LMFDB - Embedded newform 504.3.by.a.73.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(73,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.73"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.by (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.126303473664.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 2x^{5} + 92x^{4} + 14x^{3} - 441x^{2} - 686x + 2401 $ x^8 - 2x^7 - 9x^6 + 2x^5 + 92x^4 + 14x^3 - 441x^2 - 686*x + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.2
Root			$2.18070 - 1.49818i$ of defining polynomial
Character	$\chi$	$=$	504.73
Dual form			504.3.by.a.145.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.425150 - 0.245461i) q^{5} +(-6.25375 + 3.14494i) q^{7} +(5.17890 - 8.97011i) q^{11} +8.96825i q^{13} +(-0.259406 - 0.149768i) q^{17} +(-24.4164 + 14.0968i) q^{19} +(-2.82843 - 4.89898i) q^{23} +(-12.3795 + 21.4419i) q^{25} -25.4340 q^{29} +(-39.5821 - 22.8527i) q^{31} +(-1.88682 + 2.87212i) q^{35} +(5.17174 + 8.95772i) q^{37} +47.6299i q^{41} +6.83830 q^{43} +(-56.4531 + 32.5932i) q^{47} +(29.2187 - 39.3353i) q^{49} +(8.95008 - 15.5020i) q^{53} -5.08486i q^{55} +(42.0210 + 24.2608i) q^{59} +(-30.0000 + 17.3205i) q^{61} +(2.20135 + 3.81285i) q^{65} +(-40.5985 + 70.3186i) q^{67} -133.927 q^{71} +(-5.51407 - 3.18355i) q^{73} +(-4.17706 + 72.3841i) q^{77} +(-26.5241 - 45.9410i) q^{79} -116.065i q^{83} -0.147049 q^{85} +(27.1948 - 15.7009i) q^{89} +(-28.2046 - 56.0852i) q^{91} +(-6.92041 + 11.9865i) q^{95} +54.6836i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{5} - 4 q^{7} - 14 q^{11} - 12 q^{17} + 78 q^{19} - 6 q^{25} + 4 q^{29} - 24 q^{31} + 156 q^{35} + 50 q^{37} - 20 q^{43} - 12 q^{47} + 220 q^{49} + 50 q^{53} + 186 q^{59} - 240 q^{61} + 148 q^{65}+ \cdots - 144 q^{95}+O(q^{100}) $ 8 * q - 6 * q^5 - 4 * q^7 - 14 * q^11 - 12 * q^17 + 78 * q^19 - 6 * q^25 + 4 * q^29 - 24 * q^31 + 156 * q^35 + 50 * q^37 - 20 * q^43 - 12 * q^47 + 220 * q^49 + 50 * q^53 + 186 * q^59 - 240 * q^61 + 148 * q^65 + 34 * q^67 - 424 * q^71 + 294 * q^73 - 126 * q^77 - 40 * q^79 - 232 * q^85 + 132 * q^89 - 378 * q^91 - 144 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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
$5$	0.425150	−	0.245461i	0.0850300	−	0.0490921i	−0.456882	−	0.889527i	$-0.651034\pi$
$5$	0.425150	−	0.245461i	0.0850300	−	0.0490921i	0.541912	+	0.840435i	$0.317701\pi$
$6$		0			0
$7$	−6.25375	+	3.14494i	−0.893393	+	0.449277i
$7$	−6.25375	+	3.14494i	−0.893393	+	0.449277i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	5.17890	−	8.97011i	0.470809	−	0.815465i	−0.528634	−	0.848850i	$-0.677295\pi$
$11$	5.17890	−	8.97011i	0.470809	−	0.815465i	0.999443	+	0.0333851i	$0.0106288\pi$
$12$		0			0
$13$			8.96825i			0.689865i	0.938627	+	0.344933i	$0.112098\pi$
$13$			8.96825i			0.689865i	−0.938627	+	0.344933i	$0.887902\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.259406	−	0.149768i	−0.0152592	−	0.00880990i	0.492351	−	0.870397i	$-0.336138\pi$
$17$	−0.259406	−	0.149768i	−0.0152592	−	0.00880990i	−0.507610	+	0.861587i	$0.669471\pi$
$18$		0			0
$19$	−24.4164	+	14.0968i	−1.28507	+	0.741936i	−0.977771	−	0.209676i	$-0.932759\pi$
$19$	−24.4164	+	14.0968i	−1.28507	+	0.741936i	−0.307301	+	0.951612i	$0.599426\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.82843	−	4.89898i	−0.122975	−	0.212999i	0.797965	−	0.602704i	$-0.205910\pi$
$23$	−2.82843	−	4.89898i	−0.122975	−	0.212999i	−0.920940	+	0.389705i	$0.872577\pi$
$24$		0			0
$25$	−12.3795	+	21.4419i	−0.495180	+	0.857677i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−25.4340			−0.877033			−0.438517	−	0.898723i	$-0.644496\pi$
$29$	−25.4340			−0.877033			−0.438517	+	0.898723i	$0.644496\pi$
$30$		0			0
$31$	−39.5821	−	22.8527i	−1.27684	−	0.737185i	−0.300576	−	0.953758i	$-0.597179\pi$
$31$	−39.5821	−	22.8527i	−1.27684	−	0.737185i	−0.976266	+	0.216573i	$0.930512\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.88682	+	2.87212i	−0.0539092	+	0.0820606i
$36$		0			0
$37$	5.17174	+	8.95772i	0.139777	+	0.242101i	0.927412	−	0.374041i	$-0.122028\pi$
$37$	5.17174	+	8.95772i	0.139777	+	0.242101i	−0.787635	+	0.616142i	$0.788695\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			47.6299i			1.16171i	0.814009	+	0.580853i	$0.197281\pi$
$41$			47.6299i			1.16171i	−0.814009	+	0.580853i	$0.802719\pi$
$42$		0			0
$43$	6.83830			0.159030			0.0795151	−	0.996834i	$-0.474663\pi$
$43$	6.83830			0.159030			0.0795151	+	0.996834i	$0.474663\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−56.4531	+	32.5932i	−1.20113	+	0.693472i	−0.960806	−	0.277221i	$-0.910587\pi$
$47$	−56.4531	+	32.5932i	−1.20113	+	0.693472i	−0.240323	+	0.970693i	$0.577253\pi$
$48$		0			0
$49$	29.2187	−	39.3353i	0.596300	−	0.802761i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	8.95008	−	15.5020i	0.168870	−	0.292491i	−0.769153	−	0.639064i	$-0.779322\pi$
$53$	8.95008	−	15.5020i	0.168870	−	0.292491i	0.938023	+	0.346574i	$0.112655\pi$
$54$		0			0
$55$		−	5.08486i		−	0.0924520i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	42.0210	+	24.2608i	0.712220	+	0.411200i	0.811882	−	0.583821i	$-0.198443\pi$
$59$	42.0210	+	24.2608i	0.712220	+	0.411200i	−0.0996628	+	0.995021i	$0.531776\pi$
$60$		0			0
$61$	−30.0000	+	17.3205i	−0.491803	+	0.283943i	−0.725322	−	0.688409i	$-0.758309\pi$
$61$	−30.0000	+	17.3205i	−0.491803	+	0.283943i	0.233519	+	0.972352i	$0.424976\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.20135	+	3.81285i	0.0338669	+	0.0586593i
$66$		0			0
$67$	−40.5985	+	70.3186i	−0.605948	+	1.04953i	0.385953	+	0.922518i	$0.373873\pi$
$67$	−40.5985	+	70.3186i	−0.605948	+	1.04953i	−0.991901	+	0.127014i	$0.959461\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−133.927			−1.88630			−0.943150	−	0.332366i	$-0.892153\pi$
$71$	−133.927			−1.88630			−0.943150	+	0.332366i	$0.892153\pi$
$72$		0			0
$73$	−5.51407	−	3.18355i	−0.0755352	−	0.0436103i	0.461757	−	0.887007i	$-0.347219\pi$
