LMFDB - Embedded newform 162.7.d.d.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	162.d (of order $6$, degree $2$, 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:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	162.53
Dual form			162.7.d.d.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-150.644 - 86.9741i) q^{5} +(242.000 + 419.156i) q^{7} -181.019i q^{8} +O(q^{10})$	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-150.644 - 86.9741i) q^{5} +(242.000 + 419.156i) q^{7} -181.019i q^{8} -984.000 q^{10} +(1161.06 - 670.337i) q^{11} +(-1684.00 + 2916.77i) q^{13} +(2371.11 + 1368.96i) q^{14} +(-512.000 - 886.810i) q^{16} +12.7279i q^{17} +5744.00 q^{19} +(-4820.60 + 2783.17i) q^{20} +(3792.00 - 6567.94i) q^{22} +(2924.69 + 1688.57i) q^{23} +(7316.50 + 12672.5i) q^{25} +19052.3i q^{26} +15488.0 q^{28} +(25422.0 - 14677.4i) q^{29} +(19898.0 - 34464.3i) q^{31} +(-5016.55 - 2896.31i) q^{32} +(36.0000 + 62.3538i) q^{34} -84191.0i q^{35} +52526.0 q^{37} +(28139.7 - 16246.5i) q^{38} +(-15744.0 + 27269.4i) q^{40} +(32079.7 + 18521.2i) q^{41} +(-1900.00 - 3290.90i) q^{43} -42901.6i q^{44} +19104.0 q^{46} +(66503.6 - 38395.9i) q^{47} +(-58303.5 + 100985. i) q^{49} +(71686.8 + 41388.4i) q^{50} +(53888.0 + 93336.8i) q^{52} +238738. i q^{53} -233208. q^{55} +(75875.4 - 43806.7i) q^{56} +(83028.0 - 143809. i) q^{58} +(216368. + 124920. i) q^{59} +(-6625.00 - 11474.8i) q^{61} -225120. i q^{62} -32768.0 q^{64} +(507368. - 292929. i) q^{65} +(-84484.0 + 146331. i) q^{67} +(352.727 + 203.647i) q^{68} +(-238128. - 412450. i) q^{70} -531467. i q^{71} +236144. q^{73} +(257324. - 148566. i) q^{74} +(91904.0 - 159182. i) q^{76} +(561952. + 324443. i) q^{77} +(17558.0 + 30411.3i) q^{79} +178123. i q^{80} +209544. q^{82} +(-9508.92 + 5489.98i) q^{83} +(1107.00 - 1917.38i) q^{85} +(-18616.1 - 10748.0i) q^{86} +(-121344. - 210174. i) q^{88} -129328. i q^{89} -1.63011e6 q^{91} +(93590.1 - 54034.3i) q^{92} +(217200. - 376201. i) q^{94} +(-865297. - 499579. i) q^{95} +(160712. + 278361. i) q^{97} +659629. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{4} + 968 q^{7}+O(q^{10}) $ 4 * q + 64 * q^4 + 968 * q^7	$ 4 q + 64 q^{4} + 968 q^{7} - 3936 q^{10} - 6736 q^{13} - 2048 q^{16} + 22976 q^{19} + 15168 q^{22} + 29266 q^{25} + 61952 q^{28} + 79592 q^{31} + 144 q^{34} + 210104 q^{37} - 62976 q^{40} - 7600 q^{43} + 76416 q^{46} - 233214 q^{49} + 215552 q^{52} - 932832 q^{55} + 332112 q^{58} - 26500 q^{61} - 131072 q^{64} - 337936 q^{67} - 952512 q^{70} + 944576 q^{73} + 367616 q^{76} + 70232 q^{79} + 838176 q^{82} + 4428 q^{85} - 485376 q^{88} - 6520448 q^{91} + 868800 q^{94} + 642848 q^{97}+O(q^{100}) $ 4 * q + 64 * q^4 + 968 * q^7 - 3936 * q^10 - 6736 * q^13 - 2048 * q^16 + 22976 * q^19 + 15168 * q^22 + 29266 * q^25 + 61952 * q^28 + 79592 * q^31 + 144 * q^34 + 210104 * q^37 - 62976 * q^40 - 7600 * q^43 + 76416 * q^46 - 233214 * q^49 + 215552 * q^52 - 932832 * q^55 + 332112 * q^58 - 26500 * q^61 - 131072 * q^64 - 337936 * q^67 - 952512 * q^70 + 944576 * q^73 + 367616 * q^76 + 70232 * q^79 + 838176 * q^82 + 4428 * q^85 - 485376 * q^88 - 6520448 * q^91 + 868800 * q^94 + 642848 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	4.89898	−	2.82843i	0.612372	−	0.353553i
$2$	4.89898	−	2.82843i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	16.0000	−	27.7128i	0.250000	−	0.433013i
$5$	−150.644	−	86.9741i	−1.20515	−	0.695793i	−0.243453	−	0.969913i	$-0.578280\pi$
$5$	−150.644	−	86.9741i	−1.20515	−	0.695793i	−0.961696	+	0.274120i	$0.911614\pi$
$6$		0			0
$7$	242.000	+	419.156i	0.705539	+	1.22203i	0.966497	+	0.256680i	$0.0826285\pi$
$7$	242.000	+	419.156i	0.705539	+	1.22203i	−0.260957	+	0.965350i	$0.584038\pi$
$8$		−	181.019i		−	0.353553i
$9$		0			0
$10$	−984.000			−0.984000
$11$	1161.06	−	670.337i	0.872320	−	0.503634i	0.00420160	−	0.999991i	$-0.498663\pi$
$11$	1161.06	−	670.337i	0.872320	−	0.503634i	0.868119	+	0.496357i	$0.165329\pi$
$12$		0			0
$13$	−1684.00	+	2916.77i	−0.766500	+	1.32762i	0.172950	+	0.984931i	$0.444670\pi$
$13$	−1684.00	+	2916.77i	−0.766500	+	1.32762i	−0.939450	+	0.342686i	$0.888663\pi$
$14$	2371.11	+	1368.96i	0.864106	+	0.498892i
$15$		0			0
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$			12.7279i			0.00259066i	0.999999	+	0.00129533i	$0.000412317\pi$
$17$			12.7279i			0.00259066i	−0.999999	+	0.00129533i	$0.999588\pi$
$18$		0			0
$19$	5744.00			0.837440			0.418720	−	0.908115i	$-0.362479\pi$
$19$	5744.00			0.837440			0.418720	+	0.908115i	$0.362479\pi$
$20$	−4820.60	+	2783.17i	−0.602574	+	0.347897i
$21$		0			0
$22$	3792.00	−	6567.94i	0.356123	−	0.616824i
$23$	2924.69	+	1688.57i	0.240379	+	0.138783i	0.615351	−	0.788253i	$-0.289014\pi$
$23$	2924.69	+	1688.57i	0.240379	+	0.138783i	−0.374972	+	0.927036i	$0.622348\pi$
$24$		0			0
$25$	7316.50	+	12672.5i	0.468256	+	0.811043i
$26$			19052.3i			1.08399i
$27$		0			0
$28$	15488.0			0.705539
$29$	25422.0	−	14677.4i	1.04236	−	0.601805i	0.121857	−	0.992548i	$-0.461115\pi$
$29$	25422.0	−	14677.4i	1.04236	−	0.601805i	0.920500	+	0.390743i	$0.127782\pi$
$30$		0			0
$31$	19898.0	−	34464.3i	0.667920	−	1.15687i	−0.310565	−	0.950552i	$-0.600518\pi$
$31$	19898.0	−	34464.3i	0.667920	−	1.15687i	0.978485	−	0.206319i	$-0.0661484\pi$
$32$	−5016.55	−	2896.31i	−0.153093	−	0.0883883i
$33$		0			0
$34$	36.0000	+	62.3538i	0.000915937	+	0.00158645i
$35$		−	84191.0i		−	1.96364i
$36$		0			0
$37$	52526.0			1.03698			0.518489	−	0.855085i	$-0.326495\pi$
$37$	52526.0			1.03698			0.518489	+	0.855085i	$0.326495\pi$
$38$	28139.7	−	16246.5i	0.512825	−	0.296080i
$39$		0			0
$40$	−15744.0	+	27269.4i	−0.246000	+	0.426084i
$41$	32079.7	+	18521.2i	0.465457	+	0.268732i	0.714336	−	0.699803i	$-0.246729\pi$
$41$	32079.7	+	18521.2i	0.465457	+	0.268732i	−0.248879	+	0.968535i	$0.580062\pi$
$42$		0			0
$43$	−1900.00	−	3290.90i	−0.0238973	−	0.0413913i	0.853829	−	0.520553i	$-0.174274\pi$
$43$	−1900.00	−	3290.90i	−0.0238973	−	0.0413913i	−0.877727	+	0.479162i	$0.840941\pi$
$44$		−	42901.6i		−	0.503634i
$45$		0			0
