LMFDB - Embedded newform 20.5.d.c.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,5,Mod(19,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("20.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	20.d (of order $2$, degree $1$, 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:	$2.06739926168$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1816805376000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 31x^{4} + 96x^{2} + 256 $ x^8 + 6x^6 + 31x^4 + 96*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.6
Root			$0.677813 + 1.88164i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.5.d.c.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35563 + 3.76328i) q^{2} -13.9962 q^{3} +(-12.3246 + 10.2032i) q^{4} +(7.64911 + 23.8011i) q^{5} +(-18.9737 - 52.6718i) q^{6} +35.6863 q^{7} +(-55.1050 - 32.5490i) q^{8} +114.895 q^{9} +O(q^{10})$	\(q+(1.35563 + 3.76328i) q^{2} -13.9962 q^{3} +(-12.3246 + 10.2032i) q^{4} +(7.64911 + 23.8011i) q^{5} +(-18.9737 - 52.6718i) q^{6} +35.6863 q^{7} +(-55.1050 - 32.5490i) q^{8} +114.895 q^{9} +(-79.2008 + 61.0511i) q^{10} +169.874i q^{11} +(172.497 - 142.806i) q^{12} -72.8228i q^{13} +(48.3772 + 134.297i) q^{14} +(-107.059 - 333.125i) q^{15} +(47.7893 - 251.500i) q^{16} +25.2207i q^{17} +(155.754 + 432.381i) q^{18} +156.628i q^{19} +(-337.119 - 215.292i) q^{20} -499.473 q^{21} +(-639.284 + 230.286i) q^{22} +420.541 q^{23} +(771.263 + 455.564i) q^{24} +(-507.982 + 364.114i) q^{25} +(274.053 - 98.7205i) q^{26} -474.398 q^{27} +(-439.817 + 364.114i) q^{28} +439.193 q^{29} +(1108.51 - 854.486i) q^{30} -1006.00i q^{31} +(1011.25 - 161.095i) q^{32} -2377.60i q^{33} +(-94.9125 + 34.1898i) q^{34} +(272.968 + 849.371i) q^{35} +(-1416.03 + 1172.29i) q^{36} +1722.19i q^{37} +(-589.436 + 212.329i) q^{38} +1019.25i q^{39} +(353.198 - 1560.53i) q^{40} +2180.56 q^{41} +(-677.099 - 1879.66i) q^{42} +180.311 q^{43} +(-1733.26 - 2093.62i) q^{44} +(878.842 + 2734.62i) q^{45} +(570.097 + 1582.61i) q^{46} +270.757 q^{47} +(-668.871 + 3520.05i) q^{48} -1127.49 q^{49} +(-2058.90 - 1418.08i) q^{50} -352.995i q^{51} +(743.026 + 897.509i) q^{52} -924.647i q^{53} +(-643.106 - 1785.29i) q^{54} +(-4043.19 + 1299.39i) q^{55} +(-1966.49 - 1161.55i) q^{56} -2192.21i q^{57} +(595.381 + 1652.81i) q^{58} -4127.64i q^{59} +(4718.40 + 3013.28i) q^{60} -2492.07 q^{61} +(3785.86 - 1363.76i) q^{62} +4100.16 q^{63} +(1977.12 + 3587.23i) q^{64} +(1733.26 - 557.030i) q^{65} +(8947.58 - 3223.14i) q^{66} +860.976 q^{67} +(-257.332 - 310.834i) q^{68} -5886.00 q^{69} +(-2826.38 + 2178.69i) q^{70} +8034.75i q^{71} +(-6331.27 - 3739.71i) q^{72} -5770.88i q^{73} +(-6481.10 + 2334.65i) q^{74} +(7109.84 - 5096.23i) q^{75} +(-1598.11 - 1930.37i) q^{76} +6062.18i q^{77} +(-3835.71 + 1381.72i) q^{78} -4403.48i q^{79} +(6351.51 - 786.313i) q^{80} -2666.68 q^{81} +(2956.02 + 8206.06i) q^{82} -10436.9 q^{83} +(6155.79 - 5096.23i) q^{84} +(-600.279 + 192.916i) q^{85} +(244.434 + 678.560i) q^{86} -6147.05 q^{87} +(5529.24 - 9360.92i) q^{88} +12059.4 q^{89} +(-9099.75 + 7014.45i) q^{90} -2598.77i q^{91} +(-5182.98 + 4290.87i) q^{92} +14080.2i q^{93} +(367.045 + 1018.93i) q^{94} +(-3727.92 + 1198.07i) q^{95} +(-14153.7 + 2254.73i) q^{96} -8152.32i q^{97} +(-1528.46 - 4243.06i) q^{98} +19517.6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 48 q^{4} - 40 q^{5} + 312 q^{9}+O(q^{10}) $ 8 * q - 48 * q^4 - 40 * q^5 + 312 * q^9	$ 8 q - 48 q^{4} - 40 q^{5} + 312 q^{9} - 160 q^{10} + 640 q^{14} - 832 q^{16} - 400 q^{20} - 960 q^{21} + 1920 q^{24} - 2040 q^{25} + 2496 q^{26} + 2704 q^{29} - 1920 q^{30} - 2176 q^{34} - 5712 q^{36} + 6400 q^{40} + 1456 q^{41} + 1920 q^{44} + 6120 q^{45} + 7040 q^{46} - 8008 q^{49} - 12480 q^{50} - 11520 q^{54} - 14720 q^{56} + 21120 q^{60} + 6576 q^{61} + 6912 q^{64} - 1920 q^{65} + 46080 q^{66} - 12480 q^{69} - 6400 q^{70} - 23616 q^{74} - 48000 q^{76} + 19520 q^{80} - 19512 q^{81} + 24960 q^{84} + 8960 q^{85} + 37120 q^{86} + 27664 q^{89} - 48480 q^{90} + 10880 q^{94} - 76800 q^{96}+O(q^{100}) $ 8 * q - 48 * q^4 - 40 * q^5 + 312 * q^9 - 160 * q^10 + 640 * q^14 - 832 * q^16 - 400 * q^20 - 960 * q^21 + 1920 * q^24 - 2040 * q^25 + 2496 * q^26 + 2704 * q^29 - 1920 * q^30 - 2176 * q^34 - 5712 * q^36 + 6400 * q^40 + 1456 * q^41 + 1920 * q^44 + 6120 * q^45 + 7040 * q^46 - 8008 * q^49 - 12480 * q^50 - 11520 * q^54 - 14720 * q^56 + 21120 * q^60 + 6576 * q^61 + 6912 * q^64 - 1920 * q^65 + 46080 * q^66 - 12480 * q^69 - 6400 * q^70 - 23616 * q^74 - 48000 * q^76 + 19520 * q^80 - 19512 * q^81 + 24960 * q^84 + 8960 * q^85 + 37120 * q^86 + 27664 * q^89 - 48480 * q^90 + 10880 * q^94 - 76800 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.35563	+	3.76328i	0.338907	+	0.940820i
$2$	1.35563	+	3.76328i	0.338907	+	0.940820i
$3$	−13.9962			−1.55514			−0.777569	−	0.628798i	$-0.783547\pi$
$3$	−13.9962			−1.55514			−0.777569	+	0.628798i	$0.783547\pi$
$4$	−12.3246	+	10.2032i	−0.770285	+	0.637700i
$5$	7.64911	+	23.8011i	0.305964	+	0.952043i
$5$	7.64911	+	23.8011i	0.305964	+	0.952043i
$6$	−18.9737	−	52.6718i	−0.527046	−	1.46310i
$7$	35.6863			0.728291			0.364145	−	0.931342i	$-0.381361\pi$
$7$	35.6863			0.728291			0.364145	+	0.931342i	$0.381361\pi$
$8$	−55.1050	−	32.5490i	−0.861016	−	0.508579i
$9$	114.895			1.41845
$10$	−79.2008	+	61.0511i	−0.792008	+	0.610511i
$11$			169.874i			1.40392i	0.712217	+	0.701960i	$0.247691\pi$
$11$			169.874i			1.40392i	−0.712217	+	0.701960i	$0.752309\pi$
$12$	172.497	−	142.806i	1.19790	−	0.991711i
$13$		−	72.8228i		−	0.430904i	−0.976514	−	0.215452i	$-0.930877\pi$
$13$		−	72.8228i		−	0.430904i	0.976514	−	0.215452i	$-0.0691225\pi$
$14$	48.3772	+	134.297i	0.246823	+	0.685191i
$15$	−107.059	−	333.125i	−0.475817	−	1.48056i
$16$	47.7893	−	251.500i	0.186677	−	0.982421i
$17$			25.2207i			0.0872688i	0.999048	+	0.0436344i	$0.0138937\pi$
$17$			25.2207i			0.0872688i	−0.999048	+	0.0436344i	$0.986106\pi$
$18$	155.754	+	432.381i	0.480723	+	1.33451i
$19$			156.628i			0.433873i	0.976186	+	0.216937i	$0.0696065\pi$
$19$			156.628i			0.433873i	−0.976186	+	0.216937i	$0.930394\pi$
$20$	−337.119	−	215.292i	−0.842798	−	0.538231i
$21$	−499.473			−1.13259
$22$	−639.284	+	230.286i	−1.32084	+	0.475797i
$23$	420.541			0.794974			0.397487	−	0.917608i	$-0.369882\pi$
$23$	420.541			0.794974			0.397487	+	0.917608i	$0.369882\pi$
$24$	771.263	+	455.564i	1.33900	+	0.790910i
$25$	−507.982	+	364.114i	−0.812772	+	0.582583i
$26$	274.053	−	98.7205i	0.405403	−	0.146036i
$27$	−474.398			−0.650751
$28$	−439.817	+	364.114i	−0.560991	+	0.464431i
$29$	439.193			0.522227			0.261113	−	0.965308i	$-0.415910\pi$
$29$	439.193			0.522227			0.261113	+	0.965308i	$0.415910\pi$
$30$	1108.51	−	854.486i	1.23168	−	0.949429i
$31$		−	1006.00i		−	1.04683i	−0.852079	−	0.523413i	$-0.824659\pi$
$31$		−	1006.00i		−	1.04683i	0.852079	−	0.523413i	$-0.175341\pi$
$32$	1011.25	−	161.095i	0.987548	−	0.157319i
$33$		−	2377.60i		−	2.18329i
$34$	−94.9125	+	34.1898i	−0.0821042	+	0.0295760i
$35$	272.968	+	849.371i	0.222831	+	0.693364i
$36$	−1416.03	+	1172.29i	−1.09261	+	0.904547i
$37$			1722.19i			1.25799i	0.777407	+	0.628997i	$0.216534\pi$
$37$			1722.19i			1.25799i	−0.777407	+	0.628997i	$0.783466\pi$
$38$	−589.436	+	212.329i	−0.408197	+	0.147042i
$39$			1019.25i			0.670115i
$40$	353.198	−	1560.53i	0.220748	−	0.975331i
$41$	2180.56			1.29718			0.648590	−	0.761138i	$-0.275359\pi$
$41$	2180.56			1.29718			0.648590	+	0.761138i	$0.275359\pi$
$42$	−677.099	−	1879.66i	−0.383843	−	1.06557i
$43$	180.311			0.0975180			0.0487590	−	0.998811i	$-0.484473\pi$
$43$	180.311			0.0975180			0.0487590	+	0.998811i	$0.484473\pi$
$44$	−1733.26	−	2093.62i	−0.895280	−	1.08142i
$45$	878.842	+	2734.62i	0.433996	+	1.35043i
$46$	570.097	+	1582.61i	0.269422	+	0.747928i
$47$	270.757			0.122570			0.0612849	−	0.998120i	$-0.480480\pi$
$47$	270.757			0.122570			0.0612849	+	0.998120i	$0.480480\pi$
$48$	−668.871	+	3520.05i	−0.290308	+	1.52780i
$49$	−1127.49			−0.469592
$50$	−2058.90	−	1418.08i	−0.823559	−	0.567231i
$51$		−	352.995i		−	0.135715i
$52$	743.026	+	897.509i	0.274788	+	0.331919i
$53$		−	924.647i		−	0.329173i	−0.986363	−	0.164587i	$-0.947371\pi$
$53$		−	924.647i		−	0.329173i	0.986363	−	0.164587i	$-0.0526290\pi$
$54$	−643.106	−	1785.29i	−0.220544	−	0.612240i
$55$	−4043.19	+	1299.39i	−1.33659	+	0.429549i
$56$	−1966.49	−	1161.55i	−0.627070	−	0.370393i
$57$		−	2192.21i		−	0.674732i
