LMFDB - Embedded newform 1296.3.q.f.593.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1296,3,Mod(593,1296)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1296, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1296.593");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1296 = 2^{4} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1296.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$35.3134422611$
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:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1296.593
Dual form			1296.3.q.f.1025.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.67423 - 2.12132i) q^{5} +(-2.00000 + 3.46410i) q^{7} +O(q^{10})$	$q+(3.67423 - 2.12132i) q^{5} +(-2.00000 + 3.46410i) q^{7} +(-14.6969 - 8.48528i) q^{11} +(-4.00000 - 6.92820i) q^{13} +12.7279i q^{17} +16.0000 q^{19} +(-14.6969 + 8.48528i) q^{23} +(-3.50000 + 6.06218i) q^{25} +(3.67423 + 2.12132i) q^{29} +(22.0000 + 38.1051i) q^{31} +16.9706i q^{35} -34.0000 q^{37} +(-40.4166 + 23.3345i) q^{41} +(-20.0000 + 34.6410i) q^{43} +(73.4847 + 42.4264i) q^{47} +(16.5000 + 28.5788i) q^{49} -38.1838i q^{53} -72.0000 q^{55} +(29.3939 - 16.9706i) q^{59} +(-25.0000 + 43.3013i) q^{61} +(-29.3939 - 16.9706i) q^{65} +(4.00000 + 6.92820i) q^{67} -50.9117i q^{71} -16.0000 q^{73} +(58.7878 - 33.9411i) q^{77} +(-38.0000 + 65.8179i) q^{79} +(-102.879 - 59.3970i) q^{83} +(27.0000 + 46.7654i) q^{85} -12.7279i q^{89} +32.0000 q^{91} +(58.7878 - 33.9411i) q^{95} +(-88.0000 + 152.420i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{7}+O(q^{10}) $ 4 * q - 8 * q^7	$ 4 q - 8 q^{7} - 16 q^{13} + 64 q^{19} - 14 q^{25} + 88 q^{31} - 136 q^{37} - 80 q^{43} + 66 q^{49} - 288 q^{55} - 100 q^{61} + 16 q^{67} - 64 q^{73} - 152 q^{79} + 108 q^{85} + 128 q^{91} - 352 q^{97}+O(q^{100}) $ 4 * q - 8 * q^7 - 16 * q^13 + 64 * q^19 - 14 * q^25 + 88 * q^31 - 136 * q^37 - 80 * q^43 + 66 * q^49 - 288 * q^55 - 100 * q^61 + 16 * q^67 - 64 * q^73 - 152 * q^79 + 108 * q^85 + 128 * q^91 - 352 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$5$	3.67423	−	2.12132i	0.734847	−	0.424264i	−0.0853458	−	0.996351i	$-0.527199\pi$
$5$	3.67423	−	2.12132i	0.734847	−	0.424264i	0.820193	+	0.572087i	$0.193866\pi$
$6$		0			0
$7$	−2.00000	+	3.46410i	−0.285714	+	0.494872i	−0.972782	−	0.231722i	$-0.925564\pi$
$7$	−2.00000	+	3.46410i	−0.285714	+	0.494872i	0.687068	+	0.726593i	$0.258897\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−14.6969	−	8.48528i	−1.33609	−	0.771389i	−0.349861	−	0.936802i	$-0.613771\pi$
$11$	−14.6969	−	8.48528i	−1.33609	−	0.771389i	−0.986224	+	0.165412i	$0.947104\pi$
$12$		0			0
$13$	−4.00000	−	6.92820i	−0.307692	−	0.532939i	0.670165	−	0.742212i	$-0.266223\pi$
$13$	−4.00000	−	6.92820i	−0.307692	−	0.532939i	−0.977857	+	0.209274i	$0.932890\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			12.7279i			0.748701i	0.927287	+	0.374351i	$0.122134\pi$
$17$			12.7279i			0.748701i	−0.927287	+	0.374351i	$0.877866\pi$
$18$		0			0
$19$	16.0000			0.842105			0.421053	−	0.907036i	$-0.361661\pi$
$19$	16.0000			0.842105			0.421053	+	0.907036i	$0.361661\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−14.6969	+	8.48528i	−0.638997	+	0.368925i	−0.784228	−	0.620473i	$-0.786941\pi$
$23$	−14.6969	+	8.48528i	−0.638997	+	0.368925i	0.145231	+	0.989398i	$0.453608\pi$
$24$		0			0
$25$	−3.50000	+	6.06218i	−0.140000	+	0.242487i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.67423	+	2.12132i	0.126698	+	0.0731490i	0.562009	−	0.827131i	$-0.310028\pi$
$29$	3.67423	+	2.12132i	0.126698	+	0.0731490i	−0.435312	+	0.900280i	$0.643362\pi$
$30$		0			0
$31$	22.0000	+	38.1051i	0.709677	+	1.22920i	0.964977	+	0.262335i	$0.0844926\pi$
$31$	22.0000	+	38.1051i	0.709677	+	1.22920i	−0.255299	+	0.966862i	$0.582174\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			16.9706i			0.484873i
$36$		0			0
$37$	−34.0000			−0.918919			−0.459459	−	0.888199i	$-0.651957\pi$
$37$	−34.0000			−0.918919			−0.459459	+	0.888199i	$0.651957\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−40.4166	+	23.3345i	−0.985770	+	0.569135i	−0.904007	−	0.427517i	$-0.859388\pi$
$41$	−40.4166	+	23.3345i	−0.985770	+	0.569135i	−0.0817630	+	0.996652i	$0.526055\pi$
$42$		0			0
$43$	−20.0000	+	34.6410i	−0.465116	+	0.805605i	−0.999207	−	0.0398223i	$-0.987321\pi$
$43$	−20.0000	+	34.6410i	−0.465116	+	0.805605i	0.534090	+	0.845427i	$0.320654\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	73.4847	+	42.4264i	1.56350	+	0.902690i	0.996898	+	0.0787005i	$0.0250771\pi$
$47$	73.4847	+	42.4264i	1.56350	+	0.902690i	0.566606	+	0.823989i	$0.308256\pi$
$48$		0			0
$49$	16.5000	+	28.5788i	0.336735	+	0.583242i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	38.1838i		−	0.720448i	−0.932866	−	0.360224i	$-0.882700\pi$
$53$		−	38.1838i		−	0.720448i	0.932866	−	0.360224i	$-0.117300\pi$
$54$		0			0
$55$	−72.0000			−1.30909
$56$		0			0
$57$		0			0
$58$		0			0
$59$	29.3939	−	16.9706i	0.498201	−	0.287637i	−0.229769	−	0.973245i	$-0.573797\pi$
$59$	29.3939	−	16.9706i	0.498201	−	0.287637i	0.727970	+	0.685609i	$0.240464\pi$
$60$		0			0
$61$	−25.0000	+	43.3013i	−0.409836	+	0.709857i	−0.994871	−	0.101151i	$-0.967747\pi$
$61$	−25.0000	+	43.3013i	−0.409836	+	0.709857i	0.585035	+	0.811008i	$0.301081\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−29.3939	−	16.9706i	−0.452213	−	0.261086i
$66$		0			0
$67$	4.00000	+	6.92820i	0.0597015	+	0.103406i	0.894331	−	0.447405i	$-0.147652\pi$
$67$	4.00000	+	6.92820i	0.0597015	+	0.103406i	−0.834630	+	0.550811i	$0.814318\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	50.9117i		−	0.717066i	−0.933517	−	0.358533i	$-0.883277\pi$
$71$		−	50.9117i		−	0.717066i	0.933517	−	0.358533i	$-0.116723\pi$
$72$		0			0
$73$	−16.0000			−0.219178			−0.109589	−	0.993977i	$-0.534953\pi$
$73$	−16.0000			−0.219178			−0.109589	+	0.993977i	$0.534953\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	58.7878	−	33.9411i	0.763477	−	0.440794i
$78$		0			0
$79$	−38.0000	+	65.8179i	−0.481013	+	0.833138i	−0.999763	−	0.0217876i	$-0.993064\pi$
$79$	−38.0000	+	65.8179i	−0.481013	+	0.833138i	0.518750	+	0.854926i	$0.326398\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−102.879	−	59.3970i	−1.23950	−	0.715626i	−0.270509	−	0.962718i	$-0.587192\pi$
