LMFDB - Embedded newform 1008.3.cg.m.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,3,Mod(145,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1008.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1008.cg (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:	$27.4660106475$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{65})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 17x^{2} + 16x + 256 $ x^4 - x^3 + 17x^2 + 16x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$-1.76556 - 3.05805i$ of defining polynomial
Character	$\chi$	$=$	1008.145
Dual form			1008.3.cg.m.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.79669 - 2.19202i) q^{5} +(-0.500000 - 6.98212i) q^{7} +(9.79669 + 16.9684i) q^{11} -6.11609i q^{13} +(-7.59339 + 4.38404i) q^{17} +(26.2967 + 15.1824i) q^{19} +(12.0000 - 20.7846i) q^{23} +(-2.89008 - 5.00577i) q^{25} -13.5934 q^{29} +(24.2802 - 14.0182i) q^{31} +(-13.4066 + 27.6050i) q^{35} +(24.2967 - 42.0831i) q^{37} -7.14387i q^{41} -53.7802 q^{43} +(-34.5934 - 19.9725i) q^{47} +(-48.5000 + 6.98212i) q^{49} +(-30.7967 - 53.3414i) q^{53} -85.8983i q^{55} +(66.7967 - 38.5651i) q^{59} +(0.373546 + 0.215667i) q^{61} +(-13.4066 + 23.2209i) q^{65} +(-28.4835 - 49.3348i) q^{67} -123.560 q^{71} +(31.0769 - 17.9422i) q^{73} +(113.577 - 76.8859i) q^{77} +(-26.0934 + 45.1951i) q^{79} -136.883i q^{83} +38.4397 q^{85} +(-13.2198 - 7.63248i) q^{89} +(-42.7033 + 3.05805i) q^{91} +(-66.5603 - 115.286i) q^{95} -34.1524i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 9 q^{5} - 2 q^{7} + 15 q^{11} + 18 q^{17} + 81 q^{19} + 48 q^{23} + 61 q^{25} - 6 q^{29} - 48 q^{31} - 102 q^{35} + 73 q^{37} - 70 q^{43} - 90 q^{47} - 194 q^{49} - 99 q^{53} + 243 q^{59} - 192 q^{61}+ \cdots + 24 q^{95}+O(q^{100}) $ 4 * q + 9 * q^5 - 2 * q^7 + 15 * q^11 + 18 * q^17 + 81 * q^19 + 48 * q^23 + 61 * q^25 - 6 * q^29 - 48 * q^31 - 102 * q^35 + 73 * q^37 - 70 * q^43 - 90 * q^47 - 194 * q^49 - 99 * q^53 + 243 * q^59 - 192 * q^61 - 102 * q^65 + 7 * q^67 - 204 * q^71 - 45 * q^73 + 285 * q^77 - 56 * q^79 + 444 * q^85 - 198 * q^89 - 195 * q^91 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.79669	−	2.19202i	−0.759339	−	0.438404i	0.0697196	−	0.997567i	$-0.477790\pi$
$5$	−3.79669	−	2.19202i	−0.759339	−	0.438404i	−0.829058	+	0.559162i	$0.811123\pi$
$6$		0			0
$7$	−0.500000	−	6.98212i	−0.0714286	−	0.997446i
$7$	−0.500000	−	6.98212i	−0.0714286	−	0.997446i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	9.79669	+	16.9684i	0.890608	+	1.54258i	0.839147	+	0.543904i	$0.183054\pi$
$11$	9.79669	+	16.9684i	0.890608	+	1.54258i	0.0514611	+	0.998675i	$0.483612\pi$
$12$		0			0
$13$		−	6.11609i		−	0.470469i	−0.971939	−	0.235234i	$-0.924414\pi$
$13$		−	6.11609i		−	0.470469i	0.971939	−	0.235234i	$-0.0755858\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−7.59339	+	4.38404i	−0.446670	+	0.257885i	−0.706423	−	0.707790i	$-0.749692\pi$
$17$	−7.59339	+	4.38404i	−0.446670	+	0.257885i	0.259753	+	0.965675i	$0.416359\pi$
$18$		0			0
$19$	26.2967	+	15.1824i	1.38404	+	0.799074i	0.992635	−	0.121146i	$-0.0386569\pi$
$19$	26.2967	+	15.1824i	1.38404	+	0.799074i	0.391402	+	0.920220i	$0.371990\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	12.0000	−	20.7846i	0.521739	−	0.903679i	−0.477941	−	0.878392i	$-0.658617\pi$
$23$	12.0000	−	20.7846i	0.521739	−	0.903679i	0.999680	−	0.0252868i	$-0.00804990\pi$
$24$		0			0
$25$	−2.89008	−	5.00577i	−0.115603	−	0.200231i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−13.5934			−0.468737			−0.234369	−	0.972148i	$-0.575302\pi$
$29$	−13.5934			−0.468737			−0.234369	+	0.972148i	$0.575302\pi$
$30$		0			0
$31$	24.2802	−	14.0182i	0.783231	−	0.452199i	−0.0543432	−	0.998522i	$-0.517306\pi$
$31$	24.2802	−	14.0182i	0.783231	−	0.452199i	0.837574	+	0.546324i	$0.183973\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−13.4066	+	27.6050i	−0.383046	+	0.788714i
$36$		0			0
$37$	24.2967	−	42.0831i	0.656667	−	1.13738i	−0.324806	−	0.945781i	$-0.605299\pi$
$37$	24.2967	−	42.0831i	0.656667	−	1.13738i	0.981473	−	0.191600i	$-0.0613678\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	7.14387i		−	0.174241i	−0.996198	−	0.0871204i	$-0.972234\pi$
$41$		−	7.14387i		−	0.174241i	0.996198	−	0.0871204i	$-0.0277665\pi$
$42$		0			0
$43$	−53.7802			−1.25070			−0.625351	−	0.780344i	$-0.715044\pi$
$43$	−53.7802			−1.25070			−0.625351	+	0.780344i	$0.715044\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−34.5934	−	19.9725i	−0.736030	−	0.424947i	0.0845944	−	0.996415i	$-0.473041\pi$
$47$	−34.5934	−	19.9725i	−0.736030	−	0.424947i	−0.820624	+	0.571469i	$0.806374\pi$
$48$		0			0
$49$	−48.5000	+	6.98212i	−0.989796	+	0.142492i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−30.7967	−	53.3414i	−0.581070	−	1.00644i	−0.995353	−	0.0962942i	$-0.969301\pi$
$53$	−30.7967	−	53.3414i	−0.581070	−	1.00644i	0.414283	−	0.910148i	$-0.364032\pi$
$54$		0			0
$55$		−	85.8983i		−	1.56179i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	66.7967	−	38.5651i	1.13215	−	0.653646i	0.187673	−	0.982232i	$-0.439905\pi$
$59$	66.7967	−	38.5651i	1.13215	−	0.653646i	0.944474	+	0.328586i	$0.106572\pi$
$60$		0			0
$61$	0.373546	+	0.215667i	0.00612371	+	0.00353553i	0.503059	−	0.864252i	$-0.332208\pi$
$61$	0.373546	+	0.215667i	0.00612371	+	0.00353553i	−0.496935	+	0.867788i	$0.665541\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−13.4066	+	23.2209i	−0.206256	+	0.357245i
$66$		0			0
$67$	−28.4835	−	49.3348i	−0.425126	−	0.736340i	0.571306	−	0.820737i	$-0.306437\pi$
$67$	−28.4835	−	49.3348i	−0.425126	−	0.736340i	−0.996432	+	0.0843968i	$0.973104\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−123.560			−1.74029			−0.870143	−	0.492799i	$-0.835974\pi$
$71$	−123.560			−1.74029			−0.870143	+	0.492799i	$0.835974\pi$
$72$		0			0
$73$	31.0769	−	17.9422i	0.425710	−	0.245784i	−0.271807	−	0.962352i	$-0.587621\pi$
$73$	31.0769	−	17.9422i	0.425710	−	0.245784i	0.697517	+	0.716568i	$0.254288\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	113.577	−	76.8859i	1.47502	−	0.998518i
