LMFDB - Embedded newform 2916.2.e.d.1945.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2916,2,Mod(973,2916)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2916, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2916.973");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2916 = 2^{2} \cdot 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2916.e (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:	$23.2843772294$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1945.7
Root			$0.381933 - 1.68942i$ of defining polynomial
Character	$\chi$	$=$	2916.1945
Dual form			2916.2.e.d.973.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47772 + 2.55948i) q^{5} +(1.33493 - 2.31217i) q^{7} +O(q^{10})$	$q+(1.47772 + 2.55948i) q^{5} +(1.33493 - 2.31217i) q^{7} +(-1.45197 + 2.51488i) q^{11} +(-1.69505 - 2.93591i) q^{13} -4.81165 q^{17} +6.27578 q^{19} +(-0.447843 - 0.775687i) q^{23} +(-1.86730 + 3.23426i) q^{25} +(-3.05270 + 5.28743i) q^{29} +(4.18303 + 7.24522i) q^{31} +7.89062 q^{35} +9.42115 q^{37} +(5.12112 + 8.87004i) q^{41} +(0.738195 - 1.27859i) q^{43} +(2.88007 - 4.98843i) q^{47} +(-0.0640919 - 0.111010i) q^{49} +4.51324 q^{53} -8.58238 q^{55} +(5.80276 + 10.0507i) q^{59} +(-0.355294 + 0.615387i) q^{61} +(5.00961 - 8.67689i) q^{65} +(-1.35913 - 2.35408i) q^{67} +0.00129276 q^{71} -1.75616 q^{73} +(3.87655 + 6.71439i) q^{77} +(-4.99702 + 8.65509i) q^{79} +(-0.854271 + 1.47964i) q^{83} +(-7.11027 - 12.3153i) q^{85} -13.0457 q^{89} -9.05110 q^{91} +(9.27383 + 16.0627i) q^{95} +(1.59231 - 2.75796i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{5}+O(q^{10}) $ 18 * q + 6 * q^5	$ 18 q + 6 q^{5} + 6 q^{11} - 24 q^{17} + 3 q^{23} - 9 q^{25} + 24 q^{29} - 42 q^{35} + 33 q^{41} + 9 q^{47} - 9 q^{49} - 66 q^{53} + 30 q^{59} + 9 q^{61} + 39 q^{65} + 9 q^{67} - 24 q^{71} - 18 q^{73} + 39 q^{77} + 36 q^{83} - 96 q^{89} - 18 q^{91} + 12 q^{95}+O(q^{100}) $ 18 * q + 6 * q^5 + 6 * q^11 - 24 * q^17 + 3 * q^23 - 9 * q^25 + 24 * q^29 - 42 * q^35 + 33 * q^41 + 9 * q^47 - 9 * q^49 - 66 * q^53 + 30 * q^59 + 9 * q^61 + 39 * q^65 + 9 * q^67 - 24 * q^71 - 18 * q^73 + 39 * q^77 + 36 * q^83 - 96 * q^89 - 18 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2916\mathbb{Z}\right)^\times$.

$n$	$1459$	$2189$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	1.47772	+	2.55948i	0.660856	+	1.14464i	0.980391	+	0.197061i	$0.0631398\pi$
$5$	1.47772	+	2.55948i	0.660856	+	1.14464i	−0.319535	+	0.947574i	$0.603527\pi$
$6$		0			0
$7$	1.33493	−	2.31217i	0.504557	−	0.873919i	−0.495429	−	0.868648i	$-0.664989\pi$
$7$	1.33493	−	2.31217i	0.504557	−	0.873919i	0.999986	−	0.00527025i	$-0.00167758\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.45197	+	2.51488i	−0.437784	+	0.758264i	−0.997518	−	0.0704080i	$-0.977570\pi$
$11$	−1.45197	+	2.51488i	−0.437784	+	0.758264i	0.559734	+	0.828672i	$0.310903\pi$
$12$		0			0
$13$	−1.69505	−	2.93591i	−0.470122	−	0.814275i	0.529295	−	0.848438i	$-0.322457\pi$
$13$	−1.69505	−	2.93591i	−0.470122	−	0.814275i	−0.999416	+	0.0341634i	$0.989123\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.81165			−1.16700			−0.583499	−	0.812114i	$-0.698317\pi$
$17$	−4.81165			−1.16700			−0.583499	+	0.812114i	$0.698317\pi$
$18$		0			0
$19$	6.27578			1.43976			0.719881	−	0.694098i	$-0.244196\pi$
$19$	6.27578			1.43976			0.719881	+	0.694098i	$0.244196\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.447843	−	0.775687i	−0.0933817	−	0.161742i	0.815550	−	0.578686i	$-0.196434\pi$
$23$	−0.447843	−	0.775687i	−0.0933817	−	0.161742i	−0.908932	+	0.416944i	$0.863101\pi$
$24$		0			0
$25$	−1.86730	+	3.23426i	−0.373461	+	0.646853i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.05270	+	5.28743i	−0.566872	+	0.981852i	0.430000	+	0.902829i	$0.358513\pi$
$29$	−3.05270	+	5.28743i	−0.566872	+	0.981852i	−0.996873	+	0.0790232i	$0.974820\pi$
$30$		0			0
$31$	4.18303	+	7.24522i	0.751294	+	1.30128i	0.947196	+	0.320656i	$0.103903\pi$
$31$	4.18303	+	7.24522i	0.751294	+	1.30128i	−0.195901	+	0.980624i	$0.562763\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.89062			1.33376
$36$		0			0
$37$	9.42115			1.54883			0.774414	−	0.632679i	$-0.218045\pi$
$37$	9.42115			1.54883			0.774414	+	0.632679i	$0.218045\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.12112	+	8.87004i	0.799785	+	1.38527i	0.919756	+	0.392491i	$0.128386\pi$
$41$	5.12112	+	8.87004i	0.799785	+	1.38527i	−0.119971	+	0.992777i	$0.538280\pi$
$42$		0			0
$43$	0.738195	−	1.27859i	0.112574	−	0.194983i	−0.804234	−	0.594313i	$-0.797424\pi$
$43$	0.738195	−	1.27859i	0.112574	−	0.194983i	0.916807	+	0.399330i	$0.130757\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.88007	−	4.98843i	0.420101	−	0.727637i	−0.575848	−	0.817557i	$-0.695328\pi$
$47$	2.88007	−	4.98843i	0.420101	−	0.727637i	0.995949	+	0.0899202i	$0.0286612\pi$
$48$		0			0
$49$	−0.0640919	−	0.111010i	−0.00915598	−	0.0158586i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.51324			0.619942			0.309971	−	0.950746i	$-0.399681\pi$
$53$	4.51324			0.619942			0.309971	+	0.950746i	$0.399681\pi$
$54$		0			0
$55$	−8.58238			−1.15725
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.80276	+	10.0507i	0.755455	+	1.30849i	0.945148	+	0.326643i	$0.105917\pi$
$59$	5.80276	+	10.0507i	0.755455	+	1.30849i	−0.189693	+	0.981844i	$0.560749\pi$
$60$		0			0
$61$	−0.355294	+	0.615387i	−0.0454907	+	0.0787922i	−0.887874	−	0.460086i	$-0.847818\pi$
$61$	−0.355294	+	0.615387i	−0.0454907	+	0.0787922i	0.842384	+	0.538878i	$0.181152\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.00961	−	8.67689i	0.621365	−	1.07624i
$66$		0			0
$67$	−1.35913	−	2.35408i	−0.166044	−	0.287597i	0.770981	−	0.636858i	$-0.219766\pi$
$67$	−1.35913	−	2.35408i	−0.166044	−	0.287597i	−0.937026	+	0.349261i	$0.886433\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.00129276			0.000153423			7.67115e−5	−	1.00000i	$-0.499976\pi$
$71$	0.00129276			0.000153423			7.67115e−5		1.00000i	$0.499976\pi$