$58$	595.381	+	1652.81i	0.176986	+	0.491322i
$59$		−	4127.64i		−	1.18576i	−0.805290	−	0.592882i	$-0.797990\pi$
$59$		−	4127.64i		−	1.18576i	0.805290	−	0.592882i	$-0.202010\pi$
$60$	4718.40	+	3013.28i	1.31067	+	0.837023i
$61$	−2492.07			−0.669730			−0.334865	−	0.942266i	$-0.608691\pi$
$61$	−2492.07			−0.669730			−0.334865	+	0.942266i	$0.608691\pi$
$62$	3785.86	−	1363.76i	0.984875	−	0.354776i
$63$	4100.16			1.03305
$64$	1977.12	+	3587.23i	0.482696	+	0.875788i
$65$	1733.26	−	557.030i	0.410239	−	0.131841i
$66$	8947.58	−	3223.14i	2.05408	−	0.739930i
$67$	860.976			0.191797			0.0958984	−	0.995391i	$-0.469428\pi$
$67$	860.976			0.191797			0.0958984	+	0.995391i	$0.469428\pi$
$68$	−257.332	−	310.834i	−0.0556513	−	0.0672218i
$69$	−5886.00			−1.23629
$70$	−2826.38	+	2178.69i	−0.576812	+	0.444630i
$71$			8034.75i			1.59388i	0.604058	+	0.796940i	$0.293549\pi$
$71$			8034.75i			1.59388i	−0.604058	+	0.796940i	$0.706451\pi$
$72$	−6331.27	−	3739.71i	−1.22131	−	0.721395i
$73$		−	5770.88i		−	1.08292i	−0.840726	−	0.541460i	$-0.817872\pi$
$73$		−	5770.88i		−	1.08292i	0.840726	−	0.541460i	$-0.182128\pi$
$74$	−6481.10	+	2334.65i	−1.18355	+	0.426343i
$75$	7109.84	−	5096.23i	1.26397	−	0.905996i
$76$	−1598.11	−	1930.37i	−0.276681	−	0.334206i
$77$			6062.18i			1.02246i
$78$	−3835.71	+	1381.72i	−0.630458	+	0.227106i
$79$		−	4403.48i		−	0.705574i	−0.935704	−	0.352787i	$-0.885234\pi$
$79$		−	4403.48i		−	0.705574i	0.935704	−	0.352787i	$-0.114766\pi$
$80$	6351.51	−	786.313i	0.992424	−	0.122861i
$81$	−2666.68			−0.406445
$82$	2956.02	+	8206.06i	0.439623	+	1.22041i
$83$	−10436.9			−1.51500			−0.757501	−	0.652834i	$-0.773580\pi$
$83$	−10436.9			−1.51500			−0.757501	+	0.652834i	$0.773580\pi$
$84$	6155.79	−	5096.23i	0.872419	−	0.722254i
$85$	−600.279	+	192.916i	−0.0830836	+	0.0267011i
$86$	244.434	+	678.560i	0.0330495	+	0.0917469i
$87$	−6147.05			−0.812135
$88$	5529.24	−	9360.92i	0.714003	−	1.20880i
$89$	12059.4			1.52246			0.761229	−	0.648483i	$-0.224596\pi$
$89$	12059.4			1.52246			0.761229	+	0.648483i	$0.224596\pi$
$90$	−9099.75	+	7014.45i	−1.12343	+	0.865981i
$91$		−	2598.77i		−	0.313824i
$92$	−5182.98	+	4290.87i	−0.612356	+	0.506955i
$93$			14080.2i			1.62796i
$94$	367.045	+	1018.93i	0.0415397	+	0.115316i
$95$	−3727.92	+	1198.07i	−0.413066	+	0.132750i
$96$	−14153.7	+	2254.73i	−1.53577	+	0.244653i
$97$		−	8152.32i		−	0.866439i	−0.901289	−	0.433219i	$-0.857378\pi$
$97$		−	8152.32i		−	0.866439i	0.901289	−	0.433219i	$-0.142622\pi$
$98$	−1528.46	−	4243.06i	−0.159148	−	0.441802i
$99$			19517.6i			1.99139i
$100$	2545.53	−	9670.59i	0.254553	−	0.967059i
$101$	11821.9			1.15890			0.579449	−	0.815008i	$-0.303268\pi$
$101$	11821.9			1.15890			0.579449	+	0.815008i	$0.303268\pi$
$102$	1328.42	−	478.529i	0.127683	−	0.0459947i
$103$	14786.7			1.39379			0.696896	−	0.717172i	$-0.254564\pi$
$103$	14786.7			1.39379			0.696896	+	0.717172i	$0.254564\pi$
$104$	−2370.31	+	4012.90i	−0.219149	+	0.371015i
$105$	−3820.53	−	11888.0i	−0.346533	−	1.07828i
$106$	3479.71	−	1253.48i	0.309693	−	0.111559i
$107$	10294.8			0.899184			0.449592	−	0.893234i	$-0.351569\pi$
$107$	10294.8			0.899184			0.449592	+	0.893234i	$0.351569\pi$
$108$	5846.74	−	4840.38i	0.501264	−	0.414984i
$109$	3287.16			0.276673			0.138337	−	0.990385i	$-0.455824\pi$
$109$	3287.16			0.276673			0.138337	+	0.990385i	$0.455824\pi$
$110$	−10371.0	−	13454.2i	−0.857108	−	1.11192i
$111$		−	24104.2i		−	1.95635i
$112$	1705.42	−	8975.09i	0.135955	−	0.715489i
$113$			16522.8i			1.29398i	0.762500	+	0.646988i	$0.223972\pi$
$113$			16522.8i			1.29398i	−0.762500	+	0.646988i	$0.776028\pi$
$114$	8249.88	−	2971.81i	0.634802	−	0.228671i
$115$	3216.77	+	10009.3i	0.243234	+	0.756849i
$116$	−5412.86	+	4481.17i	−0.402263	+	0.333024i
$117$		−	8366.95i		−	0.611217i
$118$	15533.5	−	5595.54i	1.11559	−	0.401863i
$119$			900.031i			0.0635570i
$120$	−4943.44	+	21841.5i	−0.343294	+	1.51677i
$121$	−14216.3			−0.970990
$122$	−3378.31	−	9378.35i	−0.226976	−	0.630096i
$123$	−30519.6			−2.01729
$124$	10264.4	+	12398.5i	0.667561	+	0.806354i
$125$	−12551.9	−	9305.37i	−0.803323	−	0.595544i
$126$	5558.28	+	15430.1i	0.350106	+	0.971911i
$127$	173.676			0.0107680			0.00538398	−	0.999986i	$-0.498286\pi$
$127$	173.676			0.0107680			0.00538398	+	0.999986i	$0.498286\pi$
$128$	−10819.5	+	12303.4i	−0.660370	+	0.750940i
$129$	−2523.67			−0.151654
$130$	4445.91	+	5767.62i	0.263072	+	0.341280i
$131$			6607.20i			0.385013i	0.981296	+	0.192506i	$0.0616616\pi$
$131$			6607.20i			0.385013i	−0.981296	+	0.192506i	$0.938338\pi$
$132$	24259.1	+	29302.9i	1.39228	+	1.68175i
$133$			5589.48i			0.315986i
$134$	1167.16	+	3240.09i	0.0650012	+	0.180446i
$135$	−3628.72	−	11291.2i	−0.199107	−	0.619543i
$136$	820.908	−	1389.79i	0.0443830	−	0.0751398i
$137$		−	1214.94i		−	0.0647313i	−0.999476	−	0.0323657i	$-0.989696\pi$
$137$		−	1214.94i		−	0.0647313i	0.999476	−	0.0323657i	$-0.0103041\pi$
$138$	−7979.21	−	22150.7i	−0.418988	−	1.16313i
$139$		−	20056.1i		−	1.03805i	−0.854760	−	0.519023i	$-0.826296\pi$
$139$		−	20056.1i		−	1.03805i	0.854760	−	0.519023i	$-0.173704\pi$
$140$	−12030.5	−	7682.97i	−0.613802	−	0.391988i
$141$	−3789.57			−0.190613
$142$	−30237.0	+	10892.1i	−1.49955	+	0.540176i
$143$	12370.7			0.604955
$144$	5490.74	−	28896.0i	0.264793	−	1.39352i
$145$	3359.43	+	10453.3i	0.159783	+	0.497183i
$146$	21717.5	−	7823.16i	1.01883	−	0.367009i
$147$	15780.6			0.730281
$148$	−17571.9	−	21225.3i	−0.802223	−	0.969014i
$149$	−23237.3			−1.04668			−0.523340	−	0.852124i	$-0.675314\pi$
$149$	−23237.3			−1.04668			−0.523340	+	0.852124i	$0.675314\pi$
$150$	28816.8	+	19847.7i	1.28075	+	0.882122i
$151$			26681.2i			1.17018i	0.810970	+	0.585088i	$0.198940\pi$
$151$			26681.2i			1.17018i	−0.810970	+	0.585088i	$0.801060\pi$
$152$	5098.10	−	8631.00i	0.220659	−	0.373572i
$153$			2897.72i			0.123787i
$154$	−22813.7	+	8218.04i	−0.961953	+	0.346519i
$155$	23943.9	−	7695.00i	0.996623	−	0.320291i
$156$	−10399.6	−	12561.7i	−0.427333	−	0.516180i
$157$		−	12500.0i		−	0.507119i	−0.967320	−	0.253559i	$-0.918399\pi$
$157$		−	12500.0i		−	0.507119i	0.967320	−	0.253559i	$-0.0816013\pi$
$158$	16571.5	−	5969.48i	0.663818	−	0.239123i
$159$			12941.6i			0.511909i
$160$	11569.4	+	22836.6i	0.451929	+	0.892054i
$161$	15007.5			0.578972
$162$	−3615.03	−	10035.5i	−0.137747	−	0.382391i
$163$	−7089.40			−0.266830			−0.133415	−	0.991060i	$-0.542594\pi$
$163$	−7089.40			−0.266830			−0.133415	+	0.991060i	$0.542594\pi$
$164$	−26874.4	+	22248.7i	−0.999198	+	0.827212i
$165$	56589.4	−	18186.5i	2.07858	−	0.668008i
$166$	−14148.5	−	39276.8i	−0.513444	−	1.42534i
$167$	−41999.3			−1.50595			−0.752973	−	0.658052i	$-0.771381\pi$
$167$	−41999.3			−1.50595			−0.752973	+	0.658052i	$0.771381\pi$
$168$	27523.5	+	16257.4i	0.975180	+	0.576012i
$169$	23257.8			0.814322
$170$	−1539.75	−	1997.50i	−0.0532785	−	0.0691175i
$171$			17995.7i			0.615429i
$172$	−2222.25	+	1839.75i	−0.0751166	+	0.0621873i
$173$		−	25302.8i		−	0.845427i	−0.906263	−	0.422713i	$-0.861078\pi$
$173$		−	25302.8i		−	0.845427i	0.906263	−	0.422713i	$-0.138922\pi$
$174$	−8333.10	−	23133.1i	−0.275238	−	0.764073i
$175$	−18128.0	+	12993.9i	−0.591934	+	0.424290i
$176$	42723.3	+	8118.18i	1.37924	+	0.262080i
$177$			57771.5i			1.84402i
$178$	16348.0	+	45382.9i	0.515971	+	1.43236i
$179$		−	49260.5i		−	1.53742i	−0.639597	−	0.768711i	$-0.720899\pi$
$179$		−	49260.5i		−	1.53742i	0.639597	−	0.768711i	$-0.279101\pi$
$180$	−38733.2	−	24735.9i	−1.19547	−	0.763455i
$181$	9032.02			0.275694			0.137847	−	0.990454i	$-0.455982\pi$
$181$	9032.02			0.275694			0.137847	+	0.990454i	$0.455982\pi$
$182$	9779.91	−	3522.97i	0.295252	−	0.106357i
$183$	34879.6			1.04152
$184$	−23173.9	−	13688.2i	−0.684485	−	0.404307i
$185$	−40990.1	+	13173.3i	−1.19767	+	0.384902i
$186$	−52987.8	+	19087.5i	−1.53162	+	0.551726i
$187$	−4284.34			−0.122518
$188$	−3336.96	+	2762.58i	−0.0944136	+	0.0781628i
$189$	−16929.5			−0.473936
$190$	−9562.33	−	12405.1i	−0.264884	−	0.343631i
$191$			19872.3i			0.544729i	0.962194	+	0.272365i	$0.0878057\pi$
$191$			19872.3i			0.544729i	−0.962194	+	0.272365i	$0.912194\pi$
$192$	−27672.3	−	50207.7i	−0.750658	−	1.36197i
$193$			21521.0i			0.577761i	0.957365	+	0.288881i	$0.0932831\pi$
$193$			21521.0i			0.577761i	−0.957365	+	0.288881i	$0.906717\pi$
$194$	30679.5	−	11051.5i	0.815163	−	0.293642i
$195$	−24259.1	+	7796.32i	−0.637979	+	0.205031i
$196$	13895.8	−	11504.0i	0.361720	−	0.299459i
