LMFDB - Embedded newform 33.6.e.a.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,6,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.29266605383$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 142 x^{18} - 389 x^{17} + 14927 x^{16} - 6599 x^{15} + 1399353 x^{14} + \cdots + 25735126080400 $ x^20 - 3x^19 + 142x^18 - 389x^17 + 14927x^16 - 6599x^15 + 1399353x^14 + 1969563x^13 + 129076450x^12 + 14028509x^11 + 4158720649x^10 - 7877307064x^9 + 107078602608x^8 - 53496436514x^7 + 2527225278875x^6 - 6173773919508x^5 + 63231264058241x^4 - 118816044595930x^3 + 398041877081860x^2 - 161017247606600*x + 25735126080400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			25.5
Root			$8.61948 + 6.26242i$ of defining polynomial
Character	$\chi$	$=$	33.25
Dual form			33.6.e.a.4.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.81047 - 5.67464i) q^{2} +(2.78115 + 8.55951i) q^{3} +(18.9134 - 58.2093i) q^{4} +(25.1385 + 18.2642i) q^{5} +(70.2942 + 51.0717i) q^{6} +(56.7190 - 174.563i) q^{7} +(-87.1280 - 268.152i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})$	\(q+(7.81047 - 5.67464i) q^{2} +(2.78115 + 8.55951i) q^{3} +(18.9134 - 58.2093i) q^{4} +(25.1385 + 18.2642i) q^{5} +(70.2942 + 51.0717i) q^{6} +(56.7190 - 174.563i) q^{7} +(-87.1280 - 268.152i) q^{8} +(-65.5304 + 47.6106i) q^{9} +299.987 q^{10} +(-30.5455 + 400.147i) q^{11} +550.844 q^{12} +(-707.066 + 513.713i) q^{13} +(-547.581 - 1685.28i) q^{14} +(-86.4186 + 265.969i) q^{15} +(-617.672 - 448.765i) q^{16} +(-627.084 - 455.604i) q^{17} +(-241.650 + 743.722i) q^{18} +(462.848 + 1424.50i) q^{19} +(1538.60 - 1117.86i) q^{20} +1651.92 q^{21} +(2032.12 + 3298.67i) q^{22} +1303.68 q^{23} +(2052.94 - 1491.55i) q^{24} +(-667.313 - 2053.78i) q^{25} +(-2607.38 + 8024.68i) q^{26} +(-589.773 - 428.495i) q^{27} +(-9088.46 - 6603.16i) q^{28} +(-150.045 + 461.791i) q^{29} +(834.309 + 2567.74i) q^{30} +(-6111.03 + 4439.92i) q^{31} +1651.59 q^{32} +(-3510.02 + 851.417i) q^{33} -7483.21 q^{34} +(4614.10 - 3352.34i) q^{35} +(1531.98 + 4714.96i) q^{36} +(3612.44 - 11118.0i) q^{37} +(11698.6 + 8499.52i) q^{38} +(-6363.59 - 4623.42i) q^{39} +(2707.32 - 8332.29i) q^{40} +(2555.51 + 7865.05i) q^{41} +(12902.3 - 9374.05i) q^{42} -1748.03 q^{43} +(22714.6 + 9346.16i) q^{44} -2516.91 q^{45} +(10182.3 - 7397.90i) q^{46} +(-8232.49 - 25337.0i) q^{47} +(2123.37 - 6535.05i) q^{48} +(-13658.1 - 9923.22i) q^{49} +(-16866.5 - 12254.2i) q^{50} +(2155.72 - 6634.64i) q^{51} +(16529.9 + 50873.9i) q^{52} +(19477.4 - 14151.2i) q^{53} -7037.96 q^{54} +(-8076.25 + 9501.24i) q^{55} -51751.4 q^{56} +(-10905.8 + 7923.51i) q^{57} +(1448.57 + 4458.25i) q^{58} +(10510.2 - 32347.1i) q^{59} +(13847.4 + 10060.7i) q^{60} +(31408.0 + 22819.2i) q^{61} +(-22535.0 + 69355.7i) q^{62} +(4594.24 + 14139.6i) q^{63} +(32665.1 - 23732.6i) q^{64} -27157.2 q^{65} +(-22583.4 + 26568.0i) q^{66} -70517.1 q^{67} +(-38380.7 + 27885.2i) q^{68} +(3625.73 + 11158.8i) q^{69} +(17015.0 - 52366.6i) q^{70} +(8878.71 + 6450.76i) q^{71} +(18476.4 + 13423.9i) q^{72} +(-11126.5 + 34243.7i) q^{73} +(-34875.5 - 107336. i) q^{74} +(15723.4 - 11423.8i) q^{75} +91673.2 q^{76} +(68118.5 + 28028.1i) q^{77} -75938.9 q^{78} +(9595.02 - 6971.19i) q^{79} +(-7331.03 - 22562.6i) q^{80} +(2027.46 - 6239.88i) q^{81} +(64591.1 + 46928.2i) q^{82} +(7783.43 + 5655.00i) q^{83} +(31243.4 - 96157.2i) q^{84} +(-7442.75 - 22906.4i) q^{85} +(-13652.9 + 9919.43i) q^{86} -4370.00 q^{87} +(109962. - 26673.2i) q^{88} +93324.6 q^{89} +(-19658.2 + 14282.5i) q^{90} +(49571.4 + 152565. i) q^{91} +(24656.9 - 75886.2i) q^{92} +(-54999.2 - 39959.3i) q^{93} +(-208078. - 151177. i) q^{94} +(-14382.1 + 44263.4i) q^{95} +(4593.31 + 14136.8i) q^{96} +(-66306.2 + 48174.3i) q^{97} -162987. q^{98} +(-17049.6 - 27676.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 45 q^{3} - 124 q^{4} - 33 q^{5} - 18 q^{6} - 335 q^{7} - 472 q^{8} - 405 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 45 * q^3 - 124 * q^4 - 33 * q^5 - 18 * q^6 - 335 * q^7 - 472 * q^8 - 405 * q^9	\( 20 q - 2 q^{2} - 45 q^{3} - 124 q^{4} - 33 q^{5} - 18 q^{6} - 335 q^{7} - 472 q^{8} - 405 q^{9} + 1952 q^{10} - 835 q^{11} + 3474 q^{12} - 959 q^{13} - 3020 q^{14} + 198 q^{15} - 1428 q^{16} - 3144 q^{17} - 567 q^{18} - 930 q^{19} + 3177 q^{20} + 8460 q^{21} + 2713 q^{22} + 1400 q^{23} + 1332 q^{24} - 9388 q^{25} + 3022 q^{26} - 3645 q^{27} - 21753 q^{28} + 4494 q^{29} - 4302 q^{30} + 9208 q^{31} + 69114 q^{32} + 6615 q^{33} - 9084 q^{34} - 31371 q^{35} - 10044 q^{36} - 3153 q^{37} + 1852 q^{38} - 8631 q^{39} - 53123 q^{40} - 7497 q^{41} + 22320 q^{42} + 63624 q^{43} + 58299 q^{44} + 1782 q^{45} - 94681 q^{46} - 43031 q^{47} - 12357 q^{48} - 5640 q^{49} - 76590 q^{50} + 459 q^{51} - 80149 q^{52} - 20452 q^{53} + 13122 q^{54} + 62974 q^{55} + 169638 q^{56} - 39375 q^{57} + 93145 q^{58} + 101730 q^{59} + 28593 q^{60} + 50745 q^{61} - 171957 q^{62} - 27135 q^{63} + 199638 q^{64} - 28210 q^{65} + 46107 q^{66} + 10730 q^{67} - 420141 q^{68} + 94365 q^{69} + 292664 q^{70} + 164895 q^{71} + 11988 q^{72} - 77236 q^{73} - 328228 q^{74} + 9063 q^{75} + 79212 q^{76} + 56087 q^{77} - 280062 q^{78} - 291931 q^{79} + 18026 q^{80} - 32805 q^{81} + 424659 q^{82} - 255451 q^{83} - 26127 q^{84} - 452271 q^{85} + 252843 q^{86} + 187056 q^{87} + 171694 q^{88} + 181632 q^{89} - 40338 q^{90} + 284615 q^{91} + 1199691 q^{92} + 82872 q^{93} - 550105 q^{94} - 511091 q^{95} - 587574 q^{96} - 145083 q^{97} - 150570 q^{98} - 83430 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 45 * q^3 - 124 * q^4 - 33 * q^5 - 18 * q^6 - 335 * q^7 - 472 * q^8 - 405 * q^9 + 1952 * q^10 - 835 * q^11 + 3474 * q^12 - 959 * q^13 - 3020 * q^14 + 198 * q^15 - 1428 * q^16 - 3144 * q^17 - 567 * q^18 - 930 * q^19 + 3177 * q^20 + 8460 * q^21 + 2713 * q^22 + 1400 * q^23 + 1332 * q^24 - 9388 * q^25 + 3022 * q^26 - 3645 * q^27 - 21753 * q^28 + 4494 * q^29 - 4302 * q^30 + 9208 * q^31 + 69114 * q^32 + 6615 * q^33 - 9084 * q^34 - 31371 * q^35 - 10044 * q^36 - 3153 * q^37 + 1852 * q^38 - 8631 * q^39 - 53123 * q^40 - 7497 * q^41 + 22320 * q^42 + 63624 * q^43 + 58299 * q^44 + 1782 * q^45 - 94681 * q^46 - 43031 * q^47 - 12357 * q^48 - 5640 * q^49 - 76590 * q^50 + 459 * q^51 - 80149 * q^52 - 20452 * q^53 + 13122 * q^54 + 62974 * q^55 + 169638 * q^56 - 39375 * q^57 + 93145 * q^58 + 101730 * q^59 + 28593 * q^60 + 50745 * q^61 - 171957 * q^62 - 27135 * q^63 + 199638 * q^64 - 28210 * q^65 + 46107 * q^66 + 10730 * q^67 - 420141 * q^68 + 94365 * q^69 + 292664 * q^70 + 164895 * q^71 + 11988 * q^72 - 77236 * q^73 - 328228 * q^74 + 9063 * q^75 + 79212 * q^76 + 56087 * q^77 - 280062 * q^78 - 291931 * q^79 + 18026 * q^80 - 32805 * q^81 + 424659 * q^82 - 255451 * q^83 - 26127 * q^84 - 452271 * q^85 + 252843 * q^86 + 187056 * q^87 + 171694 * q^88 + 181632 * q^89 - 40338 * q^90 + 284615 * q^91 + 1199691 * q^92 + 82872 * q^93 - 550105 * q^94 - 511091 * q^95 - 587574 * q^96 - 145083 * q^97 - 150570 * q^98 - 83430 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	7.81047	−	5.67464i	1.38071	−	1.00314i	0.383895	−	0.923377i	$-0.374582\pi$
$2$	7.81047	−	5.67464i	1.38071	−	1.00314i	0.996814	−	0.0797669i	$-0.0254176\pi$
$3$	2.78115	+	8.55951i	0.178411	+	0.549093i
$3$	2.78115	+	8.55951i	0.178411	+	0.549093i
$4$	18.9134	−	58.2093i	0.591042	−	1.81904i
$5$	25.1385	+	18.2642i	0.449692	+	0.326720i	0.789474	−	0.613784i	$-0.210353\pi$
$5$	25.1385	+	18.2642i	0.449692	+	0.326720i	−0.339782	+	0.940504i	$0.610353\pi$
$6$	70.2942	+	51.0717i	0.797153	+	0.579165i
$7$	56.7190	−	174.563i	0.437506	−	1.34650i	−0.452991	−	0.891515i	$-0.649643\pi$
$7$	56.7190	−	174.563i	0.437506	−	1.34650i	0.890497	−	0.454989i	$-0.150357\pi$
$8$	−87.1280	−	268.152i	−0.481319	−	1.48135i
$9$	−65.5304	+	47.6106i	−0.269672	+	0.195928i
$10$	299.987			0.948641
$11$	−30.5455	+	400.147i	−0.0761141	+	0.997099i
$11$	−30.5455	+	400.147i	−0.0761141	+	0.997099i
$12$	550.844			1.10427
$13$	−707.066	+	513.713i	−1.16038	+	0.843068i	−0.989826	−	0.142280i	$-0.954557\pi$
$13$	−707.066	+	513.713i	−1.16038	+	0.843068i	−0.170557	+	0.985348i	$0.554557\pi$
$14$	−547.581	−	1685.28i	−0.746669	−	2.29801i
$15$	−86.4186	+	265.969i	−0.0991698	+	0.305213i
$16$	−617.672	−	448.765i	−0.603195	−	0.438247i
$17$	−627.084	−	455.604i	−0.526264	−	0.382353i	0.292694	−	0.956206i	$-0.405448\pi$
$17$	−627.084	−	455.604i	−0.526264	−	0.382353i	−0.818958	+	0.573853i	$0.805448\pi$
$18$	−241.650	+	743.722i	−0.175795	+	0.541040i
$19$	462.848	+	1424.50i	0.294140	+	0.905271i	0.983509	+	0.180860i	$0.0578881\pi$
$19$	462.848	+	1424.50i	0.294140	+	0.905271i	−0.689368	+	0.724411i	$0.742112\pi$
$20$	1538.60	−	1117.86i	0.860105	−	0.624903i
$21$	1651.92			0.817412
$22$	2032.12	+	3298.67i	0.895142	+	1.45306i
$23$	1303.68			0.513867			0.256933	−	0.966429i	$-0.417288\pi$
$23$	1303.68			0.513867			0.256933	+	0.966429i	$0.417288\pi$
$24$	2052.94	−	1491.55i	0.727524	−	0.528577i
$25$	−667.313	−	2053.78i	−0.213540	−	0.657209i
$26$	−2607.38	+	8024.68i	−0.756433	+	2.32806i
$27$	−589.773	−	428.495i	−0.155695	−	0.113119i
$28$	−9088.46	−	6603.16i	−2.19076	−	1.59168i
$29$	−150.045	+	461.791i	−0.0331304	+	0.101965i	−0.966254	−	0.257590i	$-0.917072\pi$
$29$	−150.045	+	461.791i	−0.0331304	+	0.101965i	0.933124	+	0.359555i	$0.117072\pi$
$30$	834.309	+	2567.74i	0.169248	+	0.520892i
$31$	−6111.03	+	4439.92i	−1.14212	+	0.829795i	−0.987413	−	0.158166i	$-0.949442\pi$
$31$	−6111.03	+	4439.92i	−1.14212	+	0.829795i	−0.154703	+	0.987961i	$0.549442\pi$
$32$	1651.59			0.285119
$33$	−3510.02	+	851.417i	−0.561079	+	0.136100i
$34$	−7483.21			−1.11017
$35$	4614.10	−	3352.34i	0.636673	−	0.462570i
$36$	1531.98	+	4714.96i	0.197014	+	0.606347i
$37$	3612.44	−	11118.0i	0.433807	−	1.33512i	−0.460497	−	0.887661i	$-0.652329\pi$
$37$	3612.44	−	11118.0i	0.433807	−	1.33512i	0.894304	−	0.447460i	$-0.147671\pi$
$38$	11698.6	+	8499.52i	1.31424	+	0.954850i
$39$	−6363.59	−	4623.42i	−0.669948	−	0.486745i
