LMFDB - Embedded newform 1584.2.cd.c.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1584,2,Mod(17,1584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1584, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 5, 9]))

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

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

chi := DirichletCharacter("1584.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1584 = 2^{4} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1584.cd (of order $10$, degree $4$, 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:	$12.6483036802$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 $ x^16 + 2x^14 - 16x^12 - 72x^10 + 26x^8 + 360x^6 + 725x^4 + 1000*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.1
Root			$1.90184 + 0.0324487i$ of defining polynomial
Character	$\chi$	$=$	1584.17
Dual form			1584.2.cd.c.1025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13811 - 0.694712i) q^{5} +(2.38116 + 3.27739i) q^{7} +(-3.31656 - 0.0200544i) q^{11} +(4.42495 - 1.43775i) q^{13} +(0.0235753 - 0.0725574i) q^{17} +(-1.40822 + 1.93825i) q^{19} +3.22717i q^{23} +(0.0437835 + 0.0318106i) q^{25} +(-1.48796 + 1.08107i) q^{29} +(-0.517528 - 1.59279i) q^{31} +(-2.81433 - 8.66162i) q^{35} +(-5.87906 + 4.27138i) q^{37} +(6.82980 + 4.96214i) q^{41} +4.28086i q^{43} +(-3.65360 + 5.02874i) q^{47} +(-2.90822 + 8.95058i) q^{49} +(-1.16884 + 0.379779i) q^{53} +(7.07723 + 2.34694i) q^{55} +(-0.341086 - 0.469465i) q^{59} +(-3.59710 - 1.16877i) q^{61} -10.4598 q^{65} -12.9984 q^{67} +(1.06563 + 0.346245i) q^{71} +(7.82153 + 10.7654i) q^{73} +(-7.83155 - 10.9174i) q^{77} +(-0.627566 + 0.203908i) q^{79} +(-3.15542 + 9.71138i) q^{83} +(-0.100813 + 0.138757i) q^{85} +6.58983i q^{89} +(15.2486 + 11.0787i) q^{91} +(4.35745 - 3.16587i) q^{95} +(5.08168 + 15.6398i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{25} - 16 q^{31} - 12 q^{37} - 24 q^{49} - 16 q^{55} - 96 q^{67} - 20 q^{73} - 100 q^{85} + 72 q^{91} + 60 q^{97}+O(q^{100}) $ 16 * q - 32 * q^25 - 16 * q^31 - 12 * q^37 - 24 * q^49 - 16 * q^55 - 96 * q^67 - 20 * q^73 - 100 * q^85 + 72 * q^91 + 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1584\mathbb{Z}\right)^\times$.

$n$	$145$	$353$	$991$	$1189$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.13811	−	0.694712i	−0.956190	−	0.310685i	−0.210962	−	0.977494i	$-0.567659\pi$
$5$	−2.13811	−	0.694712i	−0.956190	−	0.310685i	−0.745228	+	0.666809i	$0.767659\pi$
$6$		0			0
$7$	2.38116	+	3.27739i	0.899995	+	1.23874i	0.970470	+	0.241223i	$0.0775484\pi$
$7$	2.38116	+	3.27739i	0.899995	+	1.23874i	−0.0704753	+	0.997514i	$0.522452\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.31656	−	0.0200544i	−0.999982	−	0.00604662i
$11$	−3.31656	−	0.0200544i	−0.999982	−	0.00604662i
$12$		0			0
$13$	4.42495	−	1.43775i	1.22726	−	0.398761i	0.377538	−	0.925994i	$-0.376771\pi$
$13$	4.42495	−	1.43775i	1.22726	−	0.398761i	0.849721	+	0.527233i	$0.176771\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.0235753	−	0.0725574i	0.00571786	−	0.0175978i	−0.948157	−	0.317803i	$-0.897055\pi$
$17$	0.0235753	−	0.0725574i	0.00571786	−	0.0175978i	0.953875	+	0.300205i	$0.0970551\pi$
$18$		0			0
$19$	−1.40822	+	1.93825i	−0.323068	+	0.444665i	−0.939401	−	0.342821i	$-0.888618\pi$
$19$	−1.40822	+	1.93825i	−0.323068	+	0.444665i	0.616333	+	0.787486i	$0.288618\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			3.22717i			0.672912i	0.941699	+	0.336456i	$0.109228\pi$
$23$			3.22717i			0.672912i	−0.941699	+	0.336456i	$0.890772\pi$
$24$		0			0
$25$	0.0437835	+	0.0318106i	0.00875670	+	0.00636211i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.48796	+	1.08107i	−0.276307	+	0.200749i	−0.717305	−	0.696759i	$-0.754625\pi$
$29$	−1.48796	+	1.08107i	−0.276307	+	0.200749i	0.440998	+	0.897508i	$0.354625\pi$
$30$		0			0
$31$	−0.517528	−	1.59279i	−0.0929508	−	0.286073i	0.893763	−	0.448539i	$-0.148055\pi$
$31$	−0.517528	−	1.59279i	−0.0929508	−	0.286073i	−0.986714	+	0.162466i	$0.948055\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.81433	−	8.66162i	−0.475709	−	1.46408i
$36$		0			0
$37$	−5.87906	+	4.27138i	−0.966511	+	0.702211i	−0.954654	−	0.297718i	$-0.903774\pi$
$37$	−5.87906	+	4.27138i	−0.966511	+	0.702211i	−0.0118571	+	0.999930i	$0.503774\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.82980	+	4.96214i	1.06664	+	0.774956i	0.975305	−	0.220864i	$-0.0708878\pi$
$41$	6.82980	+	4.96214i	1.06664	+	0.774956i	0.0913313	+	0.995821i	$0.470888\pi$
$42$		0			0
$43$			4.28086i			0.652825i	0.945227	+	0.326413i	$0.105840\pi$
$43$			4.28086i			0.652825i	−0.945227	+	0.326413i	$0.894160\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.65360	+	5.02874i	−0.532932	+	0.733518i	−0.987574	−	0.157157i	$-0.949767\pi$
$47$	−3.65360	+	5.02874i	−0.532932	+	0.733518i	0.454642	+	0.890674i	$0.349767\pi$
$48$		0			0
$49$	−2.90822	+	8.95058i	−0.415460	+	1.27865i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.16884	+	0.379779i	−0.160552	+	0.0521666i	−0.388190	−	0.921579i	$-0.626900\pi$
$53$	−1.16884	+	0.379779i	−0.160552	+	0.0521666i	0.227638	+	0.973746i	$0.426900\pi$
$54$		0			0
$55$	7.07723	+	2.34694i	0.954294	+	0.316461i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.341086	−	0.469465i	−0.0444056	−	0.0611191i	0.786237	−	0.617925i	$-0.212027\pi$
$59$	−0.341086	−	0.469465i	−0.0444056	−	0.0611191i	−0.830642	+	0.556806i	$0.812027\pi$
$60$		0			0
$61$	−3.59710	−	1.16877i	−0.460561	−	0.149645i	0.0695411	−	0.997579i	$-0.477847\pi$
$61$	−3.59710	−	1.16877i	−0.460561	−	0.149645i	−0.530102	+	0.847934i	$0.677847\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−10.4598			−1.29738
$66$		0			0
$67$	−12.9984			−1.58801			−0.794003	−	0.607914i	$-0.792007\pi$
$67$	−12.9984			−1.58801			−0.794003	+	0.607914i	$0.792007\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.06563	+	0.346245i	0.126467	+	0.0410917i	0.371567	−	0.928406i	$-0.378821\pi$
$71$	1.06563	+	0.346245i	0.126467	+	0.0410917i	−0.245100	+	0.969498i	$0.578821\pi$
$72$		0			0
$73$	7.82153	+	10.7654i	0.915441	+	1.26000i	0.965274	+	0.261239i	$0.0841309\pi$
