LMFDB - Embedded newform 468.4.t.g.433.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,4,Mod(361,468)] 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("468.361"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(468, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	468.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,-36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$27.6128938827$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 51x^{6} - 224x^{5} + 2520x^{4} - 5712x^{3} + 16675x^{2} + 9072x + 6561 $ x^8 + 51x^6 - 224x^5 + 2520x^4 - 5712x^3 + 16675x^2 + 9072x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			433.3
Root			$1.73860 - 3.01134i$ of defining polynomial
Character	$\chi$	$=$	468.433
Dual form			468.4.t.g.361.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+11.8097i q^{5} +(-27.8750 + 16.0936i) q^{7} +(10.4661 + 6.04263i) q^{11} +(-4.16590 + 46.6867i) q^{13} +(-44.8791 - 77.7328i) q^{17} +(-16.6029 + 9.58572i) q^{19} +(-7.88869 + 13.6636i) q^{23} -14.4680 q^{25} +(131.197 - 227.240i) q^{29} -84.0297i q^{31} +(-190.060 - 329.194i) q^{35} +(-234.864 - 135.599i) q^{37} +(-143.088 - 82.6122i) q^{41} +(135.153 + 234.092i) q^{43} +238.811i q^{47} +(346.511 - 600.174i) q^{49} +94.2765 q^{53} +(-71.3613 + 123.601i) q^{55} +(214.177 - 123.655i) q^{59} +(-101.847 - 176.404i) q^{61} +(-551.354 - 49.1978i) q^{65} +(-200.442 - 115.725i) q^{67} +(-649.282 + 374.863i) q^{71} +153.347i q^{73} -388.991 q^{77} -881.413 q^{79} -197.016i q^{83} +(917.998 - 530.006i) q^{85} +(-1204.33 - 695.321i) q^{89} +(-635.234 - 1368.44i) q^{91} +(-113.204 - 196.075i) q^{95} +(-972.430 + 561.433i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 36 q^{7} - 72 q^{11} + 62 q^{13} - 88 q^{17} - 144 q^{19} + 20 q^{23} - 84 q^{25} + 484 q^{29} - 40 q^{35} + 996 q^{37} - 156 q^{41} + 504 q^{43} + 922 q^{49} + 1164 q^{53} - 1128 q^{55} - 600 q^{59}+ \cdots - 3042 q^{97}+O(q^{100}) $ 8 * q - 36 * q^7 - 72 * q^11 + 62 * q^13 - 88 * q^17 - 144 * q^19 + 20 * q^23 - 84 * q^25 + 484 * q^29 - 40 * q^35 + 996 * q^37 - 156 * q^41 + 504 * q^43 + 922 * q^49 + 1164 * q^53 - 1128 * q^55 - 600 * q^59 - 1224 * q^61 - 670 * q^65 + 960 * q^67 + 2964 * q^71 + 3972 * q^77 - 3968 * q^79 + 3870 * q^85 - 5430 * q^89 - 1720 * q^91 - 2400 * q^95 - 3042 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$5$			11.8097i			1.05629i	0.849155	+	0.528144i	$0.177112\pi$
$5$			11.8097i			1.05629i	−0.849155	+	0.528144i	$0.822888\pi$
$6$		0			0
$7$	−27.8750	+	16.0936i	−1.50511	+	0.868975i	−0.505126	+	0.863045i	$0.668554\pi$
$7$	−27.8750	+	16.0936i	−1.50511	+	0.868975i	−0.999982	+	0.00592959i	$0.998113\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	10.4661	+	6.04263i	0.286878	+	0.165629i	0.636533	−	0.771249i	$-0.280368\pi$
$11$	10.4661	+	6.04263i	0.286878	+	0.165629i	−0.349655	+	0.936879i	$0.613701\pi$
$12$		0			0
$13$	−4.16590	+	46.6867i	−0.0888778	+	0.996043i
$13$	−4.16590	+	46.6867i	−0.0888778	+	0.996043i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−44.8791	−	77.7328i	−0.640281	−	1.10900i	−0.985370	−	0.170429i	$-0.945485\pi$
$17$	−44.8791	−	77.7328i	−0.640281	−	1.10900i	0.345089	−	0.938570i	$-0.387849\pi$
$18$		0			0
$19$	−16.6029	+	9.58572i	−0.200473	+	0.115743i	−0.596876	−	0.802334i	$-0.703592\pi$
$19$	−16.6029	+	9.58572i	−0.200473	+	0.115743i	0.396403	+	0.918076i	$0.370258\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.88869	+	13.6636i	−0.0715176	+	0.123872i	−0.899567	−	0.436784i	$-0.856118\pi$
$23$	−7.88869	+	13.6636i	−0.0715176	+	0.123872i	0.828049	+	0.560656i	$0.189451\pi$
$24$		0			0
$25$	−14.4680			−0.115744
$26$		0			0
$27$		0			0
$28$		0			0
$29$	131.197	−	227.240i	0.840093	−	1.45508i	−0.0497219	−	0.998763i	$-0.515834\pi$
$29$	131.197	−	227.240i	0.840093	−	1.45508i	0.889815	−	0.456321i	$-0.150833\pi$
$30$		0			0
$31$		−	84.0297i		−	0.486844i	−0.969920	−	0.243422i	$-0.921730\pi$
$31$		−	84.0297i		−	0.486844i	0.969920	−	0.243422i	$-0.0782700\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−190.060	−	329.194i	−0.917888	−	1.58983i
$36$		0			0
$37$	−234.864	−	135.599i	−1.04355	−	0.602495i	−0.122714	−	0.992442i	$-0.539160\pi$
$37$	−234.864	−	135.599i	−1.04355	−	0.602495i	−0.920837	+	0.389947i	$0.872493\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−143.088	−	82.6122i	−0.545041	−	0.314679i	0.202079	−	0.979369i	$-0.435230\pi$
$41$	−143.088	−	82.6122i	−0.545041	−	0.314679i	−0.747119	+	0.664690i	$0.768564\pi$
$42$		0			0
$43$	135.153	+	234.092i	0.479318	+	0.830204i	0.999719	−	0.0237186i	$-0.00755056\pi$
$43$	135.153	+	234.092i	0.479318	+	0.830204i	−0.520400	+	0.853922i	$0.674217\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			238.811i			0.741153i	0.928802	+	0.370577i	$0.120840\pi$
$47$			238.811i			0.741153i	−0.928802	+	0.370577i	$0.879160\pi$
$48$		0			0
$49$	346.511	−	600.174i	1.01024	−	1.74978i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	94.2765			0.244337			0.122169	−	0.992509i	$-0.461015\pi$
$53$	94.2765			0.244337			0.122169	+	0.992509i	$0.461015\pi$
$54$		0			0
$55$	−71.3613	+	123.601i	−0.174952	+	0.303026i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	214.177	−	123.655i	0.472601	−	0.272856i	−0.244727	−	0.969592i	$-0.578698\pi$
$59$	214.177	−	123.655i	0.472601	−	0.272856i	0.717328	+	0.696736i	$0.245365\pi$
$60$		0			0
$61$	−101.847	−	176.404i	−0.213774	−	0.370267i	0.739119	−	0.673575i	$-0.235242\pi$
$61$	−101.847	−	176.404i	−0.213774	−	0.370267i	−0.952893	+	0.303308i	$0.901909\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−551.354	−	49.1978i	−1.05211	−	0.0938806i
$66$		0			0
$67$	−200.442	−	115.725i	−0.365491	−	0.211016i	0.305996	−	0.952033i	$-0.401011\pi$
$67$	−200.442	−	115.725i	−0.365491	−	0.211016i	−0.671487	+	0.741016i	$0.734344\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−649.282	+	374.863i	−1.08529	+	0.626593i	−0.932319	−	0.361638i	$-0.882218\pi$
