LMFDB - Embedded newform 324.9.g.c.53.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,9,Mod(53,324)] 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("324.53"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	324.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,-5278] 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:	$131.990669660$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	324.53
Dual form			324.9.g.c.269.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-610.940 - 352.727i) q^{5} +(-1319.50 - 2285.44i) q^{7} +(-21382.9 + 12345.4i) q^{11} +(-6959.50 + 12054.2i) q^{13} -81127.1i q^{17} -77041.0 q^{19} +(-387947. - 223981. i) q^{23} +(53519.5 + 92698.5i) q^{25} +(-507080. + 292763. i) q^{29} +(-837121. + 1.44994e6i) q^{31} +1.86169e6i q^{35} +27359.0 q^{37} +(1.13024e6 + 652544. i) q^{41} +(-999601. - 1.73136e6i) q^{43} +(-6.27741e6 + 3.62427e6i) q^{47} +(-599760. + 1.03881e6i) q^{49} -2.40559e6i q^{53} +1.74182e7 q^{55} +(-1.93393e7 - 1.11656e7i) q^{59} +(-1.24642e7 - 2.15886e7i) q^{61} +(8.50368e6 - 4.90960e6i) q^{65} +(-5.99916e6 + 1.03908e7i) q^{67} -2.18690e6i q^{71} +3.80304e7 q^{73} +(5.64295e7 + 3.25796e7i) q^{77} +(1.00092e6 + 1.73365e6i) q^{79} +(2.98200e7 - 1.72166e7i) q^{83} +(-2.86157e7 + 4.95638e7i) q^{85} -462072. i q^{89} +3.67322e7 q^{91} +(4.70674e7 + 2.71744e7i) q^{95} +(-2.62082e7 - 4.53940e7i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5278 q^{7} - 27838 q^{13} - 308164 q^{19} + 214078 q^{25} - 3348484 q^{31} + 109436 q^{37} - 3998404 q^{43} - 2399040 q^{49} + 69672960 q^{55} - 49856638 q^{61} - 23996638 q^{67} + 152121596 q^{73}+ \cdots - 104832958 q^{97}+O(q^{100}) $ 4 * q - 5278 * q^7 - 27838 * q^13 - 308164 * q^19 + 214078 * q^25 - 3348484 * q^31 + 109436 * q^37 - 3998404 * q^43 - 2399040 * q^49 + 69672960 * q^55 - 49856638 * q^61 - 23996638 * q^67 + 152121596 * q^73 + 4003682 * q^79 - 114462720 * q^85 + 146928964 * q^91 - 104832958 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−610.940	−	352.727i	−0.977504	−	0.564362i	−0.0759886	−	0.997109i	$-0.524211\pi$
$5$	−610.940	−	352.727i	−0.977504	−	0.564362i	−0.901516	+	0.432746i	$0.857545\pi$
$6$		0			0
$7$	−1319.50	−	2285.44i	−0.549563	−	0.951870i	−0.998304	−	0.0582090i	$-0.981461\pi$
$7$	−1319.50	−	2285.44i	−0.549563	−	0.951870i	0.448742	−	0.893661i	$-0.351872\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−21382.9	+	12345.4i	−1.46048	+	0.843209i	−0.999033	−	0.0439579i	$-0.986003\pi$
$11$	−21382.9	+	12345.4i	−1.46048	+	0.843209i	−0.461448	+	0.887167i	$0.652670\pi$
$12$		0			0
$13$	−6959.50	+	12054.2i	−0.243671	+	0.422051i	−0.961757	−	0.273903i	$-0.911685\pi$
$13$	−6959.50	+	12054.2i	−0.243671	+	0.422051i	0.718086	+	0.695955i	$0.245019\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	81127.1i		−	0.971338i	−0.874143	−	0.485669i	$-0.838576\pi$
$17$		−	81127.1i		−	0.971338i	0.874143	−	0.485669i	$-0.161424\pi$
$18$		0			0
$19$	−77041.0			−0.591163			−0.295582	−	0.955317i	$-0.595513\pi$
$19$	−77041.0			−0.591163			−0.295582	+	0.955317i	$0.595513\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−387947.	−	223981.i	−1.38631	−	0.800388i	−0.393415	−	0.919361i	$-0.628706\pi$
$23$	−387947.	−	223981.i	−1.38631	−	0.800388i	−0.992897	+	0.118973i	$0.962040\pi$
$24$		0			0
$25$	53519.5	+	92698.5i	0.137010	+	0.237308i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−507080.	+	292763.i	−0.716943	+	0.413927i	−0.813627	−	0.581388i	$-0.802510\pi$
$29$	−507080.	+	292763.i	−0.716943	+	0.413927i	0.0966833	+	0.995315i	$0.469177\pi$
$30$		0			0
$31$	−837121.	+	1.44994e6i	−0.906445	+	1.57001i	−0.0874793	+	0.996166i	$0.527881\pi$
$31$	−837121.	+	1.44994e6i	−0.906445	+	1.57001i	−0.818966	+	0.573842i	$0.805452\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			1.86169e6i			1.24061i
$36$		0			0
$37$	27359.0			0.0145980			0.00729900	−	0.999973i	$-0.497677\pi$
$37$	27359.0			0.0145980			0.00729900	+	0.999973i	$0.497677\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.13024e6	+	652544.i	0.399977	+	0.230927i	0.686474	−	0.727154i	$-0.259158\pi$
$41$	1.13024e6	+	652544.i	0.399977	+	0.230927i	−0.286497	+	0.958081i	$0.592491\pi$
$42$		0			0
$43$	−999601.	−	1.73136e6i	−0.292383	−	0.506423i	0.681989	−	0.731362i	$-0.261115\pi$
$43$	−999601.	−	1.73136e6i	−0.292383	−	0.506423i	−0.974373	+	0.224939i	$0.927782\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.27741e6	+	3.62427e6i	−1.28644	+	0.742726i	−0.978017	−	0.208524i	$-0.933134\pi$
$47$	−6.27741e6	+	3.62427e6i	−1.28644	+	0.742726i	−0.308422	+	0.951250i	$0.599801\pi$
$48$		0			0
$49$	−599760.	+	1.03881e6i	−0.104038	+	0.180200i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	2.40559e6i		−	0.304873i	−0.988313	−	0.152437i	$-0.951288\pi$
$53$		−	2.40559e6i		−	0.304873i	0.988313	−	0.152437i	$-0.0487120\pi$
$54$		0			0
$55$	1.74182e7			1.90350
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.93393e7	−	1.11656e7i	−1.59600	−	0.921451i	−0.992247	−	0.124280i	$-0.960338\pi$
$59$	−1.93393e7	−	1.11656e7i	−1.59600	−	0.921451i	−0.603753	−	0.797171i	$-0.706329\pi$
$60$		0			0
$61$	−1.24642e7	−	2.15886e7i	−0.900210	−	1.55921i	−0.827221	−	0.561876i	$-0.810080\pi$
$61$	−1.24642e7	−	2.15886e7i	−0.900210	−	1.55921i	−0.0729882	−	0.997333i	$-0.523254\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	8.50368e6	−	4.90960e6i	0.476380	−	0.275038i
$66$		0			0
$67$	−5.99916e6	+	1.03908e7i	−0.297708	+	0.515646i	−0.975611	−	0.219505i	$-0.929556\pi$
$67$	−5.99916e6	+	1.03908e7i	−0.297708	+	0.515646i	0.677903	+	0.735152i	$0.262889\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	2.18690e6i		−	0.0860590i	−0.999074	−	0.0430295i	$-0.986299\pi$
$71$		−	2.18690e6i		−	0.0860590i	0.999074	−	0.0430295i	$-0.0137009\pi$
$72$		0			0
$73$	3.80304e7			1.33918			0.669591	−	0.742730i	$-0.266470\pi$
$73$	3.80304e7			1.33918			0.669591	+	0.742730i	$0.266470\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.64295e7	+	3.25796e7i	1.60525	+	0.926793i
$78$		0			0
$79$	1.00092e6	+	1.73365e6i	0.0256975	+	0.0445094i	0.878588	−	0.477580i	$-0.158486\pi$
