LMFDB - Embedded newform 1500.2.i.b.557.11

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			557.11
Character	$\chi$	$=$	1500.557
Dual form			1500.2.i.b.1193.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.678567 - 1.59360i) q^{3} +(1.30038 + 1.30038i) q^{7} +(-2.07909 - 2.16272i) q^{9} +O(q^{10})$	$q+(0.678567 - 1.59360i) q^{3} +(1.30038 + 1.30038i) q^{7} +(-2.07909 - 2.16272i) q^{9} -4.00436i q^{11} +(0.272003 - 0.272003i) q^{13} +(2.24609 - 2.24609i) q^{17} +3.67327i q^{19} +(2.95467 - 1.18988i) q^{21} +(-6.44587 - 6.44587i) q^{23} +(-4.85731 + 1.84568i) q^{27} +2.72372 q^{29} +5.94348 q^{31} +(-6.38134 - 2.71723i) q^{33} +(-4.14390 - 4.14390i) q^{37} +(-0.248890 - 0.618034i) q^{39} +0.0587550i q^{41} +(5.58503 - 5.58503i) q^{43} +(-2.30319 + 2.30319i) q^{47} -3.61803i q^{49} +(-2.05524 - 5.10349i) q^{51} +(-6.59535 - 6.59535i) q^{53} +(5.85371 + 2.49256i) q^{57} +14.9857 q^{59} -9.03286 q^{61} +(0.108750 - 5.51596i) q^{63} +(0.657187 + 0.657187i) q^{67} +(-14.6461 + 5.89815i) q^{69} +7.42450i q^{71} +(6.86379 - 6.86379i) q^{73} +(5.20719 - 5.20719i) q^{77} -0.110478i q^{79} +(-0.354742 + 8.99301i) q^{81} +(-6.47173 - 6.47173i) q^{83} +(1.84823 - 4.34051i) q^{87} +0.461467 q^{89} +0.707412 q^{91} +(4.03305 - 9.47150i) q^{93} +(10.1859 + 10.1859i) q^{97} +(-8.66033 + 8.32545i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

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

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
$3$	0.678567	−	1.59360i	0.391771	−	0.920063i
$3$	0.678567	−	1.59360i	0.391771	−	0.920063i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.30038	+	1.30038i	0.491497	+	0.491497i	0.908778	−	0.417281i	$-0.137017\pi$
$7$	1.30038	+	1.30038i	0.491497	+	0.491497i	−0.417281	+	0.908778i	$0.637017\pi$
$8$		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	$-0.733012\pi$
$13$	0.272003	−	0.272003i	0.0754399	−	0.0754399i	0.743820	+	0.668380i	$0.233012\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.24609	−	2.24609i	0.544758	−	0.544758i	−0.380162	−	0.924920i	$-0.624132\pi$
$17$	2.24609	−	2.24609i	0.544758	−	0.544758i	0.924920	+	0.380162i	$0.124132\pi$
$18$		0			0
$19$			3.67327i			0.842707i	0.906897	+	0.421353i	$0.138445\pi$
$19$			3.67327i			0.842707i	−0.906897	+	0.421353i	$0.861555\pi$
$20$		0			0
$21$	2.95467	−	1.18988i	0.644762	−	0.259654i
$22$		0			0
$23$	−6.44587	−	6.44587i	−1.34406	−	1.34406i	−0.891979	−	0.452077i	$-0.850683\pi$
$23$	−6.44587	−	6.44587i	−1.34406	−	1.34406i	−0.452077	−	0.891979i	$-0.649317\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−4.85731	+	1.84568i	−0.934790	+	0.355201i
$28$		0			0
$29$	2.72372			0.505783			0.252891	−	0.967495i	$-0.418618\pi$
$29$	2.72372			0.505783			0.252891	+	0.967495i	$0.418618\pi$
$30$		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
$33$	−6.38134	−	2.71723i	−1.11085	−	0.473009i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.14390	−	4.14390i	−0.681253	−	0.681253i	0.279029	−	0.960283i	$-0.409987\pi$
$37$	−4.14390	−	4.14390i	−0.681253	−	0.681253i	−0.960283	+	0.279029i	$0.909987\pi$
$38$		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	$-0.544271\pi$
$43$	5.58503	−	5.58503i	0.851709	−	0.851709i	0.990344	+	0.138634i	$0.0442713\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.30319	+	2.30319i	−0.335955	+	0.335955i	−0.854842	−	0.518888i	$-0.826346\pi$
$47$	−2.30319	+	2.30319i	−0.335955	+	0.335955i	0.518888	+	0.854842i	$0.326346\pi$
$48$		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	0.0900009	−	0.995942i	$-0.471313\pi$
$53$	−6.59535	−	6.59535i	−0.905941	−	0.905941i	−0.995942	+	0.0900009i	$0.971313\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.85371	+	2.49256i	0.775343	+	0.330148i
$58$		0			0
$59$	14.9857			1.95097			0.975486	−	0.220060i	$-0.0706253\pi$
$59$	14.9857			1.95097			0.975486	+	0.220060i	$0.0706253\pi$
$60$		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