$78$		0			0
$79$	−26.0934	+	45.1951i	−0.330296	+	0.572090i	−0.982570	−	0.185894i	$-0.940482\pi$
$79$	−26.0934	+	45.1951i	−0.330296	+	0.572090i	0.652274	+	0.757983i	$0.273815\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	136.883i		−	1.64919i	−0.565725	−	0.824594i	$-0.691404\pi$
$83$		−	136.883i		−	1.64919i	0.565725	−	0.824594i	$-0.308596\pi$
$84$		0			0
$85$	38.4397			0.452232
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−13.2198	−	7.63248i	−0.148538	−	0.0857582i	0.423889	−	0.905714i	$-0.360665\pi$
$89$	−13.2198	−	7.63248i	−0.148538	−	0.0857582i	−0.572427	+	0.819956i	$0.693998\pi$
$90$		0			0
$91$	−42.7033	+	3.05805i	−0.469267	+	0.0336049i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−66.5603	−	115.286i	−0.700635	−	1.21354i
$96$		0			0
$97$		−	34.1524i		−	0.352087i	−0.984382	−	0.176043i	$-0.943670\pi$
$97$		−	34.1524i		−	0.352087i	0.984382	−	0.176043i	$-0.0563299\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	113.340	−	65.4372i	1.12218	−	0.647893i	0.180226	−	0.983625i	$-0.442317\pi$
$101$	113.340	−	65.4372i	1.12218	−	0.647893i	0.941957	+	0.335733i	$0.108984\pi$
$102$		0			0
$103$	140.857	+	81.3238i	1.36754	+	0.789552i	0.990614	−	0.136690i	$-0.0436464\pi$
$103$	140.857	+	81.3238i	1.36754	+	0.789552i	0.376930	+	0.926242i	$0.376980\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	51.9835	−	90.0380i	0.485827	−	0.841477i	−0.514041	−	0.857766i	$-0.671852\pi$
$107$	51.9835	−	90.0380i	0.485827	−	0.841477i	0.999867	+	0.0162892i	$0.00518525\pi$
$108$		0			0
$109$	7.89008	+	13.6660i	0.0723861	+	0.125376i	0.899947	−	0.436000i	$-0.143605\pi$
$109$	7.89008	+	13.6660i	0.0723861	+	0.125376i	−0.827561	+	0.561377i	$0.810272\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	59.6265			0.527668			0.263834	−	0.964568i	$-0.415013\pi$
$113$	59.6265			0.527668			0.263834	+	0.964568i	$0.415013\pi$
$114$		0			0
$115$	−91.1206	+	52.6085i	−0.792353	+	0.457465i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	34.4066	+	50.8259i	0.289131	+	0.427109i
$120$		0			0
$121$	−131.450	+	227.679i	−1.08637	+	1.88164i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			134.942i			1.07953i
$126$		0			0
$127$	25.0000			0.196850			0.0984252	−	0.995144i	$-0.468619\pi$
$127$	25.0000			0.196850			0.0984252	+	0.995144i	$0.468619\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	196.170	+	113.259i	1.49748	+	0.864572i	0.999996	−	0.00289939i	$-0.000922907\pi$
$131$	196.170	+	113.259i	1.49748	+	0.864572i	0.497487	+	0.867471i	$0.334256\pi$
$132$		0			0
$133$	92.8570	−	191.198i	0.698173	−	1.43758i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−123.560	−	214.013i	−0.901900	−	1.56214i	−0.825025	−	0.565096i	$-0.808839\pi$
$137$	−123.560	−	214.013i	−0.901900	−	1.56214i	−0.0768751	−	0.997041i	$-0.524494\pi$
$138$		0			0
$139$		−	147.383i		−	1.06031i	−0.847902	−	0.530154i	$-0.822134\pi$
$139$		−	147.383i		−	1.06031i	0.847902	−	0.530154i	$-0.177866\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	103.780	−	59.9175i	0.725735	−	0.419004i
$144$		0			0
$145$	51.6099	+	29.7970i	0.355930	+	0.205497i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	64.4066	−	111.556i	0.432259	−	0.748695i	−0.564808	−	0.825222i	$-0.691050\pi$
$149$	64.4066	−	111.556i	0.432259	−	0.748695i	0.997067	+	0.0765273i	$0.0243832\pi$
$150$		0			0
$151$	31.0165	+	53.7222i	0.205408	+	0.355776i	0.950262	−	0.311450i	$-0.100815\pi$
$151$	31.0165	+	53.7222i	0.205408	+	0.355776i	−0.744855	+	0.667226i	$0.767481\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−122.912			−0.792983
$156$		0			0
$157$	−217.121	+	125.355i	−1.38293	+	0.798437i	−0.992506	−	0.122196i	$-0.961006\pi$
$157$	−217.121	+	125.355i	−1.38293	+	0.798437i	−0.390428	+	0.920633i	$0.627673\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−151.121	−	73.3931i	−0.938638	−	0.455858i
$162$		0			0
$163$	−48.9669	+	84.8132i	−0.300411	+	0.520326i	−0.976229	−	0.216742i	$-0.930457\pi$
$163$	−48.9669	+	84.8132i	−0.300411	+	0.520326i	0.675818	+	0.737068i	$0.263790\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			71.7689i			0.429754i	0.976641	+	0.214877i	$0.0689351\pi$
$167$			71.7689i			0.429754i	−0.976641	+	0.214877i	$0.931065\pi$
$168$		0			0
$169$	131.593			0.778659
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−261.560	−	151.012i	−1.51191	−	0.872901i	−0.999903	−	0.0139196i	$-0.995569\pi$
$173$	−261.560	−	151.012i	−1.51191	−	0.872901i	−0.512006	−	0.858982i	$-0.671098\pi$
$174$		0			0
$175$	−33.5058	+	22.6818i	−0.191462	+	0.129610i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−69.0000	−	119.512i	−0.385475	−	0.667662i	0.606360	−	0.795190i	$-0.292629\pi$
$179$	−69.0000	−	119.512i	−0.385475	−	0.667662i	−0.991835	+	0.127528i	$0.959296\pi$
$180$		0			0
$181$		−	82.9733i		−	0.458416i	−0.973377	−	0.229208i	$-0.926386\pi$
$181$		−	82.9733i		−	0.458416i	0.973377	−	0.229208i	$-0.0736136\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−184.494	+	106.518i	−0.997266	+	0.575772i
$186$		0			0
$187$	−148.780	−	85.8983i	−0.795616	−	0.459349i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−86.1537	+	149.223i	−0.451067	+	0.781270i	−0.998453	−	0.0556101i	$-0.982290\pi$
$191$	−86.1537	+	149.223i	−0.451067	+	0.781270i	0.547386	+	0.836880i	$0.315623\pi$
$192$		0			0
$193$	−137.654	−	238.423i	−0.713232	−	1.23535i	−0.963638	−	0.267213i	$-0.913897\pi$
$193$	−137.654	−	238.423i	−0.713232	−	1.23535i	0.250406	−	0.968141i	$-0.419436\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	154.307			0.783286			0.391643	−	0.920117i	$-0.371907\pi$
$197$	154.307			0.783286			0.391643	+	0.920117i	$0.371907\pi$
$198$		0			0
$199$	162.747	−	93.9621i	0.817825	−	0.472171i	−0.0318411	−	0.999493i	$-0.510137\pi$
$199$	162.747	−	93.9621i	0.817825	−	0.472171i	0.849666	+	0.527322i	$0.176804\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.79669	+	94.9107i	0.0334812	+	0.467540i
$204$		0			0
$205$	−15.6595	+	27.1231i	−0.0763879	+	0.132308i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			594.949i			2.84665i