$79$	1.00092e6	+	1.73365e6i	0.0256975	+	0.0445094i	−0.852891	+	0.522090i	$0.825153\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.98200e7	−	1.72166e7i	0.628341	−	0.362773i	−0.151768	−	0.988416i	$-0.548497\pi$
$83$	2.98200e7	−	1.72166e7i	0.628341	−	0.362773i	0.780109	+	0.625643i	$0.215163\pi$
$84$		0			0
$85$	−2.86157e7	+	4.95638e7i	−0.548187	+	0.949487i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	462072.i		−	0.00736460i	−0.999993	−	0.00368230i	$-0.998828\pi$
$89$		−	462072.i		−	0.00736460i	0.999993	−	0.00368230i	$-0.00117212\pi$
$90$		0			0
$91$	3.67322e7			0.535651
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.70674e7	+	2.71744e7i	0.577865	+	0.333630i
$96$		0			0
$97$	−2.62082e7	−	4.53940e7i	−0.296040	−	0.512757i	0.679186	−	0.733966i	$-0.262333\pi$
$97$	−2.62082e7	−	4.53940e7i	−0.296040	−	0.512757i	−0.975226	+	0.221209i	$0.929000\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.88602e7	−	4.55299e7i	0.757831	−	0.437534i	−0.0706856	−	0.997499i	$-0.522519\pi$
$101$	7.88602e7	−	4.55299e7i	0.757831	−	0.437534i	0.828516	+	0.559965i	$0.189185\pi$
$102$		0			0
$103$	−3.45990e7	+	5.99272e7i	−0.307408	+	0.532446i	−0.977794	−	0.209566i	$-0.932795\pi$
$103$	−3.45990e7	+	5.99272e7i	−0.307408	+	0.532446i	0.670387	+	0.742012i	$0.266128\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	6.35366e7i		−	0.484718i	−0.970187	−	0.242359i	$-0.922079\pi$
$107$		−	6.35366e7i		−	0.484718i	0.970187	−	0.242359i	$-0.0779212\pi$
$108$		0			0
$109$	−1.23077e7			−0.0871907			−0.0435953	−	0.999049i	$-0.513881\pi$
$109$	−1.23077e7			−0.0871907			−0.0435953	+	0.999049i	$0.513881\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.18866e8	−	1.26363e8i	−1.34235	−	0.775005i	−0.355196	−	0.934792i	$-0.615586\pi$
$113$	−2.18866e8	−	1.26363e8i	−1.34235	−	0.775005i	−0.987152	+	0.159787i	$0.948919\pi$
$114$		0			0
$115$	1.58008e8	+	2.73678e8i	0.903418	+	1.56477i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.85411e8	+	1.07047e8i	−0.924588	+	0.533811i
$120$		0			0
$121$	1.97640e8	−	3.42322e8i	0.922004	−	1.59696i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			2.00057e8i			0.819432i
$126$		0			0
$127$	1.96635e8			0.755868			0.377934	−	0.925833i	$-0.376635\pi$
$127$	1.96635e8			0.755868			0.377934	+	0.925833i	$0.376635\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.06286e7	−	2.92304e7i	−0.171914	−	0.0992545i	0.411574	−	0.911376i	$-0.364979\pi$
$131$	−5.06286e7	−	2.92304e7i	−0.171914	−	0.0992545i	−0.583488	+	0.812122i	$0.698312\pi$
$132$		0			0
$133$	1.01656e8	+	1.76073e8i	0.324881	+	0.562711i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.12240e8	+	2.95742e8i	−1.45409	+	0.839519i	−0.998710	−	0.0507787i	$-0.983830\pi$
$137$	−5.12240e8	+	2.95742e8i	−1.45409	+	0.839519i	−0.455379	+	0.890298i	$0.650496\pi$
$138$		0			0
$139$	2.61160e8	−	4.52343e8i	0.699597	−	1.21174i	−0.269009	−	0.963138i	$-0.586696\pi$
$139$	2.61160e8	−	4.52343e8i	0.699597	−	1.21174i	0.968606	−	0.248601i	$-0.0799706\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	3.43672e8i		−	0.821864i
$144$		0			0
$145$	4.13061e8			0.934420
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.25715e8	+	2.45787e8i	0.863723	+	0.498670i	0.865257	−	0.501328i	$-0.167155\pi$
$149$	4.25715e8	+	2.45787e8i	0.863723	+	0.498670i	−0.00153453	+	0.999999i	$0.500488\pi$
$150$		0			0
$151$	4.22311e8	+	7.31464e8i	0.812315	+	1.40697i	0.911240	+	0.411877i	$0.135127\pi$
$151$	4.22311e8	+	7.31464e8i	0.812315	+	1.40697i	−0.0989242	+	0.995095i	$0.531540\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.02286e9	−	5.90550e8i	1.77211	−	1.02313i
$156$		0			0
$157$	3.36001e8	−	5.81971e8i	0.553022	−	0.957862i	−0.445033	−	0.895514i	$-0.646808\pi$
$157$	3.36001e8	−	5.81971e8i	0.553022	−	0.957862i	0.998055	−	0.0623475i	$-0.0198587\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			1.18217e9i			1.75945i
$162$		0			0
$163$	−2.35500e8			−0.333611			−0.166805	−	0.985990i	$-0.553345\pi$
$163$	−2.35500e8			−0.333611			−0.166805	+	0.985990i	$0.553345\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.08470e8	−	2.93565e8i	−0.653732	−	0.377432i	0.136153	−	0.990688i	$-0.456526\pi$
$167$	−5.08470e8	−	2.93565e8i	−0.653732	−	0.377432i	−0.789885	+	0.613256i	$0.789860\pi$
$168$		0			0
$169$	3.10996e8	+	5.38661e8i	0.381248	+	0.660342i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.87212e8	+	5.69967e8i	−1.10211	+	0.636305i	−0.936775	−	0.349932i	$-0.886205\pi$
$173$	−9.87212e8	+	5.69967e8i	−1.10211	+	0.636305i	−0.165338	+	0.986237i	$0.552871\pi$
$174$		0			0
$175$	1.41238e8	−	2.44631e8i	0.150591	−	0.260831i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	1.40519e9i		−	1.36875i	−0.729131	−	0.684374i	$-0.760076\pi$
$179$		−	1.40519e9i		−	1.36875i	0.729131	−	0.684374i	$-0.239924\pi$
$180$		0			0
$181$	2.00063e9			1.86402			0.932012	−	0.362426i	$-0.118051\pi$
$181$	2.00063e9			1.86402			0.932012	+	0.362426i	$0.118051\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.67147e7	−	9.65024e6i	−0.0142696	−	0.00823856i
$186$		0			0
$187$	1.00155e9	+	1.73473e9i	0.819041	+	1.41862i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.29905e9	−	7.50008e8i	0.976097	−	0.563550i	0.0750073	−	0.997183i	$-0.476102\pi$
$191$	1.29905e9	−	7.50008e8i	0.976097	−	0.563550i	0.901089	+	0.433633i	$0.142769\pi$
$192$		0			0
$193$	−1.26894e9	+	2.19787e9i	−0.914559	+	1.58406i	−0.107014	+	0.994258i	$0.534129\pi$
$193$	−1.26894e9	+	2.19787e9i	−0.914559	+	1.58406i	−0.807545	+	0.589806i	$0.799204\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	1.55082e9i		−	1.02967i	−0.857290	−	0.514834i	$-0.827854\pi$
$197$		−	1.55082e9i		−	1.02967i	0.857290	−	0.514834i	$-0.172146\pi$
$198$		0			0
$199$	2.67114e9			1.70328			0.851638	−	0.524130i	$-0.175610\pi$
$199$	2.67114e9			1.70328			0.851638	+	0.524130i	$0.175610\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.33819e9	+	7.72602e8i	0.788011	+	0.454958i
$204$		0			0
$205$	−4.60339e8	−	7.97331e8i	−0.260653	−	0.451464i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.64736e9	−	9.51104e8i	0.863383	−	0.498474i
$210$		0			0
