LMFDB - Embedded newform 864.2.s.a.287.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(287,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("864.287");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			287.10
Character	$\chi$	$=$	864.287
Dual form			864.2.s.a.575.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68236 + 0.971313i) q^{5} +(2.61432 - 1.50938i) q^{7} +O(q^{10})$	$q+(1.68236 + 0.971313i) q^{5} +(2.61432 - 1.50938i) q^{7} +(2.20445 + 3.81822i) q^{11} +(-2.65994 + 4.60716i) q^{13} +4.16396i q^{17} -4.66253i q^{19} +(1.30500 - 2.26033i) q^{23} +(-0.613102 - 1.06192i) q^{25} +(-1.13594 + 0.655836i) q^{29} +(0.0648938 + 0.0374664i) q^{31} +5.86431 q^{35} +8.43839 q^{37} +(-8.16220 - 4.71245i) q^{41} +(5.06694 - 2.92540i) q^{43} +(2.40374 + 4.16340i) q^{47} +(1.05643 - 1.82979i) q^{49} +8.96419i q^{53} +8.56484i q^{55} +(-1.74923 + 3.02976i) q^{59} +(6.32247 + 10.9508i) q^{61} +(-8.94999 + 5.16728i) q^{65} +(-2.38773 - 1.37856i) q^{67} +0.910434 q^{71} +6.86281 q^{73} +(11.5263 + 6.65469i) q^{77} +(10.8815 - 6.28242i) q^{79} +(-8.61553 - 14.9225i) q^{83} +(-4.04451 + 7.00530i) q^{85} -8.96419i q^{89} +16.0594i q^{91} +(4.52877 - 7.84406i) q^{95} +(-9.03909 - 15.6562i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 12 q^{25} - 24 q^{29} + 36 q^{41} + 12 q^{49} + 48 q^{65} + 24 q^{73} + 48 q^{77} + 12 q^{97}+O(q^{100}) $ 24 * q + 12 * q^25 - 24 * q^29 + 36 * q^41 + 12 * q^49 + 48 * q^65 + 24 * q^73 + 48 * q^77 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	1.68236	+	0.971313i	0.752376	+	0.434384i	0.826552	−	0.562861i	$-0.190299\pi$
$5$	1.68236	+	0.971313i	0.752376	+	0.434384i	−0.0741759	+	0.997245i	$0.523633\pi$
$6$		0			0
$7$	2.61432	−	1.50938i	0.988118	−	0.570490i	0.0834070	−	0.996516i	$-0.473420\pi$
$7$	2.61432	−	1.50938i	0.988118	−	0.570490i	0.904711	+	0.426025i	$0.140087\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.20445	+	3.81822i	0.664667	+	1.15124i	0.979376	+	0.202048i	$0.0647597\pi$
$11$	2.20445	+	3.81822i	0.664667	+	1.15124i	−0.314709	+	0.949188i	$0.601907\pi$
$12$		0			0
$13$	−2.65994	+	4.60716i	−0.737736	+	1.27780i	0.215777	+	0.976443i	$0.430772\pi$
$13$	−2.65994	+	4.60716i	−0.737736	+	1.27780i	−0.953513	+	0.301353i	$0.902562\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			4.16396i			1.00991i	0.863146	+	0.504954i	$0.168491\pi$
$17$			4.16396i			1.00991i	−0.863146	+	0.504954i	$0.831509\pi$
$18$		0			0
$19$		−	4.66253i		−	1.06966i	−0.844961	−	0.534828i	$-0.820376\pi$
$19$		−	4.66253i		−	1.06966i	0.844961	−	0.534828i	$-0.179624\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.30500	−	2.26033i	0.272112	−	0.471312i	−0.697290	−	0.716789i	$-0.745611\pi$
$23$	1.30500	−	2.26033i	0.272112	−	0.471312i	0.969402	+	0.245477i	$0.0789445\pi$
$24$		0			0
$25$	−0.613102	−	1.06192i	−0.122620	−	0.212385i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.13594	+	0.655836i	−0.210939	+	0.121786i	−0.601748	−	0.798686i	$-0.705529\pi$
$29$	−1.13594	+	0.655836i	−0.210939	+	0.121786i	0.390809	+	0.920472i	$0.372195\pi$
$30$		0			0
$31$	0.0648938	+	0.0374664i	0.0116553	+	0.00672917i	0.505816	−	0.862641i	$-0.331191\pi$
$31$	0.0648938	+	0.0374664i	0.0116553	+	0.00672917i	−0.494161	+	0.869370i	$0.664525\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.86431			0.991249
$36$		0			0
$37$	8.43839			1.38726			0.693632	−	0.720330i	$-0.256010\pi$
$37$	8.43839			1.38726			0.693632	+	0.720330i	$0.256010\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.16220	−	4.71245i	−1.27472	−	0.735960i	−0.298848	−	0.954301i	$-0.596602\pi$
$41$	−8.16220	−	4.71245i	−1.27472	−	0.735960i	−0.975873	+	0.218340i	$0.929936\pi$
$42$		0			0
$43$	5.06694	−	2.92540i	0.772702	−	0.446119i	−0.0611359	−	0.998129i	$-0.519472\pi$
$43$	5.06694	−	2.92540i	0.772702	−	0.446119i	0.833838	+	0.552010i	$0.186139\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.40374	+	4.16340i	0.350622	+	0.607294i	0.986358	−	0.164611i	$-0.0526370\pi$
$47$	2.40374	+	4.16340i	0.350622	+	0.607294i	−0.635737	+	0.771906i	$0.719304\pi$
$48$		0			0
$49$	1.05643	−	1.82979i	0.150919	−	0.261399i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			8.96419i			1.23133i	0.788009	+	0.615663i	$0.211112\pi$
$53$			8.96419i			1.23133i	−0.788009	+	0.615663i	$0.788888\pi$
$54$		0			0
$55$			8.56484i			1.15488i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.74923	+	3.02976i	−0.227731	+	0.394441i	−0.957135	−	0.289642i	$-0.906464\pi$
$59$	−1.74923	+	3.02976i	−0.227731	+	0.394441i	0.729405	+	0.684083i	$0.239797\pi$
$60$		0			0
$61$	6.32247	+	10.9508i	0.809509	+	1.40211i	0.913204	+	0.407502i	$0.133600\pi$
$61$	6.32247	+	10.9508i	0.809509	+	1.40211i	−0.103695	+	0.994609i	$0.533067\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.94999	+	5.16728i	−1.11011	+	0.640922i
$66$		0			0
$67$	−2.38773	−	1.37856i	−0.291708	−	0.168418i	0.347004	−	0.937864i	$-0.387199\pi$
$67$	−2.38773	−	1.37856i	−0.291708	−	0.168418i	−0.638712	+	0.769446i	$0.720532\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.910434			0.108049			0.0540243	−	0.998540i	$-0.482795\pi$
$71$	0.910434			0.108049			0.0540243	+	0.998540i	$0.482795\pi$
$72$		0			0
$73$	6.86281			0.803232			0.401616	−	0.915808i	$-0.368449\pi$
$73$	6.86281			0.803232			0.401616	+	0.915808i	$0.368449\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	11.5263	+	6.65469i	1.31354	+	0.758372i
$78$		0			0
$79$	10.8815	−	6.28242i	1.22426	−	0.706828i	0.258438	−	0.966028i	$-0.416792\pi$
$79$	10.8815	−	6.28242i	1.22426	−	0.706828i	0.965824	+	0.259200i	$0.0834590\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.61553	−	14.9225i	−0.945677	−	1.63796i	−0.754390	−	0.656426i	$-0.772067\pi$
$83$	−8.61553	−	14.9225i	−0.945677	−	1.63796i	−0.191286	−	0.981534i	$-0.561266\pi$
$84$		0			0