$63$	0.108750	−	5.51596i	0.0137013	−	0.694946i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.657187	+	0.657187i	0.0802881	+	0.0802881i	0.746110	−	0.665822i	$-0.231919\pi$
$67$	0.657187	+	0.657187i	0.0802881	+	0.0802881i	−0.665822	+	0.746110i	$0.731919\pi$
$68$		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	$-0.557697\pi$
$73$	6.86379	−	6.86379i	0.803346	−	0.803346i	0.983617	+	0.180271i	$0.0576974\pi$
$74$		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	$-0.998022\pi$
$79$		−	0.110478i		−	0.0124297i	0.999981	−	0.00621485i	$-0.00197826\pi$
$80$		0			0
$81$	−0.354742	+	8.99301i	−0.0394158	+	0.999223i
$82$		0			0
$83$	−6.47173	−	6.47173i	−0.710364	−	0.710364i	0.256247	−	0.966611i	$-0.417514\pi$
$83$	−6.47173	−	6.47173i	−0.710364	−	0.710364i	−0.966611	+	0.256247i	$0.917514\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.84823	−	4.34051i	0.198151	−	0.465352i
$88$		0			0
$89$	0.461467			0.0489155			0.0244577	−	0.999701i	$-0.492214\pi$
$89$	0.461467			0.0489155			0.0244577	+	0.999701i	$0.492214\pi$
$90$		0			0
$91$	0.707412			0.0741570
$92$		0			0
$93$	4.03305	−	9.47150i	0.418208	−	0.982149i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	10.1859	+	10.1859i	1.03423	+	1.03423i	0.999393	+	0.0348331i	$0.0110899\pi$
$97$	10.1859	+	10.1859i	1.03423	+	1.03423i	0.0348331	+	0.999393i	$0.488910\pi$
$98$		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	$-0.944871\pi$
$103$	−8.24812	+	8.24812i	−0.812711	+	0.812711i	0.172328	+	0.985040i	$0.444871\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.64141	+	8.64141i	−0.835397	+	0.835397i	−0.988249	−	0.152852i	$-0.951154\pi$
$107$	−8.64141	+	8.64141i	−0.835397	+	0.835397i	0.152852	+	0.988249i	$0.451154\pi$
$108$		0			0
$109$		−	13.9081i		−	1.33215i	−0.745885	−	0.666075i	$-0.767973\pi$
$109$		−	13.9081i		−	1.33215i	0.745885	−	0.666075i	$-0.232027\pi$
$110$		0			0
$111$	−9.41562	+	3.79179i	−0.893691	+	0.359900i
$112$		0			0
$113$	−7.96753	−	7.96753i	−0.749522	−	0.749522i	0.224867	−	0.974389i	$-0.427805\pi$
$113$	−7.96753	−	7.96753i	−0.749522	−	0.749522i	−0.974389	+	0.224867i	$0.927805\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.15378	−	0.0227475i	−0.106667	−	0.00210301i
$118$		0			0
$119$	5.84154			0.535493
$120$		0			0
$121$	−5.03493			−0.457721
$122$		0			0
$123$	0.0936316	+	0.0398692i	0.00844248	+	0.00359488i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−12.7056	−	12.7056i	−1.12744	−	1.12744i	−0.990592	−	0.136846i	$-0.956303\pi$
$127$	−12.7056	−	12.7056i	−1.12744	−	1.12744i	−0.136846	−	0.990592i	$-0.543697\pi$
$128$		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	−0.524044	−	0.851691i	$-0.675577\pi$
$137$	3.83501	−	3.83501i	0.327647	−	0.327647i	0.851691	+	0.524044i	$0.175577\pi$
$138$		0			0
$139$			4.14541i			0.351609i	0.984425	+	0.175804i	$0.0562527\pi$
$139$			4.14541i			0.351609i	−0.984425	+	0.175804i	$0.943747\pi$
$140$		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
$147$	−5.76568	−	2.45508i	−0.475545	−	0.202492i
$148$		0			0
$149$	8.66033			0.709482			0.354741	−	0.934965i	$-0.384569\pi$
$149$	8.66033			0.709482			0.354741	+	0.934965i	$0.384569\pi$
$150$		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
$153$	−9.52751	−	0.187840i	−0.770254	−	0.0151860i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.20857	+	8.20857i	0.655115	+	0.655115i	0.954220	−	0.299105i	$-0.0966882\pi$
$157$	8.20857	+	8.20857i	0.655115	+	0.655115i	−0.299105	+	0.954220i	$0.596688\pi$
$158$		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	$-0.631990\pi$
$163$	6.54157	−	6.54157i	0.512376	−	0.512376i	0.915254	+	0.402878i	$0.131990\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.1077	+	13.1077i	−1.01431	+	1.01431i	−0.0144114	+	0.999896i	$0.504587\pi$
$167$	−13.1077	+	13.1077i	−1.01431	+	1.01431i	−0.999896	+	0.0144114i	$0.995413\pi$
$168$		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	0.892865	+	0.450325i	$0.148692\pi$
