LMFDB - Embedded newform 1500.2.i.b.1193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(557,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("1500.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.i (of order $4$, degree $2$, 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:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1193.3
Character	$\chi$	$=$	1500.1193
Dual form			1500.2.i.b.557.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59360 - 0.678567i) q^{3} +(-1.30038 + 1.30038i) q^{7} +(2.07909 + 2.16272i) q^{9} +O(q^{10})$	$q+(-1.59360 - 0.678567i) q^{3} +(-1.30038 + 1.30038i) q^{7} +(2.07909 + 2.16272i) q^{9} -4.00436i q^{11} +(-0.272003 - 0.272003i) q^{13} +(2.24609 + 2.24609i) q^{17} -3.67327i q^{19} +(2.95467 - 1.18988i) q^{21} +(-6.44587 + 6.44587i) q^{23} +(-1.84568 - 4.85731i) q^{27} -2.72372 q^{29} +5.94348 q^{31} +(-2.71723 + 6.38134i) q^{33} +(4.14390 - 4.14390i) q^{37} +(0.248890 + 0.618034i) q^{39} +0.0587550i q^{41} +(-5.58503 - 5.58503i) q^{43} +(-2.30319 - 2.30319i) q^{47} +3.61803i q^{49} +(-2.05524 - 5.10349i) q^{51} +(-6.59535 + 6.59535i) q^{53} +(-2.49256 + 5.85371i) q^{57} -14.9857 q^{59} -9.03286 q^{61} +(-5.51596 - 0.108750i) q^{63} +(-0.657187 + 0.657187i) q^{67} +(14.6461 - 5.89815i) q^{69} +7.42450i q^{71} +(-6.86379 - 6.86379i) q^{73} +(5.20719 + 5.20719i) q^{77} +0.110478i q^{79} +(-0.354742 + 8.99301i) q^{81} +(-6.47173 + 6.47173i) q^{83} +(4.34051 + 1.84823i) q^{87} -0.461467 q^{89} +0.707412 q^{91} +(-9.47150 - 4.03305i) q^{93} +(-10.1859 + 10.1859i) q^{97} +(8.66033 - 8.32545i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{21} + 8 q^{31} - 32 q^{61} - 28 q^{81} - 88 q^{91}+O(q^{100}) $ 32 * q + 8 * q^21 + 8 * q^31 - 32 * q^61 - 28 * q^81 - 88 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	−1.59360	−	0.678567i	−0.920063	−	0.391771i
$3$	−1.59360	−	0.678567i	−0.920063	−	0.391771i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.30038	+	1.30038i	−0.491497	+	0.491497i	−0.908778	−	0.417281i	$-0.862983\pi$
$7$	−1.30038	+	1.30038i	−0.491497	+	0.491497i	0.417281	+	0.908778i	$0.362983\pi$
$8$		0			0
$9$	2.07909	+	2.16272i	0.693031	+	0.720908i
$10$		0			0
$11$		−	4.00436i		−	1.20736i	−0.797226	−	0.603681i	$-0.793700\pi$
$11$		−	4.00436i		−	1.20736i	0.797226	−	0.603681i	$-0.206300\pi$
$12$		0			0
$13$	−0.272003	−	0.272003i	−0.0754399	−	0.0754399i	0.668380	−	0.743820i	$-0.266988\pi$
$13$	−0.272003	−	0.272003i	−0.0754399	−	0.0754399i	−0.743820	+	0.668380i	$0.766988\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.24609	+	2.24609i	0.544758	+	0.544758i	0.924920	−	0.380162i	$-0.124132\pi$
$17$	2.24609	+	2.24609i	0.544758	+	0.544758i	−0.380162	+	0.924920i	$0.624132\pi$
$18$		0			0
$19$		−	3.67327i		−	0.842707i	−0.906897	−	0.421353i	$-0.861555\pi$
$19$		−	3.67327i		−	0.842707i	0.906897	−	0.421353i	$-0.138445\pi$
$20$		0			0
$21$	2.95467	−	1.18988i	0.644762	−	0.259654i
$22$		0			0
$23$	−6.44587	+	6.44587i	−1.34406	+	1.34406i	−0.452077	+	0.891979i	$0.649317\pi$
$23$	−6.44587	+	6.44587i	−1.34406	+	1.34406i	−0.891979	+	0.452077i	$0.850683\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.84568	−	4.85731i	−0.355201	−	0.934790i
$28$		0			0
$29$	−2.72372			−0.505783			−0.252891	−	0.967495i	$-0.581382\pi$
$29$	−2.72372			−0.505783			−0.252891	+	0.967495i	$0.581382\pi$
$30$		0			0
$31$	5.94348			1.06748			0.533740	−	0.845648i	$-0.320786\pi$
$31$	5.94348			1.06748			0.533740	+	0.845648i	$0.320786\pi$
$32$		0			0
$33$	−2.71723	+	6.38134i	−0.473009	+	1.11085i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.14390	−	4.14390i	0.681253	−	0.681253i	−0.279029	−	0.960283i	$-0.590013\pi$
$37$	4.14390	−	4.14390i	0.681253	−	0.681253i	0.960283	+	0.279029i	$0.0900127\pi$
$38$		0			0
$39$	0.248890	+	0.618034i	0.0398543	+	0.0989646i
$40$		0			0
$41$			0.0587550i			0.00917598i	0.999989	+	0.00458799i	$0.00146041\pi$
$41$			0.0587550i			0.00917598i	−0.999989	+	0.00458799i	$0.998540\pi$
$42$		0			0
$43$	−5.58503	−	5.58503i	−0.851709	−	0.851709i	0.138634	−	0.990344i	$-0.455729\pi$
$43$	−5.58503	−	5.58503i	−0.851709	−	0.851709i	−0.990344	+	0.138634i	$0.955729\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.30319	−	2.30319i	−0.335955	−	0.335955i	0.518888	−	0.854842i	$-0.326346\pi$
$47$	−2.30319	−	2.30319i	−0.335955	−	0.335955i	−0.854842	+	0.518888i	$0.826346\pi$
$48$		0			0
$49$			3.61803i			0.516862i
$50$		0			0
$51$	−2.05524	−	5.10349i	−0.287791	−	0.714631i
$52$		0			0
$53$	−6.59535	+	6.59535i	−0.905941	+	0.905941i	−0.995942	−	0.0900009i	$-0.971313\pi$
$53$	−6.59535	+	6.59535i	−0.905941	+	0.905941i	0.0900009	+	0.995942i	$0.471313\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.49256	+	5.85371i	−0.330148	+	0.775343i
$58$		0			0
$59$	−14.9857			−1.95097			−0.975486	−	0.220060i	$-0.929375\pi$
$59$	−14.9857			−1.95097			−0.975486	+	0.220060i	$0.929375\pi$
$60$		0			0
$61$	−9.03286			−1.15654			−0.578270	−	0.815846i	$-0.696272\pi$
$61$	−9.03286			−1.15654			−0.578270	+	0.815846i	$0.696272\pi$
$62$		0			0
$63$	−5.51596	−	0.108750i	−0.694946	−	0.0137013i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.657187	+	0.657187i	−0.0802881	+	0.0802881i	−0.746110	−	0.665822i	$-0.768081\pi$
$67$	−0.657187	+	0.657187i	−0.0802881	+	0.0802881i	0.665822	+	0.746110i	$0.268081\pi$
$68$		0			0
$69$	14.6461	−	5.89815i	1.76318	−	0.710054i
$70$		0			0
$71$			7.42450i			0.881126i	0.897722	+	0.440563i	$0.145221\pi$
$71$			7.42450i			0.881126i	−0.897722	+	0.440563i	$0.854779\pi$
$72$		0			0
$73$	−6.86379	−	6.86379i	−0.803346	−	0.803346i	0.180271	−	0.983617i	$-0.442303\pi$
$73$	−6.86379	−	6.86379i	−0.803346	−	0.803346i	−0.983617	+	0.180271i	$0.942303\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.20719	+	5.20719i	0.593414	+	0.593414i
$78$		0			0
$79$			0.110478i			0.0124297i	0.999981	+	0.00621485i	$0.00197826\pi$
$79$			0.110478i			0.0124297i	−0.999981	+	0.00621485i	$0.998022\pi$
$80$		0			0
$81$	−0.354742	+	8.99301i	−0.0394158	+	0.999223i