$83$	−102.879	−	59.3970i	−1.23950	−	0.715626i	−0.968992	+	0.247091i	$0.920525\pi$
$84$		0			0
$85$	27.0000	+	46.7654i	0.317647	+	0.550181i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	12.7279i		−	0.143010i	−0.997440	−	0.0715052i	$-0.977220\pi$
$89$		−	12.7279i		−	0.143010i	0.997440	−	0.0715052i	$-0.0227802\pi$
$90$		0			0
$91$	32.0000			0.351648
$92$		0			0
$93$		0			0
$94$		0			0
$95$	58.7878	−	33.9411i	0.618818	−	0.357275i
$96$		0			0
$97$	−88.0000	+	152.420i	−0.907216	+	1.57135i	−0.0893025	+	0.996005i	$0.528464\pi$
$97$	−88.0000	+	152.420i	−0.907216	+	1.57135i	−0.817914	+	0.575341i	$0.804870\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	25.7196	+	14.8492i	0.254650	+	0.147022i	0.621892	−	0.783103i	$-0.286364\pi$
$101$	25.7196	+	14.8492i	0.254650	+	0.147022i	−0.367242	+	0.930126i	$0.619698\pi$
$102$		0			0
$103$	−14.0000	−	24.2487i	−0.135922	−	0.235424i	0.790027	−	0.613072i	$-0.210066\pi$
$103$	−14.0000	−	24.2487i	−0.135922	−	0.235424i	−0.925949	+	0.377648i	$0.876733\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	56.0000			0.513761			0.256881	−	0.966443i	$-0.417305\pi$
$109$	56.0000			0.513761			0.256881	+	0.966443i	$0.417305\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	135.947	−	78.4889i	1.20307	−	0.694592i	0.241832	−	0.970318i	$-0.422252\pi$
$113$	135.947	−	78.4889i	1.20307	−	0.694592i	0.961236	+	0.275727i	$0.0889184\pi$
$114$		0			0
$115$	−36.0000	+	62.3538i	−0.313043	+	0.542207i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−44.0908	−	25.4558i	−0.370511	−	0.213915i
$120$		0			0
$121$	83.5000	+	144.626i	0.690083	+	1.19526i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			135.765i			1.08612i
$126$		0			0
$127$	−92.0000			−0.724409			−0.362205	−	0.932099i	$-0.617976\pi$
$127$	−92.0000			−0.724409			−0.362205	+	0.932099i	$0.617976\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−146.969	+	84.8528i	−1.12190	+	0.647731i	−0.941886	−	0.335932i	$-0.890949\pi$
$131$	−146.969	+	84.8528i	−1.12190	+	0.647731i	−0.180017	+	0.983663i	$0.557615\pi$
$132$		0			0
$133$	−32.0000	+	55.4256i	−0.240602	+	0.416734i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	135.947	+	78.4889i	0.992312	+	0.572911i	0.905964	−	0.423354i	$-0.139147\pi$
$137$	135.947	+	78.4889i	0.992312	+	0.572911i	0.0863471	+	0.996265i	$0.472481\pi$
$138$		0			0
$139$	76.0000	+	131.636i	0.546763	+	0.947021i	0.998494	+	0.0548664i	$0.0174733\pi$
$139$	76.0000	+	131.636i	0.546763	+	0.947021i	−0.451731	+	0.892154i	$0.649193\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			135.765i			0.949402i
$144$		0			0
$145$	18.0000			0.124138
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−238.825	+	137.886i	−1.60285	+	0.925408i	−0.611941	+	0.790903i	$0.709611\pi$
$149$	−238.825	+	137.886i	−1.60285	+	0.925408i	−0.990913	+	0.134505i	$0.957056\pi$
$150$		0			0
$151$	−74.0000	+	128.172i	−0.490066	+	0.848820i	−0.999935	−	0.0114328i	$-0.996361\pi$
$151$	−74.0000	+	128.172i	−0.490066	+	0.848820i	0.509868	+	0.860252i	$0.329694\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	161.666	+	93.3381i	1.04301	+	0.602181i
$156$		0			0
$157$	41.0000	+	71.0141i	0.261146	+	0.452319i	0.966547	−	0.256490i	$-0.0825661\pi$
$157$	41.0000	+	71.0141i	0.261146	+	0.452319i	−0.705400	+	0.708809i	$0.749233\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	67.8823i		−	0.421629i
$162$		0			0
$163$	−56.0000			−0.343558			−0.171779	−	0.985135i	$-0.554952\pi$
$163$	−56.0000			−0.343558			−0.171779	+	0.985135i	$0.554952\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	29.3939	−	16.9706i	0.176011	−	0.101620i	−0.409406	−	0.912352i	$-0.634264\pi$
$167$	29.3939	−	16.9706i	0.176011	−	0.101620i	0.585417	+	0.810732i	$0.300931\pi$
$168$		0			0
$169$	52.5000	−	90.9327i	0.310651	−	0.538063i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−150.644	−	86.9741i	−0.870772	−	0.502741i	−0.00316754	−	0.999995i	$-0.501008\pi$
$173$	−150.644	−	86.9741i	−0.870772	−	0.502741i	−0.867605	+	0.497254i	$0.834342\pi$
$174$		0			0
$175$	−14.0000	−	24.2487i	−0.0800000	−	0.138564i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	203.647i		−	1.13769i	−0.822444	−	0.568846i	$-0.807390\pi$
$179$		−	203.647i		−	1.13769i	0.822444	−	0.568846i	$-0.192610\pi$
$180$		0			0
$181$	−232.000			−1.28177			−0.640884	−	0.767638i	$-0.721432\pi$
$181$	−232.000			−1.28177			−0.640884	+	0.767638i	$0.721432\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−124.924	+	72.1249i	−0.675265	+	0.389864i
$186$		0			0
$187$	108.000	−	187.061i	0.577540	−	1.00033i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	29.3939	+	16.9706i	0.153895	+	0.0888511i	0.574970	−	0.818175i	$-0.305014\pi$
$191$	29.3939	+	16.9706i	0.153895	+	0.0888511i	−0.421075	+	0.907026i	$0.638347\pi$
$192$		0			0
$193$	−103.000	−	178.401i	−0.533679	−	0.924359i	−0.999226	−	0.0393357i	$-0.987476\pi$
$193$	−103.000	−	178.401i	−0.533679	−	0.924359i	0.465547	−	0.885023i	$-0.345858\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	165.463i		−	0.839914i	−0.907544	−	0.419957i	$-0.862045\pi$
$197$		−	165.463i		−	0.839914i	0.907544	−	0.419957i	$-0.137955\pi$
$198$		0			0
$199$	−20.0000			−0.100503			−0.0502513	−	0.998737i	$-0.516002\pi$
$199$	−20.0000			−0.100503			−0.0502513	+	0.998737i	$0.516002\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−14.6969	+	8.48528i	−0.0723987	+	0.0417994i
$204$		0			0
$205$	−99.0000	+	171.473i	−0.482927	+	0.836454i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−235.151	−	135.765i	−1.12512	−	0.649591i
$210$		0			0
$211$	148.000	+	256.344i	0.701422	+	1.21490i	0.967967	+	0.251076i	$0.0807844\pi$
$211$	148.000	+	256.344i	0.701422	+	1.21490i	−0.266546	+	0.963822i	$0.585882\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			169.706i			0.789328i
$216$		0			0
$217$	−176.000			−0.811060
$218$		0			0
$219$		0			0
$220$		0			0
$221$	88.1816	−	50.9117i	0.399012	−	0.230370i
$222$		0			0
$223$	−218.000	+	377.587i	−0.977578	+	1.69322i	−0.306429	+	0.951894i	$0.599134\pi$
$223$	−218.000	+	377.587i	−0.977578	+	1.69322i	−0.671149	+	0.741322i	$0.734199\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.6969	−	8.48528i	−0.0647442	−	0.0373801i	0.467278	−	0.884110i	$-0.345235\pi$