$173$	17.6669	+	17.6669i	1.34319	+	1.34319i	0.450325	+	0.892865i	$0.351308\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	10.1688	−	23.8812i	0.764334	−	1.79502i
$178$		0			0
$179$	22.9080			1.71222			0.856112	−	0.516791i	$-0.172874\pi$
$179$	22.9080			1.71222			0.856112	+	0.516791i	$0.172874\pi$
$180$		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
$183$	−6.12940	+	14.3947i	−0.453098	+	1.06409i
$184$		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	$-0.514782\pi$
$193$	13.2326	−	13.2326i	0.952500	−	0.952500i	0.998922	+	0.0464220i	$0.0147819\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.69558	−	5.69558i	0.405793	−	0.405793i	−0.474476	−	0.880269i	$-0.657362\pi$
$197$	5.69558	−	5.69558i	0.405793	−	0.405793i	0.880269	+	0.474476i	$0.157362\pi$
$198$		0			0
$199$			7.56023i			0.535931i	0.963429	+	0.267965i	$0.0863513\pi$
$199$			7.56023i			0.535931i	−0.963429	+	0.267965i	$0.913649\pi$
$200$		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
$207$	−0.539067	+	27.3422i	−0.0374677	+	1.90041i
$208$		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
$213$	11.8316	+	5.03802i	0.810691	+	0.345200i
$214$		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	$-0.704871\pi$
$223$	2.98414	−	2.98414i	0.199833	−	0.199833i	0.799928	+	0.600095i	$0.204871\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.165464	−	0.165464i	0.0109822	−	0.0109822i	−0.701594	−	0.712577i	$-0.747528\pi$
$227$	0.165464	−	0.165464i	0.0109822	−	0.0109822i	0.712577	+	0.701594i	$0.247528\pi$
$228$		0			0
$229$			8.25717i			0.545649i	0.962064	+	0.272824i	$0.0879578\pi$
$229$			8.25717i			0.545649i	−0.962064	+	0.272824i	$0.912042\pi$
$230$		0			0
$231$	−4.76472	−	11.8316i	−0.313496	−	0.778461i
$232$		0			0
$233$	−1.67114	−	1.67114i	−0.109480	−	0.109480i	0.650245	−	0.759725i	$-0.274666\pi$
$233$	−1.67114	−	1.67114i	−0.109480	−	0.109480i	−0.759725	+	0.650245i	$0.774666\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.176057	−	0.0749665i	−0.0114361	−	0.00486959i
$238$		0			0
$239$	9.91853			0.641576			0.320788	−	0.947151i	$-0.396052\pi$
$239$	9.91853			0.641576			0.320788	+	0.947151i	$0.396052\pi$
$240$		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
$243$	14.0905	+	6.66767i	0.903906	+	0.427732i
$244$		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	−0.334019	−	0.942566i	$-0.608405\pi$
$257$	9.75575	−	9.75575i	0.608547	−	0.608547i	0.942566	+	0.334019i	$0.108405\pi$
$258$		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	0.997615	+	0.0690312i	$0.0219908\pi$
$263$	17.2981	+	17.2981i	1.06665	+	1.06665i	0.0690312	+	0.997615i	$0.478009\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.313137	−	0.735393i	0.0191637	−	0.0450053i
$268$		0			0
$269$	8.67745			0.529073			0.264537	−	0.964376i	$-0.414781\pi$
$269$	8.67745			0.529073			0.264537	+	0.964376i	$0.414781\pi$
$270$		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
$273$	0.480027	−	1.12733i	0.0290525	−	0.0682291i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−10.5711	−	10.5711i	−0.635158	−	0.635158i	0.314199	−	0.949357i	$-0.398264\pi$
$277$	−10.5711	−	10.5711i	−0.635158	−	0.635158i	−0.949357	+	0.314199i	$0.898264\pi$
$278$		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	−0.364964	+	0.931022i	$0.618919\pi$
$283$	−21.8019	+	21.8019i	−1.29599	+	1.29599i	−0.931022	+	0.364964i	$0.881081\pi$
$284$		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	0.936176	+	0.351533i	$0.114339\pi$
$293$	22.0420	+	22.0420i	1.28771	+	1.28771i	0.351533	+	0.936176i	$0.385661\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	7.39078	+	19.4504i	0.428856	+	1.12863i
$298$		0			0
$299$	−3.50658			−0.202791
$300$		0			0
$301$	14.5253			0.837224
$302$		0			0
$303$	0.958300	+	0.408053i	0.0550529	+	0.0234420i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	21.3173	+	21.3173i	1.21664	+	1.21664i	0.968801	+	0.247840i	$0.0797207\pi$
$307$	21.3173	+	21.3173i	1.21664	+	1.21664i	0.247840	+	0.968801i	$0.420279\pi$
$308$		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	$-0.900270\pi$