$72$		0			0
$73$	−1.75616			−0.205543			−0.102772	−	0.994705i	$-0.532771\pi$
$73$	−1.75616			−0.205543			−0.102772	+	0.994705i	$0.532771\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.87655	+	6.71439i	0.441774	+	0.765175i
$78$		0			0
$79$	−4.99702	+	8.65509i	−0.562208	+	0.973773i	0.435095	+	0.900385i	$0.356715\pi$
$79$	−4.99702	+	8.65509i	−0.562208	+	0.973773i	−0.997303	+	0.0733889i	$0.976619\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.854271	+	1.47964i	−0.0937684	+	0.162412i	−0.909094	−	0.416591i	$-0.863225\pi$
$83$	−0.854271	+	1.47964i	−0.0937684	+	0.162412i	0.815326	+	0.579003i	$0.196558\pi$
$84$		0			0
$85$	−7.11027	−	12.3153i	−0.771217	−	1.33579i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−13.0457			−1.38284			−0.691418	−	0.722455i	$-0.743014\pi$
$89$	−13.0457			−1.38284			−0.691418	+	0.722455i	$0.743014\pi$
$90$		0			0
$91$	−9.05110			−0.948813
$92$		0			0
$93$		0			0
$94$		0			0
$95$	9.27383	+	16.0627i	0.951475	+	1.64800i
$96$		0			0
$97$	1.59231	−	2.75796i	0.161674	−	0.280028i	−0.773795	−	0.633436i	$-0.781644\pi$
$97$	1.59231	−	2.75796i	0.161674	−	0.280028i	0.935469	+	0.353408i	$0.114977\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.48987	−	9.50874i	0.546263	−	0.946155i	−0.452263	−	0.891884i	$-0.649383\pi$
$101$	5.48987	−	9.50874i	0.546263	−	0.946155i	0.998526	−	0.0542705i	$-0.0172833\pi$
$102$		0			0
$103$	2.25432	+	3.90459i	0.222125	+	0.384731i	0.955453	−	0.295144i	$-0.0953675\pi$
$103$	2.25432	+	3.90459i	0.222125	+	0.384731i	−0.733328	+	0.679875i	$0.762034\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.98188			−0.578290			−0.289145	−	0.957285i	$-0.593371\pi$
$107$	−5.98188			−0.578290			−0.289145	+	0.957285i	$0.593371\pi$
$108$		0			0
$109$	−4.37994			−0.419522			−0.209761	−	0.977753i	$-0.567269\pi$
$109$	−4.37994			−0.419522			−0.209761	+	0.977753i	$0.567269\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.01721	+	12.1542i	0.660123	+	1.14337i	0.980583	+	0.196105i	$0.0628293\pi$
$113$	7.01721	+	12.1542i	0.660123	+	1.14337i	−0.320460	+	0.947262i	$0.603837\pi$
$114$		0			0
$115$	1.32357	−	2.29249i	0.123424	−	0.213776i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.42324	+	11.1254i	−0.588817	+	1.01986i
$120$		0			0
$121$	1.28359	+	2.22325i	0.116690	+	0.202113i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.73979			0.334497
$126$		0			0
$127$	−8.48790			−0.753180			−0.376590	−	0.926380i	$-0.622903\pi$
$127$	−8.48790			−0.753180			−0.376590	+	0.926380i	$0.622903\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.53759	+	11.3234i	0.571192	+	0.989333i	0.996444	+	0.0842580i	$0.0268520\pi$
$131$	6.53759	+	11.3234i	0.571192	+	0.989333i	−0.425252	+	0.905075i	$0.639815\pi$
$132$		0			0
$133$	8.37774	−	14.5107i	0.726442	−	1.25823i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.24997	−	16.0214i	0.790278	−	1.36880i	−0.135517	−	0.990775i	$-0.543269\pi$
$137$	9.24997	−	16.0214i	0.790278	−	1.36880i	0.925795	−	0.378027i	$-0.123397\pi$
$138$		0			0
$139$	8.28772	+	14.3548i	0.702956	+	1.21755i	0.967424	+	0.253161i	$0.0814701\pi$
$139$	8.28772	+	14.3548i	0.702956	+	1.21755i	−0.264469	+	0.964394i	$0.585197\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.84460			0.823247
$144$		0			0
$145$	−18.0441			−1.49848
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.89624	−	11.9446i	−0.564962	−	0.978544i	−0.997053	−	0.0767135i	$-0.975557\pi$
$149$	−6.89624	−	11.9446i	−0.564962	−	0.978544i	0.432091	−	0.901830i	$-0.357776\pi$
$150$		0			0
$151$	0.203861	−	0.353097i	0.0165900	−	0.0287346i	−0.857611	−	0.514299i	$-0.828052\pi$
$151$	0.203861	−	0.353097i	0.0165900	−	0.0287346i	0.874201	+	0.485564i	$0.161386\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12.3627	+	21.4128i	−0.992994	+	1.71992i
$156$		0			0
$157$	−4.27436	−	7.40341i	−0.341131	−	0.590857i	0.643512	−	0.765436i	$-0.277477\pi$
$157$	−4.27436	−	7.40341i	−0.341131	−	0.590857i	−0.984643	+	0.174580i	$0.944143\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.39136			−0.188466
$162$		0			0
$163$	8.49244			0.665179			0.332590	−	0.943072i	$-0.392078\pi$
$163$	8.49244			0.665179			0.332590	+	0.943072i	$0.392078\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.19412	−	7.26443i	−0.324551	−	0.562139i	0.656871	−	0.754003i	$-0.271880\pi$
$167$	−4.19412	−	7.26443i	−0.324551	−	0.562139i	−0.981421	+	0.191865i	$0.938546\pi$
$168$		0			0
$169$	0.753624	−	1.30531i	0.0579711	−	0.100409i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.14335	−	12.3726i	0.543099	−	0.940674i	−0.455625	−	0.890172i	$-0.650584\pi$
$173$	7.14335	−	12.3726i	0.543099	−	0.940674i	0.998724	−	0.0505028i	$-0.0160824\pi$
$174$		0			0
$175$	4.98545	+	8.63505i	0.376864	+	0.652748i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.70197			−0.127212			−0.0636058	−	0.997975i	$-0.520260\pi$
$179$	−1.70197			−0.127212			−0.0636058	+	0.997975i	$0.520260\pi$
$180$		0			0
$181$	−19.7120			−1.46518			−0.732589	−	0.680671i	$-0.761688\pi$
$181$	−19.7120			−1.46518			−0.732589	+	0.680671i	$0.761688\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	13.9218	+	24.1133i	1.02355	+	1.77284i
$186$		0			0
$187$	6.98636	−	12.1007i	0.510893	−	0.884893i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.94648	+	3.37140i	−0.140842	+	0.243946i	−0.927814	−	0.373043i	$-0.878314\pi$
$191$	−1.94648	+	3.37140i	−0.140842	+	0.243946i	0.786972	+	0.616989i	$0.211648\pi$
$192$		0			0
$193$	−5.70323	−	9.87829i	−0.410528	−	0.711055i	0.584420	−	0.811452i	$-0.301322\pi$
$193$	−5.70323	−	9.87829i	−0.410528	−	0.711055i	−0.994948	+	0.100397i	$0.967989\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.07753			−0.0767707			−0.0383854	−	0.999263i	$-0.512221\pi$
$197$	−1.07753			−0.0767707			−0.0383854	+	0.999263i	$0.512221\pi$
$198$		0			0
$199$	8.78694			0.622889			0.311445	−	0.950264i	$-0.399187\pi$
$199$	8.78694			0.622889			0.311445	+	0.950264i	$0.399187\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.15030	+	14.1167i	0.572039	+	0.990801i