$73$	−5.51407	−	3.18355i	−0.0755352	−	0.0436103i	−0.537292	+	0.843396i	$0.680553\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.17706	+	72.3841i	−0.0542475	+	0.940054i
$78$		0			0
$79$	−26.5241	−	45.9410i	−0.335747	−	0.581532i	0.647881	−	0.761742i	$-0.275656\pi$
$79$	−26.5241	−	45.9410i	−0.335747	−	0.581532i	−0.983628	+	0.180210i	$0.942322\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	116.065i		−	1.39837i	−0.714940	−	0.699186i	$-0.753546\pi$
$83$		−	116.065i		−	1.39837i	0.714940	−	0.699186i	$-0.246454\pi$
$84$		0			0
$85$	−0.147049			−0.00172999
$86$		0			0
$87$		0			0
$88$		0			0
$89$	27.1948	−	15.7009i	0.305560	−	0.176415i	−0.339378	−	0.940650i	$-0.610217\pi$
$89$	27.1948	−	15.7009i	0.305560	−	0.176415i	0.644938	+	0.764235i	$0.276883\pi$
$90$		0			0
$91$	−28.2046	−	56.0852i	−0.309941	−	0.616320i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.92041	+	11.9865i	−0.0728464	+	0.126174i
$96$		0			0
$97$			54.6836i			0.563749i	0.959451	+	0.281874i	$0.0909562\pi$
$97$			54.6836i			0.563749i	−0.959451	+	0.281874i	$0.909044\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	129.836	+	74.9610i	1.28551	+	0.742188i	0.977850	−	0.209309i	$-0.0671214\pi$
$101$	129.836	+	74.9610i	1.28551	+	0.742188i	0.307658	+	0.951497i	$0.400455\pi$
$102$		0			0
$103$	39.3881	−	22.7407i	0.382409	−	0.220784i	−0.296457	−	0.955046i	$-0.595805\pi$
$103$	39.3881	−	22.7407i	0.382409	−	0.220784i	0.678866	+	0.734262i	$0.262472\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−93.8988	−	162.637i	−0.877559	−	1.51998i	−0.854012	−	0.520254i	$-0.825837\pi$
$107$	−93.8988	−	162.637i	−0.877559	−	1.51998i	−0.0235469	−	0.999723i	$-0.507496\pi$
$108$		0			0
$109$	−72.6347	+	125.807i	−0.666373	+	1.15419i	0.312538	+	0.949905i	$0.398821\pi$
$109$	−72.6347	+	125.807i	−0.666373	+	1.15419i	−0.978911	+	0.204287i	$0.934512\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	198.397			1.75572			0.877862	−	0.478913i	$-0.158969\pi$
$113$	198.397			1.75572			0.877862	+	0.478913i	$0.158969\pi$
$114$		0			0
$115$	−2.40501	−	1.38853i	−0.0209131	−	0.0120742i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.09327	+	0.120796i	0.0175905	+	0.00101509i
$120$		0			0
$121$	6.85803	+	11.8785i	0.0566780	+	0.0981691i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			24.4277i			0.195422i
$126$		0			0
$127$	231.421			1.82221			0.911107	−	0.412170i	$-0.135229\pi$
$127$	231.421			1.82221			0.911107	+	0.412170i	$0.135229\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−18.8508	+	10.8835i	−0.143899	+	0.0830802i	−0.570221	−	0.821491i	$-0.693142\pi$
$131$	−18.8508	+	10.8835i	−0.143899	+	0.0830802i	0.426322	+	0.904572i	$0.359809\pi$
$132$		0			0
$133$	108.360	−	164.946i	0.814738	−	1.24019i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	120.880	−	209.371i	0.882339	−	1.52826i	0.0336062	−	0.999435i	$-0.489301\pi$
$137$	120.880	−	209.371i	0.882339	−	1.52826i	0.848733	−	0.528821i	$-0.177366\pi$
$138$		0			0
$139$			186.378i			1.34085i	0.741978	+	0.670424i	$0.233888\pi$
$139$			186.378i			1.34085i	−0.741978	+	0.670424i	$0.766112\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	80.4462	+	46.4456i	0.562561	+	0.324795i
$144$		0			0
$145$	−10.8133	+	6.24304i	−0.0745742	+	0.0430554i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−31.8090	−	55.0948i	−0.213483	−	0.369764i	0.739319	−	0.673355i	$-0.235148\pi$
$149$	−31.8090	−	55.0948i	−0.213483	−	0.369764i	−0.952802	+	0.303591i	$0.901814\pi$
$150$		0			0
$151$	39.6384	−	68.6557i	0.262506	−	0.454673i	−0.704401	−	0.709802i	$-0.748784\pi$
$151$	39.6384	−	68.6557i	0.262506	−	0.454673i	0.966907	+	0.255129i	$0.0821178\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−22.4378			−0.144760
$156$		0			0
$157$	81.9060	+	47.2884i	0.521694	+	0.301200i	0.737628	−	0.675208i	$-0.235946\pi$
$157$	81.9060	+	47.2884i	0.521694	+	0.301200i	−0.215933	+	0.976408i	$0.569279\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	33.0953	+	21.7418i	0.205561	+	0.135042i
$162$		0			0
$163$	−86.7846	−	150.315i	−0.532421	−	0.922180i	−0.999283	−	0.0378503i	$-0.987949\pi$
$163$	−86.7846	−	150.315i	−0.532421	−	0.922180i	0.466862	−	0.884330i	$-0.345384\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	63.2343i		−	0.378649i	−0.981915	−	0.189324i	$-0.939370\pi$
$167$		−	63.2343i		−	0.378649i	0.981915	−	0.189324i	$-0.0606298\pi$
$168$		0			0
$169$	88.5705			0.524086
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−190.268	+	109.851i	−1.09981	+	0.634977i	−0.936172	−	0.351543i	$-0.885657\pi$
$173$	−190.268	+	109.851i	−1.09981	+	0.634977i	−0.163641	+	0.986520i	$0.552324\pi$
$174$		0			0
$175$	9.98473	−	173.025i	0.0570556	−	0.988715i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−37.5698	+	65.0728i	−0.209887	+	0.363535i	−0.951679	−	0.307095i	$-0.900643\pi$
$179$	−37.5698	+	65.0728i	−0.209887	+	0.363535i	0.741792	+	0.670630i	$0.233976\pi$
$180$		0			0
$181$		−	188.584i		−	1.04190i	−0.853587	−	0.520950i	$-0.825578\pi$
$181$		−	188.584i		−	1.04190i	0.853587	−	0.520950i	$-0.174422\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.39753	+	2.53892i	0.0237705	+	0.0137239i
$186$		0			0
$187$	−2.68688	+	1.55127i	−0.0143683	+	0.00829556i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	106.725	+	184.853i	0.558770	+	0.967818i	0.997599	+	0.0692478i	$0.0220599\pi$
$191$	106.725	+	184.853i	0.558770	+	0.967818i	−0.438829	+	0.898570i	$0.644607\pi$
$192$		0			0
$193$	129.565	−	224.413i	0.671320	−	1.16276i	−0.306211	−	0.951964i	$-0.599061\pi$
$193$	129.565	−	224.413i	0.671320	−	1.16276i	0.977530	−	0.210796i	$-0.0676055\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−174.822			−0.887424			−0.443712	−	0.896170i	$-0.646339\pi$
$197$	−174.822			−0.887424			−0.443712	+	0.896170i	$0.646339\pi$
$198$		0			0
$199$	118.111	+	68.1912i	0.593521	+	0.342669i	0.766488	−	0.642258i	$-0.222002\pi$
$199$	118.111	+	68.1912i	0.593521	+	0.342669i	−0.172968	+	0.984928i	$0.555336\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	159.058	−	79.9883i	0.783535	−	0.394031i