$313$	−11.3777	+	11.3777i	−0.643107	+	0.643107i	0.308211	+	0.951318i	$0.400270\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.9252	−	15.9252i	0.894447	−	0.894447i	−0.100491	−	0.994938i	$-0.532041\pi$
$317$	15.9252	−	15.9252i	0.894447	−	0.894447i	0.994938	+	0.100491i	$0.0320413\pi$
$318$		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
$327$	−22.1638	−	9.43755i	−1.22566	−	0.521898i
$328$		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
$333$	−0.346554	+	17.5777i	−0.0189910	+	0.963250i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−22.0434	−	22.0434i	−1.20078	−	1.20078i	−0.973930	−	0.226849i	$-0.927157\pi$
$337$	−22.0434	−	22.0434i	−1.20078	−	1.20078i	−0.226849	−	0.973930i	$-0.572843\pi$
$338$		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	−0.984027	−	0.178022i	$-0.943030\pi$
$347$	−15.0142	+	15.0142i	−0.806005	+	0.806005i	0.178022	+	0.984027i	$0.443030\pi$
$348$		0			0
$349$		−	24.7061i		−	1.32249i	−0.750171	−	0.661244i	$-0.770029\pi$
$349$		−	24.7061i		−	1.32249i	0.750171	−	0.661244i	$-0.229971\pi$
$350$		0			0
$351$	−0.819171	+	1.82323i	−0.0437241	+	0.0973168i
$352$		0			0
$353$	−0.314946	−	0.314946i	−0.0167629	−	0.0167629i	0.698676	−	0.715439i	$-0.253773\pi$
$353$	−0.314946	−	0.314946i	−0.0167629	−	0.0167629i	−0.715439	+	0.698676i	$0.753773\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	3.96388	−	9.30905i	0.209791	−	0.492687i
$358$		0			0
$359$	−18.0982			−0.955186			−0.477593	−	0.878581i	$-0.658491\pi$
$359$	−18.0982			−0.955186			−0.477593	+	0.878581i	$0.658491\pi$
$360$		0			0
$361$	5.50707			0.289846
$362$		0			0
$363$	−3.41654	+	8.02364i	−0.179322	+	0.421132i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.10069	−	7.10069i	−0.370653	−	0.370653i	0.497062	−	0.867715i	$-0.334412\pi$
$367$	−7.10069	−	7.10069i	−0.370653	−	0.370653i	−0.867715	+	0.497062i	$0.834412\pi$
$368$		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	$-0.645981\pi$
$373$	8.76746	−	8.76746i	0.453962	−	0.453962i	0.896667	+	0.442705i	$0.145981\pi$
$374$		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	$0.0871594\pi$
$379$			10.5287i			0.540821i	−0.962745	+	0.270410i	$0.912841\pi$
$380$		0			0
$381$	−28.8692	+	11.6260i	−1.47901	+	0.595617i
$382$		0			0
$383$	3.80842	+	3.80842i	0.194601	+	0.194601i	0.797681	−	0.603080i	$-0.206060\pi$
$383$	3.80842	+	3.80842i	0.194601	+	0.194601i	−0.603080	+	0.797681i	$0.706060\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−23.6907	−	0.467075i	−1.20426	−	0.0237428i
$388$		0			0
$389$	27.2285			1.38054			0.690270	−	0.723552i	$-0.257492\pi$
$389$	27.2285			1.38054			0.690270	+	0.723552i	$0.257492\pi$
$390$		0			0
$391$	−28.9560			−1.46437
$392$		0			0
$393$	19.1935	+	8.17277i	0.968184	+	0.412262i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	20.0718	+	20.0718i	1.00738	+	1.00738i	0.999973	+	0.00740305i	$0.00235649\pi$
$397$	20.0718	+	20.0718i	1.00738	+	1.00738i	0.00740305	+	0.999973i	$0.497644\pi$
$398$		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	$0.0453273\pi$
$409$			5.74027i			0.283838i	−0.989878	+	0.141919i	$0.954673\pi$
$410$		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
$417$	6.60610	+	2.81294i	0.323502	+	0.137750i
$418$		0			0
$419$	4.52134			0.220882			0.110441	−	0.993883i	$-0.464774\pi$
$419$	4.52134			0.220882			0.110441	+	0.993883i	$0.464774\pi$
$420$		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
$423$	9.76971	+	0.192615i	0.475020	+	0.00936528i
$424$		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	$-0.808741\pi$
$433$	−5.39988	+	5.39988i	−0.259502	+	0.259502i	0.565350	+	0.824851i	$0.308741\pi$
$434$		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	$-0.855107\pi$
$439$		−	18.4229i		−	0.879276i	0.898175	−	0.439638i	$-0.144893\pi$
$440$		0			0
$441$	−7.82481	+	7.52223i	−0.372610	+	0.358201i
$442$		0			0
$443$	16.0023	+	16.0023i	0.760293	+	0.760293i	0.976375	−	0.216082i	$-0.0693280\pi$