$210$		0			0
$211$	348.307			1.65075			0.825373	−	0.564588i	$-0.190965\pi$
$211$	348.307			1.65075			0.825373	+	0.564588i	$0.190965\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	204.187	+	117.887i	0.949706	+	0.548313i
$216$		0			0
$217$	−110.017	−	162.518i	−0.506989	−	0.748930i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	26.8132	+	46.4419i	0.121327	+	0.210144i
$222$		0			0
$223$			30.3581i			0.136135i	0.997681	+	0.0680675i	$0.0216833\pi$
$223$			30.3581i			0.136135i	−0.997681	+	0.0680675i	$0.978317\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	55.8298	−	32.2333i	0.245946	−	0.141997i	−0.371961	−	0.928249i	$-0.621314\pi$
$227$	55.8298	−	32.2333i	0.245946	−	0.141997i	0.617907	+	0.786252i	$0.287981\pi$
$228$		0			0
$229$	8.67024	+	5.00577i	0.0378613	+	0.0218592i	0.518811	−	0.854889i	$-0.326375\pi$
$229$	8.67024	+	5.00577i	0.0378613	+	0.0218592i	−0.480950	+	0.876748i	$0.659708\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.2529	−	24.6868i	0.0611713	−	0.105952i	−0.833818	−	0.552040i	$-0.813850\pi$
$233$	14.2529	−	24.6868i	0.0611713	−	0.105952i	0.894989	+	0.446088i	$0.147183\pi$
$234$		0			0
$235$	87.5603	+	151.659i	0.372597	+	0.645357i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−256.307			−1.07242			−0.536208	−	0.844086i	$-0.680144\pi$
$239$	−256.307			−1.07242			−0.536208	+	0.844086i	$0.680144\pi$
$240$		0			0
$241$	186.797	−	107.847i	0.775090	−	0.447498i	−0.0595974	−	0.998222i	$-0.518982\pi$
$241$	186.797	−	107.847i	0.775090	−	0.447498i	0.834687	+	0.550724i	$0.185648\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	199.445	+	79.8041i	0.814060	+	0.325731i
$246$		0			0
$247$	92.8570	−	160.833i	0.375939	−	0.651146i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			371.680i			1.48080i	0.672168	+	0.740398i	$0.265363\pi$
$251$			371.680i			1.48080i	−0.672168	+	0.740398i	$0.734637\pi$
$252$		0			0
$253$	470.241			1.85866
$254$		0			0
$255$		0			0
$256$		0			0
$257$	64.1206	+	37.0201i	0.249497	+	0.144047i	0.619534	−	0.784970i	$-0.287322\pi$
$257$	64.1206	+	37.0201i	0.249497	+	0.144047i	−0.370037	+	0.929017i	$0.620655\pi$
$258$		0			0
$259$	−305.978	−	148.601i	−1.18138	−	0.573749i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.65952	−	16.7308i	−0.0367282	−	0.0636151i	0.847077	−	0.531470i	$-0.178360\pi$
$263$	−9.65952	−	16.7308i	−0.0367282	−	0.0636151i	−0.883805	+	0.467855i	$0.845027\pi$
$264$		0			0
$265$			270.028i			1.01897i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	180.983	−	104.491i	0.672801	−	0.388442i	−0.124336	−	0.992240i	$-0.539680\pi$
$269$	180.983	−	104.491i	0.672801	−	0.388442i	0.797137	+	0.603798i	$0.206347\pi$
$270$		0			0
$271$	−106.357	−	61.4053i	−0.392461	−	0.226588i	0.290765	−	0.956795i	$-0.406090\pi$
$271$	−106.357	−	61.4053i	−0.392461	−	0.226588i	−0.683226	+	0.730207i	$0.739424\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	56.6265	−	98.0799i	0.205914	−	0.356654i
$276$		0			0
$277$	−13.8901	−	24.0583i	−0.0501447	−	0.0868532i	0.839864	−	0.542798i	$-0.182635\pi$
$277$	−13.8901	−	24.0583i	−0.0501447	−	0.0868532i	−0.890008	+	0.455944i	$0.849302\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−61.4942			−0.218841			−0.109420	−	0.993996i	$-0.534899\pi$
$281$	−61.4942			−0.218841			−0.109420	+	0.993996i	$0.534899\pi$
$282$		0			0
$283$	38.0107	−	21.9455i	0.134313	−	0.0775459i	−0.431338	−	0.902191i	$-0.641958\pi$
$283$	38.0107	−	21.9455i	0.134313	−	0.0775459i	0.565651	+	0.824645i	$0.308625\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−49.8794	+	3.57194i	−0.173796	+	0.0124458i
$288$		0			0
$289$	−106.060	+	183.702i	−0.366991	+	0.635647i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			223.600i			0.763139i	0.924340	+	0.381569i	$0.124616\pi$
$293$			223.600i			0.763139i	−0.924340	+	0.381569i	$0.875384\pi$
$294$		0			0
$295$	−338.142			−1.14624
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−127.121	−	73.3931i	−0.425153	−	0.245462i
$300$		0			0
$301$	26.8901	+	375.500i	0.0893358	+	1.24751i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.945494	−	1.63764i	−0.00309998	−	0.00536933i
$306$		0			0
$307$			66.8457i			0.217738i	0.994056	+	0.108869i	$0.0347230\pi$
$307$			66.8457i			0.217738i	−0.994056	+	0.108869i	$0.965277\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−25.3074	+	14.6112i	−0.0813743	+	0.0469815i	−0.540135	−	0.841578i	$-0.681627\pi$
$311$	−25.3074	+	14.6112i	−0.0813743	+	0.0469815i	0.458761	+	0.888560i	$0.348294\pi$
$312$		0			0
$313$	−214.874	−	124.057i	−0.686497	−	0.396349i	0.115801	−	0.993272i	$-0.463056\pi$
$313$	−214.874	−	124.057i	−0.686497	−	0.396349i	−0.802298	+	0.596923i	$0.796390\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.32395	−	10.9534i	0.0199494	−	0.0345533i	−0.855878	−	0.517177i	$-0.826983\pi$
$317$	6.32395	−	10.9534i	0.0199494	−	0.0345533i	0.875828	+	0.482624i	$0.160316\pi$
$318$		0			0
$319$	−133.170	−	230.658i	−0.417462	−	0.723065i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−266.241			−0.824276
$324$		0			0
$325$	−30.6157	+	17.6760i	−0.0942023	+	0.0543877i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−122.154	+	251.521i	−0.371288	+	0.764503i
$330$		0			0
$331$	−251.450	+	435.525i	−0.759669	+	1.31579i	0.183351	+	0.983048i	$0.441306\pi$
$331$	−251.450	+	435.525i	−0.759669	+	1.31579i	−0.943019	+	0.332738i	$0.892028\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			249.746i			0.745509i
$336$		0			0
$337$	−123.681			−0.367006			−0.183503	−	0.983019i	$-0.558744\pi$
$337$	−123.681			−0.367006			−0.183503	+	0.983019i	$0.558744\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	475.731	+	274.663i	1.39510	+	0.805464i
$342$		0			0
$343$	73.0000	+	335.142i	0.212828	+	0.977090i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	113.154	+	195.988i	0.326091	+	0.564807i	0.981733	−	0.190266i	$-0.0609350\pi$
$347$	113.154	+	195.988i	0.326091	+	0.564807i	−0.655641	+	0.755073i	$0.727602\pi$
$348$		0			0
$349$		−	155.669i		−	0.446043i	−0.974814	−	0.223021i	$-0.928408\pi$
