LMFDB - Embedded newform 20.5.d.c.19.5

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

$q$-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	$-0.752309\pi$
$11$		−	169.874i		−	1.40392i	0.712217	−	0.701960i	$-0.247691\pi$
$12$	172.497	+	142.806i	1.19790	+	0.991711i
$13$			72.8228i			0.430904i	0.976514	+	0.215452i	$0.0691225\pi$
$13$			72.8228i			0.430904i	−0.976514	+	0.215452i	$0.930877\pi$
$14$	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	$-0.986106\pi$
$17$		−	25.2207i		−	0.0872688i	0.999048	−	0.0436344i	$-0.0138937\pi$
$18$	155.754	−	432.381i	0.480723	−	1.33451i
$19$		−	156.628i		−	0.433873i	−0.976186	−	0.216937i	$-0.930394\pi$
$19$		−	156.628i		−	0.433873i	0.976186	−	0.216937i	$-0.0696065\pi$
$20$	−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	$0.175341\pi$
$31$			1006.00i			1.04683i	−0.852079	+	0.523413i	$0.824659\pi$
$32$	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	$-0.783466\pi$
$37$		−	1722.19i		−	1.25799i	0.777407	−	0.628997i	$-0.216534\pi$
$38$	−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	$0.0526290\pi$
$53$			924.647i			0.329173i	−0.986363	+	0.164587i	$0.947371\pi$
$54$	−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	$0.202010\pi$
$59$			4127.64i			1.18576i	−0.805290	+	0.592882i	$0.797990\pi$
$60$	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	$-0.706451\pi$
$71$		−	8034.75i		−	1.59388i	0.604058	−	0.796940i	$-0.293549\pi$
$72$	−6331.27	+	3739.71i	−1.22131	+	0.721395i
$73$			5770.88i			1.08292i	0.840726	+	0.541460i	$0.182128\pi$
$73$			5770.88i			1.08292i	−0.840726	+	0.541460i	$0.817872\pi$
$74$	−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	$0.114766\pi$
$79$			4403.48i			0.705574i	−0.935704	+	0.352787i	$0.885234\pi$
$80$	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	$0.142622\pi$
$97$			8152.32i			0.866439i	−0.901289	+	0.433219i	$0.857378\pi$
$98$	−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	$-0.776028\pi$
$113$		−	16522.8i		−	1.29398i	0.762500	−	0.646988i	$-0.223972\pi$
$114$	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	$-0.938338\pi$
$131$		−	6607.20i		−	0.385013i	0.981296	−	0.192506i	$-0.0616616\pi$
$132$	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	$0.0103041\pi$
$137$			1214.94i			0.0647313i	−0.999476	+	0.0323657i	$0.989696\pi$
$138$	−7979.21	+	22150.7i	−0.418988	+	1.16313i
$139$			20056.1i			1.03805i	0.854760	+	0.519023i	$0.173704\pi$
$139$			20056.1i			1.03805i	−0.854760	+	0.519023i	$0.826296\pi$
$140$	−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	$-0.801060\pi$
$151$		−	26681.2i		−	1.17018i	0.810970	−	0.585088i	$-0.198940\pi$
$152$	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	$0.0816013\pi$
$157$			12500.0i			0.507119i	−0.967320	+	0.253559i	$0.918399\pi$
$158$	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	$0.138922\pi$
$173$			25302.8i			0.845427i	−0.906263	+	0.422713i	$0.861078\pi$
$174$	−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	$0.279101\pi$
$179$			49260.5i			1.53742i	−0.639597	+	0.768711i	$0.720899\pi$
$180$	−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	$-0.912194\pi$
$191$		−	19872.3i		−	0.544729i	0.962194	−	0.272365i	$-0.0878057\pi$
$192$	−27672.3	+	50207.7i	−0.750658	+	1.36197i
$193$		−	21521.0i		−	0.577761i	−0.957365	−	0.288881i	$-0.906717\pi$
$193$		−	21521.0i		−	0.577761i	0.957365	−	0.288881i	$-0.0932831\pi$
$194$	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	$0.103775\pi$
$197$			24859.0i			0.640548i	−0.947325	+	0.320274i	$0.896225\pi$
$198$	−73450.4	−	26458.6i	−1.87354	−	0.674896i
$199$		−	3798.82i		−	0.0959273i	−0.998849	−	0.0479636i	$-0.984727\pi$
$199$		−	3798.82i		−	0.0959273i	0.998849	−	0.0479636i	$-0.0152732\pi$
$200$	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	$0.351379\pi$
$211$			79511.4i			1.78593i	−0.450127	+	0.892965i	$0.648621\pi$
$212$	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	$0.193302\pi$
$233$			61958.1i			1.14126i	−0.821206	+	0.570632i	$0.806698\pi$
$234$	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	$0.0184282\pi$
$239$			6610.22i			0.115723i	−0.998325	+	0.0578616i	$0.981572\pi$
$240$	−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	$-0.839098\pi$
$251$		−	61014.6i		−	0.968470i	0.874938	−	0.484235i	$-0.160902\pi$
$252$	−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	$-0.777377\pi$
$257$		−	85038.5i		−	1.28751i	0.765234	−	0.643753i	$-0.222623\pi$
