LMFDB - Embedded newform 243.4.e.c.190.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,4,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, not 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:	$14.3374641314$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			190.6
Character	$\chi$	$=$	243.190
Dual form			243.4.e.c.55.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71186 + 0.623068i) q^{2} +(-3.58609 - 3.00909i) q^{4} +(-2.34910 + 13.3224i) q^{5} +(17.5105 - 14.6931i) q^{7} +(-11.5509 - 20.0068i) q^{8} +O(q^{10})$	\(q+(1.71186 + 0.623068i) q^{2} +(-3.58609 - 3.00909i) q^{4} +(-2.34910 + 13.3224i) q^{5} +(17.5105 - 14.6931i) q^{7} +(-11.5509 - 20.0068i) q^{8} +(-12.3221 + 21.3425i) q^{10} +(5.74418 + 32.5769i) q^{11} +(64.1142 - 23.3357i) q^{13} +(39.1304 - 14.2423i) q^{14} +(-0.804842 - 4.56449i) q^{16} +(-18.6324 + 32.2722i) q^{17} +(47.5146 + 82.2977i) q^{19} +(48.5124 - 40.7067i) q^{20} +(-10.4643 + 59.3462i) q^{22} +(73.3609 + 61.5571i) q^{23} +(-54.5069 - 19.8389i) q^{25} +124.295 q^{26} -107.007 q^{28} +(134.732 + 49.0385i) q^{29} +(61.4981 + 51.6030i) q^{31} +(-30.6266 + 173.692i) q^{32} +(-52.0039 + 43.6365i) q^{34} +(154.613 + 267.798i) q^{35} +(32.8251 - 56.8548i) q^{37} +(30.0615 + 170.487i) q^{38} +(293.674 - 106.888i) q^{40} +(92.9660 - 33.8369i) q^{41} +(-76.3794 - 433.169i) q^{43} +(77.4275 - 134.108i) q^{44} +(87.2297 + 151.086i) q^{46} +(204.896 - 171.928i) q^{47} +(31.1704 - 176.776i) q^{49} +(-80.9475 - 67.9230i) q^{50} +(-300.138 - 109.241i) q^{52} -38.9538 q^{53} -447.496 q^{55} +(-496.224 - 180.611i) q^{56} +(200.089 + 167.895i) q^{58} +(37.3707 - 211.940i) q^{59} +(-40.7835 + 34.2214i) q^{61} +(73.1242 + 126.655i) q^{62} +(-179.190 + 310.366i) q^{64} +(160.277 + 908.974i) q^{65} +(-973.170 + 354.205i) q^{67} +(163.927 - 59.6647i) q^{68} +(97.8205 + 554.768i) q^{70} +(-148.085 + 256.490i) q^{71} +(49.0512 + 84.9591i) q^{73} +(91.6165 - 76.8754i) q^{74} +(77.2492 - 438.102i) q^{76} +(579.237 + 486.038i) q^{77} +(574.263 + 209.014i) q^{79} +62.7006 q^{80} +180.228 q^{82} +(-807.108 - 293.763i) q^{83} +(-386.175 - 324.039i) q^{85} +(139.142 - 789.116i) q^{86} +(585.409 - 491.217i) q^{88} +(-663.574 - 1149.34i) q^{89} +(779.800 - 1350.65i) q^{91} +(-77.8481 - 441.499i) q^{92} +(457.877 - 166.653i) q^{94} +(-1208.02 + 439.683i) q^{95} +(116.752 + 662.133i) q^{97} +(163.503 - 283.196i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8}+O(q^{10}) $ 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8	$ 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8} - 3 q^{10} - 159 q^{11} + 3 q^{13} - 336 q^{14} - 45 q^{16} - 207 q^{17} - 3 q^{19} + 681 q^{20} + 111 q^{22} + 33 q^{23} + 435 q^{25} + 1914 q^{26} - 12 q^{28} - 51 q^{29} + 111 q^{31} + 1647 q^{32} - 513 q^{34} - 1257 q^{35} - 3 q^{37} - 525 q^{38} - 6 q^{40} + 447 q^{41} + 516 q^{43} - 2211 q^{44} - 3 q^{46} + 2109 q^{47} - 591 q^{49} - 4938 q^{50} - 1350 q^{52} + 2736 q^{53} - 12 q^{55} - 7773 q^{56} - 888 q^{58} + 3048 q^{59} + 57 q^{61} - 2118 q^{62} - 195 q^{64} + 3297 q^{65} + 2082 q^{67} + 3573 q^{68} + 1524 q^{70} - 3105 q^{71} - 219 q^{73} + 9006 q^{74} - 1425 q^{76} - 8985 q^{77} - 1401 q^{79} + 9870 q^{80} - 12 q^{82} - 8511 q^{83} - 1827 q^{85} + 12507 q^{86} - 3693 q^{88} - 5202 q^{89} + 267 q^{91} + 5118 q^{92} - 2211 q^{94} + 5178 q^{95} + 1569 q^{97} - 4392 q^{98}+O(q^{100}) $ 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8 - 3 * q^10 - 159 * q^11 + 3 * q^13 - 336 * q^14 - 45 * q^16 - 207 * q^17 - 3 * q^19 + 681 * q^20 + 111 * q^22 + 33 * q^23 + 435 * q^25 + 1914 * q^26 - 12 * q^28 - 51 * q^29 + 111 * q^31 + 1647 * q^32 - 513 * q^34 - 1257 * q^35 - 3 * q^37 - 525 * q^38 - 6 * q^40 + 447 * q^41 + 516 * q^43 - 2211 * q^44 - 3 * q^46 + 2109 * q^47 - 591 * q^49 - 4938 * q^50 - 1350 * q^52 + 2736 * q^53 - 12 * q^55 - 7773 * q^56 - 888 * q^58 + 3048 * q^59 + 57 * q^61 - 2118 * q^62 - 195 * q^64 + 3297 * q^65 + 2082 * q^67 + 3573 * q^68 + 1524 * q^70 - 3105 * q^71 - 219 * q^73 + 9006 * q^74 - 1425 * q^76 - 8985 * q^77 - 1401 * q^79 + 9870 * q^80 - 12 * q^82 - 8511 * q^83 - 1827 * q^85 + 12507 * q^86 - 3693 * q^88 - 5202 * q^89 + 267 * q^91 + 5118 * q^92 - 2211 * q^94 + 5178 * q^95 + 1569 * q^97 - 4392 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	1.71186	+	0.623068i	0.605235	+	0.220288i	0.626417	−	0.779488i	$-0.284521\pi$
$2$	1.71186	+	0.623068i	0.605235	+	0.220288i	−0.0211818	+	0.999776i	$0.506743\pi$
$3$		0			0
$3$		0			0
$4$	−3.58609	−	3.00909i	−0.448261	−	0.376136i
$5$	−2.34910	+	13.3224i	−0.210110	+	1.19159i	0.679083	+	0.734061i	$0.262378\pi$
$5$	−2.34910	+	13.3224i	−0.210110	+	1.19159i	−0.889193	+	0.457532i	$0.848734\pi$
$6$		0			0
$7$	17.5105	−	14.6931i	0.945478	−	0.793350i	−0.0330521	−	0.999454i	$-0.510523\pi$
$7$	17.5105	−	14.6931i	0.945478	−	0.793350i	0.978530	+	0.206103i	$0.0660783\pi$
$8$	−11.5509	−	20.0068i	−0.510485	−	0.884185i
$9$		0			0
$10$	−12.3221	+	21.3425i	−0.389659	+	0.674910i
$11$	5.74418	+	32.5769i	0.157449	+	0.892936i	0.956513	+	0.291690i	$0.0942177\pi$
$11$	5.74418	+	32.5769i	0.157449	+	0.892936i	−0.799064	+	0.601246i	$0.794671\pi$
$12$		0			0
$13$	64.1142	−	23.3357i	1.36785	−	0.497858i	0.449379	−	0.893341i	$-0.351645\pi$
$13$	64.1142	−	23.3357i	1.36785	−	0.497858i	0.918473	+	0.395484i	$0.129423\pi$
$14$	39.1304	−	14.2423i	0.747002	−	0.271887i
$15$		0			0
$16$	−0.804842	−	4.56449i	−0.0125757	−	0.0713201i
$17$	−18.6324	+	32.2722i	−0.265825	+	0.460422i	−0.967779	−	0.251800i	$-0.918978\pi$
$17$	−18.6324	+	32.2722i	−0.265825	+	0.460422i	0.701955	+	0.712222i	$0.252311\pi$
$18$		0			0
$19$	47.5146	+	82.2977i	0.573715	+	0.993704i	0.996180	+	0.0873247i	$0.0278317\pi$
$19$	47.5146	+	82.2977i	0.573715	+	0.993704i	−0.422465	+	0.906379i	$0.638835\pi$
$20$	48.5124	−	40.7067i	0.542385	−	0.455115i
$21$		0			0
$22$	−10.4643	+	59.3462i	−0.101409	+	0.575121i
$23$	73.3609	+	61.5571i	0.665078	+	0.558067i	0.911604	−	0.411069i	$-0.134845\pi$
$23$	73.3609	+	61.5571i	0.665078	+	0.558067i	−0.246526	+	0.969136i	$0.579289\pi$
$24$		0			0
$25$	−54.5069	−	19.8389i	−0.436055	−	0.158711i
$26$	124.295			0.937545
$27$		0			0
$28$	−107.007			−0.722229
$29$	134.732	+	49.0385i	0.862729	+	0.314008i	0.735219	−	0.677830i	$-0.237079\pi$
$29$	134.732	+	49.0385i	0.862729	+	0.314008i	0.127510	+	0.991837i	$0.459301\pi$
$30$		0			0
$31$	61.4981	+	51.6030i	0.356303	+	0.298973i	0.803315	−	0.595554i	$-0.203068\pi$
$31$	61.4981	+	51.6030i	0.356303	+	0.298973i	−0.447012	+	0.894528i	$0.647512\pi$
$32$	−30.6266	+	173.692i	−0.169190	+	0.959522i
$33$		0			0
$34$	−52.0039	+	43.6365i	−0.262312	+	0.220106i
$35$	154.613	+	267.798i	0.746696	+	1.29332i
$36$		0			0
$37$	32.8251	−	56.8548i	0.145849	−	0.252618i	−0.783840	−	0.620962i	$-0.786742\pi$
$37$	32.8251	−	56.8548i	0.145849	−	0.252618i	0.929689	+	0.368344i	$0.120075\pi$
$38$	30.0615	+	170.487i	0.128332	+	0.727807i
$39$		0			0
$40$	293.674	−	106.888i	1.16085	−	0.422514i
$41$	92.9660	−	33.8369i	0.354118	−	0.128889i	−0.158835	−	0.987305i	$-0.550774\pi$
$41$	92.9660	−	33.8369i	0.354118	−	0.128889i	0.512953	+	0.858417i	$0.328551\pi$
$42$		0			0
$43$	−76.3794	−	433.169i	−0.270878	−	1.53622i	−0.751758	−	0.659439i	$-0.770794\pi$
$43$	−76.3794	−	433.169i	−0.270878	−	1.53622i	0.480880	−	0.876786i	$-0.340317\pi$
$44$	77.4275	−	134.108i	0.265287	−	0.459491i
$45$		0			0
$46$	87.2297	+	151.086i	0.279594	+	0.484271i
$47$	204.896	−	171.928i	0.635896	−	0.533580i	−0.266859	−	0.963736i	$-0.585986\pi$
$47$	204.896	−	171.928i	0.635896	−	0.533580i	0.902755	+	0.430155i	$0.141541\pi$
$48$		0			0
$49$	31.1704	−	176.776i	0.0908759	−	0.515383i
$50$	−80.9475	−	67.9230i	−0.228954	−	0.192115i
$51$		0			0
$52$	−300.138	−	109.241i	−0.800417	−	0.291328i
$53$	−38.9538			−0.100957			−0.0504784	−	0.998725i	$-0.516075\pi$
$53$	−38.9538			−0.100957			−0.0504784	+	0.998725i	$0.516075\pi$
$54$		0			0
$55$	−447.496			−1.09710
$56$	−496.224	−	180.611i	−1.18412	−	0.430985i
$57$		0			0