$211$	1.42931e9	−	2.47563e9i	0.721101	−	1.24898i	−0.239458	−	0.970907i	$-0.576970\pi$
$211$	1.42931e9	−	2.47563e9i	0.721101	−	1.24898i	0.960559	−	0.278077i	$-0.0896969\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			1.41034e9i			0.660041i
$216$		0			0
$217$	4.41832e9			1.99259
$218$		0			0
$219$		0			0
$220$		0			0
$221$	9.77923e8	+	5.64604e8i	0.409954	+	0.236687i
$222$		0			0
$223$	−1.33866e8	−	2.31863e8i	−0.0541317	−	0.0937588i	0.837690	−	0.546146i	$-0.183906\pi$
$223$	−1.33866e8	−	2.31863e8i	−0.0541317	−	0.0937588i	−0.891821	+	0.452387i	$0.850572\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.73464e9	+	1.57885e9i	−1.02990	+	0.594616i	−0.916957	−	0.398985i	$-0.869362\pi$
$227$	−2.73464e9	+	1.57885e9i	−1.02990	+	0.594616i	−0.112947	+	0.993601i	$0.536029\pi$
$228$		0			0
$229$	9.98952e6	−	1.73024e7i	0.00363248	−	0.00629163i	−0.864203	−	0.503143i	$-0.832177\pi$
$229$	9.98952e6	−	1.73024e7i	0.00363248	−	0.00629163i	0.867836	+	0.496851i	$0.165510\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			3.55234e9i			1.20529i	0.798011	+	0.602644i	$0.205886\pi$
$233$			3.55234e9i			1.20529i	−0.798011	+	0.602644i	$0.794114\pi$
$234$		0			0
$235$	5.11350e9			1.67667
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.68512e9	−	1.55025e9i	−0.822947	−	0.475129i	0.0284846	−	0.999594i	$-0.490932\pi$
$239$	−2.68512e9	−	1.55025e9i	−0.822947	−	0.475129i	−0.851432	+	0.524465i	$0.824265\pi$
$240$		0			0
$241$	7.07719e8	+	1.22580e9i	0.209794	+	0.363373i	0.951649	−	0.307186i	$-0.0993874\pi$
$241$	7.07719e8	+	1.22580e9i	0.209794	+	0.363373i	−0.741856	+	0.670560i	$0.766054\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7.32835e8	−	4.23103e8i	0.203396	−	0.117431i
$246$		0			0
$247$	5.36167e8	−	9.28668e8i	0.144050	−	0.249501i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			6.36947e8i			0.160475i	0.996776	+	0.0802376i	$0.0255679\pi$
$251$			6.36947e8i			0.160475i	−0.996776	+	0.0802376i	$0.974432\pi$
$252$		0			0
$253$	1.10606e10			2.69958
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.20715e9	−	6.96949e8i	−0.276713	−	0.159760i	0.355222	−	0.934782i	$-0.384405\pi$
$257$	−1.20715e9	−	6.96949e8i	−0.276713	−	0.159760i	−0.631934	+	0.775022i	$0.717739\pi$
$258$		0			0
$259$	−3.61002e7	−	6.25274e7i	−0.00802252	−	0.0138954i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.43650e9	+	3.13877e9i	−1.13631	+	0.656048i	−0.945514	−	0.325582i	$-0.894440\pi$
$263$	−5.43650e9	+	3.13877e9i	−1.13631	+	0.656048i	−0.190795	+	0.981630i	$0.561107\pi$
$264$		0			0
$265$	−8.48517e8	+	1.46967e9i	−0.172059	+	0.298015i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	7.75652e9i		−	1.48135i	−0.671863	−	0.740676i	$-0.734506\pi$
$269$		−	7.75652e9i		−	1.48135i	0.671863	−	0.740676i	$-0.265494\pi$
$270$		0			0
$271$	−8.57427e9			−1.58972			−0.794859	−	0.606794i	$-0.792455\pi$
$271$	−8.57427e9			−1.58972			−0.794859	+	0.606794i	$0.792455\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.28881e9	−	1.32144e9i	−0.400201	−	0.231056i
$276$		0			0
$277$	2.77625e9	+	4.80860e9i	0.471562	+	0.816770i	0.999471	−	0.0325314i	$-0.0103569\pi$
$277$	2.77625e9	+	4.80860e9i	0.471562	+	0.816770i	−0.527908	+	0.849301i	$0.677024\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−2.88177e9	+	1.66379e9i	−0.462205	+	0.266854i	−0.712971	−	0.701194i	$-0.752651\pi$
$281$	−2.88177e9	+	1.66379e9i	−0.462205	+	0.266854i	0.250766	+	0.968048i	$0.419318\pi$
$282$		0			0
$283$	2.23197e9	−	3.86589e9i	0.347971	−	0.602704i	−0.637918	−	0.770104i	$-0.720204\pi$
$283$	2.23197e9	−	3.86589e9i	0.347971	−	0.602704i	0.985889	+	0.167401i	$0.0535374\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	3.44413e9i		−	0.507635i
$288$		0			0
$289$	3.94151e8			0.0565030
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.29174e9	−	2.47784e9i	−0.582321	−	0.336203i	0.179734	−	0.983715i	$-0.442476\pi$
$293$	−4.29174e9	−	2.47784e9i	−0.582321	−	0.336203i	−0.762055	+	0.647512i	$0.775810\pi$
$294$		0			0
$295$	7.87678e9	+	1.36430e10i	1.04007	+	1.80145i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.39984e9	−	3.11760e9i	0.675610	−	0.390063i
$300$		0			0
$301$	−2.63795e9	+	4.56906e9i	−0.321366	+	0.556622i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			1.75858e10i			2.03218i
$306$		0			0
$307$	−9.36938e9			−1.05477			−0.527385	−	0.849627i	$-0.676827\pi$
$307$	−9.36938e9			−1.05477			−0.527385	+	0.849627i	$0.676827\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.26803e10	+	7.32096e9i	1.35546	+	0.782576i	0.989008	−	0.147860i	$-0.0472385\pi$
$311$	1.26803e10	+	7.32096e9i	1.35546	+	0.782576i	0.366454	+	0.930436i	$0.380572\pi$
$312$		0			0
$313$	−5.89967e9	−	1.02185e10i	−0.614681	−	1.06466i	−0.990440	−	0.137942i	$-0.955951\pi$
$313$	−5.89967e9	−	1.02185e10i	−0.614681	−	1.06466i	0.375759	−	0.926717i	$-0.377382\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.31569e10	−	7.59614e9i	1.30292	−	0.752239i	0.322013	−	0.946735i	$-0.395641\pi$
$317$	1.31569e10	−	7.59614e9i	1.30292	−	0.752239i	0.980903	+	0.194496i	$0.0623072\pi$
$318$		0			0
$319$	7.22857e9	−	1.25202e10i	0.698055	−	1.20907i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			6.25011e9i			0.574219i
$324$		0			0
$325$	−1.48988e9			−0.133542
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.65661e10	+	9.56444e9i	1.41396	+	0.816349i
$330$		0			0
$331$	4.65291e9	+	8.05908e9i	0.387626	+	0.671387i	0.992130	−	0.125215i	$-0.0399620\pi$
$331$	4.65291e9	+	8.05908e9i	0.387626	+	0.671387i	−0.604504	+	0.796602i	$0.706629\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	7.33026e9	−	4.23213e9i	0.582023	−	0.336031i
$336$		0			0
$337$	4.27012e9	−	7.39607e9i	0.331071	−	0.573432i	−0.651651	−	0.758519i	$-0.725923\pi$
$337$	4.27012e9	−	7.39607e9i	0.331071	−	0.573432i	0.982722	+	0.185087i	$0.0592568\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	4.13385e10i		−	3.05729i
$342$		0			0
$343$	−1.20478e10			−0.870423
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.12993e10	−	6.52366e9i	−0.779352	−	0.449959i	0.0568484	−	0.998383i	$-0.481895\pi$
$347$	−1.12993e10	−	6.52366e9i	−0.779352	−	0.449959i	−0.836201	+	0.548424i	$0.815228\pi$