$46$	19104.0			0.196269
$47$	66503.6	−	38395.9i	0.640548	−	0.369821i	−0.144277	−	0.989537i	$-0.546086\pi$
$47$	66503.6	−	38395.9i	0.640548	−	0.369821i	0.784826	+	0.619717i	$0.212752\pi$
$48$		0			0
$49$	−58303.5	+	100985.i	−0.495572	+	0.858355i
$50$	71686.8	+	41388.4i	0.573494	+	0.331107i
$51$		0			0
$52$	53888.0	+	93336.8i	0.383250	+	0.663808i
$53$			238738.i			1.60359i	0.597599	+	0.801795i	$0.296121\pi$
$53$			238738.i			1.60359i	−0.597599	+	0.801795i	$0.703879\pi$
$54$		0			0
$55$	−233208.			−1.40170
$56$	75875.4	−	43806.7i	0.432053	−	0.249446i
$57$		0			0
$58$	83028.0	−	143809.i	0.425540	−	0.737057i
$59$	216368.	+	124920.i	1.05351	+	0.608243i	0.923629	−	0.383287i	$-0.125208\pi$
$59$	216368.	+	124920.i	1.05351	+	0.608243i	0.129878	+	0.991530i	$0.458541\pi$
$60$		0			0
$61$	−6625.00	−	11474.8i	−0.0291875	−	0.0505542i	0.851063	−	0.525064i	$-0.175959\pi$
$61$	−6625.00	−	11474.8i	−0.0291875	−	0.0505542i	−0.880250	+	0.474510i	$0.842625\pi$
$62$		−	225120.i		−	0.944581i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	507368.	−	292929.i	1.84749	−	1.06665i
$66$		0			0
$67$	−84484.0	+	146331.i	−0.280899	+	0.486531i	−0.971606	−	0.236603i	$-0.923966\pi$
$67$	−84484.0	+	146331.i	−0.280899	+	0.486531i	0.690707	+	0.723134i	$0.257299\pi$
$68$	352.727	+	203.647i	0.00112179	+	0.000647665i
$69$		0			0
$70$	−238128.	−	412450.i	−0.694251	−	1.20248i
$71$		−	531467.i		−	1.48491i	−0.669894	−	0.742457i	$-0.733660\pi$
$71$		−	531467.i		−	1.48491i	0.669894	−	0.742457i	$-0.266340\pi$
$72$		0			0
$73$	236144.			0.607027			0.303514	−	0.952827i	$-0.401840\pi$
$73$	236144.			0.607027			0.303514	+	0.952827i	$0.401840\pi$
$74$	257324.	−	148566.i	0.635016	−	0.366627i
$75$		0			0
$76$	91904.0	−	159182.i	0.209360	−	0.362622i
$77$	561952.	+	324443.i	1.23091	+	0.710668i
$78$		0			0
$79$	17558.0	+	30411.3i	0.0356118	+	0.0616814i	0.883282	−	0.468842i	$-0.155329\pi$
$79$	17558.0	+	30411.3i	0.0356118	+	0.0616814i	−0.847670	+	0.530524i	$0.821995\pi$
$80$			178123.i			0.347897i
$81$		0			0
$82$	209544.			0.380044
$83$	−9508.92	+	5489.98i	−0.0166302	+	0.00960144i	−0.508292	−	0.861185i	$-0.669723\pi$
$83$	−9508.92	+	5489.98i	−0.0166302	+	0.00960144i	0.491662	+	0.870786i	$0.336390\pi$
$84$		0			0
$85$	1107.00	−	1917.38i	0.00180256	−	0.00312213i
$86$	−18616.1	−	10748.0i	−0.0292681	−	0.0168979i
$87$		0			0
$88$	−121344.	−	210174.i	−0.178062	−	0.308412i
$89$		−	129328.i		−	0.183453i	−0.995784	−	0.0917263i	$-0.970762\pi$
$89$		−	129328.i		−	0.183453i	0.995784	−	0.0917263i	$-0.0292385\pi$
$90$		0			0
$91$	−1.63011e6			−2.16318
$92$	93590.1	−	54034.3i	0.120189	−	0.0693914i
$93$		0			0
$94$	217200.	−	376201.i	0.261503	−	0.452936i
$95$	−865297.	−	499579.i	−1.00924	−	0.582685i
$96$		0			0
$97$	160712.	+	278361.i	0.176089	+	0.304996i	0.940538	−	0.339689i	$-0.110322\pi$
$97$	160712.	+	278361.i	0.176089	+	0.304996i	−0.764448	+	0.644685i	$0.776989\pi$
$98$			659629.i			0.700844i
$99$		0			0
$100$	468256.			0.468256
$101$	579181.	−	334390.i	0.562147	−	0.324556i	−0.191860	−	0.981422i	$-0.561452\pi$
$101$	579181.	−	334390.i	0.562147	−	0.324556i	0.754007	+	0.656867i	$0.228119\pi$
$102$		0			0
$103$	−996706.	+	1.72635e6i	−0.912127	+	1.57985i	−0.101073	+	0.994879i	$0.532228\pi$
$103$	−996706.	+	1.72635e6i	−0.912127	+	1.57985i	−0.811054	+	0.584972i	$0.801106\pi$
$104$	527992.	+	304837.i	0.469383	+	0.270999i
$105$		0			0
$106$	675252.	+	1.16957e6i	0.566955	+	0.981994i
$107$		−	260668.i		−	0.212783i	−0.994324	−	0.106391i	$-0.966070\pi$
$107$		−	260668.i		−	0.212783i	0.994324	−	0.106391i	$-0.0339296\pi$
$108$		0			0
$109$	194456.			0.150156			0.0750779	−	0.997178i	$-0.476079\pi$
$109$	194456.			0.150156			0.0750779	+	0.997178i	$0.476079\pi$
$110$	−1.14248e6	+	659612.i	−0.858363	+	0.495576i
$111$		0			0
$112$	247808.	−	429216.i	0.176385	−	0.305508i
$113$	711784.	+	410949.i	0.493302	+	0.284808i	0.725943	−	0.687755i	$-0.241404\pi$
$113$	711784.	+	410949.i	0.493302	+	0.284808i	−0.232641	+	0.972563i	$0.574737\pi$
$114$		0			0
$115$	−293724.	−	508745.i	−0.193128	−	0.334508i
$116$		−	939355.i		−	0.601805i
$117$		0			0
$118$	1.41331e6			0.860185
$119$	−5334.99	+	3080.16i	−0.00316587	+	0.00182781i
$120$		0			0
$121$	12923.5	−	22384.2i	0.00729498	−	0.0126353i
$122$	−64911.5	−	37476.7i	−0.0357472	−	0.0206387i
$123$		0			0
$124$	−636736.	−	1.10286e6i	−0.333960	−	0.578436i
$125$			172557.i			0.0883490i
$126$		0			0
$127$	3.05721e6			1.49250			0.746250	−	0.665666i	$-0.231852\pi$
$127$	3.05721e6			1.49250			0.746250	+	0.665666i	$0.231852\pi$
$128$	−160530.	+	92681.9i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	1.65706e6	−	2.87011e6i	0.754236	−	1.30637i
$131$	−2.66206e6	−	1.53694e6i	−1.18414	−	0.683664i	−0.227172	−	0.973855i	$-0.572948\pi$
$131$	−2.66206e6	−	1.53694e6i	−1.18414	−	0.683664i	−0.956969	+	0.290191i	$0.906281\pi$
$132$		0			0
$133$	1.39005e6	+	2.40763e6i	0.590847	+	1.02338i
$134$			955827.i			0.397251i
$135$		0			0
$136$	2304.00			0.000915937
$137$	−3.88336e6	+	2.24206e6i	−1.51024	+	0.871938i	−0.510312	+	0.859990i	$0.670470\pi$
$137$	−3.88336e6	+	2.24206e6i	−1.51024	+	0.871938i	−0.999929	+	0.0119482i	$0.996197\pi$
$138$		0			0
$139$	546164.	−	945984.i	0.203366	−	0.352241i	−0.746245	−	0.665672i	$-0.768145\pi$
$139$	546164.	−	945984.i	0.203366	−	0.352241i	0.949611	+	0.313431i	$0.101478\pi$
$140$	−2.33317e6	−	1.34706e6i	−0.850280	−	0.490909i
$141$		0			0
$142$	−1.50322e6	−	2.60365e6i	−0.524996	−	0.909321i
$143$			4.51539e6i			1.54414i
$144$		0			0
$145$	−5.10622e6			−1.67493
$146$	1.15686e6	−	667916.i	0.371727	−	0.214617i
$147$		0			0
$148$	840416.	−	1.45564e6i	0.259244	−	0.449024i
$149$	1.92333e6	+	1.11044e6i	0.581428	+	0.335687i	0.761701	−	0.647929i	$-0.224365\pi$
$149$	1.92333e6	+	1.11044e6i	0.581428	+	0.335687i	−0.180273	+	0.983617i	$0.557698\pi$
$150$		0			0
$151$	2.03935e6	+	3.53226e6i	0.592327	+	1.02594i	0.993918	+	0.110122i	$0.0351241\pi$
$151$	2.03935e6	+	3.53226e6i	0.592327	+	1.02594i	−0.401591	+	0.915819i	$0.631543\pi$
$152$		−	1.03978e6i		−	0.296080i
$153$		0			0
