.1749i) q^{5} +(39.0842 - 0.238046i) q^{6} +(-39.6102 - 53.2058i) q^{7} +(56.1985 + 9.90930i) q^{8} +(80.3318 - 10.3828i) q^{9} +(29.5858 + 167.789i) q^{10} +(-115.575 - 109.039i) q^{11} +(-25.7023 - 1.33997i) q^{12} +(-143.670 - 72.1536i) q^{13} +(158.292 + 240.672i) q^{14} +(103.326 + 337.635i) q^{15} +(-285.664 - 67.7036i) q^{16} +(-9.47504 + 26.0325i) q^{17} +(-350.894 + 24.7293i) q^{18} +(-263.350 + 95.8514i) q^{19} +(-13.0248 - 111.434i) q^{20} +(386.510 + 454.968i) q^{21} +(473.532 + 501.915i) q^{22} +(805.016 + 599.312i) q^{23} +(-510.470 - 56.5161i) q^{24} +(-816.946 + 410.286i) q^{25} +(604.649 + 349.095i) q^{26} +(-715.492 + 139.685i) q^{27} +(-94.8432 - 164.273i) q^{28} +(750.082 - 1140.44i) q^{29} +(-362.707 - 1489.88i) q^{30} +(-350.695 - 813.003i) q^{31} +(346.689 + 103.792i) q^{32} +(1101.05 + 912.522i) q^{33} +(47.6518 - 110.469i) q^{34} +(-1672.75 + 1993.50i) q^{35} +(231.617 - 2.82148i) q^{36} +(534.545 - 448.536i) q^{37} +(1165.94 - 349.058i) q^{38} +(1332.06 + 564.998i) q^{39} +(-130.176 - 2235.03i) q^{40} +(-1507.53 + 87.8039i) q^{41} +(-1560.80 - 2070.08i) q^{42} +(272.547 + 910.370i) q^{43} +(-292.073 - 348.079i) q^{44} +(-1123.17 - 2972.72i) q^{45} +(-3338.76 - 2801.55i) q^{46} +(586.535 + 253.007i) q^{47} +(2604.80 + 442.956i) q^{48} +(-573.270 + 1914.85i) q^{49} +(3645.41 - 1572.48i) q^{50} +(70.0522 - 239.285i) q^{51} +(-384.118 - 252.638i) q^{52} +(3716.11 - 2145.50i) q^{53} +(3137.24 - 424.926i) q^{54} +(-3116.88 + 5398.60i) q^{55} +(-1698.80 - 3382.59i) q^{56} +(2309.85 - 1013.10i) q^{57} +(-3539.90 + 4754.91i) q^{58} +(1717.48 - 1620.35i) q^{59} +(181.391 + 993.306i) q^{60} +(1896.01 - 221.612i) q^{61} +(1315.12 + 3613.27i) q^{62} +(-3734.39 - 3862.85i) q^{63} +(2937.12 + 1069.02i) q^{64} +(-1454.59 + 6137.40i) q^{65} +(-4543.10 - 4234.20i) q^{66} +(-2587.30 + 1701.70i) q^{67} +(-35.5549 + 70.7957i) q^{68} +(-7576.60 - 4917.36i) q^{69} +(7755.46 - 8220.31i) q^{70} +(-2816.68 + 496.657i) q^{71} +(4617.41 + 212.535i) q^{72} +(-1182.70 + 6707.44i) q^{73} +(-2430.74 + 1809.62i) q^{74} +(7100.18 - 4157.16i) q^{75} +(-779.827 + 184.822i) q^{76} +(-1223.57 + 10468.3i) q^{77} +(-5632.39 - 2785.87i) q^{78} +(88.8883 - 1526.15i) q^{79} +11517.8i q^{80} +(6345.40 - 1668.14i) q^{81} +6557.98 q^{82} +(-11383.1 - 662.993i) q^{83} +(946.779 + 1420.59i) q^{84} +(1079.51 + 126.177i) q^{85} +(-951.730 - 4015.66i) q^{86} +(-6077.60 + 10676.4i) q^{87} +(-5414.62 - 7273.09i) q^{88} +(5744.39 + 1012.89i) q^{89} +(4118.80 + 13171.6i) q^{90} +(1851.80 + 10502.1i) q^{91} +(2087.56 + 1969.51i) q^{92} +(3619.67 + 7099.22i) q^{93} +(-2478.99 - 1245.00i) q^{94} +(6041.81 + 9186.13i) q^{95} +(-3173.76 - 731.808i) q^{96} +(9205.02 + 2181.63i) q^{97} +(2968.89 - 8156.95i) q^{98} +(-10416.4 - 7559.32i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 630 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 2034 q^{18}+ \cdots + 4266 q^{99}+O(q^{100}) $ 630 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 2034 * q^18 - 18 * q^19 + 846 * q^20 + 2277 * q^21 - 18 * q^22 + 2979 * q^23 + 4734 * q^24 - 18 * q^25 - 27 * q^26 - 1449 * q^27 - 9 * q^28 - 3987 * q^29 - 9522 * q^30 - 18 * q^31 - 9090 * q^32 - 3231 * q^33 - 18 * q^34 + 2655 * q^35 + 10062 * q^36 - 18 * q^37 + 7326 * q^38 - 18 * q^39 - 18 * q^40 - 13410 * q^41 - 18333 * q^42 - 18 * q^43 + 4518 * q^44 + 11214 * q^45 - 18 * q^46 + 18774 * q^47 + 35127 * q^48 - 18 * q^49 + 31923 * q^50 + 12330 * q^51 - 162 * q^52 - 27 * q^53 - 13500 * q^54 - 9 * q^55 - 38808 * q^56 - 21186 * q^57 - 18 * q^58 - 31014 * q^59 - 58167 * q^60 - 18 * q^61 - 38331 * q^62 - 14058 * q^63 - 18 * q^64 + 60354 * q^65 + 99126 * q^66 - 12303 * q^67 + 72153 * q^68 + 20502 * q^69 + 21582 * q^70 - 39546 * q^71 - 138258 * q^72 - 18 * q^73 - 96786 * q^74 - 56268 * q^75 + 44046 * q^76 - 62658 * q^77 - 44523 * q^78 + 8460 * q^79 + 11574 * q^81 - 36 * q^82 + 33894 * q^83 + 153927 * q^84 - 39168 * q^85 + 117486 * q^86 + 125982 * q^87 - 72594 * q^88 + 7596 * q^89 - 1557 * q^90 - 18 * q^91 + 48312 * q^92 + 3294 * q^93 + 6030 * q^94 + 21798 * q^95 - 37665 * q^96 + 43587 * q^97 + 11079 * q^98 + 4266 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{54}\right)$

Coefficient data

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

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

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

$2$	−4.33543	−	0.252510i	−1.08386	−	0.0631275i	−0.493096	−	0.869975i	$-0.664135\pi$
$2$	−4.33543	−	0.252510i	−1.08386	−	0.0631275i	−0.590760	+	0.806847i	$0.701172\pi$
$3$	−8.98142	+	0.578015i	−0.997936	+	0.0642239i
$3$	−8.98142	+	0.578015i	−0.997936	+	0.0642239i
$4$	2.84035	+	0.331989i	0.177522	+	0.0207493i
$5$	−9.04763	−	38.1749i	−0.361905	−	1.52700i	−0.784182	−	0.620531i	$-0.786917\pi$
$5$	−9.04763	−	38.1749i	−0.361905	−	1.52700i	0.422277	−	0.906467i	$-0.361231\pi$
$6$	39.0842	−	0.238046i	1.08567	−	0.00661239i
$7$	−39.6102	−	53.2058i	−0.808372	−	1.08583i	−0.994647	−	0.103334i	$-0.967049\pi$
$7$	−39.6102	−	53.2058i	−0.808372	−	1.08583i	0.186275	−	0.982498i	$-0.440359\pi$
$8$	56.1985	+	9.90930i	0.878101	+	0.154833i
$9$	80.3318	−	10.3828i	0.991751	−	0.128183i
$10$	29.5858	+	167.789i	0.295858	+	1.67789i
$11$	−115.575	−	109.039i	−0.955162	−	0.901149i	0.0400191	−	0.999199i	$-0.487258\pi$
$11$	−115.575	−	109.039i	−0.955162	−	0.901149i	−0.995182	+	0.0980497i	$0.968740\pi$
$12$	−25.7023	−	1.33997i	−0.178488	−	0.00930535i
$13$	−143.670	−	72.1536i	−0.850116	−	0.426944i	−0.0302790	−	0.999541i	$-0.509640\pi$
$13$	−143.670	−	72.1536i	−0.850116	−	0.426944i	−0.819837	+	0.572597i	$0.805936\pi$
$14$	158.292	+	240.672i	0.807614	+	1.22792i
$15$	103.326	+	337.635i	0.459228	+	1.50060i
$16$	−285.664	−	67.7036i	−1.11587	−	0.264467i
$17$	−9.47504	+	26.0325i	−0.0327856	+	0.0900777i	−0.955005	−	0.296588i	$-0.904151\pi$
$17$	−9.47504	+	26.0325i	−0.0327856	+	0.0900777i	0.922220	+	0.386666i	$0.126373\pi$
$18$	−350.894	+	24.7293i	−1.08301	+	0.0763249i
$19$	−263.350	+	95.8514i	−0.729500	+	0.265516i	−0.679953	−	0.733255i	$-0.738000\pi$
$19$	−263.350	+	95.8514i	−0.729500	+	0.265516i	−0.0495470	+	0.998772i	$0.515778\pi$
$20$	−13.0248	−	111.434i	−0.0325619	−	0.278585i
$21$	386.510	+	454.968i	0.876440	+	1.03167i
$22$	473.532	+	501.915i	0.978372	+	1.03701i
$23$	805.016	+	599.312i	1.52177	+	1.13292i	0.949893	+	0.312577i	$0.101192\pi$
$23$	805.016	+	599.312i	1.52177	+	1.13292i	0.571877	+	0.820339i	$0.306215\pi$
$24$	−510.470	−	56.5161i	−0.886232	−	0.0981182i
$25$	−816.946	+	410.286i	−1.30711	+	0.656457i
$26$	604.649	+	349.095i	0.894452	+	0.516412i
$27$	−715.492	+	139.685i	−0.981471	+	0.191612i
$28$	−94.8432	−	164.273i	−0.120973	−	0.209532i
$29$	750.082	−	1140.44i	0.891893	−	1.35606i	−0.0422312	−	0.999108i	$-0.513447\pi$
$29$	750.082	−	1140.44i	0.891893	−	1.35606i	0.934124	−	0.356949i	$-0.116183\pi$
$30$	−362.707	−	1489.88i	−0.403008	−	1.65543i
$31$	−350.695	−	813.003i	−0.364928	−	0.845997i	−0.997444	−	0.0714504i	$-0.977237\pi$
$31$	−350.695	−	813.003i	−0.364928	−	0.845997i	0.632517	−	0.774547i	$-0.282022\pi$
$32$	346.689	+	103.792i	0.338564	+	0.101359i
$33$	1101.05	+	912.522i	1.01107	+	0.837945i
$34$	47.6518	−	110.469i	0.0412213	−	0.0955617i
$35$	−1672.75	+	1993.50i	−1.36551	+	1.62735i
$36$	231.617	−	2.82148i	0.178717	−	0.00217707i
$37$	534.545	−	448.536i	0.390463	−	0.327638i	−0.426330	−	0.904568i	$-0.640194\pi$
$37$	534.545	−	448.536i	0.390463	−	0.327638i	0.816794	+	0.576930i	$0.195749\pi$
$38$	1165.94	−	349.058i	0.807435	−	0.241730i
$39$	1332.06	+	564.998i	0.875781	+	0.371465i
$40$	−130.176	−	2235.03i	−0.0813597	−	1.39689i
$41$	−1507.53	+	87.8039i	−0.896808	+	0.0522331i	−0.500354	−	0.865821i	$-0.666797\pi$
$41$	−1507.53	+	87.8039i	−0.896808	+	0.0522331i	−0.396455	+	0.918054i	$0.629760\pi$
$42$	−1560.80	−	2070.08i	−0.884808	−	1.17351i
$43$	272.547	+	910.370i	0.147402	+	0.492358i	0.999520	−	0.0309927i	$-0.00986687\pi$
$43$	272.547	+	910.370i	0.147402	+	0.492358i	−0.852117	+	0.523351i	$0.824682\pi$
$44$	−292.073	−	348.079i	−0.150864	−	0.179793i
$45$	−1123.17	−	2972.72i	−0.554654	−	1.46801i
$46$	−3338.76	−	2801.55i	−1.57786	−	1.32398i
$47$	586.535	+	253.007i	0.265521	+	0.114534i	0.524678	−	0.851301i	$-0.324186\pi$
$47$	586.535	+	253.007i	0.265521	+	0.114534i	−0.259158	+	0.965835i	$0.583445\pi$
$48$	2604.80	+	442.956i	1.13056	+	0.192255i
$49$	−573.270	+	1914.85i	−0.238763	+	0.797524i
$50$	3645.41	−	1572.48i	1.45816	−	0.628991i
$51$	70.0522	−	239.285i	0.0269328	−	0.0919974i
$52$	−384.118	−	252.638i	−0.142055	−	0.0934313i
$53$	3716.11	−	2145.50i	1.32293	−	0.763795i	0.338736	−	0.940881i	$-0.390001\pi$
$53$	3716.11	−	2145.50i	1.32293	−	0.763795i	0.984195	+	0.177087i	$0.0566673\pi$
$54$	3137.24	−	424.926i	1.07587	−	0.145722i
$55$	−3116.88	+	5398.60i	−1.03037	+	1.78466i
$56$	−1698.80	−	3382.59i	−0.541710	−	1.07863i
$57$	2309.85	−	1013.10i	0.710942	−	0.311820i
$58$	−3539.90	+	4754.91i	−1.05229	+	1.41347i
$59$	1717.48	−	1620.35i	0.493386	−	0.465485i	−0.398875	−	0.917005i	$-0.630599\pi$
$59$	1717.48	−	1620.35i	0.493386	−	0.465485i	0.892261	+	0.451520i	$0.149118\pi$
$60$	181.391	+	993.306i	0.0503865	+	0.275918i
$61$	1896.01	−	221.612i	0.509544	−	0.0595572i	0.142563	−	0.989786i	$-0.454466\pi$
$61$	1896.01	−	221.612i	0.509544	−	0.0595572i	0.366981	+	0.930229i	$0.380391\pi$
$62$	1315.12	+	3613.27i	0.342124	+	0.939977i
$63$	−3734.39	−	3862.85i	−0.940888	−	0.973255i
$64$	2937.12	+	1069.02i	0.717070	+	0.260992i
$65$	−1454.59	+	6137.40i	−0.344282	+	1.45264i
$66$	−4543.10	−	4234.20i	−1.04295	−	0.972038i
$67$	−2587.30	+	1701.70i	−0.576366	+	0.379082i	−0.803968	−	0.594673i	$-0.797282\pi$