$227$	−14.6969	−	8.48528i	−0.0647442	−	0.0373801i	−0.532023	+	0.846730i	$0.678568\pi$
$228$		0			0
$229$	−4.00000	−	6.92820i	−0.0174672	−	0.0302542i	0.857160	−	0.515051i	$-0.172227\pi$
$229$	−4.00000	−	6.92820i	−0.0174672	−	0.0302542i	−0.874627	+	0.484797i	$0.838894\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			12.7279i			0.0546263i	0.999627	+	0.0273131i	$0.00869512\pi$
$233$			12.7279i			0.0546263i	−0.999627	+	0.0273131i	$0.991305\pi$
$234$		0			0
$235$	360.000			1.53191
$236$		0			0
$237$		0			0
$238$		0			0
$239$	117.576	−	67.8823i	0.491948	−	0.284026i	−0.233434	−	0.972373i	$-0.574996\pi$
$239$	117.576	−	67.8823i	0.491948	−	0.284026i	0.725382	+	0.688346i	$0.241663\pi$
$240$		0			0
$241$	−16.0000	+	27.7128i	−0.0663900	+	0.114991i	−0.897310	−	0.441401i	$-0.854481\pi$
$241$	−16.0000	+	27.7128i	−0.0663900	+	0.114991i	0.830920	+	0.556392i	$0.187815\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	121.250	+	70.0036i	0.494897	+	0.285729i
$246$		0			0
$247$	−64.0000	−	110.851i	−0.259109	−	0.448790i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			50.9117i			0.202835i	0.994844	+	0.101418i	$0.0323379\pi$
$251$			50.9117i			0.202835i	−0.994844	+	0.101418i	$0.967662\pi$
$252$		0			0
$253$	288.000			1.13834
$254$		0			0
$255$		0			0
$256$		0			0
$257$	157.992	−	91.2168i	0.614755	−	0.354929i	−0.160069	−	0.987106i	$-0.551172\pi$
$257$	157.992	−	91.2168i	0.614755	−	0.354929i	0.774824	+	0.632177i	$0.217838\pi$
$258$		0			0
$259$	68.0000	−	117.779i	0.262548	−	0.454747i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−323.333	−	186.676i	−1.22940	−	0.709795i	−0.262497	−	0.964933i	$-0.584546\pi$
$263$	−323.333	−	186.676i	−1.22940	−	0.709795i	−0.966905	+	0.255137i	$0.917879\pi$
$264$		0			0
$265$	−81.0000	−	140.296i	−0.305660	−	0.529419i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			343.654i			1.27752i	0.769404	+	0.638762i	$0.220553\pi$
$269$			343.654i			1.27752i	−0.769404	+	0.638762i	$0.779447\pi$
$270$		0			0
$271$	−380.000			−1.40221			−0.701107	−	0.713056i	$-0.747310\pi$
$271$	−380.000			−1.40221			−0.701107	+	0.713056i	$0.747310\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	102.879	−	59.3970i	0.374104	−	0.215989i
$276$		0			0
$277$	164.000	−	284.056i	0.592058	−	1.02547i	−0.401897	−	0.915685i	$-0.631649\pi$
$277$	164.000	−	284.056i	0.592058	−	1.02547i	0.993955	−	0.109789i	$-0.0350176\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	246.174	+	142.128i	0.876063	+	0.505795i	0.869358	−	0.494182i	$-0.164532\pi$
$281$	246.174	+	142.128i	0.876063	+	0.505795i	0.00670475	+	0.999978i	$0.497866\pi$
$282$		0			0
$283$	−104.000	−	180.133i	−0.367491	−	0.636513i	0.621681	−	0.783270i	$-0.286450\pi$
$283$	−104.000	−	180.133i	−0.367491	−	0.636513i	−0.989173	+	0.146757i	$0.953117\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	186.676i		−	0.650440i
$288$		0			0
$289$	127.000			0.439446
$290$		0			0
$291$		0			0
$292$		0			0
$293$	378.446	−	218.496i	1.29163	−	0.745720i	0.312683	−	0.949858i	$-0.398772\pi$
$293$	378.446	−	218.496i	1.29163	−	0.745720i	0.978942	+	0.204137i	$0.0654389\pi$
$294$		0			0
$295$	72.0000	−	124.708i	0.244068	−	0.422738i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	117.576	+	67.8823i	0.393229	+	0.227031i
$300$		0			0
$301$	−80.0000	−	138.564i	−0.265781	−	0.460346i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			212.132i			0.695515i
$306$		0			0
$307$	520.000			1.69381			0.846906	−	0.531743i	$-0.178463\pi$
$307$	520.000			1.69381			0.846906	+	0.531743i	$0.178463\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−323.333	+	186.676i	−1.03965	+	0.600245i	−0.919736	−	0.392539i	$-0.871597\pi$
$311$	−323.333	+	186.676i	−1.03965	+	0.600245i	−0.119919	+	0.992784i	$0.538264\pi$
$312$		0			0
$313$	47.0000	−	81.4064i	0.150160	−	0.260084i	−0.781126	−	0.624373i	$-0.785355\pi$
$313$	47.0000	−	81.4064i	0.150160	−	0.260084i	0.931286	+	0.364289i	$0.118688\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	290.265	+	167.584i	0.915661	+	0.528657i	0.882248	−	0.470785i	$-0.156029\pi$
$317$	290.265	+	167.584i	0.915661	+	0.528657i	0.0334128	+	0.999442i	$0.489362\pi$
$318$		0			0
$319$	−36.0000	−	62.3538i	−0.112853	−	0.195467i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			203.647i			0.630485i
$324$		0			0
$325$	56.0000			0.172308
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−293.939	+	169.706i	−0.893431	+	0.515823i
$330$		0			0
$331$	268.000	−	464.190i	0.809668	−	1.40239i	−0.103427	−	0.994637i	$-0.532981\pi$
$331$	268.000	−	464.190i	0.809668	−	1.40239i	0.913094	−	0.407748i	$-0.133686\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	29.3939	+	16.9706i	0.0877429	+	0.0506584i
$336$		0			0
$337$	104.000	+	180.133i	0.308605	+	0.534520i	0.978058	−	0.208335i	$-0.0668044\pi$
$337$	104.000	+	180.133i	0.308605	+	0.534520i	−0.669452	+	0.742855i	$0.733471\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	746.705i		−	2.18975i
$342$		0			0
$343$	−328.000			−0.956268
$344$		0			0
$345$		0			0
$346$		0			0
$347$	249.848	−	144.250i	0.720023	−	0.415705i	−0.0947382	−	0.995502i	$-0.530201\pi$
$347$	249.848	−	144.250i	0.720023	−	0.415705i	0.814761	+	0.579797i	$0.196868\pi$
$348$		0			0
$349$	119.000	−	206.114i	0.340974	−	0.590585i	−0.643640	−	0.765329i	$-0.722576\pi$
$349$	119.000	−	206.114i	0.340974	−	0.590585i	0.984614	+	0.174744i	$0.0559098\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−194.734	−	112.430i	−0.551656	−	0.318499i	0.198134	−	0.980175i	$-0.436512\pi$
$353$	−194.734	−	112.430i	−0.551656	−	0.318499i	−0.749789	+	0.661676i	$0.769845\pi$
$354$		0			0
$355$	−108.000	−	187.061i	−0.304225	−	0.526934i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	560.029i		−	1.55997i	−0.625799	−	0.779984i	$-0.715227\pi$
$359$		−	560.029i		−	1.55997i	0.625799	−	0.779984i	$-0.284773\pi$
$360$		0			0
$361$	−105.000			−0.290859
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−58.7878	+	33.9411i	−0.161062	+	0.0929894i
$366$		0			0
$367$	142.000	−	245.951i	0.386921	−	0.670167i	−0.605113	−	0.796140i	$-0.706872\pi$