$204$		0			0
$205$	−15.1352	+	26.2148i	−1.05708	+	1.83092i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.11221	+	15.7828i	−0.630305	+	1.09172i
$210$		0			0
$211$	−0.973415	−	1.68600i	−0.0670126	−	0.116069i	0.830572	−	0.556911i	$-0.188013\pi$
$211$	−0.973415	−	1.68600i	−0.0670126	−	0.116069i	−0.897585	+	0.440841i	$0.854680\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.36338			0.297580
$216$		0			0
$217$	22.3363			1.51628
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.15599	+	14.1266i	0.548631	+	0.950257i
$222$		0			0
$223$	−14.2957	+	24.7608i	−0.957309	+	1.65811i	−0.228314	+	0.973588i	$0.573321\pi$
$223$	−14.2957	+	24.7608i	−0.957309	+	1.65811i	−0.728995	+	0.684519i	$0.760012\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.67729	+	16.7616i	−0.642305	+	1.11250i	0.342612	+	0.939477i	$0.388688\pi$
$227$	−9.67729	+	16.7616i	−0.642305	+	1.11250i	−0.984917	+	0.173027i	$0.944645\pi$
$228$		0			0
$229$	3.68119	+	6.37600i	0.243260	+	0.421338i	0.961641	−	0.274312i	$-0.0884499\pi$
$229$	3.68119	+	6.37600i	0.243260	+	0.421338i	−0.718381	+	0.695650i	$0.755117\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	17.0740			1.11855			0.559276	−	0.828981i	$-0.311079\pi$
$233$	17.0740			1.11855			0.559276	+	0.828981i	$0.311079\pi$
$234$		0			0
$235$	17.0237			1.11051
$236$		0			0
$237$		0			0
$238$		0			0
$239$	10.8685	+	18.8249i	0.703027	+	1.21768i	0.967399	+	0.253258i	$0.0815022\pi$
$239$	10.8685	+	18.8249i	0.703027	+	1.21768i	−0.264371	+	0.964421i	$0.585164\pi$
$240$		0			0
$241$	4.60468	−	7.97554i	0.296613	−	0.513750i	−0.678746	−	0.734374i	$-0.737476\pi$
$241$	4.60468	−	7.97554i	0.296613	−	0.513750i	0.975359	+	0.220624i	$0.0708094\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.189419	−	0.328084i	0.0121016	−	0.0209605i
$246$		0			0
$247$	−10.6377	−	18.4251i	−0.676863	−	1.17236i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−20.3524			−1.28463			−0.642315	−	0.766441i	$-0.722026\pi$
$251$	−20.3524			−1.28463			−0.642315	+	0.766441i	$0.722026\pi$
$252$		0			0
$253$	2.60101			0.163524
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.37660	−	2.38434i	−0.0858698	−	0.148731i	0.819892	−	0.572519i	$-0.194034\pi$
$257$	−1.37660	−	2.38434i	−0.0858698	−	0.148731i	−0.905762	+	0.423788i	$0.860700\pi$
$258$		0			0
$259$	12.5766	−	21.7833i	0.781472	−	1.35355i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.14446	−	3.71432i	0.132233	−	0.229035i	−0.792304	−	0.610127i	$-0.791119\pi$
$263$	2.14446	−	3.71432i	0.132233	−	0.229035i	0.924537	+	0.381092i	$0.124452\pi$
$264$		0			0
$265$	6.66930	+	11.5516i	0.409692	+	0.709608i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.91806			0.299859			0.149930	−	0.988697i	$-0.452095\pi$
$269$	4.91806			0.299859			0.149930	+	0.988697i	$0.452095\pi$
$270$		0			0
$271$	2.18471			0.132712			0.0663558	−	0.997796i	$-0.478863\pi$
$271$	2.18471			0.132712			0.0663558	+	0.997796i	$0.478863\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.42252	−	9.39208i	−0.326990	−	0.566363i
$276$		0			0
$277$	0.836603	−	1.44904i	0.0502666	−	0.0870643i	−0.839797	−	0.542900i	$-0.817326\pi$
$277$	0.836603	−	1.44904i	0.0502666	−	0.0870643i	0.890064	+	0.455836i	$0.150660\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.268809	−	0.465591i	0.0160358	−	0.0277748i	−0.857896	−	0.513823i	$-0.828229\pi$
$281$	0.268809	−	0.465591i	0.0160358	−	0.0277748i	0.873932	+	0.486048i	$0.161562\pi$
$282$		0			0
$283$	−0.199278	−	0.345160i	−0.0118459	−	0.0205176i	0.860042	−	0.510224i	$-0.170437\pi$
$283$	−0.199278	−	0.345160i	−0.0118459	−	0.0205176i	−0.871888	+	0.489706i	$0.837104\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	27.3454			1.61415
$288$		0			0
$289$	6.15202			0.361883
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−14.3764	−	24.9007i	−0.839878	−	1.45471i	−0.889996	−	0.455969i	$-0.849293\pi$
$293$	−14.3764	−	24.9007i	−0.839878	−	1.45471i	0.0501175	−	0.998743i	$-0.484040\pi$
$294$		0			0
$295$	−17.1497	+	29.7041i	−0.998494	+	1.72944i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.51823	+	2.62965i	−0.0878016	+	0.152077i
$300$		0			0
$301$	−1.97088	−	3.41367i	−0.113600	−	0.196761i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.10010			−0.120251
$306$		0			0
$307$	10.4477			0.596283			0.298142	−	0.954522i	$-0.403633\pi$
$307$	10.4477			0.596283			0.298142	+	0.954522i	$0.403633\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.57034	+	2.71990i	0.0890456	+	0.154232i	0.907108	−	0.420898i	$-0.138285\pi$
$311$	1.57034	+	2.71990i	0.0890456	+	0.154232i	−0.818062	+	0.575130i	$0.804952\pi$
$312$		0			0
$313$	3.11403	−	5.39366i	0.176015	−	0.304868i	−0.764497	−	0.644628i	$-0.777012\pi$
$313$	3.11403	−	5.39366i	0.176015	−	0.304868i	0.940512	+	0.339760i	$0.110346\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.42970	−	9.40451i	0.304962	−	0.528210i	−0.672291	−	0.740287i	$-0.734689\pi$
$317$	5.42970	−	9.40451i	0.304962	−	0.528210i	0.977253	+	0.212077i	$0.0680228\pi$
$318$		0			0
$319$	−8.86483	−	15.3543i	−0.496335	−	0.859678i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−30.1969			−1.68020
$324$		0			0
$325$	12.6607			0.702288
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.68940	−	13.3184i	−0.423930	−	0.734269i
$330$		0			0
$331$	12.1286	−	21.0073i	0.666646	−	1.15467i	−0.312190	−	0.950020i	$-0.601062\pi$
$331$	12.1286	−	21.0073i	0.666646	−	1.15467i	0.978836	−	0.204646i	$-0.0656042\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4.01682	−	6.95734i	0.219462	−	0.380120i
$336$		0			0
$337$	3.67178	+	6.35972i	0.200015	+	0.346436i	0.948533	−	0.316679i	$-0.102568\pi$
$337$	3.67178	+	6.35972i	0.200015	+	0.346436i	−0.748518	+	0.663114i	$0.769234\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−24.2945			−1.31562
$342$		0			0
$343$	18.3468			0.990636
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.4105	−	19.7636i	−0.612547	−	1.06096i	−0.990809	−	0.135265i	$-0.956812\pi$