$197$		−	24859.0i		−	0.640548i	−0.947325	−	0.320274i	$-0.896225\pi$
$197$		−	24859.0i		−	0.640548i	0.947325	−	0.320274i	$-0.103775\pi$
$198$	−73450.4	+	26458.6i	−1.87354	+	0.674896i
$199$			3798.82i			0.0959273i	0.998849	+	0.0479636i	$0.0152732\pi$
$199$			3798.82i			0.0959273i	−0.998849	+	0.0479636i	$0.984727\pi$
$200$	39843.9	−	3530.18i	0.996098	−	0.0882545i
$201$	−12050.4			−0.298270
$202$	16026.1	+	44489.2i	0.392758	+	1.09031i
$203$	15673.1			0.380333
$204$	3601.67	+	4350.50i	0.0865454	+	0.104539i
$205$	16679.3	+	51899.7i	0.396891	+	1.23497i
$206$	20045.3	+	55646.7i	0.472365	+	1.31131i
$207$	48318.0			1.12763
$208$	−18314.9	−	3480.15i	−0.423330	−	0.0804399i
$209$	−26607.1			−0.609123
$210$	39558.7	−	30493.4i	0.897022	−	0.691460i
$211$		−	79511.4i		−	1.78593i	−0.450127	−	0.892965i	$-0.648621\pi$
$211$		−	79511.4i		−	1.78593i	0.450127	−	0.892965i	$-0.351379\pi$
$212$	9434.36	+	11395.9i	0.209914	+	0.253557i
$213$		−	112456.i		−	2.47870i
$214$	13955.8	+	38742.0i	0.304739	+	0.845970i
$215$	1379.22	+	4291.59i	0.0298370	+	0.0928413i
$216$	26141.7	+	15441.2i	0.560307	+	0.330958i
$217$		−	35900.4i		−	0.762394i
$218$	4456.15	+	12370.5i	0.0937664	+	0.260300i
$219$			80770.7i			1.68409i
$220$	36572.6	−	57267.8i	0.755632	−	1.18322i
$221$	1836.64			0.0376045
$222$	90711.0	−	32676.4i	1.84058	−	0.663021i
$223$	−69331.1			−1.39418			−0.697089	−	0.716984i	$-0.745522\pi$
$223$	−69331.1			−1.39418			−0.697089	+	0.716984i	$0.745522\pi$
$224$	36087.7	−	5748.88i	0.719222	−	0.114574i
$225$	−58364.4	+	41834.8i	−1.15288	+	0.826366i
$226$	−62179.8	+	22398.7i	−1.21740	+	0.438537i
$227$	−2285.09			−0.0443457			−0.0221728	−	0.999754i	$-0.507058\pi$
$227$	−2285.09			−0.0443457			−0.0221728	+	0.999754i	$0.507058\pi$
$228$	22367.5	+	27018.0i	0.430277	+	0.519736i
$229$	−6778.53			−0.129260			−0.0646300	−	0.997909i	$-0.520587\pi$
$229$	−6778.53			−0.129260			−0.0646300	+	0.997909i	$0.520587\pi$
$230$	−33307.2	+	25674.5i	−0.629626	+	0.485340i
$231$		−	84847.7i		−	1.59007i
$232$	−24201.7	−	14295.3i	−0.449646	−	0.265593i
$233$		−	61958.1i		−	1.14126i	−0.821206	−	0.570632i	$-0.806698\pi$
$233$		−	61958.1i		−	1.14126i	0.821206	−	0.570632i	$-0.193302\pi$
$234$	31487.2	−	11342.5i	0.575045	−	0.207146i
$235$	2071.05	+	6444.30i	0.0375020	+	0.116692i
$236$	42115.2	+	50871.4i	0.756161	+	0.913375i
$237$			61632.2i			1.09726i
$238$	−3387.07	+	1220.11i	−0.0597957	+	0.0215399i
$239$		−	6610.22i		−	0.115723i	−0.998325	−	0.0578616i	$-0.981572\pi$
$239$		−	6610.22i		−	0.115723i	0.998325	−	0.0578616i	$-0.0184282\pi$
$240$	−88897.3	+	11005.4i	−1.54336	+	0.191066i
$241$	−31573.2			−0.543607			−0.271804	−	0.962353i	$-0.587620\pi$
$241$	−31573.2			−0.543607			−0.271804	+	0.962353i	$0.587620\pi$
$242$	−19271.9	−	53499.8i	−0.329075	−	0.913526i
$243$	75749.8			1.28283
$244$	30713.6	−	25427.1i	0.515883	−	0.427087i
$245$	−8624.30	−	26835.5i	−0.143679	−	0.447072i
$246$	−41373.2	−	114854.i	−0.683674	−	1.89791i
$247$	11406.1			0.186958
$248$	−32744.3	+	55435.6i	−0.532393	+	0.901333i
$249$	146077.			2.35604
$250$	18003.0	−	59851.0i	0.288048	−	0.957616i
$251$			61014.6i			0.968470i	0.874938	+	0.484235i	$0.160902\pi$
$251$			61014.6i			0.968470i	−0.874938	+	0.484235i	$0.839098\pi$
$252$	−50532.7	+	41834.8i	−0.795740	+	0.658774i
$253$			71439.1i			1.11608i
$254$	235.440	+	653.593i	0.00364933	+	0.0101307i
$255$	8401.65	−	2700.09i	0.129206	−	0.0415239i
$256$	−60968.4	−	24038.0i	−0.930303	−	0.366791i
$257$			85038.5i			1.28751i	0.765234	+	0.643753i	$0.222623\pi$
$257$			85038.5i			1.28751i	−0.765234	+	0.643753i	$0.777377\pi$
$258$	−3421.16	−	9497.29i	−0.0513965	−	0.142679i
$259$			61458.7i			0.916186i
$260$	−15678.2	+	24550.0i	−0.231926	+	0.363165i
$261$	50460.9			0.740754
$262$	−24864.8	+	8956.90i	−0.362228	+	0.130483i
$263$	20477.3			0.296047			0.148024	−	0.988984i	$-0.452709\pi$
$263$	20477.3			0.296047			0.148024	+	0.988984i	$0.452709\pi$
$264$	−77388.6	+	131018.i	−1.11037	+	1.87984i
$265$	22007.6	−	7072.73i	0.313387	−	0.100715i
$266$	−21034.8	+	7577.24i	−0.297286	+	0.107090i
$267$	−168786.			−2.36763
$268$	−10611.1	+	8784.71i	−0.147738	+	0.122309i
$269$	−52590.6			−0.726781			−0.363390	−	0.931637i	$-0.618381\pi$
$269$	−52590.6			−0.726781			−0.363390	+	0.931637i	$0.618381\pi$
$270$	37572.7	−	28962.5i	0.515400	−	0.397291i
$271$			82607.9i			1.12482i	0.826858	+	0.562410i	$0.190126\pi$
$271$			82607.9i			1.12482i	−0.826858	+	0.562410i	$0.809874\pi$
$272$	6343.00	+	1205.28i	0.0857347	+	0.0162911i
$273$			36373.1i			0.488039i
$274$	4572.17	−	1647.01i	0.0609005	−	0.0219379i
$275$	−61853.6	−	86293.1i	−0.817899	−	1.14107i
$276$	72542.3	−	60056.0i	0.952298	−	0.788385i
$277$		−	99718.7i		−	1.29962i	−0.760096	−	0.649811i	$-0.774848\pi$
$277$		−	99718.7i		−	1.29962i	0.760096	−	0.649811i	$-0.225152\pi$
$278$	75476.7	−	27188.6i	0.976614	−	0.351801i
$279$		−	115584.i		−	1.48487i
$280$	12604.3	−	55689.4i	0.160769	−	0.710325i
$281$	−30209.8			−0.382591			−0.191296	−	0.981532i	$-0.561269\pi$
$281$	−30209.8			−0.382591			−0.191296	+	0.981532i	$0.561269\pi$
$282$	−5137.25	−	14261.2i	−0.0645999	−	0.179332i
$283$	49151.0			0.613705			0.306853	−	0.951757i	$-0.400724\pi$
$283$	49151.0			0.613705			0.306853	+	0.951757i	$0.400724\pi$
$284$	−81980.2	−	99024.7i	−1.01642	−	1.22774i
$285$	52176.9	−	16768.4i	0.642374	−	0.206444i
$286$	16770.1	+	46554.5i	0.205023	+	0.569154i
$287$	77816.0			0.944724
$288$	116187.	−	18509.0i	1.40079	−	0.223150i
$289$	82884.9			0.992384
$290$	−34784.4	+	26813.2i	−0.413608	+	0.318825i
$291$			114102.i			1.34743i
$292$	58881.5	+	71123.6i	0.690579	+	0.834157i
$293$			18975.5i			0.221033i	0.993874	+	0.110517i	$0.0352506\pi$
$293$			18975.5i			0.221033i	−0.993874	+	0.110517i	$0.964749\pi$
$294$	21392.6	+	59386.9i	0.247497	+	0.687063i
$295$	98242.3	−	31572.8i	1.12890	−	0.362801i
$296$	56055.8	−	94901.5i	0.639789	−	1.08315i
$297$		−	80588.0i		−	0.913602i
$298$	−31501.1	−	87448.6i	−0.354727	−	0.984737i
$299$		−	30625.0i		−	0.342558i
$300$	−35627.8	+	135352.i	−0.395864	+	1.50391i
$301$	6434.62			0.0710215
$302$	−100409.	+	36169.7i	−1.10092	+	0.396580i
$303$	−165462.			−1.80225
$304$	39392.0	+	7485.16i	0.426246	+	0.0809942i
$305$	−19062.1	−	59313.9i	−0.204914	−	0.637612i
$306$	−10904.9	+	3928.23i	−0.116461	+	0.0419521i
$307$	156013.			1.65533			0.827663	−	0.561226i	$-0.189670\pi$
$307$	156013.			1.65533			0.827663	+	0.561226i	$0.189670\pi$
$308$	−61853.6	−	74713.6i	−0.652024	−	0.787587i
$309$	−206959.			−2.16754
$310$	61417.4	+	79675.9i	0.639099	+	0.829094i
$311$		−	35745.2i		−	0.369570i	−0.982779	−	0.184785i	$-0.940841\pi$
$311$		−	35745.2i		−	0.369570i	0.982779	−	0.184785i	$-0.0591589\pi$
$312$	33175.4	−	56165.5i	0.340806	−	0.576980i
$313$		−	38787.7i		−	0.395918i	−0.980210	−	0.197959i	$-0.936569\pi$
$313$		−	38787.7i		−	0.395918i	0.980210	−	0.197959i	$-0.0634312\pi$
$314$	47040.9	−	16945.3i	0.477108	−	0.171866i
$315$	31362.6	+	97588.2i	0.316075	+	0.983504i
$316$	44929.6	+	54271.0i	0.449944	+	0.543492i
$317$			146826.i			1.46112i	0.682851	+	0.730558i	$0.260740\pi$
$317$			146826.i			1.46112i	−0.682851	+	0.730558i	$0.739260\pi$
$318$	−48702.8	+	17543.9i	−0.481615	+	0.173489i
$319$			74607.6i			0.733165i
$320$	−70256.7	+	74496.7i	−0.686100	+	0.727507i
$321$	−144088.			−1.39835
$322$	20344.6	+	56477.6i	0.196218	+	0.544709i
$323$	−3950.27			−0.0378636
$324$	32865.7	−	27208.7i	0.313078	−	0.259190i
$325$	26515.8	+	36992.7i	0.251037	+	0.350227i
$326$	−9610.58	−	26679.4i	−0.0904304	−	0.251039i
$327$	−46007.8			−0.430265
$328$	−120160.	−	70975.1i	−1.11689	−	0.659718i
$329$	9662.29			0.0892665
$330$	145155.	+	188308.i	1.33292	+	1.72918i
$331$		−	182164.i		−	1.66267i	−0.555772	−	0.831335i	$-0.687577\pi$
$331$		−	182164.i		−	1.66267i	0.555772	−	0.831335i	$-0.312423\pi$
$332$	128630.	−	106489.i	1.16698	−	0.966117i
$333$			197871.i			1.78441i
$334$	−56935.4	−	158055.i	−0.510375	−	1.41682i
$335$	6585.70	+	20492.2i	0.0586830	+	0.182599i
$336$	−23869.5	+	125617.i	−0.211429	+	1.11268i
$337$		−	203482.i		−	1.79171i	−0.444351	−	0.895853i	$-0.646566\pi$
$337$		−	203482.i		−	1.79171i	0.444351	−	0.895853i	$-0.353434\pi$
$338$	31528.9	+	87525.8i	0.275979	+	0.766130i
$339$		−	231257.i		−	2.01231i
$340$	5429.81	−	8502.37i	0.0469707	−	0.0735499i
$341$	170893.			1.46966
$342$	−67723.0	+	24395.5i	−0.579008	+	0.208573i
$343$	−125919.			−1.07029
$344$	−9936.03	−	5868.94i	−0.0839645	−	0.0495956i