$67$	−2587.30	+	1701.70i	−0.576366	+	0.379082i	0.227602	+	0.973754i	$0.426911\pi$
$68$	−35.5549	+	70.7957i	−0.00768922	+	0.0153105i
$69$	−7576.60	−	4917.36i	−1.59139	−	1.03284i
$70$	7755.46	−	8220.31i	1.58275	−	1.67761i
$71$	−2816.68	+	496.657i	−0.558755	+	0.0985235i	−0.445891	−	0.895087i	$-0.647113\pi$
$71$	−2816.68	+	496.657i	−0.558755	+	0.0985235i	−0.112863	+	0.993611i	$0.536002\pi$
$72$	4617.41	+	212.535i	0.890704	+	0.0409983i
$73$	−1182.70	+	6707.44i	−0.221937	+	1.25867i	0.646518	+	0.762899i	$0.276225\pi$
$73$	−1182.70	+	6707.44i	−0.221937	+	1.25867i	−0.868455	+	0.495768i	$0.834886\pi$
$74$	−2430.74	+	1809.62i	−0.443889	+	0.330463i
$75$	7100.18	−	4157.16i	1.26225	−	0.739050i
$76$	−779.827	+	184.822i	−0.135012	+	0.0319983i
$77$	−1223.57	+	10468.3i	−0.206370	+	1.76561i
$78$	−5632.39	−	2785.87i	−0.925771	−	0.457901i
$79$	88.8883	−	1526.15i	0.0142426	−	0.244537i	−0.983671	−	0.179975i	$-0.942398\pi$
$79$	88.8883	−	1526.15i	0.0142426	−	0.244537i	0.997914	−	0.0645612i	$-0.0205648\pi$
$80$			11517.8i			1.79965i
$81$	6345.40	−	1668.14i	0.967138	−	0.254250i
$82$	6557.98			0.975309
$83$	−11383.1	−	662.993i	−1.65237	−	0.0962393i	−0.793544	−	0.608513i	$-0.791766\pi$
$83$	−11383.1	−	662.993i	−1.65237	−	0.0962393i	−0.858822	+	0.512274i	$0.828803\pi$
$84$	946.779	+	1420.59i	0.134181	+	0.201330i
$85$	1079.51	+	126.177i	0.149414	+	0.0174640i
$86$	−951.730	−	4015.66i	−0.128682	−	0.542951i
$87$	−6077.60	+	10676.4i	−0.802960	+	1.41054i
$88$	−5414.62	−	7273.09i	−0.699201	−	0.939191i
$89$	5744.39	+	1012.89i	0.725210	+	0.127874i	0.524054	−	0.851685i	$-0.324419\pi$
$89$	5744.39	+	1012.89i	0.725210	+	0.127874i	0.201156	+	0.979559i	$0.435530\pi$
$90$	4118.80	+	13171.6i	0.508494	+	1.62613i
$91$	1851.80	+	10502.1i	0.223620	+	1.26821i
$92$	2087.56	+	1969.51i	0.246640	+	0.232693i
$93$	3619.67	+	7099.22i	0.418507	+	0.820814i
$94$	−2478.99	−	1245.00i	−0.280556	−	0.140901i
$95$	6041.81	+	9186.13i	0.669453	+	1.01785i
$96$	−3173.76	−	731.808i	−0.344375	−	0.0794062i
$97$	9205.02	+	2181.63i	0.978321	+	0.231866i	0.688517	−	0.725220i	$-0.258262\pi$
$97$	9205.02	+	2181.63i	0.978321	+	0.231866i	0.289803	+	0.957086i	$0.406410\pi$
$98$	2968.89	−	8156.95i	0.309130	−	0.849329i
$99$	−10416.4	−	7559.32i	−1.06279	−	0.771280i
$100$	−2456.62	+	894.138i	−0.245662	+	0.0894138i
$101$	−1662.15	−	14220.6i	−0.162940	−	1.39404i	−0.789061	−	0.614314i	$-0.789433\pi$
$101$	−1662.15	−	14220.6i	−0.162940	−	1.39404i	0.626122	−	0.779725i	$-0.284641\pi$
$102$	−364.128	+	1019.71i	−0.0349988	+	0.0980118i
$103$	−5250.38	−	5565.08i	−0.494899	−	0.524562i	0.430991	−	0.902356i	$-0.358164\pi$
$103$	−5250.38	−	5565.08i	−0.494899	−	0.524562i	−0.925890	+	0.377794i	$0.876683\pi$
$104$	−7359.02	−	5478.59i	−0.680383	−	0.506526i
$105$	13871.4	−	18871.4i	1.25818	−	1.71169i
$106$	−16652.7	+	8363.30i	−1.48208	+	0.744331i
$107$	1199.90	+	692.765i	0.104804	+	0.0605088i	0.551486	−	0.834184i	$-0.314061\pi$
$107$	1199.90	+	692.765i	0.104804	+	0.0605088i	−0.446682	+	0.894693i	$0.647394\pi$
$108$	−2078.62	+	159.219i	−0.178208	+	0.0136505i
$109$	−3904.16	−	6762.20i	−0.328605	−	0.569161i	0.653630	−	0.756814i	$-0.273245\pi$
$109$	−3904.16	−	6762.20i	−0.328605	−	0.569161i	−0.982235	+	0.187653i	$0.939912\pi$
$110$	14876.2	−	22618.2i	1.22944	−	1.86927i
$111$	−4541.71	+	4337.47i	−0.368615	+	0.352038i
$112$	7712.99	+	17880.7i	0.614875	+	1.42544i
$113$	−5498.91	−	1646.26i	−0.430645	−	0.128927i	0.0641422	−	0.997941i	$-0.479569\pi$
$113$	−5498.91	−	1646.26i	−0.430645	−	0.128927i	−0.494787	+	0.869014i	$0.664754\pi$
$114$	−10270.0	+	3808.97i	−0.790243	+	0.293088i
$115$	15595.2	−	36153.8i	1.17922	−	2.73375i
$116$	2509.11	−	2990.24i	0.186468	−	0.222224i
$117$	−12290.4	−	4304.53i	−0.897830	−	0.314452i
$118$	−7855.14	+	6591.25i	−0.564144	+	0.473373i
$119$	1760.39	−	527.025i	0.124312	−	0.0372167i
$120$	2461.04	+	19998.5i	0.170906	+	1.38878i
$121$	616.685	+	10588.1i	0.0421204	+	0.723179i
$122$	−8275.99	+	482.021i	−0.556032	+	0.0323852i
$123$	13489.0	−	1659.98i	0.891602	−	0.109722i
$124$	−726.189	−	2425.64i	−0.0472288	−	0.157755i
$125$	7292.72	+	8691.13i	0.466734	+	0.556232i
$126$	15214.7	+	17690.1i	0.958349	+	1.11427i
$127$	2313.62	+	1941.36i	0.143445	+	0.120364i	0.711686	−	0.702497i	$-0.247932\pi$
$127$	2313.62	+	1941.36i	0.143445	+	0.120364i	−0.568242	+	0.822862i	$0.692376\pi$
$128$	−17780.5	−	7669.74i	−1.08523	−	0.468124i
$129$	−2974.07	−	8018.88i	−0.178719	−	0.481875i
$130$	7856.02	−	26240.9i	0.464853	−	1.55272i
$131$	−11689.6	+	5042.40i	−0.681173	+	0.293829i	−0.708411	−	0.705800i	$-0.750588\pi$
$131$	−11689.6	+	5042.40i	−0.681173	+	0.293829i	0.0272388	+	0.999629i	$0.491329\pi$
$132$	2824.42	+	2957.42i	0.162100	+	0.169732i
$133$	15531.2	+	10215.0i	0.878014	+	0.577479i
$134$	11646.8	−	6724.26i	0.648628	−	0.374486i
$135$	11806.0	+	26050.0i	0.647791	+	1.42936i
$136$	−790.446	+	1369.09i	−0.0427361	+	0.0740211i
$137$	−3517.36	−	7003.64i	−0.187403	−	0.373149i	0.780238	−	0.625483i	$-0.215098\pi$
$137$	−3517.36	−	7003.64i	−0.187403	−	0.373149i	−0.967640	+	0.252334i	$0.918802\pi$
$138$	31606.1	+	23232.0i	1.65964	+	1.21991i
$139$	−2099.85	+	2820.59i	−0.108682	+	0.145986i	−0.853136	−	0.521688i	$-0.825303\pi$
$139$	−2099.85	+	2820.59i	−0.108682	+	0.145986i	0.744454	+	0.667674i	$0.232710\pi$
$140$	−5413.02	+	5106.92i	−0.276174	+	0.260557i
$141$	−5414.16	−	1933.33i	−0.272328	−	0.0972452i
$142$	12336.9	−	1441.98i	0.611830	−	0.0715126i
$143$	8737.00	+	24004.7i	0.427258	+	1.17388i
$144$	−23650.8	−	2472.76i	−1.14057	−	0.119250i
$145$	−50322.8	−	18316.0i	−2.39348	−	0.871154i
$146$	6821.21	−	28781.0i	0.320004	−	1.35020i
$147$	4041.96	−	17529.5i	0.187050	−	0.811211i
$148$	1667.20	−	1096.54i	0.0761141	−	0.0500610i
$149$	15921.3	−	31701.8i	0.717142	−	1.42795i	−0.178850	−	0.983876i	$-0.557238\pi$
$149$	15921.3	−	31701.8i	0.717142	−	1.42795i	0.895992	−	0.444070i	$-0.146466\pi$
$150$	−31832.0	+	16230.2i	−1.41476	+	0.721341i
$151$	−1654.55	+	1753.72i	−0.0725647	+	0.0769141i	−0.762639	−	0.646825i	$-0.776096\pi$
$151$	−1654.55	+	1753.72i	−0.0725647	+	0.0769141i	0.690074	+	0.723739i	$0.257578\pi$
$152$	−15749.7	+	2777.09i	−0.681686	+	0.120200i
$153$	−490.857	+	2189.61i	−0.0209687	+	0.0935372i
$154$	7948.04	−	45075.6i	0.335134	−	1.90064i
$155$	−27863.4	+	20743.5i	−1.15977	+	0.863414i
$156$	3595.95	+	2047.02i	0.147763	+	0.0841151i
$157$	−1533.39	+	363.421i	−0.0622092	+	0.0147438i	−0.261603	−	0.965176i	$-0.584251\pi$
$157$	−1533.39	+	363.421i	−0.0622092	+	0.0147438i	0.199393	+	0.979920i	$0.436103\pi$
$158$	−770.737	+	6594.08i	−0.0308739	+	0.264143i
$159$	−32135.9	+	21417.6i	−1.27115	+	0.847182i
$160$	825.537	−	14173.9i	0.0322475	−	0.553669i
$161$		−	66570.4i		−	2.56820i
$162$	−27931.2	+	5629.81i	−1.06429	+	0.214518i
$163$	35659.9			1.34216			0.671080	−	0.741385i	$-0.265831\pi$
$163$	35659.9			1.34216			0.671080	+	0.741385i	$0.265831\pi$
$164$	−4311.08	−	251.092i	−0.160287	−	0.00933565i
$165$	24873.6	−	50288.7i	0.913629	−	1.84715i
$166$	49183.4	+	5748.71i	1.78485	+	0.208619i
$167$	9564.27	+	40354.8i	0.342941	+	1.44698i	0.822146	+	0.569277i	$0.192777\pi$
$167$	9564.27	+	40354.8i	0.342941	+	1.44698i	−0.479205	+	0.877703i	$0.659075\pi$
$168$	17212.8	+	29398.6i	0.609865	+	1.04162i
$169$	−1620.64	−	2176.89i	−0.0567430	−	0.0762191i
$170$	−4648.29	−	819.620i	−0.160841	−	0.0283605i
$171$	−20160.1	+	10434.2i	−0.689448	+	0.356835i
$172$	471.896	+	2676.25i	0.0159510	+	0.0904629i
$173$	21927.5	+	20687.5i	0.732650	+	0.691220i	0.959184	−	0.282783i	$-0.0912577\pi$
$173$	21927.5	+	20687.5i	0.732650	+	0.691220i	−0.226533	+	0.974003i	$0.572739\pi$
$174$	29044.9	−	44751.9i	0.959337	−	1.47813i
$175$	54189.0	+	27214.7i	1.76944	+	0.888644i
$176$	25633.2	+	38973.3i	0.827517	+	1.25818i
$177$	−14488.8	+	15545.8i	−0.462472	+	0.496212i
$178$	−24648.6	−	5841.83i	−0.777951	−	0.184378i
$179$	−11514.1	+	31634.7i	−0.359355	+	0.987320i	0.619899	+	0.784682i	$0.287174\pi$
$179$	−11514.1	+	31634.7i	−0.359355	+	0.987320i	−0.979254	+	0.202638i	$0.935048\pi$
$180$	−2203.30	−	8816.45i	−0.0680030	−	0.272113i
$181$	−34867.9	+	12690.9i	−1.06431	+	0.387377i	−0.814046	−	0.580800i	$-0.802740\pi$
$181$	−34867.9	+	12690.9i	−1.06431	+	0.387377i	−0.250264	+	0.968178i	$0.580517\pi$
$182$	−5376.46	−	45998.6i	−0.162313	−	1.38868i
$183$	−16900.8	+	3086.32i	−0.504667	+	0.0921591i
$184$	39301.9	+	41657.6i	1.16085	+	1.23043i
$185$	−21959.2	−	16348.0i	−0.641613	−	0.477663i
$186$	−13900.2	−	31692.1i	−0.401786	−	0.916064i
$187$	3933.63	−	1975.54i	0.112489	−	0.0564941i
$188$	1581.97	+	913.351i	0.0447592	+	0.0258418i
$189$	35772.9	+	32535.4i	1.00145	+	0.910819i
$190$	−23874.2	−	41351.4i	−0.661336	−	1.14547i
$191$	16903.6	−	25700.6i	0.463353	−	0.704494i	−0.525926	−	0.850530i	$-0.676281\pi$
$191$	16903.6	−	25700.6i	0.463353	−	0.704494i	0.989279	+	0.146036i	$0.0466517\pi$
$192$	−26997.4	−	7903.65i	−0.732352	−	0.214400i
$193$	−25177.3	−	58367.6i	−0.675920	−	1.56696i	−0.816793	−	0.576930i	$-0.804250\pi$
$193$	−25177.3	−	58367.6i	−0.675920	−	1.56696i	0.140874	−	0.990028i	$-0.455009\pi$
$194$	−39356.8	−	11782.7i	−1.04572	−	0.313069i
$195$	9516.77	−	55963.3i	0.250277	−	1.47175i
$196$	−2264.00	+	5248.54i	−0.0589337	+	0.136624i
$197$	−3005.99	+	3582.40i	−0.0774560	+	0.0923084i	−0.803381	−	0.595466i	$-0.796968\pi$
$197$	−3005.99	+	3582.40i	−0.0774560	+	0.0923084i	0.725925	+	0.687774i	$0.241412\pi$
$198$	43251.0	+	35403.1i	1.10323	+	0.903049i
$199$	−41716.2	+	35004.1i	−1.05341	+	0.883919i	−0.993448	−	0.114282i	$-0.963543\pi$
$199$	−41716.2	+	35004.1i	−1.05341	+	0.883919i	−0.0599650	+	0.998200i	$0.519099\pi$