$73$	7.82153	+	10.7654i	0.915441	+	1.26000i	−0.0498335	+	0.998758i	$0.515869\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.83155	−	10.9174i	−0.892488	−	1.24416i
$78$		0			0
$79$	−0.627566	+	0.203908i	−0.0706066	+	0.0229415i	−0.344107	−	0.938930i	$-0.611818\pi$
$79$	−0.627566	+	0.203908i	−0.0706066	+	0.0229415i	0.273501	+	0.961872i	$0.411818\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.15542	+	9.71138i	−0.346352	+	1.06596i	0.614504	+	0.788914i	$0.289356\pi$
$83$	−3.15542	+	9.71138i	−0.346352	+	1.06596i	−0.960856	+	0.277048i	$0.910644\pi$
$84$		0			0
$85$	−0.100813	+	0.138757i	−0.0109347	+	0.0150503i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			6.58983i			0.698520i	0.937026	+	0.349260i	$0.113567\pi$
$89$			6.58983i			0.698520i	−0.937026	+	0.349260i	$0.886433\pi$
$90$		0			0
$91$	15.2486	+	11.0787i	1.59849	+	1.16137i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.35745	−	3.16587i	0.447065	−	0.324812i
$96$		0			0
$97$	5.08168	+	15.6398i	0.515966	+	1.58798i	0.781517	+	0.623883i	$0.214446\pi$
$97$	5.08168	+	15.6398i	0.515966	+	1.58798i	−0.265551	+	0.964097i	$0.585554\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.532095	−	1.63762i	−0.0529455	−	0.162949i	0.921087	−	0.389356i	$-0.127302\pi$
$101$	−0.532095	−	1.63762i	−0.0529455	−	0.162949i	−0.974033	+	0.226406i	$0.927302\pi$
$102$		0			0
$103$	−2.61382	+	1.89905i	−0.257548	+	0.187119i	−0.709065	−	0.705143i	$-0.750883\pi$
$103$	−2.61382	+	1.89905i	−0.257548	+	0.187119i	0.451518	+	0.892262i	$0.350883\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.9884	+	8.71006i	1.15896	+	0.842034i	0.989646	−	0.143529i	$-0.0458449\pi$
$107$	11.9884	+	8.71006i	1.15896	+	0.842034i	0.169314	+	0.985562i	$0.445845\pi$
$108$		0			0
$109$		−	14.9258i		−	1.42963i	−0.699313	−	0.714815i	$-0.746511\pi$
$109$		−	14.9258i		−	1.42963i	0.699313	−	0.714815i	$-0.253489\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.61055	+	9.09864i	−0.621868	+	0.855928i	−0.997487	−	0.0708461i	$-0.977430\pi$
$113$	−6.61055	+	9.09864i	−0.621868	+	0.855928i	0.375619	+	0.926774i	$0.377430\pi$
$114$		0			0
$115$	2.24196	−	6.90004i	0.209064	−	0.643432i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.293935	−	0.0955054i	0.0269450	−	0.00875497i
$120$		0			0
$121$	10.9992	+	0.133023i	0.999927	+	0.0120930i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.53559	+	8.99547i	0.584561	+	0.804580i
$126$		0			0
$127$	5.76481	+	1.87310i	0.511544	+	0.166211i	0.553404	−	0.832913i	$-0.313328\pi$
$127$	5.76481	+	1.87310i	0.511544	+	0.166211i	−0.0418604	+	0.999123i	$0.513328\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.15083			−0.624771			−0.312385	−	0.949955i	$-0.601128\pi$
$131$	−7.15083			−0.624771			−0.312385	+	0.949955i	$0.601128\pi$
$132$		0			0
$133$	−9.70560			−0.841582
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.1026	−	3.28252i	−0.863120	−	0.280445i	−0.156189	−	0.987727i	$-0.549921\pi$
$137$	−10.1026	−	3.28252i	−0.863120	−	0.280445i	−0.706931	+	0.707283i	$0.749921\pi$
$138$		0			0
$139$	0.0311975	+	0.0429397i	0.00264614	+	0.00364210i	0.810338	−	0.585963i	$-0.199284\pi$
$139$	0.0311975	+	0.0429397i	0.00264614	+	0.00364210i	−0.807692	+	0.589605i	$0.799284\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−14.7044	+	4.67966i	−1.22965	+	0.391333i
$144$		0			0
$145$	3.93244	−	1.27773i	0.326572	−	0.106110i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.30238	−	19.3967i	0.516311	−	1.58904i	−0.264572	−	0.964366i	$-0.585231\pi$
$149$	6.30238	−	19.3967i	0.516311	−	1.58904i	0.780883	−	0.624677i	$-0.214769\pi$
$150$		0			0
$151$	−0.698980	+	0.962063i	−0.0568822	+	0.0782916i	−0.836510	−	0.547951i	$-0.815408\pi$
$151$	−0.698980	+	0.962063i	−0.0568822	+	0.0782916i	0.779628	+	0.626243i	$0.215408\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			3.76508i			0.302419i
$156$		0			0
$157$	1.40210	+	1.01868i	0.111900	+	0.0812998i	0.642328	−	0.766430i	$-0.277969\pi$
$157$	1.40210	+	1.01868i	0.111900	+	0.0812998i	−0.530428	+	0.847730i	$0.677969\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−10.5767	+	7.68443i	−0.833561	+	0.605618i
$162$		0			0
$163$	0.309821	+	0.953532i	0.0242671	+	0.0746864i	0.962457	−	0.271435i	$-0.0874984\pi$
$163$	0.309821	+	0.953532i	0.0242671	+	0.0746864i	−0.938190	+	0.346122i	$0.887498\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.17734	−	12.8565i	−0.323252	−	0.994868i	−0.972223	−	0.234055i	$-0.924800\pi$
$167$	−4.17734	−	12.8565i	−0.323252	−	0.994868i	0.648971	−	0.760813i	$-0.275200\pi$
$168$		0			0
$169$	6.99579	−	5.08274i	0.538138	−	0.390980i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.08619	+	4.42188i	0.462724	+	0.336189i	0.794599	−	0.607135i	$-0.207681\pi$
$173$	6.08619	+	4.42188i	0.462724	+	0.336189i	−0.331875	+	0.943324i	$0.607681\pi$
$174$		0			0
$175$			0.219242i			0.0165731i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.34750	−	10.1130i	0.549178	−	0.755879i	−0.440722	−	0.897643i	$-0.645278\pi$
$179$	7.34750	−	10.1130i	0.549178	−	0.755879i	0.989900	+	0.141765i	$0.0452777\pi$
$180$		0			0
$181$	−5.56261	+	17.1200i	−0.413466	+	1.27252i	0.500150	+	0.865939i	$0.333278\pi$
$181$	−5.56261	+	17.1200i	−0.413466	+	1.27252i	−0.913616	+	0.406578i	$0.866722\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	15.5374	−	5.04842i	1.14233	−	0.371167i
$186$		0			0
$187$	−0.0796442	+	0.240168i	−0.00582416	+	0.0175629i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.7297	−	17.5209i	−0.921085	−	1.26777i	−0.963237	−	0.268654i	$-0.913421\pi$
$191$	−12.7297	−	17.5209i	−0.921085	−	1.26777i	0.0421514	−	0.999111i	$-0.486579\pi$
$192$		0			0
$193$	−4.93306	−	1.60285i	−0.355090	−	0.115376i	0.126040	−	0.992025i	$-0.459773\pi$
$193$	−4.93306	−	1.60285i	−0.355090	−	0.115376i	−0.481129	+	0.876650i	$0.659773\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.14679			0.366693			0.183347	−	0.983048i	$-0.441307\pi$
$197$	5.14679			0.366693			0.183347	+	0.983048i	$0.441307\pi$
$198$		0			0
$199$	−24.2595			−1.71971			−0.859855	−	0.510539i	$-0.829446\pi$
$199$	−24.2595			−1.71971			−0.859855	+	0.510539i	$0.829446\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.08615	−	2.30243i	−0.497350	−	0.161599i
