LMFDB - Embedded newform 756.2.l.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(289,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 2]))

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

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

chi := DirichletCharacter("756.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.l (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$-0.674693 + 1.59524i$ of defining polynomial
Character	$\chi$	$=$	756.289
Dual form			756.2.l.b.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.14520 q^{5} +(0.190437 - 2.63889i) q^{7} +O(q^{10})$	$q-4.14520 q^{5} +(0.190437 - 2.63889i) q^{7} -0.868858 q^{11} +(2.86231 + 4.95766i) q^{13} +(1.44613 + 2.50478i) q^{17} +(-2.00703 + 3.47627i) q^{19} +5.82977 q^{23} +12.1827 q^{25} +(0.900417 - 1.55957i) q^{29} +(1.48046 - 2.56422i) q^{31} +(-0.789399 + 10.9387i) q^{35} +(-2.64925 + 4.58864i) q^{37} +(5.89325 + 10.2074i) q^{41} +(-2.00703 + 3.47627i) q^{43} +(1.17218 + 2.03028i) q^{47} +(-6.92747 - 1.00508i) q^{49} +(1.09116 + 1.88995i) q^{53} +3.60159 q^{55} +(-1.52715 + 2.64510i) q^{59} +(-2.81659 - 4.87848i) q^{61} +(-11.8648 - 20.5505i) q^{65} +(1.25539 - 2.17440i) q^{67} +1.09143 q^{71} +(0.723285 + 1.25277i) q^{73} +(-0.165463 + 2.29282i) q^{77} +(1.06464 + 1.84401i) q^{79} +(-2.18784 + 3.78946i) q^{83} +(-5.99451 - 10.3828i) q^{85} +(-5.83373 + 10.1043i) q^{89} +(13.6278 - 6.60919i) q^{91} +(8.31953 - 14.4098i) q^{95} +(-3.98779 + 6.90706i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{5} - 3 q^{7}+O(q^{10}) $ 14 * q - 4 * q^5 - 3 * q^7	$ 14 q - 4 q^{5} - 3 q^{7} + 4 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} + 22 q^{23} + 18 q^{25} - q^{29} - q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 13 q^{49} + 15 q^{53} - 28 q^{55} + 14 q^{59} - 10 q^{61} - 15 q^{65} + 6 q^{67} - 2 q^{71} + 21 q^{73} - 19 q^{77} - 10 q^{79} + 25 q^{83} + 8 q^{85} + 6 q^{89} + 2 q^{91} + 28 q^{95} - 18 q^{97}+O(q^{100}) $ 14 * q - 4 * q^5 - 3 * q^7 + 4 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 + 22 * q^23 + 18 * q^25 - q^29 - q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 13 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 19 * q^77 - 10 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 - 18 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−4.14520			−1.85379			−0.926894	−	0.375322i	$-0.877532\pi$
$5$	−4.14520			−1.85379			−0.926894	+	0.375322i	$0.877532\pi$
$6$		0			0
$7$	0.190437	−	2.63889i	0.0719784	−	0.997406i
$7$	0.190437	−	2.63889i	0.0719784	−	0.997406i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.868858			−0.261971			−0.130985	−	0.991384i	$-0.541814\pi$
$11$	−0.868858			−0.261971			−0.130985	+	0.991384i	$0.541814\pi$
$12$		0			0
$13$	2.86231	+	4.95766i	0.793861	+	1.37501i	0.923560	+	0.383455i	$0.125266\pi$
$13$	2.86231	+	4.95766i	0.793861	+	1.37501i	−0.129698	+	0.991554i	$0.541401\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.44613	+	2.50478i	0.350739	+	0.607498i	0.986379	−	0.164488i	$-0.0525971\pi$
$17$	1.44613	+	2.50478i	0.350739	+	0.607498i	−0.635640	+	0.771986i	$0.719264\pi$
$18$		0			0
$19$	−2.00703	+	3.47627i	−0.460444	+	0.797512i	−0.998983	−	0.0450884i	$-0.985643\pi$
$19$	−2.00703	+	3.47627i	−0.460444	+	0.797512i	0.538539	+	0.842600i	$0.318976\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.82977			1.21559			0.607795	−	0.794094i	$-0.292054\pi$
$23$	5.82977			1.21559			0.607795	+	0.794094i	$0.292054\pi$
$24$		0			0
$25$	12.1827			2.43653
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.900417	−	1.55957i	0.167203	−	0.289604i	−0.770232	−	0.637763i	$-0.779860\pi$
$29$	0.900417	−	1.55957i	0.167203	−	0.289604i	0.937435	+	0.348159i	$0.113193\pi$
$30$		0			0
$31$	1.48046	−	2.56422i	0.265898	−	0.460548i	−0.701901	−	0.712275i	$-0.747665\pi$
$31$	1.48046	−	2.56422i	0.265898	−	0.460548i	0.967798	+	0.251727i	$0.0809984\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.789399	+	10.9387i	−0.133433	+	1.84898i
$36$		0			0
$37$	−2.64925	+	4.58864i	−0.435535	+	0.754368i	−0.997339	−	0.0729017i	$-0.976774\pi$
$37$	−2.64925	+	4.58864i	−0.435535	+	0.754368i	0.561804	+	0.827270i	$0.310107\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.89325	+	10.2074i	0.920371	+	1.59413i	0.798842	+	0.601541i	$0.205446\pi$
$41$	5.89325	+	10.2074i	0.920371	+	1.59413i	0.121528	+	0.992588i	$0.461220\pi$
$42$		0			0
$43$	−2.00703	+	3.47627i	−0.306069	+	0.530127i	−0.977499	−	0.210941i	$-0.932347\pi$
$43$	−2.00703	+	3.47627i	−0.306069	+	0.530127i	0.671430	+	0.741068i	$0.265680\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.17218	+	2.03028i	0.170980	+	0.296147i	0.938763	−	0.344564i	$-0.111973\pi$
$47$	1.17218	+	2.03028i	0.170980	+	0.296147i	−0.767783	+	0.640711i	$0.778640\pi$
$48$		0			0
$49$	−6.92747	−	1.00508i	−0.989638	−	0.143583i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.09116	+	1.88995i	0.149883	+	0.259605i	0.931184	−	0.364549i	$-0.118777\pi$
$53$	1.09116	+	1.88995i	0.149883	+	0.259605i	−0.781301	+	0.624154i	$0.785444\pi$
$54$		0			0
$55$	3.60159			0.485638
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.52715	+	2.64510i	−0.198818	+	0.344363i	−0.948146	−	0.317837i	$-0.897044\pi$
$59$	−1.52715	+	2.64510i	−0.198818	+	0.344363i	0.749327	+	0.662200i	$0.230377\pi$
$60$		0			0
$61$	−2.81659	−	4.87848i	−0.360628	−	0.624625i	0.627437	−	0.778668i	$-0.284104\pi$
$61$	−2.81659	−	4.87848i	−0.360628	−	0.624625i	−0.988064	+	0.154042i	$0.950771\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−11.8648	−	20.5505i	−1.47165	−	2.54898i
$66$		0			0
$67$	1.25539	−	2.17440i	0.153370	−	0.265645i	−0.779094	−	0.626907i	$-0.784321\pi$
$67$	1.25539	−	2.17440i	0.153370	−	0.265645i	0.932464	+	0.361262i	$0.117654\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.09143			0.129529			0.0647647	−	0.997901i	$-0.479370\pi$
$71$	1.09143			0.129529			0.0647647	+	0.997901i	$0.479370\pi$
$72$		0			0
$73$	0.723285	+	1.25277i	0.0846541	+	0.146625i	0.905244	−	0.424893i	$-0.139688\pi$
$73$	0.723285	+	1.25277i	0.0846541	+	0.146625i	−0.820590	+	0.571518i	$0.806355\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.165463	+	2.29282i	−0.0188562	+	0.261291i