$443$	16.0023	+	16.0023i	0.760293	+	0.760293i	−0.216082	+	0.976375i	$0.569328\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	5.87662	−	13.8011i	0.277954	−	0.652768i
$448$		0			0
$449$	38.4085			1.81261			0.906304	−	0.422627i	$-0.138892\pi$
$449$	38.4085			1.81261			0.906304	+	0.422627i	$0.138892\pi$
$450$		0			0
$451$	0.235276			0.0110787
$452$		0			0
$453$	−12.5328	+	29.4330i	−0.588844	+	1.38288i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	14.4035	+	14.4035i	0.673766	+	0.673766i	0.958582	−	0.284816i	$-0.0919325\pi$
$457$	14.4035	+	14.4035i	0.673766	+	0.673766i	−0.284816	+	0.958582i	$0.591932\pi$
$458$		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	$-0.630861\pi$
$463$	11.1256	−	11.1256i	0.517050	−	0.517050i	0.916678	+	0.399628i	$0.130861\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.25994	−	8.25994i	0.382225	−	0.382225i	−0.489679	−	0.871903i	$-0.662886\pi$
$467$	8.25994	−	8.25994i	0.382225	−	0.382225i	0.871903	+	0.489679i	$0.162886\pi$
$468$		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
$477$	−0.551568	+	27.9763i	−0.0252546	+	1.28094i
$478$		0			0
$479$	−10.5872			−0.483744			−0.241872	−	0.970308i	$-0.577761\pi$
$479$	−10.5872			−0.483744			−0.241872	+	0.970308i	$0.577761\pi$
$480$		0			0
$481$	−2.25430			−0.102787
$482$		0			0
$483$	−26.7152	−	11.3756i	−1.21559	−	0.517607i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	5.05605	+	5.05605i	0.229112	+	0.229112i	0.812321	−	0.583210i	$-0.198204\pi$
$487$	5.05605	+	5.05605i	0.229112	+	0.229112i	−0.583210	+	0.812321i	$0.698204\pi$
$488$		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	$-0.834918\pi$
$499$		−	22.1454i		−	0.991365i	0.868504	−	0.495682i	$-0.165082\pi$
$500$		0			0
$501$	11.9940	+	29.7829i	0.535850	+	1.33060i
$502$		0			0
$503$	−0.292413	−	0.292413i	−0.0130380	−	0.0130380i	0.700558	−	0.713596i	$-0.252935\pi$
$503$	−0.292413	−	0.292413i	−0.0130380	−	0.0130380i	−0.713596	+	0.700558i	$0.752935\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	20.4809	+	8.72096i	0.909590	+	0.387312i
$508$		0			0
$509$	−26.5321			−1.17601			−0.588007	−	0.808856i	$-0.700087\pi$
$509$	−26.5321			−1.17601			−0.588007	+	0.808856i	$0.700087\pi$
$510$		0			0
$511$	17.8511			0.789684
$512$		0			0
$513$	−6.77969	−	17.8422i	−0.299331	−	0.787753i
$514$		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	$-0.994107\pi$
$523$	−22.4419	+	22.4419i	−0.981317	+	0.981317i	0.0185119	+	0.999829i	$0.494107\pi$
$524$		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
$537$	15.5446	−	36.5061i	0.670799	−	1.57535i
$538$		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
$543$	9.97963	−	23.4369i	0.428267	−	1.00577i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−17.0695	−	17.0695i	−0.729838	−	0.729838i	0.240749	−	0.970587i	$-0.422607\pi$
$547$	−17.0695	−	17.0695i	−0.729838	−	0.729838i	−0.970587	+	0.240749i	$0.922607\pi$
$548$		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	−0.971701	−	0.236216i	$-0.924093\pi$
$557$	−17.3581	+	17.3581i	−0.735485	+	0.735485i	0.236216	+	0.971701i	$0.424093\pi$
$558$		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	0.370525	−	0.928822i	$-0.379178\pi$
$563$	−13.2471	−	13.2471i	−0.558297	−	0.558297i	−0.928822	+	0.370525i	$0.879178\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−12.1556	+	11.2330i	−0.510487	+	0.471742i
$568$		0			0
$569$	−8.65171			−0.362699			−0.181349	−	0.983419i	$-0.558046\pi$
$569$	−8.65171			−0.362699			−0.181349	+	0.983419i	$0.558046\pi$
$570$		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
$573$	14.7594	+	6.28467i	0.616581	+	0.262546i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−16.1810	−	16.1810i	−0.673624	−	0.673624i	0.284926	−	0.958550i	$-0.408031\pi$
$577$	−16.1810	−	16.1810i	−0.673624	−	0.673624i	−0.958550	+	0.284926i	$0.908031\pi$
$578$		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	−0.984387	−	0.176016i	$-0.943679\pi$
$587$	−19.5853	+	19.5853i	−0.808372	+	0.808372i	0.176016	+	0.984387i	$0.443679\pi$