$200$	−49976.8	+	14962.1i	−1.24942	+	0.374051i
$201$	22254.1	−	16779.2i	0.550830	−	0.415315i
$202$	3615.29	+	62072.1i	0.0886013	+	1.52123i
$203$	−90389.1	+	5264.57i	−2.19343	+	0.127753i
$204$	278.413	−	656.397i	0.00669004	−	0.0157727i
$205$	16991.5	+	56755.6i	0.404319	+	1.35052i
$206$	21357.4	+	25452.8i	0.503285	+	0.599792i
$207$	70890.9	+	39785.5i	1.65444	+	0.928505i
$208$	36156.1	+	30338.6i	0.835710	+	0.701244i
$209$	40888.1	+	17637.4i	0.936061	+	0.403777i
$210$	−64903.6	+	78312.8i	−1.47174	+	1.77580i
$211$	662.987	−	2214.53i	0.0148916	−	0.0497412i	−0.950221	−	0.311577i	$-0.899143\pi$
$211$	662.987	−	2214.53i	0.0148916	−	0.0497412i	0.965112	+	0.261836i	$0.0843279\pi$
$212$	11267.4	−	4860.26i	0.250698	−	0.108140i
$213$	25010.7	−	6088.77i	0.551274	−	0.134206i
$214$	−5027.17	−	3306.42i	−0.109773	−	0.0721989i
$215$	32287.4	−	18641.2i	0.698484	−	0.403270i
$216$	−41593.7	+	760.066i	−0.891498	+	0.0162909i
$217$	−29365.3	+	50862.3i	−0.623614	+	1.08013i
$218$	15218.7	+	30302.8i	0.320231	+	0.637632i
$219$	6745.34	−	60925.9i	0.140642	−	1.27032i
$220$	−10645.3	+	14299.1i	−0.219945	+	0.295437i
$221$	3239.61	−	3056.42i	0.0663297	−	0.0625789i
$222$	20785.5	−	17657.9i	0.421749	−	0.358290i
$223$	−20801.6	+	2431.35i	−0.418298	+	0.0488921i	−0.322639	−	0.946522i	$-0.604570\pi$
$223$	−20801.6	+	2431.35i	−0.418298	+	0.0488921i	−0.0956592	+	0.995414i	$0.530496\pi$
$224$	−8210.12	−	22557.1i	−0.163626	−	0.449560i
$225$	−61366.8	+	41441.2i	−1.21218	+	0.818591i
$226$	23424.4	+	8525.79i	0.458619	+	0.166924i
$227$	−15098.3	+	63704.6i	−0.293005	+	1.23629i	0.604973	+	0.796246i	$0.293184\pi$
$227$	−15098.3	+	63704.6i	−0.293005	+	1.23629i	−0.897978	+	0.440041i	$0.854964\pi$
$228$	6897.12	−	2110.72i	0.132678	−	0.0406032i
$229$	−54783.1	+	36031.4i	−1.04466	+	0.687085i	−0.951212	−	0.308539i	$-0.900160\pi$
$229$	−54783.1	+	36031.4i	−1.04466	+	0.687085i	−0.0934498	+	0.995624i	$0.529789\pi$
$230$	−76741.2	+	152804.i	−1.45068	+	2.88855i
$231$	4938.55	−	94727.5i	0.0925498	−	1.77522i
$232$	53454.4	−	56658.4i	0.993134	−	1.05266i
$233$	46085.2	−	8126.07i	0.848887	−	0.149682i	0.267751	−	0.963488i	$-0.413719\pi$
$233$	46085.2	−	8126.07i	0.848887	−	0.149682i	0.581136	+	0.813806i	$0.302608\pi$
$234$	52197.2	+	21765.4i	0.953268	+	0.397499i
$235$	4351.76	−	24680.1i	0.0788006	−	0.446900i
$236$	5416.17	−	4032.19i	0.0972453	−	0.0723964i
$237$	83.7967	+	13758.4i	0.00149187	+	0.244946i
$238$	−7765.10	+	1840.36i	−0.137086	+	0.0324900i
$239$	10368.9	−	88711.7i	0.181525	−	1.55305i	−0.528537	−	0.848910i	$-0.677259\pi$
$239$	10368.9	−	88711.7i	0.181525	−	1.55305i	0.710062	−	0.704139i	$-0.248667\pi$
$240$	−6657.44	−	103446.i	−0.115581	−	1.79593i
$241$	−1599.16	+	27456.5i	−0.0275332	+	0.472727i	0.956157	+	0.292855i	$0.0946054\pi$
$241$	−1599.16	+	27456.5i	−0.0275332	+	0.472727i	−0.983690	+	0.179872i	$0.942432\pi$
$242$		−	46059.5i		−	0.786482i
$243$	−56026.4	+	18650.0i	−0.948813	+	0.315839i
$244$	5458.92			0.0916910
$245$	78286.2	+	4559.65i	1.30423	+	0.0759625i
$246$	−58899.9	+	3790.61i	−0.973295	+	0.0626382i
$247$	44751.4	+	5230.68i	0.733520	+	0.0857362i
$248$	−11652.2	−	49164.7i	−0.189455	−	0.799374i
$249$	102620.	−	625.016i	1.65514	−	0.0100807i
$250$	−29422.5	−	39521.2i	−0.470759	−	0.632340i
$251$	87787.1	+	15479.2i	1.39342	+	0.245698i	0.819439	−	0.573167i	$-0.194285\pi$
$251$	87787.1	+	15479.2i	1.39342	+	0.245698i	0.573986	+	0.818865i	$0.305396\pi$
$252$	−9324.54	−	12211.6i	−0.146834	−	0.192297i
$253$	−27691.0	−	157044.i	−0.432611	−	2.45346i
$254$	−9540.32	−	9000.83i	−0.147875	−	0.139513i
$255$	−9768.50	−	509.274i	−0.150227	−	0.00783197i
$256$	30458.7	+	15297.0i	0.464763	+	0.233413i
$257$	31867.7	+	48452.5i	0.482486	+	0.733585i	0.991912	−	0.126930i	$-0.0405124\pi$
$257$	31867.7	+	48452.5i	0.482486	+	0.733585i	−0.509426	+	0.860515i	$0.670142\pi$
$258$	10869.0	+	35516.3i	0.163286	+	0.533566i
$259$	−45038.1	−	10674.2i	−0.671399	−	0.159125i
$260$	−6169.09	+	16949.4i	−0.0912588	+	0.250731i
$261$	48414.4	−	99401.8i	0.710712	−	1.45920i
$262$	51952.7	−	18909.2i	0.756842	−	0.275468i
$263$	−5554.19	−	47519.1i	−0.0802988	−	0.687000i	−0.972099	−	0.234571i	$-0.924632\pi$
$263$	−5554.19	−	47519.1i	−0.0802988	−	0.687000i	0.891800	−	0.452429i	$-0.149443\pi$
$264$	52834.9	+	62193.0i	0.758076	+	0.892346i
$265$	−115526.	−	122451.i	−1.64509	−	1.74369i
$266$	−64754.9	−	48208.3i	−0.915187	−	0.681331i
$267$	−52178.2	−	5776.85i	−0.731925	−	0.0810342i
$268$	−7913.80	+	3974.46i	−0.110183	+	0.0553361i
$269$	15257.0	+	8808.60i	0.210845	+	0.121731i	0.601704	−	0.798719i	$-0.294489\pi$
$269$	15257.0	+	8808.60i	0.210845	+	0.121731i	−0.390859	+	0.920451i	$0.627822\pi$
$270$	−44606.1	−	115919.i	−0.611880	−	1.59011i
$271$	−992.384	−	1718.86i	−0.0135127	−	0.0234046i	0.859190	−	0.511657i	$-0.170968\pi$
$271$	−992.384	−	1718.86i	−0.0135127	−	0.0234046i	−0.872703	+	0.488252i	$0.837635\pi$
$272$	4469.17	−	6795.04i	0.0604072	−	0.0918447i
$273$	−22702.1	−	93253.1i	−0.304608	−	1.25123i
$274$	13480.8	+	31251.9i	0.179562	+	0.416271i
$275$	139155.	+	41660.4i	1.84007	+	0.550881i
$276$	−19887.7	−	16482.4i	−0.261076	−	0.216372i
$277$	−23648.5	+	54823.3i	−0.308208	+	0.714506i	−0.999971	−	0.00761844i	$-0.997575\pi$
$277$	−23648.5	+	54823.3i	−0.308208	+	0.714506i	0.691763	+	0.722124i	$0.256834\pi$
$278$	9815.99	−	11698.2i	0.127012	−	0.151367i
$279$	−36613.2	−	61668.8i	−0.470359	−	0.792241i
$280$	−113760.	+	95456.1i	−1.45102	+	1.21755i
$281$	−69129.9	+	20696.1i	−0.875495	+	0.262106i	−0.692858	−	0.721074i	$-0.743649\pi$
$281$	−69129.9	+	20696.1i	−0.875495	+	0.262106i	−0.182637	+	0.983180i	$0.558463\pi$
$282$	22984.5	+	9748.95i	0.289026	+	0.122591i
$283$	998.967	+	17151.6i	0.0124732	+	0.214157i	0.998786	+	0.0492690i	$0.0156892\pi$
$283$	998.967	+	17151.6i	0.0124732	+	0.214157i	−0.986312	+	0.164888i	$0.947274\pi$
$284$	−8165.25	+	475.572i	−0.101235	+	0.00589630i
$285$	−59573.8	−	79012.2i	−0.733441	−	0.972757i
$286$	−31817.2	−	106277.i	−0.388982	−	1.29929i
$287$	64385.5	+	76731.6i	0.781671	+	0.931559i
$288$	28927.8	+	4738.19i	0.348764	+	0.0571252i
$289$	63392.9	+	53192.9i	0.759005	+	0.636881i
$290$	213546.	+	92114.7i	2.53919	+	1.09530i
$291$	−83935.2	−	14273.5i	−0.991192	−	0.168556i
$292$	−5586.09	+	18658.8i	−0.0655152	+	0.218836i
$293$	33751.1	−	14558.8i	0.393145	−	0.169586i	−0.190325	−	0.981721i	$-0.560954\pi$
$293$	33751.1	−	14558.8i	0.393145	−	0.169586i	0.583470	+	0.812135i	$0.301695\pi$
$294$	−21950.0	+	74977.1i	−0.253945	+	0.867429i
$295$	−77396.0	−	50904.2i	−0.889354	−	0.584937i
$296$	34485.3	−	19910.1i	0.393595	−	0.227242i
$297$	97923.9	+	61872.5i	1.11014	+	0.701431i
$298$	−77030.5	+	133421.i	−0.867422	+	1.50242i
$299$	−72413.8	−	144188.i	−0.809989	−	1.61282i
$300$	21547.1	−	9450.59i	0.239413	−	0.105007i
$301$	37641.3	−	50561.1i	0.415462	−	0.558063i
$302$	7616.00	−	7185.32i	0.0835051	−	0.0787830i
$303$	23148.2	+	126760.i	0.252134	+	1.38070i
$304$	81718.9	−	9551.57i	0.884251	−	0.103354i
$305$	−25614.5	−	70375.1i	−0.275350	−	0.756519i
$306$	2680.98	−	9368.96i	0.0286319	−	0.100057i
$307$	−59481.8	−	21649.6i	−0.631113	−	0.229706i	0.00660250	−	0.999978i	$-0.497898\pi$
$307$	−59481.8	−	21649.6i	−0.631113	−	0.229706i	−0.637716	+	0.770272i	$0.720121\pi$
$308$	−6950.73	+	29327.4i	−0.0732705	+	0.309152i
$309$	50372.6	+	46947.5i	0.527566	+	0.491695i
$310$	126038.	−	82896.3i	1.31153	−	0.862604i
$311$	−18102.2	+	36044.5i	−0.187159	+	0.372665i	−0.967570	−	0.252602i	$-0.918714\pi$
$311$	−18102.2	+	36044.5i	−0.187159	+	0.372665i	0.780411	+	0.625267i	$0.215010\pi$
$312$	69261.1	+	44951.8i	0.711509	+	0.461783i
$313$	−27203.2	+	28833.7i	−0.277672	+	0.294315i	−0.851168	−	0.524893i	$-0.824105\pi$
$313$	−27203.2	+	28833.7i	−0.277672	+	0.294315i	0.573496	+	0.819208i	$0.305587\pi$
$314$	6739.68	−	1188.39i	0.0683566	−	0.0120531i
$315$	−113677.	+	177510.i	−1.14565	+	1.78896i
$316$	759.140	−	4305.30i	0.00760235	−	0.0431151i
$317$	−54914.4	+	40882.2i	−0.546472	+	0.406833i	−0.834680	−	0.550735i	$-0.814348\pi$
$317$	−54914.4	+	40882.2i	−0.546472	+	0.406833i	0.288209	+	0.957568i	$0.406940\pi$
$318$	144731.	−	84739.8i	1.43122	−	0.837979i
$319$	−211043.	+	50018.2i	−2.07391	+	0.491526i
$320$	14236.0	−	121796.i	0.139023	−	1.18942i
$321$	−11177.3	−	5528.45i	−0.108474	−	0.0536529i
$322$	−16809.7	+	288611.i	−0.162124	+	2.78357i
$323$		−	7763.84i		−	0.0744169i
$324$	18577.0	−	2631.49i	0.176964	−	0.0250675i
$325$	146974.			1.39147
$326$	−154601.	−	9004.47i	−1.45471	−	0.0847272i
$327$	38973.5	+	58477.5i	0.364480	+	0.546881i
$328$	−85591.2	−	10004.2i	−0.795575	−	0.0929894i
$329$	−9771.39	−	41228.7i	−0.0902744	−	0.380897i
$330$	−120536.	+	211742.i	−1.10685	+	1.94437i
$331$	−17875.9	−	24011.6i	−0.163160	−	0.219161i	0.713023	−	0.701141i	$-0.247326\pi$
$331$	−17875.9	−	24011.6i	−0.163160	−	0.219161i	−0.876183	+	0.481979i	$0.839918\pi$
$332$	−32112.0	−	5662.22i	−0.291334	−	0.0513701i
$333$	38283.9	−	41581.8i	0.345245	−	0.374986i
$334$	−31275.2	−	177370.i	−0.280354	−	1.58997i
$335$	88371.2	+	83373.9i	0.787446	+	0.742917i
$336$	−79608.9	−	156136.i	−0.705153	−	1.38301i
$337$	108269.	+	54374.6i	0.953329	+	0.478780i	0.856287	−	0.516500i	$-0.172765\pi$
$337$	108269.	+	54374.6i	0.953329	+	0.478780i	0.0970424	+	0.995280i	$0.469062\pi$
$338$	6476.47	+	9846.99i	0.0566898	+	0.0861926i
$339$	50339.6	+	11607.3i	0.438036	+	0.101003i
$340$	3024.31	+	716.775i	0.0261619	+	0.00620047i
$341$	−48117.6	+	132202.i	−0.413805	+	1.13692i
$342$	90037.6	−	40146.2i	0.769789	−	0.343235i
$343$	−25067.9	+	9123.97i	−0.213074	+	0.0775525i
$344$	6295.58	+	53862.2i	0.0532009	+	0.455163i
$345$	−119170.	+	333727.i	−1.00122	+	2.80384i