$367$	142.000	−	245.951i	0.386921	−	0.670167i	0.992034	+	0.125973i	$0.0402053\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	132.272	+	76.3675i	0.356530	+	0.205842i
$372$		0			0
$373$	95.0000	+	164.545i	0.254692	+	0.441139i	0.964812	−	0.262942i	$-0.0846927\pi$
$373$	95.0000	+	164.545i	0.254692	+	0.441139i	−0.710120	+	0.704081i	$0.751359\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	33.9411i		−	0.0900295i
$378$		0			0
$379$	160.000			0.422164			0.211082	−	0.977468i	$-0.432301\pi$
$379$	160.000			0.422164			0.211082	+	0.977468i	$0.432301\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−235.151	+	135.765i	−0.613971	+	0.354477i	−0.774518	−	0.632552i	$-0.782008\pi$
$383$	−235.151	+	135.765i	−0.613971	+	0.354477i	0.160547	+	0.987028i	$0.448674\pi$
$384$		0			0
$385$	144.000	−	249.415i	0.374026	−	0.647832i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−349.052	−	201.525i	−0.897307	−	0.518060i	−0.0209813	−	0.999780i	$-0.506679\pi$
$389$	−349.052	−	201.525i	−0.897307	−	0.518060i	−0.876325	+	0.481720i	$0.840012\pi$
$390$		0			0
$391$	−108.000	−	187.061i	−0.276215	−	0.478418i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			322.441i			0.816306i
$396$		0			0
$397$	146.000			0.367758			0.183879	−	0.982949i	$-0.441135\pi$
$397$	146.000			0.367758			0.183879	+	0.982949i	$0.441135\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−282.916	+	163.342i	−0.705526	+	0.407336i	−0.809402	−	0.587254i	$-0.800209\pi$
$401$	−282.916	+	163.342i	−0.705526	+	0.407336i	0.103876	+	0.994590i	$0.466875\pi$
$402$		0			0
$403$	176.000	−	304.841i	0.436725	−	0.756429i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	499.696	+	288.500i	1.22775	+	0.708844i
$408$		0			0
$409$	−184.000	−	318.697i	−0.449878	−	0.779211i	0.548500	−	0.836151i	$-0.315199\pi$
$409$	−184.000	−	318.697i	−0.449878	−	0.779211i	−0.998378	+	0.0569395i	$0.981866\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			135.765i			0.328728i
$414$		0			0
$415$	−504.000			−1.21446
$416$		0			0
$417$		0			0
$418$		0			0
$419$	338.030	−	195.161i	0.806753	−	0.465779i	−0.0390739	−	0.999236i	$-0.512441\pi$
$419$	338.030	−	195.161i	0.806753	−	0.465779i	0.845827	+	0.533457i	$0.179107\pi$
$420$		0			0
$421$	20.0000	−	34.6410i	0.0475059	−	0.0822827i	−0.841295	−	0.540577i	$-0.818206\pi$
$421$	20.0000	−	34.6410i	0.0475059	−	0.0822827i	0.888801	+	0.458294i	$0.151539\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−77.1589	−	44.5477i	−0.181550	−	0.104818i
$426$		0			0
$427$	−100.000	−	173.205i	−0.234192	−	0.405633i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	152.735i		−	0.354374i	−0.984177	−	0.177187i	$-0.943300\pi$
$431$		−	152.735i		−	0.354374i	0.984177	−	0.177187i	$-0.0566997\pi$
$432$		0			0
$433$	542.000			1.25173			0.625866	−	0.779931i	$-0.284746\pi$
$433$	542.000			1.25173			0.625866	+	0.779931i	$0.284746\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−235.151	+	135.765i	−0.538103	+	0.310674i
$438$		0			0
$439$	−2.00000	+	3.46410i	−0.00455581	+	0.00789089i	−0.868294	−	0.496049i	$-0.834783\pi$
$439$	−2.00000	+	3.46410i	−0.00455581	+	0.00789089i	0.863739	+	0.503940i	$0.168117\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−279.242	−	161.220i	−0.630343	−	0.363929i	0.150542	−	0.988604i	$-0.451898\pi$
$443$	−279.242	−	161.220i	−0.630343	−	0.363929i	−0.780885	+	0.624675i	$0.785231\pi$
$444$		0			0
$445$	−27.0000	−	46.7654i	−0.0606742	−	0.105091i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	216.375i		−	0.481904i	−0.970537	−	0.240952i	$-0.922540\pi$
$449$		−	216.375i		−	0.481904i	0.970537	−	0.240952i	$-0.0774596\pi$
$450$		0			0
$451$	792.000			1.75610
$452$		0			0
$453$		0			0
$454$		0			0
$455$	117.576	−	67.8823i	0.258408	−	0.149192i
$456$		0			0
$457$	200.000	−	346.410i	0.437637	−	0.758009i	−0.559870	−	0.828580i	$-0.689149\pi$
$457$	200.000	−	346.410i	0.437637	−	0.758009i	0.997507	+	0.0705714i	$0.0224823\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−260.871	−	150.614i	−0.565880	−	0.326711i	0.189622	−	0.981857i	$-0.439274\pi$
$461$	−260.871	−	150.614i	−0.565880	−	0.326711i	−0.755502	+	0.655146i	$0.772607\pi$
$462$		0			0
$463$	−302.000	−	523.079i	−0.652268	−	1.12976i	−0.982571	−	0.185886i	$-0.940484\pi$
$463$	−302.000	−	523.079i	−0.652268	−	1.12976i	0.330303	−	0.943875i	$-0.392849\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			356.382i			0.763130i	0.924342	+	0.381565i	$0.124615\pi$
$467$			356.382i			0.763130i	−0.924342	+	0.381565i	$0.875385\pi$
$468$		0			0
$469$	−32.0000			−0.0682303
$470$		0			0
$471$		0			0
$472$		0			0
$473$	587.878	−	339.411i	1.24287	−	0.717571i
$474$		0			0
$475$	−56.0000	+	96.9948i	−0.117895	+	0.204200i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−455.605	−	263.044i	−0.951159	−	0.549152i	−0.0577181	−	0.998333i	$-0.518382\pi$
$479$	−455.605	−	263.044i	−0.951159	−	0.549152i	−0.893441	+	0.449181i	$0.851716\pi$
$480$		0			0
$481$	136.000	+	235.559i	0.282744	+	0.489727i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			746.705i			1.53960i
$486$		0			0
$487$	−596.000			−1.22382			−0.611910	−	0.790928i	$-0.709598\pi$
$487$	−596.000			−1.22382			−0.611910	+	0.790928i	$0.709598\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−235.151	+	135.765i	−0.478923	+	0.276506i	−0.719967	−	0.694008i	$-0.755843\pi$
$491$	−235.151	+	135.765i	−0.478923	+	0.276506i	0.241045	+	0.970514i	$0.422510\pi$
$492$		0			0
$493$	−27.0000	+	46.7654i	−0.0547667	+	0.0948588i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	176.363	+	101.823i	0.354856	+	0.204876i
$498$		0			0
$499$	112.000	+	193.990i	0.224449	+	0.388757i	0.956154	−	0.292864i	$-0.0946085\pi$
$499$	112.000	+	193.990i	0.224449	+	0.388757i	−0.731705	+	0.681621i	$0.761275\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			865.499i			1.72067i	0.509726	+	0.860337i	$0.329747\pi$
$503$			865.499i			1.72067i	−0.509726	+	0.860337i	$0.670253\pi$
$504$		0			0
$505$	126.000			0.249505
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−415.189	+	239.709i	−0.815695	+	0.470941i	−0.848929	−	0.528506i	$-0.822752\pi$
$509$	−415.189	+	239.709i	−0.815695	+	0.470941i	0.0332350	+	0.999448i	$0.489419\pi$
$510$		0			0