$78$		0			0
$79$	1.06464	+	1.84401i	0.119781	+	0.207468i	0.919681	−	0.392666i	$-0.128447\pi$
$79$	1.06464	+	1.84401i	0.119781	+	0.207468i	−0.799900	+	0.600134i	$0.795114\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.18784	+	3.78946i	−0.240147	+	0.415947i	−0.960756	−	0.277395i	$-0.910529\pi$
$83$	−2.18784	+	3.78946i	−0.240147	+	0.415947i	0.720609	+	0.693342i	$0.243862\pi$
$84$		0			0
$85$	−5.99451	−	10.3828i	−0.650196	−	1.12617i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.83373	+	10.1043i	−0.618374	+	1.07105i	0.371409	+	0.928469i	$0.378875\pi$
$89$	−5.83373	+	10.1043i	−0.618374	+	1.07105i	−0.989783	+	0.142585i	$0.954459\pi$
$90$		0			0
$91$	13.6278	−	6.60919i	1.42858	−	0.692831i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.31953	−	14.4098i	0.853566	−	1.47842i
$96$		0			0
$97$	−3.98779	+	6.90706i	−0.404899	+	0.701306i	−0.994310	−	0.106528i	$-0.966027\pi$
$97$	−3.98779	+	6.90706i	−0.404899	+	0.701306i	0.589411	+	0.807834i	$0.299360\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.76370			0.374502			0.187251	−	0.982312i	$-0.440042\pi$
$101$	3.76370			0.374502			0.187251	+	0.982312i	$0.440042\pi$
$102$		0			0
$103$	10.8556			1.06963			0.534815	−	0.844969i	$-0.320381\pi$
$103$	10.8556			1.06963			0.534815	+	0.844969i	$0.320381\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.82343	−	8.35442i	0.466298	−	0.807653i	−0.532961	−	0.846140i	$-0.678921\pi$
$107$	4.82343	−	8.35442i	0.466298	−	0.807653i	0.999259	+	0.0384875i	$0.0122540\pi$
$108$		0			0
$109$	−5.86131	−	10.1521i	−0.561412	−	0.972394i	−0.997374	−	0.0724288i	$-0.976925\pi$
$109$	−5.86131	−	10.1521i	−0.561412	−	0.972394i	0.435962	−	0.899965i	$-0.356408\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.88981	−	5.00530i	−0.271851	−	0.470859i	0.697485	−	0.716599i	$-0.254302\pi$
$113$	−2.88981	−	5.00530i	−0.271851	−	0.470859i	−0.969336	+	0.245740i	$0.920969\pi$
$114$		0			0
$115$	−24.1655			−2.25345
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.88523	−	3.33918i	0.631168	−	0.306103i
$120$		0			0
$121$	−10.2451			−0.931371
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−29.7736			−2.66303
$126$		0			0
$127$	6.47468			0.574535			0.287268	−	0.957850i	$-0.407253\pi$
$127$	6.47468			0.574535			0.287268	+	0.957850i	$0.407253\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	17.7303			1.54910			0.774551	−	0.632511i	$-0.217976\pi$
$131$	17.7303			1.54910			0.774551	+	0.632511i	$0.217976\pi$
$132$		0			0
$133$	8.79129	+	5.95833i	0.762301	+	0.516653i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.72232			−0.232583			−0.116292	−	0.993215i	$-0.537101\pi$
$137$	−2.72232			−0.232583			−0.116292	+	0.993215i	$0.537101\pi$
$138$		0			0
$139$	8.65431	+	14.9897i	0.734049	+	1.27141i	0.955139	+	0.296157i	$0.0957051\pi$
$139$	8.65431	+	14.9897i	0.734049	+	1.27141i	−0.221090	+	0.975253i	$0.570962\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.48694	−	4.30751i	−0.207968	−	0.360212i
$144$		0			0
$145$	−3.73241	+	6.46472i	−0.309959	+	0.536865i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.84685			0.560916			0.280458	−	0.959866i	$-0.409514\pi$
$149$	6.84685			0.560916			0.280458	+	0.959866i	$0.409514\pi$
$150$		0			0
$151$	9.28166			0.755331			0.377666	−	0.925942i	$-0.376727\pi$
$151$	9.28166			0.755331			0.377666	+	0.925942i	$0.376727\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.13678	+	10.6292i	−0.492918	+	0.853759i
$156$		0			0
$157$	−6.83840	+	11.8445i	−0.545764	+	0.945291i	0.452795	+	0.891615i	$0.350427\pi$
$157$	−6.83840	+	11.8445i	−0.545764	+	0.945291i	−0.998558	+	0.0536759i	$0.982906\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.11020	−	15.3841i	0.0874963	−	1.21244i
$162$		0			0
$163$	−1.65003	+	2.85793i	−0.129240	+	0.223850i	−0.923382	−	0.383882i	$-0.874587\pi$
$163$	−1.65003	+	2.85793i	−0.129240	+	0.223850i	0.794142	+	0.607732i	$0.207920\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.96228	−	10.3270i	−0.461375	−	0.799125i	0.537655	−	0.843165i	$-0.319310\pi$
$167$	−5.96228	−	10.3270i	−0.461375	−	0.799125i	−0.999030	+	0.0440399i	$0.985977\pi$
$168$		0			0
$169$	−9.88562	+	17.1224i	−0.760432	+	1.31711i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.81694	−	8.34319i	−0.366225	−	0.634321i	0.622747	−	0.782424i	$-0.286017\pi$
$173$	−4.81694	−	8.34319i	−0.366225	−	0.634321i	−0.988972	+	0.148103i	$0.952683\pi$
$174$		0			0
$175$	2.32003	−	32.1487i	0.175378	−	2.43021i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.5285	+	19.9680i	0.861682	+	1.49248i	0.870304	+	0.492515i	$0.163922\pi$
$179$	11.5285	+	19.9680i	0.861682	+	1.49248i	−0.00862183	+	0.999963i	$0.502744\pi$
$180$		0			0
$181$	−11.8325			−0.879504			−0.439752	−	0.898119i	$-0.644934\pi$
$181$	−11.8325			−0.879504			−0.439752	+	0.898119i	$0.644934\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.9817	−	19.0208i	0.807390	−	1.39844i
$186$		0			0
$187$	−1.25649	−	2.17630i	−0.0918833	−	0.159147i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.14254	−	5.44303i	−0.227386	−	0.393844i	0.729647	−	0.683824i	$-0.239685\pi$
$191$	−3.14254	−	5.44303i	−0.227386	−	0.393844i	−0.957033	+	0.289980i	$0.906351\pi$
$192$		0			0
$193$	−6.86559	+	11.8915i	−0.494196	+	0.855972i	−0.999978	−	0.00668919i	$-0.997871\pi$
$193$	−6.86559	+	11.8915i	−0.494196	+	0.855972i	0.505782	+	0.862661i	$0.331204\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.161495			0.0115061			0.00575303	−	0.999983i	$-0.498169\pi$
$197$	0.161495			0.0115061			0.00575303	+	0.999983i	$0.498169\pi$
$198$		0			0
$199$	−12.4140	−	21.5016i	−0.880003	−	1.52421i	−0.851336	−	0.524621i	$-0.824207\pi$
$199$	−12.4140	−	21.5016i	−0.880003	−	1.52421i	−0.0286672	−	0.999589i	$-0.509126\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.94405	−	2.67310i	−0.276818	−	0.187615i
$204$		0			0
$205$	−24.4287	−	42.3117i	−1.70617	−	2.95518i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.74382	−	3.02039i	0.120623	−	0.208925i
$210$		0			0
$211$	9.44607	+	16.3611i	0.650295	+	1.12634i	0.983051	+	0.183331i	$0.0586879\pi$