$85$	−4.04451	+	7.00530i	−0.438689	+	0.759831i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	8.96419i		−	0.950202i	−0.879931	−	0.475101i	$-0.842411\pi$
$89$		−	8.96419i		−	0.950202i	0.879931	−	0.475101i	$-0.157589\pi$
$90$		0			0
$91$			16.0594i			1.68348i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.52877	−	7.84406i	0.464642	−	0.804784i
$96$		0			0
$97$	−9.03909	−	15.6562i	−0.917780	−	1.58964i	−0.802779	−	0.596276i	$-0.796646\pi$
$97$	−9.03909	−	15.6562i	−0.917780	−	1.58964i	−0.115001	−	0.993365i	$-0.536687\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.58134	−	3.79974i	0.654868	−	0.378088i	−0.135451	−	0.990784i	$-0.543248\pi$
$101$	6.58134	−	3.79974i	0.654868	−	0.378088i	0.790319	+	0.612696i	$0.209915\pi$
$102$		0			0
$103$	−13.5607	−	7.82926i	−1.33617	−	0.771440i	−0.349936	−	0.936774i	$-0.613797\pi$
$103$	−13.5607	−	7.82926i	−1.33617	−	0.771440i	−0.986238	+	0.165333i	$0.947130\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.51103			0.822792			0.411396	−	0.911457i	$-0.365041\pi$
$107$	8.51103			0.822792			0.411396	+	0.911457i	$0.365041\pi$
$108$		0			0
$109$	−0.886656			−0.0849263			−0.0424631	−	0.999098i	$-0.513521\pi$
$109$	−0.886656			−0.0849263			−0.0424631	+	0.999098i	$0.513521\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.44033	−	0.831573i	−0.135494	−	0.0782278i	0.430721	−	0.902485i	$-0.358259\pi$
$113$	−1.44033	−	0.831573i	−0.135494	−	0.0782278i	−0.566215	+	0.824258i	$0.691593\pi$
$114$		0			0
$115$	4.39098	−	2.53513i	0.409461	−	0.236402i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.28498	+	10.8859i	0.576143	+	0.997909i
$120$		0			0
$121$	−4.21920	+	7.30786i	−0.383563	+	0.664351i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	12.0952i		−	1.08183i
$126$		0			0
$127$		−	7.92732i		−	0.703436i	−0.936106	−	0.351718i	$-0.885598\pi$
$127$		−	7.92732i		−	0.703436i	0.936106	−	0.351718i	$-0.114402\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.51564	+	9.55337i	−0.481904	+	0.834682i	−0.999784	−	0.0207712i	$-0.993388\pi$
$131$	−5.51564	+	9.55337i	−0.481904	+	0.834682i	0.517880	+	0.855453i	$0.326721\pi$
$132$		0			0
$133$	−7.03750	−	12.1893i	−0.610229	−	1.05695i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.101511	+	0.0586073i	−0.00867266	+	0.00500716i	−0.504330	−	0.863511i	$-0.668261\pi$
$137$	−0.101511	+	0.0586073i	−0.00867266	+	0.00500716i	0.495657	+	0.868518i	$0.334927\pi$
$138$		0			0
$139$	−3.03232	−	1.75071i	−0.257198	−	0.148494i	0.365858	−	0.930671i	$-0.380776\pi$
$139$	−3.03232	−	1.75071i	−0.257198	−	0.148494i	−0.623056	+	0.782177i	$0.714109\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−23.4549			−1.96139
$144$		0			0
$145$	−2.54809			−0.211607
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.91915	−	1.68537i	−0.239146	−	0.138071i	0.375638	−	0.926766i	$-0.377424\pi$
$149$	−2.91915	−	1.68537i	−0.239146	−	0.138071i	−0.614784	+	0.788695i	$0.710757\pi$
$150$		0			0
$151$	−9.57011	+	5.52530i	−0.778804	+	0.449643i	−0.836006	−	0.548720i	$-0.815115\pi$
$151$	−9.57011	+	5.52530i	−0.778804	+	0.449643i	0.0572021	+	0.998363i	$0.481782\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.0727833	+	0.126064i	0.00584610	+	0.0101257i
$156$		0			0
$157$	−1.84164	+	3.18981i	−0.146979	+	0.254575i	−0.930109	−	0.367282i	$-0.880288\pi$
$157$	−1.84164	+	3.18981i	−0.146979	+	0.254575i	0.783131	+	0.621857i	$0.213622\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	7.87896i		−	0.620949i
$162$		0			0
$163$			1.39773i			0.109478i	0.998501	+	0.0547392i	$0.0174327\pi$
$163$			1.39773i			0.109478i	−0.998501	+	0.0547392i	$0.982567\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.89041	+	10.2025i	−0.455814	+	0.789493i	−0.998735	−	0.0502913i	$-0.983985\pi$
$167$	−5.89041	+	10.2025i	−0.455814	+	0.789493i	0.542921	+	0.839784i	$0.317318\pi$
$168$		0			0
$169$	−7.65060	−	13.2512i	−0.588508	−	1.01933i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.11135	−	4.10574i	0.540666	−	0.312154i	−0.204683	−	0.978828i	$-0.565616\pi$
$173$	7.11135	−	4.10574i	0.540666	−	0.312154i	0.745349	+	0.666675i	$0.232283\pi$
$174$		0			0
$175$	−3.20568	−	1.85080i	−0.242327	−	0.139907i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.1876			−0.985689			−0.492844	−	0.870118i	$-0.664043\pi$
$179$	−13.1876			−0.985689			−0.492844	+	0.870118i	$0.664043\pi$
$180$		0			0
$181$	−5.98599			−0.444935			−0.222467	−	0.974940i	$-0.571411\pi$
$181$	−5.98599			−0.444935			−0.222467	+	0.974940i	$0.571411\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	14.1964	+	8.19632i	1.04374	+	0.602606i
$186$		0			0
$187$	−15.8989	+	9.17924i	−1.16264	+	0.671253i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.07853	−	8.79626i	−0.367469	−	0.636475i	0.621700	−	0.783256i	$-0.286442\pi$
$191$	−5.07853	−	8.79626i	−0.367469	−	0.636475i	−0.989169	+	0.146780i	$0.953109\pi$
$192$		0			0
$193$	6.81288	−	11.8003i	0.490402	−	0.849401i	−0.509537	−	0.860449i	$-0.670183\pi$
$193$	6.81288	−	11.8003i	0.490402	−	0.849401i	0.999939	+	0.0110476i	$0.00351664\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			5.65685i			0.403034i	0.979485	+	0.201517i	$0.0645872\pi$
$197$			5.65685i			0.403034i	−0.979485	+	0.201517i	$0.935413\pi$
$198$		0			0
$199$			13.9330i			0.987682i	0.869552	+	0.493841i	$0.164408\pi$
$199$			13.9330i			0.987682i	−0.869552	+	0.493841i	$0.835592\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.97981	+	3.42913i	−0.138955	+	0.240677i
$204$		0			0
$205$	−9.15452	−	15.8561i	−0.639379	−	1.10744i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	17.8025	−	10.2783i	1.23143	−	0.710965i
$210$		0			0
$211$	−4.72603	−	2.72857i	−0.325353	−	0.187843i	0.328423	−	0.944531i	$-0.393483\pi$
$211$	−4.72603	−	2.72857i	−0.325353	−	0.187843i	−0.653776	+	0.756688i	$0.726816\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	11.3659			0.775149
$216$		0			0
$217$	0.226204			0.0153557
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−19.1840	−	11.0759i	−1.29046	−	0.745046i