$40$	2707.32	−	8332.29i	0.267541	−	0.823406i
$41$	2555.51	+	7865.05i	0.237420	+	0.730705i	0.996791	+	0.0800467i	$0.0255069\pi$
$41$	2555.51	+	7865.05i	0.237420	+	0.730705i	−0.759371	+	0.650658i	$0.774493\pi$
$42$	12902.3	−	9374.05i	1.12861	−	0.819981i
$43$	−1748.03			−0.144171			−0.0720854	−	0.997398i	$-0.522965\pi$
$43$	−1748.03			−0.144171			−0.0720854	+	0.997398i	$0.522965\pi$
$44$	22714.6	+	9346.16i	1.76878	+	0.727783i
$45$	−2516.91			−0.185283
$46$	10182.3	−	7397.90i	0.709501	−	0.515482i
$47$	−8232.49	−	25337.0i	−0.543609	−	1.67306i	−0.724275	−	0.689511i	$-0.757825\pi$
$47$	−8232.49	−	25337.0i	−0.543609	−	1.67306i	0.180666	−	0.983544i	$-0.442175\pi$
$48$	2123.37	−	6535.05i	0.133021	−	0.409398i
$49$	−13658.1	−	9923.22i	−0.812646	−	0.590422i
$50$	−16866.5	−	12254.2i	−0.954112	−	0.693203i
$51$	2155.72	−	6634.64i	0.116056	−	0.357184i
$52$	16529.9	+	50873.9i	0.847740	+	2.60907i
$53$	19477.4	−	14151.2i	0.952450	−	0.691996i	0.00106522	−	0.999999i	$-0.499661\pi$
$53$	19477.4	−	14151.2i	0.952450	−	0.691996i	0.951385	+	0.308004i	$0.0996609\pi$
$54$	−7037.96			−0.328445
$55$	−8076.25	+	9501.24i	−0.360000	+	0.423519i
$56$	−51751.4			−2.20522
$57$	−10905.8	+	7923.51i	−0.444600	+	0.323021i
$58$	1448.57	+	4458.25i	0.0565420	+	0.174018i
$59$	10510.2	−	32347.1i	0.393081	−	1.20978i	−0.537365	−	0.843350i	$-0.680580\pi$
$59$	10510.2	−	32347.1i	0.393081	−	1.20978i	0.930446	−	0.366429i	$-0.119420\pi$
$60$	13847.4	+	10060.7i	0.496582	+	0.360788i
$61$	31408.0	+	22819.2i	1.08073	+	0.785193i	0.977809	−	0.209497i	$-0.0671827\pi$
$61$	31408.0	+	22819.2i	1.08073	+	0.785193i	0.102916	+	0.994690i	$0.467183\pi$
$62$	−22535.0	+	69355.7i	−0.744525	+	2.29141i
$63$	4594.24	+	14139.6i	0.145835	+	0.448835i
$64$	32665.1	−	23732.6i	0.996861	−	0.724262i
$65$	−27157.2			−0.797262
$66$	−22583.4	+	26568.0i	−0.638160	+	0.750757i
$67$	−70517.1			−1.91914			−0.959571	−	0.281465i	$-0.909180\pi$
$67$	−70517.1			−1.91914			−0.959571	+	0.281465i	$0.909180\pi$
$68$	−38380.7	+	27885.2i	−1.00656	+	0.731309i
$69$	3625.73	+	11158.8i	0.0916795	+	0.282161i
$70$	17015.0	−	52366.6i	0.415036	−	1.27735i
$71$	8878.71	+	6450.76i	0.209028	+	0.151868i	0.687374	−	0.726304i	$-0.258763\pi$
$71$	8878.71	+	6450.76i	0.209028	+	0.151868i	−0.478346	+	0.878171i	$0.658763\pi$
$72$	18476.4	+	13423.9i	0.420036	+	0.305174i
$73$	−11126.5	+	34243.7i	−0.244371	+	0.752097i	0.751368	+	0.659883i	$0.229394\pi$
$73$	−11126.5	+	34243.7i	−0.244371	+	0.752097i	−0.995739	+	0.0922139i	$0.970606\pi$
$74$	−34875.5	−	107336.i	−0.740357	−	2.27858i
$75$	15723.4	−	11423.8i	0.322771	−	0.234507i
$76$	91673.2			1.82057
$77$	68118.5	+	28028.1i	1.30930	+	0.538725i
$78$	−75938.9			−1.41328
$79$	9595.02	−	6971.19i	0.172973	−	0.125672i	−0.497930	−	0.867217i	$-0.665907\pi$
$79$	9595.02	−	6971.19i	0.172973	−	0.125672i	0.670903	+	0.741545i	$0.265907\pi$
$80$	−7331.03	−	22562.6i	−0.128068	−	0.394152i
$81$	2027.46	−	6239.88i	0.0343352	−	0.105673i
$82$	64591.1	+	46928.2i	1.06081	+	0.770724i
$83$	7783.43	+	5655.00i	0.124015	+	0.0901025i	0.648064	−	0.761586i	$-0.275579\pi$
$83$	7783.43	+	5655.00i	0.124015	+	0.0901025i	−0.524048	+	0.851688i	$0.675579\pi$
$84$	31243.4	−	96157.2i	0.483125	−	1.48691i
$85$	−7442.75	−	22906.4i	−0.111734	−	0.343882i
$86$	−13652.9	+	9919.43i	−0.199058	+	0.144624i
$87$	−4370.00			−0.0618990
$88$	109962.	−	26673.2i	1.51368	−	0.367171i
$89$	93324.6			1.24888			0.624441	−	0.781072i	$-0.285327\pi$
$89$	93324.6			1.24888			0.624441	+	0.781072i	$0.285327\pi$
$90$	−19658.2	+	14282.5i	−0.255822	+	0.185866i
$91$	49571.4	+	152565.i	0.627520	+	1.93131i
$92$	24656.9	−	75886.2i	0.303717	−	0.934745i
$93$	−54999.2	−	39959.3i	−0.659400	−	0.479082i
$94$	−208078.	−	151177.i	−2.42888	−	1.76469i
$95$	−14382.1	+	44263.4i	−0.163498	+	0.503195i
$96$	4593.31	+	14136.8i	0.0508684	+	0.156557i
$97$	−66306.2	+	48174.3i	−0.715525	+	0.519859i	−0.884951	−	0.465684i	$-0.845809\pi$
$97$	−66306.2	+	48174.3i	−0.715525	+	0.519859i	0.169426	+	0.985543i	$0.445809\pi$
$98$	−162987.			−1.71430
$99$	−17049.6	−	27676.1i	−0.174834	−	0.283803i
$100$	−132170.			−1.32170
$101$	3160.28	−	2296.08i	0.0308264	−	0.0223967i	−0.572265	−	0.820069i	$-0.693935\pi$
$101$	3160.28	−	2296.08i	0.0308264	−	0.0223967i	0.603092	+	0.797672i	$0.293935\pi$
$102$	−20811.9	−	64052.6i	−0.198067	−	0.609588i
$103$	−3827.32	+	11779.3i	−0.0355469	+	0.109402i	−0.967256	−	0.253804i	$-0.918318\pi$
$103$	−3827.32	+	11779.3i	−0.0355469	+	0.109402i	0.931709	+	0.363206i	$0.118318\pi$
$104$	199359.	+	144843.i	1.80739	+	1.31315i
$105$	41526.9	+	30171.0i	0.367583	+	0.267065i
$106$	71825.1	−	221055.i	0.620885	−	1.91089i
$107$	39698.1	+	122178.i	0.335205	+	1.03165i	0.966621	+	0.256210i	$0.0824739\pi$
$107$	39698.1	+	122178.i	0.335205	+	1.03165i	−0.631416	+	0.775444i	$0.717526\pi$
$108$	−36097.0	+	26226.0i	−0.297791	+	0.216358i
$109$	174532.			1.40705			0.703524	−	0.710671i	$-0.251609\pi$
$109$	174532.			1.40705			0.703524	+	0.710671i	$0.251609\pi$
$110$	−9163.23	+	120039.i	−0.0722050	+	0.945889i
$111$	105211.			0.810502
$112$	−113372.	+	82369.3i	−0.854003	+	0.620469i
$113$	−48051.2	−	147886.i	−0.354004	−	1.08951i	−0.956585	−	0.291454i	$-0.905861\pi$
$113$	−48051.2	−	147886.i	−0.354004	−	1.08951i	0.602581	−	0.798058i	$-0.294139\pi$
$114$	−40216.2	+	123773.i	−0.289827	+	0.891995i
$115$	32772.6	+	23810.7i	0.231082	+	0.167891i
$116$	24042.7	+	17468.0i	0.165897	+	0.120531i
$117$	21876.1	−	67327.7i	0.147742	−	0.454704i
$118$	−101469.	−	312288.i	−0.670851	−	2.06467i
$119$	−115099.	+	83624.5i	−0.745084	+	0.541335i
$120$	78849.8			0.499859
$121$	−159185.	−	24445.4i	−0.988413	−	0.151787i
$122$	374802.			2.27983
$123$	−60213.7	+	43747.8i	−0.358866	+	0.260732i
$124$	142865.	+	439693.i	0.834393	+	2.56800i
$125$	50741.9	−	156167.i	0.290463	−	0.893954i
$126$	116120.	+	84366.4i	0.651602	+	0.473416i
$127$	−241531.	−	175483.i	−1.32881	−	0.965439i	−0.999777	−	0.0211210i	$-0.993276\pi$
$127$	−241531.	−	175483.i	−1.32881	−	0.965439i	−0.329035	−	0.944318i	$-0.606724\pi$
$128$	104124.	−	320462.i	0.561729	−	1.72883i
$129$	−4861.53	−	14962.3i	−0.0257217	−	0.0791632i
$130$	−212110.	+	154107.i	−1.10079	+	0.799769i
$131$	−211217.			−1.07535			−0.537675	−	0.843152i	$-0.680697\pi$
$131$	−211217.			−1.07535			−0.537675	+	0.843152i	$0.680697\pi$
$132$	−16825.8	+	220419.i	−0.0840506	+	1.10107i
$133$	274918.			1.34764
$134$	−550771.	+	400159.i	−2.64978	+	1.92518i
$135$	−6999.91	−	21543.5i	−0.0330566	−	0.101738i
$136$	−67534.6	+	207850.i	−0.313097	+	0.963613i
$137$	157645.	+	114536.i	0.717593	+	0.521362i	0.885614	−	0.464422i	$-0.153738\pi$
$137$	157645.	+	114536.i	0.717593	+	0.521362i	−0.168021	+	0.985783i	$0.553738\pi$
$138$	91641.0	+	66581.1i	0.409630	+	0.297614i
$139$	−36314.4	+	111764.i	−0.159420	+	0.490643i	−0.998582	−	0.0532382i	$-0.983046\pi$
$139$	−36314.4	+	111764.i	−0.159420	+	0.490643i	0.839162	+	0.543881i	$0.183046\pi$
$140$	−107869.	−	331987.i	−0.465133	−	1.43153i
$141$	193976.	−	140932.i	0.821677	−	0.596983i
$142$	105953.			0.440951
$143$	−183963.	−	298622.i	−0.752301	−	1.22119i
$144$	61842.2			0.248530
$145$	−12206.2	+	8868.30i	−0.0482125	+	0.0350284i
$146$	107418.	+	330598.i	0.417056	+	1.28357i
$147$	46952.5	−	144505.i	0.179211	−	0.551556i
$148$	−578846.	−	420556.i	−2.17224	−	1.57823i
$149$	−108603.	−	78904.8i	−0.400753	−	0.291164i	0.369095	−	0.929392i	$-0.379668\pi$
$149$	−108603.	−	78904.8i	−0.400753	−	0.291164i	−0.769848	+	0.638228i	$0.779668\pi$
$150$	57981.8	−	178450.i	0.210409	−	0.647571i
$151$	40625.5	+	125032.i	0.144996	+	0.446252i	0.997011	−	0.0772661i	$-0.0246191\pi$
$151$	40625.5	+	125032.i	0.144996	+	0.446252i	−0.852014	+	0.523518i	$0.824619\pi$
$152$	341656.	−	248228.i	1.19944	−	0.871448i
$153$	62784.6			0.216833
$154$	691087.	−	167635.i	2.34818	−	0.569592i
$155$	−234714.			−0.784711
$156$	−389483.	+	282976.i	−1.28138	+	0.930975i
$157$	66528.9	+	204755.i	0.215408	+	0.662956i	0.999124	+	0.0418380i	$0.0133213\pi$
$157$	66528.9	+	204755.i	0.215408	+	0.662956i	−0.783717	+	0.621118i	$0.786679\pi$
$158$	35382.6	−	108896.i	0.112758	−	0.347033i
$159$	175297.	+	127361.i	0.549897	+	0.399524i
$160$	41518.4	+	30164.9i	0.128216	+	0.0931541i
$161$	73943.4	−	227574.i	0.224820	−	0.691924i
$162$	−19573.6	−	60241.5i	−0.0585982	−	0.180347i
$163$	−175207.	+	127295.i	−0.516514	+	0.375270i	−0.815289	−	0.579054i	$-0.803422\pi$
$163$	−175207.	+	127295.i	−0.516514	+	0.375270i	0.298775	+	0.954324i	$0.403422\pi$
$164$	506153.			1.46951
$165$	−103787.	−	42704.3i	−0.296780	−	0.122113i
$166$	92882.3			0.261615
$167$	−23949.9	+	17400.6i	−0.0664526	+	0.0482807i	−0.620516	−	0.784194i	$-0.713077\pi$
$167$	−23949.9	+	17400.6i	−0.0664526	+	0.0482807i	0.554063	+	0.832475i	$0.313077\pi$
$168$	−143928.	−	442966.i	−0.393435	−	1.21087i
$169$	121305.	−	373338.i	0.326709	−	1.00551i
$170$	−188117.	−	136675.i	−0.499236	−	0.362716i
$171$	−98151.9	−	71311.6i	−0.256690	−	0.186496i
$172$	−33061.1	+	101752.i	−0.0852111	+	0.262253i
$173$	99568.5	+	306440.i	0.252934	+	0.778450i	0.994230	+	0.107272i	$0.0342115\pi$
$173$	99568.5	+	306440.i	0.252934	+	0.778450i	−0.741296	+	0.671178i	$0.765789\pi$
$174$	−34131.8	+	24798.2i	−0.0854645	+	0.0620936i
$175$	−396364.			−0.978361
$176$	198439.	−	233452.i	0.482887	−	0.568088i
$177$	306106.			0.734411
$178$	728909.	−	529583.i	1.72434	−	1.25281i
$179$	148577.	+	457274.i	0.346593	+	1.06670i	0.960725	+	0.277501i	$0.0895062\pi$
$179$	148577.	+	457274.i	0.346593	+	1.06670i	−0.614132	+	0.789203i	$0.710494\pi$
$180$	−47603.2	+	146508.i	−0.109510	+	0.337038i
$181$	−39536.4	−	28724.8i	−0.0897016	−	0.0651720i	0.542030	−	0.840359i	$-0.317656\pi$
$181$	−39536.4	−	28724.8i	−0.0897016	−	0.0651720i	−0.631732	+	0.775187i	$0.717656\pi$
$182$	1.25293e6	+	910305.i	2.80380	+	2.03708i
$183$	−107971.	+	332301.i	−0.238330	+	0.733505i
$184$	−113587.	−	349584.i	−0.247334	−	0.761215i
$185$	293872.	−	213511.i	0.631291	−	0.458660i
$186$	−656324.			−1.39103
$187$	201463.	−	237010.i	0.421300	−	0.495635i
$188$	−1.63055e6			−3.36465