$347$	−11.4105	−	19.7636i	−0.612547	−	1.06096i	0.378262	−	0.925699i	$-0.376522\pi$
$348$		0			0
$349$	4.87538	−	8.44440i	0.260973	−	0.452018i	−0.705528	−	0.708682i	$-0.749290\pi$
$349$	4.87538	−	8.44440i	0.260973	−	0.452018i	0.966501	+	0.256664i	$0.0826233\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.10369	−	14.0360i	0.431316	−	0.747061i	−0.565671	−	0.824631i	$-0.691383\pi$
$353$	8.10369	−	14.0360i	0.431316	−	0.747061i	0.996987	+	0.0775701i	$0.0247162\pi$
$354$		0			0
$355$	0.00191034	+	0.00330881i	0.000101390	+	0.000175613i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.1242			−0.639893			−0.319947	−	0.947436i	$-0.603665\pi$
$359$	−12.1242			−0.639893			−0.319947	+	0.947436i	$0.603665\pi$
$360$		0			0
$361$	20.3854			1.07291
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.59511	−	4.49486i	−0.135834	−	0.235272i
$366$		0			0
$367$	−1.50184	+	2.60126i	−0.0783953	+	0.135785i	−0.902558	−	0.430569i	$-0.858313\pi$
$367$	−1.50184	+	2.60126i	−0.0783953	+	0.135785i	0.824162	+	0.566353i	$0.191646\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.02488	−	10.4354i	0.312796	−	0.541779i
$372$		0			0
$373$	11.5293	+	19.9693i	0.596963	+	1.03397i	0.993267	+	0.115851i	$0.0369595\pi$
$373$	11.5293	+	19.9693i	0.596963	+	1.03397i	−0.396303	+	0.918120i	$0.629707\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	20.6979			1.06600
$378$		0			0
$379$	−9.61297			−0.493785			−0.246893	−	0.969043i	$-0.579410\pi$
$379$	−9.61297			−0.493785			−0.246893	+	0.969043i	$0.579410\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.359756	+	0.623115i	0.0183827	+	0.0318397i	0.875070	−	0.483996i	$-0.160815\pi$
$383$	0.359756	+	0.623115i	0.0183827	+	0.0318397i	−0.856688	+	0.515835i	$0.827482\pi$
$384$		0			0
$385$	−11.4569	+	19.8439i	−0.583898	+	1.01134i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	15.7616	−	27.2999i	0.799144	−	1.38416i	−0.121030	−	0.992649i	$-0.538620\pi$
$389$	15.7616	−	27.2999i	0.799144	−	1.38416i	0.920174	−	0.391509i	$-0.128047\pi$
$390$		0			0
$391$	2.15487	+	3.73234i	0.108976	+	0.188752i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−29.5367			−1.48615
$396$		0			0
$397$	−2.22151			−0.111494			−0.0557472	−	0.998445i	$-0.517754\pi$
$397$	−2.22151			−0.111494			−0.0557472	+	0.998445i	$0.517754\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.15585	+	14.1263i	0.407284	+	0.705436i	0.994584	−	0.103933i	$-0.0331427\pi$
$401$	8.15585	+	14.1263i	0.407284	+	0.705436i	−0.587301	+	0.809369i	$0.699809\pi$
$402$		0			0
$403$	14.1809	−	24.5620i	0.706400	−	1.22352i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−13.6792	+	23.6931i	−0.678052	+	1.17442i
$408$		0			0
$409$	18.8316	+	32.6173i	0.931164	+	1.61282i	0.781335	+	0.624111i	$0.214539\pi$
$409$	18.8316	+	32.6173i	0.931164	+	1.61282i	0.149829	+	0.988712i	$0.452128\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	30.9852			1.52468
$414$		0			0
$415$	−5.04949			−0.247870
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.84576	−	17.0534i	−0.480997	−	0.833111i	0.518765	−	0.854917i	$-0.326392\pi$
$419$	−9.84576	−	17.0534i	−0.480997	−	0.833111i	−0.999762	+	0.0218058i	$0.993058\pi$
$420$		0			0
$421$	3.30321	−	5.72133i	0.160989	−	0.278841i	−0.774235	−	0.632898i	$-0.781865\pi$
$421$	3.30321	−	5.72133i	0.160989	−	0.278841i	0.935224	+	0.354058i	$0.115198\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	8.98481	−	15.5622i	0.435828	−	0.754875i
$426$		0			0
$427$	0.948587	+	1.64300i	0.0459053	+	0.0795104i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.6625			0.561765			0.280882	−	0.959742i	$-0.409373\pi$
$431$	11.6625			0.561765			0.280882	+	0.959742i	$0.409373\pi$
$432$		0			0
$433$	−33.1187			−1.59158			−0.795791	−	0.605571i	$-0.792945\pi$
$433$	−33.1187			−1.59158			−0.795791	+	0.605571i	$0.792945\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.81056	−	4.86804i	−0.134447	−	0.232870i
$438$		0			0
$439$	9.95801	−	17.2478i	0.475270	−	0.823191i	−0.524329	−	0.851516i	$-0.675684\pi$
$439$	9.95801	−	17.2478i	0.475270	−	0.823191i	0.999599	+	0.0283243i	$0.00901712\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.22662	+	14.2489i	−0.390858	+	0.676986i	−0.992563	−	0.121732i	$-0.961155\pi$
$443$	−8.22662	+	14.2489i	−0.390858	+	0.676986i	0.601705	+	0.798719i	$0.294488\pi$
$444$		0			0
$445$	−19.2778	−	33.3901i	−0.913855	−	1.58284i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.80274			0.132269			0.0661347	−	0.997811i	$-0.478933\pi$
$449$	2.80274			0.132269			0.0661347	+	0.997811i	$0.478933\pi$
$450$		0			0
$451$	−29.7428			−1.40053
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−13.3750	−	23.1661i	−0.627029	−	1.08605i
$456$		0			0
$457$	−15.9700	+	27.6608i	−0.747043	+	1.29392i	0.202191	+	0.979346i	$0.435194\pi$
$457$	−15.9700	+	27.6608i	−0.747043	+	1.29392i	−0.949234	+	0.314570i	$0.898140\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.01307	−	10.4149i	0.280057	−	0.485072i	−0.691342	−	0.722528i	$-0.742980\pi$
$461$	6.01307	−	10.4149i	0.280057	−	0.485072i	0.971398	+	0.237456i	$0.0763134\pi$
$462$		0			0
$463$	5.64894	+	9.78425i	0.262529	+	0.454713i	0.966913	−	0.255106i	$-0.0821103\pi$
$463$	5.64894	+	9.78425i	0.262529	+	0.454713i	−0.704385	+	0.709818i	$0.748777\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	26.3619			1.21988			0.609942	−	0.792446i	$-0.291193\pi$
$467$	26.3619			1.21988			0.609942	+	0.792446i	$0.291193\pi$
$468$		0			0
$469$	−7.25739			−0.335115
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.14367	+	3.71294i	0.0985660	+	0.170721i
$474$		0			0
$475$	−11.7188	+	20.2975i	−0.537694	+	0.931314i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.20611	+	14.2134i	−0.374947	+	0.649427i	−0.990319	−	0.138810i	$-0.955672\pi$
$479$	−8.20611	+	14.2134i	−0.374947	+	0.649427i	0.615372	+	0.788237i	$0.289006\pi$
$480$		0			0
$481$	−15.9693	−	27.6597i	−0.728138	−	1.26117i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.41193			0.427374