$222$		0			0
$223$	−9.87757	+	5.70282i	−0.661451	+	0.381889i	−0.792830	−	0.609443i	$-0.791393\pi$
$223$	−9.87757	+	5.70282i	−0.661451	+	0.381889i	0.131379	+	0.991332i	$0.458060\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.4469	−	23.2907i	−0.892502	−	1.54586i	−0.836866	−	0.547408i	$-0.815615\pi$
$227$	−13.4469	−	23.2907i	−0.892502	−	1.54586i	−0.0556363	−	0.998451i	$-0.517719\pi$
$228$		0			0
$229$	−1.55925	+	2.70071i	−0.103038	+	0.178468i	−0.912935	−	0.408105i	$-0.866190\pi$
$229$	−1.55925	+	2.70071i	−0.103038	+	0.178468i	0.809897	+	0.586573i	$0.199523\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	3.82047i		−	0.250288i	−0.992139	−	0.125144i	$-0.960061\pi$
$233$		−	3.82047i		−	0.250288i	0.992139	−	0.125144i	$-0.0399392\pi$
$234$		0			0
$235$			9.33914i			0.609218i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	10.2692	−	17.7868i	0.664259	−	1.15053i	−0.315227	−	0.949016i	$-0.602081\pi$
$239$	10.2692	−	17.7868i	0.664259	−	1.15053i	0.979486	−	0.201514i	$-0.0645861\pi$
$240$		0			0
$241$	10.4262	+	18.0588i	0.671613	+	1.16327i	0.977447	+	0.211182i	$0.0677314\pi$
$241$	10.4262	+	18.0588i	0.671613	+	1.16327i	−0.305834	+	0.952085i	$0.598935\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.55460	−	2.05225i	0.227095	−	0.131113i
$246$		0			0
$247$	21.4810	+	12.4021i	1.36680	+	0.789124i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.02844			0.443631			0.221815	−	0.975089i	$-0.428802\pi$
$251$	7.02844			0.443631			0.221815	+	0.975089i	$0.428802\pi$
$252$		0			0
$253$	11.5073			0.723455
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.2464	−	7.64784i	−0.826290	−	0.477059i	0.0262904	−	0.999654i	$-0.491631\pi$
$257$	−13.2464	−	7.64784i	−0.826290	−	0.477059i	−0.852581	+	0.522595i	$0.824964\pi$
$258$		0			0
$259$	22.0606	−	12.7367i	1.37078	−	0.791421i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.35108	+	7.53629i	0.268299	+	0.464707i	0.968423	−	0.249314i	$-0.0802052\pi$
$263$	4.35108	+	7.53629i	0.268299	+	0.464707i	−0.700124	+	0.714022i	$0.746872\pi$
$264$		0			0
$265$	−8.70703	+	15.0810i	−0.534869	+	0.926420i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	9.15090i		−	0.557940i	−0.960300	−	0.278970i	$-0.910007\pi$
$269$		−	9.15090i		−	0.557940i	0.960300	−	0.278970i	$-0.0899930\pi$
$270$		0			0
$271$		−	3.85013i		−	0.233879i	−0.993139	−	0.116939i	$-0.962692\pi$
$271$		−	3.85013i		−	0.233879i	0.993139	−	0.116939i	$-0.0373084\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.70310	−	4.68191i	0.163003	−	0.282330i
$276$		0			0
$277$	−3.32948	−	5.76682i	−0.200049	−	0.346495i	0.748495	−	0.663140i	$-0.230777\pi$
$277$	−3.32948	−	5.76682i	−0.200049	−	0.346495i	−0.948544	+	0.316646i	$0.897443\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.0097	+	7.51114i	−0.776092	+	0.448077i	−0.835044	−	0.550184i	$-0.814558\pi$
$281$	−13.0097	+	7.51114i	−0.776092	+	0.448077i	0.0589513	+	0.998261i	$0.481224\pi$
$282$		0			0
$283$	−14.7216	−	8.49955i	−0.875111	−	0.505246i	−0.00606768	−	0.999982i	$-0.501931\pi$
$283$	−14.7216	−	8.49955i	−0.875111	−	0.505246i	−0.869043	+	0.494736i	$0.835265\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−28.4514			−1.67943
$288$		0			0
$289$	−0.338567			−0.0199157
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.09302	−	2.94046i	−0.297538	−	0.171783i	0.343799	−	0.939043i	$-0.388286\pi$
$293$	−5.09302	−	2.94046i	−0.297538	−	0.171783i	−0.641336	+	0.767260i	$0.721620\pi$
$294$		0			0
$295$	−5.88569	+	3.39811i	−0.342678	+	0.197845i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.94247	+	12.0247i	0.401493	+	0.695407i
$300$		0			0
$301$	8.83106	−	15.2958i	0.509014	−	0.881638i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			24.5644i			1.40655i
$306$		0			0
$307$		−	7.11493i		−	0.406071i	−0.979171	−	0.203035i	$-0.934919\pi$
$307$		−	7.11493i		−	0.406071i	0.979171	−	0.203035i	$-0.0650806\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	11.7568	−	20.3633i	0.666665	−	1.15470i	−0.312166	−	0.950028i	$-0.601054\pi$
$311$	11.7568	−	20.3633i	0.666665	−	1.15470i	0.978831	−	0.204671i	$-0.0656123\pi$
$312$		0			0
$313$	6.04609	+	10.4721i	0.341745	+	0.591920i	0.984757	−	0.173936i	$-0.0556486\pi$
$313$	6.04609	+	10.4721i	0.341745	+	0.591920i	−0.643012	+	0.765856i	$0.722315\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.1235	+	8.73157i	−0.849421	+	0.490414i	−0.860456	−	0.509525i	$-0.829821\pi$
$317$	−15.1235	+	8.73157i	−0.849421	+	0.490414i	0.0110342	+	0.999939i	$0.496488\pi$
$318$		0			0
$319$	−5.00825	−	2.89152i	−0.280408	−	0.161894i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	19.4146			1.08026
$324$		0			0
$325$	6.52327			0.361846
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.5683	+	7.25629i	0.692911	+	0.400052i
$330$		0			0
$331$	−8.40914	+	4.85502i	−0.462208	+	0.266856i	−0.712972	−	0.701192i	$-0.752652\pi$
$331$	−8.40914	+	4.85502i	−0.462208	+	0.266856i	0.250764	+	0.968048i	$0.419318\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.67802	−	4.63847i	−0.146316	−	0.253427i
$336$		0			0
$337$	−2.87607	+	4.98150i	−0.156669	+	0.271360i	−0.933666	−	0.358146i	$-0.883409\pi$
$337$	−2.87607	+	4.98150i	−0.156669	+	0.271360i	0.776996	+	0.629505i	$0.216742\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			0.330372i			0.0178906i
$342$		0			0
$343$			14.7531i			0.796590i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.6350	+	21.8845i	−0.678283	+	1.17482i	0.297214	+	0.954811i	$0.403942\pi$
$347$	−12.6350	+	21.8845i	−0.678283	+	1.17482i	−0.975498	+	0.220010i	$0.929391\pi$
$348$		0			0
$349$	1.61543	+	2.79802i	0.0864722	+	0.149774i	0.906018	−	0.423240i	$-0.139107\pi$
$349$	1.61543	+	2.79802i	0.0864722	+	0.149774i	−0.819545	+	0.573014i	$0.805774\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	20.5683	−	11.8751i	1.09474	−	0.632047i	0.159904	−	0.987133i	$-0.448882\pi$