$204$		0			0
$205$	−11.1556	−	15.3543i	−0.779139	−	1.07239i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.70933	−	6.40009i	0.325751	−	0.442704i
$210$		0			0
$211$	17.8262	−	5.79210i	1.22721	−	0.398744i	0.377506	−	0.926007i	$-0.376782\pi$
$211$	17.8262	−	5.79210i	1.22721	−	0.398744i	0.849702	+	0.527263i	$0.176782\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.97397	−	9.15293i	0.202823	−	0.624225i
$216$		0			0
$217$	3.98787	−	5.48883i	0.270714	−	0.372606i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	0.354958i		−	0.0238771i
$222$		0			0
$223$	−4.44037	−	3.22612i	−0.297349	−	0.216037i	0.429100	−	0.903257i	$-0.358831\pi$
$223$	−4.44037	−	3.22612i	−0.297349	−	0.216037i	−0.726449	+	0.687220i	$0.758831\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.1352	+	8.09016i	−0.739066	+	0.536963i	−0.892419	−	0.451209i	$-0.850993\pi$
$227$	−11.1352	+	8.09016i	−0.739066	+	0.536963i	0.153352	+	0.988172i	$0.450993\pi$
$228$		0			0
$229$	−6.53035	−	20.0983i	−0.431538	−	1.32814i	−0.896593	−	0.442855i	$-0.853966\pi$
$229$	−6.53035	−	20.0983i	−0.431538	−	1.32814i	0.465056	−	0.885281i	$-0.346034\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.62458	+	14.2330i	0.302967	+	0.932435i	0.980428	+	0.196877i	$0.0630800\pi$
$233$	4.62458	+	14.2330i	0.302967	+	0.932435i	−0.677462	+	0.735558i	$0.736920\pi$
$234$		0			0
$235$	11.3053	−	8.21378i	0.737477	−	0.535808i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.37274	+	3.17698i	0.282849	+	0.205502i	0.720159	−	0.693809i	$-0.244069\pi$
$239$	4.37274	+	3.17698i	0.282849	+	0.205502i	−0.437310	+	0.899311i	$0.644069\pi$
$240$		0			0
$241$		−	11.7091i		−	0.754252i	−0.926162	−	0.377126i	$-0.876912\pi$
$241$		−	11.7091i		−	0.754252i	0.926162	−	0.377126i	$-0.123088\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	12.4362	−	17.1169i	0.794518	−	1.09356i
$246$		0			0
$247$	−3.44458	+	10.6013i	−0.219173	+	0.674546i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	21.4920	−	6.98319i	1.35657	−	0.440775i	0.461671	−	0.887051i	$-0.347250\pi$
$251$	21.4920	−	6.98319i	1.35657	−	0.440775i	0.894895	+	0.446276i	$0.147250\pi$
$252$		0			0
$253$	0.0647190	−	10.7031i	0.00406885	−	0.672900i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−16.1737	−	22.2612i	−1.00889	−	1.38862i	−0.919709	−	0.392601i	$-0.871575\pi$
$257$	−16.1737	−	22.2612i	−1.00889	−	1.38862i	−0.0891801	−	0.996016i	$-0.528425\pi$
$258$		0			0
$259$	−27.9980	−	9.09709i	−1.73971	−	0.565266i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	32.0386			1.97559			0.987793	−	0.155773i	$-0.0497868\pi$
$263$	32.0386			1.97559			0.987793	+	0.155773i	$0.0497868\pi$
$264$		0			0
$265$	2.76294			0.169726
$266$		0			0
$267$		0			0
$268$		0			0
$269$	25.7177	+	8.35619i	1.56804	+	0.509486i	0.958940	−	0.283610i	$-0.0915322\pi$
$269$	25.7177	+	8.35619i	1.56804	+	0.509486i	0.609097	+	0.793096i	$0.291532\pi$
$270$		0			0
$271$	−8.74690	−	12.0391i	−0.531336	−	0.731322i	0.455997	−	0.889981i	$-0.349283\pi$
$271$	−8.74690	−	12.0391i	−0.531336	−	0.731322i	−0.987333	+	0.158660i	$0.949283\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.144573	−	0.106380i	−0.00871807	−	0.00641495i
$276$		0			0
$277$	−7.49418	+	2.43501i	−0.450282	+	0.146305i	−0.525374	−	0.850871i	$-0.676075\pi$
$277$	−7.49418	+	2.43501i	−0.450282	+	0.146305i	0.0750927	+	0.997177i	$0.476075\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.56034	+	20.1906i	−0.391357	+	1.20447i	0.540406	+	0.841405i	$0.318271\pi$
$281$	−6.56034	+	20.1906i	−0.391357	+	1.20447i	−0.931763	+	0.363068i	$0.881729\pi$
$282$		0			0
$283$	2.52460	−	3.47482i	0.150072	−	0.206556i	−0.727362	−	0.686254i	$-0.759254\pi$
$283$	2.52460	−	3.47482i	0.150072	−	0.206556i	0.877434	+	0.479698i	$0.159254\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			34.1996i			2.01874i
$288$		0			0
$289$	13.7486	+	9.98893i	0.808740	+	0.587584i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−15.4486	+	11.2241i	−0.902518	+	0.655717i	−0.939111	−	0.343613i	$-0.888349\pi$
$293$	−15.4486	+	11.2241i	−0.902518	+	0.655717i	0.0365938	+	0.999330i	$0.488349\pi$
$294$		0			0
$295$	0.403135	+	1.24072i	0.0234714	+	0.0722376i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.63988	+	14.2801i	0.268331	+	0.825838i
$300$		0			0
$301$	−14.0300	+	10.1934i	−0.808678	+	0.587539i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.87902	+	4.99790i	0.393891	+	0.286179i
$306$		0			0
$307$			1.86240i			0.106293i	0.998587	+	0.0531463i	$0.0169250\pi$
$307$			1.86240i			0.106293i	−0.998587	+	0.0531463i	$0.983075\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.26339	−	7.24443i	0.298459	−	0.410794i	−0.633279	−	0.773923i	$-0.718292\pi$
$311$	5.26339	−	7.24443i	0.298459	−	0.410794i	0.931739	+	0.363129i	$0.118292\pi$
$312$		0			0
$313$	5.29558	−	16.2981i	0.299324	−	0.921224i	−0.682411	−	0.730969i	$-0.739068\pi$
$313$	5.29558	−	16.2981i	0.299324	−	0.921224i	0.981735	−	0.190255i	$-0.0609316\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	25.9678	−	8.43746i	1.45850	−	0.473895i	0.530888	−	0.847442i	$-0.321859\pi$
$317$	25.9678	−	8.43746i	1.45850	−	0.473895i	0.927611	+	0.373547i	$0.121859\pi$
$318$		0			0
$319$	4.95659	−	3.55558i	0.277516	−	0.199075i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.107435	+	0.147872i	0.00597785	+	0.00822781i
$324$		0			0
$325$	0.239475	+	0.0778102i	0.0132837	+	0.00431614i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−25.1809			−1.38827
$330$		0			0
$331$	5.87217			0.322764			0.161382	−	0.986892i	$-0.448405\pi$
$331$	5.87217			0.322764			0.161382	+	0.986892i	$0.448405\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	27.7919	+	9.03014i	1.51844	+	0.493370i
$336$		0			0
$337$	−9.74004	−	13.4060i	−0.530574	−	0.730272i	0.456644	−	0.889650i	$-0.349051\pi$
$337$	−9.74004	−	13.4060i	−0.530574	−	0.730272i	−0.987218	+	0.159377i	$0.949051\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.68447	+	5.29296i	0.0912193	+	0.286630i
$342$		0			0
$343$	−9.28988	+	3.01847i	−0.501606	+	0.162982i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.778158	−	2.39492i	0.0417737	−	0.128566i	−0.927995	−	0.372593i	$-0.878469\pi$