$349$		−	155.669i		−	0.446043i	0.974814	−	0.223021i	$-0.0715920\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	55.4066	−	31.9890i	0.156959	−	0.0906205i	−0.419463	−	0.907772i	$-0.637782\pi$
$353$	55.4066	−	31.9890i	0.156959	−	0.0906205i	0.576422	+	0.817152i	$0.304448\pi$
$354$		0			0
$355$	469.121	+	270.847i	1.32147	+	0.762949i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	151.494	−	262.396i	0.421989	−	0.730907i	−0.574145	−	0.818754i	$-0.694665\pi$
$359$	151.494	−	262.396i	0.421989	−	0.730907i	0.996134	+	0.0878469i	$0.0279986\pi$
$360$		0			0
$361$	280.511	+	485.859i	0.777038	+	1.34587i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−157.319			−0.431011
$366$		0			0
$367$	0.00581404	−	0.00335674i	1.58421e−5	−	9.14643e-6i	−0.499992	−	0.866030i	$-0.666664\pi$
$367$	0.00581404	−	0.00335674i	1.58421e−5	−	9.14643e-6i	0.500008	+	0.866021i	$0.333330\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−357.038	+	241.697i	−0.962367	+	0.651474i
$372$		0			0
$373$	62.8901	−	108.929i	0.168606	−	0.292034i	−0.769324	−	0.638859i	$-0.779407\pi$
$373$	62.8901	−	108.929i	0.168606	−	0.292034i	0.937930	+	0.346825i	$0.112740\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			83.1384i			0.220526i
$378$		0			0
$379$	485.076			1.27988			0.639942	−	0.768423i	$-0.278958\pi$
$379$	485.076			1.27988			0.639942	+	0.768423i	$0.278958\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−225.286	−	130.069i	−0.588214	−	0.339606i	0.176177	−	0.984359i	$-0.443627\pi$
$383$	−225.286	−	130.069i	−0.588214	−	0.339606i	−0.764391	+	0.644753i	$0.776960\pi$
$384$		0			0
$385$	−599.752	+	42.9491i	−1.55780	+	0.111556i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	42.9339	+	74.3636i	0.110370	+	0.191166i	0.915919	−	0.401362i	$-0.131463\pi$
$389$	42.9339	+	74.3636i	0.110370	+	0.191166i	−0.805550	+	0.592528i	$0.798130\pi$
$390$		0			0
$391$			210.434i			0.538195i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	198.137	−	114.395i	0.501613	−	0.289606i
$396$		0			0
$397$	401.670	+	231.904i	1.01176	+	0.584142i	0.911708	−	0.410840i	$-0.134764\pi$
$397$	401.670	+	231.904i	1.01176	+	0.584142i	0.100056	+	0.994982i	$0.468098\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−231.934	+	401.721i	−0.578389	+	1.00180i	0.417276	+	0.908780i	$0.362985\pi$
$401$	−231.934	+	401.721i	−0.578389	+	1.00180i	−0.995664	+	0.0930186i	$0.970348\pi$
$402$		0			0
$403$	−85.7364	−	148.500i	−0.212745	−	0.368486i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	952.109			2.33933
$408$		0			0
$409$	403.687	−	233.069i	0.987009	−	0.569850i	0.0826303	−	0.996580i	$-0.473668\pi$
$409$	403.687	−	233.069i	0.987009	−	0.569850i	0.904379	+	0.426730i	$0.140335\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−302.664	−	447.100i	−0.732844	−	1.08257i
$414$		0			0
$415$	−300.050	+	519.701i	−0.723011	+	1.25229i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			89.9655i			0.214715i	0.994220	+	0.107357i	$0.0342389\pi$
$419$			89.9655i			0.214715i	−0.994220	+	0.107357i	$0.965761\pi$
$420$		0			0
$421$	−413.582			−0.982379			−0.491190	−	0.871053i	$-0.663438\pi$
$421$	−413.582			−0.982379			−0.491190	+	0.871053i	$0.663438\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	43.8910	+	25.3405i	0.103273	+	0.0596246i
$426$		0			0
$427$	1.31904	−	2.71598i	0.00308909	−	0.00636061i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−35.0661	−	60.7363i	−0.0813599	−	0.140920i	0.822474	−	0.568802i	$-0.192593\pi$
$431$	−35.0661	−	60.7363i	−0.0813599	−	0.140920i	−0.903834	+	0.427883i	$0.859260\pi$
$432$		0			0
$433$			431.223i			0.995897i	0.867207	+	0.497948i	$0.165913\pi$
$433$			431.223i			0.995897i	−0.867207	+	0.497948i	$0.834087\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	631.121	−	364.378i	1.44421	−	0.833816i
$438$		0			0
$439$	81.7091	+	47.1748i	0.186126	+	0.107460i	0.590168	−	0.807281i	$-0.299062\pi$
$439$	81.7091	+	47.1748i	0.186126	+	0.107460i	−0.404042	+	0.914740i	$0.632395\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−206.291	+	357.306i	−0.465668	+	0.806560i	−0.999231	−	0.0391995i	$-0.987519\pi$
$443$	−206.291	+	357.306i	−0.465668	+	0.806560i	0.533564	+	0.845760i	$0.320853\pi$
$444$		0			0
$445$	33.4611	+	57.9564i	0.0751935	+	0.130239i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−617.802			−1.37595			−0.687975	−	0.725734i	$-0.741500\pi$
$449$	−617.802			−1.37595			−0.687975	+	0.725734i	$0.741500\pi$
$450$		0			0
$451$	121.220	−	69.9863i	0.268780	−	0.155180i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	168.835	+	81.9961i	0.371065	+	0.180211i
$456$		0			0
$457$	5.50000	−	9.52628i	0.0120350	−	0.0208453i	−0.859945	−	0.510386i	$-0.829502\pi$
$457$	5.50000	−	9.52628i	0.0120350	−	0.0208453i	0.871980	+	0.489541i	$0.162836\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	859.960i		−	1.86542i	−0.360624	−	0.932711i	$-0.617436\pi$
$461$		−	859.960i		−	1.86542i	0.360624	−	0.932711i	$-0.382564\pi$
$462$		0			0
$463$	−397.340			−0.858187			−0.429093	−	0.903260i	$-0.641167\pi$
$463$	−397.340			−0.858187			−0.429093	+	0.903260i	$0.641167\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	257.340	+	148.576i	0.551050	+	0.318149i	0.749545	−	0.661953i	$-0.230272\pi$
$467$	257.340	+	148.576i	0.551050	+	0.318149i	−0.198495	+	0.980102i	$0.563605\pi$
$468$		0			0
$469$	−330.220	+	223.542i	−0.704093	+	0.476636i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−526.868	−	912.562i	−1.11389	−	1.92931i
$474$		0			0
$475$		−	175.513i		−	0.369502i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	696.648	−	402.210i	1.45438	−	0.839687i	0.455654	−	0.890157i	$-0.349405\pi$
$479$	696.648	−	402.210i	1.45438	−	0.839687i	0.998726	+	0.0504704i	$0.0160720\pi$
$480$		0			0
$481$	−257.384	−	148.601i	−0.535102	−	0.308942i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−74.8628	+	129.666i	−0.154356	+	0.267353i
$486$		0			0
$487$	30.4008	+	52.6557i	0.0624246	+	0.108123i	0.895549	−	0.444964i	$-0.146783\pi$