$345$	−45022.6	−	140093.i	−0.378262	−	1.17701i
$346$	95221.4	−	34301.1i	0.795394	−	0.286521i
$347$	−54497.1			−0.452600			−0.226300	−	0.974058i	$-0.572663\pi$
$347$	−54497.1			−0.452600			−0.226300	+	0.974058i	$0.572663\pi$
$348$	75759.6	−	62719.6i	0.625575	−	0.517898i
$349$	−228908.			−1.87936			−0.939679	−	0.342057i	$-0.888876\pi$
$349$	−228908.			−1.87936			−0.939679	+	0.342057i	$0.888876\pi$
$350$	−73474.3	−	50605.9i	−0.599791	−	0.413109i
$351$			34547.0i			0.280412i
$352$	27365.9	+	171785.i	0.220864	+	1.38644i
$353$			82322.3i			0.660645i	0.943868	+	0.330322i	$0.107157\pi$
$353$			82322.3i			0.660645i	−0.943868	+	0.330322i	$0.892843\pi$
$354$	−217410.	+	78316.5i	−1.73490	+	0.624952i
$355$	−191236.	+	61458.7i	−1.51744	+	0.487671i
$356$	−148627.	+	123044.i	−1.17273	+	0.970872i
$357$		−	12597.1i		−	0.0988399i
$358$	185381.	−	66778.8i	1.44644	−	0.521042i
$359$			231846.i			1.79891i	0.437011	+	0.899456i	$0.356037\pi$
$359$			231846.i			1.79891i	−0.437011	+	0.899456i	$0.643963\pi$
$360$	40580.5	−	179296.i	0.313121	−	1.38346i
$361$	105789.			0.811754
$362$	12244.0	+	33990.0i	0.0934346	+	0.259379i
$363$	198974.			1.51002
$364$	26515.8	+	32028.7i	0.200125	+	0.241734i
$365$	137353.	−	44142.1i	1.03099	−	0.331335i
$366$	47283.6	+	131262.i	0.352979	+	0.979886i
$367$	111878.			0.830642			0.415321	−	0.909675i	$-0.363669\pi$
$367$	111878.			0.830642			0.415321	+	0.909675i	$0.363669\pi$
$368$	20097.4	−	105766.i	0.148403	−	0.781000i
$369$	250535.			1.83999
$370$	−105142.	−	136399.i	−0.768020	−	0.996342i
$371$		−	32997.2i		−	0.239734i
$372$	−143663.	−	173532.i	−1.03815	−	1.25399i
$373$			173753.i			1.24886i	0.781081	+	0.624430i	$0.214669\pi$
$373$			173753.i			1.24886i	−0.781081	+	0.624430i	$0.785331\pi$
$374$	−5807.97	−	16123.2i	−0.0415223	−	0.115268i
$375$	175680.	+	130240.i	1.24928	+	0.926153i
$376$	−14920.0	−	8812.87i	−0.105534	−	0.0623364i
$377$		−	31983.3i		−	0.225030i
$378$	−22950.0	−	63710.4i	−0.160620	−	0.445889i
$379$		−	16251.9i		−	0.113143i	−0.998399	−	0.0565713i	$-0.981983\pi$
$379$		−	16251.9i		−	0.113143i	0.998399	−	0.0565713i	$-0.0180168\pi$
$380$	33720.8	−	52802.4i	0.233524	−	0.365667i
$381$	−2430.82			−0.0167457
$382$	−74784.9	+	26939.4i	−0.512492	+	0.184612i
$383$	−36303.7			−0.247488			−0.123744	−	0.992314i	$-0.539490\pi$
$383$	−36303.7			−0.247488			−0.123744	+	0.992314i	$0.539490\pi$
$384$	151432.	−	172201.i	1.02697	−	1.16782i
$385$	−144286.	+	46370.3i	−0.973428	+	0.312837i
$386$	−80989.7	+	29174.5i	−0.543570	+	0.195807i
$387$	20716.7			0.138325
$388$	83179.8	+	100474.i	0.552528	+	0.667404i
$389$	159787.			1.05595			0.527975	−	0.849260i	$-0.322952\pi$
$389$	159787.			1.05595			0.527975	+	0.849260i	$0.322952\pi$
$390$	−62226.1	−	80725.0i	−0.409113	−	0.530737i
$391$			10606.3i			0.0693764i
$392$	62130.4	+	36698.7i	0.404326	+	0.238825i
$393$		−	92476.0i		−	0.598748i
$394$	93551.6	−	33699.6i	0.602641	−	0.217086i
$395$	104808.	−	33682.7i	0.671736	−	0.215880i
$396$	−199142.	−	240546.i	−1.26991	−	1.53394i
$397$			17478.7i			0.110899i	0.998461	+	0.0554495i	$0.0176592\pi$
$397$			17478.7i			0.110899i	−0.998461	+	0.0554495i	$0.982341\pi$
$398$	−14296.0	+	5149.77i	−0.0902503	+	0.0325104i
$399$		−	78231.6i		−	0.491402i
$400$	67298.5	+	145158.i	0.420616	+	0.907239i
$401$	62408.0			0.388107			0.194054	−	0.980991i	$-0.437836\pi$
$401$	62408.0			0.388107			0.194054	+	0.980991i	$0.437836\pi$
$402$	−16335.9	−	45349.1i	−0.101086	−	0.280619i
$403$	−73259.7			−0.451082
$404$	−145700.	+	120621.i	−0.892682	+	0.739030i
$405$	−20397.8	−	63469.9i	−0.124358	−	0.386953i
$406$	21246.9	+	58982.5i	0.128897	+	0.357825i
$407$	−292557.			−1.76612
$408$	−11489.6	+	19451.8i	−0.0690217	+	0.116853i
$409$	11617.5			0.0694492			0.0347246	−	0.999397i	$-0.488945\pi$
$409$	11617.5			0.0694492			0.0347246	+	0.999397i	$0.488945\pi$
$410$	−172702.	+	133126.i	−1.02738	+	0.791943i
$411$			17004.6i			0.100666i
$412$	−182240.	+	150872.i	−1.07362	+	0.888822i
$413$		−	147300.i		−	0.863581i
$414$	65501.1	+	181834.i	0.382162	+	1.06090i
$415$	−79832.6	−	248408.i	−0.463537	−	1.44235i
$416$	−11731.4	−	73642.0i	−0.0677896	−	0.425539i
$417$			280710.i			1.61430i
$418$	−36069.3	−	100130.i	−0.206436	−	0.573075i
$419$			321005.i			1.82845i	0.405201	+	0.914227i	$0.367201\pi$
$419$			321005.i			1.82845i	−0.405201	+	0.914227i	$0.632799\pi$
$420$	168382.	+	107533.i	0.954546	+	0.609596i
$421$	−266760.			−1.50507			−0.752535	−	0.658552i	$-0.771169\pi$
$421$	−266760.			−1.50507			−0.752535	+	0.658552i	$0.771169\pi$
$422$	299224.	−	107788.i	1.68024	−	0.605263i
$423$	31108.5			0.173859
$424$	−30096.4	+	50952.7i	−0.167410	+	0.283423i
$425$	−9183.20	−	12811.7i	−0.0508413	−	0.0709296i
$426$	423204.	−	152449.i	2.33201	−	0.840049i
$427$	−88932.5			−0.487759
$428$	−126878.	+	105039.i	−0.692627	+	0.573409i
$429$	−173144.			−0.940788
$430$	−14280.8	+	11008.2i	−0.0772350	+	0.0595358i
$431$		−	140280.i		−	0.755164i	−0.925976	−	0.377582i	$-0.876756\pi$
$431$		−	140280.i		−	0.755164i	0.925976	−	0.377582i	$-0.123244\pi$
$432$	−22671.2	+	119311.i	−0.121480	+	0.639312i
$433$		−	53202.7i		−	0.283765i	−0.989884	−	0.141882i	$-0.954685\pi$
$433$		−	53202.7i		−	0.283765i	0.989884	−	0.141882i	$-0.0453155\pi$
$434$	135103.	−	48667.5i	0.717275	−	0.258380i
$435$	−47019.4	−	146306.i	−0.248484	−	0.773187i
$436$	−40512.7	+	33539.5i	−0.213117	+	0.176435i
$437$			65868.6i			0.344918i
$438$	−303963.	+	109495.i	−1.58443	+	0.570749i
$439$		−	160420.i		−	0.832397i	−0.909274	−	0.416198i	$-0.863362\pi$
$439$		−	160420.i		−	0.832397i	0.909274	−	0.416198i	$-0.136638\pi$
$440$	265094.	+	59999.2i	1.36929	+	0.309913i
$441$	−129543.			−0.666094
$442$	2489.80	+	6911.79i	0.0127444	+	0.0353790i
$443$	−66393.8			−0.338314			−0.169157	−	0.985589i	$-0.554104\pi$
$443$	−66393.8			−0.338314			−0.169157	+	0.985589i	$0.554104\pi$
$444$	245941.	+	297074.i	1.24757	+	1.50695i
$445$	92243.6	+	287027.i	0.465818	+	1.44945i
$446$	−93987.1	−	260912.i	−0.472496	−	1.31167i
$447$	325235.			1.62773
$448$	70556.1	+	128015.i	0.351543	+	0.637829i
$449$	163836.			0.812675			0.406338	−	0.913723i	$-0.366806\pi$
$449$	163836.			0.812675			0.406338	+	0.913723i	$0.366806\pi$
$450$	−236556.	−	162929.i	−1.16818	−	0.804590i
$451$			370421.i			1.82114i
$452$	−168585.	−	203636.i	−0.825169	−	0.996730i
$453$		−	373436.i		−	1.81978i
$454$	−3097.72	−	8599.42i	−0.0150290	−	0.0417213i
$455$	61853.6	−	19878.3i	0.298774	−	0.0960189i
$456$	−71354.2	+	120802.i	−0.343154	+	0.580955i
$457$		−	320525.i		−	1.53472i	−0.641216	−	0.767361i	$-0.721570\pi$
$457$		−	320525.i		−	1.53472i	0.641216	−	0.767361i	$-0.278430\pi$
$458$	−9189.15	−	25509.5i	−0.0438071	−	0.121610i
$459$		−	11964.6i		−	0.0567903i
$460$	−141772.	−	90539.3i	−0.670002	−	0.427879i
$461$	−190437.			−0.896083			−0.448042	−	0.894013i	$-0.647878\pi$
$461$	−190437.			−0.896083			−0.448042	+	0.894013i	$0.647878\pi$
$462$	319305.	−	115022.i	1.49597	−	0.538885i
$463$	286156.			1.33487			0.667437	−	0.744666i	$-0.267391\pi$
$463$	286156.			1.33487			0.667437	+	0.744666i	$0.267391\pi$
$464$	20988.7	−	110457.i	0.0974878	−	0.513047i
$465$	−335124.	+	107701.i	−1.54989	+	0.498097i
$466$	233166.	−	83992.0i	1.07372	−	0.386782i
$467$	279153.			1.28000			0.639999	−	0.768376i	$-0.278935\pi$
$467$	279153.			1.28000			0.639999	+	0.768376i	$0.278935\pi$
$468$	85369.7	+	103119.i	0.389773	+	0.470811i
$469$	30725.0			0.139684
$470$	−21444.1	+	16530.0i	−0.0970762	+	0.0748302i
$471$			174953.i			0.788640i
$472$	−134351.	+	227454.i	−0.603054	+	1.02096i
$473$			30630.2i			0.136907i
$474$	−231939.	+	83550.2i	−1.03233	+	0.371870i
$475$	−57030.5	−	79564.4i	−0.252767	−	0.352640i
$476$	−9183.20	−	11092.5i	−0.0405303	−	0.0489570i
$477$		−	106237.i		−	0.466916i
$478$	24876.1	−	8960.99i	0.108875	−	0.0392193i
$479$		−	317241.i		−	1.38267i	−0.722534	−	0.691336i	$-0.757023\pi$
$479$		−	317241.i		−	1.38267i	0.722534	−	0.691336i	$-0.242977\pi$
$480$	−161928.	−	319626.i	−0.702812	−	1.38727i
$481$	125415.			0.542075
$482$	−42801.5	−	118819.i	−0.184232	−	0.511436i
$483$	−210049.			−0.900382
$484$	175209.	−	145051.i	0.747938	−	0.619200i
$485$	194034.	−	62358.0i	0.824887	−	0.265099i
$486$	102688.	+	285068.i	0.434759	+	1.20691i
$487$	−268917.			−1.13386			−0.566932	−	0.823765i	$-0.691870\pi$
$487$	−268917.			−1.13386			−0.566932	+	0.823765i	$0.691870\pi$
$488$	137325.	+	81114.4i	0.576648	+	0.340611i
$489$	99225.0			0.414957
