LMFDB - Embedded newform 20.5.d.c.19.4

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			19.4
Root			$-0.677813 + 1.88164i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.5.d.c.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35563 + 3.76328i) q^{2} +13.9962 q^{3} +(-12.3246 - 10.2032i) q^{4} +(7.64911 + 23.8011i) q^{5} +(-18.9737 + 52.6718i) q^{6} -35.6863 q^{7} +(55.1050 - 32.5490i) q^{8} +114.895 q^{9} +O(q^{10})$	\(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} +(-99.9394 - 3.47961i) 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} +(148.575 - 371.383i) 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} +(-1398.78 - 48.7015i) 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} +(1196.21 + 1062.59i) 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} +(-681.629 - 2405.28i) 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} +(2079.49 - 5197.97i) 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} +(3566.46 + 124.174i) 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} +(-5620.42 + 3061.19i) 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} +(-11482.5 - 399.789i) 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	$-0.216453\pi$
$3$	13.9962			1.55514			0.777569	+	0.628798i	$0.216453\pi$
$4$	−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	$-0.618639\pi$
$7$	−35.6863			−0.728291			−0.364145	+	0.931342i	$0.618639\pi$
$8$	55.1050	−	32.5490i	0.861016	−	0.508579i
$9$	114.895			1.41845
$10$	−99.9394	−	3.47961i	−0.999394	−	0.0347961i
$11$		−	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	$-0.930877\pi$
$13$		−	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	$-0.930394\pi$
$19$		−	156.628i		−	0.433873i	0.976186	−	0.216937i	$-0.0696065\pi$
$20$	148.575	−	371.383i	0.371438	−	0.928458i
$21$	−499.473			−1.13259
$22$	639.284	+	230.286i	1.32084	+	0.475797i
$23$	−420.541			−0.794974			−0.397487	−	0.917608i	$-0.630118\pi$
$23$	−420.541			−0.794974			−0.397487	+	0.917608i	$0.630118\pi$
$24$	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	$0.415910\pi$
$30$	−1398.78	−	48.7015i	−1.55420	−	0.0541128i
$31$			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	$0.216534\pi$
$37$			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
$40$	1196.21	+	1062.59i	0.747629	+	0.664117i
$41$	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	$-0.515527\pi$
$43$	−180.311			−0.0975180			−0.0487590	+	0.998811i	$0.515527\pi$
$44$	−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	$-0.519520\pi$
$47$	−270.757			−0.122570			−0.0612849	+	0.998120i	$0.519520\pi$
$48$	668.871	+	3520.05i	0.290308	+	1.52780i
$49$	−1127.49			−0.469592
$50$	−681.629	−	2405.28i	−0.272652	−	0.962113i
$51$			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	$0.202010\pi$
$59$			4127.64i			1.18576i	−0.805290	+	0.592882i	$0.797990\pi$
$60$	2079.49	−	5197.97i	0.577637	−	1.44388i
$61$	−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	$-0.530572\pi$
$67$	−860.976			−0.191797			−0.0958984	+	0.995391i	$0.530572\pi$
$68$	257.332	−	310.834i	0.0556513	−	0.0672218i
$69$	−5886.00			−1.23629
$70$	3566.46	+	124.174i	0.727850	+	0.0253417i
$71$		−	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	$-0.817872\pi$
$73$		−	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	$0.114766\pi$
$79$			4403.48i			0.705574i	−0.935704	+	0.352787i	$0.885234\pi$
$80$	−5620.42	+	3061.19i	−0.878191	+	0.478311i
$81$	−2666.68			−0.406445
$82$	−2956.02	+	8206.06i	−0.439623	+	1.22041i
$83$	10436.9			1.51500			0.757501	−	0.652834i	$-0.226420\pi$
$83$	10436.9			1.51500			0.757501	+	0.652834i	$0.226420\pi$
$84$	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	$0.224596\pi$
$90$	−11482.5	−	399.789i	−1.41759	−	0.0493567i
$91$			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
$100$	9975.78	+	695.501i	0.997578	+	0.0695501i
$101$	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	$-0.745436\pi$
$103$	−14786.7			−1.39379			−0.696896	+	0.717172i	$0.745436\pi$
$104$	−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	$-0.648431\pi$