$82$		0			0
$83$	−6.47173	+	6.47173i	−0.710364	+	0.710364i	−0.966611	−	0.256247i	$-0.917514\pi$
$83$	−6.47173	+	6.47173i	−0.710364	+	0.710364i	0.256247	+	0.966611i	$0.417514\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.34051	+	1.84823i	0.465352	+	0.198151i
$88$		0			0
$89$	−0.461467			−0.0489155			−0.0244577	−	0.999701i	$-0.507786\pi$
$89$	−0.461467			−0.0489155			−0.0244577	+	0.999701i	$0.507786\pi$
$90$		0			0
$91$	0.707412			0.0741570
$92$		0			0
$93$	−9.47150	−	4.03305i	−0.982149	−	0.418208i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−10.1859	+	10.1859i	−1.03423	+	1.03423i	−0.0348331	+	0.999393i	$0.511090\pi$
$97$	−10.1859	+	10.1859i	−1.03423	+	1.03423i	−0.999393	+	0.0348331i	$0.988910\pi$
$98$		0			0
$99$	8.66033	−	8.32545i	0.870396	−	0.836739i
$100$		0			0
$101$			0.601345i			0.0598360i	0.999552	+	0.0299180i	$0.00952462\pi$
$101$			0.601345i			0.0598360i	−0.999552	+	0.0299180i	$0.990475\pi$
$102$		0			0
$103$	8.24812	+	8.24812i	0.812711	+	0.812711i	0.985040	−	0.172328i	$-0.0551290\pi$
$103$	8.24812	+	8.24812i	0.812711	+	0.812711i	−0.172328	+	0.985040i	$0.555129\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.64141	−	8.64141i	−0.835397	−	0.835397i	0.152852	−	0.988249i	$-0.451154\pi$
$107$	−8.64141	−	8.64141i	−0.835397	−	0.835397i	−0.988249	+	0.152852i	$0.951154\pi$
$108$		0			0
$109$			13.9081i			1.33215i	0.745885	+	0.666075i	$0.232027\pi$
$109$			13.9081i			1.33215i	−0.745885	+	0.666075i	$0.767973\pi$
$110$		0			0
$111$	−9.41562	+	3.79179i	−0.893691	+	0.359900i
$112$		0			0
$113$	−7.96753	+	7.96753i	−0.749522	+	0.749522i	−0.974389	−	0.224867i	$-0.927805\pi$
$113$	−7.96753	+	7.96753i	−0.749522	+	0.749522i	0.224867	+	0.974389i	$0.427805\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.0227475	−	1.15378i	0.00210301	−	0.106667i
$118$		0			0
$119$	−5.84154			−0.535493
$120$		0			0
$121$	−5.03493			−0.457721
$122$		0			0
$123$	0.0398692	−	0.0936316i	0.00359488	−	0.00844248i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	12.7056	−	12.7056i	1.12744	−	1.12744i	0.136846	−	0.990592i	$-0.456303\pi$
$127$	12.7056	−	12.7056i	1.12744	−	1.12744i	0.990592	−	0.136846i	$-0.0436966\pi$
$128$		0			0
$129$	5.11046	+	12.6901i	0.449951	+	1.11730i
$130$		0			0
$131$			12.0442i			1.05230i	0.850391	+	0.526151i	$0.176365\pi$
$131$			12.0442i			1.05230i	−0.850391	+	0.526151i	$0.823635\pi$
$132$		0			0
$133$	4.77664	+	4.77664i	0.414187	+	0.414187i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.83501	+	3.83501i	0.327647	+	0.327647i	0.851691	−	0.524044i	$-0.175577\pi$
$137$	3.83501	+	3.83501i	0.327647	+	0.327647i	−0.524044	+	0.851691i	$0.675577\pi$
$138$		0			0
$139$		−	4.14541i		−	0.351609i	−0.984425	−	0.175804i	$-0.943747\pi$
$139$		−	4.14541i		−	0.351609i	0.984425	−	0.175804i	$-0.0562527\pi$
$140$		0			0
$141$	2.10748	+	5.23322i	0.177482	+	0.440717i
$142$		0			0
$143$	−1.08920	+	1.08920i	−0.0910832	+	0.0910832i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.45508	−	5.76568i	0.202492	−	0.475545i
$148$		0			0
$149$	−8.66033			−0.709482			−0.354741	−	0.934965i	$-0.615431\pi$
$149$	−8.66033			−0.709482			−0.354741	+	0.934965i	$0.615431\pi$
$150$		0			0
$151$	−18.4696			−1.50303			−0.751516	−	0.659715i	$-0.770677\pi$
$151$	−18.4696			−1.50303			−0.751516	+	0.659715i	$0.770677\pi$
$152$		0			0
$153$	−0.187840	+	9.52751i	−0.0151860	+	0.770254i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−8.20857	+	8.20857i	−0.655115	+	0.655115i	−0.954220	−	0.299105i	$-0.903312\pi$
$157$	−8.20857	+	8.20857i	−0.655115	+	0.655115i	0.299105	+	0.954220i	$0.403312\pi$
$158$		0			0
$159$	14.9857	−	6.03493i	1.18844	−	0.478601i
$160$		0			0
$161$		−	16.7641i		−	1.32120i
$162$		0			0
$163$	−6.54157	−	6.54157i	−0.512376	−	0.512376i	0.402878	−	0.915254i	$-0.368010\pi$
$163$	−6.54157	−	6.54157i	−0.512376	−	0.512376i	−0.915254	+	0.402878i	$0.868010\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.1077	−	13.1077i	−1.01431	−	1.01431i	−0.999896	−	0.0144114i	$-0.995413\pi$
$167$	−13.1077	−	13.1077i	−1.01431	−	1.01431i	−0.0144114	−	0.999896i	$-0.504587\pi$
$168$		0			0
$169$		−	12.8520i		−	0.988618i
$170$		0			0
$171$	7.94427	−	7.63708i	0.607514	−	0.584022i
$172$		0			0
$173$	17.6669	−	17.6669i	1.34319	−	1.34319i	0.450325	−	0.892865i	$-0.351308\pi$
$173$	17.6669	−	17.6669i	1.34319	−	1.34319i	0.892865	−	0.450325i	$-0.148692\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	23.8812	+	10.1688i	1.79502	+	0.764334i
$178$		0			0
$179$	−22.9080			−1.71222			−0.856112	−	0.516791i	$-0.827126\pi$
$179$	−22.9080			−1.71222			−0.856112	+	0.516791i	$0.827126\pi$
$180$		0			0
$181$	14.7069			1.09316			0.546578	−	0.837408i	$-0.315930\pi$
$181$	14.7069			1.09316			0.546578	+	0.837408i	$0.315930\pi$
$182$		0			0
$183$	14.3947	+	6.12940i	1.06409	+	0.453098i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	8.99417	−	8.99417i	0.657719	−	0.657719i
$188$		0			0
$189$	8.71642	+	3.91626i	0.634026	+	0.284866i
$190$		0			0
$191$			9.26168i			0.670151i	0.942191	+	0.335076i	$0.108762\pi$
$191$			9.26168i			0.670151i	−0.942191	+	0.335076i	$0.891238\pi$
$192$		0			0
$193$	−13.2326	−	13.2326i	−0.952500	−	0.952500i	0.0464220	−	0.998922i	$-0.485218\pi$
$193$	−13.2326	−	13.2326i	−0.952500	−	0.952500i	−0.998922	+	0.0464220i	$0.985218\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.69558	+	5.69558i	0.405793	+	0.405793i	0.880269	−	0.474476i	$-0.157362\pi$
$197$	5.69558	+	5.69558i	0.405793	+	0.405793i	−0.474476	+	0.880269i	$0.657362\pi$
$198$		0			0
$199$		−	7.56023i		−	0.535931i	−0.963429	−	0.267965i	$-0.913649\pi$
$199$		−	7.56023i		−	0.535931i	0.963429	−	0.267965i	$-0.0863513\pi$
$200$		0			0
$201$	1.49324	−	0.601345i	0.105325	−	0.0424156i
$202$		0			0
$203$	3.54187	−	3.54187i	0.248591	−	0.248591i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−27.3422	−	0.539067i	−1.90041	−	0.0374677i
$208$		0			0
$209$	−14.7091			−1.01745
$210$		0			0