$347$	0.778158	−	2.39492i	0.0417737	−	0.128566i	0.969768	+	0.244027i	$0.0784686\pi$
$348$		0			0
$349$	5.13104	−	7.06228i	0.274658	−	0.378035i	−0.649297	−	0.760535i	$-0.724937\pi$
$349$	5.13104	−	7.06228i	0.274658	−	0.378035i	0.923955	+	0.382500i	$0.124937\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	0.536500i		−	0.0285550i	−0.999898	−	0.0142775i	$-0.995455\pi$
$353$		−	0.536500i		−	0.0285550i	0.999898	−	0.0142775i	$-0.00454483\pi$
$354$		0			0
$355$	−2.03789	−	1.48062i	−0.108160	−	0.0785829i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.7871	+	9.29040i	−0.674880	+	0.490329i	−0.871655	−	0.490120i	$-0.836953\pi$
$359$	−12.7871	+	9.29040i	−0.674880	+	0.490329i	0.196775	+	0.980449i	$0.436953\pi$
$360$		0			0
$361$	4.09760	+	12.6111i	0.215663	+	0.663742i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−9.24439	−	28.4513i	−0.483873	−	1.48921i
$366$		0			0
$367$	23.4075	−	17.0065i	1.22186	−	0.887734i	0.225608	−	0.974218i	$-0.427563\pi$
$367$	23.4075	−	17.0065i	1.22186	−	0.887734i	0.996253	+	0.0864843i	$0.0275633\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.02788	−	2.92642i	−0.209117	−	0.151932i
$372$		0			0
$373$			6.60935i			0.342219i	0.985252	+	0.171109i	$0.0547352\pi$
$373$			6.60935i			0.342219i	−0.985252	+	0.171109i	$0.945265\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.02984	+	6.92297i	−0.259050	+	0.356551i
$378$		0			0
$379$	−0.478524	+	1.47275i	−0.0245801	+	0.0756498i	−0.962594	−	0.270948i	$-0.912663\pi$
$379$	−0.478524	+	1.47275i	−0.0245801	+	0.0756498i	0.938014	+	0.346597i	$0.112663\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.8467	+	4.17415i	−0.656436	+	0.213289i	−0.618250	−	0.785982i	$-0.712158\pi$
$383$	−12.8467	+	4.17415i	−0.656436	+	0.213289i	−0.0381861	+	0.999271i	$0.512158\pi$
$384$		0			0
$385$	9.16021	+	28.7833i	0.466847	+	1.46693i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.80471	+	12.1186i	0.446416	+	0.614440i	0.971623	−	0.236535i	$-0.0760119\pi$
$389$	8.80471	+	12.1186i	0.446416	+	0.614440i	−0.525206	+	0.850975i	$0.676012\pi$
$390$		0			0
$391$	0.234155	+	0.0760817i	0.0118417	+	0.00384762i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.48346			0.0746409
$396$		0			0
$397$	−20.7132			−1.03956			−0.519782	−	0.854299i	$-0.673987\pi$
$397$	−20.7132			−1.03956			−0.519782	+	0.854299i	$0.673987\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	25.7211	+	8.35730i	1.28445	+	0.417343i	0.870146	−	0.492795i	$-0.164025\pi$
$401$	25.7211	+	8.35730i	1.28445	+	0.417343i	0.414305	+	0.910138i	$0.364025\pi$
$402$		0			0
$403$	−4.58007	−	6.30392i	−0.228149	−	0.314021i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	19.5839	−	14.0484i	0.970739	−	0.696354i
$408$		0			0
$409$	−5.80668	+	1.88670i	−0.287122	+	0.0932915i	−0.449037	−	0.893513i	$-0.648233\pi$
$409$	−5.80668	+	1.88670i	−0.287122	+	0.0932915i	0.161915	+	0.986805i	$0.448233\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.726437	−	2.23574i	0.0357456	−	0.110014i
$414$		0			0
$415$	13.4932	−	18.5718i	0.662357	−	0.911656i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	35.6619i		−	1.74220i	−0.491110	−	0.871098i	$-0.663409\pi$
$419$		−	35.6619i		−	1.74220i	0.491110	−	0.871098i	$-0.336591\pi$
$420$		0			0
$421$	−11.5751	−	8.40982i	−0.564137	−	0.409870i	0.268834	−	0.963187i	$-0.413362\pi$
$421$	−11.5751	−	8.40982i	−0.564137	−	0.409870i	−0.832971	+	0.553317i	$0.813362\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.00334030	−	0.00242687i	0.000162028	−	0.000117721i
$426$		0			0
$427$	−4.73477	−	14.5721i	−0.229131	−	0.705194i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.68944	−	8.27725i	−0.129546	−	0.398701i	0.865156	−	0.501503i	$-0.167219\pi$
$431$	−2.68944	−	8.27725i	−0.129546	−	0.398701i	−0.994702	+	0.102802i	$0.967219\pi$
$432$		0			0
$433$	30.3812	−	22.0733i	1.46003	−	1.06077i	0.476673	−	0.879080i	$-0.341842\pi$
$433$	30.3812	−	22.0733i	1.46003	−	1.06077i	0.983355	−	0.181693i	$-0.0581576\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.25507	−	4.54458i	−0.299221	−	0.217397i
$438$		0			0
$439$		−	32.4669i		−	1.54956i	−0.632232	−	0.774779i	$-0.717861\pi$
$439$		−	32.4669i		−	1.54956i	0.632232	−	0.774779i	$-0.282139\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.0630	−	15.2269i	0.525618	−	0.723451i	−0.460837	−	0.887485i	$-0.652451\pi$
$443$	11.0630	−	15.2269i	0.525618	−	0.723451i	0.986455	+	0.164034i	$0.0524506\pi$
$444$		0			0
$445$	4.57804	−	14.0897i	0.217020	−	0.667918i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.86840	+	2.23168i	−0.324140	+	0.105319i	−0.466567	−	0.884486i	$-0.654509\pi$
$449$	−6.86840	+	2.23168i	−0.324140	+	0.105319i	0.142427	+	0.989805i	$0.454509\pi$
$450$		0			0
$451$	−22.5520	−	16.5942i	−1.06193	−	0.781392i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−24.9065	−	34.2809i	−1.16764	−	1.60711i
$456$		0			0
$457$	4.01554	+	1.30473i	0.187839	+	0.0610326i	0.401426	−	0.915891i	$-0.368515\pi$
$457$	4.01554	+	1.30473i	0.187839	+	0.0610326i	−0.213587	+	0.976924i	$0.568515\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	14.1922			0.660997			0.330499	−	0.943806i	$-0.392783\pi$
$461$	14.1922			0.660997			0.330499	+	0.943806i	$0.392783\pi$
$462$		0			0
$463$	40.3784			1.87654			0.938271	−	0.345902i	$-0.112427\pi$
$463$	40.3784			1.87654			0.938271	+	0.345902i	$0.112427\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.7476	+	3.49210i	0.497338	+	0.161595i	0.546936	−	0.837174i	$-0.315794\pi$
$467$	10.7476	+	3.49210i	0.497338	+	0.161595i	−0.0495980	+	0.998769i	$0.515794\pi$
$468$		0			0
$469$	−30.9513	−	42.6008i	−1.42920	−	1.96712i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.0858500	−	14.1977i	0.00394739	−	0.652813i
$474$		0			0
$475$	−0.123314	+	0.0400671i	−0.00565802	+	0.00183840i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.07597	+	21.7776i	−0.323309	+	0.995044i	0.648889	+	0.760883i	$0.275234\pi$
$479$	−7.07597	+	21.7776i	−0.323309	+	0.995044i	−0.972198	+	0.234161i	$0.924766\pi$
$480$		0			0
$481$	−19.8733	+	27.3533i	−0.906145	+	1.24720i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	36.9698i		−	1.67871i