$490$	89298.2	−	68834.6i	0.371921	−	0.286691i
$491$		−	133292.i		−	0.552891i	−0.961030	−	0.276446i	$-0.910843\pi$
$491$		−	133292.i		−	0.552891i	0.961030	−	0.276446i	$-0.0891566\pi$
$492$	376141.	−	311398.i	1.55389	−	1.28643i
$493$			11076.7i			0.0455741i
$494$	15462.4	+	42924.4i	0.0633612	+	0.175894i
$495$	−464541.	+	149293.i	−1.89589	+	0.609295i
$496$	−253009.	−	48076.0i	−1.02842	−	0.195418i
$497$			286730.i			1.16081i
$498$	198025.	+	549727.i	0.798477	+	2.21661i
$499$			155684.i			0.625235i	0.949879	+	0.312617i	$0.101206\pi$
$499$			155684.i			0.625235i	−0.949879	+	0.312617i	$0.898794\pi$
$500$	249641.	−	13385.2i	0.998566	−	0.0535407i
$501$	587832.			2.34195
$502$	−229615.	+	82713.0i	−0.911156	+	0.328221i
$503$	300512.			1.18775			0.593875	−	0.804557i	$-0.297597\pi$
$503$	300512.			1.18775			0.593875	+	0.804557i	$0.297597\pi$
$504$	−225939.	−	133456.i	−0.889469	−	0.525385i
$505$	90427.2	+	281374.i	0.354582	+	1.10332i
$506$	−268845.	+	96844.8i	−1.05003	+	0.378247i
$507$	−325522.			−1.26638
$508$	−2140.48	+	1772.06i	−0.00829439	+	0.00686673i
$509$	−178235.			−0.687952			−0.343976	−	0.938978i	$-0.611774\pi$
$509$	−178235.			−0.687952			−0.343976	+	0.938978i	$0.611774\pi$
$510$	21550.7	+	27957.4i	0.0828555	+	0.107487i
$511$		−	205941.i		−	0.788681i
$512$	7811.49	−	262028.i	0.0297985	−	0.999556i
$513$		−	74304.1i		−	0.282344i
$514$	−320024.	+	115280.i	−1.21131	+	0.436344i
$515$	113105.	+	351940.i	0.426451	+	1.32695i
$516$	31103.1	−	25749.5i	0.116817	−	0.0967097i
$517$			45994.6i			0.172078i
$518$	−231286.	+	83315.0i	−0.861966	+	0.310502i
$519$			354144.i			1.31475i
$520$	−113642.	−	25720.8i	−0.420274	−	0.0951215i
$521$	−356152.			−1.31208			−0.656040	−	0.754726i	$-0.727770\pi$
$521$	−356152.			−1.31208			−0.656040	+	0.754726i	$0.727770\pi$
$522$	68406.1	+	189899.i	0.251046	+	0.696916i
$523$	169603.			0.620057			0.310028	−	0.950727i	$-0.399661\pi$
$523$	169603.			0.620057			0.310028	+	0.950727i	$0.399661\pi$
$524$	−67414.6	−	81430.8i	−0.245523	−	0.296569i
$525$	253724.	−	181865.i	0.920539	−	0.659829i
$526$	27759.6	+	77061.8i	0.100332	+	0.278527i
$527$	25372.0			0.0913552
$528$	−597966.	−	113624.i	−2.14491	−	0.407570i
$529$	−102986.			−0.368016
$530$	56450.7	+	73232.8i	0.200964	+	0.260708i
$531$		−	474244.i		−	1.68195i
$532$	−57030.5	−	68887.8i	−0.201504	−	0.243399i
$533$		−	158794.i		−	0.558960i
$534$	−228811.	−	635190.i	−0.802406	−	2.22752i
$535$	78745.7	+	245026.i	0.275118	+	0.856061i
$536$	−47444.1	−	28023.9i	−0.165140	−	0.0975438i
$537$			689462.i			2.39090i
$538$	−71293.2	−	197913.i	−0.246311	−	0.683770i
$539$		−	191532.i		−	0.659270i
$540$	159929.	+	102134.i	0.548452	+	0.350254i
$541$	449811.			1.53687			0.768433	−	0.639930i	$-0.221037\pi$
$541$	449811.			1.53687			0.768433	+	0.639930i	$0.221037\pi$
$542$	−310877.	+	111985.i	−1.05825	+	0.381209i
$543$	−126414.			−0.428743
$544$	4062.93	+	25504.4i	0.0137291	+	0.0861821i
$545$	25143.8	+	78237.8i	0.0846522	+	0.263405i
$546$	−136882.	+	49308.3i	−0.459157	+	0.165400i
$547$	226292.			0.756302			0.378151	−	0.925744i	$-0.376560\pi$
$547$	226292.			0.756302			0.378151	+	0.925744i	$0.376560\pi$
$548$	12396.3	+	14973.6i	0.0412792	+	0.0498616i
$549$	−286325.			−0.949981
$550$	240895.	−	349754.i	0.796346	−	1.15621i
$551$			68790.0i			0.226580i
$552$	324348.	+	191583.i	1.06447	+	0.628753i
$553$		−	157144.i		−	0.513863i
$554$	375269.	−	135181.i	1.22271	−	0.440450i
$555$	573707.	−	184376.i	1.86253	−	0.598575i
$556$	204636.	+	247182.i	0.661962	+	0.799591i
$557$		−	386780.i		−	1.24668i	−0.781953	−	0.623338i	$-0.785776\pi$
$557$		−	386780.i		−	1.24668i	0.781953	−	0.623338i	$-0.214224\pi$
$558$	434975.	−	156689.i	1.39700	−	0.503233i
$559$		−	13130.7i		−	0.0420209i
$560$	226662.	−	28060.6i	0.722773	−	0.0894788i
$561$	59964.7			0.190533
$562$	−40953.2	−	113688.i	−0.129663	−	0.359949i
$563$	−462000.			−1.45756			−0.728778	−	0.684750i	$-0.759911\pi$
$563$	−462000.			−1.45756			−0.728778	+	0.684750i	$0.759911\pi$
$564$	46704.8	−	38665.8i	0.146826	−	0.121554i
$565$	−393260.	+	126385.i	−1.23192	+	0.395911i
$566$	66630.4	+	184969.i	0.207989	+	0.577386i
$567$	−95164.0			−0.296010
$568$	261523.	−	442755.i	0.810613	−	1.37236i
$569$	−80851.6			−0.249726			−0.124863	−	0.992174i	$-0.539849\pi$
$569$	−80851.6			−0.249726			−0.124863	+	0.992174i	$0.539849\pi$
$570$	133837.	+	173624.i	0.411932	+	0.534393i
$571$			141499.i			0.433991i	0.976173	+	0.216995i	$0.0696256\pi$
$571$			141499.i			0.433991i	−0.976173	+	0.216995i	$0.930374\pi$
$572$	−152464.	+	126221.i	−0.465987	+	0.385780i
$573$		−	278137.i		−	0.847129i
$574$	105489.	+	292843.i	0.320173	+	0.888816i
$575$	−213627.	+	153125.i	−0.646132	+	0.463138i
$576$	227161.	+	412153.i	0.684681	+	1.24226i
$577$		−	542683.i		−	1.63003i	−0.579442	−	0.815013i	$-0.696730\pi$
$577$		−	542683.i		−	1.63003i	0.579442	−	0.815013i	$-0.303270\pi$
$578$	112361.	+	311919.i	0.336325	+	0.933655i
$579$		−	301214.i		−	0.898498i
$580$	−148060.	−	94554.8i	−0.440132	−	0.281079i
$581$	−372452.			−1.10336
$582$	−429397.	+	154679.i	−1.26769	+	0.456653i
$583$	157074.			0.462132
$584$	−187837.	+	318005.i	−0.550750	+	0.932412i
$585$	199142.	−	63999.8i	0.581905	−	0.187011i
$586$	−71410.1	+	25723.7i	−0.207953	+	0.0749096i
$587$	−183191.			−0.531653			−0.265827	−	0.964021i	$-0.585645\pi$
$587$	−183191.			−0.531653			−0.265827	+	0.964021i	$0.585645\pi$
$588$	−194489.	+	161013.i	−0.562524	+	0.465700i
$589$	157568.			0.454190
$590$	251997.	+	326912.i	0.723922	+	0.939134i
$591$			347933.i			0.996141i
$592$	433132.	+	82302.5i	1.23588	+	0.234839i
$593$			329497.i			0.937006i	0.883462	+	0.468503i	$0.155207\pi$
$593$			329497.i			0.937006i	−0.883462	+	0.468503i	$0.844793\pi$
$594$	303275.	−	109247.i	0.859536	−	0.309626i
$595$	−21421.7	+	6884.44i	−0.0605090	+	0.0194462i
$596$	286390.	−	237095.i	0.806241	−	0.667468i
$597$		−	53169.1i		−	0.149180i
$598$	115250.	−	41516.1i	0.322285	−	0.116095i
$599$		−	192632.i		−	0.536876i	−0.963297	−	0.268438i	$-0.913493\pi$
$599$		−	192632.i		−	0.536876i	0.963297	−	0.268438i	$-0.0865074\pi$
$600$	−557665.	+	49409.2i	−1.54907	+	0.137248i
$601$	−253719.			−0.702431			−0.351215	−	0.936295i	$-0.614231\pi$
$601$	−253719.			−0.702431			−0.351215	+	0.936295i	$0.614231\pi$
$602$	8722.94	+	24215.3i	0.0240696	+	0.0668184i
$603$	98921.6			0.272055
$604$	−272233.	−	328834.i	−0.746221	−	0.901369i
$605$	−108742.	−	338362.i	−0.297088	−	0.924424i
$606$	−224305.	−	622682.i	−0.610793	−	1.69559i
$607$	151876.			0.412205			0.206102	−	0.978530i	$-0.433922\pi$
$607$	151876.			0.412205			0.206102	+	0.978530i	$0.433922\pi$
$608$	25232.1	+	158390.i	0.0682567	+	0.428471i
$609$	−219365.			−0.591470
$610$	197374.	−	152143.i	0.530432	−	0.408878i
$611$		−	19717.3i		−	0.0528158i
$612$	−29566.0	−	35713.1i	−0.0789387	−	0.0953509i
$613$			439833.i			1.17049i	0.810857	+	0.585244i	$0.199001\pi$
$613$			439833.i			1.17049i	−0.810857	+	0.585244i	$0.800999\pi$
$614$	211495.	+	587120.i	0.561001	+	1.55736i
$615$	−233448.	−	726400.i	−0.617220	−	1.92055i
$616$	197318.	−	334056.i	0.520002	−	0.880356i
$617$			315589.i			0.828994i	0.910051	+	0.414497i	$0.136042\pi$
$617$			315589.i			0.828994i	−0.910051	+	0.414497i	$0.863958\pi$
$618$	−280559.	−	778844.i	−0.734593	−	2.03926i
$619$		−	230194.i		−	0.600776i	−0.953817	−	0.300388i	$-0.902884\pi$
$619$		−	230194.i		−	0.600776i	0.953817	−	0.300388i	$-0.0971161\pi$
$620$	−216584.	+	339142.i	−0.563434	+	0.882262i
$621$	−199504.			−0.517330
$622$	134519.	−	48457.1i	0.347699	−	0.125250i
$623$	430355.			1.10879
$624$	256340.	+	48709.1i	0.658336	+	0.125095i
$625$	125467.	−	369927.i	0.321195	−	0.947013i
$626$	145969.	−	52581.6i	0.372487	−	0.134179i
$627$	372399.			0.947270
$628$	127540.	+	154057.i	0.323390	+	0.390626i
$629$	−43434.9			−0.109784
$630$	−324736.	+	250319.i	−0.818181	+	0.630686i
$631$			97407.4i			0.244643i	0.992491	+	0.122322i	$0.0390340\pi$
$631$			97407.4i			0.244643i	−0.992491	+	0.122322i	$0.960966\pi$
$632$	−143329.	+	242654.i	−0.358840	+	0.607510i
$633$			1.11286e6i			2.77737i
$634$	−552547.	+	199041.i	−1.37465	+	0.495182i
$635$	1328.47	+	4133.69i	0.00329461	+	0.0102516i
$636$	−132046.	−	159499.i	−0.326445	−	0.394316i
$637$			82107.1i			0.202349i
$638$	−280769.	+	101140.i	−0.689776	+	0.248474i
$639$			923150.i			2.26084i
$640$	−375594.	−	163406.i	−0.916977	−	0.398940i
$641$	−30226.0			−0.0735638			−0.0367819	−	0.999323i	$-0.511711\pi$