$71$	−649.282	+	374.863i	−1.08529	+	0.626593i	−0.152972	+	0.988231i	$0.548884\pi$
$72$		0			0
$73$			153.347i			0.245862i	0.992415	+	0.122931i	$0.0392294\pi$
$73$			153.347i			0.245862i	−0.992415	+	0.122931i	$0.960771\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−388.991			−0.575710
$78$		0			0
$79$	−881.413			−1.25527			−0.627637	−	0.778506i	$-0.715978\pi$
$79$	−881.413			−1.25527			−0.627637	+	0.778506i	$0.715978\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	197.016i		−	0.260546i	−0.991478	−	0.130273i	$-0.958415\pi$
$83$		−	197.016i		−	0.260546i	0.991478	−	0.130273i	$-0.0415854\pi$
$84$		0			0
$85$	917.998	−	530.006i	1.17142	−	0.676321i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1204.33	−	695.321i	−1.43437	−	0.828133i	−0.436918	−	0.899501i	$-0.643930\pi$
$89$	−1204.33	−	695.321i	−1.43437	−	0.828133i	−0.997450	+	0.0713683i	$0.977263\pi$
$90$		0			0
$91$	−635.234	−	1368.44i	−0.731765	−	1.57639i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−113.204	−	196.075i	−0.122258	−	0.211757i
$96$		0			0
$97$	−972.430	+	561.433i	−1.01789	+	0.587679i	−0.913492	−	0.406857i	$-0.866625\pi$
$97$	−972.430	+	561.433i	−1.01789	+	0.587679i	−0.104398	+	0.994536i	$0.533291\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	596.702	−	1033.52i	0.587862	−	1.01821i	−0.406650	−	0.913584i	$-0.633303\pi$
$101$	596.702	−	1033.52i	0.587862	−	1.01821i	0.994512	−	0.104623i	$-0.0333636\pi$
$102$		0			0
$103$	1367.61			1.30830			0.654149	−	0.756366i	$-0.273027\pi$
$103$	1367.61			1.30830			0.654149	+	0.756366i	$0.273027\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	868.434	−	1504.17i	0.784623	−	1.35901i	−0.144601	−	0.989490i	$-0.546190\pi$
$107$	868.434	−	1504.17i	0.784623	−	1.35901i	0.929224	−	0.369517i	$-0.120477\pi$
$108$		0			0
$109$			946.465i			0.831697i	0.909434	+	0.415848i	$0.136515\pi$
$109$			946.465i			0.831697i	−0.909434	+	0.415848i	$0.863485\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−485.712	−	841.279i	−0.404354	−	0.700361i	0.589892	−	0.807482i	$-0.299170\pi$
$113$	−485.712	−	841.279i	−0.404354	−	0.700361i	−0.994246	+	0.107121i	$0.965837\pi$
$114$		0			0
$115$	−161.362	−	93.1627i	−0.130845	−	0.0755432i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2502.01	+	1444.54i	1.92738	+	1.11278i
$120$		0			0
$121$	−592.473	−	1026.19i	−0.445134	−	0.770995i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			1305.35i			0.934029i
$126$		0			0
$127$	−801.930	+	1388.98i	−0.560313	+	0.970491i	0.437156	+	0.899386i	$0.355986\pi$
$127$	−801.930	+	1388.98i	−0.560313	+	0.970491i	−0.997469	+	0.0711048i	$0.977348\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1677.20			−1.11861			−0.559305	−	0.828962i	$-0.688932\pi$
$131$	−1677.20			−1.11861			−0.559305	+	0.828962i	$0.688932\pi$
$132$		0			0
$133$	308.538	−	534.404i	0.201155	−	0.348411i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−505.815	+	292.032i	−0.315436	+	0.182117i	−0.649356	−	0.760484i	$-0.724962\pi$
$137$	−505.815	+	292.032i	−0.315436	+	0.182117i	0.333921	+	0.942601i	$0.391628\pi$
$138$		0			0
$139$	−78.3050	−	135.628i	−0.0477823	−	0.0827614i	0.841145	−	0.540810i	$-0.181882\pi$
$139$	−78.3050	−	135.628i	−0.0477823	−	0.0827614i	−0.888927	+	0.458048i	$0.848549\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−325.711	+	463.456i	−0.190471	+	0.271022i
$144$		0			0
$145$	2683.63	+	1549.39i	1.53699	+	0.887380i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1027.99	−	593.508i	0.565207	−	0.326322i	−0.190026	−	0.981779i	$-0.560857\pi$
$149$	1027.99	−	593.508i	0.565207	−	0.326322i	0.755233	+	0.655457i	$0.227524\pi$
$150$		0			0
$151$			2022.29i			1.08988i	0.838476	+	0.544939i	$0.183447\pi$
$151$			2022.29i			1.08988i	−0.838476	+	0.544939i	$0.816553\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	992.361			0.514248
$156$		0			0
$157$	1429.86			0.726848			0.363424	−	0.931624i	$-0.381608\pi$
$157$	1429.86			0.726848			0.363424	+	0.931624i	$0.381608\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	507.831i		−	0.248588i
$162$		0			0
$163$	−961.889	+	555.347i	−0.462215	+	0.266860i	−0.712975	−	0.701189i	$-0.752653\pi$
$163$	−961.889	+	555.347i	−0.462215	+	0.266860i	0.250760	+	0.968049i	$0.419319\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	246.272	+	142.185i	0.114115	+	0.0658841i	0.555971	−	0.831202i	$-0.312347\pi$
$167$	246.272	+	142.185i	0.114115	+	0.0658841i	−0.441856	+	0.897086i	$0.645680\pi$
$168$		0			0
$169$	−2162.29	−	388.984i	−0.984201	−	0.177052i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2170.41	+	3759.26i	0.953834	+	1.65209i	0.737014	+	0.675878i	$0.236235\pi$
$173$	2170.41	+	3759.26i	0.953834	+	1.65209i	0.216820	+	0.976212i	$0.430431\pi$
$174$		0			0
$175$	403.295	−	232.843i	0.174207	−	0.100579i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−325.394	+	563.599i	−0.135872	+	0.235337i	−0.925930	−	0.377694i	$-0.876717\pi$
$179$	−325.394	+	563.599i	−0.135872	+	0.235337i	0.790058	+	0.613032i	$0.210050\pi$
$180$		0			0
$181$	454.138			0.186496			0.0932482	−	0.995643i	$-0.470275\pi$
$181$	454.138			0.186496			0.0932482	+	0.995643i	$0.470275\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1601.38	−	2773.66i	0.636408	−	1.10229i
$186$		0			0
$187$		−	1084.75i		−	0.424197i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1407.63	−	2438.09i	−0.533259	−	0.923633i	−0.999245	−	0.0388404i	$-0.987634\pi$
$191$	−1407.63	−	2438.09i	−0.533259	−	0.923633i	0.465986	−	0.884792i	$-0.345700\pi$
$192$		0			0
$193$	−999.023	−	576.786i	−0.372597	−	0.215119i	0.301995	−	0.953309i	$-0.402347\pi$
$193$	−999.023	−	576.786i	−0.372597	−	0.215119i	−0.674593	+	0.738190i	$0.735681\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	352.175	+	203.329i	0.127368	+	0.0735359i	0.562330	−	0.826913i	$-0.309905\pi$
$197$	352.175	+	203.329i	0.127368	+	0.0735359i	−0.434962	+	0.900449i	$0.643238\pi$
$198$		0			0
$199$	−404.699	−	700.960i	−0.144163	−	0.249697i	0.784898	−	0.619626i	$-0.212716\pi$