$486$		0			0
$487$	−13.5466			−0.613853			−0.306926	−	0.951733i	$-0.599301\pi$
$487$	−13.5466			−0.613853			−0.306926	+	0.951733i	$0.599301\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.92589	+	8.53190i	0.222302	+	0.385039i	0.955507	−	0.294969i	$-0.0953094\pi$
$491$	4.92589	+	8.53190i	0.222302	+	0.385039i	−0.733204	+	0.680008i	$0.761976\pi$
$492$		0			0
$493$	14.6885	−	25.4413i	0.661539	−	1.14582i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.00172575	−	0.00298909i	7.74107e−5	−	0.000134079i
$498$		0			0
$499$	−17.5495	−	30.3967i	−0.785626	−	1.36074i	−0.928625	−	0.371021i	$-0.879008\pi$
$499$	−17.5495	−	30.3967i	−0.785626	−	1.36074i	0.142999	−	0.989723i	$-0.454325\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−13.5546			−0.604369			−0.302185	−	0.953249i	$-0.597716\pi$
$503$	−13.5546			−0.604369			−0.302185	+	0.953249i	$0.597716\pi$
$504$		0			0
$505$	32.4499			1.44400
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−19.9627	−	34.5764i	−0.884831	−	1.53257i	−0.845908	−	0.533329i	$-0.820941\pi$
$509$	−19.9627	−	34.5764i	−0.884831	−	1.53257i	−0.0389228	−	0.999242i	$-0.512393\pi$
$510$		0			0
$511$	−2.34436	+	4.06054i	−0.103708	+	0.179628i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.66250	+	11.5398i	−0.293585	+	0.508503i
$516$		0			0
$517$	8.36352	+	14.4860i	0.367827	+	0.637096i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	18.5299			0.811811			0.405906	−	0.913915i	$-0.366956\pi$
$521$	18.5299			0.811811			0.405906	+	0.913915i	$0.366956\pi$
$522$		0			0
$523$	−18.9589			−0.829015			−0.414508	−	0.910046i	$-0.636046\pi$
$523$	−18.9589			−0.829015			−0.414508	+	0.910046i	$0.636046\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−20.1273	−	34.8615i	−0.876759	−	1.51859i
$528$		0			0
$529$	11.0989	−	19.2238i	0.482560	−	0.835818i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	17.3611	−	30.0703i	0.751993	−	1.30249i
$534$		0			0
$535$	−8.83953	−	15.3105i	−0.382166	−	0.661931i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.372237			0.0160334
$540$		0			0
$541$	7.63965			0.328454			0.164227	−	0.986423i	$-0.447487\pi$
$541$	7.63965			0.328454			0.164227	+	0.986423i	$0.447487\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−6.47232	−	11.2104i	−0.277244	−	0.480200i
$546$		0			0
$547$	4.08501	−	7.07545i	0.174663	−	0.302524i	−0.765382	−	0.643576i	$-0.777450\pi$
$547$	4.08501	−	7.07545i	0.174663	−	0.302524i	0.940044	+	0.341052i	$0.110783\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−19.1581	+	33.1828i	−0.816161	+	1.41363i
$552$		0			0
$553$	13.3414	+	23.1079i	0.567333	+	0.982649i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.7595			−0.498266			−0.249133	−	0.968469i	$-0.580146\pi$
$557$	−11.7595			−0.498266			−0.249133	+	0.968469i	$0.580146\pi$
$558$		0			0
$559$	−5.00511			−0.211693
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22.1530	−	38.3702i	−0.933640	−	1.61711i	−0.777042	−	0.629449i	$-0.783281\pi$
$563$	−22.1530	−	38.3702i	−0.933640	−	1.61711i	−0.156597	−	0.987663i	$-0.550053\pi$
$564$		0			0
$565$	−20.7389	+	35.9208i	−0.872492	+	1.51120i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.36679	−	9.29556i	0.224988	−	0.389690i	−0.731328	−	0.682026i	$-0.761099\pi$
$569$	5.36679	−	9.29556i	0.224988	−	0.389690i	0.956316	+	0.292336i	$0.0944325\pi$
$570$		0			0
$571$	−15.4327	−	26.7303i	−0.645840	−	1.11863i	−0.984107	−	0.177578i	$-0.943174\pi$
$571$	−15.4327	−	26.7303i	−0.645840	−	1.11863i	0.338266	−	0.941050i	$-0.390160\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.34503			0.139498
$576$		0			0
$577$	−35.3381			−1.47114			−0.735572	−	0.677447i	$-0.763086\pi$
$577$	−35.3381			−1.47114			−0.735572	+	0.677447i	$0.763086\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.28079	+	3.95044i	0.0946231	+	0.163892i
$582$		0			0
$583$	−6.55308	+	11.3503i	−0.271401	+	0.470080i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.5901	+	18.3425i	−0.437099	+	0.757077i	−0.997464	−	0.0711681i	$-0.977327\pi$
$587$	−10.5901	+	18.3425i	−0.437099	+	0.757077i	0.560366	+	0.828245i	$0.310661\pi$
$588$		0			0
$589$	26.2518	+	45.4694i	1.08168	+	1.87353i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−39.4642			−1.62060			−0.810299	−	0.586016i	$-0.800695\pi$
$593$	−39.4642			−1.62060			−0.810299	+	0.586016i	$0.800695\pi$
$594$		0			0
$595$	−37.9669			−1.55649
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.32055	−	14.4116i	−0.339968	−	0.588842i	0.644458	−	0.764640i	$-0.277083\pi$
$599$	−8.32055	−	14.4116i	−0.339968	−	0.588842i	−0.984426	+	0.175797i	$0.943750\pi$
$600$		0			0
$601$	−2.63677	+	4.56703i	−0.107556	+	0.186293i	−0.914780	−	0.403953i	$-0.867636\pi$
$601$	−2.63677	+	4.56703i	−0.107556	+	0.186293i	0.807223	+	0.590246i	$0.200969\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.79358	+	6.57067i	−0.154231	+	0.267136i
$606$		0			0
$607$	−17.4996	−	30.3102i	−0.710287	−	1.23025i	−0.964750	−	0.263170i	$-0.915232\pi$
$607$	−17.4996	−	30.3102i	−0.710287	−	1.23025i	0.254463	−	0.967083i	$-0.418101\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−19.5274			−0.789995
$612$		0			0
$613$	−26.9959			−1.09035			−0.545177	−	0.838321i	$-0.683538\pi$
$613$	−26.9959			−1.09035			−0.545177	+	0.838321i	$0.683538\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−8.95365	−	15.5082i	−0.360460	−	0.624336i	0.627576	−	0.778555i	$-0.284047\pi$
$617$	−8.95365	−	15.5082i	−0.360460	−	0.624336i	−0.988037	+	0.154219i	$0.950714\pi$
$618$		0			0
$619$	−14.7137	+	25.4848i	−0.591392	+	1.02432i	0.402653	+	0.915353i	$0.368088\pi$
$619$	−14.7137	+	25.4848i	−0.591392	+	1.02432i	−0.994045	+	0.108969i	$0.965245\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−17.4151	+	30.1638i	−0.697720	+	1.20849i
$624$		0			0
$625$	14.8629	+	25.7433i	0.594515	+	1.02973i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−45.3313			−1.80748
$630$		0			0
$631$	1.04972			0.0417888			0.0208944	−	0.999782i	$-0.493349\pi$