$258$	−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	$-0.809874\pi$
$271$		−	82607.9i		−	1.12482i	0.826858	−	0.562410i	$-0.190126\pi$
$272$	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	$0.225152\pi$
$277$			99718.7i			1.29962i	−0.760096	+	0.649811i	$0.774848\pi$
$278$	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	$-0.964749\pi$
$293$		−	18975.5i		−	0.221033i	0.993874	−	0.110517i	$-0.0352506\pi$
$294$	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	$0.0591589\pi$
$311$			35745.2i			0.369570i	−0.982779	+	0.184785i	$0.940841\pi$
$312$	33175.4	+	56165.5i	0.340806	+	0.576980i
$313$			38787.7i			0.395918i	0.980210	+	0.197959i	$0.0634312\pi$
$313$			38787.7i			0.395918i	−0.980210	+	0.197959i	$0.936569\pi$
$314$	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	$-0.739260\pi$
$317$		−	146826.i		−	1.46112i	0.682851	−	0.730558i	$-0.260740\pi$
$318$	−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	$0.312423\pi$
$331$			182164.i			1.66267i	−0.555772	+	0.831335i	$0.687577\pi$
$332$	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	$0.353434\pi$
$337$			203482.i			1.79171i	−0.444351	+	0.895853i	$0.646566\pi$
$338$	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	$-0.892843\pi$
$353$		−	82322.3i		−	0.660645i	0.943868	−	0.330322i	$-0.107157\pi$
$354$	−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	$-0.643963\pi$
$359$		−	231846.i		−	1.79891i	0.437011	−	0.899456i	$-0.356037\pi$
$360$	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	$-0.785331\pi$
$373$		−	173753.i		−	1.24886i	0.781081	−	0.624430i	$-0.214669\pi$
$374$	−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	$0.0180168\pi$
$379$			16251.9i			0.113143i	−0.998399	+	0.0565713i	$0.981983\pi$
$380$	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	$-0.982341\pi$
$397$		−	17478.7i		−	0.110899i	0.998461	−	0.0554495i	$-0.0176592\pi$
$398$	−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	$-0.632799\pi$
$419$		−	321005.i		−	1.82845i	0.405201	−	0.914227i	$-0.367201\pi$
$420$	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	$0.123244\pi$
$431$			140280.i			0.755164i	−0.925976	+	0.377582i	$0.876756\pi$
$432$	−22671.2	−	119311.i	−0.121480	−	0.639312i
$433$			53202.7i			0.283765i	0.989884	+	0.141882i	$0.0453155\pi$
$433$			53202.7i			0.283765i	−0.989884	+	0.141882i	$0.954685\pi$
$434$	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	$0.136638\pi$
$439$			160420.i			0.832397i	−0.909274	+	0.416198i	$0.863362\pi$
$440$	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	$0.278430\pi$
$457$			320525.i			1.53472i	−0.641216	+	0.767361i	$0.721570\pi$
$458$	−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	$0.242977\pi$
$479$			317241.i			1.38267i	−0.722534	+	0.691336i	$0.757023\pi$
$480$	−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	$0.0891566\pi$
$491$			133292.i			0.552891i	−0.961030	+	0.276446i	$0.910843\pi$
$492$	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	$-0.898794\pi$
$499$		−	155684.i		−	0.625235i	0.949879	−	0.312617i	$-0.101206\pi$
$500$	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	$0.214224\pi$
$557$			386780.i			1.24668i	−0.781953	+	0.623338i	$0.785776\pi$
$558$	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	$-0.930374\pi$
$571$		−	141499.i		−	0.433991i	0.976173	−	0.216995i	$-0.0696256\pi$
$572$	−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	$0.303270\pi$
$577$			542683.i			1.63003i	−0.579442	+	0.815013i	$0.696730\pi$
$578$	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	$-0.844793\pi$
$593$		−	329497.i		−	0.937006i	0.883462	−	0.468503i	$-0.155207\pi$
$594$	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	$0.0865074\pi$
$599$			192632.i			0.536876i	−0.963297	+	0.268438i	$0.913493\pi$
$600$	−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	$-0.800999\pi$
$613$		−	439833.i		−	1.17049i	0.810857	−	0.585244i	$-0.199001\pi$
$614$	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	$-0.863958\pi$
$617$		−	315589.i		−	0.828994i	0.910051	−	0.414497i	$-0.136042\pi$
$618$	−280559.	+	778844.i	−0.734593	+	2.03926i
$619$			230194.i			0.600776i	0.953817	+	0.300388i	$0.0971161\pi$
$619$			230194.i			0.600776i	−0.953817	+	0.300388i	$0.902884\pi$
$620$	−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	$-0.960966\pi$
$631$		−	97407.4i		−	0.244643i	0.992491	−	0.122322i	$-0.0390340\pi$