$199$	−404.699	−	700.960i	−0.144163	−	0.249697i	−0.929060	+	0.369929i	$0.879382\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$			8445.76i			2.92008i
$204$		0			0
$205$	975.621	−	1689.83i	0.332392	−	0.575720i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−231.692			−0.0766815
$210$		0			0
$211$	−1800.27	+	3118.16i	−0.587373	+	1.01736i	0.407202	+	0.913338i	$0.366504\pi$
$211$	−1800.27	+	3118.16i	−0.587373	+	1.01736i	−0.994575	+	0.104021i	$0.966829\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2764.55	+	1596.11i	−0.876934	+	0.506298i
$216$		0			0
$217$	1352.34	+	2342.33i	0.423055	+	0.732754i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3816.05	−	1771.43i	1.16152	−	0.539181i
$222$		0			0
$223$	2261.02	+	1305.40i	0.678964	+	0.392000i	0.799465	−	0.600713i	$-0.205117\pi$
$223$	2261.02	+	1305.40i	0.678964	+	0.392000i	−0.120501	+	0.992713i	$0.538450\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4036.43	+	2330.43i	−1.18021	+	0.681394i	−0.956063	−	0.293162i	$-0.905292\pi$
$227$	−4036.43	+	2330.43i	−1.18021	+	0.681394i	−0.224145	+	0.974556i	$0.571959\pi$
$228$		0			0
$229$		−	123.893i		−	0.0357515i	−0.999840	−	0.0178757i	$-0.994310\pi$
$229$		−	123.893i		−	0.0357515i	0.999840	−	0.0178757i	$-0.00569032\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1186.44			0.333590			0.166795	−	0.985992i	$-0.446658\pi$
$233$	1186.44			0.333590			0.166795	+	0.985992i	$0.446658\pi$
$234$		0			0
$235$	−2820.28			−0.782871
$236$		0			0
$237$		0			0
$238$		0			0
$239$			4543.56i			1.22970i	0.788644	+	0.614850i	$0.210783\pi$
$239$			4543.56i			1.22970i	−0.788644	+	0.614850i	$0.789217\pi$
$240$		0			0
$241$	5442.24	−	3142.08i	1.45463	−	0.839831i	0.455890	−	0.890036i	$-0.349321\pi$
$241$	5442.24	−	3142.08i	1.45463	−	0.839831i	0.998739	+	0.0502054i	$0.0159876\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7087.85	+	4092.17i	1.84827	+	1.06710i
$246$		0			0
$247$	−378.359	−	815.069i	−0.0974672	−	0.209966i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−462.404	−	800.908i	−0.116282	−	0.201406i	0.802010	−	0.597311i	$-0.203764\pi$
$251$	−462.404	−	800.908i	−0.116282	−	0.201406i	−0.918291	+	0.395905i	$0.870431\pi$
$252$		0			0
$253$	−165.128	+	95.3368i	−0.0410337	+	0.0236908i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	271.205	−	469.741i	0.0658261	−	0.114014i	−0.831234	−	0.555923i	$-0.812365\pi$
$257$	271.205	−	469.741i	0.0658261	−	0.114014i	0.897060	+	0.441908i	$0.145698\pi$
$258$		0			0
$259$	8729.11			2.09421
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2624.40	+	4545.59i	−0.615312	+	1.06575i	0.375017	+	0.927018i	$0.377637\pi$
$263$	−2624.40	+	4545.59i	−0.615312	+	1.06575i	−0.990330	+	0.138734i	$0.955697\pi$
$264$		0			0
$265$			1113.37i			0.258091i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−165.080	−	285.927i	−0.0374168	−	0.0648078i	0.846711	−	0.532054i	$-0.178580\pi$
$269$	−165.080	−	285.927i	−0.0374168	−	0.0648078i	−0.884127	+	0.467246i	$0.845246\pi$
$270$		0			0
$271$	−1241.78	−	716.940i	−0.278349	−	0.160705i	0.354327	−	0.935122i	$-0.384710\pi$
$271$	−1241.78	−	716.940i	−0.278349	−	0.160705i	−0.632676	+	0.774417i	$0.718043\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−151.424	−	87.4247i	−0.0332044	−	0.0191706i
$276$		0			0
$277$	−1070.54	−	1854.22i	−0.232211	−	0.402200i	0.726248	−	0.687433i	$-0.241262\pi$
$277$	−1070.54	−	1854.22i	−0.232211	−	0.402200i	−0.958458	+	0.285233i	$0.907929\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	5857.04i		−	1.24342i	−0.783246	−	0.621711i	$-0.786438\pi$
$281$		−	5857.04i		−	1.24342i	0.783246	−	0.621711i	$-0.213562\pi$
$282$		0			0
$283$	−853.748	+	1478.73i	−0.179329	+	0.310606i	−0.941651	−	0.336591i	$-0.890726\pi$
$283$	−853.748	+	1478.73i	−0.179329	+	0.310606i	0.762322	+	0.647198i	$0.224059\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5318.12			1.09379
$288$		0			0
$289$	−1571.76	+	2722.37i	−0.319919	+	0.554116i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1544.37	+	891.643i	−0.307929	+	0.177783i	−0.645999	−	0.763338i	$-0.723559\pi$
$293$	−1544.37	+	891.643i	−0.307929	+	0.177783i	0.338071	+	0.941121i	$0.390226\pi$
$294$		0			0
$295$	1460.32	+	2529.36i	0.288215	+	0.499203i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−605.045	−	425.218i	−0.117026	−	0.0822441i
$300$		0			0
$301$	−7534.80	−	4350.22i	−1.44285	−	0.833032i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2083.28	−	1202.78i	0.391108	−	0.225807i
$306$		0			0
$307$			4027.85i			0.748801i	0.927267	+	0.374400i	$0.122151\pi$
$307$			4027.85i			0.748801i	−0.927267	+	0.374400i	$0.877849\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	80.6308			0.0147014			0.00735072	−	0.999973i	$-0.497660\pi$
$311$	80.6308			0.0147014			0.00735072	+	0.999973i	$0.497660\pi$
$312$		0			0
$313$	−4628.22			−0.835790			−0.417895	−	0.908495i	$-0.637232\pi$
$313$	−4628.22			−0.835790			−0.417895	+	0.908495i	$0.637232\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	10723.3i		−	1.89993i	−0.312354	−	0.949966i	$-0.601118\pi$
$317$		−	10723.3i		−	1.89993i	0.312354	−	0.949966i	$-0.398882\pi$
$318$		0			0
$319$	2746.25	−	1585.55i	0.482009	−	0.278288i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1490.25	+	860.396i	0.256717	+	0.148216i
$324$		0			0
$325$	60.2722	−	675.463i	0.0102871	−	0.115286i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3843.34	−	6656.87i	−0.644044	−	1.11552i
$330$		0			0
$331$	4496.86	−	2596.26i	0.746736	−	0.431128i	−0.0777775	−	0.996971i	$-0.524782\pi$
$331$	4496.86	−	2596.26i	0.746736	−	0.431128i	0.824513	+	0.565843i	$0.191449\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1366.68	−	2367.15i	0.222894	−	0.386064i
$336$		0			0
$337$	2676.49			0.432635			0.216317	−	0.976323i	$-0.430595\pi$
$337$	2676.49			0.432635			0.216317	+	0.976323i	$0.430595\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	507.760	−	879.466i	0.0806356	−	0.139665i
$342$		0			0