$189$	−108251.	+	78648.9i	−0.220433	+	0.160154i
$190$	138848.	+	427331.i	0.279034	+	0.858777i
$191$	−100174.	+	308303.i	−0.198688	+	0.611498i	0.801226	+	0.598362i	$0.204181\pi$
$191$	−100174.	+	308303.i	−0.198688	+	0.611498i	−0.999914	+	0.0131359i	$0.995819\pi$
$192$	293986.	+	213594.i	0.575538	+	0.418153i
$193$	−148355.	−	107786.i	−0.286688	−	0.208291i	0.435141	−	0.900362i	$-0.356698\pi$
$193$	−148355.	−	107786.i	−0.286688	−	0.208291i	−0.721829	+	0.692071i	$0.756698\pi$
$194$	−244511.	+	752527.i	−0.466438	+	1.43555i
$195$	−75528.3	−	232452.i	−0.142240	−	0.437771i
$196$	−835945.	+	607350.i	−1.55431	+	1.12927i
$197$	−644561.			−1.18331			−0.591655	−	0.806191i	$-0.701525\pi$
$197$	−644561.			−1.18331			−0.591655	+	0.806191i	$0.701525\pi$
$198$	−290217.	−	119413.i	−0.526090	−	0.216465i
$199$	−278590.			−0.498692			−0.249346	−	0.968414i	$-0.580216\pi$
$199$	−278590.			−0.498692			−0.249346	+	0.968414i	$0.580216\pi$
$200$	−492584.	+	357883.i	−0.870774	+	0.632654i
$201$	−196119.	−	603592.i	−0.342396	−	1.05379i
$202$	11653.9	−	35866.9i	0.0200952	−	0.0618466i
$203$	72101.3	+	52384.7i	0.122801	+	0.0892204i
$204$	−345426.	−	250967.i	−0.581138	−	0.422222i
$205$	−79407.3	+	244390.i	−0.131970	+	0.406162i
$206$	36949.9	+	113720.i	0.0606660	+	0.186711i
$207$	−85430.5	+	62068.9i	−0.138576	+	0.100681i
$208$	667271.			1.06941
$209$	−584148.	+	141695.i	−0.925033	+	0.224383i
$210$	495554.			0.775430
$211$	308245.	−	223953.i	0.476639	−	0.346298i	−0.323384	−	0.946268i	$-0.604821\pi$
$211$	308245.	−	223953.i	0.476639	−	0.346298i	0.800023	+	0.599969i	$0.204821\pi$
$212$	−455348.	−	1.40142e6i	−0.695830	−	2.14155i
$213$	−30522.3	+	93937.9i	−0.0460965	+	0.141870i
$214$	1.00338e6	+	728996.i	1.49772	+	1.08816i
$215$	−43942.9	−	31926.4i	−0.0648325	−	0.0471035i
$216$	−63516.3	+	195483.i	−0.0926298	+	0.285085i
$217$	428435.	+	1.31859e6i	0.617641	+	1.90090i
$218$	1.36318e6	−	990406.i	1.94272	−	1.41147i
$219$	−324054.			−0.456570
$220$	400312.	+	649813.i	0.557624	+	0.905174i
$221$	677440.			0.933018
$222$	821747.	−	597034.i	1.11907	−	0.813049i
$223$	99211.1	+	305340.i	0.133597	+	0.411171i	0.995369	−	0.0961255i	$-0.0306450\pi$
$223$	99211.1	+	305340.i	0.133597	+	0.411171i	−0.861772	+	0.507296i	$0.830645\pi$
$224$	93676.3	−	288306.i	0.124741	−	0.383914i
$225$	141511.	+	102814.i	0.186352	+	0.135393i
$226$	−1.21450e6	−	882388.i	−1.58171	−	1.14918i
$227$	413157.	−	1.27157e6i	0.532170	−	1.63785i	−0.217515	−	0.976057i	$-0.569795\pi$
$227$	413157.	−	1.27157e6i	0.532170	−	1.63785i	0.749685	−	0.661794i	$-0.230205\pi$
$228$	254957.	+	784678.i	0.324811	+	0.999664i
$229$	826982.	−	600838.i	1.04210	−	0.757126i	0.0714017	−	0.997448i	$-0.477253\pi$
$229$	826982.	−	600838.i	1.04210	−	0.757126i	0.970693	+	0.240321i	$0.0772528\pi$
$230$	391086.			0.487475
$231$	−50458.7	+	661012.i	−0.0622166	+	0.815040i
$232$	136903.			0.166992
$233$	460295.	−	334424.i	0.555452	−	0.403559i	−0.274340	−	0.961633i	$-0.588459\pi$
$233$	460295.	−	334424.i	0.555452	−	0.403559i	0.829792	+	0.558073i	$0.188459\pi$
$234$	−211198.	−	649999.i	−0.252144	−	0.776021i
$235$	255808.	−	787295.i	0.302165	−	0.929968i
$236$	−1.68412e6	−	1.22359e6i	−1.96831	−	1.43006i
$237$	86355.1	+	62740.7i	0.0998659	+	0.0725568i
$238$	−424440.	+	1.30629e6i	−0.485707	+	1.49485i
$239$	221999.	+	683244.i	0.251395	+	0.773715i	0.994519	+	0.104560i	$0.0333436\pi$
$239$	221999.	+	683244.i	0.251395	+	0.773715i	−0.743123	+	0.669154i	$0.766656\pi$
$240$	172736.	−	125500.i	0.193577	−	0.140642i
$241$	−38689.7			−0.0429094			−0.0214547	−	0.999770i	$-0.506830\pi$
$241$	−38689.7			−0.0429094			−0.0214547	+	0.999770i	$0.506830\pi$
$242$	−1.38203e6	+	712387.i	−1.51697	+	0.781947i
$243$	59049.0			0.0641500
$244$	1.92232e6	−	1.39665e6i	2.06705	−	1.50180i
$245$	−162106.	−	498910.i	−0.172537	−	0.531016i
$246$	−222044.	+	683382.i	−0.233939	+	0.719989i
$247$	−1.05905e6	−	769444.i	−1.10452	−	0.802481i
$248$	1.72302e6	+	1.25184e6i	1.77894	+	1.29247i
$249$	−26757.1	+	82349.8i	−0.0273489	+	0.0841713i
$250$	−489876.	−	1.50768e6i	−0.495719	−	1.52567i
$251$	−770426.	+	559748.i	−0.771875	+	0.560800i	−0.902530	−	0.430628i	$-0.858292\pi$
$251$	−770426.	+	559748.i	−0.771875	+	0.560800i	0.130655	+	0.991428i	$0.458292\pi$
$252$	909951.			0.902644
$253$	−39821.5	+	521663.i	−0.0391125	+	0.512376i
$254$	−2.88227e6			−2.80318
$255$	175368.	−	127413.i	0.168889	−	0.122705i
$256$	−605981.	−	1.86502e6i	−0.577908	−	1.77862i
$257$	221193.	−	680763.i	0.208900	−	0.642930i	−0.790630	−	0.612294i	$-0.790247\pi$
$257$	221193.	−	680763.i	0.208900	−	0.642930i	0.999531	−	0.0306355i	$-0.00975312\pi$
$258$	−122876.	−	89274.9i	−0.114926	−	0.0834987i
$259$	−1.73589e6	−	1.26120e6i	−1.60795	−	1.16825i
$260$	−513633.	+	1.58080e6i	−0.471216	+	1.45025i
$261$	−12153.6	−	37405.1i	−0.0110435	−	0.0339883i
$262$	−1.64970e6	+	1.19858e6i	−1.48475	+	1.07873i
$263$	1.05112e6			0.937054			0.468527	−	0.883449i	$-0.344785\pi$
$263$	1.05112e6			0.937054			0.468527	+	0.883449i	$0.344785\pi$
$264$	534130.	+	867037.i	0.471669	+	0.765646i
$265$	748095.			0.654398
$266$	2.14724e6	−	1.56006e6i	1.86070	−	1.35188i
$267$	259550.	+	798813.i	0.222814	+	0.685752i
$268$	−1.33371e6	+	4.10475e6i	−1.13429	+	3.49100i
$269$	922648.	+	670343.i	0.777419	+	0.564828i	0.904203	−	0.427102i	$-0.140466\pi$
$269$	922648.	+	670343.i	0.777419	+	0.564828i	−0.126784	+	0.991930i	$0.540466\pi$
$270$	−176924.	−	128543.i	−0.147699	−	0.107310i
$271$	−107065.	+	329512.i	−0.0885572	+	0.272551i	−0.985521	−	0.169553i	$-0.945768\pi$
$271$	−107065.	+	329512.i	−0.0885572	+	0.272551i	0.896964	+	0.442104i	$0.145768\pi$
$272$	182874.	+	562827.i	0.149875	+	0.461267i
$273$	−1.16802e6	+	848613.i	−0.948511	+	0.689133i
$274$	1.88123e6			1.51379
$275$	842198.	−	204290.i	0.671556	−	0.162898i
$276$	718123.			0.567448
$277$	398782.	−	289732.i	0.312275	−	0.226881i	−0.420597	−	0.907247i	$-0.638179\pi$
$277$	398782.	−	289732.i	0.312275	−	0.226881i	0.732872	+	0.680367i	$0.238179\pi$
$278$	350589.	+	1.07900e6i	0.272073	+	0.837356i
$279$	189071.	−	581899.i	0.145416	−	0.447546i
$280$	−1.30095e6	−	945199.i	−0.991669	−	0.720490i
$281$	−250980.	−	182348.i	−0.189615	−	0.137764i	0.488928	−	0.872324i	$-0.337388\pi$
$281$	−250980.	−	182348.i	−0.189615	−	0.137764i	−0.678543	+	0.734561i	$0.737388\pi$
$282$	715308.	−	2.20149e6i	0.535637	−	1.64852i
$283$	653623.	+	2.01164e6i	0.485133	+	1.49309i	0.831788	+	0.555094i	$0.187318\pi$
$283$	653623.	+	2.01164e6i	0.485133	+	1.49309i	−0.346654	+	0.937993i	$0.612682\pi$
$284$	543421.	−	394818.i	0.399798	−	0.290470i
$285$	−418872.			−0.305470
$286$	−3.13141e6	−	1.28845e6i	−2.26373	−	0.931437i
$287$	1.51790e6			1.08777
$288$	−108229.	+	78633.0i	−0.0768887	+	0.0558629i
$289$	−253100.	−	778960.i	−0.178257	−	0.548619i
$290$	−45011.5	+	138531.i	−0.0314288	+	0.0967280i
$291$	−596756.	−	433568.i	−0.413109	−	0.300141i
$292$	1.78287e6	+	1.29533e6i	1.22366	+	0.889043i
$293$	−424631.	+	1.30688e6i	−0.288963	+	0.889337i	0.696219	+	0.717829i	$0.254864\pi$
$293$	−424631.	+	1.30688e6i	−0.288963	+	0.889337i	−0.985183	+	0.171508i	$0.945136\pi$
$294$	−453292.	−	1.39509e6i	−0.305851	−	0.941312i
$295$	855007.	−	621199.i	0.572025	−	0.415600i
$296$	−3.29605e6			−2.18658
$297$	189476.	−	222908.i	0.124642	−	0.146634i
$298$	−1.29600e6			−0.845403
$299$	−921786.	+	669717.i	−0.596283	+	0.433225i
$300$	−367586.	−	1.13131e6i	−0.235806	−	0.725737i
$301$	−99146.5	+	305142.i	−0.0630756	+	0.194127i
$302$	1.02682e6	+	746027.i	0.647853	+	0.470692i
$303$	28442.6	+	20664.7i	0.0177976	+	0.0129307i
$304$	353377.	−	1.08758e6i	0.219308	−	0.674961i
$305$	372775.	+	1.14728e6i	0.229455	+	0.706190i
$306$	490377.	−	356280.i	0.299383	−	0.217514i
$307$	32955.7			0.0199565			0.00997826	−	0.999950i	$-0.496824\pi$
$307$	32955.7			0.0199565			0.00997826	+	0.999950i	$0.496824\pi$
$308$	2.91985e6	−	3.43503e6i	1.75381	−	2.06326i
$309$	−111469.			−0.0664138
$310$	−1.83323e6	+	1.33192e6i	−1.08346	+	0.787178i
$311$	660495.	+	2.03279e6i	0.387229	+	1.19177i	0.934850	+	0.355043i	$0.115534\pi$
$311$	660495.	+	2.03279e6i	0.387229	+	1.19177i	−0.547621	+	0.836727i	$0.684466\pi$
$312$	−685334.	+	2.10924e6i	−0.398580	+	1.22670i
$313$	−119544.	−	86853.7i	−0.0689710	−	0.0501104i	0.552765	−	0.833337i	$-0.313573\pi$
$313$	−119544.	−	86853.7i	−0.0689710	−	0.0501104i	−0.621737	+	0.783226i	$0.713573\pi$
$314$	1.68153e6	+	1.22170e6i	0.962455	+	0.699265i
$315$	−142757.	+	439360.i	−0.0810625	+	0.249485i
$316$	−224314.	−	690368.i	−0.126369	−	0.388922i
$317$	652164.	−	473825.i	0.364509	−	0.264832i	−0.390421	−	0.920636i	$-0.627671\pi$
$317$	652164.	−	473825.i	0.364509	−	0.264832i	0.754931	+	0.655805i	$0.227671\pi$
$318$	2.09188e6			1.16003
$319$	−180201.	−	74145.7i	−0.0991474	−	0.0407952i
$320$	1.25461e6			0.684912
$321$	−935379.	+	679592.i	−0.506670	+	0.368117i
$322$	−713869.	−	2.19706e6i	−0.383689	−	1.18087i
$323$	358762.	−	1.10416e6i	0.191338	−	0.588877i
$324$	−324873.	−	236034.i	−0.171930	−	0.124914i
$325$	1.52689e6	+	1.10935e6i	0.801861	+	0.582586i
$326$	−646094.	+	1.98847e6i	−0.336707	+	1.03628i
$327$	485400.	+	1.49391e6i	0.251033	+	0.772600i
$328$	1.88638e6	−	1.37053e6i	0.968152	−	0.703404i
$329$	−4.88985e6			−2.49061
$330$	−1.05296e6	+	255414.i	−0.532263	+	0.129110i
$331$	−99812.1			−0.0500741			−0.0250370	−	0.999687i	$-0.507970\pi$
$331$	−99812.1			−0.0500741			−0.0250370	+	0.999687i	$0.507970\pi$
$332$	476384.	−	346113.i	0.237199	−	0.172335i
$333$	292608.	+	900555.i	0.144602	+	0.445040i
$334$	−88317.7	+	271814.i	−0.0433193	+	0.133323i
$335$	−1.77270e6	−	1.28794e6i	−0.863023	−	0.627023i
$336$	−1.02034e6	−	741323.i	−0.493059	−	0.358228i
$337$	544031.	−	1.67435e6i	0.260945	−	0.803106i	−0.731655	−	0.681675i	$-0.761252\pi$
$337$	544031.	−	1.67435e6i	0.260945	−	0.803106i	0.992600	−	0.121431i	$-0.0387482\pi$
$338$	−1.17111e6	−	3.60430e6i	−0.557578	−	1.71605i
$339$	1.13220e6	−	822589.i	0.535085	−	0.388762i
$340$	−1.47413e6			−0.691576
$341$	−1.58996e6	−	2.58093e6i	−0.740457	−	1.20196i
$342$	−1.17128e6			−0.541496