$107$	−10294.8			−0.899184			−0.449592	+	0.893234i	$0.648431\pi$
$108$	−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	$0.455824\pi$
$110$	−591.096	+	16977.1i	−0.0488509	+	1.40307i
$111$			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
$120$	16742.4	+	14872.2i	1.16267	+	1.03279i
$121$	−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	$-0.501714\pi$
$127$	−173.676			−0.0107680			−0.00538398	+	0.999986i	$0.501714\pi$
$128$	10819.5	+	12303.4i	0.660370	+	0.750940i
$129$	−2523.67			−0.151654
$130$	−253.395	+	7277.87i	−0.0149938	+	0.430643i
$131$		−	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	$-0.989696\pi$
$137$		−	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	$0.173704\pi$
$139$			20056.1i			1.03805i	−0.854760	+	0.519023i	$0.826296\pi$
$140$	−5302.10	+	13253.3i	−0.270515	+	0.676187i
$141$	−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	$0.675314\pi$
$150$	−9540.25	−	33664.9i	−0.424011	−	1.49622i
$151$		−	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	$-0.918399\pi$
$157$		−	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
$160$	−3900.92	−	25301.0i	−0.152380	−	0.988322i
$161$	15007.5			0.578972
$162$	3615.03	−	10035.5i	0.137747	−	0.382391i
$163$	7089.40			0.266830			0.133415	−	0.991060i	$-0.457406\pi$
$163$	7089.40			0.266830			0.133415	+	0.991060i	$0.457406\pi$
$164$	−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	$-0.228619\pi$
$167$	41999.3			1.50595			0.752973	+	0.658052i	$0.228619\pi$
$168$	−27523.5	+	16257.4i	−0.975180	+	0.576012i
$169$	23257.8			0.814322
$170$	87.7582	−	2520.54i	0.00303661	−	0.0872159i
$171$		−	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	$0.279101\pi$
$179$			49260.5i			1.53742i	−0.639597	+	0.768711i	$0.720899\pi$
$180$	17070.5	−	42669.9i	0.526867	−	1.31697i
$181$	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
$190$	−545.005	+	15653.3i	−0.0150971	+	0.433610i
$191$		−	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	$0.0932831\pi$
$193$			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	$-0.984727\pi$
$199$		−	3798.82i		−	0.0959273i	0.998849	−	0.0479636i	$-0.0152732\pi$
$200$	−16140.8	+	36598.8i	−0.403520	+	0.914971i
$201$	−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
$210$	49917.1	+	1737.97i	1.13191	+	0.0394098i
$211$			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
$220$	−63088.4	−	25239.1i	−1.30348	−	0.521469i
$221$	1836.64			0.0376045
$222$	−90711.0	−	32676.4i	−1.84058	−	0.663021i
$223$	69331.1			1.39418			0.697089	−	0.716984i	$-0.254478\pi$
$223$	69331.1			1.39418			0.697089	+	0.716984i	$0.254478\pi$
$224$	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	$-0.492942\pi$
$227$	2285.09			0.0443457			0.0221728	+	0.999754i	$0.492942\pi$
$228$	−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	$0.520587\pi$
$230$	42028.7	+	1463.32i	0.794493	+	0.0276620i
$231$			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	$0.0184282\pi$
$239$			6610.22i			0.115723i	−0.998325	+	0.0578616i	$0.981572\pi$
$240$	−78664.7	+	42845.1i	−1.36571	+	0.743839i
$241$	−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
$250$	52034.4	−	34621.8i	0.832551	−	0.553948i
$251$		−	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	$0.222623\pi$
$257$			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
$260$	−27045.2	−	10819.7i	−0.400076	−	0.160054i
$261$	50460.9			0.740754
$262$	24864.8	+	8956.90i	0.362228	+	0.130483i
$263$	−20477.3			−0.296047			−0.148024	−	0.988984i	$-0.547291\pi$
$263$	−20477.3			−0.296047			−0.148024	+	0.988984i	$0.547291\pi$
$264$	−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	$0.618381\pi$
$270$	−47411.0	−	1650.72i	−0.650357	−	0.0226436i
$271$		−	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	$-0.774848\pi$
$277$		−	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
$280$	−42688.1	−	37919.8i	−0.544491	−	0.483670i
$281$	−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	$-0.599276\pi$
$283$	−49151.0			−0.613705			−0.306853	+	0.951757i	$0.599276\pi$