$58$	200.089	+	167.895i	0.452982	+	0.380097i
$59$	37.3707	−	211.940i	0.0824619	−	0.467665i	−0.915414	−	0.402515i	$-0.868136\pi$
$59$	37.3707	−	211.940i	0.0824619	−	0.467665i	0.997875	−	0.0651501i	$-0.0207526\pi$
$60$		0			0
$61$	−40.7835	+	34.2214i	−0.0856032	+	0.0718296i	−0.684585	−	0.728933i	$-0.740017\pi$
$61$	−40.7835	+	34.2214i	−0.0856032	+	0.0718296i	0.598982	+	0.800763i	$0.295572\pi$
$62$	73.1242	+	126.655i	0.149787	+	0.259438i
$63$		0			0
$64$	−179.190	+	310.366i	−0.349981	+	0.606184i
$65$	160.277	+	908.974i	0.305844	+	1.73453i
$66$		0			0
$67$	−973.170	+	354.205i	−1.77450	+	0.645866i	−0.774591	+	0.632462i	$0.782044\pi$
$67$	−973.170	+	354.205i	−1.77450	+	0.645866i	−0.999910	+	0.0134033i	$0.995733\pi$
$68$	163.927	−	59.6647i	0.292340	−	0.106403i
$69$		0			0
$70$	97.8205	+	554.768i	0.167026	+	0.947249i
$71$	−148.085	+	256.490i	−0.247527	+	0.428729i	−0.962839	−	0.270076i	$-0.912951\pi$
$71$	−148.085	+	256.490i	−0.247527	+	0.428729i	0.715312	+	0.698805i	$0.246284\pi$
$72$		0			0
$73$	49.0512	+	84.9591i	0.0786439	+	0.136215i	0.902665	−	0.430344i	$-0.141608\pi$
$73$	49.0512	+	84.9591i	0.0786439	+	0.136215i	−0.824021	+	0.566559i	$0.808274\pi$
$74$	91.6165	−	76.8754i	0.143922	−	0.120765i
$75$		0			0
$76$	77.2492	−	438.102i	0.116593	−	0.661234i
$77$	579.237	+	486.038i	0.857276	+	0.719340i
$78$		0			0
$79$	574.263	+	209.014i	0.817843	+	0.297670i	0.716859	−	0.697218i	$-0.245579\pi$
$79$	574.263	+	209.014i	0.817843	+	0.297670i	0.100983	+	0.994888i	$0.467801\pi$
$80$	62.7006			0.0876268
$81$		0			0
$82$	180.228			0.242718
$83$	−807.108	−	293.763i	−1.06737	−	0.388491i	−0.252177	−	0.967681i	$-0.581147\pi$
$83$	−807.108	−	293.763i	−1.06737	−	0.388491i	−0.815192	+	0.579191i	$0.803369\pi$
$84$		0			0
$85$	−386.175	−	324.039i	−0.492783	−	0.413494i
$86$	139.142	−	789.116i	0.174467	−	0.989449i
$87$		0			0
$88$	585.409	−	491.217i	0.709146	−	0.595044i
$89$	−663.574	−	1149.34i	−0.790323	−	1.36888i	−0.925767	−	0.378094i	$-0.876580\pi$
$89$	−663.574	−	1149.34i	−0.790323	−	1.36888i	0.135445	−	0.990785i	$-0.456754\pi$
$90$		0			0
$91$	779.800	−	1350.65i	0.898299	−	1.55590i
$92$	−77.8481	−	441.499i	−0.0882198	−	0.500320i
$93$		0			0
$94$	457.877	−	166.653i	0.502408	−	0.182862i
$95$	−1208.02	+	439.683i	−1.30463	+	0.474848i
$96$		0			0
$97$	116.752	+	662.133i	0.122210	+	0.693087i	0.982926	+	0.184002i	$0.0589052\pi$
$97$	116.752	+	662.133i	0.122210	+	0.693087i	−0.860716	+	0.509085i	$0.829984\pi$
$98$	163.503	−	283.196i	0.168534	−	0.291909i
$99$		0			0
$100$	135.770	+	235.160i	0.135770	+	0.235160i
$101$	1303.89	−	1094.10i	1.28457	−	1.07789i	0.291979	−	0.956425i	$-0.405686\pi$
$101$	1303.89	−	1094.10i	1.28457	−	1.07789i	0.992596	−	0.121462i	$-0.0387581\pi$
$102$		0			0
$103$	−140.849	+	798.795i	−0.134741	+	0.764152i	0.840299	+	0.542122i	$0.182379\pi$
$103$	−140.849	+	798.795i	−0.134741	+	0.764152i	−0.975040	+	0.222029i	$0.928732\pi$
$104$	−1207.45	−	1013.17i	−1.13847	−	0.955286i
$105$		0			0
$106$	−66.6835	−	24.2708i	−0.0611026	−	0.0222395i
$107$	−392.858			−0.354944			−0.177472	−	0.984126i	$-0.556792\pi$
$107$	−392.858			−0.354944			−0.177472	+	0.984126i	$0.556792\pi$
$108$		0			0
$109$	847.501			0.744733			0.372366	−	0.928086i	$-0.378547\pi$
$109$	847.501			0.744733			0.372366	+	0.928086i	$0.378547\pi$
$110$	−766.053	−	278.821i	−0.664003	−	0.241677i
$111$		0			0
$112$	−81.1594	−	68.1008i	−0.0684718	−	0.0574547i
$113$	−277.950	+	1576.33i	−0.231392	+	1.31229i	0.618688	+	0.785636i	$0.287664\pi$
$113$	−277.950	+	1576.33i	−0.231392	+	1.31229i	−0.850080	+	0.526653i	$0.823447\pi$
$114$		0			0
$115$	−992.421	+	832.740i	−0.804728	+	0.675247i
$116$	−335.601	−	581.277i	−0.268618	−	0.465261i
$117$		0			0
$118$	196.026	−	339.528i	0.152930	−	0.264882i
$119$	147.915	+	838.870i	0.113944	+	0.646211i
$120$		0			0
$121$	222.473	−	80.9736i	0.167147	−	0.0608367i
$122$	−91.1381	+	33.1716i	−0.0676332	+	0.0246165i
$123$		0			0
$124$	−65.2597	−	370.106i	−0.0472620	−	0.268036i
$125$	−453.152	+	784.882i	−0.324249	+	0.561616i
$126$		0			0
$127$	−1260.78	−	2183.73i	−0.880912	−	1.52578i	−0.850328	−	0.526253i	$-0.823597\pi$
$127$	−1260.78	−	2183.73i	−0.880912	−	1.52578i	−0.0305839	−	0.999532i	$-0.509737\pi$
$128$	580.739	−	487.298i	0.401020	−	0.336496i
$129$		0			0
$130$	−291.980	+	1655.90i	−0.196987	+	1.11717i
$131$	−667.406	−	560.020i	−0.445126	−	0.373505i	0.392497	−	0.919753i	$-0.371611\pi$
$131$	−667.406	−	560.020i	−0.445126	−	0.373505i	−0.837624	+	0.546248i	$0.816056\pi$
$132$		0			0
$133$	2041.21	+	742.939i	1.33079	+	0.484368i
$134$	−1886.63			−1.21627
$135$		0			0
$136$	860.887			0.542797
$137$	−2426.56	−	883.194i	−1.51325	−	0.550776i	−0.553795	−	0.832653i	$-0.686821\pi$
$137$	−2426.56	−	883.194i	−1.51325	−	0.550776i	−0.959451	+	0.281877i	$0.909043\pi$
$138$		0			0
$139$	−585.699	−	491.460i	−0.357398	−	0.299893i	0.446354	−	0.894856i	$-0.352722\pi$
$139$	−585.699	−	491.460i	−0.357398	−	0.299893i	−0.803753	+	0.594963i	$0.797167\pi$
$140$	251.370	−	1425.59i	0.151747	−	0.860603i
$141$		0			0
$142$	−413.311	+	346.809i	−0.244256	+	0.204955i
$143$	1128.49	+	1954.60i	0.659922	+	1.14302i
$144$		0			0
$145$	−969.811	+	1679.76i	−0.555438	+	0.962046i
$146$	31.0337	+	176.001i	0.0175915	+	0.0997666i
$147$		0			0
$148$	−288.795	+	105.113i	−0.160397	+	0.0583798i
$149$	1262.04	−	459.344i	0.693893	−	0.252557i	0.0290921	−	0.999577i	$-0.490738\pi$
$149$	1262.04	−	459.344i	0.693893	−	0.252557i	0.664801	+	0.747020i	$0.268516\pi$
$150$		0			0
$151$	153.939	+	873.033i	0.0829629	+	0.470506i	0.997778	+	0.0666321i	$0.0212254\pi$
$151$	153.939	+	873.033i	0.0829629	+	0.470506i	−0.914815	+	0.403874i	$0.867663\pi$
$152$	1097.68	−	1901.23i	0.585746	−	1.01454i
$153$		0			0
$154$	688.741	+	1192.94i	0.360392	+	0.624217i
$155$	−831.942	+	698.082i	−0.431117	+	0.361751i
$156$		0			0
$157$	242.732	−	1376.60i	0.123389	−	0.699776i	−0.858862	−	0.512207i	$-0.828828\pi$
$157$	242.732	−	1376.60i	0.123389	−	0.699776i	0.982251	−	0.187569i	$-0.0600608\pi$
$158$	852.829	+	715.609i	0.429414	+	0.360321i
$159$		0			0
$160$	−2242.05	−	816.041i	−1.10781	−	0.403211i
$161$	2189.05			1.07156
$162$		0			0
$163$	128.789			0.0618869			0.0309435	−	0.999521i	$-0.490149\pi$
$163$	128.789			0.0618869			0.0309435	+	0.999521i	$0.490149\pi$
$164$	−435.203	−	158.401i	−0.207217	−	0.0754209i
$165$		0			0
$166$	−1198.63	−	1005.77i	−0.560430	−	0.470257i
$167$	15.9803	−	90.6289i	0.00740476	−	0.0419945i	−0.980882	−	0.194606i	$-0.937657\pi$
$167$	15.9803	−	90.6289i	0.00740476	−	0.0419945i	0.988286	+	0.152611i	$0.0487683\pi$
$168$		0			0
$169$	1883.08	−	1580.09i	0.857113	−	0.719203i
$170$	−459.181	−	795.324i	−0.207162	−	0.358815i
$171$		0			0
$172$	−1029.54	+	1783.22i	−0.456405	+	0.790517i
$173$	528.066	+	2994.81i	0.232070	+	1.31614i	0.848697	+	0.528880i	$0.177388\pi$
$173$	528.066	+	2994.81i	0.232070	+	1.31614i	−0.616627	+	0.787256i	$0.711501\pi$
$174$		0			0
$175$	−1245.94	+	453.484i	−0.538194	+	0.195887i
$176$	144.074	−	52.4385i	0.0617043	−	0.0224585i
$177$		0			0
$178$	−419.830	−	2380.97i	−0.176784	−	1.00259i
$179$	−180.575	+	312.765i	−0.0754012	+	0.130599i	−0.901261	−	0.433277i	$-0.857357\pi$
$179$	−180.575	+	312.765i	−0.0754012	+	0.130599i	0.825859	+	0.563876i	$0.190690\pi$
$180$		0			0
$181$	−552.436	−	956.847i	−0.226863	−	0.392939i	0.730014	−	0.683433i	$-0.239514\pi$
$181$	−552.436	−	956.847i	−0.226863	−	0.392939i	−0.956877	+	0.290494i	$0.906180\pi$
$182$	2176.46	−	1826.27i	0.886428	−	0.743801i
$183$		0			0
$184$	384.174	−	2178.76i	0.153922	−	0.872937i
$185$	680.333	+	570.867i	0.270373	+	0.226870i
$186$		0			0
$187$	−1158.36	−	421.607i	−0.452981	−	0.164872i
$188$	−1252.12			−0.485746
$189$		0			0
$190$	−2341.92			−0.894214
$191$	3387.57	+	1232.97i	1.28333	+	0.467093i	0.891532	−	0.452958i	$-0.149631\pi$
$191$	3387.57	+	1232.97i	1.28333	+	0.467093i	0.391797	+	0.920052i	$0.371854\pi$
$192$		0			0
$193$	2431.89	+	2040.60i	0.907003	+	0.761066i	0.971546	−	0.236849i	$-0.0761147\pi$
$193$	2431.89	+	2040.60i	0.907003	+	0.761066i	−0.0645437	+	0.997915i	$0.520559\pi$