$353$	20.5683	−	11.8751i	1.09474	−	0.632047i	0.934834	+	0.355086i	$0.115548\pi$
$354$		0			0
$355$	1.53168	+	0.884317i	0.0812932	+	0.0469347i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−22.9748			−1.21256			−0.606281	−	0.795250i	$-0.707339\pi$
$359$	−22.9748			−1.21256			−0.606281	+	0.795250i	$0.707339\pi$
$360$		0			0
$361$	−2.73914			−0.144166
$362$		0			0
$363$		0			0
$364$		0			0
$365$	11.5457	+	6.66594i	0.604332	+	0.348911i
$366$		0			0
$367$	21.9990	−	12.7012i	1.14834	−	0.662995i	0.199859	−	0.979825i	$-0.435952\pi$
$367$	21.9990	−	12.7012i	1.14834	−	0.662995i	0.948482	+	0.316830i	$0.102618\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	13.5303	+	23.4352i	0.702460	+	1.21670i
$372$		0			0
$373$	12.9237	−	22.3844i	0.669161	−	1.15902i	−0.308978	−	0.951069i	$-0.599987\pi$
$373$	12.9237	−	22.3844i	0.669161	−	1.15902i	0.978139	−	0.207952i	$-0.0666798\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	6.97795i		−	0.359383i
$378$		0			0
$379$		−	3.19144i		−	0.163933i	−0.996635	−	0.0819666i	$-0.973880\pi$
$379$		−	3.19144i		−	0.163933i	0.996635	−	0.0819666i	$-0.0261201\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.07378	−	5.32394i	0.157063	−	0.272041i	−0.776745	−	0.629815i	$-0.783131\pi$
$383$	3.07378	−	5.32394i	0.157063	−	0.272041i	0.933808	+	0.357774i	$0.116464\pi$
$384$		0			0
$385$	12.9276	+	22.3912i	0.658850	+	1.14116i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−25.1730	+	14.5336i	−1.27632	+	0.736885i	−0.976170	−	0.217006i	$-0.930371\pi$
$389$	−25.1730	+	14.5336i	−1.27632	+	0.736885i	−0.300152	+	0.953891i	$0.597037\pi$
$390$		0			0
$391$	9.41193	+	5.43398i	0.475982	+	0.274808i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	24.4088			1.22814
$396$		0			0
$397$	−33.7930			−1.69602			−0.848010	−	0.529980i	$-0.822199\pi$
$397$	−33.7930			−1.69602			−0.848010	+	0.529980i	$0.822199\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.93722	+	4.00521i	0.346428	+	0.200011i	0.663111	−	0.748521i	$-0.269236\pi$
$401$	6.93722	+	4.00521i	0.346428	+	0.200011i	−0.316683	+	0.948532i	$0.602569\pi$
$402$		0			0
$403$	−0.345228	+	0.199317i	−0.0171970	+	0.00992870i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	18.6020	+	32.2196i	0.922068	+	1.59707i
$408$		0			0
$409$	4.61851	−	7.99949i	0.228370	−	0.395549i	−0.728955	−	0.684562i	$-0.759994\pi$
$409$	4.61851	−	7.99949i	0.228370	−	0.395549i	0.957325	+	0.289013i	$0.0933269\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			10.5610i			0.519673i
$414$		0			0
$415$		−	33.4735i		−	1.64315i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.96784	+	8.60455i	−0.242695	+	0.420360i	−0.961481	−	0.274871i	$-0.911365\pi$
$419$	−4.96784	+	8.60455i	−0.242695	+	0.420360i	0.718786	+	0.695231i	$0.244698\pi$
$420$		0			0
$421$	14.7911	+	25.6190i	0.720876	+	1.24859i	0.960649	+	0.277764i	$0.0895934\pi$
$421$	14.7911	+	25.6190i	0.720876	+	1.24859i	−0.239774	+	0.970829i	$0.577073\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.42181	−	2.55293i	0.214489	−	0.123835i
$426$		0			0
$427$	33.0579	+	19.0860i	1.59978	+	0.923635i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	39.6306			1.90894			0.954470	−	0.298307i	$-0.0964219\pi$
$431$	39.6306			1.90894			0.954470	+	0.298307i	$0.0964219\pi$
$432$		0			0
$433$	−9.31522			−0.447661			−0.223831	−	0.974628i	$-0.571856\pi$
$433$	−9.31522			−0.447661			−0.223831	+	0.974628i	$0.571856\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.5389	−	6.08461i	−0.504142	−	0.291066i
$438$		0			0
$439$	−1.98348	+	1.14516i	−0.0946664	+	0.0546557i	−0.546586	−	0.837403i	$-0.684073\pi$
$439$	−1.98348	+	1.14516i	−0.0946664	+	0.0546557i	0.451919	+	0.892059i	$0.350739\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.3819	−	21.4461i	−0.588283	−	1.01894i	−0.994457	−	0.105141i	$-0.966471\pi$
$443$	−12.3819	−	21.4461i	−0.588283	−	1.01894i	0.406174	−	0.913796i	$-0.366863\pi$
$444$		0			0
$445$	8.70703	−	15.0810i	0.412753	−	0.714909i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			30.6070i			1.44443i	0.691667	+	0.722216i	$0.256876\pi$
$449$			30.6070i			1.44443i	−0.691667	+	0.722216i	$0.743124\pi$
$450$		0			0
$451$		−	41.5534i		−	1.95667i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−15.5987	+	27.0178i	−0.731279	+	1.26661i
$456$		0			0
$457$	9.09417	+	15.7516i	0.425408	+	0.736827i	0.996458	−	0.0840872i	$-0.0267974\pi$
$457$	9.09417	+	15.7516i	0.425408	+	0.736827i	−0.571051	+	0.820915i	$0.693464\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−30.3019	+	17.4948i	−1.41130	+	0.814813i	−0.995511	−	0.0946485i	$-0.969827\pi$
$461$	−30.3019	+	17.4948i	−1.41130	+	0.814813i	−0.415787	+	0.909462i	$0.636494\pi$
$462$		0			0
$463$	−13.9627	−	8.06138i	−0.648903	−	0.374644i	0.139133	−	0.990274i	$-0.455568\pi$
$463$	−13.9627	−	8.06138i	−0.648903	−	0.374644i	−0.788036	+	0.615630i	$0.788902\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.34589			−0.293653			−0.146826	−	0.989162i	$-0.546906\pi$
$467$	−6.34589			−0.293653			−0.146826	+	0.989162i	$0.546906\pi$
$468$		0			0
$469$	−8.32305			−0.384323
$470$		0			0
$471$		0			0
$472$		0			0
$473$	22.3396	+	12.8978i	1.02718	+	0.593041i
$474$		0			0
$475$	−4.95125	+	2.85860i	−0.227179	+	0.131162i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.745307	+	1.29091i	0.0340539	+	0.0589832i	0.882550	−	0.470218i	$-0.155825\pi$
$479$	0.745307	+	1.29091i	0.0340539	+	0.0589832i	−0.848496	+	0.529202i	$0.822492\pi$
$480$		0			0
$481$	−22.4457	+	38.8770i	−1.02343	+	1.77264i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	35.1191i		−	1.59468i
$486$		0			0
$487$		−	40.5671i		−	1.83827i	−0.393942	−	0.919135i	$-0.628889\pi$
$487$		−	40.5671i		−	1.83827i	0.393942	−	0.919135i	$-0.371111\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.02050	−	10.4278i	0.271701	−	0.470601i	−0.697596	−	0.716491i	$-0.745747\pi$