$284$	−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
$290$	−43892.7	−	1528.22i	−0.521911	−	0.0181715i
$291$		−	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
$300$	139623.	+	9734.40i	1.55137	+	0.108160i
$301$	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	$-0.810330\pi$
$307$	−156013.			−1.65533			−0.827663	+	0.561226i	$0.810330\pi$
$308$	61853.6	−	74713.6i	0.652024	−	0.787587i
$309$	−206959.			−2.16754
$310$	3500.49	−	100539.i	0.0364255	−	1.04619i
$311$			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	$-0.936569\pi$
$313$		−	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
$320$	100503.	+	19618.5i	0.981476	+	0.191587i
$321$	−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
$330$	−8273.13	+	237616.i	−0.0759699	+	2.18197i
$331$			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	$-0.646566\pi$
$337$		−	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
$340$	9366.53	+	3747.17i	0.0810253	+	0.0324150i
$341$	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	$-0.427337\pi$
$347$	54497.1			0.452600			0.226300	+	0.974058i	$0.427337\pi$
$348$	−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	$0.888876\pi$
$350$	24324.8	+	85835.5i	0.198570	+	0.700698i
$351$		−	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	$-0.643963\pi$
$359$		−	231846.i		−	1.79891i	0.437011	−	0.899456i	$-0.356037\pi$
$360$	137438.	+	122086.i	1.06048	+	0.942018i
$361$	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	$-0.636331\pi$
$367$	−111878.			−0.830642			−0.415321	+	0.909675i	$0.636331\pi$
$368$	−20097.4	−	105766.i	−0.148403	−	0.781000i
$369$	250535.			1.83999
$370$	5992.57	−	172115.i	0.0437733	−	1.25723i
$371$			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	$0.0180168\pi$
$379$			16251.9i			0.113143i	−0.998399	+	0.0565713i	$0.981983\pi$
$380$	−58169.1	−	23271.1i	−0.402833	−	0.161157i
$381$	−2430.82			−0.0167457
$382$	74784.9	+	26939.4i	0.512492	+	0.184612i
$383$	36303.7			0.247488			0.123744	−	0.992314i	$-0.460510\pi$
$383$	36303.7			0.247488			0.123744	+	0.992314i	$0.460510\pi$
$384$	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	$0.322952\pi$
$390$	−3546.58	+	101863.i	−0.0233174	+	0.669710i
$391$		−	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
$400$	−115851.	−	110357.i	−0.724067	−	0.689729i
$401$	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	$0.488945\pi$
$410$	−217924.	−	7587.50i	−1.29639	−	0.0451368i
$411$		−	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	$-0.367201\pi$
$420$	−74209.4	+	185496.i	−0.420688	+	1.05156i
$421$	−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
$430$	18020.2	+	627.412i	0.0974590	+	0.00339325i
$431$			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	$-0.954685\pi$
$433$		−	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	$0.136638\pi$
$439$			160420.i			0.832397i	−0.909274	+	0.416198i	$0.863362\pi$
$440$	180506.	−	203205.i	0.932367	−	1.04961i
$441$	−129543.			−0.666094
$442$	−2489.80	+	6911.79i	−0.0127444	+	0.0353790i
$443$	66393.8			0.338314			0.169157	−	0.985589i	$-0.445896\pi$
$443$	66393.8			0.338314			0.169157	+	0.985589i	$0.445896\pi$
$444$	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	$0.366806\pi$
$450$	−78315.6	−	276354.i	−0.386744	−	1.36471i
$451$		−	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
$460$	−62482.0	+	156182.i	−0.295284	+	0.738100i
$461$	−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	$-0.732609\pi$
$463$	−286156.			−1.33487			−0.667437	+	0.744666i	$0.732609\pi$
$464$	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	$-0.721065\pi$
$467$	−279153.			−1.28000			−0.639999	+	0.768376i	$0.721065\pi$
$468$	−85369.7	+	103119.i	−0.389773	+	0.470811i
$469$	30725.0			0.139684
$470$	27059.3	+	942.128i	0.122496	+	0.00426495i
$471$		−	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	$0.757023\pi$
$480$	−54598.2	−	354119.i	−0.236971	−	1.53698i
$481$	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	$-0.308130\pi$