$348$		0			0
$349$	−9.49522e8	−	1.64462e9i	−0.0640034	−	0.110857i	0.832248	−	0.554403i	$-0.187054\pi$
$349$	−9.49522e8	−	1.64462e9i	−0.0640034	−	0.110857i	−0.896251	+	0.443546i	$0.853720\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.32764e10	+	7.66512e9i	−0.855029	+	0.493651i	−0.862344	−	0.506322i	$-0.831005\pi$
$353$	−1.32764e10	+	7.66512e9i	−0.855029	+	0.493651i	0.00731550	+	0.999973i	$0.497671\pi$
$354$		0			0
$355$	−7.71379e8	+	1.33607e9i	−0.0485685	+	0.0841231i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			2.20067e10i			1.32488i	0.749113	+	0.662442i	$0.230480\pi$
$359$			2.20067e10i			1.32488i	−0.749113	+	0.662442i	$0.769520\pi$
$360$		0			0
$361$	−1.10482e10			−0.650526
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.32343e10	−	1.34143e10i	−1.30906	−	0.755784i
$366$		0			0
$367$	−1.37249e9	−	2.37723e9i	−0.0756565	−	0.131041i	0.825715	−	0.564087i	$-0.190772\pi$
$367$	−1.37249e9	−	2.37723e9i	−0.0756565	−	0.131041i	−0.901372	+	0.433047i	$0.857439\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−5.49785e9	+	3.17418e9i	−0.290200	+	0.167547i
$372$		0			0
$373$	3.12899e9	−	5.41958e9i	0.161648	−	0.279982i	−0.773812	−	0.633415i	$-0.781653\pi$
$373$	3.12899e9	−	5.41958e9i	0.161648	−	0.279982i	0.935460	+	0.353433i	$0.114986\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	8.14994e9i		−	0.403449i
$378$		0			0
$379$	−7.38075e9			−0.357720			−0.178860	−	0.983875i	$-0.557241\pi$
$379$	−7.38075e9			−0.357720			−0.178860	+	0.983875i	$0.557241\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.74522e10	+	1.00761e10i	0.811066	+	0.468269i	0.847326	−	0.531073i	$-0.178211\pi$
$383$	1.74522e10	+	1.00761e10i	0.811066	+	0.468269i	−0.0362600	+	0.999342i	$0.511544\pi$
$384$		0			0
$385$	−2.29834e10	−	3.98084e10i	−1.04609	−	1.81189i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.15504e9	+	4.70832e9i	−0.356146	+	0.205621i	−0.667389	−	0.744710i	$-0.732588\pi$
$389$	−8.15504e9	+	4.70832e9i	−0.356146	+	0.205621i	0.311243	+	0.950330i	$0.399255\pi$
$390$		0			0
$391$	−1.81710e10	+	3.14730e10i	−0.777447	+	1.34658i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	1.41220e9i		−	0.0580109i
$396$		0			0
$397$	−3.66441e9			−0.147517			−0.0737585	−	0.997276i	$-0.523499\pi$
$397$	−3.66441e9			−0.147517			−0.0737585	+	0.997276i	$0.523499\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.62816e10	−	1.51737e10i	−1.01642	−	0.586833i	−0.103358	−	0.994644i	$-0.532959\pi$
$401$	−2.62816e10	−	1.51737e10i	−1.01642	−	0.586833i	−0.913066	+	0.407811i	$0.866292\pi$
$402$		0			0
$403$	−1.16519e10	−	2.01817e10i	−0.441750	−	0.765133i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.85015e8	+	3.37759e8i	−0.0213201	+	0.0123092i
$408$		0			0
$409$	−1.45970e10	+	2.52827e10i	−0.521638	+	0.903503i	0.478046	+	0.878335i	$0.341345\pi$
$409$	−1.45970e10	+	2.52827e10i	−0.521638	+	0.903503i	−0.999683	+	0.0251680i	$0.991988\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			5.89318e10i			2.02558i
$414$		0			0
$415$	−2.42910e10			−0.818941
$416$		0			0
$417$		0			0
$418$		0			0
$419$	7.46657e9	+	4.31083e9i	0.242251	+	0.139864i	0.616211	−	0.787581i	$-0.288667\pi$
$419$	7.46657e9	+	4.31083e9i	0.242251	+	0.139864i	−0.373960	+	0.927445i	$0.622000\pi$
$420$		0			0
$421$	−1.17687e10	−	2.03840e10i	−0.374628	−	0.648876i	0.615643	−	0.788025i	$-0.288896\pi$
$421$	−1.17687e10	−	2.03840e10i	−0.374628	−	0.648876i	−0.990271	+	0.139150i	$0.955563\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.52036e9	−	4.34188e9i	0.230506	−	0.133083i
$426$		0			0
$427$	−3.28929e10	+	5.69722e10i	−0.989443	+	1.71377i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	9.81034e9i		−	0.284299i	−0.989845	−	0.142149i	$-0.954599\pi$
$431$		−	9.81034e9i		−	0.284299i	0.989845	−	0.142149i	$-0.0454013\pi$
$432$		0			0
$433$	−4.87335e10			−1.38636			−0.693180	−	0.720764i	$-0.743791\pi$
$433$	−4.87335e10			−1.38636			−0.693180	+	0.720764i	$0.743791\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.98878e10	+	1.72557e10i	0.819537	+	0.473160i
$438$		0			0
$439$	−9.45805e9	−	1.63818e10i	−0.254650	−	0.441066i	0.710151	−	0.704050i	$-0.248627\pi$
$439$	−9.45805e9	−	1.63818e10i	−0.254650	−	0.441066i	−0.964800	+	0.262983i	$0.915294\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.19118e10	+	3.57448e10i	−1.60753	+	0.928106i	−0.617606	+	0.786487i	$0.711898\pi$
$443$	−6.19118e10	+	3.57448e10i	−1.60753	+	0.928106i	−0.989921	+	0.141619i	$0.954769\pi$
$444$		0			0
$445$	−1.62985e8	+	2.82298e8i	−0.00415631	+	0.00719893i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	3.44073e10i		−	0.846574i	−0.905996	−	0.423287i	$-0.860876\pi$
$449$		−	3.44073e10i		−	0.846574i	0.905996	−	0.423287i	$-0.139124\pi$
$450$		0			0
$451$	−3.22237e10			−0.778879
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.24412e10	−	1.29564e10i	−0.523601	−	0.302301i
$456$		0			0
$457$	−3.42138e10	−	5.92600e10i	−0.784398	−	1.35862i	−0.929358	−	0.369179i	$-0.879639\pi$
$457$	−3.42138e10	−	5.92600e10i	−0.784398	−	1.35862i	0.144961	−	0.989437i	$-0.453694\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.11916e10	−	2.95555e10i	1.13343	−	0.654387i	0.188635	−	0.982047i	$-0.439594\pi$
$461$	5.11916e10	−	2.95555e10i	1.13343	−	0.654387i	0.944795	+	0.327661i	$0.106260\pi$
$462$		0			0
$463$	−1.19605e10	+	2.07161e10i	−0.260270	+	0.450801i	−0.966314	−	0.257368i	$-0.917145\pi$
$463$	−1.19605e10	+	2.07161e10i	−0.260270	+	0.450801i	0.706044	+	0.708168i	$0.250478\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	5.73549e10i		−	1.20588i	−0.797787	−	0.602939i	$-0.793996\pi$
$467$		−	5.73549e10i		−	1.20588i	0.797787	−	0.602939i	$-0.206004\pi$
$468$		0			0
$469$	3.16636e10			0.654438
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.27488e10	+	2.46810e10i	0.854041	+	0.493081i
$474$		0			0
$475$	−4.12320e9	−	7.14158e9i	−0.0809952	−	0.140288i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.40792e10	−	2.54491e10i	0.837321	−	0.483427i	−0.0190320	−	0.999819i	$-0.506058\pi$
$479$	4.40792e10	−	2.54491e10i	0.837321	−	0.483427i	0.856353	+	0.516392i	$0.172725\pi$