$491$	6.02050	−	10.4278i	0.271701	−	0.470601i	0.969298	+	0.245891i	$0.0790804\pi$
$492$		0			0
$493$	−2.73088	−	4.73002i	−0.122992	−	0.213029i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.38016	−	1.37419i	0.106765	−	0.0616407i
$498$		0			0
$499$	5.94438	+	3.43199i	0.266107	+	0.153637i	0.627117	−	0.778925i	$-0.284235\pi$
$499$	5.94438	+	3.43199i	0.266107	+	0.153637i	−0.361010	+	0.932562i	$0.617568\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	35.0653			1.56348			0.781741	−	0.623603i	$-0.214332\pi$
$503$	35.0653			1.56348			0.781741	+	0.623603i	$0.214332\pi$
$504$		0			0
$505$	14.7629			0.656943
$506$		0			0
$507$		0			0
$508$		0			0
$509$	11.1369	+	6.42991i	0.493635	+	0.285001i	0.726081	−	0.687609i	$-0.241340\pi$
$509$	11.1369	+	6.42991i	0.493635	+	0.285001i	−0.232446	+	0.972609i	$0.574673\pi$
$510$		0			0
$511$	17.9416	−	10.3586i	0.793688	−	0.458236i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−15.2093	−	26.3433i	−0.670203	−	1.16083i
$516$		0			0
$517$	−10.5978	+	18.3560i	−0.466093	+	0.807296i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			23.6447i			1.03589i	0.855413	+	0.517947i	$0.173303\pi$
$521$			23.6447i			1.03589i	−0.855413	+	0.517947i	$0.826697\pi$
$522$		0			0
$523$		−	18.3335i		−	0.801670i	−0.916150	−	0.400835i	$-0.868720\pi$
$523$		−	18.3335i		−	0.801670i	0.916150	−	0.400835i	$-0.131280\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.156009	+	0.270215i	−0.00679585	+	0.0117708i
$528$		0			0
$529$	8.09393	+	14.0191i	0.351910	+	0.609526i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	43.4220	−	25.0697i	1.88081	−	1.08589i
$534$		0			0
$535$	14.3186	+	8.26687i	0.619049	+	0.357408i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.31539			0.401242
$540$		0			0
$541$	11.5508			0.496606			0.248303	−	0.968682i	$-0.420127\pi$
$541$	11.5508			0.496606			0.248303	+	0.968682i	$0.420127\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.49168	−	0.861221i	−0.0638965	−	0.0368906i
$546$		0			0
$547$	−3.89458	+	2.24854i	−0.166520	+	0.0961405i	−0.580944	−	0.813944i	$-0.697316\pi$
$547$	−3.89458	+	2.24854i	−0.166520	+	0.0961405i	0.414424	+	0.910084i	$0.363983\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.05785	+	5.29636i	0.130269	+	0.225632i
$552$		0			0
$553$	18.9651	−	32.8485i	0.806477	−	1.39686i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			27.0115i			1.14451i	0.820074	+	0.572257i	$0.193932\pi$
$557$			27.0115i			1.14451i	−0.820074	+	0.572257i	$0.806068\pi$
$558$		0			0
$559$			31.1256i			1.31647i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.37475	−	14.5055i	0.352954	−	0.611334i	−0.633812	−	0.773487i	$-0.718511\pi$
$563$	8.37475	−	14.5055i	0.352954	−	0.611334i	0.986766	+	0.162153i	$0.0518439\pi$
$564$		0			0
$565$	−1.61543	−	2.79802i	−0.0679619	−	0.117713i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−34.7647	+	20.0714i	−1.45741	+	0.841437i	−0.998883	−	0.0472425i	$-0.984957\pi$
$569$	−34.7647	+	20.0714i	−1.45741	+	0.841437i	−0.458529	+	0.888680i	$0.651623\pi$
$570$		0			0
$571$	37.5848	+	21.6996i	1.57288	+	0.908101i	0.995814	+	0.0914001i	$0.0291342\pi$
$571$	37.5848	+	21.6996i	1.57288	+	0.908101i	0.577062	+	0.816700i	$0.304199\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.20040			−0.133466
$576$		0			0
$577$	20.4136			0.849829			0.424914	−	0.905234i	$-0.360304\pi$
$577$	20.4136			0.849829			0.424914	+	0.905234i	$0.360304\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−45.0474	−	26.0081i	−1.86888	−	1.07900i
$582$		0			0
$583$	−34.2272	+	19.7611i	−1.41755	+	0.818421i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.1493	+	26.2394i	0.625279	+	1.08301i	0.988487	+	0.151306i	$0.0483480\pi$
$587$	15.1493	+	26.2394i	0.625279	+	1.08301i	−0.363208	+	0.931708i	$0.618319\pi$
$588$		0			0
$589$	0.174688	−	0.302569i	0.00719791	−	0.0124671i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	35.5261i		−	1.45888i	−0.684043	−	0.729442i	$-0.739780\pi$
$593$		−	35.5261i		−	1.45888i	0.684043	−	0.729442i	$-0.260220\pi$
$594$		0			0
$595$			24.4187i			1.00107i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.29720	−	12.6391i	0.298156	−	0.516421i	−0.677558	−	0.735469i	$-0.736962\pi$
$599$	7.29720	−	12.6391i	0.298156	−	0.516421i	0.975714	+	0.219048i	$0.0702952\pi$
$600$		0			0
$601$	0.343128	+	0.594315i	0.0139965	+	0.0242426i	0.872939	−	0.487830i	$-0.162211\pi$
$601$	0.343128	+	0.594315i	0.0139965	+	0.0242426i	−0.858942	+	0.512072i	$0.828878\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14.1964	+	8.19632i	−0.577168	+	0.333228i
$606$		0			0
$607$	19.6114	+	11.3227i	0.796004	+	0.459573i	0.842072	−	0.539365i	$-0.181336\pi$
$607$	19.6114	+	11.3227i	0.796004	+	0.459573i	−0.0460679	+	0.998938i	$0.514669\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−25.5753			−1.03466
$612$		0			0
$613$	0.738126			0.0298126			0.0149063	−	0.999889i	$-0.495255\pi$
$613$	0.738126			0.0298126			0.0149063	+	0.999889i	$0.495255\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.96274	+	4.59729i	0.320568	+	0.185080i	0.651646	−	0.758524i	$-0.274079\pi$
$617$	7.96274	+	4.59729i	0.320568	+	0.185080i	−0.331078	+	0.943603i	$0.607412\pi$
$618$		0			0
$619$	−16.5675	+	9.56526i	−0.665905	+	0.384460i	−0.794523	−	0.607234i	$-0.792279\pi$
$619$	−16.5675	+	9.56526i	−0.665905	+	0.384460i	0.128618	+	0.991694i	$0.458946\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−13.5303	−	23.4352i	−0.542081	−	0.938912i
$624$		0			0
$625$	8.68270	−	15.0389i	0.347308	−	0.601555i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			35.1371i			1.40101i
$630$		0			0
$631$			16.5536i			0.658989i	0.944157	+	0.329495i	$0.106878\pi$
$631$			16.5536i			0.658989i	−0.944157	+	0.329495i	$0.893122\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.69991	−	13.3366i	0.305562	−	0.529248i
$636$		0			0