$511$	32.0000	−	55.4256i	0.0626223	−	0.108465i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−102.879	−	59.3970i	−0.199764	−	0.115334i
$516$		0			0
$517$	−720.000	−	1247.08i	−1.39265	−	2.41214i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			521.845i			1.00162i	0.865557	+	0.500811i	$0.166965\pi$
$521$			521.845i			1.00162i	−0.865557	+	0.500811i	$0.833035\pi$
$522$		0			0
$523$	736.000			1.40727			0.703633	−	0.710564i	$-0.251560\pi$
$523$	736.000			1.40727			0.703633	+	0.710564i	$0.251560\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−484.999	+	280.014i	−0.920302	+	0.531336i
$528$		0			0
$529$	−120.500	+	208.712i	−0.227788	+	0.394541i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	323.333	+	186.676i	0.606628	+	0.350237i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	560.029i		−	1.03901i
$540$		0			0
$541$	−808.000			−1.49353			−0.746765	−	0.665088i	$-0.768394\pi$
$541$	−808.000			−1.49353			−0.746765	+	0.665088i	$0.768394\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	205.757	−	118.794i	0.377536	−	0.217971i
$546$		0			0
$547$	268.000	−	464.190i	0.489945	−	0.848610i	−0.509988	−	0.860182i	$-0.670350\pi$
$547$	268.000	−	464.190i	0.489945	−	0.848610i	0.999933	+	0.0115717i	$0.00368346\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	58.7878	+	33.9411i	0.106693	+	0.0615991i
$552$		0			0
$553$	−152.000	−	263.272i	−0.274864	−	0.476079i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			165.463i			0.297061i	0.988908	+	0.148531i	$0.0474543\pi$
$557$			165.463i			0.297061i	−0.988908	+	0.148531i	$0.952546\pi$
$558$		0			0
$559$	320.000			0.572451
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−279.242	+	161.220i	−0.495989	+	0.286359i	−0.727056	−	0.686579i	$-0.759112\pi$
$563$	−279.242	+	161.220i	−0.495989	+	0.286359i	0.231067	+	0.972938i	$0.425778\pi$
$564$		0			0
$565$	333.000	−	576.773i	0.589381	−	1.02084i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	135.947	+	78.4889i	0.238922	+	0.137942i	0.614681	−	0.788776i	$-0.289285\pi$
$569$	135.947	+	78.4889i	0.238922	+	0.137942i	−0.375759	+	0.926717i	$0.622618\pi$
$570$		0			0
$571$	184.000	+	318.697i	0.322242	+	0.558139i	0.980950	−	0.194259i	$-0.0622303\pi$
$571$	184.000	+	318.697i	0.322242	+	0.558139i	−0.658709	+	0.752398i	$0.728897\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	118.794i		−	0.206598i
$576$		0			0
$577$	−142.000			−0.246101			−0.123050	−	0.992400i	$-0.539268\pi$
$577$	−142.000			−0.246101			−0.123050	+	0.992400i	$0.539268\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	411.514	−	237.588i	0.708286	−	0.408929i
$582$		0			0
$583$	−324.000	+	561.184i	−0.555746	+	0.962581i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−323.333	−	186.676i	−0.550822	−	0.318017i	0.198631	−	0.980074i	$-0.436350\pi$
$587$	−323.333	−	186.676i	−0.550822	−	0.318017i	−0.749454	+	0.662057i	$0.769684\pi$
$588$		0			0
$589$	352.000	+	609.682i	0.597623	+	1.03511i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	1107.33i		−	1.86733i	−0.358142	−	0.933667i	$-0.616590\pi$
$593$		−	1107.33i		−	1.86733i	0.358142	−	0.933667i	$-0.383410\pi$
$594$		0			0
$595$	−216.000			−0.363025
$596$		0			0
$597$		0			0
$598$		0			0
$599$	690.756	−	398.808i	1.15318	−	0.665790i	0.203521	−	0.979070i	$-0.434761\pi$
$599$	690.756	−	398.808i	1.15318	−	0.665790i	0.949661	+	0.313280i	$0.101428\pi$
$600$		0			0
$601$	−79.0000	+	136.832i	−0.131448	+	0.227674i	−0.924235	−	0.381825i	$-0.875296\pi$
$601$	−79.0000	+	136.832i	−0.131448	+	0.227674i	0.792787	+	0.609499i	$0.208629\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	613.597	+	354.260i	1.01421	+	0.585555i
$606$		0			0
$607$	166.000	+	287.520i	0.273476	+	0.473675i	0.969750	−	0.244102i	$-0.0784932\pi$
$607$	166.000	+	287.520i	0.273476	+	0.473675i	−0.696273	+	0.717777i	$0.745160\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	678.823i		−	1.11100i
$612$		0			0
$613$	578.000			0.942904			0.471452	−	0.881892i	$-0.343730\pi$
$613$	578.000			0.942904			0.471452	+	0.881892i	$0.343730\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	47.7650	−	27.5772i	0.0774150	−	0.0446956i	−0.460793	−	0.887508i	$-0.652435\pi$
$617$	47.7650	−	27.5772i	0.0774150	−	0.0446956i	0.538208	+	0.842812i	$0.319102\pi$
$618$		0			0
$619$	448.000	−	775.959i	0.723748	−	1.25357i	−0.235739	−	0.971816i	$-0.575751\pi$
$619$	448.000	−	775.959i	0.723748	−	1.25357i	0.959487	−	0.281752i	$-0.0909155\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	44.0908	+	25.4558i	0.0707718	+	0.0408601i
$624$		0			0
$625$	200.500	+	347.276i	0.320800	+	0.555642i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	432.749i		−	0.687996i
$630$		0			0
$631$	−20.0000			−0.0316957			−0.0158479	−	0.999874i	$-0.505045\pi$
$631$	−20.0000			−0.0316957			−0.0158479	+	0.999874i	$0.505045\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−338.030	+	195.161i	−0.532330	+	0.307341i
$636$		0			0
$637$	132.000	−	228.631i	0.207221	−	0.358918i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	224.128	+	129.401i	0.349654	+	0.201873i	0.664533	−	0.747259i	$-0.268631\pi$
$641$	224.128	+	129.401i	0.349654	+	0.201873i	−0.314879	+	0.949132i	$0.601964\pi$
$642$		0			0
$643$	364.000	+	630.466i	0.566096	+	0.980508i	0.996947	+	0.0780844i	$0.0248804\pi$
$643$	364.000	+	630.466i	0.566096	+	0.980508i	−0.430850	+	0.902423i	$0.641786\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	458.205i		−	0.708200i	−0.935208	−	0.354100i	$-0.884787\pi$
$647$		−	458.205i		−	0.708200i	0.935208	−	0.354100i	$-0.115213\pi$
$648$		0			0
$649$	−576.000			−0.887519
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−260.871	+	150.614i	−0.399496	+	0.230649i	−0.686266	−	0.727350i	$-0.740752\pi$
$653$	−260.871	+	150.614i	−0.399496	+	0.230649i	0.286771	+	0.957999i	$0.407418\pi$
$654$		0			0
$655$	−360.000	+	623.538i	−0.549618	+	0.951967i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	911.210	+	526.087i	1.38272	+	0.798312i	0.992480	−	0.122403i	$-0.0390601\pi$
$659$	911.210	+	526.087i	1.38272	+	0.798312i	0.390236	+	0.920715i	$0.372393\pi$
$660$		0			0
$661$	−31.0000	−	53.6936i	−0.0468986	−	0.0812308i	0.841623	−	0.540065i	$-0.181600\pi$