$632$	−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	$0.0538087\pi$
$653$			143479.i			0.336482i	−0.985746	+	0.168241i	$0.946191\pi$
$654$	−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	$0.0163082\pi$
$659$			44480.3i			0.102423i	−0.998688	+	0.0512115i	$0.983692\pi$
$660$	−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	$0.126818\pi$
$673$			351431.i			0.775908i	−0.921679	+	0.387954i	$0.873182\pi$
$674$	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	$0.0587596\pi$
$677$			168255.i			0.367104i	−0.983010	+	0.183552i	$0.941240\pi$
$678$	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	$-0.965685\pi$
$691$		−	102749.i		−	0.215189i	0.994195	−	0.107594i	$-0.0343148\pi$
$692$	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	$0.0783239\pi$
$719$			251849.i			0.487172i	−0.969879	+	0.243586i	$0.921676\pi$
$720$	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	$-0.828194\pi$
$733$		−	552245.i		−	1.02784i	0.857840	−	0.513918i	$-0.171806\pi$
$734$	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	$-0.993661\pi$
$739$		−	21750.2i		−	0.0398267i	0.999802	−	0.0199133i	$-0.00633903\pi$
$740$	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	$0.0892744\pi$
$751$			312233.i			0.553603i	−0.960927	+	0.276801i	$0.910726\pi$
$752$	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	$-0.629055\pi$
$757$		−	1.05318e6i		−	1.83786i	0.394422	−	0.918930i	$-0.370945\pi$
$758$	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	$-0.957325\pi$
$773$		−	159740.i		−	0.267335i	0.991026	−	0.133667i	$-0.0426754\pi$
$774$	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	$0.110274\pi$
$797$			431369.i			0.679098i	−0.940588	+	0.339549i	$0.889726\pi$
$798$	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	$-0.882350\pi$
$811$		−	475202.i		−	0.722498i	0.932469	−	0.361249i	$-0.117650\pi$
$812$	−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	$-0.832774\pi$
$839$		−	706063.i		−	1.00304i	0.865145	−	0.501521i	$-0.167226\pi$
$840$	−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	$0.0160261\pi$
$853$			73235.8i			0.100653i	−0.998733	+	0.0503263i	$0.983974\pi$
$854$	−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	$-0.901290\pi$
$857$		−	448249.i		−	0.610319i	0.952301	−	0.305160i	$-0.0987099\pi$
$858$	−234718.	+	651588.i	−0.318839	+	0.885112i
$859$			1.18282e6i			1.60300i	0.597995	+	0.801499i	$0.295964\pi$
$859$			1.18282e6i			1.60300i	−0.597995	+	0.801499i	$0.704036\pi$
$860$	−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	$-0.956902\pi$
$877$		−	207637.i		−	0.269964i	0.990848	−	0.134982i	$-0.0430976\pi$
$878$	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	$-0.942658\pi$
$911$		−	297399.i		−	0.358346i	0.983818	−	0.179173i	$-0.0573422\pi$
$912$	−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	$-0.688008\pi$
$919$		−	1.40295e6i		−	1.66116i	0.556897	−	0.830582i	$-0.311992\pi$
$920$	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	$-0.953056\pi$
$937$		−	258027.i		−	0.293890i	0.989145	−	0.146945i	$-0.0469441\pi$
$938$	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	$-0.740369\pi$
$953$		−	1.32267e6i		−	1.45635i	0.685392	−	0.728174i	$-0.259631\pi$
$954$	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	$0.214586\pi$
$971$			1.17709e6i			1.24846i	−0.781243	+	0.624228i	$0.785414\pi$
$972$	−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	$0.293262\pi$
$977$			1.52036e6i			1.59279i	−0.604777	+	0.796395i	$0.706738\pi$
$978$	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	$0.292102\pi$
$991$			1.55991e6i			1.58837i	−0.607677	+	0.794184i	$0.707898\pi$
$992$	−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	$-0.959341\pi$
$997$		−	253246.i		−	0.254772i	0.991853	−	0.127386i	$-0.0406587\pi$
$998$	−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.19.5	yes	8
3.2	odd	2		180.5.f.g.19.4		8
4.3	odd	2	inner	20.5.d.c.19.3	✓	8
5.2	odd	4		100.5.b.e.51.8		8
5.3	odd	4		100.5.b.e.51.1		8
5.4	even	2	inner	20.5.d.c.19.4	yes	8
8.3	odd	2		320.5.h.f.319.2		8
8.5	even	2		320.5.h.f.319.8		8
12.11	even	2		180.5.f.g.19.6		8
15.14	odd	2		180.5.f.g.19.5		8
20.3	even	4		100.5.b.e.51.2		8
20.7	even	4		100.5.b.e.51.7		8
20.19	odd	2	inner	20.5.d.c.19.6	yes	8
40.19	odd	2		320.5.h.f.319.7		8
40.29	even	2		320.5.h.f.319.1		8
60.59	even	2		180.5.f.g.19.3		8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

Properties

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