$343$	−11193.7	+	8132.69i	−0.00513734	+	0.00373249i
$344$	152302.	+	468738.i	0.0693921	+	0.213567i
$345$	−112662.	+	346738.i	−0.0509601	+	0.156839i
$346$	2.51661e6	+	1.82843e6i	1.13013	+	0.821084i
$347$	523446.	+	380306.i	0.233372	+	0.169554i	0.698325	−	0.715781i	$-0.253929\pi$
$347$	523446.	+	380306.i	0.233372	+	0.169554i	−0.464954	+	0.885335i	$0.653929\pi$
$348$	−82651.4	+	254375.i	−0.0365849	+	0.112597i
$349$	−387109.	−	1.19140e6i	−0.170126	−	0.523593i	0.829252	−	0.558875i	$-0.188767\pi$
$349$	−387109.	−	1.19140e6i	−0.170126	−	0.523593i	−0.999377	+	0.0352824i	$0.988767\pi$
$350$	−3.09579e6	+	2.24922e6i	−1.35083	+	0.981436i
$351$	637132.			0.276034
$352$	−50448.5	+	660878.i	−0.0217016	+	0.284292i
$353$	2.02804e6			0.866242			0.433121	−	0.901336i	$-0.357412\pi$
$353$	2.02804e6			0.866242			0.433121	+	0.901336i	$0.357412\pi$
$354$	2.39083e6	−	1.73704e6i	1.01401	−	0.736719i
$355$	105380.	+	324325.i	0.0443799	+	0.136587i
$356$	1.76508e6	−	5.43236e6i	0.738142	−	2.27177i
$357$	−1.03589e6	−	752621.i	−0.430174	−	0.312540i
$358$	3.75532e6	+	2.72840e6i	1.54860	+	1.12512i
$359$	−1.22221e6	+	3.76157e6i	−0.500506	+	1.54040i	0.307690	+	0.951487i	$0.400444\pi$
$359$	−1.22221e6	+	3.76157e6i	−0.500506	+	1.54040i	−0.808196	+	0.588913i	$0.799556\pi$
$360$	219293.	+	674915.i	0.0891803	+	0.274469i
$361$	188233.	−	136760.i	0.0760201	−	0.0552319i
$362$	−471801.			−0.189229
$363$	−233477.	−	1.43053e6i	−0.0929989	−	0.569811i
$364$	9.81827e6			3.88402
$365$	−905139.	+	657622.i	−0.355617	+	0.258371i
$366$	1.04238e6	+	3.20812e6i	0.406746	+	1.25184i
$367$	912923.	−	2.80969e6i	0.353809	−	1.08891i	−0.602888	−	0.797826i	$-0.705983\pi$
$367$	912923.	−	2.80969e6i	0.353809	−	1.08891i	0.956697	−	0.291086i	$-0.0940166\pi$
$368$	−805245.	−	585045.i	−0.309962	−	0.225201i
$369$	−541924.	−	393731.i	−0.207192	−	0.150533i
$370$	1.08368e6	−	3.33524e6i	0.411527	−	1.26655i
$371$	−1.36554e6	−	4.20269e6i	−0.515073	−	1.58523i
$372$	−3.36622e6	+	2.44570e6i	−1.26120	+	0.916319i
$373$	−834745.			−0.310657			−0.155329	−	0.987863i	$-0.549644\pi$
$373$	−834745.			−0.310657			−0.155329	+	0.987863i	$0.549644\pi$
$374$	228578.	−	2.99439e6i	0.0844998	−	1.10695i
$375$	1.47784e6			0.542686
$376$	−6.07689e6	+	4.41512e6i	−2.21673	+	1.61055i
$377$	−131137.	−	403597.i	−0.0475193	−	0.146249i
$378$	−399186.	+	1.22857e6i	−0.143697	+	0.442252i
$379$	−265404.	−	192827.i	−0.0949093	−	0.0689556i	0.539319	−	0.842102i	$-0.318682\pi$
$379$	−265404.	−	192827.i	−0.0949093	−	0.0689556i	−0.634228	+	0.773146i	$0.718682\pi$
$380$	2.30453e6	+	1.67434e6i	0.818698	+	0.594819i
$381$	830310.	−	2.55543e6i	0.293041	−	0.901886i
$382$	967105.	+	2.97644e6i	0.339090	+	1.04361i
$383$	2.05286e6	−	1.49149e6i	0.715092	−	0.519545i	−0.169720	−	0.985492i	$-0.554286\pi$
$383$	2.05286e6	−	1.49149e6i	0.715092	−	0.519545i	0.884813	+	0.465947i	$0.154286\pi$
$384$	3.03258e6			1.04950
$385$	1.20049e6	+	1.94872e6i	0.412768	+	0.670034i
$386$	−1.77037e6			−0.604779
$387$	114549.	−	83224.7i	0.0388789	−	0.0282472i
$388$	1.55012e6	+	4.77078e6i	0.522740	+	1.60883i
$389$	−1.46382e6	+	4.50516e6i	−0.490470	+	1.50951i	0.333430	+	0.942775i	$0.391794\pi$
$389$	−1.46382e6	+	4.50516e6i	−0.490470	+	1.50951i	−0.823900	+	0.566736i	$0.808206\pi$
$390$	−1.90899e6	−	1.38696e6i	−0.635540	−	0.461747i
$391$	−817516.	−	593960.i	−0.270430	−	0.196479i
$392$	−1.47093e6	+	4.52705e6i	−0.483477	+	1.48799i
$393$	−587426.	−	1.80791e6i	−0.191854	−	0.590467i
$394$	−5.03432e6	+	3.65765e6i	−1.63381	+	1.18703i
$395$	368528.			0.118844
$396$	−1.93347e6	+	468998.i	−0.619584	+	0.150291i
$397$	−1.78322e6			−0.567844			−0.283922	−	0.958847i	$-0.591636\pi$
$397$	−1.78322e6			−0.567844			−0.283922	+	0.958847i	$0.591636\pi$
$398$	−2.17592e6	+	1.58090e6i	−0.688549	+	0.500260i
$399$	764588.	+	2.35316e6i	0.240434	+	0.739979i
$400$	−509483.	+	1.56803e6i	−0.159214	+	0.490009i
$401$	−2.78812e6	−	2.02569e6i	−0.865866	−	0.629088i	0.0636086	−	0.997975i	$-0.479739\pi$
$401$	−2.78812e6	−	2.02569e6i	−0.865866	−	0.629088i	−0.929474	+	0.368887i	$0.879739\pi$
$402$	−4.95694e6	−	3.60143e6i	−1.52985	−	1.11150i
$403$	2.04005e6	−	6.27863e6i	0.625718	−	1.92576i
$404$	−73881.8	−	227385.i	−0.0225208	−	0.0693119i
$405$	164934.	−	119832.i	0.0499658	−	0.0363023i
$406$	860409.			0.259054
$407$	4.33848e6	+	1.78511e6i	1.29823	+	0.534170i
$408$	−1.96692e6			−0.584973
$409$	−2.36925e6	+	1.72136e6i	−0.700329	+	0.508819i	−0.880039	−	0.474901i	$-0.842484\pi$
$409$	−2.36925e6	+	1.72136e6i	−0.700329	+	0.508819i	0.179710	+	0.983720i	$0.442484\pi$
$410$	766619.	+	2.35941e6i	0.225227	+	0.693177i
$411$	−541935.	+	1.66790e6i	−0.158249	+	0.487042i
$412$	613276.	+	445571.i	0.177997	+	0.129322i
$413$	−5.05049e6	−	3.66940e6i	−1.45700	−	1.05857i
$414$	−315034.	+	969574.i	−0.0903350	+	0.278023i
$415$	92380.1	+	284317.i	0.0263304	+	0.0810368i
$416$	−1.16778e6	+	848441.i	−0.330847	+	0.240375i
$417$	−1.05764e6			−0.297851
$418$	−3.75840e6	+	4.42154e6i	−1.05211	+	1.23775i
$419$	1.18900e6			0.330861			0.165431	−	0.986221i	$-0.447099\pi$
$419$	1.18900e6			0.330861			0.165431	+	0.986221i	$0.447099\pi$
$420$	2.54165e6	−	1.84662e6i	0.703060	−	0.510803i
$421$	−1.21647e6	−	3.74392e6i	−0.334501	−	1.02949i	−0.966967	−	0.254900i	$-0.917957\pi$
$421$	−1.21647e6	−	3.74392e6i	−0.334501	−	1.02949i	0.632466	−	0.774588i	$-0.282043\pi$
$422$	1.13668e6	−	3.49835e6i	0.310712	−	0.956275i
$423$	1.74579e6	+	1.26839e6i	0.474395	+	0.344668i
$424$	−5.49171e6	−	3.98996e6i	−1.48352	−	1.07784i
$425$	−517247.	+	1.59192e6i	−0.138908	+	0.427514i
$426$	294670.	+	906902.i	0.0786706	+	0.242123i
$427$	5.76483e6	−	4.18839e6i	1.53009	−	1.11167i
$428$	7.86273e6			2.07474
$429$	2.04443e6	−	2.40515e6i	0.536326	−	0.630956i
$430$	−524385.			−0.136766
$431$	−2.10479e6	+	1.52922e6i	−0.545777	+	0.396530i	−0.826226	−	0.563339i	$-0.809517\pi$
$431$	−2.10479e6	+	1.52922e6i	−0.545777	+	0.396530i	0.280449	+	0.959869i	$0.409517\pi$
$432$	171993.	+	529339.i	0.0443405	+	0.136466i
$433$	−1.81327e6	+	5.58066e6i	−0.464774	+	1.43043i	0.394492	+	0.918899i	$0.370920\pi$
$433$	−1.81327e6	+	5.58066e6i	−0.464774	+	1.43043i	−0.859266	+	0.511528i	$0.829080\pi$
$434$	1.08288e7	+	7.86758e6i	2.75966	+	2.00501i
$435$	−109855.	−	79814.7i	−0.0278355	−	0.0202237i
$436$	3.30099e6	−	1.01594e7i	0.831625	−	2.55948i
$437$	603405.	+	1.85709e6i	0.151149	+	0.465189i
$438$	−2.53101e6	+	1.83889e6i	−0.630390	+	0.458005i
$439$	−545501.			−0.135093			−0.0675467	−	0.997716i	$-0.521517\pi$
$439$	−545501.			−0.135093			−0.0675467	+	0.997716i	$0.521517\pi$
$440$	3.25145e6	+	1.33784e6i	0.800654	+	0.329438i
$441$	1.36747e6			0.334828
$442$	5.29112e6	−	3.84422e6i	1.28823	−	0.935951i
$443$	−496538.	−	1.52819e6i	−0.120211	−	0.369970i	0.872787	−	0.488100i	$-0.162310\pi$
$443$	−496538.	−	1.52819e6i	−0.120211	−	0.369970i	−0.992998	+	0.118130i	$0.962310\pi$
$444$	1.98989e6	−	6.12426e6i	0.479041	−	1.47434i
$445$	2.34604e6	+	1.70450e6i	0.561612	+	0.408035i
$446$	2.50758e6	+	1.82186e6i	0.596922	+	0.433689i
$447$	373344.	−	1.14904e6i	0.0883773	−	0.271997i
$448$	−2.29011e6	−	7.04823e6i	−0.539089	−	1.65915i
$449$	765657.	−	556282.i	0.179233	−	0.130221i	−0.494551	−	0.869148i	$-0.664668\pi$
$449$	765657.	−	556282.i	0.179233	−	0.130221i	0.673785	+	0.738928i	$0.264668\pi$
$450$	1.68870e6			0.393116
$451$	−3.22524e6	+	782339.i	−0.746656	+	0.181115i
$452$	−9.51717e6			−2.19110
$453$	−957231.	+	695469.i	−0.219165	+	0.159233i
$454$	−3.98873e6	−	1.22760e7i	−0.908228	−	2.79524i
$455$	−1.54033e6	+	4.74065e6i	−0.348807	+	1.07352i
$456$	3.07491e6	+	2.23405e6i	0.692500	+	0.503131i
$457$	4.59115e6	+	3.33566e6i	1.02833	+	0.747123i	0.967973	−	0.251054i	$-0.0807773\pi$
$457$	4.59115e6	+	3.33566e6i	1.02833	+	0.747123i	0.0603531	+	0.998177i	$0.480777\pi$
$458$	3.04958e6	−	9.38565e6i	0.679323	−	2.09074i
$459$	174614.	+	537406.i	0.0386854	+	0.119061i
$460$	2.00584e6	−	1.45733e6i	0.441980	−	0.321117i
$461$	6.88691e6			1.50929			0.754644	−	0.656135i	$-0.227810\pi$
$461$	6.88691e6			1.50929			0.754644	+	0.656135i	$0.227810\pi$
$462$	3.35689e6	+	5.44914e6i	0.731700	+	1.18775i
$463$	−6.90209e6			−1.49633			−0.748167	−	0.663511i	$-0.769066\pi$
$463$	−6.90209e6			−1.49633			−0.748167	+	0.663511i	$0.769066\pi$
$464$	299914.	−	217900.i	0.0646699	−	0.0469854i
$465$	−652775.	−	2.00904e6i	−0.140001	−	0.430879i
$466$	1.69738e6	−	5.22401e6i	0.362089	−	1.11440i
$467$	−2.10134e6	−	1.52671e6i	−0.445865	−	0.323940i	0.342096	−	0.939665i	$-0.388863\pi$
$467$	−2.10134e6	−	1.52671e6i	−0.445865	−	0.323940i	−0.787961	+	0.615725i	$0.788863\pi$
$468$	−3.50535e6	−	2.54678e6i	−0.739804	−	0.537499i
$469$	−3.99966e6	+	1.23097e7i	−0.839636	+	2.58413i
$470$	−2.46964e6	−	7.60076e6i	−0.515690	−	1.58713i
$471$	−1.56757e6	+	1.13891e6i	−0.325593	+	0.236557i
$472$	−9.58970e6			−1.98130
$473$	53394.4	−	699469.i	0.0109734	−	0.143753i
$474$	1.03050e6			0.210671
$475$	2.61675e6	−	1.90118e6i	0.532142	−	0.386624i
$476$	2.69081e6	+	8.28147e6i	0.544335	+	1.67529i
$477$	−602618.	+	1.85467e6i	−0.121268	+	0.373224i
$478$	5.61108e6	+	4.07669e6i	1.12325	+	0.816089i
$479$	2.60636e6	+	1.89363e6i	0.519035	+	0.377101i	0.816240	−	0.577713i	$-0.196055\pi$
$479$	2.60636e6	+	1.89363e6i	0.519035	+	0.377101i	−0.297205	+	0.954814i	$0.596055\pi$
$480$	−142728.	+	439271.i	−0.0282752	+	0.0870220i
$481$	3.15721e6	+	9.71689e6i	0.622215	+	1.91498i
$482$	−302185.	+	219550.i	−0.0592454	+	0.0430443i
$483$	2.15357e6			0.420041
$484$	−4.43367e6	+	8.80371e6i	−0.860300	+	1.70825i
$485$	−2.54671e6			−0.491614
$486$	461200.	−	335082.i	0.0885725	−	0.0643517i
$487$	−1.44102e6	−	4.43500e6i	−0.275326	−	0.847367i	−0.989133	−	0.147024i	$-0.953030\pi$
$487$	−1.44102e6	−	4.43500e6i	−0.275326	−	0.847367i	0.713807	−	0.700343i	$-0.246970\pi$
$488$	3.38252e6	−	1.04103e7i	0.642970	−	1.97886i
$489$	−1.57686e6	−	1.14566e6i	−0.298210	−	0.216662i
$490$	−4.09726e6	−	2.97683e6i	−0.770909	−	0.560098i
$491$	2.61875e6	−	8.05969e6i	0.490219	−	1.50874i	−0.334057	−	0.942553i	$-0.608418\pi$
$491$	2.61875e6	−	8.05969e6i	0.490219	−	1.50874i	0.824277	−	0.566187i	$-0.191582\pi$