$487$	268917.			1.13386			0.566932	+	0.823765i	$0.308130\pi$
$488$	−137325.	+	81114.4i	−0.576648	+	0.340611i
$489$	99225.0			0.414957
$490$	112681.	+	3923.23i	0.469308	+	0.0163400i
$491$			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	$-0.101206\pi$
$500$	59752.2	+	242754.i	0.239009	+	0.971017i
$501$	587832.			2.34195
$502$	229615.	+	82713.0i	0.911156	+	0.328221i
$503$	−300512.			−1.18775			−0.593875	−	0.804557i	$-0.702403\pi$
$503$	−300512.			−1.18775			−0.593875	+	0.804557i	$0.702403\pi$
$504$	−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	$0.611774\pi$
$510$	1228.28	−	35278.1i	0.00472235	−	0.135633i
$511$			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
$520$	77380.6	−	87111.1i	0.286171	−	0.322156i
$521$	−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	$-0.600339\pi$
$523$	−169603.			−0.620057			−0.310028	+	0.950727i	$0.600339\pi$
$524$	−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
$530$	−3217.41	+	92408.7i	−0.0114539	+	0.328974i
$531$			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
$540$	70483.8	−	176183.i	0.241714	−	0.604195i
$541$	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	$-0.623440\pi$
$547$	−226292.			−0.756302			−0.378151	+	0.925744i	$0.623440\pi$
$548$	−12396.3	+	14973.6i	−0.0412792	+	0.0498616i
$549$	−286325.			−0.949981
$550$	−408595.	+	115791.i	−1.35073	+	0.382781i
$551$		−	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
$560$	200572.	−	109242.i	0.639578	−	0.348349i
$561$	59964.7			0.190533
$562$	40953.2	−	113688.i	0.129663	−	0.359949i
$563$	462000.			1.45756			0.728778	−	0.684750i	$-0.240089\pi$
$563$	462000.			1.45756			0.728778	+	0.684750i	$0.240089\pi$
$564$	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	$0.539849\pi$
$570$	−7628.03	+	219088.i	−0.0234781	+	0.674324i
$571$		−	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	$-0.696730\pi$
$577$		−	542683.i		−	1.63003i	0.579442	−	0.815013i	$-0.303270\pi$
$578$	−112361.	+	311919.i	−0.336325	+	0.933655i
$579$			301214.i			0.898498i
$580$	65253.2	−	163109.i	0.193975	−	0.484866i
$581$	−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	$-0.414355\pi$
$587$	183191.			0.531653			0.265827	+	0.964021i	$0.414355\pi$
$588$	194489.	+	161013.i	0.562524	+	0.465700i
$589$	157568.			0.454190
$590$	14362.6	−	412514.i	0.0412600	−	1.18505i
$591$		−	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	$0.0865074\pi$
$599$			192632.i			0.536876i	−0.963297	+	0.268438i	$0.913493\pi$
$600$	−225910.	+	512246.i	−0.627529	+	1.42291i
$601$	−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	$-0.566078\pi$
$607$	−151876.			−0.412205			−0.206102	+	0.978530i	$0.566078\pi$
$608$	−25232.1	+	158390.i	−0.0682567	+	0.428471i
$609$	−219365.			−0.591470
$610$	249056.	+	8671.43i	0.669325	+	0.0233040i
$611$			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	$0.0971161\pi$
$619$			230194.i			0.600776i	−0.953817	+	0.300388i	$0.902884\pi$
$620$	373611.	+	149467.i	0.971933	+	0.388831i
$621$	−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
$630$	409768.	+	14267.0i	1.03242	+	0.0359460i
$631$		−	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
$640$	−210075.	+	351626.i	−0.512877	+	0.858462i
$641$	−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	$-0.216739\pi$
$643$	642503.			1.55401			0.777004	+	0.629496i	$0.216739\pi$
$644$	−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	$-0.395546\pi$
$647$	269830.			0.644588			0.322294	+	0.946640i	$0.395546\pi$
$648$	−146948.	+	86798.0i	−0.349955	+	0.206709i
$649$	701180.			1.66472
$650$	−175159.	+	49638.2i	−0.414578	+	0.117487i
$651$		−	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	$0.0163082\pi$
$659$			44480.3i			0.102423i	−0.998688	+	0.0512115i	$0.983692\pi$
$660$	−883000.	−	353253.i	−2.02709	−	0.810956i
$661$	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
$670$	86045.5	+	2995.86i	0.191681	+	0.00667379i
$671$			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
$680$	−26799.2	+	30169.1i	−0.0579567	+	0.0652446i
$681$	31982.6			0.0689636