$194$	−212.690	+	1206.23i	−0.0787127	+	0.446402i
$195$		0			0
$196$	−643.715	+	540.141i	−0.234590	+	0.196845i
$197$	105.570	+	182.852i	0.0381804	+	0.0661304i	0.884484	−	0.466570i	$-0.154511\pi$
$197$	105.570	+	182.852i	0.0381804	+	0.0661304i	−0.846304	+	0.532701i	$0.821177\pi$
$198$		0			0
$199$	573.724	−	993.718i	0.204373	−	0.353984i	−0.745560	−	0.666439i	$-0.767818\pi$
$199$	573.724	−	993.718i	0.204373	−	0.353984i	0.949933	+	0.312455i	$0.101151\pi$
$200$	232.693	+	1319.67i	0.0822694	+	0.466573i
$201$		0			0
$202$	2913.78	−	1060.53i	1.01492	−	0.369399i
$203$	3079.75	−	1120.94i	1.06481	−	0.387559i
$204$		0			0
$205$	232.402	+	1318.02i	0.0791789	+	0.449046i
$206$	−738.818	+	1279.67i	−0.249883	+	0.432810i
$207$		0			0
$208$	−158.117	−	273.867i	−0.0527089	−	0.0912945i
$209$	−2408.07	+	2020.61i	−0.796984	+	0.668749i
$210$		0			0
$211$	66.7083	−	378.322i	0.0217649	−	0.123435i	−0.971990	−	0.235024i	$-0.924483\pi$
$211$	66.7083	−	378.322i	0.0217649	−	0.123435i	0.993754	+	0.111589i	$0.0355942\pi$
$212$	139.692	+	117.215i	0.0452550	+	0.0379735i
$213$		0			0
$214$	−672.519	−	244.777i	−0.214825	−	0.0781897i
$215$	5950.28			1.88747
$216$		0			0
$217$	1835.07			0.574067
$218$	1450.81	+	528.050i	0.450738	+	0.164055i
$219$		0			0
$220$	1604.76	+	1346.56i	0.491787	+	0.412658i
$221$	−441.507	+	2503.91i	−0.134384	+	0.762132i
$222$		0			0
$223$	85.4847	−	71.7302i	0.0256703	−	0.0215399i	−0.629862	−	0.776707i	$-0.716889\pi$
$223$	85.4847	−	71.7302i	0.0256703	−	0.0215399i	0.655533	+	0.755167i	$0.272444\pi$
$224$	2015.78	+	3491.43i	0.601272	+	1.04143i
$225$		0			0
$226$	−1457.97	+	2525.28i	−0.429128	+	0.743271i
$227$	−731.492	−	4148.49i	−0.213880	−	1.21297i	−0.882839	−	0.469675i	$-0.844371\pi$
$227$	−731.492	−	4148.49i	−0.213880	−	1.21297i	0.668959	−	0.743299i	$-0.266740\pi$
$228$		0			0
$229$	−1927.88	+	701.689i	−0.556321	+	0.202484i	−0.604853	−	0.796337i	$-0.706768\pi$
$229$	−1927.88	+	701.689i	−0.556321	+	0.202484i	0.0485315	+	0.998822i	$0.484546\pi$
$230$	−2217.74	+	807.193i	−0.635799	+	0.231412i
$231$		0			0
$232$	−575.180	−	3262.01i	−0.162769	−	0.923108i
$233$	−2172.95	+	3763.66i	−0.610965	+	1.05822i	0.380114	+	0.924940i	$0.375885\pi$
$233$	−2172.95	+	3763.66i	−0.610965	+	1.05822i	−0.991078	+	0.133282i	$0.957448\pi$
$234$		0			0
$235$	1809.18	+	3133.58i	0.502203	+	0.869840i
$236$	−771.760	+	647.583i	−0.212870	+	0.178619i
$237$		0			0
$238$	−269.462	+	1528.19i	−0.0733891	+	0.416210i
$239$	1128.98	+	947.325i	0.305555	+	0.256391i	0.782652	−	0.622460i	$-0.213867\pi$
$239$	1128.98	+	947.325i	0.305555	+	0.256391i	−0.477097	+	0.878851i	$0.658311\pi$
$240$		0			0
$241$	−2808.19	−	1022.10i	−0.750586	−	0.273191i	−0.0617335	−	0.998093i	$-0.519663\pi$
$241$	−2808.19	−	1022.10i	−0.750586	−	0.273191i	−0.688852	+	0.724902i	$0.741885\pi$
$242$	431.296			0.114565
$243$		0			0
$244$	249.229			0.0653903
$245$	2281.87	+	830.531i	0.595033	+	0.216574i
$246$		0			0
$247$	4966.83	+	4167.66i	1.27948	+	1.07361i
$248$	322.052	−	1826.45i	0.0824609	−	0.467659i
$249$		0			0
$250$	−1264.77	+	1061.27i	−0.319964	+	0.268482i
$251$	−1250.48	−	2165.90i	−0.314462	−	0.544664i	0.664861	−	0.746967i	$-0.268491\pi$
$251$	−1250.48	−	2165.90i	−0.314462	−	0.544664i	−0.979323	+	0.202303i	$0.935157\pi$
$252$		0			0
$253$	−1583.94	+	2743.46i	−0.393603	+	0.681740i
$254$	−797.668	−	4523.80i	−0.197048	−	1.11751i
$255$		0			0
$256$	3991.91	−	1452.93i	0.974586	−	0.354720i
$257$	−4057.65	+	1476.87i	−0.984862	+	0.358460i	−0.783729	−	0.621103i	$-0.786685\pi$
$257$	−4057.65	+	1476.87i	−0.984862	+	0.358460i	−0.201133	+	0.979564i	$0.564462\pi$
$258$		0			0
$259$	−260.586	−	1477.86i	−0.0625175	−	0.354554i
$260$	2160.41	−	3741.95i	0.515320	−	0.892561i
$261$		0			0
$262$	−793.578	−	1374.52i	−0.187128	−	0.324115i
$263$	2520.69	−	2115.11i	0.590998	−	0.495906i	−0.297540	−	0.954709i	$-0.596166\pi$
$263$	2520.69	−	2115.11i	0.590998	−	0.495906i	0.888538	+	0.458803i	$0.151722\pi$
$264$		0			0
$265$	91.5063	−	518.958i	0.0212120	−	0.120299i
$266$	3031.37	+	2543.62i	0.698741	+	0.586314i
$267$		0			0
$268$	4555.71	+	1658.14i	1.03837	+	0.377937i
$269$	−5133.23			−1.16349			−0.581745	−	0.813371i	$-0.697630\pi$
$269$	−5133.23			−1.16349			−0.581745	+	0.813371i	$0.697630\pi$
$270$		0			0
$271$	−2210.89			−0.495579			−0.247789	−	0.968814i	$-0.579704\pi$
$271$	−2210.89			−0.495579			−0.247789	+	0.968814i	$0.579704\pi$
$272$	162.302	+	59.0732i	0.0361802	+	0.0131685i
$273$		0			0
$274$	−3603.64	−	3023.82i	−0.794540	−	0.666699i
$275$	333.192	−	1889.62i	0.0730626	−	0.414359i
$276$		0			0
$277$	281.346	−	236.077i	0.0610268	−	0.0512076i	−0.611764	−	0.791040i	$-0.709540\pi$
$277$	281.346	−	236.077i	0.0610268	−	0.0512076i	0.672791	+	0.739833i	$0.265095\pi$
$278$	−696.425	−	1206.24i	−0.150247	−	0.260236i
$279$		0			0
$280$	3571.85	−	6186.63i	0.762354	−	1.32044i
$281$	918.247	+	5207.64i	0.194940	+	1.10556i	0.912505	+	0.409066i	$0.134145\pi$
$281$	918.247	+	5207.64i	0.194940	+	1.10556i	−0.717565	+	0.696491i	$0.754744\pi$
$282$		0			0
$283$	129.252	−	47.0439i	0.0271493	−	0.00988152i	−0.328410	−	0.944535i	$-0.606513\pi$
$283$	129.252	−	47.0439i	0.0271493	−	0.00988152i	0.355559	+	0.934654i	$0.384290\pi$
$284$	1302.84	−	474.197i	0.272217	−	0.0990789i
$285$		0			0
$286$	713.970	+	4049.13i	0.147615	+	0.837168i
$287$	1130.71	−	1958.46i	0.232557	−	0.402801i
$288$		0			0
$289$	1762.17	+	3052.16i	0.358675	+	0.621243i
$290$	−2706.79	+	2271.27i	−0.548097	+	0.459908i
$291$		0			0
$292$	79.7475	−	452.270i	0.0159824	−	0.0906408i
$293$	38.1032	+	31.9724i	0.00759731	+	0.00637490i	0.646578	−	0.762848i	$-0.276199\pi$
$293$	38.1032	+	31.9724i	0.00759731	+	0.00637490i	−0.638981	+	0.769222i	$0.720644\pi$
$294$		0			0
$295$	2735.76	+	995.736i	0.539940	+	0.196522i
$296$	−1516.64			−0.297815
$297$		0			0
$298$	2446.64			0.475604
$299$	6139.95	+	2234.76i	1.18757	+	0.432239i
$300$		0			0
$301$	−7702.02	−	6462.76i	−1.47487	−	1.23757i
$302$	−280.435	+	1590.43i	−0.0534346	+	0.303043i
$303$		0			0
$304$	337.405	−	283.116i	0.0636562	−	0.0534139i
$305$	−360.108	−	623.725i	−0.0676056	−	0.117096i
$306$		0			0
$307$	3322.84	−	5755.33i	0.617734	−	1.06995i	−0.372164	−	0.928167i	$-0.621384\pi$
$307$	3322.84	−	5755.33i	0.617734	−	1.06995i	0.989898	−	0.141780i	$-0.0452826\pi$
$308$	−614.667	−	3485.95i	−0.113714	−	0.644904i
$309$		0			0
$310$	−1859.12	+	676.666i	−0.340617	+	0.123974i
$311$	−103.806	+	37.7824i	−0.0189271	+	0.00688889i	−0.351466	−	0.936201i	$-0.614317\pi$
$311$	−103.806	+	37.7824i	−0.0189271	+	0.00688889i	0.332539	+	0.943089i	$0.392095\pi$
$312$		0			0
$313$	57.0651	+	323.632i	0.0103051	+	0.0584433i	0.989527	−	0.144350i	$-0.0461091\pi$
$313$	57.0651	+	323.632i	0.0103051	+	0.0584433i	−0.979222	+	0.202793i	$0.934998\pi$
$314$	1273.24	−	2205.32i	0.228832	−	0.396348i
$315$		0			0
$316$	−1430.41	−	2477.55i	−0.254643	−	0.441054i
$317$	−6445.21	+	5408.18i	−1.14195	+	0.958213i	−0.999501	−	0.0315891i	$-0.989943\pi$
$317$	−6445.21	+	5408.18i	−1.14195	+	0.958213i	−0.142452	+	0.989802i	$0.545499\pi$
$318$		0			0
$319$	−823.596	+	4670.84i	−0.144553	+	0.819802i
$320$	−3713.89	−	3116.33i	−0.648791	−	0.544400i
$321$		0			0
$322$	3747.35	+	1363.92i	0.648546	+	0.236051i
$323$	−3541.24			−0.610031
$324$		0			0
$325$	−3957.62			−0.675475
$326$	220.470	+	80.2445i	0.0374561	+	0.0136329i
$327$		0			0
$328$	−1750.81	−	1469.11i	−0.294733	−	0.247311i
$329$	1061.68	−	6021.09i	0.177910	−	1.00898i
$330$		0			0
$331$	2998.81	−	2516.30i	0.497974	−	0.417850i	−0.358900	−	0.933376i	$-0.616848\pi$
$331$	2998.81	−	2516.30i	0.497974	−	0.417850i	0.856874	+	0.515526i	$0.172404\pi$
$332$	2010.40	+	3482.12i	0.332335	+	0.575621i
$333$		0			0
$334$	83.8241	−	145.188i	0.0137325	−	0.0237854i
$335$	−2432.79	−	13797.0i	−0.396769	−	2.25019i
$336$		0			0
$337$	−666.630	+	242.634i	−0.107756	+	0.0392199i	−0.395335	−	0.918537i	$-0.629372\pi$
$337$	−666.630	+	242.634i	−0.107756	+	0.0392199i	0.287580	+	0.957757i	$0.407149\pi$
$338$	4208.08	−	1531.61i	0.677187	−	0.246476i