$486$		0			0
$487$	−6.10169	−	4.43314i	−0.276494	−	0.200885i	0.440893	−	0.897560i	$-0.354662\pi$
$487$	−6.10169	−	4.43314i	−0.276494	−	0.200885i	−0.717387	+	0.696675i	$0.754662\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−30.8965	+	22.4476i	−1.39434	+	1.01305i	−0.398967	+	0.916965i	$0.630631\pi$
$491$	−30.8965	+	22.4476i	−1.39434	+	1.01305i	−0.995373	+	0.0960820i	$0.969369\pi$
$492$		0			0
$493$	0.0433602	+	0.133449i	0.00195285	+	0.00601024i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.40266	+	4.31695i	0.0629181	+	0.193642i
$498$		0			0
$499$	−6.51994	+	4.73701i	−0.291873	+	0.212058i	−0.724079	−	0.689717i	$-0.757735\pi$
$499$	−6.51994	+	4.73701i	−0.291873	+	0.212058i	0.432207	+	0.901775i	$0.357735\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.0846	+	15.3188i	0.940115	+	0.683033i	0.948448	−	0.316932i	$-0.102653\pi$
$503$	21.0846	+	15.3188i	0.940115	+	0.683033i	−0.00833362	+	0.999965i	$0.502653\pi$
$504$		0			0
$505$			3.87106i			0.172260i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	16.4364	−	22.6228i	0.728531	−	1.00274i	−0.270666	−	0.962673i	$-0.587244\pi$
$509$	16.4364	−	22.6228i	0.728531	−	1.00274i	0.999197	−	0.0400639i	$-0.0127561\pi$
$510$		0			0
$511$	−16.6581	+	51.2684i	−0.736911	+	2.26798i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.90792	−	2.24452i	0.304399	−	0.0989054i
$516$		0			0
$517$	12.2182	−	16.6049i	0.537357	−	0.730282i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−18.9804	−	26.1242i	−0.831545	−	1.14452i	−0.987633	−	0.156781i	$-0.949888\pi$
$521$	−18.9804	−	26.1242i	−0.831545	−	1.14452i	0.156088	−	0.987743i	$-0.450112\pi$
$522$		0			0
$523$	−16.5104	−	5.36454i	−0.721948	−	0.234575i	−0.0750804	−	0.997177i	$-0.523921\pi$
$523$	−16.5104	−	5.36454i	−0.721948	−	0.234575i	−0.646868	+	0.762602i	$0.723921\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.127769			−0.00556572
$528$		0			0
$529$	12.5853			0.547189
$530$		0			0
$531$		0			0
$532$		0			0
$533$	37.3558	+	12.1376i	1.61806	+	0.525740i
$534$		0			0
$535$	−19.5814	−	26.9515i	−0.846578	−	1.16522i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.82480	−	29.6269i	0.423184	−	1.27612i
$540$		0			0
$541$	−9.58312	+	3.11375i	−0.412011	+	0.133870i	−0.507686	−	0.861542i	$-0.669499\pi$
$541$	−9.58312	+	3.11375i	−0.412011	+	0.133870i	0.0956753	+	0.995413i	$0.469499\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−10.3691	+	31.9129i	−0.444165	+	1.36700i
$546$		0			0
$547$	−14.0244	+	19.3029i	−0.599639	+	0.825333i	−0.995675	−	0.0929023i	$-0.970386\pi$
$547$	−14.0244	+	19.3029i	−0.599639	+	0.825333i	0.396036	+	0.918235i	$0.370386\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	4.40642i		−	0.187720i
$552$		0			0
$553$	−2.16262	−	1.57124i	−0.0919640	−	0.0668158i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−31.6776	+	23.0151i	−1.34222	+	0.975181i	−0.342862	+	0.939386i	$0.611396\pi$
$557$	−31.6776	+	23.0151i	−1.34222	+	0.975181i	−0.999359	+	0.0357950i	$0.988604\pi$
$558$		0			0
$559$	6.15482	+	18.9426i	0.260321	+	0.801185i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.55147	−	4.77494i	−0.0653868	−	0.201240i	0.913025	−	0.407903i	$-0.133740\pi$
$563$	−1.55147	−	4.77494i	−0.0653868	−	0.201240i	−0.978412	+	0.206663i	$0.933740\pi$
$564$		0			0
$565$	20.4550	−	14.8614i	0.860548	−	0.625225i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	7.69308	+	5.58935i	0.322511	+	0.234318i	0.737246	−	0.675624i	$-0.236126\pi$
$569$	7.69308	+	5.58935i	0.322511	+	0.234318i	−0.414735	+	0.909942i	$0.636126\pi$
$570$		0			0
$571$			39.8291i			1.66680i	0.552673	+	0.833398i	$0.313608\pi$
$571$			39.8291i			1.66680i	−0.552673	+	0.833398i	$0.686392\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.102658	+	0.141297i	−0.00428115	+	0.00589249i
$576$		0			0
$577$	−4.03506	+	12.4186i	−0.167982	+	0.516994i	−0.999244	−	0.0388866i	$-0.987619\pi$
$577$	−4.03506	+	12.4186i	−0.167982	+	0.516994i	0.831262	+	0.555881i	$0.187619\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−39.3415	+	12.7828i	−1.63216	+	0.530321i
$582$		0			0
$583$	3.88415	−	1.23612i	0.160865	−	0.0511949i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.9608	+	19.2153i	0.576222	+	0.793102i	0.993275	−	0.115780i	$-0.0369369\pi$
$587$	13.9608	+	19.2153i	0.576222	+	0.793102i	−0.417053	+	0.908882i	$0.636937\pi$
$588$		0			0
$589$	3.81602	+	1.23990i	0.157236	+	0.0510891i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	37.1489			1.52552			0.762761	−	0.646680i	$-0.223843\pi$
$593$	37.1489			1.52552			0.762761	+	0.646680i	$0.223843\pi$
$594$		0			0
$595$	−0.694814			−0.0284846
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.26902	−	0.737248i	−0.0927095	−	0.0301231i	0.262295	−	0.964988i	$-0.415521\pi$
$599$	−2.26902	−	0.737248i	−0.0927095	−	0.0301231i	−0.355004	+	0.934865i	$0.615521\pi$
$600$		0			0
$601$	3.99333	+	5.49635i	0.162891	+	0.224201i	0.882658	−	0.470015i	$-0.155751\pi$
$601$	3.99333	+	5.49635i	0.162891	+	0.224201i	−0.719767	+	0.694216i	$0.755751\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−23.4250	−	7.92570i	−0.952363	−	0.322225i
$606$		0			0
$607$	38.5143	−	12.5141i	1.56325	−	0.507930i	0.605575	−	0.795788i	$-0.292943\pi$
$607$	38.5143	−	12.5141i	1.56325	−	0.507930i	0.957673	+	0.287859i	$0.0929433\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.93688	+	27.5049i	−0.361547	+	1.11273i
$612$		0			0
$613$	0.119072	−	0.163888i	0.00480926	−	0.00661938i	−0.806606	−	0.591090i	$-0.798698\pi$
$613$	0.119072	−	0.163888i	0.00480926	−	0.00661938i	0.811415	+	0.584471i	$0.198698\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			8.08426i			0.325460i	0.986671	+	0.162730i	$0.0520299\pi$
$617$			8.08426i			0.325460i	−0.986671	+	0.162730i	$0.947970\pi$
$618$		0			0
$619$	16.9785	+	12.3356i	0.682424	+	0.495810i	0.874161	−	0.485636i	$-0.161412\pi$
$619$	16.9785	+	12.3356i	0.682424	+	0.495810i	−0.191737	+	0.981446i	$0.561412\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−21.5974	+	15.6914i	−0.865282	+	0.628664i
$624$		0			0
$625$	−7.80814	−	24.0310i	−0.312326	−	0.961239i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.171320	+	0.527268i	0.00683097	+	0.0210236i