$154$	3.67066e6			1.00504
$155$	−5.99501e6	+	3.46122e6i	−1.60989	+	0.929468i
$156$		0			0
$157$	−3.07784e6	+	5.33097e6i	−0.795329	+	1.37755i	0.127301	+	0.991864i	$0.459369\pi$
$157$	−3.07784e6	+	5.33097e6i	−0.795329	+	1.37755i	−0.922630	+	0.385686i	$0.873965\pi$
$158$	172033.	+	99323.0i	0.0436154	+	0.0251813i
$159$		0			0
$160$	503808.	+	872621.i	0.123000	+	0.213042i
$161$			1.63454e6i			0.391667i
$162$		0			0
$163$	800696.			0.184886			0.0924432	−	0.995718i	$-0.470532\pi$
$163$	800696.			0.184886			0.0924432	+	0.995718i	$0.470532\pi$
$164$	1.02655e6	−	592680.i	0.232728	−	0.134366i
$165$		0			0
$166$	−31056.0	+	53790.6i	−0.00678924	+	0.0117593i
$167$	−4.16097e6	−	2.40234e6i	−0.893398	−	0.515804i	−0.0183455	−	0.999832i	$-0.505840\pi$
$167$	−4.16097e6	−	2.40234e6i	−0.893398	−	0.515804i	−0.875052	+	0.484028i	$0.839173\pi$
$168$		0			0
$169$	−3.25831e6	−	5.64355e6i	−0.675044	−	1.16921i
$170$		−	12524.3i		−	0.00254921i
$171$		0			0
$172$	−121600.			−0.0238973
$173$	−3.09164e6	+	1.78496e6i	−0.597106	+	0.344739i	−0.767902	−	0.640567i	$-0.778699\pi$
$173$	−3.09164e6	+	1.78496e6i	−0.597106	+	0.344739i	0.170796	+	0.985306i	$0.445366\pi$
$174$		0			0
$175$	−3.54119e6	+	6.13351e6i	−0.660746	+	1.14445i
$176$	−1.18892e6	−	686425.i	−0.218080	−	0.125909i
$177$		0			0
$178$	−365796.	−	633577.i	−0.0648603	−	0.112341i
$179$		−	7.43698e6i		−	1.29669i	−0.761345	−	0.648347i	$-0.775461\pi$
$179$		−	7.43698e6i		−	1.29669i	0.761345	−	0.648347i	$-0.224539\pi$
$180$		0			0
$181$	−1.03812e7			−1.75070			−0.875350	−	0.483491i	$-0.839369\pi$
$181$	−1.03812e7			−1.75070			−0.875350	+	0.483491i	$0.839369\pi$
$182$	−7.98589e6	+	4.61065e6i	−1.32467	+	0.764801i
$183$		0			0
$184$	305664.	−	529426.i	0.0490671	−	0.0849868i
$185$	−7.91271e6	−	4.56840e6i	−1.24971	−	0.721521i
$186$		0			0
$187$	8532.00	+	14777.9i	0.00130475	+	0.00225989i
$188$		−	2.45734e6i		−	0.369821i
$189$		0			0
$190$	−5.65210e6			−0.824041
$191$	1.12532e7	−	6.49703e6i	1.61501	−	0.932426i	0.626825	−	0.779160i	$-0.284354\pi$
$191$	1.12532e7	−	6.49703e6i	1.61501	−	0.932426i	0.988185	−	0.153266i	$-0.0489793\pi$
$192$		0			0
$193$	1.96598e6	−	3.40517e6i	0.273468	−	0.473660i	−0.696279	−	0.717771i	$-0.745163\pi$
$193$	1.96598e6	−	3.40517e6i	0.273468	−	0.473660i	0.969747	+	0.244110i	$0.0784959\pi$
$194$	1.57465e6	+	909124.i	0.215665	+	0.124514i
$195$		0			0
$196$	1.86571e6	+	3.23151e6i	0.247786	+	0.429178i
$197$			5.37967e6i			0.703651i	0.936066	+	0.351825i	$0.114439\pi$
$197$			5.37967e6i			0.703651i	−0.936066	+	0.351825i	$0.885561\pi$
$198$		0			0
$199$	−565900.			−0.0718093			−0.0359046	−	0.999355i	$-0.511431\pi$
$199$	−565900.			−0.0718093			−0.0359046	+	0.999355i	$0.511431\pi$
$200$	2.29398e6	−	1.32443e6i	0.286747	−	0.165553i
$201$		0			0
$202$	1.89160e6	−	3.27634e6i	0.229496	−	0.397498i
$203$	1.23043e7	+	7.10387e6i	1.47085	+	0.849194i
$204$		0			0
$205$	−3.22174e6	−	5.58022e6i	−0.373963	−	0.647723i
$206$			1.12764e7i			1.28994i
$207$		0			0
$208$	3.44883e6			0.383250
$209$	6.66912e6	−	3.85042e6i	0.730516	−	0.421763i
$210$		0			0
$211$	6.75825e6	−	1.17056e7i	0.719427	−	1.24608i	−0.241799	−	0.970326i	$-0.577738\pi$
$211$	6.75825e6	−	1.17056e7i	0.719427	−	1.24608i	0.961227	−	0.275759i	$-0.0889291\pi$
$212$	6.61609e6	+	3.81980e6i	0.694375	+	0.400897i
$213$		0			0
$214$	−737280.	−	1.27701e6i	−0.0752300	−	0.130302i
$215$			661003.i			0.0665102i
$216$		0			0
$217$	1.92613e7			1.88497
$218$	952636.	−	550005.i	0.0919512	−	0.0530881i
$219$		0			0
$220$	−3.73133e6	+	6.46285e6i	−0.350425	+	0.606954i
$221$	−37124.5	−	21433.8i	−0.00343941	−	0.00198574i
$222$		0			0
$223$	2.67742e6	+	4.63742e6i	0.241436	+	0.418179i	0.961123	−	0.276119i	$-0.0890484\pi$
$223$	2.67742e6	+	4.63742e6i	0.241436	+	0.418179i	−0.719688	+	0.694298i	$0.755715\pi$
$224$		−	2.80363e6i		−	0.249446i
$225$		0			0
$226$	4.64935e6			0.402779
$227$	−1.17834e7	+	6.80317e6i	−1.00738	+	0.581612i	−0.910424	−	0.413676i	$-0.864245\pi$
$227$	−1.17834e7	+	6.80317e6i	−1.00738	+	0.581612i	−0.0969580	+	0.995288i	$0.530911\pi$
$228$		0			0
$229$	−2.17320e6	+	3.76410e6i	−0.180965	+	0.313440i	−0.942209	−	0.335025i	$-0.891255\pi$
$229$	−2.17320e6	+	3.76410e6i	−0.180965	+	0.313440i	0.761245	+	0.648465i	$0.224589\pi$
$230$	−2.87790e6	−	1.66155e6i	−0.236533	−	0.136562i
$231$		0			0
$232$	−2.65690e6	−	4.60188e6i	−0.212770	−	0.368529i
$233$		−	2.02333e7i		−	1.59956i	−0.600297	−	0.799778i	$-0.704951\pi$
$233$		−	2.02333e7i		−	1.59956i	0.600297	−	0.799778i	$-0.295049\pi$
$234$		0			0
$235$	−1.33578e7			−1.02927
$236$	6.92379e6	−	3.99745e6i	0.526754	−	0.304121i
$237$		0			0
$238$	−17424.0	+	30179.3i	−0.00129246	+	0.00223861i
$239$	1.76623e7	+	1.01973e7i	1.29376	+	0.746953i	0.979319	−	0.202324i	$-0.0648494\pi$
$239$	1.76623e7	+	1.01973e7i	1.29376	+	0.746953i	0.314442	+	0.949277i	$0.398183\pi$
$240$		0			0
$241$	1.56046e6	+	2.70280e6i	0.111481	+	0.193092i	0.916368	−	0.400337i	$-0.131107\pi$
$241$	1.56046e6	+	2.70280e6i	0.111481	+	0.193092i	−0.804886	+	0.593429i	$0.797774\pi$
$242$		−	146213.i		−	0.0103167i
$243$		0			0
$244$	−424000.			−0.0291875
$245$	1.75661e7	−	1.01418e7i	1.19448	−	0.689631i
$246$		0			0
$247$	−9.67290e6	+	1.67539e7i	−0.641897	+	1.11180i
$248$	−6.23871e6	−	3.60192e6i	−0.409016	−	0.236145i
$249$		0			0
$250$	488064.	+	845352.i	0.0312361	+	0.0541025i
$251$			5.09519e6i			0.322210i	0.986937	+	0.161105i	$0.0515058\pi$
$251$			5.09519e6i			0.322210i	−0.986937	+	0.161105i	$0.948494\pi$
$252$		0			0
$253$	4.52765e6			0.279583
$254$	1.49772e7	−	8.64710e6i	0.913966	−	0.527678i
$255$		0			0
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	−1.25031e7	−	7.21869e6i	−0.736580	−	0.425264i	0.0842448	−	0.996445i	$-0.473152\pi$
$257$	−1.25031e7	−	7.21869e6i	−0.736580	−	0.425264i	−0.820824	+	0.571181i	$0.806486\pi$
$258$		0			0
$259$	1.27113e7	+	2.20166e7i	0.731628	+	1.26722i
$260$		−	1.87474e7i		−	1.06665i
$261$		0			0
$262$	−1.73885e7			−0.966847
$263$	2.70691e7	−	1.56283e7i	1.48801	−	0.859104i	0.488105	−	0.872785i	$-0.337688\pi$