$661$	−31.0000	−	53.6936i	−0.0468986	−	0.0812308i	−0.888522	+	0.458834i	$0.848267\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			271.529i			0.408314i
$666$		0			0
$667$	−72.0000			−0.107946
$668$		0			0
$669$		0			0
$670$		0			0
$671$	734.847	−	424.264i	1.09515	−	0.632286i
$672$		0			0
$673$	335.000	−	580.237i	0.497771	−	0.862165i	−0.502226	−	0.864737i	$-0.667485\pi$
$673$	335.000	−	580.237i	0.497771	−	0.862165i	0.999997	+	0.00257172i	$0.000818604\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1120.64	−	647.003i	−1.65531	−	0.955691i	−0.974839	−	0.222912i	$-0.928444\pi$
$677$	−1120.64	−	647.003i	−1.65531	−	0.955691i	−0.680466	−	0.732779i	$-0.738223\pi$
$678$		0			0
$679$	−352.000	−	609.682i	−0.518409	−	0.897911i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	560.029i		−	0.819954i	−0.912096	−	0.409977i	$-0.865537\pi$
$683$		−	560.029i		−	0.819954i	0.912096	−	0.409977i	$-0.134463\pi$
$684$		0			0
$685$	666.000			0.972263
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−264.545	+	152.735i	−0.383955	+	0.221676i
$690$		0			0
$691$	−20.0000	+	34.6410i	−0.0289436	+	0.0501317i	−0.880134	−	0.474725i	$-0.842548\pi$
$691$	−20.0000	+	34.6410i	−0.0289436	+	0.0501317i	0.851191	+	0.524856i	$0.175881\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	558.484	+	322.441i	0.803574	+	0.463943i
$696$		0			0
$697$	−297.000	−	514.419i	−0.426112	−	0.738047i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	954.594i		−	1.36176i	−0.732395	−	0.680880i	$-0.761597\pi$
$701$		−	954.594i		−	1.36176i	0.732395	−	0.680880i	$-0.238403\pi$
$702$		0			0
$703$	−544.000			−0.773826
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−102.879	+	59.3970i	−0.145514	+	0.0840127i
$708$		0			0
$709$	−484.000	+	838.313i	−0.682652	+	1.18239i	0.291517	+	0.956566i	$0.405840\pi$
$709$	−484.000	+	838.313i	−0.682652	+	1.18239i	−0.974169	+	0.225822i	$0.927493\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−646.665	−	373.352i	−0.906964	−	0.523636i
$714$		0			0
$715$	288.000	+	498.831i	0.402797	+	0.697665i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			1170.97i			1.62861i	0.580439	+	0.814304i	$0.302881\pi$
$719$			1170.97i			1.62861i	−0.580439	+	0.814304i	$0.697119\pi$
$720$		0			0
$721$	112.000			0.155340
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−25.7196	+	14.8492i	−0.0354754	+	0.0204817i
$726$		0			0
$727$	−254.000	+	439.941i	−0.349381	+	0.605146i	−0.986140	−	0.165918i	$-0.946941\pi$
$727$	−254.000	+	439.941i	−0.349381	+	0.605146i	0.636759	+	0.771063i	$0.280275\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−440.908	−	254.558i	−0.603158	−	0.348233i
$732$		0			0
$733$	572.000	+	990.733i	0.780355	+	1.35161i	0.931735	+	0.363138i	$0.118295\pi$
$733$	572.000	+	990.733i	0.780355	+	1.35161i	−0.151380	+	0.988476i	$0.548372\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	135.765i		−	0.184212i
$738$		0			0
$739$	304.000			0.411367			0.205683	−	0.978619i	$-0.434058\pi$
$739$	304.000			0.411367			0.205683	+	0.978619i	$0.434058\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	734.847	−	424.264i	0.989027	−	0.571015i	0.0840436	−	0.996462i	$-0.473217\pi$
$743$	734.847	−	424.264i	0.989027	−	0.571015i	0.904983	+	0.425447i	$0.139883\pi$
$744$		0			0
$745$	−585.000	+	1013.25i	−0.785235	+	1.36007i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	94.0000	+	162.813i	0.125166	+	0.216795i	0.921798	−	0.387671i	$-0.126720\pi$
$751$	94.0000	+	162.813i	0.125166	+	0.216795i	−0.796632	+	0.604465i	$0.793387\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			627.911i			0.831670i
$756$		0			0
$757$	−1240.00			−1.63804			−0.819022	−	0.573761i	$-0.805484\pi$
$757$	−1240.00			−1.63804			−0.819022	+	0.573761i	$0.805484\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	135.947	−	78.4889i	0.178642	−	0.103139i	−0.408012	−	0.912976i	$-0.633778\pi$
$761$	135.947	−	78.4889i	0.178642	−	0.103139i	0.586655	+	0.809837i	$0.300445\pi$
$762$		0			0
$763$	−112.000	+	193.990i	−0.146789	+	0.254246i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−235.151	−	135.765i	−0.306585	−	0.177007i
$768$		0			0
$769$	455.000	+	788.083i	0.591678	+	1.02482i	0.994007	+	0.109320i	$0.0348674\pi$
$769$	455.000	+	788.083i	0.591678	+	1.02482i	−0.402329	+	0.915495i	$0.631799\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			1387.34i			1.79475i	0.441266	+	0.897376i	$0.354529\pi$
$773$			1387.34i			1.79475i	−0.441266	+	0.897376i	$0.645471\pi$
$774$		0			0
$775$	−308.000			−0.397419
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−646.665	+	373.352i	−0.830122	+	0.479271i
$780$		0			0
$781$	−432.000	+	748.246i	−0.553137	+	0.958061i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	301.287	+	173.948i	0.383805	+	0.221590i
$786$		0			0
$787$	−680.000	−	1177.79i	−0.864041	−	1.49656i	−0.867997	−	0.496570i	$-0.834593\pi$
$787$	−680.000	−	1177.79i	−0.864041	−	1.49656i	0.00395593	−	0.999992i	$-0.498741\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			627.911i			0.793819i
$792$		0			0
$793$	400.000			0.504414
$794$		0			0
$795$		0			0
$796$		0			0
$797$	91.8559	−	53.0330i	0.115252	−	0.0665408i	−0.441266	−	0.897376i	$-0.645470\pi$
$797$	91.8559	−	53.0330i	0.115252	−	0.0665408i	0.556518	+	0.830836i	$0.312137\pi$
$798$		0			0
$799$	−540.000	+	935.307i	−0.675845	+	1.17060i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	235.151	+	135.765i	0.292841	+	0.169072i
$804$		0			0
$805$	−144.000	−	249.415i	−0.178882	−	0.309833i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			1107.33i			1.36876i	0.729124	+	0.684381i	$0.239928\pi$
$809$			1107.33i			1.36876i	−0.729124	+	0.684381i	$0.760072\pi$
$810$		0			0
$811$	160.000			0.197287			0.0986436	−	0.995123i	$-0.468550\pi$
$811$	160.000			0.197287			0.0986436	+	0.995123i	$0.468550\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−205.757	+	118.794i	−0.252463	+	0.145759i
$816$		0			0
$817$	−320.000	+	554.256i	−0.391677	+	0.678404i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	378.446	+	218.496i	0.460958	+	0.266134i	0.712447	−	0.701726i	$-0.247587\pi$
$821$	378.446	+	218.496i	0.460958	+	0.266134i	−0.251489	+	0.967860i	$0.580920\pi$
$822$		0			0
$823$	166.000	+	287.520i	0.201701	+	0.349357i	0.949077	−	0.315045i	$-0.102020\pi$