$487$	30.4008	+	52.6557i	0.0624246	+	0.108123i	−0.833124	+	0.553086i	$0.813450\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	514.955			1.04879			0.524394	−	0.851475i	$-0.324292\pi$
$491$	514.955			1.04879			0.524394	+	0.851475i	$0.324292\pi$
$492$		0			0
$493$	103.220	−	59.5940i	0.209371	−	0.120880i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	61.7802	+	862.713i	0.124306	+	1.73584i
$498$		0			0
$499$	444.450	−	769.811i	0.890682	−	1.54271i	0.0516230	−	0.998667i	$-0.483561\pi$
$499$	444.450	−	769.811i	0.890682	−	1.54271i	0.839059	−	0.544040i	$-0.183106\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			822.920i			1.63602i	0.575202	+	0.818012i	$0.304924\pi$
$503$			822.920i			1.63602i	−0.575202	+	0.818012i	$0.695076\pi$
$504$		0			0
$505$	−573.759			−1.13616
$506$		0			0
$507$		0			0
$508$		0			0
$509$	492.038	+	284.078i	0.966676	+	0.558111i	0.898221	−	0.439544i	$-0.144860\pi$
$509$	492.038	+	284.078i	0.966676	+	0.558111i	0.0684546	+	0.997654i	$0.478193\pi$
$510$		0			0
$511$	−140.813	−	208.011i	−0.275564	−	0.407067i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−356.527	−	617.523i	−0.692286	−	1.19907i
$516$		0			0
$517$		−	782.658i		−	1.51385i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−118.407	+	68.3621i	−0.227268	+	0.131213i	−0.609311	−	0.792931i	$-0.708554\pi$
$521$	−118.407	+	68.3621i	−0.227268	+	0.131213i	0.382043	+	0.924145i	$0.375221\pi$
$522$		0			0
$523$	−12.6157	−	7.28370i	−0.0241219	−	0.0139268i	0.487891	−	0.872905i	$-0.337767\pi$
$523$	−12.6157	−	7.28370i	−0.0241219	−	0.0139268i	−0.512012	+	0.858978i	$0.671100\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−122.912	+	212.891i	−0.233230	+	0.403967i
$528$		0			0
$529$	−23.5000	−	40.7032i	−0.0444234	−	0.0769437i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−43.6926			−0.0819748
$534$		0			0
$535$	−394.731	+	227.898i	−0.737814	+	0.425977i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−593.615	−	754.564i	−1.10133	−	1.39993i
$540$		0			0
$541$	462.450	−	800.988i	0.854807	−	1.48057i	−0.0220176	−	0.999758i	$-0.507009\pi$
$541$	462.450	−	800.988i	0.854807	−	1.48057i	0.876824	−	0.480811i	$-0.159658\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	69.1809i		−	0.126937i
$546$		0			0
$547$	−103.626			−0.189445			−0.0947225	−	0.995504i	$-0.530196\pi$
$547$	−103.626			−0.189445			−0.0947225	+	0.995504i	$0.530196\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−357.461	−	206.380i	−0.648750	−	0.374556i
$552$		0			0
$553$	328.604	+	159.590i	0.594221	+	0.288589i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	206.203	+	357.155i	0.370203	+	0.641211i	0.989597	−	0.143870i	$-0.0459546\pi$
$557$	206.203	+	357.155i	0.370203	+	0.641211i	−0.619393	+	0.785081i	$0.712621\pi$
$558$		0			0
$559$			328.925i			0.588416i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−594.412	+	343.184i	−1.05579	+	0.609562i	−0.924266	−	0.381750i	$-0.875322\pi$
$563$	−594.412	+	343.184i	−1.05579	+	0.609562i	−0.131528	+	0.991313i	$0.541988\pi$
$564$		0			0
$565$	−226.383	−	130.702i	−0.400679	−	0.231332i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−73.3074	+	126.972i	−0.128836	+	0.223150i	−0.923226	−	0.384258i	$-0.874457\pi$
$569$	−73.3074	+	126.972i	−0.128836	+	0.223150i	0.794390	+	0.607408i	$0.207791\pi$
$570$		0			0
$571$	178.131	+	308.533i	0.311964	+	0.540337i	0.978787	−	0.204878i	$-0.0656799\pi$
$571$	178.131	+	308.533i	0.311964	+	0.540337i	−0.666824	+	0.745216i	$0.732347\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−138.724			−0.241259
$576$		0			0
$577$	−148.115	+	85.5141i	−0.256698	+	0.148205i	−0.622827	−	0.782359i	$-0.714016\pi$
$577$	−148.115	+	85.5141i	−0.256698	+	0.148205i	0.366129	+	0.930564i	$0.380683\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−955.731	+	68.4413i	−1.64498	+	0.117799i
$582$		0			0
$583$	603.412	−	1045.14i	1.03501	−	1.79269i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	24.8384i		−	0.0423142i	−0.999776	−	0.0211571i	$-0.993265\pi$
$587$		−	24.8384i		−	0.0423142i	0.999776	−	0.0211571i	$-0.00673502\pi$
$588$		0			0
$589$	851.317			1.44536
$590$		0			0
$591$		0			0
$592$		0			0
$593$	117.846	+	68.0386i	0.198729	+	0.114736i	0.596062	−	0.802938i	$-0.296731\pi$
$593$	117.846	+	68.0386i	0.198729	+	0.114736i	−0.397333	+	0.917674i	$0.630064\pi$
$594$		0			0
$595$	−19.2198	−	268.390i	−0.0323023	−	0.451076i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−494.615	−	856.698i	−0.825734	−	1.43021i	−0.901357	−	0.433077i	$-0.857428\pi$
$599$	−494.615	−	856.698i	−0.825734	−	1.43021i	0.0756226	−	0.997137i	$-0.475906\pi$
$600$		0			0
$601$			78.8184i			0.131145i	0.997848	+	0.0655727i	$0.0208874\pi$
$601$			78.8184i			0.131145i	−0.997848	+	0.0655727i	$0.979113\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	998.154	−	576.284i	1.64984	−	0.952536i
$606$		0			0
$607$	−727.850	−	420.225i	−1.19909	−	0.692297i	−0.238741	−	0.971083i	$-0.576735\pi$
$607$	−727.850	−	420.225i	−1.19909	−	0.692297i	−0.960353	+	0.278786i	$0.910068\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−122.154	+	211.576i	−0.199924	+	0.346279i
$612$		0			0
$613$	−423.714	−	733.894i	−0.691214	−	1.19722i	−0.971440	−	0.237283i	$-0.923743\pi$
$613$	−423.714	−	733.894i	−0.691214	−	1.19722i	0.280227	−	0.959934i	$-0.409590\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	649.669			1.05295			0.526474	−	0.850191i	$-0.323514\pi$
$617$	649.669			1.05295			0.526474	+	0.850191i	$0.323514\pi$
$618$		0			0
$619$	422.659	−	244.022i	0.682809	−	0.394220i	−0.118104	−	0.993001i	$-0.537682\pi$
$619$	422.659	−	244.022i	0.682809	−	0.394220i	0.800912	+	0.598781i	$0.204348\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−46.6810	+	96.1187i	−0.0749293	+	0.154284i
$624$		0			0
$625$	223.543	−	387.188i	0.357669	−	0.619500i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			426.071i			0.677378i
$630$		0			0
$631$	820.473			1.30027			0.650137	−	0.759817i	$-0.274712\pi$
$631$	820.473			1.30027			0.650137	+	0.759817i	$0.274712\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−94.9173	−	54.8005i	−0.149476	−	0.0863001i