$211$	24.0673			1.65686			0.828431	−	0.560092i	$-0.189234\pi$
$211$	24.0673			1.65686			0.828431	+	0.560092i	$0.189234\pi$
$212$		0			0
$213$	5.03802	−	11.8316i	0.345200	−	0.810691i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−7.72877	+	7.72877i	−0.524663	+	0.524663i
$218$		0			0
$219$	6.28057	+	15.5957i	0.424401	+	1.05386i
$220$		0			0
$221$		−	1.22189i		−	0.0821929i
$222$		0			0
$223$	−2.98414	−	2.98414i	−0.199833	−	0.199833i	0.600095	−	0.799928i	$-0.295129\pi$
$223$	−2.98414	−	2.98414i	−0.199833	−	0.199833i	−0.799928	+	0.600095i	$0.795129\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.165464	+	0.165464i	0.0109822	+	0.0109822i	0.712577	−	0.701594i	$-0.247528\pi$
$227$	0.165464	+	0.165464i	0.0109822	+	0.0109822i	−0.701594	+	0.712577i	$0.747528\pi$
$228$		0			0
$229$		−	8.25717i		−	0.545649i	−0.962064	−	0.272824i	$-0.912042\pi$
$229$		−	8.25717i		−	0.545649i	0.962064	−	0.272824i	$-0.0879578\pi$
$230$		0			0
$231$	−4.76472	−	11.8316i	−0.313496	−	0.778461i
$232$		0			0
$233$	−1.67114	+	1.67114i	−0.109480	+	0.109480i	−0.759725	−	0.650245i	$-0.774666\pi$
$233$	−1.67114	+	1.67114i	−0.109480	+	0.109480i	0.650245	+	0.759725i	$0.274666\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.0749665	−	0.176057i	0.00486959	−	0.0114361i
$238$		0			0
$239$	−9.91853			−0.641576			−0.320788	−	0.947151i	$-0.603948\pi$
$239$	−9.91853			−0.641576			−0.320788	+	0.947151i	$0.603948\pi$
$240$		0			0
$241$	0.978901			0.0630565			0.0315283	−	0.999503i	$-0.489963\pi$
$241$	0.978901			0.0630565			0.0315283	+	0.999503i	$0.489963\pi$
$242$		0			0
$243$	6.66767	−	14.0905i	0.427732	−	0.903906i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.999139	+	0.999139i	−0.0635737	+	0.0635737i
$248$		0			0
$249$	14.7048	−	5.92181i	0.931880	−	0.375280i
$250$		0			0
$251$		−	18.3748i		−	1.15981i	−0.814686	−	0.579903i	$-0.803090\pi$
$251$		−	18.3748i		−	1.15981i	0.814686	−	0.579903i	$-0.196910\pi$
$252$		0			0
$253$	25.8116	+	25.8116i	1.62276	+	1.62276i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.75575	+	9.75575i	0.608547	+	0.608547i	0.942566	−	0.334019i	$-0.108405\pi$
$257$	9.75575	+	9.75575i	0.608547	+	0.608547i	−0.334019	+	0.942566i	$0.608405\pi$
$258$		0			0
$259$			10.7773i			0.669667i
$260$		0			0
$261$	−5.66287	−	5.89066i	−0.350523	−	0.364623i
$262$		0			0
$263$	17.2981	−	17.2981i	1.06665	−	1.06665i	0.0690312	−	0.997615i	$-0.478009\pi$
$263$	17.2981	−	17.2981i	1.06665	−	1.06665i	0.997615	−	0.0690312i	$-0.0219908\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.735393	+	0.313137i	0.0450053	+	0.0191637i
$268$		0			0
$269$	−8.67745			−0.529073			−0.264537	−	0.964376i	$-0.585219\pi$
$269$	−8.67745			−0.529073			−0.264537	+	0.964376i	$0.585219\pi$
$270$		0			0
$271$	−10.4505			−0.634826			−0.317413	−	0.948287i	$-0.602814\pi$
$271$	−10.4505			−0.634826			−0.317413	+	0.948287i	$0.602814\pi$
$272$		0			0
$273$	−1.12733	−	0.480027i	−0.0682291	−	0.0290525i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.5711	−	10.5711i	0.635158	−	0.635158i	−0.314199	−	0.949357i	$-0.601736\pi$
$277$	10.5711	−	10.5711i	0.635158	−	0.635158i	0.949357	+	0.314199i	$0.101736\pi$
$278$		0			0
$279$	12.3570	+	12.8541i	0.739797	+	0.769555i
$280$		0			0
$281$		−	18.1986i		−	1.08564i	−0.839850	−	0.542818i	$-0.817357\pi$
$281$		−	18.1986i		−	1.08564i	0.839850	−	0.542818i	$-0.182643\pi$
$282$		0			0
$283$	21.8019	+	21.8019i	1.29599	+	1.29599i	0.931022	+	0.364964i	$0.118919\pi$
$283$	21.8019	+	21.8019i	1.29599	+	1.29599i	0.364964	+	0.931022i	$0.381081\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.0764037	−	0.0764037i	−0.00450997	−	0.00450997i
$288$		0			0
$289$		−	6.91013i		−	0.406478i
$290$		0			0
$291$	23.1441	−	9.32043i	1.35673	−	0.546373i
$292$		0			0
$293$	22.0420	−	22.0420i	1.28771	−	1.28771i	0.351533	−	0.936176i	$-0.385661\pi$
$293$	22.0420	−	22.0420i	1.28771	−	1.28771i	0.936176	−	0.351533i	$-0.114339\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−19.4504	+	7.39078i	−1.12863	+	0.428856i
$298$		0			0
$299$	3.50658			0.202791
$300$		0			0
$301$	14.5253			0.837224
$302$		0			0
$303$	0.408053	−	0.958300i	0.0234420	−	0.0550529i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−21.3173	+	21.3173i	−1.21664	+	1.21664i	−0.247840	+	0.968801i	$0.579721\pi$
$307$	−21.3173	+	21.3173i	−1.21664	+	1.21664i	−0.968801	+	0.247840i	$0.920279\pi$
$308$		0			0
$309$	−7.54726	−	18.7411i	−0.429349	−	1.06614i
$310$		0			0
$311$			29.6948i			1.68384i	0.539603	+	0.841920i	$0.318574\pi$
$311$			29.6948i			1.68384i	−0.539603	+	0.841920i	$0.681426\pi$
$312$		0			0
$313$	11.3777	+	11.3777i	0.643107	+	0.643107i	0.951318	−	0.308211i	$-0.0997304\pi$
$313$	11.3777	+	11.3777i	0.643107	+	0.643107i	−0.308211	+	0.951318i	$0.599730\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.9252	+	15.9252i	0.894447	+	0.894447i	0.994938	−	0.100491i	$-0.0320413\pi$
$317$	15.9252	+	15.9252i	0.894447	+	0.894447i	−0.100491	+	0.994938i	$0.532041\pi$
$318$		0			0
$319$			10.9068i			0.610662i
$320$		0			0
$321$	7.90714	+	19.6347i	0.441333	+	1.09590i
$322$		0			0
$323$	8.25051	−	8.25051i	0.459071	−	0.459071i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	9.43755	−	22.1638i	0.521898	−	1.22566i
$328$		0			0
$329$	5.99004			0.330241
$330$		0			0
$331$	5.25924			0.289074			0.144537	−	0.989499i	$-0.453831\pi$
$331$	5.25924			0.289074			0.144537	+	0.989499i	$0.453831\pi$
$332$		0			0
$333$	17.5777	+	0.346554i	0.963250	+	0.0189910i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	22.0434	−	22.0434i	1.20078	−	1.20078i	0.226849	−	0.973930i	$-0.427157\pi$
$337$	22.0434	−	22.0434i	1.20078	−	1.20078i	0.973930	−	0.226849i	$-0.0728425\pi$
$338$		0			0
$339$	18.1035	−	7.29052i	0.983248	−	0.395966i
$340$		0			0
$341$		−	23.7999i		−	1.28883i
$342$		0			0
$343$	−13.8075	−	13.8075i	−0.745533	−	0.745533i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.0142	−	15.0142i	−0.806005	−	0.806005i	0.178022	−	0.984027i	$-0.443030\pi$