$211$	9.44607	+	16.3611i	0.650295	+	1.12634i	−0.332757	+	0.943013i	$0.607979\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.31953	−	14.4098i	0.567387	−	0.982743i
$216$		0			0
$217$	−6.48477	−	4.39508i	−0.440215	−	0.298357i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−8.27856	+	14.3389i	−0.556876	+	0.964538i
$222$		0			0
$223$	7.04717	−	12.2061i	0.471914	−	0.817378i	−0.527570	−	0.849512i	$-0.676897\pi$
$223$	7.04717	−	12.2061i	0.471914	−	0.817378i	0.999484	+	0.0321333i	$0.0102301\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−25.9782			−1.72424			−0.862118	−	0.506708i	$-0.830862\pi$
$227$	−25.9782			−1.72424			−0.862118	+	0.506708i	$0.830862\pi$
$228$		0			0
$229$	24.9157			1.64648			0.823239	−	0.567695i	$-0.192165\pi$
$229$	24.9157			1.64648			0.823239	+	0.567695i	$0.192165\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.05923	−	5.29874i	0.200417	−	0.347132i	−0.748246	−	0.663421i	$-0.769104\pi$
$233$	3.05923	−	5.29874i	0.200417	−	0.347132i	0.948663	+	0.316289i	$0.102437\pi$
$234$		0			0
$235$	−4.85893	−	8.41591i	−0.316961	−	0.548993i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.71988	+	13.3712i	0.499357	+	0.864912i	1.00000		0.000742080i	$-0.000236211\pi$
$239$	7.71988	+	13.3712i	0.499357	+	0.864912i	−0.500643	+	0.865654i	$0.666903\pi$
$240$		0			0
$241$	9.84518			0.634183			0.317092	−	0.948395i	$-0.397294\pi$
$241$	9.84518			0.634183			0.317092	+	0.948395i	$0.397294\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	28.7157	+	4.16627i	1.83458	+	0.266173i
$246$		0			0
$247$	−22.9789			−1.46211
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−26.8843			−1.69692			−0.848461	−	0.529258i	$-0.822470\pi$
$251$	−26.8843			−1.69692			−0.848461	+	0.529258i	$0.822470\pi$
$252$		0			0
$253$	−5.06524			−0.318449
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.0127			−0.686954			−0.343477	−	0.939161i	$-0.611605\pi$
$257$	−11.0127			−0.686954			−0.343477	+	0.939161i	$0.611605\pi$
$258$		0			0
$259$	11.6044	+	7.86494i	0.721063	+	0.488703i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.31095			0.450812			0.225406	−	0.974265i	$-0.427629\pi$
$263$	7.31095			0.450812			0.225406	+	0.974265i	$0.427629\pi$
$264$		0			0
$265$	−4.52309	−	7.83423i	−0.277851	−	0.481253i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.08048	+	3.60349i	0.126849	+	0.219709i	0.922454	−	0.386107i	$-0.126180\pi$
$269$	2.08048	+	3.60349i	0.126849	+	0.219709i	−0.795605	+	0.605815i	$0.792847\pi$
$270$		0			0
$271$	−4.18300	+	7.24516i	−0.254099	+	0.440112i	−0.964650	−	0.263533i	$-0.915112\pi$
$271$	−4.18300	+	7.24516i	−0.254099	+	0.440112i	0.710551	+	0.703645i	$0.248446\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−10.5850			−0.638300
$276$		0			0
$277$	−2.79856			−0.168149			−0.0840745	−	0.996459i	$-0.526793\pi$
$277$	−2.79856			−0.168149			−0.0840745	+	0.996459i	$0.526793\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.44314	−	9.42779i	0.324710	−	0.562415i	−0.656743	−	0.754114i	$-0.728067\pi$
$281$	5.44314	−	9.42779i	0.324710	−	0.562415i	0.981454	+	0.191699i	$0.0613998\pi$
$282$		0			0
$283$	1.01212	−	1.75304i	0.0601642	−	0.104207i	−0.834374	−	0.551198i	$-0.814171\pi$
$283$	1.01212	−	1.75304i	0.0601642	−	0.104207i	0.894539	+	0.446990i	$0.147504\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	28.0585	−	13.6078i	1.65624	−	0.803241i
$288$		0			0
$289$	4.31739	−	7.47794i	0.253964	−	0.439879i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.65448	+	16.7220i	0.564021	+	0.976912i	0.997140	+	0.0755757i	$0.0240795\pi$
$293$	9.65448	+	16.7220i	0.564021	+	0.976912i	−0.433120	+	0.901336i	$0.642587\pi$
$294$		0			0
$295$	6.33035	−	10.9645i	0.368567	−	0.638377i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	16.6866	+	28.9020i	0.965011	+	1.67145i
$300$		0			0
$301$	8.79129	+	5.95833i	0.506721	+	0.343433i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	11.6753	+	20.2223i	0.668527	+	1.15792i
$306$		0			0
$307$	−13.1378			−0.749813			−0.374907	−	0.927063i	$-0.622325\pi$
$307$	−13.1378			−0.749813			−0.374907	+	0.927063i	$0.622325\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.76606	+	11.7192i	−0.383668	+	0.664533i	−0.991583	−	0.129469i	$-0.958673\pi$
$311$	−6.76606	+	11.7192i	−0.383668	+	0.664533i	0.607915	+	0.794002i	$0.292006\pi$
$312$		0			0
$313$	12.6000	+	21.8238i	0.712194	+	1.23356i	0.964032	+	0.265787i	$0.0856318\pi$
$313$	12.6000	+	21.8238i	0.712194	+	1.23356i	−0.251838	+	0.967770i	$0.581035\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.14888	−	10.6502i	−0.345356	−	0.598173i	0.640063	−	0.768323i	$-0.278908\pi$
$317$	−6.14888	−	10.6502i	−0.345356	−	0.598173i	−0.985418	+	0.170149i	$0.945575\pi$
$318$		0			0
$319$	−0.782335	+	1.35504i	−0.0438023	+	0.0758679i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−11.6097			−0.645982
$324$		0			0
$325$	34.8705	+	60.3975i	1.93427	+	3.35025i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	5.58091	−	2.70662i	0.307685	−	0.149221i
$330$		0			0
$331$	9.96285	+	17.2562i	0.547608	+	0.948484i	0.998438	+	0.0558745i	$0.0177947\pi$
$331$	9.96285	+	17.2562i	0.547608	+	0.948484i	−0.450830	+	0.892610i	$0.648872\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.20383	+	9.01330i	−0.284316	+	0.492449i
$336$		0			0
$337$	−0.966380	−	1.67382i	−0.0526421	−	0.0911788i	0.838504	−	0.544896i	$-0.183431\pi$
$337$	−0.966380	−	1.67382i	−0.0526421	−	0.0911788i	−0.891146	+	0.453717i	$0.850098\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.28631	+	2.22795i	−0.0696574	+	0.120650i
$342$		0			0
$343$	−3.97155	+	18.0894i	−0.214444	+	0.976736i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.48241	−	14.6920i	0.455360	−	0.788706i	−0.543349	−	0.839507i	$-0.682844\pi$
$347$	8.48241	−	14.6920i	0.455360	−	0.788706i	0.998709	+	0.0508006i	$0.0161773\pi$
$348$		0			0
$349$	−6.25767	+	10.8386i	−0.334966	+	0.580177i	−0.983478	−	0.181027i	$-0.942058\pi$
$349$	−6.25767	+	10.8386i	−0.334966	+	0.580177i	0.648513	+	0.761204i	$0.275391\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−32.3857			−1.72372			−0.861859	−	0.507149i	$-0.830700\pi$
$353$	−32.3857			−1.72372			−0.861859	+	0.507149i	$0.830700\pi$