$637$	5.62009	+	9.73428i	0.222676	+	0.385686i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.62226	−	1.51396i	0.103573	−	0.0597978i	−0.447319	−	0.894375i	$-0.647621\pi$
$641$	2.62226	−	1.51396i	0.103573	−	0.0597978i	0.550892	+	0.834577i	$0.314288\pi$
$642$		0			0
$643$	4.77000	+	2.75396i	0.188110	+	0.108606i	0.591098	−	0.806600i	$-0.298695\pi$
$643$	4.77000	+	2.75396i	0.188110	+	0.108606i	−0.402987	+	0.915206i	$0.632028\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−22.6014			−0.888551			−0.444276	−	0.895890i	$-0.646539\pi$
$647$	−22.6014			−0.888551			−0.444276	+	0.895890i	$0.646539\pi$
$648$		0			0
$649$	−15.4244			−0.605460
$650$		0			0
$651$		0			0
$652$		0			0
$653$	34.0192	+	19.6410i	1.33127	+	0.768611i	0.985495	−	0.169705i	$-0.0542814\pi$
$653$	34.0192	+	19.6410i	1.33127	+	0.768611i	0.345779	+	0.938316i	$0.387615\pi$
$654$		0			0
$655$	−18.5586	+	10.7148i	−0.725146	+	0.418663i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.48091	−	7.76116i	−0.174551	−	0.302332i	0.765454	−	0.643490i	$-0.222514\pi$
$659$	−4.48091	−	7.76116i	−0.174551	−	0.302332i	−0.940006	+	0.341158i	$0.889181\pi$
$660$		0			0
$661$	3.44282	−	5.96314i	0.133910	−	0.231939i	−0.791270	−	0.611466i	$-0.790580\pi$
$661$	3.44282	−	5.96314i	0.133910	−	0.231939i	0.925181	+	0.379527i	$0.123913\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	27.3425i		−	1.06030i
$666$		0			0
$667$			3.42347i			0.132557i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−27.8751	+	48.2811i	−1.07611	+	1.86387i
$672$		0			0
$673$	−10.5054	−	18.1959i	−0.404954	−	0.701401i	0.589362	−	0.807869i	$-0.299379\pi$
$673$	−10.5054	−	18.1959i	−0.404954	−	0.701401i	−0.994316	+	0.106468i	$0.966046\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.85645	−	3.95858i	0.263515	−	0.152140i	−0.362422	−	0.932014i	$-0.618050\pi$
$677$	6.85645	−	3.95858i	0.263515	−	0.152140i	0.625937	+	0.779874i	$0.284717\pi$
$678$		0			0
$679$	−47.2620	−	27.2868i	−1.81375	−	1.04717i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−25.1669			−0.962983			−0.481492	−	0.876451i	$-0.659905\pi$
$683$	−25.1669			−0.962983			−0.481492	+	0.876451i	$0.659905\pi$
$684$		0			0
$685$	−0.227704			−0.00870013
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−41.2994	−	23.8442i	−1.57338	−	0.908393i
$690$		0			0
$691$	−16.0586	+	9.27142i	−0.610897	+	0.352701i	−0.773316	−	0.634020i	$-0.781404\pi$
$691$	−16.0586	+	9.27142i	−0.610897	+	0.352701i	0.162420	+	0.986722i	$0.448070\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.40098	−	5.89067i	−0.129007	−	0.223446i
$696$		0			0
$697$	19.6224	−	33.9871i	0.743253	−	1.28735i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	44.2203i		−	1.67018i	−0.550116	−	0.835088i	$-0.685417\pi$
$701$		−	44.2203i		−	1.67018i	0.550116	−	0.835088i	$-0.314583\pi$
$702$		0			0
$703$		−	39.3442i		−	1.48390i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	11.4705	−	19.8674i	0.431391	−	0.747192i
$708$		0			0
$709$	5.89832	+	10.2162i	0.221516	+	0.383677i	0.955268	−	0.295740i	$-0.0955662\pi$
$709$	5.89832	+	10.2162i	0.221516	+	0.383677i	−0.733753	+	0.679417i	$0.762233\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.169373	−	0.0977877i	0.00634308	−	0.00366218i
$714$		0			0
$715$	−39.4596	−	22.7820i	−1.47570	−	0.851999i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.11638			−0.0416339			−0.0208169	−	0.999783i	$-0.506627\pi$
$719$	−1.11638			−0.0416339			−0.0208169	+	0.999783i	$0.506627\pi$
$720$		0			0
$721$	−47.2692			−1.76040
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.39290	+	0.804189i	0.0517309	+	0.0298668i
$726$		0			0
$727$	11.6152	−	6.70606i	0.430785	−	0.248714i	−0.268896	−	0.963169i	$-0.586659\pi$
$727$	11.6152	−	6.70606i	0.430785	−	0.248714i	0.699681	+	0.714455i	$0.253325\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	12.1813	+	21.0986i	0.450540	+	0.780358i
$732$		0			0
$733$	3.97824	−	6.89052i	0.146940	−	0.254507i	−0.783155	−	0.621826i	$-0.786391\pi$
$733$	3.97824	−	6.89052i	0.146940	−	0.254507i	0.930095	+	0.367319i	$0.119724\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	12.1559i		−	0.447767i
$738$		0			0
$739$			2.13143i			0.0784058i	0.999231	+	0.0392029i	$0.0124819\pi$
$739$			2.13143i			0.0784058i	−0.999231	+	0.0392029i	$0.987518\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	26.7656	−	46.3594i	0.981934	−	1.70076i	0.327095	−	0.944992i	$-0.393930\pi$
$743$	26.7656	−	46.3594i	0.981934	−	1.70076i	0.654839	−	0.755768i	$-0.272736\pi$
$744$		0			0
$745$	−3.27404	−	5.67081i	−0.119952	−	0.207762i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	22.2505	−	12.8463i	0.813016	−	0.469395i
$750$		0			0
$751$	31.0885	+	17.9489i	1.13443	+	0.654966i	0.945046	−	0.326936i	$-0.106016\pi$
$751$	31.0885	+	17.9489i	1.13443	+	0.654966i	0.189388	+	0.981902i	$0.439350\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−21.4672			−0.781271
$756$		0			0
$757$	−15.9513			−0.579762			−0.289881	−	0.957063i	$-0.593616\pi$
$757$	−15.9513			−0.579762			−0.289881	+	0.957063i	$0.593616\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−12.5944	−	7.27140i	−0.456548	−	0.263588i	0.254044	−	0.967193i	$-0.418239\pi$
$761$	−12.5944	−	7.27140i	−0.456548	−	0.263588i	−0.710592	+	0.703605i	$0.751573\pi$
$762$		0			0
$763$	−2.31800	+	1.33830i	−0.0839172	+	0.0484496i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.30572	−	16.1180i	−0.336010	−	0.581987i
$768$		0			0
$769$	0.545353	−	0.944579i	0.0196659	−	0.0340624i	−0.856025	−	0.516934i	$-0.827073\pi$
$769$	0.545353	−	0.944579i	0.0196659	−	0.0340624i	0.875691	+	0.482872i	$0.160406\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			31.0697i			1.11750i	0.829336	+	0.558750i	$0.188719\pi$
$773$			31.0697i			1.11750i	−0.829336	+	0.558750i	$0.811281\pi$
$774$		0			0
$775$		−	0.0918830i		−	0.00330054i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−21.9719	+	38.0564i	−0.787225	+	1.36351i