$347$	−15.0142	−	15.0142i	−0.806005	−	0.806005i	−0.984027	+	0.178022i	$0.943030\pi$
$348$		0			0
$349$			24.7061i			1.32249i	0.750171	+	0.661244i	$0.229971\pi$
$349$			24.7061i			1.32249i	−0.750171	+	0.661244i	$0.770029\pi$
$350$		0			0
$351$	−0.819171	+	1.82323i	−0.0437241	+	0.0973168i
$352$		0			0
$353$	−0.314946	+	0.314946i	−0.0167629	+	0.0167629i	−0.715439	−	0.698676i	$-0.753773\pi$
$353$	−0.314946	+	0.314946i	−0.0167629	+	0.0167629i	0.698676	+	0.715439i	$0.253773\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	9.30905	+	3.96388i	0.492687	+	0.209791i
$358$		0			0
$359$	18.0982			0.955186			0.477593	−	0.878581i	$-0.341509\pi$
$359$	18.0982			0.955186			0.477593	+	0.878581i	$0.341509\pi$
$360$		0			0
$361$	5.50707			0.289846
$362$		0			0
$363$	8.02364	+	3.41654i	0.421132	+	0.179322i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	7.10069	−	7.10069i	0.370653	−	0.370653i	−0.497062	−	0.867715i	$-0.665588\pi$
$367$	7.10069	−	7.10069i	0.370653	−	0.370653i	0.867715	+	0.497062i	$0.165588\pi$
$368$		0			0
$369$	−0.127071	+	0.122157i	−0.00661504	+	0.00635924i
$370$		0			0
$371$		−	17.1529i		−	0.890534i
$372$		0			0
$373$	−8.76746	−	8.76746i	−0.453962	−	0.453962i	0.442705	−	0.896667i	$-0.354019\pi$
$373$	−8.76746	−	8.76746i	−0.453962	−	0.453962i	−0.896667	+	0.442705i	$0.854019\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.740860	+	0.740860i	0.0381562	+	0.0381562i
$378$		0			0
$379$		−	10.5287i		−	0.540821i	−0.962745	−	0.270410i	$-0.912841\pi$
$379$		−	10.5287i		−	0.540821i	0.962745	−	0.270410i	$-0.0871594\pi$
$380$		0			0
$381$	−28.8692	+	11.6260i	−1.47901	+	0.595617i
$382$		0			0
$383$	3.80842	−	3.80842i	0.194601	−	0.194601i	−0.603080	−	0.797681i	$-0.706060\pi$
$383$	3.80842	−	3.80842i	0.194601	−	0.194601i	0.797681	+	0.603080i	$0.206060\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.467075	−	23.6907i	0.0237428	−	1.20426i
$388$		0			0
$389$	−27.2285			−1.38054			−0.690270	−	0.723552i	$-0.742508\pi$
$389$	−27.2285			−1.38054			−0.690270	+	0.723552i	$0.742508\pi$
$390$		0			0
$391$	−28.9560			−1.46437
$392$		0			0
$393$	8.17277	−	19.1935i	0.412262	−	0.968184i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−20.0718	+	20.0718i	−1.00738	+	1.00738i	−0.00740305	+	0.999973i	$0.502356\pi$
$397$	−20.0718	+	20.0718i	−1.00738	+	1.00738i	−0.999973	+	0.00740305i	$0.997644\pi$
$398$		0			0
$399$	−4.37076	−	10.8533i	−0.218812	−	0.543345i
$400$		0			0
$401$			26.7585i			1.33626i	0.744046	+	0.668129i	$0.232904\pi$
$401$			26.7585i			1.33626i	−0.744046	+	0.668129i	$0.767096\pi$
$402$		0			0
$403$	−1.61664	−	1.61664i	−0.0805307	−	0.0805307i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−16.5937	−	16.5937i	−0.822518	−	0.822518i
$408$		0			0
$409$		−	5.74027i		−	0.283838i	−0.989878	−	0.141919i	$-0.954673\pi$
$409$		−	5.74027i		−	0.283838i	0.989878	−	0.141919i	$-0.0453273\pi$
$410$		0			0
$411$	−3.50914	−	8.71376i	−0.173093	−	0.429818i
$412$		0			0
$413$	19.4871	−	19.4871i	0.958897	−	0.958897i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.81294	+	6.60610i	−0.137750	+	0.323502i
$418$		0			0
$419$	−4.52134			−0.220882			−0.110441	−	0.993883i	$-0.535226\pi$
$419$	−4.52134			−0.220882			−0.110441	+	0.993883i	$0.535226\pi$
$420$		0			0
$421$	−18.4599			−0.899680			−0.449840	−	0.893109i	$-0.648519\pi$
$421$	−18.4599			−0.899680			−0.449840	+	0.893109i	$0.648519\pi$
$422$		0			0
$423$	0.192615	−	9.76971i	0.00936528	−	0.475020i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	11.7461	−	11.7461i	0.568435	−	0.568435i
$428$		0			0
$429$	2.47483	−	0.996646i	0.119486	−	0.0481185i
$430$		0			0
$431$			14.5744i			0.702023i	0.936371	+	0.351011i	$0.114162\pi$
$431$			14.5744i			0.702023i	−0.936371	+	0.351011i	$0.885838\pi$
$432$		0			0
$433$	5.39988	+	5.39988i	0.259502	+	0.259502i	0.824851	−	0.565350i	$-0.191259\pi$
$433$	5.39988	+	5.39988i	0.259502	+	0.259502i	−0.565350	+	0.824851i	$0.691259\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	23.6774	+	23.6774i	1.13264	+	1.13264i
$438$		0			0
$439$			18.4229i			0.879276i	0.898175	+	0.439638i	$0.144893\pi$
$439$			18.4229i			0.879276i	−0.898175	+	0.439638i	$0.855107\pi$
$440$		0			0
$441$	−7.82481	+	7.52223i	−0.372610	+	0.358201i
$442$		0			0
$443$	16.0023	−	16.0023i	0.760293	−	0.760293i	−0.216082	−	0.976375i	$-0.569328\pi$
$443$	16.0023	−	16.0023i	0.760293	−	0.760293i	0.976375	+	0.216082i	$0.0693280\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	13.8011	+	5.87662i	0.652768	+	0.277954i
$448$		0			0
$449$	−38.4085			−1.81261			−0.906304	−	0.422627i	$-0.861108\pi$
$449$	−38.4085			−1.81261			−0.906304	+	0.422627i	$0.861108\pi$
$450$		0			0
$451$	0.235276			0.0110787
$452$		0			0
$453$	29.4330	+	12.5328i	1.38288	+	0.588844i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14.4035	+	14.4035i	−0.673766	+	0.673766i	−0.958582	−	0.284816i	$-0.908068\pi$
$457$	−14.4035	+	14.4035i	−0.673766	+	0.673766i	0.284816	+	0.958582i	$0.408068\pi$
$458$		0			0
$459$	6.76440	−	15.0555i	0.315735	−	0.702732i
$460$		0			0
$461$			15.4834i			0.721132i	0.932734	+	0.360566i	$0.117416\pi$
$461$			15.4834i			0.721132i	−0.932734	+	0.360566i	$0.882584\pi$
$462$		0			0
$463$	−11.1256	−	11.1256i	−0.517050	−	0.517050i	0.399628	−	0.916678i	$-0.369139\pi$
$463$	−11.1256	−	11.1256i	−0.517050	−	0.517050i	−0.916678	+	0.399628i	$0.869139\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.25994	+	8.25994i	0.382225	+	0.382225i	0.871903	−	0.489679i	$-0.162886\pi$
$467$	8.25994	+	8.25994i	0.382225	+	0.382225i	−0.489679	+	0.871903i	$0.662886\pi$
$468$		0			0
$469$		−	1.70918i		−	0.0789227i
$470$		0			0
$471$	18.6512	−	7.51107i	0.859402	−	0.346092i
$472$		0			0
$473$	−22.3645	+	22.3645i	−1.02832	+	1.02832i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−27.9763	−	0.551568i	−1.28094	−	0.0252546i
$478$		0			0
$479$	10.5872			0.483744			0.241872	−	0.970308i	$-0.422239\pi$
$479$	10.5872			0.483744			0.241872	+	0.970308i	$0.422239\pi$
$480$		0			0