$631$	1.04972			0.0417888			0.0208944	+	0.999782i	$0.493349\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.5427	−	21.7246i	−0.497743	−	0.862116i
$636$		0			0
$637$	−0.217278	+	0.376336i	−0.00860885	+	0.0149110i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	16.7462	−	29.0052i	0.661433	−	1.14564i	−0.318806	−	0.947820i	$-0.603282\pi$
$641$	16.7462	−	29.0052i	0.661433	−	1.14564i	0.980239	−	0.197816i	$-0.0633849\pi$
$642$		0			0
$643$	11.8091	+	20.4540i	0.465707	+	0.806628i	0.999233	−	0.0391558i	$-0.0124669\pi$
$643$	11.8091	+	20.4540i	0.465707	+	0.806628i	−0.533526	+	0.845783i	$0.679134\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	43.5704			1.71293			0.856465	−	0.516205i	$-0.172656\pi$
$647$	43.5704			1.71293			0.856465	+	0.516205i	$0.172656\pi$
$648$		0			0
$649$	−33.7016			−1.32290
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−10.3437	−	17.9158i	−0.404780	−	0.701100i	0.589515	−	0.807757i	$-0.299319\pi$
$653$	−10.3437	−	17.9158i	−0.404780	−	0.701100i	−0.994296	+	0.106657i	$0.965985\pi$
$654$		0			0
$655$	−19.3214	+	33.4657i	−0.754950	+	1.30761i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	7.50160	−	12.9932i	0.292221	−	0.506142i	−0.682114	−	0.731246i	$-0.738939\pi$
$659$	7.50160	−	12.9932i	0.292221	−	0.506142i	0.974335	+	0.225105i	$0.0722724\pi$
$660$		0			0
$661$	21.4087	+	37.0810i	0.832703	+	1.44228i	0.895887	+	0.444282i	$0.146541\pi$
$661$	21.4087	+	37.0810i	0.832703	+	1.44228i	−0.0631838	+	0.998002i	$0.520125\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	49.5198			1.92029
$666$		0			0
$667$	5.46852			0.211742
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.03175	−	1.78704i	−0.0398302	−	0.0689879i
$672$		0			0
$673$	18.7217	−	32.4269i	0.721669	−	1.24997i	−0.238662	−	0.971103i	$-0.576709\pi$
$673$	18.7217	−	32.4269i	0.721669	−	1.24997i	0.960331	−	0.278864i	$-0.0899578\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.3417	+	23.1084i	−0.512762	+	0.888130i	0.487129	+	0.873330i	$0.338044\pi$
$677$	−13.3417	+	23.1084i	−0.512762	+	0.888130i	−0.999890	+	0.0147993i	$0.995289\pi$
$678$		0			0
$679$	−4.25125	−	7.36338i	−0.163148	−	0.282580i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−25.5345			−0.977052			−0.488526	−	0.872549i	$-0.662465\pi$
$683$	−25.5345			−0.977052			−0.488526	+	0.872549i	$0.662465\pi$
$684$		0			0
$685$	54.6754			2.08904
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−7.65017	−	13.2505i	−0.291448	−	0.504803i
$690$		0			0
$691$	4.25877	−	7.37640i	0.162011	−	0.280612i	−0.773579	−	0.633700i	$-0.781535\pi$
$691$	4.25877	−	7.37640i	0.162011	−	0.280612i	0.935590	+	0.353089i	$0.114869\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−24.4938	+	42.4246i	−0.929104	+	1.60926i
$696$		0			0
$697$	−24.6411	−	42.6796i	−0.933347	−	1.61660i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−8.06432			−0.304585			−0.152293	−	0.988335i	$-0.548666\pi$
$701$	−8.06432			−0.304585			−0.152293	+	0.988335i	$0.548666\pi$
$702$		0			0
$703$	59.1251			2.22994
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−14.6572	−	25.3871i	−0.551242	−	0.954779i
$708$		0			0
$709$	7.21574	−	12.4980i	0.270993	−	0.469374i	−0.698123	−	0.715977i	$-0.745981\pi$
$709$	7.21574	−	12.4980i	0.270993	−	0.469374i	0.969116	+	0.246604i	$0.0793147\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.74668	−	6.48944i	0.140314	−	0.243031i
$714$		0			0
$715$	14.5476	+	25.1971i	0.544048	+	0.942318i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10.0809			0.375955			0.187977	−	0.982173i	$-0.439807\pi$
$719$	10.0809			0.375955			0.187977	+	0.982173i	$0.439807\pi$
$720$		0			0
$721$	12.0375			0.448298
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−11.4006	−	19.7465i	−0.423409	−	0.733366i
$726$		0			0
$727$	24.0032	−	41.5748i	0.890230	−	1.54192i	0.0506304	−	0.998717i	$-0.483877\pi$
$727$	24.0032	−	41.5748i	0.890230	−	1.54192i	0.839599	−	0.543206i	$-0.182790\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.55194	+	6.15214i	−0.131373	+	0.227545i
$732$		0			0
$733$	−23.0786	−	39.9733i	−0.852427	−	1.47645i	−0.879012	−	0.476800i	$-0.841797\pi$
$733$	−23.0786	−	39.9733i	−0.852427	−	1.47645i	0.0265854	−	0.999647i	$-0.491537\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.89364			0.290766
$738$		0			0
$739$	10.8329			0.398496			0.199248	−	0.979949i	$-0.436150\pi$
$739$	10.8329			0.398496			0.199248	+	0.979949i	$0.436150\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.24978	+	5.62878i	0.119223	+	0.206500i	0.919460	−	0.393184i	$-0.128626\pi$
$743$	3.24978	+	5.62878i	0.119223	+	0.206500i	−0.800237	+	0.599684i	$0.795293\pi$
$744$		0			0
$745$	20.3814	−	35.3016i	0.746717	−	1.29335i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−7.98540	+	13.8311i	−0.291780	+	0.505378i
$750$		0			0
$751$	10.3943	+	18.0035i	0.379294	+	0.656956i	0.990960	−	0.134160i	$-0.0428337\pi$
$751$	10.3943	+	18.0035i	0.379294	+	0.656956i	−0.611666	+	0.791116i	$0.709500\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.20499			0.0438543
$756$		0			0
$757$	−26.9259			−0.978639			−0.489319	−	0.872105i	$-0.662755\pi$
$757$	−26.9259			−0.978639			−0.489319	+	0.872105i	$0.662755\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−21.1643	−	36.6577i	−0.767206	−	1.32884i	−0.939072	−	0.343720i	$-0.888313\pi$
$761$	−21.1643	−	36.6577i	−0.767206	−	1.32884i	0.171866	−	0.985120i	$-0.445020\pi$
$762$		0			0
$763$	−5.84693	+	10.1272i	−0.211673	+	0.366628i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	19.6719	−	34.0728i	0.710312	−	1.23030i
$768$		0			0
$769$	−13.0569	−	22.6151i	−0.470842	−	0.815523i	0.528601	−	0.848870i	$-0.322717\pi$
$769$	−13.0569	−	22.6151i	−0.470842	−	0.815523i	−0.999444	+	0.0333472i	$0.989383\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−49.5067			−1.78063			−0.890316	−	0.455344i	$-0.849516\pi$
$773$	−49.5067			−1.78063			−0.890316	+	0.455344i	$0.849516\pi$
$774$		0			0