$354$		0			0
$355$	−4.52421			−0.240120
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.98559	+	15.5635i	−0.474242	+	0.821410i	−0.999565	−	0.0294922i	$-0.990611\pi$
$359$	−8.98559	+	15.5635i	−0.474242	+	0.821410i	0.525323	+	0.850903i	$0.323944\pi$
$360$		0			0
$361$	1.44368	+	2.50052i	0.0759830	+	0.131606i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.99816	−	5.19297i	−0.156931	−	0.271812i
$366$		0			0
$367$	8.16840			0.426387			0.213194	−	0.977010i	$-0.431614\pi$
$367$	8.16840			0.426387			0.213194	+	0.977010i	$0.431614\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.19517	−	2.51954i	0.269720	−	0.130808i
$372$		0			0
$373$	−5.16161			−0.267258			−0.133629	−	0.991031i	$-0.542663\pi$
$373$	−5.16161			−0.267258			−0.133629	+	0.991031i	$0.542663\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.3091			0.530945
$378$		0			0
$379$	21.0017			1.07878			0.539392	−	0.842055i	$-0.318654\pi$
$379$	21.0017			1.07878			0.539392	+	0.842055i	$0.318654\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−29.5589			−1.51039			−0.755194	−	0.655501i	$-0.772458\pi$
$383$	−29.5589			−1.51039			−0.755194	+	0.655501i	$0.772458\pi$
$384$		0			0
$385$	0.685876	−	9.50419i	0.0349555	−	0.484379i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.5379			0.838505			0.419252	−	0.907870i	$-0.362292\pi$
$389$	16.5379			0.838505			0.419252	+	0.907870i	$0.362292\pi$
$390$		0			0
$391$	8.43063	+	14.6023i	0.426355	+	0.738469i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.41315	−	7.64379i	−0.222049	−	0.384601i
$396$		0			0
$397$	15.4394	−	26.7418i	0.774881	−	1.34213i	−0.159980	−	0.987120i	$-0.551143\pi$
$397$	15.4394	−	26.7418i	0.774881	−	1.34213i	0.934861	−	0.355014i	$-0.115524\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.6323			−0.530951			−0.265475	−	0.964118i	$-0.585529\pi$
$401$	−10.6323			−0.530951			−0.265475	+	0.964118i	$0.585529\pi$
$402$		0			0
$403$	16.9501			0.844343
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.30183	−	3.98688i	0.114097	−	0.197622i
$408$		0			0
$409$	7.39782	−	12.8134i	0.365799	−	0.633582i	−0.623105	−	0.782138i	$-0.714129\pi$
$409$	7.39782	−	12.8134i	0.365799	−	0.633582i	0.988904	+	0.148556i	$0.0474625\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	6.68931	+	4.53371i	0.329159	+	0.223089i
$414$		0			0
$415$	9.06904	−	15.7080i	0.445182	−	0.771078i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.56134	+	2.70432i	0.0762765	+	0.132115i	0.901641	−	0.432486i	$-0.142363\pi$
$419$	1.56134	+	2.70432i	0.0762765	+	0.132115i	−0.825364	+	0.564601i	$0.809030\pi$
$420$		0			0
$421$	−0.644580	+	1.11645i	−0.0314149	+	0.0544122i	−0.881305	−	0.472547i	$-0.843335\pi$
$421$	−0.644580	+	1.11645i	−0.0314149	+	0.0544122i	0.849891	+	0.526959i	$0.176668\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	17.6178	+	30.5149i	0.854587	+	1.48019i
$426$		0			0
$427$	−13.4101	+	6.50363i	−0.648962	+	0.314733i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.5916	+	20.0773i	0.558350	+	0.967090i	0.997634	+	0.0687421i	$0.0218986\pi$
$431$	11.5916	+	20.0773i	0.558350	+	0.967090i	−0.439285	+	0.898348i	$0.644768\pi$
$432$		0			0
$433$	35.6437			1.71293			0.856464	−	0.516207i	$-0.172657\pi$
$433$	35.6437			1.71293			0.856464	+	0.516207i	$0.172657\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.7005	+	20.2659i	−0.559711	+	0.969448i
$438$		0			0
$439$	−8.00620	−	13.8671i	−0.382115	−	0.661843i	0.609249	−	0.792979i	$-0.291471\pi$
$439$	−8.00620	−	13.8671i	−0.382115	−	0.661843i	−0.991364	+	0.131136i	$0.958138\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.17778	+	12.4323i	0.341027	+	0.590676i	0.984624	−	0.174689i	$-0.0558920\pi$
$443$	7.17778	+	12.4323i	0.341027	+	0.590676i	−0.643597	+	0.765365i	$0.722559\pi$
$444$		0			0
$445$	24.1819	−	41.8844i	1.14633	−	1.98551i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−5.72475			−0.270168			−0.135084	−	0.990834i	$-0.543130\pi$
$449$	−5.72475			−0.270168			−0.135084	+	0.990834i	$0.543130\pi$
$450$		0			0
$451$	−5.12040	−	8.86879i	−0.241110	−	0.417615i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−56.4900	+	27.3964i	−2.64829	+	1.28436i
$456$		0			0
$457$	−7.33175	−	12.6990i	−0.342965	−	0.594033i	0.642017	−	0.766690i	$-0.278098\pi$
$457$	−7.33175	−	12.6990i	−0.342965	−	0.594033i	−0.984982	+	0.172658i	$0.944765\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.9720	−	22.4681i	0.604164	−	1.04644i	−0.388018	−	0.921652i	$-0.626840\pi$
$461$	12.9720	−	22.4681i	0.604164	−	1.04644i	0.992183	−	0.124792i	$-0.0398263\pi$
$462$		0			0
$463$	−6.46277	−	11.1939i	−0.300351	−	0.520223i	0.675865	−	0.737026i	$-0.263770\pi$
$463$	−6.46277	−	11.1939i	−0.300351	−	0.520223i	−0.976215	+	0.216803i	$0.930437\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.3104	−	28.2504i	0.754755	−	1.30727i	−0.190741	−	0.981640i	$-0.561089\pi$
$467$	16.3104	−	28.2504i	0.754755	−	1.30727i	0.945496	−	0.325633i	$-0.105577\pi$
$468$		0			0
$469$	−5.49892	−	3.72692i	−0.253916	−	0.172093i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.74382	−	3.02039i	0.0801811	−	0.138878i
$474$		0			0
$475$	−24.4509	+	42.3503i	−1.12189	+	1.94316i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	25.3478			1.15817			0.579084	−	0.815268i	$-0.303410\pi$
$479$	25.3478			1.15817			0.579084	+	0.815268i	$0.303410\pi$
$480$		0			0
$481$	−30.3319			−1.38302
$482$		0			0
$483$		0			0
$484$		0			0
$485$	16.5302	−	28.6311i	0.750597	−	1.30007i
$486$		0			0
$487$	17.7383	+	30.7236i	0.803799	+	1.39222i	0.917099	+	0.398660i	$0.130525\pi$
$487$	17.7383	+	30.7236i	0.803799	+	1.39222i	−0.113299	+	0.993561i	$0.536142\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.2554	−	22.9590i	−0.598208	−	1.03613i	−0.993085	−	0.117393i	$-0.962546\pi$
$491$	−13.2554	−	22.9590i	−0.598208	−	1.03613i	0.394877	−	0.918734i	$-0.370787\pi$
$492$		0			0
$493$	5.20849			0.234579
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.207849	−	2.88017i	0.00932332	−	0.129193i
$498$		0			0
$499$	−6.00261			−0.268714			−0.134357	−	0.990933i	$-0.542897\pi$