$682$	−231668.	+	643120.i	−0.498077	+	1.38268i
$683$	506300.			1.08534			0.542671	−	0.839946i	$-0.317413\pi$
$683$	506300.			1.08534			0.542671	+	0.839946i	$0.317413\pi$
$684$	−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
$690$	588243.	+	20481.0i	1.23555	+	0.0430182i
$691$		−	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
$700$	−355998.	−	24819.8i	−0.726527	−	0.0506527i
$701$	−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	$0.658329\pi$
$710$	−27957.8	+	802988.i	−0.0554608	+	1.59291i
$711$			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	$0.921676\pi$
$720$	−645756.	+	351714.i	−1.24567	+	0.678461i
$721$	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	$-0.475941\pi$
$727$	79819.7			0.151022			0.0755112	+	0.997145i	$0.475941\pi$
$728$	84587.6	+	143205.i	0.159604	+	0.270207i
$729$	−844210.			−1.58853
$730$	−20080.4	+	576739.i	−0.0376814	+	1.08226i
$731$		−	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	$-0.993661\pi$
$739$		−	21750.2i		−	0.0398267i	0.999802	−	0.0199133i	$-0.00633903\pi$
$740$	639594.	+	255876.i	1.16799	+	0.467267i
$741$	−159643.			−0.290745
$742$	−124178.	−	44731.9i	−0.225546	−	0.0812474i
$743$	−345994.			−0.626746			−0.313373	−	0.949630i	$-0.601459\pi$
$743$	−345994.			−0.626746			−0.313373	+	0.949630i	$0.601459\pi$
$744$	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
$750$	728286.	−	484575.i	1.29473	−	0.861466i
$751$			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	$0.370945\pi$
$757$			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
$760$	166431.	−	187360.i	0.288143	−	0.324376i
$761$	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	$0.688217\pi$
$770$	21094.0	−	605850.i	0.0355777	−	1.02184i
$771$			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
$780$	−378531.	−	151435.i	−0.622174	−	0.248906i
$781$	−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	$-0.562793\pi$
$787$	−242785.			−0.391988			−0.195994	+	0.980605i	$0.562793\pi$
$788$	−253642.	+	306377.i	−0.408478	+	0.493405i
$789$	−286605.			−0.460394
$790$	15322.4	−	440082.i	0.0245512	−	0.705146i
$791$		−	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
$800$	572353.	−	286376.i	0.894302	−	0.447463i
$801$	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	$0.481241\pi$
$810$	266507.	+	9279.03i	0.406199	+	0.0141427i
$811$		−	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
$820$	323977.	−	809823.i	0.481822	−	1.20438i
$821$	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	$-0.350504\pi$
$823$	613089.			0.905157			0.452578	+	0.891725i	$0.350504\pi$
$824$	−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	$-0.841374\pi$
$827$	−1.20150e6			−1.75676			−0.878378	+	0.477967i	$0.841374\pi$
$828$	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	$0.370240\pi$
$830$	−1.04305e6	−	36316.2i	−1.51409	−	0.0527162i
$831$		−	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	$-0.167226\pi$
$840$	−597473.	−	530734.i	−0.846759	−	0.752174i
$841$	−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
$850$	60662.8	−	17191.1i	0.0839624	−	0.0237940i
$851$		−	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	$0.295964\pi$
$859$			1.18282e6i			1.60300i	−0.597995	+	0.801499i	$0.704036\pi$
$860$	−26789.7	+	66964.4i	−0.0362219	+	0.0905413i
$861$	−1.08913e6			−1.46918
$862$	−527913.	−	190167.i	−0.710474	−	0.255930i
$863$	1.04231e6			1.39951			0.699754	−	0.714384i	$-0.253293\pi$
$863$	1.04231e6			1.39951			0.699754	+	0.714384i	$0.253293\pi$
$864$	−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
$870$	−614333.	−	21389.3i	−0.811643	−	0.0282591i
$871$			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
$880$	520017.	+	954765.i	0.671509	+	1.23291i
$881$	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	$-0.580163\pi$
$883$	−388576.			−0.498373			−0.249187	+	0.968456i	$0.580163\pi$
$884$	−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	$-0.436886\pi$
$887$	309960.			0.393966			0.196983	+	0.980407i	$0.436886\pi$
$888$	784570.	+	1.32826e6i	0.994960	+	1.68445i