$263$	2.70691e7	−	1.56283e7i	1.48801	−	0.859104i	0.999906	+	0.0136808i	$0.00435487\pi$
$264$		0			0
$265$	2.07640e7	−	3.59643e7i	1.11577	−	1.93256i
$266$	1.36196e7	+	7.86330e6i	0.723637	+	0.417792i
$267$		0			0
$268$	2.70349e6	+	4.68258e6i	0.140449	+	0.243266i
$269$			251338.i			0.0129122i	0.999979	+	0.00645612i	$0.00205506\pi$
$269$			251338.i			0.0129122i	−0.999979	+	0.00645612i	$0.997945\pi$
$270$		0			0
$271$	2.96399e7			1.48925			0.744627	−	0.667481i	$-0.232627\pi$
$271$	2.96399e7			1.48925			0.744627	+	0.667481i	$0.232627\pi$
$272$	11287.2	−	6516.70i	0.000560895	−	0.000323833i
$273$		0			0
$274$	−1.26830e7	+	2.19676e7i	−0.616553	+	1.06790i
$275$	1.69898e7	+	9.80904e6i	0.816938	+	0.471660i
$276$		0			0
$277$	−6.61064e6	−	1.14500e7i	−0.311031	−	0.538722i	0.667555	−	0.744561i	$-0.267341\pi$
$277$	−6.61064e6	−	1.14500e7i	−0.311031	−	0.538722i	−0.978586	+	0.205839i	$0.934008\pi$
$278$		−	6.17914e6i		−	0.287603i
$279$		0			0
$280$	−1.52402e7			−0.694251
$281$	−5.30320e6	+	3.06180e6i	−0.239011	+	0.137993i	−0.614722	−	0.788744i	$-0.710732\pi$
$281$	−5.30320e6	+	3.06180e6i	−0.239011	+	0.137993i	0.375711	+	0.926737i	$0.377399\pi$
$282$		0			0
$283$	3.37162e6	−	5.83982e6i	0.148758	−	0.257656i	−0.782011	−	0.623265i	$-0.785806\pi$
$283$	3.37162e6	−	5.83982e6i	0.148758	−	0.257656i	0.930769	+	0.365609i	$0.119139\pi$
$284$	−1.47284e7	−	8.50347e6i	−0.642987	−	0.371229i
$285$		0			0
$286$	1.27715e7	+	2.21208e7i	0.545937	+	0.945590i
$287$			1.79286e7i			0.758403i
$288$		0			0
$289$	2.41374e7			0.999993
$290$	−2.50153e7	+	1.44426e7i	−1.02568	+	0.592176i
$291$		0			0
$292$	3.77830e6	−	6.54421e6i	0.151757	−	0.262851i
$293$	8.68096e6	+	5.01195e6i	0.345116	+	0.199253i	0.662532	−	0.749034i	$-0.269482\pi$
$293$	8.68096e6	+	5.01195e6i	0.345116	+	0.199253i	−0.317416	+	0.948286i	$0.602815\pi$
$294$		0			0
$295$	−2.17297e7	−	3.76369e7i	−0.846422	−	1.46605i
$296$		−	9.50822e6i		−	0.366627i
$297$		0			0
$298$	1.25632e7			0.474734
$299$	−9.85036e6	+	5.68711e6i	−0.368501	+	0.212754i
$300$		0			0
$301$	919600.	−	1.59279e6i	0.0337209	−	0.0584064i
$302$	1.99815e7	+	1.15363e7i	0.725450	+	0.418839i
$303$		0			0
$304$	−2.94093e6	−	5.09384e6i	−0.104680	−	0.181311i
$305$			2.30481e6i			0.0812337i
$306$		0			0
$307$	−5.23060e6			−0.180774			−0.0903871	−	0.995907i	$-0.528810\pi$
$307$	−5.23060e6			−0.180774			−0.0903871	+	0.995907i	$0.528810\pi$
$308$	1.79825e7	−	1.03822e7i	0.615456	−	0.355334i
$309$		0			0
$310$	−1.95796e7	+	3.39129e7i	−0.657233	+	1.13836i
$311$	−2.70392e7	−	1.56111e7i	−0.898901	−	0.518981i	−0.0220578	−	0.999757i	$-0.507022\pi$
$311$	−2.70392e7	−	1.56111e7i	−0.898901	−	0.518981i	−0.876844	+	0.480776i	$0.840355\pi$
$312$		0			0
$313$	−1.12389e7	−	1.94664e7i	−0.366515	−	0.634822i	0.622503	−	0.782617i	$-0.286116\pi$
$313$	−1.12389e7	−	1.94664e7i	−0.366515	−	0.634822i	−0.989018	+	0.147795i	$0.952782\pi$
$314$			3.48218e7i			1.12477i
$315$		0			0
$316$	1.12371e6			0.0356118
$317$	−2.39206e7	+	1.38106e7i	−0.750921	+	0.433544i	−0.826026	−	0.563631i	$-0.809404\pi$
$317$	−2.39206e7	+	1.38106e7i	−0.750921	+	0.433544i	0.0751058	+	0.997176i	$0.476071\pi$
$318$		0			0
$319$	1.96776e7	−	3.40827e7i	0.606179	−	1.04993i
$320$	4.93629e6	+	2.84997e6i	0.150644	+	0.0869741i
$321$		0			0
$322$	4.62317e6	+	8.00756e6i	0.138475	+	0.239846i
$323$			73109.2i			0.00216952i
$324$		0			0
$325$	−4.92839e7			−1.43567
$326$	3.92259e6	−	2.26471e6i	0.113219	−	0.0653672i
$327$		0			0
$328$	3.35270e6	−	5.80705e6i	0.0950110	−	0.164564i
$329$	3.21878e7	+	1.85836e7i	0.903864	+	0.521846i
$330$		0			0
$331$	2.88069e6	+	4.98950e6i	0.0794352	+	0.137586i	0.903006	−	0.429627i	$-0.141355\pi$
$331$	2.88069e6	+	4.98950e6i	0.0794352	+	0.137586i	−0.823571	+	0.567213i	$0.808022\pi$
$332$			351359.i			0.00960144i
$333$		0			0
$334$	−2.71793e7			−0.729456
$335$	2.54540e7	−	1.46958e7i	0.677050	−	0.390895i
$336$		0			0
$337$	2.00526e7	−	3.47321e7i	0.523939	−	0.907489i	−0.475673	−	0.879622i	$-0.657795\pi$
$337$	2.00526e7	−	3.47321e7i	0.523939	−	0.907489i	0.999612	−	0.0278665i	$-0.00887132\pi$
$338$	−3.19248e7	−	1.84318e7i	−0.826756	−	0.477328i
$339$		0			0
$340$	−35424.0	−	61356.2i	−0.000901282	−	0.00156107i
$341$		−	5.33535e7i		−	1.34555i
$342$		0			0
$343$	504328.			0.0124977
$344$	−595716.	+	343937.i	−0.0146340	+	0.00844896i
$345$		0			0
$346$	−1.00973e7	+	1.74890e7i	−0.243767	+	0.422217i
$347$	−5.87275e7	−	3.39064e7i	−1.40557	−	0.811508i	−0.410616	−	0.911808i	$-0.634686\pi$
$347$	−5.87275e7	−	3.39064e7i	−1.40557	−	0.811508i	−0.994957	+	0.100301i	$0.968020\pi$
$348$		0			0
$349$	2.10319e7	+	3.64284e7i	0.494769	+	0.856965i	0.999982	−	0.00602956i	$-0.00191928\pi$
$349$	2.10319e7	+	3.64284e7i	0.494769	+	0.856965i	−0.505213	+	0.862995i	$0.668586\pi$
$350$			4.00639e7i			0.934436i
$351$		0			0
$352$	−7.76602e6			−0.178062
$353$	−1.52399e7	+	8.79878e6i	−0.346465	+	0.200032i	−0.663127	−	0.748507i	$-0.730771\pi$
$353$	−1.52399e7	+	8.79878e6i	−0.346465	+	0.200032i	0.316662	+	0.948538i	$0.397438\pi$
$354$		0			0
$355$	−4.62239e7	+	8.00621e7i	−1.03319	+	1.78954i
$356$	−3.58405e6	−	2.06925e6i	−0.0794373	−	0.0458632i
$357$		0			0
$358$	−2.10349e7	−	3.64336e7i	−0.458450	−	0.794059i
$359$		−	1.39920e7i		−	0.302410i	−0.988502	−	0.151205i	$-0.951685\pi$
$359$		−	1.39920e7i		−	0.302410i	0.988502	−	0.151205i	$-0.0483154\pi$
$360$		0			0
$361$	−1.40523e7			−0.298694
$362$	−5.08572e7	+	2.93624e7i	−1.07208	+	0.618966i
$363$		0			0
$364$	−2.60818e7	+	4.51750e7i	−0.540796	+	0.936686i
$365$	−3.55736e7	−	2.05384e7i	−0.731559	−	0.422365i
$366$		0			0
$367$	1.32927e7	+	2.30237e7i	0.268916	+	0.465776i	0.968582	−	0.248694i	$-0.0800013\pi$
$367$	1.32927e7	+	2.30237e7i	0.268916	+	0.465776i	−0.699666	+	0.714470i	$0.746668\pi$
$368$		−	3.45819e6i		−	0.0693914i
$369$		0			0
$370$	−5.16856e7			−1.02039
$371$	−1.00068e8	+	5.77745e7i	−1.95963	+	1.13140i
$372$		0			0
$373$	−8.94146e6	+	1.54871e7i	−0.172299	+	0.298430i	−0.939223	−	0.343307i	$-0.888453\pi$
$373$	−8.94146e6	+	1.54871e7i	−0.172299	+	0.298430i	0.766924	+	0.641737i	$0.221786\pi$