$641$	−30226.0			−0.0735638			−0.0367819	+	0.999323i	$0.511711\pi$
$642$	−195329.	−	542243.i	−0.473911	−	1.31560i
$643$	−642503.			−1.55401			−0.777004	−	0.629496i	$-0.783261\pi$
$643$	−642503.			−1.55401			−0.777004	+	0.629496i	$0.783261\pi$
$644$	−184961.	+	153125.i	−0.445974	+	0.369211i
$645$	−19303.9	−	60066.1i	−0.0464007	−	0.144381i
$646$	−5355.09	−	14866.0i	−0.0128322	−	0.0356228i
$647$	−269830.			−0.644588			−0.322294	−	0.946640i	$-0.604454\pi$
$647$	−269830.			−0.644588			−0.322294	+	0.946640i	$0.604454\pi$
$648$	146948.	+	86798.0i	0.349955	+	0.206709i
$649$	701180.			1.66472
$650$	−103268.	+	149935.i	−0.244422	+	0.354875i
$651$			502470.i			1.18563i
$652$	87373.8	−	72334.6i	0.205535	−	0.170157i
$653$		−	143479.i		−	0.336482i	−0.985746	−	0.168241i	$-0.946191\pi$
$653$		−	143479.i		−	0.336482i	0.985746	−	0.168241i	$-0.0538087\pi$
$654$	−62369.4	−	173140.i	−0.145820	−	0.404802i
$655$	−157258.	+	50539.2i	−0.366549	+	0.117800i
$656$	104207.	−	548410.i	0.242154	−	1.27438i
$657$		−	663044.i		−	1.53607i
$658$	13098.5	+	36361.9i	0.0302530	+	0.0839837i
$659$		−	44480.3i		−	0.102423i	−0.998688	−	0.0512115i	$-0.983692\pi$
$659$		−	44480.3i		−	0.102423i	0.998688	−	0.0512115i	$-0.0163082\pi$
$660$	−511879.	+	801534.i	−1.17511	+	1.84007i
$661$	414413.			0.948485			0.474242	−	0.880394i	$-0.342722\pi$
$661$	414413.			0.948485			0.474242	+	0.880394i	$0.342722\pi$
$662$	685533.	−	246946.i	1.56427	−	0.563490i
$663$	−25706.1			−0.0584801
$664$	575123.	+	339709.i	1.30444	+	0.770498i
$665$	−133036.	+	42754.5i	−0.300832	+	0.0966805i
$666$	−744644.	+	268239.i	−1.67880	+	0.604747i
$667$	184699.			0.415157
$668$	517623.	−	428528.i	1.16001	−	0.960342i
$669$	970375.			2.16814
$670$	−68190.0	+	52563.5i	−0.151905	+	0.117094i
$671$		−	423338.i		−	0.940248i
$672$	−505092.	+	80462.7i	−1.11849	+	0.178179i
$673$		−	351431.i		−	0.775908i	−0.921679	−	0.387954i	$-0.873182\pi$
$673$		−	351431.i		−	0.775908i	0.921679	−	0.387954i	$-0.126818\pi$
$674$	765761.	−	275846.i	1.68567	−	0.607221i
$675$	240986.	−	172735.i	0.528912	−	0.379116i
$676$	−286643.	+	237304.i	−0.627259	+	0.519293i
$677$		−	168255.i		−	0.367104i	−0.983010	−	0.183552i	$-0.941240\pi$
$677$		−	168255.i		−	0.367104i	0.983010	−	0.183552i	$-0.0587596\pi$
$678$	870284.	−	313498.i	1.89322	−	0.681985i
$679$		−	290926.i		−	0.631019i
$680$	39357.6	+	8907.88i	0.0851159	+	0.0192644i
$681$	31982.6			0.0689636
$682$	231668.	+	643120.i	0.498077	+	1.38268i
$683$	−506300.			−1.08534			−0.542671	−	0.839946i	$-0.682587\pi$
$683$	−506300.			−1.08534			−0.542671	+	0.839946i	$0.682587\pi$
$684$	−183614.	−	221790.i	−0.392459	−	0.474055i
$685$	28916.9	−	9293.23i	0.0616270	−	0.0198055i
$686$	−170699.	−	473867.i	−0.362729	−	1.00695i
$687$	94873.9			0.201017
$688$	8616.93	−	45348.1i	0.0182044	−	0.0958038i
$689$	−67335.4			−0.141842
$690$	466175.	−	359347.i	0.979154	−	0.754771i
$691$			102749.i			0.215189i	0.994195	+	0.107594i	$0.0343148\pi$
$691$			102749.i			0.215189i	−0.994195	+	0.107594i	$0.965685\pi$
$692$	258169.	+	311845.i	0.539129	+	0.651219i
$693$			696512.i			1.45031i
$694$	−73877.7	−	205088.i	−0.153389	−	0.425815i
$695$	477356.	−	153411.i	0.988264	−	0.317605i
$696$	338733.	+	200080.i	0.699261	+	0.413034i
$697$			54995.2i			0.113203i
$698$	−310313.	−	861444.i	−0.636927	−	1.76814i
$699$			867180.i			1.77482i
$700$	90840.3	−	345107.i	0.185388	−	0.704300i
$701$	−368530.			−0.749959			−0.374979	−	0.927033i	$-0.622350\pi$
$701$	−368530.			−0.749959			−0.374979	+	0.927033i	$0.622350\pi$
$702$	−130010.	+	46832.8i	−0.263817	+	0.0950333i
$703$	−269744.			−0.545810
$704$	−609378.	+	335862.i	−1.22954	+	0.677666i
$705$	−28986.9	−	90195.9i	−0.0583208	−	0.181472i
$706$	−309802.	+	111598.i	−0.621548	+	0.223897i
$707$	421880.			0.844015
$708$	−589454.	−	712008.i	−1.17593	−	1.42042i
$709$	−479705.			−0.954293			−0.477147	−	0.878824i	$-0.658329\pi$
$709$	−479705.			−0.954293			−0.477147	+	0.878824i	$0.658329\pi$
$710$	−490530.	−	636358.i	−0.973081	−	1.26237i
$711$		−	505937.i		−	1.00082i
$712$	−664533.	−	392522.i	−1.31086	−	0.774290i
$713$		−	423064.i		−	0.832199i
$714$	47406.2	−	17076.9i	0.0929906	−	0.0334975i
$715$	94625.0	+	294436.i	0.185095	+	0.575943i
$716$	502615.	+	607114.i	0.980414	+	1.18425i
$717$			92518.3i			0.179965i
$718$	−872500.	+	314296.i	−1.69245	+	0.609663i
$719$		−	251849.i		−	0.487172i	−0.969879	−	0.243586i	$-0.921676\pi$
$719$		−	251849.i		−	0.487172i	0.969879	−	0.243586i	$-0.0783239\pi$
$720$	729755.	−	90343.2i	1.40771	−	0.174273i
$721$	527684.			1.01509
$722$	143410.	+	398112.i	0.275109	+	0.763714i
$723$	441907.			0.845384
$724$	−111316.	+	92155.6i	−0.212363	+	0.175810i
$725$	−223102.	+	159916.i	−0.424451	+	0.304240i
$726$	269735.	+	748795.i	0.511756	+	1.42066i
$727$	−79819.7			−0.151022			−0.0755112	−	0.997145i	$-0.524059\pi$
$727$	−79819.7			−0.151022			−0.0755112	+	0.997145i	$0.524059\pi$
$728$	−84587.6	+	143205.i	−0.159604	+	0.270207i
$729$	−844210.			−1.58853
$730$	352319.	+	457059.i	0.661135	+	0.857682i
$731$			4547.56i			0.00851028i
$732$	−429875.	+	355883.i	−0.802269	+	0.664179i
$733$			552245.i			1.02784i	0.857840	+	0.513918i	$0.171806\pi$
$733$			552245.i			1.02784i	−0.857840	+	0.513918i	$0.828194\pi$
$734$	151665.	+	421030.i	0.281510	+	0.781485i
$735$	120708.	+	375596.i	0.223440	+	0.695258i
$736$	425272.	−	67747.2i	0.785075	−	0.125065i
$737$			146258.i			0.269267i
$738$	339631.	+	942832.i	0.623584	+	1.73110i
$739$			21750.2i			0.0398267i	0.999802	+	0.0199133i	$0.00633903\pi$
$739$			21750.2i			0.0398267i	−0.999802	+	0.0199133i	$0.993661\pi$
$740$	370775.	−	580585.i	0.677091	−	1.06024i
$741$	−159643.			−0.290745
$742$	124178.	−	44731.9i	0.225546	−	0.0812474i
$743$	345994.			0.626746			0.313373	−	0.949630i	$-0.398541\pi$
$743$	345994.			0.626746			0.313373	+	0.949630i	$0.398541\pi$
$744$	458297.	−	775890.i	0.827944	−	1.40170i
$745$	−177745.	−	553074.i	−0.320247	−	0.996484i
$746$	−653880.	+	235544.i	−1.17495	+	0.423247i
$747$	−1.19914e6			−2.14896
$748$	52802.6	−	43714.0i	0.0943740	−	0.0781299i
$749$	367381.			0.654867
$750$	−251974.	+	837689.i	−0.447955	+	1.48922i
$751$		−	312233.i		−	0.553603i	−0.960927	−	0.276801i	$-0.910726\pi$
$751$		−	312233.i		−	0.553603i	0.960927	−	0.276801i	$-0.0892744\pi$
$752$	12939.3	−	68095.3i	0.0228810	−	0.120415i
$753$		−	853975.i		−	1.50610i
$754$	120362.	−	43357.3i	0.211713	−	0.0762641i
$755$	−635041.	+	204087.i	−1.11406	+	0.358032i
$756$	208648.	−	172735.i	0.365066	−	0.302229i
$757$			1.05318e6i			1.83786i	0.394422	+	0.918930i	$0.370945\pi$
$757$			1.05318e6i			1.83786i	−0.394422	+	0.918930i	$0.629055\pi$
$758$	61160.5	−	22031.5i	0.106447	−	0.0383448i
$759$		−	999879.i		−	1.73566i
$760$	244423.	+	55320.7i	0.423170	+	0.0957768i
$761$	162550.			0.280683			0.140342	−	0.990103i	$-0.455180\pi$
$761$	162550.			0.280683			0.140342	+	0.990103i	$0.455180\pi$
$762$	−3295.28	−	9147.84i	−0.00567521	−	0.0157546i
$763$	117306.			0.201499
$764$	−202761.	−	244917.i	−0.347374	−	0.419597i
$765$	−68968.9	+	22165.0i	−0.117850	+	0.0378743i
$766$	−49214.3	−	136621.i	−0.0838753	−	0.232842i
$767$	−300587.			−0.510950
$768$	853328.	+	336442.i	1.44675	+	0.570411i
$769$	−659297.			−1.11488			−0.557441	−	0.830217i	$-0.688217\pi$
$769$	−659297.			−1.11488			−0.557441	+	0.830217i	$0.688217\pi$
$770$	−370103.	−	480129.i	−0.624224	−	0.809798i
$771$		−	1.19022e6i		−	2.00225i
$772$	−219583.	−	265237.i	−0.368439	−	0.445041i
$773$			159740.i			0.267335i	0.991026	+	0.133667i	$0.0426754\pi$
$773$			159740.i			0.267335i	−0.991026	+	0.133667i	$0.957325\pi$
$774$	28084.2	+	77962.9i	0.0468791	+	0.130139i
$775$	366299.	+	511030.i	0.609862	+	0.850830i
$776$	−265350.	+	449234.i	−0.440652	+	0.746017i
$777$		−	860190.i		−	1.42480i
$778$	216612.	+	601324.i	0.357868	+	0.993458i
$779$			341537.i			0.562812i
$780$	219436.	−	343607.i	0.360677	−	0.564772i
$781$	−1.36490e6			−2.23768
$782$	−39914.6	+	14378.2i	−0.0652707	+	0.0235121i
$783$	−208352.			−0.339840
$784$	−53882.0	+	283564.i	−0.0876621	+	0.461337i
$785$	297513.	−	95613.7i	0.482799	−	0.155160i
$786$	348013.	−	125363.i	0.563314	−	0.202919i
$787$	242785.			0.391988			0.195994	−	0.980605i	$-0.437207\pi$
$787$	242785.			0.391988			0.195994	+	0.980605i	$0.437207\pi$
$788$	253642.	+	306377.i	0.408478	+	0.493405i
$789$	−286605.			−0.460394
$790$	268838.	+	348759.i	0.430760	+	0.558820i
$791$			589636.i			0.942391i