$780$		0			0
$781$	2.00701	+	3.47624i	0.0718163	+	0.124390i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.19661	+	3.57762i	−0.221167	+	0.127691i
$786$		0			0
$787$	0.0751371	+	0.0433804i	0.00267835	+	0.00154635i	0.501339	−	0.865251i	$-0.332841\pi$
$787$	0.0751371	+	0.0433804i	0.00267835	+	0.00154635i	−0.498660	+	0.866798i	$0.666174\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−5.02062			−0.178513
$792$		0			0
$793$	−67.2697			−2.38882
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.88596	−	2.24356i	−0.137648	−	0.0794710i	0.429595	−	0.903022i	$-0.358656\pi$
$797$	−3.88596	−	2.24356i	−0.137648	−	0.0794710i	−0.567242	+	0.823551i	$0.691990\pi$
$798$		0			0
$799$	−17.3362	+	10.0091i	−0.613312	+	0.354096i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	15.1287	+	26.2037i	0.533881	+	0.924710i
$804$		0			0
$805$	7.65294	−	13.2553i	0.269731	−	0.467187i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	30.9732i		−	1.08896i	−0.838774	−	0.544480i	$-0.816727\pi$
$809$		−	30.9732i		−	1.08896i	0.838774	−	0.544480i	$-0.183273\pi$
$810$		0			0
$811$			25.5248i			0.896298i	0.893959	+	0.448149i	$0.147917\pi$
$811$			25.5248i			0.896298i	−0.893959	+	0.448149i	$0.852083\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.35763	+	2.35148i	−0.0475557	+	0.0823689i
$816$		0			0
$817$	−13.6398	−	23.6248i	−0.477195	−	0.826525i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	38.1380	−	22.0190i	1.33102	−	0.768467i	0.345567	−	0.938394i	$-0.387686\pi$
$821$	38.1380	−	22.0190i	1.33102	−	0.768467i	0.985457	+	0.169927i	$0.0543531\pi$
$822$		0			0
$823$	37.3847	+	21.5841i	1.30315	+	0.752373i	0.980943	−	0.194297i	$-0.0622425\pi$
$823$	37.3847	+	21.5841i	1.30315	+	0.752373i	0.322205	+	0.946670i	$0.395576\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	7.24861			0.252059			0.126029	−	0.992027i	$-0.459777\pi$
$827$	7.24861			0.252059			0.126029	+	0.992027i	$0.459777\pi$
$828$		0			0
$829$	13.5377			0.470185			0.235092	−	0.971973i	$-0.424461\pi$
$829$	13.5377			0.470185			0.235092	+	0.971973i	$0.424461\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	7.61918	+	4.39893i	0.263989	+	0.152414i
$834$		0			0
$835$	−19.8196	+	11.4429i	−0.685887	+	0.395997i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−20.6704	−	35.8022i	−0.713622	−	1.23603i	−0.963489	−	0.267749i	$-0.913720\pi$
$839$	−20.6704	−	35.8022i	−0.713622	−	1.23603i	0.249867	−	0.968280i	$-0.419613\pi$
$840$		0			0
$841$	−13.6398	+	23.6248i	−0.470336	+	0.814647i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	29.7245i		−	1.02255i
$846$		0			0
$847$			25.4734i			0.875277i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.0121	−	19.0736i	0.377491	−	0.653834i
$852$		0			0
$853$	4.39474	+	7.61191i	0.150473	+	0.260627i	0.931401	−	0.363994i	$-0.118587\pi$
$853$	4.39474	+	7.61191i	0.150473	+	0.260627i	−0.780928	+	0.624620i	$0.785254\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.5978	−	16.5109i	0.976881	−	0.564003i	0.0755543	−	0.997142i	$-0.475927\pi$
$857$	28.5978	−	16.5109i	0.976881	−	0.564003i	0.901327	+	0.433139i	$0.142594\pi$
$858$		0			0
$859$	−17.0192	−	9.82606i	−0.580689	−	0.335261i	0.180718	−	0.983535i	$-0.442158\pi$
$859$	−17.0192	−	9.82606i	−0.580689	−	0.335261i	−0.761407	+	0.648274i	$0.775491\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−11.3994			−0.388040			−0.194020	−	0.980998i	$-0.562153\pi$
$863$	−11.3994			−0.388040			−0.194020	+	0.980998i	$0.562153\pi$
$864$		0			0
$865$	15.9518			0.542379
$866$		0			0
$867$		0			0
$868$		0			0
$869$	47.9753	+	27.6986i	1.62745	+	0.939609i
$870$		0			0
$871$	12.7025	−	7.33378i	0.430407	−	0.248496i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−18.2562	−	31.6206i	−0.617172	−	1.06897i
$876$		0			0
$877$	−17.5243	+	30.3531i	−0.591755	+	1.02495i	0.402241	+	0.915534i	$0.368231\pi$
$877$	−17.5243	+	30.3531i	−0.591755	+	1.02495i	−0.993996	+	0.109416i	$0.965102\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			22.1147i			0.745064i	0.928019	+	0.372532i	$0.121510\pi$
$881$			22.1147i			0.745064i	−0.928019	+	0.372532i	$0.878490\pi$
$882$		0			0
$883$		−	48.4270i		−	1.62970i	−0.579673	−	0.814849i	$-0.696820\pi$
$883$		−	48.4270i		−	1.62970i	0.579673	−	0.814849i	$-0.303180\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.6506	+	23.6436i	−0.458343	+	0.793873i	−0.998874	−	0.0474512i	$-0.984890\pi$
$887$	−13.6506	+	23.6436i	−0.458343	+	0.793873i	0.540531	+	0.841324i	$0.318223\pi$
$888$		0			0
$889$	−11.9653	−	20.7245i	−0.401304	−	0.695078i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	19.4120	−	11.2075i	0.649596	−	0.375045i
$894$		0			0
$895$	−22.1864	−	12.8093i	−0.741608	−	0.428168i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.0982874			−0.00327807
$900$		0			0
$901$	−37.3265			−1.24353
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−10.0706	−	5.81427i	−0.334758	−	0.193273i
$906$		0			0
$907$	17.0823	−	9.86248i	0.567209	−	0.327478i	−0.188825	−	0.982011i	$-0.560468\pi$
$907$	17.0823	−	9.86248i	0.567209	−	0.327478i	0.756034	+	0.654532i	$0.227135\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	17.0924	+	29.6049i	0.566296	+	0.980854i	0.996928	+	0.0783259i	$0.0249575\pi$
$911$	17.0924	+	29.6049i	0.566296	+	0.980854i	−0.430632	+	0.902528i	$0.641709\pi$
$912$		0			0
$913$	37.9850	−	65.7919i	1.25712	−	2.17739i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			33.3007i			1.09969i
$918$		0			0
$919$			33.2819i			1.09787i	0.835866	+	0.548934i	$0.184966\pi$
$919$			33.2819i			1.09787i	−0.835866	+	0.548934i	$0.815034\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.42170	+	4.19451i	−0.0797114	+	0.138064i
$924$		0			0
$925$	−5.17360	−	8.96093i	−0.170107	−	0.294634i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	27.4859	−	15.8690i	0.901784	−	0.520645i	0.0240056	−	0.999712i	$-0.492358\pi$