$636$		0			0
$637$	42.7033	+	296.631i	0.0670382	+	0.465668i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.93387	−	17.2060i	−0.0154975	−	0.0268424i	0.858173	−	0.513361i	$-0.171600\pi$
$641$	−9.93387	−	17.2060i	−0.0154975	−	0.0268424i	−0.873670	+	0.486519i	$0.838267\pi$
$642$		0			0
$643$			1013.95i			1.57691i	0.615092	+	0.788456i	$0.289119\pi$
$643$			1013.95i			1.57691i	−0.615092	+	0.788456i	$0.710881\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	115.582	−	66.7312i	0.178643	−	0.103139i	−0.408012	−	0.912976i	$-0.633778\pi$
$647$	115.582	−	66.7312i	0.178643	−	0.103139i	0.586655	+	0.809837i	$0.300445\pi$
$648$		0			0
$649$	1308.77	+	755.621i	2.01660	+	1.16428i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	302.378	−	523.735i	0.463060	−	0.802044i	−0.536051	−	0.844185i	$-0.680085\pi$
$653$	302.378	−	523.735i	0.463060	−	0.802044i	0.999112	+	0.0421413i	$0.0134180\pi$
$654$		0			0
$655$	−496.532	−	860.019i	−0.758064	−	1.31301i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	335.451			0.509031			0.254515	−	0.967069i	$-0.418084\pi$
$659$	335.451			0.509031			0.254515	+	0.967069i	$0.418084\pi$
$660$		0			0
$661$	608.186	−	351.136i	0.920100	−	0.531220i	0.0364328	−	0.999336i	$-0.488401\pi$
$661$	608.186	−	351.136i	0.920100	−	0.531220i	0.883667	+	0.468116i	$0.155067\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−771.660	+	522.375i	−1.16039	+	0.785526i
$666$		0			0
$667$	−163.121	+	282.533i	−0.244559	+	0.423588i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			8.45130i			0.0125951i
$672$		0			0
$673$	−1119.48			−1.66342			−0.831711	−	0.555209i	$-0.812638\pi$
$673$	−1119.48			−1.66342			−0.831711	+	0.555209i	$0.812638\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−225.709	−	130.313i	−0.333396	−	0.192486i	0.323952	−	0.946074i	$-0.394988\pi$
$677$	−225.709	−	130.313i	−0.333396	−	0.192486i	−0.657348	+	0.753587i	$0.728322\pi$
$678$		0			0
$679$	−238.456	+	17.0762i	−0.351187	+	0.0251490i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	100.258	+	173.652i	0.146790	+	0.254248i	0.930039	−	0.367460i	$-0.119772\pi$
$683$	100.258	+	173.652i	0.146790	+	0.254248i	−0.783249	+	0.621708i	$0.786439\pi$
$684$		0			0
$685$			1083.39i			1.58159i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−326.241	+	188.355i	−0.473500	+	0.273375i
$690$		0			0
$691$	−860.933	−	497.060i	−1.24592	−	0.719334i	−0.275629	−	0.961264i	$-0.588886\pi$
$691$	−860.933	−	497.060i	−1.24592	−	0.719334i	−0.970294	+	0.241930i	$0.922220\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−323.066	+	559.567i	−0.464843	+	0.805132i
$696$		0			0
$697$	31.3190	+	54.2462i	0.0449341	+	0.0778281i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	148.231			0.211457			0.105729	−	0.994395i	$-0.466283\pi$
$701$	148.231			0.211457			0.105729	+	0.994395i	$0.466283\pi$
$702$		0			0
$703$	1277.85	−	737.764i	1.81770	−	1.04945i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−513.560	−	758.638i	−0.726394	−	1.07304i
$708$		0			0
$709$	−355.988	+	616.590i	−0.502099	+	0.869661i	0.497898	+	0.867236i	$0.334105\pi$
$709$	−355.988	+	616.590i	−0.502099	+	0.869661i	−0.999997	+	0.00242571i	$0.999228\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	672.872i		−	0.943719i
$714$		0			0
$715$	−525.362			−0.734772
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−649.109	−	374.763i	−0.902794	−	0.521228i	−0.0246885	−	0.999695i	$-0.507859\pi$
$719$	−649.109	−	374.763i	−0.902794	−	0.521228i	−0.878106	+	0.478467i	$0.841193\pi$
$720$		0			0
$721$	497.384	−	1024.14i	0.689853	−	1.42045i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	39.2860	+	68.0453i	0.0541876	+	0.0938556i
$726$		0			0
$727$			865.702i			1.19079i	0.803434	+	0.595393i	$0.203004\pi$
$727$			865.702i			1.19079i	−0.803434	+	0.595393i	$0.796996\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	408.374	−	235.775i	0.558651	−	0.322537i
$732$		0			0
$733$	83.5710	+	48.2498i	0.114012	+	0.0658251i	0.555922	−	0.831235i	$-0.312365\pi$
$733$	83.5710	+	48.2498i	0.114012	+	0.0658251i	−0.441909	+	0.897060i	$0.645699\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	558.088	−	966.636i	0.757242	−	1.31158i
$738$		0			0
$739$	−210.450	−	364.511i	−0.284777	−	0.493249i	0.687778	−	0.725921i	$-0.258586\pi$
$739$	−210.450	−	364.511i	−0.284777	−	0.493249i	−0.972555	+	0.232673i	$0.925253\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	920.043			1.23828			0.619141	−	0.785280i	$-0.287481\pi$
$743$	920.043			1.23828			0.619141	+	0.785280i	$0.287481\pi$
$744$		0			0
$745$	−489.064	+	282.361i	−0.656462	+	0.379009i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−654.648	−	317.936i	−0.874029	−	0.424480i
$750$		0			0
$751$	−160.181	+	277.442i	−0.213290	+	0.369430i	−0.952742	−	0.303780i	$-0.901751\pi$
$751$	−160.181	+	277.442i	−0.213290	+	0.369430i	0.739452	+	0.673209i	$0.235085\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	271.956i		−	0.360206i
$756$		0			0
$757$	330.813			0.437006			0.218503	−	0.975836i	$-0.429883\pi$
$757$	330.813			0.437006			0.218503	+	0.975836i	$0.429883\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−230.615	−	133.146i	−0.303042	−	0.174961i	0.340767	−	0.940148i	$-0.389313\pi$
$761$	−230.615	−	133.146i	−0.303042	−	0.174961i	−0.643809	+	0.765187i	$0.722647\pi$
$762$		0			0
$763$	91.4727	−	61.9225i	0.119886	−	0.0811566i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−235.868	−	408.535i	−0.307520	−	0.532640i
$768$		0			0
$769$		−	241.301i		−	0.313785i	−0.987616	−	0.156893i	$-0.949852\pi$
$769$		−	241.301i		−	0.313785i	0.987616	−	0.156893i	$-0.0501477\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	805.208	−	464.887i	1.04167	−	0.601406i	0.121362	−	0.992608i	$-0.461274\pi$
$773$	805.208	−	464.887i	1.04167	−	0.601406i	0.920305	+	0.391202i	$0.127941\pi$
$774$		0			0
$775$	−140.343	−	81.0272i	−0.181088	−	0.104551i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	108.461	−	187.860i	0.139231	−	0.241156i
$780$		0			0