$792$	635280.	−	1.07552e6i	1.01278	−	1.71462i
$793$			181479.i			0.288590i
$794$	−65777.1	+	23694.5i	−0.104336	+	0.0375844i
$795$	−308024.	+	98991.6i	−0.487360	+	0.156626i
$796$	−38760.1	−	46818.7i	−0.0611728	−	0.0738913i
$797$		−	431369.i		−	0.679098i	−0.940588	−	0.339549i	$-0.889726\pi$
$797$		−	431369.i		−	0.679098i	0.940588	−	0.339549i	$-0.110274\pi$
$798$	294408.	−	106053.i	0.462320	−	0.166539i
$799$			6828.66i			0.0106965i
$800$	−455039.	+	450043.i	−0.710999	+	0.703193i
$801$	1.38556e6			2.15954
$802$	84601.9	+	234859.i	0.131532	+	0.365139i
$803$	980325.			1.52033
$804$	148516.	−	122953.i	0.229753	−	0.190207i
$805$	114794.	+	357196.i	0.177145	+	0.551207i
$806$	−99312.8	−	275697.i	−0.152875	−	0.424387i
$807$	736070.			1.13024
$808$	−651447.	−	384792.i	−0.997830	−	0.589391i
$809$	77096.8			0.117798			0.0588992	−	0.998264i	$-0.481241\pi$
$809$	77096.8			0.117798			0.0588992	+	0.998264i	$0.481241\pi$
$810$	211203.	−	162804.i	0.321907	−	0.248139i
$811$			475202.i			0.722498i	0.932469	+	0.361249i	$0.117650\pi$
$811$			475202.i			0.722498i	−0.932469	+	0.361249i	$0.882350\pi$
$812$	−193165.	+	159916.i	−0.292965	+	0.242539i
$813$		−	1.15620e6i		−	1.74925i
$814$	−396597.	−	1.10097e6i	−0.598551	−	1.66160i
$815$	−54227.6	−	168735.i	−0.0816405	−	0.254034i
$816$	−88778.1	−	16869.4i	−0.133329	−	0.0253349i
$817$			28241.8i			0.0423105i
$818$	15749.0	+	43720.0i	0.0235368	+	0.0653392i
$819$		−	298585.i		−	0.445144i
$820$	−735108.	−	469458.i	−1.09326	−	0.698182i
$821$	980753.			1.45503			0.727517	−	0.686090i	$-0.240674\pi$
$821$	980753.			1.45503			0.727517	+	0.686090i	$0.240674\pi$
$822$	−63993.2	+	23051.9i	−0.0947087	+	0.0341164i
$823$	−613089.			−0.905157			−0.452578	−	0.891725i	$-0.649496\pi$
$823$	−613089.			−0.905157			−0.452578	+	0.891725i	$0.649496\pi$
$824$	−814824.	−	481294.i	−1.20008	−	0.708853i
$825$	865718.	+	1.20778e6i	1.27195	+	1.77451i
$826$	554332.	−	199684.i	0.812474	−	0.292673i
$827$	1.20150e6			1.75676			0.878378	−	0.477967i	$-0.158626\pi$
$827$	1.20150e6			1.75676			0.878378	+	0.477967i	$0.158626\pi$
$828$	−595497.	+	492998.i	−0.868599	+	0.719092i
$829$	544920.			0.792909			0.396454	−	0.918054i	$-0.370240\pi$
$829$	544920.			0.792909			0.396454	+	0.918054i	$0.370240\pi$
$830$	826607.	−	637181.i	1.19989	−	0.924926i
$831$			1.39569e6i			2.02109i
$832$	261232.	−	143980.i	0.377381	−	0.207996i
$833$		−	28436.1i		−	0.0409807i
$834$	−1.05639e6	+	380537.i	−1.51877	+	0.547098i
$835$	−321257.	−	999629.i	−0.460766	−	1.43372i
$836$	327921.	−	271478.i	0.469198	−	0.388438i
$837$			477244.i			0.681223i
$838$	−1.20803e6	+	435163.i	−1.72025	+	0.619675i
$839$			706063.i			1.00304i	0.865145	+	0.501521i	$0.167226\pi$
$839$			706063.i			1.00304i	−0.865145	+	0.501521i	$0.832774\pi$
$840$	−176413.	+	779443.i	−0.250018	+	1.10465i
$841$	−514391.			−0.727279
$842$	−361627.	−	1.00389e6i	−0.510078	−	1.41600i
$843$	422823.			0.594982
$844$	811271.	+	979942.i	1.13889	+	1.37567i
$845$	177902.	+	553561.i	0.249153	+	0.775269i
$846$	42171.5	+	117070.i	0.0589221	+	0.163570i
$847$	−507325.			−0.707163
$848$	−232549.	−	44188.3i	−0.323387	−	0.0614491i
$849$	−687930.			−0.954396
$850$	35764.8	−	51926.8i	0.0495015	−	0.0718710i
$851$			724254.i			1.00007i
$852$	1.14741e6	+	1.38597e6i	1.58067	+	1.90931i
$853$		−	73235.8i		−	0.100653i	−0.998733	−	0.0503263i	$-0.983974\pi$
$853$		−	73235.8i		−	0.100653i	0.998733	−	0.0503263i	$-0.0160261\pi$
$854$	−120559.	−	334678.i	−0.165305	−	0.458893i
$855$	−428318.	+	137651.i	−0.585914	+	0.188299i
$856$	−567292.	−	335084.i	−0.774211	−	0.457305i
$857$			448249.i			0.610319i	0.952301	+	0.305160i	$0.0987099\pi$
$857$			448249.i			0.610319i	−0.952301	+	0.305160i	$0.901290\pi$
$858$	−234718.	−	651588.i	−0.318839	−	0.885112i
$859$		−	1.18282e6i		−	1.60300i	−0.597995	−	0.801499i	$-0.704036\pi$
$859$		−	1.18282e6i		−	1.60300i	0.597995	−	0.801499i	$-0.295964\pi$
$860$	−60786.2	−	38819.5i	−0.0821880	−	0.0524872i
$861$	−1.08913e6			−1.46918
$862$	527913.	−	190167.i	0.710474	−	0.255930i
$863$	−1.04231e6			−1.39951			−0.699754	−	0.714384i	$-0.746707\pi$
$863$	−1.04231e6			−1.39951			−0.699754	+	0.714384i	$0.746707\pi$
$864$	−479734.	+	76423.2i	−0.642648	+	0.102376i
$865$	602233.	−	193544.i	0.804882	−	0.258670i
$866$	200217.	−	72123.0i	0.266971	−	0.0961697i
$867$	−1.16008e6			−1.54329
$868$	366299.	+	442456.i	0.486179	+	0.587260i
$869$	748039.			0.990568
$870$	486851.	−	375284.i	0.643217	−	0.495817i
$871$		−	62698.7i		−	0.0826461i
$872$	−181139.	−	106994.i	−0.238220	−	0.140710i
$873$		−	936658.i		−	1.22900i
$874$	−247882.	+	89293.3i	−0.324506	+	0.116895i
$875$	−447931.	−	332074.i	−0.585053	−	0.433729i
$876$	−824119.	−	995463.i	−1.07394	−	1.29723i
$877$			207637.i			0.269964i	0.990848	+	0.134982i	$0.0430976\pi$
$877$			207637.i			0.269964i	−0.990848	+	0.134982i	$0.956902\pi$
$878$	603707.	−	217470.i	0.783135	−	0.282105i
$879$		−	265585.i		−	0.343737i
$880$	133574.	+	1.07896e6i	0.172487	+	1.39328i
$881$	953855.			1.22894			0.614470	−	0.788940i	$-0.289370\pi$
$881$	953855.			1.22894			0.614470	+	0.788940i	$0.289370\pi$
$882$	−175611.	−	487506.i	−0.225744	−	0.626675i
$883$	388576.			0.498373			0.249187	−	0.968456i	$-0.419837\pi$
$883$	388576.			0.498373			0.249187	+	0.968456i	$0.419837\pi$
$884$	−22635.8	+	18739.6i	−0.0289662	+	0.0239804i
$885$	−1.37502e6	+	441900.i	−1.75559	+	0.564206i
$886$	−90005.2	−	249858.i	−0.114657	−	0.318293i
$887$	−309960.			−0.393966			−0.196983	−	0.980407i	$-0.563114\pi$
$887$	−309960.			−0.393966			−0.196983	+	0.980407i	$0.563114\pi$
$888$	−784570.	+	1.32826e6i	−0.994960	+	1.68445i
$889$	6197.86			0.00784221
$890$	−955113.	+	736239.i	−1.20580	+	0.929478i
$891$		−	453001.i		−	0.570616i
$892$	854475.	−	707399.i	1.07391	−	0.889068i
$893$			42408.1i			0.0531797i
$894$	440897.	+	1.22395e6i	0.551649	+	1.53140i
$895$	1.17245e6	−	376799.i	1.46369	−	0.470396i
$896$	−386108.	+	439062.i	−0.480942	+	0.546903i
$897$			428635.i			0.532724i
$898$	222101.	+	616561.i	0.275421	+	0.764581i
$899$		−	441828.i		−	0.546681i
$900$	292467.	−	1.11110e6i	0.361071	−	1.37173i
$901$	23320.2			0.0287265
$902$	−1.39400e6	+	502152.i	−1.71336	+	0.617195i
$903$	−90060.4			−0.110448
$904$	537800.	−	910488.i	0.658088	−	1.11413i
$905$	69087.0	+	214972.i	0.0843527	+	0.262473i
$906$	1.40534e6	−	506240.i	1.71209	−	0.616737i
$907$	47309.4			0.0575087			0.0287543	−	0.999587i	$-0.490846\pi$
$907$	47309.4			0.0575087			0.0287543	+	0.999587i	$0.490846\pi$
$908$	28162.7	−	23315.2i	0.0341588	−	0.0282792i
$909$	1.35828e6			1.64384
$910$	158658.	+	205825.i	0.191593	+	0.248551i
$911$			297399.i			0.358346i	0.983818	+	0.179173i	$0.0573422\pi$
$911$			297399.i			0.358346i	−0.983818	+	0.179173i	$0.942658\pi$
$912$	−551339.	−	104764.i	−0.662872	−	0.125957i
$913$		−	1.77295e6i		−	2.12694i
$914$	1.20623e6	−	434512.i	1.44390	−	0.520127i
$915$	266798.	+	830171.i	0.318669	+	0.991575i
$916$	83542.3	−	69162.7i	0.0995670	−	0.0824291i
$917$			235786.i			0.280401i
$918$	45026.3	−	16219.6i	0.0534294	−	0.0192466i
$919$			1.40295e6i			1.66116i	0.556897	+	0.830582i	$0.311992\pi$
$919$			1.40295e6i			1.66116i	−0.556897	+	0.830582i	$0.688008\pi$
$920$	148534.	−	656267.i	0.175489	−	0.775363i
$921$	−2.18359e6			−2.57426
$922$	−258161.	−	716666.i	−0.303689	−	0.843053i
$923$	585113.			0.686810
$924$	865718.	+	1.04571e6i	1.01399	+	1.22481i
$925$	−627075.	−	874844.i	−0.732886	−	1.02246i
$926$	387920.	+	1.07688e6i	0.452398	+	1.25588i
$927$	1.69892e6			1.97703
$928$	444133.	−	70751.9i	0.515724	−	0.0821565i
$929$	−1.02250e6			−1.18476			−0.592381	−	0.805658i	$-0.701812\pi$
$929$	−1.02250e6			−1.18476			−0.592381	+	0.805658i	$0.701812\pi$
$930$	−859612.	−	1.11516e6i	−0.993886	−	1.28936i
$931$		−	176597.i		−	0.203744i
$932$	632171.	+	763606.i	0.727784	+	0.879098i
$933$			500298.i			0.574732i
$934$	378428.	+	1.05053e6i	0.433799	+	1.20425i
$935$	−32771.4	−	101972.i	−0.0374862	−	0.116643i
$936$	−272336.	+	461061.i	−0.310852	+	0.526268i
$937$			258027.i			0.293890i	0.989145	+	0.146945i	$0.0469441\pi$
$937$			258027.i			0.293890i	−0.989145	+	0.146945i	$0.953056\pi$
$938$	41651.6	+	115627.i	0.0473398	+	0.131417i
$939$			542881.i			0.615706i
$940$	−91277.2	−	58291.8i	−0.103302	−	0.0659708i
$941$	813979.			0.919251			0.459625	−	0.888113i	$-0.347984\pi$
$941$	813979.			0.919251			0.459625	+	0.888113i	$0.347984\pi$
$942$	−658396.	+	237170.i	−0.741968	+	0.267275i
$943$	917015.			1.03122