$204$		0			0
$205$	11.6913	+	20.2499i	0.0570306	+	0.0987798i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			292.023i			1.39724i
$210$		0			0
$211$	78.7551			0.373247			0.186623	−	0.982432i	$-0.440246\pi$
$211$	78.7551			0.373247			0.186623	+	0.982432i	$0.440246\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.90730	−	1.67853i	0.0135223	−	0.00780713i
$216$		0			0
$217$	319.407	+	18.4320i	1.47192	+	0.0849400i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.34316	−	2.32642i	0.00607764	−	0.0105268i
$222$		0			0
$223$			13.4235i			0.0601952i	0.999547	+	0.0300976i	$0.00958181\pi$
$223$			13.4235i			0.0601952i	−0.999547	+	0.0300976i	$0.990418\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	170.282	+	98.3125i	0.750142	+	0.433095i	0.825745	−	0.564043i	$-0.190755\pi$
$227$	170.282	+	98.3125i	0.750142	+	0.433095i	−0.0756031	+	0.997138i	$0.524088\pi$
$228$		0			0
$229$	−175.428	+	101.283i	−0.766062	+	0.442286i	−0.831468	−	0.555573i	$-0.812499\pi$
$229$	−175.428	+	101.283i	−0.766062	+	0.442286i	0.0654062	+	0.997859i	$0.479166\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−190.078	−	329.224i	−0.815783	−	1.41298i	−0.908764	−	0.417310i	$-0.862973\pi$
$233$	−190.078	−	329.224i	−0.815783	−	1.41298i	0.0929805	−	0.995668i	$-0.470361\pi$
$234$		0			0
$235$	−16.0007	+	27.7140i	−0.0680880	+	0.117932i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	85.8505			0.359207			0.179604	−	0.983739i	$-0.442518\pi$
$239$	85.8505			0.359207			0.179604	+	0.983739i	$0.442518\pi$
$240$		0			0
$241$	128.636	+	74.2679i	0.533758	+	0.308165i	0.742546	−	0.669796i	$-0.233618\pi$
$241$	128.636	+	74.2679i	0.533758	+	0.308165i	−0.208787	+	0.977961i	$0.566952\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.76708	−	23.8955i	0.0112942	−	0.0975325i
$246$		0			0
$247$	−126.424	−	218.972i	−0.511836	−	0.886526i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	149.761i		−	0.596659i	−0.954463	−	0.298329i	$-0.903571\pi$
$251$		−	149.761i		−	0.596659i	0.954463	−	0.298329i	$-0.0964294\pi$
$252$		0			0
$253$	−58.5925			−0.231591
$254$		0			0
$255$		0			0
$256$		0			0
$257$	61.7360	−	35.6433i	0.240218	−	0.138690i	−0.375059	−	0.927001i	$-0.622378\pi$
$257$	61.7360	−	35.6433i	0.240218	−	0.138690i	0.615277	+	0.788311i	$0.289044\pi$
$258$		0			0
$259$	−60.5143	−	39.7545i	−0.233646	−	0.153492i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−29.6583	+	51.3696i	−0.112769	+	0.195322i	−0.916886	−	0.399150i	$-0.869305\pi$
$263$	−29.6583	+	51.3696i	−0.112769	+	0.195322i	0.804117	+	0.594472i	$0.202639\pi$
$264$		0			0
$265$		−	8.78757i		−	0.0331606i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−430.588	−	248.600i	−1.60070	−	0.924165i	−0.991347	−	0.131266i	$-0.958096\pi$
$269$	−430.588	−	248.600i	−1.60070	−	0.924165i	−0.609353	−	0.792899i	$-0.708571\pi$
$270$		0			0
$271$	−435.450	+	251.407i	−1.60683	+	0.927702i	−0.616753	+	0.787157i	$0.711552\pi$
$271$	−435.450	+	251.407i	−1.60683	+	0.927702i	−0.990074	+	0.140546i	$0.955114\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	128.224	+	222.091i	0.466270	+	0.807604i
$276$		0			0
$277$	−185.233	+	320.833i	−0.668712	+	1.15824i	0.309553	+	0.950882i	$0.399821\pi$
$277$	−185.233	+	320.833i	−0.668712	+	1.15824i	−0.978265	+	0.207360i	$0.933513\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	288.212			1.02566			0.512832	−	0.858489i	$-0.328596\pi$
$281$	288.212			1.02566			0.512832	+	0.858489i	$0.328596\pi$
$282$		0			0
$283$	305.915	+	176.620i	1.08097	+	0.624099i	0.931158	−	0.364616i	$-0.118800\pi$
$283$	305.915	+	176.620i	1.08097	+	0.624099i	0.149813	+	0.988714i	$0.452133\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−149.793	−	297.865i	−0.521927	−	1.03786i
$288$		0			0
$289$	−144.455	−	250.204i	−0.499845	−	0.865757i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			367.107i			1.25292i	0.779452	+	0.626462i	$0.215498\pi$
$293$			367.107i			1.25292i	−0.779452	+	0.626462i	$0.784502\pi$
$294$		0			0
$295$	23.8203			0.0807467
$296$		0			0
$297$		0			0
$298$		0			0
$299$	43.9353	−	25.3660i	0.146941	−	0.0848362i
$300$		0			0
$301$	−42.7650	+	21.5060i	−0.142076	+	0.0714486i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−8.50300	+	14.7276i	−0.0278787	+	0.0482873i
$306$		0			0
$307$			369.042i			1.20209i	0.799214	+	0.601046i	$0.205249\pi$
$307$			369.042i			1.20209i	−0.799214	+	0.601046i	$0.794751\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	358.023	+	206.705i	1.15120	+	0.664645i	0.949179	−	0.314736i	$-0.101916\pi$
$311$	358.023	+	206.705i	1.15120	+	0.664645i	0.202020	+	0.979381i	$0.435249\pi$
$312$		0			0
$313$	−414.383	+	239.244i	−1.32391	+	0.764359i	−0.984350	−	0.176226i	$-0.943611\pi$
$313$	−414.383	+	239.244i	−1.32391	+	0.764359i	−0.339559	+	0.940585i	$0.610278\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−172.202	−	298.263i	−0.543224	−	0.940892i	−0.998716	−	0.0506524i	$-0.983870\pi$
$317$	−172.202	−	298.263i	−0.543224	−	0.940892i	0.455492	−	0.890240i	$-0.349463\pi$
$318$		0			0
$319$	−131.720	+	228.146i	−0.412915	+	0.715190i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	8.44501			0.0261455
$324$		0			0
$325$	−192.296	−	111.022i	−0.591681	−	0.341607i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	250.540	−	381.371i	0.761519	−	1.15918i
$330$		0			0
$331$	−254.688	−	441.133i	−0.769450	−	1.33273i	−0.937861	−	0.347010i	$-0.887197\pi$
$331$	−254.688	−	441.133i	−0.769450	−	1.33273i	0.168411	−	0.985717i	$-0.446136\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			39.8613i			0.118989i
$336$		0			0
$337$	−539.169			−1.59991			−0.799953	−	0.600062i	$-0.795142\pi$
$337$	−539.169			−1.59991			−0.799953	+	0.600062i	$0.795142\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−409.983	+	236.704i	−1.20230	+	0.694147i
$342$		0			0
$343$	−59.0194	+	337.884i	−0.172068	+	0.985085i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−338.796	+	586.813i	−0.976359	+	1.69110i	−0.300982	+	0.953630i	$0.597314\pi$