$346$	−89841.2	−	95226.2i	−0.750453	−	0.795434i
$347$	155632.	+	115864.i	1.29253	+	0.962251i	0.999982	+	0.00599995i	$0.00190986\pi$
$347$	155632.	+	115864.i	1.29253	+	0.962251i	0.292546	+	0.956251i	$0.405498\pi$
$348$	−20807.0	+	28306.9i	−0.171811	+	0.233741i
$349$	−23897.2	+	12001.6i	−0.196199	+	0.0985348i	−0.544186	−	0.838964i	$-0.683162\pi$
$349$	−23897.2	+	12001.6i	−0.196199	+	0.0985348i	0.347987	+	0.937499i	$0.386865\pi$
$350$	−228060.	−	131671.i	−1.86172	−	1.07486i
$351$	112873.	+	31556.8i	0.916171	+	0.256141i
$352$	−28751.1	−	49798.4i	−0.232044	−	0.401911i
$353$	15764.2	−	23968.4i	0.126510	−	0.192348i	−0.766679	−	0.642030i	$-0.778092\pi$
$353$	15764.2	−	23968.4i	0.126510	−	0.192348i	0.893189	+	0.449682i	$0.148463\pi$
$354$	66740.5	−	63739.2i	0.532578	−	0.508628i
$355$	44444.1	+	103033.i	0.352661	+	0.817561i
$356$	15979.8	+	4784.04i	0.126087	+	0.0377481i
$357$	−15506.1	+	5750.96i	−0.121665	+	0.0451236i
$358$	57906.6	−	134243.i	0.451816	−	1.04743i
$359$	−88251.7	+	105174.i	−0.684753	+	0.816057i	−0.990710	−	0.135988i	$-0.956579\pi$
$359$	−88251.7	+	105174.i	−0.684753	+	0.816057i	0.305957	+	0.952045i	$0.401023\pi$
$360$	−33663.1	−	178192.i	−0.259746	−	1.37494i
$361$	−39666.2	+	33283.9i	−0.304373	+	0.255399i
$362$	154372.	−	46215.8i	1.17801	−	0.352674i
$363$	−11658.8	−	94739.5i	−0.0884789	−	0.718981i
$364$	1773.18	+	30444.3i	0.0133829	+	0.229776i
$365$	266757.	−	15536.8i	2.00230	−	0.116621i
$366$	74051.5	−	9112.88i	0.552805	−	0.0680289i
$367$	37693.4	+	125905.i	0.279855	+	0.934782i	0.976163	+	0.217039i	$0.0696398\pi$
$367$	37693.4	+	125905.i	0.279855	+	0.934782i	−0.696308	+	0.717744i	$0.745175\pi$
$368$	−189388.	−	225704.i	−1.39848	−	1.66665i
$369$	−120191.	+	22705.9i	−0.882715	+	0.166757i
$370$	91074.5	+	76420.5i	0.665263	+	0.558222i
$371$	−261349.	−	112735.i	−1.89877	−	0.819051i
$372$	7924.27	+	21366.0i	0.0572629	+	0.154396i
$373$	42287.2	−	141249.i	0.303942	−	1.01524i	−0.660474	−	0.750849i	$-0.729644\pi$
$373$	42287.2	−	141249.i	0.303942	−	1.01524i	0.964416	−	0.264389i	$-0.0851703\pi$
$374$	−17552.8	+	7571.54i	−0.125488	+	0.0541304i
$375$	−70522.6	−	73843.3i	−0.501494	−	0.525108i
$376$	30455.3	+	20030.7i	0.215420	+	0.141684i
$377$	−190051.	+	109726.i	−1.33717	+	0.772017i
$378$	−146875.	−	150088.i	−1.02793	−	1.05042i
$379$	78254.0	−	135540.i	0.544789	−	0.943602i	−0.453832	−	0.891087i	$-0.649943\pi$
$379$	78254.0	−	135540.i	0.544789	−	0.943602i	0.998620	−	0.0525141i	$-0.0167234\pi$
$380$	14111.2	+	28097.6i	0.0977228	+	0.194582i
$381$	−21901.7	−	16098.8i	−0.150879	−	0.110903i
$382$	−79773.9	+	107155.i	−0.546681	+	0.734320i
$383$	50555.1	−	47696.3i	0.344642	−	0.325153i	−0.494385	−	0.869243i	$-0.664607\pi$
$383$	50555.1	−	47696.3i	0.344642	−	0.325153i	0.839027	+	0.544091i	$0.183125\pi$
$384$	164127.	+	58607.8i	1.11306	+	0.397459i
$385$	410697.	−	48003.6i	2.77077	−	0.323856i
$386$	94416.1	+	259406.i	0.633682	+	1.74103i
$387$	31346.4	+	70301.9i	0.209298	+	0.469402i
$388$	25421.2	+	9252.56i	0.168862	+	0.0614608i
$389$	−41626.0	+	175634.i	−0.275084	+	1.16067i	0.643500	+	0.765446i	$0.277482\pi$
$389$	−41626.0	+	175634.i	−0.275084	+	1.16067i	−0.918584	+	0.395225i	$0.870667\pi$
$390$	−55390.5	+	240222.i	−0.364172	+	1.57937i
$391$	−23229.1	+	15278.0i	−0.151943	+	0.0999342i
$392$	−51191.7	+	101931.i	−0.333141	+	0.663338i
$393$	102075.	−	52044.7i	0.660896	−	0.336970i
$394$	13936.8	−	14772.2i	0.0897784	−	0.0951595i
$395$	−59065.0	+	10414.8i	−0.378561	+	0.0667505i
$396$	−27076.8	−	24929.3i	−0.172666	−	0.158971i
$397$	19612.7	−	111229.i	0.124439	−	0.705728i	−0.857201	−	0.514983i	$-0.827798\pi$
$397$	19612.7	−	111229.i	0.124439	−	0.705728i	0.981640	−	0.190745i	$-0.0610905\pi$
$398$	189696.	−	141224.i	1.19755	−	0.891542i
$399$	−145397.	−	82768.2i	−0.913289	−	0.519897i
$400$	261150.	−	61893.6i	1.63219	−	0.386835i
$401$	3821.20	−	32692.5i	0.0237636	−	0.203310i	−0.976141	−	0.217138i	$-0.930328\pi$
$401$	3821.20	−	32692.5i	0.0237636	−	0.203310i	0.999904	+	0.0138282i	$0.00440179\pi$
$402$	−100718.	+	67125.4i	−0.623238	+	0.415370i
$403$	−8276.84	+	142108.i	−0.0509629	+	0.874999i
$404$		−	40943.3i		−	0.250853i
$405$	−121092.	−	227142.i	−0.738252	−	1.38480i
$406$	393205.			2.38543
$407$	−110688.	−	6446.83i	−0.668207	−	0.0389186i
$408$	6307.97	−	12753.3i	0.0378939	−	0.0766129i
$409$	−128271.	−	14992.7i	−0.766797	−	0.0896257i	−0.276303	−	0.961070i	$-0.589109\pi$
$409$	−128271.	−	14992.7i	−0.766797	−	0.0896257i	−0.490494	+	0.871445i	$0.663183\pi$
$410$	−59334.1	−	250350.i	−0.352969	−	1.48929i
$411$	35639.1	+	60869.6i	0.210981	+	0.360343i
$412$	−13065.4	−	17549.8i	−0.0769710	−	0.103390i
$413$	−154242.	−	27197.0i	−0.904278	−	0.159449i
$414$	−297296.	−	190388.i	−1.73456	−	1.11081i
$415$	77680.8	+	440549.i	0.451042	+	2.55799i
$416$	−42319.8	−	39926.6i	−0.244544	−	0.230715i
$417$	17229.3	−	26546.7i	0.0990823	−	0.152665i
$418$	−172814.	−	86790.3i	−0.989067	−	0.496728i
$419$	−83022.9	−	126230.i	−0.472900	−	0.719010i	0.517735	−	0.855541i	$-0.326775\pi$
$419$	−83022.9	−	126230.i	−0.472900	−	0.719010i	−0.990636	+	0.136531i	$0.956405\pi$
$420$	45664.7	−	48996.2i	0.258870	−	0.277756i
$421$	−150374.	−	35639.4i	−0.848418	−	0.201079i	−0.216663	−	0.976247i	$-0.569517\pi$
$421$	−150374.	−	35639.4i	−0.848418	−	0.201079i	−0.631755	+	0.775168i	$0.717665\pi$
$422$	−3433.52	+	9433.52i	−0.0192803	+	0.0529723i
$423$	49744.4	+	14234.6i	0.278012	+	0.0795545i
$424$	230100.	−	83749.7i	1.27993	−	0.465856i
$425$	−2940.15	−	25154.6i	−0.0162776	−	0.139264i
$426$	−109970.	+	20082.0i	−0.605974	+	0.110659i
$427$	−86892.6	−	92100.8i	−0.476570	−	0.505135i
$428$	3178.16	+	2366.05i	0.0173495	+	0.0129163i
$429$	−92345.8	−	210546.i	−0.501767	−	1.14402i
$430$	−144687.	+	72664.5i	−0.782514	+	0.392993i
$431$	113201.	+	65356.4i	0.609389	+	0.351831i	0.772726	−	0.634740i	$-0.218893\pi$
$431$	113201.	+	65356.4i	0.609389	+	0.351831i	−0.163337	+	0.986570i	$0.552226\pi$
$432$	213847.	+	8538.35i	1.14587	+	0.0457516i
$433$	−83854.1	−	145240.i	−0.447248	−	0.774656i	0.550958	−	0.834533i	$-0.314263\pi$
$433$	−83854.1	−	145240.i	−0.447248	−	0.774656i	−0.998206	+	0.0598769i	$0.980929\pi$
$434$	140155.	−	213095.i	0.744094	−	1.13134i
$435$	462557.	+	135416.i	2.44448	+	0.715637i
$436$	−8844.19	−	20503.1i	−0.0465249	−	0.107857i
$437$	−269446.	−	80666.7i	−1.41094	−	0.422408i
$438$	−44628.4	+	262437.i	−0.232628	+	1.36797i
$439$	14445.0	−	33487.2i	0.0749527	−	0.173760i	−0.876620	−	0.481183i	$-0.840207\pi$
$439$	14445.0	−	33487.2i	0.0749527	−	0.173760i	0.951573	+	0.307423i	$0.0994666\pi$
$440$	−228660.	+	272507.i	−1.18110	+	1.40758i
$441$	−26170.2	+	159776.i	−0.134565	+	0.821550i
$442$	−14816.9	+	12432.8i	−0.0758424	+	0.0636393i
$443$	−334401.	+	100113.i	−1.70396	+	0.510133i	−0.983119	−	0.182966i	$-0.941430\pi$
$443$	−334401.	+	100113.i	−1.70396	+	0.510133i	−0.720843	+	0.693099i	$0.756245\pi$
$444$	−14340.0	+	10812.1i	−0.0727418	+	0.0548460i
$445$	−13306.0	−	228456.i	−0.0671937	−	1.15367i
$446$	90797.6	−	5288.36i	0.456462	−	0.0265859i
$447$	−124671.	+	293930.i	−0.623953	+	1.47106i
$448$	−59461.7	−	198616.i	−0.296266	−	0.989596i
$449$	122390.	+	145859.i	0.607092	+	0.723504i	0.978794	−	0.204848i	$-0.0656702\pi$
$449$	122390.	+	145859.i	0.607092	+	0.723504i	−0.371702	+	0.928352i	$0.621226\pi$
$450$	276516.	−	164169.i	1.36551	−	0.810713i
$451$	183807.	+	154232.i	0.903667	+	0.758267i
$452$	−15072.3	−	6501.55i	−0.0737738	−	0.0318229i
$453$	13846.5	−	16707.2i	0.0674751	−	0.0814157i
$454$	81543.5	−	272374.i	0.395619	−	1.32146i
$455$	384162.	−	165711.i	1.85563	−	0.800440i
$456$	139849.	−	34045.8i	0.672559	−	0.163732i
$457$	−3196.86	−	2102.61i	−0.0153071	−	0.0100676i	0.541832	−	0.840487i	$-0.317731\pi$
$457$	−3196.86	−	2102.61i	−0.0153071	−	0.0100676i	−0.557139	+	0.830419i	$0.688101\pi$
$458$	246606.	−	142378.i	1.17564	−	0.678754i
$459$	3142.97	−	19949.5i	0.0149181	−	0.0946908i
$460$	56298.6	−	97512.0i	0.266061	−	0.460832i
$461$	−48395.0	−	96362.3i	−0.227719	−	0.453425i	0.750537	−	0.660829i	$-0.229795\pi$
$461$	−48395.0	−	96362.3i	−0.227719	−	0.453425i	−0.978255	+	0.207404i	$0.933499\pi$
$462$	−45330.3	+	409437.i	−0.212376	+	1.91824i
$463$	−89305.2	+	119958.i	−0.416596	+	0.559585i	−0.960041	−	0.279859i	$-0.909712\pi$
$463$	−89305.2	+	119958.i	−0.416596	+	0.559585i	0.543445	+	0.839445i	$0.317120\pi$
$464$	−291483.	+	275000.i	−1.35387	+	1.27731i
$465$	238263.	−	202412.i	1.10192	−	0.936117i
$466$	−201851.	+	23593.0i	−0.929521	+	0.108645i
$467$	−119593.	−	328580.i	−0.548369	−	1.50663i	−0.835911	−	0.548864i	$-0.815060\pi$
$467$	−119593.	−	328580.i	−0.548369	−	1.50663i	0.287542	−	0.957768i	$-0.407162\pi$
$468$	−33480.0	−	16306.7i	−0.152860	−	0.0744515i
$469$	193024.	+	70254.9i	0.877537	+	0.319397i
$470$	−25098.7	+	105900.i	−0.113620	+	0.479401i
$471$	13562.0	−	4150.36i	0.0611338	−	0.0187087i
$472$	112576.	−	74042.4i	0.505315	−	0.332351i
$473$	67766.4	−	134934.i	0.302895	−	0.603114i
$474$	3110.84	−	59669.7i	0.0138459	−	0.265581i
$475$	175816.	−	186354.i	0.779240	−	0.825946i
$476$	5175.08	−	912.506i	0.0228404	−	0.00402737i
$477$	276246.	−	210935.i	1.21411	−	0.927071i
$478$	−67354.2	+	381985.i	−0.294788	+	1.67182i
$479$	−46116.4	+	34332.4i	−0.200995	+	0.149635i	−0.692950	−	0.720985i	$-0.743690\pi$
$479$	−46116.4	+	34332.4i	−0.200995	+	0.149635i	0.491956	+	0.870620i	$0.336282\pi$
$480$	778.250	+	127779.i	0.00337782	+	0.554597i
$481$	−109161.	+	25871.7i	−0.471822	+	0.111824i
$482$	13866.1	−	118632.i	0.0596842	−	0.510631i
$483$	38478.7	+	597897.i	0.164940	+	2.56290i
$484$	−1763.53	+	30278.6i	−0.00752820	+	0.129254i
$485$		−	371140.i		−	1.57781i