$492$	1.40769e6	+	4.33242e6i	0.262177	+	0.806896i
$493$	304485.	−	221221.i	0.0564219	−	0.0409929i
$494$	−1.26380e7			−2.33002
$495$	76880.2	−	1.00713e6i	0.0141027	−	0.184746i
$496$	5.76709e6			1.05257
$497$	1.62966e6	−	1.18402e6i	0.295941	−	0.215014i
$498$	258320.	+	795027.i	0.0466750	+	0.143651i
$499$	−1.71648e6	+	5.28279e6i	−0.308594	+	0.949755i	0.669717	+	0.742616i	$0.266415\pi$
$499$	−1.71648e6	+	5.28279e6i	−0.308594	+	0.949755i	−0.978312	+	0.207139i	$0.933585\pi$
$500$	−8.13070e6	−	5.90730e6i	−1.45446	−	1.05673i
$501$	−215549.	−	156606.i	−0.0383665	−	0.0278749i
$502$	−2.84103e6	+	8.74378e6i	−0.503172	+	1.54860i
$503$	3.13560e6	+	9.65039e6i	0.552587	+	1.70069i	0.702231	+	0.711949i	$0.252187\pi$
$503$	3.13560e6	+	9.65039e6i	0.552587	+	1.70069i	−0.149644	+	0.988740i	$0.547813\pi$
$504$	3.39129e6	−	2.46391e6i	0.594687	−	0.432065i
$505$	121381.			0.0211798
$506$	2.64923e6	+	4.30041e6i	0.459984	+	0.746678i
$507$	3.53295e6			0.610405
$508$	−1.47829e7	+	1.07404e7i	−2.54156	+	1.84655i
$509$	1.01503e6	+	3.12393e6i	0.173653	+	0.534449i	0.999569	−	0.0293434i	$-0.00934165\pi$
$509$	1.01503e6	+	3.12393e6i	0.173653	+	0.534449i	−0.825916	+	0.563793i	$0.809342\pi$
$510$	646689.	−	1.99030e6i	0.110096	−	0.338839i
$511$	5.34662e6	+	3.88454e6i	0.905789	+	0.658094i
$512$	−6.59306e6	−	4.79014e6i	−1.11151	−	0.807557i
$513$	337416.	−	1.03846e6i	0.0566073	−	0.174219i
$514$	−2.13546e6	−	6.57227e6i	−0.356520	−	1.09726i
$515$	−311352.	+	226211.i	−0.0517290	+	0.0375833i
$516$	−962891.			−0.159204
$517$	1.03900e7	−	2.52028e6i	1.70958	−	0.414689i
$518$	−2.07150e7			−3.39203
$519$	−2.34606e6	+	1.70452e6i	−0.382315	+	0.277768i
$520$	2.36615e6	+	7.28226e6i	0.383737	+	1.18102i
$521$	2.75439e6	−	8.47714e6i	0.444561	−	1.36822i	−0.438404	−	0.898778i	$-0.644456\pi$
$521$	2.75439e6	−	8.47714e6i	0.444561	−	1.36822i	0.882965	−	0.469439i	$-0.155544\pi$
$522$	−307186.	−	223184.i	−0.0493429	−	0.0358497i
$523$	−7.19933e6	−	5.23062e6i	−1.15090	−	0.836179i	−0.162301	−	0.986741i	$-0.551891\pi$
$523$	−7.19933e6	−	5.23062e6i	−1.15090	−	0.836179i	−0.988600	+	0.150563i	$0.951891\pi$
$524$	−3.99482e6	+	1.22948e7i	−0.635578	+	1.95611i
$525$	−1.10235e6	−	3.39268e6i	−0.174550	−	0.537211i
$526$	8.20977e6	−	5.96475e6i	1.29380	−	0.940000i
$527$	5.85497e6			0.918329
$528$	2.55012e6	+	1.04928e6i	0.398086	+	0.163797i
$529$	−4.73677e6			−0.735941
$530$	5.84297e6	−	4.24517e6i	0.903533	−	0.656456i
$531$	851328.	+	2.62012e6i	0.131027	+	0.403260i
$532$	5.19962e6	−	1.60028e7i	0.796512	−	2.45141i
$533$	−5.84730e6	−	4.24831e6i	−0.891532	−	0.647736i
$534$	6.56018e6	+	4.76625e6i	0.995549	+	0.723309i
$535$	−1.23354e6	+	3.79644e6i	−0.186324	+	0.573445i
$536$	6.14401e6	+	1.89093e7i	0.923719	+	2.84292i
$537$	−3.50082e6	+	2.54350e6i	−0.523883	+	0.380624i
$538$	1.10103e7			1.63999
$539$	4.38794e6	−	5.16216e6i	0.650563	−	0.765349i
$540$	−1.38642e6			−0.204603
$541$	−1.77269e6	+	1.28794e6i	−0.260400	+	0.189191i	−0.710323	−	0.703876i	$-0.751451\pi$
$541$	−1.77269e6	+	1.28794e6i	−0.260400	+	0.189191i	0.449924	+	0.893067i	$0.351451\pi$
$542$	1.03363e6	+	3.18120e6i	0.151136	+	0.465149i
$543$	135914.	−	418300.i	0.0197817	−	0.0608819i
$544$	−1.03568e6	−	752468.i	−0.150048	−	0.109016i
$545$	4.38748e6	+	3.18769e6i	0.632738	+	0.459711i
$546$	−4.30718e6	+	1.32561e7i	−0.618317	+	1.90298i
$547$	−780471.	−	2.40204e6i	−0.111529	−	0.343251i	0.879678	−	0.475569i	$-0.157758\pi$
$547$	−780471.	−	2.40204e6i	−0.111529	−	0.343251i	−0.991207	+	0.132318i	$0.957758\pi$
$548$	9.64864e6	−	7.01014e6i	1.37251	−	0.997185i
$549$	−3.14461e6			−0.445283
$550$	5.41869e6	−	6.37477e6i	0.763814	−	0.898582i
$551$	−727269.			−0.102051
$552$	2.67637e6	−	1.94449e6i	0.373851	−	0.271618i
$553$	−672693.	−	2.07034e6i	−0.0935414	−	0.287891i
$554$	1.47055e6	−	4.52589e6i	0.203566	−	0.626512i
$555$	2.64485e6	+	1.92160e6i	0.364476	+	0.264807i
$556$	5.81889e6	+	4.22767e6i	0.798276	+	0.579982i
$557$	369749.	−	1.13797e6i	0.0504974	−	0.155415i	−0.922628	−	0.385691i	$-0.873963\pi$
$557$	369749.	−	1.13797e6i	0.0504974	−	0.155415i	0.973125	+	0.230276i	$0.0739630\pi$
$558$	−1.82534e6	−	5.61781e6i	−0.248175	−	0.763804i
$559$	1.23597e6	−	897986.i	0.167293	−	0.121546i
$560$	−4.35441e6			−0.586758
$561$	2.58899e6	+	1.06527e6i	0.347314	+	0.142906i
$562$	−2.99503e6			−0.400000
$563$	−1.23837e6	+	899732.i	−0.164657	+	0.119631i	−0.667062	−	0.745002i	$-0.732449\pi$
$563$	−1.23837e6	+	899732.i	−0.164657	+	0.119631i	0.502405	+	0.864632i	$0.332449\pi$
$564$	−4.53482e6	−	1.39567e7i	−0.600291	−	1.84751i
$565$	1.49309e6	−	4.59526e6i	0.196773	−	0.605605i
$566$	1.65205e7	+	1.20028e7i	2.16761	+	1.57486i
$567$	−974259.	−	707840.i	−0.127267	−	0.0924650i
$568$	956203.	−	2.94289e6i	0.124360	−	0.382739i
$569$	−2.43303e6	−	7.48810e6i	−0.315041	−	0.969596i	−0.975738	−	0.218943i	$-0.929739\pi$
$569$	−2.43303e6	−	7.48810e6i	−0.315041	−	0.969596i	0.660697	−	0.750653i	$-0.270261\pi$
$570$	−3.27159e6	+	2.37695e6i	−0.421766	+	0.306431i
$571$	−7.61662e6			−0.977625			−0.488812	−	0.872389i	$-0.662570\pi$
$571$	−7.61662e6			−0.977625			−0.488812	+	0.872389i	$0.662570\pi$
$572$	−2.08620e7	+	5.06044e6i	−2.66603	+	0.646693i
$573$	−2.91752e6			−0.371217
$574$	1.18555e7	−	8.61351e6i	1.50189	−	1.09119i
$575$	−869962.	−	2.67747e6i	−0.109731	−	0.337718i
$576$	−1.01064e6	+	3.11041e6i	−0.126922	+	0.390627i
$577$	−5.75982e6	−	4.18475e6i	−0.720226	−	0.523275i	0.166230	−	0.986087i	$-0.446841\pi$
$577$	−5.75982e6	−	4.18475e6i	−0.720226	−	0.523275i	−0.886457	+	0.462812i	$0.846841\pi$
$578$	−6.39714e6	−	4.64780e6i	−0.796465	−	0.578665i
$579$	510000.	−	1.56962e6i	0.0632228	−	0.194580i
$580$	285358.	+	878242.i	0.0352225	+	0.108404i
$581$	1.42862e6	−	1.03796e6i	0.175581	−	0.127567i
$582$	−7.12129e6			−0.871467
$583$	5.06762e6	+	8.22611e6i	0.617493	+	1.00236i
$584$	1.01520e7			1.23174
$585$	1.77962e6	−	1.29297e6i	0.215000	−	0.156206i
$586$	4.09950e6	+	1.26170e7i	0.493159	+	1.51779i
$587$	−2.70597e6	+	8.32811e6i	−0.324136	+	0.997588i	0.647693	+	0.761901i	$0.275734\pi$
$587$	−2.70597e6	+	8.32811e6i	−0.324136	+	0.997588i	−0.971829	+	0.235687i	$0.924266\pi$
$588$	−7.52350e6	−	5.46615e6i	−0.897381	−	0.651985i
$589$	−9.15315e6	−	6.65015e6i	−1.08713	−	0.789847i
$590$	3.15293e6	−	9.70371e6i	0.372893	−	1.14765i
$591$	−1.79262e6	−	5.51712e6i	−0.211115	−	0.649747i
$592$	−7.22065e6	+	5.24611e6i	−0.846783	+	0.615224i
$593$	4.79253e6			0.559665			0.279833	−	0.960049i	$-0.409721\pi$
$593$	4.79253e6			0.559665			0.279833	+	0.960049i	$0.409721\pi$
$594$	214978.	−	2.81622e6i	0.0249993	−	0.327492i
$595$	−4.42077e6			−0.511923
$596$	−6.64705e6	+	4.82936e6i	−0.766502	+	0.556896i
$597$	−774801.	−	2.38459e6i	−0.0889722	−	0.273828i
$598$	−3.39918e6	+	1.04616e7i	−0.388706	+	1.19631i
$599$	−8.93752e6	−	6.49349e6i	−1.01777	−	0.739454i	−0.0519464	−	0.998650i	$-0.516542\pi$
$599$	−8.93752e6	−	6.49349e6i	−1.01777	−	0.739454i	−0.965825	+	0.259196i	$0.916542\pi$
$600$	−4.43326e6	−	3.22095e6i	−0.502742	−	0.365263i
$601$	716407.	−	2.20487e6i	0.0809047	−	0.248999i	−0.902420	−	0.430857i	$-0.858211\pi$
$601$	716407.	−	2.20487e6i	0.0809047	−	0.248999i	0.983325	+	0.181858i	$0.0582112\pi$
$602$	957187.	+	2.94592e6i	0.107648	+	0.331306i
$603$	4.62101e6	−	3.35736e6i	0.517540	−	0.376015i
$604$	8.04642e6			0.897450
$605$	−3.55520e6	−	3.52191e6i	−0.394890	−	0.391192i
$606$	339415.			0.0375447
$607$	−7.29214e6	+	5.29805e6i	−0.803311	+	0.583639i	−0.911883	−	0.410449i	$-0.865372\pi$
$607$	−7.29214e6	+	5.29805e6i	−0.803311	+	0.583639i	0.108573	+	0.994088i	$0.465372\pi$
$608$	764433.	+	2.35268e6i	0.0838650	+	0.258110i
$609$	−247862.	+	762842.i	−0.0270812	+	0.0833472i
$610$	9.42197e6	+	6.84546e6i	1.02522	+	0.744866i
$611$	1.88369e7	+	1.36858e7i	2.04129	+	1.48309i
$612$	1.18747e6	−	3.65465e6i	0.128157	−	0.394428i
$613$	2.86967e6	+	8.83194e6i	0.308447	+	0.949303i	0.978368	+	0.206871i	$0.0663279\pi$
$613$	2.86967e6	+	8.83194e6i	0.308447	+	0.949303i	−0.669921	+	0.742432i	$0.733672\pi$
$614$	257400.	−	187012.i	0.0275541	−	0.0200193i
$615$	−2.31271e6			−0.246566
$616$	1.58077e6	−	2.07082e7i	0.167848	−	2.19882i
$617$	1.35949e7			1.43768			0.718840	−	0.695176i	$-0.244673\pi$
$617$	1.35949e7			1.43768			0.718840	+	0.695176i	$0.244673\pi$
$618$	−870626.	+	632547.i	−0.0916981	+	0.0666226i
$619$	−4.47984e6	−	1.37875e7i	−0.469933	−	1.44630i	−0.852671	−	0.522448i	$-0.825019\pi$
$619$	−4.47984e6	−	1.37875e7i	−0.469933	−	1.44630i	0.382739	−	0.923857i	$-0.374981\pi$
$620$	−4.43923e6	+	1.36625e7i	−0.463797	+	1.42742i
$621$	−768875.	−	558620.i	−0.0800067	−	0.0581283i
$622$	1.66941e7	+	1.21290e7i	1.73017	+	1.25704i
$623$	5.29328e6	−	1.62910e7i	0.546393	−	1.68162i
$624$	1.85578e6	+	5.71151e6i	0.190794	+	0.587205i
$625$	−1.33168e6	+	967519.i	−0.136364	+	0.0990740i
$626$	−1.42656e6			−0.145497
$627$	−2.83745e6	−	4.60594e6i	−0.288243	−	0.467896i
$628$	1.31769e7			1.33326
$629$	−7.33069e6	+	5.32606e6i	−0.738785	+	0.536759i
$630$	1.37821e6	+	4.24170e6i	0.138345	+	0.425783i
$631$	−4.30637e6	+	1.32537e7i	−0.430565	+	1.32514i	0.467000	+	0.884258i	$0.345335\pi$
$631$	−4.30637e6	+	1.32537e7i	−0.430565	+	1.32514i	−0.897564	+	0.440884i	$0.854665\pi$
$632$	−2.70533e6	−	1.96554e6i	−0.269419	−	0.195744i
$633$	2.77420e6	+	2.01558e6i	0.275188	+	0.199936i
$634$	2.40492e6	−	7.40159e6i	0.237617	−	0.731311i
$635$	−2.86669e6	−	8.82275e6i	−0.282128	−	0.868300i
$636$	1.07290e7	−	7.79510e6i	1.05176	−	0.764151i
$637$	1.47549e7			1.44075
$638$	−1.82821e6	+	443464.i	−0.177817	+	0.0431327i
$639$	−888950.			−0.0861242
$640$	8.47052e6	−	6.15419e6i	0.817448	−	0.593911i
$641$	−2.01764e6	−	6.20966e6i	−0.193954	−	0.596929i	−0.999987	−	0.00505876i	$-0.998390\pi$
$641$	−2.01764e6	−	6.20966e6i	−0.193954	−	0.596929i	0.806033	−	0.591870i	$-0.201610\pi$
$642$	−3.44930e6	+	1.06159e7i	−0.330289	+	1.01652i
$643$	−1.59523e7	−	1.15900e7i	−1.52158	−	1.10549i	−0.960697	−	0.277599i	$-0.910461\pi$
$643$	−1.59523e7	−	1.15900e7i	−1.52158	−	1.10549i	−0.560884	−	0.827894i	$-0.689539\pi$