$347$	−338.796	+	586.813i	−0.976359	+	1.69110i	−0.675376	+	0.737473i	$0.736019\pi$
$348$		0			0
$349$			380.017i			1.08887i	0.838802	+	0.544437i	$0.183257\pi$
$349$			380.017i			1.08887i	−0.838802	+	0.544437i	$0.816743\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−365.769	−	211.177i	−1.03617	−	0.598235i	−0.117427	−	0.993082i	$-0.537464\pi$
$353$	−365.769	−	211.177i	−1.03617	−	0.598235i	−0.918747	+	0.394846i	$0.870798\pi$
$354$		0			0
$355$	−56.9392	+	32.8739i	−0.160392	+	0.0926025i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−153.041	−	265.076i	−0.426299	−	0.738372i	0.570242	−	0.821477i	$-0.306850\pi$
$359$	−153.041	−	265.076i	−0.426299	−	0.738372i	−0.996541	+	0.0831051i	$0.973516\pi$
$360$		0			0
$361$	216.939	−	375.750i	0.600940	−	1.04086i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.12574			−0.00856368
$366$		0			0
$367$	409.023	+	236.149i	1.11450	+	0.643459i	0.939992	−	0.341196i	$-0.110832\pi$
$367$	409.023	+	236.149i	1.11450	+	0.643459i	0.174512	+	0.984655i	$0.444165\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.21873	+	125.093i	−0.0194575	+	0.337178i
$372$		0			0
$373$	−208.308	−	360.799i	−0.558465	−	0.967291i	−0.997625	−	0.0688814i	$-0.978057\pi$
$373$	−208.308	−	360.799i	−0.558465	−	0.967291i	0.439159	−	0.898409i	$-0.355276\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	228.098i		−	0.605035i
$378$		0			0
$379$	109.766			0.289621			0.144811	−	0.989459i	$-0.453743\pi$
$379$	109.766			0.289621			0.144811	+	0.989459i	$0.453743\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	231.360	−	133.576i	0.604073	−	0.348762i	−0.166569	−	0.986030i	$-0.553269\pi$
$383$	231.360	−	133.576i	0.604073	−	0.348762i	0.770642	+	0.637268i	$0.219935\pi$
$384$		0			0
$385$	15.9916	+	31.7994i	0.0415366	+	0.0825959i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−49.6383	+	85.9761i	−0.127605	+	0.221018i	−0.922748	−	0.385403i	$-0.874062\pi$
$389$	−49.6383	+	85.9761i	−0.127605	+	0.221018i	0.795143	+	0.606422i	$0.207396\pi$
$390$		0			0
$391$			1.69443i			0.00433359i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−22.5534	−	13.0212i	−0.0570972	−	0.0329651i
$396$		0			0
$397$	−303.640	+	175.307i	−0.764837	+	0.441579i	−0.831030	−	0.556228i	$-0.812248\pi$
$397$	−303.640	+	175.307i	−0.764837	+	0.441579i	0.0661929	+	0.997807i	$0.478915\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	336.391	+	582.647i	0.838881	+	1.45299i	0.890831	+	0.454335i	$0.150123\pi$
$401$	336.391	+	582.647i	0.838881	+	1.45299i	−0.0519493	+	0.998650i	$0.516543\pi$
$402$		0			0
$403$	204.949	−	354.982i	0.508558	−	0.880849i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	107.136			0.263233
$408$		0			0
$409$	459.393	+	265.231i	1.12321	+	0.648486i	0.942219	−	0.334999i	$-0.108736\pi$
$409$	459.393	+	265.231i	1.12321	+	0.648486i	0.180992	+	0.983485i	$0.442069\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−339.087	−	19.5677i	−0.821034	−	0.0473793i
$414$		0			0
$415$	−28.4894	−	49.3450i	−0.0686490	−	0.118904i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			164.046i			0.391517i	0.980652	+	0.195759i	$0.0627169\pi$
$419$			164.046i			0.391517i	−0.980652	+	0.195759i	$0.937283\pi$
$420$		0			0
$421$	−278.128			−0.660637			−0.330319	−	0.943870i	$-0.607156\pi$
$421$	−278.128			−0.660637			−0.330319	+	0.943870i	$0.607156\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.42264	−	3.70811i	0.0151121	−	0.00872497i
$426$		0			0
$427$	133.140	−	202.666i	0.311804	−	0.474628i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−347.432	+	601.770i	−0.806107	+	1.39622i	0.109435	+	0.993994i	$0.465096\pi$
$431$	−347.432	+	601.770i	−0.806107	+	1.39622i	−0.915541	+	0.402224i	$0.868237\pi$
$432$		0			0
$433$		−	324.716i		−	0.749921i	−0.927041	−	0.374960i	$-0.877656\pi$
$433$		−	324.716i		−	0.749921i	0.927041	−	0.374960i	$-0.122344\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	138.120	+	79.7435i	0.316064	+	0.182479i
$438$		0			0
$439$	8.14985	−	4.70532i	0.0185646	−	0.0107183i	−0.490689	−	0.871335i	$-0.663255\pi$
$439$	8.14985	−	4.70532i	0.0185646	−	0.0107183i	0.509254	+	0.860617i	$0.329922\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−164.820	−	285.477i	−0.372055	−	0.644418i	0.617827	−	0.786314i	$-0.288013\pi$
$443$	−164.820	−	285.477i	−0.372055	−	0.644418i	−0.989882	+	0.141896i	$0.954680\pi$
$444$		0			0
$445$	7.70792	−	13.3505i	0.0173212	−	0.0300011i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	127.813			0.284662			0.142331	−	0.989819i	$-0.454540\pi$
$449$	127.813			0.284662			0.142331	+	0.989819i	$0.454540\pi$
$450$		0			0
$451$	427.246	+	246.670i	0.947330	+	0.546941i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−25.7579	−	16.9215i	−0.0566107	−	0.0371901i
$456$		0			0
$457$	43.0590	+	74.5804i	0.0942210	+	0.163196i	0.909283	−	0.416178i	$-0.136631\pi$
$457$	43.0590	+	74.5804i	0.0942210	+	0.163196i	−0.815062	+	0.579373i	$0.803297\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			397.368i			0.861970i	0.902359	+	0.430985i	$0.141834\pi$
$461$			397.368i			0.861970i	−0.902359	+	0.430985i	$0.858166\pi$
$462$		0			0
$463$	−190.911			−0.412335			−0.206167	−	0.978517i	$-0.566099\pi$
$463$	−190.911			−0.412335			−0.206167	+	0.978517i	$0.566099\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−649.505	+	374.992i	−1.39080	+	0.802981i	−0.993404	−	0.114665i	$-0.963420\pi$
$467$	−649.505	+	374.992i	−1.39080	+	0.802981i	−0.397399	+	0.917646i	$0.630087\pi$
$468$		0			0
$469$	32.7449	−	567.435i	0.0698185	−	1.20988i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	35.4149	−	61.3403i	0.0748729	−	0.129684i
$474$		0			0
$475$		−	698.045i		−	1.46957i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−146.651	−	84.6693i	−0.306162	−	0.176763i	0.339046	−	0.940770i	$-0.389896\pi$
$479$	−146.651	−	84.6693i	−0.306162	−	0.176763i	−0.645208	+	0.764007i	$0.723229\pi$
$480$		0			0