$781$	−1210.48	−	2096.62i	−1.54991	−	2.68453i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1099.12			1.40015
$786$		0			0
$787$	−961.097	+	554.890i	−1.22122	+	0.705070i	−0.965177	−	0.261597i	$-0.915751\pi$
$787$	−961.097	+	554.890i	−1.22122	+	0.705070i	−0.256039	+	0.966666i	$0.582418\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−29.8132	−	416.319i	−0.0376906	−	0.526320i
$792$		0			0
$793$	1.31904	−	2.28465i	0.00166336	−	0.00288102i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	231.047i		−	0.289896i	−0.989439	−	0.144948i	$-0.953699\pi$
$797$		−	231.047i		−	0.289896i	0.989439	−	0.144948i	$-0.0463014\pi$
$798$		0			0
$799$	350.241			0.438350
$800$		0			0
$801$		0			0
$802$		0			0
$803$	608.901	+	351.549i	0.758282	+	0.437795i
$804$		0			0
$805$	412.879	+	609.911i	0.512894	+	0.757653i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−159.473	−	276.215i	−0.197123	−	0.341428i	0.750471	−	0.660903i	$-0.229827\pi$
$809$	−159.473	−	276.215i	−0.197123	−	0.341428i	−0.947595	+	0.319476i	$0.896493\pi$
$810$		0			0
$811$		−	196.807i		−	0.242672i	−0.992612	−	0.121336i	$-0.961282\pi$
$811$		−	196.807i		−	0.242672i	0.992612	−	0.121336i	$-0.0387178\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	371.825	−	214.673i	0.456227	−	0.263403i
$816$		0			0
$817$	−1414.24	−	816.512i	−1.73102	−	0.999403i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−692.005	+	1198.59i	−0.842881	+	1.45991i	0.0445687	+	0.999006i	$0.485809\pi$
$821$	−692.005	+	1198.59i	−0.842881	+	1.45991i	−0.887449	+	0.460906i	$0.847525\pi$
$822$		0			0
$823$	138.253	+	239.461i	0.167987	+	0.290961i	0.937712	−	0.347414i	$-0.112940\pi$
$823$	138.253	+	239.461i	0.167987	+	0.290961i	−0.769725	+	0.638375i	$0.779607\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1467.81			1.77486			0.887431	−	0.460940i	$-0.152488\pi$
$827$	1467.81			1.77486			0.887431	+	0.460940i	$0.152488\pi$
$828$		0			0
$829$	68.1859	−	39.3671i	0.0822507	−	0.0474875i	−0.458311	−	0.888792i	$-0.651545\pi$
$829$	68.1859	−	39.3671i	0.0822507	−	0.0474875i	0.540561	+	0.841305i	$0.318212\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	337.669	−	265.644i	0.405365	−	0.318900i
$834$		0			0
$835$	157.319	−	272.485i	0.188406	−	0.326329i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	591.398i		−	0.704884i	−0.935834	−	0.352442i	$-0.885351\pi$
$839$		−	591.398i		−	0.704884i	0.935834	−	0.352442i	$-0.114649\pi$
$840$		0			0
$841$	−656.220			−0.780285
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−499.620	−	288.456i	−0.591266	−	0.341368i
$846$		0			0
$847$	1655.41	+	803.963i	1.95443	+	0.949189i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−583.121	−	1009.99i	−0.685218	−	1.18683i
$852$		0			0
$853$			1048.80i			1.22954i	0.788707	+	0.614770i	$0.210751\pi$
$853$			1048.80i			1.22954i	−0.788707	+	0.614770i	$0.789249\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−92.8132	+	53.5857i	−0.108300	+	0.0625271i	−0.553172	−	0.833067i	$-0.686583\pi$
$857$	−92.8132	+	53.5857i	−0.108300	+	0.0625271i	0.444872	+	0.895594i	$0.353249\pi$
$858$		0			0
$859$	1304.52	+	753.162i	1.51864	+	0.876790i	0.999759	+	0.0219460i	$0.00698618\pi$
$859$	1304.52	+	753.162i	1.51864	+	0.876790i	0.518885	+	0.854844i	$0.326347\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−187.681	+	325.073i	−0.217475	+	0.376678i	−0.954035	−	0.299694i	$-0.903115\pi$
$863$	−187.681	+	325.073i	−0.217475	+	0.376678i	0.736560	+	0.676372i	$0.236449\pi$
$864$		0			0
$865$	662.043	+	1146.69i	0.765367	+	1.32566i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1022.52			−1.17666
$870$		0			0
$871$	−301.736	+	174.208i	−0.346425	+	0.200009i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	942.178	−	67.4708i	1.07678	−	0.0771095i
$876$		0			0
$877$	−704.395	+	1220.05i	−0.803187	+	1.39116i	0.114321	+	0.993444i	$0.463531\pi$
$877$	−704.395	+	1220.05i	−0.803187	+	1.39116i	−0.917508	+	0.397717i	$0.869803\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	1236.04i		−	1.40299i	−0.712673	−	0.701497i	$-0.752515\pi$
$881$		−	1236.04i		−	1.40299i	0.712673	−	0.701497i	$-0.247485\pi$
$882$		0			0
$883$	72.9437			0.0826089			0.0413045	−	0.999147i	$-0.486849\pi$
$883$	72.9437			0.0826089			0.0413045	+	0.999147i	$0.486849\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1249.01	+	721.116i	1.40813	+	0.812983i	0.995208	−	0.0977838i	$-0.0311754\pi$
$887$	1249.01	+	721.116i	1.40813	+	0.812983i	0.412921	+	0.910767i	$0.364509\pi$
$888$		0			0
$889$	−12.5000	−	174.553i	−0.0140607	−	0.196348i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−606.461	−	1050.42i	−0.679128	−	1.17628i
$894$		0			0
$895$			604.998i			0.675975i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−330.050	+	190.554i	−0.367130	+	0.211962i
$900$		0			0
$901$	467.702	+	270.028i	0.519093	+	0.299698i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−181.879	+	315.024i	−0.200972	+	0.348093i
$906$		0			0
$907$	−604.878	−	1047.68i	−0.666900	−	1.15510i	−0.978766	−	0.204979i	$-0.934287\pi$
$907$	−604.878	−	1047.68i	−0.666900	−	1.15510i	0.311866	−	0.950126i	$-0.399046\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1328.22			−1.45798			−0.728989	−	0.684525i	$-0.760009\pi$
$911$	−1328.22			−1.45798			−0.728989	+	0.684525i	$0.760009\pi$
$912$		0			0
$913$	2322.67	−	1341.00i	2.54400	−	1.46878i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	692.702	−	1426.31i	0.755401	−	1.55541i
$918$		0			0
$919$	−244.429	+	423.363i	−0.265973	+	0.460678i	−0.967818	−	0.251651i	$-0.919026\pi$
$919$	−244.429	+	423.363i	−0.265973	+	0.460678i	0.701845	+	0.712329i	$0.252360\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			755.707i			0.818750i
$924$		0			0
$925$	−280.878			−0.303651
$926$		0			0
$927$		0			0
$928$		0			0
$929$	824.055	+	475.768i	0.887034	+	0.512129i	0.872971	−	0.487772i	$-0.162190\pi$
$929$	824.055	+	475.768i	0.887034	+	0.512129i	0.0140628	+	0.999901i	$0.495524\pi$
$930$		0			0
$931$	−1381.39	−	552.740i	−1.48378	−	0.593706i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	376.582	+	652.259i	0.402761	+	0.697603i