$823$	166.000	+	287.520i	0.201701	+	0.349357i	−0.747376	+	0.664402i	$0.768686\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			101.823i			0.123124i	0.998103	+	0.0615619i	$0.0196082\pi$
$827$			101.823i			0.123124i	−0.998103	+	0.0615619i	$0.980392\pi$
$828$		0			0
$829$	632.000			0.762364			0.381182	−	0.924500i	$-0.375517\pi$
$829$	632.000			0.762364			0.381182	+	0.924500i	$0.375517\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−363.749	+	210.011i	−0.436674	+	0.252114i
$834$		0			0
$835$	72.0000	−	124.708i	0.0862275	−	0.149350i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−631.968	−	364.867i	−0.753240	−	0.434883i	0.0736234	−	0.997286i	$-0.476544\pi$
$839$	−631.968	−	364.867i	−0.753240	−	0.434883i	−0.826863	+	0.562403i	$0.809877\pi$
$840$		0			0
$841$	−411.500	−	712.739i	−0.489298	−	0.847490i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	445.477i		−	0.527192i
$846$		0			0
$847$	−668.000			−0.788666
$848$		0			0
$849$		0			0
$850$		0			0
$851$	499.696	−	288.500i	0.587187	−	0.339012i
$852$		0			0
$853$	−223.000	+	386.247i	−0.261430	+	0.452810i	−0.966622	−	0.256206i	$-0.917527\pi$
$853$	−223.000	+	386.247i	−0.261430	+	0.452810i	0.705192	+	0.709016i	$0.250861\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−371.098	−	214.253i	−0.433019	−	0.250004i	0.267613	−	0.963527i	$-0.413765\pi$
$857$	−371.098	−	214.253i	−0.433019	−	0.250004i	−0.700632	+	0.713523i	$0.747099\pi$
$858$		0			0
$859$	364.000	+	630.466i	0.423749	+	0.733954i	0.996303	−	0.0859129i	$-0.0273807\pi$
$859$	364.000	+	630.466i	0.423749	+	0.733954i	−0.572554	+	0.819867i	$0.694047\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	916.410i		−	1.06189i	−0.847407	−	0.530945i	$-0.821837\pi$
$863$		−	916.410i		−	1.06189i	0.847407	−	0.530945i	$-0.178163\pi$
$864$		0			0
$865$	−738.000			−0.853179
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1116.97	−	644.881i	1.28535	−	0.742096i
$870$		0			0
$871$	32.0000	−	55.4256i	0.0367394	−	0.0636345i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−470.302	−	271.529i	−0.537488	−	0.310319i
$876$		0			0
$877$	455.000	+	788.083i	0.518814	+	0.898612i	0.999761	+	0.0218627i	$0.00695967\pi$
$877$	455.000	+	788.083i	0.518814	+	0.898612i	−0.480947	+	0.876750i	$0.659707\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			929.138i			1.05464i	0.849667	+	0.527320i	$0.176803\pi$
$881$			929.138i			1.05464i	−0.849667	+	0.527320i	$0.823197\pi$
$882$		0			0
$883$	−1064.00			−1.20498			−0.602492	−	0.798125i	$-0.705825\pi$
$883$	−1064.00			−1.20498			−0.602492	+	0.798125i	$0.705825\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1205.15	+	695.793i	−1.35868	+	0.784434i	−0.989446	−	0.144902i	$-0.953713\pi$
$887$	−1205.15	+	695.793i	−1.35868	+	0.784434i	−0.369234	+	0.929337i	$0.620380\pi$
$888$		0			0
$889$	184.000	−	318.697i	0.206974	−	0.358490i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1175.76	+	678.823i	1.31664	+	0.760160i
$894$		0			0
$895$	−432.000	−	748.246i	−0.482682	−	0.836029i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			186.676i			0.207649i
$900$		0			0
$901$	486.000			0.539401
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−852.422	+	492.146i	−0.941903	+	0.543808i
$906$		0			0
$907$	−884.000	+	1531.13i	−0.974642	+	1.68813i	−0.293529	+	0.955950i	$0.594830\pi$
$907$	−884.000	+	1531.13i	−0.974642	+	1.68813i	−0.681112	+	0.732179i	$0.738504\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	205.757	+	118.794i	0.225859	+	0.130399i	0.608660	−	0.793431i	$-0.291707\pi$
$911$	205.757	+	118.794i	0.225859	+	0.130399i	−0.382801	+	0.923831i	$0.625041\pi$
$912$		0			0
$913$	1008.00	+	1745.91i	1.10405	+	1.91228i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	678.823i		−	0.740264i
$918$		0			0
$919$	−380.000			−0.413493			−0.206746	−	0.978395i	$-0.566288\pi$
$919$	−380.000			−0.413493			−0.206746	+	0.978395i	$0.566288\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−352.727	+	203.647i	−0.382152	+	0.220636i
$924$		0			0
$925$	119.000	−	206.114i	0.128649	−	0.222826i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	576.855	+	333.047i	0.620942	+	0.358501i	0.777236	−	0.629210i	$-0.216621\pi$
$929$	576.855	+	333.047i	0.620942	+	0.358501i	−0.156294	+	0.987711i	$0.549955\pi$
$930$		0			0
$931$	264.000	+	457.261i	0.283566	+	0.491151i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	916.410i		−	0.980118i
$936$		0			0
$937$	−178.000			−0.189968			−0.0949840	−	0.995479i	$-0.530280\pi$
$937$	−178.000			−0.189968			−0.0949840	+	0.995479i	$0.530280\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	378.446	−	218.496i	0.402174	−	0.232196i	−0.285247	−	0.958454i	$-0.592076\pi$
$941$	378.446	−	218.496i	0.402174	−	0.232196i	0.687422	+	0.726258i	$0.258742\pi$
$942$		0			0
$943$	396.000	−	685.892i	0.419936	−	0.727351i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1557.88	−	899.440i	−1.64506	−	0.949778i	−0.978994	−	0.203889i	$-0.934642\pi$
$947$	−1557.88	−	899.440i	−1.64506	−	0.949778i	−0.666070	−	0.745889i	$-0.732025\pi$
$948$		0			0
$949$	64.0000	+	110.851i	0.0674394	+	0.116808i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	1310.98i		−	1.37563i	−0.725886	−	0.687815i	$-0.758570\pi$
$953$		−	1310.98i		−	1.37563i	0.725886	−	0.687815i	$-0.241430\pi$
$954$		0			0
$955$	144.000			0.150785
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−543.787	+	313.955i	−0.567035	+	0.327378i
$960$		0			0
$961$	−487.500	+	844.375i	−0.507284	+	0.878642i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−756.892	−	436.992i	−0.784344	−	0.452841i
$966$		0			0
$967$	850.000	+	1472.24i	0.879007	+	1.52249i	0.852432	+	0.522838i	$0.175127\pi$
$967$	850.000	+	1472.24i	0.879007	+	1.52249i	0.0265754	+	0.999647i	$0.491540\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			458.205i			0.471890i	0.971766	+	0.235945i	$0.0758185\pi$
$971$			458.205i			0.471890i	−0.971766	+	0.235945i	$0.924181\pi$
$972$		0			0
$973$	−608.000			−0.624872
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−657.688	+	379.716i	−0.673171	+	0.388655i	−0.797277	−	0.603614i	$-0.793727\pi$
$977$	−657.688	+	379.716i	−0.673171	+	0.388655i	0.124106	+	0.992269i	$0.460394\pi$
$978$		0			0