$481$	−80.3351	+	46.3815i	−0.167017	+	0.0964272i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.4227	+	23.2488i	0.0276756	+	0.0479356i
$486$		0			0
$487$	−181.494	+	314.356i	−0.372677	+	0.645496i	−0.989976	−	0.141233i	$-0.954893\pi$
$487$	−181.494	+	314.356i	−0.372677	+	0.645496i	0.617299	+	0.786728i	$0.288227\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	749.523			1.52652			0.763262	−	0.646089i	$-0.223597\pi$
$491$	749.523			1.52652			0.763262	+	0.646089i	$0.223597\pi$
$492$		0			0
$493$	6.59773	+	3.80920i	0.0133828	+	0.00772657i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	837.548	−	421.193i	1.68521	−	0.847472i
$498$		0			0
$499$	72.9754	+	126.397i	0.146243	+	0.253301i	0.929836	−	0.367974i	$-0.119948\pi$
$499$	72.9754	+	126.397i	0.146243	+	0.253301i	−0.783593	+	0.621275i	$0.786615\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	820.446i		−	1.63111i	−0.578683	−	0.815553i	$-0.696433\pi$
$503$		−	820.446i		−	1.63111i	0.578683	−	0.815553i	$-0.303567\pi$
$504$		0			0
$505$	73.5999			0.145742
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−148.845	+	85.9359i	−0.292427	+	0.168833i	−0.639036	−	0.769177i	$-0.720666\pi$
$509$	−148.845	+	85.9359i	−0.292427	+	0.168833i	0.346609	+	0.938010i	$0.387333\pi$
$510$		0			0
$511$	44.4957	+	2.56770i	0.0870757	+	0.00502486i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	11.1639	−	19.3364i	0.0216775	−	0.0375465i
$516$		0			0
$517$			675.187i			1.30597i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−499.992	−	288.671i	−0.959678	−	0.554070i	−0.0636038	−	0.997975i	$-0.520259\pi$
$521$	−499.992	−	288.671i	−0.959678	−	0.554070i	−0.896074	+	0.443905i	$0.853593\pi$
$522$		0			0
$523$	−67.2420	+	38.8222i	−0.128570	+	0.0742298i	−0.562905	−	0.826521i	$-0.690316\pi$
$523$	−67.2420	+	38.8222i	−0.128570	+	0.0742298i	0.434336	+	0.900751i	$0.356983\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.84523	+	11.8563i	0.0129890	+	0.0224977i
$528$		0			0
$529$	248.500	−	430.415i	0.469754	−	0.813638i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−427.157			−0.801420
$534$		0			0
$535$	−79.8422	−	46.0969i	−0.149238	−	0.0861624i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−201.521	−	465.809i	−0.373880	−	0.864209i
$540$		0			0
$541$	36.9433	+	63.9877i	0.0682871	+	0.118277i	0.898147	−	0.439695i	$-0.144913\pi$
$541$	36.9433	+	63.9877i	0.0682871	+	0.118277i	−0.829860	+	0.557971i	$0.811580\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			71.3158i			0.130855i
$546$		0			0
$547$	−47.2310			−0.0863456			−0.0431728	−	0.999068i	$-0.513747\pi$
$547$	−47.2310			−0.0863456			−0.0431728	+	0.999068i	$0.513747\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	621.005	−	358.537i	1.12705	−	0.650703i
$552$		0			0
$553$	310.356	+	203.887i	0.561223	+	0.368692i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	466.647	−	808.257i	0.837787	−	1.45109i	−0.0539545	−	0.998543i	$-0.517183\pi$
$557$	466.647	−	808.257i	0.837787	−	1.45109i	0.891741	−	0.452546i	$-0.149484\pi$
$558$		0			0
$559$			61.3276i			0.109709i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	669.452	+	386.509i	1.18908	+	0.686516i	0.958098	−	0.286442i	$-0.0924725\pi$
$563$	669.452	+	386.509i	1.18908	+	0.686516i	0.230983	+	0.972958i	$0.425806\pi$
$564$		0			0
$565$	84.3484	−	48.6986i	0.149289	−	0.0861922i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	119.707	+	207.339i	0.210382	+	0.364392i	0.951834	−	0.306613i	$-0.0991959\pi$
$569$	119.707	+	207.339i	0.210382	+	0.364392i	−0.741452	+	0.671006i	$0.765863\pi$
$570$		0			0
$571$	−78.9427	+	136.733i	−0.138253	+	0.239462i	−0.926836	−	0.375467i	$-0.877482\pi$
$571$	−78.9427	+	136.733i	−0.138253	+	0.239462i	0.788582	+	0.614929i	$0.210816\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	140.058			0.243579
$576$		0			0
$577$	428.402	+	247.338i	0.742465	+	0.428663i	0.822965	−	0.568092i	$-0.192318\pi$
$577$	428.402	+	247.338i	0.742465	+	0.428663i	−0.0804997	+	0.996755i	$0.525652\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	365.017	+	725.841i	0.628257	+	1.24930i
$582$		0			0
$583$	−92.7031	−	160.567i	−0.159011	−	0.275414i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			185.278i			0.315635i	0.987468	+	0.157818i	$0.0504458\pi$
$587$			185.278i			0.315635i	−0.987468	+	0.157818i	$0.949554\pi$
$588$		0			0
$589$	1288.60			2.18778
$590$		0			0
$591$		0			0
$592$		0			0
$593$	371.431	−	214.446i	0.626359	−	0.361628i	−0.152982	−	0.988229i	$-0.548888\pi$
$593$	371.431	−	214.446i	0.626359	−	0.361628i	0.779340	+	0.626601i	$0.215554\pi$
$594$		0			0
$595$	0.919606	−	0.462459i	0.00154556	−	0.000777243i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	322.911	−	559.299i	0.539084	−	0.933721i	−0.459869	−	0.887987i	$-0.652104\pi$
$599$	322.911	−	559.299i	0.539084	−	0.933721i	0.998954	−	0.0457347i	$-0.0145629\pi$
$600$		0			0
$601$			872.204i			1.45125i	0.688088	+	0.725627i	$0.258450\pi$
$601$			872.204i			1.45125i	−0.688088	+	0.725627i	$0.741550\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.83139	+	3.36675i	0.00963866	+	0.00556488i
$606$		0			0
$607$	203.992	−	117.775i	0.336065	−	0.194027i	−0.322465	−	0.946581i	$-0.604512\pi$
$607$	203.992	−	117.775i	0.336065	−	0.194027i	0.658531	+	0.752554i	$0.271178\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−292.304	−	506.285i	−0.478402	−	0.828617i
$612$		0			0
$613$	333.951	−	578.421i	0.544782	−	0.943590i	−0.453838	−	0.891084i	$-0.649946\pi$
$613$	333.951	−	578.421i	0.544782	−	0.943590i	0.998621	−	0.0525064i	$-0.0167210\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	257.921			0.418025			0.209012	−	0.977913i	$-0.432975\pi$
$617$	257.921			0.418025			0.209012	+	0.977913i	$0.432975\pi$
$618$		0			0
$619$	−200.464	−	115.738i	−0.323852	−	0.186976i	0.329257	−	0.944241i	$-0.393202\pi$
$619$	−200.464	−	115.738i	−0.323852	−	0.186976i	−0.653108	+	0.757265i	$0.726535\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−120.691	+	183.716i	−0.193726	+	0.294889i
$624$		0			0