$343$			11266.2i			1.77353i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4924.23	−	8529.02i	−0.761806	−	1.31949i	−0.941919	−	0.335840i	$-0.890980\pi$
$347$	−4924.23	−	8529.02i	−0.761806	−	1.31949i	0.180113	−	0.983646i	$-0.442354\pi$
$348$		0			0
$349$	−5638.99	−	3255.67i	−0.864894	−	0.499347i	0.000754175	−	1.00000i	$-0.499760\pi$
$349$	−5638.99	−	3255.67i	−0.864894	−	0.499347i	−0.865648	+	0.500653i	$0.833093\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9609.82	−	5548.23i	−1.44895	−	0.836552i	−0.450531	−	0.892761i	$-0.648765\pi$
$353$	−9609.82	−	5548.23i	−1.44895	−	0.836552i	−0.998419	+	0.0562092i	$0.982099\pi$
$354$		0			0
$355$	−4427.01	−	7667.80i	−0.661862	−	1.14638i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			7844.27i			1.15322i	0.817021	+	0.576608i	$0.195624\pi$
$359$			7844.27i			1.15322i	−0.817021	+	0.576608i	$0.804376\pi$
$360$		0			0
$361$	−3245.73	+	5621.77i	−0.473207	+	0.819619i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1810.98			−0.259701
$366$		0			0
$367$	−1637.80	+	2836.75i	−0.232949	+	0.403479i	−0.958675	−	0.284505i	$-0.908171\pi$
$367$	−1637.80	+	2836.75i	−0.232949	+	0.403479i	0.725726	+	0.687984i	$0.241504\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2627.96	+	1517.25i	−0.367754	+	0.212323i
$372$		0			0
$373$	812.650	+	1407.55i	0.112808	+	0.195389i	0.916901	−	0.399114i	$-0.130682\pi$
$373$	812.650	+	1407.55i	0.112808	+	0.195389i	−0.804093	+	0.594503i	$0.797349\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10062.5	+	7071.82i	1.37466	+	0.966093i
$378$		0			0
$379$	−11188.2	−	6459.52i	−1.51636	−	0.875470i	−0.999816	−	0.0192081i	$-0.993885\pi$
$379$	−11188.2	−	6459.52i	−1.51636	−	0.875470i	−0.516542	−	0.856262i	$-0.672781\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4300.61	−	2482.96i	0.573762	−	0.331261i	−0.184889	−	0.982759i	$-0.559192\pi$
$383$	4300.61	−	2482.96i	0.573762	−	0.331261i	0.758650	+	0.651498i	$0.225859\pi$
$384$		0			0
$385$		−	4593.86i		−	0.608116i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8704.29			−1.13451			−0.567256	−	0.823542i	$-0.691995\pi$
$389$	−8704.29			−1.13451			−0.567256	+	0.823542i	$0.691995\pi$
$390$		0			0
$391$	1416.15			0.183165
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	10409.2i		−	1.32593i
$396$		0			0
$397$	−3805.52	+	2197.12i	−0.481092	+	0.277759i	−0.720871	−	0.693069i	$-0.756258\pi$
$397$	−3805.52	+	2197.12i	−0.481092	+	0.277759i	0.239779	+	0.970827i	$0.422925\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2814.32	+	1624.85i	0.350475	+	0.202347i	0.664894	−	0.746937i	$-0.268476\pi$
$401$	2814.32	+	1624.85i	0.350475	+	0.202347i	−0.314419	+	0.949284i	$0.601810\pi$
$402$		0			0
$403$	3923.07	+	350.059i	0.484918	+	0.0432697i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1638.75	−	2838.39i	−0.199581	−	0.345685i
$408$		0			0
$409$	5685.82	−	3282.71i	0.687398	−	0.396870i	−0.115238	−	0.993338i	$-0.536763\pi$
$409$	5685.82	−	3282.71i	0.687398	−	0.396870i	0.802637	+	0.596468i	$0.203430\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3980.12	+	6893.77i	−0.474211	+	0.821357i
$414$		0			0
$415$	2326.69			0.275212
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−5682.35	+	9842.12i	−0.662532	+	1.14754i	0.317416	+	0.948286i	$0.397185\pi$
$419$	−5682.35	+	9842.12i	−0.662532	+	1.14754i	−0.979948	+	0.199253i	$0.936148\pi$
$420$		0			0
$421$		−	3657.27i		−	0.423383i	−0.977337	−	0.211692i	$-0.932103\pi$
$421$		−	3657.27i		−	0.423383i	0.977337	−	0.211692i	$-0.0678972\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	649.310	+	1124.64i	0.0741086	+	0.128360i
$426$		0			0
$427$	5677.98	+	3278.18i	0.643505	+	0.371528i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11576.7	−	6683.84i	−1.29381	−	0.746982i	−0.314483	−	0.949263i	$-0.601831\pi$
$431$	−11576.7	−	6683.84i	−1.29381	−	0.746982i	−0.979328	+	0.202281i	$0.935165\pi$
$432$		0			0
$433$	3031.38	+	5250.50i	0.336440	+	0.582731i	0.983760	−	0.179487i	$-0.0574437\pi$
$433$	3031.38	+	5250.50i	0.336440	+	0.582731i	−0.647320	+	0.762218i	$0.724110\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	302.475i		−	0.0331106i
$438$		0			0
$439$	−855.711	+	1482.13i	−0.0930315	+	0.161135i	−0.908785	−	0.417264i	$-0.862989\pi$
$439$	−855.711	+	1482.13i	−0.0930315	+	0.161135i	0.815754	+	0.578399i	$0.196322\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14253.1			−1.52864			−0.764320	−	0.644837i	$-0.776925\pi$
$443$	−14253.1			−1.52864			−0.764320	+	0.644837i	$0.776925\pi$
$444$		0			0
$445$	8211.50	−	14222.7i	0.874747	−	1.51511i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	3059.23	−	1766.25i	0.321546	−	0.185644i	−0.330536	−	0.943793i	$-0.607229\pi$
$449$	3059.23	−	1766.25i	0.321546	−	0.185644i	0.652081	+	0.758149i	$0.273896\pi$
$450$		0			0
$451$	−998.389	−	1729.26i	−0.104240	−	0.180549i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	16160.8	−	7501.90i	1.66512	−	0.772955i
$456$		0			0
$457$	−4838.91	−	2793.74i	−0.495305	−	0.285965i	0.231468	−	0.972843i	$-0.425647\pi$
$457$	−4838.91	−	2793.74i	−0.495305	−	0.285965i	−0.726773	+	0.686878i	$0.758981\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2328.04	+	1344.09i	−0.235201	+	0.135793i	−0.612969	−	0.790107i	$-0.710025\pi$
$461$	−2328.04	+	1344.09i	−0.235201	+	0.135793i	0.377768	+	0.925900i	$0.376692\pi$
$462$		0			0
$463$		−	19314.2i		−	1.93868i	−0.245723	−	0.969340i	$-0.579025\pi$
$463$		−	19314.2i		−	1.93868i	0.245723	−	0.969340i	$-0.420975\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5482.16			0.543221			0.271611	−	0.962407i	$-0.412444\pi$
$467$	5482.16			0.543221			0.271611	+	0.962407i	$0.412444\pi$
$468$		0			0
$469$	7449.77			0.733472
$470$		0			0
$471$		0			0
$472$		0			0
$473$			3266.72i			0.317556i
$474$		0			0
$475$	240.211	−	138.686i	0.0232035	−	0.0133965i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4389.48	+	2534.27i	0.418707	+	0.241740i	0.694524	−	0.719470i	$-0.255615\pi$