$630$		0			0
$631$	−19.6268	+	14.2597i	−0.781332	+	0.567671i	−0.905378	−	0.424606i	$-0.860413\pi$
$631$	−19.6268	+	14.2597i	−0.781332	+	0.567671i	0.124047	+	0.992276i	$0.460413\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−11.0245	−	8.00977i	−0.437494	−	0.317858i
$636$		0			0
$637$			43.7871i			1.73491i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.48633	+	13.0568i	−0.374688	+	0.515713i	−0.954167	−	0.299273i	$-0.903256\pi$
$641$	−9.48633	+	13.0568i	−0.374688	+	0.515713i	0.579480	+	0.814987i	$0.303256\pi$
$642$		0			0
$643$	−3.88866	+	11.9681i	−0.153354	+	0.471975i	−0.997990	−	0.0633656i	$-0.979817\pi$
$643$	−3.88866	+	11.9681i	−0.153354	+	0.471975i	0.844637	+	0.535340i	$0.179817\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−28.7701	+	9.34797i	−1.13107	+	0.367507i	−0.813982	−	0.580890i	$-0.802705\pi$
$647$	−28.7701	+	9.34797i	−1.13107	+	0.367507i	−0.317087	+	0.948396i	$0.602705\pi$
$648$		0			0
$649$	1.12182	+	1.56385i	0.0440352	+	0.0613865i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−11.5162	−	15.8507i	−0.450664	−	0.620286i	0.521876	−	0.853021i	$-0.325232\pi$
$653$	−11.5162	−	15.8507i	−0.450664	−	0.620286i	−0.972540	+	0.232735i	$0.925232\pi$
$654$		0			0
$655$	15.2892	+	4.96777i	0.597399	+	0.194107i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.34943			−0.0525664			−0.0262832	−	0.999655i	$-0.508367\pi$
$659$	−1.34943			−0.0525664			−0.0262832	+	0.999655i	$0.508367\pi$
$660$		0			0
$661$	28.7859			1.11964			0.559821	−	0.828614i	$-0.310870\pi$
$661$	28.7859			1.11964			0.559821	+	0.828614i	$0.310870\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	20.7516	+	6.74260i	0.804712	+	0.261467i
$666$		0			0
$667$	−3.48879	−	4.80191i	−0.135086	−	0.185931i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	11.9066	+	3.94843i	0.459648	+	0.152428i
$672$		0			0
$673$	20.6864	−	6.72140i	0.797400	−	0.259091i	0.118148	−	0.992996i	$-0.462304\pi$
$673$	20.6864	−	6.72140i	0.797400	−	0.259091i	0.679252	+	0.733905i	$0.262304\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.84208	+	17.9801i	−0.224529	+	0.691030i	0.773810	+	0.633418i	$0.218349\pi$
$677$	−5.84208	+	17.9801i	−0.224529	+	0.691030i	−0.998339	+	0.0576121i	$0.981651\pi$
$678$		0			0
$679$	−39.1574	+	53.8955i	−1.50272	+	2.06832i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			33.7466i			1.29128i	0.763642	+	0.645640i	$0.223409\pi$
$683$			33.7466i			1.29128i	−0.763642	+	0.645640i	$0.776591\pi$
$684$		0			0
$685$	19.3199	+	14.0367i	0.738176	+	0.536316i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.62602	+	3.36100i	−0.176237	+	0.128044i
$690$		0			0
$691$	8.50814	+	26.1854i	0.323665	+	0.996138i	0.972040	+	0.234817i	$0.0754490\pi$
$691$	8.50814	+	26.1854i	0.323665	+	0.996138i	−0.648375	+	0.761321i	$0.724551\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.0368728	−	0.113483i	−0.00139867	−	0.00430465i
$696$		0			0
$697$	0.521055	−	0.378569i	0.0197364	−	0.0143393i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−8.43699	−	6.12983i	−0.318661	−	0.231521i	0.416943	−	0.908933i	$-0.363101\pi$
$701$	−8.43699	−	6.12983i	−0.318661	−	0.231521i	−0.735604	+	0.677412i	$0.763101\pi$
$702$		0			0
$703$		−	17.4101i		−	0.656636i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.10011	−	5.64332i	0.154201	−	0.212239i
$708$		0			0
$709$	−6.19477	+	19.0655i	−0.232649	+	0.716021i	0.764775	+	0.644297i	$0.222850\pi$
$709$	−6.19477	+	19.0655i	−0.232649	+	0.716021i	−0.997425	+	0.0717239i	$0.977150\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5.14021	−	1.67015i	0.192502	−	0.0625478i
$714$		0			0
$715$	34.6907	+	0.209765i	1.29736	+	0.00784477i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.01752	+	8.28241i	0.224416	+	0.308882i	0.906347	−	0.422535i	$-0.138860\pi$
$719$	6.01752	+	8.28241i	0.224416	+	0.308882i	−0.681931	+	0.731417i	$0.738860\pi$
$720$		0			0
$721$	−12.4479	−	4.04456i	−0.463583	−	0.150627i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.0995374			−0.00369673
$726$		0			0
$727$	14.4456			0.535759			0.267880	−	0.963452i	$-0.413677\pi$
$727$	14.4456			0.535759			0.267880	+	0.963452i	$0.413677\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.310608	+	0.100923i	0.0114883	+	0.00373276i
$732$		0			0
$733$	4.29622	+	5.91324i	0.158685	+	0.218411i	0.880955	−	0.473200i	$-0.156901\pi$
$733$	4.29622	+	5.91324i	0.158685	+	0.218411i	−0.722270	+	0.691611i	$0.756901\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	43.1100	+	0.260675i	1.58798	+	0.00960207i
$738$		0			0
$739$	12.4909	−	4.05854i	0.459485	−	0.149296i	−0.0701229	−	0.997538i	$-0.522339\pi$
$739$	12.4909	−	4.05854i	0.459485	−	0.149296i	0.529608	+	0.848243i	$0.322339\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.9307	−	33.6412i	0.401008	−	1.23418i	−0.523175	−	0.852225i	$-0.675253\pi$
$743$	10.9307	−	33.6412i	0.401008	−	1.23418i	0.924183	−	0.381950i	$-0.124747\pi$
$744$		0			0
$745$	−26.9503	+	37.0939i	−0.987383	+	1.35902i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			60.0306i			2.19347i
$750$		0			0
$751$	−18.6629	−	13.5594i	−0.681018	−	0.494789i	0.192677	−	0.981262i	$-0.438283\pi$
$751$	−18.6629	−	13.5594i	−0.681018	−	0.494789i	−0.873695	+	0.486473i	$0.838283\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.16285	−	1.57140i	0.0787141	−	0.0571892i
$756$		0			0
$757$	3.02640	+	9.31430i	0.109996	+	0.338534i	0.990871	−	0.134816i	$-0.0430445\pi$
$757$	3.02640	+	9.31430i	0.109996	+	0.338534i	−0.880874	+	0.473350i	$0.843044\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.9642	−	46.0550i	−0.542452	−	1.66949i	−0.726973	−	0.686666i	$-0.759074\pi$
$761$	−14.9642	−	46.0550i	−0.542452	−	1.66949i	0.184522	−	0.982828i	$-0.440926\pi$
$762$		0			0
$763$	48.9176	−	35.5407i	1.77094	−	1.28666i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.18426	−	1.58696i	−0.0788691	−	0.0573017i
$768$		0			0
$769$			33.4223i			1.20524i	0.798029	+	0.602619i	$0.205876\pi$
$769$			33.4223i			1.20524i	−0.798029	+	0.602619i	$0.794124\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.82924	−	5.27050i	0.137728	−	0.189567i	−0.734581	−	0.678521i	$-0.762621\pi$