$481$	−2.25430			−0.102787
$482$		0			0
$483$	−11.3756	+	26.7152i	−0.517607	+	1.21559i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−5.05605	+	5.05605i	−0.229112	+	0.229112i	−0.812321	−	0.583210i	$-0.801796\pi$
$487$	−5.05605	+	5.05605i	−0.229112	+	0.229112i	0.583210	+	0.812321i	$0.301796\pi$
$488$		0			0
$489$	5.98573	+	14.8635i	0.270684	+	0.672152i
$490$		0			0
$491$			35.3324i			1.59453i	0.603630	+	0.797265i	$0.293720\pi$
$491$			35.3324i			1.59453i	−0.603630	+	0.797265i	$0.706280\pi$
$492$		0			0
$493$	−6.11774	−	6.11774i	−0.275529	−	0.275529i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.65466	−	9.65466i	−0.433070	−	0.433070i
$498$		0			0
$499$			22.1454i			0.991365i	0.868504	+	0.495682i	$0.165082\pi$
$499$			22.1454i			0.991365i	−0.868504	+	0.495682i	$0.834918\pi$
$500$		0			0
$501$	11.9940	+	29.7829i	0.535850	+	1.33060i
$502$		0			0
$503$	−0.292413	+	0.292413i	−0.0130380	+	0.0130380i	−0.713596	−	0.700558i	$-0.752935\pi$
$503$	−0.292413	+	0.292413i	−0.0130380	+	0.0130380i	0.700558	+	0.713596i	$0.252935\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−8.72096	+	20.4809i	−0.387312	+	0.909590i
$508$		0			0
$509$	26.5321			1.17601			0.588007	−	0.808856i	$-0.299913\pi$
$509$	26.5321			1.17601			0.588007	+	0.808856i	$0.299913\pi$
$510$		0			0
$511$	17.8511			0.789684
$512$		0			0
$513$	−17.8422	+	6.77969i	−0.787753	+	0.299331i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−9.22281	+	9.22281i	−0.405619	+	0.405619i
$518$		0			0
$519$	−40.1421	+	16.1657i	−1.76204	+	0.709596i
$520$		0			0
$521$		−	15.4558i		−	0.677131i	−0.940943	−	0.338565i	$-0.890058\pi$
$521$		−	15.4558i		−	0.677131i	0.940943	−	0.338565i	$-0.109942\pi$
$522$		0			0
$523$	22.4419	+	22.4419i	0.981317	+	0.981317i	0.999829	−	0.0185119i	$-0.00589287\pi$
$523$	22.4419	+	22.4419i	0.981317	+	0.981317i	−0.0185119	+	0.999829i	$0.505893\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.3496	+	13.3496i	0.581518	+	0.581518i
$528$		0			0
$529$		−	60.0984i		−	2.61297i
$530$		0			0
$531$	−31.1567	−	32.4099i	−1.35208	−	1.40647i
$532$		0			0
$533$	0.0159815	−	0.0159815i	0.000692236	−	0.000692236i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	36.5061	+	15.5446i	1.57535	+	0.670799i
$538$		0			0
$539$	14.4879			0.624039
$540$		0			0
$541$	−22.2465			−0.956454			−0.478227	−	0.878236i	$-0.658720\pi$
$541$	−22.2465			−0.956454			−0.478227	+	0.878236i	$0.658720\pi$
$542$		0			0
$543$	−23.4369	−	9.97963i	−1.00577	−	0.428267i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	17.0695	−	17.0695i	0.729838	−	0.729838i	−0.240749	−	0.970587i	$-0.577393\pi$
$547$	17.0695	−	17.0695i	0.729838	−	0.729838i	0.970587	+	0.240749i	$0.0773932\pi$
$548$		0			0
$549$	−18.7802	−	19.5356i	−0.801517	−	0.833758i
$550$		0			0
$551$			10.0050i			0.426226i
$552$		0			0
$553$	−0.143663	−	0.143663i	−0.00610916	−	0.00610916i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.3581	−	17.3581i	−0.735485	−	0.735485i	0.236216	−	0.971701i	$-0.424093\pi$
$557$	−17.3581	−	17.3581i	−0.735485	−	0.735485i	−0.971701	+	0.236216i	$0.924093\pi$
$558$		0			0
$559$			3.03828i			0.128506i
$560$		0			0
$561$	−20.4362	+	8.22992i	−0.862818	+	0.347468i
$562$		0			0
$563$	−13.2471	+	13.2471i	−0.558297	+	0.558297i	−0.928822	−	0.370525i	$-0.879178\pi$
$563$	−13.2471	+	13.2471i	−0.558297	+	0.558297i	0.370525	+	0.928822i	$0.379178\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−11.2330	−	12.1556i	−0.471742	−	0.510487i
$568$		0			0
$569$	8.65171			0.362699			0.181349	−	0.983419i	$-0.441954\pi$
$569$	8.65171			0.362699			0.181349	+	0.983419i	$0.441954\pi$
$570$		0			0
$571$	−33.9749			−1.42180			−0.710902	−	0.703291i	$-0.751713\pi$
$571$	−33.9749			−1.42180			−0.710902	+	0.703291i	$0.751713\pi$
$572$		0			0
$573$	6.28467	−	14.7594i	0.262546	−	0.616581i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	16.1810	−	16.1810i	0.673624	−	0.673624i	−0.284926	−	0.958550i	$-0.591969\pi$
$577$	16.1810	−	16.1810i	0.673624	−	0.673624i	0.958550	+	0.284926i	$0.0919690\pi$
$578$		0			0
$579$	12.1082	+	30.0665i	0.503198	+	1.24952i
$580$		0			0
$581$		−	16.8314i		−	0.698283i
$582$		0			0
$583$	26.4102	+	26.4102i	1.09380	+	1.09380i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−19.5853	−	19.5853i	−0.808372	−	0.808372i	0.176016	−	0.984387i	$-0.443679\pi$
$587$	−19.5853	−	19.5853i	−0.808372	−	0.808372i	−0.984387	+	0.176016i	$0.943679\pi$
$588$		0			0
$589$		−	21.8320i		−	0.899573i
$590$		0			0
$591$	−5.21161	−	12.9413i	−0.214377	−	0.532333i
$592$		0			0
$593$	−24.0775	+	24.0775i	−0.988744	+	0.988744i	−0.999937	−	0.0111937i	$-0.996437\pi$
$593$	−24.0775	+	24.0775i	−0.988744	+	0.988744i	0.0111937	+	0.999937i	$0.496437\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5.13013	+	12.0480i	−0.209962	+	0.493090i
$598$		0			0
$599$	27.5084			1.12396			0.561982	−	0.827149i	$-0.310039\pi$
$599$	27.5084			1.12396			0.561982	+	0.827149i	$0.310039\pi$
$600$		0			0
$601$	26.0170			1.06125			0.530627	−	0.847606i	$-0.321957\pi$
$601$	26.0170			1.06125			0.530627	+	0.847606i	$0.321957\pi$
$602$		0			0
$603$	−2.78767	−	0.0549604i	−0.113523	−	0.00223816i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−7.95535	+	7.95535i	−0.322898	+	0.322898i	−0.849878	−	0.526980i	$-0.823324\pi$
$607$	−7.95535	+	7.95535i	−0.322898	+	0.322898i	0.526980	+	0.849878i	$0.323324\pi$
$608$		0			0
$609$	−8.04770	+	3.24091i	−0.326109	+	0.131328i
$610$		0			0
$611$			1.25295i			0.0506888i
$612$		0			0
$613$	−11.7384	−	11.7384i	−0.474109	−	0.474109i	0.429133	−	0.903241i	$-0.358819\pi$
$613$	−11.7384	−	11.7384i	−0.474109	−	0.474109i	−0.903241	+	0.429133i	$0.858819\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.1548	−	26.1548i	−1.05295	−	1.05295i	−0.998517	−	0.0544346i	$-0.982664\pi$
$617$	−26.1548	−	26.1548i	−1.05295	−	1.05295i	−0.0544346	−	0.998517i	$-0.517336\pi$
$618$		0			0
$619$		−	3.28083i		−	0.131868i	−0.997824	−	0.0659338i	$-0.978997\pi$