$499$	−6.00261			−0.268714			−0.134357	+	0.990933i	$0.542897\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	22.9460			1.02311			0.511556	−	0.859250i	$-0.329069\pi$
$503$	22.9460			1.02311			0.511556	+	0.859250i	$0.329069\pi$
$504$		0			0
$505$	−15.6013			−0.694248
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−29.8697			−1.32395			−0.661975	−	0.749526i	$-0.730281\pi$
$509$	−29.8697			−1.32395			−0.661975	+	0.749526i	$0.730281\pi$
$510$		0			0
$511$	3.44365	−	1.67010i	0.152338	−	0.0738807i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−44.9984			−1.98287
$516$		0			0
$517$	−1.01846	−	1.76402i	−0.0447918	−	0.0775817i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−15.5980	−	27.0166i	−0.683362	−	1.18362i	−0.973949	−	0.226769i	$-0.927184\pi$
$521$	−15.5980	−	27.0166i	−0.683362	−	1.18362i	0.290587	−	0.956849i	$-0.406149\pi$
$522$		0			0
$523$	−3.07911	+	5.33318i	−0.134640	+	0.233203i	−0.925460	−	0.378846i	$-0.876321\pi$
$523$	−3.07911	+	5.33318i	−0.134640	+	0.233203i	0.790820	+	0.612049i	$0.209654\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.56375			0.373043
$528$		0			0
$529$	10.9862			0.477661
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−33.7366	+	58.4335i	−1.46129	+	2.53103i
$534$		0			0
$535$	−19.9941	+	34.6307i	−0.864419	+	1.49722i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.01899	+	0.873275i	0.259256	+	0.0376146i
$540$		0			0
$541$	−13.5137	+	23.4064i	−0.580999	+	1.00632i	0.414362	+	0.910112i	$0.364005\pi$
$541$	−13.5137	+	23.4064i	−0.580999	+	1.00632i	−0.995361	+	0.0962083i	$0.969329\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	24.2963	+	42.0824i	1.04074	+	1.80261i
$546$		0			0
$547$	14.9426	−	25.8814i	0.638900	−	1.10661i	−0.346775	−	0.937948i	$-0.612723\pi$
$547$	14.9426	−	25.8814i	0.638900	−	1.10661i	0.985675	−	0.168658i	$-0.0539434\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.61432	+	6.26019i	0.153975	+	0.266693i
$552$		0			0
$553$	5.06889	−	2.45830i	0.215551	−	0.104538i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−10.6650	−	18.4722i	−0.451889	−	0.782694i	0.546615	−	0.837384i	$-0.315916\pi$
$557$	−10.6650	−	18.4722i	−0.451889	−	0.782694i	−0.998503	+	0.0546900i	$0.982583\pi$
$558$		0			0
$559$	−22.9789			−0.971905
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.7317	−	27.2482i	0.663014	−	1.14837i	−0.316805	−	0.948491i	$-0.602610\pi$
$563$	15.7317	−	27.2482i	0.663014	−	1.14837i	0.979820	−	0.199884i	$-0.0640564\pi$
$564$		0			0
$565$	11.9788	+	20.7480i	0.503954	+	0.872873i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	14.6696	+	25.4084i	0.614980	+	1.06518i	0.990388	+	0.138317i	$0.0441694\pi$
$569$	14.6696	+	25.4084i	0.614980	+	1.06518i	−0.375408	+	0.926860i	$0.622497\pi$
$570$		0			0
$571$	13.7473	−	23.8111i	0.575308	−	0.996463i	−0.420700	−	0.907200i	$-0.638215\pi$
$571$	13.7473	−	23.8111i	0.575308	−	0.996463i	0.996008	−	0.0892631i	$-0.0284512\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	71.0221			2.96183
$576$		0			0
$577$	−20.2293	−	35.0381i	−0.842156	−	1.45866i	−0.888068	−	0.459712i	$-0.847953\pi$
$577$	−20.2293	−	35.0381i	−0.842156	−	1.45866i	0.0459122	−	0.998945i	$-0.485381\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	9.58331	+	6.49513i	0.397583	+	0.269463i
$582$		0			0
$583$	−0.948067	−	1.64210i	−0.0392649	−	0.0680089i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.6559	−	23.6528i	0.563641	−	0.976255i	−0.433533	−	0.901137i	$-0.642733\pi$
$587$	13.6559	−	23.6528i	0.563641	−	0.976255i	0.997175	−	0.0751177i	$-0.0239333\pi$
$588$		0			0
$589$	5.94263	+	10.2929i	0.244862	+	0.424113i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.2898	+	24.7507i	−0.586813	+	1.01639i	0.407833	+	0.913056i	$0.366284\pi$
$593$	−14.2898	+	24.7507i	−0.586813	+	1.01639i	−0.994647	+	0.103334i	$0.967049\pi$
$594$		0			0
$595$	−28.5406	+	13.8416i	−1.17005	+	0.567449i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	19.9919	−	34.6270i	0.816848	−	1.41482i	−0.0911461	−	0.995838i	$-0.529053\pi$
$599$	19.9919	−	34.6270i	0.816848	−	1.41482i	0.907994	−	0.418984i	$-0.137614\pi$
$600$		0			0
$601$	−12.6948	+	21.9880i	−0.517831	+	0.896910i	0.481954	+	0.876196i	$0.339927\pi$
$601$	−12.6948	+	21.9880i	−0.517831	+	0.896910i	−0.999785	+	0.0207133i	$0.993406\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	42.4679			1.72657
$606$		0			0
$607$	−37.2939			−1.51371			−0.756856	−	0.653581i	$-0.773266\pi$
$607$	−37.2939			−1.51371			−0.756856	+	0.653581i	$0.773266\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.71029	+	11.6226i	−0.271469	+	0.470199i
$612$		0			0
$613$	−11.7319	−	20.3203i	−0.473848	−	0.820729i	0.525704	−	0.850668i	$-0.323802\pi$
$613$	−11.7319	−	20.3203i	−0.473848	−	0.820729i	−0.999552	+	0.0299390i	$0.990469\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.56888	−	11.3776i	−0.264453	−	0.458047i	0.702967	−	0.711223i	$-0.251858\pi$
$617$	−6.56888	−	11.3776i	−0.264453	−	0.458047i	−0.967420	+	0.253176i	$0.918525\pi$
$618$		0			0
$619$	21.5553			0.866380			0.433190	−	0.901303i	$-0.357388\pi$
$619$	21.5553			0.866380			0.433190	+	0.901303i	$0.357388\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	25.5532	+	17.3188i	1.02377	+	0.693862i
$624$		0			0
$625$	62.5040			2.50016
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−15.3247			−0.611036
$630$		0			0
$631$	−6.15223			−0.244916			−0.122458	−	0.992474i	$-0.539078\pi$
$631$	−6.15223			−0.244916			−0.122458	+	0.992474i	$0.539078\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−26.8388			−1.06507
$636$		0			0
$637$	−14.8457	−	37.2209i	−0.588207	−	1.47475i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4.47364			0.176698			0.0883491	−	0.996090i	$-0.471841\pi$
$641$	4.47364			0.176698			0.0883491	+	0.996090i	$0.471841\pi$
$642$		0			0
$643$	8.98009	+	15.5540i	0.354140	+	0.613389i	0.986970	−	0.160902i	$-0.0514402\pi$
$643$	8.98009	+	15.5540i	0.354140	+	0.613389i	−0.632830	+	0.774291i	$0.718107\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.02992	−	10.4441i	−0.237061	−	0.410601i	0.722809	−	0.691048i	$-0.242851\pi$
$647$	−6.02992	−	10.4441i	−0.237061	−	0.410601i	−0.959870	+	0.280447i	$0.909517\pi$
$648$		0			0