$480$		0			0
$481$	−1.90405e8	+	3.29791e8i	−0.00355712	+	0.00616110i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			3.69774e10i			0.668296i
$486$		0			0
$487$	7.54226e9			0.134087			0.0670433	−	0.997750i	$-0.478643\pi$
$487$	7.54226e9			0.134087			0.0670433	+	0.997750i	$0.478643\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.17096e10	−	5.29486e10i	−1.57793	−	0.911021i	−0.995147	−	0.0983960i	$-0.968629\pi$
$491$	−9.17096e10	−	5.29486e10i	−1.57793	−	0.911021i	−0.582787	−	0.812625i	$-0.698038\pi$
$492$		0			0
$493$	2.37510e10	+	4.11380e10i	0.402063	+	0.696394i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.99804e9	+	2.88562e9i	−0.0819170	+	0.0472948i
$498$		0			0
$499$	1.53106e10	−	2.65187e10i	0.246939	−	0.427711i	−0.715736	−	0.698371i	$-0.753909\pi$
$499$	1.53106e10	−	2.65187e10i	0.246939	−	0.427711i	0.962675	+	0.270660i	$0.0872418\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			5.46233e10i			0.853308i	0.904415	+	0.426654i	$0.140308\pi$
$503$			5.46233e10i			0.853308i	−0.904415	+	0.426654i	$0.859692\pi$
$504$		0			0
$505$	−6.42385e10			−0.987710
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.96944e10	+	1.13705e10i	0.293407	+	0.169399i	0.639477	−	0.768810i	$-0.279151\pi$
$509$	1.96944e10	+	1.13705e10i	0.293407	+	0.169399i	−0.346070	+	0.938209i	$0.612484\pi$
$510$		0			0
$511$	−5.01811e10	−	8.69162e10i	−0.735964	−	1.27473i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.22758e10	−	2.44080e10i	0.600985	−	0.346979i
$516$		0			0
$517$	8.94862e10	−	1.54995e11i	1.25255	−	2.16947i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	7.23199e10i		−	0.981538i	−0.871290	−	0.490769i	$-0.836716\pi$
$521$		−	7.23199e10i		−	0.981538i	0.871290	−	0.490769i	$-0.163284\pi$
$522$		0			0
$523$	−1.34399e11			−1.79634			−0.898168	−	0.439652i	$-0.855102\pi$
$523$	−1.34399e11			−1.79634			−0.898168	+	0.439652i	$0.855102\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.17629e11	+	6.79132e10i	1.52501	+	0.880464i
$528$		0			0
$529$	6.11798e10	+	1.05967e11i	0.781241	+	1.35315i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.57318e10	+	9.08276e9i	−0.194926	+	0.112541i
$534$		0			0
$535$	−2.24111e10	+	3.88171e10i	−0.273557	+	0.473814i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	2.96172e10i		−	0.350904i
$540$		0			0
$541$	2.43319e10			0.284044			0.142022	−	0.989863i	$-0.454640\pi$
$541$	2.43319e10			0.284044			0.142022	+	0.989863i	$0.454640\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7.51926e9	+	4.34124e9i	0.0852293	+	0.0492072i
$546$		0			0
$547$	4.30671e9	+	7.45944e9i	0.0481056	+	0.0833214i	0.889076	−	0.457760i	$-0.151348\pi$
$547$	4.30671e9	+	7.45944e9i	0.0481056	+	0.0833214i	−0.840970	+	0.541082i	$0.818015\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.90660e10	−	2.25548e10i	0.423831	−	0.244699i
$552$		0			0
$553$	2.64143e9	−	4.57509e9i	0.0282448	−	0.0489214i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			9.83454e10i			1.02172i	0.859663	+	0.510862i	$0.170674\pi$
$557$			9.83454e10i			1.02172i	−0.859663	+	0.510862i	$0.829326\pi$
$558$		0			0
$559$	2.78269e10			0.284982
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.59836e10	+	9.22814e9i	0.159089	+	0.0918503i	0.577431	−	0.816439i	$-0.304055\pi$
$563$	1.59836e10	+	9.22814e9i	0.159089	+	0.0918503i	−0.418342	+	0.908290i	$0.637389\pi$
$564$		0			0
$565$	8.91428e10	+	1.54400e11i	0.874767	+	1.51514i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.23535e11	+	7.13227e10i	−1.17853	+	0.680423i	−0.955673	−	0.294429i	$-0.904870\pi$
$569$	−1.23535e11	+	7.13227e10i	−1.17853	+	0.680423i	−0.222853	+	0.974852i	$0.571537\pi$
$570$		0			0
$571$	−4.73284e10	+	8.19752e10i	−0.445223	+	0.771148i	−0.998068	−	0.0621358i	$-0.980209\pi$
$571$	−4.73284e10	+	8.19752e10i	−0.445223	+	0.771148i	0.552845	+	0.833284i	$0.313542\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	4.79495e10i		−	0.438644i
$576$		0			0
$577$	−6.51933e10			−0.588165			−0.294083	−	0.955780i	$-0.595014\pi$
$577$	−6.51933e10			−0.588165			−0.294083	+	0.955780i	$0.595014\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.86950e10	−	4.54346e10i	−0.690625	−	0.398733i
$582$		0			0
$583$	2.96981e10	+	5.14386e10i	0.257072	+	0.445261i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.42227e10	−	1.97585e10i	0.288245	−	0.166418i	−0.348905	−	0.937158i	$-0.613447\pi$
$587$	3.42227e10	−	1.97585e10i	0.288245	−	0.166418i	0.637150	+	0.770740i	$0.280113\pi$
$588$		0			0
$589$	6.44926e10	−	1.11705e11i	0.535857	−	0.928132i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			1.40557e11i			1.13667i	0.822798	+	0.568334i	$0.192412\pi$
$593$			1.40557e11i			1.13667i	−0.822798	+	0.568334i	$0.807588\pi$
$594$		0			0
$595$	1.51034e11			1.20505
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.13177e11	−	6.53426e10i	−0.879124	−	0.507562i	−0.00875424	−	0.999962i	$-0.502787\pi$
$599$	−1.13177e11	−	6.53426e10i	−0.879124	−	0.507562i	−0.870369	+	0.492399i	$0.836120\pi$
$600$		0			0
$601$	6.12844e9	+	1.06148e10i	0.0469734	+	0.0813603i	0.888556	−	0.458768i	$-0.151709\pi$
$601$	6.12844e9	+	1.06148e10i	0.0469734	+	0.0813603i	−0.841583	+	0.540128i	$0.818376\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.41492e11	+	1.39426e11i	−1.80253	+	1.04069i
$606$		0			0
$607$	−3.95568e10	+	6.85144e10i	−0.291385	+	0.504693i	−0.974137	−	0.225957i	$-0.927449\pi$
$607$	−3.95568e10	+	6.85144e10i	−0.291385	+	0.504693i	0.682753	+	0.730649i	$0.260783\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	1.00892e11i		−	0.723924i
$612$		0			0
$613$	−1.81518e10			−0.128552			−0.0642760	−	0.997932i	$-0.520474\pi$
$613$	−1.81518e10			−0.128552			−0.0642760	+	0.997932i	$0.520474\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.50679e11	−	8.69948e10i	−1.03971	−	0.600278i	−0.119960	−	0.992779i	$-0.538277\pi$
$617$	−1.50679e11	−	8.69948e10i	−1.03971	−	0.600278i	−0.919752	+	0.392501i	$0.871610\pi$
$618$		0			0
$619$	2.94108e10	+	5.09410e10i	0.200329	+	0.346980i	0.948634	−	0.316374i	$-0.102466\pi$