$936$		0			0
$937$		−	309.707i		−	0.330530i	−0.986249	−	0.165265i	$-0.947152\pi$
$937$		−	309.707i		−	0.330530i	0.986249	−	0.165265i	$-0.0528480\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1015.42	+	586.254i	−1.07909	+	0.623011i	−0.930650	−	0.365910i	$-0.880758\pi$
$941$	−1015.42	+	586.254i	−1.07909	+	0.623011i	−0.148437	+	0.988922i	$0.547424\pi$
$942$		0			0
$943$	−148.483	−	85.7264i	−0.157458	−	0.0909082i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	362.428	−	627.744i	0.382712	−	0.662876i	−0.608737	−	0.793372i	$-0.708324\pi$
$947$	362.428	−	627.744i	0.382712	−	0.662876i	0.991449	+	0.130496i	$0.0416569\pi$
$948$		0			0
$949$	−109.736	−	190.069i	−0.115634	−	0.200283i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−27.5371			−0.0288951			−0.0144476	−	0.999896i	$-0.504599\pi$
$953$	−27.5371			−0.0288951			−0.0144476	+	0.999896i	$0.504599\pi$
$954$		0			0
$955$	654.198	−	377.702i	0.685025	−	0.395499i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1432.48	+	969.719i	−1.49373	+	1.01118i
$960$		0			0
$961$	−87.4826	+	151.524i	−0.0910328	+	0.157674i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			1206.96i			1.25074i
$966$		0			0
$967$	−1279.81			−1.32349			−0.661744	−	0.749730i	$-0.730183\pi$
$967$	−1279.81			−1.32349			−0.661744	+	0.749730i	$0.730183\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	963.686	+	556.384i	0.992467	+	0.573001i	0.906011	−	0.423254i	$-0.139112\pi$
$971$	963.686	+	556.384i	0.992467	+	0.573001i	0.0864565	+	0.996256i	$0.472446\pi$
$972$		0			0
$973$	−1029.04	+	73.6914i	−1.05760	+	0.0757362i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−217.879	−	377.378i	−0.223009	−	0.386262i	0.732712	−	0.680539i	$-0.238254\pi$
$977$	−217.879	−	377.378i	−0.223009	−	0.386262i	−0.955720	+	0.294277i	$0.904921\pi$
$978$		0			0
$979$		−	299.092i		−	0.305508i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−243.835	+	140.778i	−0.248052	+	0.143213i	−0.618872	−	0.785492i	$-0.712410\pi$
$983$	−243.835	+	140.778i	−0.248052	+	0.143213i	0.370820	+	0.928705i	$0.379077\pi$
$984$		0			0
$985$	−585.858	−	338.245i	−0.594780	−	0.343396i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−645.362	+	1117.80i	−0.652540	+	1.13023i
$990$		0			0
$991$	−308.786	−	534.833i	−0.311590	−	0.539690i	0.667117	−	0.744953i	$-0.267528\pi$
$991$	−308.786	−	534.833i	−0.311590	−	0.539690i	−0.978707	+	0.205263i	$0.934195\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−823.868			−0.828008
$996$		0			0
$997$	−1303.91	+	752.814i	−1.30784	+	0.755079i	−0.981734	−	0.190256i	$-0.939068\pi$
$997$	−1303.91	+	752.814i	−1.30784	+	0.755079i	−0.326101	+	0.945335i	$0.605735\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.3.cg.m.145.1		4
3.2	odd	2		336.3.bh.f.145.2		4
4.3	odd	2		252.3.z.e.145.1		4
7.3	odd	6	inner	1008.3.cg.m.577.1		4
12.11	even	2		84.3.m.b.61.2	✓	4
21.2	odd	6		2352.3.f.f.97.3		4
21.5	even	6		2352.3.f.f.97.2		4
21.17	even	6		336.3.bh.f.241.2		4
28.3	even	6		252.3.z.e.73.1		4
28.11	odd	6		1764.3.z.h.325.2		4
28.19	even	6		1764.3.d.f.685.2		4
28.23	odd	6		1764.3.d.f.685.3		4
28.27	even	2		1764.3.z.h.901.2		4
60.23	odd	4		2100.3.be.d.649.2		8
60.47	odd	4		2100.3.be.d.649.3		8
60.59	even	2		2100.3.bd.f.901.1		4
84.11	even	6		588.3.m.d.325.1		4
84.23	even	6		588.3.d.b.97.1		4
84.47	odd	6		588.3.d.b.97.4		4
84.59	odd	6		84.3.m.b.73.2	yes	4
84.83	odd	2		588.3.m.d.313.1		4
420.59	odd	6		2100.3.bd.f.1501.2		4
420.143	even	12		2100.3.be.d.1249.3		8
420.227	even	12		2100.3.be.d.1249.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.m.b.61.2	✓	4	12.11	even	2
84.3.m.b.73.2	yes	4	84.59	odd	6
252.3.z.e.73.1		4	28.3	even	6
252.3.z.e.145.1		4	4.3	odd	2
336.3.bh.f.145.2		4	3.2	odd	2
336.3.bh.f.241.2		4	21.17	even	6
588.3.d.b.97.1		4	84.23	even	6
588.3.d.b.97.4		4	84.47	odd	6
588.3.m.d.313.1		4	84.83	odd	2
588.3.m.d.325.1		4	84.11	even	6
1008.3.cg.m.145.1		4	1.1	even	1	trivial
1008.3.cg.m.577.1		4	7.3	odd	6	inner
1764.3.d.f.685.2		4	28.19	even	6
1764.3.d.f.685.3		4	28.23	odd	6
1764.3.z.h.325.2		4	28.11	odd	6
1764.3.z.h.901.2		4	28.27	even	2
2100.3.bd.f.901.1		4	60.59	even	2
2100.3.bd.f.1501.2		4	420.59	odd	6
2100.3.be.d.649.2		8	60.23	odd	4
2100.3.be.d.649.3		8	60.47	odd	4
2100.3.be.d.1249.2		8	420.227	even	12
2100.3.be.d.1249.3		8	420.143	even	12
2352.3.f.f.97.2		4	21.5	even	6
2352.3.f.f.97.3		4	21.2	odd	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cg (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.79669 - 2.19202i) q^{5} +(-0.500000 - 6.98212i) q^{7} +(9.79669 + 16.9684i) q^{11} -6.11609i q^{13} +(-7.59339 + 4.38404i) q^{17} +(26.2967 + 15.1824i) q^{19} +(12.0000 - 20.7846i) q^{23} +(-2.89008 - 5.00577i) q^{25} -13.5934 q^{29} +(24.2802 - 14.0182i) q^{31} +(-13.4066 + 27.6050i) q^{35} +(24.2967 - 42.0831i) q^{37} -7.14387i q^{41} -53.7802 q^{43} +(-34.5934 - 19.9725i) q^{47} +(-48.5000 + 6.98212i) q^{49} +(-30.7967 - 53.3414i) q^{53} -85.8983i q^{55} +(66.7967 - 38.5651i) q^{59} +(0.373546 + 0.215667i) q^{61} +(-13.4066 + 23.2209i) q^{65} +(-28.4835 - 49.3348i) q^{67} -123.560 q^{71} +(31.0769 - 17.9422i) q^{73} +(113.577 - 76.8859i) q^{77} +(-26.0934 + 45.1951i) q^{79} -136.883i q^{83} +38.4397 q^{85} +(-13.2198 - 7.63248i) q^{89} +(-42.7033 + 3.05805i) q^{91} +(-66.5603 - 115.286i) q^{95} -34.1524i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 9 q^{5} - 2 q^{7} + 15 q^{11} + 18 q^{17} + 81 q^{19} + 48 q^{23} + 61 q^{25} - 6 q^{29} - 48 q^{31} - 102 q^{35} + 73 q^{37} - 70 q^{43} - 90 q^{47} - 194 q^{49} - 99 q^{53} + 243 q^{59} - 192 q^{61}+ \cdots + 24 q^{95}+O(q^{100}) \) 4 * q + 9 * q^5 - 2 * q^7 + 15 * q^11 + 18 * q^17 + 81 * q^19 + 48 * q^23 + 61 * q^25 - 6 * q^29 - 48 * q^31 - 102 * q^35 + 73 * q^37 - 70 * q^43 - 90 * q^47 - 194 * q^49 - 99 * q^53 + 243 * q^59 - 192 * q^61 - 102 * q^65 + 7 * q^67 - 204 * q^71 - 45 * q^73 + 285 * q^77 - 56 * q^79 + 444 * q^85 - 198 * q^89 - 195 * q^91 + 24 * q^95

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