$619$		−	3.28083i		−	0.131868i	0.997824	−	0.0659338i	$-0.0210026\pi$
$620$		0			0
$621$	43.2066	+	19.4126i	1.73382	+	0.778999i
$622$		0			0
$623$	0.600082	−	0.600082i	0.0240418	−	0.0240418i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	23.4404	+	9.98113i	0.936119	+	0.398608i
$628$		0			0
$629$	18.6152			0.742236
$630$		0			0
$631$	11.2288			0.447011			0.223506	−	0.974703i	$-0.428250\pi$
$631$	11.2288			0.447011			0.223506	+	0.974703i	$0.428250\pi$
$632$		0			0
$633$	−38.3535	−	16.3313i	−1.52442	−	0.649110i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.984114	−	0.984114i	0.0389920	−	0.0389920i
$638$		0			0
$639$	−16.0571	+	15.4362i	−0.635210	+	0.610648i
$640$		0			0
$641$		−	36.8170i		−	1.45418i	−0.686540	−	0.727092i	$-0.740871\pi$
$641$		−	36.8170i		−	1.45418i	0.686540	−	0.727092i	$-0.259129\pi$
$642$		0			0
$643$	−14.7257	−	14.7257i	−0.580725	−	0.580725i	0.354378	−	0.935102i	$-0.384693\pi$
$643$	−14.7257	−	14.7257i	−0.580725	−	0.580725i	−0.935102	+	0.354378i	$0.884693\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.3595	+	13.3595i	0.525216	+	0.525216i	0.919142	−	0.393926i	$-0.128884\pi$
$647$	13.3595	+	13.3595i	0.525216	+	0.525216i	−0.393926	+	0.919142i	$0.628884\pi$
$648$		0			0
$649$			60.0082i			2.35553i
$650$		0			0
$651$	17.5610	−	7.07204i	0.688271	−	0.277175i
$652$		0			0
$653$	−7.05323	+	7.05323i	−0.276014	+	0.276014i	−0.831516	−	0.555502i	$-0.812526\pi$
$653$	−7.05323	+	7.05323i	−0.276014	+	0.276014i	0.555502	+	0.831516i	$0.312526\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.574018	−	29.1149i	0.0223946	−	1.13588i
$658$		0			0
$659$	5.30757			0.206754			0.103377	−	0.994642i	$-0.467035\pi$
$659$	5.30757			0.206754			0.103377	+	0.994642i	$0.467035\pi$
$660$		0			0
$661$	13.6655			0.531527			0.265763	−	0.964038i	$-0.414376\pi$
$661$	13.6655			0.531527			0.265763	+	0.964038i	$0.414376\pi$
$662$		0			0
$663$	−0.829132	+	1.94719i	−0.0322008	+	0.0756227i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	17.5568	−	17.5568i	0.679800	−	0.679800i
$668$		0			0
$669$	2.73057	+	6.78045i	0.105570	+	0.262148i
$670$		0			0
$671$			36.1709i			1.39636i
$672$		0			0
$673$	−26.5577	−	26.5577i	−1.02372	−	1.02372i	−0.999712	−	0.0240106i	$-0.992356\pi$
$673$	−26.5577	−	26.5577i	−1.02372	−	1.02372i	−0.0240106	−	0.999712i	$-0.507644\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.2749	+	12.2749i	0.471764	+	0.471764i	0.902485	−	0.430721i	$-0.141741\pi$
$677$	12.2749	+	12.2749i	0.471764	+	0.471764i	−0.430721	+	0.902485i	$0.641741\pi$
$678$		0			0
$679$		−	26.4912i		−	1.01664i
$680$		0			0
$681$	−0.151404	−	0.375961i	−0.00580182	−	0.0144068i
$682$		0			0
$683$	−12.9023	+	12.9023i	−0.493694	+	0.493694i	−0.909468	−	0.415774i	$-0.863511\pi$
$683$	−12.9023	+	12.9023i	−0.493694	+	0.493694i	0.415774	+	0.909468i	$0.363511\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−5.60304	+	13.1586i	−0.213769	+	0.502031i
$688$		0			0
$689$	3.58790			0.136688
$690$		0			0
$691$	33.6681			1.28080			0.640398	−	0.768043i	$-0.278769\pi$
$691$	33.6681			1.28080			0.640398	+	0.768043i	$0.278769\pi$
$692$		0			0
$693$	−0.435476	+	22.0879i	−0.0165424	+	0.839051i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.131969	+	0.131969i	−0.00499869	+	0.00499869i
$698$		0			0
$699$	3.79711	−	1.52915i	0.143620	−	0.0578376i
$700$		0			0
$701$		−	40.1058i		−	1.51477i	−0.652966	−	0.757387i	$-0.726476\pi$
$701$		−	40.1058i		−	1.51477i	0.652966	−	0.757387i	$-0.273524\pi$
$702$		0			0
$703$	−15.2217	−	15.2217i	−0.574096	−	0.574096i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.781975	−	0.781975i	−0.0294092	−	0.0294092i
$708$		0			0
$709$			2.24990i			0.0844968i	0.999107	+	0.0422484i	$0.0134521\pi$
$709$			2.24990i			0.0844968i	−0.999107	+	0.0422484i	$0.986548\pi$
$710$		0			0
$711$	−0.238932	+	0.229693i	−0.00896067	+	0.00861417i
$712$		0			0
$713$	−38.3109	+	38.3109i	−1.43475	+	1.43475i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	15.8061	+	6.73039i	0.590290	+	0.251351i
$718$		0			0
$719$	2.61154			0.0973940			0.0486970	−	0.998814i	$-0.484493\pi$
$719$	2.61154			0.0973940			0.0486970	+	0.998814i	$0.484493\pi$
$720$		0			0
$721$	−21.4513			−0.798890
$722$		0			0
$723$	−1.55997	−	0.664250i	−0.0580160	−	0.0247037i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−8.39344	+	8.39344i	−0.311296	+	0.311296i	−0.845411	−	0.534116i	$-0.820645\pi$
$727$	−8.39344	+	8.39344i	−0.311296	+	0.311296i	0.534116	+	0.845411i	$0.320645\pi$
$728$		0			0
$729$	−20.1869	+	17.9301i	−0.747664	+	0.664077i
$730$		0			0
$731$		−	25.0890i		−	0.927950i
$732$		0			0
$733$	−17.6275	−	17.6275i	−0.651086	−	0.651086i	0.302169	−	0.953254i	$-0.402289\pi$
$733$	−17.6275	−	17.6275i	−0.651086	−	0.651086i	−0.953254	+	0.302169i	$0.902289\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.63162	+	2.63162i	0.0969368	+	0.0969368i
$738$		0			0
$739$		−	27.3573i		−	1.00636i	−0.864183	−	0.503178i	$-0.832164\pi$
$739$		−	27.3573i		−	1.00636i	0.864183	−	0.503178i	$-0.167836\pi$
$740$		0			0
$741$	2.27021	−	0.914241i	0.0833982	−	0.0335855i
$742$		0			0
$743$	−9.28334	+	9.28334i	−0.340573	+	0.340573i	−0.856583	−	0.516010i	$-0.827417\pi$
$743$	−9.28334	+	9.28334i	−0.340573	+	0.340573i	0.516010	+	0.856583i	$0.327417\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−27.4519	−	0.541229i	−1.00441	−	0.0198025i
$748$		0			0
$749$	22.4742			0.821190
$750$		0			0
$751$	1.76472			0.0643957			0.0321978	−	0.999482i	$-0.489749\pi$
$751$	1.76472			0.0643957			0.0321978	+	0.999482i	$0.489749\pi$
$752$		0			0
$753$	−12.4685	+	29.2820i	−0.454378	+	1.06709i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	7.77796	−	7.77796i	0.282695	−	0.282695i	−0.551488	−	0.834183i	$-0.685940\pi$
$757$	7.77796	−	7.77796i	0.282695	−	0.282695i	0.834183	+	0.551488i	$0.185940\pi$
$758$		0			0
$759$	−23.6183	−	58.6481i	−0.857291	−	2.12879i
$760$		0			0
$761$		−	2.93947i		−	0.106556i	−0.998580	−	0.0532779i	$-0.983033\pi$
$761$		−	2.93947i		−	0.106556i	0.998580	−	0.0532779i	$-0.0169669\pi$