$929$	27.4859	−	15.8690i	0.901784	−	0.520645i	0.877779	+	0.479066i	$0.159025\pi$
$930$		0			0
$931$	−8.53144	−	4.92563i	−0.279607	−	0.161431i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−35.6637			−1.16633
$936$		0			0
$937$	30.7310			1.00394			0.501969	−	0.864886i	$-0.332609\pi$
$937$	30.7310			1.00394			0.501969	+	0.864886i	$0.332609\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	24.0527	+	13.8868i	0.784095	+	0.452697i	0.837880	−	0.545855i	$-0.183795\pi$
$941$	24.0527	+	13.8868i	0.784095	+	0.452697i	−0.0537847	+	0.998553i	$0.517128\pi$
$942$		0			0
$943$	−21.3034	+	12.2995i	−0.693734	+	0.400527i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	11.4561	+	19.8426i	0.372273	+	0.644796i	0.989915	−	0.141663i	$-0.0452450\pi$
$947$	11.4561	+	19.8426i	0.372273	+	0.644796i	−0.617641	+	0.786460i	$0.711912\pi$
$948$		0			0
$949$	−18.2547	+	31.6181i	−0.592573	+	1.02637i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			8.34110i			0.270195i	0.990832	+	0.135097i	$0.0431347\pi$
$953$			8.34110i			0.270195i	−0.990832	+	0.135097i	$0.956865\pi$
$954$		0			0
$955$		−	19.7314i		−	0.638492i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.176921	+	0.306436i	−0.00571308	+	0.00989534i
$960$		0			0
$961$	−15.4972	−	26.8419i	−0.499909	−	0.865869i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	22.9235	−	13.2349i	0.737933	−	0.426046i
$966$		0			0
$967$	−49.6181	−	28.6470i	−1.59561	−	0.921227i	−0.992319	−	0.123708i	$-0.960522\pi$
$967$	−49.6181	−	28.6470i	−1.59561	−	0.921227i	−0.603293	−	0.797519i	$-0.706145\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23.2853			−0.747259			−0.373630	−	0.927578i	$-0.621887\pi$
$971$	−23.2853			−0.747259			−0.373630	+	0.927578i	$0.621887\pi$
$972$		0			0
$973$	−10.5699			−0.338857
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−35.8129	−	20.6766i	−1.14576	−	0.661504i	−0.197908	−	0.980221i	$-0.563415\pi$
$977$	−35.8129	−	20.6766i	−1.14576	−	0.661504i	−0.947850	+	0.318717i	$0.896748\pi$
$978$		0			0
$979$	34.2272	−	19.7611i	1.09391	−	0.631568i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.9396	−	39.7326i	−0.731661	−	1.26727i	−0.956173	−	0.292802i	$-0.905412\pi$
$983$	−22.9396	−	39.7326i	−0.731661	−	1.26727i	0.224512	−	0.974471i	$-0.427921\pi$
$984$		0			0
$985$	−5.49458	+	9.51689i	−0.175072	+	0.303233i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	15.2706i		−	0.485578i
$990$		0			0
$991$			41.4407i			1.31641i	0.752840	+	0.658204i	$0.228683\pi$
$991$			41.4407i			1.31641i	−0.752840	+	0.658204i	$0.771317\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−13.5333	+	23.4403i	−0.429034	+	0.743108i
$996$		0			0
$997$	9.03515	+	15.6493i	0.286146	+	0.495620i	0.972886	−	0.231283i	$-0.0742924\pi$
$997$	9.03515	+	15.6493i	0.286146	+	0.495620i	−0.686740	+	0.726903i	$0.740959\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.s.a.287.10		24
3.2	odd	2		288.2.s.a.95.6	✓	24
4.3	odd	2	inner	864.2.s.a.287.9		24
8.3	odd	2		1728.2.s.g.1151.3		24
8.5	even	2		1728.2.s.g.1151.4		24
9.2	odd	6	inner	864.2.s.a.575.9		24
9.4	even	3		2592.2.c.c.2591.8		24
9.5	odd	6		2592.2.c.c.2591.18		24
9.7	even	3		288.2.s.a.191.7	yes	24
12.11	even	2		288.2.s.a.95.7	yes	24
24.5	odd	2		576.2.s.g.383.7		24
24.11	even	2		576.2.s.g.383.6		24
36.7	odd	6		288.2.s.a.191.6	yes	24
36.11	even	6	inner	864.2.s.a.575.10		24
36.23	even	6		2592.2.c.c.2591.17		24
36.31	odd	6		2592.2.c.c.2591.7		24
72.5	odd	6		5184.2.c.m.5183.8		24
72.11	even	6		1728.2.s.g.575.4		24
72.13	even	6		5184.2.c.m.5183.18		24
72.29	odd	6		1728.2.s.g.575.3		24
72.43	odd	6		576.2.s.g.191.7		24
72.59	even	6		5184.2.c.m.5183.7		24
72.61	even	6		576.2.s.g.191.6		24
72.67	odd	6		5184.2.c.m.5183.17		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.s.a.95.6	✓	24	3.2	odd	2
288.2.s.a.95.7	yes	24	12.11	even	2
288.2.s.a.191.6	yes	24	36.7	odd	6
288.2.s.a.191.7	yes	24	9.7	even	3
576.2.s.g.191.6		24	72.61	even	6
576.2.s.g.191.7		24	72.43	odd	6
576.2.s.g.383.6		24	24.11	even	2
576.2.s.g.383.7		24	24.5	odd	2
864.2.s.a.287.9		24	4.3	odd	2	inner
864.2.s.a.287.10		24	1.1	even	1	trivial
864.2.s.a.575.9		24	9.2	odd	6	inner
864.2.s.a.575.10		24	36.11	even	6	inner
1728.2.s.g.575.3		24	72.29	odd	6
1728.2.s.g.575.4		24	72.11	even	6
1728.2.s.g.1151.3		24	8.3	odd	2
1728.2.s.g.1151.4		24	8.5	even	2
2592.2.c.c.2591.7		24	36.31	odd	6
2592.2.c.c.2591.8		24	9.4	even	3
2592.2.c.c.2591.17		24	36.23	even	6
2592.2.c.c.2591.18		24	9.5	odd	6
5184.2.c.m.5183.7		24	72.59	even	6
5184.2.c.m.5183.8		24	72.5	odd	6
5184.2.c.m.5183.17		24	72.67	odd	6
5184.2.c.m.5183.18		24	72.13	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.68236 + 0.971313i) q^{5} +(2.61432 - 1.50938i) q^{7} +O(q^{10})\)	\(q+(1.68236 + 0.971313i) q^{5} +(2.61432 - 1.50938i) q^{7} +(2.20445 + 3.81822i) q^{11} +(-2.65994 + 4.60716i) q^{13} +4.16396i q^{17} -4.66253i q^{19} +(1.30500 - 2.26033i) q^{23} +(-0.613102 - 1.06192i) q^{25} +(-1.13594 + 0.655836i) q^{29} +(0.0648938 + 0.0374664i) q^{31} +5.86431 q^{35} +8.43839 q^{37} +(-8.16220 - 4.71245i) q^{41} +(5.06694 - 2.92540i) q^{43} +(2.40374 + 4.16340i) q^{47} +(1.05643 - 1.82979i) q^{49} +8.96419i q^{53} +8.56484i q^{55} +(-1.74923 + 3.02976i) q^{59} +(6.32247 + 10.9508i) q^{61} +(-8.94999 + 5.16728i) q^{65} +(-2.38773 - 1.37856i) q^{67} +0.910434 q^{71} +6.86281 q^{73} +(11.5263 + 6.65469i) q^{77} +(10.8815 - 6.28242i) q^{79} +(-8.61553 - 14.9225i) q^{83} +(-4.04451 + 7.00530i) q^{85} -8.96419i q^{89} +16.0594i q^{91} +(4.52877 - 7.84406i) q^{95} +(-9.03909 - 15.6562i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 12 q^{25} - 24 q^{29} + 36 q^{41} + 12 q^{49} + 48 q^{65} + 24 q^{73} + 48 q^{77} + 12 q^{97}+O(q^{100}) \) 24 * q + 12 * q^25 - 24 * q^29 + 36 * q^41 + 12 * q^49 + 48 * q^65 + 24 * q^73 + 48 * q^77 + 12 * q^97

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