$486$	247608.	−	66708.4i	1.04832	−	0.282428i
$487$	12691.1			0.0535107			0.0267554	−	0.999642i	$-0.491482\pi$
$487$	12691.1			0.0535107			0.0267554	+	0.999642i	$0.491482\pi$
$488$	108749.	+	6333.91i	0.456653	+	0.0265970i
$489$	−320276.	+	20611.9i	−1.33939	+	0.0861988i
$490$	−338253.	−	39536.1i	−1.40880	−	0.164665i
$491$	−86969.2	−	366952.i	−0.360747	−	1.52211i	−0.786683	−	0.617357i	$-0.788203\pi$
$491$	−86969.2	−	366952.i	−0.360747	−	1.52211i	0.425937	−	0.904753i	$-0.359945\pi$
$492$	38864.7	−	236.709i	0.160556	−	0.000977878i
$493$	22581.5	+	30332.2i	0.0929093	+	0.124799i
$494$	−192695.	−	33977.4i	−0.789619	−	0.139231i
$495$	−194332.	+	466041.i	−0.793112	+	1.90201i
$496$	45137.8	+	255989.i	0.183475	+	1.04054i
$497$	137994.	+	130191.i	0.558662	+	0.527070i
$498$	−445060.	−	23202.9i	−1.79457	−	0.0935584i
$499$	15864.8	+	7967.61i	0.0637138	+	0.0319983i	0.480371	−	0.877065i	$-0.340502\pi$
$499$	15864.8	+	7967.61i	0.0637138	+	0.0319983i	−0.416657	+	0.909064i	$0.636798\pi$
$500$	17828.5	+	27107.0i	0.0713141	+	0.108428i
$501$	−109226.	−	356915.i	−0.435163	−	1.42197i
$502$	−376686.	−	89276.2i	−1.49476	−	0.354265i
$503$	136570.	−	375222.i	0.539782	−	1.48304i	−0.307318	−	0.951607i	$-0.599432\pi$
$503$	136570.	−	375222.i	0.539782	−	1.48304i	0.847101	−	0.531433i	$-0.178346\pi$
$504$	−171589.	−	254091.i	−0.675503	−	1.00030i
$505$	−527832.	+	192115.i	−2.06973	+	0.753319i
$506$	80397.3	+	687843.i	0.314008	+	2.68651i
$507$	15813.9	+	18614.8i	0.0615210	+	0.0724175i
$508$	5926.98	+	6282.24i	0.0229671	+	0.0243437i
$509$	199241.	+	148329.i	0.769030	+	0.572522i	0.908589	−	0.417692i	$-0.137161\pi$
$509$	199241.	+	148329.i	0.769030	+	0.572522i	−0.139559	+	0.990214i	$0.544568\pi$
$510$	42222.0	+	4674.56i	0.162330	+	0.0179722i
$511$	403722.	−	202757.i	1.54611	−	0.776485i
$512$	140128.	+	80903.1i	0.534547	+	0.308621i
$513$	175036.	−	105367.i	0.665107	−	0.400378i
$514$	−125925.	−	218109.i	−0.476637	−	0.825559i
$515$	−164943.	+	250784.i	−0.621898	+	0.945551i
$516$	−5785.21	−	23763.8i	−0.0217280	−	0.0892517i
$517$	−40201.0	−	93196.4i	−0.150403	−	0.348673i
$518$	192564.	+	57649.9i	0.717656	+	0.214852i
$519$	−208898.	−	173129.i	−0.775531	−	0.642739i
$520$	−142563.	+	330498.i	−0.527230	+	1.22226i
$521$	61956.8	−	73837.2i	0.228251	−	0.272019i	−0.639748	−	0.768585i	$-0.720961\pi$
$521$	61956.8	−	73837.2i	0.228251	−	0.272019i	0.867999	+	0.496565i	$0.165406\pi$
$522$	−234997.	+	418724.i	−0.862425	+	1.53669i
$523$	259365.	−	217633.i	0.948218	−	0.795650i	−0.0307783	−	0.999526i	$-0.509799\pi$
$523$	259365.	−	217633.i	0.948218	−	0.795650i	0.978997	+	0.203877i	$0.0653541\pi$
$524$	−34876.6	+	10441.4i	−0.127020	+	0.0380272i
$525$	−502425.	−	213105.i	−1.82286	−	0.773170i
$526$	12080.7	+	207418.i	0.0436638	+	0.749679i
$527$	24487.3	−	1426.22i	0.0881699	−	0.00513531i
$528$	−252749.	−	335219.i	−0.906613	−	1.20243i
$529$	208617.	+	696828.i	0.745482	+	2.49008i
$530$	469936.	+	560048.i	1.67297	+	1.99376i
$531$	121144.	−	147998.i	0.429648	−	0.524889i
$532$	40722.7	+	34170.4i	0.143884	+	0.120733i
$533$	222922.	+	96159.2i	0.784691	+	0.338483i
$534$	224756.	+	38220.6i	0.788186	+	0.134034i
$535$	15590.0	−	52074.1i	0.0544676	−	0.181934i
$536$	−162265.	+	69994.4i	−0.564801	+	0.243632i
$537$	85127.6	−	290780.i	0.295204	−	1.00836i
$538$	−63921.1	−	42041.6i	−0.220841	−	0.145249i
$539$	275049.	−	158800.i	0.946745	−	0.546604i
$540$	24884.8	+	77910.7i	0.0853388	+	0.267184i
$541$	280466.	−	485781.i	0.958265	−	1.65976i	0.231553	−	0.972822i	$-0.425619\pi$
$541$	280466.	−	485781.i	0.958265	−	1.65976i	0.726713	−	0.686942i	$-0.241047\pi$
$542$	3868.38	+	7702.57i	0.0131683	+	0.0262203i
$543$	305827.	−	134136.i	1.03723	−	0.454932i
$544$	−5986.86	+	8041.75i	−0.0202303	+	0.0271739i
$545$	−222823.	+	210223.i	−0.750183	+	0.707761i
$546$	74876.1	+	410025.i	0.251164	+	1.37539i
$547$	242751.	−	28373.5i	0.811308	−	0.0948282i	0.299685	−	0.954038i	$-0.403119\pi$
$547$	242751.	−	28373.5i	0.811308	−	0.0948282i	0.511623	+	0.859210i	$0.329044\pi$
$548$	−7665.40	−	21060.5i	−0.0255255	−	0.0701307i
$549$	150009.	−	37488.4i	0.497706	−	0.124381i
$550$	−592778.	−	215754.i	−1.95960	−	0.713235i
$551$	−88220.6	+	372232.i	−0.290581	+	1.22606i
$552$	−377066.	−	351427.i	−1.23748	−	1.15334i
$553$	−84721.0	+	55721.9i	−0.277039	+	0.182211i
$554$	116370.	−	231711.i	0.379158	−	0.754966i
$555$	206674.	+	134136.i	0.670966	+	0.435470i
$556$	−6900.73	+	7314.35i	−0.0223226	+	0.0236606i
$557$	−317103.	+	55913.8i	−1.02209	+	0.180222i	−0.659483	−	0.751719i	$-0.729225\pi$
$557$	−317103.	+	55913.8i	−1.02209	+	0.180222i	−0.362608	+	0.931942i	$0.618114\pi$
$558$	143162.	+	276606.i	0.459790	+	0.888368i
$559$	26529.8	−	150458.i	0.0849004	−	0.481494i
$560$	612811.	−	456221.i	1.95412	−	1.45479i
$561$	−34187.7	+	20016.9i	−0.108629	+	0.0636020i
$562$	304934.	−	72270.6i	0.965457	−	0.228817i
$563$	16641.3	−	142375.i	0.0525012	−	0.449176i	−0.941263	−	0.337674i	$-0.890360\pi$
$563$	16641.3	−	142375.i	0.0525012	−	0.449176i	0.993764	−	0.111502i	$-0.0355662\pi$
$564$	−14736.3	−	7288.79i	−0.0463265	−	0.0229138i
$565$	−13094.0	+	224815.i	−0.0410181	+	0.704253i
$566$		−	74611.8i		−	0.232903i
$567$	−340097.	−	271536.i	−1.05788	−	0.844621i
$568$	−163215.			−0.505898
$569$	408614.	+	23799.1i	1.26209	+	0.0735081i	0.676098	−	0.736812i	$-0.263670\pi$
$569$	408614.	+	23799.1i	1.26209	+	0.0735081i	0.585988	+	0.810320i	$0.300707\pi$
$570$	238326.	+	357595.i	0.733538	+	1.10063i
$571$	−310540.	−	36296.9i	−0.952458	−	0.111326i	−0.374351	−	0.927287i	$-0.622134\pi$
$571$	−310540.	−	36296.9i	−0.952458	−	0.111326i	−0.578107	+	0.815961i	$0.696208\pi$
$572$	16846.8	+	71082.4i	0.0514904	+	0.217255i
$573$	−136963.	+	240599.i	−0.417151	+	0.732797i
$574$	−259763.	−	348922.i	−0.788412	−	1.05902i
$575$	−903544.	−	159319.i	−2.73284	−	0.481873i
$576$	247043.	+	55381.1i	0.744609	+	0.166923i
$577$	−72868.8	−	413260.i	−0.218872	−	1.24128i	−0.874060	−	0.485819i	$-0.838522\pi$
$577$	−72868.8	−	413260.i	−0.218872	−	1.24128i	0.655188	−	0.755466i	$-0.272590\pi$
$578$	−261403.	−	246621.i	−0.782448	−	0.738202i
$579$	259866.	+	509671.i	0.775160	+	1.52031i
$580$	−136854.	−	68730.5i	−0.406819	−	0.204312i
$581$	415614.	+	631911.i	1.23123	+	1.87199i
$582$	360291.	+	83076.1i	1.06367	+	0.245262i
$583$	−663432.	−	157236.i	−1.95191	−	0.462611i
$584$	−132932.	+	365228.i	−0.389766	+	1.07087i
$585$	−53126.5	+	508131.i	−0.155238	+	1.48479i
$586$	−150002.	+	54596.1i	−0.436818	+	0.158989i
$587$	3373.09	+	28858.6i	0.00978929	+	0.0837527i	0.997250	−	0.0741133i	$-0.0236127\pi$
$587$	3373.09	+	28858.6i	0.00978929	+	0.0837527i	−0.987461	+	0.157866i	$0.949539\pi$
$588$	17300.2	−	48447.9i	0.0500375	−	0.140127i
$589$	170283.	+	180489.i	0.490841	+	0.520261i
$590$	322691.	+	240235.i	0.927006	+	0.690131i
$591$	24927.4	−	33912.5i	0.0713676	−	0.0970924i
$592$	−183067.	+	91939.9i	−0.522357	+	0.262338i
$593$	75578.6	+	43635.3i	0.214926	+	0.124088i	0.603599	−	0.797288i	$-0.293733\pi$
$593$	75578.6	+	43635.3i	0.214926	+	0.124088i	−0.388673	+	0.921376i	$0.627066\pi$
$594$	−408918.	−	292971.i	−1.15895	−	0.830331i
$595$	−36046.5	−	62434.3i	−0.101819	−	0.176356i
$596$	55746.7	−	84758.7i	0.156937	−	0.238612i
$597$	354438.	−	338499.i	0.994470	−	0.949748i
$598$	277536.	+	643401.i	0.776099	+	1.79920i
$599$	−588121.	−	176072.i	−1.63913	−	0.490723i	−0.671060	−	0.741403i	$-0.734161\pi$
$599$	−588121.	−	176072.i	−1.63913	−	0.490723i	−0.968070	+	0.250680i	$0.919346\pi$
$600$	440214.	−	163268.i	1.22282	−	0.453522i
$601$	−139549.	+	323511.i	−0.386347	+	0.895654i	0.608432	+	0.793606i	$0.291799\pi$
$601$	−139549.	+	323511.i	−0.386347	+	0.895654i	−0.994780	+	0.102048i	$0.967461\pi$
$602$	−175958.	+	209699.i	−0.485531	+	0.578633i
$603$	−190174.	+	163564.i	−0.523019	+	0.449834i
$604$	−5281.71	+	4431.88i	−0.0144777	+	0.0121483i
$605$	398619.	−	119339.i	1.08905	−	0.326040i
$606$	−68349.0	−	555406.i	−0.186117	−	1.51239i
$607$	−54.2219	−	930.954i	−0.000147163	−	0.00252668i	0.998234	−	0.0594081i	$-0.0189213\pi$
$607$	−54.2219	−	930.954i	−0.000147163	−	0.00252668i	−0.998381	+	0.0568814i	$0.981884\pi$
$608$	−101249.	+	5897.09i	−0.273895	+	0.0159526i
$609$	808780.	−	99529.6i	2.18070	−	0.268360i
$610$	93279.2	+	311574.i	0.250683	+	0.837340i
$611$	−66011.9	−	78670.0i	−0.176824	−	0.210730i
$612$	−2121.14	+	6056.31i	−0.00566325	+	0.0161698i
$613$	−32379.3	−	27169.5i	−0.0861682	−	0.0723037i	0.598686	−	0.800984i	$-0.295690\pi$
$613$	−32379.3	−	27169.5i	−0.0861682	−	0.0723037i	−0.684854	+	0.728680i	$0.740134\pi$
$614$	252412.	+	108880.i	0.669536	+	0.288809i
$615$	−185414.	−	499925.i	−0.490220	−	1.32177i
$616$	−172496.	+	576178.i	−0.454588	+	1.51843i
$617$	−106400.	+	45896.3i	−0.279492	+	0.120561i	−0.531212	−	0.847239i	$-0.678263\pi$
$617$	−106400.	+	45896.3i	−0.279492	+	0.120561i	0.251720	+	0.967800i	$0.419004\pi$
$618$	−206532.	−	216257.i	−0.540767	−	0.566230i
$619$	218138.	+	143472.i	0.569313	+	0.374443i	0.801288	−	0.598279i	$-0.204149\pi$
$619$	218138.	+	143472.i	0.569313	+	0.374443i	−0.231975	+	0.972722i	$0.574519\pi$
$620$	−86028.4	+	49668.5i	−0.223799	+	0.129211i
$621$	−659698.	−	316354.i	−1.71065	−	0.820334i
$622$	87582.5	−	151697.i	0.226379	−	0.392100i
$623$	−173645.	−	345755.i	−0.447390	−	0.890826i
$624$	−342270.	−	251585.i	−0.879021	−	0.646123i
$625$	−75394.7	+	101273.i	−0.193010	+	0.259258i
$626$	125218.	−	118137.i	0.319535	−	0.301466i
$627$	−377428.	−	134775.i	−0.960061	−	0.342826i
$628$	−4476.03	+	523.173i	−0.0113494	+	0.00132656i
$629$	6611.67	+	18165.4i	0.0167113	+	0.0459139i
$630$	537660.	−	740875.i	1.35465	−	1.86665i
$631$	−165732.	−	60321.4i	−0.416243	−	0.151500i	0.125405	−	0.992106i	$-0.459977\pi$