$644$	−1.18484e7	−	8.60839e6i	−1.12576	−	0.817913i
$645$	151062.	−	464922.i	0.0142974	−	0.0440028i
$646$	−3.46359e6	−	1.06598e7i	−0.326547	−	1.00501i
$647$	−4.12442e6	+	2.99657e6i	−0.387349	+	0.281426i	−0.764368	−	0.644780i	$-0.776949\pi$
$647$	−4.12442e6	+	2.99657e6i	−0.387349	+	0.281426i	0.377019	+	0.926205i	$0.376949\pi$
$648$	−1.84989e6			−0.173064
$649$	1.26226e7	+	5.19370e6i	1.17635	+	0.484022i
$650$	1.82209e7			1.69155
$651$	−1.00949e7	+	7.33439e6i	−0.933578	+	0.678284i
$652$	4.09602e6	+	1.26063e7i	0.377349	+	1.16136i
$653$	−4.11385e6	+	1.26611e7i	−0.377542	+	1.16196i	0.564205	+	0.825635i	$0.309183\pi$
$653$	−4.11385e6	+	1.26611e7i	−0.377542	+	1.16196i	−0.941747	+	0.336321i	$0.890817\pi$
$654$	1.22686e7	+	8.91365e6i	1.12163	+	0.814913i
$655$	−5.30968e6	−	3.85771e6i	−0.483577	−	0.351339i
$656$	1.95109e6	−	6.00484e6i	0.177018	−	0.544806i
$657$	−901244.	−	2.77374e6i	−0.0814571	−	0.250699i
$658$	−3.81920e7	+	2.77481e7i	−3.43881	+	2.49844i
$659$	−1.07283e7			−0.962315			−0.481158	−	0.876634i	$-0.659784\pi$
$659$	−1.07283e7			−0.962315			−0.481158	+	0.876634i	$0.659784\pi$
$660$	−4.44876e6	+	5.23370e6i	−0.397538	+	0.467680i
$661$	7.60595e6			0.677096			0.338548	−	0.940949i	$-0.390064\pi$
$661$	7.60595e6			0.677096			0.338548	+	0.940949i	$0.390064\pi$
$662$	−779579.	+	566397.i	−0.0691377	+	0.0502315i
$663$	1.88406e6	+	5.79855e6i	0.166461	+	0.512313i
$664$	838246.	−	2.57985e6i	0.0737821	−	0.227078i
$665$	6.91103e6	+	5.02116e6i	0.606023	+	0.440301i
$666$	7.39573e6	+	5.37331e6i	0.646093	+	0.469414i
$667$	−195610.	+	602027.i	−0.0170246	+	0.0523964i
$668$	559905.	+	1.72321e6i	0.0485482	+	0.149416i
$669$	−2.33764e6	+	1.69840e6i	−0.201936	+	0.146715i
$670$	−2.11542e7			−1.82058
$671$	−1.00904e7	+	1.18708e7i	−0.865174	+	1.01783i
$672$	2.72829e6			0.233060
$673$	1.73127e7	−	1.25784e7i	1.47342	−	1.07050i	0.493815	−	0.869567i	$-0.335602\pi$
$673$	1.73127e7	−	1.25784e7i	1.47342	−	1.07050i	0.979605	−	0.200935i	$-0.0643979\pi$
$674$	−5.25222e6	−	1.61647e7i	−0.445341	−	1.37062i
$675$	−486472.	+	1.49721e6i	−0.0410959	+	0.126480i
$676$	−1.94374e7	−	1.41221e7i	−1.63596	−	1.18859i
$677$	−1.64778e7	−	1.19718e7i	−1.38175	−	1.00390i	−0.996715	−	0.0809943i	$-0.974190\pi$
$677$	−1.64778e7	−	1.19718e7i	−1.38175	−	1.00390i	−0.385032	−	0.922903i	$-0.625810\pi$
$678$	4.17509e6	−	1.28496e7i	0.348812	−	1.07353i
$679$	4.64863e6	+	1.43070e7i	0.386947	+	1.19090i
$680$	−5.49394e6	+	3.99158e6i	−0.455629	+	0.331034i
$681$	1.20330e7			0.994277
$682$	−2.70642e7	−	1.11358e7i	−2.22809	−	0.916773i
$683$	946068.			0.0776016			0.0388008	−	0.999247i	$-0.487646\pi$
$683$	946068.			0.0776016			0.0388008	+	0.999247i	$0.487646\pi$
$684$	−6.00738e6	+	4.36462e6i	−0.490959	+	0.356702i
$685$	1.87106e6	+	5.75852e6i	0.152356	+	0.468904i
$686$	−41277.9	+	127040.i	−0.00334894	+	0.0103070i
$687$	7.44284e6	+	5.40754e6i	0.601654	+	0.437127i
$688$	1.07971e6	+	784454.i	0.0869631	+	0.0631824i
$689$	−6.50218e6	+	2.00116e7i	−0.521808	+	1.60596i
$690$	1.08767e6	+	3.34750e6i	0.0869710	+	0.267669i
$691$	1.29122e6	−	938125.i	0.102874	−	0.0747421i	−0.535159	−	0.844751i	$-0.679748\pi$
$691$	1.29122e6	−	938125.i	0.102874	−	0.0747421i	0.638033	+	0.770009i	$0.279748\pi$
$692$	1.97209e7			1.56553
$693$	−5.79827e6	+	1.40647e6i	−0.458633	+	0.111250i
$694$	6.24645e6			0.492306
$695$	−2.95418e6	+	2.14633e6i	−0.231993	+	0.168553i
$696$	380749.	+	1.17183e6i	0.0297931	+	0.0916938i
$697$	1.98083e6	−	6.09635e6i	0.154442	−	0.475322i
$698$	−9.78426e6	−	7.10868e6i	−0.760133	−	0.552269i
$699$	4.14265e6	+	3.00981e6i	0.320690	+	0.232995i
$700$	−7.49657e6	+	2.30721e7i	−0.578253	+	1.77968i
$701$	−6.30010e6	−	1.93897e7i	−0.484231	−	1.49031i	−0.833092	−	0.553135i	$-0.813432\pi$
$701$	−6.30010e6	−	1.93897e7i	−0.484231	−	1.49031i	0.348861	−	0.937174i	$-0.386568\pi$
$702$	4.97630e6	−	3.61549e6i	0.381122	−	0.276901i
$703$	1.75096e7			1.33625
$704$	8.49877e6	+	1.37958e7i	0.646286	+	1.04910i
$705$	7.45030e6			0.564548
$706$	1.58399e7	−	1.15084e7i	1.19603	−	0.868966i
$707$	−221563.	−	681901.i	−0.0166705	−	0.0513066i
$708$	5.78950e6	−	1.78182e7i	0.434068	−	1.33592i
$709$	4.01215e6	+	2.91500e6i	0.299752	+	0.217783i	0.727487	−	0.686122i	$-0.240688\pi$
$709$	4.01215e6	+	2.91500e6i	0.299752	+	0.217783i	−0.427735	+	0.903904i	$0.640688\pi$
$710$	2.66349e6	+	1.93514e6i	0.198292	+	0.144068i
$711$	−296863.	+	913649.i	−0.0220232	+	0.0677806i
$712$	−8.13119e6	−	2.50252e7i	−0.601110	−	1.85003i
$713$	−7.96681e6	+	5.78823e6i	−0.586895	+	0.426404i
$714$	−1.23617e7			−0.907468
$715$	829529.	−	1.08669e7i	0.0606829	−	0.794950i
$716$	2.94277e7			2.14523
$717$	−5.23082e6	+	3.80041e6i	−0.379990	+	0.276079i
$718$	1.17995e7	+	3.63152e7i	0.854189	+	2.62892i
$719$	−2.03383e6	+	6.25950e6i	−0.146721	+	0.451562i	−0.997228	−	0.0744019i	$-0.976295\pi$
$719$	−2.03383e6	+	6.25950e6i	−0.146721	+	0.451562i	0.850507	+	0.525964i	$0.176295\pi$
$720$	1.55462e6	+	1.12950e6i	0.111762	+	0.0811998i
$721$	1.83915e6	+	1.33622e6i	0.131758	+	0.0957280i
$722$	694130.	−	2.13631e6i	0.0495562	−	0.152518i
$723$	−107602.	−	331165.i	−0.00765551	−	0.0235612i
$724$	−2.41982e6	+	1.75810e6i	−0.171568	+	0.124652i
$725$	1.04854e6			0.0740869
$726$	−9.94131e6	−	9.84822e6i	−0.700007	−	0.693452i
$727$	−2.20512e7			−1.54737			−0.773687	−	0.633568i	$-0.781590\pi$
$727$	−2.20512e7			−1.54737			−0.773687	+	0.633568i	$0.781590\pi$
$728$	3.65916e7	−	2.65854e7i	2.55890	−	1.85915i
$729$	164224.	+	505430.i	0.0114451	+	0.0352243i
$730$	−3.33779e6	+	1.02727e7i	−0.231821	+	0.713470i
$731$	1.09616e6	+	796408.i	0.0758719	+	0.0551242i
$732$	1.73009e7	+	1.25698e7i	1.19341	+	0.867066i
$733$	−1.85938e6	+	5.72260e6i	−0.127823	+	0.393399i	−0.994405	−	0.105636i	$-0.966312\pi$
$733$	−1.85938e6	+	5.72260e6i	−0.127823	+	0.393399i	0.866582	+	0.499035i	$0.166312\pi$
$734$	−8.81360e6	−	2.71255e7i	−0.603828	−	1.85839i
$735$	3.81959e6	−	2.77509e6i	0.260794	−	0.189478i
$736$	2.15314e6			0.146513
$737$	2.15398e6	−	2.82172e7i	0.146074	−	1.91358i
$738$	−6.46695e6			−0.437078
$739$	−5.36647e6	+	3.89897e6i	−0.361474	+	0.262626i	−0.753667	−	0.657257i	$-0.771717\pi$
$739$	−5.36647e6	+	3.89897e6i	−0.361474	+	0.262626i	0.392193	+	0.919883i	$0.371717\pi$
$740$	−6.87021e6	−	2.11443e7i	−0.461201	−	1.41943i
$741$	3.64069e6	−	1.12049e7i	0.243578	−	0.749655i
$742$	−3.45142e7	−	2.50760e7i	−2.30138	−	1.67205i
$743$	1.21202e7	+	8.80585e6i	0.805449	+	0.585193i	0.912508	−	0.409060i	$-0.134143\pi$
$743$	1.21202e7	+	8.80585e6i	0.805449	+	0.585193i	−0.107059	+	0.994253i	$0.534143\pi$
$744$	−5.92320e6	+	1.82297e7i	−0.392305	+	1.20739i
$745$	−1.28899e6	−	3.96711e6i	−0.0850862	−	0.261868i
$746$	−6.51975e6	+	4.73687e6i	−0.428927	+	0.311634i
$747$	−779289.			−0.0510972
$748$	−9.98583e6	−	1.62097e7i	−0.652574	−	1.05930i
$749$	2.35795e7			1.53578
$750$	1.15426e7	−	8.38619e6i	0.749291	−	0.544392i
$751$	1.14047e6	+	3.51001e6i	0.0737878	+	0.227096i	0.981148	−	0.193259i	$-0.0619057\pi$
$751$	1.14047e6	+	3.51001e6i	0.0737878	+	0.227096i	−0.907360	+	0.420354i	$0.861906\pi$
$752$	−6.28537e6	+	1.93444e7i	−0.405309	+	1.24741i
$753$	−6.93384e6	−	5.03773e6i	−0.445642	−	0.323778i
$754$	−3.31450e6	−	2.40813e6i	−0.212320	−	0.154259i
$755$	−1.26235e6	+	3.88513e6i	−0.0805961	+	0.248049i
$756$	2.53071e6	+	7.78873e6i	0.161042	+	0.495635i
$757$	1.80996e7	−	1.31501e7i	1.14796	−	0.834045i	0.159755	−	0.987157i	$-0.448929\pi$
$757$	1.80996e7	−	1.31501e7i	1.14796	−	0.834045i	0.988209	+	0.153112i	$0.0489295\pi$
$758$	−3.16715e6			−0.200214
$759$	−4.57593e6	+	1.10997e6i	−0.288320	+	0.0699372i
$760$	1.31224e7			0.824100
$761$	−1.07492e7	+	7.80972e6i	−0.672842	+	0.488848i	−0.870975	−	0.491327i	$-0.836512\pi$
$761$	−1.07492e7	+	7.80972e6i	−0.672842	+	0.488848i	0.198134	+	0.980175i	$0.436512\pi$
$762$	−8.01603e6	−	2.46708e7i	−0.500118	−	1.53920i
$763$	9.89929e6	−	3.04669e7i	0.615592	−	1.89460i
$764$	1.60515e7	+	1.16621e7i	0.994907	+	0.722842i
$765$	1.57831e6	+	1.14671e6i	0.0975079	+	0.0708437i
$766$	7.57013e6	−	2.32985e7i	0.466156	−	1.43468i
$767$	9.18574e6	+	2.82708e7i	0.563801	+	1.73520i
$768$	1.42783e7	−	1.03738e7i	0.873522	−	0.634651i
$769$	−2.07446e6			−0.126500			−0.0632498	−	0.997998i	$-0.520146\pi$
$769$	−2.07446e6			−0.126500			−0.0632498	+	0.997998i	$0.520146\pi$
$770$	2.04346e7	+	8.40805e6i	1.24205	+	0.511056i
$771$	6.44217e6			0.390298
$772$	−9.08008e6	+	6.59706e6i	−0.548335	+	0.398389i
$773$	977545.	+	3.00858e6i	0.0588421	+	0.181097i	0.976157	−	0.217065i	$-0.0696482\pi$
$773$	977545.	+	3.00858e6i	0.0588421	+	0.181097i	−0.917315	+	0.398162i	$0.869648\pi$
$774$	422411.	−	1.30005e6i	0.0253445	−	0.0780022i
$775$	1.31966e7	+	9.58788e6i	0.789237	+	0.573414i
$776$	1.86952e7	+	1.35828e7i	1.11449	+	0.809723i
$777$	5.96747e6	−	1.83660e7i	0.354599	−	1.09134i
$778$	1.41321e7	+	4.34940e7i	0.837060	+	2.57621i
$779$	−1.00210e7	+	7.28065e6i	−0.591651	+	0.429860i
$780$	−1.49594e7			−0.880394
$781$	−2.85246e6	+	3.35575e6i	−0.167337	+	0.196862i
$782$	−9.75569e6			−0.570481
$783$	286368.	−	208058.i	0.0166924	−	0.0121278i
$784$	3.98305e6	+	1.22586e7i	0.231433	+	0.712279i
$785$	−2.06725e6	+	6.36233e6i	−0.119734	+	0.368504i
$786$	−1.48473e7	−	1.07872e7i	−0.857218	−	0.622806i
$787$	−4.52393e6	−	3.28683e6i	−0.260363	−	0.189165i	0.449944	−	0.893057i	$-0.351444\pi$
$787$	−4.52393e6	−	3.28683e6i	−0.260363	−	0.189165i	−0.710307	+	0.703892i	$0.751444\pi$
$788$	−1.21908e7	+	3.75195e7i	−0.699386	+	2.15249i
$789$	2.92334e6	+	8.99711e6i	0.167181	+	0.514530i
$790$	2.87838e6	−	2.09126e6i	0.164089	−	0.119218i
$791$	−2.85409e7			−1.62191
$792$	−5.93591e6	+	6.98326e6i	−0.336260	+	0.395590i
$793$	−3.39300e7			−1.91603
$794$	−1.39278e7	+	1.01191e7i	−0.784027	+	0.569629i
$795$	2.08057e6	+	6.40333e6i	0.116752	+	0.359325i
$796$	−5.26907e6	+	1.62165e7i	−0.294748	+	0.907142i
$797$	1.84195e7	+	1.33825e7i	1.02714	+	0.746264i	0.967735	−	0.251970i	$-0.0810784\pi$
$797$	1.84195e7	+	1.33825e7i	1.02714	+	0.746264i	0.0594088	+	0.998234i	$0.481078\pi$
$798$	1.93251e7	+	1.40405e7i	1.07427	+	0.780506i