$374$	83596.2	+	48264.3i	0.00159798	+	0.000922595i
$375$		0			0
$376$	−6.95040e6	−	1.20384e7i	−0.130751	−	0.226468i
$377$			9.88671e7i			1.84513i
$378$		0			0
$379$	7.20978e7			1.32435			0.662177	−	0.749347i	$-0.269633\pi$
$379$	7.20978e7			1.32435			0.662177	+	0.749347i	$0.269633\pi$
$380$	−2.76895e7	+	1.59865e7i	−0.504620	+	0.291342i
$381$		0			0
$382$	3.67527e7	−	6.36576e7i	0.659325	−	1.14198i
$383$	−7.52272e6	−	4.34324e6i	−0.133899	−	0.0773068i	0.431554	−	0.902087i	$-0.357965\pi$
$383$	−7.52272e6	−	4.34324e6i	−0.133899	−	0.0773068i	−0.565453	+	0.824780i	$0.691299\pi$
$384$		0			0
$385$	−5.64363e7	−	9.77506e7i	−0.988955	−	1.71292i
$386$		−	2.22425e7i		−	0.386742i
$387$		0			0
$388$	1.02856e7			0.176089
$389$	−4.28173e7	+	2.47206e7i	−0.727395	+	0.419962i	−0.817468	−	0.575974i	$-0.804623\pi$
$389$	−4.28173e7	+	2.47206e7i	−0.727395	+	0.419962i	0.0900736	+	0.995935i	$0.471290\pi$
$390$		0			0
$391$	−21492.0	+	37225.2i	−0.000359539	+	0.000622741i
$392$	1.82802e7	+	1.05541e7i	0.303474	+	0.175211i
$393$		0			0
$394$	1.52160e7	+	2.63549e7i	0.248778	+	0.430896i
$395$		−	6.10837e6i		−	0.0991137i
$396$		0			0
$397$	1.56911e7			0.250774			0.125387	−	0.992108i	$-0.459983\pi$
$397$	1.56911e7			0.250774			0.125387	+	0.992108i	$0.459983\pi$
$398$	−2.77233e6	+	1.60061e6i	−0.0439740	+	0.0253884i
$399$		0			0
$400$	7.49210e6	−	1.29767e7i	0.117064	−	0.202761i
$401$	4.10941e7	+	2.37257e7i	0.637304	+	0.367947i	0.783575	−	0.621297i	$-0.213394\pi$
$401$	4.10941e7	+	2.37257e7i	0.637304	+	0.367947i	−0.146272	+	0.989244i	$0.546727\pi$
$402$		0			0
$403$	6.70165e7	+	1.16076e8i	1.02392	+	1.77348i
$404$		−	2.14010e7i		−	0.324556i
$405$		0			0
$406$	8.03711e7			1.20094
$407$	6.09857e7	−	3.52101e7i	0.904576	−	0.522257i
$408$		0			0
$409$	5.77558e7	−	1.00036e8i	0.844162	−	1.46213i	−0.0421850	−	0.999110i	$-0.513432\pi$
$409$	5.77558e7	−	1.00036e8i	0.844162	−	1.46213i	0.886347	−	0.463022i	$-0.153235\pi$
$410$	−3.15665e7	−	1.82249e7i	−0.458009	−	0.264432i
$411$		0			0
$412$	3.18946e7	+	5.52431e7i	0.456064	+	0.789925i
$413$			1.20923e8i			1.71656i
$414$		0			0
$415$	1.90994e6			0.0267225
$416$	1.68958e7	−	9.75477e6i	0.234692	−	0.135499i
$417$		0			0
$418$	2.17812e7	−	3.77262e7i	0.298232	−	0.516553i
$419$	−1.27040e8	−	7.33466e7i	−1.72702	−	0.997098i	−0.901577	−	0.432618i	$-0.857590\pi$
$419$	−1.27040e8	−	7.33466e7i	−1.72702	−	0.997098i	−0.825447	−	0.564480i	$-0.809077\pi$
$420$		0			0
$421$	−6.96194e7	−	1.20584e8i	−0.933005	−	1.61601i	−0.778153	−	0.628075i	$-0.783843\pi$
$421$	−6.96194e7	−	1.20584e8i	−0.933005	−	1.61601i	−0.154852	−	0.987938i	$-0.549490\pi$
$422$		−	7.64609e7i		−	1.01742i
$423$		0			0
$424$	4.32161e7			0.566955
$425$	−161295.	+	93123.8i	−0.00210114	+	0.00121309i
$426$		0			0
$427$	3.20650e6	−	5.55382e6i	0.0411858	−	0.0713359i
$428$	−7.22384e6	−	4.17069e6i	−0.0921376	−	0.0531957i
$429$		0			0
$430$	1.86960e6	+	3.23824e6i	0.0235149	+	0.0407290i
$431$		−	1.00392e8i		−	1.25391i	−0.779056	−	0.626954i	$-0.784301\pi$
$431$		−	1.00392e8i		−	1.25391i	0.779056	−	0.626954i	$-0.215699\pi$
$432$		0			0
$433$	−4.00631e7			−0.493493			−0.246747	−	0.969080i	$-0.579362\pi$
$433$	−4.00631e7			−0.493493			−0.246747	+	0.969080i	$0.579362\pi$
$434$	9.43605e7	−	5.44791e7i	1.15431	−	0.666439i
$435$		0			0
$436$	3.11130e6	−	5.38892e6i	0.0375389	−	0.0650193i
$437$	1.67994e7	+	9.69915e6i	0.201303	+	0.116222i
$438$		0			0
$439$	6.92959e7	+	1.20024e8i	0.819057	+	1.41865i	0.906378	+	0.422468i	$0.138836\pi$
$439$	6.92959e7	+	1.20024e8i	0.819057	+	1.41865i	−0.0873208	+	0.996180i	$0.527831\pi$
$440$			4.22152e7i			0.495576i
$441$		0			0
$442$	−242496.			−0.00280826
$443$	−9.65121e7	+	5.57213e7i	−1.11012	+	0.640929i	−0.938861	−	0.344296i	$-0.888117\pi$
$443$	−9.65121e7	+	5.57213e7i	−1.11012	+	0.640929i	−0.171261	+	0.985226i	$0.554784\pi$
$444$		0			0
$445$	−1.12482e7	+	1.94825e7i	−0.127645	+	0.221088i
$446$	2.62332e7	+	1.51458e7i	0.295697	+	0.170721i
$447$		0			0
$448$	−7.92986e6	−	1.37349e7i	−0.0881924	−	0.152754i
$449$		−	6.11166e7i		−	0.675181i	−0.941293	−	0.337591i	$-0.890388\pi$
$449$		−	6.11166e7i		−	0.675181i	0.941293	−	0.337591i	$-0.109612\pi$
$450$		0			0
$451$	4.96619e7			0.541370
$452$	2.27771e7	−	1.31504e7i	0.246651	−	0.142404i
$453$		0			0
$454$	−3.84845e7	+	6.66572e7i	−0.411262	+	0.712327i
$455$	2.45566e8	+	1.41778e8i	2.60696	+	1.50513i
$456$		0			0
$457$	−1.78332e7	−	3.08881e7i	−0.186845	−	0.323625i	0.757352	−	0.653007i	$-0.226493\pi$
$457$	−1.78332e7	−	3.08881e7i	−0.186845	−	0.323625i	−0.944197	+	0.329382i	$0.893160\pi$
$458$			2.45870e7i			0.255923i
$459$		0			0
$460$	−1.87983e7			−0.193128
$461$	1.31621e8	−	7.59914e7i	1.34345	−	0.775642i	0.356139	−	0.934433i	$-0.384093\pi$
$461$	1.31621e8	−	7.59914e7i	1.34345	−	0.775642i	0.987312	+	0.158791i	$0.0507595\pi$
$462$		0			0
$463$	−5.74891e7	+	9.95740e7i	−0.579218	+	1.00324i	0.416351	+	0.909204i	$0.363309\pi$
$463$	−5.74891e7	+	9.95740e7i	−0.579218	+	1.00324i	−0.995569	+	0.0940314i	$0.970025\pi$
$464$	−2.60322e7	−	1.50297e7i	−0.260589	−	0.150451i
$465$		0			0
$466$	−5.72284e7	−	9.91226e7i	−0.565528	−	0.979523i
$467$			8.81705e7i			0.865711i	0.901463	+	0.432855i	$0.142494\pi$
$467$			8.81705e7i			0.865711i	−0.901463	+	0.432855i	$0.857506\pi$
$468$		0			0
$469$	−8.17805e7			−0.792741
$470$	−6.54396e7	+	3.77816e7i	−0.630300	+	0.363904i
$471$		0			0
$472$	2.26130e7	−	3.91669e7i	0.215046	−	0.372471i
$473$	−4.41202e6	−	2.54728e6i	−0.0416921	−	0.0240710i
$474$		0			0
$475$	4.20260e7	+	7.27911e7i	0.392136	+	0.679200i
$476$			197130.i			0.00182781i
$477$		0			0
$478$	1.15370e8			1.05635
$479$	−7.74563e7	+	4.47194e7i	−0.704774	+	0.406902i	−0.809123	−	0.587639i	$-0.800057\pi$
$479$	−7.74563e7	+	4.47194e7i	−0.704774	+	0.406902i	0.104349	+	0.994541i	$0.466724\pi$
$480$		0			0
$481$	−8.84538e7	+	1.53206e8i	−0.794843	+	1.37671i
$482$	1.52894e7	+	8.82732e6i	0.136536	+	0.0788293i
$483$		0			0
$484$	−413552.	−	716293.i	−0.00364749	−	0.00631764i
$485$		−	5.59111e7i		−	0.490087i
$486$		0			0
$487$	−7.51688e7			−0.650805			−0.325403	−	0.945576i	$-0.605500\pi$