$479$	4389.48	+	2534.27i	0.418707	+	0.241740i	−0.275817	+	0.961210i	$0.588948\pi$
$480$		0			0
$481$	7309.08	−	10400.1i	0.692859	−	0.985873i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6630.33	−	11484.1i	−0.620758	−	1.07518i
$486$		0			0
$487$	−11806.8	+	6816.65i	−1.09860	+	0.634275i	−0.935852	−	0.352393i	$-0.885368\pi$
$487$	−11806.8	+	6816.65i	−1.09860	+	0.634275i	−0.162744	+	0.986668i	$0.552035\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−332.094	+	575.204i	−0.0305238	+	0.0528688i	−0.880884	−	0.473333i	$-0.843051\pi$
$491$	−332.094	+	575.204i	−0.0305238	+	0.0528688i	0.850360	+	0.526201i	$0.176384\pi$
$492$		0			0
$493$	−23552.0			−2.15158
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12065.8	−	20898.6i	1.08899	−	1.88618i
$498$		0			0
$499$		−	14754.0i		−	1.32361i	−0.749676	−	0.661805i	$-0.769791\pi$
$499$		−	14754.0i		−	1.32361i	0.749676	−	0.661805i	$-0.230209\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−2641.84	−	4575.80i	−0.234182	−	0.405616i	0.724852	−	0.688904i	$-0.241908\pi$
$503$	−2641.84	−	4575.80i	−0.234182	−	0.405616i	−0.959035	+	0.283288i	$0.908575\pi$
$504$		0			0
$505$	12205.5	+	7046.85i	1.07552	+	0.620952i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6582.35	−	3800.32i	−0.573197	−	0.330936i	0.185228	−	0.982696i	$-0.440698\pi$
$509$	−6582.35	−	3800.32i	−0.573197	−	0.330936i	−0.758425	+	0.651760i	$0.774031\pi$
$510$		0			0
$511$	−2467.92	−	4274.56i	−0.213648	−	0.370050i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			16151.0i			1.38194i
$516$		0			0
$517$	−1443.05	+	2499.43i	−0.122757	+	0.212621i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10834.5			−0.911074			−0.455537	−	0.890217i	$-0.650553\pi$
$521$	−10834.5			−0.911074			−0.455537	+	0.890217i	$0.650553\pi$
$522$		0			0
$523$	−4518.24	+	7825.83i	−0.377761	+	0.654301i	−0.990736	−	0.135801i	$-0.956639\pi$
$523$	−4518.24	+	7825.83i	−0.377761	+	0.654301i	0.612975	+	0.790102i	$0.289973\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6531.86	+	3771.17i	−0.539910	+	0.311717i
$528$		0			0
$529$	5959.04	+	10321.4i	0.489770	+	0.848307i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4452.98	−	6336.17i	0.361876	−	0.514916i
$534$		0			0
$535$	17763.7	+	10255.9i	1.43550	+	0.828788i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7253.25	−	4187.67i	0.579628	−	0.334649i
$540$		0			0
$541$			8389.76i			0.666735i	0.942797	+	0.333368i	$0.108185\pi$
$541$			8389.76i			0.666735i	−0.942797	+	0.333368i	$0.891815\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−11177.4			−0.878511
$546$		0			0
$547$	−23840.9			−1.86355			−0.931777	−	0.363032i	$-0.881742\pi$
$547$	−23840.9			−1.86355			−0.931777	+	0.363032i	$0.881742\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			5030.48i			0.388939i
$552$		0			0
$553$	24569.4	−	14185.1i	1.88933	−	1.09080i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	16297.7	+	9409.46i	1.23977	+	0.715784i	0.969048	−	0.246873i	$-0.0794030\pi$
$557$	16297.7	+	9409.46i	1.23977	+	0.715784i	0.270726	+	0.962657i	$0.412736\pi$
$558$		0			0
$559$	−11492.0	+	5334.66i	−0.869519	+	0.403635i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4276.04	+	7406.32i	0.320095	+	0.554421i	0.980507	−	0.196482i	$-0.0629517\pi$
$563$	4276.04	+	7406.32i	0.320095	+	0.554421i	−0.660412	+	0.750903i	$0.729618\pi$
$564$		0			0
$565$	9935.21	−	5736.10i	0.739783	−	0.427114i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13111.9	+	22710.4i	−0.966041	+	1.67323i	−0.259250	+	0.965810i	$0.583475\pi$
$569$	−13111.9	+	22710.4i	−0.966041	+	1.67323i	−0.706792	+	0.707422i	$0.749858\pi$
$570$		0			0
$571$	−3528.25			−0.258586			−0.129293	−	0.991606i	$-0.541271\pi$
$571$	−3528.25			−0.258586			−0.129293	+	0.991606i	$0.541271\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	114.133	−	197.685i	0.00827773	−	0.0143375i
$576$		0			0
$577$			26672.4i			1.92441i	0.272322	+	0.962206i	$0.412208\pi$
$577$			26672.4i			1.92441i	−0.272322	+	0.962206i	$0.587792\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3170.71	+	5491.83i	0.226408	+	0.392150i
$582$		0			0
$583$	986.711	+	569.678i	0.0700950	+	0.0404694i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4017.05	−	2319.24i	−0.282455	−	0.163076i	0.352079	−	0.935970i	$-0.385475\pi$
$587$	−4017.05	−	2319.24i	−0.282455	−	0.163076i	−0.634534	+	0.772895i	$0.718808\pi$
$588$		0			0
$589$	805.484	+	1395.14i	0.0563487	+	0.0975989i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			5932.05i			0.410793i	0.978679	+	0.205396i	$0.0658484\pi$
$593$			5932.05i			0.410793i	−0.978679	+	0.205396i	$0.934152\pi$
$594$		0			0
$595$	−17059.5	+	29547.9i	−1.17541	+	2.03587i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8927.94			0.608991			0.304496	−	0.952514i	$-0.401512\pi$
$599$	8927.94			0.608991			0.304496	+	0.952514i	$0.401512\pi$
$600$		0			0
$601$	−5217.26	+	9036.57i	−0.354104	+	0.613327i	−0.986964	−	0.160940i	$-0.948548\pi$
$601$	−5217.26	+	9036.57i	−0.354104	+	0.613327i	0.632860	+	0.774266i	$0.281881\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	12119.0	−	6996.91i	0.814392	−	0.470190i
$606$		0			0
$607$	−4468.87	−	7740.30i	−0.298823	−	0.517577i	0.677044	−	0.735943i	$-0.263261\pi$
$607$	−4468.87	−	7740.30i	−0.298823	−	0.517577i	−0.975867	+	0.218366i	$0.929927\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−11149.3	−	994.863i	−0.738220	−	0.0658721i
$612$		0			0
$613$	−20757.2	−	11984.2i	−1.36766	−	0.789620i	−0.377032	−	0.926200i	$-0.623055\pi$
$613$	−20757.2	−	11984.2i	−1.36766	−	0.789620i	−0.990629	+	0.136580i	$0.956389\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11348.4	−	6551.98i	0.740467	−	0.427509i	−0.0817724	−	0.996651i	$-0.526058\pi$
$617$	11348.4	−	6551.98i	0.740467	−	0.427509i	0.822239	+	0.569142i	$0.192725\pi$
$618$		0			0
$619$			25051.3i			1.62665i	0.581810	+	0.813324i	$0.302345\pi$
$619$			25051.3i			1.62665i	−0.581810	+	0.813324i	$0.697655\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	44761.0			2.87851