$619$	2.94108e10	+	5.09410e10i	0.200329	+	0.346980i	−0.748305	+	0.663354i	$0.769132\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.05604e9	+	6.09704e8i	−0.00701015	+	0.00404731i
$624$		0			0
$625$	9.14713e10	−	1.58433e11i	0.599466	−	1.03831i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	2.21956e9i		−	0.0141796i
$630$		0			0
$631$	1.13829e11			0.718020			0.359010	−	0.933334i	$-0.383114\pi$
$631$	1.13829e11			0.718020			0.359010	+	0.933334i	$0.383114\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.20132e11	−	6.93583e10i	−0.738864	−	0.426583i
$636$		0			0
$637$	−8.34806e9	−	1.44593e10i	−0.0507023	−	0.0878190i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.04568e11	−	1.18107e11i	1.21173	−	0.699592i	0.248593	−	0.968608i	$-0.420032\pi$
$641$	2.04568e11	−	1.18107e11i	1.21173	−	0.699592i	0.963136	+	0.269016i	$0.0866984\pi$
$642$		0			0
$643$	−7.58520e10	+	1.31380e11i	−0.443735	+	0.768571i	−0.997963	−	0.0637936i	$-0.979680\pi$
$643$	−7.58520e10	+	1.31380e11i	−0.443735	+	0.768571i	0.554228	+	0.832365i	$0.313013\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	8.87726e9i		−	0.0506596i	−0.999679	−	0.0253298i	$-0.991936\pi$
$647$		−	8.87726e9i		−	0.0506596i	0.999679	−	0.0253298i	$-0.00806359\pi$
$648$		0			0
$649$	5.51374e11			3.10791
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.99815e11	+	1.15363e11i	1.09894	+	0.634475i	0.935943	−	0.352152i	$-0.114550\pi$
$653$	1.99815e11	+	1.15363e11i	1.09894	+	0.634475i	0.162999	+	0.986626i	$0.447883\pi$
$654$		0			0
$655$	2.06207e10	+	3.57161e10i	0.112031	+	0.194043i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.02511e11	−	5.91849e10i	0.543538	−	0.313812i	−0.202974	−	0.979184i	$-0.565061\pi$
$659$	1.02511e11	−	5.91849e10i	0.543538	−	0.313812i	0.746512	+	0.665372i	$0.231727\pi$
$660$		0			0
$661$	1.13003e11	−	1.95726e11i	0.591946	−	1.02528i	−0.402024	−	0.915629i	$-0.631693\pi$
$661$	1.13003e11	−	1.95726e11i	0.591946	−	1.02528i	0.993970	−	0.109652i	$-0.0349736\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	1.43427e11i		−	0.733403i
$666$		0			0
$667$	2.62294e11			1.32521
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.33040e11	+	3.07751e11i	2.62948	+	1.51813i
$672$		0			0
$673$	−1.45420e11	−	2.51874e11i	−0.708864	−	1.22779i	−0.965279	−	0.261222i	$-0.915875\pi$
$673$	−1.45420e11	−	2.51874e11i	−0.708864	−	1.22779i	0.256415	−	0.966567i	$-0.417459\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	5.46120e10	−	3.15302e10i	0.259976	−	0.150097i	−0.364348	−	0.931263i	$-0.618708\pi$
$677$	5.46120e10	−	3.15302e10i	0.259976	−	0.150097i	0.624324	+	0.781166i	$0.285375\pi$
$678$		0			0
$679$	−6.91635e10	+	1.19795e11i	−0.325385	+	0.563584i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			6.54747e10i			0.300878i	0.988619	+	0.150439i	$0.0480687\pi$
$683$			6.54747e10i			0.300878i	−0.988619	+	0.150439i	$0.951931\pi$
$684$		0			0
$685$	4.17264e11			1.89517
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.89975e10	+	1.67417e10i	0.128672	+	0.0742889i
$690$		0			0
$691$	3.64439e10	+	6.31227e10i	0.159850	+	0.276869i	0.934815	−	0.355136i	$-0.115566\pi$
$691$	3.64439e10	+	6.31227e10i	0.159850	+	0.276869i	−0.774964	+	0.632005i	$0.782232\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.19107e11	+	1.84236e11i	−1.36772	+	0.789653i
$696$		0			0
$697$	5.29390e10	−	9.16931e10i	0.224308	−	0.388513i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			2.18377e10i			0.0904347i	0.998977	+	0.0452173i	$0.0143980\pi$
$701$			2.18377e10i			0.0904347i	−0.998977	+	0.0452173i	$0.985602\pi$
$702$		0			0
$703$	−2.10776e9			−0.00862980
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.08112e11	−	1.20154e11i	−0.832951	−	0.480904i
$708$		0			0
$709$	1.48096e11	+	2.56510e11i	0.586082	+	1.01512i	0.994740	+	0.102436i	$0.0326636\pi$
$709$	1.48096e11	+	2.56510e11i	0.586082	+	1.01512i	−0.408658	+	0.912688i	$0.634003\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.49517e11	−	3.74999e11i	2.51323	−	1.45102i
$714$		0			0
$715$	−1.21222e11	+	2.09963e11i	−0.463829	+	0.803376i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			4.64816e11i			1.73927i	0.493699	+	0.869633i	$0.335644\pi$
$719$			4.64816e11i			1.73927i	−0.493699	+	0.869633i	$0.664356\pi$
$720$		0			0
$721$	1.82614e11			0.675759
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.42774e10	−	3.13371e10i	−0.196457	−	0.113424i
$726$		0			0
$727$	1.93507e11	+	3.35164e11i	0.692722	+	1.19983i	0.970942	+	0.239313i	$0.0769222\pi$
$727$	1.93507e11	+	3.35164e11i	0.692722	+	1.19983i	−0.278220	+	0.960517i	$0.589744\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.40460e11	+	8.10947e10i	−0.491908	+	0.284003i
$732$		0			0
$733$	5.72572e10	−	9.91724e10i	0.198342	−	0.343538i	−0.749649	−	0.661836i	$-0.769778\pi$
$733$	5.72572e10	−	9.91724e10i	0.198342	−	0.343538i	0.947991	+	0.318297i	$0.103111\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	2.96249e11i		−	1.00412i
$738$		0			0
$739$	9.88171e10			0.331325			0.165663	−	0.986183i	$-0.447024\pi$
$739$	9.88171e10			0.331325			0.165663	+	0.986183i	$0.447024\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−2.80555e11	−	1.61978e11i	−0.920581	−	0.531498i	−0.0367607	−	0.999324i	$-0.511704\pi$
$743$	−2.80555e11	−	1.61978e11i	−0.920581	−	0.531498i	−0.883820	+	0.467826i	$0.845037\pi$
$744$		0			0
$745$	−1.73391e11	−	3.00322e11i	−0.562862	−	0.974905i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.45209e11	+	8.38366e10i	−0.461389	+	0.266383i
$750$		0			0
$751$	−1.28902e11	+	2.23264e11i	−0.405227	+	0.701874i	−0.994348	−	0.106171i	$-0.966141\pi$
$751$	−1.28902e11	+	2.23264e11i	−0.405227	+	0.701874i	0.589121	+	0.808045i	$0.299474\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	5.95841e11i		−	1.83376i
$756$		0			0
$757$	−2.74781e11			−0.836765			−0.418382	−	0.908271i	$-0.637403\pi$
$757$	−2.74781e11			−0.836765			−0.418382	+	0.908271i	$0.637403\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.84005e10	+	3.94910e10i	0.203948	+	0.117750i	0.598496	−	0.801126i	$-0.295765\pi$
$761$	6.84005e10	+	3.94910e10i	0.203948	+	0.117750i	−0.394547	+	0.918876i	$0.629099\pi$
$762$		0			0