$649$	1.32688	−	2.29822i	0.0520845	−	0.0902131i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	48.2733			1.88908			0.944540	−	0.328397i	$-0.106508\pi$
$653$	48.2733			1.88908			0.944540	+	0.328397i	$0.106508\pi$
$654$		0			0
$655$	−73.4955			−2.87171
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−14.5795	+	25.2525i	−0.567937	+	0.983696i	0.428832	+	0.903384i	$0.358925\pi$
$659$	−14.5795	+	25.2525i	−0.567937	+	0.983696i	−0.996770	+	0.0803122i	$0.974408\pi$
$660$		0			0
$661$	7.27428	−	12.5994i	0.282937	−	0.490061i	−0.689170	−	0.724600i	$-0.742025\pi$
$661$	7.27428	−	12.5994i	0.282937	−	0.490061i	0.972107	+	0.234539i	$0.0753581\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−36.4416	−	24.6985i	−1.41315	−	0.957766i
$666$		0			0
$667$	5.24922	−	9.09192i	0.203251	−	0.352040i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.44722	+	4.23871i	0.0944738	+	0.163633i
$672$		0			0
$673$	11.6825	−	20.2348i	0.450329	−	0.779993i	−0.548077	−	0.836428i	$-0.684640\pi$
$673$	11.6825	−	20.2348i	0.450329	−	0.779993i	0.998406	+	0.0564349i	$0.0179733\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.85875	−	15.3438i	−0.340469	−	0.589710i	0.644051	−	0.764983i	$-0.277253\pi$
$677$	−8.85875	−	15.3438i	−0.340469	−	0.589710i	−0.984520	+	0.175273i	$0.943919\pi$
$678$		0			0
$679$	17.4675	+	11.8387i	0.670343	+	0.454328i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−21.7769	−	37.7186i	−0.833269	−	1.44326i	−0.895432	−	0.445198i	$-0.853133\pi$
$683$	−21.7769	−	37.7186i	−0.833269	−	1.44326i	0.0621637	−	0.998066i	$-0.480200\pi$
$684$		0			0
$685$	11.2846			0.431161
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.24650	+	10.8193i	−0.237973	+	0.412181i
$690$		0			0
$691$	−11.7672	−	20.3814i	−0.447645	−	0.775345i	0.550587	−	0.834778i	$-0.314404\pi$
$691$	−11.7672	−	20.3814i	−0.447645	−	0.775345i	−0.998232	+	0.0594333i	$0.981071\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−35.8738	−	62.1353i	−1.36077	−	2.35693i
$696$		0			0
$697$	−17.0449	+	29.5225i	−0.645620	+	1.11825i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−45.1804			−1.70644			−0.853219	−	0.521552i	$-0.825353\pi$
$701$	−45.1804			−1.70644			−0.853219	+	0.521552i	$0.825353\pi$
$702$		0			0
$703$	−10.6343	−	18.4191i	−0.401079	−	0.694689i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.716748	−	9.93199i	0.0269561	−	0.373531i
$708$		0			0
$709$	13.5064	+	23.3937i	0.507242	+	0.878568i	0.999965	+	0.00838223i	$0.00266818\pi$
$709$	13.5064	+	23.3937i	0.507242	+	0.878568i	−0.492723	+	0.870186i	$0.663998\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.63071	−	14.9488i	0.323223	−	0.559838i
$714$		0			0
$715$	10.3089	+	17.8555i	0.385529	+	0.667757i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	11.2096	−	19.4156i	0.418048	−	0.724080i	−0.577695	−	0.816253i	$-0.696048\pi$
$719$	11.2096	−	19.4156i	0.418048	−	0.724080i	0.995743	+	0.0921724i	$0.0293811\pi$
$720$		0			0
$721$	2.06730	−	28.6466i	0.0769902	−	1.06686i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.9695	−	18.9997i	0.407396	−	0.705631i
$726$		0			0
$727$	21.9820	−	38.0740i	0.815268	−	1.41208i	−0.0938680	−	0.995585i	$-0.529923\pi$
$727$	21.9820	−	38.0740i	0.815268	−	1.41208i	0.909136	−	0.416500i	$-0.136744\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−11.6097			−0.429401
$732$		0			0
$733$	0.866772			0.0320149			0.0160075	−	0.999872i	$-0.494904\pi$
$733$	0.866772			0.0320149			0.0160075	+	0.999872i	$0.494904\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.09075	+	1.88924i	−0.0401785	+	0.0695911i
$738$		0			0
$739$	13.0442	+	22.5932i	0.479838	+	0.831103i	0.999733	−	0.0231270i	$-0.00736222\pi$
$739$	13.0442	+	22.5932i	0.479838	+	0.831103i	−0.519895	+	0.854230i	$0.674029\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−22.5842	−	39.1170i	−0.828533	−	1.43506i	−0.899189	−	0.437561i	$-0.855842\pi$
$743$	−22.5842	−	39.1170i	−0.828533	−	1.43506i	0.0706551	−	0.997501i	$-0.477491\pi$
$744$		0			0
$745$	−28.3816			−1.03982
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−21.1278	−	14.3195i	−0.771994	−	0.523222i
$750$		0			0
$751$	−20.5988			−0.751662			−0.375831	−	0.926688i	$-0.622643\pi$
$751$	−20.5988			−0.751662			−0.375831	+	0.926688i	$0.622643\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−38.4743			−1.40022
$756$		0			0
$757$	−39.0856			−1.42059			−0.710294	−	0.703905i	$-0.751438\pi$
$757$	−39.0856			−1.42059			−0.710294	+	0.703905i	$0.751438\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	28.8872			1.04716			0.523581	−	0.851976i	$-0.324596\pi$
$761$	28.8872			1.04716			0.523581	+	0.851976i	$0.324596\pi$
$762$		0			0
$763$	−27.9065	+	13.5340i	−1.01028	+	0.489964i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−17.4847			−0.631336
$768$		0			0
$769$	−11.1407	−	19.2962i	−0.401742	−	0.695838i	0.592194	−	0.805796i	$-0.298262\pi$
$769$	−11.1407	−	19.2962i	−0.401742	−	0.695838i	−0.993936	+	0.109957i	$0.964929\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	21.3593	+	36.9955i	0.768242	+	1.33063i	0.938515	+	0.345238i	$0.112202\pi$
$773$	21.3593	+	36.9955i	0.768242	+	1.33063i	−0.170273	+	0.985397i	$0.554465\pi$
$774$		0			0
$775$	18.0359	−	31.2391i	0.647868	−	1.12214i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−47.3116			−1.69512
$780$		0			0
$781$	−0.948302			−0.0339329
$782$		0			0
$783$		0			0
$784$		0			0
$785$	28.3465	−	49.0976i	1.01173	−	1.75237i
$786$		0			0
$787$	0.143384	−	0.248349i	0.00511110	−	0.00885268i	−0.863459	−	0.504420i	$-0.831706\pi$
$787$	0.143384	−	0.248349i	0.00511110	−	0.00885268i	0.868570	+	0.495567i	$0.165040\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−13.7588	+	6.67270i	−0.489205	+	0.237254i
$792$		0			0
$793$	16.1239	−	27.9274i	0.572577	−	0.991732i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.457746	+	0.792840i	0.0162142	+	0.0280838i	0.874019	−	0.485892i	$-0.161505\pi$
$797$	0.457746	+	0.792840i	0.0162142	+	0.0280838i	−0.857804	+	0.513976i	$0.828172\pi$
$798$		0			0
$799$	−3.39026	+	5.87211i	−0.119939	+	0.207740i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.628433	−	1.08848i	−0.0221769	−	0.0384115i
$804$		0			0