$979$	−108.000	+	187.061i	−0.110317	+	0.191074i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	911.210	+	526.087i	0.926969	+	0.535186i	0.885852	−	0.463969i	$-0.153575\pi$
$983$	911.210	+	526.087i	0.926969	+	0.535186i	0.0411171	+	0.999154i	$0.486908\pi$
$984$		0			0
$985$	−351.000	−	607.950i	−0.356345	−	0.617208i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	678.823i		−	0.686373i
$990$		0			0
$991$	772.000			0.779011			0.389506	−	0.921024i	$-0.372646\pi$
$991$	772.000			0.779011			0.389506	+	0.921024i	$0.372646\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−73.4847	+	42.4264i	−0.0738540	+	0.0426396i
$996$		0			0
$997$	−97.0000	+	168.009i	−0.0972919	+	0.168514i	−0.910563	−	0.413371i	$-0.864351\pi$
$997$	−97.0000	+	168.009i	−0.0972919	+	0.168514i	0.813271	+	0.581885i	$0.197685\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1296.3.q.f.593.2		4
3.2	odd	2	inner	1296.3.q.f.593.1		4
4.3	odd	2		162.3.d.b.107.2		4
9.2	odd	6		144.3.e.b.17.1		2
9.4	even	3	inner	1296.3.q.f.1025.1		4
9.5	odd	6	inner	1296.3.q.f.1025.2		4
9.7	even	3		144.3.e.b.17.2		2
12.11	even	2		162.3.d.b.107.1		4
36.7	odd	6		18.3.b.a.17.1	✓	2
36.11	even	6		18.3.b.a.17.2	yes	2
36.23	even	6		162.3.d.b.53.2		4
36.31	odd	6		162.3.d.b.53.1		4
45.2	even	12		3600.3.c.b.449.3		4
45.7	odd	12		3600.3.c.b.449.4		4
45.29	odd	6		3600.3.l.d.1601.1		2
45.34	even	6		3600.3.l.d.1601.2		2
45.38	even	12		3600.3.c.b.449.1		4
45.43	odd	12		3600.3.c.b.449.2		4
72.11	even	6		576.3.e.c.449.2		2
72.29	odd	6		576.3.e.f.449.2		2
72.43	odd	6		576.3.e.c.449.1		2
72.61	even	6		576.3.e.f.449.1		2
144.11	even	12		2304.3.h.f.2177.3		4
144.29	odd	12		2304.3.h.c.2177.2		4
144.43	odd	12		2304.3.h.f.2177.1		4
144.61	even	12		2304.3.h.c.2177.4		4
144.83	even	12		2304.3.h.f.2177.2		4
144.101	odd	12		2304.3.h.c.2177.3		4
144.115	odd	12		2304.3.h.f.2177.4		4
144.133	even	12		2304.3.h.c.2177.1		4
180.7	even	12		450.3.b.b.449.3		4
180.43	even	12		450.3.b.b.449.2		4
180.47	odd	12		450.3.b.b.449.1		4
180.79	odd	6		450.3.d.f.251.2		2
180.83	odd	12		450.3.b.b.449.4		4
180.119	even	6		450.3.d.f.251.1		2
252.11	even	6		882.3.s.b.863.1		4
252.47	odd	6		882.3.s.d.557.2		4
252.79	odd	6		882.3.s.b.557.1		4
252.83	odd	6		882.3.b.a.197.2		2
252.115	even	6		882.3.s.d.863.2		4
252.151	odd	6		882.3.s.b.863.2		4
252.187	even	6		882.3.s.d.557.1		4
252.191	even	6		882.3.s.b.557.2		4
252.223	even	6		882.3.b.a.197.1		2
252.227	odd	6		882.3.s.d.863.1		4
396.43	even	6		2178.3.c.d.485.2		2
396.263	odd	6		2178.3.c.d.485.1		2
468.47	odd	12		3042.3.d.a.3041.2		4
468.83	odd	12		3042.3.d.a.3041.3		4
468.151	even	12		3042.3.d.a.3041.4		4
468.155	even	6		3042.3.c.e.1691.1		2
468.187	even	12		3042.3.d.a.3041.1		4
468.259	odd	6		3042.3.c.e.1691.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.b.a.17.1	✓	2	36.7	odd	6
18.3.b.a.17.2	yes	2	36.11	even	6
144.3.e.b.17.1		2	9.2	odd	6
144.3.e.b.17.2		2	9.7	even	3
162.3.d.b.53.1		4	36.31	odd	6
162.3.d.b.53.2		4	36.23	even	6
162.3.d.b.107.1		4	12.11	even	2
162.3.d.b.107.2		4	4.3	odd	2
450.3.b.b.449.1		4	180.47	odd	12
450.3.b.b.449.2		4	180.43	even	12
450.3.b.b.449.3		4	180.7	even	12
450.3.b.b.449.4		4	180.83	odd	12
450.3.d.f.251.1		2	180.119	even	6
450.3.d.f.251.2		2	180.79	odd	6
576.3.e.c.449.1		2	72.43	odd	6
576.3.e.c.449.2		2	72.11	even	6
576.3.e.f.449.1		2	72.61	even	6
576.3.e.f.449.2		2	72.29	odd	6
882.3.b.a.197.1		2	252.223	even	6
882.3.b.a.197.2		2	252.83	odd	6
882.3.s.b.557.1		4	252.79	odd	6
882.3.s.b.557.2		4	252.191	even	6
882.3.s.b.863.1		4	252.11	even	6
882.3.s.b.863.2		4	252.151	odd	6
882.3.s.d.557.1		4	252.187	even	6
882.3.s.d.557.2		4	252.47	odd	6
882.3.s.d.863.1		4	252.227	odd	6
882.3.s.d.863.2		4	252.115	even	6
1296.3.q.f.593.1		4	3.2	odd	2	inner
1296.3.q.f.593.2		4	1.1	even	1	trivial
1296.3.q.f.1025.1		4	9.4	even	3	inner
1296.3.q.f.1025.2		4	9.5	odd	6	inner
2178.3.c.d.485.1		2	396.263	odd	6
2178.3.c.d.485.2		2	396.43	even	6
2304.3.h.c.2177.1		4	144.133	even	12
2304.3.h.c.2177.2		4	144.29	odd	12
2304.3.h.c.2177.3		4	144.101	odd	12
2304.3.h.c.2177.4		4	144.61	even	12
2304.3.h.f.2177.1		4	144.43	odd	12
2304.3.h.f.2177.2		4	144.83	even	12
2304.3.h.f.2177.3		4	144.11	even	12
2304.3.h.f.2177.4		4	144.115	odd	12
3042.3.c.e.1691.1		2	468.155	even	6
3042.3.c.e.1691.2		2	468.259	odd	6
3042.3.d.a.3041.1		4	468.187	even	12
3042.3.d.a.3041.2		4	468.47	odd	12
3042.3.d.a.3041.3		4	468.83	odd	12
3042.3.d.a.3041.4		4	468.151	even	12
3600.3.c.b.449.1		4	45.38	even	12
3600.3.c.b.449.2		4	45.43	odd	12
3600.3.c.b.449.3		4	45.2	even	12
3600.3.c.b.449.4		4	45.7	odd	12
3600.3.l.d.1601.1		2	45.29	odd	6
3600.3.l.d.1601.2		2	45.34	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1296.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.67423 - 2.12132i) q^{5} +(-2.00000 + 3.46410i) q^{7} +O(q^{10})\)	\(q+(3.67423 - 2.12132i) q^{5} +(-2.00000 + 3.46410i) q^{7} +(-14.6969 - 8.48528i) q^{11} +(-4.00000 - 6.92820i) q^{13} +12.7279i q^{17} +16.0000 q^{19} +(-14.6969 + 8.48528i) q^{23} +(-3.50000 + 6.06218i) q^{25} +(3.67423 + 2.12132i) q^{29} +(22.0000 + 38.1051i) q^{31} +16.9706i q^{35} -34.0000 q^{37} +(-40.4166 + 23.3345i) q^{41} +(-20.0000 + 34.6410i) q^{43} +(73.4847 + 42.4264i) q^{47} +(16.5000 + 28.5788i) q^{49} -38.1838i q^{53} -72.0000 q^{55} +(29.3939 - 16.9706i) q^{59} +(-25.0000 + 43.3013i) q^{61} +(-29.3939 - 16.9706i) q^{65} +(4.00000 + 6.92820i) q^{67} -50.9117i q^{71} -16.0000 q^{73} +(58.7878 - 33.9411i) q^{77} +(-38.0000 + 65.8179i) q^{79} +(-102.879 - 59.3970i) q^{83} +(27.0000 + 46.7654i) q^{85} -12.7279i q^{89} +32.0000 q^{91} +(58.7878 - 33.9411i) q^{95} +(-88.0000 + 152.420i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{7}+O(q^{10}) \) 4 * q - 8 * q^7	\( 4 q - 8 q^{7} - 16 q^{13} + 64 q^{19} - 14 q^{25} + 88 q^{31} - 136 q^{37} - 80 q^{43} + 66 q^{49} - 288 q^{55} - 100 q^{61} + 16 q^{67} - 64 q^{73} - 152 q^{79} + 108 q^{85} + 128 q^{91} - 352 q^{97}+O(q^{100}) \) 4 * q - 8 * q^7 - 16 * q^13 + 64 * q^19 - 14 * q^25 + 88 * q^31 - 136 * q^37 - 80 * q^43 + 66 * q^49 - 288 * q^55 - 100 * q^61 + 16 * q^67 - 64 * q^73 - 152 * q^79 + 108 * q^85 + 128 * q^91 - 352 * q^97

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