$487$	−7.51688e7			−0.650805			−0.325403	+	0.945576i	$0.605500\pi$
$488$	−2.07717e6	+	1.19925e6i	−0.0178736	+	0.0103193i
$489$		0			0
$490$	5.73706e7	−	9.93689e7i	0.487642	−	0.844621i
$491$	−3.90424e7	−	2.25411e7i	−0.329831	−	0.190428i	0.325935	−	0.945392i	$-0.394321\pi$
$491$	−3.90424e7	−	2.25411e7i	−0.329831	−	0.190428i	−0.655766	+	0.754964i	$0.727654\pi$
$492$		0			0
$493$	186813.	+	323570.i	0.00155907	+	0.00270039i
$494$			1.09436e8i			0.907780i
$495$		0			0
$496$	−4.07511e7			−0.333960
$497$	2.22768e8	−	1.28615e8i	1.81461	−	1.04767i
$498$		0			0
$499$	−4.57729e7	+	7.92810e7i	−0.368389	+	0.638069i	−0.989314	−	0.145801i	$-0.953424\pi$
$499$	−4.57729e7	+	7.92810e7i	−0.368389	+	0.638069i	0.620925	+	0.783870i	$0.286757\pi$
$500$	4.78203e6	+	2.76091e6i	0.0382562	+	0.0220873i
$501$		0			0
$502$	1.44114e7	+	2.49612e7i	0.113919	+	0.197313i
$503$		−	1.61043e8i		−	1.26543i	−0.774386	−	0.632713i	$-0.781941\pi$
$503$		−	1.61043e8i		−	1.26543i	0.774386	−	0.632713i	$-0.218059\pi$
$504$		0			0
$505$	−1.16333e8			−0.903295
$506$	2.21809e7	−	1.28061e7i	0.171209	−	0.0988476i
$507$		0			0
$508$	4.89154e7	−	8.47239e7i	0.373125	−	0.646272i
$509$	−2.07841e7	−	1.19997e7i	−0.157608	−	0.0909951i	0.419122	−	0.907930i	$-0.362338\pi$
$509$	−2.07841e7	−	1.19997e7i	−0.157608	−	0.0909951i	−0.576730	+	0.816935i	$0.695671\pi$
$510$		0			0
$511$	5.71468e7	+	9.89812e7i	0.428282	+	0.741806i
$512$			5.93164e6i			0.0441942i
$513$		0			0
$514$	−8.16702e7			−0.601415
$515$	3.00295e8	−	1.73375e8i	2.19850	−	1.26930i
$516$		0			0
$517$	5.14764e7	−	8.91597e7i	0.372509	−	0.645204i
$518$	1.24545e8	+	7.19059e7i	0.896058	+	0.517339i
$519$		0			0
$520$	−5.30258e7	−	9.18434e7i	−0.377118	−	0.653187i
$521$		−	9.00897e7i		−	0.637033i	−0.947917	−	0.318517i	$-0.896815\pi$
$521$		−	9.00897e7i		−	0.637033i	0.947917	−	0.318517i	$-0.103185\pi$
$522$		0			0
$523$	−3.77691e7			−0.264016			−0.132008	−	0.991249i	$-0.542143\pi$
$523$	−3.77691e7			−0.264016			−0.132008	+	0.991249i	$0.542143\pi$
$524$	−8.51858e7	+	4.91820e7i	−0.592070	+	0.341832i
$525$		0			0
$526$	8.84073e7	−	1.53126e8i	0.607478	−	1.05218i
$527$	438660.	+	253260.i	0.00299706	+	0.00173035i
$528$		0			0
$529$	−6.83154e7	−	1.18326e8i	−0.461479	−	0.799304i
$530$		−	2.34918e8i		−	1.57793i
$531$		0			0
$532$	8.89631e7			0.590847
$533$	−1.08045e8	+	6.23796e7i	−0.713545	+	0.411965i
$534$		0			0
$535$	−2.26714e7	+	3.92679e7i	−0.148053	+	0.256435i
$536$	2.64887e7	+	1.52932e7i	0.172015	+	0.0993128i
$537$		0			0
$538$	710892.	+	1.23130e6i	0.00456517	+	0.00790710i
$539$			1.56332e8i			0.998347i
$540$		0			0
$541$	2.54800e7			0.160919			0.0804595	−	0.996758i	$-0.474361\pi$
$541$	2.54800e7			0.160919			0.0804595	+	0.996758i	$0.474361\pi$
$542$	1.45205e8	−	8.38343e7i	0.911978	−	0.526531i
$543$		0			0
$544$	36864.0	−	63850.3i	0.000228984	−	0.000396612i
$545$	−2.92936e7	−	1.69126e7i	−0.180960	−	0.104477i
$546$		0			0
$547$	−1.02608e8	−	1.77722e8i	−0.626930	−	1.08587i	−0.988164	−	0.153399i	$-0.950978\pi$
$547$	−1.02608e8	−	1.77722e8i	−0.626930	−	1.08587i	0.361234	−	0.932475i	$-0.382355\pi$
$548$			1.43492e8i			0.871938i
$549$		0			0
$550$	1.10977e8			0.667027
$551$	1.46024e8	−	8.43071e7i	0.872911	−	0.503975i
$552$		0			0
$553$	−8.49807e6	+	1.47191e7i	−0.0502510	+	0.0870373i
$554$	−6.47707e7	−	3.73954e7i	−0.380934	−	0.219932i
$555$		0			0
$556$	−1.74772e7	−	3.02715e7i	−0.101683	−	0.176120i
$557$		−	2.41143e8i		−	1.39543i	−0.716375	−	0.697715i	$-0.754200\pi$
$557$		−	2.41143e8i		−	1.39543i	0.716375	−	0.697715i	$-0.245800\pi$
$558$		0			0
$559$	1.27984e7			0.0732690
$560$	−7.46614e7	+	4.31058e7i	−0.425140	+	0.245455i
$561$		0			0
$562$	−1.73202e7	+	2.99994e7i	−0.0975760	+	0.169007i
$563$	1.46252e8	+	8.44386e7i	0.819552	+	0.473168i	0.850262	−	0.526360i	$-0.176444\pi$
$563$	1.46252e8	+	8.44386e7i	0.819552	+	0.473168i	−0.0307102	+	0.999528i	$0.509777\pi$
$564$		0			0
$565$	−7.14838e7	−	1.23814e8i	−0.396335	−	0.686472i
$566$		−	3.81456e7i		−	0.210375i
$567$		0			0
$568$	−9.62058e7			−0.524996
$569$	−2.11306e8	+	1.21998e8i	−1.14703	+	0.662238i	−0.948162	−	0.317788i	$-0.897060\pi$
$569$	−2.11306e8	+	1.21998e8i	−1.14703	+	0.662238i	−0.198869	+	0.980026i	$0.563727\pi$
$570$		0			0
$571$	−1.20751e8	+	2.09147e8i	−0.648608	+	1.12342i	0.334848	+	0.942272i	$0.391315\pi$
$571$	−1.20751e8	+	2.09147e8i	−0.648608	+	1.12342i	−0.983456	+	0.181149i	$0.942018\pi$
$572$	1.25134e8	+	7.22463e7i	0.668633	+	0.386036i
$573$		0			0
$574$	5.07096e7	+	8.78317e7i	0.268136	+	0.464425i
$575$			4.94177e7i			0.259944i
$576$		0			0
$577$	−4.93979e7			−0.257147			−0.128573	−	0.991700i	$-0.541040\pi$
$577$	−4.93979e7			−0.257147			−0.128573	+	0.991700i	$0.541040\pi$
$578$	1.18249e8	−	6.82709e7i	0.612368	−	0.353551i
$579$		0			0
$580$	−8.16996e7	+	1.41508e8i	−0.418732	+	0.725264i
$581$	−4.60232e6	−	2.65715e6i	−0.0234665	−	0.0135484i
$582$		0			0
$583$	1.60035e8	+	2.77188e8i	0.807623	+	1.39884i
$584$		−	4.27466e7i		−	0.214617i
$585$		0			0
$586$	5.67038e7			0.281786
$587$	−1.49001e8	+	8.60260e7i	−0.736675	+	0.425320i	−0.820859	−	0.571131i	$-0.806505\pi$
$587$	−1.49001e8	+	8.60260e7i	−0.736675	+	0.425320i	0.0841840	+	0.996450i	$0.473172\pi$
$588$		0			0
$589$	1.14294e8	−	1.97963e8i	0.559343	−	0.968810i
$590$	−2.12906e8	−	1.22922e8i	−1.03665	−	0.598511i
$591$		0			0
$592$	−2.68933e7	−	4.65806e7i	−0.129622	−	0.224512i
$593$			2.70643e8i			1.29788i	0.760841	+	0.648938i	$0.224787\pi$
$593$			2.70643e8i			1.29788i	−0.760841	+	0.648938i	$0.775213\pi$
$594$		0			0
$595$	1.07158e6			0.00508712
$596$	6.15467e7	−	3.55340e7i	0.290714	−	0.167844i
$597$		0			0
$598$	−3.21711e7	+	5.57220e7i	−0.150440	+	0.260569i
$599$	1.50082e8	+	8.66497e7i	0.698308	+	0.403169i	0.806717	−	0.590938i	$-0.201242\pi$
$599$	1.50082e8	+	8.66497e7i	0.698308	+	0.403169i	−0.108409	+	0.994106i	$0.534575\pi$
$600$		0			0
$601$	2.15545e8	+	3.73335e8i	0.992921	+	1.71979i	0.599323	+	0.800507i	$0.295437\pi$
$601$	2.15545e8	+	3.73335e8i	0.992921	+	1.71979i	0.393598	+	0.919282i	$0.371230\pi$