$805$	−4.60201	+	63.7702i	−0.162200	+	2.24760i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	14.3721	+	24.8932i	0.505297	+	0.875199i	0.999981	+	0.00612685i	$0.00195025\pi$
$809$	14.3721	+	24.8932i	0.505297	+	0.875199i	−0.494685	+	0.869073i	$0.664716\pi$
$810$		0			0
$811$	14.3005			0.502157			0.251079	−	0.967967i	$-0.419215\pi$
$811$	14.3005			0.502157			0.251079	+	0.967967i	$0.419215\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.83969	−	11.8467i	0.239584	−	0.414971i
$816$		0			0
$817$	−8.05632	−	13.9540i	−0.281855	−	0.488187i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.8125	+	30.8521i	0.621660	+	1.07675i	0.989177	+	0.146730i	$0.0468749\pi$
$821$	17.8125	+	30.8521i	0.621660	+	1.07675i	−0.367516	+	0.930017i	$0.619792\pi$
$822$		0			0
$823$	11.2157	−	19.4261i	0.390953	−	0.677151i	−0.601622	−	0.798781i	$-0.705479\pi$
$823$	11.2157	−	19.4261i	0.390953	−	0.677151i	0.992576	+	0.121630i	$0.0388121\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	26.6728			0.927505			0.463753	−	0.885965i	$-0.346503\pi$
$827$	26.6728			0.927505			0.463753	+	0.885965i	$0.346503\pi$
$828$		0			0
$829$	−16.0078	−	27.7263i	−0.555973	−	0.962973i	−0.997827	−	0.0658866i	$-0.979012\pi$
$829$	−16.0078	−	27.7263i	−0.555973	−	0.962973i	0.441854	−	0.897087i	$-0.354321\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.50053	−	18.8053i	−0.259878	−	0.651563i
$834$		0			0
$835$	24.7148	+	42.8074i	0.855292	+	1.48141i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−9.10375	+	15.7682i	−0.314296	+	0.544377i	−0.979288	−	0.202474i	$-0.935102\pi$
$839$	−9.10375	+	15.7682i	−0.314296	+	0.544377i	0.664991	+	0.746851i	$0.268435\pi$
$840$		0			0
$841$	12.8785	+	22.3062i	0.444086	+	0.769180i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	40.9778	−	70.9757i	1.40968	−	2.44164i
$846$		0			0
$847$	−1.95104	+	27.0356i	−0.0670386	+	0.928956i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−15.4445	+	26.7507i	−0.529432	+	0.917003i
$852$		0			0
$853$	20.9242	−	36.2419i	0.716432	−	1.24090i	−0.245972	−	0.969277i	$-0.579107\pi$
$853$	20.9242	−	36.2419i	0.716432	−	1.24090i	0.962404	−	0.271621i	$-0.0875596\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−15.7141			−0.536783			−0.268391	−	0.963310i	$-0.586492\pi$
$857$	−15.7141			−0.536783			−0.268391	+	0.963310i	$0.586492\pi$
$858$		0			0
$859$	24.2046			0.825849			0.412924	−	0.910765i	$-0.364507\pi$
$859$	24.2046			0.825849			0.412924	+	0.910765i	$0.364507\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−26.0542	+	45.1272i	−0.886896	+	1.53615i	−0.0433714	+	0.999059i	$0.513810\pi$
$863$	−26.0542	+	45.1272i	−0.886896	+	1.53615i	−0.843525	+	0.537090i	$0.819523\pi$
$864$		0			0
$865$	19.9672	+	34.5842i	0.678904	+	1.17590i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.925022	−	1.60219i	−0.0313792	−	0.0543504i
$870$		0			0
$871$	14.3732			0.487018
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.66999	+	78.5691i	−0.191680	+	2.65612i
$876$		0			0
$877$	−13.9768			−0.471964			−0.235982	−	0.971757i	$-0.575831\pi$
$877$	−13.9768			−0.471964			−0.235982	+	0.971757i	$0.575831\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−28.1210			−0.947421			−0.473710	−	0.880681i	$-0.657086\pi$
$881$	−28.1210			−0.947421			−0.473710	+	0.880681i	$0.657086\pi$
$882$		0			0
$883$	−35.1633			−1.18334			−0.591670	−	0.806180i	$-0.701531\pi$
$883$	−35.1633			−1.18334			−0.591670	+	0.806180i	$0.701531\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.9219			0.903950			0.451975	−	0.892031i	$-0.350720\pi$
$887$	26.9219			0.903950			0.451975	+	0.892031i	$0.350720\pi$
$888$		0			0
$889$	1.23302	−	17.0860i	0.0413541	−	0.573045i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−9.41041			−0.314907
$894$		0			0
$895$	−47.7880	−	82.7713i	−1.59738	−	2.76674i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.66605	−	4.61774i	−0.0889179	−	0.154010i
$900$		0			0
$901$	−3.15594	+	5.46625i	−0.105140	+	0.182107i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	49.0481			1.63041
$906$		0			0
$907$	−44.7142			−1.48471			−0.742355	−	0.670007i	$-0.766291\pi$
$907$	−44.7142			−1.48471			−0.742355	+	0.670007i	$0.766291\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	13.7822	−	23.8715i	0.456626	−	0.790899i	−0.542154	−	0.840279i	$-0.682391\pi$
$911$	13.7822	−	23.8715i	0.456626	−	0.790899i	0.998780	+	0.0493800i	$0.0157246\pi$
$912$		0			0
$913$	1.90093	−	3.29250i	0.0629115	−	0.108966i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.37650	−	46.7882i	0.111502	−	1.54508i
$918$		0			0
$919$	−21.3836	+	37.0376i	−0.705381	+	1.22176i	0.261173	+	0.965292i	$0.415891\pi$
$919$	−21.3836	+	37.0376i	−0.705381	+	1.22176i	−0.966554	+	0.256464i	$0.917442\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.12402	+	5.41096i	0.102828	+	0.178104i
$924$		0			0
$925$	−32.2750	+	55.9019i	−1.06119	+	1.83804i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	23.9748	+	41.5256i	0.786589	+	1.36241i	0.928045	+	0.372468i	$0.121488\pi$
$929$	23.9748	+	41.5256i	0.786589	+	1.36241i	−0.141456	+	0.989945i	$0.545178\pi$
$930$		0			0
$931$	17.3976	−	22.0645i	0.570182	−	0.723136i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5.20838	+	9.02118i	0.170332	+	0.295024i
$936$		0			0
$937$	33.9136			1.10791			0.553955	−	0.832547i	$-0.313118\pi$
$937$	33.9136			1.10791			0.553955	+	0.832547i	$0.313118\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.27395	+	7.40270i	−0.139327	+	0.241321i	−0.927242	−	0.374463i	$-0.877827\pi$
$941$	−4.27395	+	7.40270i	−0.139327	+	0.241321i	0.787915	+	0.615784i	$0.211161\pi$
$942$		0			0
$943$	34.3563	+	59.5068i	1.11879	+	1.93781i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.411563	+	0.712848i	0.0133740	+	0.0231645i	0.872635	−	0.488373i	$-0.162409\pi$
$947$	0.411563	+	0.712848i	0.0133740	+	0.0231645i	−0.859261	+	0.511538i	$0.829076\pi$
$948$		0			0
$949$	−4.14053	+	7.17161i	−0.134407	+	0.232800i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	44.6726			1.44709			0.723544	−	0.690278i	$-0.242512\pi$
$953$	44.6726			1.44709			0.723544	+	0.690278i	$0.242512\pi$
$954$		0			0