$762$		0			0
$763$	−18.0857	−	18.0857i	−0.654748	−	0.654748i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.07615	+	4.07615i	0.147181	+	0.147181i
$768$		0			0
$769$			8.88726i			0.320483i	0.987078	+	0.160241i	$0.0512273\pi$
$769$			8.88726i			0.320483i	−0.987078	+	0.160241i	$0.948773\pi$
$770$		0			0
$771$	−8.92678	−	22.1666i	−0.321490	−	0.798312i
$772$		0			0
$773$	5.61335	−	5.61335i	0.201898	−	0.201898i	−0.598915	−	0.800813i	$-0.704401\pi$
$773$	5.61335	−	5.61335i	0.201898	−	0.201898i	0.800813	+	0.598915i	$0.204401\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	7.31310	−	17.1746i	0.262356	−	0.616136i
$778$		0			0
$779$	0.215823			0.00773266
$780$		0			0
$781$	29.7304			1.06384
$782$		0			0
$783$	5.02712	+	13.2300i	0.179655	+	0.472800i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−33.0682	+	33.0682i	−1.17875	+	1.17875i	−0.198692	+	0.980062i	$0.563669\pi$
$787$	−33.0682	+	33.0682i	−1.17875	+	1.17875i	−0.980062	+	0.198692i	$0.936331\pi$
$788$		0			0
$789$	−39.3041	+	15.8282i	−1.39926	+	0.563500i
$790$		0			0
$791$		−	20.7216i		−	0.736775i
$792$		0			0
$793$	2.45696	+	2.45696i	0.0872492	+	0.0872492i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.45586	−	1.45586i	−0.0515692	−	0.0515692i	0.680852	−	0.732421i	$-0.261610\pi$
$797$	−1.45586	−	1.45586i	−0.0515692	−	0.0515692i	−0.732421	+	0.680852i	$0.761610\pi$
$798$		0			0
$799$		−	10.3464i		−	0.366028i
$800$		0			0
$801$	−0.959434	−	0.998026i	−0.0338999	−	0.0352635i
$802$		0			0
$803$	−27.4851	+	27.4851i	−0.969929	+	0.969929i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	13.8283	+	5.88823i	0.486781	+	0.207276i
$808$		0			0
$809$	30.5920			1.07556			0.537778	−	0.843087i	$-0.319264\pi$
$809$	30.5920			1.07556			0.537778	+	0.843087i	$0.319264\pi$
$810$		0			0
$811$	36.2708			1.27364			0.636820	−	0.771012i	$-0.280249\pi$
$811$	36.2708			1.27364			0.636820	+	0.771012i	$0.280249\pi$
$812$		0			0
$813$	16.6539	+	7.09140i	0.584079	+	0.248706i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−20.5153	+	20.5153i	−0.717741	+	0.717741i
$818$		0			0
$819$	1.47078	+	1.52994i	0.0513931	+	0.0534603i
$820$		0			0
$821$		−	32.1333i		−	1.12146i	−0.827998	−	0.560731i	$-0.810520\pi$
$821$		−	32.1333i		−	1.12146i	0.827998	−	0.560731i	$-0.189480\pi$
$822$		0			0
$823$	3.53568	+	3.53568i	0.123246	+	0.123246i	0.766040	−	0.642793i	$-0.222225\pi$
$823$	3.53568	+	3.53568i	0.123246	+	0.123246i	−0.642793	+	0.766040i	$0.722225\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.22925	−	1.22925i	−0.0427452	−	0.0427452i	0.685411	−	0.728156i	$-0.259623\pi$
$827$	−1.22925	−	1.22925i	−0.0427452	−	0.0427452i	−0.728156	+	0.685411i	$0.759623\pi$
$828$		0			0
$829$		−	6.70948i		−	0.233030i	−0.993189	−	0.116515i	$-0.962828\pi$
$829$		−	6.70948i		−	0.233030i	0.993189	−	0.116515i	$-0.0371723\pi$
$830$		0			0
$831$	−24.0193	+	9.67288i	−0.833221	+	0.335549i
$832$		0			0
$833$	−8.12644	+	8.12644i	−0.281564	+	0.281564i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−10.9698	−	28.8693i	−0.379171	−	0.997870i
$838$		0			0
$839$	21.7502			0.750900			0.375450	−	0.926843i	$-0.377488\pi$
$839$	21.7502			0.750900			0.375450	+	0.926843i	$0.377488\pi$
$840$		0			0
$841$	−21.5813			−0.744184
$842$		0			0
$843$	−12.3490	+	29.0012i	−0.425321	+	0.998854i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	6.54731	−	6.54731i	0.224968	−	0.224968i
$848$		0			0
$849$	−19.9493	−	49.5374i	−0.684659	−	1.70012i
$850$		0			0
$851$			53.4221i			1.83128i
$852$		0			0
$853$	20.4722	+	20.4722i	0.700956	+	0.700956i	0.964616	−	0.263660i	$-0.0849296\pi$
$853$	20.4722	+	20.4722i	0.700956	+	0.700956i	−0.263660	+	0.964616i	$0.584930\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	24.4310	+	24.4310i	0.834548	+	0.834548i	0.988135	−	0.153587i	$-0.0490825\pi$
$857$	24.4310	+	24.4310i	0.834548	+	0.834548i	−0.153587	+	0.988135i	$0.549082\pi$
$858$		0			0
$859$			53.3779i			1.82123i	0.413254	+	0.910616i	$0.364392\pi$
$859$			53.3779i			1.82123i	−0.413254	+	0.910616i	$0.635608\pi$
$860$		0			0
$861$	0.0699115	+	0.173602i	0.00238258	+	0.00591633i
$862$		0			0
$863$	−18.0378	+	18.0378i	−0.614013	+	0.614013i	−0.943989	−	0.329976i	$-0.892959\pi$
$863$	−18.0378	+	18.0378i	−0.614013	+	0.614013i	0.329976	+	0.943989i	$0.392959\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.68899	+	11.0120i	−0.159246	+	0.373986i
$868$		0			0
$869$	0.442392			0.0150071
$870$		0			0
$871$	0.357513			0.0121139
$872$		0			0
$873$	−43.2069	−	0.851849i	−1.46233	−	0.0288307i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9.63257	+	9.63257i	−0.325269	+	0.325269i	−0.850784	−	0.525515i	$-0.823873\pi$
$877$	−9.63257	+	9.63257i	−0.325269	+	0.325269i	0.525515	+	0.850784i	$0.323873\pi$
$878$		0			0
$879$	−50.0830	+	20.1691i	−1.68926	+	0.680286i
$880$		0			0
$881$			0.656732i			0.0221259i	0.999939	+	0.0110629i	$0.00352151\pi$
$881$			0.656732i			0.0221259i	−0.999939	+	0.0110629i	$0.996478\pi$
$882$		0			0
$883$	−9.76211	−	9.76211i	−0.328521	−	0.328521i	0.523503	−	0.852024i	$-0.324625\pi$
$883$	−9.76211	−	9.76211i	−0.328521	−	0.328521i	−0.852024	+	0.523503i	$0.824625\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.87587	−	7.87587i	−0.264446	−	0.264446i	0.562412	−	0.826857i	$-0.309874\pi$
$887$	−7.87587	−	7.87587i	−0.264446	−	0.264446i	−0.826857	+	0.562412i	$0.809874\pi$
$888$		0			0
$889$			33.0441i			1.10826i
$890$		0			0
$891$	36.0113	+	1.42052i	1.20642	+	0.0475891i
$892$		0			0
$893$	−8.46025	+	8.46025i	−0.283111	+	0.283111i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−5.58808	−	2.37945i	−0.186580	−	0.0794476i
$898$		0			0
$899$	−16.1884			−0.539913
$900$		0			0
$901$	−29.6275			−0.987036
$902$		0			0
$903$	−23.1475	−	9.85639i	−0.770299	−	0.328000i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−1.83851	+	1.83851i	−0.0610468	+	0.0610468i	−0.736971	−	0.675924i	$-0.763745\pi$
$907$	−1.83851	+	1.83851i	−0.0610468	+	0.0610468i	0.675924	+	0.736971i	$0.263745\pi$