$763$	1.62400e10	+	2.81285e10i	0.0479168	+	0.0829942i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.69184e11	−	1.55413e11i	0.777799	−	0.449063i
$768$		0			0
$769$	1.28801e11	−	2.23089e11i	0.368309	−	0.637930i	−0.620992	−	0.783817i	$-0.713270\pi$
$769$	1.28801e11	−	2.23089e11i	0.368309	−	0.637930i	0.989301	+	0.145886i	$0.0466034\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	2.55605e11i		−	0.715898i	−0.933741	−	0.357949i	$-0.883476\pi$
$773$		−	2.55605e11i		−	0.715898i	0.933741	−	0.357949i	$-0.116524\pi$
$774$		0			0
$775$	−1.79209e11			−0.496768
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.70748e10	−	5.02726e10i	−0.236452	−	0.136515i
$780$		0			0
$781$	2.69983e10	+	4.67624e10i	0.0725658	+	0.125688i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.10553e11	+	2.37033e11i	−1.08116	+	0.624209i
$786$		0			0
$787$	−1.79969e11	+	3.11716e11i	−0.469137	+	0.812569i	−0.999378	−	0.0352783i	$-0.988768\pi$
$787$	−1.79969e11	+	3.11716e11i	−0.469137	+	0.812569i	0.530241	+	0.847847i	$0.322102\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			6.66941e11i			1.70366i
$792$		0			0
$793$	3.46977e11			0.877422
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.78732e10	−	3.34131e10i	−0.143431	−	0.0828101i	0.426567	−	0.904456i	$-0.359723\pi$
$797$	−5.78732e10	−	3.34131e10i	−0.143431	−	0.0828101i	−0.569998	+	0.821646i	$0.693056\pi$
$798$		0			0
$799$	2.94026e11	+	5.09268e11i	0.721438	+	1.24957i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8.13201e11	+	4.69502e11i	−1.95585	+	1.12921i
$804$		0			0
$805$	4.16984e11	−	7.22237e11i	0.992969	−	1.71987i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			1.52798e11i			0.356717i	0.983966	+	0.178358i	$0.0570786\pi$
$809$			1.52798e11i			0.356717i	−0.983966	+	0.178358i	$0.942921\pi$
$810$		0			0
$811$	−7.47417e11			−1.72774			−0.863872	−	0.503712i	$-0.831967\pi$
$811$	−7.47417e11			−1.72774			−0.863872	+	0.503712i	$0.831967\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.43876e11	+	8.30670e10i	0.326106	+	0.188277i
$816$		0			0
$817$	7.70103e10	+	1.33386e11i	0.172846	+	0.299379i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.87212e10	+	1.08087e10i	−0.0412061	+	0.0237903i	−0.520462	−	0.853885i	$-0.674240\pi$
$821$	−1.87212e10	+	1.08087e10i	−0.0412061	+	0.0237903i	0.479255	+	0.877675i	$0.340907\pi$
$822$		0			0
$823$	1.48416e11	−	2.57064e11i	0.323505	−	0.560328i	−0.657703	−	0.753277i	$-0.728472\pi$
$823$	1.48416e11	−	2.57064e11i	0.323505	−	0.560328i	0.981209	+	0.192949i	$0.0618053\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			7.77124e11i			1.66138i	0.556737	+	0.830689i	$0.312053\pi$
$827$			7.77124e11i			1.66138i	−0.556737	+	0.830689i	$0.687947\pi$
$828$		0			0
$829$	−6.11841e10			−0.129545			−0.0647725	−	0.997900i	$-0.520632\pi$
$829$	−6.11841e10			−0.129545			−0.0647725	+	0.997900i	$0.520632\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.42760e10	+	4.86568e10i	0.175035	+	0.101056i
$834$		0			0
$835$	2.07097e11	+	3.58702e11i	0.426017	+	0.737884i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.98324e11	−	3.45443e11i	1.20750	−	0.697153i	0.245291	−	0.969449i	$-0.421116\pi$
$839$	5.98324e11	−	3.45443e11i	1.20750	−	0.697153i	0.962214	+	0.272296i	$0.0877830\pi$
$840$		0			0
$841$	−7.87028e10	+	1.36317e11i	−0.157328	+	0.272500i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	4.38786e11i		−	0.860649i
$846$		0			0
$847$	−1.04314e12			−2.02680
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.06138e10	−	6.12791e9i	−0.0202374	−	0.0116841i
$852$		0			0
$853$	−4.03386e11	−	6.98685e11i	−0.761947	−	1.31973i	−0.941846	−	0.336045i	$-0.890911\pi$
$853$	−4.03386e11	−	6.98685e11i	−0.761947	−	1.31973i	0.179899	−	0.983685i	$-0.442423\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.85262e11	+	1.06961e11i	−0.343449	+	0.198290i	−0.661796	−	0.749684i	$-0.730206\pi$
$857$	−1.85262e11	+	1.06961e11i	−0.343449	+	0.198290i	0.318347	+	0.947974i	$0.396872\pi$
$858$		0			0
$859$	3.13829e11	−	5.43567e11i	0.576395	−	0.998345i	−0.419494	−	0.907758i	$-0.637792\pi$
$859$	3.13829e11	−	5.43567e11i	0.576395	−	0.998345i	0.995889	−	0.0905867i	$-0.0288742\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	2.94626e11i		−	0.531163i	−0.964088	−	0.265581i	$-0.914436\pi$
$863$		−	2.94626e11i		−	0.531163i	0.964088	−	0.265581i	$-0.0855639\pi$
$864$		0			0
$865$	8.04170e11			1.43643
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.28052e10	−	2.47136e10i	−0.0750615	−	0.0433368i
$870$		0			0
$871$	−8.35023e10	−	1.44630e11i	−0.145086	−	0.251297i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.57218e11	−	2.63975e11i	0.779993	−	0.450329i
$876$		0			0
$877$	2.34559e11	−	4.06268e11i	0.396510	−	0.686775i	−0.596783	−	0.802403i	$-0.703555\pi$
$877$	2.34559e11	−	4.06268e11i	0.396510	−	0.686775i	0.993293	+	0.115628i	$0.0368880\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			5.66926e11i			0.941072i	0.882381	+	0.470536i	$0.155939\pi$
$881$			5.66926e11i			0.941072i	−0.882381	+	0.470536i	$0.844061\pi$
$882$		0			0
$883$	−9.08701e11			−1.49478			−0.747392	−	0.664384i	$-0.768694\pi$
$883$	−9.08701e11			−1.49478			−0.747392	+	0.664384i	$0.768694\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.30853e11	+	2.48753e11i	0.696040	+	0.401859i	0.805871	−	0.592091i	$-0.201697\pi$
$887$	4.30853e11	+	2.48753e11i	0.696040	+	0.401859i	−0.109831	+	0.993950i	$0.535031\pi$
$888$		0			0
$889$	−2.59460e11	−	4.49397e11i	−0.415397	−	0.719488i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.83618e11	−	2.79217e11i	0.760496	−	0.439072i
$894$		0			0
$895$	−4.95648e11	+	8.58488e11i	−0.772470	+	1.33796i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	9.80312e11i		−	1.50081i
$900$		0			0
$901$	−1.95159e11			−0.296135
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.22226e12	−	7.05674e11i	−1.82209	−	1.05199i
$906$		0			0
$907$	−6.79916e10	−	1.17765e11i	−0.100468	−	0.174015i	0.811410	−	0.584478i	$-0.198701\pi$
$907$	−6.79916e10	−	1.17765e11i	−0.100468	−	0.174015i	−0.911877	+	0.410463i	$0.865367\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.89607e11	+	1.09469e11i	−0.275283	+	0.158935i	−0.631286	−	0.775550i	$-0.717473\pi$