$588$		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	0.0111937	−	0.999937i	$-0.496437\pi$
$593$	−24.0775	−	24.0775i	−0.988744	−	0.988744i	−0.999937	+	0.0111937i	$0.996437\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	12.0480	+	5.13013i	0.493090	+	0.209962i
$598$		0			0
$599$	−27.5084			−1.12396			−0.561982	−	0.827149i	$-0.689961\pi$
$599$	−27.5084			−1.12396			−0.561982	+	0.827149i	$0.689961\pi$
$600$		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
$603$	0.0549604	−	2.78767i	0.00223816	−	0.113523i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	7.95535	+	7.95535i	0.322898	+	0.322898i	0.849878	−	0.526980i	$-0.176676\pi$
$607$	7.95535	+	7.95535i	0.322898	+	0.322898i	−0.526980	+	0.849878i	$0.676676\pi$
$608$		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	$-0.641181\pi$
$613$	11.7384	−	11.7384i	0.474109	−	0.474109i	0.903241	+	0.429133i	$0.141181\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.1548	+	26.1548i	−1.05295	+	1.05295i	−0.0544346	+	0.998517i	$0.517336\pi$
$617$	−26.1548	+	26.1548i	−1.05295	+	1.05295i	−0.998517	+	0.0544346i	$0.982664\pi$
$618$		0			0
$619$			3.28083i			0.131868i	0.997824	+	0.0659338i	$0.0210026\pi$
$619$			3.28083i			0.131868i	−0.997824	+	0.0659338i	$0.978997\pi$
$620$		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
$627$	9.98113	−	23.4404i	0.398608	−	0.936119i
$628$		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
$633$	16.3313	−	38.3535i	0.649110	−	1.52442i
$634$		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	$-0.615307\pi$
$643$	14.7257	−	14.7257i	0.580725	−	0.580725i	0.935102	+	0.354378i	$0.115307\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.3595	−	13.3595i	0.525216	−	0.525216i	−0.393926	−	0.919142i	$-0.628884\pi$
$647$	13.3595	−	13.3595i	0.525216	−	0.525216i	0.919142	+	0.393926i	$0.128884\pi$
$648$		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	0.555502	−	0.831516i	$-0.312526\pi$
$653$	−7.05323	−	7.05323i	−0.276014	−	0.276014i	−0.831516	+	0.555502i	$0.812526\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−29.1149	−	0.574018i	−1.13588	−	0.0223946i
$658$		0			0
$659$	−5.30757			−0.206754			−0.103377	−	0.994642i	$-0.532965\pi$
$659$	−5.30757			−0.206754			−0.103377	+	0.994642i	$0.532965\pi$
$660$		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
$663$	−1.94719	−	0.829132i	−0.0756227	−	0.0322008i
$664$		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	0.0240106	−	0.999712i	$-0.492356\pi$
$673$	26.5577	−	26.5577i	1.02372	−	1.02372i	0.999712	−	0.0240106i	$-0.00764354\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.2749	−	12.2749i	0.471764	−	0.471764i	−0.430721	−	0.902485i	$-0.641741\pi$
$677$	12.2749	−	12.2749i	0.471764	−	0.471764i	0.902485	+	0.430721i	$0.141741\pi$
$678$		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	0.415774	−	0.909468i	$-0.363511\pi$
$683$	−12.9023	−	12.9023i	−0.493694	−	0.493694i	−0.909468	+	0.415774i	$0.863511\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	13.1586	+	5.60304i	0.502031	+	0.213769i
$688$		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
$693$	−22.0879	−	0.435476i	−0.839051	−	0.0165424i
$694$		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	$-0.986548\pi$
$709$		−	2.24990i		−	0.0844968i	0.999107	−	0.0422484i	$-0.0134521\pi$
$710$		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
$717$	6.73039	−	15.8061i	0.251351	−	0.590290i
$718$		0			0
$719$	−2.61154			−0.0973940			−0.0486970	−	0.998814i	$-0.515507\pi$
$719$	−2.61154			−0.0973940			−0.0486970	+	0.998814i	$0.515507\pi$
$720$		0			0
$721$	−21.4513			−0.798890
$722$		0			0
$723$	0.664250	−	1.55997i	0.0247037	−	0.0580160i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	8.39344	+	8.39344i	0.311296	+	0.311296i	0.845411	−	0.534116i	$-0.179355\pi$
$727$	8.39344	+	8.39344i	0.311296	+	0.311296i	−0.534116	+	0.845411i	$0.679355\pi$
$728$		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	$-0.597711\pi$