$339$		0			0
$340$	409.796	+	2324.07i	0.0653656	+	0.370707i
$341$	−1327.81	+	2299.83i	−0.210865	+	0.365229i
$342$		0			0
$343$	1868.63	+	3236.56i	0.294159	+	0.509498i
$344$	−7784.08	+	6531.62i	−1.22003	+	1.02373i
$345$		0			0
$346$	−961.993	+	5455.73i	−0.149471	+	0.847694i
$347$	−6968.17	−	5846.99i	−1.07801	−	0.904561i	−0.0822593	−	0.996611i	$-0.526214\pi$
$347$	−6968.17	−	5846.99i	−1.07801	−	0.904561i	−0.995754	+	0.0920500i	$0.970658\pi$
$348$		0			0
$349$	−5954.55	−	2167.28i	−0.913295	−	0.332412i	−0.157727	−	0.987483i	$-0.550417\pi$
$349$	−5954.55	−	2167.28i	−0.913295	−	0.332412i	−0.755568	+	0.655071i	$0.772639\pi$
$350$	−2415.43			−0.368886
$351$		0			0
$352$	−5834.27			−0.883431
$353$	−8788.43	−	3198.73i	−1.32510	−	0.482298i	−0.420012	−	0.907518i	$-0.637974\pi$
$353$	−8788.43	−	3198.73i	−1.32510	−	0.482298i	−0.905090	+	0.425221i	$0.860196\pi$
$354$		0			0
$355$	−3069.20	−	2575.36i	−0.458863	−	0.385031i
$356$	−1078.84	+	6118.40i	−0.160613	+	0.910884i
$357$		0			0
$358$	−503.994	+	422.901i	−0.0744048	+	0.0624330i
$359$	−5947.18	−	10300.8i	−0.874318	−	1.51436i	−0.857488	−	0.514505i	$-0.827976\pi$
$359$	−5947.18	−	10300.8i	−0.874318	−	1.51436i	−0.0168303	−	0.999858i	$-0.505357\pi$
$360$		0			0
$361$	−1085.77	+	1880.61i	−0.158299	+	0.274181i
$362$	−349.515	−	1982.20i	−0.0507461	−	0.287795i
$363$		0			0
$364$	−6860.66	+	2497.08i	−0.987902	+	0.359567i
$365$	−1247.09	+	453.903i	−0.178837	+	0.0650914i
$366$		0			0
$367$	1410.51	+	7999.39i	0.200621	+	1.13778i	0.904183	+	0.427145i	$0.140481\pi$
$367$	1410.51	+	7999.39i	0.200621	+	1.13778i	−0.703562	+	0.710634i	$0.748408\pi$
$368$	221.933	−	384.399i	0.0314376	−	0.0544515i
$369$		0			0
$370$	808.949	+	1401.14i	0.113663	+	0.196870i
$371$	−682.100	+	572.350i	−0.0954524	+	0.0800941i
$372$		0			0
$373$	1610.69	−	9134.66i	0.223588	−	1.26803i	−0.641779	−	0.766890i	$-0.721803\pi$
$373$	1610.69	−	9134.66i	0.223588	−	1.26803i	0.865367	−	0.501139i	$-0.167086\pi$
$374$	−1720.26	−	1443.47i	−0.237841	−	0.199572i
$375$		0			0
$376$	−5806.47	−	2113.38i	−0.796399	−	0.289866i
$377$	9782.59			1.33642
$378$		0			0
$379$	1420.08			0.192466			0.0962329	−	0.995359i	$-0.469321\pi$
$379$	1420.08			0.192466			0.0962329	+	0.995359i	$0.469321\pi$
$380$	5655.11	+	2058.29i	0.763424	+	0.277864i
$381$		0			0
$382$	5030.83	+	4221.37i	0.673821	+	0.565403i
$383$	1210.15	−	6863.08i	0.161451	−	0.915632i	−0.791198	−	0.611560i	$-0.790542\pi$
$383$	1210.15	−	6863.08i	0.161451	−	0.915632i	0.952649	−	0.304072i	$-0.0983465\pi$
$384$		0			0
$385$	−7835.89	+	6575.09i	−1.03728	+	0.870383i
$386$	2891.64	+	5008.47i	0.381297	+	0.660425i
$387$		0			0
$388$	1573.73	−	2725.79i	0.205913	−	0.356652i
$389$	−1774.46	−	10063.4i	−0.231281	−	1.31166i	−0.850305	−	0.526290i	$-0.823583\pi$
$389$	−1774.46	−	10063.4i	−0.231281	−	1.31166i	0.619024	−	0.785372i	$-0.287529\pi$
$390$		0			0
$391$	−3353.47	+	1220.56i	−0.433740	+	0.157869i
$392$	−3896.78	+	1418.31i	−0.502085	+	0.182744i
$393$		0			0
$394$	66.7919	+	378.796i	0.00854042	+	0.0484352i
$395$	−4133.58	+	7159.57i	−0.526539	+	0.911992i
$396$		0			0
$397$	−6593.97	−	11421.1i	−0.833607	−	1.44385i	−0.895160	−	0.445745i	$-0.852939\pi$
$397$	−6593.97	−	11421.1i	−0.833607	−	1.44385i	0.0615530	−	0.998104i	$-0.480395\pi$
$398$	1601.29	−	1343.64i	0.201672	−	0.169223i
$399$		0			0
$400$	−46.6849	+	264.763i	−0.00583561	+	0.0330954i
$401$	−2848.67	−	2390.31i	−0.354752	−	0.297672i	0.447943	−	0.894062i	$-0.352157\pi$
$401$	−2848.67	−	2390.31i	−0.354752	−	0.297672i	−0.802695	+	0.596390i	$0.796601\pi$
$402$		0			0
$403$	5147.09	+	1873.39i	0.636216	+	0.231564i
$404$	−7968.10			−0.981257
$405$		0			0
$406$	5970.54			0.729835
$407$	2040.70	+	742.756i	0.248535	+	0.0904595i
$408$		0			0
$409$	9331.48	+	7830.04i	1.12815	+	0.946628i	0.998987	−	0.0449960i	$-0.0143275\pi$
$409$	9331.48	+	7830.04i	1.12815	+	0.946628i	0.129160	+	0.991624i	$0.458772\pi$
$410$	−423.374	+	2401.07i	−0.0509974	+	0.289221i
$411$		0			0
$412$	2908.74	−	2440.72i	0.347824	−	0.291859i
$413$	−2459.66	−	4260.26i	−0.293056	−	0.507588i
$414$		0			0
$415$	5809.62	−	10062.6i	0.687188	−	1.19024i
$416$	2089.62	+	11850.8i	0.246279	+	1.39672i
$417$		0			0
$418$	−5381.26	+	1958.62i	−0.629680	+	0.229185i
$419$	−4548.20	+	1655.41i	−0.530296	+	0.193012i	−0.593271	−	0.805003i	$-0.702164\pi$
$419$	−4548.20	+	1655.41i	−0.530296	+	0.193012i	0.0629744	+	0.998015i	$0.479941\pi$
$420$		0			0
$421$	−2653.87	−	15050.9i	−0.307225	−	1.74236i	−0.612841	−	0.790206i	$-0.709973\pi$
$421$	−2653.87	−	15050.9i	−0.307225	−	1.74236i	0.305616	−	0.952155i	$-0.401138\pi$
$422$	349.916	−	606.072i	0.0403640	−	0.0699126i
$423$		0			0
$424$	449.953	+	779.341i	0.0515369	+	0.0892645i
$425$	1655.84	−	1389.41i	0.188988	−	0.158580i
$426$		0			0
$427$	−211.322	+	1198.47i	−0.0239499	+	0.135827i
$428$	1408.82	+	1182.14i	0.159108	+	0.133507i
$429$		0			0
$430$	10186.1	+	3707.43i	1.14236	+	0.415786i
$431$	12236.8			1.36757			0.683786	−	0.729683i	$-0.260332\pi$
$431$	12236.8			1.36757			0.683786	+	0.729683i	$0.260332\pi$
$432$		0			0
$433$	6472.96			0.718407			0.359204	−	0.933259i	$-0.383048\pi$
$433$	6472.96			0.718407			0.359204	+	0.933259i	$0.383048\pi$
$434$	3141.39	+	1143.37i	0.347446	+	0.126460i
$435$		0			0
$436$	−3039.21	−	2550.20i	−0.333835	−	0.280121i
$437$	−1580.29	+	8962.29i	−0.172988	+	0.981063i
$438$		0			0
$439$	5825.29	−	4888.00i	0.633316	−	0.531415i	−0.268641	−	0.963240i	$-0.586575\pi$
$439$	5825.29	−	4888.00i	0.633316	−	0.531415i	0.901957	+	0.431825i	$0.142130\pi$
$440$	5169.01	+	8952.98i	0.560052	+	0.970038i
$441$		0			0
$442$	−2315.90	+	4011.26i	−0.249222	+	0.431666i
$443$	−631.503	−	3581.43i	−0.0677282	−	0.384106i	−0.999764	−	0.0217388i	$-0.993080\pi$
$443$	−631.503	−	3581.43i	−0.0677282	−	0.384106i	0.932035	−	0.362367i	$-0.118031\pi$
$444$		0			0
$445$	16870.8	−	6140.48i	1.79720	−	0.654128i
$446$	191.031	−	69.5296i	0.0202816	−	0.00738188i
$447$		0			0
$448$	1422.52	+	8067.52i	0.150017	+	0.850791i
$449$	1687.18	−	2922.28i	0.177334	−	0.307151i	−0.763633	−	0.645651i	$-0.776586\pi$
$449$	1687.18	−	2922.28i	0.177334	−	0.307151i	0.940967	+	0.338500i	$0.109919\pi$
$450$		0			0
$451$	1636.31	+	2834.18i	0.170845	+	0.295912i
$452$	5740.07	−	4816.49i	0.597323	−	0.501214i
$453$		0			0
$454$	1332.58	−	7557.43i	0.137756	−	0.781250i
$455$	16162.1	+	13561.6i	1.66526	+	1.39732i
$456$		0			0
$457$	−5692.95	−	2072.07i	−0.582725	−	0.212094i	0.0338018	−	0.999429i	$-0.489238\pi$
$457$	−5692.95	−	2072.07i	−0.582725	−	0.212094i	−0.616527	+	0.787334i	$0.711461\pi$
$458$	−3737.46			−0.381310
$459$		0			0
$460$	6064.70			0.614713
$461$	8110.31	+	2951.91i	0.819381	+	0.298230i	0.717493	−	0.696566i	$-0.245289\pi$
$461$	8110.31	+	2951.91i	0.819381	+	0.298230i	0.101888	+	0.994796i	$0.467512\pi$
$462$		0			0
$463$	−1606.22	−	1347.78i	−0.161226	−	0.135284i	0.558606	−	0.829433i	$-0.311337\pi$
$463$	−1606.22	−	1347.78i	−0.161226	−	0.135284i	−0.719831	+	0.694149i	$0.755781\pi$
$464$	115.397	−	654.452i	0.0115457	−	0.0654788i
$465$		0			0
$466$	−6064.81	+	5088.98i	−0.602891	+	0.505885i
$467$	−8814.78	−	15267.6i	−0.873446	−	1.51285i	−0.858409	−	0.512966i	$-0.828547\pi$
$467$	−8814.78	−	15267.6i	−0.873446	−	1.51285i	−0.0150374	−	0.999887i	$-0.504787\pi$
$468$		0			0
$469$	−11836.3	+	20501.1i	−1.16535	+	2.01845i
$470$	1144.63	+	6491.51i	0.112336	+	0.637087i
$471$		0			0
$472$	−4671.91	+	1700.44i	−0.455598	+	0.165824i
$473$	13672.6	−	4976.41i	1.32910	−	0.483753i
$474$		0			0
$475$	−957.178	−	5428.43i	−0.0924597	−	0.524365i
$476$	1993.79	−	3453.35i	0.191986	−	0.332530i
$477$		0			0
$478$	1342.41	+	2325.12i	0.128453	+	0.222487i
$479$	539.569	−	452.752i	0.0514687	−	0.0431874i	−0.616690	−	0.787206i	$-0.711527\pi$
$479$	539.569	−	452.752i	0.0514687	−	0.0431874i	0.668159	+	0.744018i	$0.267083\pi$
$480$		0			0
$481$	777.812	−	4411.19i	0.0737322	−	0.418156i
$482$	−4170.40	−	3499.38i	−0.394100	−	0.330690i
$483$		0			0
$484$	−1041.47	−	379.062i	−0.0978085	−	0.0355994i
$485$	−9095.48			−0.851555