$631$	−165732.	−	60321.4i	−0.416243	−	0.151500i	−0.541648	+	0.840606i	$0.682199\pi$
$632$	20118.5	−	84886.6i	0.0503688	−	0.212523i
$633$	−4674.53	+	20272.8i	−0.0116662	+	0.0505950i
$634$	248400.	−	163376.i	0.617979	−	0.406451i
$635$	53178.5	−	105887.i	0.131883	−	0.262600i
$636$	−98387.5	+	50164.7i	−0.243235	+	0.124018i
$637$	220525.	−	233743.i	0.543474	−	0.576049i
$638$	927593.	−	163560.i	2.27885	−	0.401823i
$639$	−221112.	+	69142.4i	−0.541516	+	0.169333i
$640$	−131921.	+	748161.i	−0.322073	+	1.82656i
$641$	−137066.	+	102042.i	−0.333591	+	0.248350i	−0.750901	−	0.660415i	$-0.770380\pi$
$641$	−137066.	+	102042.i	−0.333591	+	0.248350i	0.417310	+	0.908764i	$0.362973\pi$
$642$	47062.2	+	26790.6i	0.114183	+	0.0649998i
$643$	620834.	−	147140.i	1.50160	−	0.355885i	0.604101	−	0.796908i	$-0.293532\pi$
$643$	620834.	−	147140.i	1.50160	−	0.355885i	0.897496	+	0.441023i	$0.145384\pi$
$644$	22100.7	−	189083.i	0.0532885	−	0.455913i
$645$	−279212.	+	186087.i	−0.671143	+	0.447297i
$646$	−1960.45	+	33659.5i	−0.00469775	+	0.0806572i
$647$			356905.i			0.852598i	0.904582	+	0.426299i	$0.140183\pi$
$647$			356905.i			0.852598i	−0.904582	+	0.426299i	$0.859817\pi$
$648$	373132.	−	30868.3i	0.888611	−	0.0735127i
$649$	−375179.			−0.890735
$650$	−637194.	−	37112.4i	−1.50815	−	0.0878399i
$651$	234343.	−	473789.i	0.552956	−	1.11795i
$652$	101287.	+	11838.7i	0.238263	+	0.0278489i
$653$	76160.8	+	321348.i	0.178610	+	0.753614i	0.986430	+	0.164184i	$0.0524992\pi$
$653$	76160.8	+	321348.i	0.178610	+	0.753614i	−0.807820	+	0.589429i	$0.799353\pi$
$654$	−154201.	−	263366.i	−0.360521	−	0.615750i
$655$	298257.	+	400628.i	0.695196	+	0.933811i
$656$	436593.	+	76983.1i	1.01454	+	0.178891i
$657$	−25366.6	+	551100.i	−0.0587668	+	1.27673i
$658$	31952.5	+	181211.i	0.0737994	+	0.418537i
$659$	−153364.	−	144691.i	−0.353144	−	0.333174i	0.489143	−	0.872204i	$-0.337310\pi$
$659$	−153364.	−	144691.i	−0.353144	−	0.333174i	−0.842287	+	0.539030i	$0.818791\pi$
$660$	87344.9	−	134580.i	0.200516	−	0.308953i
$661$	613228.	+	307975.i	1.40352	+	0.704875i	0.979625	−	0.200836i	$-0.0643658\pi$
$661$	613228.	+	307975.i	1.40352	+	0.704875i	0.423896	+	0.905711i	$0.360662\pi$
$662$	71436.7	+	108614.i	0.163007	+	0.247840i
$663$	−27329.6	+	29323.5i	−0.0621737	+	0.0667096i
$664$	−633146.	−	150058.i	−1.43604	−	0.340348i
$665$	249438.	−	685324.i	0.564051	−	1.54972i
$666$	−176477.	+	170608.i	−0.397868	+	0.384636i
$667$	1.28731e6	−	468543.i	2.89355	−	1.05317i
$668$	13768.5	+	117797.i	0.0308556	+	0.263986i
$669$	185422.	−	33860.6i	0.414295	−	0.0756559i
$670$	−362074.	−	383776.i	−0.806580	−	0.854925i
$671$	−243295.	−	181127.i	−0.540367	−	0.402289i
$672$	86776.9	+	197849.i	0.192161	+	0.438123i
$673$	−677350.	+	340178.i	−1.49549	+	0.751063i	−0.993502	−	0.113813i	$-0.963694\pi$
$673$	−677350.	+	340178.i	−1.49549	+	0.751063i	−0.501986	+	0.864876i	$0.667397\pi$
$674$	−455661.	−	263076.i	−1.00305	−	0.579110i
$675$	527208.	−	407672.i	1.15711	−	0.894752i
$676$	−3880.47	−	6721.18i	−0.00849164	−	0.0147079i
$677$	−431739.	+	656427.i	−0.941985	+	1.43222i	−0.0406115	+	0.999175i	$0.512931\pi$
$677$	−431739.	+	656427.i	−0.941985	+	1.43222i	−0.901373	+	0.433043i	$0.857440\pi$
$678$	−215313.	−	63034.0i	−0.468392	−	0.137125i
$679$	−248538.	−	576175.i	−0.539079	−	1.24973i
$680$	59416.7	+	17788.2i	0.128496	+	0.0384693i
$681$	98781.7	−	580885.i	0.213001	−	1.25255i
$682$	241993.	−	561002.i	0.520276	−	1.20613i
$683$	261872.	−	312086.i	0.561367	−	0.669011i	−0.408468	−	0.912773i	$-0.633937\pi$
$683$	261872.	−	312086.i	0.561367	−	0.669011i	0.969835	+	0.243761i	$0.0783813\pi$
$684$	−60725.9	+	22943.9i	−0.129796	+	0.0490405i
$685$	−235540.	+	197641.i	−0.501976	+	0.421208i
$686$	110984.	−	33226.4i	0.235837	−	0.0706049i
$687$	471203.	−	355279.i	0.998377	−	0.752758i
$688$	−16221.5	−	278512.i	−0.0342700	−	0.588393i
$689$	−688698.	+	40112.1i	−1.45074	+	0.0844961i
$690$	600921.	−	1.41676e6i	1.26217	−	2.97575i
$691$	−130613.	−	436279.i	−0.273547	−	0.913709i	−0.978811	−	0.204765i	$-0.934357\pi$
$691$	−130613.	−	436279.i	−0.273547	−	0.913709i	0.705265	−	0.708944i	$-0.250828\pi$
$692$	55413.7	+	66039.5i	0.115719	+	0.137909i
$693$	10398.7	+	853642.i	0.0216528	+	1.77750i
$694$	−645474.	−	541617.i	−1.34017	−	1.12454i
$695$	126675.	+	54642.1i	0.262253	+	0.113125i
$696$	−447347.	+	539770.i	−0.923478	+	1.11427i
$697$	11998.2	−	40076.8i	0.0246974	−	0.0824949i
$698$	106635.	−	45997.9i	0.218872	−	0.0944121i
$699$	−409214.	+	99621.6i	−0.837522	+	0.203892i
$700$	144881.	+	95289.6i	0.295675	+	0.194468i
$701$	−206013.	+	118942.i	−0.419236	+	0.242046i	−0.694750	−	0.719251i	$-0.744485\pi$
$701$	−206013.	+	118942.i	−0.419236	+	0.242046i	0.275514	+	0.961297i	$0.411152\pi$
$702$	−481385.	−	165314.i	−0.976829	−	0.335455i
$703$	−97779.3	+	169359.i	−0.197850	+	0.342686i
$704$	−222891.	−	443813.i	−0.449725	−	0.895477i
$705$	−24819.5	+	224177.i	−0.0499362	+	0.451038i
$706$	−74396.9	+	99932.4i	−0.149261	+	0.200492i
$707$	−690780.	+	651717.i	−1.38198	+	1.30383i
$708$	−46314.3	+	39345.4i	−0.0923949	+	0.0784924i
$709$	835718.	−	97681.4i	1.66252	−	0.194321i	0.767720	−	0.640786i	$-0.221391\pi$
$709$	835718.	−	97681.4i	1.66252	−	0.194321i	0.894801	+	0.446465i	$0.147317\pi$
$710$	−166667.	−	457915.i	−0.330624	−	0.908381i
$711$	−8705.18	−	123521.i	−0.0172202	−	0.244345i
$712$	312789.	+	113846.i	0.617008	+	0.224573i
$713$	204927.	−	864657.i	0.403108	−	1.70085i
$714$	68677.9	−	21017.4i	0.134716	−	0.0412271i
$715$	837330.	−	550720.i	1.63789	−	1.07726i
$716$	−43206.5	+	86031.1i	−0.0842796	+	0.167815i
$717$	−41850.8	+	802751.i	−0.0814077	+	1.56150i
$718$	409166.	−	433691.i	0.793690	−	0.841262i
$719$	875216.	−	154324.i	1.69300	−	0.298522i	0.757760	−	0.652533i	$-0.226294\pi$
$719$	875216.	−	154324.i	1.69300	−	0.298522i	0.935241	+	0.354011i	$0.115182\pi$
$720$	119586.	+	925242.i	0.230684	+	1.78480i
$721$	−88125.5	+	499785.i	−0.169524	+	0.961418i
$722$	180374.	−	134284.i	0.346019	−	0.257602i
$723$	−1507.56	−	247523.i	−0.00288401	−	0.473520i
$724$	−103250.	+	24470.7i	−0.196976	+	0.0466842i
$725$	−144868.	+	1.23943e6i	−0.275612	+	2.35801i
$726$	26623.1	+	413680.i	0.0505110	+	0.784858i
$727$	7379.92	−	126708.i	0.0139631	−	0.239738i	−0.984104	−	0.177593i	$-0.943169\pi$
$727$	7379.92	−	126708.i	0.0139631	−	0.239738i	0.998067	−	0.0621447i	$-0.0197940\pi$
$728$			608550.i			1.14824i
$729$	492417.	−	199887.i	0.926570	−	0.376123i
$730$	−1.16043e6			−2.17757
$731$	−26281.6	−	1530.73i	−0.0491832	−	0.00286459i
$732$	−49028.8	+	3155.34i	−0.0915017	+	0.00588876i
$733$	−178687.	−	20885.5i	−0.332571	−	0.0388720i	−0.0518312	−	0.998656i	$-0.516506\pi$
$733$	−178687.	−	20885.5i	−0.332571	−	0.0388720i	−0.280740	+	0.959784i	$0.590580\pi$
$734$	−131625.	−	555369.i	−0.244313	−	1.03084i
$735$	−705756.	+	4298.47i	−1.30641	+	0.00795682i
$736$	216887.	+	291330.i	0.400385	+	0.537810i
$737$	484578.	+	85444.2i	0.892132	+	0.157307i
$738$	526814.	−	68090.1i	0.967263	−	0.125018i
$739$	−118422.	−	671602.i	−0.216841	−	1.22977i	−0.877683	−	0.479242i	$-0.840912\pi$
$739$	−118422.	−	671602.i	−0.216841	−	1.22977i	0.660841	−	0.750526i	$-0.270200\pi$
$740$	−56944.5	−	53724.3i	−0.103989	−	0.0981087i
$741$	−404954.	−	21112.0i	−0.737512	−	0.0384497i
$742$	1.10459e6	+	554748.i	2.00629	+	1.00760i
$743$	207523.	+	315524.i	0.375914	+	0.571550i	0.973051	−	0.230589i	$-0.0740654\pi$
$743$	207523.	+	315524.i	0.375914	+	0.571550i	−0.597137	+	0.802139i	$0.703695\pi$
$744$	133072.	+	434833.i	0.240403	+	0.785556i
$745$	−1.35427e6	−	320967.i	−2.44001	−	0.578293i
$746$	−219000.	+	601697.i	−0.393519	+	1.08119i
$747$	−921312.	+	64929.5i	−1.65107	+	0.116359i
$748$	11828.7	−	4305.31i	0.0211415	−	0.00769487i
$749$	−10669.4	−	91282.4i	−0.0190185	−	0.162713i
$750$	287099.	+	337950.i	0.510399	+	0.600800i
$751$	561930.	+	595611.i	0.996329	+	1.05605i	0.998428	+	0.0560490i	$0.0178503\pi$
$751$	561930.	+	595611.i	0.996329	+	1.05605i	−0.00209923	+	0.999998i	$0.500668\pi$
$752$	−150422.	−	111985.i	−0.265997	−	0.198028i
$753$	−797400.	−	88283.3i	−1.40633	−	0.155700i
$754$	851659.	−	427719.i	1.49804	−	0.752343i
$755$	81917.8	+	47295.3i	0.143709	+	0.0829705i
$756$	90806.1	+	104288.i	0.158881	+	0.182470i
$757$	358436.	+	620830.i	0.625489	+	1.08338i	0.988446	+	0.151573i	$0.0484340\pi$
$757$	358436.	+	620830.i	0.625489	+	1.08338i	−0.362957	+	0.931806i	$0.618233\pi$
$758$	−373490.	+	567863.i	−0.650040	+	0.988338i
$759$	339478.	+	1.39447e6i	0.589289	+	2.42061i
$760$	248512.	+	576116.i	0.430250	+	0.997431i
$761$	525023.	+	157182.i	0.906587	+	0.271414i	0.705958	−	0.708253i	$-0.250517\pi$
$761$	525023.	+	157182.i	0.906587	+	0.271414i	0.200628	+	0.979667i	$0.435702\pi$
$762$	90888.2	+	75325.8i	0.156530	+	0.129728i
$763$	−205143.	+	475576.i	−0.352378	+	0.816903i
$764$	56544.4	−	67387.0i	0.0968730	−	0.115449i
$765$	88029.4	−	1072.34i	0.150420	−	0.00183236i
$766$	−231222.	+	194018.i	−0.394068	+	0.330662i
$767$	−363663.	+	108874.i	−0.618171	+	0.185068i
$768$	−282405.	−	119783.i	−0.478795	−	0.203082i
$769$	19031.0	+	326750.i	0.0321818	+	0.552539i	0.975411	+	0.220396i	$0.0707349\pi$
$769$	19031.0	+	326750.i	0.0321818	+	0.552539i	−0.943229	+	0.332144i	$0.892228\pi$
$770$	−1.79267e6	+	104411.i	−3.02356	+	0.176102i
$771$	−314224.	−	416752.i	−0.528604	−	0.701083i
$772$	−52135.0	−	174143.i	−0.0874772	−	0.292194i
$773$	−255264.	−	304211.i	−0.427199	−	0.509116i	0.508913	−	0.860818i	$-0.330047\pi$
$773$	−255264.	−	304211.i	−0.427199	−	0.509116i	−0.936112	+	0.351702i	$0.885603\pi$
$774$	−118148.	−	312704.i	−0.197217	−	0.521977i
$775$	620063.	+	520295.i	1.03236	+	0.866255i