$625$	−303.491	−	525.663i	−0.485586	−	0.841060i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	3.09825i		−	0.00492568i
$630$		0			0
$631$	−146.992			−0.232951			−0.116476	−	0.993194i	$-0.537160\pi$
$631$	−146.992			−0.232951			−0.116476	+	0.993194i	$0.537160\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	98.3887	−	56.8047i	0.154943	−	0.0894563i
$636$		0			0
$637$	352.769	+	262.041i	0.553797	+	0.411367i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.09951	+	5.36851i	−0.00483543	+	0.00837521i	−0.868433	−	0.495807i	$-0.834873\pi$
$641$	−3.09951	+	5.36851i	−0.00483543	+	0.00837521i	0.863598	+	0.504182i	$0.168206\pi$
$642$		0			0
$643$		−	436.122i		−	0.678261i	−0.940739	−	0.339130i	$-0.889867\pi$
$643$		−	436.122i		−	0.678261i	0.940739	−	0.339130i	$-0.110133\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	77.8134	+	44.9256i	0.120268	+	0.0694368i	0.558927	−	0.829217i	$-0.311213\pi$
$647$	77.8134	+	44.9256i	0.120268	+	0.0694368i	−0.438659	+	0.898654i	$0.644546\pi$
$648$		0			0
$649$	435.244	−	251.288i	0.670639	−	0.387193i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−25.9180	−	44.8913i	−0.0396907	−	0.0687462i	0.845498	−	0.533979i	$-0.179304\pi$
$653$	−25.9180	−	44.8913i	−0.0396907	−	0.0687462i	−0.885188	+	0.465233i	$0.845971\pi$
$654$		0			0
$655$	−5.34294	+	9.25425i	−0.00815716	+	0.0141286i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−212.500			−0.322459			−0.161229	−	0.986917i	$-0.551546\pi$
$659$	−212.500			−0.322459			−0.161229	+	0.986917i	$0.551546\pi$
$660$		0			0
$661$	−1000.48	−	577.625i	−1.51358	−	0.873865i	−0.999874	−	0.0158974i	$-0.994939\pi$
$661$	−1000.48	−	577.625i	−1.51358	−	0.873865i	−0.513704	−	0.857967i	$-0.671727\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.58169	−	96.7249i	0.00839351	−	0.145451i
$666$		0			0
$667$	71.9381	+	124.601i	0.107853	+	0.186807i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			358.805i			0.534731i
$672$		0			0
$673$	563.787			0.837722			0.418861	−	0.908050i	$-0.362429\pi$
$673$	563.787			0.837722			0.418861	+	0.908050i	$0.362429\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−417.611	+	241.108i	−0.616855	+	0.356141i	−0.775643	−	0.631171i	$-0.782574\pi$
$677$	−417.611	+	241.108i	−0.616855	+	0.356141i	0.158789	+	0.987313i	$0.449241\pi$
$678$		0			0
$679$	−171.977	−	341.978i	−0.253279	−	0.503649i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−30.2784	+	52.4437i	−0.0443315	+	0.0767844i	−0.887340	−	0.461116i	$-0.847449\pi$
$683$	−30.2784	+	52.4437i	−0.0443315	+	0.0767844i	0.843008	+	0.537901i	$0.180782\pi$
$684$		0			0
$685$		−	118.686i		−	0.173264i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	139.026	+	80.2666i	0.201779	+	0.116497i
$690$		0			0
$691$	97.0468	−	56.0300i	0.140444	−	0.0810853i	−0.428132	−	0.903716i	$-0.640828\pi$
$691$	97.0468	−	56.0300i	0.140444	−	0.0810853i	0.568576	+	0.822631i	$0.307495\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	45.7484	+	79.2386i	0.0658251	+	0.114012i
$696$		0			0
$697$	7.13345	−	12.3555i	0.0102345	−	0.0177267i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1102.36			−1.57255			−0.786274	−	0.617878i	$-0.787992\pi$
$701$	−1102.36			−1.57255			−0.786274	+	0.617878i	$0.787992\pi$
$702$		0			0
$703$	−252.550	−	145.810i	−0.359247	−	0.207411i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1047.71	−	60.4601i	−1.48191	−	0.0855164i
$708$		0			0
$709$	337.594	+	584.730i	0.476155	+	0.824725i	0.999627	−	0.0273180i	$-0.00869667\pi$
$709$	337.594	+	584.730i	0.476155	+	0.824725i	−0.523471	+	0.852043i	$0.675363\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			258.549i			0.362622i
$714$		0			0
$715$	45.6023			0.0637794
$716$		0			0
$717$		0			0
$718$		0			0
$719$	194.756	−	112.443i	0.270871	−	0.156387i	−0.358412	−	0.933563i	$-0.616682\pi$
$719$	194.756	−	112.443i	0.270871	−	0.156387i	0.629283	+	0.777176i	$0.283348\pi$
$720$		0			0
$721$	−174.805	+	266.088i	−0.242448	+	0.369054i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	314.860	−	545.353i	0.434289	−	0.752211i
$726$		0			0
$727$		−	1063.86i		−	1.46336i	−0.681648	−	0.731680i	$-0.738736\pi$
$727$		−	1063.86i		−	1.46336i	0.681648	−	0.731680i	$-0.261264\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.77390	−	1.02416i	−0.00242667	−	0.00140104i
$732$		0			0
$733$	291.563	−	168.334i	0.397767	−	0.229651i	−0.287753	−	0.957705i	$-0.592908\pi$
$733$	291.563	−	168.334i	0.397767	−	0.229651i	0.685520	+	0.728054i	$0.259575\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	420.511	+	728.346i	0.570571	+	0.988258i
$738$		0			0
$739$	−602.668	+	1043.85i	−0.815519	+	1.41252i	0.0934364	+	0.995625i	$0.470215\pi$
$739$	−602.668	+	1043.85i	−0.815519	+	1.41252i	−0.908955	+	0.416894i	$0.863119\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−521.516			−0.701906			−0.350953	−	0.936393i	$-0.614142\pi$
$743$	−521.516			−0.701906			−0.350953	+	0.936393i	$0.614142\pi$
$744$		0			0
$745$	−27.0472	−	15.6157i	−0.0363050	−	0.0209607i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1098.70	+	721.788i	1.46689	+	0.963669i
$750$		0			0
$751$	494.756	+	856.942i	0.658796	+	1.14107i	0.980928	+	0.194374i	$0.0622674\pi$
$751$	494.756	+	856.942i	0.658796	+	1.14107i	−0.322131	+	0.946695i	$0.604399\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	38.9186i		−	0.0515478i
$756$		0			0
$757$	265.725			0.351024			0.175512	−	0.984477i	$-0.443842\pi$
$757$	265.725			0.351024			0.175512	+	0.984477i	$0.443842\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	42.5450	−	24.5634i	0.0559067	−	0.0322778i	−0.471786	−	0.881713i	$-0.656391\pi$
$761$	42.5450	−	24.5634i	0.0559067	−	0.0322778i	0.527693	+	0.849435i	$0.323057\pi$
$762$		0			0
$763$	58.5838	−	1015.20i	0.0767808	−	1.33053i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−217.577	+	376.854i	−0.283673	+	0.491336i
$768$		0			0
$769$		−	831.567i		−	1.08136i	−0.841228	−	0.540681i	$-0.818167\pi$