$889$	6197.86			0.00784221
$890$	−1.20521e6	−	41962.0i	−1.52154	−	0.0529757i
$891$			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
$900$	1.14616e6	+	79909.4i	1.41502	+	0.0986535i
$901$	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	$-0.509154\pi$
$907$	−47309.4			−0.0575087			−0.0287543	+	0.999587i	$0.509154\pi$
$908$	−28162.7	−	23315.2i	−0.0341588	−	0.0282792i
$909$	1.35828e6			1.64384
$910$	9042.72	−	259720.i	0.0109198	−	0.313634i
$911$		−	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	$-0.311992\pi$
$920$	−503054.	−	446862.i	−0.594345	−	0.527956i
$921$	−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	$0.701812\pi$
$930$	48993.7	−	1.40717e6i	0.0566466	−	1.62697i
$931$			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
$940$	−40227.7	+	100554.i	−0.0455271	+	0.113801i
$941$	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	$-0.206107\pi$
$947$	1.43058e6			1.59518			0.797592	+	0.603197i	$0.206107\pi$
$948$	628846.	−	759590.i	0.699725	−	0.845206i
$949$	−420252.			−0.466635
$950$	−376735.	+	106762.i	−0.417435	+	0.118296i
$951$			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
$960$	1.40667e6	+	274585.i	1.52633	+	0.297944i
$961$	−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	$-0.371125\pi$
$967$	736666.			0.787803			0.393902	+	0.919153i	$0.371125\pi$
$968$	−783387.	+	462725.i	−0.836037	+	0.493824i
$969$	55288.9			0.0588831
$970$	−28366.9	+	814738.i	−0.0301487	+	0.865914i
$971$			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	$-0.706738\pi$
$977$		−	1.52036e6i		−	1.59279i	0.604777	−	0.796395i	$-0.293262\pi$
$978$	−134512.	+	373411.i	−0.140632	+	0.390400i
$979$		−	2.04858e6i		−	2.13741i
$980$	−167517.	+	418731.i	−0.174425	+	0.435997i
$981$	377677.			0.392448
$982$	−501613.	−	180694.i	−0.520171	−	0.187378i
$983$	1.19830e6			1.24010			0.620051	−	0.784562i	$-0.287112\pi$
$983$	1.19830e6			1.24010			0.620051	+	0.784562i	$0.287112\pi$
$984$	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
$990$	−67913.8	+	1.95058e6i	−0.0692928	+	1.99019i
$991$			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	$0.0406587\pi$
$997$			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.19.4	yes	8
3.2	odd	2		180.5.f.g.19.5		8
4.3	odd	2	inner	20.5.d.c.19.6	yes	8
5.2	odd	4		100.5.b.e.51.1		8
5.3	odd	4		100.5.b.e.51.8		8
5.4	even	2	inner	20.5.d.c.19.5	yes	8
8.3	odd	2		320.5.h.f.319.7		8
8.5	even	2		320.5.h.f.319.1		8
12.11	even	2		180.5.f.g.19.3		8
15.14	odd	2		180.5.f.g.19.4		8
20.3	even	4		100.5.b.e.51.7		8
20.7	even	4		100.5.b.e.51.2		8
20.19	odd	2	inner	20.5.d.c.19.3	✓	8
40.19	odd	2		320.5.h.f.319.2		8
40.29	even	2		320.5.h.f.319.8		8
60.59	even	2		180.5.f.g.19.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.d.c.19.3	✓	8	20.19	odd	2	inner
20.5.d.c.19.4	yes	8	1.1	even	1	trivial
20.5.d.c.19.5	yes	8	5.4	even	2	inner
20.5.d.c.19.6	yes	8	4.3	odd	2	inner
100.5.b.e.51.1		8	5.2	odd	4
100.5.b.e.51.2		8	20.7	even	4
100.5.b.e.51.7		8	20.3	even	4
100.5.b.e.51.8		8	5.3	odd	4
180.5.f.g.19.3		8	12.11	even	2
180.5.f.g.19.4		8	15.14	odd	2
180.5.f.g.19.5		8	3.2	odd	2
180.5.f.g.19.6		8	60.59	even	2
320.5.h.f.319.1		8	8.5	even	2
320.5.h.f.319.2		8	40.19	odd	2
320.5.h.f.319.7		8	8.3	odd	2
320.5.h.f.319.8		8	40.29	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} +(-99.9394 - 3.47961i) 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} +(148.575 - 371.383i) 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} +(-1398.78 - 48.7015i) 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} +(1196.21 + 1062.59i) 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} +(-681.629 - 2405.28i) 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} +(2079.49 - 5197.97i) 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} +(3566.46 + 124.174i) 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} +(-5620.42 + 3061.19i) 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} +(-11482.5 - 399.789i) 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

Related objects

Downloads

Learn more