$733$	17.6275	−	17.6275i	0.651086	−	0.651086i	0.953254	+	0.302169i	$0.0977106\pi$
$734$		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	$0.167836\pi$
$739$			27.3573i			1.00636i	−0.864183	+	0.503178i	$0.832164\pi$
$740$		0			0
$741$	2.27021	−	0.914241i	0.0833982	−	0.0335855i
$742$		0			0
$743$	−9.28334	−	9.28334i	−0.340573	−	0.340573i	0.516010	−	0.856583i	$-0.327417\pi$
$743$	−9.28334	−	9.28334i	−0.340573	−	0.340573i	−0.856583	+	0.516010i	$0.827417\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.541229	+	27.4519i	−0.0198025	+	1.00441i
$748$		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
$753$	−29.2820	−	12.4685i	−1.06709	−	0.454378i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−7.77796	−	7.77796i	−0.282695	−	0.282695i	0.551488	−	0.834183i	$-0.314060\pi$
$757$	−7.77796	−	7.77796i	−0.282695	−	0.282695i	−0.834183	+	0.551488i	$0.814060\pi$
$758$		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	$-0.948773\pi$
$769$		−	8.88726i		−	0.320483i	0.987078	−	0.160241i	$-0.0512273\pi$
$770$		0			0
$771$	−8.92678	−	22.1666i	−0.321490	−	0.798312i
$772$		0			0
$773$	5.61335	+	5.61335i	0.201898	+	0.201898i	0.800813	−	0.598915i	$-0.204401\pi$
$773$	5.61335	+	5.61335i	0.201898	+	0.201898i	−0.598915	+	0.800813i	$0.704401\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−17.1746	−	7.31310i	−0.616136	−	0.262356i
$778$		0			0
$779$	−0.215823			−0.00773266
$780$		0			0
$781$	29.7304			1.06384
$782$		0			0
$783$	−13.2300	+	5.02712i	−0.472800	+	0.179655i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	33.0682	+	33.0682i	1.17875	+	1.17875i	0.980062	+	0.198692i	$0.0636693\pi$
$787$	33.0682	+	33.0682i	1.17875	+	1.17875i	0.198692	+	0.980062i	$0.436331\pi$
$788$		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	−0.732421	−	0.680852i	$-0.761610\pi$
$797$	−1.45586	+	1.45586i	−0.0515692	+	0.0515692i	0.680852	+	0.732421i	$0.261610\pi$
$798$		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
$807$	5.88823	−	13.8283i	0.207276	−	0.486781i
$808$		0			0
$809$	−30.5920			−1.07556			−0.537778	−	0.843087i	$-0.680736\pi$
$809$	−30.5920			−1.07556			−0.537778	+	0.843087i	$0.680736\pi$
$810$		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
$813$	−7.09140	+	16.6539i	−0.248706	+	0.584079i
$814$		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	$-0.777775\pi$
$823$	−3.53568	+	3.53568i	−0.123246	+	0.123246i	0.642793	+	0.766040i	$0.277775\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.22925	+	1.22925i	−0.0427452	+	0.0427452i	−0.728156	−	0.685411i	$-0.759623\pi$
$827$	−1.22925	+	1.22925i	−0.0427452	+	0.0427452i	0.685411	+	0.728156i	$0.259623\pi$
$828$		0			0
$829$			6.70948i			0.233030i	0.993189	+	0.116515i	$0.0371723\pi$
$829$			6.70948i			0.233030i	−0.993189	+	0.116515i	$0.962828\pi$
$830$		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
$837$	−28.8693	+	10.9698i	−0.997870	+	0.379171i
$838$		0			0
$839$	−21.7502			−0.750900			−0.375450	−	0.926843i	$-0.622512\pi$
$839$	−21.7502			−0.750900			−0.375450	+	0.926843i	$0.622512\pi$
$840$		0			0
$841$	−21.5813			−0.744184
$842$		0			0
$843$	−29.0012	−	12.3490i	−0.998854	−	0.425321i
$844$		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	$-0.915070\pi$
$853$	−20.4722	+	20.4722i	−0.700956	+	0.700956i	0.263660	+	0.964616i	$0.415070\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	24.4310	−	24.4310i	0.834548	−	0.834548i	−0.153587	−	0.988135i	$-0.549082\pi$
$857$	24.4310	−	24.4310i	0.834548	−	0.834548i	0.988135	+	0.153587i	$0.0490825\pi$
$858$		0			0
$859$		−	53.3779i		−	1.82123i	−0.413254	−	0.910616i	$-0.635608\pi$
$859$		−	53.3779i		−	1.82123i	0.413254	−	0.910616i	$-0.364392\pi$
$860$		0			0
$861$	0.0699115	+	0.173602i	0.00238258	+	0.00591633i
$862$		0			0
$863$	−18.0378	−	18.0378i	−0.614013	−	0.614013i	0.329976	−	0.943989i	$-0.392959\pi$
$863$	−18.0378	−	18.0378i	−0.614013	−	0.614013i	−0.943989	+	0.329976i	$0.892959\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	11.0120	+	4.68899i	0.373986	+	0.159246i