$486$		0			0
$487$	−15835.5			−1.47346			−0.736731	−	0.676185i	$-0.763632\pi$
$487$	−15835.5			−1.47346			−0.736731	+	0.676185i	$0.763632\pi$
$488$	1155.75	+	420.659i	0.107210	+	0.0390212i
$489$		0			0
$490$	3388.77	+	2843.51i	0.312426	+	0.262157i
$491$	263.720	−	1495.63i	0.0242394	−	0.137468i	−0.970287	−	0.241959i	$-0.922210\pi$
$491$	263.720	−	1495.63i	0.0242394	−	0.137468i	0.994526	+	0.104491i	$0.0333212\pi$
$492$		0			0
$493$	−4092.97	+	3434.41i	−0.373911	+	0.313748i
$494$	5905.80	+	10229.1i	0.537884	+	0.931642i
$495$		0			0
$496$	186.045	−	322.239i	0.0168421	−	0.0291713i
$497$	1175.59	+	6667.08i	0.106101	+	0.601729i
$498$		0			0
$499$	2226.72	−	810.459i	0.199763	−	0.0727076i	−0.240201	−	0.970723i	$-0.577213\pi$
$499$	2226.72	−	810.459i	0.199763	−	0.0727076i	0.439964	+	0.898015i	$0.354991\pi$
$500$	3986.82	−	1451.08i	0.356592	−	0.129789i
$501$		0			0
$502$	−791.156	−	4486.87i	−0.0703407	−	0.398922i
$503$	3378.26	−	5851.33i	0.299462	−	0.518683i	−0.676551	−	0.736396i	$-0.736526\pi$
$503$	3378.26	−	5851.33i	0.299462	−	0.518683i	0.976013	+	0.217712i	$0.0698595\pi$
$504$		0			0
$505$	11513.0	+	19941.1i	1.01450	+	1.75717i
$506$	−4420.85	+	3709.54i	−0.388401	+	0.325907i
$507$		0			0
$508$	−2049.77	+	11624.8i	−0.179023	+	1.01529i
$509$	−1776.16	−	1490.37i	−0.154670	−	0.129783i	0.562169	−	0.827022i	$-0.309967\pi$
$509$	−1776.16	−	1490.37i	−0.154670	−	0.129783i	−0.716839	+	0.697239i	$0.754412\pi$
$510$		0			0
$511$	2107.22	+	766.965i	0.182423	+	0.0663964i
$512$	1674.06			0.144500
$513$		0			0
$514$	−7866.34			−0.675038
$515$	−10311.0	−	3752.90i	−0.882247	−	0.321112i
$516$		0			0
$517$	6777.84	+	5687.28i	0.576574	+	0.483803i
$518$	474.717	−	2692.25i	0.0402661	−	0.228361i
$519$		0			0
$520$	16334.3	−	13706.1i	1.37752	−	1.15587i
$521$	8391.50	+	14534.5i	0.705640	+	1.22220i	0.966460	+	0.256816i	$0.0826736\pi$
$521$	8391.50	+	14534.5i	0.705640	+	1.22220i	−0.260821	+	0.965387i	$0.583993\pi$
$522$		0			0
$523$	−8351.57	+	14465.3i	−0.698257	+	1.20942i	0.270813	+	0.962632i	$0.412707\pi$
$523$	−8351.57	+	14465.3i	−0.698257	+	1.20942i	−0.969070	+	0.246785i	$0.920626\pi$
$524$	708.229	+	4016.57i	0.0590441	+	0.334856i
$525$		0			0
$526$	5632.93	−	2050.22i	0.466935	−	0.169950i
$527$	−2811.20	+	1023.19i	−0.232368	+	0.0845750i
$528$		0			0
$529$	−520.233	−	2950.39i	−0.0427577	−	0.242491i
$530$	479.992	−	831.371i	0.0393388	−	0.0681367i
$531$		0			0
$532$	−5084.39	−	8806.42i	−0.414354	−	0.717682i
$533$	5170.84	−	4338.85i	0.420214	−	0.352601i
$534$		0			0
$535$	922.863	−	5233.81i	0.0745773	−	0.422949i
$536$	18327.5	+	15378.6i	1.47692	+	1.23928i
$537$		0			0
$538$	−8787.40	−	3198.35i	−0.704185	−	0.256302i
$539$	5937.87			0.474513
$540$		0			0
$541$	19710.2			1.56637			0.783185	−	0.621789i	$-0.213594\pi$
$541$	19710.2			1.56637			0.783185	+	0.621789i	$0.213594\pi$
$542$	−3784.74	−	1377.53i	−0.299942	−	0.109170i
$543$		0			0
$544$	−5034.79	−	4224.69i	−0.396810	−	0.332963i
$545$	−1990.87	+	11290.8i	−0.156476	+	0.887418i
$546$		0			0
$547$	−969.597	+	813.588i	−0.0757897	+	0.0635951i	−0.679895	−	0.733309i	$-0.737975\pi$
$547$	−969.597	+	813.588i	−0.0757897	+	0.0635951i	0.604106	+	0.796904i	$0.293530\pi$
$548$	6044.24	+	10468.9i	0.471162	+	0.816077i
$549$		0			0
$550$	1747.74	−	3027.18i	0.135498	−	0.234690i
$551$	2365.99	+	13418.2i	0.182930	+	1.03745i
$552$		0			0
$553$	13126.7	−	4777.72i	1.00941	−	0.367395i
$554$	628.718	−	228.835i	0.0482160	−	0.0175492i
$555$		0			0
$556$	621.524	+	3524.84i	0.0474074	+	0.268861i
$557$	−9473.52	+	16408.6i	−0.720657	+	1.24821i	0.240080	+	0.970753i	$0.422826\pi$
$557$	−9473.52	+	16408.6i	−0.720657	+	1.24821i	−0.960737	+	0.277462i	$0.910507\pi$
$558$		0			0
$559$	−15005.3	−	25989.9i	−1.13534	−	1.96647i
$560$	1097.92	−	921.264i	0.0828492	−	0.0695188i
$561$		0			0
$562$	−1672.80	+	9486.90i	−0.125556	+	0.712065i
$563$	−6467.94	−	5427.24i	−0.484176	−	0.406272i	0.367758	−	0.929922i	$-0.380126\pi$
$563$	−6467.94	−	5427.24i	−0.484176	−	0.406272i	−0.851934	+	0.523650i	$0.824570\pi$
$564$		0			0
$565$	−20347.6	−	7405.92i	−1.51510	−	0.551450i
$566$	250.574			0.0186085
$567$		0			0
$568$	6842.07			0.505434
$569$	10151.5	+	3694.85i	0.747933	+	0.272225i	0.687736	−	0.725961i	$-0.258605\pi$
$569$	10151.5	+	3694.85i	0.747933	+	0.272225i	0.0601970	+	0.998187i	$0.480827\pi$
$570$		0			0
$571$	−9242.18	−	7755.11i	−0.677361	−	0.568374i	0.237873	−	0.971296i	$-0.423550\pi$
$571$	−9242.18	−	7755.11i	−0.677361	−	0.568374i	−0.915234	+	0.402923i	$0.867994\pi$
$572$	1834.70	−	10405.1i	0.134113	−	0.760591i
$573$		0			0
$574$	3155.88	−	2648.10i	0.229484	−	0.192560i
$575$	−2777.45	−	4810.69i	−0.201440	−	0.348903i
$576$		0			0
$577$	258.925	−	448.472i	0.0186815	−	0.0323572i	−0.856534	−	0.516091i	$-0.827386\pi$
$577$	258.925	−	448.472i	0.0186815	−	0.0323572i	0.875215	+	0.483734i	$0.160720\pi$
$578$	1114.89	+	6322.84i	0.0802305	+	0.455010i
$579$		0			0
$580$	8532.38	−	3105.53i	0.610841	−	0.222328i
$581$	−18449.2	+	6714.94i	−1.31738	+	0.479488i
$582$		0			0
$583$	−223.758	−	1268.99i	−0.0158955	−	0.0901480i
$584$	1133.18	−	1962.72i	0.0802930	−	0.139072i
$585$		0			0
$586$	45.3065	+	78.4732i	0.00319385	+	0.00553191i
$587$	13523.6	−	11347.6i	0.950900	−	0.797900i	−0.0285491	−	0.999592i	$-0.509089\pi$
$587$	13523.6	−	11347.6i	0.950900	−	0.797900i	0.979449	+	0.201693i	$0.0646443\pi$
$588$		0			0
$589$	−1324.75	+	7513.04i	−0.0926748	+	0.525585i
$590$	4062.84	+	3409.13i	0.283499	+	0.237884i
$591$		0			0
$592$	−285.932	−	104.071i	−0.0198509	−	0.00722513i
$593$	12632.6			0.874803			0.437402	−	0.899266i	$-0.355899\pi$
$593$	12632.6			0.874803			0.437402	+	0.899266i	$0.355899\pi$
$594$		0			0
$595$	−11523.2			−0.793961
$596$	−5907.99	−	2150.33i	−0.406041	−	0.147787i
$597$		0			0
$598$	9118.36	+	7651.21i	0.623541	+	0.523213i
$599$	3255.98	−	18465.6i	0.222096	−	1.25957i	−0.646063	−	0.763284i	$-0.723586\pi$
$599$	3255.98	−	18465.6i	0.222096	−	1.25957i	0.868159	−	0.496286i	$-0.165303\pi$
$600$		0			0
$601$	−18704.7	+	15695.1i	−1.26952	+	1.06525i	−0.274919	+	0.961467i	$0.588651\pi$
$601$	−18704.7	+	15695.1i	−1.26952	+	1.06525i	−0.994600	+	0.103786i	$0.966904\pi$
$602$	−9158.07	−	15862.2i	−0.620025	−	1.07392i
$603$		0			0
$604$	2074.99	−	3593.99i	0.139785	−	0.242115i
$605$	556.152	+	3154.10i	0.0373732	+	0.211954i
$606$		0			0
$607$	−6735.60	+	2451.56i	−0.450395	+	0.163930i	−0.557251	−	0.830344i	$-0.688144\pi$
$607$	−6735.60	+	2451.56i	−0.450395	+	0.163930i	0.106856	+	0.994275i	$0.465922\pi$
$608$	−15749.7	+	5732.41i	−1.05055	+	0.382368i
$609$		0			0
$610$	−227.833	−	1292.10i	−0.0151224	−	0.0857635i
$611$	9124.68	−	15804.4i	0.604165	−	1.04644i
$612$		0			0
$613$	−1526.50	−	2643.98i	−0.100579	−	0.174208i	0.811344	−	0.584569i	$-0.198736\pi$
$613$	−1526.50	−	2643.98i	−0.100579	−	0.174208i	−0.911923	+	0.410361i	$0.865403\pi$
$614$	9274.21	−	7781.98i	0.609571	−	0.511491i
$615$		0			0
$616$	3033.34	−	17202.9i	0.198404	−	1.12520i
$617$	−12916.0	−	10837.8i	−0.842756	−	0.707156i	0.115426	−	0.993316i	$-0.463177\pi$
$617$	−12916.0	−	10837.8i	−0.842756	−	0.707156i	−0.958182	+	0.286160i	$0.907621\pi$
$618$		0			0
$619$	13344.2	+	4856.90i	0.866478	+	0.315372i	0.736740	−	0.676176i	$-0.236364\pi$
$619$	13344.2	+	4856.90i	0.866478	+	0.315372i	0.129738	+	0.991548i	$0.458586\pi$
$620$	5084.01			0.329321
$621$		0			0
$622$	−201.243			−0.0129729
$623$	−28506.9	−	10375.7i	−1.83323	−	0.667242i
$624$		0			0
$625$	−14946.3	−	12541.5i	−0.956565	−	0.802653i
$626$	−103.957	+	589.570i	−0.00663731	+	0.0376421i
$627$		0			0
$628$	−5012.77	+	4206.22i	−0.318521	+	0.267271i
$629$	1223.22	+	2118.68i	0.0775405	+	0.134304i
$630$		0			0
$631$	−575.775	+	997.271i	−0.0363252	+	0.0629172i	−0.883616	−	0.468211i	$-0.844899\pi$
$631$	−575.775	+	997.271i	−0.0363252	+	0.0629172i	0.847291	+	0.531129i	$0.178232\pi$
$632$	−2451.56	−	13903.5i	−0.154300	−	0.875081i
$633$		0			0
$634$	−14403.0	+	5242.26i	−0.902233	+	0.328386i
$635$	32054.2	−	11666.8i	2.00320	−	0.729106i
$636$		0			0