$624$		0			0
$625$	−17224.2			−1.10235
$626$		0			0
$627$		0			0
$628$		0			0
$629$			24342.2i			1.54306i
$630$		0			0
$631$	48.2319	−	27.8467i	0.00304292	−	0.00175683i	−0.498478	−	0.866902i	$-0.666107\pi$
$631$	48.2319	−	27.8467i	0.00304292	−	0.00175683i	0.501521	+	0.865146i	$0.332774\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−16403.4	−	9470.51i	−1.02512	−	0.591852i
$636$		0			0
$637$	26576.6	+	18677.7i	1.65307	+	1.16175i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8949.61	+	15501.2i	0.551464	+	0.955164i	0.998169	+	0.0604827i	$0.0192640\pi$
$641$	8949.61	+	15501.2i	0.551464	+	0.955164i	−0.446705	+	0.894681i	$0.647403\pi$
$642$		0			0
$643$	22413.1	−	12940.2i	1.37463	−	0.793643i	0.383123	−	0.923697i	$-0.374848\pi$
$643$	22413.1	−	12940.2i	1.37463	−	0.793643i	0.991507	+	0.130054i	$0.0415151\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	68.8528	−	119.257i	0.00418375	−	0.00724646i	−0.863926	−	0.503619i	$-0.832002\pi$
$647$	68.8528	−	119.257i	0.00418375	−	0.00724646i	0.868110	+	0.496372i	$0.165335\pi$
$648$		0			0
$649$	2988.81			0.180772
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8047.59	−	13938.8i	0.482277	−	0.835328i	−0.517516	−	0.855673i	$-0.673143\pi$
$653$	8047.59	−	13938.8i	0.482277	−	0.835328i	0.999793	+	0.0203456i	$0.00647666\pi$
$654$		0			0
$655$		−	19807.2i		−	1.18157i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3527.57	−	6109.93i	−0.208520	−	0.361167i	0.742729	−	0.669593i	$-0.233531\pi$
$659$	−3527.57	−	6109.93i	−0.208520	−	0.361167i	−0.951248	+	0.308426i	$0.900198\pi$
$660$		0			0
$661$	3501.02	+	2021.31i	0.206012	+	0.118941i	0.599457	−	0.800407i	$-0.295383\pi$
$661$	3501.02	+	2021.31i	0.206012	+	0.118941i	−0.393445	+	0.919348i	$0.628717\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6311.13	+	3643.73i	0.368022	+	0.212478i
$666$		0			0
$667$	2069.95	+	3585.25i	0.120163	+	0.208128i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	2461.70i		−	0.141629i
$672$		0			0
$673$	11358.9	−	19674.2i	0.650598	−	1.12687i	−0.332380	−	0.943146i	$-0.607852\pi$
$673$	11358.9	−	19674.2i	0.650598	−	1.12687i	0.982978	−	0.183724i	$-0.0588151\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19237.7			−1.09212			−0.546058	−	0.837747i	$-0.683872\pi$
$677$	−19237.7			−1.09212			−0.546058	+	0.837747i	$0.683872\pi$
$678$		0			0
$679$	18071.0	−	31299.9i	1.02136	−	1.76904i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	21722.4	−	12541.5i	1.21696	−	0.702614i	0.252696	−	0.967546i	$-0.418683\pi$
$683$	21722.4	−	12541.5i	1.21696	−	0.702614i	0.964267	+	0.264932i	$0.0853494\pi$
$684$		0			0
$685$	−3448.80	−	5973.50i	−0.192368	−	0.333191i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−392.746	+	4401.46i	−0.0217162	+	0.243370i
$690$		0			0
$691$	9752.83	+	5630.80i	0.536925	+	0.309994i	0.743832	−	0.668367i	$-0.233006\pi$
$691$	9752.83	+	5630.80i	0.536925	+	0.309994i	−0.206907	+	0.978361i	$0.566340\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1601.72	−	924.755i	0.0874198	−	0.0504719i
$696$		0			0
$697$			14830.2i			0.805933i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−15678.7			−0.844761			−0.422381	−	0.906419i	$-0.638805\pi$
$701$	−15678.7			−0.844761			−0.422381	+	0.906419i	$0.638805\pi$
$702$		0			0
$703$	5199.25			0.278938
$704$		0			0
$705$		0			0
$706$		0			0
$707$			38412.4i			2.04335i
$708$		0			0
$709$	15238.3	−	8797.84i	0.807174	−	0.466022i	−0.0387995	−	0.999247i	$-0.512353\pi$
$709$	15238.3	−	8797.84i	0.807174	−	0.466022i	0.845974	+	0.533225i	$0.179020\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1148.15	+	662.884i	0.0603064	+	0.0348179i
$714$		0			0
$715$	−5473.26	−	3846.53i	−0.286277	−	0.201192i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8305.36	−	14385.3i	−0.430790	−	0.746150i	0.566152	−	0.824301i	$-0.308432\pi$
$719$	−8305.36	−	14385.3i	−0.430790	−	0.746150i	−0.996942	+	0.0781513i	$0.975098\pi$
$720$		0			0
$721$	−38122.1	+	22009.8i	−1.96913	+	1.13688i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1898.16	+	3287.71i	−0.0972357	+	0.168417i
$726$		0			0
$727$	8614.24			0.439456			0.219728	−	0.975561i	$-0.429483\pi$
$727$	8614.24			0.439456			0.219728	+	0.975561i	$0.429483\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	12131.1	−	21011.7i	0.613797	−	1.06313i
$732$		0			0
$733$			22282.4i			1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$733$			22282.4i			1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1398.57	−	2422.39i	−0.0699009	−	0.121072i
$738$		0			0
$739$	23374.0	+	13495.0i	1.16350	+	0.671748i	0.952141	−	0.305660i	$-0.0988771\pi$
$739$	23374.0	+	13495.0i	1.16350	+	0.671748i	0.211361	+	0.977408i	$0.432210\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7976.16	+	4605.04i	0.393832	+	0.227379i	0.683819	−	0.729652i	$-0.260318\pi$
$743$	7976.16	+	4605.04i	0.393832	+	0.227379i	−0.289987	+	0.957030i	$0.593651\pi$
$744$		0			0
$745$	7009.12	+	12140.2i	0.344690	+	0.597021i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			55905.1i			2.72727i
$750$		0			0
$751$	11115.8	−	19253.2i	0.540109	−	0.935496i	−0.458788	−	0.888546i	$-0.651716\pi$
$751$	11115.8	−	19253.2i	0.540109	−	0.935496i	0.998897	−	0.0469505i	$-0.0149503\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−23882.5			−1.15123
$756$		0			0
$757$	10967.4	−	18996.2i	0.526576	−	0.912057i	−0.472944	−	0.881092i	$-0.656809\pi$
$757$	10967.4	−	18996.2i	0.526576	−	0.912057i	0.999520	−	0.0309645i	$-0.00985788\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	20991.7	−	12119.6i	0.999932	−	0.577311i	0.0917041	−	0.995786i	$-0.470769\pi$
$761$	20991.7	−	12119.6i	0.999932	−	0.577311i	0.908228	+	0.418475i	$0.137435\pi$
$762$		0			0
$763$	−15232.1	−	26382.7i	−0.722724	−	1.25179i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4880.81	+	10514.3i	0.229773	+	0.494982i
$768$		0			0
$769$	−26825.0	−	15487.4i	−1.25791	−	0.726256i	−0.285243	−	0.958455i	$-0.592074\pi$