$799$	−6.38116e6	+	1.96392e7i	−0.353617	+	1.08832i
$800$	−1.10213e6	−	3.39199e6i	−0.0608844	−	0.187383i
$801$	−6.11560e6	+	4.44324e6i	−0.336789	+	0.244691i
$802$	−3.32716e7			−1.82657
$803$	−1.33627e7	−	5.49822e6i	−0.731316	−	0.300908i
$804$	−3.88439e7			−2.11925
$805$	6.01530e6	−	4.37037e6i	0.327165	−	0.237700i
$806$	−1.96952e7	−	6.06156e7i	−1.06788	−	3.28660i
$807$	−3.17178e6	+	9.76173e6i	−0.171443	+	0.527647i
$808$	−891049.	−	647385.i	−0.0480146	−	0.0348846i
$809$	3.50596e6	+	2.54723e6i	0.188337	+	0.136835i	0.677958	−	0.735100i	$-0.262865\pi$
$809$	3.50596e6	+	2.54723e6i	0.188337	+	0.136835i	−0.489621	+	0.871935i	$0.662865\pi$
$810$	608211.	−	1.87188e6i	0.0325718	−	0.100246i
$811$	−9.22401e6	−	2.83886e7i	−0.492456	−	1.51562i	−0.820884	−	0.571096i	$-0.806519\pi$
$811$	−9.22401e6	−	2.83886e7i	−0.492456	−	1.51562i	0.328427	−	0.944529i	$-0.393481\pi$
$812$	4.41296e6	−	3.20620e6i	0.234876	−	0.170648i
$813$	−3.11822e6			−0.165455
$814$	4.40154e7	−	1.06767e7i	2.32833	−	0.564777i
$815$	−6.72940e6			−0.354881
$816$	−4.30892e6	+	3.13061e6i	−0.226539	+	0.164590i
$817$	−809072.	−	2.49007e6i	−0.0424065	−	0.130514i
$818$	−8.73685e6	+	2.68892e7i	−0.456532	+	1.40506i
$819$	−1.05121e7	−	7.63752e6i	−0.547623	−	0.397871i
$820$	1.27239e7	+	9.24449e6i	0.660826	+	0.480118i
$821$	1.40082e6	−	4.31128e6i	0.0725312	−	0.223228i	−0.908219	−	0.418496i	$-0.862558\pi$
$821$	1.40082e6	−	4.31128e6i	0.0725312	−	0.223228i	0.980750	+	0.195268i	$0.0625575\pi$
$822$	5.23198e6	+	1.61024e7i	0.270076	+	0.831210i
$823$	2.36151e7	−	1.71574e7i	1.21532	−	0.882980i	0.219615	−	0.975587i	$-0.429520\pi$
$823$	2.36151e7	−	1.71574e7i	1.21532	−	0.882980i	0.995703	+	0.0926062i	$0.0295198\pi$
$824$	3.49210e6			0.179172
$825$	4.09090e6	+	6.64064e6i	0.209259	+	0.339684i
$826$	−6.02692e7			−3.07359
$827$	2.00777e7	−	1.45873e7i	1.02082	−	0.741670i	0.0543700	−	0.998521i	$-0.482685\pi$
$827$	2.00777e7	−	1.45873e7i	1.02082	−	0.741670i	0.966451	+	0.256851i	$0.0826850\pi$
$828$	1.99721e6	+	6.14678e6i	0.101239	+	0.311582i
$829$	1.01248e7	−	3.11610e7i	0.511683	−	1.57480i	−0.277555	−	0.960710i	$-0.589524\pi$
$829$	1.01248e7	−	3.11610e7i	0.511683	−	1.57480i	0.789238	−	0.614087i	$-0.210476\pi$
$830$	2.33493e6	+	1.69642e6i	0.117646	+	0.0854750i
$831$	3.58904e6	+	2.60759e6i	0.180292	+	0.130990i
$832$	−1.09046e7	+	3.35610e7i	−0.546139	+	1.68084i
$833$	4.04375e6	+	1.24454e7i	0.201917	+	0.621435i
$834$	−8.26068e6	+	6.00174e6i	−0.411245	+	0.298787i
$835$	−919874.			−0.0456575
$836$	−2.80020e6	+	3.66828e7i	−0.138571	+	1.81529i
$837$	5.50661e6			0.271688
$838$	9.28663e6	−	6.74713e6i	0.456823	−	0.331902i
$839$	1.22220e6	+	3.76154e6i	0.0599428	+	0.184485i	0.976544	−	0.215318i	$-0.0690787\pi$
$839$	1.22220e6	+	3.76154e6i	0.0599428	+	0.184485i	−0.916601	+	0.399803i	$0.869079\pi$
$840$	4.47228e6	−	1.37643e7i	0.218691	−	0.673062i
$841$	1.64031e7	+	1.19176e7i	0.799718	+	0.581029i
$842$	−3.07466e7	−	2.23387e7i	−1.49457	−	1.08587i
$843$	862793.	−	2.65540e6i	0.0418155	−	0.128695i
$844$	−7.20621e6	−	2.21784e7i	−0.348217	−	1.07170i
$845$	9.86814e6	−	7.16963e6i	0.475438	−	0.345426i
$846$	2.08331e7			1.00075
$847$	−1.32961e7	+	2.64013e7i	−0.636818	+	1.26450i
$848$	−1.83812e7			−0.877778
$849$	−1.54009e7	+	1.11894e7i	−0.733290	+	0.532766i
$850$	4.99365e6	+	1.53689e7i	0.237067	+	0.729616i
$851$	4.70946e6	−	1.44942e7i	0.222919	−	0.686075i
$852$	4.89079e6	+	3.55336e6i	0.230823	+	0.167703i
$853$	6.20501e6	+	4.50820e6i	0.291991	+	0.212144i	0.724131	−	0.689663i	$-0.242241\pi$
$853$	6.20501e6	+	4.50820e6i	0.291991	+	0.212144i	−0.432140	+	0.901807i	$0.642241\pi$
$854$	2.12584e7	−	6.54266e7i	0.997438	−	3.06980i
$855$	−1.16495e6	−	3.58534e6i	−0.0544993	−	0.167732i
$856$	2.93036e7	−	2.12903e7i	1.36690	−	0.993109i
$857$	4.16106e6			0.193531			0.0967657	−	0.995307i	$-0.469150\pi$
$857$	4.16106e6			0.193531			0.0967657	+	0.995307i	$0.469150\pi$
$858$	2.31959e6	−	3.03867e7i	0.107570	−	1.40918i
$859$	2.65770e7			1.22892			0.614459	−	0.788949i	$-0.289374\pi$
$859$	2.65770e7			1.22892			0.614459	+	0.788949i	$0.289374\pi$
$860$	−2.68952e6	+	1.95405e6i	−0.124002	+	0.0900928i
$861$	4.22150e6	+	1.29924e7i	0.194070	+	0.597287i
$862$	−7.76162e6	+	2.38878e7i	−0.355782	+	1.09499i
$863$	−1.24291e7	−	9.03024e6i	−0.568082	−	0.412736i	0.266326	−	0.963883i	$-0.414190\pi$
$863$	−1.24291e7	−	9.03024e6i	−0.568082	−	0.412736i	−0.834408	+	0.551147i	$0.814190\pi$
$864$	−974061.	−	707697.i	−0.0443917	−	0.0322525i
$865$	−3.09389e6	+	9.52201e6i	−0.140593	+	0.432701i
$866$	1.75058e7	+	5.38772e7i	0.793207	+	2.44124i
$867$	5.96361e6	−	4.33282e6i	0.269440	−	0.195759i
$868$	8.48573e7			3.82287
$869$	2.49642e6	+	4.05236e6i	0.112142	+	0.182036i
$870$	−1.31094e6			−0.0587199
$871$	4.98602e7	−	3.62256e7i	2.22694	−	1.61797i
$872$	−1.52066e7	−	4.68012e7i	−0.677238	−	2.08433i
$873$	2.05146e6	−	6.31376e6i	0.0911021	−	0.280383i
$874$	1.52512e7	+	1.10806e7i	0.675344	+	0.490666i
$875$	−2.43831e7	−	1.77153e7i	−1.07663	−	0.782220i
$876$	−6.12895e6	+	1.88630e7i	−0.269852	+	0.830519i
$877$	8.25391e6	+	2.54029e7i	0.362377	+	1.11528i	0.951607	+	0.307317i	$0.0994311\pi$
$877$	8.25391e6	+	2.54029e7i	0.362377	+	1.11528i	−0.589230	+	0.807965i	$0.700569\pi$
$878$	−4.26061e6	+	3.09552e6i	−0.186525	+	0.135518i
$879$	−1.23672e7			−0.539883
$880$	9.25229e6	−	2.24431e6i	0.402757	−	0.0976957i
$881$	−2.41492e7			−1.04825			−0.524123	−	0.851643i	$-0.675607\pi$
$881$	−2.41492e7			−1.04825			−0.524123	+	0.851643i	$0.675607\pi$
$882$	1.06806e7	−	7.75991e6i	0.462300	−	0.335881i
$883$	8.47847e6	+	2.60941e7i	0.365945	+	1.12626i	0.949387	+	0.314108i	$0.101706\pi$
$883$	8.47847e6	+	2.60941e7i	0.365945	+	1.12626i	−0.583442	+	0.812155i	$0.698294\pi$
$884$	1.28127e7	−	3.94333e7i	0.551453	−	1.69720i
$885$	7.69506e6	+	5.59079e6i	0.330259	+	0.239947i
$886$	−1.25501e7	−	9.11818e6i	−0.537109	−	0.390233i
$887$	−6.92411e6	+	2.13102e7i	−0.295498	+	0.909449i	0.687556	+	0.726132i	$0.258684\pi$
$887$	−6.92411e6	+	2.13102e7i	−0.295498	+	0.909449i	−0.983054	+	0.183318i	$0.941316\pi$
$888$	−9.16683e6	−	2.82126e7i	−0.390110	−	1.20063i
$889$	−4.43322e7	+	3.22092e7i	−1.88133	+	1.36687i
$890$	2.79961e7			1.18474
$891$	2.43494e6	+	1.00188e6i	0.102753	+	0.0422788i
$892$	1.96501e7			0.826898
$893$	3.22822e7	−	2.34544e7i	1.35467	−	0.984226i
$894$	−3.60437e6	−	1.10931e7i	−0.150829	−	0.464204i
$895$	−4.61674e6	+	1.42089e7i	−0.192654	+	0.592927i
$896$	−5.00350e7	−	3.63526e7i	−2.08211	−	1.51274i
$897$	−8.29607e6	−	6.02745e6i	−0.344264	−	0.250122i
$898$	2.82344e6	−	8.68965e6i	0.116839	−	0.359593i
$899$	−1.13339e6	−	3.48820e6i	−0.0467712	−	0.143947i
$900$	8.66117e6	−	6.29271e6i	0.356427	−	0.258959i
$901$	−1.86613e7			−0.765827
$902$	−2.07511e7	+	2.44125e7i	−0.849231	+	0.999070i
$903$	−2.88760e6			−0.117847
$904$	−3.54695e7	+	2.57701e7i	−1.44356	+	1.04880i
$905$	−469250.	−	1.44420e6i	−0.0190451	−	0.0586147i
$906$	−3.52989e6	+	1.08639e7i	−0.142870	+	0.439708i
$907$	−1.19018e7	−	8.64715e6i	−0.480390	−	0.349023i	0.321087	−	0.947050i	$-0.395952\pi$
$907$	−1.19018e7	−	8.64715e6i	−0.480390	−	0.349023i	−0.801477	+	0.598026i	$0.795952\pi$
$908$	−6.62029e7	−	4.80992e7i	−2.66478	−	1.93608i
$909$	−97776.8	+	300926.i	−0.00392488	+	0.0120795i
$910$	1.48708e7	+	4.57675e7i	0.595291	+	1.83212i
$911$	6.93748e6	−	5.04038e6i	0.276953	−	0.201218i	−0.440634	−	0.897687i	$-0.645246\pi$
$911$	6.93748e6	−	5.04038e6i	0.276953	−	0.201218i	0.717587	+	0.696469i	$0.245246\pi$
$912$	1.02920e7			0.409743
$913$	−2.50058e6	+	2.94179e6i	−0.0992805	+	0.116798i
$914$	5.47877e7			2.16929
$915$	−8.78345e6	+	6.38155e6i	−0.346826	+	0.251984i
$916$	−1.93333e7	−	5.95019e7i	−0.761322	−	2.34311i
$917$	−1.19800e7	+	3.68707e7i	−0.470472	+	1.44796i
$918$	4.41340e6	+	3.20652e6i	0.172849	+	0.125582i
$919$	−1.57124e7	−	1.14157e7i	−0.613695	−	0.445876i	0.237019	−	0.971505i	$-0.423830\pi$
$919$	−1.57124e7	−	1.14157e7i	−0.613695	−	0.445876i	−0.850714	+	0.525630i	$0.823830\pi$
$920$	3.52948e6	−	1.08626e7i	0.137480	−	0.423121i
$921$	91654.9	+	282085.i	0.00356046	+	0.0109580i
$922$	5.37900e7	−	3.90807e7i	2.08389	−	1.51403i
$923$	−9.59167e6			−0.370587
$924$	3.75227e7	+	1.54391e7i	1.44582	+	0.594898i
$925$	−2.52445e7			−0.970090
$926$	−5.39086e7	+	3.91669e7i	−2.06600	+	1.50104i
$927$	−310013.	−	954121.i	−0.0118490	−	0.0364673i
$928$	−247812.	+	762687.i	−0.00944610	+	0.0290721i
$929$	7.44492e6	+	5.40905e6i	0.283022	+	0.205628i	0.720235	−	0.693731i	$-0.244034\pi$
$929$	7.44492e6	+	5.40905e6i	0.283022	+	0.205628i	−0.437212	+	0.899358i	$0.644034\pi$
$930$	−1.64990e7	−	1.19872e7i	−0.625534	−	0.454477i
$931$	7.81398e6	−	2.40490e7i	0.295460	−	0.909331i
$932$	−1.07609e7	−	3.31185e7i	−0.405796	−	1.24891i
$933$	−1.55628e7	+	1.13070e7i	−0.585306	+	0.425250i
$934$	−2.50759e7			−0.940568
$935$	9.39329e6	−	2.27851e6i	0.351389	−	0.0852357i
$936$	−1.99601e7			−0.744685
$937$	−8.85005e6	+	6.42994e6i	−0.329304	+	0.239253i	−0.740135	−	0.672458i	$-0.765239\pi$
$937$	−8.85005e6	+	6.42994e6i	−0.329304	+	0.239253i	0.410831	+	0.911711i	$0.365239\pi$
$938$	3.86138e7	+	1.18841e8i	1.43296	+	4.41021i
$939$	410955.	−	1.26479e6i	0.0152101	−	0.0468117i
$940$	−4.09897e7	−	2.97808e7i	−1.51306	−	1.09930i
$941$	7.95641e6	+	5.78067e6i	0.292916	+	0.212816i	0.724531	−	0.689242i	$-0.242056\pi$
$941$	7.95641e6	+	5.78067e6i	0.292916	+	0.212816i	−0.431615	+	0.902058i	$0.642056\pi$
$942$	−5.78059e6	+	1.77908e7i	−0.212249	+	0.653234i
$943$	3.33156e6	+	1.02535e7i	0.122003	+	0.375485i
$944$	−2.10081e7	+	1.52633e7i	−0.767286	+	0.557466i
$945$	−4.15773e6			−0.151453
$946$	−3.55220e6	−	5.76618e6i	−0.129053	−	0.209488i
$947$	3.36186e7			1.21816			0.609080	−	0.793109i	$-0.291539\pi$
$947$	3.36186e7			1.21816			0.609080	+	0.793109i	$0.291539\pi$
$948$	5.28536e6	−	3.84004e6i	0.191009	−	0.138776i
$949$	−9.72432e6	−	2.99284e7i	−0.350505	−	1.07874i
$950$	9.64952e6	−	2.96982e7i	0.346894	−	1.06763i
$951$	5.86948e6	+	4.26442e6i	0.210450	+	0.152901i
$952$	3.24525e7	+	2.35781e7i	1.16053	+	0.843173i