$776$	495690.	+	213820.i	0.823164	+	0.355078i
$777$	410676.	+	69837.1i	0.680233	+	0.115676i
$778$	224816.	−	750937.i	0.371422	−	1.24064i
$779$	388592.	−	167622.i	0.640353	−	0.276221i
$780$	45610.2	−	155796.i	0.0749674	−	0.256075i
$781$	379692.	+	249727.i	0.622486	+	0.409415i
$782$	104566.	−	60371.3i	0.170993	−	0.0987226i
$783$	−377374.	+	920754.i	−0.615530	+	1.50183i
$784$	293405.	−	508192.i	0.477348	−	0.826791i
$785$	27747.1	+	55249.1i	0.0450276	+	0.0896574i
$786$	−455679.	+	199861.i	−0.737588	+	0.323507i
$787$	−584106.	+	784590.i	−0.943066	+	1.26676i	0.0206389	+	0.999787i	$0.493430\pi$
$787$	−584106.	+	784590.i	−0.943066	+	1.26676i	−0.963705	+	0.266970i	$0.913977\pi$
$788$	−9727.38	+	9177.31i	−0.0156655	+	0.0147796i
$789$	77351.2	+	423579.i	0.124255	+	0.680425i
$790$	258702.	−	30237.9i	0.414520	−	0.0484504i
$791$	130222.	+	357783.i	0.208129	+	0.571829i
$792$	−510481.	−	528042.i	−0.813821	−	0.841817i
$793$	−288390.	−	104965.i	−0.458599	−	0.166916i
$794$	−113116.	+	477273.i	−0.179425	+	0.757053i
$795$	1.10837e6	+	1.03301e6i	1.75368	+	1.63444i
$796$	−130110.	+	85574.5i	−0.205345	+	0.135057i
$797$	359786.	−	716393.i	0.566406	−	1.12781i	−0.410045	−	0.912066i	$-0.634487\pi$
$797$	359786.	−	716393.i	0.566406	−	1.12781i	0.976451	−	0.215742i	$-0.0692169\pi$
$798$	609456.	+	395549.i	0.957055	+	0.621148i
$799$	−12143.8	+	12871.7i	−0.0190223	+	0.0201624i
$800$	−325811.	+	57449.3i	−0.509080	+	0.0897645i
$801$	471974.	+	21724.5i	0.735618	+	0.0338598i
$802$	−24821.7	+	140771.i	−0.0385907	+	0.218859i
$803$	868063.	−	646249.i	1.34623	−	1.00223i
$804$	68779.8	−	40270.6i	0.106402	−	0.0622982i
$805$	−2.54132e6	+	602304.i	−3.92164	+	0.929446i
$806$	71767.2	−	614008.i	0.110473	−	0.945157i
$807$	−142121.	−	70295.0i	−0.218228	−	0.107939i
$808$	47506.0	−	815646.i	0.0727655	−	1.24934i
$809$		−	509608.i		−	0.778644i	−0.921102	−	0.389322i	$-0.872709\pi$
$809$		−	509608.i		−	0.778644i	0.921102	−	0.389322i	$-0.127291\pi$
$810$	467629.	+	1.01534e6i	0.712740	+	1.54753i
$811$	−713895.			−1.08541			−0.542703	−	0.839924i	$-0.682599\pi$
$811$	−713895.			−1.08541			−0.542703	+	0.839924i	$0.682599\pi$
$812$	−258485.	−	15055.0i	−0.392033	−	0.0228333i
$813$	9906.54	+	14864.2i	0.0149879	+	0.0224885i
$814$	478251.	+	55899.5i	0.721783	+	0.0843644i
$815$	−322637.	−	1.36131e6i	−0.485735	−	2.04948i
$816$	−36211.8	+	63612.3i	−0.0543839	+	0.0955347i
$817$	−159035.	−	213622.i	−0.238259	−	0.320038i
$818$	552322.	+	97389.2i	0.825440	+	0.145547i
$819$	257799.	+	824423.i	0.384338	+	1.22909i
$820$	29419.6	+	166847.i	0.0437531	+	0.248136i
$821$	−278.877	−	263.107i	−0.000413739	−	0.000390343i	0.686035	−	0.727569i	$-0.259350\pi$
$821$	−278.877	−	263.107i	−0.000413739	−	0.000390343i	−0.686448	+	0.727178i	$0.740831\pi$
$822$	−139141.	−	272895.i	−0.205926	−	0.403879i
$823$	−1.02097e6	−	512748.i	−1.50734	−	0.757015i	−0.512522	−	0.858674i	$-0.671289\pi$
$823$	−1.02097e6	−	512748.i	−1.50734	−	0.757015i	−0.994819	+	0.101659i	$0.967585\pi$
$824$	−239917.	−	364776.i	−0.353352	−	0.537245i
$825$	−1.27389e6	−	293736.i	−1.87165	−	0.431567i
$826$	661837.	+	156858.i	0.970042	+	0.229904i
$827$	23675.9	−	65048.9i	0.0346174	−	0.0951106i	−0.921180	−	0.389137i	$-0.872773\pi$
$827$	23675.9	−	65048.9i	0.0346174	−	0.0951106i	0.955797	+	0.294027i	$0.0949954\pi$
$828$	188147.	+	136540.i	0.274433	+	0.199158i
$829$	−552771.	+	201192.i	−0.804333	+	0.292753i	−0.711281	−	0.702908i	$-0.751885\pi$
$829$	−552771.	+	201192.i	−0.804333	+	0.292753i	−0.0930523	+	0.995661i	$0.529662\pi$
$830$	−225536.	−	1.92959e6i	−0.327386	−	2.80097i
$831$	180708.	−	506061.i	0.261683	−	0.732825i
$832$	−344841.	−	365510.i	−0.498163	−	0.528022i
$833$	−44416.6	−	33066.9i	−0.0640111	−	0.0476545i
$834$	−81399.8	+	110741.i	−0.117028	+	0.159212i
$835$	1.45401e6	−	730231.i	2.08542	−	1.04734i
$836$	110281.	+	63670.8i	0.157793	+	0.0911020i
$837$	364484.	+	532711.i	0.520269	+	0.760397i
$838$	328065.	+	568226.i	0.467167	+	0.809157i
$839$	179148.	−	272382.i	0.254501	−	0.386949i	−0.685527	−	0.728047i	$-0.740428\pi$
$839$	179148.	−	272382.i	0.254501	−	0.386949i	0.940028	+	0.341098i	$0.110799\pi$
$840$	966553.	−	923086.i	1.36983	−	1.30823i
$841$	−457850.	−	1.06142e6i	−0.647338	−	1.50070i
$842$	642938.	+	192483.i	0.906870	+	0.271499i
$843$	608922.	−	225839.i	0.856854	−	0.317792i
$844$	2618.32	−	6069.94i	0.00367567	−	0.00852117i
$845$	−68439.9	+	81563.5i	−0.0958508	+	0.114231i
$846$	−212069.	−	74274.0i	−0.296303	−	0.103776i
$847$	538920.	−	452207.i	0.751203	−	0.630334i
$848$	−1.20682e6	+	361297.i	−1.67822	+	0.502427i
$849$	−18886.0	−	153468.i	−0.0262014	−	0.212914i
$850$	6395.02	+	109798.i	0.00885124	+	0.151970i
$851$	699130.	−	40719.7i	0.965382	−	0.0562271i
$852$	73060.6	−	8990.95i	0.100648	−	0.0123859i
$853$	−233817.	−	781002.i	−0.321349	−	1.07338i	−0.954215	−	0.299120i	$-0.903307\pi$
$853$	−233817.	−	781002.i	−0.321349	−	1.07338i	0.632866	−	0.774261i	$-0.281878\pi$
$854$	353460.	+	421237.i	0.484646	+	0.577579i
$855$	580727.	+	675207.i	0.794401	+	0.923645i
$856$	60567.9	+	50822.5i	0.0826600	+	0.0693600i
$857$	−464717.	−	200459.i	−0.632742	−	0.272938i	0.0554560	−	0.998461i	$-0.482339\pi$
$857$	−464717.	−	200459.i	−0.632742	−	0.272938i	−0.688198	+	0.725523i	$0.741598\pi$
$858$	347193.	+	936126.i	0.471625	+	1.27163i
$859$	−110285.	+	368378.i	−0.149462	+	0.499237i	−0.999628	−	0.0272774i	$-0.991316\pi$
$859$	−110285.	+	368378.i	−0.149462	+	0.499237i	0.850166	+	0.526515i	$0.176501\pi$
$860$	97896.3	−	42228.3i	0.132364	−	0.0570962i
$861$	−622625.	−	651943.i	−0.839886	−	0.879434i
$862$	−474270.	−	311932.i	−0.638280	−	0.419803i
$863$	−326364.	+	188426.i	−0.438209	+	0.253000i	−0.702837	−	0.711350i	$-0.748084\pi$
$863$	−326364.	+	188426.i	−0.438209	+	0.253000i	0.264629	+	0.964350i	$0.414751\pi$
$864$	−262552.	−	25835.0i	−0.351712	−	0.0346083i
$865$	591353.	−	1.02425e6i	0.790341	−	1.36891i
$866$	326869.	+	650849.i	0.435851	+	0.867850i
$867$	−600104.	−	441106.i	−0.798341	−	0.586820i
$868$	−100294.	+	134718.i	−0.133117	+	0.178807i
$869$	−176683.	+	166692.i	−0.233968	+	0.220737i
$870$	−1.97119e6	−	703888.i	−2.60429	−	0.929962i
$871$	494501.	−	57798.8i	0.651824	−	0.0761873i
$872$	−152399.	−	418713.i	−0.200424	−	0.550659i
$873$	762107.	+	79680.4i	0.999971	+	0.104550i
$874$	1.14779e6	+	417762.i	1.50259	+	0.546898i
$875$	173552.	−	732272.i	0.226680	−	0.956437i
$876$	39385.9	−	170812.i	0.0513254	−	0.222592i
$877$	−992087.	+	652506.i	−1.28988	+	0.848370i	−0.994266	−	0.106937i	$-0.965896\pi$
$877$	−992087.	+	652506.i	−1.28988	+	0.848370i	−0.295617	+	0.955306i	$0.595525\pi$
$878$	−71080.9	+	141534.i	−0.0922070	+	0.183599i
$879$	−294718.	+	150267.i	−0.381442	+	0.194485i
$880$	1.25588e6	−	1.33116e6i	1.62175	−	1.71896i
$881$	−177610.	+	31317.4i	−0.228831	+	0.0403491i	−0.286888	−	0.957964i	$-0.592621\pi$
$881$	−177610.	+	31317.4i	−0.228831	+	0.0403491i	0.0580567	+	0.998313i	$0.481510\pi$
$882$	153804.	−	686088.i	0.197711	−	0.881947i
$883$	35337.0	−	200406.i	0.0453219	−	0.257033i	−0.953725	−	0.300680i	$-0.902786\pi$
$883$	35337.0	−	200406.i	0.0453219	−	0.257033i	0.999047	+	0.0436466i	$0.0138976\pi$
$884$	10216.3	−	7605.77i	0.0130735	−	0.00973282i
$885$	724549.	+	412456.i	0.925085	+	0.526612i
$886$	1.47505e6	−	349593.i	1.87905	−	0.445344i
$887$	96008.2	−	821403.i	0.122028	−	1.04402i	−0.783988	−	0.620777i	$-0.786817\pi$
$887$	96008.2	−	821403.i	0.122028	−	1.04402i	0.906016	−	0.423243i	$-0.139108\pi$
$888$	−298218.	+	198754.i	−0.378188	+	0.252052i
$889$	11648.4	−	199996.i	0.0147388	−	0.253056i
$890$			993814.i			1.25466i
$891$	−915259.	−	499102.i	−1.15289	−	0.628686i
$892$	−59890.9			−0.0752716
$893$	−178715.	−	10409.0i	−0.224108	−	0.0130528i
$894$	614724.	−	1.24283e6i	0.769140	−	1.55503i
$895$	1.31183e6	+	153331.i	1.63769	+	0.191418i
$896$	296214.	+	1.24982e6i	0.368968	+	1.55680i
$897$	733722.	+	1.25315e6i	0.911898	+	1.55747i
$898$	−493783.	−	663266.i	−0.612327	−	0.822498i
$899$	−1.19023e6	−	209871.i	−1.47270	−	0.259676i
$900$	−188061.	+	97334.3i	−0.232174	+	0.120166i
$901$	20642.3	+	117068.i	0.0254278	+	0.144208i
$902$	−757936.	−	715076.i	−0.931578	−	0.878899i
$903$	−308847.	+	475867.i	−0.378764	+	0.583593i
$904$	−292717.	−	147008.i	−0.358188	−	0.179889i
$905$	799944.	+	1.21626e6i	0.976703	+	1.48501i
$906$	−64249.3	+	68936.6i	−0.0782729	+	0.0839834i
$907$	−238669.	−	56565.5i	−0.290122	−	0.0687602i	0.0829778	−	0.996551i	$-0.473557\pi$
$907$	−238669.	−	56565.5i	−0.290122	−	0.0687602i	−0.373100	+	0.927791i	$0.621705\pi$
$908$	−64033.6	+	175931.i	−0.0776670	+	0.213388i
$909$	−281173.	−	1.12511e6i	−0.340287	−	1.36165i
$910$	−1.70735e6	+	621424.i	−2.06177	+	0.750421i
$911$	116346.	+	995401.i	0.140189	+	1.19939i	0.861856	+	0.507153i	$0.169302\pi$
$911$	116346.	+	995401.i	0.140189	+	1.19939i	−0.721667	+	0.692240i	$0.756624\pi$
$912$	−728431.	+	133021.i	−0.875788	+	0.159931i
$913$	1.24331e6	+	1.31783e6i	1.49155	+	1.58095i
$914$	13328.8	+	9922.95i	0.0159551	+	0.0118781i
$915$	270732.	+	617263.i	0.323368	+	0.737273i
$916$	−167565.	+	84154.4i	−0.199707	+	0.100297i
$917$	731313.	+	422224.i	0.869690	+	0.502116i
$918$	−18663.6	+	85696.2i	−0.0221467	+	0.101689i
$919$	215402.	+	373086.i	0.255046	+	0.441752i	0.964908	−	0.262589i	$-0.0845762\pi$
$919$	215402.	+	373086.i	0.255046	+	0.441752i	−0.709862	+	0.704340i	$0.751243\pi$
$920$	1.23469e6	−	1.87725e6i	1.45875	−	2.21792i
$921$	546745.	+	160063.i	0.644563	+	0.188700i
$922$	185480.	+	429992.i	0.218191	+	0.505823i
$923$	440507.	+	131879.i	0.517070	+	0.154801i
$924$	45475.7	−	267420.i	0.0532642	−	0.313220i
$925$	−252666.	+	585746.i	−0.295300	+	0.684582i