$769$	−26825.0	−	15487.4i	−1.25791	−	0.726256i	−0.972668	+	0.232199i	$0.925408\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−27865.7	+	16088.3i	−1.29658	+	0.748583i	−0.979813	−	0.199918i	$-0.935932\pi$
$773$	−27865.7	+	16088.3i	−1.29658	+	0.748583i	−0.316772	+	0.948502i	$0.602599\pi$
$774$		0			0
$775$			1215.74i			0.0563493i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3167.59			0.145688
$780$		0			0
$781$	−9060.63			−0.415128
$782$		0			0
$783$		0			0
$784$		0			0
$785$			16886.1i			0.767760i
$786$		0			0
$787$	−22531.5	+	13008.6i	−1.02053	+	0.589206i	−0.914259	−	0.405131i	$-0.867226\pi$
$787$	−22531.5	+	13008.6i	−1.02053	+	0.589206i	−0.106276	+	0.994337i	$0.533893\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	27078.5	+	15633.8i	1.21719	+	0.702747i
$792$		0			0
$793$	8660.02	−	4020.02i	0.387801	−	0.180019i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9450.96	+	16369.5i	0.420038	+	0.727527i	0.995943	−	0.0899897i	$-0.0286834\pi$
$797$	9450.96	+	16369.5i	0.420038	+	0.727527i	−0.575905	+	0.817517i	$0.695350\pi$
$798$		0			0
$799$	18563.5	−	10717.6i	0.821938	−	0.474546i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−926.621	+	1604.95i	−0.0407220	+	0.0705325i
$804$		0			0
$805$	5997.31			0.262580
$806$		0			0
$807$		0			0
$808$		0			0
$809$	363.787	−	630.098i	0.0158097	−	0.0273833i	−0.858012	−	0.513629i	$-0.828301\pi$
$809$	363.787	−	630.098i	0.0158097	−	0.0273833i	0.873822	+	0.486246i	$0.161634\pi$
$810$		0			0
$811$			23940.1i			1.03656i	0.855210	+	0.518281i	$0.173428\pi$
$811$			23940.1i			1.03656i	−0.855210	+	0.518281i	$0.826572\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6558.46	−	11359.6i	−0.281881	−	0.488232i
$816$		0			0
$817$	−4487.89	−	2591.08i	−0.192180	−	0.110955i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6548.34	−	3780.69i	−0.278366	−	0.160715i	0.354317	−	0.935125i	$-0.384713\pi$
$821$	−6548.34	−	3780.69i	−0.278366	−	0.160715i	−0.632684	+	0.774410i	$0.718047\pi$
$822$		0			0
$823$	10413.0	+	18035.9i	0.441038	+	0.763901i	0.997767	−	0.0667938i	$-0.0212770\pi$
$823$	10413.0	+	18035.9i	0.441038	+	0.763901i	−0.556729	+	0.830695i	$0.687944\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			34592.6i			1.45454i	0.686353	+	0.727268i	$0.259210\pi$
$827$			34592.6i			1.45454i	−0.686353	+	0.727268i	$0.740790\pi$
$828$		0			0
$829$	−10442.0	+	18086.1i	−0.437474	+	0.757727i	−0.997494	−	0.0707518i	$-0.977460\pi$
$829$	−10442.0	+	18086.1i	−0.437474	+	0.757727i	0.560020	+	0.828479i	$0.310794\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−62204.3			−2.58734
$834$		0			0
$835$	−1679.16	+	2908.39i	−0.0695925	+	0.120538i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	38090.7	−	21991.7i	1.56739	−	0.904932i	0.570916	−	0.821009i	$-0.306588\pi$
$839$	38090.7	−	21991.7i	1.56739	−	0.904932i	0.996472	−	0.0839231i	$-0.0267450\pi$
$840$		0			0
$841$	−22230.9	−	38505.0i	−0.911513	−	1.57879i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4593.76	−	25535.9i	0.187018	−	1.03960i
$846$		0			0
$847$	33030.4	+	19070.1i	1.33995	+	0.773621i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3705.54	−	2139.39i	0.149265	−	0.0861779i
$852$		0			0
$853$			16552.4i			0.664412i	0.943207	+	0.332206i	$0.107793\pi$
$853$			16552.4i			0.664412i	−0.943207	+	0.332206i	$0.892207\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12869.9			0.512983			0.256492	−	0.966546i	$-0.417433\pi$
$857$	12869.9			0.512983			0.256492	+	0.966546i	$0.417433\pi$
$858$		0			0
$859$	21172.2			0.840961			0.420481	−	0.907302i	$-0.361861\pi$
$859$	21172.2			0.840961			0.420481	+	0.907302i	$0.361861\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	47889.1i		−	1.88895i	−0.328584	−	0.944475i	$-0.606571\pi$
$863$		−	47889.1i		−	1.88895i	0.328584	−	0.944475i	$-0.393429\pi$
$864$		0			0
$865$	−44395.6	+	25631.8i	−1.74508	+	1.00752i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9224.99	−	5326.05i	−0.360111	−	0.207910i
$870$		0			0
$871$	6237.85	−	8875.88i	0.242665	−	0.345290i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−21007.8	−	36386.5i	−0.811648	−	1.40582i
$876$		0			0
$877$	−37745.6	+	21792.4i	−1.45334	+	0.839085i	−0.998669	−	0.0515750i	$-0.983576\pi$
$877$	−37745.6	+	21792.4i	−1.45334	+	0.839085i	−0.454669	+	0.890660i	$0.650243\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−21279.2	+	36856.7i	−0.813751	+	1.40946i	0.0964705	+	0.995336i	$0.469245\pi$
$881$	−21279.2	+	36856.7i	−0.813751	+	1.40946i	−0.910221	+	0.414122i	$0.864089\pi$
$882$		0			0
$883$	−22522.3			−0.858364			−0.429182	−	0.903218i	$-0.641198\pi$
$883$	−22522.3			−0.858364			−0.429182	+	0.903218i	$0.641198\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3089.40	+	5351.00i	−0.116947	+	0.202558i	−0.918556	−	0.395290i	$-0.870644\pi$
$887$	−3089.40	+	5351.00i	−0.116947	+	0.202558i	0.801609	+	0.597848i	$0.203977\pi$
$888$		0			0
$889$		−	51623.9i		−	1.94759i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2289.18	−	3964.97i	−0.0857832	−	0.148581i
$894$		0			0
$895$	−6655.92	−	3842.79i	−0.248584	−	0.143520i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−19094.9	−	11024.5i	−0.708399	−	0.408995i
$900$		0			0
$901$	−4231.04	−	7328.38i	−0.156445	−	0.270970i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			5363.22i			0.196994i
$906$		0			0
$907$	13077.7	−	22651.3i	0.478764	−	0.829244i	−0.520939	−	0.853594i	$-0.674418\pi$
$907$	13077.7	−	22651.3i	0.478764	−	0.829244i	0.999703	+	0.0243499i	$0.00775157\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−29386.6			−1.06874			−0.534369	−	0.845251i	$-0.679451\pi$
$911$	−29386.6			−1.06874			−0.534369	+	0.845251i	$0.679451\pi$
$912$		0			0
$913$	1190.49	−	2062.00i	0.0431540	−	0.0747450i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	46752.0	−	26992.3i	1.68363	−	0.972044i
$918$		0			0
$919$	−11348.9	−	19656.9i	−0.407363	−	0.705573i	0.587231	−	0.809420i	$-0.300218\pi$