$911$	−1.89607e11	+	1.09469e11i	−0.275283	+	0.158935i	0.356003	+	0.934485i	$0.384139\pi$
$912$		0			0
$913$	−4.25092e11	+	7.36281e11i	−0.611787	+	1.05965i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			1.54278e11i			0.218186i
$918$		0			0
$919$	−8.19281e11			−1.14860			−0.574302	−	0.818643i	$-0.694727\pi$
$919$	−8.19281e11			−1.14860			−0.574302	+	0.818643i	$0.694727\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.63614e10	+	1.52198e10i	0.0363213	+	0.0209701i
$924$		0			0
$925$	1.46424e9	+	2.53614e9i	0.00200007	+	0.00346422i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−8.43450e11	+	4.86966e11i	−1.13239	+	0.653786i	−0.944535	−	0.328410i	$-0.893487\pi$
$929$	−8.43450e11	+	4.86966e11i	−1.13239	+	0.653786i	−0.187856	+	0.982197i	$0.560154\pi$
$930$		0			0
$931$	4.62061e10	−	8.00313e10i	0.0615036	−	0.106527i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	1.41309e12i		−	1.84894i
$936$		0			0
$937$	2.32658e11			0.301828			0.150914	−	0.988547i	$-0.451778\pi$
$937$	2.32658e11			0.301828			0.150914	+	0.988547i	$0.451778\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.74131e11	+	2.73740e11i	0.604700	+	0.349124i	0.770888	−	0.636970i	$-0.219813\pi$
$941$	4.74131e11	+	2.73740e11i	0.604700	+	0.349124i	−0.166189	+	0.986094i	$0.553146\pi$
$942$		0			0
$943$	−2.92315e11	−	5.06305e11i	−0.369662	−	0.640274i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.21095e11	+	6.99143e10i	−0.150566	+	0.0869293i	−0.573390	−	0.819282i	$-0.694372\pi$
$947$	−1.21095e11	+	6.99143e10i	−0.150566	+	0.0869293i	0.422824	+	0.906212i	$0.361039\pi$
$948$		0			0
$949$	−2.64673e11	+	4.58426e11i	−0.326320	+	0.565203i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			1.90654e11i			0.231140i	0.993299	+	0.115570i	$0.0368694\pi$
$953$			1.90654e11i			0.231140i	−0.993299	+	0.115570i	$0.963131\pi$
$954$		0			0
$955$	−1.05819e12			−1.27219
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.35180e12	+	7.80463e11i	1.59823	+	0.922736i
$960$		0			0
$961$	−9.75098e11	−	1.68892e12i	−1.14329	−	1.98023i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.55049e12	−	8.95178e11i	1.78797	−	1.03229i
$966$		0			0
$967$	−5.19179e11	+	8.99244e11i	−0.593760	+	1.02842i	0.399960	+	0.916532i	$0.369024\pi$
$967$	−5.19179e11	+	8.99244e11i	−0.593760	+	1.02842i	−0.993721	+	0.111890i	$0.964309\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			1.21983e12i			1.37222i	0.727500	+	0.686108i	$0.240682\pi$
$971$			1.21983e12i			1.37222i	−0.727500	+	0.686108i	$0.759318\pi$
$972$		0			0
$973$	−1.37840e12			−1.53789
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.26675e12	+	7.31358e11i	1.39031	+	0.802697i	0.993349	−	0.115138i	$-0.0367311\pi$
$977$	1.26675e12	+	7.31358e11i	1.39031	+	0.802697i	0.396962	+	0.917835i	$0.370064\pi$
$978$		0			0
$979$	5.70447e9	+	9.88044e9i	0.00620990	+	0.0107559i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.52702e11	−	4.34573e11i	0.806137	−	0.465424i	−0.0394753	−	0.999221i	$-0.512569\pi$
$983$	7.52702e11	−	4.34573e11i	0.806137	−	0.465424i	0.845613	+	0.533797i	$0.179235\pi$
$984$		0			0
$985$	−5.47016e11	+	9.47460e11i	−0.581106	+	1.00650i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			8.95568e11i			0.936081i
$990$		0			0
$991$	1.22632e11			0.127148			0.0635738	−	0.997977i	$-0.479750\pi$
$991$	1.22632e11			0.127148			0.0635738	+	0.997977i	$0.479750\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.63191e12	−	9.42184e11i	−1.66496	−	0.961265i
$996$		0			0
$997$	−5.77449e10	−	1.00017e11i	−0.0584431	−	0.101226i	0.835324	−	0.549759i	$-0.185280\pi$
$997$	−5.77449e10	−	1.00017e11i	−0.0584431	−	0.101226i	−0.893767	+	0.448532i	$0.851947\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.9.g.c.53.1		4
3.2	odd	2	inner	324.9.g.c.53.2		4
9.2	odd	6	inner	324.9.g.c.269.1		4
9.4	even	3		108.9.c.c.53.2	yes	2
9.5	odd	6		108.9.c.c.53.1	✓	2
9.7	even	3	inner	324.9.g.c.269.2		4
36.23	even	6		432.9.e.c.161.1		2
36.31	odd	6		432.9.e.c.161.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.9.c.c.53.1	✓	2	9.5	odd	6
108.9.c.c.53.2	yes	2	9.4	even	3
324.9.g.c.53.1		4	1.1	even	1	trivial
324.9.g.c.53.2		4	3.2	odd	2	inner
324.9.g.c.269.1		4	9.2	odd	6	inner
324.9.g.c.269.2		4	9.7	even	3	inner
432.9.e.c.161.1		2	36.23	even	6
432.9.e.c.161.2		2	36.31	odd	6

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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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	324.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-610.940 - 352.727i) q^{5} +(-1319.50 - 2285.44i) q^{7} +(-21382.9 + 12345.4i) q^{11} +(-6959.50 + 12054.2i) q^{13} -81127.1i q^{17} -77041.0 q^{19} +(-387947. - 223981. i) q^{23} +(53519.5 + 92698.5i) q^{25} +(-507080. + 292763. i) q^{29} +(-837121. + 1.44994e6i) q^{31} +1.86169e6i q^{35} +27359.0 q^{37} +(1.13024e6 + 652544. i) q^{41} +(-999601. - 1.73136e6i) q^{43} +(-6.27741e6 + 3.62427e6i) q^{47} +(-599760. + 1.03881e6i) q^{49} -2.40559e6i q^{53} +1.74182e7 q^{55} +(-1.93393e7 - 1.11656e7i) q^{59} +(-1.24642e7 - 2.15886e7i) q^{61} +(8.50368e6 - 4.90960e6i) q^{65} +(-5.99916e6 + 1.03908e7i) q^{67} -2.18690e6i q^{71} +3.80304e7 q^{73} +(5.64295e7 + 3.25796e7i) q^{77} +(1.00092e6 + 1.73365e6i) q^{79} +(2.98200e7 - 1.72166e7i) q^{83} +(-2.86157e7 + 4.95638e7i) q^{85} -462072. i q^{89} +3.67322e7 q^{91} +(4.70674e7 + 2.71744e7i) q^{95} +(-2.62082e7 - 4.53940e7i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5278 q^{7} - 27838 q^{13} - 308164 q^{19} + 214078 q^{25} - 3348484 q^{31} + 109436 q^{37} - 3998404 q^{43} - 2399040 q^{49} + 69672960 q^{55} - 49856638 q^{61} - 23996638 q^{67} + 152121596 q^{73}+ \cdots - 104832958 q^{97}+O(q^{100}) \) 4 * q - 5278 * q^7 - 27838 * q^13 - 308164 * q^19 + 214078 * q^25 - 3348484 * q^31 + 109436 * q^37 - 3998404 * q^43 - 2399040 * q^49 + 69672960 * q^55 - 49856638 * q^61 - 23996638 * q^67 + 152121596 * q^73 + 4003682 * q^79 - 114462720 * q^85 + 146928964 * q^91 - 104832958 * q^97

Introduction

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