$637$	−2126.73	−	12061.3i	−0.132282	−	0.750211i
$638$	−4320.13	+	7482.69i	−0.268081	+	0.464330i
$639$		0			0
$640$	5127.77	+	8881.57i	0.316708	+	0.548554i
$641$	2071.81	−	1738.45i	0.127662	−	0.107121i	−0.576721	−	0.816941i	$-0.695668\pi$
$641$	2071.81	−	1738.45i	0.127662	−	0.107121i	0.704383	+	0.709820i	$0.251224\pi$
$642$		0			0
$643$	−4578.33	+	25965.0i	−0.280796	+	1.59247i	0.439130	+	0.898423i	$0.355287\pi$
$643$	−4578.33	+	25965.0i	−0.280796	+	1.59247i	−0.719927	+	0.694050i	$0.755825\pi$
$644$	−7850.12	−	6587.03i	−0.480339	−	0.403052i
$645$		0			0
$646$	−6062.12	−	2206.43i	−0.369212	−	0.134382i
$647$	1482.35			0.0900730			0.0450365	−	0.998985i	$-0.485660\pi$
$647$	1482.35			0.0900730			0.0450365	+	0.998985i	$0.485660\pi$
$648$		0			0
$649$	7119.00			0.430578
$650$	−6774.91	−	2465.87i	−0.408821	−	0.148799i
$651$		0			0
$652$	−461.850	−	387.538i	−0.0277415	−	0.0232779i
$653$	−4541.81	+	25757.9i	−0.272182	+	1.54362i	0.475592	+	0.879666i	$0.342234\pi$
$653$	−4541.81	+	25757.9i	−0.272182	+	1.54362i	−0.747774	+	0.663954i	$0.768877\pi$
$654$		0			0
$655$	9028.63	−	7575.92i	0.538592	−	0.451932i
$656$	−229.271	−	397.109i	−0.0136456	−	0.0236349i
$657$		0			0
$658$	5569.00	−	9645.79i	0.329943	−	0.571477i
$659$	3801.12	+	21557.2i	0.224690	+	1.27428i	0.863277	+	0.504730i	$0.168408\pi$
$659$	3801.12	+	21557.2i	0.224690	+	1.27428i	−0.638588	+	0.769549i	$0.720481\pi$
$660$		0			0
$661$	−12684.2	+	4616.68i	−0.746383	+	0.271661i	−0.687083	−	0.726579i	$-0.741109\pi$
$661$	−12684.2	+	4616.68i	−0.746383	+	0.271661i	−0.0593003	+	0.998240i	$0.518887\pi$
$662$	6701.38	−	2439.10i	0.393439	−	0.143200i
$663$		0			0
$664$	3445.59	+	19540.9i	0.201378	+	1.14207i
$665$	−14692.7	+	25448.6i	−0.856782	+	1.48399i
$666$		0			0
$667$	6865.41	+	11891.2i	0.398545	+	0.690300i
$668$	−330.017	+	276.917i	−0.0191149	+	0.0160393i
$669$		0			0
$670$	4431.88	−	25134.4i	0.255550	−	1.44930i
$671$	−1349.10	−	1132.03i	−0.0776174	−	0.0651287i
$672$		0			0
$673$	30486.5	+	11096.2i	1.74617	+	0.635553i	0.999559	−	0.0297115i	$-0.00945884\pi$
$673$	30486.5	+	11096.2i	1.74617	+	0.635553i	0.746608	+	0.665264i	$0.231681\pi$
$674$	−1292.36			−0.0738572
$675$		0			0
$676$	−11507.5			−0.654729
$677$	−28765.4	−	10469.7i	−1.63300	−	0.594364i	−0.647207	−	0.762314i	$-0.724063\pi$
$677$	−28765.4	−	10469.7i	−1.63300	−	0.594364i	−0.985796	+	0.167950i	$0.946285\pi$
$678$		0			0
$679$	11773.1	+	9878.84i	0.665408	+	0.558343i
$680$	−2022.31	+	11469.1i	−0.114047	+	0.646794i
$681$		0			0
$682$	−3705.98	+	3109.69i	−0.208078	+	0.174598i
$683$	−2113.19	−	3660.16i	−0.118388	−	0.205054i	0.800741	−	0.599011i	$-0.204439\pi$
$683$	−2113.19	−	3660.16i	−0.118388	−	0.205054i	−0.919129	+	0.393957i	$0.871106\pi$
$684$		0			0
$685$	17466.5	−	30252.9i	0.974249	−	1.68745i
$686$	1182.24	+	6704.84i	0.0657992	+	0.373166i
$687$		0			0
$688$	−1915.72	+	697.265i	−0.106157	+	0.0386381i
$689$	−2497.49	+	909.012i	−0.138094	+	0.0502621i
$690$		0			0
$691$	4694.40	+	26623.2i	0.258442	+	1.46570i	0.787081	+	0.616850i	$0.211591\pi$
$691$	4694.40	+	26623.2i	0.258442	+	1.46570i	−0.528639	+	0.848847i	$0.677298\pi$
$692$	7117.96	−	12328.7i	0.391018	−	0.677262i
$693$		0			0
$694$	−8285.49	−	14350.9i	−0.453188	−	0.784945i
$695$	7923.30	−	6648.44i	0.432443	−	0.362863i
$696$		0			0
$697$	−640.188	+	3630.68i	−0.0347903	+	0.197306i
$698$	−8843.02	−	7420.18i	−0.479532	−	0.402375i
$699$		0			0
$700$	5832.62	+	2122.90i	0.314932	+	0.114626i
$701$	−19177.6			−1.03328			−0.516640	−	0.856203i	$-0.672817\pi$
$701$	−19177.6			−1.03328			−0.516640	+	0.856203i	$0.672817\pi$
$702$		0			0
$703$	6238.68			0.334703
$704$	−11140.1	−	4054.65i	−0.596388	−	0.217068i
$705$		0			0
$706$	−13051.6	−	10951.6i	−0.695754	−	0.583807i
$707$	6756.20	−	38316.3i	0.359396	−	2.03824i
$708$		0			0
$709$	12097.5	−	10151.0i	0.640808	−	0.537702i	−0.263458	−	0.964671i	$-0.584863\pi$
$709$	12097.5	−	10151.0i	0.640808	−	0.537702i	0.904266	+	0.426969i	$0.140419\pi$
$710$	−3649.43	−	6320.99i	−0.192902	−	0.334116i
$711$		0			0
$712$	−15329.8	+	26552.0i	−0.806895	+	1.39758i
$713$	1335.02	+	7571.29i	0.0701220	+	0.397682i
$714$		0			0
$715$	−28690.9	+	10442.6i	−1.50067	+	0.546199i
$716$	1588.70	−	578.238i	0.0829223	−	0.0301813i
$717$		0			0
$718$	−3762.66	−	21339.1i	−0.195573	−	1.10915i
$719$	4886.52	−	8463.70i	0.253458	−	0.439002i	−0.711017	−	0.703174i	$-0.751765\pi$
$719$	4886.52	−	8463.70i	0.253458	−	0.439002i	0.964476	+	0.264172i	$0.0850986\pi$
$720$		0			0
$721$	9270.40	+	16056.8i	0.478846	+	0.829385i
$722$	−3030.44	+	2542.84i	−0.156207	+	0.131073i
$723$		0			0
$724$	−898.151	+	5093.67i	−0.0461043	+	0.261470i
$725$	−6370.97	−	5345.88i	−0.326361	−	0.273850i
$726$		0			0
$727$	4022.46	+	1464.06i	0.205206	+	0.0746890i	0.442578	−	0.896730i	$-0.354064\pi$
$727$	4022.46	+	1464.06i	0.205206	+	0.0746890i	−0.237372	+	0.971419i	$0.576286\pi$
$728$	−36029.7			−1.83427
$729$		0			0
$730$	−2417.66			−0.122577
$731$	15402.5	+	5606.04i	0.779317	+	0.283648i
$732$		0			0
$733$	9912.79	+	8317.82i	0.499505	+	0.419135i	0.857418	−	0.514620i	$-0.172067\pi$
$733$	9912.79	+	8317.82i	0.499505	+	0.419135i	−0.357913	+	0.933755i	$0.616512\pi$
$734$	−2569.56	+	14572.7i	−0.129216	+	0.732818i
$735$		0			0
$736$	−12938.8	+	10856.9i	−0.648002	+	0.543738i
$737$	−17129.0	−	29668.2i	−0.856110	−	1.48283i
$738$		0			0
$739$	12267.7	−	21248.4i	0.610658	−	1.05769i	−0.380472	−	0.924793i	$-0.624238\pi$
$739$	12267.7	−	21248.4i	0.610658	−	1.05769i	0.991130	−	0.132898i	$-0.0424283\pi$
$740$	−721.947	−	4094.36i	−0.0358639	−	0.203394i
$741$		0			0
$742$	−1524.27	+	554.791i	−0.0754149	+	0.0274488i
$743$	−11071.1	+	4029.54i	−0.546646	+	0.198963i	−0.600556	−	0.799583i	$-0.705054\pi$
$743$	−11071.1	+	4029.54i	−0.546646	+	0.198963i	0.0539098	+	0.998546i	$0.482832\pi$
$744$		0			0
$745$	3154.92	+	17892.4i	0.155151	+	0.879903i
$746$	8448.79	−	14633.7i	0.414654	−	0.718202i
$747$		0			0
$748$	2885.32	+	4997.52i	0.141040	+	0.244288i
$749$	−6879.14	+	5772.28i	−0.335592	+	0.281595i
$750$		0			0
$751$	4813.96	−	27301.3i	0.233907	−	1.32655i	−0.610998	−	0.791632i	$-0.709232\pi$
$751$	4813.96	−	27301.3i	0.233907	−	1.32655i	0.844904	−	0.534917i	$-0.179657\pi$
$752$	−949.672	−	796.869i	−0.0460518	−	0.0386421i
$753$		0			0
$754$	16746.5	+	6095.22i	0.808847	+	0.294396i
$755$	−11992.5			−0.578083
$756$		0			0
$757$	−8933.57			−0.428925			−0.214462	−	0.976732i	$-0.568800\pi$
$757$	−8933.57			−0.428925			−0.214462	+	0.976732i	$0.568800\pi$
$758$	2430.98	+	884.805i	0.116487	+	0.0423978i
$759$		0			0
$760$	22750.4	+	19089.9i	1.08585	+	0.911136i
$761$	−1912.40	+	10845.7i	−0.0910964	+	0.516633i	0.904777	+	0.425885i	$0.140037\pi$
$761$	−1912.40	+	10845.7i	−0.0910964	+	0.516633i	−0.995874	+	0.0907486i	$0.971074\pi$
$762$		0			0
$763$	14840.2	−	12452.4i	0.704128	−	0.590834i
$764$	−8438.00	−	14615.0i	−0.399576	−	0.692086i
$765$		0			0
$766$	6347.77	−	10994.7i	0.299418	−	0.518607i
$767$	−2549.76	−	14460.4i	−0.120035	−	0.680750i
$768$		0			0
$769$	24566.0	−	8941.30i	1.15198	−	0.419287i	0.305754	−	0.952110i	$-0.401091\pi$
$769$	24566.0	−	8941.30i	1.15198	−	0.419287i	0.846226	+	0.532824i	$0.178869\pi$
$770$	−17510.7	+	6373.37i	−0.819535	+	0.298286i
$771$		0			0
$772$	−2580.64	−	14635.6i	−0.120310	−	0.682312i
$773$	2067.63	−	3581.24i	0.0962062	−	0.166634i	−0.813905	−	0.580998i	$-0.802663\pi$
$773$	2067.63	−	3581.24i	0.0962062	−	0.166634i	0.910111	+	0.414364i	$0.135996\pi$
$774$		0			0
$775$	−2328.32	−	4032.78i	−0.107917	−	0.186918i
$776$	11898.6	−	9984.10i	0.550431	−	0.461866i
$777$		0			0
$778$	3232.58	−	18332.9i	0.148963	−	0.844813i
$779$	7201.94	+	6043.14i	0.331240	+	0.277944i
$780$		0			0
$781$	−9206.27	−	3350.81i	−0.421800	−	0.153523i
$782$	−6501.19			−0.297292
$783$		0			0
$784$	−831.981			−0.0379000
$785$	17769.5	+	6467.55i	0.807923	+	0.294060i
$786$		0			0
$787$	−26691.4	−	22396.8i	−1.20895	−	1.01443i	−0.999328	−	0.0366510i	$-0.988331\pi$
$787$	−26691.4	−	22396.8i	−1.20895	−	1.01443i	−0.209626	−	0.977782i	$-0.567225\pi$