$769$		−	831.567i		−	1.08136i	0.841228	−	0.540681i	$-0.181833\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1211.82	+	699.646i	1.56769	+	0.905105i	0.996438	+	0.0843281i	$0.0268744\pi$
$773$	1211.82	+	699.646i	1.56769	+	0.905105i	0.571249	+	0.820777i	$0.306459\pi$
$774$		0			0
$775$	980.013	−	565.811i	1.26453	−	0.730079i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−671.429	−	1162.95i	−0.861911	−	1.49287i
$780$		0			0
$781$	−693.596	+	1201.34i	−0.888087	+	1.53821i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	46.4298			0.0591462
$786$		0			0
$787$	123.205	+	71.1325i	0.156550	+	0.0903843i	0.576229	−	0.817289i	$-0.304524\pi$
$787$	123.205	+	71.1325i	0.156550	+	0.0903843i	−0.419678	+	0.907673i	$0.637857\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1240.72	+	623.946i	−1.56855	+	0.788806i
$792$		0			0
$793$	−155.335	−	269.047i	−0.195882	−	0.339278i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	500.787i		−	0.628340i	−0.949367	−	0.314170i	$-0.898274\pi$
$797$		−	500.787i		−	0.628340i	0.949367	−	0.314170i	$-0.101726\pi$
$798$		0			0
$799$	19.5257			0.0244377
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−57.1136	+	32.9746i	−0.0711253	+	0.0410642i
$804$		0			0
$805$	19.4072	+	1.11993i	0.0241083	+	0.00139121i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−467.439	+	809.627i	−0.577798	+	1.00078i	0.417934	+	0.908478i	$0.362754\pi$
$809$	−467.439	+	809.627i	−0.577798	+	1.00078i	−0.995731	+	0.0922977i	$0.970579\pi$
$810$		0			0
$811$			495.665i			0.611178i	0.952164	+	0.305589i	$0.0988533\pi$
$811$			495.665i			0.611178i	−0.952164	+	0.305589i	$0.901147\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−73.7930	−	42.6044i	−0.0905435	−	0.0522753i
$816$		0			0
$817$	−166.966	+	96.3981i	−0.204365	+	0.117990i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	325.872	+	564.426i	0.396920	+	0.687486i	0.993344	−	0.115183i	$-0.0367456\pi$
$821$	325.872	+	564.426i	0.396920	+	0.687486i	−0.596424	+	0.802670i	$0.703412\pi$
$822$		0			0
$823$	71.9474	−	124.617i	0.0874209	−	0.151417i	−0.818999	−	0.573794i	$-0.805471\pi$
$823$	71.9474	−	124.617i	0.0874209	−	0.151417i	0.906420	+	0.422377i	$0.138804\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−211.134			−0.255302			−0.127651	−	0.991819i	$-0.540744\pi$
$827$	−211.134			−0.255302			−0.127651	+	0.991819i	$0.540744\pi$
$828$		0			0
$829$	−1164.24	−	672.177i	−1.40440	−	0.810828i	−0.409556	−	0.912285i	$-0.634316\pi$
$829$	−1164.24	−	672.177i	−1.40440	−	0.810828i	−0.994840	+	0.101457i	$0.967650\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−13.4707	+	5.82779i	−0.0161713	+	0.00699614i
$834$		0			0
$835$	−15.5215	−	26.8841i	−0.0185887	−	0.0321965i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	256.252i		−	0.305425i	−0.988271	−	0.152713i	$-0.951199\pi$
$839$		−	256.252i		−	0.305425i	0.988271	−	0.152713i	$-0.0488009\pi$
$840$		0			0
$841$	−194.113			−0.230812
$842$		0			0
$843$		0			0
$844$		0			0
$845$	37.6558	−	21.7406i	0.0445630	−	0.0257285i
$846$		0			0
$847$	−80.2455	−	52.7168i	−0.0947408	−	0.0622395i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	29.2558	−	50.6725i	0.0343781	−	0.0595447i
$852$		0			0
$853$			674.045i			0.790206i	0.918637	+	0.395103i	$0.129291\pi$
$853$			674.045i			0.790206i	−0.918637	+	0.395103i	$0.870709\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−342.885	−	197.965i	−0.400099	−	0.230997i	0.286428	−	0.958102i	$-0.407532\pi$
$857$	−342.885	−	197.965i	−0.400099	−	0.230997i	−0.686527	+	0.727104i	$0.740866\pi$
$858$		0			0
$859$	−926.466	+	534.896i	−1.07854	+	0.622696i	−0.930502	−	0.366286i	$-0.880629\pi$
$859$	−926.466	+	534.896i	−1.07854	+	0.622696i	−0.148038	+	0.988982i	$0.547296\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−202.670	−	351.034i	−0.234843	−	0.406760i	0.724384	−	0.689397i	$-0.242124\pi$
$863$	−202.670	−	351.034i	−0.234843	−	0.406760i	−0.959227	+	0.282637i	$0.908791\pi$
$864$		0			0
$865$	−53.9282	+	93.4064i	−0.0623447	+	0.107984i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−549.461			−0.632292
$870$		0			0
$871$	−630.635	−	364.097i	−0.724036	−	0.418022i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−76.8237	−	152.765i	−0.0877986	−	0.174588i
$876$		0			0
$877$	440.516	+	762.996i	0.502299	+	0.870007i	0.999996	+	0.00265646i	$0.000845578\pi$
$877$	440.516	+	762.996i	0.502299	+	0.870007i	−0.497698	+	0.867351i	$0.665821\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	330.169i		−	0.374767i	−0.982287	−	0.187383i	$-0.939999\pi$
$881$		−	330.169i		−	0.374767i	0.982287	−	0.187383i	$-0.0600007\pi$
$882$		0			0
$883$	−813.993			−0.921850			−0.460925	−	0.887439i	$-0.652482\pi$
$883$	−813.993			−0.921850			−0.460925	+	0.887439i	$0.652482\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−321.939	+	185.872i	−0.362953	+	0.209551i	−0.670375	−	0.742022i	$-0.733867\pi$
$887$	−321.939	+	185.872i	−0.362953	+	0.209551i	0.307422	+	0.951573i	$0.400534\pi$
$888$		0			0
$889$	−1447.25	+	727.805i	−1.62795	+	0.818679i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	918.919	−	1591.61i	1.02902	−	1.78232i
$894$		0			0
$895$			36.8876i			0.0412152i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1006.73	+	581.236i	1.11983	+	0.646536i
$900$		0			0
$901$	−4.64341	+	2.68088i	−0.00515362	+	0.00297545i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−46.2899	−	80.1765i	−0.0511491	−	0.0885928i
$906$		0			0
$907$	−358.081	+	620.214i	−0.394797	+	0.683809i	−0.993075	−	0.117480i	$-0.962518\pi$
$907$	−358.081	+	620.214i	−0.394797	+	0.683809i	0.598278	+	0.801289i	$0.295852\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−161.244			−0.176997			−0.0884985	−	0.996076i	$-0.528207\pi$
$911$	−161.244			−0.176997			−0.0884985	+	0.996076i	$0.528207\pi$
$912$		0			0
$913$	−1041.12	−	601.088i	−1.14032	−	0.658366i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	83.6601	−	127.347i	0.0912324	−	0.138874i
$918$		0			0
$919$	575.804	+	997.322i	0.626555	+	1.08523i	0.988238	+	0.152924i	$0.0488690\pi$