$944$	−1.03810e6	−	197257.i	−1.16492	−	0.221355i
$945$	−129495.	−	402940.i	−0.145008	−	0.451208i
$946$	−115270.	+	41523.0i	−0.128805	+	0.0463988i
$947$	−1.43058e6			−1.59518			−0.797592	−	0.603197i	$-0.793893\pi$
$947$	−1.43058e6			−1.59518			−0.797592	+	0.603197i	$0.793893\pi$
$948$	−628846.	−	759590.i	−0.699725	−	0.845206i
$949$	−420252.			−0.466635
$950$	222111.	−	322481.i	0.246106	−	0.357320i
$951$		−	2.05501e6i		−	2.27224i
$952$	29295.1	−	49596.2i	0.0323237	−	0.0547236i
$953$			1.32267e6i			1.45635i	0.685392	+	0.728174i	$0.259631\pi$
$953$			1.32267e6i			1.45635i	−0.685392	+	0.728174i	$0.740369\pi$
$954$	399800.	−	144018.i	0.439284	−	0.158241i
$955$	−472981.	+	152005.i	−0.518606	+	0.166668i
$956$	67445.4	+	81468.1i	0.0737967	+	0.0891398i
$957$		−	1.04423e6i		−	1.14017i
$958$	1.19387e6	−	430061.i	1.30084	−	0.468596i
$959$		−	43356.7i		−	0.0471432i
$960$	983329.	−	1.04267e6i	1.06698	−	1.13137i
$961$	−88513.9			−0.0958439
$962$	170016.	+	471972.i	0.183713	+	0.509995i
$963$	1.18281e6			1.27545
$964$	389126.	−	322148.i	0.418732	−	0.346658i
$965$	−512224.	+	164617.i	−0.550054	+	0.176774i
$966$	−284748.	−	790474.i	−0.305145	−	0.847097i
$967$	−736666.			−0.787803			−0.393902	−	0.919153i	$-0.628875\pi$
$967$	−736666.			−0.787803			−0.393902	+	0.919153i	$0.628875\pi$
$968$	783387.	+	462725.i	0.836037	+	0.493824i
$969$	55288.9			0.0588831
$970$	497708.	+	645670.i	0.528970	+	0.686226i
$971$		−	1.17709e6i		−	1.24846i	−0.781243	−	0.624228i	$-0.785414\pi$
$971$		−	1.17709e6i		−	1.24846i	0.781243	−	0.624228i	$-0.214586\pi$
$972$	−933582.	+	772890.i	−0.988143	+	0.818060i
$973$		−	715727.i		−	0.755999i
$974$	−364551.	−	1.01201e6i	−0.384274	−	1.06676i
$975$	−371122.	−	517759.i	−0.390398	−	0.544651i
$976$	−119094.	+	626755.i	−0.125023	+	0.657957i
$977$		−	1.52036e6i		−	1.59279i	−0.604777	−	0.796395i	$-0.706738\pi$
$977$		−	1.52036e6i		−	1.59279i	0.604777	−	0.796395i	$-0.293262\pi$
$978$	134512.	+	373411.i	0.140632	+	0.390400i
$979$			2.04858e6i			2.13741i
$980$	380099.	+	242740.i	0.395771	+	0.252749i
$981$	377677.			0.392448
$982$	501613.	−	180694.i	0.520171	−	0.187378i
$983$	−1.19830e6			−1.24010			−0.620051	−	0.784562i	$-0.712888\pi$
$983$	−1.19830e6			−1.24010			−0.620051	+	0.784562i	$0.712888\pi$
$984$	1.68178e6	+	993384.i	1.73692	+	1.02595i
$985$	591672.	−	190150.i	0.609830	−	0.195985i
$986$	−41684.9	+	15015.9i	−0.0428770	+	0.0154454i
$987$	−135236.			−0.138822
$988$	−140575.	+	116379.i	−0.144011	+	0.119223i
$989$	75828.1			0.0775243
$990$	−1.19157e6	−	1.54581e6i	−1.21577	−	1.57720i
$991$		−	1.55991e6i		−	1.58837i	−0.607677	−	0.794184i	$-0.707898\pi$
$991$		−	1.55991e6i		−	1.58837i	0.607677	−	0.794184i	$-0.292102\pi$
$992$	−162062.	−	1.01732e6i	−0.164686	−	1.03379i
$993$			2.54961e6i			2.58568i
$994$	−1.07905e6	+	388699.i	−1.09211	+	0.393406i
$995$	−90415.9	+	29057.6i	−0.0913269	+	0.0293503i
$996$	−1.80033e6	+	1.49045e6i	−1.81482	+	1.50245i
$997$			253246.i			0.254772i	0.991853	+	0.127386i	$0.0406587\pi$
$997$			253246.i			0.254772i	−0.991853	+	0.127386i	$0.959341\pi$
$998$	−585883.	+	211049.i	−0.588233	+	0.211896i
$999$		−	817005.i		−	0.818642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.5.d.c.19.6	yes	8
3.2	odd	2		180.5.f.g.19.3		8
4.3	odd	2	inner	20.5.d.c.19.4	yes	8
5.2	odd	4		100.5.b.e.51.2		8
5.3	odd	4		100.5.b.e.51.7		8
5.4	even	2	inner	20.5.d.c.19.3	✓	8
8.3	odd	2		320.5.h.f.319.1		8
8.5	even	2		320.5.h.f.319.7		8
12.11	even	2		180.5.f.g.19.5		8
15.14	odd	2		180.5.f.g.19.6		8
20.3	even	4		100.5.b.e.51.8		8
20.7	even	4		100.5.b.e.51.1		8
20.19	odd	2	inner	20.5.d.c.19.5	yes	8
40.19	odd	2		320.5.h.f.319.8		8
40.29	even	2		320.5.h.f.319.2		8
60.59	even	2		180.5.f.g.19.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.d.c.19.3	✓	8	5.4	even	2	inner
20.5.d.c.19.4	yes	8	4.3	odd	2	inner
20.5.d.c.19.5	yes	8	20.19	odd	2	inner
20.5.d.c.19.6	yes	8	1.1	even	1	trivial
100.5.b.e.51.1		8	20.7	even	4
100.5.b.e.51.2		8	5.2	odd	4
100.5.b.e.51.7		8	5.3	odd	4
100.5.b.e.51.8		8	20.3	even	4
180.5.f.g.19.3		8	3.2	odd	2
180.5.f.g.19.4		8	60.59	even	2
180.5.f.g.19.5		8	12.11	even	2
180.5.f.g.19.6		8	15.14	odd	2
320.5.h.f.319.1		8	8.3	odd	2
320.5.h.f.319.2		8	40.29	even	2
320.5.h.f.319.7		8	8.5	even	2
320.5.h.f.319.8		8	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35563 + 3.76328i) q^{2} -13.9962 q^{3} +(-12.3246 + 10.2032i) q^{4} +(7.64911 + 23.8011i) q^{5} +(-18.9737 - 52.6718i) q^{6} +35.6863 q^{7} +(-55.1050 - 32.5490i) q^{8} +114.895 q^{9} +O(q^{10})\)	\(q+(1.35563 + 3.76328i) q^{2} -13.9962 q^{3} +(-12.3246 + 10.2032i) q^{4} +(7.64911 + 23.8011i) q^{5} +(-18.9737 - 52.6718i) q^{6} +35.6863 q^{7} +(-55.1050 - 32.5490i) q^{8} +114.895 q^{9} +(-79.2008 + 61.0511i) q^{10} +169.874i q^{11} +(172.497 - 142.806i) q^{12} -72.8228i q^{13} +(48.3772 + 134.297i) q^{14} +(-107.059 - 333.125i) q^{15} +(47.7893 - 251.500i) q^{16} +25.2207i q^{17} +(155.754 + 432.381i) q^{18} +156.628i q^{19} +(-337.119 - 215.292i) q^{20} -499.473 q^{21} +(-639.284 + 230.286i) q^{22} +420.541 q^{23} +(771.263 + 455.564i) q^{24} +(-507.982 + 364.114i) q^{25} +(274.053 - 98.7205i) q^{26} -474.398 q^{27} +(-439.817 + 364.114i) q^{28} +439.193 q^{29} +(1108.51 - 854.486i) q^{30} -1006.00i q^{31} +(1011.25 - 161.095i) q^{32} -2377.60i q^{33} +(-94.9125 + 34.1898i) q^{34} +(272.968 + 849.371i) q^{35} +(-1416.03 + 1172.29i) q^{36} +1722.19i q^{37} +(-589.436 + 212.329i) q^{38} +1019.25i q^{39} +(353.198 - 1560.53i) q^{40} +2180.56 q^{41} +(-677.099 - 1879.66i) q^{42} +180.311 q^{43} +(-1733.26 - 2093.62i) q^{44} +(878.842 + 2734.62i) q^{45} +(570.097 + 1582.61i) q^{46} +270.757 q^{47} +(-668.871 + 3520.05i) q^{48} -1127.49 q^{49} +(-2058.90 - 1418.08i) q^{50} -352.995i q^{51} +(743.026 + 897.509i) q^{52} -924.647i q^{53} +(-643.106 - 1785.29i) q^{54} +(-4043.19 + 1299.39i) q^{55} +(-1966.49 - 1161.55i) q^{56} -2192.21i q^{57} +(595.381 + 1652.81i) q^{58} -4127.64i q^{59} +(4718.40 + 3013.28i) q^{60} -2492.07 q^{61} +(3785.86 - 1363.76i) q^{62} +4100.16 q^{63} +(1977.12 + 3587.23i) q^{64} +(1733.26 - 557.030i) q^{65} +(8947.58 - 3223.14i) q^{66} +860.976 q^{67} +(-257.332 - 310.834i) q^{68} -5886.00 q^{69} +(-2826.38 + 2178.69i) q^{70} +8034.75i q^{71} +(-6331.27 - 3739.71i) q^{72} -5770.88i q^{73} +(-6481.10 + 2334.65i) q^{74} +(7109.84 - 5096.23i) q^{75} +(-1598.11 - 1930.37i) q^{76} +6062.18i q^{77} +(-3835.71 + 1381.72i) q^{78} -4403.48i q^{79} +(6351.51 - 786.313i) q^{80} -2666.68 q^{81} +(2956.02 + 8206.06i) q^{82} -10436.9 q^{83} +(6155.79 - 5096.23i) q^{84} +(-600.279 + 192.916i) q^{85} +(244.434 + 678.560i) q^{86} -6147.05 q^{87} +(5529.24 - 9360.92i) q^{88} +12059.4 q^{89} +(-9099.75 + 7014.45i) q^{90} -2598.77i q^{91} +(-5182.98 + 4290.87i) q^{92} +14080.2i q^{93} +(367.045 + 1018.93i) q^{94} +(-3727.92 + 1198.07i) q^{95} +(-14153.7 + 2254.73i) q^{96} -8152.32i q^{97} +(-1528.46 - 4243.06i) q^{98} +19517.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 48 q^{4} - 40 q^{5} + 312 q^{9}+O(q^{10}) \) 8 * q - 48 * q^4 - 40 * q^5 + 312 * q^9	\( 8 q - 48 q^{4} - 40 q^{5} + 312 q^{9} - 160 q^{10} + 640 q^{14} - 832 q^{16} - 400 q^{20} - 960 q^{21} + 1920 q^{24} - 2040 q^{25} + 2496 q^{26} + 2704 q^{29} - 1920 q^{30} - 2176 q^{34} - 5712 q^{36} + 6400 q^{40} + 1456 q^{41} + 1920 q^{44} + 6120 q^{45} + 7040 q^{46} - 8008 q^{49} - 12480 q^{50} - 11520 q^{54} - 14720 q^{56} + 21120 q^{60} + 6576 q^{61} + 6912 q^{64} - 1920 q^{65} + 46080 q^{66} - 12480 q^{69} - 6400 q^{70} - 23616 q^{74} - 48000 q^{76} + 19520 q^{80} - 19512 q^{81} + 24960 q^{84} + 8960 q^{85} + 37120 q^{86} + 27664 q^{89} - 48480 q^{90} + 10880 q^{94} - 76800 q^{96}+O(q^{100}) \) 8 * q - 48 * q^4 - 40 * q^5 + 312 * q^9 - 160 * q^10 + 640 * q^14 - 832 * q^16 - 400 * q^20 - 960 * q^21 + 1920 * q^24 - 2040 * q^25 + 2496 * q^26 + 2704 * q^29 - 1920 * q^30 - 2176 * q^34 - 5712 * q^36 + 6400 * q^40 + 1456 * q^41 + 1920 * q^44 + 6120 * q^45 + 7040 * q^46 - 8008 * q^49 - 12480 * q^50 - 11520 * q^54 - 14720 * q^56 + 21120 * q^60 + 6576 * q^61 + 6912 * q^64 - 1920 * q^65 + 46080 * q^66 - 12480 * q^69 - 6400 * q^70 - 23616 * q^74 - 48000 * q^76 + 19520 * q^80 - 19512 * q^81 + 24960 * q^84 + 8960 * q^85 + 37120 * q^86 + 27664 * q^89 - 48480 * q^90 + 10880 * q^94 - 76800 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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