$602$		−	1.04041e7i		−	0.0476886i
$603$		0			0
$604$	1.30519e8			0.592327
$605$	−3.89369e6	+	2.24802e6i	−0.0175831	+	0.0101516i
$606$		0			0
$607$	−8.34953e6	+	1.44618e7i	−0.0373332	+	0.0646631i	−0.884088	−	0.467320i	$-0.845220\pi$
$607$	−8.34953e6	+	1.44618e7i	−0.0373332	+	0.0646631i	0.846755	+	0.531983i	$0.178553\pi$
$608$	−2.88151e7	−	1.66364e7i	−0.128206	−	0.0740199i
$609$		0			0
$610$	6.51900e6	+	1.12912e7i	0.0287205	+	0.0497453i
$611$			2.58635e8i			1.13387i
$612$		0			0
$613$	−1.92321e8			−0.834920			−0.417460	−	0.908695i	$-0.637080\pi$
$613$	−1.92321e8			−0.834920			−0.417460	+	0.908695i	$0.637080\pi$
$614$	−2.56246e7	+	1.47944e7i	−0.110701	+	0.0639133i
$615$		0			0
$616$	5.87305e7	−	1.01724e8i	0.251259	−	0.435193i
$617$	1.61967e8	+	9.35117e7i	0.689558	+	0.398117i	0.803447	−	0.595377i	$-0.202997\pi$
$617$	1.61967e8	+	9.35117e7i	0.689558	+	0.398117i	−0.113888	+	0.993494i	$0.536331\pi$
$618$		0			0
$619$	−1.27437e8	−	2.20727e8i	−0.537307	−	0.930643i	−0.999048	−	0.0436278i	$-0.986108\pi$
$619$	−1.27437e8	−	2.20727e8i	−0.537307	−	0.930643i	0.461741	−	0.887015i	$-0.347225\pi$
$620$			2.21518e8i			0.929468i
$621$		0			0
$622$	−1.76619e8			−0.733950
$623$	5.42088e7	−	3.12975e7i	0.224185	−	0.129433i
$624$		0			0
$625$	1.29328e8	−	2.24003e8i	0.529729	−	0.917517i
$626$	−1.10118e8	−	6.35769e7i	−0.448887	−	0.259165i
$627$		0			0
$628$	9.84908e7	+	1.70591e8i	0.397665	+	0.688775i
$629$			668547.i			0.00268646i
$630$		0			0
$631$	9.23602e7			0.367618			0.183809	−	0.982962i	$-0.441157\pi$
$631$	9.23602e7			0.367618			0.183809	+	0.982962i	$0.441157\pi$
$632$	5.50504e6	−	3.17834e6i	0.0218077	−	0.0125907i
$633$		0			0
$634$	−7.81243e7	+	1.35315e8i	−0.306562	+	0.530981i
$635$	−4.60549e8	−	2.65898e8i	−1.79869	−	1.03847i
$636$		0			0
$637$	−1.96366e8	−	3.40116e8i	−0.759711	−	1.31586i
$638$		−	2.22627e8i		−	0.857267i
$639$		0			0
$640$	3.22437e7			0.123000
$641$	−3.67771e8	+	2.12333e8i	−1.39638	+	0.806200i	−0.994011	−	0.109278i	$-0.965146\pi$
$641$	−3.67771e8	+	2.12333e8i	−1.39638	+	0.806200i	−0.402368	+	0.915478i	$0.631813\pi$
$642$		0			0
$643$	−1.87973e8	+	3.25579e8i	−0.707071	+	1.22468i	0.258868	+	0.965913i	$0.416650\pi$
$643$	−1.87973e8	+	3.25579e8i	−0.707071	+	1.22468i	−0.965939	+	0.258770i	$0.916683\pi$
$644$	4.52976e7	+	2.61526e7i	0.169597	+	0.0979168i
$645$		0			0
$646$	206784.	+	358160.i	0.000767042	+	0.00132856i
$647$			2.63747e7i			0.0973813i	0.998814	+	0.0486906i	$0.0155048\pi$
$647$			2.63747e7i			0.0973813i	−0.998814	+	0.0486906i	$0.984495\pi$
$648$		0			0
$649$	3.34955e8			1.22533
$650$	−2.41441e8	+	1.39396e8i	−0.879166	+	0.507587i
$651$		0			0
$652$	1.28111e7	−	2.21895e7i	0.0462216	−	0.0800581i
$653$	−2.24090e8	−	1.29378e8i	−0.804790	−	0.464645i	0.0403536	−	0.999185i	$-0.487152\pi$
$653$	−2.24090e8	−	1.29378e8i	−0.804790	−	0.464645i	−0.845143	+	0.534540i	$0.820485\pi$
$654$		0			0
$655$	2.67348e8	+	4.63060e8i	0.951377	+	1.64783i
$656$		−	3.79315e7i		−	0.134366i
$657$		0			0
$658$	2.10250e8			0.738002
$659$	−1.20676e8	+	6.96725e7i	−0.421663	+	0.243447i	−0.695789	−	0.718247i	$-0.744945\pi$
$659$	−1.20676e8	+	6.96725e7i	−0.421663	+	0.243447i	0.274126	+	0.961694i	$0.411612\pi$
$660$		0			0
$661$	2.36272e8	−	4.09236e8i	0.818104	−	1.41700i	−0.0889731	−	0.996034i	$-0.528359\pi$
$661$	2.36272e8	−	4.09236e8i	0.818104	−	1.41700i	0.907077	−	0.420964i	$-0.138308\pi$
$662$	2.82249e7	+	1.62957e7i	0.0972878	+	0.0561691i
$663$		0			0
$664$	993792.	+	1.72130e6i	0.00339462	+	0.00587966i
$665$		−	4.83593e8i		−	1.64443i
$666$		0			0
$667$	9.91354e7			0.334081
$668$	−1.33151e8	+	7.68747e7i	−0.446699	+	0.257902i
$669$		0			0
$670$	8.31323e7	−	1.43989e8i	0.276405	−	0.478747i
$671$	−1.53840e7	−	8.88197e6i	−0.0509216	−	0.0293996i
$672$		0			0
$673$	−2.74417e8	−	4.75304e8i	−0.900254	−	1.55929i	−0.827164	−	0.561961i	$-0.810047\pi$
$673$	−2.74417e8	−	4.75304e8i	−0.900254	−	1.55929i	−0.0730906	−	0.997325i	$-0.523286\pi$
$674$		−	2.26869e8i		−	0.740961i
$675$		0			0
$676$	−2.08532e8			−0.675044
$677$	−8.72609e7	+	5.03801e7i	−0.281225	+	0.162365i	−0.633978	−	0.773351i	$-0.718579\pi$
$677$	−8.72609e7	+	5.03801e7i	−0.281225	+	0.162365i	0.352753	+	0.935717i	$0.385246\pi$
$678$		0			0
$679$	−7.77846e7	+	1.34727e8i	−0.248476	+	0.430373i
$680$	−347083.	−	200388.i	−0.00110384	−	0.000637303i
$681$		0			0
$682$	−1.50906e8	−	2.61378e8i	−0.475724	−	0.823977i
$683$		−	313056.i		−	0.000982562i	−1.00000		0.000491281i	$-0.999844\pi$
$683$		−	313056.i		−	0.000982562i	1.00000		0.000491281i	$-0.000156380\pi$
$684$		0			0
$685$	7.80005e8			2.42675
$686$	2.47069e6	−	1.42645e6i	0.00765326	−	0.00441861i
$687$		0			0
$688$	−1.94560e6	+	3.36988e6i	−0.00597432	+	0.0103478i
$689$	−6.96344e8	−	4.02034e8i	−2.12895	−	1.22915i
$690$		0			0
$691$	1.86406e8	+	3.22865e8i	0.564971	+	0.978558i	0.997052	+	0.0767236i	$0.0244459\pi$
$691$	1.86406e8	+	3.22865e8i	0.564971	+	0.978558i	−0.432082	+	0.901834i	$0.642221\pi$
$692$			1.14238e8i			0.344739i
$693$		0			0
$694$	−3.83607e8			−1.14765
$695$	−1.64552e8	+	9.50043e7i	−0.490173	+	0.283002i
$696$		0			0
$697$	−235737.	+	408308.i	−0.000696193	+	0.00120584i
$698$	2.06070e8	+	1.18975e8i	0.605966	+	0.349855i
$699$		0			0
$700$	1.13318e8	+	1.96272e8i	0.330373	+	0.572223i
$701$			6.21170e8i			1.80325i	0.432517	+	0.901626i	$0.357626\pi$
$701$			6.21170e8i			1.80325i	−0.432517	+	0.901626i	$0.642374\pi$
$702$		0			0
$703$	3.01709e8			0.868406
$704$	−3.80456e7	+	2.19656e7i	−0.109040	+	0.0629543i
$705$		0			0
$706$	−4.97734e7	+	8.62101e7i	−0.141444	+	0.244988i
$707$	2.80323e8	+	1.61845e8i	0.793234	+	0.457974i
$708$		0			0
$709$	1.23255e8	+	2.13484e8i	0.345833	+	0.599000i	0.985505	−	0.169648i	$-0.0542631\pi$
$709$	1.23255e8	+	2.13484e8i	0.345833	+	0.599000i	−0.639672	+	0.768648i	$0.720930\pi$
$710$			5.22964e8i			1.46116i
$711$		0			0
$712$	−2.34109e7			−0.0648603
$713$	1.16391e8	−	6.71984e7i	0.321108	−	0.185392i
$714$		0			0
$715$	3.92722e8	−	6.80215e8i	1.07440	−	1.86092i
$716$	−2.06100e8	−	1.18992e8i	−0.561485	−	0.324173i
$717$		0			0