$955$	13.0264	+	22.5625i	0.421526	+	0.730104i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.518430	+	7.18390i	−0.0167410	+	0.231980i
$960$		0			0
$961$	11.1165	+	19.2544i	0.358597	+	0.621108i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	28.4592	−	49.2928i	0.916135	−	1.58679i
$966$		0			0
$967$	−18.2289	−	31.5735i	−0.586203	−	1.01533i	−0.994724	−	0.102585i	$-0.967289\pi$
$967$	−18.2289	−	31.5735i	−0.586203	−	1.01533i	0.408521	−	0.912749i	$-0.366045\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−8.63674	+	14.9593i	−0.277166	+	0.480066i	−0.970679	−	0.240378i	$-0.922729\pi$
$971$	−8.63674	+	14.9593i	−0.277166	+	0.480066i	0.693513	+	0.720444i	$0.256062\pi$
$972$		0			0
$973$	41.2043	−	19.9832i	1.32095	−	0.640631i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.51775	−	7.82497i	0.144536	−	0.250343i	−0.784664	−	0.619921i	$-0.787165\pi$
$977$	4.51775	−	7.82497i	0.144536	−	0.250343i	0.929200	+	0.369578i	$0.120498\pi$
$978$		0			0
$979$	5.06868	−	8.77921i	0.161996	−	0.280585i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	22.8573			0.729034			0.364517	−	0.931197i	$-0.381234\pi$
$983$	22.8573			0.729034			0.364517	+	0.931197i	$0.381234\pi$
$984$		0			0
$985$	−0.669430			−0.0213298
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−11.7005	+	20.2659i	−0.372055	+	0.644417i
$990$		0			0
$991$	−4.37884	−	7.58437i	−0.139098	−	0.240925i	0.788057	−	0.615602i	$-0.211087\pi$
$991$	−4.37884	−	7.58437i	−0.139098	−	0.240925i	−0.927156	+	0.374677i	$0.877754\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	51.4584	+	89.1285i	1.63134	+	2.82556i
$996$		0			0
$997$	6.93070			0.219498			0.109749	−	0.993959i	$-0.464995\pi$
$997$	6.93070			0.219498			0.109749	+	0.993959i	$0.464995\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.l.b.289.1		14
3.2	odd	2		252.2.l.b.205.3	yes	14
4.3	odd	2		3024.2.t.j.289.1		14
7.2	even	3		5292.2.j.h.3529.7		14
7.3	odd	6		5292.2.i.i.2125.1		14
7.4	even	3		756.2.i.b.613.7		14
7.5	odd	6		5292.2.j.g.3529.1		14
7.6	odd	2		5292.2.l.i.3313.7		14
9.2	odd	6		2268.2.k.e.1297.1		14
9.4	even	3		756.2.i.b.37.7		14
9.5	odd	6		252.2.i.b.121.7	yes	14
9.7	even	3		2268.2.k.f.1297.7		14
12.11	even	2		1008.2.t.j.961.5		14
21.2	odd	6		1764.2.j.g.1177.3		14
21.5	even	6		1764.2.j.h.1177.5		14
21.11	odd	6		252.2.i.b.25.7	✓	14
21.17	even	6		1764.2.i.i.1537.1		14
21.20	even	2		1764.2.l.i.961.5		14
28.11	odd	6		3024.2.q.j.2881.7		14
36.23	even	6		1008.2.q.j.625.1		14
36.31	odd	6		3024.2.q.j.2305.7		14
63.4	even	3	inner	756.2.l.b.361.1		14
63.5	even	6		1764.2.j.h.589.5		14
63.11	odd	6		2268.2.k.e.1621.1		14
63.13	odd	6		5292.2.i.i.1549.1		14
63.23	odd	6		1764.2.j.g.589.3		14
63.25	even	3		2268.2.k.f.1621.7		14
63.31	odd	6		5292.2.l.i.361.7		14
63.32	odd	6		252.2.l.b.193.3	yes	14
63.40	odd	6		5292.2.j.g.1765.1		14
63.41	even	6		1764.2.i.i.373.1		14
63.58	even	3		5292.2.j.h.1765.7		14
63.59	even	6		1764.2.l.i.949.5		14
84.11	even	6		1008.2.q.j.529.1		14
252.67	odd	6		3024.2.t.j.1873.1		14
252.95	even	6		1008.2.t.j.193.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.7	✓	14	21.11	odd	6
252.2.i.b.121.7	yes	14	9.5	odd	6
252.2.l.b.193.3	yes	14	63.32	odd	6
252.2.l.b.205.3	yes	14	3.2	odd	2
756.2.i.b.37.7		14	9.4	even	3
756.2.i.b.613.7		14	7.4	even	3
756.2.l.b.289.1		14	1.1	even	1	trivial
756.2.l.b.361.1		14	63.4	even	3	inner
1008.2.q.j.529.1		14	84.11	even	6
1008.2.q.j.625.1		14	36.23	even	6
1008.2.t.j.193.5		14	252.95	even	6
1008.2.t.j.961.5		14	12.11	even	2
1764.2.i.i.373.1		14	63.41	even	6
1764.2.i.i.1537.1		14	21.17	even	6
1764.2.j.g.589.3		14	63.23	odd	6
1764.2.j.g.1177.3		14	21.2	odd	6
1764.2.j.h.589.5		14	63.5	even	6
1764.2.j.h.1177.5		14	21.5	even	6
1764.2.l.i.949.5		14	63.59	even	6
1764.2.l.i.961.5		14	21.20	even	2
2268.2.k.e.1297.1		14	9.2	odd	6
2268.2.k.e.1621.1		14	63.11	odd	6
2268.2.k.f.1297.7		14	9.7	even	3
2268.2.k.f.1621.7		14	63.25	even	3
3024.2.q.j.2305.7		14	36.31	odd	6
3024.2.q.j.2881.7		14	28.11	odd	6
3024.2.t.j.289.1		14	4.3	odd	2
3024.2.t.j.1873.1		14	252.67	odd	6
5292.2.i.i.1549.1		14	63.13	odd	6
5292.2.i.i.2125.1		14	7.3	odd	6
5292.2.j.g.1765.1		14	63.40	odd	6
5292.2.j.g.3529.1		14	7.5	odd	6
5292.2.j.h.1765.7		14	63.58	even	3
5292.2.j.h.3529.7		14	7.2	even	3
5292.2.l.i.361.7		14	63.31	odd	6
5292.2.l.i.3313.7		14	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-4.14520 q^{5} +(0.190437 - 2.63889i) q^{7} +O(q^{10})\)	\(q-4.14520 q^{5} +(0.190437 - 2.63889i) q^{7} -0.868858 q^{11} +(2.86231 + 4.95766i) q^{13} +(1.44613 + 2.50478i) q^{17} +(-2.00703 + 3.47627i) q^{19} +5.82977 q^{23} +12.1827 q^{25} +(0.900417 - 1.55957i) q^{29} +(1.48046 - 2.56422i) q^{31} +(-0.789399 + 10.9387i) q^{35} +(-2.64925 + 4.58864i) q^{37} +(5.89325 + 10.2074i) q^{41} +(-2.00703 + 3.47627i) q^{43} +(1.17218 + 2.03028i) q^{47} +(-6.92747 - 1.00508i) q^{49} +(1.09116 + 1.88995i) q^{53} +3.60159 q^{55} +(-1.52715 + 2.64510i) q^{59} +(-2.81659 - 4.87848i) q^{61} +(-11.8648 - 20.5505i) q^{65} +(1.25539 - 2.17440i) q^{67} +1.09143 q^{71} +(0.723285 + 1.25277i) q^{73} +(-0.165463 + 2.29282i) q^{77} +(1.06464 + 1.84401i) q^{79} +(-2.18784 + 3.78946i) q^{83} +(-5.99451 - 10.3828i) q^{85} +(-5.83373 + 10.1043i) q^{89} +(13.6278 - 6.60919i) q^{91} +(8.31953 - 14.4098i) q^{95} +(-3.98779 + 6.90706i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{5} - 3 q^{7}+O(q^{10}) \) 14 * q - 4 * q^5 - 3 * q^7	\( 14 q - 4 q^{5} - 3 q^{7} + 4 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} + 22 q^{23} + 18 q^{25} - q^{29} - q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 13 q^{49} + 15 q^{53} - 28 q^{55} + 14 q^{59} - 10 q^{61} - 15 q^{65} + 6 q^{67} - 2 q^{71} + 21 q^{73} - 19 q^{77} - 10 q^{79} + 25 q^{83} + 8 q^{85} + 6 q^{89} + 2 q^{91} + 28 q^{95} - 18 q^{97}+O(q^{100}) \) 14 * q - 4 * q^5 - 3 * q^7 + 4 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 + 22 * q^23 + 18 * q^25 - q^29 - q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 13 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 19 * q^77 - 10 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 - 18 * q^97

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