$953$	6.12525e6	−	1.88516e7i	0.218470	−	0.672381i	−0.780419	−	0.625257i	$-0.784994\pi$
$953$	6.12525e6	−	1.88516e7i	0.218470	−	0.672381i	0.998889	−	0.0471242i	$-0.0150056\pi$
$954$	5.81783e6	+	1.79054e7i	0.206962	+	0.636963i
$955$	−8.14914e6	+	5.92070e6i	−0.289137	+	0.210070i
$956$	4.39699e7			1.55600
$957$	133484.	−	1.74865e6i	0.00471139	−	0.0617194i
$958$	3.11026e7			1.09492
$959$	2.89352e7	−	2.10226e7i	1.01597	−	0.738143i
$960$	3.48927e6	+	1.07389e7i	0.122196	+	0.376080i
$961$	8.78485e6	−	2.70370e7i	0.306850	−	0.944387i
$962$	7.97991e7	+	5.79774e7i	2.78010	+	2.01986i
$963$	−8.41841e6	−	6.11633e6i	−0.292526	−	0.212532i
$964$	−731752.	+	2.25210e6i	−0.0253613	+	0.0780540i
$965$	−1.76080e6	−	5.41919e6i	−0.0608684	−	0.187334i
$966$	1.68204e7	−	1.22207e7i	0.579954	−	0.421361i
$967$	−2.76797e7			−0.951907			−0.475953	−	0.879470i	$-0.657897\pi$
$967$	−2.76797e7			−0.951907			−0.475953	+	0.879470i	$0.657897\pi$
$968$	7.31438e6	+	4.48157e7i	0.250893	+	1.53724i
$969$	1.04488e7			0.357485
$970$	−1.98910e7	+	1.44516e7i	−0.678776	+	0.493160i
$971$	8.53166e6	+	2.62577e7i	0.290393	+	0.893736i	0.984730	+	0.174087i	$0.0556974\pi$
$971$	8.53166e6	+	2.62577e7i	0.290393	+	0.893736i	−0.694338	+	0.719649i	$0.744303\pi$
$972$	1.11681e6	−	3.43720e6i	0.0379154	−	0.116692i
$973$	1.74502e7	+	1.26783e7i	0.590906	+	0.429318i
$974$	−3.64221e7	−	2.64622e7i	−1.23018	−	0.893776i
$975$	−5.24898e6	+	1.61547e7i	−0.176833	+	0.544236i
$976$	−9.15935e6	−	2.81896e7i	−0.307780	−	0.947249i
$977$	6.59288e6	−	4.79001e6i	0.220973	−	0.160546i	−0.471792	−	0.881710i	$-0.656393\pi$
$977$	6.59288e6	−	4.79001e6i	0.220973	−	0.160546i	0.692764	+	0.721164i	$0.256393\pi$
$978$	−1.88172e7			−0.629084
$979$	−2.85064e6	+	3.73436e7i	−0.0950575	+	1.24526i
$980$	−3.21072e7			−1.06792
$981$	−1.14372e7	+	8.30958e6i	−0.379442	+	0.275681i
$982$	−2.52821e7	−	7.78104e7i	−0.836633	−	2.57489i
$983$	1.58234e7	−	4.86993e7i	0.522294	−	1.60746i	−0.247310	−	0.968936i	$-0.579547\pi$
$983$	1.58234e7	−	4.86993e7i	0.522294	−	1.60746i	0.769605	−	0.638521i	$-0.220453\pi$
$984$	1.69774e7	+	1.23348e7i	0.558963	+	0.406110i
$985$	−1.62033e7	−	1.17724e7i	−0.532125	−	0.386611i
$986$	1.12282e6	−	3.45568e6i	0.0367804	−	0.113199i
$987$	−1.35994e7	−	4.18547e7i	−0.444352	−	1.36758i
$988$	−6.48190e7	+	4.70938e7i	−2.11256	+	1.53487i
$989$	−2.27887e6			−0.0740846
$990$	−5.11465e6	−	8.30246e6i	−0.165855	−	0.269227i
$991$	5.95505e6			0.192620			0.0963100	−	0.995351i	$-0.469296\pi$
$991$	5.95505e6			0.192620			0.0963100	+	0.995351i	$0.469296\pi$
$992$	−1.00929e7	+	7.33291e6i	−0.325639	+	0.236590i
$993$	−277593.	−	854342.i	−0.00893377	−	0.0274953i
$994$	6.00953e6	−	1.84954e7i	0.192919	−	0.593743i
$995$	−7.00335e6	−	5.08823e6i	−0.224258	−	0.162933i
$996$	4.28746e6	+	3.11502e6i	0.136947	+	0.0994976i
$997$	1.20516e7	−	3.70909e7i	0.383978	−	1.18176i	−0.553241	−	0.833021i	$-0.686609\pi$
$997$	1.20516e7	−	3.70909e7i	0.383978	−	1.18176i	0.937219	−	0.348741i	$-0.113391\pi$
$998$	1.65714e7	+	5.10014e7i	0.526662	+	1.62090i
$999$	−6.89452e6	+	5.00916e6i	−0.218570	+	0.158800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.6.e.a.25.5	yes	20
3.2	odd	2		99.6.f.c.91.1		20
11.2	odd	10		363.6.a.q.1.10		10
11.4	even	5	inner	33.6.e.a.4.5	✓	20
11.9	even	5		363.6.a.u.1.1		10
33.2	even	10		1089.6.a.bl.1.1		10
33.20	odd	10		1089.6.a.bh.1.10		10
33.26	odd	10		99.6.f.c.37.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.e.a.4.5	✓	20	11.4	even	5	inner
33.6.e.a.25.5	yes	20	1.1	even	1	trivial
99.6.f.c.37.1		20	33.26	odd	10
99.6.f.c.91.1		20	3.2	odd	2
363.6.a.q.1.10		10	11.2	odd	10
363.6.a.u.1.1		10	11.9	even	5
1089.6.a.bh.1.10		10	33.20	odd	10
1089.6.a.bl.1.1		10	33.2	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(7.81047 - 5.67464i) q^{2} +(2.78115 + 8.55951i) q^{3} +(18.9134 - 58.2093i) q^{4} +(25.1385 + 18.2642i) q^{5} +(70.2942 + 51.0717i) q^{6} +(56.7190 - 174.563i) q^{7} +(-87.1280 - 268.152i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})\)	\(q+(7.81047 - 5.67464i) q^{2} +(2.78115 + 8.55951i) q^{3} +(18.9134 - 58.2093i) q^{4} +(25.1385 + 18.2642i) q^{5} +(70.2942 + 51.0717i) q^{6} +(56.7190 - 174.563i) q^{7} +(-87.1280 - 268.152i) q^{8} +(-65.5304 + 47.6106i) q^{9} +299.987 q^{10} +(-30.5455 + 400.147i) q^{11} +550.844 q^{12} +(-707.066 + 513.713i) q^{13} +(-547.581 - 1685.28i) q^{14} +(-86.4186 + 265.969i) q^{15} +(-617.672 - 448.765i) q^{16} +(-627.084 - 455.604i) q^{17} +(-241.650 + 743.722i) q^{18} +(462.848 + 1424.50i) q^{19} +(1538.60 - 1117.86i) q^{20} +1651.92 q^{21} +(2032.12 + 3298.67i) q^{22} +1303.68 q^{23} +(2052.94 - 1491.55i) q^{24} +(-667.313 - 2053.78i) q^{25} +(-2607.38 + 8024.68i) q^{26} +(-589.773 - 428.495i) q^{27} +(-9088.46 - 6603.16i) q^{28} +(-150.045 + 461.791i) q^{29} +(834.309 + 2567.74i) q^{30} +(-6111.03 + 4439.92i) q^{31} +1651.59 q^{32} +(-3510.02 + 851.417i) q^{33} -7483.21 q^{34} +(4614.10 - 3352.34i) q^{35} +(1531.98 + 4714.96i) q^{36} +(3612.44 - 11118.0i) q^{37} +(11698.6 + 8499.52i) q^{38} +(-6363.59 - 4623.42i) q^{39} +(2707.32 - 8332.29i) q^{40} +(2555.51 + 7865.05i) q^{41} +(12902.3 - 9374.05i) q^{42} -1748.03 q^{43} +(22714.6 + 9346.16i) q^{44} -2516.91 q^{45} +(10182.3 - 7397.90i) q^{46} +(-8232.49 - 25337.0i) q^{47} +(2123.37 - 6535.05i) q^{48} +(-13658.1 - 9923.22i) q^{49} +(-16866.5 - 12254.2i) q^{50} +(2155.72 - 6634.64i) q^{51} +(16529.9 + 50873.9i) q^{52} +(19477.4 - 14151.2i) q^{53} -7037.96 q^{54} +(-8076.25 + 9501.24i) q^{55} -51751.4 q^{56} +(-10905.8 + 7923.51i) q^{57} +(1448.57 + 4458.25i) q^{58} +(10510.2 - 32347.1i) q^{59} +(13847.4 + 10060.7i) q^{60} +(31408.0 + 22819.2i) q^{61} +(-22535.0 + 69355.7i) q^{62} +(4594.24 + 14139.6i) q^{63} +(32665.1 - 23732.6i) q^{64} -27157.2 q^{65} +(-22583.4 + 26568.0i) q^{66} -70517.1 q^{67} +(-38380.7 + 27885.2i) q^{68} +(3625.73 + 11158.8i) q^{69} +(17015.0 - 52366.6i) q^{70} +(8878.71 + 6450.76i) q^{71} +(18476.4 + 13423.9i) q^{72} +(-11126.5 + 34243.7i) q^{73} +(-34875.5 - 107336. i) q^{74} +(15723.4 - 11423.8i) q^{75} +91673.2 q^{76} +(68118.5 + 28028.1i) q^{77} -75938.9 q^{78} +(9595.02 - 6971.19i) q^{79} +(-7331.03 - 22562.6i) q^{80} +(2027.46 - 6239.88i) q^{81} +(64591.1 + 46928.2i) q^{82} +(7783.43 + 5655.00i) q^{83} +(31243.4 - 96157.2i) q^{84} +(-7442.75 - 22906.4i) q^{85} +(-13652.9 + 9919.43i) q^{86} -4370.00 q^{87} +(109962. - 26673.2i) q^{88} +93324.6 q^{89} +(-19658.2 + 14282.5i) q^{90} +(49571.4 + 152565. i) q^{91} +(24656.9 - 75886.2i) q^{92} +(-54999.2 - 39959.3i) q^{93} +(-208078. - 151177. i) q^{94} +(-14382.1 + 44263.4i) q^{95} +(4593.31 + 14136.8i) q^{96} +(-66306.2 + 48174.3i) q^{97} -162987. q^{98} +(-17049.6 - 27676.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 45 q^{3} - 124 q^{4} - 33 q^{5} - 18 q^{6} - 335 q^{7} - 472 q^{8} - 405 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 45 * q^3 - 124 * q^4 - 33 * q^5 - 18 * q^6 - 335 * q^7 - 472 * q^8 - 405 * q^9	\( 20 q - 2 q^{2} - 45 q^{3} - 124 q^{4} - 33 q^{5} - 18 q^{6} - 335 q^{7} - 472 q^{8} - 405 q^{9} + 1952 q^{10} - 835 q^{11} + 3474 q^{12} - 959 q^{13} - 3020 q^{14} + 198 q^{15} - 1428 q^{16} - 3144 q^{17} - 567 q^{18} - 930 q^{19} + 3177 q^{20} + 8460 q^{21} + 2713 q^{22} + 1400 q^{23} + 1332 q^{24} - 9388 q^{25} + 3022 q^{26} - 3645 q^{27} - 21753 q^{28} + 4494 q^{29} - 4302 q^{30} + 9208 q^{31} + 69114 q^{32} + 6615 q^{33} - 9084 q^{34} - 31371 q^{35} - 10044 q^{36} - 3153 q^{37} + 1852 q^{38} - 8631 q^{39} - 53123 q^{40} - 7497 q^{41} + 22320 q^{42} + 63624 q^{43} + 58299 q^{44} + 1782 q^{45} - 94681 q^{46} - 43031 q^{47} - 12357 q^{48} - 5640 q^{49} - 76590 q^{50} + 459 q^{51} - 80149 q^{52} - 20452 q^{53} + 13122 q^{54} + 62974 q^{55} + 169638 q^{56} - 39375 q^{57} + 93145 q^{58} + 101730 q^{59} + 28593 q^{60} + 50745 q^{61} - 171957 q^{62} - 27135 q^{63} + 199638 q^{64} - 28210 q^{65} + 46107 q^{66} + 10730 q^{67} - 420141 q^{68} + 94365 q^{69} + 292664 q^{70} + 164895 q^{71} + 11988 q^{72} - 77236 q^{73} - 328228 q^{74} + 9063 q^{75} + 79212 q^{76} + 56087 q^{77} - 280062 q^{78} - 291931 q^{79} + 18026 q^{80} - 32805 q^{81} + 424659 q^{82} - 255451 q^{83} - 26127 q^{84} - 452271 q^{85} + 252843 q^{86} + 187056 q^{87} + 171694 q^{88} + 181632 q^{89} - 40338 q^{90} + 284615 q^{91} + 1199691 q^{92} + 82872 q^{93} - 550105 q^{94} - 511091 q^{95} - 587574 q^{96} - 145083 q^{97} - 150570 q^{98} - 83430 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 45 * q^3 - 124 * q^4 - 33 * q^5 - 18 * q^6 - 335 * q^7 - 472 * q^8 - 405 * q^9 + 1952 * q^10 - 835 * q^11 + 3474 * q^12 - 959 * q^13 - 3020 * q^14 + 198 * q^15 - 1428 * q^16 - 3144 * q^17 - 567 * q^18 - 930 * q^19 + 3177 * q^20 + 8460 * q^21 + 2713 * q^22 + 1400 * q^23 + 1332 * q^24 - 9388 * q^25 + 3022 * q^26 - 3645 * q^27 - 21753 * q^28 + 4494 * q^29 - 4302 * q^30 + 9208 * q^31 + 69114 * q^32 + 6615 * q^33 - 9084 * q^34 - 31371 * q^35 - 10044 * q^36 - 3153 * q^37 + 1852 * q^38 - 8631 * q^39 - 53123 * q^40 - 7497 * q^41 + 22320 * q^42 + 63624 * q^43 + 58299 * q^44 + 1782 * q^45 - 94681 * q^46 - 43031 * q^47 - 12357 * q^48 - 5640 * q^49 - 76590 * q^50 + 459 * q^51 - 80149 * q^52 - 20452 * q^53 + 13122 * q^54 + 62974 * q^55 + 169638 * q^56 - 39375 * q^57 + 93145 * q^58 + 101730 * q^59 + 28593 * q^60 + 50745 * q^61 - 171957 * q^62 - 27135 * q^63 + 199638 * q^64 - 28210 * q^65 + 46107 * q^66 + 10730 * q^67 - 420141 * q^68 + 94365 * q^69 + 292664 * q^70 + 164895 * q^71 + 11988 * q^72 - 77236 * q^73 - 328228 * q^74 + 9063 * q^75 + 79212 * q^76 + 56087 * q^77 - 280062 * q^78 - 291931 * q^79 + 18026 * q^80 - 32805 * q^81 + 424659 * q^82 - 255451 * q^83 - 26127 * q^84 - 452271 * q^85 + 252843 * q^86 + 187056 * q^87 + 171694 * q^88 + 181632 * q^89 - 40338 * q^90 + 284615 * q^91 + 1199691 * q^92 + 82872 * q^93 - 550105 * q^94 - 511091 * q^95 - 587574 * q^96 - 145083 * q^97 - 150570 * q^98 - 83430 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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