$788$	171.636	−	973.394i	0.00775922	−	0.0440047i
$789$		0			0
$790$	−11537.0	+	9680.71i	−0.519581	+	0.435980i
$791$	18294.1	+	31686.3i	0.822329	+	1.42432i
$792$		0			0
$793$	−1816.22	+	3145.79i	−0.0813316	+	0.140870i
$794$	−4171.87	−	23659.8i	−0.186466	−	1.05750i
$795$		0			0
$796$	−5047.61	+	1837.18i	−0.224758	+	0.0818054i
$797$	−16527.2	+	6015.40i	−0.734533	+	0.267348i	−0.682082	−	0.731275i	$-0.738925\pi$
$797$	−16527.2	+	6015.40i	−0.734533	+	0.267348i	−0.0524508	+	0.998624i	$0.516703\pi$
$798$		0			0
$799$	1730.80	+	9815.88i	0.0766351	+	0.434619i
$800$	5115.22	−	8859.82i	0.226063	−	0.391553i
$801$		0			0
$802$	−3387.20	−	5866.81i	−0.149135	−	0.258309i
$803$	−2485.95	+	2085.96i	−0.109249	+	0.0916710i
$804$		0			0
$805$	−5142.29	+	29163.4i	−0.225145	+	1.27686i
$806$	7643.87	+	6413.97i	0.334050	+	0.280301i
$807$		0			0
$808$	−36950.5	−	13448.9i	−1.60881	−	0.585558i
$809$	28644.6			1.24486			0.622428	−	0.782677i	$-0.286146\pi$
$809$	28644.6			1.24486			0.622428	+	0.782677i	$0.286146\pi$
$810$		0			0
$811$	30919.2			1.33874			0.669370	−	0.742929i	$-0.266564\pi$
$811$	30919.2			1.33874			0.669370	+	0.742929i	$0.266564\pi$
$812$	−14417.3	−	5247.46i	−0.623088	−	0.226785i
$813$		0			0
$814$	3030.62	+	2542.99i	0.130495	+	0.109499i
$815$	−302.539	+	1715.79i	−0.0130031	+	0.0737440i
$816$		0			0
$817$	32019.7	−	26867.7i	1.37115	−	1.15053i
$818$	11095.6	+	19218.1i	0.474264	+	0.821450i
$819$		0			0
$820$	3132.62	−	5425.85i	0.133409	−	0.231072i
$821$	2899.55	+	16444.2i	0.123258	+	0.699032i	0.982327	+	0.187172i	$0.0599322\pi$
$821$	2899.55	+	16444.2i	0.123258	+	0.699032i	−0.859069	+	0.511860i	$0.828957\pi$
$822$		0			0
$823$	13294.9	−	4838.96i	0.563102	−	0.204952i	−0.0447564	−	0.998998i	$-0.514251\pi$
$823$	13294.9	−	4838.96i	0.563102	−	0.204952i	0.607858	+	0.794046i	$0.292029\pi$
$824$	17608.3	−	6408.89i	0.744434	−	0.270952i
$825$		0			0
$826$	−1556.18	−	8825.53i	−0.0655525	−	0.371767i
$827$	−7204.22	+	12478.1i	−0.302920	+	0.524674i	−0.976796	−	0.214171i	$-0.931295\pi$
$827$	−7204.22	+	12478.1i	−0.302920	+	0.524674i	0.673876	+	0.738845i	$0.264628\pi$
$828$		0			0
$829$	6216.40	+	10767.1i	0.260440	+	0.451095i	0.966359	−	0.257198i	$-0.0827991\pi$
$829$	6216.40	+	10767.1i	0.260440	+	0.451095i	−0.705919	+	0.708292i	$0.749466\pi$
$830$	16214.9	−	13605.9i	0.678106	−	0.568999i
$831$		0			0
$832$	−4246.03	+	24080.4i	−0.176928	+	1.00341i
$833$	5124.19	+	4299.71i	0.213136	+	0.178843i
$834$		0			0
$835$	1169.86	+	425.793i	0.0484845	+	0.0176469i
$836$	14715.7			0.608797
$837$		0			0
$838$	−8817.33			−0.363472
$839$	−17377.4	−	6324.84i	−0.715057	−	0.260260i	−0.0412313	−	0.999150i	$-0.513128\pi$
$839$	−17377.4	−	6324.84i	−0.715057	−	0.260260i	−0.673826	+	0.738890i	$0.735350\pi$
$840$		0			0
$841$	−2935.06	−	2462.81i	−0.120344	−	0.100980i
$842$	4834.63	−	27418.6i	0.197877	−	1.12222i
$843$		0			0
$844$	−1377.63	+	1155.96i	−0.0561846	+	0.0471445i
$845$	16627.1	+	28798.9i	0.676910	+	1.17244i
$846$		0			0
$847$	2705.87	−	4686.70i	0.109769	−	0.190126i
$848$	31.3516	+	177.804i	0.00126960	+	0.00720025i
$849$		0			0
$850$	3700.27	−	1346.79i	0.149316	−	0.0543464i
$851$	5907.89	−	2150.30i	0.237979	−	0.0866172i
$852$		0			0
$853$	5556.18	+	31510.7i	0.223025	+	1.26484i	0.866426	+	0.499306i	$0.166412\pi$
$853$	5556.18	+	31510.7i	0.223025	+	1.26484i	−0.643401	+	0.765529i	$0.722477\pi$
$854$	−1108.48	+	1919.95i	−0.0444163	+	0.0769312i
$855$		0			0
$856$	4537.88	+	7859.84i	0.181193	+	0.313836i
$857$	−25794.0	+	21643.8i	−1.02813	+	0.862704i	−0.990627	−	0.136593i	$-0.956385\pi$
$857$	−25794.0	+	21643.8i	−1.02813	+	0.862704i	−0.0375030	+	0.999297i	$0.511940\pi$
$858$		0			0
$859$	−5686.82	+	32251.5i	−0.225881	+	1.28103i	0.635113	+	0.772419i	$0.280953\pi$
$859$	−5686.82	+	32251.5i	−0.225881	+	1.28103i	−0.860994	+	0.508615i	$0.830158\pi$
$860$	−21338.2	−	17904.9i	−0.846079	−	0.709945i
$861$		0			0
$862$	20947.7	+	7624.32i	0.827703	+	0.301259i
$863$	22733.2			0.896696			0.448348	−	0.893859i	$-0.352013\pi$
$863$	22733.2			0.896696			0.448348	+	0.893859i	$0.352013\pi$
$864$		0			0
$865$	−41138.6			−1.61706
$866$	11080.8	+	4033.09i	0.434806	+	0.158256i
$867$		0			0
$868$	−6580.72	−	5521.88i	−0.257332	−	0.215927i
$869$	−3510.37	+	19908.3i	−0.137032	+	0.777149i
$870$		0			0
$871$	−54128.4	+	45419.1i	−2.10571	+	1.76690i
$872$	−9789.43	−	16955.8i	−0.380174	−	0.658481i
$873$		0			0
$874$	−8289.36	+	14357.6i	−0.320814	+	0.555667i
$875$	3597.40	+	20401.9i	0.138988	+	0.788238i
$876$		0			0
$877$	−10552.0	+	3840.60i	−0.406288	+	0.147877i	−0.537076	−	0.843534i	$-0.680471\pi$
$877$	−10552.0	+	3840.60i	−0.406288	+	0.147877i	0.130789	+	0.991410i	$0.458249\pi$
$878$	13017.7	−	4738.04i	0.500370	−	0.182120i
$879$		0			0
$880$	360.164	+	2042.59i	0.0137967	+	0.0782452i
$881$	−15460.7	+	26778.7i	−0.591242	+	1.02406i	0.402824	+	0.915278i	$0.368029\pi$
$881$	−15460.7	+	26778.7i	−0.591242	+	1.02406i	−0.994066	+	0.108783i	$0.965305\pi$
$882$		0			0
$883$	−18630.1	−	32268.3i	−0.710027	−	1.22980i	−0.964847	−	0.262814i	$-0.915350\pi$
$883$	−18630.1	−	32268.3i	−0.710027	−	1.22980i	0.254820	−	0.966989i	$-0.417984\pi$
$884$	9117.76	−	7650.71i	0.346904	−	0.291087i
$885$		0			0
$886$	1150.43	−	6524.39i	0.0436223	−	0.247394i
$887$	32112.3	+	26945.4i	1.21559	+	1.02000i	0.999044	+	0.0437267i	$0.0139231\pi$
$887$	32112.3	+	26945.4i	1.21559	+	1.02000i	0.216544	+	0.976273i	$0.430521\pi$
$888$		0			0
$889$	−54162.5	−	19713.5i	−2.04337	−	0.743724i
$890$	32706.5			1.23183
$891$		0			0
$892$	−522.398			−0.0196089
$893$	23884.8	+	8693.36i	0.895045	+	0.325770i
$894$		0			0
$895$	−3742.60	−	3140.42i	−0.139778	−	0.117288i
$896$	3009.14	−	17065.7i	0.112197	−	0.636299i
$897$		0			0
$898$	4709.00	−	3951.32i	0.174990	−	0.146834i
$899$	5755.24	+	9968.37i	0.213513	+	0.369815i
$900$		0			0
$901$	725.802	−	1257.13i	0.0268368	−	0.0464827i
$902$	1035.26	+	5871.26i	0.0382156	+	0.216731i
$903$		0			0
$904$	34747.9	−	12647.2i	1.27843	−	0.465310i
$905$	14045.2	−	5112.05i	0.515889	−	0.187768i
$906$		0			0
$907$	−9206.60	−	52213.2i	−0.337045	−	1.91148i	−0.406027	−	0.913861i	$-0.633086\pi$
$907$	−9206.60	−	52213.2i	−0.337045	−	1.91148i	0.0689820	−	0.997618i	$-0.478025\pi$
$908$	−9859.99	+	17078.0i	−0.360369	+	0.624178i
$909$		0			0
$910$	19217.6	+	33285.8i	0.700061	+	1.21254i
$911$	4496.75	−	3773.22i	0.163539	−	0.137225i	−0.557346	−	0.830280i	$-0.688180\pi$
$911$	4496.75	−	3773.22i	0.163539	−	0.137225i	0.720885	+	0.693055i	$0.243736\pi$
$912$		0			0
$913$	4933.72	−	27980.5i	0.178841	−	1.01426i
$914$	−8454.53	−	7094.19i	−0.305964	−	0.256734i
$915$		0			0
$916$	9024.98	+	3284.82i	0.325539	+	0.118486i
$917$	−19915.0			−0.717178
$918$		0			0
$919$	−29491.3			−1.05857			−0.529285	−	0.848444i	$-0.677540\pi$
$919$	−29491.3			−1.05857			−0.529285	+	0.848444i	$0.677540\pi$
$920$	28123.9	+	10236.3i	1.00785	+	0.366826i
$921$		0			0
$922$	12044.5	+	10106.5i	0.430222	+	0.360999i
$923$	−3508.96	+	19900.3i	−0.125134	+	0.709671i
$924$		0			0
$925$	−2917.13	+	2447.76i	−0.103692	+	0.0870075i
$926$	−1909.88	−	3308.00i	−0.0677780	−	0.117395i
$927$		0			0
$928$	−12644.0	+	21900.0i	−0.447262	+	0.774681i
$929$	−3894.20	−	22085.1i	−0.137529	−	0.779966i	−0.973065	−	0.230530i	$-0.925954\pi$
$929$	−3894.20	−	22085.1i	−0.137529	−	0.779966i	0.835536	−	0.549435i	$-0.185157\pi$
$930$		0			0
$931$	16029.3	−	5834.20i	0.564275	−	0.205379i
$932$	19117.6	−	6958.23i	0.671907	−	0.244554i
$933$		0			0
$934$	−5576.93	−	31628.3i	−0.195378	−	1.10804i
$935$	8337.93	−	14441.7i	0.291636	−	0.505128i
$936$		0			0
$937$	−1850.02	−	3204.33i	−0.0645012	−	0.111719i	0.831971	−	0.554818i	$-0.187212\pi$
$937$	−1850.02	−	3204.33i	−0.0645012	−	0.111719i	−0.896473	+	0.443099i	$0.853879\pi$
$938$	−33035.8	+	27720.3i	−1.14995	+	0.964926i
$939$		0			0
$940$	2941.36	−	16681.3i	0.102060	−	0.578812i
$941$	27001.6	+	22657.0i	0.935416	+	0.784907i	0.976782	−	0.214237i	$-0.0687265\pi$
$941$	27001.6	+	22657.0i	0.935416	+	0.784907i	−0.0413661	+	0.999144i	$0.513171\pi$
$942$		0			0