$718$	−3.95754e7	−	6.85466e7i	−0.106918	−	0.185188i
$719$		−	9.60389e7i		−	0.258381i	−0.991620	−	0.129191i	$-0.958762\pi$
$719$		−	9.60389e7i		−	0.258381i	0.991620	−	0.129191i	$-0.0412379\pi$
$720$		0			0
$721$	−9.64811e8			−2.57417
$722$	−6.88421e7	+	3.97460e7i	−0.182912	+	0.105604i
$723$		0			0
$724$	−1.66099e8	+	2.87692e8i	−0.437675	+	0.758075i
$725$	3.72001e8	+	2.14775e8i	0.976179	+	0.563597i
$726$		0			0
$727$	−1.95685e8	−	3.38937e8i	−0.509278	−	0.882096i	−0.999942	−	0.0107471i	$-0.996579\pi$
$727$	−1.95685e8	−	3.38937e8i	−0.509278	−	0.882096i	0.490664	−	0.871349i	$-0.336754\pi$
$728$			2.95082e8i			0.764801i
$729$		0			0
$730$	−2.32366e8			−0.597315
$731$	41886.3	−	24183.1i	0.000107231	−	6.19097e-5i
$732$		0			0
$733$	−1.74539e7	+	3.02311e7i	−0.0443181	+	0.0767611i	−0.887334	−	0.461128i	$-0.847445\pi$
$733$	−1.74539e7	+	3.02311e7i	−0.0443181	+	0.0767611i	0.843015	+	0.537889i	$0.180778\pi$
$734$	1.30242e8	+	7.51951e7i	0.329353	+	0.190152i
$735$		0			0
$736$	−9.78125e6	−	1.69416e7i	−0.0245336	−	0.0424934i
$737$			2.26531e8i			0.565881i
$738$		0			0
$739$	−3.02999e8			−0.750773			−0.375386	−	0.926868i	$-0.622490\pi$
$739$	−3.02999e8			−0.750773			−0.375386	+	0.926868i	$0.622490\pi$
$740$	−2.53207e8	+	1.46189e8i	−0.624856	+	0.360761i
$741$		0			0
$742$	−3.26822e8	+	5.66072e8i	−0.800018	+	1.38567i
$743$	−2.12720e8	−	1.22814e8i	−0.518612	−	0.299421i	0.217754	−	0.976004i	$-0.430127\pi$
$743$	−2.12720e8	−	1.22814e8i	−0.518612	−	0.299421i	−0.736367	+	0.676583i	$0.763460\pi$
$744$		0			0
$745$	−1.93159e8	−	3.34560e8i	−0.467138	−	0.809107i
$746$			1.01161e8i			0.243667i
$747$		0			0
$748$	546048.			0.00130475
$749$	1.09261e8	−	6.30816e7i	0.260027	−	0.150127i
$750$		0			0
$751$	4.11635e7	−	7.12973e7i	0.0971835	−	0.168327i	−0.813334	−	0.581797i	$-0.802350\pi$
$751$	4.11635e7	−	7.12973e7i	0.0971835	−	0.168327i	0.910518	+	0.413470i	$0.135683\pi$
$752$	−6.80997e7	−	3.93174e7i	−0.160137	−	0.0924552i
$753$		0			0
$754$	2.79638e8	+	4.84348e8i	0.652353	+	1.12991i
$755$		−	7.09484e8i		−	1.64855i
$756$		0			0
$757$	−6.03579e8			−1.39138			−0.695691	−	0.718341i	$-0.744902\pi$
$757$	−6.03579e8			−1.39138			−0.695691	+	0.718341i	$0.744902\pi$
$758$	3.53205e8	−	2.03923e8i	0.810998	−	0.468230i
$759$		0			0
$760$	−9.04335e7	+	1.56635e8i	−0.206010	+	0.356820i
$761$	2.01769e8	+	1.16491e8i	0.457825	+	0.264325i	0.711129	−	0.703061i	$-0.248184\pi$
$761$	2.01769e8	+	1.16491e8i	0.457825	+	0.264325i	−0.253304	+	0.967387i	$0.581517\pi$
$762$		0			0
$763$	4.70584e7	+	8.15075e7i	0.105941	+	0.183495i
$764$		−	4.15810e8i		−	0.932426i
$765$		0			0
$766$	−4.91382e7			−0.109328
$767$	−7.28729e8	+	4.20732e8i	−1.61503	+	0.932436i
$768$		0			0
$769$	−4.07898e8	+	7.06500e8i	−0.896958	+	1.55358i	−0.0655965	+	0.997846i	$0.520895\pi$
$769$	−4.07898e8	+	7.06500e8i	−0.896958	+	1.55358i	−0.831362	+	0.555731i	$0.812438\pi$
$770$	−5.52961e8	−	3.19252e8i	−1.21122	−	0.699297i
$771$		0			0
$772$	−6.29113e7	−	1.08966e8i	−0.136734	−	0.236830i
$773$		−	3.66587e8i		−	0.793667i	−0.917891	−	0.396833i	$-0.870109\pi$
$773$		−	3.66587e8i		−	0.793667i	0.917891

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-150.644 - 86.9741i) q^{5} +(242.000 + 419.156i) q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-150.644 - 86.9741i) q^{5} +(242.000 + 419.156i) q^{7} -181.019i q^{8} -984.000 q^{10} +(1161.06 - 670.337i) q^{11} +(-1684.00 + 2916.77i) q^{13} +(2371.11 + 1368.96i) q^{14} +(-512.000 - 886.810i) q^{16} +12.7279i q^{17} +5744.00 q^{19} +(-4820.60 + 2783.17i) q^{20} +(3792.00 - 6567.94i) q^{22} +(2924.69 + 1688.57i) q^{23} +(7316.50 + 12672.5i) q^{25} +19052.3i q^{26} +15488.0 q^{28} +(25422.0 - 14677.4i) q^{29} +(19898.0 - 34464.3i) q^{31} +(-5016.55 - 2896.31i) q^{32} +(36.0000 + 62.3538i) q^{34} -84191.0i q^{35} +52526.0 q^{37} +(28139.7 - 16246.5i) q^{38} +(-15744.0 + 27269.4i) q^{40} +(32079.7 + 18521.2i) q^{41} +(-1900.00 - 3290.90i) q^{43} -42901.6i q^{44} +19104.0 q^{46} +(66503.6 - 38395.9i) q^{47} +(-58303.5 + 100985. i) q^{49} +(71686.8 + 41388.4i) q^{50} +(53888.0 + 93336.8i) q^{52} +238738. i q^{53} -233208. q^{55} +(75875.4 - 43806.7i) q^{56} +(83028.0 - 143809. i) q^{58} +(216368. + 124920. i) q^{59} +(-6625.00 - 11474.8i) q^{61} -225120. i q^{62} -32768.0 q^{64} +(507368. - 292929. i) q^{65} +(-84484.0 + 146331. i) q^{67} +(352.727 + 203.647i) q^{68} +(-238128. - 412450. i) q^{70} -531467. i q^{71} +236144. q^{73} +(257324. - 148566. i) q^{74} +(91904.0 - 159182. i) q^{76} +(561952. + 324443. i) q^{77} +(17558.0 + 30411.3i) q^{79} +178123. i q^{80} +209544. q^{82} +(-9508.92 + 5489.98i) q^{83} +(1107.00 - 1917.38i) q^{85} +(-18616.1 - 10748.0i) q^{86} +(-121344. - 210174. i) q^{88} -129328. i q^{89} -1.63011e6 q^{91} +(93590.1 - 54034.3i) q^{92} +(217200. - 376201. i) q^{94} +(-865297. - 499579. i) q^{95} +(160712. + 278361. i) q^{97} +659629. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{4} + 968 q^{7}+O(q^{10}) \) 4 * q + 64 * q^4 + 968 * q^7	\( 4 q + 64 q^{4} + 968 q^{7} - 3936 q^{10} - 6736 q^{13} - 2048 q^{16} + 22976 q^{19} + 15168 q^{22} + 29266 q^{25} + 61952 q^{28} + 79592 q^{31} + 144 q^{34} + 210104 q^{37} - 62976 q^{40} - 7600 q^{43} + 76416 q^{46} - 233214 q^{49} + 215552 q^{52} - 932832 q^{55} + 332112 q^{58} - 26500 q^{61} - 131072 q^{64} - 337936 q^{67} - 952512 q^{70} + 944576 q^{73} + 367616 q^{76} + 70232 q^{79} + 838176 q^{82} + 4428 q^{85} - 485376 q^{88} - 6520448 q^{91} + 868800 q^{94} + 642848 q^{97}+O(q^{100}) \) 4 * q + 64 * q^4 + 968 * q^7 - 3936 * q^10 - 6736 * q^13 - 2048 * q^16 + 22976 * q^19 + 15168 * q^22 + 29266 * q^25 + 61952 * q^28 + 79592 * q^31 + 144 * q^34 + 210104 * q^37 - 62976 * q^40 - 7600 * q^43 + 76416 * q^46 - 233214 * q^49 + 215552 * q^52 - 932832 * q^55 + 332112 * q^58 - 26500 * q^61 - 131072 * q^64 - 337936 * q^67 - 952512 * q^70 + 944576 * q^73 + 367616 * q^76 + 70232 * q^79 + 838176 * q^82 + 4428 * q^85 - 485376 * q^88 - 6520448 * q^91 + 868800 * q^94 + 642848 * q^97

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