$908$		0			0
$909$	−1.30054	+	1.25025i	−0.0431362	+	0.0414682i
$910$		0			0
$911$		−	5.04798i		−	0.167247i	−0.996497	−	0.0836235i	$-0.973351\pi$
$911$		−	5.04798i		−	0.167247i	0.996497	−	0.0836235i	$-0.0266493\pi$
$912$		0			0
$913$	25.9151	+	25.9151i	0.857666	+	0.857666i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.6620	−	15.6620i	−0.517203	−	0.517203i
$918$		0			0
$919$		−	12.9237i		−	0.426312i	−0.977018	−	0.213156i	$-0.931626\pi$
$919$		−	12.9237i		−	0.426312i	0.977018	−	0.213156i	$-0.0683743\pi$
$920$		0			0
$921$	48.4363	−	19.5059i	1.59603	−	0.642741i
$922$		0			0
$923$	2.01948	−	2.01948i	0.0664721	−	0.0664721i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.689789	+	34.9870i	−0.0226556	+	1.14912i
$928$		0			0
$929$	41.4696			1.36057			0.680287	−	0.732946i	$-0.261855\pi$
$929$	41.4696			1.36057			0.680287	+	0.732946i	$0.261855\pi$
$930$		0			0
$931$	13.2900			0.435563
$932$		0			0
$933$	20.1499	−	47.3215i	0.659679	−	1.54924i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	36.1771	−	36.1771i	1.18186	−	1.18186i	0.202592	−	0.979263i	$-0.435063\pi$
$937$	36.1771	−	36.1771i	1.18186	−	1.18186i	0.979263	−	0.202592i	$-0.0649365\pi$
$938$		0			0
$939$	−10.4109	−	25.8520i	−0.339748	−	0.843649i
$940$		0			0
$941$			42.8764i			1.39773i	0.715254	+	0.698865i	$0.246311\pi$
$941$			42.8764i			1.39773i	−0.715254	+	0.698865i	$0.753689\pi$
$942$		0			0
$943$	−0.378727	−	0.378727i	−0.0123330	−	0.0123330i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	35.2738	+	35.2738i	1.14625	+	1.14625i	0.987285	+	0.158961i	$0.0508143\pi$
$947$	35.2738	+	35.2738i	1.14625	+	1.14625i	0.158961	+	0.987285i	$0.449186\pi$
$948$		0			0
$949$			3.73394i			0.121209i
$950$		0			0
$951$	−14.5720	−	36.1846i	−0.472529	−	1.17337i
$952$		0			0
$953$	−10.5733	+	10.5733i	−0.342502	+	0.342502i	−0.857307	−	0.514805i	$-0.827864\pi$
$953$	−10.5733	+	10.5733i	−0.342502	+	0.342502i	0.514805	+	0.857307i	$0.327864\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	7.40098	−	17.3810i	0.239240	−	0.561848i
$958$		0			0
$959$	−9.97392			−0.322075
$960$		0			0
$961$	4.32496			0.139515
$962$		0			0
$963$	0.722680	−	36.6553i	0.0232880	−	1.18120i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	9.57606	−	9.57606i	0.307945	−	0.307945i	−0.536167	−	0.844112i	$-0.680128\pi$
$967$	9.57606	−	9.57606i	0.307945	−	0.307945i	0.844112	+	0.536167i	$0.180128\pi$
$968$		0			0
$969$	−18.7465	+	7.54945i	−0.602225	+	0.242523i
$970$		0			0
$971$			8.97640i			0.288066i	0.989573	+	0.144033i	$0.0460072\pi$
$971$			8.97640i			0.288066i	−0.989573	+	0.144033i	$0.953993\pi$
$972$		0			0
$973$	5.39060	+	5.39060i	0.172815	+	0.172815i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−24.3924	−	24.3924i	−0.780383	−	0.780383i	0.199512	−	0.979895i	$-0.436064\pi$
$977$	−24.3924	−	24.3924i	−0.780383	−	0.780383i	−0.979895	+	0.199512i	$0.936064\pi$
$978$		0			0
$979$			1.84788i			0.0590586i
$980$		0			0
$981$	−30.0793	+	28.9162i	−0.960358	+	0.923222i
$982$		0			0
$983$	−21.3796	+	21.3796i	−0.681904	+	0.681904i	−0.960429	−	0.278525i	$-0.910154\pi$
$983$	−21.3796	+	21.3796i	−0.681904	+	0.681904i	0.278525	+	0.960429i	$0.410154\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−9.54569	−	4.06464i	−0.303843	−	0.129379i
$988$		0			0
$989$	72.0007			2.28949
$990$		0			0
$991$	−43.0754			−1.36833			−0.684167	−	0.729325i	$-0.739834\pi$
$991$	−43.0754			−1.36833			−0.684167	+	0.729325i	$0.739834\pi$
$992$		0			0
$993$	−8.38110	−	3.56875i	−0.265966	−	0.113251i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	6.23446	−	6.23446i	0.197447	−	0.197447i	−0.601457	−	0.798905i	$-0.705413\pi$
$997$	6.23446	−	6.23446i	0.197447	−	0.197447i	0.798905	+	0.601457i	$0.205413\pi$
$998$		0			0
$999$	−27.7765	−	12.4799i	−0.878810	−	0.394846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.i.b.1193.3	yes	32
3.2	odd	2	inner	1500.2.i.b.1193.6	yes	32
5.2	odd	4	inner	1500.2.i.b.557.6	yes	32
5.3	odd	4	inner	1500.2.i.b.557.11	yes	32
5.4	even	2	inner	1500.2.i.b.1193.14	yes	32
15.2	even	4	inner	1500.2.i.b.557.3	✓	32
15.8	even	4	inner	1500.2.i.b.557.14	yes	32
15.14	odd	2	inner	1500.2.i.b.1193.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1500.2.i.b.557.3	✓	32	15.2	even	4	inner
1500.2.i.b.557.6	yes	32	5.2	odd	4	inner
1500.2.i.b.557.11	yes	32	5.3	odd	4	inner
1500.2.i.b.557.14	yes	32	15.8	even	4	inner
1500.2.i.b.1193.3	yes	32	1.1	even	1	trivial
1500.2.i.b.1193.6	yes	32	3.2	odd	2	inner
1500.2.i.b.1193.11	yes	32	15.14	odd	2	inner
1500.2.i.b.1193.14	yes	32	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59360 - 0.678567i) q^{3} +(-1.30038 + 1.30038i) q^{7} +(2.07909 + 2.16272i) q^{9} +O(q^{10})\)	\(q+(-1.59360 - 0.678567i) q^{3} +(-1.30038 + 1.30038i) q^{7} +(2.07909 + 2.16272i) q^{9} -4.00436i q^{11} +(-0.272003 - 0.272003i) q^{13} +(2.24609 + 2.24609i) q^{17} -3.67327i q^{19} +(2.95467 - 1.18988i) q^{21} +(-6.44587 + 6.44587i) q^{23} +(-1.84568 - 4.85731i) q^{27} -2.72372 q^{29} +5.94348 q^{31} +(-2.71723 + 6.38134i) q^{33} +(4.14390 - 4.14390i) q^{37} +(0.248890 + 0.618034i) q^{39} +0.0587550i q^{41} +(-5.58503 - 5.58503i) q^{43} +(-2.30319 - 2.30319i) q^{47} +3.61803i q^{49} +(-2.05524 - 5.10349i) q^{51} +(-6.59535 + 6.59535i) q^{53} +(-2.49256 + 5.85371i) q^{57} -14.9857 q^{59} -9.03286 q^{61} +(-5.51596 - 0.108750i) q^{63} +(-0.657187 + 0.657187i) q^{67} +(14.6461 - 5.89815i) q^{69} +7.42450i q^{71} +(-6.86379 - 6.86379i) q^{73} +(5.20719 + 5.20719i) q^{77} +0.110478i q^{79} +(-0.354742 + 8.99301i) q^{81} +(-6.47173 + 6.47173i) q^{83} +(4.34051 + 1.84823i) q^{87} -0.461467 q^{89} +0.707412 q^{91} +(-9.47150 - 4.03305i) q^{93} +(-10.1859 + 10.1859i) q^{97} +(8.66033 - 8.32545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{21} + 8 q^{31} - 32 q^{61} - 28 q^{81} - 88 q^{91}+O(q^{100}) \) 32 * q + 8 * q^21 + 8 * q^31 - 32 * q^61 - 28 * q^81 - 88 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more