$943$	8902.97	+	3240.42i	0.307445	+	0.111901i
$944$	−997.474			−0.0343909
$945$		0			0
$946$	26506.2			0.910984
$947$	40054.9	+	14578.8i	1.37446	+	0.500261i	0.920493	−	0.390760i	$-0.127788\pi$
$947$	40054.9	+	14578.8i	1.37446	+	0.500261i	0.453963	+	0.891021i	$0.350010\pi$
$948$		0			0
$949$	5127.46	+	4302.45i	0.175389	+	0.147169i
$950$	1743.72	−	9889.12i	0.0595513	−	0.337732i
$951$		0			0
$952$	15074.6	−	12649.1i	0.513203	−	0.430628i
$953$	−7330.68	−	12697.1i	−0.249175	−	0.431584i	0.714122	−	0.700021i	$-0.246826\pi$
$953$	−7330.68	−	12697.1i	−0.249175	−	0.431584i	−0.963297	+	0.268437i	$0.913493\pi$
$954$		0			0
$955$	−24383.9	+	42234.2i	−0.826226	+	1.43106i
$956$	−1198.03	−	6794.39i	−0.0405305	−	0.229860i
$957$		0			0
$958$	1205.76	−	438.862i	0.0406644	−	0.0148006i
$959$	−55467.0	+	20188.3i	−1.86770	+	0.679787i
$960$		0			0
$961$	−4054.01	−	22991.4i	−0.136082	−	0.771758i
$962$	4079.98	−	7066.73i	0.136740	−	0.236841i
$963$		0			0
$964$	6994.83	+	12115.4i	0.233702	+	0.404783i
$965$	−32898.5	+	27605.1i	−1.09745	+	0.920871i
$966$		0			0
$967$	−1029.82	+	5840.41i	−0.0342470	+	0.194224i	−0.997131	−	0.0756897i	$-0.975884\pi$
$967$	−1029.82	+	5840.41i	−0.0342470	+	0.194224i	0.962884	+	0.269914i	$0.0869953\pi$
$968$	−4189.80	−	3515.66i	−0.139117	−	0.116733i
$969$		0			0
$970$	−15570.2	−	5667.10i	−0.515391	−	0.187587i
$971$	13692.5			0.452538			0.226269	−	0.974065i	$-0.427347\pi$
$971$	13692.5			0.452538			0.226269	+	0.974065i	$0.427347\pi$
$972$		0			0
$973$	−17476.9			−0.575832
$974$	−27108.3	−	9866.61i	−0.891792	−	0.324586i
$975$		0			0
$976$	189.028	+	158.613i	0.00619941	+	0.00520192i
$977$	2739.78	−	15538.1i	0.0897169	−	0.508810i	−0.906522	−	0.422159i	$-0.861272\pi$
$977$	2739.78	−	15538.1i	0.0897169	−	0.508810i	0.996239	−	0.0866510i	$-0.0276165\pi$
$978$		0			0
$979$	33630.4	−	28219.2i	1.09789	−	0.921236i
$980$	−5683.84	−	9844.69i	−0.185269	−	0.320895i
$981$		0			0
$982$	1383.33	−	2396.00i	0.0449531	−	0.0778610i
$983$	−7849.92	−	44519.1i	−0.254704	−	1.44450i	−0.796832	−	0.604201i	$-0.793493\pi$
$983$	−7849.92	−	44519.1i	−0.254704	−	1.44450i	0.542129	−	0.840296i	$-0.317619\pi$
$984$		0			0
$985$	−2684.03	+	976.907i	−0.0868227	+	0.0316009i
$986$	−9146.47	+	3329.04i	−0.295419	+	0.107524i
$987$		0			0
$988$	−5270.63	−	29891.2i	−0.169718	−	0.962517i
$989$	21061.4	−	36479.4i	0.677161	−	1.17288i
$990$		0			0
$991$	1253.68	+	2171.44i	0.0401862	+	0.0696045i	0.885419	−	0.464794i	$-0.153872\pi$
$991$	1253.68	+	2171.44i	0.0401862	+	0.0696045i	−0.845233	+	0.534398i	$0.820538\pi$
$992$	−10846.5	+	9101.31i	−0.347155	+	0.291297i
$993$		0			0
$994$	−2141.60	+	12145.6i	−0.0683374	+	0.387561i
$995$	11891.0	+	9977.73i	0.378864	+	0.317905i
$996$		0			0
$997$	51228.1	+	18645.5i	1.62729	+	0.592286i	0.984752	−	0.173966i	$-0.0556582\pi$
$997$	51228.1	+	18645.5i	1.62729	+	0.592286i	0.642540	+	0.766252i	$0.277880\pi$
$998$	4316.81			0.136920
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.4.e.c.190.6		48
3.2	odd	2		243.4.e.b.190.3		48
9.2	odd	6		243.4.e.a.28.6		48
9.4	even	3		27.4.e.a.22.3	yes	48
9.5	odd	6		81.4.e.a.37.6		48
9.7	even	3		243.4.e.d.28.3		48
27.2	odd	18		81.4.e.a.46.6		48
27.7	even	9	inner	243.4.e.c.55.6		48
27.11	odd	18		243.4.e.a.217.6		48
27.13	even	9		729.4.a.d.1.9		24
27.14	odd	18		729.4.a.c.1.16		24
27.16	even	9		243.4.e.d.217.3		48
27.20	odd	18		243.4.e.b.55.3		48
27.25	even	9		27.4.e.a.16.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.16.3	✓	48	27.25	even	9
27.4.e.a.22.3	yes	48	9.4	even	3
81.4.e.a.37.6		48	9.5	odd	6
81.4.e.a.46.6		48	27.2	odd	18
243.4.e.a.28.6		48	9.2	odd	6
243.4.e.a.217.6		48	27.11	odd	18
243.4.e.b.55.3		48	27.20	odd	18
243.4.e.b.190.3		48	3.2	odd	2
243.4.e.c.55.6		48	27.7	even	9	inner
243.4.e.c.190.6		48	1.1	even	1	trivial
243.4.e.d.28.3		48	9.7	even	3
243.4.e.d.217.3		48	27.16	even	9
729.4.a.c.1.16		24	27.14	odd	18
729.4.a.d.1.9		24	27.13	even	9

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.71186 + 0.623068i) q^{2} +(-3.58609 - 3.00909i) q^{4} +(-2.34910 + 13.3224i) q^{5} +(17.5105 - 14.6931i) q^{7} +(-11.5509 - 20.0068i) q^{8} +O(q^{10})\)	\(q+(1.71186 + 0.623068i) q^{2} +(-3.58609 - 3.00909i) q^{4} +(-2.34910 + 13.3224i) q^{5} +(17.5105 - 14.6931i) q^{7} +(-11.5509 - 20.0068i) q^{8} +(-12.3221 + 21.3425i) q^{10} +(5.74418 + 32.5769i) q^{11} +(64.1142 - 23.3357i) q^{13} +(39.1304 - 14.2423i) q^{14} +(-0.804842 - 4.56449i) q^{16} +(-18.6324 + 32.2722i) q^{17} +(47.5146 + 82.2977i) q^{19} +(48.5124 - 40.7067i) q^{20} +(-10.4643 + 59.3462i) q^{22} +(73.3609 + 61.5571i) q^{23} +(-54.5069 - 19.8389i) q^{25} +124.295 q^{26} -107.007 q^{28} +(134.732 + 49.0385i) q^{29} +(61.4981 + 51.6030i) q^{31} +(-30.6266 + 173.692i) q^{32} +(-52.0039 + 43.6365i) q^{34} +(154.613 + 267.798i) q^{35} +(32.8251 - 56.8548i) q^{37} +(30.0615 + 170.487i) q^{38} +(293.674 - 106.888i) q^{40} +(92.9660 - 33.8369i) q^{41} +(-76.3794 - 433.169i) q^{43} +(77.4275 - 134.108i) q^{44} +(87.2297 + 151.086i) q^{46} +(204.896 - 171.928i) q^{47} +(31.1704 - 176.776i) q^{49} +(-80.9475 - 67.9230i) q^{50} +(-300.138 - 109.241i) q^{52} -38.9538 q^{53} -447.496 q^{55} +(-496.224 - 180.611i) q^{56} +(200.089 + 167.895i) q^{58} +(37.3707 - 211.940i) q^{59} +(-40.7835 + 34.2214i) q^{61} +(73.1242 + 126.655i) q^{62} +(-179.190 + 310.366i) q^{64} +(160.277 + 908.974i) q^{65} +(-973.170 + 354.205i) q^{67} +(163.927 - 59.6647i) q^{68} +(97.8205 + 554.768i) q^{70} +(-148.085 + 256.490i) q^{71} +(49.0512 + 84.9591i) q^{73} +(91.6165 - 76.8754i) q^{74} +(77.2492 - 438.102i) q^{76} +(579.237 + 486.038i) q^{77} +(574.263 + 209.014i) q^{79} +62.7006 q^{80} +180.228 q^{82} +(-807.108 - 293.763i) q^{83} +(-386.175 - 324.039i) q^{85} +(139.142 - 789.116i) q^{86} +(585.409 - 491.217i) q^{88} +(-663.574 - 1149.34i) q^{89} +(779.800 - 1350.65i) q^{91} +(-77.8481 - 441.499i) q^{92} +(457.877 - 166.653i) q^{94} +(-1208.02 + 439.683i) q^{95} +(116.752 + 662.133i) q^{97} +(163.503 - 283.196i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8}+O(q^{10}) \) 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8	\( 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8} - 3 q^{10} - 159 q^{11} + 3 q^{13} - 336 q^{14} - 45 q^{16} - 207 q^{17} - 3 q^{19} + 681 q^{20} + 111 q^{22} + 33 q^{23} + 435 q^{25} + 1914 q^{26} - 12 q^{28} - 51 q^{29} + 111 q^{31} + 1647 q^{32} - 513 q^{34} - 1257 q^{35} - 3 q^{37} - 525 q^{38} - 6 q^{40} + 447 q^{41} + 516 q^{43} - 2211 q^{44} - 3 q^{46} + 2109 q^{47} - 591 q^{49} - 4938 q^{50} - 1350 q^{52} + 2736 q^{53} - 12 q^{55} - 7773 q^{56} - 888 q^{58} + 3048 q^{59} + 57 q^{61} - 2118 q^{62} - 195 q^{64} + 3297 q^{65} + 2082 q^{67} + 3573 q^{68} + 1524 q^{70} - 3105 q^{71} - 219 q^{73} + 9006 q^{74} - 1425 q^{76} - 8985 q^{77} - 1401 q^{79} + 9870 q^{80} - 12 q^{82} - 8511 q^{83} - 1827 q^{85} + 12507 q^{86} - 3693 q^{88} - 5202 q^{89} + 267 q^{91} + 5118 q^{92} - 2211 q^{94} + 5178 q^{95} + 1569 q^{97} - 4392 q^{98}+O(q^{100}) \) 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8 - 3 * q^10 - 159 * q^11 + 3 * q^13 - 336 * q^14 - 45 * q^16 - 207 * q^17 - 3 * q^19 + 681 * q^20 + 111 * q^22 + 33 * q^23 + 435 * q^25 + 1914 * q^26 - 12 * q^28 - 51 * q^29 + 111 * q^31 + 1647 * q^32 - 513 * q^34 - 1257 * q^35 - 3 * q^37 - 525 * q^38 - 6 * q^40 + 447 * q^41 + 516 * q^43 - 2211 * q^44 - 3 * q^46 + 2109 * q^47 - 591 * q^49 - 4938 * q^50 - 1350 * q^52 + 2736 * q^53 - 12 * q^55 - 7773 * q^56 - 888 * q^58 + 3048 * q^59 + 57 * q^61 - 2118 * q^62 - 195 * q^64 + 3297 * q^65 + 2082 * q^67 + 3573 * q^68 + 1524 * q^70 - 3105 * q^71 - 219 * q^73 + 9006 * q^74 - 1425 * q^76 - 8985 * q^77 - 1401 * q^79 + 9870 * q^80 - 12 * q^82 - 8511 * q^83 - 1827 * q^85 + 12507 * q^86 - 3693 * q^88 - 5202 * q^89 + 267 * q^91 + 5118 * q^92 - 2211 * q^94 + 5178 * q^95 + 1569 * q^97 - 4392 * q^98

Introduction

L-functions

Modular forms

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Database

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