$775$	−31.2439			−1.12231
$776$		0			0
$777$		0			0
$778$		0			0
$779$	32.1390	+	55.6664i	1.15150	+	1.99446i
$780$		0			0
$781$	−0.00187705	+	0.00325115i	−6.71661e−5	+	0.000116335i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	12.6326	−	21.8803i	0.450877	−	0.780942i
$786$		0			0
$787$	7.96014	+	13.7874i	0.283748	+	0.491466i	0.972305	−	0.233716i	$-0.0750886\pi$
$787$	7.96014	+	13.7874i	0.283748	+	0.491466i	−0.688557	+	0.725183i	$0.741755\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	37.4700			1.33228
$792$		0			0
$793$	2.40896			0.0855447
$794$		0			0
$795$		0			0
$796$		0			0
$797$	7.74751	+	13.4191i	0.274431	+	0.475328i	0.969991	−	0.243139i	$-0.0781772\pi$
$797$	7.74751	+	13.4191i	0.274431	+	0.475328i	−0.695560	+	0.718468i	$0.744844\pi$
$798$		0			0
$799$	−13.8579	+	24.0026i	−0.490257	+	0.849150i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.54988	−	4.41653i	0.0899835	−	0.155856i
$804$		0			0
$805$	−3.53376	−	6.12065i	−0.124549	−	0.215725i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−36.9909			−1.30053			−0.650265	−	0.759708i	$-0.725342\pi$
$809$	−36.9909			−1.30053			−0.650265	+	0.759708i	$0.725342\pi$
$810$		0			0
$811$	51.5190			1.80908			0.904539	−	0.426391i	$-0.140215\pi$
$811$	51.5190			1.80908			0.904539	+	0.426391i	$0.140215\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12.5494	+	21.7363i	0.439587	+	0.761388i
$816$		0			0
$817$	4.63275	−	8.02416i	0.162079	−	0.280730i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.49710	+	16.4495i	−0.331451	+	0.574090i	−0.982797	−	0.184691i	$-0.940872\pi$
$821$	−9.49710	+	16.4495i	−0.331451	+	0.574090i	0.651345	+	0.758781i	$0.274205\pi$
$822$		0			0
$823$	11.0875	+	19.2042i	0.386487	+	0.669416i	0.991974	−	0.126440i	$-0.0403550\pi$
$823$	11.0875	+	19.2042i	0.386487	+	0.669416i	−0.605487	+	0.795855i	$0.707022\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	38.7943			1.34901			0.674505	−	0.738271i	$-0.264357\pi$
$827$	38.7943			1.34901			0.674505	+	0.738271i	$0.264357\pi$
$828$		0			0
$829$	56.8904			1.97588			0.987942	−	0.154826i	$-0.0494816\pi$
$829$	56.8904			1.97588			0.987942	+	0.154826i	$0.0494816\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.308388	+	0.534144i	0.0106850	+	0.0185070i
$834$		0			0
$835$	12.3955	−	21.4696i	0.428963	−	0.742985i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	28.0367	−	48.5610i	0.967934	−	1.67651i	0.266416	−	0.963858i	$-0.414160\pi$
$839$	28.0367	−	48.5610i	0.967934	−	1.67651i	0.701517	−	0.712652i	$-0.252506\pi$
$840$		0			0
$841$	−4.13798	−	7.16718i	−0.142689	−	0.247144i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.45457			0.153242
$846$		0			0
$847$	6.85404			0.235508
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.21920	−	7.30787i	−0.144632	−	0.250510i
$852$		0			0
$853$	−11.8382	+	20.5044i	−0.405333	+	0.702057i	−0.994360	−	0.106056i	$-0.966178\pi$
$853$	−11.8382	+	20.5044i	−0.405333	+	0.702057i	0.589027	+	0.808113i	$0.299511\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.04065	−	12.1948i	0.240504	−	0.416565i	−0.720354	−	0.693607i	$-0.756021\pi$
$857$	7.04065	−	12.1948i	0.240504	−	0.416565i	0.960858	+	0.277041i	$0.0893539\pi$
$858$		0			0
$859$	−19.9083	−	34.4823i	−0.679264	−	1.17652i	−0.975203	−	0.221313i	$-0.928966\pi$
$859$	−19.9083	−	34.4823i	−0.679264	−	1.17652i	0.295939	−	0.955207i	$-0.404368\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6.52665			−0.222170			−0.111085	−	0.993811i	$-0.535433\pi$
$863$	−6.52665			−0.222170			−0.111085	+	0.993811i	$0.535433\pi$
$864$		0			0
$865$	42.2234			1.43564
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−14.5110	−	25.1338i	−0.492252	−	0.852605i
$870$		0			0
$871$	−4.60758	+	7.98056i	−0.156122	+	0.270411i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.99237	−	8.64705i	0.168773	−	0.292324i
$876$		0			0
$877$	2.98215	+	5.16523i	0.100700	+	0.174418i	0.911973	−	0.410250i	$-0.134558\pi$
$877$	2.98215	+	5.16523i	0.100700	+	0.174418i	−0.811273	+	0.584667i	$0.801225\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	35.3732			1.19175			0.595876	−	0.803077i	$-0.296805\pi$
$881$	35.3732			1.19175			0.595876	+	0.803077i	$0.296805\pi$
$882$		0			0
$883$	−24.6548			−0.829701			−0.414851	−	0.909890i	$-0.636166\pi$
$883$	−24.6548			−0.829701			−0.414851	+	0.909890i	$0.636166\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.2155	−	21.1579i	−0.410157	−	0.710412i	0.584750	−	0.811214i	$-0.301193\pi$
$887$	−12.2155	−	21.1579i	−0.410157	−	0.710412i	−0.994907	+	0.100802i	$0.967859\pi$
$888$		0			0
$889$	−11.3308	+	19.6255i	−0.380022	+	0.658218i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	18.0747	−	31.3062i	0.604846	−	1.04762i
$894$		0			0
$895$	−2.51504	−	4.35617i	−0.0840685	−	0.145611i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−51.0782			−1.70355
$900$		0			0
$901$	−21.7162			−0.723471
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−29.1287	−	50.4524i	−0.968271	−	1.67709i
$906$		0			0
$907$	15.5127	−	26.8688i	0.515091	−	0.892163i	−0.484756	−	0.874649i	$-0.661092\pi$
$907$	15.5127	−	26.8688i	0.515091	−	0.892163i	0.999847	−	0.0175138i	$-0.00557509\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−13.6657	+	23.6698i	−0.452766	+	0.784214i	−0.998557	−	0.0537076i	$-0.982896\pi$
$911$	−13.6657	+	23.6698i	−0.452766	+	0.784214i	0.545791	+	0.837922i	$0.316229\pi$
$912$		0			0
$913$	−2.48074	−	4.29678i	−0.0821007	−	0.142203i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	34.9090			1.15280
$918$		0			0
$919$	13.7346			0.453064			0.226532	−	0.974004i	$-0.427261\pi$
$919$	13.7346			0.453064			0.226532	+	0.974004i	$0.427261\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.00219130	−	0.00379544i	−7.21275e−5	−	0.000124928i
$924$		0			0
$925$	−17.5921	+	30.4705i	−0.578426	+	1.00186i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.75464	−	3.03913i	0.0575679	−	0.0997106i	−0.835805	−	0.549026i	$-0.814999\pi$