$919$	−11348.9	−	19656.9i	−0.407363	−	0.705573i	−0.994593	+	0.103847i	$0.966885\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−14796.3	−	31874.5i	−0.527655	−	1.13669i
$924$		0			0
$925$	3398.01	+	1961.84i	0.120785	+	0.0697351i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	35327.4	−	20396.3i	1.24764	−	0.720324i	0.277000	−	0.960870i	$-0.410660\pi$
$929$	35327.4	−	20396.3i	1.24764	−	0.720324i	0.970638	+	0.240546i	$0.0773266\pi$
$930$		0			0
$931$			13286.2i			0.467710i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	12810.5			0.448074
$936$		0			0
$937$	22015.2			0.767560			0.383780	−	0.923424i	$-0.374622\pi$
$937$	22015.2			0.767560			0.383780	+	0.923424i	$0.374622\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	7774.05i		−	0.269316i	−0.990892	−	0.134658i	$-0.957006\pi$
$941$		−	7774.05i		−	0.269316i	0.990892	−	0.134658i	$-0.0429936\pi$
$942$		0			0
$943$	2257.56	−	1303.40i	0.0779600	−	0.0450102i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13746.3	−	7936.44i	−0.471695	−	0.272333i	0.245254	−	0.969459i	$-0.421129\pi$
$947$	−13746.3	−	7936.44i	−0.471695	−	0.272333i	−0.716949	+	0.697126i	$0.754462\pi$
$948$		0			0
$949$	−7159.28	−	638.829i	−0.244889	−	0.0218517i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−21907.7	−	37945.3i	−0.744659	−	1.28979i	−0.950354	−	0.311171i	$-0.899279\pi$
$953$	−21907.7	−	37945.3i	−0.744659	−	1.28979i	0.205695	−	0.978616i	$-0.434055\pi$
$954$		0			0
$955$	28793.0	−	16623.6i	0.975622	−	0.563275i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	9399.73	−	16280.8i	0.316510	−	0.548212i
$960$		0			0
$961$	22730.0			0.762983
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6811.65	−	11798.1i	0.227228	−	0.393570i
$966$		0			0
$967$			6323.57i			0.210292i	0.994457	+	0.105146i	$0.0335310\pi$
$967$			6323.57i			0.210292i	−0.994457	+	0.105146i	$0.966469\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−24755.4	−	42877.5i	−0.818164	−	1.41710i	−0.907034	−	0.421058i	$-0.861659\pi$
$971$	−24755.4	−	42877.5i	−0.818164	−	1.41710i	0.0888698	−	0.996043i	$-0.471674\pi$
$972$		0			0
$973$	4365.50	+	2520.42i	0.143835	+	0.0830433i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4897.51	−	2827.58i	−0.160374	−	0.0925918i	0.417665	−	0.908601i	$-0.362848\pi$
$977$	−4897.51	−	2827.58i	−0.160374	−	0.0925918i	−0.578039	+	0.816009i	$0.696182\pi$
$978$		0			0
$979$	−8403.12	−	14554.6i	−0.274326	−	0.475146i
$980$		0			0
$981$		0			0
$982$		0			0
$983$		−	4051.62i		−	0.131461i	−0.997837	−	0.0657307i	$-0.979062\pi$
$983$		−	4051.62i		−	0.131461i	0.997837	−	0.0657307i	$-0.0209378\pi$
$984$		0			0
$985$	−2401.24	+	4159.07i	−0.0776750	+	0.134537i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4264.73			−0.137119
$990$		0			0
$991$	10104.2	−	17500.9i	0.323884	−	0.560984i	−0.657402	−	0.753540i	$-0.728345\pi$
$991$	10104.2	−	17500.9i	0.323884	−	0.560984i	0.981286	+	0.192556i	$0.0616778\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8278.09	−	4779.36i	0.263752	−	0.152277i
$996$		0			0
$997$	23139.1	+	40078.2i	0.735029	+	1.27311i	0.954711	+	0.297536i	$0.0961649\pi$
$997$	23139.1	+	40078.2i	0.735029	+	1.27311i	−0.219681	+	0.975572i	$0.570502\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.4.t.g.433.3		8
3.2	odd	2		52.4.h.a.17.1	✓	8
12.11	even	2		208.4.w.c.17.4		8
13.10	even	6	inner	468.4.t.g.361.2		8
39.2	even	12		676.4.e.h.653.1		16
39.5	even	4		676.4.e.h.529.1		16
39.8	even	4		676.4.e.h.529.2		16
39.11	even	12		676.4.e.h.653.2		16
39.17	odd	6		676.4.d.d.337.8		8
39.20	even	12		676.4.a.g.1.8		8
39.23	odd	6		52.4.h.a.49.1	yes	8
39.29	odd	6		676.4.h.e.361.1		8
39.32	even	12		676.4.a.g.1.7		8
39.35	odd	6		676.4.d.d.337.7		8
39.38	odd	2		676.4.h.e.485.1		8
156.23	even	6		208.4.w.c.49.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.4.h.a.17.1	✓	8	3.2	odd	2
52.4.h.a.49.1	yes	8	39.23	odd	6
208.4.w.c.17.4		8	12.11	even	2
208.4.w.c.49.4		8	156.23	even	6
468.4.t.g.361.2		8	13.10	even	6	inner
468.4.t.g.433.3		8	1.1	even	1	trivial
676.4.a.g.1.7		8	39.32	even	12
676.4.a.g.1.8		8	39.20	even	12
676.4.d.d.337.7		8	39.35	odd	6
676.4.d.d.337.8		8	39.17	odd	6
676.4.e.h.529.1		16	39.5	even	4
676.4.e.h.529.2		16	39.8	even	4
676.4.e.h.653.1		16	39.2	even	12
676.4.e.h.653.2		16	39.11	even	12
676.4.h.e.361.1		8	39.29	odd	6
676.4.h.e.485.1		8	39.38	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	468.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+11.8097i q^{5} +(-27.8750 + 16.0936i) q^{7} +(10.4661 + 6.04263i) q^{11} +(-4.16590 + 46.6867i) q^{13} +(-44.8791 - 77.7328i) q^{17} +(-16.6029 + 9.58572i) q^{19} +(-7.88869 + 13.6636i) q^{23} -14.4680 q^{25} +(131.197 - 227.240i) q^{29} -84.0297i q^{31} +(-190.060 - 329.194i) q^{35} +(-234.864 - 135.599i) q^{37} +(-143.088 - 82.6122i) q^{41} +(135.153 + 234.092i) q^{43} +238.811i q^{47} +(346.511 - 600.174i) q^{49} +94.2765 q^{53} +(-71.3613 + 123.601i) q^{55} +(214.177 - 123.655i) q^{59} +(-101.847 - 176.404i) q^{61} +(-551.354 - 49.1978i) q^{65} +(-200.442 - 115.725i) q^{67} +(-649.282 + 374.863i) q^{71} +153.347i q^{73} -388.991 q^{77} -881.413 q^{79} -197.016i q^{83} +(917.998 - 530.006i) q^{85} +(-1204.33 - 695.321i) q^{89} +(-635.234 - 1368.44i) q^{91} +(-113.204 - 196.075i) q^{95} +(-972.430 + 561.433i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 36 q^{7} - 72 q^{11} + 62 q^{13} - 88 q^{17} - 144 q^{19} + 20 q^{23} - 84 q^{25} + 484 q^{29} - 40 q^{35} + 996 q^{37} - 156 q^{41} + 504 q^{43} + 922 q^{49} + 1164 q^{53} - 1128 q^{55} - 600 q^{59}+ \cdots - 3042 q^{97}+O(q^{100}) \) 8 * q - 36 * q^7 - 72 * q^11 + 62 * q^13 - 88 * q^17 - 144 * q^19 + 20 * q^23 - 84 * q^25 + 484 * q^29 - 40 * q^35 + 996 * q^37 - 156 * q^41 + 504 * q^43 + 922 * q^49 + 1164 * q^53 - 1128 * q^55 - 600 * q^59 - 1224 * q^61 - 670 * q^65 + 960 * q^67 + 2964 * q^71 + 3972 * q^77 - 3968 * q^79 + 3870 * q^85 - 5430 * q^89 - 1720 * q^91 - 2400 * q^95 - 3042 * q^97

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