$773$	3.82924	−	5.27050i	0.137728	−	0.189567i	0.872310	+	0.488954i	$0.162621\pi$
$774$		0			0
$775$	0.0280083	−	0.0862007i	0.00100609	−	0.00309642i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−19.2357	+	6.25007i	−0.689192	+	0.223932i
$780$		0			0
$781$	−3.52729	−	1.16971i	−0.126216	−	0.0418556i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.29014	−	3.15211i	−0.0817386	−	0.112503i
$786$		0			0
$787$	−27.5749	−	8.95962i	−0.982939	−	0.319376i	−0.226911	−	0.973916i	$-0.572863\pi$
$787$	−27.5749	−	8.95962i	−0.982939	−	0.319376i	−0.756028	+	0.654539i	$0.772863\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−45.5606			−1.61995
$792$		0			0
$793$	−17.5974			−0.624901
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−25.7264	−	8.35900i	−0.911274	−	0.296091i	−0.184392	−	0.982853i	$-0.559032\pi$
$797$	−25.7264	−	8.35900i	−0.911274	−	0.296091i	−0.726882	+	0.686762i	$0.759032\pi$
$798$		0			0
$799$	0.278738	+	0.383650i	0.00986103	+	0.0135725i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−25.7247	−	35.8610i	−0.907805	−	1.26551i
$804$		0			0
$805$	27.9526	−	9.08234i	0.985199	−	0.320110i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−12.9385	+	39.8205i	−0.454892	+	1.40001i	0.416370	+	0.909195i	$0.363302\pi$
$809$	−12.9385	+	39.8205i	−0.454892	+	1.40001i	−0.871262	+	0.490818i	$0.836698\pi$
$810$		0			0
$811$	7.51871	−	10.3486i	0.264018	−	0.363389i	−0.656341	−	0.754464i	$-0.727897\pi$
$811$	7.51871	−	10.3486i	0.264018	−	0.363389i	0.920359	+	0.391075i	$0.127897\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		−	2.25399i		−	0.0789538i
$816$		0			0
$817$	−8.29738	−	6.02840i	−0.290289	−	0.210907i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.59682	+	6.97250i	−0.334931	+	0.243342i	−0.742520	−	0.669824i	$-0.766370\pi$
$821$	−9.59682	+	6.97250i	−0.334931	+	0.243342i	0.407589	+	0.913166i	$0.366370\pi$
$822$		0			0
$823$	−8.11976	−	24.9900i	−0.283037	−	0.871098i	−0.986980	−	0.160842i	$-0.948579\pi$
$823$	−8.11976	−	24.9900i	−0.283037	−	0.871098i	0.703943	−	0.710256i	$-0.251421\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	7.99992	+	24.6212i	0.278184	+	0.856163i	0.988359	+	0.152138i	$0.0486159\pi$
$827$	7.99992	+	24.6212i	0.278184	+	0.856163i	−0.710175	+	0.704025i	$0.751384\pi$
$828$		0			0
$829$	−14.0195	+	10.1858i	−0.486918	+	0.353766i	−0.803998	−	0.594632i	$-0.797298\pi$
$829$	−14.0195	+	10.1858i	−0.486918	+	0.353766i	0.317080	+	0.948399i	$0.397298\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.580869	+	0.422026i	0.0201259	+	0.0146223i
$834$		0			0
$835$			30.3907i			1.05171i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	18.2513	−	25.1207i	0.630104	−	0.867264i	−0.367935	−	0.929851i	$-0.619935\pi$
$839$	18.2513	−	25.1207i	0.630104	−	0.867264i	0.998039	+	0.0625873i	$0.0199352\pi$
$840$		0			0
$841$	−7.91617	+	24.3635i	−0.272971	+	0.840120i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−18.4888	+	6.00737i	−0.636033	+	0.206660i
$846$		0			0
$847$	25.7549	+	36.3654i	0.884949	+	1.24953i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−13.7845	−	18.9727i	−0.472527	−	0.650377i
$852$		0			0
$853$	0.303737	+	0.0986902i	0.0103998	+	0.00337909i	0.314212	−	0.949353i	$-0.398260\pi$
$853$	0.303737	+	0.0986902i	0.0103998	+	0.00337909i	−0.303812	+	0.952732i	$0.598260\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.2476			−0.452528			−0.226264	−	0.974066i	$-0.572651\pi$
$857$	−13.2476			−0.452528			−0.226264	+	0.974066i	$0.572651\pi$
$858$		0			0
$859$	8.58152			0.292798			0.146399	−	0.989226i	$-0.453232\pi$
$859$	8.58152			0.292798			0.146399	+	0.989226i	$0.453232\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	51.0889	+	16.5998i	1.73909	+	0.565063i	0.994712	−	0.102700i	$-0.0327482\pi$
$863$	51.0889	+	16.5998i	1.73909	+	0.565063i	0.744374	+	0.667763i	$0.232748\pi$
$864$		0			0
$865$	−9.94098	−	13.6826i	−0.338004	−	0.465222i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.08545	−	0.663690i	0.0707441	−	0.0225141i
$870$		0			0
$871$	−57.5172	+	18.6885i	−1.94889	+	0.633234i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−13.9193	+	42.8394i	−0.470560	+	1.44823i
$876$		0			0
$877$	−25.8716	+	35.6092i	−0.873623	+	1.20244i	0.104524	+	0.994522i	$0.466668\pi$
$877$	−25.8716	+	35.6092i	−0.873623	+	1.20244i	−0.978147	+	0.207916i	$0.933332\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	7.44194i		−	0.250725i	−0.992111	−	0.125363i	$-0.959991\pi$
$881$		−	7.44194i		−	0.250725i	0.992111	−	0.125363i	$-0.0400095\pi$
$882$		0			0
$883$	−7.59369	−	5.51714i	−0.255548	−	0.185667i	0.452634	−	0.891696i	$-0.350484\pi$
$883$	−7.59369	−	5.51714i	−0.255548	−	0.185667i	−0.708182	+	0.706030i	$0.750484\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−19.5658	+	14.2154i	−0.656957	+	0.477307i	−0.865634	−	0.500678i	$-0.833084\pi$
$887$	−19.5658	+	14.2154i	−0.656957	+	0.477307i	0.208677	+	0.977985i	$0.433084\pi$
$888$		0			0
$889$	7.58806	+	23.3537i	0.254496	+	0.783257i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.60189	−	14.1632i	−0.153996	−	0.473952i
$894$		0			0
$895$	−22.7353	+	16.5182i	−0.759958	+	0.552142i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.49197	+	1.81052i	0.0831119	+	0.0603843i
$900$		0			0
$901$			0.0937613i			0.00312364i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	23.7869	−	32.7399i	0.790703	−	1.08831i
$906$		0			0
$907$	11.0734	−	34.0803i	0.367685	−	1.13162i	−0.580597	−	0.814191i	$-0.697181\pi$
$907$	11.0734	−	34.0803i	0.367685	−	1.13162i	0.948282	−	0.317428i	$-0.102819\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	8.33061	−	2.70678i	0.276005	−	0.0896796i	−0.167744	−	0.985831i	$-0.553648\pi$
$911$	8.33061	−	2.70678i	0.276005	−	0.0896796i	0.443749	+	0.896151i	$0.353648\pi$
$912$		0			0
$913$	10.6599	−	32.1451i	0.352791	−	1.06385i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−17.0273	−	23.4360i	−0.562290	−	0.773926i
$918$		0			0
$919$	39.4876	+	12.8303i	1.30258	+	0.423233i	0.876477	−	0.481443i	$-0.159887\pi$
$919$	39.4876	+	12.8303i	1.30258	+	0.423233i	0.426100	+	0.904676i	$0.359887\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.21318			0.171594