$868$		0			0
$869$	−0.442392			−0.0150071
$870$		0			0
$871$	0.357513			0.0121139
$872$		0			0
$873$	0.851849	−	43.2069i	0.0288307	−	1.46233i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	9.63257	+	9.63257i	0.325269	+	0.325269i	0.850784	−	0.525515i	$-0.176127\pi$
$877$	9.63257	+	9.63257i	0.325269	+	0.325269i	−0.525515	+	0.850784i	$0.676127\pi$
$878$		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	$-0.675375\pi$
$883$	9.76211	−	9.76211i	0.328521	−	0.328521i	0.852024	+	0.523503i	$0.175375\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.87587	+	7.87587i	−0.264446	+	0.264446i	−0.826857	−	0.562412i	$-0.809874\pi$
$887$	−7.87587	+	7.87587i	−0.264446	+	0.264446i	0.562412	+	0.826857i	$0.309874\pi$
$888$		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
$897$	−2.37945	+	5.58808i	−0.0794476	+	0.186580i
$898$		0			0
$899$	16.1884			0.539913
$900$		0			0
$901$	−29.6275			−0.987036
$902$		0			0
$903$	9.85639	−	23.1475i	0.328000	−	0.770299i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.83851	+	1.83851i	0.0610468	+	0.0610468i	0.736971	−	0.675924i	$-0.236255\pi$
$907$	1.83851	+	1.83851i	0.0610468	+	0.0610468i	−0.675924	+	0.736971i	$0.736255\pi$
$908$		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	$0.0683743\pi$
$919$			12.9237i			0.426312i	−0.977018	+	0.213156i	$0.931626\pi$
$920$		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
$927$	34.9870	+	0.689789i	1.14912	+	0.0226556i
$928$		0			0
$929$	−41.4696			−1.36057			−0.680287	−	0.732946i	$-0.738145\pi$
$929$	−41.4696			−1.36057			−0.680287	+	0.732946i	$0.738145\pi$
$930$		0			0
$931$	13.2900			0.435563
$932$		0			0
$933$	47.3215	+	20.1499i	1.54924	+	0.659679i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−36.1771	−	36.1771i	−1.18186	−	1.18186i	−0.979263	−	0.202592i	$-0.935063\pi$
$937$	−36.1771	−	36.1771i	−1.18186	−	1.18186i	−0.202592	−	0.979263i	$-0.564937\pi$
$938$		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	0.158961	−	0.987285i	$-0.449186\pi$
$947$	35.2738	−	35.2738i	1.14625	−	1.14625i	0.987285	−	0.158961i	$-0.0508143\pi$
$948$		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	0.514805	−	0.857307i	$-0.327864\pi$
$953$	−10.5733	−	10.5733i	−0.342502	−	0.342502i	−0.857307	+	0.514805i	$0.827864\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−17.3810	−	7.40098i	−0.561848	−	0.239240i
$958$		0			0
$959$	9.97392			0.322075
$960$		0			0
$961$	4.32496			0.139515
$962$		0			0
$963$	36.6553	+	0.722680i	1.18120	+	0.0232880i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−9.57606	−	9.57606i	−0.307945	−	0.307945i	0.536167	−	0.844112i	$-0.319872\pi$
$967$	−9.57606	−	9.57606i	−0.307945	−	0.307945i	−0.844112	+	0.536167i	$0.819872\pi$
$968$		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	−0.979895	−	0.199512i	$-0.936064\pi$
$977$	−24.3924	+	24.3924i	−0.780383	+	0.780383i	0.199512	+	0.979895i	$0.436064\pi$
$978$		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	0.278525	−	0.960429i	$-0.410154\pi$
$983$	−21.3796	−	21.3796i	−0.681904	−	0.681904i	−0.960429	+	0.278525i	$0.910154\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.06464	+	9.54569i	−0.129379	+	0.303843i
$988$		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
$993$	3.56875	−	8.38110i	0.113251	−	0.265966i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−6.23446	−	6.23446i	−0.197447	−	0.197447i	0.601457	−	0.798905i	$-0.294587\pi$
$997$	−6.23446	−	6.23446i	−0.197447	−	0.197447i	−0.798905	+	0.601457i	$0.794587\pi$
$998$		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.557.11	yes	32
3.2	odd	2	inner	1500.2.i.b.557.14	yes	32
5.2	odd	4	inner	1500.2.i.b.1193.3	yes	32
5.3	odd	4	inner	1500.2.i.b.1193.14	yes	32
5.4	even	2	inner	1500.2.i.b.557.6	yes	32
15.2	even	4	inner	1500.2.i.b.1193.6	yes	32
15.8	even	4	inner	1500.2.i.b.1193.11	yes	32
15.14	odd	2	inner	1500.2.i.b.557.3	✓	32

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

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