$929$	1.75464	−	3.03913i	0.0575679	−	0.0997106i	0.893373	+	0.449316i	$0.148332\pi$
$930$		0			0
$931$	−0.402226	−	0.696676i	−0.0131824	−	0.0228326i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	41.2955			1.35051
$936$		0			0
$937$	3.26305			0.106599			0.0532996	−	0.998579i	$-0.483026\pi$
$937$	3.26305			0.106599			0.0532996	+	0.998579i	$0.483026\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.03294	+	1.78910i	0.0336728	+	0.0583230i	0.882371	−	0.470555i	$-0.155946\pi$
$941$	1.03294	+	1.78910i	0.0336728	+	0.0583230i	−0.848698	+	0.528878i	$0.822613\pi$
$942$		0			0
$943$	4.58692	−	7.94477i	0.149371	−	0.258717i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.10807	−	7.11539i	0.133494	−	0.231219i	−0.791527	−	0.611134i	$-0.790714\pi$
$947$	4.10807	−	7.11539i	0.133494	−	0.231219i	0.925021	+	0.379915i	$0.124047\pi$
$948$		0			0
$949$	2.97678	+	5.15593i	0.0966303	+	0.167369i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−25.2636			−0.818370			−0.409185	−	0.912452i	$-0.634187\pi$
$953$	−25.2636			−0.818370			−0.409185	+	0.912452i	$0.634187\pi$
$954$		0			0
$955$	−11.5054			−0.372306
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−24.6962	−	42.7750i	−0.797481	−	1.38128i
$960$		0			0
$961$	−19.4955	+	33.7671i	−0.628886	+	1.08926i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	16.8555	−	29.1947i	0.542599	−	0.939810i
$966$		0			0
$967$	26.2765	+	45.5122i	0.844995	+	1.46357i	0.885626	+	0.464400i	$0.153730\pi$
$967$	26.2765	+	45.5122i	0.844995	+	1.46357i	−0.0406305	+	0.999174i	$0.512937\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	20.8321			0.668535			0.334267	−	0.942478i	$-0.391511\pi$
$971$	20.8321			0.668535			0.334267	+	0.942478i	$0.391511\pi$
$972$		0			0
$973$	44.2542			1.41873
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.898283	−	1.55587i	−0.0287386	−	0.0497768i	0.851298	−	0.524682i	$-0.175816\pi$
$977$	−0.898283	−	1.55587i	−0.0287386	−	0.0497768i	−0.880037	+	0.474905i	$0.842482\pi$
$978$		0			0
$979$	18.9418	−	32.8082i	0.605384	−	1.04856i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−24.1895	+	41.8975i	−0.771526	+	1.33632i	0.165201	+	0.986260i	$0.447173\pi$
$983$	−24.1895	+	41.8975i	−0.771526	+	1.33632i	−0.936727	+	0.350062i	$0.886161\pi$
$984$		0			0
$985$	−1.59228	−	2.75792i	−0.0507344	−	0.0878745i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.32238			−0.0420493
$990$		0			0
$991$	43.6880			1.38780			0.693898	−	0.720073i	$-0.255892\pi$
$991$	43.6880			1.38780			0.693898	+	0.720073i	$0.255892\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	12.9846	+	22.4900i	0.411640	+	0.712981i
$996$		0			0
$997$	12.1649	−	21.0703i	0.385267	−	0.667302i	−0.606539	−	0.795053i	$-0.707443\pi$
$997$	12.1649	−	21.0703i	0.385267	−	0.667302i	0.991806	+	0.127752i	$0.0407761\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2916.2.e.d.1945.7		18
3.2	odd	2		2916.2.e.c.1945.3		18
9.2	odd	6		2916.2.a.d.1.7		9
9.4	even	3	inner	2916.2.e.d.973.7		18
9.5	odd	6		2916.2.e.c.973.3		18
9.7	even	3		2916.2.a.c.1.3		9
27.2	odd	18		972.2.i.a.109.1		18
27.4	even	9		972.2.i.b.541.1		18
27.5	odd	18		972.2.i.a.865.1		18
27.7	even	9		324.2.i.a.253.1		18
27.11	odd	18		972.2.i.c.433.3		18
27.13	even	9		324.2.i.a.73.1		18
27.14	odd	18		108.2.i.a.25.1	yes	18
27.16	even	9		972.2.i.b.433.1		18
27.20	odd	18		108.2.i.a.13.1	✓	18
27.22	even	9		972.2.i.d.865.3		18
27.23	odd	18		972.2.i.c.541.3		18
27.25	even	9		972.2.i.d.109.3		18
108.47	even	18		432.2.u.d.337.3		18
108.95	even	18		432.2.u.d.241.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.13.1	✓	18	27.20	odd	18
108.2.i.a.25.1	yes	18	27.14	odd	18
324.2.i.a.73.1		18	27.13	even	9
324.2.i.a.253.1		18	27.7	even	9
432.2.u.d.241.3		18	108.95	even	18
432.2.u.d.337.3		18	108.47	even	18
972.2.i.a.109.1		18	27.2	odd	18
972.2.i.a.865.1		18	27.5	odd	18
972.2.i.b.433.1		18	27.16	even	9
972.2.i.b.541.1		18	27.4	even	9
972.2.i.c.433.3		18	27.11	odd	18
972.2.i.c.541.3		18	27.23	odd	18
972.2.i.d.109.3		18	27.25	even	9
972.2.i.d.865.3		18	27.22	even	9
2916.2.a.c.1.3		9	9.7	even	3
2916.2.a.d.1.7		9	9.2	odd	6
2916.2.e.c.973.3		18	9.5	odd	6
2916.2.e.c.1945.3		18	3.2	odd	2
2916.2.e.d.973.7		18	9.4	even	3	inner
2916.2.e.d.1945.7		18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2916 = 2^{2} \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2916.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.47772 + 2.55948i) q^{5} +(1.33493 - 2.31217i) q^{7} +O(q^{10})\)	\(q+(1.47772 + 2.55948i) q^{5} +(1.33493 - 2.31217i) q^{7} +(-1.45197 + 2.51488i) q^{11} +(-1.69505 - 2.93591i) q^{13} -4.81165 q^{17} +6.27578 q^{19} +(-0.447843 - 0.775687i) q^{23} +(-1.86730 + 3.23426i) q^{25} +(-3.05270 + 5.28743i) q^{29} +(4.18303 + 7.24522i) q^{31} +7.89062 q^{35} +9.42115 q^{37} +(5.12112 + 8.87004i) q^{41} +(0.738195 - 1.27859i) q^{43} +(2.88007 - 4.98843i) q^{47} +(-0.0640919 - 0.111010i) q^{49} +4.51324 q^{53} -8.58238 q^{55} +(5.80276 + 10.0507i) q^{59} +(-0.355294 + 0.615387i) q^{61} +(5.00961 - 8.67689i) q^{65} +(-1.35913 - 2.35408i) q^{67} +0.00129276 q^{71} -1.75616 q^{73} +(3.87655 + 6.71439i) q^{77} +(-4.99702 + 8.65509i) q^{79} +(-0.854271 + 1.47964i) q^{83} +(-7.11027 - 12.3153i) q^{85} -13.0457 q^{89} -9.05110 q^{91} +(9.27383 + 16.0627i) q^{95} +(1.59231 - 2.75796i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{5}+O(q^{10}) \) 18 * q + 6 * q^5	\( 18 q + 6 q^{5} + 6 q^{11} - 24 q^{17} + 3 q^{23} - 9 q^{25} + 24 q^{29} - 42 q^{35} + 33 q^{41} + 9 q^{47} - 9 q^{49} - 66 q^{53} + 30 q^{59} + 9 q^{61} + 39 q^{65} + 9 q^{67} - 24 q^{71} - 18 q^{73} + 39 q^{77} + 36 q^{83} - 96 q^{89} - 18 q^{91} + 12 q^{95}+O(q^{100}) \) 18 * q + 6 * q^5 + 6 * q^11 - 24 * q^17 + 3 * q^23 - 9 * q^25 + 24 * q^29 - 42 * q^35 + 33 * q^41 + 9 * q^47 - 9 * q^49 - 66 * q^53 + 30 * q^59 + 9 * q^61 + 39 * q^65 + 9 * q^67 - 24 * q^71 - 18 * q^73 + 39 * q^77 + 36 * q^83 - 96 * q^89 - 18 * q^91 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more