$926$	417467.	−	497517.i	0.486855	−	0.580211i
$927$	−479553.	−	392539.i	−0.558056	−	0.456797i
$928$	378414.	−	317527.i	0.439412	−	0.368710i
$929$	−877021.	+	262563.i	−1.01620	+	0.304230i	−0.751239	−	0.660030i	$-0.770544\pi$
$929$	−877021.	+	262563.i	−1.01620	+	0.304230i	−0.264959	+	0.964260i	$0.585358\pi$
$930$	−1.08408e6	+	817378.i	−1.25342	+	0.945055i
$931$	−32571.1	−	559225.i	−0.0375780	−	0.645189i
$932$	133596.	−	7781.08i	0.153802	−	0.00895794i
$933$	141749.	−	334194.i	0.162839	−	0.383916i
$934$	435518.	+	1.45473e6i	0.499244	+	1.66759i
$935$	−111006.	−	132292.i	−0.126977	−	0.151325i
$936$	−648046.	−	363697.i	−0.739698	−	0.415134i
$937$	−507297.	−	425673.i	−0.577807	−	0.484838i	0.306419	−	0.951897i	$-0.400869\pi$
$937$	−507297.	−	425673.i	−0.577807	−	0.484838i	−0.884226	+	0.467059i	$0.845314\pi$
$938$	−819101.	−	353326.i	−0.930961	−	0.401578i
$939$	227657.	−	274692.i	0.258196	−	0.311540i
$940$	20554.0	−	68655.3i	0.0232617	−	0.0776995i
$941$	−570144.	+	245936.i	−0.643881	+	0.277743i	−0.692877	−	0.721056i	$-0.743657\pi$
$941$	−570144.	+	245936.i	−0.643881	+	0.277743i	0.0489962	+	0.998799i	$0.484398\pi$
$942$	−59845.0	+	14569.1i	−0.0674413	+	0.0164183i
$943$	−1.26621e6	−	832801.i	−1.42391	−	0.936521i
$944$	−600324.	+	346597.i	−0.673662	+	0.388939i
$945$	918375.	−	1.66000e6i	1.02839	−	1.85885i
$946$	−327868.	+	567885.i	−0.366368	+	0.634568i
$947$	−52666.3	−	104867.i	−0.0587263	−	0.116934i	0.862355	−	0.506304i	$-0.168989\pi$
$947$	−52666.3	−	104867.i	−0.0587263	−	0.116934i	−0.921081	+	0.389371i	$0.872692\pi$
$948$	−4329.63	+	39106.5i	−0.00481764	+	0.0435143i
$949$	653884.	−	878319.i	0.726053	−	0.975258i
$950$	−809293.	+	763529.i	−0.896724	+	0.846015i
$951$	469579.	−	398922.i	0.519215	−	0.441090i
$952$	104153.	−	12173.8i	0.114921	−	0.0134323i
$953$	370488.	+	1.01791e6i	0.407933	+	1.12079i	0.958275	+	0.285848i	$0.0922751\pi$
$953$	370488.	+	1.01791e6i	0.407933	+	1.12079i	−0.550342	+	0.834939i	$0.685503\pi$
$954$	−1.25091e6	+	844741.i	−1.37445	+	0.928168i
$955$	−1.13406e6	−	412763.i	−1.24345	−	0.452579i
$956$	58902.7	−	248530.i	0.0644495	−	0.271934i
$957$	1.86656e6	−	571221.i	2.03806	−	0.623706i
$958$	208603.	−	137201.i	0.227295	−	0.149494i
$959$	−233311.	+	464560.i	−0.253687	+	0.505132i
$960$	−57459.0	+	1.10213e6i	−0.0623470	+	1.19589i
$961$	95771.4	−	101512.i	0.103702	−	0.109918i
$962$	479794.	−	84600.5i	0.518447	−	0.0914162i
$963$	103583.	+	43192.7i	0.111696	+	0.0465755i
$964$	−13657.4	+	77455.1i	−0.0146965	+	0.0833482i
$965$	−2.00038e6	+	1.48923e6i	−2.14812	+	1.59922i
$966$	−15846.8	−	2.60185e6i	−0.0169820	−	2.78823i
$967$	1.00572e6	−	238360.i	1.07553	−	0.254906i	0.345571	−	0.938393i	$-0.387685\pi$
$967$	1.00572e6	−	238360.i	1.07553	−	0.254906i	0.729964	+	0.683486i	$0.239537\pi$
$968$	−70263.7	+	601144.i	−0.0749860	+	0.641546i
$969$	4487.62	+	69730.3i	0.00477934	+	0.0742632i
$970$	−93716.4	+	1.60905e6i	−0.0996030	+	1.71012i
$971$		−	1.82099e6i		−	1.93138i	−0.259693	−	0.965691i	$-0.583621\pi$
$971$		−	1.82099e6i		−	1.93138i	0.259693	−	0.965691i	$-0.416379\pi$
$972$	−165326.	+	34372.3i	−0.174989	+	0.0363811i
$973$	233248.			0.246372
$974$	−55021.3	−	3204.62i	−0.0579979	−	0.00337800i
$975$	−1.32003e6	+	84953.1i	−1.38860	+	0.0893656i
$976$	−556626.	−	65060.3i	−0.584338	−	0.0682993i
$977$	−74481.9	−	314264.i	−0.0780300	−	0.329235i	0.920004	−	0.391909i	$-0.128185\pi$
$977$	−74481.9	−	314264.i	−0.0780300	−	0.329235i	−0.998034	+	0.0626744i	$0.980037\pi$
$978$	1.39374e6	−	8488.69i	1.45715	−	0.00887489i
$979$	−553461.	−	743427.i	−0.577459	−	0.775663i
$980$	220846.	+	38941.2i	0.229953	+	0.0405468i
$981$	−383838.	−	502683.i	−0.398851	−	0.522344i
$982$	284390.	+	1.61285e6i	0.294911	+	1.67252i
$983$	355388.	+	335291.i	0.367787	+	0.346989i	0.847842	−	0.530250i	$-0.177902\pi$
$983$	355388.	+	335291.i	0.367787	+	0.346989i	−0.480055	+	0.877238i	$0.659383\pi$
$984$	774513.	+	40378.7i	0.799905	+	0.0417025i
$985$	163955.	+	82341.2i	0.168986	+	0.0848682i
$986$	−90241.3	−	137205.i	−0.0928221	−	0.141129i
$987$	111592.	+	364644.i	0.114551	+	0.374313i
$988$	125373.	+	29713.9i	0.128437	+	0.0304401i
$989$	−326191.	+	896204.i	−0.333488	+	0.916250i
$990$	960193.	−	1.97142e6i	0.979689	−	2.01144i
$991$	1.04152e6	−	379081.i	1.06052	−	0.385998i	0.247897	−	0.968786i	$-0.420261\pi$
$991$	1.04152e6	−	379081.i	1.06052	−	0.385998i	0.812624	+	0.582789i	$0.198038\pi$
$992$	−37199.2	−	318259.i	−0.0378016	−	0.323413i
$993$	174430.	+	205325.i	0.176898	+	0.208230i
$994$	−565390.	−	599279.i	−0.572237	−	0.606535i
$995$	1.71371e6	+	1.27581e6i	1.73098	+	1.28866i
$996$	291684.	+	32293.5i	0.294032	+	0.0325534i
$997$	727570.	−	365399.i	0.731955	−	0.367602i	−0.0434588	−	0.999055i	$-0.513838\pi$
$997$	727570.	−	365399.i	0.731955	−	0.367602i	0.775414	+	0.631454i	$0.217541\pi$
$998$	−66768.8	−	38549.0i	−0.0670367	−	0.0387037i
$999$	−319809.	+	395592.i	−0.320449	+	0.396384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.h.a.2.9	✓	630
81.41	odd	54	inner	81.5.h.a.41.9	yes	630

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.5.h.a.2.9	✓	630	1.1	even	1	trivial
81.5.h.a.41.9	yes	630	81.41	odd	54	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	81.h (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.33543 - 0.252510i) q^{2} +(-8.98142 + 0.578015i) q^{3} +(2.84035 + 0.331989i) q^{4} +(-9.04763 - 38.1749i) q^{5} +(39.0842 - 0.238046i) q^{6} +(-39.6102 - 53.2058i) q^{7} +(56.1985 + 9.90930i) q^{8} +(80.3318 - 10.3828i) q^{9} +(29.5858 + 167.789i) q^{10} +(-115.575 - 109.039i) q^{11} +(-25.7023 - 1.33997i) q^{12} +(-143.670 - 72.1536i) q^{13} +(158.292 + 240.672i) q^{14} +(103.326 + 337.635i) q^{15} +(-285.664 - 67.7036i) q^{16} +(-9.47504 + 26.0325i) q^{17} +(-350.894 + 24.7293i) q^{18} +(-263.350 + 95.8514i) q^{19} +(-13.0248 - 111.434i) q^{20} +(386.510 + 454.968i) q^{21} +(473.532 + 501.915i) q^{22} +(805.016 + 599.312i) q^{23} +(-510.470 - 56.5161i) q^{24} +(-816.946 + 410.286i) q^{25} +(604.649 + 349.095i) q^{26} +(-715.492 + 139.685i) q^{27} +(-94.8432 - 164.273i) q^{28} +(750.082 - 1140.44i) q^{29} +(-362.707 - 1489.88i) q^{30} +(-350.695 - 813.003i) q^{31} +(346.689 + 103.792i) q^{32} +(1101.05 + 912.522i) q^{33} +(47.6518 - 110.469i) q^{34} +(-1672.75 + 1993.50i) q^{35} +(231.617 - 2.82148i) q^{36} +(534.545 - 448.536i) q^{37} +(1165.94 - 349.058i) q^{38} +(1332.06 + 564.998i) q^{39} +(-130.176 - 2235.03i) q^{40} +(-1507.53 + 87.8039i) q^{41} +(-1560.80 - 2070.08i) q^{42} +(272.547 + 910.370i) q^{43} +(-292.073 - 348.079i) q^{44} +(-1123.17 - 2972.72i) q^{45} +(-3338.76 - 2801.55i) q^{46} +(586.535 + 253.007i) q^{47} +(2604.80 + 442.956i) q^{48} +(-573.270 + 1914.85i) q^{49} +(3645.41 - 1572.48i) q^{50} +(70.0522 - 239.285i) q^{51} +(-384.118 - 252.638i) q^{52} +(3716.11 - 2145.50i) q^{53} +(3137.24 - 424.926i) q^{54} +(-3116.88 + 5398.60i) q^{55} +(-1698.80 - 3382.59i) q^{56} +(2309.85 - 1013.10i) q^{57} +(-3539.90 + 4754.91i) q^{58} +(1717.48 - 1620.35i) q^{59} +(181.391 + 993.306i) q^{60} +(1896.01 - 221.612i) q^{61} +(1315.12 + 3613.27i) q^{62} +(-3734.39 - 3862.85i) q^{63} +(2937.12 + 1069.02i) q^{64} +(-1454.59 + 6137.40i) q^{65} +(-4543.10 - 4234.20i) q^{66} +(-2587.30 + 1701.70i) q^{67} +(-35.5549 + 70.7957i) q^{68} +(-7576.60 - 4917.36i) q^{69} +(7755.46 - 8220.31i) q^{70} +(-2816.68 + 496.657i) q^{71} +(4617.41 + 212.535i) q^{72} +(-1182.70 + 6707.44i) q^{73} +(-2430.74 + 1809.62i) q^{74} +(7100.18 - 4157.16i) q^{75} +(-779.827 + 184.822i) q^{76} +(-1223.57 + 10468.3i) q^{77} +(-5632.39 - 2785.87i) q^{78} +(88.8883 - 1526.15i) q^{79} +11517.8i q^{80} +(6345.40 - 1668.14i) q^{81} +6557.98 q^{82} +(-11383.1 - 662.993i) q^{83} +(946.779 + 1420.59i) q^{84} +(1079.51 + 126.177i) q^{85} +(-951.730 - 4015.66i) q^{86} +(-6077.60 + 10676.4i) q^{87} +(-5414.62 - 7273.09i) q^{88} +(5744.39 + 1012.89i) q^{89} +(4118.80 + 13171.6i) q^{90} +(1851.80 + 10502.1i) q^{91} +(2087.56 + 1969.51i) q^{92} +(3619.67 + 7099.22i) q^{93} +(-2478.99 - 1245.00i) q^{94} +(6041.81 + 9186.13i) q^{95} +(-3173.76 - 731.808i) q^{96} +(9205.02 + 2181.63i) q^{97} +(2968.89 - 8156.95i) q^{98} +(-10416.4 - 7559.32i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 630 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 2034 q^{18}+ \cdots + 4266 q^{99}+O(q^{100}) \) 630 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 2034 * q^18 - 18 * q^19 + 846 * q^20 + 2277 * q^21 - 18 * q^22 + 2979 * q^23 + 4734 * q^24 - 18 * q^25 - 27 * q^26 - 1449 * q^27 - 9 * q^28 - 3987 * q^29 - 9522 * q^30 - 18 * q^31 - 9090 * q^32 - 3231 * q^33 - 18 * q^34 + 2655 * q^35 + 10062 * q^36 - 18 * q^37 + 7326 * q^38 - 18 * q^39 - 18 * q^40 - 13410 * q^41 - 18333 * q^42 - 18 * q^43 + 4518 * q^44 + 11214 * q^45 - 18 * q^46 + 18774 * q^47 + 35127 * q^48 - 18 * q^49 + 31923 * q^50 + 12330 * q^51 - 162 * q^52 - 27 * q^53 - 13500 * q^54 - 9 * q^55 - 38808 * q^56 - 21186 * q^57 - 18 * q^58 - 31014 * q^59 - 58167 * q^60 - 18 * q^61 - 38331 * q^62 - 14058 * q^63 - 18 * q^64 + 60354 * q^65 + 99126 * q^66 - 12303 * q^67 + 72153 * q^68 + 20502 * q^69 + 21582 * q^70 - 39546 * q^71 - 138258 * q^72 - 18 * q^73 - 96786 * q^74 - 56268 * q^75 + 44046 * q^76 - 62658 * q^77 - 44523 * q^78 + 8460 * q^79 + 11574 * q^81 - 36 * q^82 + 33894 * q^83 + 153927 * q^84 - 39168 * q^85 + 117486 * q^86 + 125982 * q^87 - 72594 * q^88 + 7596 * q^89 - 1557 * q^90 - 18 * q^91 + 48312 * q^92 + 3294 * q^93 + 6030 * q^94 + 21798 * q^95 - 37665 * q^96 + 43587 * q^97 + 11079 * q^98 + 4266 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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