$919$	575.804	+	997.322i	0.626555	+	1.08523i	−0.361683	+	0.932301i	$0.617798\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	1201.09i		−	1.30129i
$924$		0			0
$925$	−256.094			−0.276859
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−784.559	+	452.965i	−0.844519	+	0.487583i	−0.858798	−	0.512315i	$-0.828788\pi$
$929$	−784.559	+	452.965i	−0.844519	+	0.487583i	0.0142785	+	0.999898i	$0.495455\pi$
$930$		0			0
$931$	−158.913	+	1372.32i	−0.170691	+	1.47402i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.761551	+	1.31904i	−0.000814493	+	0.00141074i
$936$		0			0
$937$			1077.46i			1.14991i	0.818186	+	0.574954i	$0.194980\pi$
$937$			1077.46i			1.14991i	−0.818186	+	0.574954i	$0.805020\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−293.347	−	169.364i	−0.311740	−	0.179983i	0.335965	−	0.941874i	$-0.390938\pi$
$941$	−293.347	−	169.364i	−0.311740	−	0.179983i	−0.647705	+	0.761891i	$0.724271\pi$
$942$		0			0
$943$	233.338	−	134.718i	0.247442	−	0.142861i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	412.641	+	714.714i	0.435735	+	0.754714i	0.997355	−	0.0726805i	$-0.0231553\pi$
$947$	412.641	+	714.714i	0.435735	+	0.754714i	−0.561621	+	0.827395i	$0.689822\pi$
$948$		0			0
$949$	28.5509	−	49.4515i	0.0300852	−	0.0521091i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	156.655			0.164381			0.0821905	−	0.996617i	$-0.473808\pi$
$953$	156.655			0.164381			0.0821905	+	0.996617i	$0.473808\pi$
$954$		0			0
$955$	90.7484	+	52.3936i	0.0950245	+	0.0548624i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−97.4966	+	1689.52i	−0.101665	+	1.76175i
$960$		0			0
$961$	563.995	+	976.869i	0.586884	+	1.01651i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	127.212i		−	0.131826i
$966$		0			0
$967$	−1148.52			−1.18771			−0.593856	−	0.804572i	$-0.702395\pi$
$967$	−1148.52			−1.18771			−0.593856	+	0.804572i	$0.702395\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1073.94	−	620.041i	1.10602	−	0.638559i	0.168222	−	0.985749i	$-0.446197\pi$
$971$	1073.94	−	620.041i	1.10602	−	0.638559i	0.937795	+	0.347190i	$0.112864\pi$
$972$		0			0
$973$	−586.147	−	1165.56i	−0.602412	−	1.19790i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	117.611	−	203.708i	0.120379	−	0.208503i	−0.799538	−	0.600616i	$-0.794922\pi$
$977$	117.611	−	203.708i	0.120379	−	0.208503i	0.919917	+	0.392112i	$0.128256\pi$
$978$		0			0
$979$		−	325.254i		−	0.332231i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1298.66	−	749.780i	−1.32112	−	0.762747i	−0.337210	−	0.941429i	$-0.609483\pi$
$983$	−1298.66	−	749.780i	−1.32112	−	0.762747i	−0.983907	+	0.178682i	$0.942817\pi$
$984$		0			0
$985$	−74.3258	+	42.9120i	−0.0754577	+	0.0435655i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−19.3416	−	33.5007i	−0.0195568	−	0.0338733i
$990$		0			0
$991$	−197.226	+	341.606i	−0.199017	+	0.344708i	−0.948210	−	0.317644i	$-0.897108\pi$
$991$	−197.226	+	341.606i	−0.199017	+	0.344708i	0.749193	+	0.662352i	$0.230442\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	66.9530			0.0672894
$996$		0			0
$997$	−885.726	−	511.374i	−0.888391	−	0.512913i	−0.0149751	−	0.999888i	$-0.504767\pi$
$997$	−885.726	−	511.374i	−0.888391	−	0.512913i	−0.873416	+	0.486975i	$0.838100\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.by.a.73.2		8
3.2	odd	2		168.3.z.a.73.3	✓	8
4.3	odd	2		1008.3.cg.n.577.2		8
7.3	odd	6		3528.3.f.f.2449.4		8
7.4	even	3		3528.3.f.f.2449.5		8
7.5	odd	6	inner	504.3.by.a.145.2		8
12.11	even	2		336.3.bh.h.241.3		8
21.2	odd	6		1176.3.z.d.313.2		8
21.5	even	6		168.3.z.a.145.3	yes	8
21.11	odd	6		1176.3.f.a.97.7		8
21.17	even	6		1176.3.f.a.97.2		8
21.20	even	2		1176.3.z.d.913.2		8
28.19	even	6		1008.3.cg.n.145.2		8
84.11	even	6		2352.3.f.k.97.3		8
84.47	odd	6		336.3.bh.h.145.3		8
84.59	odd	6		2352.3.f.k.97.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.z.a.73.3	✓	8	3.2	odd	2
168.3.z.a.145.3	yes	8	21.5	even	6
336.3.bh.h.145.3		8	84.47	odd	6
336.3.bh.h.241.3		8	12.11	even	2
504.3.by.a.73.2		8	1.1	even	1	trivial
504.3.by.a.145.2		8	7.5	odd	6	inner
1008.3.cg.n.145.2		8	28.19	even	6
1008.3.cg.n.577.2		8	4.3	odd	2
1176.3.f.a.97.2		8	21.17	even	6
1176.3.f.a.97.7		8	21.11	odd	6
1176.3.z.d.313.2		8	21.2	odd	6
1176.3.z.d.913.2		8	21.20	even	2
2352.3.f.k.97.3		8	84.11	even	6
2352.3.f.k.97.6		8	84.59	odd	6
3528.3.f.f.2449.4		8	7.3	odd	6
3528.3.f.f.2449.5		8	7.4	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.by (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.425150 - 0.245461i) q^{5} +(-6.25375 + 3.14494i) q^{7} +(5.17890 - 8.97011i) q^{11} +8.96825i q^{13} +(-0.259406 - 0.149768i) q^{17} +(-24.4164 + 14.0968i) q^{19} +(-2.82843 - 4.89898i) q^{23} +(-12.3795 + 21.4419i) q^{25} -25.4340 q^{29} +(-39.5821 - 22.8527i) q^{31} +(-1.88682 + 2.87212i) q^{35} +(5.17174 + 8.95772i) q^{37} +47.6299i q^{41} +6.83830 q^{43} +(-56.4531 + 32.5932i) q^{47} +(29.2187 - 39.3353i) q^{49} +(8.95008 - 15.5020i) q^{53} -5.08486i q^{55} +(42.0210 + 24.2608i) q^{59} +(-30.0000 + 17.3205i) q^{61} +(2.20135 + 3.81285i) q^{65} +(-40.5985 + 70.3186i) q^{67} -133.927 q^{71} +(-5.51407 - 3.18355i) q^{73} +(-4.17706 + 72.3841i) q^{77} +(-26.5241 - 45.9410i) q^{79} -116.065i q^{83} -0.147049 q^{85} +(27.1948 - 15.7009i) q^{89} +(-28.2046 - 56.0852i) q^{91} +(-6.92041 + 11.9865i) q^{95} +54.6836i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{5} - 4 q^{7} - 14 q^{11} - 12 q^{17} + 78 q^{19} - 6 q^{25} + 4 q^{29} - 24 q^{31} + 156 q^{35} + 50 q^{37} - 20 q^{43} - 12 q^{47} + 220 q^{49} + 50 q^{53} + 186 q^{59} - 240 q^{61} + 148 q^{65}+ \cdots - 144 q^{95}+O(q^{100}) \) 8 * q - 6 * q^5 - 4 * q^7 - 14 * q^11 - 12 * q^17 + 78 * q^19 - 6 * q^25 + 4 * q^29 - 24 * q^31 + 156 * q^35 + 50 * q^37 - 20 * q^43 - 12 * q^47 + 220 * q^49 + 50 * q^53 + 186 * q^59 - 240 * q^61 + 148 * q^65 + 34 * q^67 - 424 * q^71 + 294 * q^73 - 126 * q^77 - 40 * q^79 - 232 * q^85 + 132 * q^89 - 378 * q^91 - 144 * q^95

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