$924$		0			0
$925$	−0.393281			−0.0129310
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−51.5363	−	16.7451i	−1.69085	−	0.549390i	−0.703883	−	0.710316i	$-0.748552\pi$
$929$	−51.5363	−	16.7451i	−1.69085	−	0.549390i	−0.986967	+	0.160925i	$0.948552\pi$
$930$		0			0
$931$	−13.2531	−	18.2413i	−0.434351	−	0.597833i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.337136	−	0.458176i	0.0110255	−	0.0149839i
$936$		0			0
$937$	−16.5444	+	5.37559i	−0.540480	+	0.175613i	−0.566520	−	0.824048i	$-0.691710\pi$
$937$	−16.5444	+	5.37559i	−0.540480	+	0.175613i	0.0260393	+	0.999661i	$0.491710\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6.64708	−	20.4576i	0.216689	−	0.666899i	−0.782341	−	0.622851i	$-0.785974\pi$
$941$	6.64708	−	20.4576i	0.216689	−	0.666899i	0.999029	−	0.0440486i	$-0.0140256\pi$
$942$		0			0
$943$	−16.0137	+	22.0410i	−0.521478	+	0.717753i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	44.7887i		−	1.45544i	−0.685875	−	0.727719i	$-0.740580\pi$
$947$		−	44.7887i		−	1.45544i	0.685875	−	0.727719i	$-0.259420\pi$
$948$		0			0
$949$	50.0878	+	36.3909i	1.62592	+	1.18130i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−8.11741	+	5.89765i	−0.262949	+	0.191043i	−0.711446	−	0.702741i	$-0.751959\pi$
$953$	−8.11741	+	5.89765i	−0.262949	+	0.191043i	0.448497	+	0.893784i	$0.351959\pi$
$954$		0			0
$955$	15.0454	+	46.3049i	0.486857	+	1.49839i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−13.2977	−	40.9262i	−0.429406	−	1.32158i
$960$		0			0
$961$	22.8104	−	16.5727i	0.735819	−	0.534604i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	9.43388	+	6.85412i	0.303688	+	0.220642i
$966$		0			0
$967$		−	4.32167i		−	0.138976i	−0.997583	−	0.0694878i	$-0.977863\pi$
$967$		−	4.32167i		−	0.138976i	0.997583	−	0.0694878i	$-0.0221365\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−33.7344	+	46.4314i	−1.08259	+	1.49005i	−0.225947	+	0.974140i	$0.572548\pi$
$971$	−33.7344	+	46.4314i	−1.08259	+	1.49005i	−0.856640	+	0.515914i	$0.827452\pi$
$972$		0			0
$973$	−0.0664437	+	0.204493i	−0.00213009	+	0.00655574i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.28130	−	1.06616i	0.104978	−	0.0341095i	−0.256057	−	0.966662i	$-0.582423\pi$
$977$	3.28130	−	1.06616i	0.104978	−	0.0341095i	0.361035	+	0.932552i	$0.382423\pi$
$978$		0			0
$979$	0.132155	−	21.8556i	0.00422369	−	0.698508i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−0.608167	−	0.837070i	−0.0193975	−	0.0266984i	0.799208	−	0.601054i	$-0.205253\pi$
$983$	−0.608167	−	0.837070i	−0.0193975	−	0.0266984i	−0.818606	+	0.574356i	$0.805253\pi$
$984$		0			0
$985$	−11.0044	−	3.57554i	−0.350628	−	0.113926i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−13.8151			−0.439294
$990$		0			0
$991$	−9.78910			−0.310961			−0.155481	−	0.987839i	$-0.549693\pi$
$991$	−9.78910			−0.310961			−0.155481	+	0.987839i	$0.549693\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	51.8693	+	16.8534i	1.64437	+	0.534288i
$996$		0			0
$997$	−6.82690	−	9.39642i	−0.216210	−	0.297588i	0.687111	−	0.726552i	$-0.258878\pi$
$997$	−6.82690	−	9.39642i	−0.216210	−	0.297588i	−0.903321	+	0.428965i	$0.858878\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1584.2.cd.c.17.1		16
3.2	odd	2	inner	1584.2.cd.c.17.4		16
4.3	odd	2		99.2.j.a.17.1	✓	16
11.2	odd	10	inner	1584.2.cd.c.1025.4		16
12.11	even	2		99.2.j.a.17.4	yes	16
33.2	even	10	inner	1584.2.cd.c.1025.1		16
36.7	odd	6		891.2.u.c.215.1		32
36.11	even	6		891.2.u.c.215.4		32
36.23	even	6		891.2.u.c.512.1		32
36.31	odd	6		891.2.u.c.512.4		32
44.3	odd	10		1089.2.d.g.1088.3		16
44.19	even	10		1089.2.d.g.1088.13		16
44.35	even	10		99.2.j.a.35.4	yes	16
132.35	odd	10		99.2.j.a.35.1	yes	16
132.47	even	10		1089.2.d.g.1088.14		16
132.107	odd	10		1089.2.d.g.1088.4		16
396.79	even	30		891.2.u.c.134.1		32
396.167	odd	30		891.2.u.c.431.1		32
396.211	even	30		891.2.u.c.431.4		32
396.299	odd	30		891.2.u.c.134.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.17.1	✓	16	4.3	odd	2
99.2.j.a.17.4	yes	16	12.11	even	2
99.2.j.a.35.1	yes	16	132.35	odd	10
99.2.j.a.35.4	yes	16	44.35	even	10
891.2.u.c.134.1		32	396.79	even	30
891.2.u.c.134.4		32	396.299	odd	30
891.2.u.c.215.1		32	36.7	odd	6
891.2.u.c.215.4		32	36.11	even	6
891.2.u.c.431.1		32	396.167	odd	30
891.2.u.c.431.4		32	396.211	even	30
891.2.u.c.512.1		32	36.23	even	6
891.2.u.c.512.4		32	36.31	odd	6
1089.2.d.g.1088.3		16	44.3	odd	10
1089.2.d.g.1088.4		16	132.107	odd	10
1089.2.d.g.1088.13		16	44.19	even	10
1089.2.d.g.1088.14		16	132.47	even	10
1584.2.cd.c.17.1		16	1.1	even	1	trivial
1584.2.cd.c.17.4		16	3.2	odd	2	inner
1584.2.cd.c.1025.1		16	33.2	even	10	inner
1584.2.cd.c.1025.4		16	11.2	odd	10	inner

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:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1584.cd (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.13811 - 0.694712i) q^{5} +(2.38116 + 3.27739i) q^{7} +(-3.31656 - 0.0200544i) q^{11} +(4.42495 - 1.43775i) q^{13} +(0.0235753 - 0.0725574i) q^{17} +(-1.40822 + 1.93825i) q^{19} +3.22717i q^{23} +(0.0437835 + 0.0318106i) q^{25} +(-1.48796 + 1.08107i) q^{29} +(-0.517528 - 1.59279i) q^{31} +(-2.81433 - 8.66162i) q^{35} +(-5.87906 + 4.27138i) q^{37} +(6.82980 + 4.96214i) q^{41} +4.28086i q^{43} +(-3.65360 + 5.02874i) q^{47} +(-2.90822 + 8.95058i) q^{49} +(-1.16884 + 0.379779i) q^{53} +(7.07723 + 2.34694i) q^{55} +(-0.341086 - 0.469465i) q^{59} +(-3.59710 - 1.16877i) q^{61} -10.4598 q^{65} -12.9984 q^{67} +(1.06563 + 0.346245i) q^{71} +(7.82153 + 10.7654i) q^{73} +(-7.83155 - 10.9174i) q^{77} +(-0.627566 + 0.203908i) q^{79} +(-3.15542 + 9.71138i) q^{83} +(-0.100813 + 0.138757i) q^{85} +6.58983i q^{89} +(15.2486 + 11.0787i) q^{91} +(4.35745 - 3.16587i) q^{95} +(5.08168 + 15.6398i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{25} - 16 q^{31} - 12 q^{37} - 24 q^{49} - 16 q^{55} - 96 q^{67} - 20 q^{73} - 100 q^{85} + 72 q^{91} + 60 q^{97}+O(q^{100}) \) 16 * q - 32 * q^25 - 16 * q^31 - 12 * q^37 - 24 * q^49 - 16 * q^55 - 96 * q^67 - 20 * q^73 - 100 * q^85 + 72 * q^91 + 60 * q^97

Introduction

L-functions

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